diff --git "a/txt-clean-pdf-without-outline-all2-onefile/abaqus.txt" "b/txt-clean-pdf-without-outline-all2-onefile/abaqus.txt" new file mode 100644--- /dev/null +++ "b/txt-clean-pdf-without-outline-all2-onefile/abaqus.txt" @@ -0,0 +1,164501 @@ +User’s Manual +CAUTION: This documentation is intended for qualified users who will exercise sound engineering judgment and expertise in the use of the Abaqus +Software. The Abaqus Software is inherently complex, and the examples and procedures in this documentation are not intended to be exhaustive or to apply +to any particular situation. Users are cautioned to satisfy themselves as to the accuracy and results of their analyses. +Dassault Systèmes and its subsidiaries, including Dassault Systèmes Simulia Corp., shall not be responsible for the accuracy or usefulness of any analysis +performed using the Abaqus Software or the procedures, examples, or explanations in this documentation. Dassault Systèmes and its subsidiaries shall not +be responsible for the consequences of any errors or omissions that may appear in this documentation. +The Abaqus Software is available only under license from Dassault Systèmes or its subsidiary and may be used or reproduced only in accordance with the +terms of such license. This documentation is subject to the terms and conditions of either the software license agreement signed by the parties, or, absent +such an agreement, the then current software license agreement to which the documentation relates. +This documentation and the software described in this documentation are subject to change without prior notice. +No part of this documentation may be reproduced or distributed in any form without prior written permission of Dassault Systèmes or its subsidiary. +The Abaqus Software is a product of Dassault Systèmes Simulia Corp., Providence, RI, USA. +© Dassault Systèmes, 2012 +Abaqus, the 3DS logo, SIMULIA, CATIA, and Unified FEA are trademarks or registered trademarks of Dassault Systèmes or its subsidiaries in the United +States and/or other countries. +Other company, product, and service names may be trademarks or service marks of their respective owners. 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Bhd., Kuala Lumpur, Tel: +603 2039 9000, abaqus.my@worleyparsons.com +Kimeca.NET SA de CV, Mexico, Tel: +52 55 2459 2635 +Matrix Applied Computing Ltd., Auckland, Tel: +64 9 623 1223, abaqus-tech@matrix.co.nz +BudSoft Sp. z o.o., Poznań, Tel: +48 61 8508 466, info@budsoft.com.pl +TESIS Ltd., Moscow, Tel: +7 495 612 44 22, info@tesis.com.ru +WorleyParsons Pte Ltd., Singapore, Tel: +65 6735 8444, abaqus.sg@worleyparsons.com +Finite Element Analysis Services (Pty) Ltd., Parklands, Tel: +27 21 556 6462, feas@feas.co.za +Thailand +Turkey +Simutech Solution Corporation, Taipei, R.O.C., Tel: +886 2 2507 9550, camilla@simutech.com.tw +WorleyParsons Pte Ltd., Singapore, Tel: +65 6735 8444, abaqus.sg@worleyparsons.com +A-Ztech Ltd., Istanbul, Tel: +90 216 361 8850, info@a-ztech.com.tr +Preface +Support +Both technical engineering support (for problems with creating a model or performing an analysis) and +systems support (for installation, licensing, and hardware-related problems) for Abaqus are offered through +a network of local support offices. Regional contact information is listed in the front of each Abaqus manual +and is accessible from the Locations page at www.simulia.com. +Support for SIMULIA products +SIMULIA provides a knowledge database of answers and solutions to questions that we have answered, +as well as guidelines on how to use Abaqus, SIMULIA Scenario Definition, Isight, and other SIMULIA +products. You can also submit new requests for support. All support incidents are tracked. If you contact +us by means outside the system to discuss an existing support problem and you know the incident or support +request number, please mention it so that we can query the database to see what the latest action has been. +Many questions about Abaqus can also be answered by visiting the Products page and the Support +page at www.simulia.com. +Anonymous ftp site +To facilitate data transfer with SIMULIA, an anonymous ftp account is available at ftp.simulia.com. +Login as user anonymous, and type your e-mail address as your password. Contact support before placing +files on the site. +Training +All offices and representatives offer regularly scheduled public training classes. The courses are offered in +a traditional classroom form and via the Web. We also provide training seminars at customer sites. All +training classes and seminars include workshops to provide as much practical experience with Abaqus as +possible. For a schedule and descriptions of available classes, see www.simulia.com or call your local office +or representative. +Feedback +We welcome any suggestions for improvements to Abaqus software, the support program, or documentation. +We will ensure that any enhancement requests you make are considered for future releases. If you wish to +make a suggestion about the service or products, refer to www.simulia.com. Complaints should be made by +contacting your local office or through www.simulia.com by visiting the Quality Assurance section of the +1.1.1 +1.2.1 +1.2.2 +1.3.1 +1.4.1 +2.1.1 +2.1.2 +2.1.3 +2.1.4 +2.1.5 +2.1.6 +2.2.1 +2.2.2 +2.2.3 +2.2.4 +2.2.5 +2.3.1 +2.3.2 +2.3.3 +2.3.4 +Contents +Volume I +PART I +INTRODUCTION, SPATIAL MODELING, AND EXECUTION +1. +Introduction +Introduction: general +Abaqus syntax and conventions +Input syntax rules +Conventions +Abaqus model definition +Defining a model in Abaqus +Parametric modeling +Parametric input +2. Spatial Modeling +Node definition +Node definition +Parametric shape variation +Nodal thicknesses +Normal definitions at nodes +Transformed coordinate systems +Adjusting nodal coordinates +Element definition +Element definition +Element foundations +Defining reinforcement +Defining rebar as an element property +Orientations +Surface definition +Surfaces: overview +Element-based surface definition +Node-based surface definition +Analytical rigid surface definition +Eulerian surface definition +Operating on surfaces +Rigid body definition +Rigid body definition +Integrated output section definition +Integrated output section definition +Mass adjustment +Adjust and/or redistribute mass of an element set +Nonstructural mass definition +Nonstructural mass definition +Distribution definition +Distribution definition +Display body definition +Display body definition +Assembly definition +Defining an assembly +Matrix definition +Defining matrices +3. Job Execution +Execution procedures: overview +Execution procedure for Abaqus: overview +Execution procedures +Obtaining information +Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD execution +SIMULIA Co-Simulation Engine controller execution +Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD co-simulation execution +Abaqus/CAE execution +Abaqus/Viewer execution +Python execution +Parametric studies +Abaqus documentation +Licensing utilities +ASCII translation of results (.fil) files +Joining results (.fil) files +Querying the keyword/problem database +ii +Abaqus ID:usb-toc +Printed on: Fri February 3 -- 18:01:12 2012 +2.3.5 +2.3.6 +2.4.1 +2.5.1 +2.6.1 +2.7.1 +2.8.1 +2.9.1 +2.10.1 +2.11.1 +3.1.1 +3.2.1 +3.2.2 +3.2.3 +3.2.4 +3.2.5 +3.2.6 +3.2.7 +3.2.8 +3.2.9 +3.2.10 +Making user-defined executables and subroutines +Input file and output database upgrade utility +Generating output database reports +Joining output database (.odb) files from restarted analyses +Combining output from substructures +Combining data from multiple output databases +Network output database file connector +Mapping thermal and magnetic loads +Fixed format conversion utility +Translating Nastran bulk data files to Abaqus input files +Translating Abaqus files to Nastran bulk data files +Translating ANSYS input files to Abaqus input files +Translating PAM-CRASH input files to partial Abaqus input files +Translating RADIOSS input files to partial Abaqus input files +Translating Abaqus output database files to Nastran Output2 results files +Translating LS-DYNA data files to Abaqus input files +Exchanging Abaqus data with ZAERO +Encrypting and decrypting Abaqus input data +Job execution control +Environment file settings +Using the Abaqus environment settings +Managing memory and disk resources +Managing memory and disk use in Abaqus +Parallel execution +Parallel execution: overview +Parallel execution in Abaqus/Standard +Parallel execution in Abaqus/Explicit +Parallel execution in Abaqus/CFD +File extension definitions +File extensions used by Abaqus +FORTRAN unit numbers +FORTRAN unit numbers used by Abaqus +CONTENTS +3.2.14 +3.2.15 +3.2.16 +3.2.17 +3.2.18 +3.2.19 +3.2.20 +3.2.21 +3.2.22 +3.2.23 +3.2.24 +3.2.25 +3.2.26 +3.2.27 +3.2.28 +3.2.29 +3.2.30 +3.2.31 +3.2.32 +3.2.33 +3.3.1 +3.4.1 +3.5.1 +3.5.2 +3.5.3 +3.5.4 +3.6.1 +3.7.1 +4.1.2 +4.1.3 +4.1.4 +4.2.1 +4.2.2 +4.2.3 +4.3.1 +5.1.1 +5.1.2 +5.1.3 +5.1.4 +CONTENTS +4. Output +PART II +OUTPUT +Output +Output to the data and results files +Output to the output database +Error indicator output +Output variables +Abaqus/Standard output variable identifiers +Abaqus/Explicit output variable identifiers +Abaqus/CFD output variable identifiers +The postprocessing calculator +The postprocessing calculator +5. File Output Format +Accessing the results file +Accessing the results file: overview +Results file output format +Accessing the results file information +Utility routines for accessing the results file +OI.1 Abaqus/Standard Output Variable Index +OI.2 Abaqus/Explicit Output Variable Index +OI.3 Abaqus/CFD Output Variable Index +6.1.1 +6.1.2 +6.1.3 +6.1.4 +6.1.5 +6.1.6 +6.2.1 +6.2.2 +6.2.3 +6.2.4 +6.2.5 +6.2.6 +6.2.7 +6.3.1 +6.3.2 +6.3.3 +6.3.4 +6.3.5 +6.3.6 +6.3.7 +6.3.8 +6.3.9 +6.3.10 +6.3.11 +6.4.1 +6.5.1 +6.5.2 +Volume II +PART III +ANALYSIS PROCEDURES, SOLUTION, AND CONTROL +6. Analysis Procedures +Introduction +Solving analysis problems: overview +Defining an analysis +General and linear perturbation procedures +Multiple load case analysis +Direct linear equation solver +Iterative linear equation solver +Static stress/displacement analysis +Static stress analysis procedures: overview +Static stress analysis +Eigenvalue buckling prediction +Unstable collapse and postbuckling analysis +Quasi-static analysis +Direct cyclic analysis +Low-cycle fatigue analysis using the direct cyclic approach +Dynamic stress/displacement analysis +Dynamic analysis procedures: overview +Implicit dynamic analysis using direct integration +Explicit dynamic analysis +Direct-solution steady-state dynamic analysis +Natural frequency extraction +Complex eigenvalue extraction +Transient modal dynamic analysis +Mode-based steady-state dynamic analysis +Subspace-based steady-state dynamic analysis +Response spectrum analysis +Random response analysis +Steady-state transport analysis +Steady-state transport analysis +Heat transfer and thermal-stress analysis +Heat transfer analysis procedures: overview +Uncoupled heat transfer analysis +6.5.4 +6.6.1 +6.6.2 +6.7.1 +6.7.2 +6.7.3 +6.7.4 +6.7.5 +6.7.6 +6.8.1 +6.8.2 +6.9.1 +6.10.1 +6.11.1 +6.12.1 +7.1.1 +7.2.1 +7.2.2 +7.2.3 +7.2.4 +CONTENTS +Fully coupled thermal-stress analysis +Adiabatic analysis +Fluid dynamic analysis +Fluid dynamic analysis procedures: overview +Incompressible fluid dynamic analysis +Electromagnetic analysis +Electromagnetic analysis procedures +Piezoelectric analysis +Coupled thermal-electrical analysis +Fully coupled thermal-electrical-structural analysis +Eddy current analysis +Magnetostatic analysis +Coupled pore fluid flow and stress analysis +Coupled pore fluid diffusion and stress analysis +Geostatic stress state +Mass diffusion analysis +Mass diffusion analysis +Acoustic and shock analysis +Acoustic, shock, and coupled acoustic-structural analysis +Abaqus/Aqua analysis +Abaqus/Aqua analysis +Annealing +Annealing procedure +7. Analysis Solution and Control +Solving nonlinear problems +Solving nonlinear problems +Analysis convergence controls +Convergence and time integration criteria: overview +Commonly used control parameters +Convergence criteria for nonlinear problems +Time integration accuracy in transient problems +ANALYSIS TECHNIQUES +8. Analysis Techniques: Introduction +Analysis techniques: overview +9. Analysis Continuation Techniques +Restarting an analysis +Restarting an analysis +Importing and transferring results +Transferring results between Abaqus analyses: overview +Transferring results between Abaqus/Explicit and Abaqus/Standard +Transferring results from one Abaqus/Standard analysis to another +Transferring results from one Abaqus/Explicit analysis to another +10. Modeling Abstractions +Substructuring +Using substructures +Defining substructures +Submodeling +Submodeling: overview +Node-based submodeling +Surface-based submodeling +Generating global matrices +Generating matrices +CONTENTS +8.1.1 +9.1.1 +9.2.1 +9.2.2 +9.2.3 +9.2.4 +10.1.1 +10.1.2 +10.2.1 +10.2.2 +10.2.3 +10.3.1 +Symmetric model generation, results transfer, and analysis of cyclic symmetry models +Symmetric model generation +Transferring results from a symmetric mesh or a partial three-dimensional mesh to +a full three-dimensional mesh +Analysis of models that exhibit cyclic symmetry +Periodic media analysis +Periodic media analysis +Meshed beam cross-sections +Meshed beam cross-sections +vii +10.4.1 +10.4.2 +10.4.3 +10.5.1 +Modeling discontinuities as an enriched feature using the extended finite element method +Modeling discontinuities as an enriched feature using the extended finite element +10.7.1 +11.1.1 +11.2.1 +11.3.1 +11.4.1 +11.4.2 +11.4.3 +11.5.1 +11.5.2 +11.5.3 +11.5.4 +11.6.1 +11.7.1 +11.8.1 +12.1.1 +12.2.1 +12.2.2 +12.2.3 +12.2.4 +method +11. Special-Purpose Techniques +Inertia relief +Inertia relief +Mesh modification or replacement +Element and contact pair removal and reactivation +Geometric imperfections +Introducing a geometric imperfection into a model +Fracture mechanics +Fracture mechanics: overview +Contour integral evaluation +Crack propagation analysis +Surface-based fluid modeling +Surface-based fluid cavities: overview +Fluid cavity definition +Fluid exchange definition +Inflator definition +Mass scaling +Mass scaling +Selective subcycling +Selective subcycling +Steady-state detection +Steady-state detection +12. Adaptivity Techniques +Adaptivity techniques: overview +Adaptivity techniques +ALE adaptive meshing +ALE adaptive meshing: overview +Defining ALE adaptive mesh domains in Abaqus/Explicit +ALE adaptive meshing and remapping in Abaqus/Explicit +Modeling techniques for Eulerian adaptive mesh domains in Abaqus/Explicit +12.2.5 +12.2.6 +12.2.7 +12.3.1 +12.3.2 +12.3.3 +12.4.1 +13.1.1 +13.2.1 +13.2.2 +13.2.3 +14.1.1 +14.1.2 +14.1.3 +14.1.4 +15.1.1 +15.1.2 +16.1.1 +16.1.2 +16.1.3 +17.1.1 +17.2.1 +Output and diagnostics for ALE adaptive meshing in Abaqus/Explicit +Defining ALE adaptive mesh domains in Abaqus/Standard +ALE adaptive meshing and remapping in Abaqus/Standard +Adaptive remeshing +Adaptive remeshing: overview +Selection of error indicators influencing adaptive remeshing +Solution-based mesh sizing +Analysis continuation after mesh replacement +Mesh-to-mesh solution mapping +13. Optimization Techniques +Structural optimization: overview +Structural optimization: overview +Optimization models +Design responses +Objectives and constraints +Creating Abaqus optimization models +14. Eulerian Analysis +Eulerian analysis +Defining Eulerian boundaries +Eulerian mesh motion +Defining adaptive mesh refinement in the Eulerian domain +15. Particle Methods +Smoothed particle hydrodynamic analyses +Smoothed particle hydrodynamic analysis +Finite element conversion to SPH particles +16. Sequentially Coupled Multiphysics Analyses +Predefined fields for sequential coupling +Sequentially coupled thermal-stress analysis +Predefined loads for sequential coupling +17. Co-simulation +Co-simulation: overview +Preparing an Abaqus analysis for co-simulation +Preparing an Abaqus analysis for co-simulation +Co-simulation between Abaqus solvers +Abaqus/Standard to Abaqus/Explicit co-simulation +Abaqus/CFD to Abaqus/Standard or to Abaqus/Explicit co-simulation +18. Extending Abaqus Analysis Functionality +User subroutines and utilities +User subroutines: overview +Available user subroutines +Available utility routines +19. Design Sensitivity Analysis +Design sensitivity analysis +20. Parametric Studies +Scripting parametric studies +Scripting parametric studies +Parametric studies: commands +aStudy.combine(): Combine parameter samples for parametric studies. +aStudy.constrain(): Constrain parameter value combinations in parametric studies. +aStudy.define(): Define parameters for parametric studies. +aStudy.execute(): Execute the analysis of parametric study designs. +aStudy.gather(): Gather the results of a parametric study. +aStudy.generate(): Generate the analysis job data for a parametric study. +aStudy.output(): Specify the source of parametric study results. +aStudy=ParStudy(): Create a parametric study. +aStudy.report(): Report parametric study results. +aStudy.sample(): Sample parameters for parametric studies. +17.3.1 +17.3.2 +18.1.1 +18.1.2 +18.1.3 +19.1.1 +20.1.1 +20.2.1 +20.2.2 +20.2.3 +20.2.4 +20.2.5 +20.2.6 +20.2.7 +20.2.8 +20.2.9 +20.2.10 +21.1.1 +21.1.2 +21.1.3 +21.2.1 +22.1.1 +22.2.1 +22.2.2 +22.2.3 +22.3.1 +22.4.1 +22.5.1 +22.5.2 +22.5.3 +22.6.1 +22.6.2 +22.7.1 +22.7.2 +Volume III +PART V MATERIALS +21. Materials: Introduction +Introduction +Material library: overview +Material data definition +Combining material behaviors +General properties +Density +22. Elastic Mechanical Properties +Overview +Elastic behavior: overview +Linear elasticity +Linear elastic behavior +No compression or no tension +Plane stress orthotropic failure measures +Porous elasticity +Elastic behavior of porous materials +Hypoelasticity +Hypoelastic behavior +Hyperelasticity +Hyperelastic behavior of rubberlike materials +Hyperelastic behavior in elastomeric foams +Anisotropic hyperelastic behavior +Stress softening in elastomers +Mullins effect +Energy dissipation in elastomeric foams +Viscoelasticity +Time domain viscoelasticity +Frequency domain viscoelasticity +Nonlinear viscoelasticity +Hysteresis in elastomers +Parallel network viscoelastic model +Rate sensitive elastomeric foams +Low-density foams +23. +Inelastic Mechanical Properties +Overview +Inelastic behavior +Metal plasticity +Classical metal plasticity +Models for metals subjected to cyclic loading +Rate-dependent yield +Rate-dependent plasticity: creep and swelling +Annealing or melting +Anisotropic yield/creep +Johnson-Cook plasticity +Dynamic failure models +Porous metal plasticity +Cast iron plasticity +Two-layer viscoplasticity +ORNL – Oak Ridge National Laboratory constitutive model +Deformation plasticity +Other plasticity models +Extended Drucker-Prager models +Modified Drucker-Prager/Cap model +Mohr-Coulomb plasticity +Critical state (clay) plasticity model +Crushable foam plasticity models +Fabric materials +Fabric material behavior +Jointed materials +Jointed material model +Concrete +Concrete smeared cracking +Cracking model for concrete +Concrete damaged plasticity +xii +Abaqus ID:usb-toc +Printed on: Fri February 3 -- 18:01:12 2012 +22.8.1 +22.8.2 +22.9.1 +23.1.1 +23.2.1 +23.2.2 +23.2.3 +23.2.4 +23.2.5 +23.2.6 +23.2.7 +23.2.8 +23.2.9 +23.2.10 +23.2.11 +23.2.12 +23.2.13 +23.3.1 +23.3.2 +23.3.3 +23.3.4 +23.3.5 +23.4.1 +23.5.1 +23.7.1 +24.1.1 +24.2.1 +24.2.2 +24.2.3 +24.3.1 +24.3.2 +24.3.3 +24.4.1 +24.4.2 +24.4.3 +25.1.1 +25.2.1 +26.1.1 +26.1.2 +26.1.3 +26.1.4 +26.2.1 +26.2.2 +26.2.3 +26.2.4 +Permanent set in rubberlike materials +Permanent set in rubberlike materials +24. Progressive Damage and Failure +Progressive damage and failure: overview +Progressive damage and failure +Damage and failure for ductile metals +Damage and failure for ductile metals: overview +Damage initiation for ductile metals +Damage evolution and element removal for ductile metals +Damage and failure for fiber-reinforced composites +Damage and failure for fiber-reinforced composites: overview +Damage initiation for fiber-reinforced composites +Damage evolution and element removal for fiber-reinforced composites +Damage and failure for ductile materials in low-cycle fatigue analysis +Damage and failure for ductile materials in low-cycle fatigue analysis: overview +Damage initiation for ductile materials in low-cycle fatigue +Damage evolution for ductile materials in low-cycle fatigue +25. Hydrodynamic Properties +Overview +Hydrodynamic behavior: overview +Equations of state +Equation of state +26. Other Material Properties +Mechanical properties +Material damping +Thermal expansion +Field expansion +Viscosity +Heat transfer properties +Thermal properties: overview +Conductivity +Specific heat +Latent heat +Acoustic properties +Acoustic medium +Mass diffusion properties +Diffusivity +Solubility +Electromagnetic properties +Electrical conductivity +Piezoelectric behavior +Magnetic permeability +Pore fluid flow properties +Pore fluid flow properties +Permeability +Porous bulk moduli +Sorption +Swelling gel +Moisture swelling +User materials +User-defined mechanical material behavior +User-defined thermal material behavior +26.3.1 +26.4.1 +26.4.2 +26.5.1 +26.5.2 +26.5.3 +26.6.1 +26.6.2 +26.6.3 +26.6.4 +26.6.5 +26.6.6 +26.7.1 +26.7.2 +27.1.1 +27.1.2 +27.1.3 +27.1.4 +28.1.1 +28.1.2 +28.1.3 +28.1.4 +28.1.5 +28.1.6 +28.1.7 +28.2.1 +28.2.2 +28.3.1 +28.3.2 +28.4.1 +28.4.2 +28.5.1 +28.5.2 +29.1.1 +29.1.2 +29.1.3 +Volume IV +PART VI +ELEMENTS +27. Elements: Introduction +Element library: overview +Choosing the element’s dimensionality +Choosing the appropriate element for an analysis type +Section controls +28. Continuum Elements +General-purpose continuum elements +Solid (continuum) elements +One-dimensional solid (link) element library +Two-dimensional solid element library +Three-dimensional solid element library +Cylindrical solid element library +Axisymmetric solid element library +Axisymmetric solid elements with nonlinear, asymmetric deformation +Fluid continuum elements +Fluid (continuum) elements +Fluid element library +Infinite elements +Infinite elements +Infinite element library +Warping elements +Warping elements +Warping element library +Particle elements +Particle elements +Particle element library +29. Structural Elements +Membrane elements +Membrane elements +General membrane element library +Cylindrical membrane element library +Axisymmetric membrane element library +Truss elements +Truss elements +Truss element library +Beam elements +Beam modeling: overview +Choosing a beam cross-section +Choosing a beam element +Beam element cross-section orientation +Beam section behavior +Using a beam section integrated during the analysis to define the section behavior +Using a general beam section to define the section behavior +Beam element library +Beam cross-section library +Frame elements +Frame elements +Frame section behavior +Frame element library +Elbow elements +Pipes and pipebends with deforming cross-sections: elbow elements +Elbow element library +Shell elements +Shell elements: overview +Choosing a shell element +Defining the initial geometry of conventional shell elements +Shell section behavior +Using a shell section integrated during the analysis to define the section behavior +Using a general shell section to define the section behavior +Three-dimensional conventional shell element library +Continuum shell element library +Axisymmetric shell element library +Axisymmetric shell elements with nonlinear, asymmetric deformation +29.1.4 +29.2.1 +29.2.2 +29.3.1 +29.3.2 +29.3.3 +29.3.4 +29.3.5 +29.3.6 +29.3.7 +29.3.8 +29.3.9 +29.4.1 +29.4.2 +29.4.3 +29.5.1 +29.5.2 +29.6.1 +29.6.2 +29.6.3 +29.6.4 +29.6.5 +29.6.6 +29.6.7 +29.6.8 +29.6.9 +29.6.10 +30.1.1 +30.1.2 +30.2.1 +30.2.2 +30.3.1 +30.3.2 +30.4.1 +30.4.2 +31.1.1 +31.1.2 +31.1.3 +31.1.4 +31.1.5 +31.2.1 +31.2.2 +31.2.3 +31.2.4 +31.2.5 +31.2.6 +31.2.7 +31.2.8 +31.2.9 +31.2.10 +32.1.1 +32.1.2 +30. +Inertial, Rigid, and Capacitance Elements +Point mass elements +Point masses +Mass element library +Rotary inertia elements +Rotary inertia +Rotary inertia element library +Rigid elements +Rigid elements +Rigid element library +Capacitance elements +Point capacitance +Capacitance element library +31. Connector Elements +Connector elements +Connectors: overview +Connector elements +Connector actuation +Connector element library +Connection-type library +Connector element behavior +Connector behavior +Connector elastic behavior +Connector damping behavior +Connector functions for coupled behavior +Connector friction behavior +Connector plastic behavior +Connector damage behavior +Connector stops and locks +Connector failure behavior +Connector uniaxial behavior +32. Special-Purpose Elements +Spring elements +Springs +Spring element library +Dashpot elements +Dashpots +Dashpot element library +Flexible joint elements +Flexible joint element +Flexible joint element library +Distributing coupling elements +Distributing coupling elements +Distributing coupling element library +Cohesive elements +Cohesive elements: overview +Choosing a cohesive element +Modeling with cohesive elements +Defining the cohesive element’s initial geometry +Defining the constitutive response of cohesive elements using a continuum approach +Defining the constitutive response of cohesive elements using a traction-separation +description +Defining the constitutive response of fluid within the cohesive element gap +Two-dimensional cohesive element library +Three-dimensional cohesive element library +Axisymmetric cohesive element library +Gasket elements +Gasket elements: overview +Choosing a gasket element +Including gasket elements in a model +Defining the gasket element’s initial geometry +Defining the gasket behavior using a material model +Defining the gasket behavior directly using a gasket behavior model +Two-dimensional gasket element library +Three-dimensional gasket element library +Axisymmetric gasket element library +Surface elements +Surface elements +General surface element library +Cylindrical surface element library +Axisymmetric surface element library +32.2.1 +32.2.2 +32.3.1 +32.3.2 +32.4.1 +32.4.2 +32.5.1 +32.5.2 +32.5.3 +32.5.4 +32.5.5 +32.5.6 +32.5.7 +32.5.8 +32.5.9 +32.5.10 +32.6.1 +32.6.2 +32.6.3 +32.6.4 +32.6.5 +32.6.6 +32.6.7 +32.6.8 +32.6.9 +32.7.1 +32.7.2 +32.7.3 +32.7.4 +32.8.1 +32.8.2 +32.9.1 +32.9.2 +32.10.1 +32.10.2 +32.11.1 +32.11.2 +32.12.1 +32.12.2 +32.13.1 +32.13.2 +32.14.1 +32.14.2 +32.15.1 +32.15.2 +Tube support elements +Tube support elements +Tube support element library +Line spring elements +Line spring elements for modeling part-through cracks in shells +Line spring element library +Elastic-plastic joints +Elastic-plastic joints +Elastic-plastic joint element library +Drag chain elements +Drag chains +Drag chain element library +Pipe-soil elements +Pipe-soil interaction elements +Pipe-soil interaction element library +Acoustic interface elements +Acoustic interface elements +Acoustic interface element library +Eulerian elements +Eulerian elements +Eulerian element library +User-defined elements +User-defined elements +User-defined element library +EI.1 Abaqus/Standard Element Index +EI.2 Abaqus/Explicit Element Index +EI.3 Abaqus/CFD Element Index +Volume V +PART VII +PRESCRIBED CONDITIONS +33. Prescribed Conditions +Overview +Prescribed conditions: overview +Amplitude curves +Initial conditions +Initial conditions in Abaqus/Standard and Abaqus/Explicit +Initial conditions in Abaqus/CFD +Boundary conditions +Boundary conditions in Abaqus/Standard and Abaqus/Explicit +Boundary conditions in Abaqus/CFD +Loads +Applying loads: overview +Concentrated loads +Distributed loads +Thermal loads +Electromagnetic loads +Acoustic and shock loads +Pore fluid flow +Prescribed assembly loads +Prescribed assembly loads +Predefined fields +Predefined fields +PART VIII +CONSTRAINTS +34. Constraints +Overview +Kinematic constraints: overview +Multi-point constraints +Linear constraint equations +xx +Abaqus ID:usb-toc +Printed on: Fri February 3 -- 18:01:12 2012 +33.1.1 +33.1.2 +33.2.1 +33.2.2 +33.3.1 +33.3.2 +33.4.1 +33.4.2 +33.4.3 +33.4.4 +33.4.5 +33.4.6 +33.4.7 +33.5.1 +34.2.2 +34.2.3 +34.3.1 +34.3.2 +34.3.3 +34.3.4 +34.4.1 +34.5.1 +34.6.1 +35.1.1 +35.2.1 +35.2.2 +35.2.3 +35.2.4 +35.2.5 +35.2.6 +35.3.1 +35.3.2 +35.3.3 +35.3.4 +35.3.5 +35.3.6 +35.3.7 +35.3.8 +General multi-point constraints +Kinematic coupling constraints +Surface-based constraints +Mesh tie constraints +Coupling constraints +Shell-to-solid coupling +Mesh-independent fasteners +Embedded elements +Embedded elements +Element end release +Element end release +Overconstraint checks +Overconstraint checks +PART IX +INTERACTIONS +35. Defining Contact Interactions +Overview +Contact interaction analysis: overview +Defining general contact in Abaqus/Standard +Defining general contact interactions in Abaqus/Standard +Surface properties for general contact in Abaqus/Standard +Contact properties for general contact in Abaqus/Standard +Controlling initial contact status in Abaqus/Standard +Stabilization for general contact in Abaqus/Standard +Numerical controls for general contact in Abaqus/Standard +Defining contact pairs in Abaqus/Standard +Defining contact pairs in Abaqus/Standard +Assigning surface properties for contact pairs in Abaqus/Standard +Assigning contact properties for contact pairs in Abaqus/Standard +Modeling contact interference fits in Abaqus/Standard +Adjusting initial surface positions and specifying initial clearances in Abaqus/Standard +contact pairs +Adjusting contact controls in Abaqus/Standard +Defining tied contact in Abaqus/Standard +Extending master surfaces and slide lines +Contact modeling if substructures are present +Contact modeling if asymmetric-axisymmetric elements are present +Defining general contact in Abaqus/Explicit +Defining general contact interactions in Abaqus/Explicit +Assigning surface properties for general contact in Abaqus/Explicit +Assigning contact properties for general contact in Abaqus/Explicit +Controlling initial contact status for general contact in Abaqus/Explicit +Contact controls for general contact in Abaqus/Explicit +Defining contact pairs in Abaqus/Explicit +Defining contact pairs in Abaqus/Explicit +Assigning surface properties for contact pairs in Abaqus/Explicit +Assigning contact properties for contact pairs in Abaqus/Explicit +Adjusting initial surface positions and specifying initial clearances for contact pairs +in Abaqus/Explicit +Contact controls for contact pairs in Abaqus/Explicit +36. Contact Property Models +Mechanical contact properties +Mechanical contact properties: overview +Contact pressure-overclosure relationships +Contact damping +Contact blockage +Frictional behavior +User-defined interfacial constitutive behavior +Pressure penetration loading +Interaction of debonded surfaces +Breakable bonds +Surface-based cohesive behavior +Thermal contact properties +Thermal contact properties +Electrical contact properties +Electrical contact properties +Pore fluid contact properties +Pore fluid contact properties +37. Contact Formulations and Numerical Methods +Contact formulations and numerical methods in Abaqus/Standard +Contact formulations in Abaqus/Standard +xxii +Abaqus ID:usb-toc +Printed on: Fri February 3 -- 18:01:12 2012 +35.3.9 +35.3.10 +35.4.1 +35.4.2 +35.4.3 +35.4.4 +35.4.5 +35.5.1 +35.5.2 +35.5.3 +35.5.4 +35.5.5 +36.1.1 +36.1.2 +36.1.3 +36.1.4 +36.1.5 +36.1.6 +36.1.7 +36.1.8 +36.1.9 +36.1.10 +36.2.1 +37.1.2 +37.1.3 +37.2.1 +37.2.2 +37.2.3 +38.1.1 +38.1.2 +38.2.1 +38.2.2 +39.1.1 +39.2.1 +39.2.2 +39.3.1 +39.3.2 +39.4.1 +39.4.2 +39.5.1 +39.5.2 +40.1.1 +Contact constraint enforcement methods in Abaqus/Standard +Smoothing contact surfaces in Abaqus/Standard +Contact formulations and numerical methods in Abaqus/Explicit +Contact formulation for general contact in Abaqus/Explicit +Contact formulations for contact pairs in Abaqus/Explicit +Contact constraint enforcement methods in Abaqus/Explicit +38. Contact Difficulties and Diagnostics +Resolving contact difficulties in Abaqus/Standard +Contact diagnostics in an Abaqus/Standard analysis +Common difficulties associated with contact modeling in Abaqus/Standard +Resolving contact difficulties in Abaqus/Explicit +Contact diagnostics in an Abaqus/Explicit analysis +Common difficulties associated with contact modeling using contact pairs in +Abaqus/Explicit +39. Contact Elements in Abaqus/Standard +Contact modeling with elements +Contact modeling with elements +Gap contact elements +Gap contact elements +Gap element library +Tube-to-tube contact elements +Tube-to-tube contact elements +Tube-to-tube contact element library +Slide line contact elements +Slide line contact elements +Axisymmetric slide line element library +Rigid surface contact elements +Rigid surface contact elements +Axisymmetric rigid surface contact element library +40. Defining Cavity Radiation in Abaqus/Standard +Cavity radiation +Printed on: +Execution +• Chapter 1, “Introduction” +• Chapter 2, “Spatial Modeling” +Introduction +Introduction +Abaqus syntax and conventions +Abaqus model definition +Parametric modeling +INTRODUCTION +1.1 +1.2 +1.3 +1.1 +Introduction +• “Introduction: general,” Section 1.1.1 +INTRODUCTION: GENERAL +INTRODUCTION +Overview of the Abaqus finite element system +The Abaqus finite element system includes: +• Abaqus/Standard, a general-purpose finite element program; +• Abaqus/Explicit, an explicit dynamics finite element program; +• Abaqus/CFD, a general-purpose computational fluid dynamics program; +• Abaqus/CAE, an interactive environment used to create finite element models, submit Abaqus +analyses, monitor and diagnose jobs, and evaluate results; and +• Abaqus/Viewer, a subset of Abaqus/CAE that contains only the postprocessing capabilities of the +Visualization module. +Several add-on options are available to further extend the capabilities of Abaqus/Standard and +Abaqus/Explicit. The Abaqus/Aqua option works with Abaqus/Standard and Abaqus/Explicit. The +Abaqus/Design and Abaqus/AMS options work with Abaqus/Standard. Abaqus/Aqua contains optional +features that are specifically designed for the analysis of beam-like structures installed underwater +and subject to loading by water currents and wave action. The Abaqus/Design option enables you to +perform design sensitivity analysis (DSA). Abaqus/AMS is an optional eigensolver that works within +Abaqus/Standard providing very fast solution of large symmetric eigenvalue problems. The Abaqus +co-simulation technique provides several applications, available as separate add-on capabilities, for +coupling between Abaqus and third-party analysis programs. Abaqus/Foundation is an optional subset +of Abaqus/Standard that provides more cost-efficient access to the linear static and dynamic analysis +functionality in Abaqus/Standard. These options are available only if your license includes them. +For a comprehensive list of Abaqus products, utilities, and add-on options, see “Abaqus products,” +Section 1.2 of the Abaqus Release Notes. +Overview of this manual +This manual is a reference guide to using Abaqus/Standard (including Abaqus/Aqua, Abaqus/Design, and +Abaqus/Foundation), Abaqus/Explicit (including Abaqus/Aqua), and Abaqus/CFD. Abaqus/Standard +solves a system of equations implicitly at each solution “increment.” In contrast, Abaqus/Explicit +marches a solution forward through time in small time increments without solving a coupled system +of equations at each increment (or even forming a global stiffness matrix). Abaqus/CFD provides a +computational fluid dynamics capability with extensive support for preprocessing, simulation, and +postprocessingin Abaqus/CAE. +Throughout the manual the term Abaqus is most commonly used to refer collectively to both +Abaqus/Standard and Abaqus/Explicit and, when applicable, Abaqus/CFD; +the individual product +names are used to indicate when information applies to only that product. Product identifiers appear at +the beginning of each section in the manual (excluding overview sections) indicating the products to +which the information in the section applies. +The manual is divided into several parts: +• Part I, “Introduction, Spatial Modeling, and Execution,” discusses basic modeling concepts in +Abaqus, such as defining nodes, elements, and surfaces; the conventions and input formats that +should be followed when using Abaqus; and the execution procedures for Abaqus/Standard, +Abaqus/Explicit, Abaqus/CFD, Abaqus/CAE, and several utilities that are provided with the +Abaqus system. +• Part II, “Output,” describes how to obtain output from Abaqus and the format of the results (.fil) +file. It also describes the output variable identifiers that are available. +• Part III, “Analysis Procedures, Solution, and Control,” describes the analysis types (static stress +analysis, dynamics, eigenvalue extraction, etc.) +that are available. Detailed discussions of the +differences between how Abaqus/Standard and Abaqus/Explicit solve finite element analyses are +provided in this chapter. +• Part IV, “Analysis Techniques,” discusses various analysis techniques available in Abaqus such as +submodeling, removing elements or surfaces, and importing results from a previous simulation to +define the initial conditions for the current model. +• Part V, “Materials,” describes the material modeling options and how to calibrate some of the more +advanced material models. +• Part VI, “Elements,” describes the elements available in Abaqus. +• Part VII, “Prescribed Conditions,” describes the use of prescribed conditions, such as distributed +loads and nodal velocities. +• Part VIII, “Constraints,” discusses the use of constraints, such as multi-point constraints. +• Part IX, “Interactions,” discusses the contact and interaction models available in Abaqus. +The manual also includes indexes of all of +Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD. +the output variables and elements available in +Using Abaqus +Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD can be run as batch applications or through +the interactive Abaqus/CAE environment . The main input to the Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD +analysis products is a file containing the options required for the simulation and the data associated +with those options. There may also be supplementary files, such as restart or results files from previous +analyses, or auxiliary data files, such as a file containing an acceleration record or an earthquake record +for dynamic analysis. The input file is usually created by Abaqus/CAE or another preprocessor. Both +input file usage and Abaqus/CAE usage information are provided in this manual. +As described in “Defining a model in Abaqus,” Section 1.3.1, the main input file consists of two +sections: model input and history input. The input is organized around a few natural concepts and +conventions, which means that even though input files for complex simulations can be large, they can +be managed without difficulty. The basic syntax rules that govern an Abaqus input file are discussed +in “Input syntax rules,” Section 1.2.1. The Abaqus Keywords Reference Manual contains a complete +description of all the input options available in Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD. +For a detailed introduction to using Abaqus for your analyses, it is recommended that you follow the +self-paced tutorials in Getting Started with Abaqus: Interactive Edition. Refer to the Abaqus/CAE User’s +Manual for detailed information on working with Abaqus/CAE. +In addition, many analyses that demonstrate the numerous capabilities of Abaqus are discussed in +the Abaqus Example Problems Manual, the Abaqus Benchmarks Manual, and the Abaqus Verification +Manual. As a supplement to the Abaqus Analysis User’s Manual, these examples can help you become +familiar with the functionality that Abaqus provides and the structure of the Abaqus input file. For +example, “Beam impact on cylinder,” Section 1.6.12 of the Abaqus Verification Manual, discusses the +various modeling techniques that can be used to analyze the dynamic response of a cantilever beam. +Reviewing the results of an Abaqus simulation +Information on requesting output from an Abaqus simulation is discussed in “Output,” Section 4.1.1. +Requested results from an Abaqus simulation are viewed through the Visualization module in +Abaqus/CAE (also licensed separately as Abaqus/Viewer). The output database file is read by the +Visualization module in Abaqus/CAE to create contour plots, animations, X–Y plots, and tabular output +of Abaqus results. See Part V, “Viewing results,” of the Abaqus/CAE User’s Manual for detailed +information on using the Visualization module in Abaqus/CAE. +1.2 +Abaqus syntax and conventions +• “Input syntax rules,” Section 1.2.1 +• “Conventions,” Section 1.2.2 +1.2.1 +INPUT SYNTAX RULES +Products: Abaqus/Standard Abaqus/Explicit +Reference +• “Defining a model in Abaqus,” Section 1.3.1 +Overview +This section describes the syntax rules that govern an Abaqus input file. +All data definitions in Abaqus are accomplished with option blocks—sets of data describing a part +of the problem definition. You choose those options that are relevant for a particular application. Options +are defined by lines in the input file. Three types of input lines are used in an Abaqus input file: keyword +lines, data lines, and comment lines. Only 7-bit ASCII characters are supported, and a carriage return is +required at the end of each line in an input file. +• Keyword lines introduce options and often have parameters, which appear as words or phrases +separated by commas on the keyword line. Parameters are used to define the behavior of an option. +Parameters can stand alone or have a value, and they may be required or optional. +• Data lines, which are used to provide numeric or alphanumeric entries, follow most keyword lines. +• Any line that begins with stars in columns 1 and 2 (**) is a comment line. Such lines can be placed +anywhere in the file. They are ignored by Abaqus, so they will be printed only in the initial listing +of the file. There is no restriction on how many or where such lines occur in the file. +Relevant parameters and data lines (including the number of entries per data line) are described in the +sections of the Abaqus Keywords Reference Manual describing each option. This section describes the +general rules that apply to all keyword and data lines. +Keyword lines +The following rules apply when entering a keyword line: +• The first non-blank character of each keyword line must be a star (*). +• The keyword must be followed by a comma (,) if any parameters are given. +• Parameters must be separated by commas. +• Blanks on a keyword line are ignored. +• A line can include no more than 256 characters, including blanks. +• Keywords and parameters are not case sensitive. +• Parameter values usually are not case sensitive. The only exceptions to this rule are those imposed +externally to Abaqus, such as file names on case-sensitive operating systems. +• Keywords, parameters, and, in most cases, parameter values need not be spelled out completely, +but there must be enough characters given to distinguish them from other keywords, parameters, +and parameter values that begin in the same way. Abaqus first searches each associated text string +for an exact match. If an exact match is not found, Abaqus then searches based upon the minimum +number of unique characters in each keyword, parameter, or parameter value, as the case may be. +Embedded blanks can be omitted from any item in a keyword line. If a parameter value is used to +provide a number or a file name, the complete value should be provided. +• If a parameter has a value, the equal sign (=) is used. The value can be an integer, a floating point +number, or a character string, depending on the context. For example, +*ELASTIC, TYPE=ISOTROPIC, DEPENDENCIES=1 +• When the parameter value is a character string that represents the name of an item, you should not +use case as a method of distinguishing values unless the values are enclosed within quotation marks. +For example, Abaqus does not distinguish between the following definitions: +*MATERIAL, NAME=STEEL +*MATERIAL, NAME=Steel +• The same parameter should not appear more than once on a single keyword line. If a parameter has +multiple settings on a single keyword line, Abaqus ignores all but one of the settings. +• Continuation of a keyword line is sometimes necessary; for example, because of a large number +of parameters. If the last character on a keyword line is a comma, the next line is interpreted as a +continuation of the line. For example, the *ELASTIC keyword line above could also be given as +*ELASTIC, TYPE=ISOTROPIC, +DEPENDENCIES=1 +• Certain keywords must be used in conjunction with other keywords; for example, the *ELASTIC +and *DENSITY keywords must be used in conjunction with the *MATERIAL keyword. These +related keywords must be grouped in a block in the input file; unrelated keywords cannot be specified +within this block. +• Some options allow the INPUT or FILE parameter to be set equal to the name of an alternate file. +Such file names can include a full path name or a relative path name. Relative path names must be +with respect to the directory from which the job was submitted. If no path is specified, the file is +assumed to be in the directory from which the job was submitted. A substructure library must be in +the same directory from which the job was submitted; a full path name cannot be used to specify a +substructure library name. +For files referenced by the INPUT parameter, the file name must include any extension (e.g., +elem.inp). For files referenced by the FILE parameter, the name must be given without an +extension in most cases since Abaqus assumes that the file to be read has the correct extension for the +file type that is relevant to the option: .res for restart files (“Restarting an analysis,” Section 9.1.1) +and .fil for results files (“Output,” Section 4.1.1). However, special rules may apply when a +results file (.fil) or an output database file (.odb) is relevant for the option . +The file or substructure library name must have the correct case on computers with case- +sensitive operating systems. Regardless of whether the user specifies only a file name, a relative +path name, or a full path name, the complete name including the path can have a maximum of +80 characters. +Data lines +Data lines are used to provide data that are more easily given in lists than as parameters on an option. +Most options require one or more data lines; if they are required, the data lines must immediately follow +the keyword line introducing the option. The following rules apply when entering a data line: +• A data line can include no more than 256 characters, including blanks. Trailing blanks are ignored. +• All data items must be separated by commas (,). An empty data field is specified by omitting data +between commas. Abaqus will use values of zero for any required numeric data that are omitted +unless a default value is specified. +• A line must contain only the number of items specified. +• Empty data fields at the end of a line can be ignored. +• Floating point numbers can occupy a maximum of 20 spaces including the sign, decimal point, and +any exponential notation. +Floating point numbers can be given with or without an exponent. Any exponent, if input, +must be preceded by E or D and an optional (−) or (+). The following line shows four acceptable +ways of entering the same floating point number: +-12.345 +-1234.5E-2 +-1234.5D-2 +-1.2345E1 +• Integer data items can occupy a maximum of 9 digits. +• Character strings can be up to 80 characters long and are not case sensitive. +• Continuation lines are allowed in specific instances . If +allowed, such lines are indicated by a comma as the last character of the preceding line. A single +data item cannot be entered over multiple lines. +In many cases the choice of parameters used with an option determines the type of data lines required. For +example, there are five different ways to define a linear elastic material (“Elastic behavior: overview,” +Section 22.1.1). The data lines you specify must be consistent with the value of the TYPE parameter +given on the *ELASTIC option. +Sets +One of the most useful features of the Abaqus data definition method is the availability of sets. A set can +be a set of nodes or a set of elements. You provide a name (1–80 characters, the first of which must be a +letter) for each set. That name then provides a means of referencing all of the members of the set. As an +example suppose that, for the structure shown in Figure 1.2.1–1, we wish to apply symmetry boundary +conditions at all of the nodes in the set MIDDLE and that the edge SUPPORT is pinned. We assemble the +relevant nodes into sets and specify the boundary conditions by +*BOUNDARY +NSET middle +NSET support +Figure 1.2.1–1 Example of the use of sets. +MIDDLE, ZSYMM +SUPPORT, PINNED +Sets are the basic reference throughout Abaqus, and the use of sets is recommended. Choosing +meaningful set names makes it simple to identify which data belong to which part of the model. +Further discussion of sets is provided in “Node definition,” Section 2.1.1, and “Element definition,” +Section 2.2.1. +Labels +Labels such as set names, surface names, and rebar names are case insensitive unless enclosed +within quotation marks (except when they are accessed from user subroutines; see “User subroutines: +overview,” Section 18.1.1). Labels can be up to 80 characters long. All spaces within a label are ignored +unless the label is enclosed in quotation marks, in which case all spaces within the label are maintained. +A label that is not enclosed within quotation marks must begin with a letter, may not include a period +(.), and should not contain characters such as commas and equal signs. These restrictions do not apply +to labels enclosed within quotation marks except if the label is a material name. A material name must +always start with a letter, even if the name is enclosed within quotation marks. +Labels cannot begin and end with a double underscore (e.g., __STEEL__). This label format is +reserved for internal use by Abaqus. +The following are examples of labels entered with and without the use of quotation marks: +*ELEMENT, TYPE=SPRINGA, ELSET="One element" +1,1,2 +*SPRING, ELSET="One element" +1.0E-5, +*NSET, ELSET="One element", NSET=NODESET +*BOUNDARY +nodeset,1,2 +Repeating data lines +Some options list only a single data line. In cases where only one data line is allowed, this is indicated +by the data line title “First (and only) line.” An example of this is the *DYNAMIC option. In many cases +the single data line shown can be repeated to define one variable as a function of another; this choice is +indicated by a note after the data line. For example, a table of biaxial test data can be given to define a +hyperelastic material: +*BIAXIAL TEST DATA +, +, +, +Etc. +There is no limit on the number of data lines allowed, but the data must be given in a certain order, as +explained below. +Many options require more than one data line; these are indicated by the data line titles “First line:”, +“Second line:”, etc. For example, exactly two data lines must be used to define a local orientation for a +shell element (*ORIENTATION), and at least three data lines are required to define anisotropic elasticity +(*ELASTIC). +In many cases the data lines can be repeated, which is indicated by a note after the data lines. As +with repetition of a single data line, it is important that sets of data lines be given in the correct order so +that Abaqus can interpolate the data properly. +Example: Multiple data lines due to field variable dependence +Any time an option can be defined as a function of field variables, you must determine the number of data +lines required to define the option completely. For example, two data lines are required if stress- +based failure criteria (*FAIL STRESS) are defined as a function of two field variables. This pair of data +lines is repeated as often as necessary to define the failure criteria completely: +first +pair +⎭ +⎬ +⎫ +⎭ +second +⎬ +pair +⎫ +⎭ +⎬ +⎫ +third +pair +*FAIL STRESS, DEPENDENCIES=2 +X1, X1, Y1, Y1, S1, , σ1 +fv1, fv1 +1 2 +t c t c biax +t c t c biax +X2, X2, Y2, Y2, S2, , σ2 +fv2, fv2 +1 2 +t c t c biax +X3, X3, Y3, Y3, S3, , σ3 +fv3, fv3 + 1 2 +Etc. +(In this example the last field on the first data line of each pair was omitted, which means that the stress- +based failure criteria are not temperature dependent.) +If the stress-based failure criteria were defined as a function of nine field variables, a set of three +data lines would be repeated as often as necessary: +*FAIL STRESS, DEPENDENCIES=9 +X1, X1, Y1, Y1, S1, , σ1 +t c t c biax +fv1, fv1, fv1, fv1, fv1, fv1, fv1, fv1 +1 2 3 4 5 6 7 8 +fv1 +⎭ +⎬ +⎫ +first +set +⎭ +second +⎬ +set +⎫ +X2, X2, Y2, Y2, S2, , σ2 +t c t c biax +fv2, fv2, fv2, fv2, fv2, fv2, fv2, fv2 +1 2 3 4 5 6 7 8 +fv2 +Etc. +Ordering the data lines +Whenever one variable is defined as a function of another, the data must be given in the proper order so +that Abaqus can interpolate for intermediate values correctly. The variable being defined is assumed to be +constant outside the range of independent variables given, except for nonlinear elastic gasket thickness +behavior involving damage where the data are extrapolated based on the last slope computed from the +user-specified data. +If the property being defined is a function of only one variable (such as the *BIAXIAL TEST DATA +shown above), the data should be given in the order of increasing value of the independent variable. +If the property being defined is a function of multiple independent variables, the variation of the +property with respect to the first variable must be given at fixed values of the other variables, in ascending +values of the second variable, then of the third variable, and so on. The data lines must always be ordered +so that the independent variables are given increasing values. This process ensures that the value of the +material property is completely and uniquely defined at any values of the independent variables upon +which the property depends. +As an example, consider isotropic elasticity defined as a function of three field variables (but not of +temperature): +*ELASTIC, DEPENDENCIES=3 +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, 1, 1, 1 +, 2, 1, 1 +, 1, 2, 1 +, 2, 2, 1 +, 1, 3, 1 +, 2, 3, 1 +, 1, 1, 2 +, 2, 1, 2 +, 1, 2, 2 +, , 2, 2, 2 +, , 1, 3, 2 +, , 2, 3, 2 +, , 1, 1, 3 +, , 2, 1, 3 +, , 1, 2, 3 +, , 2, 2, 3 +, , 1, 3, 3 +, , 2, 3, 3 +1.2.2 +CONVENTIONS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD Abaqus/CAE +References +• Chapter 2, “Spatial Modeling” +• Part II, “Output” +• “Boundary conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1 +• “Boundary conditions in Abaqus/CFD,” Section 33.3.2 +Overview +The conventions that are used throughout Abaqus are defined in this section. The following topics are +discussed: +• Degrees of freedom +• Coordinate systems +• Self-consistent units +• Time measures +• Local directions on surfaces in space +• Stress and strain conventions +• Stress and strain measures in geometrically nonlinear analysis +• Conventions for finite rotations +• Conventions for tabular data input +Degrees of freedom +Except for axisymmetric elements, fluid continuum elements, and electromagnetic elements, the degrees +of freedom are always referred to as follows: +x-displacement +y-displacement +z-displacement +Rotation about the x-axis, in radians +Rotation about the y-axis, in radians +Rotation about the z-axis, in radians +Warping amplitude (for open-section beam elements) +Pore pressure, hydrostatic fluid pressure, or acoustic pressure +Electric potential +10 +11 +12 +13 +14 +Connector material flow (units of length) +Temperature (or normalized concentration in mass diffusion analysis) +Second temperature (for shells or beams) +Third temperature (for shells or beams) +Etc. +Here the x-, y-, and z-directions coincide with the global X-, Y-, and Z-directions, respectively; however, +if a local transformation is defined at a node , they +coincide with the local directions defined by the transformation. +A maximum of 20 temperature values (degrees of freedom 11 through 30) can be defined for shell +or beam elements in Abaqus/Standard. +Axisymmetric elements +The displacement and rotation degrees of freedom in axisymmetric elements are referred to as follows: +r-displacement +z-displacement +Rotation about the z-axis (for axisymmetric elements with twist), in radians +Rotation in the r–z plane (for axisymmetric shells), in radians +Here the r- and z-directions coincide with the global X- and Y-directions, respectively; however, if a +local transformation is defined at a node , they +coincide with the local directions defined by the transformation. +Fluid continuum elements +Fluid continuum elements in Abaqus/CFD are used to define the element shape and to discretize the +continuum. Degrees of freedom in a fluid flow analysis are not determined by the element type but by +the analysis procedure and options specified (e.g., turbulence models and auxiliary transport equations). +Electromagnetic elements +Electromagnetic elements in Abaqus/Standard are used to define the element shape and to discretize the +continuum. The eddy current and magnetostatic analyses formulations use magnetic vector potential as a +degree of freedom . +Activation of degrees of freedom +Abaqus/Standard and Abaqus/Explicit activate only those degrees of freedom needed at a node. Thus, +some of the degrees of freedom listed above may not be used at all nodes in a model, because each +element type uses only those degrees of freedom that are relevant. For example, two-dimensional solid +(continuum) stress/displacement elements use only degrees of freedom 1 and 2. The degrees of freedom +actually used at any node are the envelope of those needed in each element that shares the node. +In Abaqus/CFD the active degrees of freedom in a fluid flow analysis are determined by the analysis +procedure and the options specified. For example, using the energy equation in conjunction with the +incompressible flow procedure activates the velocity, pressure, and temperature degrees of freedom. +For more information, see “Active degrees of freedom” in “Boundary conditions in Abaqus/CFD,” +Section 33.3.2. +Internal variables in Abaqus/Standard +In addition to the degrees of freedom listed above, Abaqus/Standard uses internal variables (such as +Lagrange multipliers to impose constraints) for some elements. Normally you need not be concerned +with these variables, but they may appear in error and warning messages and are checked for satisfaction +of nonlinear constraints during iteration. Internal variables are always associated with internal nodes, +which have negative numbers to distinguish them from user-defined nodes. +Coordinate systems +The basic coordinate system in Abaqus is a right-handed, rectangular Cartesian system. You can choose +other systems locally for input , for output of nodal variables +(displacements, velocities, etc.) and point load or boundary condition specification , and for material or kinematic joint specification . All coordinate systems must be right-handed. +Units +Abaqus has no units built into it except for rotation and angle measures. Therefore, the units chosen must +be self-consistent, which means that derived units of the chosen system can be expressed in terms of the +fundamental units without conversion factors. +Rotation and angle measures +In Abaqus rotational degrees of freedom are expressed in radians, and all other angle measures are +expressed in degrees (for example, phase angles). +International System of units (SI) +The International System of units (SI) is an example of a self-consistent set of units. The fundamental +units in the SI system are length in meters (m), mass in kilograms (kg), time in seconds (s), temperature +in degrees kelvin (K), and electric current in amperes (A). The units of secondary or derived quantities +are based on these fundamental units. An example of a derived unit is the unit of force. A unit of force +in the SI system is called a newton (N): +Similarly, a unit of electrical charge in the SI system is called a coulomb (C): +newton +kg m s +coulomb +A s +Another example is the unit of energy, called a joule (J): +joule +N m +A volt s +kg m s +The unit of electrical potential in the SI system is the volt, which is chosen such that +joule +volt C +volt A s +Sometimes the standard units are not convenient to work with. For example, Young’s modulus is +frequently specified in terms of megapascals (MPa) (or, equivalently, N/mm2 ), where 1 pascal = 1 N/m2 . +In this case the fundamental units could be tonnes (1 tonne = 1000 kilograms), millimeters, and seconds. +American or English units +American or English units can cause confusion since the naming conventions are not as clear as in the +SI system. For example, 1 pound force (lbf) will give 1 pound mass (lbm) an acceleration of g ft/sec2 , +where g is the value of acceleration due to gravity. If pounds force, feet (ft), and seconds are taken as +fundamental units, the derived unit of mass is lbf sec2 /ft. Since density is commonly given in handbooks +as lbm/in3 , it must be converted to lbf sec2/ft4 by +lbm in +lbf sec +ft +Frequently it is not made clear in handbooks whether lb stands for lbm or lbf. You need to check that the +values used make up a consistent set of units. +Two other units that cause difficulty are the slug, defined as the mass that will be accelerated at +1 ft/sec2 by 1 lbf, and the poundal, defined as the force required to accelerate 1 lbm at 1 ft/sec2 . Useful +conversions are +and +slug +lbm +lbf +poundals +where g is the magnitude of the acceleration due to gravity in ft/sec2 . +Symbols used in Abaqus for units +Units are indicated for the value to be given on load and flux types as follows: +Dimension +Indicator Example (S.I. units) +length +mass +meter +kilogram +Dimension +Indicator Example (S.I. units) +time +temperature +electric current +force +energy +electric charge +electric potential +mass concentration +second +degree Celsius +ampere +newton +joule +coulomb +volt +Parts per million +Time +Abaqus has two measures of time—step time and total time. Except for certain linear perturbation +procedures, step time is measured from the beginning of each step. Total time starts at zero and is the total +accumulated time over all general analysis steps (including restart steps; see “Restarting an analysis,” +Section 9.1.1). Total time does not accumulate during linear perturbation steps. +Local directions on surfaces in space +Local directions are needed on surfaces in space; for example, to define the tangential slip directions on +an element-based contact surface or to define stress and strain components in a shell. The convention +used in Abaqus for such directions is as follows. +The default local 1-direction is the projection of the global x-axis onto the surface. If the global +x-axis is within 0.1° of being normal to the surface, the local 1-direction is the projection of the global +z-axis onto the surface. The local 2-direction is then at right angles to the local 1-direction, so that the +local 1-direction, local 2-direction, and the positive normal to the surface form a right-handed set . The positive normal direction is defined in an element by the right-hand rotation rule +going around the nodes of the element. The local surface directions can be redefined; see “Orientations,” +Section 2.2.5. +The local 1- and 2-directions become local 2- and 3-directions, respectively, when considering +gasket elements or the local systems associated with integrated output sections (“Integrated output section +definition,” Section 2.5.1) or user-defined sections (“Section output from Abaqus/Standard” in “Output +to the data and results files,” Section 4.1.2). +For “line”-type surfaces defined on beam, pipe, or truss elements in space, the default local +1-direction and 2-direction are tangential and transverse to the elements. In this case the local surface +directions can also be redefined as described in “Orientations,” Section 2.2.5. +surface normal +projection of x-axis +onto surface +surface +normal +Figure 1.2.2–1 Default local surface directions. +Rotation of the local directions +For geometrically linear analysis, stress and strain components are given by default in the material +directions in the reference (initial) configuration. +For geometrically nonlinear analysis, small-strain shell elements in Abaqus/Standard (S4R5, +S8R, S8R5, S8RT, S9R5, STRI3, and STRI65) use a total Lagrangian strain, and the stress and strain +components are given relative to material directions in the reference configuration. Gasket elements +are small-strain small-displacement elements, and the components are output by default in the behavior +directions in the reference configuration. +For finite-membrane-strain elements (all membrane elements, S3/S3R, S4, S4R, SAX, and SAXA +elements) and for small-strain shell elements in Abaqus/Explicit, the material directions rotate with the +average rigid body motion of the surface to form the material directions in the current configuration. +Stress and strain components in these elements are given relative to these material directions in the +current configuration. +For a more thorough discussion of the definition of the rotated coordinate directions in membrane +elements; S3/S3R, S4, and S4R elements; S3RS, S4RS, and S4RSW elements; and SAXA elements, see: +• “Membrane elements,” Section 3.4.1 of the Abaqus Theory Manual, +• “Finite-strain shell element formulation,” Section 3.6.5 of the Abaqus Theory Manual, +• “Small-strain shell elements in Abaqus/Explicit,” Section 3.6.6 of the Abaqus Theory Manual, and +• “Axisymmetric shell element allowing asymmetric loading,” Section 3.6.7 of the Abaqus Theory +Manual. +You can determine whether the local system associated with a user-defined section is fixed or rotates +with the average rigid body motion; see “Section output from Abaqus/Standard” in “Output to the data +and results files,” Section 4.1.2, for details. +You can determine whether the local system associated with an integrated output section is fixed, +translates with average rigid body motion, or translates and rotates with the average rigid body motion; +see “Integrated output section definition,” Section 2.5.1, for details. +See “Contact formulations in Abaqus/Standard,” Section 37.1.1, for information on how the slip +directions evolve during an Abaqus/Standard contact analysis. +Convention used for stress and strain components +When defining material properties, the convention used for stress and strain components in Abaqus is +that they are ordered: +Direct stress in the 1-direction +Direct stress in the 2-direction +Direct stress in the 3-direction +Shear stress in the 1–2 plane +Shear stress in the 1–3 plane +Shear stress in the 2–3 plane +For example, a fully anisotropic, linear elasticity matrix is +symm. +The 1-, 2-, and 3-directions depend on the element type chosen. For solid elements the defaults for +these directions are the global spatial directions. For shell and membrane elements the defaults for the +1- and 2-directions are local directions in the surface of the shell or membrane, as defined in Part VI, +“Elements.” In both cases the 1-, 2-, and 3-directions can be changed as described in “Orientations,” +Section 2.2.5. +For geometrically nonlinear analysis with solid elements, the default (global) directions do not rotate +with the material. However, user-defined orientations do rotate with the material. +, +, +Abaqus/Explicit stores the stress and strain components internally in a different order: +, +. For geometrically nonlinear analysis, the internally stored components rotate with the +material, regardless of whether or not a user-defined orientation is used. This distinction is important +when a user subroutine (such as VUMAT) is used. +, +, +Nonisotropic material behavior +When nonisotropic material behavior is defined in continuum elements, a user-defined orientation is +necessary for the anisotropic behavior to be associated with material directions. See “State storage,” +Section 1.5.4 of the Abaqus Theory Manual, for a description of how material directions rotate. +Zero-valued stress components +Stress components that are always zero are omitted from storage. For example, in plane stress Abaqus +stores only the two direct components and one shear component of stress and strain in the plane where +the stress values are nonzero. +Shear strains +Abaqus always reports shear strain as engineering shear strain, +: +Stress and strain measures +The stress measure used in Abaqus is Cauchy or “true” stress, which corresponds to the force per +current area. See “Stress measures,” Section 1.5.2 of the Abaqus Theory Manual, and “Stress rates,” +Section 1.5.3 of the Abaqus Theory Manual, for more details on stress measures. +For geometrically nonlinear analysis, a large number of different strain measures exist. Unlike +“true” stress, there is no clearly preferred “true” strain. For the same physical deformation different +strain measures will report different values in large-strain analysis. The optimal choice of strain measure +depends on analysis type, material behavior, and (to some degree) personal preference. See “Strain +measures,” Section 1.4.2 of the Abaqus Theory Manual, for more details on strain measures. +By default, the strain output in Abaqus/Standard is the “integrated” total strain (output variable E). +For large-strain shells, membranes, and solid elements in Abaqus/Standard two other measures of total +strain can be requested: logarithmic strain (output variable LE) and nominal strain (output variable NE). +Logarithmic strain (output variable LE) is the default strain output in Abaqus/Explicit; nominal +strain (output variable NE) can be requested as well. The “integrated” total strain is not available in +Abaqus/Explicit. +Total (integrated) strain +The default “integrated” strain measure, E, output by Abaqus/Standard to the data (.dat) and results +(.fil) files for all elements that can handle finite strain is obtained by integrating the strain rate +numerically in a material frame of reference: +are the total strains at increments +and n, respectively; +is the total strain increment from increment n to +1.2.2–8 +is the incremental +. For elements that use +where +rotation tensor; and +orientations), the above equation simplifies to +CONVENTIONS +The strain increment is obtained by integration of the rate of deformation +over the time increment: +This strain measure is appropriate for elastic-(visco)plastic or elastic-creeping materials, because the +plastic strains and creep strains are obtained by the same integration procedure. In such materials the +elastic strains are small (because the yield stress is small compared to the elastic modulus), and the total +strains can be compared directly with the plastic strains and creep strains. +If the principal directions of straining rotate with respect to the material axes, the resulting strain +measure cannot be related to the total deformation, regardless whether a spatial or corotational coordinate +system is used. If the principal directions remain fixed in the material axes, the strain is the integration +of the rate of deformation, +which is equivalent to the logarithmic strain discussed later. +Green’s strain +For small-strain shells and beams in Abaqus/Standard, the default strain measure, E, is Green’s strain: +is the deformation gradient and +is the identity tensor. This strain measure is appropriate for +where +the small-strain, large-rotation approximation used in these elements. The components of +represent +strain along directions in the original configuration. The small-strain shells and beams should not be +used in finite-strain analysis with either elastic-plastic or hyperelastic material behavior, since incorrect +analysis results may be obtained or program failure may occur. +Nominal strain +The nominal strain, NE, is +is the left stretch tensor, +where +are the principal +stretch directions in the current configuration. The principal values of nominal strain are, therefore, the +ratios of change in length to length in the reference configuration in the principal directions, thus giving +a direct measure of deformation. +are the principal stretches, and +Logarithmic strain +The logarithmic strain, LE, is +where the variables are as defined earlier for nominal strain. This is also the strain output for hyperelastic +materials. For a hyper-viscoleastic material, the logarithmic elastic strain EE is computed from the +current (relaxed) stress state, and the viscoelastic strain CE is computed as LE +EE. +Stress invariants +Many of the constitutive models in Abaqus are formulated in terms of stress invariants. These invariants +are defined as the equivalent pressure stress, +the Mises equivalent stress, +and the third invariant of deviatoric stress, +where +is the deviatoric stress, defined as +Finite rotations +The following convention is used for finite rotations in space: Define +global X, Y, and Z-axes (that is, degrees of freedom 4, 5, and 6 at a node). Then define +, +, +as “rotations” about the +where +The direction +according to the right-hand rule . +is then the axis of rotation, and +is the angular rotation (in radians) about the axis +Same vector rotated +by ( φ , φ , φ ) +y z +Initial vector +Figure 1.2.2–2 Definition of finite rotation. +The value of +, any multiple of +exceeds +for the rotation components. If rotations larger than +direction in Abaqus/Standard, the rotation output varies discontinuously between 0 and +Abaqus/Explicit the rotation output varies in all cases between +is not uniquely determined. In large-rotation problems where the overall rotation +can be added or subtracted, which may lead to discontinuous output values +about one axis occur in the positive (negative) +). In +and +( +. +This convention provides straightforward input of kinematic boundary conditions and moments in +most cases and simple interpretation of the output. The rotations output by Abaqus represent a single +rotation from the reference configuration to the current configuration about a fixed axis. The output does +not follow the history of rotation at a node. In addition, this convention reduces to the usual convention +for small rotations, even in the case of small rotations superposed on an initial finite rotation (such as +might be considered in the study of small vibrations about a predeformed state). +Compound rotations +Because finite rotations are not additive, the way they must be specified is a bit different from the way +the increment in rotation specified over a step must be the +other boundary conditions are specified: +rotation needed to rotate the node from the configuration at the beginning of the step to that desired at +the end of the step. It is not enough to rotate the node over this step to a total rotation vector that would +have taken the node into its final configuration if applied on the node in some other initial reference +configuration. +is needed to rotate from the rotation +boundary condition +at the beginning of the step (and at the end of the previous step) to +its final position at the end of the step, the boundary condition must be specified such that the rotation +vector is +at the end of the step. If the direction of the rotation vector +is constant, this method of specifying rotation boundary conditions and the total rotation vector will be +the same. +If an increment of rotation +Example +As an example of how to specify compound finite rotations and to interpret finite rotation output, consider +the following example of the rotation of a beam. +The beam initially lies along the x-axis. We want to perform the compound rotation, where (Step 1) +the beam is rotated by 60° about the z-axis, followed by (Step 2) a 90° spin of the beam about itself, +followed by (Step 3) a 90° rotation of the beam about an axis perpendicular to the beam in the x–y plane, +such that the beam finishes on the z-axis. +This compound rotation is achieved in three steps with applied rotation vectors +, +, and +, +where +, +For this example +represents the magnitude of each +finite rotation about the (unit length) rotation axis. The rotation vectors above are applied in each of the +three steps on the configuration at the beginning of that step. It is most straightforward to prescribe these +rotations with velocity-type boundary conditions. For convenience, the default amplitude reference in +Abaqus for a velocity-type boundary condition is a constant value of one. +. Here +, and +A typical Abaqus step definition for this example, where node 1 is pinned at the origin and the +rotation is applied to node 2, is as follows: +*STEP, NLGEOM +Step 1: Rotate 60 degrees about the z-axis +*STATIC +*BOUNDARY, TYPE=VELOCITY +2, 4, 5 +2, 6, 6, 1.047198 +*END STEP +** +*STEP, NLGEOM +Step 2: Rotate 90 degrees about the beam axis +*STATIC +*BOUNDARY, TYPE=VELOCITY +2, 4, 4, 0.785398 +2, 5, 5, 1.36035 +2, 6, 6 +*END STEP +** +*STEP, NLGEOM +Step 3: Rotate beam onto z-axis +*STATIC +*BOUNDARY, TYPE=VELOCITY +2, 4, 4, 1.36035 +2, 5, 5, -0.785398 +2, 6, 6 +*END STEP +The above method for applying finite-rotation boundary conditions (using a velocity-type boundary +condition with the default constant amplitude definition) is strongly recommended. However, if the +rotation boundary conditions are applied as displacement-type boundary conditions, the input syntax +would change. +The Abaqus/Standard convention for boundary condition specification within a step is to specify +the total or final boundary state. In such a case the specified boundary conditions from all of the previous +steps must be added to the incremental rotation vector components. The Abaqus/Standard step definitions +from above would change to: +*STEP, NLGEOM +Step 1: Rotate 60 degrees about the z-axis +*STATIC +*BOUNDARY +2, 4, 5 +2, 6, 6, 1.047198 +*END STEP +** +*STEP, NLGEOM +Step 2: Rotate 90 degrees about the beam axis +*STATIC +*BOUNDARY +2, 4, 4, 0.785398 +2, 5, 5, 1.36035 +2, 6, 6, 1.047198 +*END STEP +** +*STEP, NLGEOM +Step 3: Rotate beam onto z-axis +*STATIC +*BOUNDARY +2, 4, 4, 2.145748 +2, 5, 5, 0.574952 +2, 6, 6, 1.047198 +*END STEP +The boundary conditions in Steps 2 and 3 are the sum of the incremental rotation components plus the +rotation boundary conditions specified in the previous steps. +In Abaqus/Explicit references to amplitude definitions should be used such that there are no jumps +in displacement across the steps. It is often convenient to use amplitude definitions given in terms of +total time for this purpose. The displacement boundary conditions will be applied incrementally based +on the increment in the value of amplitude curve over the time increment. Therefore, any sudden jumps +in displacement at the beginning of a step introduced either without the amplitude curves or with two +amplitude curves will be ignored . The Abaqus/Explicit step definitions for the above example would change to: +*AMPLITUDE, TIME=TOTAL TIME, NAME=RAMPUR1 +0., 0., 0.001, 0., 0.002, 0.785398, 0.003, 2.145748 +*AMPLITUDE, TIME=TOTAL TIME, NAME=RAMPUR2 +0., 0., 0.001, 0., 0.002, 1.36035, 0.003, 0.574952 +*AMPLITUDE, TIME=TOTAL TIME, NAME=RAMPUR3 +0., 0., 0.001, 1.047198, 0.002, 1.047198, 0.003, 1.047198 +*STEP +Step 1: Rotate 60 degrees about the z-axis +*DYNAMIC, EXPLICIT +, 0.001 +*BOUNDARY, AMP=RAMPUR1 +2, 4, 4, 1.0 +*BOUNDARY, AMP=RAMPUR2 +2, 5, 5, 1.0 +*BOUNDARY, AMP=RAMPUR3 +2, 6, 6, 1.0 +*END STEP +** +*STEP +Step 2: Rotate 90 degrees about the beam axis +*DYNAMIC, EXPLICIT +, 0.001 +*END STEP +** +*STEP +Step 3: Rotate beam onto z-axis +*DYNAMIC, EXPLICIT +, 0.001 +*END STEP +The boundary conditions in Steps 2 and 3 are the sum of the incremental rotation components plus the +rotation boundary conditions specified in the previous steps. +The Abaqus output of the rotation field at the end of Step 3 is +We see that none of the individual components of the specified boundary conditions appears in the +final rotation output. The final rotation output represents the rotation vector required to obtain the final +orientation in a single step. +Suppose that in Step 3 of the previous example we want to apply the rotation vector +at node 1 +instead of at node 2. If the rotation is applied incrementally, the Abaqus/Standard step definition is as +follows: +*STEP, NLGEOM +Step 3: Rotate beam onto z-axis +*STATIC +*BOUNDARY, TYPE=VELOCITY, OP=NEW +1, 1, 3 +1, 4, 4, 1.36035 +1, 5, 5, -0.785398 +1, 6, 6 +*END STEP +and the Abaqus/Explicit step definition is similar. +conditions that are in effect at node 2. +It is necessary to remove the rotation boundary +As mentioned previously, using velocity-type boundary conditions is the preferred method for +applying finite-rotation boundary conditions. If the rotation boundary condition is to be applied as a +displacement-type boundary condition, we must first retrieve the rotation field at node 1 at the end of +Step 2. The Abaqus output of this rotation field is +These rotation vector components must then be added to the incremental rotation vector components we +wish to prescribe in Step 3. The Abaqus/Standard step definition would change to +*STEP +Step 3: Rotate beam onto z-axis +*STATIC +*BOUNDARY, OP=NEW +1, 1, 3 +1, 4, 4, 2.772 +1, 5, 5, 0.0301 +1, 6, 6, 0.8155 +*END STEP +and the Abaqus/Explicit step definition would change to: +*STEP +Step 3: Rotate beam onto z-axis +*DYNAMIC, EXPLICIT +, 0.001 +*AMPLITUDE, TIME=STEP TIME, NAME=NODE1UR1 +0., 1.412, 0.001, 2.772 +*AMPLITUDE, TIME=STEP TIME, NAME=NODE1UR2 +0., 0.8155, 0.001, 0.0301 +*AMPLITUDE, TIME=STEP TIME, NAME=NODE1UR3 +0., 0.8155, 0.001, 0.8155 +*BOUNDARY, OP=NEW +1, 1, 3 +*BOUNDARY, OP=NEW, AMP=NODE1UR1 +1, 4, 4, 1. +*BOUNDARY, OP=NEW, AMP=NODE1UR2 +1, 5, 5, 1. +*BOUNDARY, OP=NEW, AMP=NODE1UR3 +1, 6, 6, 1. +*END STEP +The boundary conditions are again specified in the Abaqus/Explicit input using amplitude curves to avoid +any sudden jump in their values at the beginning of the step. As stated above and in “Boundary conditions +in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1, any jumps in the displacement values will be +ignored and the boundary will be maintained at the previous values. +As this last procedure clearly demonstrates, it is simpler to apply finite-rotation boundary conditions +as velocity-type boundary conditions rather than as displacement-type boundary conditions. The +recommended method of specifying finite-rotation boundary conditions is also described in “Boundary +conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1. For further discussion of how +finite rotations are accumulated, see “Rotation variables,” Section 1.3.1 of the Abaqus Theory Manual. +1.3 +Abaqus model definition +• “Defining a model in Abaqus,” Section 1.3.1 +1.3.1 +DEFINING A MODEL IN Abaqus +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD +References +• “Input syntax rules,” Section 1.2.1 +• Abaqus Keywords Reference Manual +• Abaqus/CAE User’s Manual +Overview +An analysis in Abaqus is defined by an input file, which +• contains keyword lines and data lines; and +• is divided into model data and history data. +The input file +An Abaqus input file is an ASCII data file. It can be created by using a text editor or by using a graphical +preprocessor such as Abaqus/CAE. The input file consists of a series of lines containing Abaqus options +(keyword lines) and data (data lines). The input syntax for keyword and data lines is described in “Input +syntax rules,” Section 1.2.1. +Most input files have the same basic structure. The following portions of the input file are specified +to define a finite element model: +1. An input file often begins with the *HEADING option, which is used to define a title for the analysis. +Any number of data lines can be used to give the title; they will appear at the beginning of the output +files (“Output,” Section 4.1.1). The first heading line will appear as a heading at the top of each page +of the output. +While including a title can be helpful for users examining your input file, the *HEADING +option is not required. +2. After the heading the input file usually contains a model data section to define nodes, elements, +materials, initial conditions, etc. The model data section is explained below. +3. If the model is organized into an assembly of part instances, the model data are further categorized +and must fall within the proper level: part, assembly, instance, or model. Models defined in terms +of an assembly of part instances are discussed in “Defining an assembly,” Section 2.10.1. +4. Finally, the input file contains history data to define the analysis type, loading, output requests, etc. +Step definitions divide the model data from the history data in an input file: everything appearing +before the first step definition is model data, and everything appearing within and following the first +step definition is history data. The history data section is explained below. +The input file is processed by the “analysis input file processor” prior to executing the appropriate analysis +product, Abaqus/Standard, Abaqus/Explicit, or Abaqus/CFD. The functions of the analysis input file +processor are to interpret the Abaqus options, to perform the necessary consistency checking, and to +prepare the data for the analysis products. +Most computational mechanics modeling options (element types, loading types, etc.) are available +in both Abaqus/Standard and Abaqus/Explicit, although some options are available in only one analysis +product or the other. All of the step procedure types used in an input file must be from the same analysis +product; however, it is possible to import a solution from Abaqus/Standard into Abaqus/Explicit and vice +versa , which allows each analysis product to be +used at the various stages of an analysis for which it is best suited (for example, a static preloading in +Abaqus/Standard followed by a dynamic analysis in Abaqus/Explicit). +Model data +Model data define the nodes, elements, materials, initial conditions, etc. +Required model data +The following model data must be included in an input file to define a finite element model: +• Geometry: The geometry of a model is described by elements and their nodes. The rules +and methods for defining nodes and elements are described in “Node definition,” Section 2.1.1; +“Element definition,” Section 2.2.1; and “Defining an assembly,” Section 2.10.1. Cross-sections +for structural elements (such as beams) must be defined. Special features can be defined with +special elements such as springs, dashpots, point masses, etc. The element types available for +modeling are described in Part VI, “Elements,” along with explanations of how to define the +elements. You can view the initial mesh or the configuration after adjustment for initial overclosure +in the Visualization module of Abaqus/CAE after a data check run . +• Material definitions: A material type must be associated with most portions of the geometry. +The material library is described in Part V, “Materials.” Special elements such as springs or dashpots +do not have an associated material, but their properties must be defined. +Optional model data +The following model data can be included as necessary: +• Parts and an assembly: The geometry of a model can be defined by organizing it into +parts, which are positioned relative to one another in an assembly (“Defining an assembly,” +Section 2.10.1). +• Initial conditions: Nonzero initial conditions such as initial stresses, temperatures, or velocities +can be specified (“Initial conditions,” Section 33.2). +• Boundary conditions: Zero-valued boundary conditions (including symmetry conditions) +can be imposed on individual solution variables such as displacements or rotations (“Boundary +conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1). +• Kinematic constraints: Equations involving several of the fundamental solution variables in the +model (“Linear constraint equations,” Section 34.2.1) or multi-point constraints (“General multi- +point constraints,” Section 34.2.2) can be defined. +• Interactions: Contact and other interactions between parts can be defined (“Contact interaction +analysis: overview,” Section 35.1.1). +• Amplitude definitions: Amplitude curves can be defined for +later use in specifying +time-dependent loading or boundary conditions (“Amplitude curves,” Section 33.1.2). +• Output control: You can control model definition output to the data file (“Output,” Section 4.1.1). +• Environment properties: Environment properties, such as the attributes of a fluid surrounding +the model, may have to be defined. +• Analysis continuation: +It is possible to write restart data or to use the results from a previous +analysis and continue the analysis with new model or history data (“Restarting an analysis,” +Section 9.1.1), with a new mesh (“Submodeling: overview,” Section 10.2.1; “Mesh-to-mesh +solution mapping,” Section 12.4.1; and “Symmetric model generation,” Section 10.4.1), or with the +same or a different Abaqus program (“Transferring results between Abaqus analyses: overview,” +Section 9.2.1). +History data +The purpose of an analysis is to predict the response of a model to some form of external loading or +to some nonequilibrium initial conditions. An Abaqus analysis is based on the concept of steps, which +are described in the history data portion of the input file. (For more information on steps, see “Defining +an analysis,” Section 6.1.2.) The history input data are combined within a step as needed to define the +history of the analysis. +Multiple steps can be defined in an analysis. Steps can be introduced simply to change the output +requests or to change the loads, boundary conditions, analysis procedure, etc. There is no limit on the +number of steps in an analysis. +There are two kinds of steps in Abaqus: general response analysis steps, which can be linear or +nonlinear; and, in Abaqus/Standard, linear perturbation steps . A general analysis step contributes to the response history of the system; +a linear perturbation step allows the investigation of the linearized response of the system at any stage +during the response history. +The state at the end of a general step provides the initial conditions for the next step, making it easy +to simulate consecutive loadings of a model, such as a dynamic response following a static preload or +the loading of a product during its usage following a simulation of the manufacturing process. +The optional history data described below prescribing the loading; boundary conditions; output +controls; auxiliary controls; and, in Abaqus/Explicit, contact conditions are continued from one general +analysis step to the next general analysis step unless modified. For example, the solution controls +prescribed in a general analysis step in Abaqus/Standard will remain in effect for all subsequent general analysis steps until +they are modified or reset. For linear perturbation steps only the output controls are continued from +one linear perturbation step to the next if there are no intermediate general analysis steps and the +output controls are not redefined . Similarly, conditions specified in an +Abaqus/CFD analysis are continued from one step to the next unless modified. +Input File Usage: +Use the following option to begin a step definition: +*STEP +Use the following option to end a step definition: +*END STEP +Required history data +The following history data must be included in an input file to define an analysis procedure: +• Response type: An option to define the analysis procedure type must appear immediately after +the beginning of the step definition. +Abaqus can perform many types of analyses—linear or nonlinear, static or dynamic, etc. . The type of analysis can be changed from step to step. For +example, in Abaqus/Standard a static preload can be analyzed first, then the response type can be +changed to transient dynamic. In this way a linear or nonlinear dynamic analysis can be performed +based on the conditions at the end of the static solution. +Optional history data +The following history data can be included as necessary: +• Loading: Usually some form of external loading is defined. For example, concentrated or +distributed loads can be applied (“Applying loads: overview,” Section 33.4.1), temperature changes +leading to thermal expansion can be prescribed (“Thermal expansion,” Section 26.1.2), or contact +conditions can be used to apply loads (“Contact interaction analysis: overview,” Section 35.1.1). +The loading can be prescribed as a function of time (“Amplitude curves,” Section 33.1.2). +This feature can be used to prescribe loadings such as the ground motion during a seismic event, +known accelerations, or the temperature and pressure history during a transient in an engine. If an +amplitude curve is not defined, Abaqus assumes either that the loading varies linearly over the step +or that the load is applied instantaneously at the beginning of the step, depending on the chosen +response type . +• Boundary conditions: Boundary conditions can be added, modified, or removed during an +analysis (“Boundary conditions,” Section 33.3). +• Output control: Quantities such as stress, strain, reaction force, temperature, and energy are +available as output. The output options are described in “Output to the data and results files,” +Section 4.1.2, and “Output to the output database,” Section 4.1.3; and all of the output variables +are listed in “Output variables,” Section 4.2. The available output files are described in “Output,” +Section 4.1.1. +• Contact: Contact surfaces and contact interactions can be added, modified, or removed as +step-dependent history data during an Abaqus/Explicit analysis . +• Auxiliary controls: You can overwrite the solution controls that are built +into Abaqus. +In some procedures these values are given in the procedure definition. More generally in +Abaqus/Standard they are given by defining solution controls (“Commonly used control +parameters,” Section 7.2.2). Solution controls for contact problems (“Adjusting contact controls +in Abaqus/Standard,” Section 35.3.6; “Common difficulties associated with contact modeling +using contact pairs in Abaqus/Explicit,” Section 38.2.2; or “Contact controls for general contact in +Abaqus/Explicit,” Section 35.4.5) can also be defined. +• Element and surface removal/reactivation: +In Abaqus/Standard portions of the model can be +removed or reactivated from step to step. See “Element and contact pair removal and reactivation,” +Section 11.2.1. +• Co-simulation: The steps in the Abaqus model must be defined such that the co-simulation fits +entirely within a single Abaqus step. Further, there can be only one co-simulation in the Abaqus +job. +Including model or history data from an external file +You can specify an external file that contains a portion of the Abaqus input file. This file can include +model and history definition data, comment lines, and other references to external files. When a reference +to an external file is encountered, Abaqus will immediately process the data within the specified file. +When the end-of-file is reached, Abaqus will return to processing the original file. +A maximum of five levels of nested external file references can be used. UNIX environment +variables can be used to specify the file names. +Input File Usage: +*INCLUDE, INPUT=file_name +Including an encrypted data file +You can include an encrypted file by reference in an Abaqus input file or in another data file. When +you refer to the encrypted file, you must also provide the file’s password. If the password is correct, +Abaqus processes the data within the specified file as it would for an unencrypted external file. Material +and connector behavior definitions within an encrypted input file are not written to the output database. +In addition, all material and connector behavior definitions output to the data file are suppressed if an +encrypted file is used as input for any portion of the model. See “Encrypting and decrypting Abaqus +input data,” Section 3.2.32, for details about the encryption utility. +Some encrypted files are eligible for inclusion only by users with a license for a particular Abaqus +feature (such as Abaqus/Explicit) or to users at a particular site. If you attempt to include an encrypted +file for which you do not have the proper privileges, Abaqus issues an error message. +You cannot include encrypted input files that contain parametric input. +Input File Usage: +*INCLUDE, INPUT=file_name, PASSWORD=password +1.4 +Parametric modeling +• “Parametric input,” Section 1.4.1 +1.4.1 +PARAMETRIC INPUT +Products: Abaqus/Standard Abaqus/Explicit +References +• “Scripting parametric studies,” Section 20.1.1 +• “Parametric shape variation,” Section 2.1.2 +• *PARAMETER +• *PARAMETER DEPENDENCE +• *PARAMETER SHAPE VARIATION +• Chapter 4, “Introduction to Python,” of the Abaqus Scripting User’s Manual +Overview +The parametric input capability allows you to create an Abaqus input file in which: +• Any number of input parameters is defined by assigning a value to each one of them. +• The parameters defined in the input file are used in place of input quantities. +• The parameters are evaluated according to their definition and are substituted for the parametrized +input quantities before an analysis is run. +Parametric input allows greater flexibility in building and manipulating models. The different kinds of +parameters and the different ways of parametrizing the Abaqus input quantities are discussed in this +section. +Introduction +You must define all the parameters you wish to use in an analysis by assigning a value to them. The +Python language (Lutz, 1999) is used to perform parameter evaluation and substitution; hence, parameter +definitions are required to follow the Python syntax rules discussed later in this section. These parameters +can then be used in place of input quantities. +Input File Usage: +Use the following option to define parameters: +*PARAMETER +Use these parameters in place of input quantities by delimiting them with < >. +For example, the following input defines the two parameters width and +height, which are then used to define beam section properties: +*PARAMETER +width = 2.5 +height = width*2 +*BEAM SECTION, SECTION=RECT, ELSET=name, +MATERIAL=name +, +In this simple example models with beams of different cross-sections can be +obtained simply by changing the values of the parameters. +Parameters +Parameters are user-named variables to which you assign values. When a parameter is used instead of a +value, the value of that parameter is substituted. There are two basic types of parameters: independent +parameters and dependent parameters. +Independent parameters +Independent parameters are those that do not depend on any other parameters. The following are +examples of independent parameters: +thickness = 10.0 +area = 5.0**2 +length = 3.0*sin(45*pi/180.0) # convert degrees to radians +Python expressions using numbers and numerical operations (such as addition, multiplication, and +exponentiation) can be used to define independent parameters. Arithmetic support in Python is +discussed later in this section. +Dependent parameters +Dependent parameters are those that depend on other parameters (dependent or independent). Dependent +parameters can be defined in one of two ways: using a mathematical expression or using a tabular +dependence. +Expressional dependence +Python parametric expressions involving operations between numbers and parameters are used to +define expressionally dependent parameters. In the following example area and mom_inertia are +dependent parameters: +width = 2.0 +height = 5.0 +area = width*height +mom_inertia = area*height**2/12.0 +Tabular dependence +Tabular dependence between parameters is defined by specifying the dependent and independent +parameters as well as a dependence table. The table that defines the dependence between the parameters +must have as many values per line as the number of dependent parameters plus the number of +independent parameters for which it is going to be used. The table must contain only real values; +dependent parameter values are given first, followed by independent parameter values. Parameter +names and character strings cannot be used in a table. +The evaluation of tabularly dependent parameters by interpolation between values in a table will +result in these parameters being assigned real values. +If it is necessary that the tabularly dependent +parameters be integer numbers, the real numbers must be converted to integer numbers as described +later in the Python language section. +When the tabularly dependent parameters are functions of only one independent parameter, the +tabular data must be given in order of increasing values of the independent parameter. Abaqus then +interpolates linearly for values between those given. The dependent parameters are assumed to be +constant outside the range of the independent parameters used in a table. When the tabularly dependent +parameters depend on several independent parameters, the variation of the dependent parameters +with respect to the first independent parameter must be given at fixed values of the other independent +parameters, in ascending values of the second independent parameter, then of the third independent +parameter, and so on. The table lines must always be ordered so that the independent parameters are +given increasing values. This process ensures that the value of each dependent parameter is completely +and uniquely defined for all values of the independent parameters. +The fact that the definition of the dependence table is separate from the assignment of the +dependence to particular parameters means that the same table can be used for multiple sets of +dependent/independent parameters. This is useful when there are different instances of the same kind +of input data; for example, multiple material definitions that use the same dependence but different sets +of parameters. +Because the evaluation of parameters is procedural , a parameter +dependence table must always be defined before it is used to specify tabular parameter dependencies. +Independent parameters in tabular dependence definitions are treated as independent for the purpose +of defining this dependency; however, these “independent” parameters can be defined to depend on other +parameters in a preceding parameter definition. +Input File Usage: +Use the following option to define a parameter dependence table: +*PARAMETER DEPENDENCE, TABLE=name, NUMBER VALUES=n +table with n values per line +Use the following option to define the dependent and independent parameters +that are used in the dependence table: +*PARAMETER, TABLE=name, DEPENDENT=(parList), +INDEPENDENT=(parList) +Rules for parameters +Some general rules apply to all parameters used in Abaqus input files. These rules are described in the +following subsections. +Parameter evaluation +Parameters are evaluated by ordered execution of the parameter definitions as they appear in the input +file. For example, the input +*PARAMETER +x = 2 +y = x + 3 +x = 4 +gives x=4 and y=5, not x=4 and y=7. The input +*PARAMETER +y = x + 3 +x = 4 +is flagged as an error because y cannot be evaluated by ordered execution of the input. In other words, +there is no deferred execution of the parameter definitions. +It is possible to define parameters anywhere in the input file, even after parameters have been used +in place of input quantities, since the parameter definitions are always processed before any other input +options are processed. +Parameters can also be defined and used in place of input quantities in an input file used for a restart +analysis. However, parameters defined in the input file for the original analysis (from which the restart +run is continued) are not available in the restart analysis. +Parameter substitution +When the parameterized data are processed, Abaqus assigns the parameter values as determined at the +end of parameter evaluation. An error is reported if a parameter used in place of input quantities has not +been assigned a value. Later, the analysis input file processor performs its usual checks on the validity +of the parameter values with respect to the options in which they are being used. +Data given to define a parameter, a parameter dependence table, or a parameter shape variation +cannot be parameterized. For example, the input +*PARAMETER SHAPE VARIATION + +is not valid; however, the analysis input file processor will not report an error for this input. +Data types +The data type of a parameter is deduced from its definition. An integer parameter results from assigning +an integer literal value to the parameter. Similarly, a real parameter arises from assigning a real literal +value to the parameter. Integers are promoted to reals if they are used in operations containing reals. A +character string parameter results from assigning a character string literal value to the parameter. +The input option context in which the parameter is used dictates the data type that the parameter must +have. Parameters of real data type should be used in place of real Abaqus input quantities. Parameters +of integer (or character string) type should be used in place of integer (or character string) type input +quantities, respectively. In some instances, mismatches between the input context and the type of the +substituted parameter will cause the analysis input file processor to flag these instances as input errors. +For example, the input +*PARAMETER +int_pts = 5.0 +*SHELL SECTION +10.0, +will cause the analysis input file processor to report an error because the number of integration points +specified for a shell section must be an integer. However, the input +*PARAMETER +thick = 5/4 +*SHELL SECTION +, +will be accepted by the analysis input file processor without a warning being flagged; as a result of doing +integer division, this input gives a shell thickness of 1 (not 1.25). In conclusion, you can rely on the +analysis input file processor to catch only some data type errors. +Continuous and discrete parameters +From the point of view of design activities (sensitivity analysis, parametric studies, etc.) parameters can +be continuous valued or discrete valued. A continuous-valued parameter is differentiable and can, thus, +be used for design sensitivity analysis purposes. A discrete-valued parameter is not differentiable and +can, thus, not be used for design sensitivity analysis purposes; however, it can be used for parametric +studies. Examples of continuous-valued parameters may be a shell thickness or a material property. +Examples of discrete-valued parameters may be the number of integration points through the thickness +of a shell, or an element type. Continuous-valued parameters generally coincide with physical (design) +input quantities, while discrete-valued parameters generally coincide with finite element (numerical +approximation) input quantities. +Auxiliary input files +Parameters can be defined in *INCLUDE input files but not in any other auxiliary input files. Names of +auxiliary input files can be parameterized, except those used in the *INCLUDE option. +Parametrization of input quantities +Abaqus treats parametrization of “size” and “shape” quantities somewhat differently. Parametrization of +shape input quantities is discussed in a separate section . +Size input quantities are understood to include all Abaqus input quantities except those that relate +to shape. Size input quantities include section properties, material properties, orientation properties, +prescribed conditions, interaction definitions and properties, and analysis procedure data. +Parametrizing individual input quantities +The following example shows the parametrization of shell section input using three independent +parameters of differing data types: +*ELSET, ELSET=, GEN +1, 111, 10 +*PARAMETER +shell_set = 'lining' +shell_thick = 1.E2 +num_int_pts = 5 +*SHELL SECTION, ELSET=, MATERIAL=name +, +Parametrizing groups of input quantities (expressional dependence) +The following example shows the parametrization of a three-layer composite shell section using +expressional-dependent parameters. In this example the thickness parameter can be used to change +the thickness of the layers of the composite section uniformly. +*PARAMETER +thickness = 10. +layer1_thick = 0.15*thickness +layer2_thick = 0.6*thickness +layer3_thick = 0.25*thickness +*SHELL SECTION, ELSET=, COMPOSITE +,num int pts, material name, orientation +,num int pts, material name, orientation +,num int pts, material name, orientation +This parametrization requires that dependent parameters be created for the three input quantities +(layer1_thick, layer2_thick, layer3_thick) that each depend on the independent +parameter (thickness). +Parametrizing groups of input quantities (tabular dependence) +The following example shows the parametrization of the section properties of a box beam. The height +and wall thicknesses of the beam section are parameters that depend tabularly on the section width. +*PARAMETER +a = 60. +*PARAMETER DEPENDENCE, TABLE=sectprop, NUMBER VALUES=6 +25.0, 1.04, +50.0, 4.17, +75.0, 9.38, +*PARAMETER, TABLE=sectprop, DEPENDENT=(b, t1, t2, t3, t4), +INDEPENDENT=(a) +*BEAM SECTION, SECTION=BOX, ELSET=beams, MATERIAL=steel +, , , , , +1.04, 1.04, 1.04, 50.0 +3.13, 2.08, 2.50, 100.0 +6.24, 3.13, 4.90, 150.0 +The above parametrization creates dependent parameters (b, t1, t2, t3, t4) that each depend on the +independent parameter (a). Usage of tabular dependence allows the definition of the dependencies of +input quantities on parameters to be confined to the parameter definitions; i.e., separate from the options +where parametrization of input quantities is done. An advantage of this method of parametrization is +that the same parameter dependence table can be used for different parameters in different input options. +For example, you may wish to use beams of different cross-section dimensions in different parts of the +structure being modeled. The parameter dependence table can be reused with new dependent (bb, tt1, +tt2, tt3, tt4) and independent (aa) parameters. +*PARAMETER +aa = 65. +*PARAMETER, TABLE=sectprop, DEPENDENT=(bb, tt1, tt2, tt3, tt4), +INDEPENDENT=(aa) +*BEAM SECTION, SECTION=BOX, ELSET=columns, MATERIAL=steel +, , , , , +In options where predefined field variable dependence is supported, this method of parametrization +provides a clear separation between predefined field variable dependence and parameter dependence; +therefore, field variable and parameter dependence can never be confused. Consider, for example, the +case of perfect plasticity properties for a metal where the yield stress depends on a field variable and is +also parametrized to depend tabularly on the carbon content of the metal alloy. +*PARAMETER +carbon = 0.01 +*PARAMETER DEPENDENCE, TABLE=yield_data, NUMBER=4 +ys_fv1 val 1, ys_fv2 val 1, ys_fv3 val 1, carbon val 1 +ys_fv1 val 2, ys_fv2 val 2, ys_fv3 val 2, carbon val 2 +ys_fv1 val 3, ys_fv2 val 3, ys_fv3 val 3, carbon val 3 +ys_fv1 val 4, ys_fv2 val 4, ys_fv3 val 4, carbon val 4 +*PARAMETER, TABLE=yield_data, DEPENDENT=(ys_fv1, ys_fv2, ys_fv3), +INDEPENDENT=(carbon) +*MATERIAL, NAME=alloy +*PLASTIC, DEPENDENCIES=1 +, , , fv val 1 +, , , fv val 2 +, , , fv val 3 +Consider, for example, the case of metal creep properties where the creep material data are parameters +that depend tabularly on the carbon content of the metal alloy. In addition, one of the creep parameters, +A, also depends on a predefined field variable. +*PARAMETER +carbon = 0.01 +*PARAMETER DEPENDENCE, TABLE=creepdata, NUMBER=6 +A_fv1 val 1, A_fv2 val 1, A_fv3 val 1, n val 1, m val 1, carbon val 1 +A_fv1 val 2, A_fv2 val 2, A_fv3 val 2, n val 2, m val 2, carbon val 2 +A_fv1 val 3, A_fv2 val 3, A_fv3 val 3, n val 3, m val 3, carbon val 3 +A_fv1 val 4, A_fv2 val 4, A_fv3 val 4, n val 4, m val 4, carbon val 4 +*PARAMETER, TABLE=creepdata, DEPENDENT=(A_fv1, A_fv2, A_fv3, +n, m), INDEPENDENT=(carbon) +*MATERIAL, NAME=alloy +*CREEP, DEPENDENCIES=1 +, , , , fv val 1 +, , , , fv val 2 +, , , , fv val 3 +This example shows that any combination of dependencies on predefined field variables and/or dependent +parameters can be defined. +Python language +Parameter statements in parameter definitions are required to follow the syntax and semantics of the +Python language (note that the parameter dependence table and parameter shape variation definitions +follow the usual Abaqus input syntax rules). The subset of the Python language that is endorsed is +documented here. +Statement length and continuation lines +Python statements in parameter definitions can be continued over multiple lines by terminating each line +with a backslash character (\). The *PARAMETER keyword lines can be continued onto the following +line using a trailing comma since they are treated like other Abaqus keyword lines. +Comments +Comments in a parameter definition start with the number character (#) and continue to the end of the +line. However, comments in a parameter dependence table or parameter shape variation definition are +indicated by the usual Abaqus input syntax convention (**). +Parameter names +Parameter names must begin with a letter and can contain the underscore character (_) and numbers. +Parameter names are case sensitive. +Data types +Data types are limited to character strings, integers, and reals. +Strings are delimited with single or double quotation marks (’ ’ or ” ”). Backward single quotation +marks (‘ ‘) are not permitted. Character strings should not contain the backslash character (\). +Integers are created by assignment to integer literals (for example, aInt = 2). +Reals are created by assignment to real literals (for example, aReal = 1.0). Real numbers can be +given with or without an exponent. Any exponent must be preceded by E or e. The following line shows +five acceptable ways of entering the same real number: +-12.345, -1234.5E-2, -0.12345E+2, -0.12345E2, -0.12345e2 +The syntax +-0.12345D+2 +(allowed elsewhere in the Abaqus input file) is not valid in Python. +Type conversion +If integers and reals are mixed in expressions, integers are promoted automatically to reals. Explicit type +conversion can be obtained using: +int(aReal) +float(anInt) +str(anIntOrReal) +’anIntOrReal’ +aReal converted to integer type +anInt converted to real type (float is the same as real) +anIntOrReal converted to character string type +anIntOrReal converted to character string type +Numeric operators +Standard support for operators is provided: +− x ++ x +x + y +x − y +x * y +x / y +x**y +Functions +x negated +x unchanged +sum of x and y +difference of x and y +product of x and y +quotient of x and y +x to the power y +The following utility functions are supported: +abs(x) +acos(x) +asin(x) +atan(x) +cos(x) +log(x) +log10(x) +pow(x,y) +absolute value of x +arc cosine of x (result is in radians) +arc sine of x (result is in radians) +arc tangent of x (result is in radians) +cosine of x (x is in radians) +natural logarithm of x +base 10 logarithm of x +x to the power y (equivalent to x**y) +sin(x) +sqrt(x) +tan(x) +sine of x (x is in radians) +square root of x +tangent of x (x is in radians) +Character string operators +’abc’ + ’def’ +concatenation of character string ’abc’ and character string ’def’ +Execution of parametrized input +Jobs with parametrized input files are submitted to Abaqus in the usual way; for example, +abaqus job=job-name input=input-file +where it is assumed that an input file named input-file.inp exists. +Abaqus searches input-file.inp and any *INCLUDE input files for parameter, parameter +dependence table, and parameter shape variation (“Parametric shape variation,” Section 2.1.2) +definitions, as well as parameter names inside < > that may have been used in place of input quantities. +If any of the above are found, Abaqus will interpret the parametrized input file and perform the tasks +of parameter evaluation and substitution. +As a result, a modified input file that is free of parameter and parameter dependence table +This file is named job-name.pes and is +definitions and instances is produced. +subsequently submitted for execution of an analysis. The execution procedure of a parametrized input +file, except for the additional processing of parameter shape variation definitions in the analysis input +file processor, does not differ from that of a non-parametrized input file. All the files generated by the +parametrized input job will be named job-name with the appropriate extension appended to it. +Parameter check jobs +You can specify an execution mode in which only parameter processing (evaluation and substitution) is +carried out. The parameter check execution mode is mutually exclusive of other execution modes, such +as complete analysis, data check, continuation of a data check, conversion of results, or recovery . +A parameter check run is useful in situations where you have defined complex parametrization in +the input. In these cases you may want to study the results of parameter evaluation and substitution +before proceeding further. +A parameter check run does not permit continuation of the execution in a subsequent run; the job +must be rerun from the beginning. +Input File Usage: +Enter the following input on the command line: +abaqus job=job-name input=input-file parametercheck +Display of parametric input +Display of the results of parameter evaluation and substitution in the data file is described in this section. +Visualization of parameter shape variations is described in “Parametric shape variation,” Section 2.1.2. +Data file display +The data (.dat) file contains information about the model definition generated by the analysis input +file processor. You can control the amount of output generated by the analysis input file processor; see +“Controlling the amount of analysis input file processor information written to the data file” in “Output,” +Section 4.1.1, for details. In particular, you can specify whether or not the original input (.inp) file is +echoed to the data file (by default, it is not). +In the case of parametric input this file will generally contain a number of parameter, parameter +dependence table, and parameter shape variation definitions, as well as a number of +instances. To verify the definition of parametric input, you can create a modified version of the original +input file showing the parameters and their values (this file is named job-name.par). You can also +create the job-name.pes file, which is the modified version of the original input file that is free of +parameter and parameter dependence table definitions, as well as instances. +Input File Usage: +Use the following option to print the contents of the job-name.par file to the +data file: +*PREPRINT, PARVALUES=YES +Use the following option to print the contents of the job-name.pes file to the +data file: +*PREPRINT, PARSUBSTITUTION=YES +Additional reference +• Lutz, M., and D. Ascher, Learning Python, O’Reilly & Associates, Inc., 1999. +Spatial Modeling +Node definition +Element definition +Surface definition +Rigid body definition +Integrated output section definition +Mass adjustment +Nonstructural mass definition +Distribution definition +Display body definition +Assembly definition +Matrix definition +SPATIAL MODELING +2.1 +2.2 +2.3 +2.4 +2.5 +2.6 +2.7 +2.8 +2.9 +2.10 +2.1 +Node definition +• “Node definition,” Section 2.1.1 +• “Parametric shape variation,” Section 2.1.2 +• “Nodal thicknesses,” Section 2.1.3 +• “Normal definitions at nodes,” Section 2.1.4 +• “Transformed coordinate systems,” Section 2.1.5 +• “Adjusting nodal coordinates,” Section 2.1.6 +2.1.1 +NODE DEFINITION +Products: Abaqus/Standard Abaqus/Explicit +References +• *NCOPY +• *NFILL +• *NGEN +• *NMAP +• *NODE +• *NSET +• *SYSTEM +Overview +This section describes the methods for defining nodes in an Abaqus input file. In a preprocessor such as +Abaqus/CAE, you define the model geometry rather than the nodes and elements; when you mesh the +geometry, the preprocessor automatically creates the nodes and elements needed for analysis. Although +the concepts discussed in this section apply in general to the node definitions in the input file that is +created by Abaqus/CAE, the methods and techniques described here apply only if you are creating the +input file manually. +Node definition consists of: +• assigning a node number to the node; +• optionally specifying a local coordinate system in which to define nodes; +• defining individual nodes by specifying their coordinates; +• grouping nodes into node sets; +• creating nodes from existing nodes by generating them incrementally, by copying existing nodes, +or by filling in nodes between the bounds of a region; and +• mapping a set of nodes from one coordinate system to another. +If any node is specified more than once, the last specification given is used. +Abaqus will eliminate all unnecessary nodes before proceeding with the analysis. This feature is +useful because it allows points to be defined as nodes for mesh generation purposes only. +Assigning a node number to the node +Each individual node must have a numeric label called the node number, which is assigned when the +node is defined. The node number must be a positive integer, and the maximum node number allowed +is 999999999 (for information on integer input, see “Input syntax rules,” Section 1.2.1). The nodes do +not need to be numbered continuously. +An Abaqus model can be defined in terms of an assembly of part instances . In such a model all nodes must belong to either a part, part instance, or, in +the case of reference nodes, to the assembly. Node numbers must be unique within a part, part instance, +or the assembly; but they can be repeated in different parts or part instances. +Specifying a local coordinate system in which to define nodes +Sometimes it is convenient to define nodal coordinates in a local coordinate system and then transform +these coordinates to the global coordinate system. You can define a nodal coordinate system; Abaqus +will translate and rotate the local ( +) coordinate values into the global coordinate system. The +transformation is done immediately after input and will be applied to all nodal coordinates entered or +generated after the nodal coordinate system is defined. +The transformation affects only the input of nodal coordinates in node definitions. Nodal coordinate +system definitions cannot be used +• for applying loads and boundary conditions—see “Transformed coordinate systems,” Section 2.1.5, +instead; or +• for output of components of stress, strain, and element section forces—see “Orientations,” +Section 2.2.5, instead. +In addition to defining nodal coordinate systems, you can define individual nodes or node sets in local +rectangular, cylindrical, or spherical systems . If a nodal coordinate system is in effect and you specify a local coordinate system for a +particular node or node set definition, the input coordinates are first transformed according to the local +system specified in the node definition and then according to the nodal coordinate system. +Defining the nodal coordinate system +You set up the coordinate system specification by specifying the global coordinates of three points in +the local system: the origin of the local system (point a in Figure 2.1.1–1), a point on the local +-axis +(point b in Figure 2.1.1–1), and a point in the +plane of the local system on (or near) the local +-axis (point c in Figure 2.1.1–1). +(global) +(local) +Figure 2.1.1–1 Nodal coordinate system. +If only one point (the origin) is given, Abaqus assumes that you need a translation only. If only two +points are given, the direction of the +-axis +will be projected onto the +-axis will be the same as that of the Z-axis; that is, the +plane. +To change the nodal coordinate system that is in effect, define another nodal coordinate system; +to revert to input in the global coordinate system, use a nodal coordinate system definition without any +associated data. +Input File Usage: +Use the following option to define a nodal coordinate system: +*SYSTEM +, +, +, +, +, +, +, +For example, in the following input, nodes 1 through 3 are defined in the +first nodal coordinate system, nodes 4 and 5 are defined in the second nodal +coordinate system, and nodes 6 and 7 are defined in the global coordinate +system: +*SYSTEM +0, 0, 0, 5, 5, 5 +*NODE +1, 0, 0, 1 +2, 0, 0, 2 +3, 0, 1, 2 +*SYSTEM +2, 3, 4 +*NODE +4, 0, 0, 1 +5, 1, 4, 0 +*SYSTEM +*NODE +6, 1, 0, 1 +7, 0, 4, 2 +Defining a nodal coordinate system within part definitions +When you define a nodal coordinate system within a part (or part instance) definition, it is in effect only +within that part (or part instance) definition. Nodes defined in other parts are not affected. +You specify the local ( +) coordinate values relative to the part coordinate system, which +subsequently may be translated and/or rotated according to the positioning data given for the instance +. +Defining individual nodes by specifying their coordinates +You can define individual nodes by specifying the node number and the coordinates that define the +node. Abaqus uses a right-handed, rectangular Cartesian coordinate system for all nodes except for +axisymmetric models, when the coordinates of the nodes must be given as the radial and axial positions. +For more information about direction definitions, see “Conventions,” Section 1.2.2. +In a model defined in terms of an assembly of part instances, give nodal coordinates in the local +coordinate system of the part (or part instance). See “Defining an assembly,” Section 2.10.1. +Input File Usage: +*NODE +Reading node definitions from a file +Node definitions can be read into Abaqus from an alternate file. The syntax of such file names is described +in “Input syntax rules,” Section 1.2.1. +Input File Usage: +*NODE, INPUT=file_name +Specifying a local coordinate system for the nodal coordinates +You can specify that a local rectangular Cartesian, cylindrical, or spherical coordinate system be used +for a particular node definition. These coordinate systems are shown in Figure 2.1.1–2. +(X,Y,Z) +Rectangular Cartesian +(default) +(R,θ,Z) +(R,θ, φ) +Cylindrical +(θ and φ are given in degrees) +Spherical +Figure 2.1.1–2 Coordinate systems. +This coordinate system specification is entirely local to the node definition. As the nodal data +are read, the coordinates are transformed to rectangular Cartesian coordinates immediately. If a nodal +coordinate system is also in effect , +these are local rectangular Cartesian coordinates as defined by the nodal coordinate system, which are +subsequently transformed to global Cartesian coordinates. +Input File Usage: +Use the following option to specify the nodal coordinates in a rectangular +Cartesian system (this is the default): +*NODE, SYSTEM=R +Use the following option to specify the nodal coordinates in a cylindrical +system: +*NODE, SYSTEM=C +Use the following option to specify the nodal coordinates in a spherical system: +the following lines define node number 1 with coordinates +*NODE, SYSTEM=S +For example, +(10cos20°, 10sin20°, 5.) in a local cylindrical system (R, +*NODE, NSET=DISC, SYSTEM=C +1, 10., 20., 5. +, Z): +If the following lines appeared in the input file before the above node definition, +the coordinates of node 1 would be transformed first to rectangular Cartesian +coordinates in the nodal coordinate system defined by the *SYSTEM option +and then to coordinates in the global system: +*SYSTEM +2, 0, 2 +Grouping nodes into node sets +Node sets are used as convenient cross-references when defining loads, constraints, properties, etc. Node +sets are the fundamental references of the model and should be used to assist the input definition. The +members of a node set can be individual nodes or other node sets. An individual node can belong to +several node sets. +Nodes can be grouped into node sets when they are created or after they have already been defined. +In either case each node set is assigned a name. Node set names can be up to 80 characters long. +The same name can be used for a node set and for an element set. +By default, the nodes within a node set will be arranged in ascending order, and duplicate nodes +will be removed. Such a set is called a sorted node set. You may choose to create an unsorted node set +as described later, which is often useful for features that match two or more node sets. For example, if +you define multi-point constraints (“General multi-point constraints,” Section 34.2.2) between two node +sets, a constraint will be created between the first node in Set 1 and the first node in Set 2, then between +the second node in Set 1 and the second node in Set 2, etc. It is important to ensure that the nodes are +combined in the desired way. Therefore, it is sometimes better to specify that a node set be stored in +unsorted order. +Once nodes are assigned to a node set, additional nodes can be added to the same node set; however, +nodes cannot be removed from a node set. +Creating an unsorted node set +You can choose to assign nodes to a new node set (or to add nodes to an existing node set) in the order +in which they are given. The node numbers will not be rearranged, and duplicates will not be removed. +This unsorted node set will affect node copies, node fills, linear constraint equations, multi-point +constraints, and substructure nodes associated with retained degrees of freedom. An unsorted node set +can be created only by directly defining an unsorted node set as described here or by copying an unsorted +node set. Any additions or modifications to a node set using other means will result in a sorted node set. +Input File Usage: +*NSET, NSET=name, UNSORTED +Assigning nodes to a node set as they are created +There are several ways that nodes can be assigned to node sets as they are created. +Input File Usage: +Use any of the following options: +*NODE, NSET=name +*NCOPY, NEW SET=name +*NFILL, NSET=name +*NGEN, NSET=name +*NMAP, NSET=name +Assigning previously defined nodes to a node set +You can assign nodes that you have defined previously (by specifying their coordinates, by filling in nodes +between two bounds, or by generating them incrementally) to a node set by listing the nodes forming the +set directly, by generating the node set, or by generating a node set from an element set. +Listing the nodes that define the set directly +You can list the nodes that form a node set directly. Previously defined node sets, as well as individual +nodes, can be assigned to node sets. +Input File Usage: +*NSET, NSET=name +For example, the following lines add nodes 1, 3, 10, 11, and all the nodes in set +A11 to set A12: +*NSET, NSET=A12 +1, 3 +10, 11, +A11 +Node set A11 can be assigned to node set A12 only if the definition of A11 +occurs before the definition of A12. +All the nodes in node set A12 will be sorted into ascending numerical order. If +the UNSORTED parameter were included on the *NSET option, node set A12 +would contain the nodes in the order in which they are specified on the data +lines. +Generating the node set +To generate a node set, you must specify a first node, +numbers between these nodes, i. All nodes going from +set. Therefore, i must be an integer such that +is +. +; a last node, +to +; and the increment in node +in increments of i will be added to the +is a whole number (not a fraction). The default +Input File Usage: +*NSET, NSET=name, GENERATE +For example, the following lines add all nodes from 100 to 120 in increments +of 10 to set A13: +*NSET, NSET=A13, GENERATE +100, 120, 10 +Generating a node set from an element set +You can specify the name of a previously defined element set (“Element definition,” Section 2.2.1), +in which case the nodes that define the elements contained in this element set will be assigned to the +specified node set. This method can be used only to define sorted node sets. +Input File Usage: +*NSET, NSET=name, ELSET=name +For example, the following lines add all nodes that define elements 50 and 100 +(nodes 1, 2, 3, and 4) to node set A14: +*ELEMENT, TYPE=B21 +50, 1, 2 +100, 3, 4 +*ELSET, ELSET=B1 +50, 100 +*NSET, NSET=A14, ELSET=B1 +Element set B1 can be assigned to node set A14 since the definition of B1 +occurs before the definition of A14. +Limitation on updating node sets that are used to define other node sets +If a node set is constructed from previously defined node sets, subsequent updates to these sets are not +taken into account. +Input File Usage: +*NSET, NSET=name +For example, the following lines add nodes 1 and 2, but not 3, to the set SET-AB +while adding nodes 1 and 3 to set SET-A: +*NSET, NSET=SET-A +1, +*NSET, NSET=SET-B +2, +*NSET, NSET=SET-AB +SET-A, SET-B +*NSET, NSET=SET-A +3, +Defining part and assembly sets +In a model defined in terms of an assembly of part instances, all node sets must be defined within a part, +part instance, or the assembly definition. If a node set is defined within a part (or part instance) definition, +you can refer to the node numbers directly. To define an assembly-level node set, you must identify the +nodes to be added to the set by prefixing each node number with the part instance name and a “.” (as +explained in “Defining an assembly,” Section 2.10.1). An assembly-level node set can have the same +name as a part-level node set. +Example +The following input defines a node set, set1, that belongs to part PartA and will be inherited by every +instance of PartA: +*PART, NAME=PartA +... +*NSET, NSET=set1 +1,3,26,500 +*END PART +A node set with the same name is defined at the assembly level as follows: +*ASSEMBLY, NAME=Assembly-1 +*INSTANCE, NAME=PartA-1, PART=PartA +... +*END INSTANCE +*INSTANCE, NAME=PartA-2, PART=PartA +... +*END INSTANCE +*NSET, NSET=set1 +PartA-1.1, PartA-1.3, PartA-1.26, PartA-1.500 +PartA-2.1, PartA-2.3, PartA-2.26, PartA-2.500 +*END ASSEMBLY +Assembly-level node set set1 contains all the nodes from node sets set1 belonging to part instances +PartA-1 and PartA-2. Therefore, the nodes are assigned to two separate node sets: one at the part +instance level and one at the assembly level. An assembly-level node set called set1 could be created +with entirely different nodes than those that belong to the part set; part- and assembly-level node sets +assembly-level node sets set1, the assembly-level set could alternatively be defined by +NODE DEFINITION +*ASSEMBLY, NAME=Assembly-1 +*INSTANCE, NAME=PartA-1, PART=PartA +... +*END INSTANCE +*INSTANCE, NAME=PartA-2, PART=PartA +... +*END INSTANCE +*NSET, NSET=set1 +PartA-1.set1, PartA-2.set1 +*END ASSEMBLY +This node set definition is equivalent to the previous example, where the nodes are listed individually. +Alternate method for defining assembly-level node sets +Sometimes it is not convenient to define an assembly-level node set by referring to part-level node sets. +In such cases a set definition containing many nodes can get quite lengthy. Therefore, an alternate method +is provided. +Input File Usage: +*NSET, NSET=NsetName, INSTANCE=InstanceName +The following example shows two equivalent ways to define an assembly-level +node set; once by prefixing each node number with a part instance name (as +shown above) and once using the more compact INSTANCE notation: +*ASSEMBLY, NAME=Assembly-1 +*INSTANCE, NAME=PartA-1, PART=PartA +... +*END INSTANCE +*INSTANCE, NAME=PartA-2, PART=PartA +... +*END INSTANCE +*NSET, NSET=set2 +PartA-1.11, PartA-1.12, PartA-1.13, PartA-1.14, +PartA-2.21, PartA-2.22, PartA-2.23, PartA-2.24 +*NSET, NSET=set3, INSTANCE=PartA-1 +11, 12, 13, 14 +*NSET, NSET=set3, INSTANCE=PartA-2 +21, 22, 23, 24 +*END ASSEMBLY +When the *NSET option is used more than once with the same name, as it +is with set3, the nodes in the second use of *NSET are appended to the set +created by the first use of *NSET. +Internal node sets created by Abaqus/CAE +In Abaqus/CAE many modeling operations are performed by picking geometry with the mouse. For +example, a concentrated load can be applied by picking a point on a geometric part instance. Since the +*CLOAD option refers to a node set, this “picked” geometry must be translated into a node set in the +input file. Such sets are assigned a name by Abaqus/CAE and marked as internal. You can view these +internal sets using display groups in the Visualization module of Abaqus/CAE . +Input File Usage: +*NSET, NSET=NsetName, INTERNAL +Transferring of node sets +If the results of an Abaqus/Explicit analysis are imported into an Abaqus/Standard analysis (or vice +versa) or results from an Abaqus/Standard analysis are imported into another Abaqus/Standard analysis +, all node set definitions +in the original analysis are imported by default. Alternatively, you can import only selected node set +definitions; see “Importing element set and node set definitions” in “Transferring results between Abaqus +analyses: overview,” Section 9.2.1, for details. +If a three-dimensional model is generated from a symmetric model , all node sets in the original model will be used (and expanded) in the +generated model. +Creating nodes from existing nodes by generating them incrementally +You can generate nodes incrementally from existing nodes. All of the nodes along a straight or curved +line can be generated by giving the coordinates of the two end nodes and defining the type of curve. +The two end nodes must already be defined, usually by specifying their coordinates, but it is also +possible to have them defined by an earlier generation. +Defining a straight line between the two end nodes +To define a straight line between the two end nodes, specify the number of the first end node, +number of the last end node, +i. Therefore, i must be an integer such that +is +; the +; and the increment in node numbers between each node along the line, +is a whole number (not a fraction). The default +. +Input File Usage: +*NGEN +For example, in the following input node number 1 with coordinates (0., 0., +0.) and node number 6 with coordinates (10., 0., 0.) are defined and nodes 2, +3, 4, and 5 with coordinates (2., 0., 0.), (4., 0., 0.), (6., 0., 0.), and (8., 0., 0.), +respectively, are generated automatically: +*NODE +1, 0., 0., 0. +6, 10., 0., 0. +1, 6, 1 +Defining a circular arc between the two end nodes +NODE DEFINITION +To define a circular arc between the two end nodes, specify the number of the first end node, +number of the last end node, +i. Therefore, i must be an integer such that +is +; the +; and the increment in node numbers between each node along the arc, +is a whole number (not a fraction). The default +. +In addition, you must specify the coordinates of one extra point, the center of the circle, either +by giving the node number of a node that has already been defined or by giving the nodal coordinates +directly. If both are supplied, the node number will take precedence over the coordinates. +If the coordinates are defined directly, they can be specified in a local coordinate system as described +later. +The coordinates of the end nodes will be adjusted radially if the circle cannot be passed through +both points. An arc of a circle of 180° through 360° will require more extensive definition. For this case +you must define the plane of the circular disc by giving the normal to the disc; the nodes will then be +numbered according to the right-hand rule about this normal. +Input File Usage: +*NGEN, LINE=C +Defining a parabola between the two end nodes +To define a parabola between the two end nodes, specify the number of the first end node, +of the last end node, +Therefore, i must be an integer such that +; the number +; and the increment in node numbers between each node along the parabola, i. +is a whole number (not a fraction). The default is +. +In addition, you must specify the coordinates of one extra point, the midpoint on the arc between +the two end points, either by giving the node number of a node that has already been defined or by +giving the nodal coordinates directly. If both are supplied, the node number will take precedence over +the coordinates. +If the coordinates are defined directly, they can be specified in a local coordinate system as described +later. +Input File Usage: +*NGEN, LINE=P +Defining the extra point and the normal direction in a local coordinate system +You can specify the coordinates of the extra point that is required for a circle or a parabola in a local +rectangular Cartesian system, a cylindrical system, or a spherical system. These coordinate systems are +shown in Figure 2.1.1–2. +If a nodal coordinate system is in effect , the coordinates and normal direction specified in the node definition are assumed to be +in the nodal coordinate system. If a nodal coordinate system is in effect and you specify the extra point +for a circle or parabola in a local coordinate system, the input is first transformed according to the local +system specified in the node definition and subsequently according to the nodal coordinate system. +Input File Usage: +Use the following option to specify the extra point in a rectangular Cartesian +system (this is the default): +*NGEN, SYSTEM=RC +Use the following option to specify the extra point in a cylindrical system: +*NGEN, SYSTEM=C +Use the following option to specify the extra point in a spherical system: +*NGEN, SYSTEM=S +Creating nodes by copying existing nodes +You can create new nodes by copying existing nodes. The coordinates of the new nodes can be translated +and rotated, reflected from the nodes being copied, or projected from the nodes being copied by using a +polar projection with respect to a pole node. +You must identify the existing node set to copy and specify an integer constant, n, that will be added +to the node numbers of existing nodes to define node numbers for the nodes being created. +You can assign the newly created nodes to a node set. If you do not specify a node set name for the +newly created nodes, they are not assigned to a node set. +Input File Usage: +*NCOPY, OLD SET=name, CHANGE NUMBER=n, NEW SET=new_name +Translating and rotating the coordinates of the old nodes +You can create new nodes by translating and/or rotating the nodes in the old node set . +You specify the value of the translation in the X-, Y-, and Z-directions. +In addition, you specify the coordinates of the first point defining the rotation axis (point a in +Figure 2.1.1–3), the coordinates of the second point defining the rotation axis (point b in Figure 2.1.1–3), +and the angle of rotation (in degrees) about the a–b axis. The rotation can be applied multiple times as +described later. +If you specify both translation and rotation, the translation is applied once before the rotation. +Input File Usage: +*NCOPY, OLD SET=name, CHANGE NUMBER=n, SHIFT +Applying the rotation multiple times +You can specify the number of times the rotation should be applied, m. For example, if nodes are to +be created at angles of 30°, 60°, and 90°, set m=3. The identifiers of the nodes created are incremented +sequentially by the value of n, as described above. +Input File Usage: +*NCOPY, OLD SET=name, CHANGE NUMBER=n, SHIFT, MULTIPLE=m +Reflecting the coordinates of the old nodes +You can create new nodes by reflecting the coordinates of the old nodes through a line, a plane, or a point. +Figure 2.1.1–3 Translation and rotation of existing nodes. +Reflecting the coordinates through a line +To reflect the old nodal coordinates through a line, you specify the coordinates of points a and b . +Input File Usage: +*NCOPY, OLD SET=name, CHANGE NUMBER=n, REFLECT=LINE +Old set +New Set +a, b define the line +Figure 2.1.1–4 Reflection of coordinates through a line. +Reflecting the coordinates through a plane +To reflect the old nodal coordinates through a plane, you specify the coordinates of points a, b, and c . +Input File Usage: +*NCOPY, OLD SET=name, CHANGE NUMBER=n, REFLECT=MIRROR +New Set +Old Set +a, b, c define the mirror plane +Figure 2.1.1–5 Reflection of coordinates through a plane. +Reflecting the coordinates through a point +To reflect the old nodal coordinates through a point, you specify the coordinates of point a . +Input File Usage: +*NCOPY, OLD SET=name, CHANGE NUMBER=n, REFLECT=POINT +Projecting the nodes in the old set from a pole node +You can create new nodes by projecting the nodes in the old set from a pole node. Each new node will +be located such that the corresponding old node is equidistant between the pole node and the new node. +The pole node is identified by giving its number or, alternatively, its coordinates. +This method is particularly useful for creating nodes that are associated with infinite elements +(“Infinite elements,” Section 28.3.1). In this case the pole node should be located at the center of the +far-field solution. +Input File Usage: +*NCOPY, OLD SET=name, CHANGE NUMBER=n, POLE +New Set +Old set +a is the point through which the nodes are reflected +Figure 2.1.1–6 Reflection of coordinates through a point. +pole +node +old set +new set +Figure 2.1.1–7 Projection of existing nodes from a pole node. +Creating nodes by filling in nodes between two bounds +You can create nodes by filling in nodes between two bounds. In this case you specify the two node sets +whose members form the bounds, the number of intervals along each line between the bounding nodes, +and the increment in node numbers from the node number at the first bound set end. +Let l equal the number of lines of nodes to be created between the two bounding node sets; the +number of intervals along each line between the bounding nodes is then given by +. +node ( +must be numbered such that +Let n equal the increment in node numbers from the node number at the first bound set end; for each +) in the first bounding node set, the corresponding node in the other bounding node set ( +) +is a whole number. +The node sets that define the bounds of the region are used as they exist at the time the node fill +definition appears in the input file: only those nodes that have been added to the sets prior to the node fill +definition are used. Both sorted and unsorted node sets can be used. Nodes that have not yet been given +coordinates are assumed to be at the origin, (0.,0.,0.). +The nodes created by this method lie on straight lines between corresponding nodes in the two sets. +If the sets do not have the same number of nodes, the extra nodes in the longer set are ignored. By default, +the spacing between nodes along the lines is uniform. +Input File Usage: +*NFILL +Example +For example, Figure 2.1.1–8 shows a simple quarter-cylinder model. +OUTSIDE A +6501 +OUTSIDE B +6101 +INSIDE B +6105 +6505 +1501 +1101 +INSIDE A +1105 +1505 +Figure 2.1.1–8 Filling a three-dimensional region. +The quarter circles INSIDEA (nodes 1101–1105), OUTSIDEA (nodes 1501–1505), INSIDEB (nodes +6101–6105), and OUTSIDEB (6501–6505) have already been defined by specifying their coordinates +the nodes on those planes into sets A and B and then filling between those sets with the following options: +NODE DEFINITION +*NFILL, NSET=A +INSIDEA, OUTSIDEA, 4, 100 +*NFILL, NSET=B +INSIDEB, OUTSIDEB, 4, 100 +*NFILL +A, B, 5, 1000 +Concentrating the nodes toward one bound or the other +You can concentrate the nodes toward one bound or the other by specifying b, the ratio of adjacent +distances between nodes along each line of nodes generated as the nodes go from the first bounding node +set to the second. +Thus, if b is less than one, the nodes are concentrated toward the first bounding node set; if b is +greater than one, the nodes are concentrated toward the second bounding set. The value of b must be +positive. +The bias intervals along the line from the first bounding node are L, +, +… (where L is the length of the first interval). In Abaqus/Standard the bias value can be applied at every +interval along the line or at every second interval along the line as described later. +, +, +, +, +Input File Usage: +*NFILL, BIAS=b +Example +For example, suppose the lines of nodes shown in Figure 2.1.1–9 have already been generated by other +methods and placed into node sets INSIDE and OUTSIDE. The following option will fill the region as +shown in Figure 2.1.1–10: +*NFILL, BIAS=0.6 +INSIDE, OUTSIDE, 5, 100 +Applying the bias value at every second interval along the line +In Abaqus/Standard you can apply the bias value at every second interval along the line. In this case the +nodes will be positioned along the line correctly for use with second-order elements, so that the midside +nodes are at the middle of the interval between the corner nodes of the elements. +The bias intervals along the line from the first bounding node are L, L, +, … +, +, +, +(where L is the length of the first interval). +Input File Usage: +*NFILL, BIAS=b, TWO STEP +Creating quarter-point spacing +In Abaqus/Standard you can create quarter-point spacing for fracture mechanics calculations with +second-order isoparametric elements (“Fracture mechanics: overview,” Section 11.4.1). This spacing +105 +104 +103 +102 +101 +605 +604 +603 +602 +601 +Inside Outside +Figure 2.1.1–9 Node sets defining bias example. +5 0 4 +105 +4 0 4 +3 0 4 +2 0 4 +104 +103 +3 0 3 +2 0 3 +4 0 3 +5 0 3 +202 302 402 +502 +201 301 401 +501 +102 +101 +605 +604 +603 +602 +601 +Figure 2.1.1–10 Result of bias example. +gives a square root singularity in the strain field at the crack tip by placing the first node away from +that point at one-quarter of the distance to the second point. The remaining nodes on each line are +spaced so that the size of the elements will grow as the square of the distance from the singularity, with +the midside nodes exactly at the midsides of the elements. This spacing produces a reasonable mesh +gradation for this type of problem; however, better results can be obtained for crude meshes by making +the size of the crack element smaller than the quarter-point spacing technique does. +Input File Usage: +*NFILL, SINGULAR +Example +Figure 2.1.1–11 shows a simple fracture mechanics example. +507 506 505 504 503 +Node set TOP +107 106 105 104 103 +Node set MID +108 +109 +102 +101 +Nodes 101-109 in +node set OUTER +Nodes 1-9 at crack tip (node set TIP) +Figure 2.1.1–11 Node fill used in a singular problem. +(The mesh shown is very coarse, and a finer mesh would probably be used in an actual case.) The nodes +on the top edge have been placed in node set TOP, those on the horizontal line at the upper end of the +focused region are in node set MID, all of the nodes around the focused region are in node set OUTER, +and there are multiple nodes at the crack tip in node set TIP. The following options are used to fill in the +region as shown in Figure 2.1.1–12 (note the quarter-point nodes adjacent to the crack tip): +*NFILL, BIAS=0.8 +MID, TOP, 4, 100 +*NFILL, SINGULAR=1 +TIP, OUTER, 5, 20 +Mapping a set of nodes from one coordinate system to another +You can map a set of nodes from one coordinate system to another. You can also rotate, translate, or scale +the nodes in a set by using a more direct method instead of coordinate system mapping. These capabilities +503 +403 +303 +203 +103 +102 +101 +82 +22 +62 +42 +21 41 61 81 +Figure 2.1.1–12 Node fill used in a singular problem. +are useful for many geometric situations: a mesh can be generated quite easily in a local coordinate +system (for example, on the surface of a cylinder) using other methods and then can be mapped into the +global (X, Y, Z) system. In other cases some parts of your model need to be translated or rotated along +a given axis or scaled with respect to one point. +The mapping capability cannot be used in a model defined in terms of an assembly of part instances. +The following different mappings are provided: a simple scaling; a simple shift and/or rotation; +skewed Cartesian; cylindrical; spherical; toroidal; and, in Abaqus/Standard only, blended quadratic. +The first five of these mappings are shown in Figure 2.1.1–13. Blended quadratic mapping is shown in +Figure 2.1.1–14. +In all cases the coordinates of the nodes in the set are assumed to be defined in the local system: +these local coordinates at each node are replaced with the global Cartesian (X, Y, Z) coordinates defined +by the mapping. All angular coordinates should be given in degrees. +You can use either coordinates or node numbers to define the new coordinate system, the axis of +rotation and translation, or the reference point used for scaling. +The mapping capability can be used several times in succession on the same nodes, if required. +Scaling the local coordinates before they are mapped +For all mappings except the blended quadratic mapping, you can specify a scaling factor to be applied +to the local coordinates before they are mapped. +This facility is useful for “stretching” some of the coordinates that are given. For example, in +cases where the local system uses some angular coordinates and some distance coordinates (cylindrical, +spherical, etc.), it may be preferable to generate the mesh in a system that uses distance measures in the +angular directions and then scale onto the angular coordinate system for the mapping. +Two different scaling methods are available. +^ +^ +^ +^ +^ +^ +rectangular skewed Cartesian +^ +(R, θ, φ) +(θ = 0) +(φ = 0) +^ +(R, θ, Z) +(θ = 0) + spherical cylindrical +(r, θ, φ) +b (φ = 0) +φ + toroidal +Figure 2.1.1–13 Coordinate systems; angles are in degrees. +5134 +136 +138 +5126 +10134 +10136 +10138 +10130 +5138 +10001 +10126 +10124 +10122 +5122 +134 +130 +126 +124 +122 +ORIGINAL CONFIGURATION +10134 +10136 +5134 +10130 +5138 +10138 +10001 +134 +136 +138 +10126 +10124 +130 +126 +5126 +10122 +5122 +124 +122 +MAPPED CONFIGURATION +Figure 2.1.1–14 Use of blended quadratic mapping to develop a solid mesh onto a curved block. +Specifying the scaling factors directly +A first method of scaling the nodes with respect to the origin of the local system is to specify the scale +factors directly. In this case the scaling is done at the same time as the mapping from one coordinate +system to another. +Input File Usage: +*NMAP, NSET=name +first data line +second data line +scale factor for first local coord, scale factor for second local coord, +scale factor for third local coord +Specifying the scaling with respect to a reference point +Alternatively, you can scale with respect to a point other than the origin. The reference point with respect +to which the scaling is done can be defined by using either its coordinates or the user node number. +Input File Usage: +Use the following option to define the scaling reference point by using its +coordinates (default): +*NMAP, TYPE=SCALE, DEFINITION=COORDINATES +X-coordinate of reference point, Y-coordinate of reference point, +Z-coordinate of reference point +scale factor for first local coord, scale factor for second local coord, +scale factor for third local coord +Use the following option to define the scaling reference point by using its node +number: +*NMAP, TYPE=SCALE, DEFINITION=NODES +Local node number of the reference point +scale factor for first local coord, scale factor for second local coord, +scale factor for third local coord +Introducing a simple shift and/or rotation by mapping from one coordinate system to another +In the case of a simple shift and/or rotation, point a in Figure 2.1.1–13 defines the origin of the local +rectangular coordinate system defining the map. The local +-axis is defined by the line joining points a +and b. The local – plane is defined by the plane passing through points a, b, and c. +Input File Usage: +*NMAP, NSET=name, TYPE=RECTANGULAR +Introducing a pure shift by specifying the axis and magnitude of the translation +You can define a pure translation (or shift) to move a set of nodes by a prescribed value along a desired +axis. You must specify the axis of translation by providing either the coordinates or the two node numbers +defining this axis, and you must prescribe the magnitude of the translation. +Input File Usage: +Use the following option to specify the axis of translation using coordinates +(default): +*NMAP, NSET=name, TYPE=TRANSLATION, +DEFINITION=COORDINATES +Use the following option to specify the axis of translation using node numbers: +*NMAP, NSET=name, TYPE=TRANSLATION, DEFINITION=NODES +Introducing a pure rotation by specifying the axis, origin, and angle of the rotation +You can define a rotation of a set of nodes by providing the axis of rotation, the origin of rotation, and the +magnitude of the rotation. You must specify the axis of rotation by providing either the coordinates or +the two node numbers defining this axis. You must specify the origin of the rotation by providing either +the coordinates or the node number at the origin of rotation. Finally, you must specify the angle of the +rotation in degrees. +Input File Usage: +Use the following option to specify the axis of rotation using coordinates +(default): +*NMAP, NSET=name, TYPE=ROTATION, +DEFINITION=COORDINATES +Use the following option to specify the axis of rotation using node numbers: +*NMAP, NSET=name, TYPE=ROTATION, DEFINITION=NODES +Mapping from cylindrical coordinates +For mapping from cylindrical coordinates, point a in Figure 2.1.1–13 defines the origin of the local +cylindrical coordinate system defining the map. The line going through point a and point b defines the +-axis of the local cylindrical coordinate system. The local – plane for +is defined by the plane +passing through points a, b, and c. +Input File Usage: +*NMAP, NSET=name, TYPE=CYLINDRICAL +Mapping from skewed Cartesian coordinates +For mapping from skewed Cartesian coordinates, point a in Figure 2.1.1–13 defines the origin of the +local diamond coordinate system defining the map. The line going through point a and point b defines +the -axis of the local coordinate system. The line going through point a and point c defines the -axis +of the local coordinate system. The line going through point a and point d defines the -axis of the local +coordinate system. +Input File Usage: +*NMAP, NSET=name, TYPE=DIAMOND +Mapping from spherical coordinates +For mapping from spherical coordinates, point a in Figure 2.1.1–13 defines the origin of the local +spherical coordinate system defining the map. The line going through point a and point b defines the +polar axis of the local spherical coordinate system. The plane passing through point a and perpendicular +to the polar axis defines the +plane. The plane passing through points a, b, and c defines the local +plane. +Input File Usage: +*NMAP, NSET=name, TYPE=SPHERICAL +Mapping from toroidal coordinates +For mapping from toroidal coordinates, point a in Figure 2.1.1–13 defines the origin of the local toroidal +coordinate system defining the map. The axis of the local toroidal system lies in the plane defined by +points a, b, and c. The R-coordinate of the toroidal system is defined by the distance between points a +and b. The line between points a and b defines the +the -coordinate +is defined in a plane perpendicular to the plane defined by the points a, b, and c and perpendicular to the +axis of the toroidal system. +lies in the plane defined by the points a, b, and c. +position. For every value of +Input File Usage: +*NMAP, NSET=name, TYPE=TOROIDAL +Mapping by means of blended quadratics +To map by means of blended quadratics in Abaqus/Standard, you define the new (mapped) coordinates +of up to 20 “control nodes”: these are the corner and midedge nodes of the block of nodes being mapped. +The mapping in this case is like that of a 20-node brick isoparametric element. Any of the midedge nodes +can be omitted, thus allowing linear interpolation along that edge of the block. Abaqus/Standard does +not check whether the nodes in the set lie within the physical space of the block defined by the corner +and midedge nodes: these control nodes simply define mapping functions that are then applied to all of +the nodes in the set. +The control nodes should define a “well”-shaped block; for example, midedge nodes should be close +to the midpoint of the edge. Otherwise, the mapping can be very distorted. For example, the nodes of a +crack-tip 20-node element with midside nodes at the quarter points will not map correctly and, therefore, +should not be used as the control nodes. +Blended mapping is only available for three-dimensional analyses. +Input File Usage: +*NMAP, NSET=name, TYPE=BLENDED +2.1.2 +PARAMETRIC SHAPE VARIATION +Products: Abaqus/Standard Abaqus/Explicit +References +• “Parametric input,” Section 1.4.1 +• *PARAMETER SHAPE VARIATION +Overview +Shape parametrization can be accomplished in an Abaqus input file by: +• parametrizing nodal coordinates; or +• relating nodal coordinates to shape parameters using shape variations. +The different approaches to shape parametrization are described in this section. +Parametrization of nodal coordinates +Any individual nodal coordinates can be parametrized directly. This is usually of limited value +because it often leads to designs with irregular shape that cannot be manufactured easily. In addition, +parametrization of individual nodal coordinates generally requires an excessive number of parameters +to define the parametrized shape. +Parametrization of nodal coordinates used in conjunction with node generation in Abaqus provides +a more practical method of shape parametrization. However, this method is still of somewhat limited +practical use because the simple node generation capabilities available in Abaqus cannot describe +complex shapes. +Direct parametrization of individual nodal coordinates +The simplest form of parametrization of nodal coordinates is to define individual parameters and use them +in place of the nodal coordinates to be parametrized, as described in “Parametric input,” Section 1.4.1. +For example, +*PARAMETER +x_coord_node_1 = 10. +y_coord_node_1 = 20. +*NODE +1, , +Parametrization of nodal coordinates using node generation +Shape parametrization can be accomplished by parametrizing the coordinates of some nodes, then using +these nodes to generate other nodes and their coordinates. For example: +*PARAMETER +x_coord_node_1 = 10. +x_coord_node_11 = 20. +*NODE +1, , 50. +11, , 50. +*NGEN +1, 11, 1 +This method of shape parametrization reduces the number of user-defined parameters necessary for shape +parametrization by implicitly making the nodal coordinates of the generated nodes dependent on the +shape parameters. +Shape change by linear combination of shape variations +The definition of shape in Abaqus includes a basic shape plus any number of additional shape variations +that are added to the basic shape using a linear combination. Mathematically, we can express the nodal +coordinates, +, as +is the basic shape, +where +shape parameter. +shape variation, and +This calculation is always done in the global rectangular Cartesian coordinate system. Although it is not +necessarily so, it is frequently the case that the input to define a shape variation is simply the gradient of +the basic shape +taken with respect to the corresponding shape parameter. +is the value of the +is the +You specify the basic shape of a model in the Abaqus input file by providing nodal definitions either +directly or through node generation; see “Node definition,” Section 2.1.1. +You can specify shape variations and associated shape parameters, as described here. +In addition, you can specify perturbations of the shape as a linear combination of other shapes +(for example, buckling mode shapes); see “Introducing a geometric imperfection into a model,” +Section 11.3.1. +The definition of the nodal coordinates for a model in the Abaqus input file is then possible using a +combination of four types of methods: +• You can directly define individual nodes and their respective coordinates; these coordinates are part +of the definition of the basic shape, +, and can be parametrized. +• Node generation can be used to create nodes and their coordinates according to geometrically simple +mappings that rely on existing node definitions; these generated coordinates are also part of the +definition of the basic shape, +. If necessary, the node generation input can be parametrized. +• Parameter shape variations can be used to vary the coordinates of nodes defined using the above +methods. +• Geometric imperfections can be used to perturb nodal coordinates previously defined using any +combination of the above three types of methods. +Shape parametrization using shape variations +Instead of parametrizing nodal coordinates directly, you can specify shape variations. Each shape +variation must be associated with a single shape parameter. The names of the parameters associated +with the shape variations must be chosen such that the names remain unique when interpreted in a +case-insensitive manner. The values of the shape parameters are assigned using parameter definitions. +A parameter shape variation can be defined more than once for the same parameter so that different +parts of a shape variation can be specified separately. In these cases if the same node is specified in +multiple parameter shape variation definitions, the last definition for the node prevails. +A node that is specified under a parameter shape variation definition that has not also been defined +directly or through node generation will be ignored. +You can specify shape variations using a combination of three possibilities: directly specifying +them, reading them from an alternate input file, and reading them from the results files of auxiliary +analyses. These methods are described in the following sections. +Defining shape variations directly or reading them from an alternate input file +You can define the shape variation data directly by specifying the node number and corresponding +variations of coordinate components. Alternatively, the data can be given in an ASCII file. +Input File Usage: +Use the following option to specify the shape variation data directly: +*PARAMETER SHAPE VARIATION, PARAMETER=name +Use the following option to specify the shape variation data in an alternate input +file: +*PARAMETER SHAPE VARIATION, PARAMETER=name, +INPUT=input file +Defining shape variations in alternative coordinate systems +By default, the shape variation data are interpreted in the global rectangular Cartesian coordinate system. +You can specify the shape variation data (either directly or in an alternate input file) in cylindrical or +spherical coordinate systems. In such cases the computation of the shape variation is done as follows. +The nodal coordinate components that define the basic shape are first transformed from the global +rectangular Cartesian coordinate system in which they are stored to the specified coordinate system. The +shape variation coordinate components are then added to give updated coordinate components, which +are transformed back to the global rectangular Cartesian coordinate system. Finally, the shape variation +is taken as the difference between the updated coordinate components and the original coordinate +components, using the components expressed in the global rectangular Cartesian coordinate system. +The value of the shape parameter associated with the shape variation is not used at any point in the +calculation of the shape variation. +Input File Usage: +Use the following option to specify the shape variation data in a rectangular +coordinate system (the default): +*PARAMETER SHAPE VARIATION, PARAMETER=name, SYSTEM=R +Use the following option to specify the shape variation data in a cylindrical +coordinate system: +*PARAMETER SHAPE VARIATION, PARAMETER=name, SYSTEM=C +Use the following option to specify the shape variation data in a spherical +coordinate system: +*PARAMETER SHAPE VARIATION, PARAMETER=name, SYSTEM=S +Using auxiliary analyses to generate shape variations +Auxiliary models are additional finite element models that are used to generate shape variations for a +primary model. Rather than defining shape variations directly on a node-by-node basis, auxiliary models +can be used to simplify this process. Auxiliary analyses are finite element analyses of these auxiliary +models. +An auxiliary model usually has the same geometry, element connectivity, and material type as the +primary model. However, the boundary conditions are usually different. Applying loading to an auxiliary +model results in sets of displacements that we may interpret as shape variations. For example, we may +be interested in studying the sensitivity of the nonlinear buckling behavior of a structure with respect +to imperfections in the structure. In this case we could perform an auxiliary eigenvalue linear buckling +analysis and then use the resulting mode shapes as shape variations to be added to the basic geometry of +the primary model. (This particular problem could also be addressed by using a geometric imperfection.) +Abaqus reads the shape variation data from auxiliary analyses through the user node labels. Abaqus +does not check model compatibility between both analysis runs. Shape variation data cannot be read from +the results file for models defined in terms of an assembly of part instances (“Defining an assembly,” +Section 2.10.1). +Reading shape variations from a static analysis results file +To define a shape variation based on the deformed geometry of a previous static analysis, specify the +results file and step from a previous static analysis. Optionally, you can specify the increment number +from which displacement data are read. +(By default, Abaqus will read data from the last increment +available for the specified step on the results file.) In addition, you can read shape variation data for a +specified node set. +Input File Usage: +*PARAMETER SHAPE VARIATION, PARAMETER=name, +FILE=results file, STEP=step, INC=inc, NSET=name +Reading shape variations from an eigenvalue analysis results file +To define a shape variation based on a mode shape from a previous eigenvalue analysis, specify the +results file and step from a previous eigenfrequency extraction or eigenvalue buckling prediction analysis. +Optionally, you can specify the mode number from which eigenvector data are read. (By default, Abaqus +will read data from the first eigenvector available for the specified step on the results file.) In addition, +you can read eigenmode data for a specified node set. +Input File Usage: +*PARAMETER SHAPE VARIATION, PARAMETER=name, +FILE=results file, STEP=step, MODE=mode, NSET=name +Shape parametrization and design sensitivity analysis +For the purpose of design sensitivity analysis with Abaqus/Design (“Design sensitivity analysis,” +Section 19.1.1) if the parameter specified for a parameter shape variation is also specified as a design +parameter, the shape variation is used to define the design gradient of the nodal coordinates and nodal +normals with respect to the design parameter. If you wish to perform design sensitivity analysis for the +basic shape, all shape parameters must be given a value of zero. In addition, if any parameter specified +in a parameter shape variation definition is also specified as a design parameter, the parameters of all +parameter shape variations must be specified as design parameters. +In DSA calculations for shell and beam elements Abaqus always computes the design gradients of +nodal normals using the design gradients of nodal coordinates. To overwrite the gradients computed by +Abaqus, you must provide the nodal normal as part of the node definition and design gradients of the +normals using a parameter shape variation. To prescribe a design-independent normal, you must provide +a zero design gradient explicitly. For shape variations read from the results file, Abaqus computes the +gradients of the normals based on the displacements and ignores the nodal rotations. +For beam elements Abaqus computes the design gradients for the +-direction of the beam cross- +section using the gradients of the node coordinates and the gradients for the +-direction specified using a +parameter shape variation. You cannot provide the shape variation for the +-direction. Abaqus ignores +any such design gradients implicitly provided in either the beam section definition or as an extra node in +the beam element connectivity. +In cases where the data defining a shape variation are given in a cylindrical or spherical coordinate +system it is important that you understand how the shape variation is calculated from the data. This +calculation is described in the previous section. +Visualization of shape variations +Shape variations can be visualized only after the parametrized input file has been processed by the +analysis input file processor. Therefore, at least a data check run must be executed before parameter +shape variations can be visualized using Abaqus/CAE. +The shape variations associated with each individual shape parameter can be visualized as displaced +shape plots at step zero of the analysis. The basic shape is interpreted as the undeformed shape, and the +shape generated by adding the +displaced +shape. +shape variation to the basic shape is interpreted as the +The combination of all shape variations added to the basic shape represents the true undeformed +shape of the analysis. +Using Abaqus/CAE to compute shape variations +A capability for computing shape variations is provided by the Abaqus Scripting Interface command +_computeShapeVariations( ). Using the command requires some familiarity with the Abaqus +Scripting Interface and the execution of scripts in Abaqus/CAE. The procedure that must be followed +is described and illustrated in “Design sensitivity analysis: overview,” Section 13.1.1 of the Abaqus +Example Problems Manual. +2.1.3 +NODAL THICKNESSES +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Membrane elements,” Section 29.1.1 +• “Using a shell section integrated during the analysis to define the section behavior,” Section 29.6.5 +• “Using a general shell section to define the section behavior,” Section 29.6.6 +• *NODAL THICKNESS +• *MEMBRANE SECTION +• *RIGID BODY +• *SHELL GENERAL SECTION +• *SHELL SECTION +Overview +Nodal thicknesses are used to define continuously varying thicknesses for: +• shell structures; +• membrane structures; or +• in Abaqus/Explicit rigid elements. +Defining nodal thicknesses +You can specify the thickness of a shell, membrane, or rigid element at a particular node or node set. +Input File Usage: +*NODAL THICKNESS +node_number or node_set_name, thickness +Abaqus/CAE Usage: +Use the following option for a conventional shell composite layup: +Property module: composite layup editor: Shell Parameters: Nodal +distribution: select an analytical field or a node-based discrete field +Use the following option for a homogeneous shell section: +Property module: shell section editor: Basic: Nodal distribution: +select an analytical field or a node-based discrete field +Use the following option for a composite shell section: +Property module: shell section editor: Advanced: Nodal distribution: +select an analytical field or a node-based discrete field +Reading nodal thicknesses from an alternate file +The nodal thickness data can be stored in a separate file and read from there at the start of the analysis. +For details on the syntax of such file names, see “Input syntax rules,” Section 1.2.1. +Input File Usage: +Abaqus/CAE Usage: +*NODAL THICKNESS, INPUT=file_name +Reading nodal +Abaqus/CAE. +thicknesses from an alternate file is not supported in +Generating continuously varying thicknesses between two nodes or node sets +Abaqus can linearly interpolate the thickness between two bounding nodes or node sets. The thicknesses +at the bounding nodes must first be defined. +Input File Usage: +Use the following options: +*NODAL THICKNESS +first bounding node or node set, thickness +second bounding node or node set, thickness +*NODAL THICKNESS, GENERATE +first bounding node or node set, second bounding node or node set, +number of intervals, increment in node numbers +Abaqus/CAE Usage: +Generating thicknesses between bounding nodes or node sets is not supported +in Abaqus/CAE. +Specifying a continuously varying thickness for shell, membrane, and rigid elements +You must specify that a shell or membrane element is going to have a continuously varying thickness +rather than a homogeneous thickness when you define the element section. See “Membrane elements,” +Section 29.1.1; “Using a shell section integrated during the analysis to define the section behavior,” +Section 29.6.5; and “Using a general shell section to define the section behavior,” Section 29.6.6, for +details. +In Abaqus/Explicit you must specify that a rigid element is going to have a continuously varying +thickness when you define the rigid body to which the element belongs; see “Rigid elements,” +Section 30.3.1. In Abaqus/Standard rigid elements cannot have a continuously varying thickness. +Every node that is part of a shell, membrane, or rigid element using a continuously varying thickness +must have a nodal thickness defined. Abaqus will issue an error message if there is a node with no nodal +thickness in an element that is using a continuously varying thickness. +Specifying a continuously varying thickness for a composite shell +When a composite shell structure has a continuously varying thickness, the total thickness of the shell at +any node is defined by the nodal thickness value. The total thickness at an integration point is interpolated +from the nodal thicknesses. The layer thicknesses given in the shell section definition are used as relative +thicknesses and are scaled proportionally such that the sum of the layer thicknesses equals the total +thickness at the integration point. +Example +For example, if a composite shell section were defined with the following input: +*SHELL SECTION, COMPOSITE, NODAL THICKNESS, ELSET=name +1.5, 3, STEEL +2.5, 3, FOAM +1.0, 3, STEEL +and the total thickness at a point was only 1.0, the thicknesses of the individual layers at the point would +be 0.3 for the first steel layer, 0.5 for the foam layer, and 0.2 for the second steel layer. +Creating a discontinuity in the shell, membrane, or rigid element thicknesses +You can specify only a single thickness at each node. Therefore, use separate nodes along the interface +on shell, membrane, or rigid elements where there is a discontinuity in the thickness and assign the +appropriate thickness to each group of nodes. For elements that are not part of a rigid body, multi-point +constraints must be used to make the displacements (and rotations, for shells) the same at corresponding +nodes. +2.1.4 +NORMAL DEFINITIONS AT NODES +Products: Abaqus/Standard Abaqus/Explicit +References +• *NORMAL +• *NODE +Overview +Normals can be defined at nodes: +• with a user-specified normal definition; +• following the nodal coordinates as part of the node definition for beam and shell elements; +• on rigid master surfaces used in contact pairs in Abaqus/Standard; +• in beam and shell elements; +• for line spring elements to give the direction normal to the flaw in the structure; +• for gasket elements to give the thickness direction of the elements; and +• for contour integral evaluation. +The normals defined at nodes do not affect the element face normals, which are defined by the element +connectivity. They need not be of unit length. +Contact surfaces in Abaqus/Standard +User-specified surface normals for contact surfaces in Abaqus/Standard are relevant only when the small- +sliding contact approach is used or when the finite-sliding contact approach is used with rigid elements +that make up the master surface. User-specified surface normals defined on deformable master surfaces +in contact pairs are ignored when finite sliding is used. +The small-sliding contact formulation uses the surface normals at each node along the master surface +to define a normal vector that varies smoothly from point to point on the surface. For a detailed discussion +on how the “master plane” is constructed for each slave node using the surface normals, see “Contact +formulations in Abaqus/Standard,” Section 37.1.1. +For master surfaces composed of rigid elements Abaqus/Standard smooths any discontinuous +surface normal transitions between the rigid elements. The surface normals at the nodes are used to +control the surface normal interpolation. For a detailed discussion on the smoothing of such master +surfaces, see “Analytical rigid surface definition,” Section 2.3.4. +To define the normal, specify the components of the normal in the global coordinate system. +Input File Usage: +*NORMAL, TYPE=CONTACT SURFACE +Elements +User-specified normals may be necessary for beam and shell elements, line spring elements, gasket +elements, or elements involved in contour integral evaluations. In such cases specify the components of +the normal in the global coordinate system. +Input File Usage: +*NORMAL, TYPE=ELEMENT +Beam and shell elements +User-specified normals may be needed to define the desired normal directions at shell surface +intersections or at beam intersections where the automatically determined normals may be inappropriate +for the model . +The nodal normals can also be defined as part of the node definition. While you can define a +single normal for all elements connected to a node as part of the node definition, a user-specified normal +definition defines a normal for a particular element at a node, thus allowing you to define separate normals +for each element connected to a node. User-specified normal definitions supersede normals defined as +part of a node definition. +Input File Usage: +*NODE +Specify the normals in the fifth, sixth, and seventh positions on the data line. +For example, +the following lines define some normals as part of node +definitions; the normal to be used at node 7 in element 2 is then redefined using +a user-specified normal definition: +*NODE +6, 5., 5., , -0.5, .8 +7, 10., 8., , -0.5, .8 +9, 14., 4., , .6, .6 +*NORMAL +2, 7, .6, .6 +Line spring elements +For line spring elements user-specified normals can be used to give the direction normal to the flaw in +the structure. See “Line spring elements for modeling part-through cracks in shells,” Section 32.9.1, for +a description of these elements. +Gasket elements +For gasket elements user-specified normals can be used to specify the thickness direction of the elements. +The nodal thickness directions can also be defined as part of the gasket section definition. Thickness +directions defined by user-specified normals supersede thickness directions defined as part of the gasket +section definition. See “Defining the gasket element’s initial geometry,” Section 32.6.4, for a description +of the definition of the thickness direction for these elements. +Contour integral evaluation +For contour integral evaluations (“Contour integral evaluation,” Section 11.4.2) surface normals should +be specified at all surface nodes lying within the bounds of the requested contours. These nodes are +printed out under the “Contour Integral” information in the data (.dat) file. For accurate contour integral +evaluation it is important that the virtual crack extension direction is in the plane of the surface for the +following cases: when a crack front intersects the external surface of a three-dimensional solid, when +the crack front intersects a surface of material discontinuity, or when the crack is in a curved shell. If no +normals are specified, Abaqus will calculate the normals automatically. +The nodal normal data specified as part of a node definition will not be activated for solid elements +unless a user-specified normal definition is used in the model; it suffices to include a user-specified normal +definition for only one node to activate the utilization of the nodal normal data specified as part of a node +definition. +The coordinate system in which normals are defined +Abaqus models can be defined in terms of an assembly of part instances . Normals at nodes defined within a part (or part instance) are defined relative to the part +coordinate system. These normals are rotated according to the positioning data given for each instance of +the part. Normals can be defined at reference nodes at the assembly level if necessary. Normals defined +at the assembly level are defined in the global coordinate system. +For models that are not defined in terms of an assembly of part instances, normals are defined in the +global coordinate system. +2.1.5 +TRANSFORMED COORDINATE SYSTEMS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Prescribed conditions: overview,” Section 33.1.1 +• *TRANSFORM +• “Transforming results into a new coordinate system,” Section 42.6.8 of the Abaqus/CAE User’s +Manual, in the online HTML version of this manual +• “An overview of the methods for creating a datum coordinate system,” Section 62.5.4 of the +Abaqus/CAE User’s Manual +Overview +A nodal transformation is used to define a local coordinate system for: +• the definition of concentrated forces and moments; +• the definition of displacement and rotation boundary conditions; +• the definition of linear constraint equations; and +• the output of vector-valued quantities. +A nodal transformation cannot be used to specify a local coordinate system for defining: +• nodal coordinates—see “Specifying a local coordinate system in which to define nodes” in “Node +definition,” Section 2.1.1, or “Specifying a local coordinate system for the nodal coordinates” in +“Node definition,” Section 2.1.1, instead; or +• material properties or rebars—see “Orientations,” Section 2.2.5, instead. +Defining a local coordinate system +Normally displacement and rotation components are associated with the global, rectangular Cartesian +axis system. When a transformed coordinate system is associated with a node, all input data for +concentrated forces and moments and for displacement and rotation boundary conditions at the node +are given in the local system. The following transformations are available: +• Rectangular Cartesian +• Cylindrical +• Spherical +The coordinate transformation defined at a node must be consistent with the degrees of freedom that +exist at the node. For example, a transformed coordinate system should not be defined at a node that is +connected only to a SPRING1 or SPRING2 element, since these elements have only one active degree +of freedom per node. +Input File Usage: +You must identify the node set for which the local transformed system is +defined. +Abaqus/CAE Usage: +*TRANSFORM, NSET=name +In Abaqus/CAE you define a local coordinate system independent of its use and +then refer to it when you apply a load or boundary condition at a node. +Any module: Tools→Datum: Type: CSYS +Interaction module: load or boundary condition editor: CSYS: +Edit: select local coordinate system +Defining a local coordinate system in a model that contains an assembly of part instances +In a model defined in terms of an assembly of part instances, you can define a nodal transformation at +the part, part instance, or assembly level. A nodal transformation defined at the part or part instance +level will be rotated according to the positioning data given for each instance of that part (or for the +part instance). See “Defining an assembly,” Section 2.10.1. Multiple transformation definitions are not +allowed at a node, even if one of them is at the part level and another is at the assembly level. +Large-displacement analysis +The transformed coordinate system is always a set of fixed Cartesian axes at a node (even for cylindrical +or spherical transforms). These transformed directions are fixed in space; the directions do not rotate +as the node moves. Therefore, even in large-displacement analysis, the displacement components must +always be given with respect to these fixed directions in space. +Defining a rectangular Cartesian coordinate transformation +In a rectangular Cartesian transformation the transformed directions are parallel at all nodes of the set. +The coordinates of two points must be given, as shown in Figure 2.1.5–1. +Z1 +Y1 +a X1 +(global) +Figure 2.1.5–1 Cartesian transformation. +The first point, a, must be on a line through the global origin; this point defines the transformed +-direction. The second point, b, must be in the plane containing the global origin and the transformed +- and +-axis. +-directions. This second point should be on or near the positive +*TRANSFORM, NSET=name, TYPE=R (default) +Any module: Tools→Datum: Type: CSYS: select any method, +and click OK: Rectangular +Abaqus/CAE Usage: +Input File Usage: +Defining a cylindrical coordinate transformation +The radial, tangential, and axial directions must be defined based on the original coordinates of each +node in the node set for which the transformation is invoked. The global ( +) coordinates of the +two points defining the axis of the cylindrical system (points a and b as shown in Figure 2.1.5–2) must +be given. +(radial) +(axial) +(tangential) +(global) +Figure 2.1.5–2 Cylindrical transformation. +The origin of the local coordinate system is at the node of interest. The local +line through the node, perpendicular to the line through points a and b. The local +line that is parallel to the line through points a and b. The local +system with +-axis is defined by a +-axis is defined by a +-axis forms a right-handed coordinate +and +. +A cylindrical coordinate system cannot be defined for a node that lies along the line joining points +a and b. +Input File Usage: +Abaqus/CAE Usage: +*TRANSFORM, NSET=name, TYPE=C +Any module: Tools→Datum: Type: CSYS: select any method, +and click OK: Cylindrical +Defining a spherical coordinate transformation +The radial, circumferential, and meridional directions must be defined based on the original coordinates +of each node in the node set for which the transformation is invoked. The global ( +) coordinates +of the center of the spherical system, a, and of a point on the polar axis, b, must be given as shown in +Figure 2.1.5–3. + (meridional) + (circumferential) +1 +(radial) +(global) +Figure 2.1.5–3 Spherical transformation. +The origin of the local coordinate system is at the node of interest. The local +-axis is defined by +-axis lies in a plane containing the polar axis (the line +-axis forms a right-handed +-axis. The local +a line through the node and point a. The local +between points a and b) and is perpendicular to the local +coordinate system with +and +. +A spherical coordinate system cannot be defined for a node that lies along the line joining points a +and b. +Input File Usage: +Abaqus/CAE Usage: +*TRANSFORM, NSET=name, TYPE=S +Any module: Tools→Datum: Type: CSYS: select any method, +and click OK: Spherical +Output at a node associated with a coordinate transformation +Printed and file output of vector-valued quantities from Abaqus/Standard at transformed nodes can be +in the local or global system . By default, the values are written to the data file in the local system, +whereas the values are written to the results file in the global system (since this is more convenient for +postprocessing). Consequently, reaction forces printed using the default will not appear to equilibrate +loads applied in the global system. However, these reaction forces and loads should equilibrate if you +output them to the data file in the global system. +File output from Abaqus/Explicit is always in the global system. +Output database output of field vector-valued quantities at transformed nodes is in the global system. +The local transformations are also written to the output database. You can apply these transformations to +the results in the Visualization module of Abaqus/CAE to view the vector components in the transformed +systems. +Output database output of history vector-valued quantities at transformed nodes can be in the local +or global system . By default, the values are written +in the global system (since this is more convenient for postprocessing). +2.1.6 +ADJUSTING NODAL COORDINATES +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• *ADJUST +• “Defining adjust points constraints,” Section 15.15.5 of the Abaqus/CAE User’s Manual +Overview +Nodal adjustment is used for: +• adjusting user-specified nodal coordinates so that the nodes lie on a given surface; and +• specifying the direction along which the nodes are moved. +Adjusting nodal coordinates +In general, user-specified nodal coordinates are not modified during input file processing. However, +there are some situations where mesh coordinates are known only in a generic way and it is inconvenient +to determine their coordinates for their actual usage. For example, when using fasteners the specified +reference node should be positioned at its projection point on the associated surface. Since that location +may be known only approximately, you can use nodal adjustment to move the reference node to that +location automatically. For typical usage of the nodal adjustment feature, refer to “About assembled +fasteners,” Section 29.1.3 of the Abaqus/CAE User’s Manual. +When using this feature, the nodes are adjusted to lie on the specified surface without regard for +shell thickness or shell offsets. Therefore, it is not advisable to use this feature as a way of correcting +initial overclosures for contact or for tie constraints. In addition, care should be taken when choosing the +nodes to be adjusted because the feature does not respect any constraints relating the relative position of +the adjusted node with other nodes (e.g., rigid body definitions). +Input File Usage: +Use the following option to identify the nodes to be moved and the surface onto +which the nodes are to be moved: +Abaqus/CAE Usage: +*ADJUST, NODE SET=name, SURFACE=name +Use the following option to move the control point of a coupling constraint onto +the coupling surface: +Interaction module: Constraint→Create: Coupling; Adjust +control point to lie on surface +Use the following option to move any point or points onto any surface: +Interaction module: Constraint→Create: Adjust points +Specifying the nodal adjustment direction +A node can be moved to the surface using a normal adjustment or a directed adjustment. By default, +the node is adjusted to the closest point on the specified surface along the normal to the surface. You +can specify an orientation to move the node to the surface along a given direction rather than along the +normal to the surface. The vector along the local Z-direction from the orientation definition is used to +move the node to the surface . If no projection can be found, the nodal +coordinates are left unmodified. +Input File Usage: +Abaqus/CAE Usage: +*ADJUST, ORIENTATION=name +The orientation projection option is not supported in Abaqus/CAE. +2.2 +Element definition +• “Element definition,” Section 2.2.1 +• “Element foundations,” Section 2.2.2 +• “Defining reinforcement,” Section 2.2.3 +• “Defining rebar as an element property,” Section 2.2.4 +• “Orientations,” Section 2.2.5 +2.2.1 +ELEMENT DEFINITION +Products: Abaqus/Standard Abaqus/Explicit +References +• *ELCOPY +• *ELEMENT +• *ELGEN +• *ELSET +Overview +This section describes the methods for defining elements in an Abaqus input file. In a preprocessor such +as Abaqus/CAE, you define the model geometry rather than the nodes and elements; when you mesh the +geometry, the preprocessor automatically creates the nodes and elements needed for analysis. Although +the concepts discussed in this section apply in general to the element definitions in the input file that is +created by Abaqus/CAE, the methods and techniques described here apply only if you are creating the +input file manually. +Element definition consists of: +• assigning an element number to the element; +• defining individual elements by specifying their nodes; +• grouping elements into element sets; and +• creating elements from existing elements by generating them incrementally or by copying existing +elements. +If any element is specified more than once, the last specification given is used. +Assigning an element number to the element +Each individual element must have a numeric label called the element number, which is assigned when +the element is defined. The element number must be a positive integer, and the maximum element number +allowed is 999999999 (for information on integer input, see “Input syntax rules,” Section 1.2.1). The +elements do not need to be numbered continuously. +An Abaqus model can be defined in terms of an assembly of part instances . In such a model almost all elements must belong to a part or part instance. +The only exceptions are mass, rotary inertia, capacitance, connector, spring, and dashpot elements, which +can belong to a part or to the assembly. Element numbers must be unique within a part, part instance, or +the assembly; but they can be repeated in different parts or part instances. +Defining individual elements by specifying their nodes +You can define individual elements by specifying the element number and the nodes that define the +element. In addition, you must specify the element type. The element must be chosen from one of the +element types specified in Part VI, “Elements”; or, in Abaqus/Standard, it can be a user-defined element +(“User-defined elements,” Section 32.15.1) or a substructure (“Using substructures,” Section 10.1.1). +Input File Usage: +*ELEMENT, TYPE=name +For example, the following lines create element number 11, which is of type +C3D8R, by defining its nodes (2, 3, 9, 7, 5, 8, 12, 16): +*ELEMENT, TYPE=C3D8R +11, 2, 3, 9, 7, 5, 8, 12, 16 +Using large node numbers with elements that use many nodes +The following rules apply when defining elements: +• The connectivity for each element is considered a logical record, and any number of input lines can +be used to specify it. Abaqus will read the first line for an element and consider the next line a +continuation line if a comma ends the line and the element definition is not complete. +• Any number of continuation lines can be used. +• For elements such as C3D27 with a variable number of nodes elements,” +Section 28.1.1), the last line should not end with a comma or Abaqus will interpret the next element +definition as a continuation of the current element. +For example, +*ELEMENT, TYPE=C3D20 +100001, 100001, 100002, 100003, 100004, 100005, 100006, 100007, +100008, 100009, 100010, 100011, 100012, 100013, 100014, 100015, +100016, 100017, 100018, 100019, 100020 +Reading element definitions from a file +Element definitions can be read into Abaqus from an alternate file. The syntax of such file names is +described in “Input syntax rules,” Section 1.2.1. +Input File Usage: +*ELEMENT, INPUT=file_name +Reading substructure definitions from a substructure library +Substructure definitions can be read from the substructure library in which the substructure resides +(“Using substructures,” Section 10.1.1). +Input File Usage: +*ELEMENT, FILE=substructure_library_name +If the FILE parameter is used without a value, the default substructure library +name is used. +Defining axisymmetric elements with asymmetric deformation +You can define a positive offset number that will be used to specify nodes for axisymmetric elements with +asymmetric deformation . +The default offset is 100000. +Input File Usage: +*ELEMENT, OFFSET=number +Defining gasket elements +There are several methods for defining gasket elements. +overview,” +Section 32.6.1; “Including gasket elements in a model,” Section 32.6.3; and “Defining the gasket +element’s initial geometry,” Section 32.6.4, for more information on gasket elements; they are available +only in Abaqus/Standard.) + face of the solid element coincides +with the first (SNEG) face of the gasket element. If the equivalent solid element is oriented differently, +specify the face number on the solid element that corresponds to the first face of the gasket element. The +solid element must have the same number of nodes on each face as the corresponding gasket element; +If both +any nodes between the faces will be ignored. The 18-node gasket element is an exception. +element faces are part of contact surfaces, the connectivity of a 20-node brick element can be used, and +Abaqus/Standard will generate the node numbers and coordinates of the midface nodes automatically. +Abaqus/Standard will transform the solid element connectivity to the normal gasket element +connectivity immediately upon reading the data. Hence, all output to the data (.dat), results (.fil), +and output database (.odb) files will use the normal gasket element connectivity. +Input File Usage: +Use the following option to specify solid element connectivity for a gasket +element in which the first face of the solid element corresponds to the first face +of the gasket element: +*ELEMENT, TYPE=name, SOLID ELEMENT NUMBERING +Use the following option to specify solid element connectivity for a gasket +element and the face of the solid element that corresponds to the first face of +the gasket element: +*ELEMENT, TYPE=name, SOLID ELEMENT NUMBERING=face number +Examples +The following lines create GK3D12M element number 11 that has node numbers 1, 2, 3, 4, 5, 6, 1001, +1002, 1003, 1004, 1005, and 1006: +*ELEMENT, TYPE=GK3D12M +11, 1, 2, 3, 4, 5, 6, 1001, 1002, 1003, 1004, 1005, 1006 +The same element connectivity is also created by the following lines: +*ELEMENT, TYPE=GK3D12M, OFFSET=1000 +11, 1, 2, 3, 4, 5, 6 +The equivalent solid element would be C3D15, with the following input: +*ELEMENT, TYPE=GK3D12M, SOLID ELEMENT NUMBERING +11, 1, 2, 3, 1001, 1002, 1003, 4, 5, 6, 1004, 1005, 1006, +501, 502, 503 +where nodes 501, 502, and 503 would not be used. +Defining cohesive elements + +• In the first method you specify the element number and all of the nodes that define the element. +• In the second method you specify only the nodes on the bottom face of the cohesive element and +Abaqus will create the remaining nodes, numbering them according to an offset number that you +specify. +• In the third method, which is applicable only to pore pressure cohesive elements, you specify the +nodes on the bottom and top faces. Abaqus will create the remaining middle-face nodes according +to an offset number that you specify. +Defining a cohesive element by specifying all nodes +With this method you specify all nodes that define the cohesive element. See “Two-dimensional cohesive +element library,” Section 32.5.8; “Three-dimensional cohesive element library,” Section 32.5.9; and +“Axisymmetric cohesive element library,” Section 32.5.10, for the element node numbering definition. +Input File Usage: +Use the following option to specify the element number and the nodes that +define the element: +*ELEMENT, TYPE=name +For example, the following lines create COH3D8 element number 11 that has +node numbers 1, 2, 3, 4, 1001, 1002, 1003, and 1004: +*ELEMENT, TYPE=COH3D8 +11, 1, 2, 3, 4, 1001, 1002, 1003, 1004 +Defining a cohesive element by specifying only the bottom face nodes +With this method you specify only the nodes on the bottom face of the cohesive element and a positive +offset number. With displacement cohesive elements, the offset number is added to the bottom face node +numbers to create the corresponding nodes on the top face. With pore pressure cohesive elements, the +offset number first is added to the bottom face node numbers to create the corresponding nodes on the +top face, then the offset number is added to the top face node numbers to create the corresponding nodes +on the middle face. +Input File Usage: +Use the following option to specify the nodes on the bottom face of the element +and a positive offset number for nodes on the remaining face or faces: +*ELEMENT, TYPE=name, OFFSET=offset number +For example, the following lines create COH3D8 element number 11 that has +node numbers 1, 2, 3, 4, 1001, 1002, 1003, and 1004: +*ELEMENT, TYPE=COH3D8, OFFSET=1000 +11, 1, 2, 3, 4 +and the following lines create pore pressure cohesive element COH3D8P +element number 11 that has node numbers 1, 2, 3, 4, 1001, 1002, 1003, 1004, +2001, 2002, 2003, and 2004 (nodes 1, 2, 3, and 4 define the bottom face; nodes +1001, 1002, 1003, and 1004 define the top face; and nodes 2001, 2002, 2003, +and 2004 define the middle face): +*ELEMENT, TYPE=COH3D8P, OFFSET=1000 +11, 1, 2, 3, 4 +Defining a pore pressure cohesive element by specifying only the bottom and top face nodes +With this method you specify only the nodes on the bottom and top faces of the pore pressure cohesive +element and a positive offset number. The offset number is added to the bottom face node numbers to +create the corresponding nodes on the middle face. +Input File Usage: +Use the following option to specify the nodes on the bottom and top faces of the +pore pressure cohesive element and a positive offset number for the remaining +middle-face nodes: +*ELEMENT, TYPE=name, OFFSET=offset number +For example, the following lines create a pore pressure cohesive element +COH3D8P element number 11 that has node numbers 1, 2, 3, 4, 1001, 1002, +1003, 1004, 2001, 2002, 2003, and 2004 (nodes 1, 2, 3, and 4 define the bottom +face; nodes 1001, 1002, 1003, and 1004 define the top face; and nodes 2001, +2002, 2003, and 2004 define the middle face): +*ELEMENT, TYPE=COH3D8P, OFFSET=2000 +11, 1, 2, 3, 4, 1001, 1002, 1003, 1004 +Grouping elements into element sets +Element sets are used as convenient cross-references for defining loads, properties, etc. Element sets are +the fundamental references of the model and should be used to assist the input definition. The members +of an element set can be individual elements or other element sets. An individual element can belong to +several element sets. +Elements can be grouped into element sets when they are created or after they have already been +defined. In either case each element set is assigned a name. Element set names can be up to 80 characters +long. +The same name can be used for a node set and for an element set. +All elements within an element set will be arranged in ascending order of their element number, and +duplicates will be removed. +Once elements are assigned to an element set, additional elements can be added to the same element +set; however, elements cannot be removed from an element set. +Assigning elements to an element set as they are created +There are several ways that elements can be assigned to element sets as they are created. +Input File Usage: +Use any one of the following options: +*ELEMENT, ELSET=name +*ELGEN, ELSET=name +*ELCOPY, NEW SET=name +Assigning previously defined elements to an element set +You can assign elements that you have defined previously (by specifying their nodes, by generating them +incrementally, or by copying existing elements) to an element set by listing the elements forming the set +directly or by generating the element set. +Listing the elements that form the set directly +You can list the elements that form the element set directly. Previously defined element sets, as well as +individual elements, can be assigned to element sets. +Input File Usage: +*ELSET, ELSET=name +For example, the following lines add elements 3, 13, and 20 to set LEFT: +*ELSET, ELSET=LEFT +20 +3, 13 +The following lines add elements 5 and 16 to the existing set LEFT: +*ELSET, ELSET=LEFT +5, 16 +** The above data line is equivalent to +specifying 5, 16, LEFT +The following lines add elements 22, 14, and all elements in set LEFT to set B: +*ELSET, ELSET=B +22, 14, LEFT +Thus, element set B contains the following elements: 3, 5, 13, 14, 16, 20, and +22. Element set LEFT can be assigned to element set B since the definition of +LEFT occurs before the definition of B. +Generating the element set +To generate an element set, you must specify a first element, +element numbers between these elements, i. All elements going from to +to the set. Therefore, i must be an integer such that +default is +; a last element, +; and the increment in +in steps of i will be added +is a whole number (not a fraction). The +. +Input File Usage: +*ELSET, ELSET=name, GENERATE +For example, the following lines add elements 1, 3, 5, …, 19, 21 and elements +39, 49, 59, …, 129, 139 to set UP: +*ELSET, ELSET=UP, GENERATE +1, 21, 2 +39, 139, 10 +Limitation on updating element sets that are used to define other element sets +If an element set is constructed from previously defined element sets, subsequent updates to these sets +are not taken into account. +Input File Usage: +*ELSET, ELSET=name +For example, the following lines add elements 1 and 2, but not 3, to the set +SET-AB while adding elements 1 and 3 to set SET-A: +*ELSET, ELSET=SET-A +1, +*ELSET, ELSET=SET-B +2, +*ELSET, ELSET=SET-AB +SET-A, SET-B +*ELSET, ELSET=SET-A +3, +Defining part and assembly sets +In a model defined in terms of an assembly of part instances, all element sets must be defined within a +part, part instance, or the assembly definition. If an element set is defined within a part (or part instance), +you can refer to the element numbers directly. To define an assembly-level element set, you must identify +the elements to be added to the set by prefixing each element number with the part instance name and a +“.” (as explained in “Defining an assembly,” Section 2.10.1). An assembly-level element set can have +the same name as a part-level element set. +Example +The following input defines an element set, set1, that belongs to part PartA and will be inherited by +every instance of PartA: +*PART, NAME=PartA +... +*ELSET, ELSET=set1 +1,3,26,500 +*END PART +An element set with the same name is defined at the assembly level as follows: +*ASSEMBLY, NAME=Assembly-1 +*INSTANCE, NAME=PartA-1, PART=PartA +... +*END INSTANCE +*INSTANCE, NAME=PartA-2, PART=PartA +... +*END INSTANCE +*ELSET, ELSET=set1 +PartA-1.1, PartA-1.3, PartA-1.26, PartA-1.500 +PartA-2.1, PartA-2.3, PartA-2.26, PartA-2.500 +*END ASSEMBLY +Assembly-level element set set1 contains all the elements from element sets set1 belonging to part +instances PartA-1 and PartA-2. Therefore, the elements are assigned to two separate element sets: +one at the part instance level and one at the assembly level. An assembly-level element set called set1 +could be created with entirely different elements than those that belong to the part set; part- and assembly- +level element sets are independent. However, since in this example the same elements are assigned +to both the part- and assembly-level element sets set1, the assembly-level set could alternatively be +defined by +*ASSEMBLY, NAME=Assembly-1 +*INSTANCE, NAME=PartA-1, PART=PartA +... +*END INSTANCE +*INSTANCE, NAME=PartA-2, PART=PartA +... +*END INSTANCE +*ELSET, ELSET=set1 +PartA-1.set1, PartA-2.set1 +*END ASSEMBLY +This element set definition is equivalent to the previous example, where the elements are listed +individually. +Alternate method for defining assembly-level element sets +Sometimes it is not convenient to define an assembly-level element set by referring to part-level element +sets. In such cases a set definition containing many elements can get quite lengthy. Therefore, an alternate +method is provided. +Input File Usage: +*ELSET, ELSET=ElsetName, INSTANCE=InstanceName +The following example shows two equivalent ways to define an assembly-level +element set; once by prefixing each element number with a part instance name +(as shown above) and once using the more compact INSTANCE notation: +*ASSEMBLY, NAME=Assembly-1 +*INSTANCE, NAME=PartA-1, PART=PartA +... +*END INSTANCE +*INSTANCE, NAME=PartA-2, PART=PartA +... +*END INSTANCE +*ELSET, ELSET=set2 +PartA-1.11, PartA-1.12, PartA-1.13, PartA-1.14, +PartA-2.21, PartA-2.22, PartA-2.23, PartA-2.24 +*ELSET, ELSET=set3, INSTANCE=PartA-1 +11, 12, 13, 14 +*ELSET, ELSET=set3, INSTANCE=PartA-2 +21, 22, 23, 24 +*END ASSEMBLY +When the *ELSET option is used more than once with the same name, as it is +with set3, the elements in the second use of *ELSET are appended to the set +created by the first use of *ELSET. +Internal element sets created by Abaqus/CAE +In Abaqus/CAE many modeling operations are performed by picking geometry with the mouse. For +example, a surface can be created by picking a face on a geometric part instance. Since the *SURFACE +option refers to an element set, this “picked” geometry must be translated into an element set in the input +file. Such sets are assigned a name by Abaqus/CAE and marked as internal. You can view these internal +sets using display groups in the Visualization module of Abaqus/CAE . +Input File Usage: +*ELSET, ELSET=ElsetName, INTERNAL +Transferring of element sets +If the results of an Abaqus/Explicit analysis are imported into an Abaqus/Standard analysis (or vice versa) +or results from an Abaqus/Standard analysis are imported into another Abaqus/Standard analysis , all element set definitions +in the original analysis are imported by default. Alternatively, you can import only selected element set +definitions; see “Importing element set and node set definitions” in “Transferring results between Abaqus +analyses: overview,” Section 9.2.1, for details. +If a three-dimensional model is generated from a symmetric model , all element sets in the original model will be used (and expanded) in the +generated model. +Creating elements from existing elements by generating them incrementally +You can generate elements incrementally from existing elements. The newly created elements are always +the same element type as that of the master element. +Abaqus first generates a row of elements by copying the node pattern of a given element with +prescribed increments in the node and element numbers. This row can then be repeated to form a layer, +which can also be repeated to form a block. +To generate a row of elements, you must specify the following information: +• The master element number. The master element must exist at the time that the generation is +specified, although it can be an element that has just been defined in this same element generation. +• The number of elements to be defined in the first row generated, including the master element. +• The increment in node numbers of corresponding nodes from element to element in the row. The +default is 1. All element node numbers (except special-purpose nodes, discussed later) will increase +by the same value. +• The increment in element numbers in the row. The default is 1. +To copy this newly created master row to create a layer of elements, you must specify the following +additional information: +• The number of rows to be defined, including the master row. +• The increment in node numbers of corresponding nodes from row to row. +• The increment in element numbers of corresponding elements from row to row. +To copy this newly created master layer to create a block of elements, you must specify the following +additional information: +• The number of layers to be defined, including the master layer. +• The increment in node numbers of corresponding nodes from layer to layer. +• The increment in element numbers of corresponding elements from layer to layer. +Input File Usage: +*ELGEN +For example, the elements forming the quarter cylinder shown in Figure 2.2.1–1 +can be generated by the following lines: +*ELGEN +1, 3, 1, 1, 5, 10, 10, 6, 100, 100 +Incrementing special-purpose nodes +By default, the following nodes are not incremented: +• rigid body reference nodes for IRS-type and drag chain elements; and +• nodes used to define the direction of the first cross-section axis for beams or frames in space. +You can specify that all nodes should be incremented. You define the increment between node numbers +as described above. Usually the incrementation of all nodes is needed only for nodes used to define the +direction of the first cross-section axis for beams in space. +Input File Usage: +*ELGEN, ALL NODES +Creating elements by copying existing elements +You can create new elements by copying existing elements. You must identify the existing element set +to copy and specify an integer constant that will be added to the node numbers of the existing elements +to define the node numbers of the new elements. Likewise, you must specify an integer constant that +will be added to the element numbers of existing elements to define element numbers for the elements +being created. +301 +211 +201 +111 +501 +411 +401 +311 +321 +221 +511 +521 +421 +121 +431 +331 +231 +441 +341 +131 +141 +241 +531 +541 +101 +11 +22 +21 +31 +32 +13 +12 +23 +33 +43 +42 +41 +a. Element numbers +(Only visible elements shown). +501 +411 +601 +511 +421 +401 +301 +311 +211 +321 +221 +201 +101 +111 +11 +611 +621 +521 +12 +121 +21 +13 +22 +23 +14 +24 +33 +32 +131 +31 +42 +41 +43 +34 +44 +54 +431 +441 +331 +231 +341 +241 +141 +451 +351 +251 +53 +52 +51 +151 +631 +531 +641 +541 +651 +551 +b. Node numbers +(Only visible nodes shown). +Figure 2.2.1–1 Element generation example. +You can assign the newly created elements to an element set. If you do not specify an element set +name for the newly created elements, they are not assigned to an element set. +Input File Usage: +*ELCOPY, OLD SET=name, NEW SET=new_name, +SHIFT NODES=number, ELEMENT SHIFT=number +For example, the following data lines will generate new elements in set B that +are copies of all elements in set A at the time this option is processed, with 1000 +added to each element number and to each node number in the definitions of +the new elements. The members of set A at the time the line is processed are +those elements defined to be in set A by all element generation and element set +definition lines that appear in the input file prior to this *ELCOPY option. +*ELCOPY, OLD SET=A, NEW SET=B, ELEMENT SHIFT=1000, +SHIFT NODES=1000 +Special considerations for continuum elements +When copying existing elements, you can choose to modify the node numbering sequence for the +elements being created to avoid creating continuum elements that violate the Abaqus convention for +counterclockwise element numbering. This modification is normally required when the nodes have +been generated by copying existing nodes (“Creating nodes by copying existing nodes” in “Node +definition,” Section 2.1.1). +Input File Usage: +*ELCOPY, REFLECT +For example, assume element 1 is in element set A and is defined by nodes 1, +2, 3, 4. The following data line will generate element number 11, also in set A, +with nodes 11, 14, 13, and 12: +*ELCOPY, OLD SET=A, NEW SET=A, ELEMENT SHIFT=10, +SHIFT NODES=10, REFLECT +If the REFLECT parameter is not used, the new element will be defined by the +node sequence 11, 12, 13, 14 and will violate the counterclockwise element +numbering convention used with continuum elements . +13 +12 +14 +11 +Figure 2.2.1–2 Example of modification of node numbering sequence. +2.2.2 +ELEMENT FOUNDATIONS +Products: Abaqus/Standard Abaqus/CAE +References +• *FOUNDATION +• “Defining foundations,” Section 15.13.20 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +Elastic element foundations: +• can be defined for stress/displacement elements in Abaqus/Standard according to the load identifiers +described in Part VI, “Elements”; +• act like springs to ground; and +• are a simple way of including the stiffness effects of a support (such as the soil under a building) +without modeling the details of the support. +Defining element foundation behavior +Foundation pressures act normal to the element faces on which they are applied. In large-displacement +analysis the direction of action of the foundation is based on the deformed configuration; foundations +rotate with the element sides. +Convergence difficulties may arise with large-deformation problems since no corresponding +foundation load stiffness terms are included in the element stiffness matrices. +To define the foundation behavior, you specify the foundation stiffness per unit area (per unit length +for beams). +Input File Usage: +Use the following option in the model definition portion of the input file: +Abaqus/CAE Usage: +*FOUNDATION +Interaction module: Create Interaction: Step: Initial, Elastic foundation +2.2.3 +DEFINING REINFORCEMENT +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• *EMBEDDED ELEMENT +• *MEMBRANE SECTION +• *PRESTRESS HOLD +• *REBAR +• *REBAR LAYER +• *SHELL SECTION +• *SURFACE SECTION +• “Defining rebar layers,” Section 12.13.19 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +Rebar: +• are used to define layers of uniaxial reinforcement in membrane, shell, and surface elements (such +layers are treated as a smeared layer with a constant thickness equal to the area of each reinforcing +bar divided by the reinforcing bar spacing); +• can be used to add layers of reinforcement in a solid by embedding reinforced surface or membrane +elements in the “host” solid elements as described in “Embedded elements,” Section 34.4.1; +• can be used to add additional stiffness, volume, and mass to the model; +• can be used to add discrete axial reinforcement in beam elements in Abaqus/Standard; +• can be used in coupled temperature-displacement analysis but do not contribute to the thermal +conductivity and specific heat; +• can be used in coupled thermal-electrical-structural analysis but do not contribute to the electrical +conductivity, thermal conductivity and specific heat; +• cannot be used in heat transfer or mass diffusion analysis; and +• have material properties that are distinct from those of the underlying or host element. +• do not include the mass or volume of the underlying elements. +Defining a rebar layer +You can specify one or multiple layers of reinforcement in membrane, shell, or surface elements. For +each layer you specify the rebar properties including the rebar layer name; the cross-sectional area of +each rebar; the rebar spacing in the plane of the membrane, shell, or surface element; the position of +the rebars in the thickness direction (for shell elements only), measured from the midsurface of the shell +(positive in the direction of the positive normal to the shell); the rebar material name; the initial angular +orientation, in degrees, measured relative to the local 1-direction; and the isoparametric direction from +which the rebar angle output will be measured. +You can model rebar layers in solid (continuum) elements by embedding a set of surface or +membrane elements with rebar layers defined as discussed above in a set of host continuum elements. +Input File Usage: +Use the following options to define one or more rebar layers in membrane +elements: +*MEMBRANE SECTION, ELSET=memb_set_name +*REBAR LAYER +Use the following options to define one or more rebar layers in shell elements: +*SHELL SECTION, ELSET=shell_set_name +*REBAR LAYER +Use the following options to define one or more rebar layers in surface elements: +*SURFACE SECTION, ELSET=surf_set_name +*REBAR LAYER +Use the following option to model rebar layers in solid (continuum) elements: +*EMBEDDED ELEMENT, HOST ELSET=solid_set_name +memb_set_name or surf_set_name +Abaqus/CAE Usage: +Property module: membrane, shell, or surface section editor: Rebar Layers +Interaction module: Create Constraint: Embedded region +Assigning a name to the rebar layer +You must assign each layer of rebar in a particular element or element set a separate name. This name +can be used in defining rebar prestress and output requests. +Input File Usage: +*REBAR LAYER +rebar layer name +Abaqus/CAE Usage: +Property module: membrane, shell, or surface section editor: Rebar +Layers: Layer Name rebar layer name +Specifying rebar geometry +The rebar geometry is always defined with respect to a local coordinate system. Defining an appropriate +local system is described in the next section. The rebar geometry can be constant, vary as a function of +radial position in a cylindrical coordinate system, or vary according to the tire “lift” equation. In each +case you must specify the spacing, s, and the area, A, which are used to determine the thickness of the +equivalent rebar layer, +, of the rebar with respect to this +local system. +, as well as the angular orientation, +In addition, for shell elements you must specify the position of the rebars in the shell thickness +direction measured from the midsurface of the shell (positive in the direction of the positive normal to +the shell). If the shell’s thickness is defined by nodal thicknesses (“Nodal thicknesses,” Section 2.1.3), +this distance will be scaled by the ratio of the thickness defined by the nodal thickness to the thickness +defined by the section definition. If the shell’s thickness is defined with a distribution (“Distribution +definition,” Section 2.8.1), this distance is scaled by the ratio of the element thickness defined by the +distribution to the default thickness. +Defining rebar with constant spacing +You can specify the geometry to be constant in the local rebar coordinate system. In this case the spacing, +s, is specified as a length measure. +Input File Usage: +Abaqus/CAE Usage: +*REBAR LAYER, GEOMETRY=CONSTANT +Property module: membrane, shell, or surface section editor: Rebar +Layers: Rebar geometry: Constant +Defining rebar spacing as a function of radial position +You can specify the spacing, s, in terms of angular spacing in degrees as shown in Figure 2.2.3–1. +middle surface +of shell +position in shell +thickness direction +rebar angular spacing +in degrees +radial rebar (orientation angle 0o) +Figure 2.2.3–1 Example of radial rebars in axisymmetric shell elements. +Angular spacing values can also be used for non-radial rebars as well as for rebars having nonzero +orientation angles from the meridional plane. In these cases the orientation angles of the rebars do not +change. The angular spacing option is used only to compute the spacing between rebars in units of length +by multiplying the angular spacing by the radial distance of the concerned point on the rebar from the +axis of axisymmetry. A local cylindrical coordinate system must be defined for the rebar if the rebar is +associated with three-dimensional elements. +Input File Usage: +Abaqus/CAE Usage: +*REBAR LAYER, GEOMETRY=ANGULAR +Property module: membrane, shell, or surface section editor: Rebar +Layers: Rebar geometry: Angular +Defining rebar using the tire “lift” equation +Structural tire analysis is often performed using the cured tire geometry as the reference configuration +for the finite element model. However, the cord geometry is more conveniently specified with respect +to the “green,” or uncured, tire configuration. The tire lift equation provides mapping from the uncured +geometry to the cured geometry . +αο +αο +revolution axis +rο +rd +a) uncured geometry +rd +revolution axis +b) cured geometry +Figure 2.2.3–2 Mapping between uncured and cured tire rebar geometry. +You can specify the spacing and orientation of the rebar cords with respect to the uncured configuration +and let Abaqus map these properties to the reference configuration of the cured tire. Using a cylindrical +coordinate system, the spacing, s, and angular orientation, +, in the cured tire are obtained from +and +where r is the position of the rebar along the radial direction in the cured geometry, +the rebar in the uncured geometry, +is the spacing in the uncured geometry, +is the position of +is the angle measured +with respect to the projected local 1-direction in the uncured geometry, and e is the cord extension ratio. +In a tire e represents the pre-strain that occurs during the curing process; e =1 means a 100% extension. +When +is equal to 90°, the rebar is assumed to have a constant spacing of +. +A local cylindrical coordinate system must be defined for the rebar if the rebar is associated with +three-dimensional elements. +Input File Usage: +Abaqus/CAE Usage: +*REBAR LAYER, GEOMETRY=LIFT EQUATION +Property module: membrane, shell, or surface section editor: Rebar +Layers: Rebar geometry: Lift equation–based +Local rebar orientation system +The rebar geometry, such as rebar orientation and spacing, is defined with respect to a local orientation +system. This local rebar orientation system is entirely independent from the local orientation system +used for the underlying assignment. +The rebar angle is always defined with respect to the local 1-direction as shown in Figure 2.2.3–3. +Default projected local surface directions +or user-defined local surface directions +Initial rebar angle, α +Figure 2.2.3–3 Rebar in a three-dimensional shell, membrane, or surface element. +Rebar defined with either angular spacing or spacing defined by the tire lift equation is specified with +respect to a cylindrical orientation system. For axisymmetric analysis the global coordinate system +is used as the cylindrical system. For three-dimensional analysis you must provide a user-defined +cylindrical orientation definition. +Local orientation system for three-dimensional elements +You can define the local system by referring to a user-defined local coordinate system. +See +“Orientations,” Section 2.2.5, for a description of how the local coordinate system is calculated from +the user-defined directions for definition of rebar in shell, membrane, and surface elements. +If you do not specify a user-defined orientation, the local 1-direction is based on the default projected +local coordinate system. See “Conventions,” Section 1.2.2, for a definition of the default projected local +directions on a surface in space. +A positive angle +defines a rotation from local direction 1 to local direction 2 around the element’s +normal direction or the user-defined normal direction. If the shell, membrane, or surface element is +curved in space, the local 1-direction will vary across the element and the initial rebar angular orientation +will also vary accordingly. The orientation definition that can optionally be associated with a shell or +membrane section definition has no influence on the rebar angular orientation definitions. For example, +in a membrane section, shell section, or surface section, the following data would result in the rebar layer +definition shown in Figure 2.2.3–4: A=0.01; s=0.1; distance of rebar from the shell midsurface=0.0; +=30.; and the rebar definition refers to a local rectangular orientation defined to have its X-axis go +plane include the point (−0.7071, −0.7071, 0.0), and +through the point (−0.7071, 0.7071, 0.0), its +an additional rotation of 0.0 degrees about the 3-direction. +OR1 +OR2 +ORn = user-defined local directions +1, 2 = default local directions +Figure 2.2.3–4 Rebar defined relative to user-defined local coordinate directions. +The following data would result in the rebar layer definition shown in Figure 2.2.3–5: A=0.01, s=0.1, +distance of rebar from the shell midsurface=0.0, and =45. +Input File Usage: +Abaqus/CAE Usage: +Use the following options to define the local 1-direction for a rebar layer: +*ORIENTATION, NAME=name +*REBAR LAYER, ORIENTATION=name +Property module: +Tools→Datum: Type: CSYS +Assign→Rebar Reference Orientation +Local orientation system for axisymmetric elements +Rebars in an axisymmetric membrane element or an axisymmetric surface element must lie in the element +reference surface, whereas rebars in an axisymmetric shell can lie in the shell reference surface or can +be offset from the midsurface. Rebars in axisymmetric membrane, shell, and surface elements can be +local directions +α = 45° +Figure 2.2.3–5 Rebar defined relative to default local coordinate directions. +defined to have any angular orientation with respect to the r–z plane. See Figure 2.2.3–6 for an example +of circumferential rebars and Figure 2.2.3–1 for an example of radial rebars in axisymmetric shells. +CL +10 +circumferential rebar (90o orientation) +middle surface +of shell +spacing +of rebar +position in shell +thickness direction +20 +Figure 2.2.3–6 Example of circumferential rebars in axisymmetric shell elements. +You cannot specify a user-defined orientation for rebar layers in axisymmetric membrane, shell, and +surface elements. Instead, in the rebar layer definition you specify the angular orientation of the rebar +layer, in degrees, with respect to the r–z plane; this orientation is measured positive about the positive +normal to the membrane, shell, or surface element. +If you specify an orientation angle other than 0° or 90° for rebar in an axisymmetric membrane +without twist, axisymmetric shell, or axisymmetric surface without twist, Abaqus assumes that the +rebars are balanced (i.e., half the rebar lie at the specified angle +and the other half at an angle of +) and internal calculations are handled accordingly. Such a rebar definition should not be used +with the symmetric model generation capability (“Symmetric model generation,” Section 10.4.1). The +recommended modeling technique is to define unbalanced rebar in axisymmetric elements with twist. +Balanced rebar, on the other hand, can be defined in regular axisymmetric elements or in axisymmetric +elements with twist and should be defined by specifying half the rebar at the specified angle +and the +other half at an angle of +. +Large-displacement considerations +In geometrically nonlinear analyses as the rebar-reinforced element deforms, the initially defined +geometric properties and orientation of the rebar layer can change as a result of finite-strain effects. +The deformation of the rebar layer is determined from the deformation gradient of the underlying shell, +membrane, or surface element. Rebars rotate with the actual deformation and not with the average rigid +body rotation of the material point in the underlying element. See “Rebar modeling in shell, membrane, +and surface elements,” Section 3.7.3 of the Abaqus Theory Manual, for details. +For example, consider a plate modeled with a first-order element under large pure shear deformation +as shown in Figure 2.2.3–7, where rebars are initially aligned with the element isoparametric directions. +Figure 2.2.3–7 Rebar orientation evolves in a geometrically nonlinear analysis. +As a result of finite-strain effects, rebars rotate but remain aligned with the element isoparametric +directions. If the same problem is modeled using anisotropic material properties rather than rebars and +the material directions (1 and 2) are initially aligned with the element isoparametric directions, under +such large shear deformation the material directions rotate and are no longer aligned with the element +isoparametric directions. The material directions in this case are determined based on the average rigid +body rotation of the material point. Hence, if the material is not truly a continuum, the anisotropic +behavior is better modeled with rebars. +Defining rebar in Abaqus/Standard beam elements +You must use element-based rebar, described in “Defining rebar as an element property,” Section 2.2.4, +to model discrete rebar in beam elements in Abaqus/Standard. You specify the elements that contain the +rebar, the cross-sectional area of each rebar, and the location of each rebar with respect to the local beam +section axis . +Rebar +Local beam +section axes +Figure 2.2.3–8 Rebar location in a beam section. +Each individual rebar must be assigned a separate name in a particular element or element set. This name +can be used in defining rebar prestress and output requests. +Input File Usage: +Abaqus/CAE Usage: +*REBAR, ELEMENT=BEAM, MATERIAL=mat, NAME=name +Rebar in Abaqus/Standard beam elements are not supported in Abaqus/CAE. +Defining the rebar material +The material properties of the rebars are distinct from those of the underlying element and are defined by +a separate material definition (“Material data definition,” Section 21.1.2). You must associate each rebar +layer (or, for beam elements in Abaqus/Standard, each rebar definition) with a set of material properties. +The following material behavior cannot be used in Abaqus/Standard to define rebar materials: +• “Porous metal plasticity,” Section 23.2.9. +The following material behaviors cannot be used in Abaqus/Explicit to define rebar materials: +• “Defining fully anisotropic elasticity” in “Linear elastic behavior,” Section 22.2.1; +• “Defining orthotropic elasticity by specifying the terms in the elastic stiffness matrix” in “Linear +elastic behavior,” Section 22.2.1; +• “Equation of state,” Section 25.2.1; +• “Anisotropic yield/creep,” Section 23.2.6; +• “Porous metal plasticity,” Section 23.2.9; +• “Extended Drucker-Prager models,” Section 23.3.1; +• “Modified Drucker-Prager/Cap model,” Section 23.3.2; +• “Crushable foam plasticity models,” Section 23.3.5; or +• “Cracking model for concrete,” Section 23.6.2. +Although Abaqus/Standard will allow for a rebar material to be defined with orthotropic elasticity +(“Defining orthotropic elasticity by specifying the terms in the elastic stiffness matrix” in “Linear elastic +behavior,” Section 22.2.1) or anisotropic elasticity (“Defining fully anisotropic elasticity” in “Linear +elastic behavior,” Section 22.2.1), +is the only meaningful material constant in these definitions. +, using the corresponding stress component, +, as discussed in “Linear elastic behavior,” Section 22.2.1; no other strain or stress components exist +is used to compute the strain in the rebar direction, +in rebars. +If a nonzero density is specified for the material in a rebar layer, the mass of the rebar is taken into +account for dynamic analysis as well as for gravity, centrifugal, and rotary acceleration distributed loads. +The mass is not taken into account for rebar in beam elements (available only in Abaqus/Standard); +you should adapt the density of the beam material to account for the rebar mass. +Input File Usage: +Abaqus/CAE Usage: +*REBAR LAYER +rebar layer name, A, s, distance of rebar from shell midsurface, +rebar material name +Property module: membrane, shell, or surface section editor: Rebar +Layers: Material rebar material name +Initial conditions +Initial conditions (“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1) can be +used to define prestress or solution-dependent values for rebars. +Defining prestress in rebar +For structures in which reinforcing is defined (such as reinforced concrete structures), you can use initial +conditions to define the prestress in the rebars. +In such cases in Abaqus/Standard the structure must be brought to a state of equilibrium before +it is actively loaded by means of an initial static analysis step (“Static stress analysis,” Section 6.2.2) +with no external loads applied (or, perhaps, with the “dead” loads only)—see “Initial conditions in +Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1. +Input File Usage: +*INITIAL CONDITIONS, TYPE=STRESS, REBAR +element number or element set name, rebar name, prestress value +Abaqus/CAE Usage: +Rebar prestress is not supported in Abaqus/CAE. +Holding prestress in rebar in Abaqus/Standard +If prestress is defined in the rebars and unless the prestress is held fixed, it will be allowed to change +during an equilibrating static analysis step; this is a result of the straining of the structure as the self- +equilibrating stress state establishes itself. An example is the pretension type of concrete prestressing in +which reinforcing tendons are initially stretched to a desired tension before being covered by concrete. +After the concrete cures and bonds to the rebar, release of the initial rebar tension transfers load to the +concrete, introducing compressive stresses in the concrete. The resulting deformation in the concrete +reduces the stress in the rebar. +Alternatively, you can keep the initial stress defined in some or all of the rebars constant during +this initial equilibrium solution. An example is the post-tension type of concrete prestressing; the rebars +are allowed to slide through the concrete (normally they are in conduits), and the prestress loading is +maintained by some external source (prestressing jacks). The magnitude of the prestress in the rebar is +normally part of the design requirements and must not be reduced as the concrete compresses under the +loading of the prestressing. Normally, the prestress is held constant only in the first step of an analysis. +This is generally the more common assumption for prestressing. +If the prestress is not held constant in analysis steps following the step in which it is held constant, +the stress in the rebar will change due to additional deformation in the concrete. If there is no additional +deformation, the stress in the rebar will remain at the level set by the initial conditions. If the loading +history is such that no plastic deformation is induced in the concrete or rebar in steps subsequent to the +steps in which the prestress is held constant, the stress in the rebar will return to the level set by the initial +conditions upon removal of the loading applied in those steps. +Input File Usage: +Abaqus/CAE Usage: +*PRESTRESS HOLD +Rebar prestress is not supported in Abaqus/CAE. +Defining the initial values of solution-dependent state variables for rebars +You can define the initial values of solution-dependent state variables for rebars within elements. See +“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1, for details. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=SOLUTION, REBAR +Initial solution-dependent state variables are not supported in Abaqus/CAE. +Output +Rebar force output is available at the rebar integration locations with output variable RBFOR. The rebar +force is equal to the rebar stress times the current rebar cross-sectional area. The current cross-sectional +area of the rebar is calculated by assuming the rebar is made of an incompressible material, regardless +of the actual material definition. For rebars in membrane, shell, or surface elements output variables +RBANG and RBROT identify the current orientation of rebar within the element and the relative +rotation of the rebar as a result of finite deformation, respectively. These quantities are measured with +respect to the user-specified isoparametric direction in the element, not the default local element system +or the orientation-defined system. See “Rebar modeling in shell, membrane, and surface elements,” +Section 3.7.3 of the Abaqus Theory Manual. +See “Abaqus/Standard output variable identifiers,” Section 4.2.1, and “Abaqus/Explicit output +variable identifiers,” Section 4.2.2, for information on additional output quantities such as stress and +strain. For rebars in membrane, shell, or surface elements with multiple integration points, output +quantities are available at the integration points and at the centroid of the element. +Specifying the direction for rebar angle output +The output quantities RBANG and RBROT can be measured from either of the isoparametric directions +in the plane of the membrane, shell, or surface elements. You can specify the desired isoparametric +direction from which the rebar angle will be measured (1 or 2). The rebar angle is measured from the +isoparametric direction to the rebar with a positive angle defined as a counterclockwise rotation around +the element’s normal direction. The default direction is the first isoparametric direction. +In axisymmetric shell, surface, and membrane elements the first isoparametric direction coincides +with the meridional direction, and the second isoparametric direction coincides with the hoop direction. +In triangular elements Abaqus defines the isoparametric directions as follows: for a 3-node triangle the +first isoparametric direction is a straight line going from node 1 to the midpoint of the second element +edge, and the second isoparametric direction is a straight line going from the midpoint of the first element +edge to the midpoint of the third element edge; for a 6-node triangle the first isoparametric direction is a +straight line going from node 1 to node 5, and the second isoparametric direction is a straight line going +from node 4 to node 6 . +Input File Usage: +*REBAR LAYER +rebar layer name, A, s, distance of rebar from shell midsurface, +rebar material name, angular orientation of rebar, isoparametric direction +Abaqus/CAE Usage: +You cannot specify the direction for rebar angle output in Abaqus/CAE; the +first isoparametric direction is always used. +Example +As an example, a user-defined local coordinate system is used to define rebar in a shell element ( = +and the output value of RBANG is 75°, as illustrated in Figure 2.2.3–9: +), +*REBAR LAYER, ORIENTATION=ORIENT +Rbname, 0.01, 0.1, 0.0, Rbmat, 30., 2 +*ORIENTATION, SYSTEM=RECTANGULAR, NAME=ORIENT +-0.7071, 0.7071, 0.0, -0.7071, -0.7071, 0.0 +3, 0.0 +The rebars are located at the midsurface of the shell. Output variable RBANG is measured from the +second isoparametric direction to the rebar. +If the first isoparametric direction were chosen instead, +output variable RBANG would report an angle of 165°. +Visualizing rebar orientation and results in rebar +Abaqus/CAE supports visualization of rebar direction and results in rebar layers. Plots of rebar +orientation are available only if you request element output for rebars . Element variables for rebar can be contoured as field output +or plotted as history output in the Visualization module. Each rebar layer will have a unique name +and represents one additional section point in a membrane, shell, or surface element. You can select a +RBANG = 75 +2, ISO2 +OR1 +OR2 +ISOn = isoparametric directions +ORn = user-defined local directions +1, 2 = default local directions +1, ISO1 +Figure 2.2.3–9 RBANG measurement for rebar defined relative +to user-defined local coordinate directions. +named rebar layer in a membrane, shell, or surface element to display its results in the Visualization +module. Abaqus/CAE does not yet support rebar in beams. +2.2.4 +DEFINING REBAR AS AN ELEMENT PROPERTY +Products: Abaqus/Standard Abaqus/Explicit +References +• *PRESTRESS HOLD +• *REBAR +Overview +The preferred method for defining rebar in shell and membrane elements is defining layers of +reinforcement as part of the element section definition (documented in “Defining reinforcement,” +Section 2.2.3). The preferred method for defining rebar in solids is embedding reinforced surface or +membrane elements in “host” solid elements as described in “Embedded elements,” Section 34.4.1. +This section describes an alternative method of defining rebar in shell, membrane, and continuum +elements as an element property. This method is more cumbersome than the method described in +“Defining reinforcement,” Section 2.2.3, and does not allow visualization of the rebar and rebar results +in Abaqus/CAE. +Element-based rebars: +• are used to define uniaxial reinforcement in solid, membrane, and shell elements; +• can be defined as individual reinforcing bars in solid elements; +• can be defined as layers of uniformly spaced reinforcing bars in shell, membrane, and solid elements +(such layers are treated as a smeared layer with a constant thickness equal to the area of each +reinforcing bar divided by the reinforcing bar spacing); +• can be used with coupled temperature-displacement elements but do not contribute to the thermal +conductivity and specific heat; +• can be used with coupled thermal-electrical-structural elements but do not contribute to the electrical +conductivity, thermal conductivity and specific heat; +• do not contribute to the mass of the model in Abaqus/Standard; +• cannot be used in elements intended for heat transfer or mass diffusion analysis; +• cannot be used with triangular shell and membrane elements or with triangular, triangular prism, +and tetrahedral solid elements; and +• have material properties that are distinct from those of the underlying element. +Assigning a name to the rebar set +You must assign a name to the rebar set. This name can be used in defining rebar prestress and output +requests. Each layer of rebar must be assigned a separate name in a particular element or element set. +Input File Usage: +*REBAR, ELEMENT=elem, MATERIAL=mat, NAME=name +Defining rebars in three-dimensional shell and membrane elements +Both isoparametric and skew rebars can be defined in three-dimensional shell and membrane elements. +Rebars cannot be used with triangular shells or membranes. +If triangular-shaped shells or membranes are needed, collapsed quadrilateral shells or membranes +can be used. The resulting rebar directions will depend on the type of rebar (isoparametric or skew) used. +The rebar must be defined carefully since the element is distorted. This technique should be used only +in regions of the mesh where results are not critical and stress gradients are not high. +The stiffness calculations for the rebars use the same integration points as the calculations for +the underlying shell or membrane elements. See “Shell elements: overview,” Section 29.6.1, and +“Membrane elements,” Section 29.1.1, for more information about shell and membrane elements. +Defining isoparametric rebars in three-dimensional shell and membrane elements +Isoparametric rebars are aligned along the mapping of constant isoparametric lines in the element . +Similar to +edge 1 or 3 +(cid:0)(cid:0) +(cid:0)(cid:0) +(cid:0)(cid:0) +(cid:0)(cid:0) +(cid:0)(cid:0) +(cid:0)(cid:0) +(cid:0)(cid:0) +Similar to +edge 2 or 4 +physical space +(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0) +(cid:0)(cid:0) +(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0) +(cid:0)(cid:0) +(cid:0)(cid:0) +isoparametric space +Edge Corner nodes +1 1-2 +2 2-3 +3 3-4 +4 4-1 +Figure 2.2.4–1 “Isoparametric” rebar in an undistorted +three-dimensional shell or membrane element. +If opposite edges of the element containing the rebar are not parallel, the rebar directions will be different +at each of the integration points within an element . +The spacing of the rebar will be fixed in physical space. The spacing, s, and the area of the rebar, A, +are used to determine the thickness of the equivalent smeared layer, +. If the edges of the element +containing the rebar are not parallel, the number of actual rebar with this spacing passing through one +edge will be different than the number passing through the opposite edge (opposite in isoparametric +space). +You specify the elements that contain the rebars; the cross-sectional area, A, of each rebar; the rebar +spacing in the plane of the shell, s; and the edge number to which the rebars are parallel when plotted +in isoparametric space . In addition, for shell elements you specify the position of +the rebars in the shell thickness direction measured from the midsurface of the shell (positive in the +direction of the positive normal to the shell). If the shell’s thickness is defined by nodal thicknesses +Figure 2.2.4–2 “Isoparametric” rebar directions in a distorted three-dimensional shell or +membrane element (dashed lines indicate rebar directions). +(“Nodal thicknesses,” Section 2.1.3), this distance is scaled by the ratio of the thickness defined by the +nodal thickness to the thickness defined by the section definition. If the shell’s thickness is defined with +a distribution (“Distribution definition,” Section 2.8.1), this distance is scaled by the ratio of the element +thickness defined by the distribution to the default thickness. If the shell has a composite section whose +layer thicknesses are defined with distributions (“Distribution definition,” Section 2.8.1), this distance is +scaled by the ratio of the sum of the element layer thicknesses defined by the distributions to the sum of +the default layer thicknesses. +Input File Usage: +Use the following option to define isoparametric rebars in three-dimensional +shell elements: +*REBAR, ELEMENT=SHELL, MATERIAL=mat, +GEOMETRY=ISOPARAMETRIC +Use the following option to define isoparametric rebars in general membrane +elements: +*REBAR, ELEMENT=MEMBRANE, MATERIAL=mat, +GEOMETRY=ISOPARAMETRIC +Defining skew rebars in three-dimensional shell and membrane elements +Skew rebars need not be similar to an element edge; they can lie at any prescribed angle from the local +1-axis. The direction of the rebars must be defined in one of two ways, as indicated in Figure 2.2.4–3: +1. The rebars can be defined relative to the default projected local coordinate system . +2. The rebars can be defined relative to a user-defined local coordinate system . +Projected local surface directions +or user-defined local +surface directions +Skew angle, α +Figure 2.2.4–3 “Skew” rebar in a three-dimensional shell or membrane. +The orientation definition that can optionally be associated with a shell or membrane section definition +has no influence on the rebar angular orientation definitions. If the shell or membrane is curved in space, +the local 1-direction will vary across the element and the skew rebar will also vary accordingly. +For shell elements the definition of a local coordinate system using distributions (“Distribution +definition,” Section 2.8.1) has no influence on the rebar angular orientation definitions. +If the rebar cross-sectional area is A, the rebar spacing, s, should be given so that the thickness of +the equivalent “smeared” layer of reinforcing is +. +Defining skew rebars relative to the default projected local coordinate system +To define skew rebars relative to the default projected local coordinate system, you specify the elements +that contain the rebars; the cross-sectional area, A, of each rebar; the rebar spacing in the plane of the +shell, s; the position of the rebars in the thickness direction (for shell elements only), measured from the +midsurface of the shell (positive in the direction of the positive normal to the shell); and the angle +, in +degrees, between the default local 1-direction and the rebars. See “Conventions,” Section 1.2.2, for a +definition of the default projected local directions on a surface in space. If the shell’s thickness is defined +by nodal thicknesses (“Nodal thicknesses,” Section 2.1.3), the rebar position in the thickness direction +will be scaled by the ratio of the thickness defined by the nodal thickness to the thickness defined by +the section definition. If the shell’s thickness is defined with a distribution (“Distribution definition,” +Section 2.8.1), the rebar position in the thickness direction is scaled by the ratio of the element thickness +defined by the distribution to the default thickness. A positive angle +defines a rotation from local +direction 1 to local direction 2 around the element’s normal direction. For example, in a membrane the +following data would result in the rebar definition shown in Figure 2.2.4–4: A=0.05, s=0.1, and =45. +When a user-defined local orientation definition is not used to define the angular orientation of the +rebar and the normal to the shell is nearly parallel to the global 1-axis, the local 1-axis may change +significantly within an element or from one element to the next . +local directions +α = 45° +Figure 2.2.4–4 Skew rebar defined relative to default local coordinate directions. +Input File Usage: +Use the following option to define skew rebars relative to the default projected +local coordinate system in three-dimensional shell elements: +*REBAR, ELEMENT=SHELL, MATERIAL=mat, GEOMETRY=SKEW +Use the following option to define skew rebars relative to the default projected +local coordinate system in general membrane elements: +*REBAR, ELEMENT=MEMBRANE, MATERIAL=mat, +GEOMETRY=SKEW +Defining skew rebars relative to a user-defined local coordinate system +To define skew rebars relative to a user-defined local coordinate system, you specify the elements that +contain the rebars; the cross-sectional area, A, of each rebar; the rebar spacing in the plane, s; the position +of the rebars in the thickness direction (for shell elements only), measured from the midsurface of the +shell (positive in the direction of the positive normal to the shell); and the angle, +, in degrees, between +the user-defined 1-direction and the rebars. See “Orientations,” Section 2.2.5, for a description of how the +local coordinate system is calculated from the user-defined directions for definition of rebar in shells and +membranes. A positive angle +defines a rotation from local direction 1 to local direction 2 around the +user-defined normal direction. For example, in a shell the following data would result in the skew rebar +definition shown in Figure 2.2.4–5: A=0.01; s=0.1; distance of rebar from the shell midsurface=0.0; +=30.; and the rebar definition refers to a local rectangular orientation defined to have its X-axis go +through the point (−0.7071, 0.7071, 0.0), its X–Y plane include the point (−0.7071, −0.7071, 0.0), and +an additional rotation of 0.0 degrees about the 3-direction. +Input File Usage: +Use the following option to define skew rebars relative to a user-defined local +coordinate system in three-dimensional shell elements: +*REBAR, ELEMENT=SHELL, MATERIAL=mat, GEOMETRY=SKEW, +ORIENTATION=name +OR1 +OR2 +ORn = user-defined local directions +1, 2 = default local directions +Figure 2.2.4–5 Skew rebar defined relative to user-defined local coordinate directions. +Use the following option to define skew rebars relative to a user-defined local +coordinate system in general membrane elements: +*REBAR, ELEMENT=MEMBRANE, MATERIAL=mat, +GEOMETRY=SKEW, ORIENTATION=name +Defining rebars in axisymmetric shell and membrane elements +Rebars in an axisymmetric membrane must lie in the membrane reference surface, whereas rebars in an +axisymmetric shell can lie in the shell reference surface or can be offset from the midsurface. Rebars in +axisymmetric shells and membranes can be defined to have any orientation with respect to the r–z plane. +See Figure 2.2.4–6 for an example of circumferential rebars and Figure 2.2.4–7 for an example of radial +rebars in axisymmetric shells. +You specify the cross-sectional area, A, of each rebar; the rebar spacing, s; for shell elements the +position of the rebars in the shell thickness direction, measured from the midsurface of the shell (positive +in the direction of the positive normal to the shell); the angular orientation with respect to the r–z plane, +, measured in degrees; and the radial position at which the rebar spacing is measured. The angular +orientation is measured positive about the positive normal to the shell or membrane element. If the +shell’s thickness is defined by nodal thicknesses (“Nodal thicknesses,” Section 2.1.3), the distance from +the midsurface will be scaled by the ratio of the thickness defined by the nodal thickness to the thickness +defined by the section definition. If the shell’s thickness is defined with a distribution (“Distribution +definition,” Section 2.8.1) the distance from the midsurface will be scaled by the ratio of the element +thickness defined by the distribution to the default thickness. +If an orientation angle other than 0 or 90° is specified for rebar in an axisymmetric shell or +membrane without twist, Abaqus assumes that the rebars are balanced (i.e., half the rebar lie at the +specified angle +) and internal calculations are handled accordingly. +and the other half at an angle of +10 +circumferential rebar (90o orientation) +middle surface +of shell +spacing +of rebar +position in shell +thickness direction +20 +CL +Figure 2.2.4–6 Example of circumferential rebars in axisymmetric shell elements. +radial position where +rebar spacing is given +middle surface +of shell +position in shell +thickness direction +rebar spacing +radial rebar (orientation angle 0o) +Figure 2.2.4–7 Example of radial rebars in axisymmetric shell elements. +See “Rebar modeling in two dimensions,” Section 3.7.1 of the Abaqus Theory Manual, for details. If +the symmetric model generation capability (“Symmetric model generation,” Section 10.4.1) is used +to create a three-dimensional model from an axisymmetric shell or membrane model, only balanced +rebars will be translated appropriately. The definition of balanced rebars in the axisymmetric model will +result in balanced rebars in the three-dimensional model; such a translation with unbalanced rebars is +not available. Unbalanced rebars in generalized axisymmetric membranes with twist will be translated +properly. +If the radial position for the rebar spacing is given, the total cross-sectional area of rebar will +remain constant as the radial position changes; this behavior corresponds to the number of rebar in the +circumferential direction remaining constant and implies that the thickness of the smeared layer of rebar +decreases and that the spacing of the rebars increases as r increases . If the radial +position for the rebar spacing is omitted (or is set to zero), Abaqus assumes that the spacing of the rebar +remains constant; the thickness of the corresponding smeared layer is held fixed such that +. +Input File Usage: +Use the following option to define rebars in an axisymmetric shell element: +*REBAR, ELEMENT=AXISHELL, MATERIAL=mat +Use the following option to define rebars in an axisymmetric membrane +element: +*REBAR, ELEMENT=AXIMEMBRANE, MATERIAL=mat +Defining rebars in continuum elements +Two- or three-dimensional continuum (solid) elements can contain rebars; rebars cannot be defined in +triangular, prism, tetrahedral, or infinite elements. If triangular or wedge-shaped elements are needed, +collapsed quadrilateral or brick elements can be used. Be careful when collapsing elements that contain +rebar. It is important to check that the location and orientation of the rebar are correct. +Rebars are defined as single bars or in layers. In the latter case the layer is a surface in each element; +you provide the rebar orientation in the surface. +Defining layers of rebars in planar and axisymmetric continuum elements +By default, the rebars form a layer that lies in a surface that is at right angles to the plane of the model. +You define the line where this rebar surface intersects the plane of the model, as described below. +The orientation of the rebars within the rebar surface is defined by giving an angle, in degrees, +between the line of intersection in the plane of the model and the rebars. This angle is measured in +physical three-dimensional space, not in isoparametric space. See ��Rebar modeling in two dimensions,” +Section 3.7.1 of the Abaqus Theory Manual, for details. The positive direction along the line of +intersection is from the lower to the higher numbered element edge that is intersected, and a positive +angle indicates rebars oriented down into the plane of the model (where the plane is parallel to the z-axis +in plane strain analysis or the -axis for axisymmetric analysis), as shown in Figure 2.2.4–8. +If an orientation angle other than 0 or 90° is specified for rebar in an axisymmetric element without +twist, it is assumed that the rebar in the element are balanced (i.e., half the rebar lie at the specified angle +and the other half at the angle +). +Defining isoparametric rebars +For isoparametric rebars the intersection of the rebar layer with the plane of the model will lie along the +mapping of a constant isoparametric line in the element. You specify the elements that contain the rebars; +the cross-sectional area, A, of each rebar; the rebar spacing, s; the rebar orientation, +(as described +gle +n a +n t a tio +O rie +edge 4 +Rebar +Positive direction +from lower to +higher numbered +edge. +edge 1 +rebar +spacing +edge 2 +edge 3 +Figure 2.2.4–8 Orientation of rebars in plane and axisymmetric solid elements. +above); the fractional distance from the edge, f (the ratio of the distance between the edge and the rebar +to the distance across the element); and the edge number from which the rebars are defined. In addition, +for axisymmetric elements you specify the radial position at which the rebar spacing is measured. +If the radial position for the rebar spacing is given for rebar in axisymmetric elements, the total +cross-sectional area of rebar will remain constant as the radial position changes; this behavior corresponds +to the number of rebar remaining constant as r increases; that is, the thickness of the smeared layer +If the radial position for the rebar spacing is omitted (or is set to +of rebar decreases as r increases. +zero), Abaqus assumes that the spacing of the rebar remains constant; the thickness of the corresponding +smeared layer is held fixed such that +. +Figure 2.2.4–9 shows an example of isoparametric rebar. +In the isoparametric mapping of the +element, the line of rebars is parallel to one of the edges of the element. In this figure the line for rebar +layer A can be defined using edges 1 or 3 and rebar layer B can be defined by edges 2 or 4. The fractional +distance from edge 1 for rebar layer A is the ratio +; alternatively, layer A can +be defined from edge 3, so that +. +Input File Usage: +Use the following option to define layers of isoparametric rebars in planar and +axisymmetric continuum elements: +*REBAR, ELEMENT=CONTINUUM, MATERIAL=mat, +GEOMETRY=ISOPARAMETRIC +rebar layer B, +defined with +edge 2 or 4 +4L +A4L +rebar layer A, defined with +edge 1 and f = = +A2L +L2 +A4L +L4 +Actual element +Edge Corner nodes + 1 1-2 + 2 2-3 + 3 3-4 + 4 4-1 +L2 +LA2 +rebar layer B +rebar layer A +Isoparametric mapping of +element with rebar +Figure 2.2.4–9 Isoparametric rebar layer definition in solid elements. +Defining skew rebars +For skew rebars the intersection of the rebar layer with the plane of the model can intersect any two edges +of an element. You specify the elements that contain the rebars; the cross-sectional area, A, of each rebar; +the rebar spacing, s; and the rebar orientation, +(as described above). In addition, for axisymmetric +elements you specify the radial position at which the rebar spacing is measured. You also specify the +fractional distance along the element edge, from the first node of the edge (as listed in Figure 2.2.4–10) +to where the rebar layer intersects the edge, for all edges. Only the two values corresponding to the two +edges that the rebar intersects can be nonzero. +Figure 2.2.4–10 shows an example of skew rebar. In the isoparametric mapping of the element, +the line of rebars intersects two of the element edges. The intersection points are located by defining +a fractional distance along each intersected edge. In this figure rebar layer A is defined by the ratio +along edge 2. Rebar layer B is defined by the +along edge 1 and the ratio +ratio +along edge 3 and the ratio +along edge 4. +Defining skew rebars in continuum elements can increase the run time for an Abaqus/Explicit +analysis significantly. The element’s stable time increment will, in most cases, be determined by +the stable time increment of the rebar, which is proportional to the rebar length. The rebar length is +determined by factors including the rebar surface position in the element, the rebar spacing, the rebar +area, and the rebar orientation within the rebar surface. If a skew rebar in a continuum element is defined +Edge Corner nodes + 1 1-2 + 2 2-3 + 3 3-4 + 4 4-1 +rebar layer A defined with +A2L +L2 +f1 = , f2 = , f3 = 0 and f4 = 0 +A1L +L1 +B3L +rebar layer B +L2 +A2 +rebar layer A +Isoparametric mapping of +element with rebar +rebar layer B defined with +f1 = 0, f2 = 0, f3 = and f4 = +B3L +L3 +B4L +L4 +3L +4L +B4L +A1L +1L +Actual element +Figure 2.2.4–10 Skew rebar layer definition in solid elements. +such that it intersects two adjacent element edges, the resulting rebar length could be considerably less +than the average element edge length, thus resulting in a very small element stable time increment. +Input File Usage: +Use the following option to define layers of skew rebars in planar and +axisymmetric continuum elements: +*REBAR, ELEMENT=CONTINUUM, MATERIAL=mat, +GEOMETRY=SKEW +Defining single rebars in two-dimensional axisymmetric and generalized plane strain continuum +elements +You can define single rebars in axisymmetric and generalized plane strain continuum elements. In this +case the rebar is assumed to be at right angles with the plane of the model—in the thickness direction for +generalized plane strain elements or the hoop direction for axisymmetric elements. +The intersection of the rebar with the plane of the model is defined by the fractional distances along +edges 1 and 2 of the intersections of constant isoparametric lines that pass through the rebar location . The fractional distances are measured from the first edge node listed in Figure 2.2.4–11. +Edge Corner nodes + 1 1-2 + 2 2-3 +single rebar defined with +2l +f1 = and f2 = +L2 +1l +L1 +1l +L2 +2l +1L +Actual element +single rebar +Isoparametric mapping of +element with rebar +Figure 2.2.4–11 Single rebar in a solid element. +You specify the elements that contain the rebars; the cross-sectional area, A, of each rebar; and the +fractional distances locating the rebar’s position in the element, +and +. +Input File Usage: +Use the following option to define single rebars in axisymmetric and +generalized plane strain continuum elements: +*REBAR, ELEMENT=CONTINUUM, MATERIAL=mat, SINGLE +Defining layers of rebars in three-dimensional continuum elements +By default, the rebars in three-dimensional continuum elements are defined as layers lying in surfaces. +The surfaces are most easily defined with respect to the isoparametric mapped cube of the element. +Therefore, you must consider how the rebar will be defined before generating the mesh; if the rebar +surfaces are not taken into account in designing the mesh, the rebar definition can be very inefficient. +In the isoparametric mapped cube the rebar surface always has two edges (opposite to one +another) that are parallel to an isoparametric direction. The isoparametric directions are defined in +Figure 2.2.4–12. You specify this isoparametric direction (1, 2, or 3). +actual element +⇒ +isoparametric mapping +Isoparametric direction: 1 (parallel to the 1-2 edge of the element and intersecting + face 1-4-8-5) +Edge Corner nodes + 1 1-4 + 2 4-8 + 3 8-5 + 4 5-1 +Isoparametric direction: 2 (parallel to the 1-4 edge of the element and intersecting + face 1-5-6-2) +Edge Corner nodes + 1 1-5 + 2 5-6 + 3 6-2 + 4 2-1 +Isoparametric direction: 3 (parallel to the 1-5 edge of the element and intersecting + face 1-2-3-4) +Edge Corner nodes + 1 1-2 + 2 2-3 + 3 3-4 + 4 4-1 +Figure 2.2.4–12 Isoparametric direction and edge definitions for three-dimensional elements. +A particular face of the element, which is perpendicular to this isoparametric direction in the +isoparametric mapped cube, is used to define the position of the other two edges of the surface; the faces +are defined in Figure 2.2.4–12, where the edges of the faces are also defined. +If isoparametric rebars are defined, the two edges of the rebar surface that are not parallel to the +user-specified isoparametric direction will be parallel to one of the other two isoparametric directions; +in the isoparametric-mapped cube one isoparametric coordinate is constant on the rebar surface. +Figure 2.2.4–13 illustrates this concept with an element containing two layers of isoparametric rebars. +The position of each surface is given by the fractional distance f from an edge of the face defined in +Figure 2.2.4–12 for the isoparametric direction chosen; you must specify the edge from which the +fractional distance is measured. +If skew rebars are defined, the two edges of the rebar surface, which are not parallel to the user- +specified isoparametric direction, are generally not parallel to one of the other isoparametric directions. +The positions of these two edges of the rebar surface are specified by the intersection of the rebar surface +with edges of the intersecting face, defined in Figure 2.2.4–12, for the isoparametric direction chosen; the +intersections are given by the fractional distance f along each edge of the face. (Note that the fractional +distance is along the edge for skew rebars; for isoparametric rebars the fractional distances are measured +from an edge.) The fractional distance along an edge is measured from the first node of the edge. All +four fractional distances must be given, but only two can be nonzero. +The orientation angle, +, of the rebars within the rebar layer is defined in the isoparametric-mapped +cube; it is measured in degrees and is the angle between the line of intersection of the rebar surface +with the face for the isoparametric direction chosen and the rebar. The positive direction of the line of +intersection is from the lower numbered edge to the higher numbered edge; the positive direction for +the rebars points into the elements. An example is shown in Figure 2.2.4–14. The orientation angle +is defined in the rebar layer in the isoparametric-mapped cube; therefore, the definition is the same for +isoparametric and skew rebar. +If the rebar layer is not flat in physical space, the orientation angle at each integration point may +be different. Since it is possible to define only one orientation angle per element, an average value +orientation angle for the element must be used; for reasonable meshes this approximation should not +affect the results significantly. +Defining isoparametric rebars +You specify the elements that contain the rebars; the cross-sectional area, A, of each rebar; the rebar +spacing, s; the rebar orientation, +(as described above); the fractional distance, f, from the edge; the +number of the edge from which the fractional distance is measured; and the isoparametric direction of +the rebar surface. +Input File Usage: +Use the following option to define layers of +three-dimensional continuum elements: +isoparametric rebars in +*REBAR, ELEMENT=CONTINUUM, MATERIAL=mat, +GEOMETRY=ISOPARAMETRIC +30o +REBAR AS ELEMENT PROPERTY +L3 +WA +f4L3 +layer b +element in +physical space +layer a +45o +L1 +120o +f4L1 +LA +135o +f3L4 +L4 +layer b +2.0 +corresponding +isoparametric-mapped +cube +63.4o +layer a +139.3o +153.4o +49.3o +2.0 +2.0 +0.5 +Figure 2.2.4–13 Element with two layers of isoparametric rebar. +Edge Corner nodes +1 1-5 +2 5-6 +3 6-2 +4 2-1 +edge 2 +f3L3 +edge 1 +Orientation +angle, α +L3 +L1 +f1L1 +edge 3 +Positive direction along line +of intersection +edge 4 +positive +direction +of rebar +Figure 2.2.4–14 Orientation example for three-dimensional skew rebar modeling, isoparametric +direction 2. Shown in the mapped isoparametric element. +Example: isoparametric rebar +For example, the following input defines the isoparametric rebar shown in Figure 2.2.4–13: +*HEADING +ISOPARAMETRIC REBAR +*NODE +0., +1, +2, 10., +3, 10., +4, +0., +0., +5, +6, 10., +7, 10., +0., +8, +0. +0. +5. +5. +7.5 +0., +0., 12.5 +5., 12.5 +5., 7.5 +*ELEMENT, TYPE=C3D8R, ELSET=ONE +1,1,2,3,4,5,6,7,8 +*REBAR, ELEMENT=CONTINUUM, MATERIAL=STEEL, +GEOMETRY=ISOPARAMETRIC, NAME=LAYER_A +ONE,.04,2.5,49.32628,0.25,4,2 +*REBAR, ELEMENT=CONTINUUM, MATERIAL=STEEL, +GEOMETRY=ISOPARAMETRIC, NAME=LAYER_B +ONE,.04,1.,63.43494,0.5,3,2 +*MATERIAL, NAME=STEEL +*ELASTIC +30.E6, +… +Rebar layers A and B are defined using isoparametric direction 2. From Figure 2.2.4–12 the position of +the layers must be given with respect to the face with nodes 1-5-6-2. +. It could also be given from edge 2 (edge with nodes 5–6), so that +The fractional distance defining the position of intersection of layer A with this face can be measured +from edge 4 (edge with nodes 2–1) along edge 3 (edge with nodes 6–2), as shown in Figure 2.2.4–13. For +layer A, +. +, equal to 30° for +layer A. This angle must be transformed into the corresponding angle in the isoparametric-mapped cube. +This transformation can be done as follows: consider a single rebar that intersects the intersecting line +(described above) and an adjacent edge . +The orientation of rebar for layer A in physical space is defined by an angle, +β = 120o +β = 30o +rebar layer A in physical space +α = 139.3o +α = 49.3o +rebar layer A in +isoparametric-mapped cube +Figure 2.2.4–15 Example defining isoparametric rebar. +. The length of the rebar layer along the intersecting line is L, and the +From the figure +length of the opposite edge is W. Consider the same rebar in the rebar layer in the isoparametric-mapped +cube. The orientation angle, +. (The 2 is +included because the isoparametric-mapped cube is a 2 × 2 × 2 cube.) This expression can be simplified +to give +, is given by +, where +and +For layer A, +must be specified. +, +, +, and +, where +is the orientation angle that +The fractional distance defining the position of the intersection of layer B with this face can be +. It could also be measured from edge 1 (edge +. The orientation angle for layer B in the rebar layer is 45°. In +measured from edge 3 (edge with nodes 6–2); +with nodes 1–5), such that +the isoparametric-mapped cube +, +, and +. +, +Since an isoparametric rebar layer always lies in two of the isoparametric directions, an alternative +but equivalent definition can be given. For example, layer A also lies in isoparametric direction 1, with +the intersecting face having nodes 1-4-8-5. The fractional distance for layer A, measured from edge 1 +(edge with nodes 1–4), is +. The positive sense of the line of intersection is from edge 2 (edge +with nodes 4–8) to edge 4 (edge with nodes 5–1); therefore, +, and +, +, +. +Layer B also lies in isoparametric direction 3, with the intersecting face having nodes 1-2-3-4. The +fractional distance for layer B, measured from edge 2 (edge with nodes 2–3), is +. The positive +sense of the intersecting line is from edge 1 (edge with nodes 1–2) to edge 3 (edge with nodes 3–4); +therefore, the orientation angle of the rebar in physical space is +, and in the +isoparametric-mapped cube +, +, +. +Defining skew rebars +You specify the elements that contain the rebars; the cross-sectional area, A, of each rebar; the rebar +spacing, s; the rebar orientation, +(as described above); and the isoparametric direction. In addition, +you specify the fractional distance f along the element edge for each edge of the intersecting face defined +in Figure 2.2.4–12. Only the values corresponding to the two edges that the rebar intersects can be +nonzero. +Input File Usage: +Use the following option to define layers of skew rebars in three-dimensional +continuum elements: +*REBAR, ELEMENT=CONTINUUM, MATERIAL=mat, +GEOMETRY=SKEW +Example: skew rebar +For example, the following input defines the skew rebar shown in Figure 2.2.4–16: +*HEADING +*NODE +0., +1, +2, 10., +3, 10., +4, +0., +0., +5, +6, 10., +7, 10., +0., +8, +0. +0. +5. +5. +7.5 +0., +0., 12.5 +5., 12.5 +5., 7.5 +L1 +30o +f1L1 +f3L3 +L3 +Figure 2.2.4–16 Example defining skew rebar. +*ELEMENT, TYPE=C3D8R, ELSET=ONE +1,1,2,3,4,5,6,7,8 +*REBAR, ELEMENT=CONTINUUM, MATERIAL=STEEL, GEOMETRY=SKEW, +NAME=LAYER_A +ONE, .04, 2.5, 55.28, , 2 +.2, 0., .4, .0 +*MATERIAL, NAME=STEEL +*ELASTIC +30.E6, +… +The rebar layer is defined using isoparametric direction 2. The intersecting face is defined in +Figure 2.2.4–12 and has nodes 1-5-6-2. The position of the rebar layer is given by its intersection +with the edges of this face; the fractional distances, +, are shown in Figure 2.2.4–16. The +orientation angle +of the rebar in physical space is 30°. Following the same procedure for calculating +, and the orientation angle in the +as was described for isoparametric rebar, +and +, +isoparametric-mapped cube +is 55.28°. +Defining single rebars in three-dimensional continuum elements +You can define single rebars in three-dimensional continuum elements; in this case the rebar is assumed to +be placed along one of the element’s isoparametric directions. The rebar is then located by its intersection +with the intersecting face (defined in Figure 2.2.4–12). The intersections of constant isoparametric lines +with edges 1 and 2 of the intersecting face are given by fractional distances along edges 1 and 2, measured +from the first node of each edge, as shown in Figure 2.2.4–11. +You specify the elements that contain the rebars; the cross-sectional area, A, of each rebar; the +fractional distances locating the rebar’s position in the element, +; and the isoparametric +direction. Give the fractional distances with respect to edge 1 and edge 2 for the isoparametric direction +chosen, as defined in Figure 2.2.4–12. +and +Input File Usage: +Use the following option to define single rebars in three-dimensional continuum +elements: +*REBAR, ELEMENT=CONTINUUM, MATERIAL=mat, SINGLE +Defining the rebar material +The material properties of the rebars are distinct from those of the underlying element and are defined +by a separate material definition (“Material data definition,” Section 21.1.2). You must associate each +rebar definition with a set of material properties. +The following material behavior cannot be used in Abaqus/Standard to define rebar materials: +• “Porous metal plasticity,” Section 23.2.9. +The following material behaviors cannot be used in Abaqus/Explicit to define rebar materials: +• “Defining fully anisotropic elasticity” in “Linear elastic behavior,” Section 22.2.1; +• “Defining orthotropic elasticity by specifying the terms in the elastic stiffness matrix” in “Linear +elastic behavior,” Section 22.2.1; +• “Equation of state,” Section 25.2.1; +• “Anisotropic yield/creep,” Section 23.2.6; +• “Porous metal plasticity,” Section 23.2.9; +• “Extended Drucker-Prager models,” Section 23.3.1; +• “Modified Drucker-Prager/Cap model,” Section 23.3.2; +• “Crushable foam plasticity models,” Section 23.3.5; or +• “Cracking model for concrete,” Section 23.6.2. +Although Abaqus/Standard will allow for a rebar material to be defined with orthotropic elasticity +(“Defining orthotropic elasticity by specifying the terms in the elastic stiffness matrix” in “Linear elastic +behavior,” Section 22.2.1) or anisotropic elasticity (“Defining fully anisotropic elasticity” in “Linear +elastic behavior,” Section 22.2.1), +is the only meaningful material constant in these definitions. +, using the corresponding stress component, +, as discussed in “Linear elastic behavior,” Section 22.2.1; no other strain or stress components exist +is used to compute the strain in the rebar direction, +in rebars. +In Abaqus/Standard density is ignored for the rebar material properties. Hence, the mass of the +rebar is neglected in eigenvalue extraction and implicit dynamic procedures and for gravity, centrifugal, +and rotary acceleration distributed loads. +Input File Usage: +Use the following option to associate a material definition with a rebar +definition: +*REBAR, ELEMENT=elem, MATERIAL=mat +Initial conditions +Initial conditions (“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1) can be +used to define rebar prestress or solution-dependent values for rebars. +Defining prestress in rebar +For structures in which reinforcing is defined (such as reinforced concrete structures), you can use initial +conditions to define the prestress in the rebars. +In such cases in Abaqus/Standard the structure must be brought to a state of equilibrium before it +is actively loaded by means of an initial static analysis step (“Static stress analysis,” Section 6.2.2) with +no external loads applied (or, perhaps, with the “dead” loads only)—see “Defining initial stresses” in +“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1. +Input File Usage: +*INITIAL CONDITIONS, TYPE=STRESS, REBAR +element number or element set name, rebar name, prestress value +Holding prestress in rebar in Abaqus/Standard +If prestress is defined in the rebars and unless the prestress is held fixed, it will be allowed to change +during an equilibrating static analysis step; this is a result of the straining of the structure as the self- +equilibrating stress state establishes itself. An example is the pretension type of concrete prestressing in +which reinforcing tendons are initially stretched to a desired tension before being covered by concrete. +After the concrete cures and bonds to the rebar, release of the initial rebar tension transfers load to the +concrete, introducing compressive stresses in the concrete. The resulting deformation in the concrete +reduces the stress in the rebar. +Alternatively, you can keep the initial stress defined in some or all of the rebars constant during +this initial equilibrium solution. An example is the post-tension type of concrete prestressing; the rebars +are allowed to slide through the concrete (normally they are in conduits), and the prestress loading is +maintained by some external source (prestressing jacks). The magnitude of the prestress in the rebar is +normally part of the design requirements and must not be reduced as the concrete compresses under the +loading of the prestressing. Normally, the prestress is held constant only in the first step of an analysis. +This is generally the more common assumption for prestressing. +If the prestress is not held constant in analysis steps following the step in which it is held constant, +the stress in the rebar will change due to additional deformation in the concrete. If there is no additional +deformation, the stress in the rebar will remain at the level set by the initial conditions. If the loading +history is such that no plastic deformation is induced in the concrete or rebar in steps subsequent to the +steps in which the prestress is held constant, the stress in the rebar will return to the level set by the initial +conditions upon removal of the loading applied in those steps. +Input File Usage: +*PRESTRESS HOLD +Defining the initial values of solution-dependent state variables for rebars +You can define the initial values of solution-dependent state variables for rebars within elements. See +“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1, for details. +Input File Usage: +*INITIAL CONDITIONS, TYPE=SOLUTION, REBAR +Output +Rebar force output is available at the rebar integration locations with output variable RBFOR. The rebar +force is equal to the rebar stress times the current rebar cross-sectional area. The current cross-sectional +area of the rebar is calculated by assuming the rebar is made of an incompressible material, regardless of +the actual material definition. For rebars in membrane or shell elements output variables RBANG and +RBROT identify the current orientation of isoparametric or skew rebar within the element and the relative +rotation of the rebar as a result of finite deformation, respectively. These quantities are measured with +respect to the user-specified isoparametric direction in the element, not the default local element system +or the orientation-defined system. See “Rebar modeling in shell, membrane, and surface elements,” +Section 3.7.3 of the Abaqus Theory Manual. +See “Abaqus/Standard output variable identifiers,” Section 4.2.1, and “Abaqus/Explicit output +variable identifiers,” Section 4.2.2, for information on additional output quantities such as stress and +strain. For rebars in membrane or shell elements with multiple integration points, output quantities are +available at the integration points and at the centroid of the element. +Specifying the direction for rebar angle output in shell and membrane elements +The output quantities RBANG and RBROT can be measured from either of the isoparametric directions +in the plane of the shell or the membrane. You can specify the desired isoparametric direction from which +the rebar angle will be measured (1 or 2). In axisymmetric shells and membranes the first isoparametric +direction coincides with the meridional direction, and the second isoparametric direction coincides with +the hoop direction. The rebar angle is measured from the isoparametric direction to the rebar with a +positive angle defined as a counterclockwise rotation around the element’s normal direction. The default +direction is the first isoparametric direction. +Input File Usage: +Use any of the following options: +*REBAR, ELEMENT=SHELL, MATERIAL=mat, ISODIRECTION=n +*REBAR, ELEMENT=AXISHELL, MATERIAL=mat, ISODIRECTION=n +*REBAR, ELEMENT=MEMBRANE, MATERIAL=mat, ISODIRECTION=n +*REBAR, ELEMENT=AXIMEMBRANE, MATERIAL=mat, +ISODIRECTION=n +Example +As an example, a user-defined local coordinate system is used to define skewed rebar in a shell element +(skew angle +), and the output value of RBANG is 75°, as illustrated in Figure 2.2.4–17: +*REBAR, ELEMENT=SHELL, MATERIAL=MAT1, NAME=REBARB, +RBANG = 75 +2, ISO2 +OR1 +OR2 +ISOn = isoparametric directions +ORn = user-defined local directions +1, 2 = default local directions +1, ISO1 +Figure 2.2.4–17 RBANG measurement for skew rebar defined +relative to user-defined local coordinate directions. +GEOMETRY=SKEW, ORIENTATION=ORIENT, ISODIRECTION=2 +ELSET1, 0.01, 0.1, 0.0, 30. +*ORIENTATION, SYSTEM=RECTANGULAR, NAME=ORIENT +-0.7071, 0.7071, 0.0, -0.7071, -0.7071, 0.0 +3, 0.0 +The rebars are located at the midsurface of the shell. Output variable RBANG is measured from the +second isoparametric direction to the rebar. +If the first isoparametric direction were chosen instead, +output variable RBANG would report an angle of 165°. +Visualizing rebar orientation and results in rebar +Abaqus/CAE does not support visualization of element-based rebar or rebar results. Abaqus/CAE does +support visualization of rebar defined as described in “Defining reinforcement,” Section 2.2.3. +2.2.5 +ORIENTATIONS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Distribution definition,” Section 2.8.1 +• “Material library: overview,” Section 21.1.1 +• “Material data definition,” Section 21.1.2 +• “Fabric material behavior,” Section 23.4.1 +• “Distributed loads,” Section 33.4.3 +• “Kinematic coupling constraints,” Section 34.2.3 +• “Coupling constraints,” Section 34.3.2 +• “Inertia relief,” Section 11.1.1 +• *ORIENTATION +• “Creating datum coordinate systems,” Section 62.9 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +A user-defined orientation is used to define a local coordinate system for: +• definition of material properties—for example, anisotropic materials or jointed materials (a local +coordinate system must be defined if anisotropic material properties are defined for solid elements); +• definition of local material directions, such as the in-plane fill and warp yarn directions of a fabric +material or the fiber directions of anisotropic hyperelastic materials; +• definition of rebars in shell, membrane, and surface elements; +• definition of rotary inertia and connector elements; +• definition of coupling constraints; +• definition of loading directions for distributed general tractions, shear tractions, and general edge +loads; +• definition of slip directions for contact in Abaqus/Standard; +• material calculations at integration points; +• output of components of stress, strain, and element section force; and +• definition of a local system of rigid body motion directions for inertia relief in Abaqus/Standard. +A user-defined orientation cannot be used: +• at points where the smeared crack concrete material behavior (“Concrete smeared cracking,” +Section 23.6.1) is also used in Abaqus/Standard; +• to specify a local coordinate system for defining nodal coordinates—see “Specifying a local +coordinate system in which to define nodes” in “Node definition,” Section 2.1.1, or “Specifying a +local coordinate system for the nodal coordinates” in “Node definition,” Section 2.1.1, instead; or +• to specify a local coordinate system for applying loads and boundary conditions—see “Transformed +coordinate systems,” Section 2.1.5, instead. +Considerable generality is provided in the way the local system can be defined, since this system must +often change from point to point because of the shape and construction of the structure being modeled. +You can define the local orientation directly. The direct data methods provided in Abaqus are intended +to give sufficient generality to model most cases easily: they are particularly useful for regular geometry. +Distributions (“Distribution definition,” Section 2.8.1) can be used to define spatially varying local +coordinate systems for solid continuum, shell, and membrane (in Abaqus/Standard) elements directly +for arbitrary geometries. +In Abaqus/Standard you can alternatively define the local orientation in user subroutine ORIENT. +Assigning a name to an orientation +You must assign a name to each orientation definition. This name is used by various features to refer to +the orientation definition. +Input File Usage: +Abaqus/CAE Usage: +*ORIENTATION, NAME=name +Any module: Tools→Datum: Type: CSYS: select any method, +and click OK: Name: name +Defining a local coordinate system in a model that contains an assembly of part instances +In a model defined in terms of an assembly of part instances, you can define a local orientation at +the part, part instance, or assembly level. An orientation defined at the part or part instance level is +rotated according to the positioning data given for each instance of that part (or for the part instance). +This includes the case when an orientation is defined using a distribution. See “Defining an assembly,” +Section 2.10.1, and “Distribution definition,” Section 2.8.1. +Defining a local coordinate system directly +A two-stage process is used to define the local system directly. +1. You define the local coordinate system at the particular location at which it is required. You can +select a rectangular, cylindrical, or spherical coordinate system. The coordinate system is defined +in terms of points a, b, and c, as shown in Figure 2.2.5–1. You can select the method for defining +points a, b, and c, as described below. +, or +2. Optionally, you can specify an additional rotation by identifying one of these local directions ( +, +) as a rotation axis and giving a rotation, in degrees, about that axis. The local system is +then rotated through this angle about the specified axis. This method of defining a local system is +required for contact surfaces in Abaqus/Standard, shells, membranes, gasket elements, and when +the orientation is associated with a composite solid section. The additional rotation is illustrated in +Figure 2.2.5–2. +Rectangular system +(a on X'-axis) +Cylindrical system +Spherical system +Rectangular system +(a on Z'-axis) +Y +b +a +X +X (radial) +Y (tangential) +Z (meridional) +X (global) +X (global) +Y (circumferential) +X (radial) +X (global) +Y +X +b +a +Z +c +X (global) +Figure 2.2.5–1 Orientation systems. +a. 1-direction specified. +b. 2-direction specified. +c. 3-direction specified. +2 (3) +1 (2) +1 (2) +2 (3) +2 (3) +1 (2) +Figure 2.2.5–2 Specifying rotation about a local axis for shell elements, membrane elements, gasket +elements (in parentheses), composite solids (in parentheses), and contact surfaces in Abaqus/Standard. +. The local +The local coordinate system for composite solids is indicated by +coordinate system for other element types is indicated by 1, 2, and 3; the axis labels in parentheses +are oriented for gasket elements. +, and +, +Available coordinate systems +Rectangular, cylindrical, and spherical coordinate systems are available. +Defining a rectangular coordinate system +A rectangular Cartesian coordinate system is shown in Figure 2.2.5–1(a). The rectangular coordinate +system is the default. Alternatively, you can define a rectangular Cartesian coordinate system as shown +in Figure 2.2.5–1(d). +Input File Usage: +Abaqus/CAE Usage: +*ORIENTATION, NAME=name, SYSTEM=RECTANGULAR +*ORIENTATION, NAME=name, SYSTEM=Z RECTANGULAR +Any module: Tools→Datum: Type: CSYS: select any method, +and click OK: Rectangular +Defining a cylindrical coordinate system +A cylindrical coordinate system is shown in Figure 2.2.5–1(b). The local axes are +=radial, +=tangential, +=axial. +Input File Usage: +Abaqus/CAE Usage: +*ORIENTATION, NAME=name, SYSTEM=CYLINDRICAL +Any module: Tools→Datum: Type: CSYS: select any method, +and click OK: Cylindrical +Defining a spherical coordinate system +A spherical coordinate system is shown in Figure 2.2.5–1(c). +The local axes are +=radial, +=circumferential, +=meridional. +Input File Usage: +Abaqus/CAE Usage: +*ORIENTATION, NAME=name, SYSTEM=SPHERICAL +Any module: Tools→Datum: Type: CSYS: select any method, +and click OK: Spherical +Methods for defining a coordinate system +You can define a coordinate system by specifying the locations of points a, b, and c directly; by specifying +the locations of points a, b, and c relative to global node numbers; by specifying the locations of points +a, b, and c relative to local node numbers; by specifying an offset from another coordinate system; or by +specifying two lines in the coordinate system. +Defining a coordinate system by specifying the locations of points a, b, and c directly +You can specify the coordinates of points a, b, and c directly. These coordinates should be appropriate +to the system chosen. This method is the default. +You can define a rectangular Cartesian coordinate system +(a, b, and c) that lie on the +point a must lie on the +-axis, and point b must lie on the +intuitive to select point b such that it is on or near the local +- +- +-axis. +by specifying three points +plane, as shown in Figure 2.2.5–1(a). Point c is the origin of the system, +plane. Although not necessary, it is +by specifying three points (a, b, and c) that lie on the +Alternatively in Abaqus/Standard you can define a rectangular Cartesian coordinate system +plane, as shown in +-axis, and point b must +plane. Although not necessary, it is intuitive to select point b such that it is on or near +Figure 2.2.5–1(d). Point c is the origin of the system, point a must lie on the +lie on the +the local +- +-axis. +- +For rectangular coordinate systems the default location of the origin (point c) is the global origin. +You define a cylindrical coordinate system by giving the two points, a and b, on the polar axis of +the cylindrical system, as shown in Figure 2.2.5–1(b). +You define a spherical coordinate system by giving the center of the sphere, a, and point b on the +polar axis, as shown in Figure 2.2.5–1(c). +To define a spatially varying local coordinate system directly on solid continuum and shell elements, +you can specify the coordinates of points a and b on an element-by-element basis using a distribution. +Using a distribution to define the coordinates of the optional point c is not currently supported. See +“Distribution definition,” Section 2.8.1. +Input File Usage: +Abaqus/CAE Usage: +*ORIENTATION, NAME=name, DEFINITION=COORDINATES +Any module: Tools→Datum: Type: CSYS, Method: 3 points +Defining a coordinate system by giving global node numbers for points a, b, and c +You can locate points a, b, and c at nodes by specifying three global node numbers. For a rectangular +coordinate system the default location of the origin (point c) is the global origin. +Input File Usage: +Abaqus/CAE Usage: +*ORIENTATION, NAME=name, DEFINITION=NODES +You cannot define a coordinate system by giving global node numbers in +Abaqus/CAE. +Defining a coordinate system by giving local node numbers for points a, b, and c +You can locate points a, b, and c by specifying the local node numbers of an element. Local node +numbers refer to the order in which nodes are specified in the element connectivity. For example, local +node number 2 corresponds to the second node specified for the element definition. This definition +method allows for variation of the local coordinate system on an element-by-element basis with a single +orientation definition. For example, if local node number 2 is given as the location of point c and local +node number 3 is given as the location of point a, the local +-direction is defined to be parallel to the +(2, 3) side of the element. By default, the origin (point c) of the local coordinate system is the first node +of the element (local node number 1). +Input File Usage: +Abaqus/CAE Usage: +*ORIENTATION, NAME=name, DEFINITION=OFFSET TO NODES +You cannot define a coordinate system by giving local node numbers in +Abaqus/CAE. +Defining a coordinate system by giving an offset from another coordinate system +You can define a coordinate system by specifying an offset from an existing coordinate system. +Input File Usage: +You cannot define a coordinate system by giving an offset from another +coordinate system in the input file. +Abaqus/CAE Usage: +Any module: Tools→Datum: Type: CSYS: Offset from CSYS +Defining a coordinate system by giving two edges +You can define a coordinate system by specifying two edges. The first edge defines the X- or R-axis, +and the X–Y or +plane passes through the second. +Input File Usage: +You cannot define a coordinate system by giving two edges in the input file. +Abaqus/CAE Usage: +Any module: Tools→Datum: Type: CSYS: 2 lines +Defining local material directions for anisotropic hyperelastic materials +When modeling anisotropic hyperelastic materials with an invariant-based formulation (“Invariant-based +formulation” in “Anisotropic hyperelastic behavior,” Section 22.5.3) you must define the local +directions that characterize each family of fibers. These directions need not be orthogonal in the initial +configuration. You can specify these local directions with respect to an orthogonal orientation system +at a material point. Up to three local directions can be specified as part of the definition of a local +orientation system. The local directions can be output as field variables to the output database . +Input File Usage: +Use the following option to define an orthogonal system and N local directions +with respect to that system to identify the preferred directions of an anisotropic +hyperelastic material: +Abaqus/CAE Usage: +*ORIENTATION, LOCAL DIRECTIONS=N +Local material directions cannot be defined in Abaqus/CAE. +Defining yarn directions in the reference configuration for a fabric material +In general, the yarn directions in a fabric material may not be orthogonal to each other in the reference +configuration . You can specify these local directions +with respect to the in-plane axes of an orthogonal orientation system at a material point. Both the local +directions and the orthogonal system are defined together as a single orientation definition. If the local +directions are not specified, these directions are assumed to match the in-plane axes of the orthogonal +system defined. The local direction may not remain orthogonal with deformation. Abaqus updates the +local directions with deformation and computes the nominal strains along these directions and the angle +between them (the fabric shear strain). The constitutive behavior for the fabric defines the nominal +stresses in the local system in terms of the fabric strain. The local directions can be output as field +variables to the output database . +Input File Usage: +Use the following option to define an orthogonal system and the local +directions with respect to that system to identify the yarn directions in the +reference configuration: +Abaqus/CAE Usage: +*ORIENTATION, LOCAL DIRECTIONS=2 +Yarn directions for fabric materials cannot be defined in Abaqus/CAE. +Defining a local coordinate system in Abaqus/Standard using a user subroutine +In some cases the simplest way to specify a local system is by means of a user subroutine. User subroutine +ORIENT is provided in Abaqus/Standard. In this case the user subroutine is called each time that an +orientation definition is needed. In a model defined in terms of an assembly of part instances, the local +directions defined by user subroutine ORIENT must be defined relative to the coordinate system of the +assembly. +Input File Usage: +*ORIENTATION, NAME=name, SYSTEM=USER +Abaqus/CAE Usage: +You can enter the name of an orientation defined in user subroutine ORIENT +whenever a user-defined orientation is allowed. +Multiple references to an orientation definition +Because the orientation is independent of the material definition and they can both be referenced in any +element property definition, the ability to describe complex structural components (such as laminated +composite shells) is quite general and straightforward to use. +An orientation definition can be used as often as needed and with different material or element type +definitions; for example, it can be used for different layers of a shell where the orientation is the same. +Large-displacement considerations +In large-displacement analysis a user-defined orientation rotates with the average rigid body motion of the +material point, the rigid body when the orientation is used with ROTARYI elements, the first node of the +joint in JOINTC elements, the pipeline edge for pipe-soil interaction elements, the appropriate surface for +contact in Abaqus/Standard, or the reference node when the orientation is used with coupling constraints. +However, when an orientation is defined for spring, dashpot, or gasket elements in Abaqus/Standard, the +local directions always remain fixed in space. +Because the material directions rotate with the average rigid body motion at a material point, using +anisotropic elasticity to model a material that is not truly a continuum can give significant errors if shear +deformation is large. For example, an individual fiber in a reinforcing belt of a tire can shear relatively +easily with respect to fibers in other directions. The fibers rotate with the actual deformation of the +material point and not with the average rigid body motion. In this case the anisotropic behavior is better +modeled with rebars or as a fabric material. The fabric material model in Abaqus/Explicit tracks the +current yarn directions as local directions with respect to the orthogonal coordinate system. +Use with two-dimensional solid elements +When a user-defined orientation is used with two-dimensional solid elements such as plane stress, plane +strain, or torsionless axisymmetric elements, the orientation must redefine only the X- and Y-directions: +the third direction must remain unchanged (Z-direction for plane strain and plane stress elements, +-direction for axisymmetric elements). When a user-defined orientation is used with axisymmetric +elements with twist, all three directions can be redefined. For axisymmetric elements, including the +CGAX and CAXA families of elements, the global 1-, 2-, and 3-directions are the radial, axial, and +hoop directions, respectively. Cylindrical or spherical orientations may be appropriate for axisymmetric +elements only if the local +-direction is in the global 3-, or hoop, direction. +Use with shell, membrane, or gasket elements or contact surfaces +When a user-defined orientation is used with shell, membrane, or gasket elements or with contact +surfaces, Abaqus first rotates and then projects the orientation system onto the element or contact +surface using the algorithm described in this section. +Abaqus first rotates (through the additional rotation angle) the user-defined local coordinate system +about the specified rotation axis. If you do not specify a rotation axis or an additional angle, Abaqus +will by default use the local 1-axis and a rotation of 0°. After the rotation, Abaqus follows a cyclic +permutation (1, 2, 3) of the axes and projects the axis following the axis for additional rotation onto +the contact surface or onto the surface of the element to form the local material 1-direction (or the local +material 2-direction for gaskets). The remaining material direction is then defined by the cross product +of the element normal and the projected direction. Thus, for example: +1. If you choose the user-defined 1-axis as the axis for additional rotation, Abaqus projects the 2-axis +onto the element or contact surface. This will be local direction 1 for contact surfaces, shells, and +membranes and local direction 2 for gaskets. +2. Abaqus takes the positive element or contact surface normal as the local 3-direction for contact +surfaces, shells, and membranes and the local 1-direction for gaskets. +3. Abaqus computes the local 2-direction (3-direction for gaskets) by taking the cross product of the +element or contact surface normal and the local 1-direction (2-direction for gaskets), such that the +three local axes form an orthonormal, right-handed local coordinate system. +When the axis for additional rotation points in a direction that is opposite to the element or contact surface +normal, the local 2-direction (3-direction for gaskets) is reversed with respect to the corresponding user- +defined axis; see Figure 2.2.5–3. This does not apply in the case of an orientation used to define rebars; +see below. +S1 +S2 +S1 +normal defined by +local orientation +definition is opposite +to element normal +S2 +orientation used +by Abaqus +S = user-defined directions +Figure 2.2.5–3 The local 3-direction (1-direction for gaskets) will +be in the same direction as the element or contact surface normal. +As an example, +the orientation of the spiral-wound layer of the cylindrical shell shown in +Figure 2.2.5–4 would be given by defining a cylindrical coordinate system and then specifying the +(in degrees). The local 1- and 2-directions for +rotation axis as the 1-axis and giving the rotation angle +material property specification and material calculations are then those indicated in the figure. +Figure 2.2.5–4 Spiral-wound cylindrical shell layer: material orientation example. +The projected directions are most easily understood when the axis for additional rotation is +approximately perpendicular to the element or contact surface. +To define a spatially varying local coordinate system directly on solid continuum and shell elements, +as well as membrane elements in Abaqus/Standard, you can specify the additional angle of rotation on +an element-by-element basis using a distribution. See “Distribution definition,” Section 2.8.1. +Defining rebars in shell, membrane, and surface elements +The orientation of skew rebars in shell, membrane, and surface elements can be defined relative to a +user-defined orientation . In this case the local coordinate +system is calculated as follows: +1. The local 1-direction follows a cyclic permutation of the additional rotation direction; for example, +if you choose the user-defined 1-axis as the axis for additional rotation, Abaqus projects the 2-axis +onto the element. This will be the local 1-direction. +2. The axis for additional rotation is made orthogonal to the element to create the local 3-direction. +This local 3-direction need not be in the same direction as the element normal; in fact it will be +in the opposite direction when the dot product of the axis for additional rotation and the element +normal is negative. +3. Abaqus computes the local 2-direction by taking the cross product of the local 3-direction and the +local 1-direction, such that the three local axes form an orthonormal, right-handed local coordinate +system. +Since the local 3-direction may be opposite to the element normal, the definition of rebars is independent +of the element connectivity. +Special considerations when defining orientations on contact surfaces in Abaqus/Standard +When a user-defined orientation is used to define the tangential slip directions on a surface of a +three-dimensional contact pair in Abaqus/Standard , you cannot define points a and b by giving local node numbers . +For geometrically nonlinear analysis the tangential slip directions of a contact pair rotate with the +surface on which the directions were defined initially. These rotated tangential slip directions are further +rotated to ensure that the normal vector, computed using the cross product of the rotated tangential +slip directions, corresponds to the normal vector on the master surface when the slave node comes into +contact. +Arbitrary slip directions can be defined for a “line”-type slave surface defined on three-dimensional +beam, truss, or pipe elements. When this surface comes into contact with the master surface during a +large-displacement analysis, the slip directions are projected onto the master surface. +Use with laminated shells +There are two ways in which a user-defined orientation can be used in the section definition of a laminated +shell. In each case the name referenced in the shell section definition is the name of the user-defined +orientation. +The first is to associate the user-defined orientation with the entire composite shell section definition. +Then each layer’s orientation angle can be given relative to this section orientation (or the default shell +coordinate directions if no section orientation is used). The angle is given as an additional rotation about +the shell normal after the orientation directions have been projected onto the shell surface. Section forces +(available only from Abaqus/Standard) are given in the local system specified for the section. +The second is to specify the name of each layer’s orientation separately; this method allows different +orientation definitions to be referenced for the different layers. Section forces and strains are still reported +in the local orientation defined for the entire section (or the default shell coordinate directions if no section +orientation is used). The individual layer orientations are used for material calculations and for output +of stress and strain. +See “Using a shell section integrated during the analysis to define the section behavior,” +Section 29.6.5, and “Using a general shell section to define the section behavior,” Section 29.6.6, for +more information. +Use with laminated three-dimensional solid elements +When a user-defined orientation is used with composite solid elements (available only in +Abaqus/Standard), one of the local directions must be identified as the axis for additional rotation. +There are two ways in which this orientation can be used with a composite solid section definition to +specify the material orientation for individual layers. +In each case the name referenced in the solid +section definition is the name of the user-defined orientation. +The first is to associate the user-defined orientation with the entire composite solid section definition. +Then each layer’s orientation angle can be given relative to this section orientation. The angle is given +as an additional rotation about the local direction defined as the axis for additional rotation. +The second is to specify the name of each layer’s orientation separately; this method allows different +orientation definitions to be referenced for the different layers. (In this case any user-defined orientation +associated with the entire solid section will be ignored.) +See “Defining the element’s section properties” in “Solid (continuum) elements,” Section 28.1.1, +for more information. +Use with pipe-soil interaction elements +An arbitrary user-defined orientation can be defined for pipe-soil interaction elements (available only in +Abaqus/Standard). In a large-displacement analysis the local orientation system rotates with the rigid +body motion of the underlying pipeline. In a small-displacement analysis the local system is defined by +the initial geometry of the PSI element and remains fixed in space during the analysis. +Use with beam, frame, and truss elements +See “Beam element cross-section orientation,” Section 29.3.4, for information on defining local material +directions for beams, frames, or trusses. +Use with the fabric material model +The fill and the warp yarn directions in the fabric plane are allowed to rotate with respect to each other +under shear deformations (“Fabric material behavior,” Section 23.4.1). The current yarn directions are +tracked with respect to the orthogonal coordinate system that also rotates with the material. +Use with the jointed material model +When a user-defined orientation is used to define a joint system orientation for the jointed material +model available in Abaqus/Standard (“Jointed material model,” Section 23.5.1), only the local coordinate +system need be defined. It is assumed that the first direction is the direction normal to the plane of the +joint and the other directions are in the plane of the joint. An additional axis of rotation cannot be used. +Use with rotary inertia and connector elements +A user-defined orientation must be used to define the local directions for certain connection types used +to define connector elements . +A user-defined orientation can be used with SPRING1, SPRING2, DASHPOT1, DASHPOT2, +JOINTC, JOINT2D, JOINT3D, and ROTARYI elements to provide a local system for defining the +direction of action of such elements. Points a, b, and c cannot be defined by giving +local node numbers when the orientation is used for these elements. If you do not specify an axis for +additional rotation, the local 1-direction with no additional rotation will be chosen as the default. +Use with the kinematic coupling constraint +User-defined orientations can be used in Abaqus/Standard to define the local coordinate systems in +which constraint directions are specified for a kinematic coupling constraint (see “Kinematic coupling +constraints,” Section 34.2.3). In this case you cannot define points a, b, and c by giving local node +numbers . +Use with surface-based coupling constraints +User-defined orientations can be used to define the local coordinate systems in which surface-based +coupling constraint directions are specified . In this case +you cannot define points a, b, and c by giving local node numbers . +Use with inertia relief +A user-defined orientation can be used in Abaqus/Standard to define a local system of directions along +which the inertia relief loads are computed . In this case you cannot +define points a, b, and c by giving local node numbers . +Use with distributed general traction, shear traction, and general edge loads +User-defined orientations can be used in Abaqus to define the local coordinate systems in which the +loading directions for distributed general tractions, shear tractions, and general edge loads are specified. +See “Distributed loads,” Section 33.4.3. +Orientations defined with distributions +Spatially varying local coordinate systems (for material definitions, material calculations, and output) +defined with a distribution can be applied only to solid continuum, membrane (in Abaqus/Standard), +and shell elements. +See “Solid (continuum) elements,” Section 28.1.1; “Membrane elements,” +Section 29.1.1; “Using a shell section integrated during the analysis to define the section behavior,” +Section 29.6.5; and “Using a general shell section to define the section behavior,” Section 29.6.6. +Output +When a user-defined orientation is used in an element section definition, the stress, the strain, and the +element section force components are output in the local system. +For a fabric material the output of the regular material point tensors such as stress and strain are given +in an orthogonal coordinate system even when the local yarn directions are non-orthogonal. However, +the nominal fabric stress SFABRIC and the nominal fabric strain EFABRIC are also available for output +. +This use of a local system is indicated by a footnote in the printed output +Abaqus/Standard. An orientation used with the jointed material model does not affect the output. +tables from +When a user-defined orientation is used in Abaqus/Standard with kinematic or distributing coupling +constraints, the local system is indicated in the analysis input file processor output tables. +Local coordinate systems are written automatically to the output database with the exception of +systems defined by specifying points a and b relative to local or global node numbers or systems defined +through a user subroutine. Any additional rotations specified are ignored. +Material directions are written automatically to the output database. They can also be written to the +Abaqus/Standard results file (with at least one output variable specified; see “Output of local directions +to the results file” in “Output to the data and results files,” Section 4.1.2). The material directions can be +visualized in Abaqus/CAE by selecting Plot→Material Orientations in the Visualization module. +2.3 +Surface definition +• “Surfaces: overview,” Section 2.3.1 +• “Element-based surface definition,” Section 2.3.2 +• “Node-based surface definition,” Section 2.3.3 +• “Analytical rigid surface definition,” Section 2.3.4 +• “Eulerian surface definition,” Section 2.3.5 +• “Operating on surfaces,” Section 2.3.6 +2.3.1 +SURFACES: OVERVIEW +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Element-based surface definition,” Section 2.3.2 +• “Node-based surface definition,” Section 2.3.3 +• “Analytical rigid surface definition,” Section 2.3.4 +• “Eulerian surface definition,” Section 2.3.5 +• “Operating on surfaces,” Section 2.3.6 +• “Integrated output section definition,” Section 2.5.1 +• “Acoustic, shock, and coupled acoustic-structural analysis,” Section 6.10.1 +• “Distributed loads,” Section 33.4.3 +• “Prescribed assembly loads,” Section 33.5.1 +• “Mesh tie constraints,” Section 34.3.1 +• “Coupling constraints,” Section 34.3.2 +• “Shell-to-solid coupling,” Section 34.3.3 +• “Contact interaction analysis: overview,” Section 35.1.1 +• “Defining tied contact in Abaqus/Standard,” Section 35.3.7 +• “Cavity radiation,” Section 40.1.1 +Overview +In Abaqus surfaces: +• can be used to define contact and interactions, including acoustic-structural interactions; +• can define regions used to prescribe distributed surface loads; +• can be used to tie dissimilar meshes together; +• can define cavities used for a cavity radiation analysis in Abaqus/Standard; +• can define pre-tensioned sections used in prescribing assembly loads in Abaqus/Standard; +• can define sections used for tracking the average motion of a surface in Abaqus/Explicit; +• can define sections for output quantities such as the total force transmitted through a surface; +• are geometric entities that have an area associated with them but have zero volume; +• have an identifiable orientation defined by their normals; +• are defined by specifying nodes or node sets, an analytic curve or surface, an Eulerian material +instance, or element faces, edges, or ends; and +• can be deformable, rigid, or partially deformable and partially rigid. +This section describes the general rules that apply when creating surfaces in Abaqus. +Why use surfaces? +Surfaces can be used to model the interaction of two or more distinct bodies in a mechanical, acoustic, +coupled acoustic-structural, coupled thermal-mechanical, coupled thermal-electrical-structural, thermal, +coupled thermal-electrical, or cavity radiation analysis. A rigid surface can be used to represent a body +that is much stiffer than the rest of the model in a mechanical or coupled thermal-mechanical analysis, +with the limitation that no heat can be transferred to the rigid body. +In acoustic-structural analysis, +surfaces can be used to define impedance boundary conditions, including first-order conditions for +modeling acoustic radiation. +Surfaces can be used to define a region on which a distributed surface load is prescribed; this +can facilitate user input of distributed surface loads for complex models. In addition, surfaces can be +used to define multi-point or coupling constraints. Surfaces can also define pre-tension sections used in +prescribing assembly loads in Abaqus/Standard. +Finally, surfaces can be used to define sections to obtain output of accumulated quantities; +this provides a “free body diagram” output, allowing analyses of “force-flow” through a statically +indeterminate structure. +The following types of surfaces can be defined in Abaqus: +• Element-based surfaces are defined on the faces, edges, or ends of elements. The elements can be +deformable or rigid, leading to a surface that is deformable or rigid. When some of the deformable +elements underlying a surface are part of a rigid body, the surface will become partially deformable +and partially rigid. +In Abaqus/Explicit a default element-based surface that includes all bodies in the model is +provided for use with the general contact algorithm. +• Node-based surfaces are defined on nodes and, hence, are by definition discontinuous. A user- +defined area can be associated with each node on the surface. +• Analytical surfaces are defined directly in geometric terms and are always rigid. +• Eulerian material surfaces are defined on material instances in an Eulerian section. These surfaces +are available in Abaqus/Explicit for use with the general contact algorithm. +Element-based surfaces contain more intrinsic information than either node-based surfaces or +analytical rigid surfaces. When an element-based surface is used in a mechanical contact analysis, +Abaqus can associate a surface area with each node and can calculate the contact stress acting on the +surface. In contrast, Abaqus may not be able to calculate accurate contact stresses when a node-based +surface (“Node-based surface definition,” Section 2.3.3) is used because the actual area associated +with each node may not be correct. In addition, when a surface formed by shell, membrane, or rigid +elements is used, Abaqus can consider the thickness and possibly the offset of the reference surface of +these elements in some applications that refer to surfaces. For example, these thicknesses are accounted +for by all contact algorithms available in Abaqus/Explicit and by the surface-to-surface, small-sliding +contact formulation in Abaqus/Standard. +Contact between two node-based surfaces or a node-based surface with itself is not allowed; +contact between two analytical rigid surfaces is not allowed. Contact between two rigid surfaces defined +using rigid elements is not allowed in Abaqus/Standard and is allowed only with penalty contact in +Abaqus/Explicit. +Surface definitions cannot change from step to step; however, new surfaces can be defined upon +restart. +Internal surfaces created by Abaqus/CAE +In Abaqus/CAE many modeling operations are performed by picking geometry with the mouse. For +example, a contact pair can be defined by picking faces on geometric part instances. Each such face +must be translated into a surface in the input file. Such a surface is assigned a name by Abaqus/CAE and +is marked as internal. These internal surfaces can be viewed using display groups in the Visualization +module of Abaqus/CAE . +Input File Usage: +*SURFACE, NAME=surface_name, INTERNAL +Restrictions on surfaces +Refer to the subsequent sections on the different surface types available in Abaqus for details on the +In addition, some features +general restrictions that apply to all surface definitions of a given type. +in Abaqus that use surfaces impose other restrictions on surface characteristics. These limitations are +discussed in the following sections: +• “Integrated output section definition,” Section 2.5.1 +• “Distributed loads,” Section 33.4.3 +• “Mesh tie constraints,” Section 34.3.1 +• “Coupling constraints,” Section 34.3.2 +• “Shell-to-solid coupling,” Section 34.3.3 +• “Contact interaction analysis: overview,” Section 35.1.1 +• “Defining contact pairs in Abaqus/Standard,” Section 35.3.1 +• “Defining general contact interactions in Abaqus/Explicit,” Section 35.4.1 +• “Defining contact pairs in Abaqus/Explicit,” Section 35.5.1 +In models that are defined in terms of an assembly of part instances, all surfaces must belong to a +part, part instance, or the assembly. All of the general restrictions on surfaces still apply in such models. +Additional rules are given in “Defining an assembly,” Section 2.10.1. +2.3.2 +ELEMENT-BASED SURFACE DEFINITION +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Surfaces: overview,” Section 2.3.1 +• “Integrated output section definition,” Section 2.5.1 +• “Distributed loads,” Section 33.4.3 +• “Prescribed assembly loads,” Section 33.5.1 +• “Mesh tie constraints,” Section 34.3.1 +• “Coupling constraints,” Section 34.3.2 +• “Shell-to-solid coupling,” Section 34.3.3 +• “Contact interaction analysis: overview,” Section 35.1.1 +• “Cavity radiation,” Section 40.1.1 +• *SURFACE +• “What is a surface?,” Section 73.2.3 of the Abaqus/CAE User’s Manual +Overview +An element-based surface: +• can be defined on solid, structural, rigid, surface, gasket, or acoustic elements; +• can be deformable or rigid; +• can be defined on any combination of elements in many cases; +• can be defined on the exterior of any body; and +• can be defined on the interior of any body that is modeled with continuum, shell, membrane, surface, +beam, pipe, truss, or rigid elements (e.g., to define a cross-section through a body) either by simply +cutting the body with a plane or by identifying the elements and the corresponding interior facets. +For details about defining node-based surfaces, see “Node-based surface definition,” Section 2.3.3. +For details about defining analytical +rigid surface definition,” +Section 2.3.4. For details about defining surfaces using Boolean combinations of existing surfaces, see +“Operating on surfaces,” Section 2.3.6. +rigid surfaces, see “Analytical +Defining element-based surfaces +You must assign a name to all element-based surfaces; this name can be used with various features to +define a contact model, a surface-based load, or a surface-based constraint. In addition, you must specify +the region of your model on which the surface is defined. In an input file you can define element-based +surfaces on element faces, edges, or ends. In Abaqus/CAE you can define element-based surfaces on +geometric or element faces, edges, or ends. The methods for defining surfaces depend on the underlying +element type and are discussed later in this section. +In an input file you need only specify an element number or element set name and all exposed +element faces of these elements (or “contact edges” of beam, pipe, and truss elements) will be included +in the surface. Optionally(and the only available method in Abaqus/CAE), you can specify individual +faces, edges, or ends, which allows you direct control over which faces, edges, or ends are to be included +in the surface. +For general contact in Abaqus/Explicit the surface perimeter edges are generated automatically +from the surface facets for use in edge-to-edge contact constraints; you can specify that geometric +feature edges should be included as well . +Input File Usage: +*SURFACE, NAME=surface_name, TYPE=ELEMENT (default) +An element number or element set name is specified as the first entry of each +data line. Optionally, an element face, edge, or end identifier can be specified +as the second entry on a data line. The face and edge identifiers used in Abaqus +are discussed later in this section. +Multiple data lines can be used to define a surface. For example, SURF_1 can +be specified by the following input: +*SURFACE, NAME=SURF_1, TYPE=ELEMENT +ELSET_1, +ELSET_2, S2 +Abaqus/CAE Usage: +Any module except Sketch, Job, and Visualization: Tools→Surface→Create: +Name: surface_name +General restrictions on element-based surfaces +Elements defining a single surface must satisfy the following rules, regardless of how the surface is used +in Abaqus: +• Two-dimensional, axisymmetric, and three-dimensional elements cannot be mixed in the same +surface definition. +• In Abaqus/Standard deformable elements cannot be combined with rigid elements to define a single +surface, but can be combined with other deformable elements that are part of a rigid body . +• The following element types cannot be mixed with other element types in the same surface +definition: +– Coupled thermal-electrical-structural elements +– Coupled temperature-displacement elements +– Heat transfer elements +– Pore pressure elements +– Coupled thermal-electrical elements +– Acoustic finite or infinite elements +• The axisymmetric solid Fourier elements with nonlinear, asymmetric deformation (CAXA +elements) cannot form element-based surfaces. +Surface discretization +For element-based surfaces Abaqus uses a faceted geometry defined by the finite element mesh as the +surface definition. The surface in a coarse finite element model may not be a very good approximation +for contact modeling if the physical surface is curved. Therefore, sufficient mesh refinement must be +used to ensure that the faceted surface is a reasonable approximation of the curved physical surface. +Alternatively, some curved surface geometries may be more effectively modeled with analytical rigid +surfaces . +Creating surfaces on solid, continuum shell, and cohesive elements +There are three ways to define the facets of an element-based surface on solid, continuum shell, and +cohesive elements: +1. by instructing Abaqus to generate the “free surface” from the exposed faces of elements, +2. by specifying the particular faces for each element, and +3. in Abaqus/Explicit by instructing Abaqus to generate an interior surface from element faces that are +not exposed (i.e., not part of the “free surface” of the model). +The automatic free surface generation approach is the simplest method of defining exterior surfaces on +solid elements. Specifying the element faces gives you exact control over which element faces (any +combination of exterior and interior faces) form the surface. Automatic generation of an interior surface +is the simplest method of defining interior surfaces on solid elements (interior surfaces can be useful for +modeling surface erosion due to element failure). +It is possible to use all three approaches in the same surface definition when creating a single surface. +Generating the free surface automatically +You can define the facets of a surface by specifying a series of elements. The faces of these elements +that are on the exterior (free) surface of the model are included in the surface definition. +When the free surface generation method is used to define surfaces, the specified elements can be a +mixture of continuum and structural elements. +Multi-point constraints (“General multi-point constraints,” Section 34.2.2) involving nodes +on exposed surfaces are not taken into account during free surface generation, which can result +in faces that are not on the exterior of a body being included in surface definitions. For example, +the nodes of the elements in element set REFINED shown in Figure 2.3.2–1 are used in linear, +mesh-refinement constraints. The surfaces generated with and without multi-point constraints are +shown in Figure 2.3.2–1. +with MPCs: +Surface SURF generated by +specifying element set REFINED +⇒ +element set "REFINED" +resulting surface "SURF" + without MPCs: +⇒ +element set "REFINED" +resulting surface "SURF" +Figure 2.3.2–1 Effect of multi-point constraints on automatic surface generation. +Input File Usage: +*SURFACE, NAME=surface_name, TYPE=ELEMENT +element number or element set, +For example, if the name of the shaded element set in Figure 2.3.2–2 is ESETA, +the surface named ASURF is specified by +*SURFACE, NAME=ASURF, TYPE=ELEMENT +ESETA, +Abaqus/CAE Usage: +The automatic free surface generation method is not supported in Abaqus/CAE. +Special treatment of cohesive elements for automatic free surface generation +The definition of exposed faces of elements for the purpose of automatic free surface generation has the +following unique aspects regarding cohesive elements: +• Faces of non-cohesive elements along an interface of shared nodes with cohesive elements are +considered exposed. +• The top and bottom faces of all cohesive elements are considered exposed; side faces of cohesive +elements are never considered exposed. +See “Modeling with cohesive elements,” Section 32.5.3, for examples of surfaces on or near cohesive +elements. +FEM model +perimeter +⇒ +user-specified element set +automatically generated surface +Figure 2.3.2–2 Automatic free surface generation. +Creating surface facets by specifying solid, continuum shell, and cohesive element faces +You can define the facets of a surface by identifying the element faces that should be included in the +surface definition. +Input File Usage: +*SURFACE, NAME=surface_name, TYPE=ELEMENT +element number or set, face identifier +Element face numbers are defined in Part VI, “Elements.” Table 2.3.2–1 +contains a list of valid face identifiers for all solid, continuum shell, and +cohesive elements. The face identifier can refer to individual elements or to +entire element sets. When you specify the element faces to define surfaces, the +specified elements cannot be a mixture of continuum and structural elements; +however, each data line of the surface definition can refer to different element +types. +Abaqus/CAE Usage: +Any module except Sketch, Job, and Visualization: Tools→Surface→Create: +Name: surface_name, pick faces in viewport +Generating an interior surface automatically +In Abaqus/Explicit you can define the facets of a surface on the interior of a solid element mesh. The +faces of the specified elements that are not on the exterior (free) surface of the model will be included +in the surface definition. For example, interior surfaces are used with the general contact algorithm +in Abaqus/Explicit for modeling surface erosion due to element failure . +Table 2.3.2–1 Surface definition face identifier labels for solid, continuum shell, and cohesive elements. +Face Labels +SPOS, SNEG +S1, S2, S3 +S1, S2, S3, S4 +S1, S2, S3, S4, S5 +S1, S2, S3, S4, S5, S6 +Elements +DCCAX2(D) +CPEG3(H)(T) +CPS3(T) +CPE3(H)(T) +CAX3(H)(T) +CGAX3(H) +AC2D3 +ACAX3 +DC2D3(E) +DCAX3(E) +CGAX4(R)(H)(T) +CPEG4(H)(I)(R)(T) +CPS4(I)(R)(T) +CPE4(H)(I)(R)(T)(P) +CAX4(H)(I)(R)(T)(P) +C3D4(H)(T) +AC2D4(R) +ACAX4(R) +AC3D4 +DC2D4(E) +DCAX4(E) +DC3D4(E) +DCC2D4(D) +COH2D4 +C3D6(H)(T) +AC3D6 +CCL9(H) +DC3D6(E) +SC6R +C3D8(H)(I)(R)(T)(P) +C3D27(R)(H) +AC3D8(R) +CCL12(H) +DC3D8(E) +DCC3D8(D) +SC8R +CPEG6(M)(H)(T) +CPS6M(T) +CPE6(M)(H)(T) +CAX6(M)(H)(T) +CGAX6(M)(H)(T) +AC2D6 +ACAX6 +DC2D6(E) +DCAX6(E) +CGAX8(R)(H) +CPEG8(R)(H)(T) +CPS8(R)(T) +CPE8(H)(R)(T)(P) +CAX8(R)(H)(T)(P) +C3D10(M)(H)(I)(T) +AC2D8 +ACAX8 +AC3D10 +DC2D8(E) +DCAX8(E) +DC3D10(E) +DCCAX4(D) +COHAX4 +C3D15(H)(V) +AC3D15 +CCL18(H) +DC3D15(E) +COH3D6 +C3D20(H)(R)(T)(P) +AC3D20 +CCL24(R)(H) +DC3D20(E) +COH3D8 +The automatic generation of an interior surface is equivalent to constructing a surface consisting of +all faces of the elements and then subtracting the free surfaces of those elements. Shell elements, beam +elements, pipe elements, membrane elements, etc. are ignored since they do not have any interior faces +by definition. +Multi-point constraints are not taken into account when generating interior surfaces. This can result +in faces that are on the interior of a body being excluded from the surface definition. +Input File Usage: +*SURFACE, NAME=surface_name, TYPE=ELEMENT +element number or element set, INTERIOR +For example, if the name of the shaded element set in Figure 2.3.2–3 is ESETA, +the surface named ASURFINTR (the elements in the figure have been reduced +in size to differentiate faces that share the same nodes) is specified by +*SURFACE, NAME=ASURFINTR, TYPE=ELEMENT +ESETA, INTERIOR +Abaqus/CAE Usage: +The generation of interior surfaces is not supported in Abaqus/CAE. +FEM model +⇒ +user-specified element set +surface ASURFINTR +drawn with solid lines +Figure 2.3.2–3 Automatic interior surface generation. +Creating surfaces on structural, surface, and rigid elements +There are five ways to define surfaces on structural, surface, and rigid elements: +1. You can create a single-sided surface with a well-defined orientation by indicating either the top or +bottom surface of each specified element. +2. You can create a double-sided surface by specifying only the elements and letting Abaqus generate +the “free surface” from the exposed faces. +3. You can create an edge-based surface. +4. You can create a cross-section surface on the ends of beam, pipe, and truss elements. +5. You can create a three-dimensional curve-type surface along the length of beam, pipe, and truss +elements by specifying only the elements and letting Abaqus generate the “free surface.” +It is possible to use any or all of the above approaches in the same surface definition as long as it +makes sense in the use of that surface with other features in Abaqus. Table 2.3.2–2 contains a list of +valid face and edge identifiers for structural, surface, and rigid elements. +Table 2.3.2–2 Surface definition face and edge identifier labels +for structural, surface, and rigid elements. +Face and Edge +Labels +SPOS, SNEG +Elements +SAX2(T) +MAX2 +MGAX2 +M3D8(R) +MCL6 +DS4 +DSAX1 +SFMAX1 +SFMGAX1 +SFM3D3 +SFM3D6 +SFMCL9 +RAX2 +B22(H) (Abaqus/Standard) +PIPE22(H) +T2D3(H)(T) +END1, END2 +SAX1 +MAX1 +MGAX1 +M3D6 +M3D9(R) +MCL9 +DS8 +DSAX2 +SFMAX2 +SFMGAX2 +SFM3D4(R) +SFM3D8(R) +SFMCL6 +B21(H) +B23(H) +PIPE21(H) +T2D2(H)(T) +B22 (Abaqus/Explicit) +B32(H)(OS) +ELBOW31(B)(C) +PIPE31(H) +T3D2(H)(T) +STRI3 +S3(R)(S) +M3D3 +B31(H)(OS) +B33(H) +ELBOW32 +PIPE32(H) +T3D3(H)(T) +STRI65 +R3D3 +END1, END2; must use +node-based surfaces with +the contact pair algorithm +in Abaqus/Explicit. +SPOS, SNEG, +E1, E2, E3 +ACIN2D2 +ACINAX2 +S4(R)(S)(W)(5) +S9R5 +M3D4(R) +ACIN3D3 +Elements +ACIN2D3 +ACINAX3 +S8R5(T) +R3D4 +ACIN3D6 +ACIN3D4 +ACIN3D8 +Face and Edge +Labels +SPOS +E1, E2 +SPOS, SNEG, +E1, E2, E3, E4 +SPOS +E1, E2, E3 +SPOS +E1, E2, E3, E4 +Defining single-sided surfaces +You can define a single-sided surface on the positive or negative face of structural, surface, or rigid +elements. The positive face is defined as the one in the direction of the positive element normal, and the +negative face is defined as the one in the direction opposite to the element normal. The definition of the +element normal for all elements is given in Part VI, “Elements.” +You must ensure that all of the specified elements have their normals oriented consistently. If they +are oriented as shown in Figure 2.3.2–4, the surface normals will reverse direction as the surface is +traversed and improper results may occur when the surface is used with features requiring an orientation +such as distributed surface loads. Further, an error message will be issued and the analysis will terminate +if this condition is detected for surfaces used with mesh tie constraints in Abaqus/Standard or with contact +pairs. To correct the surface orientations in this figure, two separate element sets with different face +identifiers should be used. +Input File Usage: +Use the following option to define a surface on the positive face of a structural, +surface, or rigid element: +*SURFACE, NAME=surface_name, TYPE=ELEMENT +element number or element set, SPOS +Use the following option to define a surface on the negative face of a structural, +surface, or rigid element: +*SURFACE, NAME=surface_name, TYPE=ELEMENT +element number or element set, SNEG +For example, single-sided surfaces on the positive faces of the elements in +element set SHELL can be defined using input similar to +*SURFACE, NAME=BSURF, TYPE=ELEMENT +SHELL, SPOS +element set SHELL +element normals +Figure 2.3.2–4 Inconsistent orientation of structural element +normals can result in an invalid surface. +Abaqus/CAE Usage: +Any module except Sketch, Job, and Visualization: Tools→Surface→Create: +Name: surface_name, pick face in viewport, click mouse button 2, +and specify the side of the selected face +Defining double-sided surfaces +You can create double-sided surface facets on three-dimensional shell, membrane, surface, and rigid +elements using the automatic surface facet generation approach (i.e., specifying only the element +numbers or sets). Some applications that refer to surfaces do not allow the use of double-sided surfaces: +examples include contact pairs in Abaqus/Standard and features requiring an oriented surface such +as distributed surface loads. When double-sided surfaces can be used, they are often preferred to +single-sided surfaces. +In some applications, such as when defining the contact domain for general +contact, it does not matter whether single- or double-sided surfaces are used. +When double-sided surfaces are used with contact pairs in Abaqus/Explicit, the normals of all the +underlying elements do not need to have a consistent positive orientation: Abaqus/Explicit will define +the contact surface such that its facets have consistent normals, even if the underlying elements do not +have consistent normals. The facet normals will be the same as the element normals if the element +normals are all consistent; otherwise, an arbitrary positive orientation is chosen for the surface. The +positive orientation is significant only with respect to the sign of the contact pressure output variable +for the contact pair algorithm, CPRESS . +Although contact is enforced unconditionally on both sides of a surface when self-contact is used +with contact pairs, contact is enforced on both sides of a surface used in two-body contact only when that +surface is double-sided (if allowed). The use of single-sided surfaces with contact pairs is sometimes +desirable: the resolution of large initial overclosures in contact pairs is more robust with single-sided +surfaces than with double-sided surfaces . However, single-sided contact is +generally more limiting than double-sided contact; it may cause an analysis to fail due to excessive +element distortion or not enforce the contact conditions realistically if a slave node unexpectedly moves +behind a master surface. This condition can occur, for example, when large deformations or rigid-body +motions are present or due to complex tool shapes in a forming analysis. +Input File Usage: +Use the following option to define a double-sided surface on three-dimensional +shell, membrane, surface, or rigid elements in Abaqus/Explicit: +*SURFACE, NAME=surface_name, TYPE=ELEMENT +element number or element set, +For example, double-sided surfaces on the elements in element set SHELL can +be defined using input similar to +*SURFACE, NAME=BSURF, TYPE=ELEMENT +SHELL, +Abaqus/CAE Usage: +Any module except Sketch, Job, and Visualization: Tools→Surface→Create: +Name: surface_name, pick face in viewport, click mouse +button 2, and choose Both sides +Defining edge-based surfaces +You can define an edge-based surface on three-dimensional shell, membrane, surface, or rigid elements +by specifying the individual edges. Alternatively, you can specify that all the edges of the elements that +are on the exterior (free) surface of the model are used to form the surface; this method cannot be used +to define edge-based surfaces that are in the interior of the model. It is possible to use both methods in +the same surface definition when creating a single surface. +Input File Usage: +Use the following option to specify the individual edges that form the surface: +*SURFACE, NAME=surface_name, TYPE=ELEMENT +element number or element set, edge identifier +The individual edge identifiers used in Abaqus are listed in Table 2.3.2–2. +Use the following option to specify that all the edges of the elements that are +on the exterior (free) surface of the model are used to form the surface: +*SURFACE, NAME=surface_name, TYPE=ELEMENT +element number or element set, EDGE +For example, if the shaded element set in Figure 2.3.2–2 is composed of three- +dimensional shell elements and is named ESETA, the surface named ESURF +could be specified by the following input: +*SURFACE, NAME=ESURF, TYPE=ELEMENT +ESETA, EDGE +Abaqus/CAE Usage: +Any module except Sketch, Job, and Visualization: Tools→Surface→Create: +Name: surface_name, pick edges in viewport +In Abaqus/CAE you can specify that all the edges of the elements that are on +the exterior (free) surface of the model are used to form the surface by directly +picking all the free edges in the viewport. +Defining a surface over the cross-section at the ends of beam, pipe, and truss elements +To define a surface over the cross-section of beam, pipe, or truss elements, you must specify the end +on which the surface is defined. Surfaces created on the ends of these elements can be used only for +integrated output request and integrated output section +definitions. +Input File Usage: +Use the following option to define a surface over the cross-section of a beam, +pipe, or truss element: +*SURFACE, NAME=surface_name, TYPE=ELEMENT +element number or element set, END1 or END2 +Abaqus/CAE Usage: +Any module except Sketch, Job, and Visualization: Tools→Surface→Create: +Name: surface_name, pick three-dimensional wire region in viewport, click +mouse button 2, and choose End (Magenta) or End (Yellow) +Defining a surface along the length of three-dimensional beam, pipe, and truss elements +You cannot specify the faces to define a surface along the length of three-dimensional beams, pipes, or +trusses because their element connectivity cannot define a unique element or surface normal. Instead, +you must specify that Abaqus should generate a surface for these elements. Therefore, the use of surfaces +along the length of these elements is restricted. +In Abaqus/Standard element-based surfaces created along the length of three-dimensional beam, +pipe, or truss elements can be used in tie constraints but can be used only as slave surfaces in contact +interactions. However, there are several advantages to using an element-based surface rather than a +node-based surface when modeling contact in Abaqus/Standard with three-dimensional beams, pipes, or +trusses: +1. The default slip directions are parallel and orthogonal to the element axis. +2. Abaqus/Standard calculates the contact results as contact forces per unit length rather than just +contact forces. +3. It can be easier to define an element-based surface than a node-based surface. +In Abaqus/Standard a surface definition is not allowed for cases where three or more three-dimensional +beams, pipes, or trusses are joined at a common node because of the lack of uniquely defined element +tangents. +In Abaqus/Explicit element-based surfaces created along the length of three-dimensional beam, +pipe, or truss elements can be used only with the general contact algorithm or tie constraints. To +define contact for these elements using the contact pair algorithm, the nodes forming the beam, pipe, +or truss elements can be included in a node-based surface definition (“Node-based surface definition,” +Section 2.3.3) and a contact pair can be defined for this node-based surface and a non-node-based +surface. +Surfaces along the length of three-dimensional beam, pipe, or truss elements cannot be used to +prescribe a distributed surface load since the loading direction is not unique. +Input File Usage: +Use the following option to define a surface along the length of a +three-dimensional beam, pipe, or truss element: +*SURFACE, NAME=surface_name, TYPE=ELEMENT +element number or element set, +Abaqus/CAE Usage: +Any module except Sketch, Job, and Visualization: Tools→Surface→Create: +Name: surface_name, pick three-dimensional wire region in viewport, +click mouse button 2, and choose Circumferential +Surfaces along the length of two-dimensional beam, pipe, and truss elements +Surfaces created along the length of two-dimensional beam, pipe, and truss elements can be used as +master surfaces in a contact pair simulation because the underlying elements have unique element +normals that lie in the plane of the model. These surfaces can also be used to prescribe distributed +surface loads. +Shell, membrane, or rigid element thickness and shell offset +Some applications that refer to surfaces will account for underlying element thicknesses and any offset of +the midsurface relative to the reference surface for surfaces based on shell, membrane, or rigid elements. +For example, all of the contact algorithms available in Abaqus/Explicit can account for these effects. Of +the contact algorithms available in Abaqus/Standard, only the surface-to-surface small-sliding contact +formulation can account for these effects. See the following sections for additional details on applications +that can account for surface thickness and offset: +• “Mesh tie constraints,” Section 34.3.1 +• “Contact formulations in Abaqus/Standard,” Section 37.1.1 +• “Assigning surface properties for general contact in Abaqus/Explicit,” Section 35.4.2 +• “Assigning surface properties for contact pairs in Abaqus/Explicit,” Section 35.5.2 +Creating surfaces on gasket elements +When surfaces are defined on gasket elements, automatic surface facet generation cannot be used because +only the top and bottom element faces can be used to create surfaces . Abaqus/Standard cannot create surfaces on gasket link elements since the top and bottom +surfaces are each reduced to a single node. For other gasket elements you must specify the top and +bottom surfaces directly. The positive face of the element is in the thickness direction of the element. +The definition of the thickness direction of all gasket elements is given in “Defining the gasket element’s +initial geometry,” Section 32.6.4. The negative face is defined as the face in the direction opposite to the +thickness direction of the element. +Input File Usage: +Use the following option to define a surface on the positive face of a gasket +element: +*SURFACE, NAME=surface_name, TYPE=ELEMENT +element number or element set, SPOS +Use the following option to define a surface on the negative face of a gasket +element: +*SURFACE, NAME=surface_name, TYPE=ELEMENT +element number or element set, SNEG +For example, single-sided surfaces on the positive faces of the elements in +element set GASKET can be defined using input similar to +*SURFACE, NAME=BSURF, TYPE=ELEMENT +GASKET, SPOS +Abaqus/CAE Usage: +Any module except Sketch, Job, and Visualization: Tools→Surface→Create: +Name: surface_name, pick top or bottom faces in viewport +Surfaces on three-dimensional gasket line elements +There are several advantages to using an element-based surface rather than a node-based surface when +modeling contact in Abaqus/Standard with three-dimensional gasket line elements: +1. The slip directions are parallel and orthogonal to the gasket line element, which is useful for output +purposes and for anisotropic friction definition. +2. Abaqus/Standard calculates the contact results as contact forces per unit length rather than just +contact forces. +Surfaces created on three-dimensional gasket line elements can be used only as slave surfaces because +Abaqus/Standard cannot form unique normals for these surfaces. +Creating interior cross-section surfaces +To study the “force-flow” through various paths in a model, you must create interior surfaces that cut +through one or more components (similar to a cross-section) so that you can request integrated output +of the total force transmitted across these surfaces . Abaqus provides a simple method to create +such an interior surface over the element facets, edges, or ends by cutting through a region of the model +with a plane. The region can be identified using one or more element sets. If no element sets are specified, +the region consists of the whole model. The cutting plane is defined by specifying the coordinates of a +point on the plane and a vector normal to the plane. Alternatively, the cutting plane can be defined by +specifying the global node numbers of point a on the plane and point b that lies off the cutting plane with +the normal determined as the vector from point a to point b. Abaqus then automatically forms a surface +close to the specified cutting plane by selecting the element facets, edges, or ends of the continuum +solid, shell, membrane, surface, beam, pipe, truss, or rigid elements in the selected region. The surface +generated in this manner is an approximation for the cutting plane. +Multi-point mesh constraints are ignored while generating the interior surface based on the cutting +plane; therefore, the result may be a surface that is not continuous if these constraints stitch disjointed +meshes together in a region that is cut by the cutting plane. When the cutting plane intersects a beam, +pipe, or truss element, the entire element is shown in the Visualization module of Abaqus/CAE as being +part of the surface. However, if this surface is used for integrated output, only the element nodal forces +from the element end that lies on the positive side as defined by the normal to the cutting plane are +included in the integrated output. Point mass and rotary elements, connector elements, spot welds, and +spring elements will not be part of the generated surface even if they are cut by the cutting plane. +Input File Usage: +Use the following option to define the cutting surface by specifying coordinates +of a point on the plane and a vector normal to the plane: +*SURFACE, NAME=surface_name, TYPE=CUTTING SURFACE, +DEFINITION=COORDINATES +Use the following option to define the cutting surface by specifying global node +numbers of points a and b: +*SURFACE, NAME=surface_name, TYPE=CUTTING SURFACE, +DEFINITION=NODES +Abaqus/CAE Usage: +Interior cross-section surfaces are not supported in Abaqus/CAE. +Whole-model free surface in an Abaqus/Explicit input file +In an Abaqus/Explicit input file you can create a surface containing the exposed faces of all elements (and +“contact edges” of beam, pipe, and truss elements) in the model except cohesive elements by specifying +a blank element set name and a blank face identifier. This “free” surface of the model can be used as +the base surface for the cropping and combining operations; without modifications this surface is similar +to the default all-inclusive surface commonly used in general contact . +Input File Usage: +Abaqus/CAE Usage: +*SURFACE, NAME=surface_name, TYPE=ELEMENT +, +The whole-model automatic free surface generation method is not supported in +Abaqus/CAE. +Trimming the perimeter of an open surface +An “open” surface is one that has ends in two dimensions or an outside edge in three dimensions. The +ends of a two-dimensional surface and the edge of a three-dimensional surface are called the surface’s +“perimeter.” Since Abaqus allows a surface to be defined as only a part of the surface of a body, it may +have a perimeter even though it is defined on a closed body. Abaqus automatically performs surface +“trimming” on solid element meshes. You can change the default setting when a surface is created, +providing some basic control over the extent of surfaces. +Surface trimming: +• is a recursive procedure that removes undesirable convex corners near the perimeter of an open +surface ; +• has no effect on closed surfaces (ones with no ends or edges); +• is performed automatically, unless the surface is used as a master surface in a finite-sliding +simulation in Abaqus/Standard or the surface is used with the contact pair algorithm in +Abaqus/Explicit; +• can be used only for external surfaces on solid element meshes (either specified surfaces or +automatically generated free surfaces); and +• has no effect on surfaces used with the contact pair algorithm in Abaqus/Explicit. +Input File Usage: +Use the following option to suppress automatic surface trimming: +Abaqus/CAE Usage: +*SURFACE, TYPE=ELEMENT, NAME=surface_name, TRIM=NO +Automatic surface trimming cannot be suppressed in Abaqus/CAE. +The effect of surface trimming +The effect of surface trimming is best explained by means of an example. Figure 2.3.2–5 illustrates the +effect of trimming for two different surfaces defined on the same simple two-dimensional mesh. +In Case I the surface definition consists of a single layer of elements on the perimeter of the model. +Using automatic surface facet generation, the resulting default surface (curve) includes the vertical +element faces A and B since these faces lie on the perimeter of the model. Trimming the default surface +created in Case I eliminates faces A and B since their presence results in the two spurious corners near +the perimeter of the curve. +Abaqus uses a special criterion in deciding to remove faces A and B from the original open curve. +A face is removed if one of its end nodes is an endpoint and either of the following is true: another face +node is a node on an element corner belonging to the curve or the face normal differs by more than 30° +from the normal of an adjacent face also belonging to the curve. To be a node on an element corner +belonging to the curve means to be a node on two different faces of the same element, both of which +are part of the curve. The face removal criterion is applied recursively to the curve definition until all +corners on or near the perimeter of the curve have been removed. This procedure is generalized for +three-dimensional surface definitions. +In Case II in Figure 2.3.2–5 trimming would not result in the elimination of faces A and B because +neither of the endpoints of these two faces meets the criterion described above. +Why Abaqus will, by default, trim most surfaces +Trimming of surfaces used for application of distributed loads is usually desired since loads are normally +applied to specific sides of a body. Any surface that is used for application of a distributed load will, by +default, be trimmed. +In Abaqus/Standard trimming the slave surface in contact or interaction simulations results in more +accurate estimates of the contact pressures, heat fluxes, and electrical current densities along the perimeter +of the surface. Any surface that is used as a slave surface in a contact or interaction simulation will, by +default, be trimmed. If the slave surface is left untrimmed, the nodes at the corners of the surface will be +assigned additional contact area from the element faces around the corners that may never be involved +in the interaction between the surfaces. This additional contact area introduces errors into the estimates +of the contact output variables at those nodes. Master surfaces in small-sliding simulations will, by +DEFINING ELEMENT-BASED SURFACES +user-specified element set +automatically generated surface +trim +⇒ +Case I +trim +⇒ +Case II +automatically generated surface +Figure 2.3.2–5 Case I: Faces A and B are removed when trimming is done since one node of each of the +faces is an end node and the other is a corner node. Case II: Faces A and B are not removed when trimming +is done since one node of each of the faces is an end node but the other is not a corner node. +default, be trimmed; Abaqus/Standard will normally form a better approximate surface. However, master +surfaces in finite-sliding contact simulations will, by default, be left untrimmed, and they should extend +far enough away from all expected regions of contact. This practice protects against the possibility of +the slave surface nodes sliding off the master surface . +2.3.3 +NODE-BASED SURFACE DEFINITION +Products: Abaqus/Standard Abaqus/Explicit +References +• “Surfaces: overview,” Section 2.3.1 +• “Mesh tie constraints,” Section 34.3.1 +• “Contact interaction analysis: overview,” Section 35.1.1 +• *SURFACE +Overview +A node-based “surface”: +• can be used only as a “slave surface” in contact calculations; +• can be used as a “slave” or “master surface” in a surface-based tie constraint; +• is convenient in three-dimensional cases where Abaqus cannot construct a unique physical surface +on the elements, such as a pipe modeled with pipe elements contacting the ocean floor or cables +modeled with trusses contacting the ground after they break; +• should be used with caution or not at all if accurate contact stresses are needed or if heat will be +exchanged between the two surfaces; +• can be assigned a nonzero thickness for use with the general contact algorithm in Abaqus/Explicit; +• should not be used to model a shell or membrane surface if the thickness and midsurface offset need +to be considered in the problem; +• must either contain nodes that are all part of the same rigid body or not contain any nodes that are part +of a rigid body if the node-based surface is to be used in a penalty contact pair in Abaqus/Explicit; +• in Abaqus/Standard does not provide heat conduction between surfaces in fully coupled +temperature-displacement analysis or pore fluid flow between surfaces in coupled pore +pressure–displacement analysis; +• in Abaqus/Standard does not provide heat conduction and electrical conduction between surfaces +in a fully coupled thermal-electrical-structural analysis; and +• does not include circumferential friction when used with axisymmetric elements with twist (CGAX, +MGAX elements). +Alternatives to node-based surfaces are element-based surfaces and, in the case of rigid surfaces, analytical rigid surfaces . See “Operating on surfaces,” Section 2.3.6, for information on +defining surfaces using Boolean combinations of existing surfaces. +Creating a node-based surface +You create a node-based surface by specifying the nodes or node sets that form the surface. You must +assign a name to the node-based surface; this name will be used when defining contact interactions that +involve the surface. +An optional associated area can be defined for each node. If no area is defined for a node and the +surface is defined in a contact pair, the area specified as part of the contact property definition is used. If +no area is specified as part of the contact property definition, a unit area is used. +In Abaqus/Explicit the area used in contact pair calculations for a node in a node-based surface +is always 1.0, regardless of the user-specified value. Therefore, the contact pressure output variable in +Abaqus/CAE should be interpreted as the contact force when a node-based surface is used for contact +pairs in Abaqus/Explicit. +In models that are defined in terms of an assembly of part instances, all surfaces must belong to a +part, part instance, or the assembly. Additional rules are given in “Defining an assembly,” Section 2.10.1. +When the nodes of shell and membrane elements are used in a node-based surface, the thickness +and midsurface offset of the shell or membrane at each node are not considered. However, a nonzero +thickness can be assigned to node-based surfaces when used with the general contact algorithm +in Abaqus/Explicit,” +in Abaqus/Explicit . +Input File Usage: +*SURFACE, NAME=name, TYPE=NODE +node number or node set, area +2.3.4 +ANALYTICAL RIGID SURFACE DEFINITION +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Surfaces: overview,” Section 2.3.1 +• “Contact interaction analysis: overview,” Section 35.1.1 +• “RSURFU,” Section 1.1.16 of the Abaqus User Subroutines Reference Manual +• *RIGID BODY +• *SURFACE +Overview +An analytical rigid surface: +• can be two-dimensional or three-dimensional; +• must be defined as model data; +• can be used with the infinitesimal-sliding, small-sliding, or finite-sliding mechanical contact +formulations; +• should be oriented such that the analytical rigid surface’s outward normal points toward any body +it may contact; and +• is associated with a node, known as the rigid body reference node, whose motion governs the motion +of the surface. +What are analytical rigid surfaces and why use them? +Analytical rigid surfaces are geometric surfaces with profiles that can be described with straight and +curved line segments. These profiles can be swept along a generator vector or rotated about an axis to +form a three-dimensional surface. An analytical rigid surface is associated with a rigid body reference +node, whose motion governs the motion of the surface. An analytical rigid surface does not contribute +to the rigid body’s mass or inertia properties . The degrees +of freedom of the rigid body reference node become active only when the analytical surface is used in a +contact interaction or when an element (such as a spring element or a mass element) is connected to the +rigid body reference node. +Analytical rigid surfaces are always single-sided with their orientation specified through their +definition. Therefore, contact interaction is recognized only on the outer boundary of an analytical rigid +surface. To model contact on both sides of a thin structure, use an analytical rigid surface that wraps +around the boundary of the thin structure. +Advantages +Using analytical rigid surfaces instead of defining element-based rigid surfaces provides two important +advantages in contact modeling. +• Many curved geometries can be modeled exactly with analytical rigid surfaces because of the ability +to parameterize the surface with curved line segments. The result is a smoother surface description, +which can reduce contact noise and provide a better approximation to the physical contact constraint. +• Using analytical rigid surfaces instead of rigid surfaces formed by element faces may result in +decreased computational cost incurred by the contact algorithm. +The use of curved line segments instead of many linear facets will decrease the time spent in +contact tracking operations. Additional computational savings may be realized in three dimensions +because of the intrinsic two-dimensional descriptions of the analytical surfaces. +Disadvantages +There are also some disadvantages to using analytical rigid surfaces for contact modeling. +• An analytical rigid surface must always act as a master surface in a contact interaction. Therefore, +contact cannot be modeled between two analytical rigid surfaces. +• Contact forces and pressures cannot be contoured on an analytical rigid surface. However, contact +forces and pressures can be plotted on the slave surface. +• The use of a very large number (thousands) of segments to define an analytical rigid surface can +degrade performance. In most cases it is not necessary to use a large number of segments to define +an analytical rigid surface, because curved segment types are allowed. In rare cases in which a very +large number of segments would be necessary, the analysis may be more efficient if an element- +based rigid surface is used instead . +• An analytical rigid surface does not contribute to the mass and rotary inertia properties of the rigid +body with which it is associated. Therefore, if the mass distribution on an analytical rigid surface +needs to be accounted for, equivalent mass and rotary inertia properties must be defined for the +rigid body by using MASS and ROTARYI elements, or a finite element discretization of the surface +should be used instead of an analytical rigid surface . +• In Abaqus/Explicit reaction force output for a rigid body containing an analytical rigid surface is +calculated only for constraints that are active at the reference node (e.g., constraints specified as +boundary conditions). If the net contact force on the rigid body corresponding to an unconstrained +degree of freedom is desired, it must be calculated from the rigid body’s acceleration and mass. +Creating an analytical rigid surface +You can define the following types of simple, two- or three-dimensional, geometric analytical surfaces: +• planar (two-dimensional) surfaces, +• three-dimensional cylindrical (swept) surfaces, and +• three-dimensional surfaces of revolution. +In Abaqus/Standard if none of these surfaces is adequate, you can define a more general analytical surface +with user subroutine RSURFU. +Analytical rigid surfaces are useful when the cross-sections of the surfaces can be represented by +straight and curved line segments. The curved segments can be either circular or parabolic arcs. In two- +dimensional simulations the line segments are defined in the global coordinate system of the deformable +model. In three-dimensional simulations a local, two-dimensional coordinate system must be created, +and the line segments are then defined in that system. The two standard types of three-dimensional +analytical rigid surfaces available are shown in Figure 2.3.4–1. +surface of revolution +cylindrical surface +Figure 2.3.4–1 Examples of three-dimensional rigid surfaces. +You must indicate which type of analytical surface (planar, cylindrical, or revolution) is being +created and assign a name to the surface. In addition, you must define the analytical surface as part +of a rigid body by specifying the name of the analytical surface and the rigid body reference node that +will control the motion of the surface in a rigid body definition. +An Abaqus model can be defined in terms of an assembly of part instances . A part can contain only one analytical surface. A part containing an +analytical surface definition cannot also contain elements. +Input File Usage: +Use both of the following options to create an analytical rigid surface: +Abaqus/CAE Usage: +*SURFACE, TYPE=analytical_surface_type, NAME=name +*RIGID BODY, ANALYTICAL SURFACE=name, REF NODE=n +Part module: Create Part: Name: analytical_rigid_part: select +Analytical rigid as the Type +Then do one of the following: +Any module except Sketch, Job, and Visualization: Tools→Surface→Create: +select analytical_rigid_part +Interaction module: Create Constraint: Rigid body: Analytical +Surface: Edit: select analytical_rigid_part +Interaction module: Create Interaction: any valid type: select +analytical_rigid_part as one of the regions involved in contact +Defining a surface profile +The surface profile is the collection of line segments defining the cross-section of the surface. The surface +type determines whether the profile is swept (cylindrical surfaces), revolved (surfaces of revolution), or, +in the two-dimensional case, used as is (planar surfaces). +You construct a profile by providing the endpoint of each line segment in the profile; the starting +point is always the endpoint of the previous segment, or, in the case of the first segment, the point specified +as the starting point. The center points of circular arcs must be given. Abaqus can define only arcs that +are less than 179.74°; thus, it will use the shorter arc defined by the data provided (use two adjacent arcs +to define a longer arc). For parabolic arcs you must give a third point that lies on the parabola and within +the arc. +Two-dimensional rigid surfaces +To define a planar rigid surface, specify the line segments forming the rigid surface’s profile in the global +coordinate system. If the analytical surface is being defined inside a part, specify the line segments in +the local part coordinate system. +Input File Usage: +*SURFACE, TYPE=SEGMENTS, NAME=name +data lines to define the line segments forming the surface +For example, the definition of the two-dimensional rigid surface depicted in +Figure 2.3.4–2 is +*SURFACE, TYPE=SEGMENTS, NAME=BSURF +START, +CIRCL, +LINE, +CIRCL, +*RIGID BODY, ANALYTICAL SURFACE=BSURF, REF NODE=101 +where +are the global coordinates of the points shown in Figure 2.3.4–2. +, +, +and +, +, +, +, +, +, +Abaqus/CAE Usage: +Part module: Create Part: Name: analytical_rigid_part: select 2D Planar or +Axisymmetric as the Modeling Space and Analytical rigid as the Type +Three-dimensional cylindrical rigid surfaces +To define a cylindrical rigid surface in a model that is not defined in terms of an assembly of part +instances, specify the points a, b, and c shown in Figure 2.3.4–3 that define the local coordinate system. +Give the coordinates of these points—( +)—in the default global +), ( +coordinate system. As shown in Figure 2.3.4–3, point a defines the origin of the local system; point b +defines the local x-axis; and point c defines the generator vector, which is the negative local z-axis. If the +segment +, Abaqus will automatically adjust point c within the plane defined +by points a, b, and c, such that they become perpendicular. The line segments forming the profile of the +rigid surface are defined in the local x–y plane. The three-dimensional surface is formed by sweeping +this profile along the generator vector. The resulting surface extends to infinity in both the positive and +negative directions of the generator vector. +is not perpendicular to +), and ( +rigid reference node +101 +BSURF +ASURF +Figure 2.3.4–2 Two-dimensional analytical rigid surface contacting a deformable body. +Start +Line segment +Outward +normal +Circular arc segment +Local y-axis +Generator +direction +b +Local x-axis +Local z-axis +Figure 2.3.4–3 Cylindrical rigid surface. +To define a cylindrical rigid surface within a part, specify the line segments forming the profile of +the rigid surface in the part coordinate system. For an analytical surface defined within a part (or part +instance), point a is located at the origin of the part coordinate system, point b is located on the part +x-axis, and point c is located on the negative part z-axis. If the segment +, +Abaqus will automatically adjust point c within the plane defined by points a, b, and c, such that they +become perpendicular. You cannot redefine this analytical surface coordinate system; instead, you can +position the surface in the model by giving positioning data when you instance the part . +is not perpendicular to +Input File Usage: +*SURFACE, TYPE=CYLINDER, NAME=name +data lines to define the line segments forming the surface +, +, +and +are points in the local +For example, the following input, where +coordinate system, would define the rigid surface shown in Figure 2.3.4–3 +in a model that is not defined in terms of an assembly of part instances (the +reference node is not shown in the figure): +*SURFACE, TYPE=CYLINDER, NAME=CSURF +, +, +, +, +, +START, +LINE, +CIRCL, … +… +*RIGID BODY, ANALYTICAL SURFACE=CSURF, REF NODE=n +Leave the first two data lines blank to define a cylindrical rigid surface within +a part. +, +, +Abaqus/CAE Usage: +Part module: Create Part: Name: analytical_rigid_part: select +3D as the Modeling Space, Analytical rigid as the Type, and +Extruded shell as the Base Feature +Three-dimensional surfaces of revolution +To define a rigid surface of revolution in a model that is not defined in terms of an assembly of part +instances, specify the two points a and b shown in Figure 2.3.4–4 that define the local coordinate system. +Give the coordinates of these points—( +)—in the default global coordinate +system. As shown in Figure 2.3.4–4, point a defines the origin of the local system, and the vector from +a to b defines the local z-axis, which is the axis of a cylindrical coordinate system. The line segments +forming the profile of the surface of revolution are defined in the local r–z plane, where the local r-axis +aligns with the radial axis of the cylindrical coordinate system. The three-dimensional surface is formed +by revolving this profile about the axis of the cylindrical system, the local z-axis. +) and ( +To define a rigid surface of revolution within a part, specify the line segments forming the cross- +section of the rigid surface in the local part coordinate system. For an analytical surface defined within a +local z +Start +line segment +local r +circular arc segment +Figure 2.3.4–4 Rigid surface of revolution. +part (or part instance), point a is located at the origin of the part coordinate system, the part x-axis aligns +with the radial axis of the cylindrical coordinate system, and point b is located on the part y-axis. You +cannot redefine this local axis; instead, you can position the surface in the model by giving positioning +data when you instance the part . +*SURFACE, TYPE=REVOLUTION, NAME=name +Input File Usage: +data lines to define the line segments forming the surface +For example, the following input would define the rigid surface shown in +Figure 2.3.4–4 (the reference node is not shown in the figure): +*SURFACE, TYPE=REVOLUTION, NAME=REVSURF +, +, +, +, +, +, +START, +LINE, … +CIRCL, … +… +*RIGID BODY, ANALYTICAL SURFACE=REVSURF, +REF NODE=999 +Leave the first data line blank to define a rigid surface of revolution within a +part. +Abaqus/CAE Usage: +Part module: Create Part: Name: analytical_rigid_part: select +3D as the Modeling Space, Analytical rigid as the Type, and +Revolved shell as the Base Feature +Defining the surface normals +The outward surface normal for analytical rigid surfaces is determined by the direction of the line +segments forming the profile of the surface. The sequence of line segments defines a vector +along +the rigid surface from the starting point of the first segment to the ending point of the last segment. +The outward surface normal is created by taking the cross product of the vector +, the unit normal +to the plane in which the surface is defined, and the vector +. +Figure 2.3.4–5 shows the vector +in the definition plane of an analytical rigid surface. +, the tangent to the surface: +Line segment +Start +e2 +e3 +e1 +Circular segments +Line segment +Figure 2.3.4–5 Orientation of surface normals for a rigid surface. +, and +is defined such that +and +The unit vector +, +form a right-handed orthonormal coordinate system. +In-plane coordinate directions +depend on the type of analytical rigid surface being defined. For +two-dimensional analytical rigid surfaces they correspond to the global X- and Y-axes in planar models +and the r- and z-axes in axisymmetric models. For cylindrical rigid surfaces they correspond to the local +x- and y-axes, and for rigid surfaces of revolution they correspond to the local r- and z-axes. The outward +normals for a cylindrical rigid surface and rigid surface of revolution are shown in Figure 2.3.4–3 and +Figure 2.3.4–4, respectively. +If the line segments are specified in the wrong order, the surface normals of a rigid surface will +appear in exactly the opposite direction to what was intended. Such a mistake can be corrected only by +specifying the line segments in the opposite sequence. +Smoothing analytical rigid surfaces +In many cases it can be beneficial to smooth surfaces to more accurately represent the surface geometry. +In particular, it can be very difficult to obtain a converged solution in a finite-sliding Abaqus/Standard +simulation if the master surface does not have continuous normal and surface tangent vectors ; therefore, it is important to smooth any +sharp corners on the master surface so that discontinuities in these vectors are eliminated. +By default, Abaqus does not smooth master surfaces that are analytical rigid surfaces. Smooth +transitions between adjacent line segments can always be created by manually inserting additional curved +line segments. Alternatively, smooth surfaces can be generated automatically by Abaqus. You specify +the radius of curvature, r, in the units of length used in the model, that Abaqus will use to construct a +smooth transition between any discontinuous line segments forming the rigid surface. The default value +of zero provides no smoothing of the surface. +The effect of a fillet radius on adjoining line segments and on adjoining line and circular arc +segments is illustrated in Figure 2.3.4–6. +END +START +fillet radius +Y-local +X-local +OUTWARD +NORMAL +Figure 2.3.4–6 Effect of fillet radius on an analytical rigid surface. +The sharp corners have been smoothed using the fillet radius so that the normal and tangent surface +vectors are continuous along the entire master surface. Any value r can be used in a model. However, if +r is greater than the length of either of the two adjacent segments, no smoothing will occur. Therefore, +a practical limit on the size of r is the length of the smallest line segment forming the surface. +Input File Usage: +*SURFACE, TYPE=analytical_surface_type, NAME=name, +FILLET RADIUS=r +Abaqus/CAE Usage: When you create an analytical rigid part in Abaqus/CAE, you can create a +fillet radius between segments or join the segments using arcs. See “Sketching +simple objects,” Section 20.10 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual. +Surface tangent conventions +, is always along the direction +Abaqus forms analytical rigid surfaces such that the first surface tangent, +of the line segments forming the surface . The second surface tangent, +, is defined such that the +outward surface normal and the two surface tangents form a right-handed orthonormal system, as shown +in Figure 2.3.4–7. +a. Two-dimensional cases +b. Three-dimensional cases +t1 +t2 +t1 +Figure 2.3.4–7 Surface tangent and outward normal definitions for analytical rigid surfaces. +Creating an analytical rigid surface in a user subroutine +More complicated analytical rigid surfaces can be defined in Abaqus/Standard by user subroutine +RSURFU. Writing subroutine RSURFU to create a smooth surface is usually difficult, and convergence +problems are often caused by inadequate surface definition in this subroutine. When using RSURFU, +ensure that the outward surface normal and the two surface tangents form a right-handed orthonormal +system. In two-dimensional cases the second surface tangent is always (0, 0, −1). You must also ensure +that the surface is smooth in finite-sliding simulations and that the orientation of the rigid surface relative +to the deformable surface is reasonable (i.e., the rigid surface cannot be inside the deformable surface). +Input File Usage: +Abaqus/CAE Usage: +*SURFACE, TYPE=USER, NAME=name +User subroutine RSURFU is not supported in Abaqus/CAE. +Defining analytical rigid surfaces when drag chain or rigid surface elements are used +An alternative method of defining analytical rigid surfaces must be used to define the surface of the +seabed when three-dimensional drag chain elements (available only in Abaqus/Standard) are used. This +alternative method must also be used when rigid surface elements are used; these elements are required +only when CAXA or SAXA elements contact a rigid surface. For this method the rigid surface must be +flat and parallel to the x–y plane. +In a model defined in terms of an assembly of part instances, the rigid surface definition must appear +inside the same part definition as the drag chain or rigid surface elements. +You must indicate which type of analytical surface (planar, cylindrical, or user-defined) is being +created. Cylindrical rigid surfaces are not valid for use with CAXA or SAXA elements. In addition, you +must assign a name to the surface and identify the rigid body reference node that will control the motion +of the surface. +Input File Usage: +Abaqus/CAE Usage: +*RIGID SURFACE, TYPE=surface_type, NAME=name, REF NODE=n +Drag chain and rigid surface elements are not supported in Abaqus/CAE. +Two-dimensional rigid surfaces +To define a planar rigid surface, define the line segments forming the rigid surface’s cross-section in +the global coordinate system. You must provide the endpoint of each line segment; the starting point is +always the endpoint of the previous segment, or, in the case of the first segment, the point specified as the +starting point. The centers of the circular arcs, points c and f in Figure 2.3.4–2, must be given. Abaqus +can define only arcs that are less than, but not equal to, 179.74°; thus, it will use the shorter arc defined +by the data provided (use two adjacent arcs to define a longer arc). For parabolic arcs you must give a +third point that lies on the parabola and within the arc. +Input File Usage: +*RIGID SURFACE, TYPE=SEGMENTS, NAME=name, REF NODE=n +START, starting point X- or r-coordinate, starting point Y- or z-coordinate +data lines to define the endpoints of the line segments forming the surface, +beginning with the word LINE (for straight line segments), CIRCL (for +circular arc segments), or PARAB (for parabolic arc segments) +Abaqus/CAE Usage: +Drag chain and rigid surface elements are not supported in Abaqus/CAE. +Three-dimensional cylindrical rigid surfaces +To define a cylindrical rigid surface, specify the points a, b, and c shown in Figure 2.3.4–3 that define +the local coordinate system. Give the coordinates of these points—( +), and +( +)—in the default global coordinate system. As shown in Figure 2.3.4–3, point a defines the +origin of the local system; point b defines the local x-axis; and point c defines the generator vector, +which is the negative local z-axis. The line segments forming the cross-section of the rigid surface are +defined in the local x–y plane. The three-dimensional surface is formed by sweeping this cross-section +along the generator vector. The resulting surface extends to infinity in both the positive and negative +directions of the generator vector. +), ( +Input File Usage: +*RIGID SURFACE, TYPE=CYLINDER, NAME=name, REF NODE=n +START, starting point x-coordinate, starting point y-coordinate +data lines to define the endpoints of the line segments forming the surface, +beginning with the word LINE (for straight line segments), CIRCL (for +circular arc segments), or PARAB (for parabolic arc segments) +Abaqus/CAE Usage: +Drag chain and rigid surface elements are not supported in Abaqus/CAE. +2.3.5 +EULERIAN SURFACE DEFINITION +Product: Abaqus/Explicit +References +• “Surfaces: overview,” Section 2.3.1 +• “Eulerian analysis,” Section 14.1.1 +• “Contact interaction analysis: overview,” Section 35.1.1 +• *EULERIAN SECTION +• *SURFACE +Overview +An Eulerian surface: +• must be three-dimensional; +• must be defined as model data; +• can be used with the general contact algorithm in Abaqus/Explicit; and +• is created by specifying the name of an Eulerian material instance. +What are Eulerian surfaces and why use them? +An Eulerian surface represents the exterior surface of a particular Eulerian material instance in an +Abaqus/Explicit analysis. Since Eulerian materials flow through the Eulerian mesh, their surfaces +cannot be defined by a simple list of element faces. Instead, these surfaces often lie within Eulerian +elements and must be computed in each time increment using element volume fraction data. +You can use Eulerian surfaces to define specific interactions with Lagrangian surfaces in +Abaqus/Explicit’s general contact algorithm. Once defined, you can reference Eulerian surfaces in +inclusions, exclusions, and interaction definitions. You cannot combine or crop Eulerian surfaces. +Eulerian surface definitions are not required for the use of Eulerian-Lagrangian contact. If you +specify “automatic” contact for the entire model, the exterior surface of all Eulerian materials will +automatically be considered for contact. +Advantages of creating Eulerian surfaces +You can use Eulerian surfaces to: +• Assign contact properties for contact interactions involving a particular Eulerian material instance. +• Exclude interactions between Eulerian materials and Lagrangian bodies that are unlikely to make +contact, simplifying the contact problem and reducing computational cost. +Creating an Eulerian surface +To create an Eulerian surface, you must specify the name of a material instance that is present in the +model. The material instance names are defined as part of the Eulerian section . Abaqus/Explicit calculates the exterior boundary of the specified material instance and +defines a surface corresponding to that boundary. The surface is recalculated in each time increment as +the material deforms. +Input File Usage: +*SURFACE, TYPE=EULERIAN MATERIAL, NAME=name +material instance name, +2.3.6 +OPERATING ON SURFACES +Products: Abaqus/Standard Abaqus/Explicit +References +• “Surfaces: overview,” Section 2.3.1 +• “Coupling constraints,” Section 34.3.2 +• “Mesh-independent fasteners,” Section 34.3.4 +• “Defining general contact interactions in Abaqus/Explicit,” Section 35.4.1 +• *SURFACE +Overview +Combined surfaces: +• are created by performing a Boolean operation (union, intersection, or difference) on existing +surfaces; +• can be formed from element-based or node-based surfaces; +• cannot be formed from Eulerian surfaces; +• can be used in the same way as other element-based or mode-based surfaces in Abaqus/Standard; +and +• cannot be used with contact pairs in Abaqus/Explicit (but can be used with general contact in +Abaqus/Explicit). +Cropped surfaces: +• are created by cropping an existing surface and keeping only that part of the surface that is enclosed +in a specified rectangular box; +• can be formed from element-based or node-based surfaces; +• cannot be formed from Eulerian surfaces; +• can be used in the same way as other element-based or mode-based surfaces in Abaqus/Standard; +and +• cannot be used with contact pairs in Abaqus/Explicit (but can be used with general contact in +Abaqus/Explicit). +Creating a combined surface +You must assign a name to the combined surface; this name can be used with other features that refer to +surfaces. +In models that are defined in terms of an assembly of part instances, all surfaces must belong to +a part, part instance, or the assembly. Surfaces can be created at the part level and combined at the +assembly level. Additional rules are given in “Defining an assembly,” Section 2.10.1. +The surfaces being combined must be the same type; i.e., an element-based surface can be combined +with another element-based surface but not with a node-based surface. Combined surfaces can be used +to create another combined surface. +Union of existing surfaces +Any number of existing surfaces can be combined to create a new surface. If the surfaces being combined +are element-based surfaces, the new surface will also be an element-based surface and any overlap among +the surfaces will be merged. Similarly, if the surfaces being combined are node-based surfaces, the new +surface will be a node-based surface and any overlap among the surfaces will be merged. +Input File Usage: +*SURFACE, NAME=name, COMBINE=UNION +list of surface names +Intersection or difference of existing surfaces +The intersection or difference of two existing surfaces can be used to create a new surface. The +difference operation subtracts the second surface from the first surface. When the intersection or +difference operations are performed on element-based surfaces, they act only on the facets. A warning +message is issued if the intersection operation results in an empty surface. +Input File Usage: +Use the following option to create a new surface based on the intersection of +two existing surfaces: +*SURFACE, NAME=name, COMBINE=INTERSECTION +first surface name, second surface name +Use the following option to create a new surface based on the difference of two +existing surfaces: +*SURFACE, NAME=name, COMBINE=DIFFERENCE +first surface name, second surface name +Creating a cropped surface +You can create a new surface that will contain only those faces of an existing surface that have nodes +inside a specified cropping box. For a node-based surface the new surface will contain only those nodes +that are enclosed inside the cropping box. If the face has at least one node inside the box, the entire face +is accepted as valid. You must assign a name to the new surface and specify the name of the existing +surface from which the new surface is to be generated. Only one surface can be specified. +To define the location of the box, specify the coordinates of the lower corner of the box ( +, +, +). The +cutting box can be rotated about the lower corner ( +) if an optional rotation is defined. +The coordinates of the two points, a and b, that define the rotation are given in the unrotated system. +) and the coordinates of the opposite (upper) corner of the box ( +, +, +, +, +These points should be defined such that point a lies on the rotated X-axis and point b lies on the X–Y +plane and close to the Y-axis. +Input File Usage: +*SURFACE, NAME=name, CROP +old_surface_name +, +, +, +, +, +, +, +, +, +, +For example, to crop the surface that contains all exposed faces in the model, +use the following input: +*SURFACE, TYPE=ELEMENT, NAME=entire_surface +, +*SURFACE, NAME=name, CROP +entire_surface +, +, +, +, +, +, +, +, +2.3.6–3 +, +2.4 +Rigid body definition +• “Rigid body definition,” Section 2.4.1 +2.4.1 +RIGID BODY DEFINITION +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Surfaces: overview,” Section 2.3.1 +• “Element-based surface definition,” Section 2.3.2 +• “Analytical rigid surface definition,” Section 2.3.4 +• “Rigid elements,” Section 30.3.1 +• *RIGID BODY +• “Defining rigid body constraints,” Section 15.15.2 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +A rigid body: +• can be two-dimensional planar, axisymmetric, or three-dimensional; +• is associated with a node, called the rigid body reference node, whose motion governs the motion +of the entire rigid body; +• can consist of nodes, elements, and surfaces; +• can act as a method of constraint; +• can be used with connector elements in multibody dynamic simulations; +• can be used to prescribe the motion of a rigid surface for contact modeling; +• can be computationally efficient and, in Abaqus/Explicit, does not affect the global time increment; +and +• can have temperature gradients or be isothermal in a fully coupled temperature-displacement +analysis where thermal interactions are considered. +What is a rigid body? +A rigid body is a collection of nodes, elements, and/or surfaces whose motion is governed by the motion +of a single node, called the rigid body reference node. The relative positions of the nodes and elements +that are part of the rigid body remain constant throughout a simulation. Therefore, the constituent +elements do not deform but can undergo large rigid body motions. The mass and inertia of a rigid body +can be calculated based on contributions from its elements or can be assigned specifically. Analytical +surfaces can also be made part of the rigid body, whereas any surfaces based on the nodes or elements +of a rigid body are associated automatically with the rigid body. +The motion of a rigid body can be prescribed by applying boundary conditions at the rigid body +reference node. Loads on a rigid body are generated from concentrated loads applied to nodes and +from distributed loads applied to elements that are part of the rigid body. Rigid bodies interact with the +remainder of the model in several ways. Rigid bodies can connect at the nodes to deformable elements, +and surfaces defined on rigid bodies can continue on these deformable elements, provided that compatible +element types are used. Rigid bodies can also be connected to other rigid bodies by connector elements +. Surfaces defined on rigid bodies can contact surfaces +defined on other bodies in the model. +Determining when to use a rigid body +Rigid bodies can be used to model very stiff components, either fixed or undergoing large motions. For +example, rigid bodies are ideally suited for modeling tooling (i.e., punch, die, drawbead, blank holder, +roller, etc.). They can also be used to model constraints between deformable components, and they +provide a convenient method of specifying certain contact interactions. Rigid bodies can be used with +connector elements to model a wide variety of multibody dynamic problems. +It may be useful to make parts of a model rigid for model verification purposes. For example, in +complex models elements far away from the particular region of interest could be included as part of a +rigid body, resulting in faster run times at the model development stage. When you are satisfied with the +model, you can remove the rigid body definitions and incorporate an accurate deformable finite element +representation throughout. +In multibody dynamic simulations rigid bodies are useful for many reasons. Although the motion +of the rigid body is governed by the six degrees of freedom at the reference node, rigid bodies allow +accurate representation of the geometry, mass, and rotary inertia of the rigid body. Furthermore, rigid +bodies provide accurate visualization and postprocessing of the model. +The principal advantage to representing portions of a model with rigid bodies rather than deformable +finite elements is computational efficiency. Element-level calculations are not performed for elements +that are part of a rigid body. Although some computational effort is required to update the motion of the +nodes of the rigid body and to assemble concentrated and distributed loads, the motion of the rigid body +is determined completely by a maximum of six degrees of freedom at the reference node. +Rigid bodies are particularly effective for modeling relatively stiff parts of a model +in +Abaqus/Explicit for which tracking waves and stress distributions are not important. Element stable +time increment estimates in the stiff region can result in a very small global time increment. Since rigid +bodies and elements that are part of a rigid body do not affect the global time increment, using a rigid +body instead of a deformable finite element representation in a stiff region can result in a much larger +global time increment, without significantly affecting the overall accuracy of the solution. +Creating a rigid body +You must assign a rigid body reference node to the rigid body. +Input File Usage: +Abaqus/CAE Usage: +*RIGID BODY, REF NODE=n +Interaction module: +Tools→Reference Point: select a point to act as a reference point +Create Constraint: Rigid body: Point: Edit: select reference point region +The rigid body reference node +A rigid body reference node has both translational and rotational degrees of freedom and must be defined +for every rigid body. If the reference node has not been assigned coordinates, Abaqus will assign it the +coordinates of the global origin by default. Alternatively, you can specify that the reference node should +be placed at the center of mass of the rigid body. In fully coupled temperature-displacement analysis +where a rigid body is considered as isothermal, a single temperature degree of freedom describing the +temperature of the rigid body exists at the rigid body reference node. The rigid body reference node: +• can be connected to mass, rotary inertia, capacitance, or deformable elements; +• cannot be a rigid body reference node for another rigid body; and +• can have a temperature degree of freedom if the body is an isothermal rigid body. +Positioning the reference node at the center of mass +The specific location of the rigid body reference node relative to the rest of the rigid body or to its center of +mass is important if nonzero boundary conditions are to be applied to the rigid body or concentrated loads +are to be applied at the reference node. In many problems of rigid body dynamics, it may be desirable +to apply loads and boundary conditions to the rigid body at its center of mass. In addition, it may be +useful to monitor the configuration of the rigid body at its center of mass for output purposes. However, +it may be difficult to locate the center of mass a priori when the rigid body mass and inertia properties +(discussed below) contain contributions from a finite element discretization or a complex arrangement +of MASS and ROTARYI elements. +By default, the rigid body reference node will not be repositioned. You can specify that it should +be repositioned at the calculated center of mass. In this case if a MASS element is defined at the rigid +body reference node, the calculated center of mass used for repositioning includes all mass contributions +except the mass at the reference node. The MASS element is then repositioned at the center of mass and +included in the mass properties of the rigid body. If the only mass contribution to the rigid body is from +a MASS element defined at the rigid body reference node, the reference node will not be repositioned. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to indicate that the reference node should not be +repositioned (the default): +*RIGID BODY, REF NODE=n, POSITION=INPUT +Use the following option to specify that the rigid body reference node should +be repositioned at the calculated center of mass: +*RIGID BODY, REF NODE=n, POSITION=CENTER OF MASS +Interaction module: Create Constraint: Rigid body: toggle Adjust +point to center of mass at start of analysis +The collection of nodes that constitute the rigid body +In addition to the rigid body reference node, rigid bodies consist of a collection of nodes that is generated +by assigning elements and nodes to the rigid body. These nodes provide a connection to other elements. +Nodes that are part of a rigid body are one of two types: +• pin nodes, which have only translational degrees of freedom associated with the rigid body, or +• tie nodes, which have both translational and rotational degrees of freedom associated with the rigid +body. +The rigid body node type is determined by the type of elements on the rigid body to which the node +is attached. You can also specify the node type when you assign nodes directly to a rigid body. For +pin nodes only the translational degrees of freedom are part of the rigid body, and the motion of these +degrees of freedom is constrained by the motion of the rigid body reference node. For tie nodes both +the translational and rotational degrees of freedom are part of the rigid body and are constrained by the +motion of the rigid body reference node. +The node type has important implications when the node is connected to rotary inertia elements, +deformable structural elements, or connector elements or when the node has concentrated moments or +follower loads applied to it. Rotary inertia elements and applied concentrated moments affect the rigid +body only when associated with a tie node. Rigid body connections to deformable elements always +involve the translational degrees of freedom; rigid body connections to deformable shell, beam, pipe, +and connector elements also involve the rotational degrees of freedom if the connection is at a tie node. +The behavior of the two types of connections is illustrated in Figure 2.4.1–1, which shows an octagonal +rigid body connected to two deformable shell elements through nodes at opposite ends subjected to an +applied rotational velocity. +tie node +pin node +initial configuration +Final configuration after counterclockwise rotation through 45 +Figure 2.4.1–1 Rigid body with tie node and pin node connections. +The shell elements are assumed to be stiff (negligible bending is shown in the figure). When the nodes +common to the rigid body and the shell elements are tie nodes, the rotation applied to the rigid body is +transmitted directly to the shell elements. When the common nodes are pin nodes, the rigid body rotation +is not transmitted directly to the shell elements, which can result in large relative motions between the +rigid body and the adjacent shell structure. +Assigning elements to a rigid body +To include elements in the rigid body definition, you specify the region of your model containing all of +the elements that are part of the rigid body. Elements in this region or nodes connected to the elements +in this region cannot be part of any other rigid body. Table 2.4.1–1 lists the continuum, structural, and +rigid element types that can be included in a rigid body and the respective node types generated in the +rigid body. +Table 2.4.1–1 List of valid elements that can be included in a rigid body +(* indicates all elements beginning with the preceding label). +Elements +Generate Pin Nodes Generate Tie Nodes +Nodal Degrees of +Freedom +Pin +Nodes +Tie +Nodes +B21*, B22*, B23*, +FRAME2D, PIPE2*, +RB2D2 +CGAX*, MGAX*, +SAX1, SAX2* +B31*, B32*, B33*, +FRAME3D, PIPE*, +RB3D2, S3*, S4*, S8*, +S9* +CPE3*, CPE4*, +CPE6*, CPE8*, CPS3, +CPS4*, CPS6*, CPS8*, +GK2D2, GKPS*, +GKPE*, R2D2, T2D2* +CAX3, CAX4*, +CAX6*, CAX8*, +GKAX*, MAX*, +RAX2 +C3D4*, C3D6*, +C3D8*, C3D10*, +C3D15*, C3D20*, +C3D27*, GK3D*, +M3D3, M3D4*, M3D6, +M3D8*, M3D9*, +SFM3D*, SFMAX*, +SFMGAX*, R3D3, +R3D4, T3D2*, CCL*, +MCL*, SFMCL* +2.4.1–5 +Rigid Body +Geometry +Planar +Axisymmetric +Three- +When connector elements are included in the rigid body, the type of generated nodes depends on +whether the rotational degrees of freedom are active for their connection type. If connector elements that +activate material flow degree of freedom at nodes are included in the rigid body, the material and flow +through the rigid body as that degree of freedom is constrained to the motion of the rigid body. +The following elements cannot be declared as rigid: +• Acoustic elements +• Axisymmetric-asymmetric continuum and shell elements +• Coupled thermal-electrical elements +• Diffusive heat transfer/mass diffusion elements and forced convection/diffusion elements +• Eulerian elements +• Generalized plane strain elements +• Gasket elements with thickness-direction behavior +• Heat capacitance elements +• Inertial elements (mass and rotary inertia) +• Infinite elements +• Piezoelectric elements +• Special-purpose elements +• Substructures +• Thermal-electrical-structural elements +• User-defined elements +If elements of more than one type or section definition are part of a rigid body, the specified region +will contain elements with different section definitions. When continuum or structural elements are +assigned to a rigid body, they are no longer deformable and their motion is governed by the motion +of the rigid body reference node. Element stiffness calculations are not performed for these elements, +and they do not affect the global time increment in Abaqus/Explicit. However, the mass and inertia of +the rigid body includes contributions from these elements as calculated from their section and material +density definitions . Mass and rotary inertia elements, as well as point heat +capacitance elements, should not be included in the specified region. Contributions to a rigid body from +mass, rotary inertia, and heat capacitance elements are accounted for automatically when these elements +are connected to nodes that are part of the rigid body. +A list of nodes that are part of a rigid body is generated automatically when you assign elements to +a rigid body. The node list is constructed as a unique list including all the nodes that are connected to +elements in the specified region. Nodes in this list cannot be part of any other rigid body. The type of each +node, pin or tie, is determined by the type of elements on the rigid body to which it is connected. Shell, +beam, pipe, and rigid beam elements generate tie nodes; solid, membrane, truss, and rigid (other than +beam) elements generate pin nodes . For nodes that are connected to both elements +that generate pin nodes and elements that generate tie nodes, the common node is defined as the tie type. +All elements that are part of a rigid body must be of like geometry. Therefore, elements contained +in the specified region must be either planar, axisymmetric, or three-dimensional. The geometry of the +elements determines the geometry of the rigid body as shown in Table 2.4.1–1. +Input File Usage: +Use the following option to assign elements to a rigid body: +Abaqus/CAE Usage: +*RIGID BODY, REF NODE=n, ELSET=name +Interaction module: Create Constraint: Rigid body: Body +(elements): Edit: select body regions +Assigning nodes to a rigid body +To assign nodes directly to a rigid body, you specify all the desired pin nodes and all the tie nodes +separately. These nodes become part of the rigid body in addition to any nodes that have been generated +from elements assigned to the rigid body. The following rules apply when assigning nodes directly to a +rigid body: +• The rigid body reference node cannot be contained in either the set of pin nodes or the set of tie +nodes. +• Nodes that are part of the set of pin nodes cannot also be contained in the set of tie nodes. +• Nodes that are contained in the set of pin nodes or the set of tie nodes cannot be part of any other +rigid body definition. +• Nodes that are generated automatically from elements assigned to the rigid body that are also +contained in the set of pin nodes are classified as pin nodes, regardless of their element connections. +• Nodes that are generated automatically from elements assigned to the rigid body that are also +contained in the set of tie nodes are classified as tie nodes, regardless of their element connections. +The types of nodes generated by elements included in a rigid body can, therefore, be overridden by +assigning the nodes directly to the rigid body, thereby allowing you greater flexibility to define a +constraint with a rigid body by easily specifying the type of connection the rigid body makes with its +attached deformable finite elements. +Input File Usage: +Use the following option to assign nodes to a rigid body: +Abaqus/CAE Usage: +*RIGID BODY, REF NODE=n, PIN NSET=name, TIE NSET=name +Interaction module: Create Constraint: Rigid body: Pin (nodes): Edit: +select pin regions, and Tie (nodes): Edit: select tie regions +Assigning analytical surfaces to a rigid body +You can assign an analytical surface to a rigid body. The procedure for creating and naming an analytical +rigid surface is described in “Analytical rigid surface definition,” Section 2.3.4. Only one analytical +surface can be defined as part of the rigid body definition. +Input File Usage: +Use the following option to assign an analytical rigid surface to a rigid body: +*RIGID BODY, REF NODE=n or name, ANALYTICAL SURFACE=name +Abaqus/CAE Usage: +Interaction module: Create Constraint: Rigid body: Analytical +Surface: Edit: select analytical surface regions +Defining a rigid body in a model that is defined in terms of an assembly of part instances +An Abaqus model can be defined in terms of an assembly of part instances . A rigid body in such a model can be created from deformable elements at either the part +level or the assembly level. In either case all node and element definitions must belong to one or more +parts. If all nodes making up the rigid body belong to the same part, create a rigid part by defining the +rigid body at the part level. +Multiple deformable part instances can be combined into a single rigid body by creating an +assembly-level node or element set that spans the part instances, then defining the rigid body at the +assembly level to refer to that set. The rigid body reference node can also be defined at the assembly +level, if necessary. +Rigid body mass and inertial properties +When a rigid body is not constrained fully, the mass and inertia properties of the rigid body are important +to its dynamic response. In Abaqus/Explicit an error message will be issued if there is no mass (or rotary +inertia) corresponding to an unconstrained degree of freedom. Abaqus automatically calculates the mass, +center of mass, and rotary inertia of each rigid body and prints the results to the data (.dat) file if model +definition data are requested . The following rules are used to determine the mass +and inertia of a rigid body: +• The mass of each continuum, structural, and rigid element that is part of the rigid body contributes +to the rigid body’s mass, center of mass, and rotary inertia properties. +• Point mass elements that are connected to any node that is part of a rigid body or to the rigid body +reference node contribute to the rigid body’s mass, center of mass, and rotary inertia properties. +• Rotary inertia elements that are connected to any tie node or to the rigid body reference node +contribute to the rigid body’s rotary inertia properties. +Since the rotational degrees of freedom at a pin node are not part of a rigid body, rotary inertia elements +connected to a pin node do not contribute to the rigid body inertia but are rather associated with the +independent rotation of the node. +Defining mass and inertia properties by discretization +In many cases it is desirable to model rigid components for which the mass, center of mass, and +rotary inertia are not readily available. +In Abaqus it is not necessary to define the mass and inertia +properties of the rigid body directly. Instead, a finite element discretization can be used to model the +rigid components, and Abaqus will automatically calculate the properties from the discretization. Rigid +structures with one-dimensional rod or beam geometries can be modeled with beam or truss elements, +structures containing two-dimensional surface geometries can be modeled with shell or membrane +elements, and solid geometries can be modeled with solid elements. The mass contributions to the rigid +body for each of these elements are based on that element’s section properties +and the material density . Although both shell and membrane elements +in a rigid body can yield similar mass contributions given similar section and density definitions, they +will generate different node types (tie nodes for shells and pin nodes for membranes), which may affect +the overall results. The same holds true for beam and truss elements. +In situations where one portion of a rigid component can be modeled with a finite element +discretization but it is not convenient to do so for other portions, point mass and rotary inertia elements +can be used to represent the mass distribution of these other portions. The mass, center of mass, and +rotary inertia for the rigid body will then include the contributions from both the finite elements and +the point mass and rotary inertia elements. +Abaqus uses the lumped mass formulation for low-order elements. As a consequence, the second +mass moments of inertia can deviate from the theoretical values, especially for coarse meshes. This +inaccuracy can be circumvented by adding point mass and rotary inertia elements with the correct inertia +properties and eliminating the mass contribution from the solid elements. Alternatively, second-order +elements could be used in Abaqus/Standard. +Defining mass and inertia properties directly +When the mass, center of mass, and rotary inertia properties of the actual rigid component are known +or can be approximated, it is not necessary to use a finite element discretization or to use an array of +point masses to generate the rigid body properties. You can assign these properties directly by locating +the rigid body reference node at the center of mass and by specifying the rigid body mass and rotary inertia at the reference node . +It may also be desirable to input mass properties directly at the center of mass but to specify boundary +In this case you should place the rigid body +conditions at a location other than the center of mass. +reference node at the desired boundary condition location. In addition, you must define a tie node at the +center of mass of the rigid body by correctly specifying its coordinates to coincide with the coordinates +of the center of mass of the rigid body and then assigning it to a tie node set in the rigid body definition. +You can then define the rigid body mass and rotary inertia at the tie node. +For most applications where mass properties are input directly, it may be necessary to assign +additional elements or nodes to a rigid body so that the rigid body can interact with the rest of the +model. For example, contact pair definitions could require rigid surfaces formed with element faces on +the rigid body and additional pin or tie nodes may be necessary to provide the desired constraints with +deformable elements attached to the rigid body. Abaqus will account for the mass and rotary inertia +contributions from all elements on a rigid body; therefore, if you want to assign the rigid body mass +properties directly, you should take care to ensure that contributions from other element types that are +part of the rigid body do not affect the desired input mass properties. If rigid elements are part of the +rigid body definition, you can set their mass contribution to zero by not specifying a density for these +elements in the rigid body definition. +If other element types are used to define the rigid body, you +should set their density to zero. +Kinematics of a rigid body +The motion of a rigid body is defined entirely by the motion of its reference node. The active degrees +of freedom at the reference node depend on the geometry of the rigid body . The geometry of a rigid body is planar, axisymmetric, or three-dimensional and is +determined by the type of elements that are assigned to the rigid body. In the case where no elements +are assigned to a rigid body, the geometry of the rigid body is assumed to be three-dimensional. +The calculated mass and rotary inertia properties for each of the active degrees of freedom for all +rigid bodies are printed to the data (.dat) file if model definition data are requested . +These properties include the contributions from elements that are part of the rigid body, as well as point +mass and rotary inertia elements at the nodes of the rigid body. +Although this calculated mass represents the true mass of the rigid body, Abaqus/Explicit actually +uses an augmented mass in the integration of the equation of motion, which is conceptually similar to an +added mass formulation. Essentially, the calculated mass and rotary inertia of the rigid body is augmented +with the mass contributions of all of its attached deformable elements to create a larger, augmented mass +and rotary inertia. Rotary inertia contributions from adjacent deformable elements are also included in +the augmented rotary inertia if the nodal connection is at a tie node. +Rigid body motions +A rigid body can undergo free rigid body motion in each of its active translational degrees of freedom, +as well as each of its active rotational degrees of freedom. +Boundary conditions +Boundary conditions for rigid bodies should be defined as described in “Boundary conditions in +Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1, at the rigid body reference node. Reaction +forces and moments can be recovered for all degrees of freedom that are constrained at the reference +node. If a nodal transformation is defined at the rigid body reference node, boundary conditions are +applied in the local system . +In Abaqus/Standard, if boundary conditions are applied to any nodes on a rigid body other than the +rigid body reference node, Abaqus will attempt to transfer these boundary conditions to the reference +node. If successful, you are warned that this transfer has taken place. Otherwise, an error message is +produced . +In Abaqus/Explicit, +if boundary conditions are applied to any nodes on a rigid body other +than the rigid body reference node, these boundary conditions are ignored with the exception of the +symmetry-type boundary conditions that can affect the contact logic at the perimeter of a surface in the +Abaqus/Explicit contact pair algorithm . +Constraints +In Abaqus/Standard nodes on a rigid body, excluding the rigid body reference node, cannot be used in a +multi-point constraint or linear constraint equation definition. +In Abaqus/Explicit a multi-point constraint or linear constraint equation can be defined for any node +on a rigid body, including the reference node. +Connector elements +Connector elements can be used at any node of a rigid body, including the reference node, to define a +connection between rigid bodies, between a rigid body and a deformable body, or from a rigid body to +ground. Connector elements are convenient for providing multiple points of attachment on rigid bodies; +modeling complex nonlinear kinematic constraints; specifying zero or nonzero boundary conditions at a +point on a rigid body that is not the rigid body reference node; applying force actuation; and modeling +discrete interactions, such as spring, dashpot, node-to-node contact, friction, locking mechanisms, and +failure joints. Unlike multi-point constraints or linear constraint equations, connector elements retain +degrees of freedom in the connection, thereby allowing output of information related to the connection +(such as constraint forces and moments, relative displacements, velocities, accelerations, etc.). See +“Connector elements,” Section 31.1.2, for a detailed description of connector elements. +Planar rigid body +A rigid body with a planar geometry has three active degrees of freedom: 1, 2, and 6 ( +, and +). Here, the x- and y-directions coincide with the global X- and Y-directions, respectively. If a nodal +transformation is defined at the rigid body reference node, the x- and y-directions coincide with the user- +defined local directions. The coordinate transformation defined at the reference node must be consistent +with the geometry; the local directions must remain in the global X–Y plane. All nodes and elements +that are part of a planar rigid body should lie in the global X–Y plane. +, +Planar rigid bodies should be connected only to planar deformable elements. To model the +connection of a rigid component with a planar geometry to three-dimensional deformable elements, +model the planar rigid component as a three-dimensional rigid body consisting of the appropriate +three-dimensional elements. +Axisymmetric rigid body +, +A rigid body with an axisymmetric geometry has three active degrees of freedom in Abaqus: 1, 2, and +6 ( +). Classical axisymmetric theory admits only one rigid body mode, which is displacement +in the z-direction. To maximize the flexibility of using rigid bodies for axisymmetric analysis, Abaqus +allows for three active degrees of freedom, although only the axial displacement is a rigid body mode. +, +The r- and z-directions coincide with the global X- and Y-directions, respectively. +If a nodal +transformation is defined at the rigid body reference node, the r- and z-directions coincide with the +user-defined local directions. The coordinate transformation defined at the reference node must be +consistent with the geometry; the local directions must remain in the global X–Y plane. All nodes and +elements that are part of an axisymmetric rigid body should lie in the global X–Y plane. +Translation in the r-direction is associated with a radial mode, and rotation in the r–z plane is +associated with a rotary mode . For an axisymmetric rigid body in Abaqus each +of these modes develop no hoop stress, but mass and inertia computed for these degrees of freedom +represent the modal mass associated with their modal motion. The mass properties for an axisymmetric +rigid body are, therefore, calculated based on the initial configuration assuming the following: +• Point masses defined on nodes of the rigid body are assumed +to account for the entire mass around the circumference of the body. +• Mass contributions from axisymmetric elements assigned to the rigid body include the integrated +value around the circumference. +• The center of mass of the rigid body is located at the center of mass of the circumferential slice, as +shown in Figure 2.4.1–2. +If the rigid body reference node is positioned at the center of mass, the reference node for an axisymmetric +rigid body will, thus, be repositioned at the center of mass of the circumferential slice. +These assumptions are consistent with the manner in which Abaqus handles other axisymmetric +features but are noted here because of the deviation from classical rigid body theory. +Axisymmetric rigid bodies should be connected only to axisymmetric deformable elements. To +model the connection of a rigid component with an axisymmetric geometry to three-dimensional +deformable elements, model the axisymmetric rigid component as a three-dimensional rigid body +consisting of the appropriate three-dimensional elements. +Three-dimensional rigid body +, +A rigid body with a three-dimensional geometry has six active degrees of freedom: 1, 2, 3, 4, 5, and +6 ( +). Here, the x-, y-, and z-directions coincide with the global X-, Y- and Z- +directions, respectively. If a nodal transformation is defined at the rigid body reference node, the x-, y-, +and z-directions coincide with the user-defined local directions. +, +, +, +, +In general, three-dimensional rigid bodies will possess a full, nonisotropic inertia tensor and can +behave in a nonintuitive manner when they are spun about an axis that is not one of the principal inertia +axes. Classical phenomena of rigid body dynamics (e.g., precession, gyroscopic moments, etc.) can be +simulated using three-dimensional rigid bodies in Abaqus. +In most cases three-dimensional rigid bodies should be connected only to three-dimensional +deformable elements. If it is physically relevant, a three-dimensional rigid body can be connected to +two-dimensional plane stress, plane strain, or axisymmetric elements; however, you should always +constrain the z-displacement, x-axis rotation, and y-axis rotation of the rigid body. The above procedure +is useful when incorporating a two-dimensional plane strain approximation in one region of a model +and a three-dimensional discretization in another. Rigid bodies can be used to constrain the two finite +element geometries at their interface as shown in Figure 2.4.1–3. A unique rigid body should be used at +each node in the plane along the interface to handle the constraint properly. +Defining loads on rigid bodies +Loads on a rigid body are assembled from contributions of all of the loads on nodes and elements that +are part of the rigid body. Loads are defined on nodes and elements that are part of a rigid body in the +original configuration +rigid body +center of mass +radial mode +rotary mode +Figure 2.4.1–2 Axisymmetric rigid body modes. +same manner that they are specified if the nodes and elements are not part of a rigid body. Contributions +include: +• applied concentrated forces on pin nodes, tie nodes, and the rigid body reference node; +• applied concentrated moments on tie nodes and the rigid body reference node; and +• applied distributed loads on all elements and surfaces that are part of the rigid body. +rigid body +3D mesh +2D mesh +rigid body +Figure 2.4.1–3 Rigid body nodes used to connect a +two-dimensional and three-dimensional mesh. +Unless the point of action is through the rigid body center of mass, each of these loads will create both +a force at and a torque about the center of mass, which will tend to rotate an unconstrained rigid body. +If a nodal transformation is defined at any rigid body nodes, concentrated loads defined at these nodes +are interpreted in the local system. The local system defined by the nodal transformation does not rotate +with the rigid body. +Concentrated moments defined on rigid body pin nodes do not contribute load to the rigid body +but are rather associated with the independent rotation of that node. Independent rotation of a pin node +exists only if it is connected to a deformable element with rotational degrees of freedom or a rotary +inertia element. Follower forces can be defined at pin nodes if the independent rotation exists. However, the results may +be nonintuitive since the direction of the force is determined by the independent rotation even though +the follower force acts on the rigid body. +Rigid bodies with temperature degrees of freedom +Only rigid bodies that contain coupled temperature-displacement elements have temperature degrees of +freedom. If it is reasonable to assume that a rigid body used in a fully coupled temperature-displacement +analysis has a uniform temperature, you can define the rigid body as isothermal. A transient heat transfer +process involving an isothermal rigid body assumes that the internal resistance of the body to heat is +negligible in comparison with the external resistance. Thus, the body temperature can be a function of +time but cannot be a function of position. The temperature degree of freedom that is created at the rigid +body reference node describes the temperature of the body. +Thermal +interactions for rigid bodies with analytical rigid surfaces are available only in +Abaqus/Explicit and are activated by specifying that the rigid body is isothermal. +By default, rigid bodies are not considered isothermal and all nodes on a rigid body connected to +coupled temperature-displacement elements will have independent temperature degrees of freedom. The +fact that the nodes are part of a rigid body does not affect the ability of the coupled elements to conduct +heat within the rigid body. However, the mechanical response will be rigid. +The lumped heat capacitance associated with the rigid body reference node of an isothermal body +is calculated automatically if the rigid body is composed of coupled temperature-displacement elements +for which a specific heat and a density property are defined. Otherwise, you should specify a point +heat capacitance for the rigid body . An error message will be +issued in Abaqus/Explicit if no heat capacitance is associated with an isothermal rigid body for which +temperature is not prescribed at the reference node. +• The capacitance of each coupled temperature-displacement element that is part of the rigid body +contributes to the isothermal rigid body’s capacitance. For an axisymmetric isothermal rigid body, +capacitance contributions from axisymmetric elements assigned to the rigid body include the +integrated value around the circumference. +• HEATCAP elements that are connected to any node that is part of a rigid body or the rigid +body reference node contribute to the isothermal rigid body’s capacitance. For an axisymmetric +isothermal rigid body the point capacitances defined on nodes of the rigid body are assumed to +account for the capacitance integrated around the circumference of the body. +Thermal loads acting on the reference node of an isothermal body are assembled from contributions +of all the thermal loads on nodes and elements that are part of the rigid body. Heat transfer between +a deformable body and an isothermal rigid body can occur during contact, as well as when the bodies +are not in contact if gap conductance and gap radiation are defined . Heat transfer between two isothermal rigid bodies can occur only via gap conduction +and gap radiation. +Input File Usage: +Abaqus/CAE Usage: +*RIGID BODY, ISOTHERMAL=YES +Interaction module: Create Constraint: Rigid body: toggle on +Constrain selected regions to be isothermal +Modeling contact with a rigid body +Contact with a rigid body is modeled by specifying a contact interaction formed with a rigid surface +and with a surface defined on another body . A rigid surface can be formed by nodes, element +faces, or an analytical surface . +Contact modeling can be a primary factor when choosing the appropriate rigid body geometry. +Contact interactions should be formed with surfaces of like geometry. For example, a planar rigid +body should be used to model contact either with deformable surfaces formed by two-dimensional plane +stress or plane strain elements or via node-based surfaces with two-dimensional beam, pipe, or truss +elements. Similarly, an axisymmetric rigid body should be used to model contact with surfaces formed by +axisymmetric elements, and a three-dimensional rigid body should be used to model contact either with +surfaces formed by three-dimensional element faces or via node-based surfaces with three-dimensional +beam, pipe, or truss elements. +A rigid body must contain only two-dimensional or only three-dimensional elements. Nodes +cannot be shared between two rigid bodies. Contact between two analytical rigid surfaces or between +an analytical rigid surface and itself cannot be modeled. +Limitations in Abaqus/Standard +Contact between rigid bodies is allowed if the slave surface belongs to an elastic body that has been +declared as rigid. In this case softened contact should be prescribed to avoid possible overconstraints. +Contact between two rigid surfaces defined using rigid elements is not allowed. +Rigid beams and trusses cannot be included in a contact pair definition because surfaces from beams +and trusses can be node-based surfaces only. A node-based surface must be a slave surface, and elements +that are part of a rigid body should be part of the master surface in a contact pair. +Limitations in Abaqus/Explicit +Contact between two rigid surfaces can be modeled in Abaqus/Explicit only if the penalty contact pair +algorithm or the general contact algorithm is used; kinematic contact pairs cannot be used for rigid- +to-rigid contact. Therefore, when converting two deformable regions of a model to two distinct rigid +bodies for the purpose of model development, any contact interaction definitions between these rigid +bodies must use penalty contact pairs or general contact. +For rigid-to-rigid contact involving analytical rigid surfaces, at least one of the rigid surfaces must +be formed by element faces since contact between two analytical rigid surfaces cannot be modeled in +Abaqus. +The penalty contact pair algorithm, which introduces numerical softening to the contact +enforcement through the use of penalty springs, or the general contact algorithm must be used for all +contact interactions involving a rigid body if an equation constraint, a multi-point constraint, a tie +constraint, or a connector element is defined for a node on the rigid body. +Rigid beams and trusses cannot be included in a kinematic contact pair definition because surfaces +from beams and trusses can be node-based surfaces only. A node-based surface must be a slave surface, +and elements that are part of a rigid body must be part of the master surface in a kinematic contact pair. +When a rigid surface acts as a slave surface in a penalty contact pair or in general contact, initial +penetrations of the rigid slave nodes into the master surface will not be corrected with strain-free +corrections . For contact pairs any initial penetrations of this type may cause +artificially large contact forces in the initial increments. For general contact these initial penetrations +are stored as contact offsets. +Using rigid bodies in geometrically linear Abaqus/Standard analysis +If rigid bodies are used in a geometrically linear Abaqus/Standard analysis , the rigid body constraints are linearized. Consequently, except +for analytical rigid surfaces, the distance between any two nodes belonging to the rigid body may not +remain constant during the analysis if the magnitudes of the rotations are not small. +2.5 +Integrated output section definition +• “Integrated output section definition,” Section 2.5.1 +2.5.1 +INTEGRATED OUTPUT SECTION DEFINITION +Products: Abaqus/Explicit Abaqus/CAE +References +• “Output to the output database,” Section 4.1.3 +• *INTEGRATED OUTPUT SECTION +• *INTEGRATED OUTPUT +• *SURFACE +• “Defining integrated output sections,” Section 14.13.1 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +An integrated output section: +• can be two-dimensional or three-dimensional; +• can be used to track the average motion of a surface; +• can be used in association with integrated output requests to study the “force-flow” in the model; +and +• does not impose any constraint on the motion of the surface. +Introduction +An integrated output section is a way to associate a surface with a coordinate system and/or a reference +node for one or both of the following purposes: +• tracking the average motion of the surface; and/or +• expressing the force and the moment transmitted through the surface in a local coordinate system, +with the moment taken about a point that moves with the surface. +The average motion of a surface can be obtained as the displacement and/or rotation history at the +reference node on an integrated output section definition. You must define a reference node that is not +connected to any other part of the finite element model and select whether the reference node follows +only the average translation of the surface or both the translation and the rotation. Since the reference +node is not connected to the rest of the model, an integrated output section definition used to track the +average surface motion does not form a constraint on the motion of any nodes in the model. +The “force-flow” in a complicated model can be studied using integrated output sections defined +over a number of interior cross-section-like surfaces cutting through various parts of the model. It can +be equally useful to sum forces over an exterior surface in contact or to sum forces transmitted through +a tie constraint between surfaces, which is done by associating an integrated output section definition +with an integrated output request. The vector output quantities can be expressed in a coordinate system +of choice by specifying an orientation on an integrated output section definition. This coordinate system +can rotate by an amount given by the rotational degrees of freedom at the reference node. In addition, +the output of the integrated moment across the surface can be taken about a location that can translate by +an amount given by the translational degrees of freedom at the reference node. Integrated output over +a given surface can be requested with different coordinate systems and reference nodes by employing +multiple integrated output section definitions over the same surface. +Creating an integrated output section +You must assign a name to each integrated output section. This name is used to associate the section +with an integrated output request. In addition, you must identify the surface over which the section is +being defined . +Input File Usage: +*INTEGRATED OUTPUT SECTION, NAME=section_name, +SURFACE=surface_name +Abaqus/CAE Usage: +Step module: Output→Integrated Output Sections→Create: +Name: section_name: select surface region +Creating interior cross-section surfaces +To study the “force-flow” through various paths in a model, you must create interior surfaces that cut +through one or more regions (similar to a cross-section) so that you can request integrated output of the +total force and moment transmitted across these surfaces. You can create such interior surfaces over the +element facets, edges, or ends by simply cutting through one or more regions of the model with a plane; +see “Creating interior cross-section surfaces” in “Element-based surface definition,” Section 2.3.2, for +more information. +The integrated output section reference node +A reference node can be associated with an integrated output section for one or both of the following +purposes: +• tracking the average motion of the surface; and/or +• computing the variables from an integrated output request in a coordinate system that moves with +the motion of the reference node. +If the average surface motion must be tracked, you must define a reference node that is not connected to +any other part of the finite element model and select whether the reference node follows only the average +translation of the surface or both the translation and the rotation. The rotational degrees of freedom will +be activated in addition to the translational degrees of freedom at the reference node if it is selected to +follow the average rotation of the surface. Further, the initial position of the reference node may be +adjusted to lie at the center of the surface automatically. +When an integrated output section with a reference node is associated with an integrated output +request, the total moment transmitted through the section is computed with respect to the current location +of the reference node. If the reference node has active rotational degrees of freedom, the coordinate +system used to express the integrated output variables rotates with the rotation of the reference node. +Positioning the reference node at the center of the surface +The reference node can be repositioned automatically at the center of the surface in the initial +configuration when the reference node is not connected to the rest of the model. +The default is to leave the reference node in its specified position. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to position the reference node at the center of the +surface: +*INTEGRATED OUTPUT SECTION, REF NODE=n, POSITION=CENTER +Step module: integrated output section editor: Anchor at reference point: +Edit: select reference point: Move point to center of surface +Setting the reference node to track the average motion of the surface +It is often meaningful to obtain integrated output over a surface using a coordinate system and a point +that moves with the average surface motion. When the reference node is not connected to the rest of the +model, it can be specified to translate with the average translation of the surface without any rotation or +to both translate and rotate with the average motion of the surface. The average motion is based on the +mass weighted motion of the individual nodes that are on the surface and are not part of any rigid body. +By default, the reference node does not track the average motion of the surface. +Input File Usage: +Abaqus/CAE Usage: +Use the following option if the reference node must translate with the average +translation of the surface: +*INTEGRATED OUTPUT SECTION, REF NODE=n, +REF NODE MOTION=AVERAGE TRANSLATION +Use the following option if the reference node must both translate and rotate +with the average translation of the surface: +*INTEGRATED OUTPUT SECTION, REF NODE=n, +REF NODE MOTION=AVERAGE +Step module: integrated output section editor: Anchor at reference +point: Edit: select reference point: Point motion: Average translation +and rotation or Average translation +The integrated output section local coordinate system +You can define a local coordinate system on an integrated output section and associate the section with an +integrated output request to express the integrated output variables in the local coordinate system. You +can specify an orientation as the local coordinate system and, possibly, further project it onto the surface. +Alternatively, you can form a local coordinate system by projecting the global coordinate system onto +the surface following the Abaqus conventions . If a local system is +not defined explicitly, the local system is initialized to the global coordinate system. +The initial coordinate system, whether explicitly defined or initialized to the global coordinate +system, will rotate with the deformation if a reference node is specified and that reference node has +active rotational degrees of freedom. If the reference node is not connected to the rest of the model +and its motion is based on both the average translation and rotation of the surface, the rotational and +translational degrees of freedom are activated at the reference node. +Input File Usage: +Use the following option to define the initial coordinate system for the section: +Abaqus/CAE Usage: +*INTEGRATED OUTPUT SECTION, ORIENTATION=orientation_name +Step module: integrated output section editor: CSYS: Edit: select orientation +Projecting the coordinate system onto the section surface +Either the coordinate system defined by the specified orientation or the global coordinate system can +be projected onto the section surface to obtain a local coordinate system. Projection onto the surface is +based on the average normal of the surface; the local 1-direction is formed perpendicular to the surface +. +Input File Usage: +Use the following option to project the coordinate system onto the section +surface: +Abaqus/CAE Usage: +*INTEGRATED OUTPUT SECTION, PROJECT ORIENTATION=YES +Step module: integrated output section editor: Project +orientation onto surface +defined section +anchor point +anchor point +elements used to +define the section +defined section +2-D and axisymmetric +3-D +Figure 2.5.1–1 User-defined local coordinate system. +Associating an integrated output section with an integrated output request +An integrated output request is used to obtain history output of variables such as total force transmitted +across a surface . Such a request may refer to an integrated output section definition to identify the surface +where output is needed and to provide a local coordinate system and/or a reference node as a point +about which the total moment across the surface is computed. +Input File Usage: +Use both of the following options to associate an integrated output section with +an integrated output request: +Abaqus/CAE Usage: +*INTEGRATED OUTPUT SECTION, NAME=section_name +*INTEGRATED OUTPUT, SECTION=section_name +Step module: +Output→Integrated Output Sections→Create: Name: section_name +History output request editor: Domain: Integrated output +section: section_name +Limitations +Integrated output sections are subject to the following limitations: +• The surface associated with an integrated output section cannot be an analytical rigid surface. +• The surface associated with an integrated output section can contain facets over rigid or +axisymmetric elements. However, such an integrated output section cannot be associated with an +integrated output request . +2.6 +Mass adjustment +• “Adjust and/or redistribute mass of an element set,” Section 2.6.1 +ADJUST AND/OR REDISTRIBUTE MASS OF AN ELEMENT SET +MASS ADJUST +Product: Abaqus/Explicit +References +• “Density,” Section 21.2.1 +• “Point masses,” Section 30.1.1 +• “Nonstructural mass definition,” Section 2.7.1 +• “Mass scaling,” Section 11.6.1 +• *MASS ADJUST +Overview +Mass adjustment: +• is useful to set the net mass of one or more components in the model to a known value; +• is useful to account for any errors in mass due to modeling approximations; +• is useful to account for mass from nonstructural features otherwise omitted from the model, such +as paint; +• can be applied over all element types that have mass; +• adjusts the mass of the individual elements in an element set in proportion to their pre-adjusted mass +including any nonstructural mass, so as to meet the specified target value for the set; +• can be used to redistribute mass among elements in the set to raise the minimum stable time +increment to a target value; +• can be specified only once in an Abaqus/Explicit analysis during the model definition; and +• can be applied in a hierarchical fashion to adjust the mass for individual parts first and then for an +assembly of these parts. +Adjusting the total mass of an element set to a known value +The mass of a component in a numerical model may differ from its actual value for a number of reasons +including modeling approximations and omission of minor features from the model. You can specify +mass adjustment in the numerical model for such components by identifying the element sets defining +these components and their respective total mass values. For a given element set, the mass is adjusted +at the start of the analysis such that the adjustment in each element in that set is in proportion to the pre- +adjusted mass of that element, thus preserving the center of mass and the principal directions of the rotary +inertia. The pre-adjusted mass of an element includes the mass due to any associated material density; +any mass directly specified on the section definition as in the case of beam, pipe, shell, membrane, rigid, +and surface elements; and any nonstructural mass applied directly to that element. “Knee bolster impact +with general contact,” Section 2.1.9 of the Abaqus Example Problems Manual, is an example of setting +the total mass of an element set using mass adjustment. +When mass is adjusted for an element with active rotational degrees of freedom, the rotary inertia +contribution from that element is also modified proportionally to correspond with the scaling in the +element mass from mass adjustment, thus preserving the principal directions of the rotary inertia. The +adjusted mass value is considered when calculating the stable time increment of an element. Loads such +as mass proportional damping and gravity take the adjusted +mass into account. +Mass adjustment can be applied in a hierarchical fashion to adjust the mass for individual parts first +and then for an assembly of these parts. In this scenario, the mass adjustment defined over the assembly +may further modify the adjusted mass of the individual parts. You must associate all of the mass-adjusted +element sets in the desired order with a single mass adjustment definition. +Abaqus/Explicit automatically calculates the mass, center of mass, and rotary inertia of each +element set and prints the results to the data (.dat) file if model definition data are requested . The contributions from mass adjustment are also listed in these tables. +Redistribution of mass to raise the minimum stable time increment to a target value +You can increase the minimum stable time increment in the initial configuration for an element set to +a specified target value by redistributing mass among the elements in that set. The redistribution of +mass to affect the stable time increment and adjustment of mass to achieve a target total mass can be +requested independently of each other. If both options are requested for a given element set, the mass +is first adjusted to meet the target total mass for the set and then redistributed among the elements to +achieve the target time increment. +You can set a default target time increment that is applicable for all of the mass-adjusted element sets +as well as specific targets for any of the individual element sets. Within each set, the mass is transferred to +the elements with time increments below the target value from the remaining elements. Abaqus/Explicit +prints the amount of mass available for redistribution along with the percentage of this amount that is +redistributed to the data (.dat) file if model definition data are requested . If a sufficient +amount of mass is not available to meet the specified target time increment, the analysis terminates with +an error message. “Impact of a water-filled bottle,” Section 2.3.2 of the Abaqus Example Problems +Manual, is an example of maintaining the target stable time increment of an element set using mass +adjustment. +When compared to the fixed mass scaling functionality, the redistribution feature above does not +alter the total mass of the set. However, both features affect the center of mass and the principal directions +of rotary inertia. The redistribution feature is performed only in the initial configuration at the start of +the analysis; whereas the fixed mass scaling is performed in the configuration at the start of the step +requesting that mass scaling. When you specify mass adjustment and mass scaling, the mass scaling +adds mass as necessary on top of the adjusted mass. +Defining mass adjustment +To adjust the total mass of one or more components in the model, you first identify the corresponding +element sets. If you specify multiple elements sets, the mass is adjusted in the order in which the element +sets are specified. For element sets that share elements, you must determine the order in which to specify +the element sets to obtain the desired results. +Defining total mass for an element set without altering its center of mass +You must specify the total mass for each mass-adjusted element set. +*MASS ADJUST +element_set_name, element_set_mass +Input File Usage: +Defining mass redistribution to raise the time increment +You can redistribute the mass of an element set to achieve a target time increment and specify the total +mass for each mass-adjusted element set, or you can redistribute the mass without changing the existing +total mass of the element set. You can set a default target time increment that is applicable for all of the +mass-adjusted sets as well as specific targets for any of the individual sets. When both a default target +and a specific target are specified, the specific target is used for that set. +Input File Usage: +Use the following option to raise the time increment and specify the total mass: +*MASS ADJUST, TARGET DT=min_stable_time_increment +element_set_name, element_set_mass, +element_set_min_stable_time_increment +Use the following option to raise the time increment without altering the total +mass: +*MASS ADJUST, TARGET DT=min_stable_time_increment +element_set_name, CURRENT, element_set_min_stable_time_increment +2.7 +Nonstructural mass definition +• “Nonstructural mass definition,” Section 2.7.1 +2.7.1 +NONSTRUCTURAL MASS DEFINITION +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Point masses,” Section 30.1.1 +• “Density,” Section 21.2.1 +• “Adjust and/or redistribute mass of an element set,” Section 2.6.1 +• *NONSTRUCTURAL MASS +• “Defining nonstructural mass,” Section 33.4 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +A nonstructural mass: +• is a contribution to the model mass from features that have negligible structural stiffness (such as +paint on sheet metal panels in a car); +• can be used to bring the net mass of one or more components in the model up to a known value; +• can be positive to add mass to the model and negative to remove mass from the model, with the +corresponding increase or decrease in the element stable time increment in an Abaqus/Explicit +analysis; +• can be specified in the form of a total mass of the nonstructural features to be distributed over one +or more components in the model; +• can be specified in the form of an increase in density over the smeared region; +• can be specified in the form of mass per unit area to be applied over a smeared region consisting of +shells, membranes, and/or surface elements; and +• can be specified in the form of mass per unit length to be applied over a smeared region consisting +of beam, pipe, and/or truss elements. +Nonstructural mass +The mass contribution from nonstructural features can be included in the model even if the features +themselves are omitted. The nonstructural mass is smeared over an element set that is typically adjacent +to the nonstructural feature. This element set can contain solid, shell, membrane, surface, beam, pipe, or +truss elements. The nonstructural mass can be specified in the following forms: +• a total mass value, +• a mass per unit volume, +• a mass per unit area (for element sets that contain conventional shell, membrane, and/or surface +elements), or +• a mass per unit length (for element sets that contain beam, pipe, and/or truss elements). +When a total mass is spread over an element set region, it can be distributed either in proportion to the +underlying element “structural” mass or in proportion to the element volume in the initial configuration. +A “structural” mass is defined as the sum of all the mass contributions to an element outside of +the nonstructural features. This may include the mass due to any material definitions associated with +the element; any “mass per unit area” given on the section definition for shell, membrane, and surface +elements; mass from any rebars included in shell, membrane, and surface elements; and any additional +inertia given on the section definition of beam/pipe elements. A nonstructural mass contribution to an +element is not allowed if that element has no structural mass. +A given element +in the model can have contributions from multiple nonstructural mass +specifications. The nonstructural mass in a given element will participate in any mass proportional +distributed loads, such as gravity loading, defined on that element. When a nonstructural mass is +added to a shell, beam, or pipe element with active rotational degrees of freedom, the nonstructural +contribution affects both the element mass and the element rotary inertia. The element stable time +increment increases with a positive nonstructural mass and decreases with a negative nonstructural +mass. In general, it is easier to use a nonstructural mass definition to bring an additional mass into the +model than to do the same with a group of point masses. It is also more beneficial in an Abaqus/Explicit +analysis due to a possibly higher time increment. +Any mass proportional damping specified as part of the material definition will also apply to the nonstructural mass contribution assigned to the element or element +set using that material definition. +Defining nonstructural mass +To define a nonstructural mass contribution to the model mass, you must first identify the region over +which the contribution must be added. You then specify the value of the nonstructural mass using the +appropriate units and, if the total mass from the nonstructural features is known, determine how the +nonstructural mass is distributed over the region. +Input File Usage: +Abaqus/CAE Usage: +*NONSTRUCTURAL MASS, ELSET=element_set_name +Property or Interaction module: Special→Inertia→Create: +Nonstructural mass: select region +Specifying the units of the nonstructural mass +The nonstructural mass can be specified in different types of units, depending on the types of elements +contained in the specified region. +Specifying units of mass +A total nonstructural mass with units of “mass” can be spread over a region containing solid, shell, +membrane, beam, pipe, and/or truss elements. +Input File Usage: +*NONSTRUCTURAL MASS, UNITS=TOTAL MASS +total mass of the nonstructural feature +Abaqus/CAE Usage: +Property or Interaction module: Special→Inertia→Create: +Nonstructural mass: select region: Units: Total Mass: Magnitude: +total mass of the nonstructural feature +Specifying units of mass per unit volume +A nonstructural mass with units of “mass per unit volume” can be spread over a region containing solid, +shell, membrane, beam, pipe, and/or truss elements. +Input File Usage: +*NONSTRUCTURAL MASS, UNITS=MASS PER VOLUME +added density due to the nonstructural feature +Abaqus/CAE Usage: +Property or Interaction module: Special→Inertia→Create: Nonstructural +mass: select region: Units: Mass per Volume: Magnitude: added +density due to the nonstructural feature +Specifying units of mass per unit area +A nonstructural mass with units of “mass per unit area” can be spread over a region containing +conventional shells, membranes, and/or surface elements. +Input File Usage: +*NONSTRUCTURAL MASS, UNITS=MASS PER AREA +added mass per unit area due to the nonstructural feature +Abaqus/CAE Usage: +Property or Interaction module: Special→Inertia→Create: Nonstructural +mass: select region: Units: Mass per Area: Magnitude: added +mass per unit area due to the nonstructural feature +Specifying units of mass per unit length +A nonstructural mass with units of “mass per unit length” can be spread over a region containing beam, +pipe, and/or truss elements. +Input File Usage: +*NONSTRUCTURAL MASS, UNITS=MASS PER LENGTH +added mass per unit length due to the nonstructural feature +Abaqus/CAE Usage: +Property or Interaction module: Special→Inertia→Create: Nonstructural +mass: select region: Units: Mass per Length: Magnitude: added +mass per unit length due to the nonstructural feature +Controlling the distribution of the total mass from nonstructural features +There are two methods available for distributing the nonstructural mass over the region when the total +mass from the nonstructural features is known. +Distributing the nonstructural mass in proportion to the element structural mass +If you do not want to change the center of mass for the region, distribute the nonstructural mass in +proportion to the element structural mass. This method results in a uniform scaling of the structural +density of the region. Abaqus uses mass proportional distribution by default. +The element structural mass in shell, membrane, and surface elements includes any mass +the rebar are defined as a rebar layer . +Input File Usage: +*NONSTRUCTURAL MASS, UNITS=TOTAL MASS, +DISTRIBUTION=MASS PROPORTIONAL +total mass of the nonstructural feature +Abaqus/CAE Usage: +Property or Interaction module: Special→Inertia→Create: Nonstructural +mass: select region: Units: Total Mass: Magnitude: total mass of the +nonstructural feature: Distribution: Mass Proportional +Distributing the nonstructural mass in proportion to the element volume +Alternatively, you can distribute the nonstructural mass in proportion to the element volume in the initial +configuration. This method results in a uniform value added to the underlying structural density over +the region. Therefore, the center of mass for the region may be altered if the region has nonuniform +structural density. +Input File Usage: +*NONSTRUCTURAL MASS, UNITS=TOTAL MASS, +DISTRIBUTION=VOLUME PROPORTIONAL +total mass of the nonstructural feature +Abaqus/CAE Usage: +Property or Interaction module: Special→Inertia→Create: Nonstructural +mass: select region: Units: Total Mass: Magnitude: total mass of the +nonstructural feature: Distribution: Volume Proportional +2.8 +Distribution definition +• “Distribution definition,” Section 2.8.1 +2.8.1 +DISTRIBUTION DEFINITION +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD Abaqus/CAE +References +• “Orientations,” Section 2.2.5 +• “Material library: overview,” Section 21.1.1 +• “Material data definition,” Section 21.1.2 +• “Combining material behaviors,” Section 21.1.3 +• “Density,” Section 21.2.1 +• “Linear elastic behavior,” Section 22.2.1 +• “Thermal expansion,” Section 26.1.2 +• “Solid (continuum) elements,” Section 28.1.1 +• “Membrane elements,” Section 29.1.1 +• “Using a shell section integrated during the analysis to define the section behavior,” Section 29.6.5 +• “Using a general shell section to define the section behavior,” Section 29.6.6 +• “Connectors: overview,” Section 31.1.1 +• “Controlling initial contact status for general contact in Abaqus/Explicit,” Section 35.4.4 +• “Boundary conditions in Abaqus/CFD,” Section 33.3.2 +• *DISTRIBUTION +• *DISTRIBUTION TABLE +• Chapter 63, “The Discrete Field toolset,” of the Abaqus/CAE User’s Manual +Overview +A distribution: +• is a spatially varying field defined over elements or nodes in an Abaqus model; +• can be used to define shell thicknesses on an element-by-element basis; +• can be used to define shell stiffness on an element-by-element basis; +• can be used to define local coordinate systems on solid continuum and shell elements on an element- +by-element basis; +• can be used to define orientation angles on the layers of composite shell elements; +• can be used to define orientation angles for connector elements; +• can be used to define thicknesses on the layers of conventional composite shell elements; +• can be used to specify initial contact clearances; +• can be used to specify pressure that varies with the total volume of fluid crossing a surface in an +Abaqus/CFD analysis; and +• in an Abaqus/Standard analysis can be used to define mass density, linear elastic material behavior, +and thermal expansion for solid continuum elements; shell offsets; orientation angles on the layers +of composite solid continuum elements; local coordinate systems on membrane elements; and +membrane thickness on an element-by-element basis. +Distributions +A distribution is a spatial analogy of an amplitude definition . +Amplitude definitions are used to provide arbitrary time variations of loads, displacements, and other +prescribed variables. Distributions are used to specify arbitrary spatial variations of selected element +properties, material properties, +local coordinate systems, and spatial variations of initial contact +clearances. +The two main components of a distribution are its location and field data. The location identifies +where the distribution is defined, either on elements or nodes. Field data are a specified number of +floating point values defined for each element or node in the distribution. +To define a distribution, you must assign it a unique name. You must also specify the number and +physical dimension of each data value in the distribution by referring to a distribution table. +Input File Usage: +Abaqus/CAE Usage: +*DISTRIBUTION, NAME=name, TABLE=distribution table name +Abaqus/CAE supports distributions using discrete fields. +Property, Interaction, or Load module: Tools→Discrete Field→Create +Specifying the location of a distribution +You can define a distribution on elements or nodes. Currently distributions on nodes are supported +only for defining initial contact clearances as described in “Controlling initial contact status for general +contact in Abaqus/Explicit,” Section 35.4.4. For a distribution used with fluid boundary definitions in +Abaqus/CFD, you specify that no location is required. All other applications of distributions require +distributions defined on elements. +There is no limit on the number of distributions to which a given element or node may belong. +Elements and nodes cannot be combined within the same distribution definition. +Defining a distribution on elements +Defining a distribution on elements requires you to specify field data for each element or element set +included in the distribution definition. All distributions on elements require that default data be defined. +Default data are used for all elements that are not specifically assigned a value in the distribution. +*DISTRIBUTION, LOCATION=ELEMENT +blank space, field data +element set or element number, field data +Input File Usage: +Default data are defined by using a blank space instead of an element number or +element set for the first data item on the first data line of a distribution definition. +Only one set of default data can be defined for a distribution. If you specify only +default data, all elements that reference that distribution use the default values. +If an element is specified more than once in a given distribution definition, the +last specification given is used. +Abaqus/CAE Usage: +Property, Interaction, or Load module: Tools→Discrete +Field→Create: Definition: Elements +Defining a distribution on nodes +Defining a distribution on nodes requires you to specify field data for each node or node set included in +the distribution definition. +Input File Usage: +*DISTRIBUTION, LOCATION=NODE +node set or node number, field data +If a node is specified more than once in a given distribution definition, the last +specification given is used. +Abaqus/CAE Usage: +Defining a distribution on nodes for initial contact clearances is not supported +in Abaqus/CAE. +Defining a distribution used in Abaqus/CFD +For a distribution used to define fluid boundary conditions for pressure that varies with the total volume +of fluid crossing a surface, you specify field data and that no location is required. +Input File Usage: +*DISTRIBUTION, LOCATION=NONE +field data, field data +Abaqus/CAE Usage: +Defining a distribution used in Abaqus/CFD is not supported in Abaqus/CAE. +Defining a distribution table +Every distribution definition must refer to a distribution table. A distribution table defines the number of +field data items needed for each element or node in a distribution. The distribution table also defines the +physical dimension of each data value in a distribution. A distribution table can be referred to as many +times as needed by different distributions. The distribution table consists of a list of predefined labels +shown in Table 2.8.1–1 and Table 2.8.1–2. The combination of labels needed for a given distribution is +determined by how the distribution is applied. +Input File Usage: +Use the following option to define a distribution table: +*DISTRIBUTION TABLE, NAME=distribution table name +list of distribution table labels +Abaqus/CAE Usage: +Abaqus/CAE creates a distribution table when you specify a distribution by +selecting a discrete field. +Defining a distribution table used in Abaqus/CFD is not supported in +Abaqus/CAE. +Table 2.8.1–1 Distribution table labels—Abaqus/Standard and Abaqus/Explicit. +Data label +Physical dimension +Number of data +items per label +ANGLE +COORD3D +DENSITY +EXPANSION +LENGTH +MODULUS +RATIO +SHELLSTIFF1 +SHELLSTIFF2 +SHELLSTIFF3 +angle in degrees +(L, L, L) +ML−3 +−1 +FL−2 +dimensionless +FL-1 +FL +Table 2.8.1–2 Distribution table labels—Abaqus/CFD. +Data label +Physical dimension +PRESSURE +VOLUME +FL−2 +L3 +Number of data +items per label +Applying distributions +The data defined in a distribution are not used in an Abaqus analysis unless the distribution is referred +to by name by a feature that supports distributions, and the distribution is applied only to the elements +or nodes that are associated with the referenced feature. In addition, a distribution definition can be +referenced more than one time in a given model. These points are illustrated in the examples below. +Examples +The simple examples below illustrate how distributions are defined. A large number of illustrative +example problems using distributions can be found in “Spatially varying element properties,” +Section 5.1.4 of the Abaqus Verification Manual. +Example 1 +A distribution for shell thickness is defined and applied to two different shell section definitions through +the SHELL THICKNESS parameter—as noted above the distribution dist0 would not be used if it is +not referred to by a feature that supports distributions. See “Using a shell section integrated during the +analysis to define the section behavior,” Section 29.6.5, for more details. The distribution table defines +both the number of data values (one) and the physical dimension (LENGTH) of the thickness data. The +thicknesses defined in distribution dist0 are assigned only to shell elements that belong to the element +set elset1 or elset2. The default thickness (t0 ) defined in the first data line of dist0 will be +assigned to all elements in elset1 and elset2 that are not explicitly assigned a thickness in dist0. +*DISTRIBUTION TABLE, NAME=tab0 +LENGTH +*DISTRIBUTION, NAME=dist0, LOCATION=element, TABLE=tab0 +, t0 +element set or number, t1 +element set or number, t2 +… +*SHELL SECTION, ELSET=elset1, SHELL THICKNESS=dist0 +*SHELL SECTION, ELSET=elset2, SHELL THICKNESS=dist0 +Example 2 +A distribution for spatially varying isotropic elastic material behavior is defined and applied to a material +definition (“Linear elastic behavior,” Section 22.2.1). This material is then referred to by a solid section +definition. This is important because like any material definition, a material defined by a distribution is +not used unless it is referred to by a section definition, and then it is applied only to the elements associated +with the section definition. The distribution table defines both the number of data values (two) and the +physical dimensions (MODULUS and RATIO) of the isotropic elastic data. Other material behaviors (in +this case plasticity) can also be included in the material definition. The default elastic constants (E0 , +0 ) +in distribution dist1 will be assigned to all elements in elset3 that are not explicitly assigned elastic +constants in dist1. +*DISTRIBUTION TABLE, NAME=tab1 +MODULUS, RATIO +*DISTRIBUTION, NAME=dist1, LOCATION=element, TABLE=tab1 +, E0, 0 +element set or number, E1, 1 +element set or number, E2, 2 +… +*MATERIAL, NAME=MAT +*ELASTIC +dist1 +*PLASTIC +… +*SOLID SECTION, ELSET=elset3, MATERIAL=MAT +Example 3 +A spatially varying local coordinate system ( “Orientations,” Section 2.2.5) is defined by specifying both +spatially varying coordinates for points a and b as well as a spatially varying additional rotation angle. +This orientation is then referred to by a general shell section definition. This is important because like +any orientation definition, an orientation defined by a distribution is not used unless it is referred to by +a section definition, and then it is applied only to the elements associated with the section definition. +The distribution table for the coordinates specifies COORD3D twice to indicate that data for two three- +dimensional coordinates points must be specified for each element in the distribution. +*DISTRIBUTION TABLE, NAME=tab2 +COORD3D, COORD3D +*DISTRIBUTION, NAME=dist2, LOCATION=element, TABLE=tab2 +, aX0,aY0 ,aZ0 ,bX0,bY0 ,bZ0 +element set or number, aX1,aY1 ,aZ1 ,bX1,bY1 ,bZ1 +element set or number, aX2,aY2 ,aZ2 ,bX2,bY2 ,bZ2 +… +*DISTRIBUTION TABLE, NAME=tab3 +ANGLE +*DISTRIBUTION, NAME=dist3, LOCATION=element, TABLE=tab3 +, 0 +element set or number, 1 +element set or number, 2 +… +*ORIENTATION, NAME=ORI, DEFINITION=COORDINATES +dist2 +3, dist3 +*SHELL GENERAL SECTION, ELSET=elset4, ORIENTATION=ORI +Example 4 +Spatially varying thicknesses and orientation angles are defined on the layers of a composite shell +element. The distribution table for the thicknesses specifies LENGTH, and the distribution table for +the orientation angles specifies ANGLE. A distribution of thicknesses is used on layers 1 and 3, while +a distribution of angles is used on layers 2 and 3. +*DISTRIBUTION TABLE, NAME=tableThick +LENGTH +*DISTRIBUTION, NAME=thickPly1, LOCATION=element, TABLE=tableThick +, t0 +element set or number, t1 +element set or number, t2 +… +*DISTRIBUTION, NAME=thickPly3, LOCATION=element, TABLE=tableThick +, t0 +element set or number, t1 +element set or number, t2 +… +*DISTRIBUTION TABLE, NAME=tableOriAngle +ANGLE +*DISTRIBUTION, NAME=oriAnglePly2, LOCATION=element, +TABLE=tableOriAngle +, +element set or number, +element set or number, +… +*DISTRIBUTION, NAME=oriAnglePly3, LOCATION=element, +TABLE=tableOriAngle +, +element set or number, +element set or number, +… +*SHELL SECTION, ELSET=elset1, COMPOSITE +thickPly1, 3, mat1, 0. +1., 3, mat2, oriAnglePly2 +thickPly3, 3, mat3, oriAnglePly3 +2.9 +Display body definition +• “Display body definition,” Section 2.9.1 +2.9.1 +DISPLAY BODY DEFINITION +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• *DISPLAY BODY +• “Defining display body constraints,” Section 15.15.3 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +A display body: +• can be two-dimensional planar, axisymmetric, or three-dimensional; +• is associated with a part instance and up to three reference nodes, such that the motion of the part +instance is governed by the motion of the reference nodes; +• is used for display purposes only and does not take part in the analysis; +• can be used to make the analysis more efficient while improving visualization of analysis results; +and +• is especially useful for mechanism or multibody dynamic analyses. +What is a display body? +A display body is a part instance that is used for display only. None of the nodes or elements of the +instance take part in the analysis, but they are still available during postprocessing. The motion of the +display body is governed by the motion of the associated reference nodes, if any. +It behaves like a +rigid body since the relative positions of the nodes and elements of the part instance remain constant +throughout a simulation. The nodes and elements of the part instance cannot be used to define prescribed +conditions, interactions, constraints, etc. Section properties do not have to be assigned to the elements. +A display body is useful in cases where the physical model is different from the idealized model +used for the analysis. An idealized model may be difficult to visualize; it may help to include more +details in the model for realistic postprocessing purposes. Display bodies allow this without increasing +the analysis time. +Display bodies are especially useful in mechanism or multibody dynamics problems where rigid +parts interact with each other via connectors. In such cases a part can be represented by a very simple +rigid body and a more complex display body. In this case, the rigid body can be as simple as just a node, +along with mass and rotary inertia elements attached to that node. +Display bodies can also be used to model stationary objects that are not involved in the analysis but +aid in visualization. +Creating a display body +You must specify the part instance to be made a display body. +Input File Usage: +Abaqus/CAE Usage: +*DISPLAY BODY, INSTANCE=name +Interaction module: Create Constraint: Display body: select part instance +The reference nodes +If the display body is not associated with any reference nodes, it will remain fixed in space during the +analysis. However, you can specify that the motion of the display body should be governed by the motion +of selected reference nodes. These nodes must belong to another part instance in the assembly. They +cannot belong to another display body definition. If you specify only one reference node, the display +body will translate and rotate based on the translations and rotations of that node during the analysis. +If the reference node has no rotational degrees of freedom, the display body will not rotate during the +analysis. +If you specify three reference nodes, the display body will translate and rotate based on the +translations of all three nodes. The new position of the part instance at any time will be calculated from +the new position and orientation of the coordinate system defined by the three reference nodes: the first +node will be the origin, the second will be a point in the x-direction, and the third node will be a point +in the X–Y plane. Care should be taken when specifying the three nodes so that they do not become +colinear at any stage of the analysis. If this occurs, the position of the part instance may change abruptly +through that increment. +Input File Usage: +Abaqus/CAE Usage: +*DISPLAY BODY, INSTANCE=name +first reference node number, second reference node number, +third reference node number +Interaction module: Create Constraint: Display body: select part +instance, choose Follow single point or Follow three points, +click Edit, and select the reference points +Using display bodies with connectors +Display bodies can be used effectively in models containing rigid part instances that interact with each +other using connector elements. Such models need both rigid bodies and display bodies. The rigid body +should contain any nodes used by connectors, used to define mass and inertia properties, and used to apply +loads or boundary conditions. The display body should contain the nodes and elements representing the +physical part. Care should be taken to ensure that the nodes in the rigid body are not part of the display +body. The reference node of the display body will typically be the same as the rigid body reference node. +Figure 2.9.1–1(a) illustrates a model containing rigid bodies and a display body. Part instance A +is included in a display body definition. Figure 2.9.1–1(b) shows the same model without the display +body. This model will actually be involved in the analysis. The connector node and reference node form +a rigid body that represents the analysis version of part instance A. Both these nodes are assembly-level +nodes and are not included in the display body. +Connector node +Connector +Reference +node +Reference +node +Connector node +Connector +(a) + (b) +Figure 2.9.1–1 Example of a display body. +Input file template +The following input shows how display bodies can be used in a model with rigid part instances and +connectors: +*ASSEMBLY +... +*INSTANCE, NAME=INST1 +... +*END INSTANCE +*NODE, NSET=INST1-REFNODE +1001, -10, 0, 0 +*NODE, NSET=INST1-CONNECTOR-NODE +1002, -5, -5, 0 +*RIGID BODY, TIE NSET=INST1-CONNECTOR-NODE, +REF NODE=INST1-REFNODE +*DISPLAY BODY, INSTANCE=INST1 +1001 +... +*END ASSEMBLY +2.10 +Assembly definition +• “Defining an assembly,” Section 2.10.1 +2.10.1 +DEFINING AN ASSEMBLY +Products: Abaqus/Standard Abaqus/Explicit +References +• *ASSEMBLY +• *INSTANCE +• *PART +Overview +A finite element model in Abaqus can be defined as an assembly of part instances. The organization of +such a model: +• is consistent with models generated by Abaqus/CAE and displayed in the Visualization module +(Abaqus/Viewer); and +• allows reuse of part definitions, which is valuable for creating large, complex models. +allows reuse of part definitions, which is valuable for creating large, complex models. +By default, input files written by Abaqus/CAE are written in terms of an assembly of part instances. +For input files not written by Abaqus/CAE, the use of part and assembly definitions in the input file is +currently optional. However, since the Visualization module displays results in terms of an assembly of +part instances, an assembly and at least one part instance will be created automatically by the analysis +input file processor if they are not defined in the input file. +Introduction +A physical model is typically created by assembling various components. The assembly interface in +Abaqus allows analysts to create a finite element mesh using an organizational scheme that parallels +the physical assembly. In Abaqus the components that are assembled together are called part instances. +This section explains how to organize an Abaqus finite element model in terms of an assembly of part +instances. +The mesh is created by defining parts, then assembling instances of each part. Each part can be +used (instanced) one or more times, and each part instance has its own position within the assembly. +This organization of the model definition matches the way models are created in Abaqus/CAE, where +the assembly can be created interactively or imported from an input file . +Terminology +Assembly +An assembly is a collection of positioned part instances. An analysis is conducted by defining +boundary conditions, constraints, interactions, and a loading history for the assembly. +Part +A part is a finite element idealization of an object. Parts are the building blocks of an assembly +and can be either rigid or deformable. Parts are reusable; they can be instanced multiple times in +the assembly. Parts are not analyzed directly; a part is like a blueprint for its instances. +Part instance +A part instance is a usage of a part within the assembly. All characteristics (such as mesh and +section definitions) defined for a part become characteristics for each instance of that part—they are +inherited by the part instances. Each part instance is positioned independently within the assembly. +Example +A hinge can be modeled using two flanges and a pin, as shown in Figure 2.10.1–1. The flange geometry +is defined by creating a part, which is instanced twice inside the hinge assembly. Another part, the pin, +is created and instanced once. The pin is modeled as a rigid body created from an analytical surface . +The Hinge Assembly +Part instance Flange-2 +Part instance Flange-1 + Ref Pt + Ref +Part instance Pin-1 +Figure 2.10.1–1 The hinge assembly. +This hinge example is used throughout this section to illustrate the keyword interface for parts and +assemblies. This example is also used to illustrate the interactive assembly process . +Defining parts, part instances, and the assembly +Everything defined within a part, instance, or the assembly is local to that part, instance, or the assembly. +This means that node/element identifiers and names (like set and surface names) need not be unique +throughout a model; they need only be unique within the part, instance, or assembly where they are +being defined . +Names should not use an underscore to join part instance names to element set, node set, orientation +names, or distribution names because the names may conflict with internal names used by Abaqus. +For example, consider Figure 2.10.1–2. In this model the assembly (Hinge) contains three part +instances (Flange-1, Flange-2, and Pin-1). Multiple sets named top can be defined: in this case +one is defined within the assembly and one is defined within each of the Flange part instances. The set +name top can be reused, and each set named top is independent from the others. +assembly +part instance +set: top +Hinge +Flange-1 +Pin-1 +Flange-2 +set: top +set: top +Figure 2.10.1–2 The organization of the Hinge assembly. +Input File Usage: +Use the following options to begin and end each part, instance, and assembly +definition: +*PART/*END PART +*INSTANCE/*END INSTANCE +*ASSEMBLY/*END ASSEMBLY +If any one of these options appears in an input file, they must all appear except +when you import a part instance from a previous analysis; in this case *PART +and *END PART are not required. The model must be consistently defined as +an assembly of part instances. +Defining a part +A part definition must appear outside the assembly definition. Multiple parts can be defined in a model; +each part must have a unique name. +Input File Usage: +Use the following options to define a part: +*PART, NAME=PartName +Node, element, section, set, and surface definitions +*END PART +Defining part instances +A part instance definition must appear within the assembly definition. If the part instance is not imported +from a previous analysis, each part instance must have a unique name and refer to a part name. A part +instance name of Assembly is not allowed. In addition, you can specify data that are used to position +the instance within the assembly. Give a translation and rotation for the part instance relative to the origin +of the assembly (global) coordinate system. +If the part instance is to be imported from a previous analysis, each part instance must specify the +name of the instance to be imported. For more information on defining part instances for use with the +import capability, see “Transferring results between Abaqus analyses: overview,” Section 9.2.1. +Additional sets and surfaces can be defined at the instance level, as explained later in this section. +Input File Usage: +Use the following options to instance a part that is not imported from a previous +analysis: +*INSTANCE, NAME=InstanceName, PART=PartName + +Additional set and surface definitions (optional) +*END INSTANCE +Repeat these options, each time referring to the same part name, to instance a +part multiple times. +Use the following options to import a part instance from a previous analysis: +*INSTANCE, INSTANCE=instance-name +Additional set and surface definitions (optional) +*IMPORT +*END INSTANCE +Defining the assembly +Only one assembly can be defined in a model. All part instance definitions must appear within the +assembly definition. +Sets and surfaces can be defined at the assembly level by including the appropriate definitions within +the assembly definition. +Input File Usage: +Use the following options to create an assembly: +*ASSEMBLY, NAME=name +Part instance definitions +Set and surface definitions +Connector and constraint definitions +Rigid body definitions +*END ASSEMBLY +Example +The hinge assembly shown in Figure 2.10.1–1 can be defined using the following syntax in the input file: +*PART, NAME=Flange +*NODE, NSET=Flange +1, ... +2, ... +... +360, ... +*ELEMENT, ELSET=Flange +1, ... +2, ... +... +200, ... +*SOLID SECTION, ELSET=Flange, MATERIAL=Steel +*ELSET, ELSET=Flat, GENERATE +176, 200, 1 +*SURFACE, NAME=Flat +Flat, S1 +*END PART +*PART, NAME=Pin +*NODE, NSET=RefPt +1, ... +*SURFACE, TYPE=REVOLUTION, NAME=Pin +... +*RIGID BODY, REF NODE=1, ANALYTICAL SURFACE=Pin +*END PART +*ASSEMBLY, NAME=Hinge +*INSTANCE, NAME=Flange-1, PART=Flange + +*END INSTANCE +*INSTANCE, NAME=Flange-2, PART=Flange + +*END INSTANCE +*INSTANCE, NAME=Pin-1, PART=Pin + +*END INSTANCE +*ELSET, ELSET=Top +... +*NSET, NSET=Output +... +*END ASSEMBLY +*MATERIAL, NAME=Steel +... +Notes +• All of the nodes and elements that describe the Flange part are defined between the *PART and +*END PART options. The section definition (*SOLID SECTION) must also appear within the part +definition. +• At least one element set must be defined within the Flange part so that the section definition can +refer to it. Additional node and element sets can also be defined in the part. +• The Flange part is instanced twice in the Hinge assembly. Therefore, the model contains two +element sets named Flat: one belongs to part instance Flange-1, and the other belongs to part +instance Flange-2. +• When a meshed part is instanced, the node and element numbers are repeated in each part instance. +• The Pin part is instanced once. It is a rigid body created from an analytical surface . +• Keywords can be indented to help clarify the definition of each part, part instance, and assembly. +Organizing the model definition +In a traditional Abaqus model without an assembly definition, the components of the model fall into one +of two categories: model data (step independent) and history data (step dependent). In an Abaqus model +that is organized into an assembly of part instances, all components are further categorized and must fall +within the proper level: part, assembly, instance, step, or model. Step-level components correspond to +history data; all step-dependent component definitions must appear within a step definition . Model-level data include everything that does not fall into part-, assembly-, +instance-, or step-level data (for example, material definitions; see Figure 2.10.1–3). The proper level +within which a keyword option must appear in the input file is indicated at the top of each section in the +Abaqus Keywords Reference Manual. +Rules for defining an assembly +The organization shown in Figure 2.10.1–3 is achieved by following a few basic rules. +Referring to items between levels +When creating a model, it is often necessary to refer to something outside of the current level; for +example, a section definition within a part must refer to a material, which is defined at the model level. +Loads defined within a step must refer to sets within the assembly. But some references between levels +are not allowed; for example, a set in one part instance cannot refer to nodes in another part instance. +The following references are allowed: +An Abaqus model +Part +Assembly +Mesh +Node Set +Element Set +Surface +Local Coordinate +System +Section +Definition +Constraint +Reference Point +Part level +Model data +Node Set +Element Set +Surface +Section +Definition +Constraint +Reference +Point +Local +Coordinate +System +Part Instance +Mesh +Node Set +Element Set +Surface +Local +Coordinate +System +Section +Definition +Constraint +Reference +Point +Part instance level +Assembly level +Material +Amplitude +Physical +Constants +Interaction +Property +Interaction +Initial +Condition +Boundary +Condition +Model level +Analysis Step +Output Database +Request +Restart Output +Request +Diagnostic Output +Request +Load +Boundary +Condition +Predefined +Fields +Interaction +Property +Interaction +Step level +History data +Figure 2.10.1–3 Organization of a model defined in terms of an assembly of part instances. +A definition +within: +Can refer to +items within: +the assembly +an instance +an instance +a part +a step +the model +the model +the model +the assembly +an instance +the model +These rules are illustrated in Figure 2.10.1–4. +Naming conventions +The Abaqus naming conventions allow for a model that contains an assembly. When something is defined +within a part, instance, or the assembly and is referred to from outside its level, the complete name must +be used to identify it (set Flat of instance Flange-2 in assembly Hinge, for example). A complete +Part instance +Part instance +Model +Step +Assembly +Part +Allowable reference between levels +Figure 2.10.1–4 Allowable references between levels. +name is given in the input file using “dot” notation: each name in the hierarchy is separated by a “.” +(period). For example, some complete names in the Hinge assembly are +Hinge.Flange-2.Flat +Hinge.Output +An element set that belongs to part +instance Flange-2. +A node set that belongs to assembly +Hinge. +Such names would be used to refer to the sets from outside the assembly. The same syntax is used to +refer to individual nodes or elements. +Hinge.Flange-1.3 +Hinge.Flange-2.11 +A node or element that belongs to part +instance Flange-1. +A node or element that belongs to part +instance Flange-2. +As always, the context determines whether a node or element is being referred to. The “.” has special +meaning; it is used to separate the individual names in a complete name. Therefore, the “.” cannot be +used in labels such as set and surface names. For example, +*ELSET, ELSET=Set.1 +*ELSET, ELSET=Set1 +Error +OK +Complete names are limited to 80 characters, including the periods. +However, when referring to a name in an input file that is not defined in terms of an assembly of part +instances, the “.” in the name should be replaced by underscores. Such a situation can occur, for example, +when an element set from a previous analysis is referred to by the current analysis but the current input +file is not defined in terms of an assembly of part instances. +Quoted labels +Labels for set and surface names can be defined by enclosing the label in quotation marks . Any subsequent use of the label in a complete name must be enclosed in +quotation marks as well. For example, +*PART, NAME=Flange +... +*ELSET, ELSET="Set 1" +... +*END PART +... +*ELEMENT OUTPUT, ELSET=Hinge.Flange-1."Set 1" +Example +An assembly node set Top can be defined by the following syntax: +*ASSEMBLY, NAME=Hinge +... +*NSET, NSET=Top +Flange-1.2, Flange-1.5, ... +Flange-2.1, Flange-2.4, ... +*END ASSEMBLY +Since the node set is defined within the assembly level, Hinge. is not part of the complete names given +on the data lines. However, the prefix Hinge. would be required to request output for this node set, +since the output request exists within the step definition, which is outside the assembly level. +*STEP +... +*NODE OUTPUT, NSET=Hinge.Top +*END STEP +Similarly, a boundary condition could be applied to a set defined for part instance Flange-2. +*STEP +... +*BOUNDARY +Hinge.Flange-2.FixedEnd, 1, 3 +*END STEP +The mesh (nodes and elements) +• The mesh can be defined either on a part or on an instance of that part (not both). Typically, parts +are meshed and instances inherit that mesh, but it is not required. If, for example, you want to use +fully integrated elements for one part instance and reduced-integration elements for another, or if +you want to define a more refined mesh on one part instance than on another, you must mesh the +instances separately. +– If the mesh is defined on a part, it is inherited by every instance of that part. +– If the mesh is defined on a part, it cannot be redefined (overridden) on an instance of that part. +In other words, if the node and element definitions appear within the part definition, they cannot +appear within the instance definition for that part. +– If a mesh is not defined on a part, it must be defined on every instance of that part. +• A part definition is required even if no mesh is defined on it. In such cases the empty part definition +is used only to relate various instances to each other via the instance definitions. This allows the +Visualization module to group information by part. +• Rebar must be defined within a part along with the elements that are being reinforced. +• Reference nodes can be created at the assembly level. +• Only mass, rotary inertia, capacitance, connector, spring, and dashpot elements can be created at the +part or the assembly level. All other element types must be defined within a part (or part instance). +To define assembly-level elements that refer to part-level nodes, include the part instance name +when defining the element connectivity. For example: +*ELEMENT, TYPE=MASS +1, Instance-1.10 +Section definitions +• Sections must be assigned where the mesh is defined (either within a part definition or within each +instance of the part). +• If a part is meshed, all instances of that part have the same element types and are made of the same +materials. +• The set referred to by a section definition must be created at the same level as the mesh and section +definition. +• If the part is meshed, the section assignment cannot be overridden at the instance level. +Sets and surfaces +• Sets and surfaces (rigid or deformable) can be created within a part, part instance, or the assembly. +– Sets and surfaces can be created on a part if a mesh is defined on the part. +– Sets and surfaces defined on a part are inherited by each instance of that part. +– Assembly-level sets and, in Abaqus/Standard, slave surfaces can span part instances. +• If an element set or node set definition with the same name appears more than once at the same +level, the new members are appended to the set. +• A surface definition cannot appear more than once with the same surface name within the same +level. +• New sets and surfaces can be created on a part instance. If a set or surface is defined on a part +instance and a set or surface with that name was not defined on the part, the set or surface is added +to the instance. +• Sets and surfaces cannot be redefined on a part instance. If a set or surface is defined on a part +instance and a set or surface with that name was also defined on the part, an error will be generated. +• Sets and surfaces are not step dependent. All sets and surfaces must be defined within a part, part +instance, or the assembly. +Defining assembly-level sets +You can refer to a part instance from an element set or node set definition as a shortcut to using the +complete name when defining assembly-level sets. Specify the name of the instance that contains the +specified elements or nodes. To add elements or nodes from more than one instance to the set, repeat +the element set or node set definition . +Input File Usage: +Use the following options to define assembly-level sets: +*NSET, NSET=NsetName, INSTANCE=InstanceName +*ELSET, ELSET=ElsetName, INSTANCE=InstanceName +Adding sets and surfaces on restart +• Existing sets and surfaces cannot be redefined on restart. +• Analytical surfaces cannot be created on restart. +• New sets and surfaces (excluding analytical surfaces) can be added to part instances or the assembly +on restart. To add a set or surface, give the complete name. As in the original analysis, you can refer +to the part instance name from the element set or node set definition to define an assembly-level set +in the restart analysis. For example, +*HEADING +*RESTART, READ, STEP=1 +** Add element set "Bottom" to assembly "Hinge": +*ELSET, ELSET=Hinge.Bottom +Flange-1.40, Flange-2.99 +** Add node set "Top" to assembly "Hinge": +*NSET, NSET=Hinge.Top, Instance=Flange-1 +21, 22, 23, 24, 26, 28, 31 +*NSET, NSET=Hinge.Top, Instance=Flange-2 +21, 22, 23, 24, 26, 28, 31 +** +** Add element set "Right" to part instance "Flange-2": +*ELSET, ELSET=Hinge.Flange-2.Right +16, 18, 20, 29 +** +** Add surface "surfR" to part instance "Flange-2": +*SURFACE, TYPE=ELEMENT, NAME=Hinge.Flange-2.surfR +Right, S1 +** +*STEP +... +*END STEP +Rigid bodies +Rigid bodies can be defined at the part or assembly level. +• To define a rigid body at the part level, include the rigid body and rigid body reference node +definitions within the part definition. +– Rigid elements, deformable elements, and analytical surfaces cannot be combined within a +part. +– If a rigid body is defined within a part, all deformable, rigid, or connector elements in the part +must belong to the rigid body. +– Mass, rotary inertia, spring, dashpot, and heat capacitance elements can be included in a part +that contains a rigid body definition, but these elements cannot belong to the rigid body. +– To create a part-level rigid body from an analytical surface, include the surface definition within +the part definition. Only one analytical surface is allowed per part. +• To define a rigid body at the assembly level, include the rigid body and reference node definitions +within the assembly definition. +– A rigid body can be created at the assembly level from any combination of rigid elements, +deformable elements, and up to one analytical surface. +– The rigid body definition can refer to assembly-level or part-level sets. +– A part that contains a rigid body definition cannot be included in an assembly-level rigid body. +• You can define a discrete surface at the part or assembly level independent from the rigid body +definition. +• An analytical surface definition can appear only within a part definition, even if the rigid body is +defined at the assembly level. +Materials +• Materials are defined at the model level so that they can be reused. The material definition cannot +appear within a part, part instance, or the assembly. +• All materials in a model must have unique names. +Interactions +An interaction is a relationship between surfaces or between a surface and its environment. Interactions +in Abaqus include contact, radiation, film conditions, and element foundations. +• Interactions are defined at the model level in Abaqus/Standard and at the model level or within steps +in Abaqus/Explicit; they cannot be defined within a part, assembly, or instance. +Constraints +Constraints are inflexible coupling mechanisms such as MPCs and equations . +• Constraints can be defined within a part or the assembly. They can be defined within a part instance +if the mesh is defined within the part instance. Constraints should be defined at the assembly level +if they constrain the motion of one part instance relative to another. +• Constraints are translated and rotated according to the positioning data given for a part instance. +Distributions +Distributions are used to specify arbitrary spatial variations of selected element properties, material +properties, local coordinate systems, and spatial variations of initial contact clearances . +• Distributions should be defined at the level at which they are used. For example, if a distribution is +used to define shell thicknesses, the distribution should be defined at the same level as the section +definition that refers to it. If a distribution is used to define a material property, it should be defined +at the model level with the material definition. +Examples +In the following examples most parameters and data lines are omitted for clarity. +Example 1 +*PART, NAME=PartA +*NODE ... +*ELEMENT ... +*SOLID SECTION, ELSET=setA, +MATERIAL=Mat1 +*SURFACE, NAME=surf1 +setB, ... +*ELSET, ELSET=setA +*NSET, NSET=setA +*SURFACE, NAME=surf2 +setA, ... +Notes +The mesh is defined on the part. +error +Section assignment must appear within the +part level if the mesh is defined on the part. +Element set setB is not defined at the part +level. +Sets and surfaces can be defined on the part +since the mesh is defined on the part. +Example 1 +Notes +*END PART +*ASSEMBLY, NAME=Assembly-1 +*INSTANCE, NAME=I1, PART=PartA +*NODE +*ELEMENT +*SOLID SECTION +*ELSET, ELSET=setA +*NSET, NSET=setA +*SURFACE, NAME=surf2 +*ELSET, ELSET=setB +*NSET, NSET=setB +*SURFACE, NAME=surf3 +setA, ... +*END INSTANCE +*END ASSEMBLY +error +error +error +error +error +error +Mesh and section assignment cannot be +defined on the instance if they are defined +on the part. +Sets and surfaces cannot be redefined on the +instance. +New sets and surfaces can be defined on the +instance. +Set and surface definitions can refer to +inherited sets. +In the second example the instances are meshed. +Example 2 +Notes +*PART, NAME=PartB +*END PART +*PART, NAME=PartC +*SOLID SECTION, ... +*END PART +*ASSEMBLY, NAME=Assembly-1 +*INSTANCE, NAME=I1, PART=PartB +*NODE ... +*ELEMENT ... +*SOLID SECTION, ELSET=setA, +MATERIAL=Mat1 +*ELSET, ELSET=setA +*NSET, NSET=setA +*SURFACE, NAME=surf2 +setA, ... +*END INSTANCE +The *PART and *END PART options are +required, even when the instance is meshed. +Section cannot be defined on the part if +mesh is not defined on the part. +error +The mesh is defined on the part instance. +Section assignment must appear within the +same level as the mesh definition. +Sets and surfaces are defined on the instance +since the mesh is defined on the instance. +Example 2 +Notes +*INSTANCE, NAME=I3, PART=PartC + +*END INSTANCE +*END ASSEMBLY +Coordinate system definitions +error +The mesh and section must be defined for +each instance since the part is not meshed. +Abaqus provides several methods for defining local coordinate systems. +Nodal coordinate systems +You can define nodal coordinates in a local coordinate system . The coordinate system can +be defined within a part definition to define the nodes in that part. The nodal coordinate system +definition remains in effect until another nodal coordinate system is defined within the same level +or until the level ends. +Nodal transformations +A nodal transformation is used for applying loads and boundary conditions . It can be defined at the part or assembly level to define a local +coordinate system for application of loads and boundary conditions or for the definition of linear +constraint equations. +User-defined orientations +A user-defined orientation is used for defining material properties, coupling, connectors, and rebar +. It can be defined at the part level for reference from a section, +connector, rebar, or coupling definition. An orientation definition can also be used at the assembly +level for reference from a connector or coupling definition. +Distributions +Distributions can be used to specify arbitrary spatial variations of local coordinate systems for +continuum and shell elements . A distribution used by an +orientation should be defined at the level in which the orientation is defined. +Normal definitions at nodes +Normals can be defined at nodes as part of the node definition for beam, pipe, and shell elements +or with a user-specified normal definition . These +normals can be defined at the part or assembly level. +A local coordinate system defined for a part using any of these methods is inherited by all instances of +the part. +Translating and rotating a part instance +The assembly’s coordinate system is the global coordinate system. You can position part instances within +the assembly by giving a translation and/or rotation relative to the global origin. Specify a translation +by giving a translation vector. Specify a rotation by giving two points, a and b, to define a rotation axis +plus a right-handed angular rotation around that axis. +Local coordinate systems defined within a part or part instance will be translated and rotated +according to the specified positioning data, as shown in Figure 2.10.1–5. (In this figure details such as +element and section definitions are omitted for clarity.) Results given in a local coordinate system are +output in the transformed local system. Equations will also be translated and rotated according to the +positioning data for an instance. All data within a part (or part instance) definition are defined relative +to the part’s local coordinate system; positioning data are applied to a part instance after everything +within that instance is defined. +Limitations +The following capabilities are not supported in a model defined in terms of an assembly of part instances: +• “Mapping a set of nodes from one coordinate system to another” in “Node definition,” Section 2.1.1 +• “Using auxiliary analyses to generate shape variations” in “Parametric shape variation,” +Section 2.1.2 +• “Symmetric model generation,” Section 10.4.1 +• “Transferring results from a symmetric mesh or a partial three-dimensional mesh to a full three- +dimensional mesh,” Section 10.4.2 +• “Reading the element matrices from an Abaqus/Standard results file” in “User-defined elements,” +Section 32.15.1 +The substructure library is not organized in terms of an assembly of part instances, so substructures +cannot be generated from models that have an assembly defined. None of the substructure options are +supported in models that have an assembly defined. +Input file template +This template shows an input file that is written in terms of parts and assemblies with the part instances +defined in this analysis. For templates that show how to import a part instance from a previous +analysis to transfer model data and results, see “Transferring results between Abaqus/Explicit and +Abaqus/Standard,” Section 9.2.2, and “Transferring results from one Abaqus/Standard analysis to +another,” Section 9.2.3. +*HEADING +*PART, NAME=Part-1 +Node, element, section, set, and surface definitions +Connector and constraint definitions +*END PART +*PART, NAME=Part-2 +*Part, Name=P +*System +*Node +*End part +*Part, Name=Q +*Node +*End part +Local coordinate system defined relative to part coordinate system +Nodes defined in local coordinate system +Local coordinate system only applies +within this part definition +Nodes defined in part coordinate system +*Assembly, Name=Assembly-1 +*Instance, Name=Instance-1, Part=Q + +*End Instance +*Instance, Name=Instance-2, Part=P + +*End Instance +*Instance, Name=Instance-3, Part=P + +*End Instance +*End assembly +Instances positioned relative +to global coordinate system +Instance-2 +Instance-1 +Instance-3 +Assembly-1 coordinate system +Position given relative to the assembly (global) coordinate system +(defined by ∗INSTANCE) +Part-local coordinate system (defined by ∗NORMAL, ∗ORIENTATION, +∗SYSTEM, or ∗TRANSFORM) +Figure 2.10.1–5 Defining local coordinate systems. +**The instance is meshed, so the part definition is empty +*END PART +*MATERIAL, NAME=mat1 +Suboptions and data lines to define this material +*ASSEMBLY, NAME=Assembly-1 +*INSTANCE, NAME=i1, PART=Part-1 + +Additional set and surface definitions (optional) +*END INSTANCE +*INSTANCE, NAME=i2, PART=Part-2 + +Node, element, section, set, and surface definitions +Connector and constraint definitions +*END INSTANCE +Assembly-level set and surface definitions +Assembly-level connectors and constraints +Assembly-level reference node definitions +Assembly-level rigid body definitions +*END ASSEMBLY +*MATERIAL, NAME=mat2 +Suboptions and data lines to define this material +*AMPLITUDE +*INITIAL CONDITIONS +*BOUNDARY +Zero-valued boundary conditions +*PHYSICAL CONSTANTS +*CONNECTOR BEHAVIOR +Suboptions and data lines to define this connector behavior +Interaction and interaction property definitions in Abaqus/Standard or Abaqus/Explicit +*STEP +Loads and boundary conditions +Predefined field definitions +Output requests +Contact interaction definitions in Abaqus/Explicit +*END STEP +2.11 +Matrix definition +• “Defining matrices,” Section 2.11.1 +2.11.1 +DEFINING MATRICES +Product: Abaqus/Standard +References +• “Generating matrices,” Section 10.3.1 +• *MATRIX ASSEMBLE +• *MATRIX GENERATE +• *MATRIX INPUT +• *MATRIX OUTPUT +Overview +A matrix: +• can be used to represent stiffness, mass, viscous damping, or structural damping for a part of the +model or for the entire model; +• is defined by giving it a unique name and by specifying matrix data, which may be scaled; +• can be symmetric or unsymmetric; +• can be given in text format in lower triangular, upper triangular, or square form or read from binary +.sim files generated by the matrix generation procedure; +• can be used to provide linear elastic response with large translations but not large rotations; +• can be used in static and natural frequency extraction procedures; +• can be used in matrix generation and substructure generation procedures; +• can be used in transient modal dynamics, mode-based steady-state dynamics, subspace-based +steady-state dynamics, random response, response spectrum, and complex eigenvalue extraction +procedures that use the SIM architecture; +• can have loads, boundary conditions, and constraints applied directly to any matrix nodal degrees +of freedom; +• can be used in submodeling analysis; and +• cannot be used in direct steady-state dynamic or mode-based analyses that do not use the SIM +architecture. +What is a matrix in Abaqus/Standard? +Designing complex models of structures like automobiles typically involves subcontracting the work +on various parts. When the entire model has to be put together, information about the parts needs to +be exchanged between different vendors. Often, to avoid the exchange of proprietary information, this +information is exchanged in terms of matrices representing the stiffness, mass, and damping for each +part. During an analysis these matrices are added to the corresponding global finite element matrices to +complete the assembly of the entire model. +Abaqus/Standard provides the capability to input stiffness, mass, viscous damping, and structural +damping matrices directly. You can define as many different matrices as are necessary to build the model. +Including matrices in a model +You must assign a name to the matrix to include it in the matrix usage model. +Input File Usage: +*MATRIX INPUT, NAME=name +Specifying a matrix type +For matrices given in text format, you can specify the matrix type as symmetric (default) or unsymmetric. +If symmetric, it can be entered as a lower triangular, upper triangular, or square matrix. +For matrices read from a .sim file, the matrix type is automatically set according to the matrix data +stored on the SIM database. +Input File Usage: +Use one of the following options to specify the type for matrices given in text +format: +*MATRIX INPUT, NAME=name, TYPE=SYMMETRIC +*MATRIX INPUT, NAME=name, TYPE=UNSYMMETRIC +Scaling the matrix data +You can define a multiplication scale factor for all matrix entries. +Input File Usage: +*MATRIX INPUT, NAME=name, SCALE FACTOR=sval +Providing matrix data directly +You can specify data directly to define a symmetric matrix in lower triangular, upper triangular, or square +format. For a square matrix to be symmetric, corresponding entries above and below the diagonal must +have exactly the same values. You can specify data directly to define an unsymmetric matrix by providing +data for each matrix entry. +Input File Usage: +*MATRIX INPUT +row node label, degree of freedom for row node, column node label, +degree of freedom for column node, matrix entry +Repeat this data line to specify data for each matrix entry. +Reading the matrix data in text format from an alternate file +Matrix data in text format can be contained in an alternate file. Typically, an alternate file is used for large +matrices. To ensure acceptable performance, the data lines in the alternate file are read without extensive +checking for data format. You should make sure that the data entries are specified in the proper format +without any comments or blank lines. Matrix data output in text format can be generated in the matrix +generation procedure . +Input File Usage: +*MATRIX INPUT, NAME=name, INPUT=input_file_name +Reading the matrix data from the SIM database +Matrix data in binary format can be read from the .sim file generated by the matrix generation procedure +. The .sim file can contain +stiffness, mass, viscous damping, and structural damping matrices. You specify each matrix to be read +from the .sim file. +Input File Usage: +Use the following options: +*MATRIX INPUT, NAME=stif_name, INPUT=sim_file_name, +MATRIX=STIFFNESS +*MATRIX INPUT, NAME=mass_name, INPUT=sim_file_name, +MATRIX=MASS +*MATRIX INPUT, NAME=dmpv_name, INPUT=sim_file_name, +MATRIX=VISCOUS DAMPING +*MATRIX INPUT, NAME=dmps_name, INPUT=sim_file_name, +MATRIX=STRUCTURAL DAMPING +Defining the stiffness, mass, and damping with matrices included in a model +You can assemble the stiffness, mass, viscous damping, and structural damping matrices that you have +specified into the corresponding global finite element matrices for the model. Many matrices with +different names can be defined and assembled. +Input File Usage: +Use the following option to assemble matrices generated from the same original +model: +*MATRIX ASSEMBLE, STIFFNESS=stif_name, MASS=mass_name, +VISCOUS DAMPING=dmpv_name, +STRUCTURAL DAMPING=dmps_name +To assemble matrices generated from different original models, repeat the +*MATRIX ASSEMBLE option for each model. +Connecting a part of a model represented by matrices +A part of the model represented by user-defined matrices is connected to other parts and finite elements +through shared nodes. You must define these nodes directly in the model . In addition, there may be nodes that are used only by matrices but that are not shared. +You do not need to define nodes that are not shared and have no loads, boundary conditions, or +constraints associated with them; these nodes will be defined for you and placed at the origin of the +global coordinate system. +Input File Usage: +Use the following option to define the shared nodes directly: +*NODE +Remapping user-defined nodes in assembled matrices +The nodes defined in the assembled matrices can be remapped (renamed) to different node labels in the +matrix usage model. You must define all the new node labels in the matrix usage model, create a node +set from them, and specify this node set when assembling the matrices. The size of the node set and the +order of the nodes in the set must fully correspond to the combined set of nodes of all the matrices that +are assembled. The matrix nodes are assumed to be sorted in ascending order of their original labels that +were defined at generation or specified in the matrix data. +Input File Usage: +Use the following option to create a node set for the matrix nodes: +*NSET, NSET=nset_name, UNSORTED +Use the following option to assemble matrices with node remapping: +*MATRIX ASSEMBLE, STIFFNESS=stif_name, MASS=mass_name, +VISCOUS DAMPING=dmpv_name, +STRUCTURAL DAMPING=dmps_name, NSET=nset_name +Multiple instantiation of matrices +With the node remapping feature, the same matrix can be used multiple times in the matrix usage model. +You define the matrix once and assemble it several times, specifying the relevant node sets for remapping. +Input File Usage: +*MATRIX INPUT, NAME=name +*MATRIX ASSEMBLE, STIFFNESS=name +*MATRIX ASSEMBLE, STIFFNESS=name, NSET=nset1_name +*MATRIX ASSEMBLE, STIFFNESS=name, NSET=nset2_name +Internal nodes in matrix data +Internal nodes are nodes with internal degrees of freedom associated with them (for example, Lagrange +multipliers and generalized displacements) that are created internally by Abaqus/Standard. By +definition, user-defined nodes have positive node labels, and internal nodes have negative node labels. +You can use the matrix generation procedure to designate some of the user-defined nodes as internal +nodes to hide them in the matrix usage model . +When using matrix data that contains internal nodes, these nodes are remapped automatically to +unique internal node labels in the matrix usage model. For assembled matrices that originate from the +same model, the internal nodes are shared. For assembled matrices that originate from different models, +the internal nodes are mapped to different internal nodes in the matrix usage model, even if they have +the same negative node labels. +Using matrices in nonlinear analyses +When you use matrices in a nonlinear analysis procedure, nonlinearities are not accounted for. Since +the matrix data remain unchanged during the analysis, only linear elastic material behavior can be +represented and only large translations can be modeled correctly in a geometrically nonlinear analysis. +Changes to the matrix due to large rotations or load stiffness are not computed in a geometrically +nonlinear analysis. +Using matrices in linear perturbation analyses +Matrices can be used in a static perturbation analysis as well as in a natural frequency extraction analysis +using the Lanczos or AMS eigensolver. For certain quantities (such as participation factors and global +inertia properties) to be computed properly, the coordinates of the nodes associated with the matrices +should be defined in the model using matrices. Matrices can also be used in modal analysis procedures +using the high-performance SIM architecture; namely, steady-state dynamic, modal dynamic, random +response, response spectrum, and complex frequency extraction analyses. Matrices can be used in the +substructure generation and matrix generation procedures as well. +Matrices cannot be used in the direct-solution steady-state dynamic analysis procedure and in modal +procedures that are not based on the high-performance SIM architecture. +Constraints and transformations +Kinematic constraints (for example, coupling constraints, +linear constraint equations, multi-point +constraints, or surface-based tie constraints) can be applied to any nodes in a model containing matrices. +Since kinematic constraints in Abaqus/Standard are usually imposed by eliminating degrees of freedom +at the dependent nodes, matrix nodes should not be used as dependent nodes. +To apply contact constraints on matrix nodes, a node-based surface must be defined on these nodes +and this surface should be used as the slave surface in the contact pair definition. +Nodal transformations defined at nodes that appear in the matrix do not affect the matrix. The +matrix entries corresponding to these nodes are assumed to be in the local coordinates defined by the +nodal transformations. +Initial conditions +Initial conditions can be specified as usual; however, only node-based initial conditions can be applied +to nodes that appear in matrices. See “Initial conditions in Abaqus/Standard and Abaqus/Explicit,” +Section 33.2.1. +Boundary conditions +Boundary conditions can be specified as usual. See “Boundary conditions in Abaqus/Standard and +Abaqus/Explicit,” Section 33.3.1. Matrix nodes can be defined as driven nodes in a submodel analysis +; they cannot be defined as driving nodes in a global +model. For shell-to-solid submodeling, matrix nodes that are defined as driven nodes are treated as lying +within the center zone no matter how far they are from the shell reference surface. +Loads +Concentrated nodal forces can be applied at displacement degrees of freedom (1–6) of any node as usual. +Distributed pressure forces can be applied to surface elements defined over matrix nodes (see “Surface +elements,” Section 32.7.1). Body forces cannot be applied to parts of the model represented by matrices. +User-defined loads can be applied with the same restrictions as above for distributed pressure forces and +body forces. +Predefined fields can be applied at any nodes as usual ; however, +matrix data are not affected by predefined fields. For example, if temperatures are specified as a +predefined field on nodes that appear on a matrix, only the elements that share these nodes with the +matrix experience thermal strains if thermal expansion is specified for those elements. The matrix does +not experience any thermal strains, but it may experience linear elastic forces due to displacements at +shared nodes. +Elements +All elements that can be used in static stress analysis are available . +Output +All nodal output variables that apply to static analysis are available . +Limitations +The following are known limitations to using matrices: +• An analysis that contains matrices cannot be restarted. In addition, matrices cannot be introduced +in a restart analysis. +• Matrices cannot be used in a model containing parts and assemblies. +• Matrices containing acoustic pressure and mechanical degrees of freedom will disable the coupled +acoustic structural eigenvalue extraction. +• Matrices containing Lagrange multiplier degrees of freedom can produce inaccurate results +in Abaqus/Standard analysis procedures that use the direct sparse solver, except for analysis +procedures based on the AMS eigensolver or using the eigenmodes extracted with the AMS +eigensolver. To address this limitation, you can set the constraint optimization solver control +for the analysis procedure. Setting this solver control is helpful if the matrix data contain up to +several hundred Lagrange multipliers. However, for matrices with a larger number of Lagrange +multipliers, using the constraint optimization solver control can significantly affect performance +or the analysis may fail due to insufficient memory. Setting this solver control does not help for +matrices generated from models using hybrid elements. +• In an Abaqus/Standard analysis using matrix input data for the mass matrix, inertia quantities for +the global model that are reported in the data (.dat) file, including coordinates of the center of +mass and moments of inertia, may be calculated incorrectly. +• Matrices cannot be used in analyses with inertia relief loads. +DEFINING MATRICES +*HEADING +… +*NODE +Data lines to specify nodes +*NSET, NSET=NSET1, UNSORTED +Data lines to specify a node set with the nodes in a particular order +… +*BOUNDARY +Data lines to specify zero-valued boundary conditions +*MATRIX INPUT, NAME=MAT1, SCALE FACTOR=sval +Data lines to specify a stiffness matrix +*MATRIX INPUT, NAME=MAT2, SCALE FACTOR=sval +Data lines to specify a mass matrix +*MATRIX INPUT, NAME=MAT3, SCALE FACTOR=sval +Data lines to specify a viscous damping matrix +*MATRIX INPUT, NAME=MAT4, INPUT=input_file_name +*MATRIX INPUT, NAME=MAT5, INPUT=input_file_name +*MATRIX INPUT, NAME=MAT6, INPUT=sim_file_name, MATRIX=STIFFNESS +*MATRIX ASSEMBLE, STIFFNESS=MAT1, MASS=MAT2, +VISCOUS DAMPING=MAT3, STRUCTURAL DAMPING=MAT4 +*MATRIX ASSEMBLE, STIFFNESS=MAT6, MASS=MAT5 +*MATRIX ASSEMBLE, STIFFNESS=MAT6, MASS=MAT5, NSET=NSET1 +*STEP(,NLGEOM)(,PERTURBATION) +Use NLGEOM to include nonlinear geometric effects; it will remain active in all subsequent steps. +*STATIC +*BOUNDARY +Data lines to prescribe zero-valued or nonzero boundary conditions +*CLOAD and/or *DLOAD +Data lines to specify loads +*END STEP +*STEP +*FREQUENCY +*BOUNDARY +Data lines to prescribe zero-valued or nonzero boundary conditions +*END STEP +*STEP +*STEADY STATE DYNAMICS +*CLOAD and/or *DLOAD +Data lines to specify loads +*END STEP +Job Execution +Execution procedures: overview +Execution procedures +Environment file settings +Managing memory and disk resources +Parallel execution +File extension definitions +FORTRAN unit numbers +JOB EXECUTION +3.1 +3.2 +3.3 +3.4 +3.5 +3.6 +3.1 +Execution procedures: overview +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +EXECUTION PROCEDURE FOR Abaqus: OVERVIEW +EXECUTION PROCEDURE: OVERVIEW +Overview +Abaqus is executed by using the Abaqus execution procedure. In the following discussion the command +to run the execution procedure is assumed to be abaqus. However, you can customize the execution +procedure to run Abaqus using any alias you choose. +The abaqus command is described in “Execution procedures,” Section 3.2. The following sections +contain further information about running Abaqus jobs: +• “Using the Abaqus environment settings,” Section 3.3.1 +• “Managing memory and disk use in Abaqus,” Section 3.4.1 +• “Parallel execution,” Section 3.5 +• “File extensions used by Abaqus,” Section 3.6.1 +• “FORTRAN unit numbers used by Abaqus,” Section 3.7.1 +Conventions +The following conventions are used in these sections: +• Each discussion includes a “Command summary” section that provides the syntax for the command +in the left column and the syntax for its options in the right column. The full command must appear +first, followed by the options. In some cases the command has multiple words, such as abaqus cae; +you must enter all words of the command before issuing any option statements. +• Options are presented in boldface. They can appear in any order and can be abbreviated. +• Default options are underlined ( __ ). +• Items enclosed in square brackets ([ ]) are optional. +• Items appearing in a list separated by bars ( | ) are mutually exclusive. +• One value must be selected from a list of values enclosed by curly brackets ({ }). +• You must supply values in italics. +• Blanks are used as separators between options and must not precede nor follow an equal sign. +• An alternate syntax of -option value can be used instead of the option=value format. +The abaqus procedure will prompt for any information required that is not provided on the command +line. If abaqus is typed with no options, prompts are issued for all options. +Environment settings +The Abaqus execution procedure uses “environment” settings to customize the execution of a job. +These settings can be changed using the Abaqus environment file, abaqus_v6.env. The execution +procedure looks for this file in two places other than the installation location when running a job. The +first place it looks is in your home directory. If it exists, the settings in this file will be applied to all +jobs that you run. The second place the execution procedure looks is in the current directory. If the file +exists, the settings defined there will be applied to all jobs run from that directory. +If the same job parameter is defined in more than one environment file or is defined more than once +within the same environment file, the last definition encountered will be used. Some exceptions to this +rule are noted in “Using the Abaqus environment settings,” Section 3.3.1. These environment files can +be used to customize the behavior of Abaqus, including modification of the default options. See “Using +the Abaqus environment settings,” Section 3.3.1, for further information on the environment files. +Selecting TCP/UDP port numbers +Several of the execution procedure command line options, such as port and listenerport, require that +you specify a port number. TCP/UDP port numbers can range from 0 to 65535. +Port numbers 0 to 1023 are well-known ports used by system processes (such as FTP, SSH, SMTP, +etc.) and should never be used. Port numbers 1024 to 49151 are registered ports with the Internet +Assigned Number Authority (IANA) by software vendors. These ports can be used, but you should be +careful that you are not conflicting with any software installed on your system that may be using this +port. Port numbers 49152 to 65535 are unreserved and can be used freely, as long as no other application +uses them. +Ports may be blocked by a firewall. Contact your system administrator to ensure that the ports that +you want to specify are not blocked. +You can use the netstat command to obtain information on TCP/UDP network connections. +3.2 +Execution procedures +• “Obtaining information,” Section 3.2.1 +• “Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD execution,” Section 3.2.2 +• “SIMULIA Co-Simulation Engine controller execution,” Section 3.2.3 +• “Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD co-simulation execution,” Section 3.2.4 +• “Abaqus/CAE execution,” Section 3.2.5 +• “Abaqus/Viewer execution,” Section 3.2.6 +• “Python execution,” Section 3.2.7 +• “Parametric studies,” Section 3.2.8 +• “Abaqus documentation,” Section 3.2.9 +• “Licensing utilities,” Section 3.2.10 +• “ASCII translation of results (.fil) files,” Section 3.2.11 +• “Joining results (.fil) files,” Section 3.2.12 +• “Querying the keyword/problem database,” Section 3.2.13 +• “Fetching sample input files,” Section 3.2.14 +• “Making user-defined executables and subroutines,” Section 3.2.15 +• “Input file and output database upgrade utility,” Section 3.2.16 +• “Generating output database reports,” Section 3.2.17 +• “Joining output database (.odb) files from restarted analyses,” Section 3.2.18 +• “Combining output from substructures,” Section 3.2.19 +• “Combining data from multiple output databases,” Section 3.2.20 +• “Network output database file connector,” Section 3.2.21 +• “Mapping thermal and magnetic loads,” Section 3.2.22 +• “Fixed format conversion utility,” Section 3.2.23 +• “Translating Nastran bulk data files to Abaqus input files,” Section 3.2.24 +• “Translating Abaqus files to Nastran bulk data files,” Section 3.2.25 +• “Translating ANSYS input files to Abaqus input files,” Section 3.2.26 +• “Translating PAM-CRASH input files to partial Abaqus input files,” Section 3.2.27 +• “Translating RADIOSS input files to partial Abaqus input files,” Section 3.2.28 +• “Translating Abaqus output database files to Nastran Output2 results files,” Section 3.2.29 +• “Translating LS-DYNA data files to Abaqus input files,” Section 3.2.30 +• “Exchanging Abaqus data with ZAERO,” Section 3.2.31 +• “Encrypting and decrypting Abaqus input data,” Section 3.2.32 +• “Job execution control,” Section 3.2.33 +3.2.1 +OBTAINING INFORMATION +Products: Abaqus/Standard Abaqus/Explicit +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +The Abaqus execution procedure can be used to obtain help regarding command syntax or information +about the installation and computing environment. +Command summary +abaqus +Command line options +help +{help | information={environment | local | memory | +release | support | system | all} [job=job-name] | +whereami} +This option prints a summary of the abaqus command syntax. +information +This option writes information about the installation and the environment that is in effect to the screen. +The following information is output for all information requests: the current release, the directory in +which Abaqus is located, and the directory in which the information files are located. +If information=environment, the current settings of the environment file options are displayed. +If information=local, the local installation notes are output. +If information=memory, some suggestions for setting memory parameters for analysis jobs are +output. +If information=release, information is provided about where to locate the current release notes. +If information=support, information on diagnosing hardware-related issues is provided. Please +send this information to systems support when requesting assistance. +If information=system, information is provided about system software and hardware resources +(operating system level, compiler levels, processor type, graphics board, memory, etc). +If information=all, information on all of the above information topics is output. +job +If a job-name is specified, the information text is written to the file job-name.log. +whereami +This option prints the location of the Abaqus release directory. +Examples +Use the following command to display the local installation notes: +abaqus information=local +The following command will write the local installation notes to the file support.log: +abaqus information=local job=support +Abaqus/Standard, Abaqus/Explicit, AND Abaqus/CFD EXECUTION +ANALYSIS EXECUTION +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD are executed by running the Abaqus execution +procedure. Several parameters can be set either on the command line or in the environment file . Alternatively, you can use the convenient +Abaqus/CAE user interface to submit an Abaqus analysis from an input file and set the analysis +parameters; see “Understanding analysis jobs,” Section 19.2 of the Abaqus/CAE User’s Manual. +Abaqus enforces a character limit on file names. For any command line reference to a file, the total +length of the file name, including the path description, cannot exceed 256 characters. +job=job-name +[analysis | datacheck | parametercheck | continue | +convert={select | odb | state | all} | +recover | syntaxcheck | information={environment | local | +memory | release | support | system | all}] +[input=input-file] [user={source-file | object-file}] +[oldjob=oldjob-name] [fil={append | new}] +[globalmodel={results file-name | output database file-name}] +[cpus=number-of-cpus] [parallel={domain | loop}] +[domains=number-of-domains] +[dynamic_load_balancing] +[mp_mode={mpi | threads}] +[standard_parallel={all | solver}] +[gpus=number-of-gpgpus] [memory=memory-size] +[interactive | background | queue=[queue-name] [after=time] ] +[double={explicit | both | off | constraint}] +[scratch=scratch-dir] +[output_precision={single | full} ] +[field={odb | exodus | nemesis} ] +[history={odb | csv} ] +[madymo=MADYMO-input-file] +3.2.2–1 +Command summary +Command line options +Required option +job +[host=co-simulation hostname] +[port=co-simulation port-number] +[listenerport=Co-Simulation Engine listener port-number] +[remoteconnections=Co-Simulation +remote job host:port-number] +[timeout=co-simulation timeout value in seconds] +[unconnected_regions={yes | no}] +Engine +host:port-number, +The value of this option specifies the name of all files generated during the run and the name of files that +are read in the continue, convert, and recover phases. +If this option is omitted from the command line, you will be prompted for its value (except when +only the informational options described in “Obtaining information,” Section 3.2.1, are used). If the +input option is not supplied, the procedure will look for an input file called job-name.inp in the current +directory. +Mutually exclusive options that determine which phases of an analysis are performed +All options are order independent. If none of these options is present, the analysis option is assumed. +The convert option is an exception to the mutual exclusion rule: convert can appear with any +option except datacheck, parametercheck, syntaxcheck, and information. +The convert and +parametercheck options are not available for Abaqus/CFD. +analysis +This option indicates that a complete Abaqus analysis (or a restart of an Abaqus analysis) is to be +performed. +datacheck +This option indicates that the run is for data checking only. No analysis will be performed. If this option +is used, all files necessary to continue the analysis are saved. +parametercheck +This option indicates that the run is for input parameter checking only (parameter definitions must have +been used; see “Parametric input,” Section 1.4.1). No analysis or data checking will be performed. This +option is not applicable for Abaqus/CFD. +continue +This option indicates that the run is to begin at the point at which a previous data check run ended. +convert +The value of this parameter indicates which files will be postprocessed. This option is not applicable for +Abaqus/CFD. +Results can be converted either immediately following an analysis run, as a separate run subsequent +to an analysis run, or while an analysis is running as follows: +1. To run an analysis including a subsequent conversion of the results, use the convert option in +conjunction with the job and analysis options. +2. To convert the results of a previously run analysis, use the convert option in conjunction with the +job option. +3. To convert results from a job that is currently running, use the convert option in conjunction with +the oldjob option (to name the running job) and the job option (to supply a new name for the files +generated by the convert option). +If convert=select, +the Abaqus/Explicit selected results file (job-name.sel) will be +converted into a standard Abaqus results file (job-name.fil). If the analysis is run in parallel with +parallel=domain, the separate selected results files (job-name.sel.n) will be converted into a single +selected results file (job-name.sel) prior to being converted into a standard Abaqus results file. +If convert=odb, the output database (job-name.odb) will be converted using the postprocessing +calculator . This conversion is necessary only if the +types of output listed in “The postprocessing calculator,” Section 4.3.1, are requested. +If convert=state, the separate Abaqus/Explicit state files (job-name.abq.n) will be converted +into a single Abaqus/Explicit state file (job-name.abq) if the analysis is run in parallel with +parallel=domain. +If convert=all, all of the applicable convert options will be executed. +recover +This option applies only to Abaqus/Explicit. It indicates that an analysis is to be restarted at the last +available step and increment in the state file. This capability is available to restart after a catastrophic +failure, such as exceeding a CPU limit or a disk quota ( see “Restarting an analysis,” Section 9.1.1). If the +original analysis was run in parallel with parallel=domain, it must be restarted with parallel=domain +and the same number of processors. +syntaxcheck +This option indicates that the run is for checking the syntax of the input file only. This option does not use +any license tokens. No analysis will be performed, and the continue option cannot be used to continue +with an analysis. Only the data (.dat) and output database (.odb) files are generated for viewing. In +an Abaqus/Explicit analysis, the model data in the output database may not be complete. +information +This option writes information about the installation and the environment that is in effect to the screen +or to the file job-name.log. For output information for each value of this option, see “Obtaining +information,” Section 3.2.1. If the information option is used in conjunction with the analysis option, +the job must be run in the background to write the information text to the log file. +Additional options available for the analysis module +input +This option is used to specify the input file name, which may be given with or without the .inp extension +(if the extension is not supplied, Abaqus will append it automatically). If this option is not supplied, the +procedure will look for an input file called job-name.inp in the current directory. If job-name.inp +cannot be found, the procedure will prompt for the input file name. +user +This option specifies the name of a source or object file that contains any user subroutines to be used in the +analysis. The name of the user routine may contain a path name and may be given with or without a file +extension. Abaqus/Standard and Abaqus/Explicit only accept user subroutines written in FORTRAN. +Abaqus/CFD accepts user subroutines written in C or C++. +If an extension is given, the program will take the appropriate action based on the file type. If the +file name has no extension, the program will search for a FORTRAN, C, or C++ source file depending +on the analysis type. If the source file does not exist, an object file will be searched for instead. The +execution procedure creates a shared library using the user subroutine file that is used by the analysis +during execution. +If the same user subroutine will be needed often, consider setting the usub_lib_dir environment +file parameter and using the abaqus make execution procedure to create a shared library containing the +user subroutine. This will avoid the need to recompile and/or relink the user subroutine each time it +is needed. The user option is not required if the user subroutine called by the analysis is contained in +the user library. User libraries contained in the directory given by the usub_lib_dir environment file +parameter will not be used if the user option is specified. +The user option cannot be used to specify an object file when the double option is used to run an +Abaqus/Explicit analysis because Abaqus/Explicit double precision runs need both single precision and +double precision objects. In this case you must set the usub_lib_dir environment file parameter and +place the single and double precision object files in the specified directory; alternatively, you can supply +the user subroutine source. +oldjob +This option specifies the name of the files from a previous run from which a restart or postprocessing +(Abaqus/Standard only; see “Recovering additional results output from restart data in Abaqus/Standard” +in “Output,” Section 4.1.1) run is to be started or from which results are to be imported. A path or +file extension is not allowed. This option is required when a restart, postprocessing, symmetric model +generation, or import analysis reads data from the restart or the results file. The oldjob-name must be +different from the current job-name. +fil +This option specifies whether the data from the old results file specified in a restart run are included at the +beginning of the new results file (default). If fil=new is used, the new results file will contain only the +data from the point in the analysis where the restart occurred. This feature is used for Abaqus/Standard +runs to join the output from restarted analyses into a single, continuous results file. Non-restart jobs +cannot use this feature to append results file output to an old results file; the abaqus append execution +procedure must be used for this purpose. Setting fil=new is not allowed for Abaqus/Explicit runs. This +option is not applicable for Abaqus/CFD. +globalmodel +This option specifies the name of the global model’s results file or output database file from which the +results are to be interpolated to drive a submodel analysis. This option is required whenever a submodel +analysis or submodel boundary condition reads data from the global model’s results. The file extension +is optional. If both a results file and an output database file exist for the global model and no extension +is given, the results file will be used. This option is not applicable for Abaqus/CFD. +cpus +This option specifies the number of processors to use during an analysis run if parallel processing is +available. The default value for this parameter is 1 and can be changed in the environment file . +parallel +This option specifies the method to use for thread-based parallel processing in Abaqus/Explicit. The +possible values are domain and loop. If parallel=domain, the domain-level method is used to break +the model into geometric domains. If parallel=loop, the loop-level method is used to parallelize low- +level loops. See “Parallel execution in Abaqus/Explicit,” Section 3.5.3, for more information on these +methods. The default value is domain, which can be changed in the environment file . +domains +This option specifies the number of parallel domains in Abaqus/Explicit. If the value is greater than +1, the domain decomposition will be performed regardless of the values of the parallel and cpus +options. However, if parallel=domain, the value of cpus must be evenly divisible into the value of +domains. The default value is set equal to the number of processors used during the analysis run if +parallel=domain and 1 if parallel=loop. The default value can be changed in the environment file +(see“Using the Abaqus environment settings,” Section 3.3.1). A restart analysis uses the same number +of parallel domains as the original analysis, and the value specified with this option will be ignored. +dynamic_load_balancing +For domain-parallel execution in Abaqus/Explicit (parallel=domain) where the number of domains is +larger than the number of cpus, this option activates the dynamic load balancing scheme. Abaqus/Explicit +will attempt to improve computational efficiency by periodically reassigning domains to processors in a +way that minimizes load imbalance . +mp_mode +If this option is set equal to mpi, the MPI-based parallelization method will be used when applicable. +Set mp_mode=threads to use the thread-based parallelization method. The default value is mpi on +Windows platforms if MPI components are installed; otherwise, thread-based parallel execution is the +default behavior. On all other platforms, the default value is mpi. The default setting can be changed +in the environment file . For Abaqus/CFD +only mp_mode=mpi can be used. +standard_parallel +This option specifies the parallel execution mode in Abaqus/Standard. The possible values are all +If standard_parallel=all, both the element operations and the solver will run in +and solver. +If standard_parallel=solver, only the solver will run in parallel. The default value is +parallel. +standard_parallel=all on platforms where MPI-based parallelization is supported. +The parallel execution mode can also be set in the environment file . +gpus +This option specifies acceleration of the Abaqus/Standard direct solver. This option is meaningful only +on computers equipped with appropriate GPGPU hardware. By default, GPGPU solver acceleration +is not activated. The value of this parameter is the number of GPGPUs to use in an Abaqus/Standard +analysis. +GPGPU-based solver acceleration can also be set in the environment file . +memory +Maximum amount of memory or maximum percentage of the physical memory that can be allocated +during the input file preprocessing and during the Abaqus/Standard analysis phase . The default values can be changed in the environment +file . This option is not applicable for +Abaqus/CFD. +interactive +This option will cause the job to run interactively. For Abaqus/Standard and Abaqus/CFD the log file +will be output to the screen; for Abaqus/Explicit the status file and the log file will be output to the screen. +The default run_mode can be set in the environment file . +background +This option will submit the job to run in the background, which is the default. Log file output will be +saved in the file job-name.log in the current directory. The default method for submitting the job can +be set in the environment file by using the run_mode parameter . +queue +This option will submit the job to a batch queue. +If the option appears with no value, the job will +be submitted to the system default queue. Quoted strings are allowed. The available queues are +site specific. Contact your site administrator to find out more about local queuing capabilities. Use +information=local to see what local queuing capabilities have been installed. The default method +for submitting the job can be set in the environment file by using the run_mode parameter . +after +This option is used in conjunction with the queue option to specify the time at which the job will start +in the selected batch queue. This capability is supported for each individual site through the Abaqus +environment file. +double +This option is used to specify that the double precision executable is to be used for Abaqus/Explicit. +The possible values are both, constraint, explicit, and off. This capability is also supported +through the Abaqus environment file with the environment variable double_precision . +If double=both, both the Abaqus/Explicit packager and analysis will run in double precision. +If double=constraint, the constraint packaging and constraint solver in Abaqus/Explicit will +run in double precision, while the Abaqus/Explicit packager and Abaqus/Explicit analysis continue to +run in single precision. +If double=explicit, +the Abaqus/Explicit analysis will run in double precision, while the +packager will still run in single precision. The default value is explicit. +If double=off, +the environment file setting is overridden if necessary to invoke both the +Abaqus/Explicit packager and Abaqus/Explicit analysis in single precision. For a discussion of when to +use the double precision executable, see “Defining an analysis,” Section 6.1.2. +scratch +This option is used to specify the name of the directory used for scratch files. On UNIX platforms the +default value is the value of the $TMPDIR environment variable or /tmp if $TMPDIR is not defined. +On Windows platforms the default value is the value of the %TEMP% environment variable or \TEMP +if this variable is not defined. During the analysis a subdirectory will be created under this directory to +hold the analysis scratch files. The default value for this parameter can be set in the environment file . +output_precision +This option specifies the precision of the nodal field output written to the output database file +(job-name.odb). +Using output_precision=full results in double precision field output for +Abaqus/Standard analyses. To obtain double precision field output for Abaqus/Explicit analyses, use +the double option in addition to using output_precision=full. Nodal history output is available only +in single precision. This option cannot be used with the recover option. +field +This option specifies the format of field output for Abaqus/CFD. If field=odb, field output is written to +the output database file. If field=exodus, the field output is written to files in EXODUS-II format, one +file per processor. To obtain a single file for parallel execution, use field=nemesis; the file is written in +EXODUS-II format using the NEMESIS library. The default value is odb. For more information, see +“Alternate output formats in Abaqus/CFD” in “Output,” Section 4.1.1. +history +This option specifies the format of history output for Abaqus/CFD. If history=odb, history output +is written to the output database file. If history=csv, history output is written to a file in comma- +separated values format. +The default value depends on the setting for the field option. When field=odb, the default +is history=odb. When field=exodus or nemesis, the default is history=csv. For more +information, see “Alternate output formats in Abaqus/CFD” in “Output,” Section 4.1.1. +madymo +This option is used to specify the MADYMO input file name for a co-simulation analysis that couples +Abaqus/Explicit and MADYMO. The MADYMO input file name must be given with the .saf +extension. For more information, see the Abaqus User’s Guide for Crash Safety Simulation Using +Abaqus/Explicit and MADYMO. +port +host +This option is used to specify the TCP/UDP port number for co-simulation between solvers using the +direct coupling interface, which includes co-simulation between Abaqus and certain third-party analysis +programs. Set port equal to the port number used for the connection. The default value is 48000. The +default port number that Abaqus uses to initiate communication can be set with the cosimulation_port +parameter in the environment file . This +option is used in conjunction with the host option. For more information, see “Selecting TCP/UDP port +numbers” in “Execution procedure for Abaqus: overview,” Section 3.1.1. +This option is used to specify the host name for co-simulation between solvers using the direct coupling +interface, which includes co-simulation between Abaqus and certain third-party analysis programs. This +option specifies the name of the machine that is hosting the connection. Refer to the third-party program +documentation to determine if the host option is required. This option is used in conjunction with the +port option. +listenerport +This option is used to specify the TCP/UDP port number for co-simulation between Abaqus solvers and +between Abaqus and certain third-party analysis programs using the SIMULIA Co-Simulation Engine. +Set listenerport equal to the port number used for the connection. Refer to the third-party program +documentation to determine if the listenerport option is required. This option is used in conjunction +with the remoteconnections option. For more information, see “Selecting TCP/UDP port numbers” in +“Execution procedure for Abaqus: overview,” Section 3.1.1. +remoteconnections +for co-simulation between +This option is used to specify the remote socket connections +Abaqus +solvers and between Abaqus and certain third-party analysis programs using the +SIMULIA Co-Simulation Engine. The remote connections list consists of a pair of entries; the first entry +identifies the host name and the listener TCP/UDP port number for the SIMULIA Co-Simulation Engine +controller, and the second entry identifies the host name and the listener TCP/UDP port number for the +remote job. The host name and port number for the controller must be the first entry. +Each entry is separated by a comma, and the host (machine) name and port number within an entry +are separated by a colon (e.g., enter discovery:20000,atlantis:30000 for an analysis where +the co-simulation controller is running on machine “discovery” using a listener port of “20000” and the +remote job is running on machine “atlantis” using a listener port of “30000”). Refer to the third-party +program documentation to determine if the remoteconnections option is required. This option is used in +conjunction with the listenerport option. For more information, see “Selecting TCP/UDP port numbers” +in “Execution procedure for Abaqus: overview,” Section 3.1.1. +timeout +This option is used to specify a timeout value in seconds for the co-simulation connection using the direct +coupling interface or the SIMULIA Co-Simulation Engine. Abaqus terminates if it does not receive +any communication from the coupled analysis program during the time specified. The default value is +3600 seconds. The default timeout value that Abaqus uses can be set with the cosimulation_timeout +parameter in the environment file . +Additional option available for the datacheck module +unconnected_regions +This option is used to request that Abaqus/Standard create element and node sets for unconnected regions +in the analysis output database. Set unconnected_regions=yes to create element and node sets that are +named MESH COMPONENT N, where N is the component number. +Examples +The following examples illustrate the different functions and capabilities of the abaqus execution procedure. +Running analyses in Abaqus/Standard +Use the following command to run a heat transfer analysis called “c8” in the background: +abaqus analysis job=c8 background +The following command will run the job c8 in the background and output the current environment settings +to the log file: +abaqus analysis job=c8 information=environment background +The follow-up analysis to the heat transfer analysis c8 is “c10,” which is a static analysis that uses +temperature data from c8 as input. The temperature data are read in from the c8 results file as predefined +fields. The execution procedure scans the Abaqus/Standard input file for file dependencies of this sort. +In this example the procedure will look for the c8 results file in the current directory with the extension +.fil. The results file identifier can include a path name , and +the execution procedure will then look in the directory specified. In either case an error message will be +issued if the file does not exist. The following command is used to run the job c10 in the “long” queue: +abaqus analysis job=c10 queue=long +This job is next restarted as “c11,” using the final results from c10 as the starting point for a creep analysis. +The following command is used to run this job in the default queue: +abaqus analysis job=c11 oldjob=c10 queue= +The following command is used to run an Abaqus/Standard analysis called “draw_imp” that imports the +results from a previously run Abaqus/Explicit analysis called “draw_exp”: +abaqus analysis job=draw_imp oldjob=draw_exp +Running analyses in Abaqus/Explicit +Use the following command to submit an Abaqus/Explicit analysis called “beam” to the default queue: +abaqus analysis job=beam convert=all queue= +Equivalent results would be obtained from the following series of commands: +abaqus datacheck job=beam interactive +abaqus continue job=beam queue= +abaqus convert=all job=beam interactive +Note that the CPU-intensive analysis option is run in batch, while the other options are run interactively. +Running analyses in Abaqus/CFD +Use the following command to submit an Abaqus/CFD analysis called “cylinder” using 128 cores in +parallel: +abaqus analysis job=cylinder cpus=128 +Running different phases of an analysis +Use the following command to perform a parameter check run on an input file called “parmodel”: +abaqus job=parmodel parametercheck +Use the following command to perform a data check run on an input file called “parmodel” (the parameter +check is done again if this job is run after the previous one): +abaqus job=parmodel datacheck +The following command will continue the previous datacheck job to execute the analysis: +abaqus job=parmodel continue +Running an Abaqus/Standard to Abaqus/Explicit, Abaqus/Standard to Abaqus/CFD, or +Abaqus/Explicit to Abaqus/CFD co-simulation +This example illustrates submitting the co-simulation analyses (“Job1” and “Job2”) separately, +which also involves invoking the SIMULIA Co-Simulation Engine (CSE) controller, as described in +“SIMULIA Co-Simulation Engine controller execution,” Section 3.2.3. You can submit these jobs +using the co-simulation procedure, where the port assignments described below, as well as the launching +of the CSE controller, are performed automatically . +Use the following command for the first Abaqus analysis, running on “einstein”, to initiate +listening communication via port 55555 and to connect to the SIMULIA Co-Simulation Engine listening +on port 66666 on machine “godel” and to the other Abaqus analysis listening on port 77777 on machine +“feynman”: +abaqus job=Job1 listenerport=55555 +remoteconnections=godel:66666,feynman:77777 +Use the following command for the second Abaqus analysis, running on machine “feynman”, to +initiate listening communication via port 77777 and to connect to the SIMULIA Co-Simulation Engine +listening on port 66666 on machine “godel” and to the other Abaqus analysis listening on port 66666 on +machine “einstein”: +abaqus job=Job2 listenerport=77777 +remoteconnections=godel:66666,einstein:55555 +Use the following command for the SIMULIA Co-Simulation Engine, running on machine “godel” +and listening on port 66666 to connect to the Abaqus analyses described above: +abaqus cse job=csecontrol listenerport=66666 +remoteconnections=feynman:77777,einstein:55555 +Running a co-simulation using Abaqus/Explicit and MADYMO +Use the following command to launch an Abaqus/Explicit analysis called “vehicle” for co-simulation +with a MADYMO model called “dummy”: +abaqus job=vehicle madymo=dummy.saf +3.2.3 +SIMULIA Co-Simulation Engine CONTROLLER EXECUTION +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +Co-simulation between Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD is governed by an +additional process called the SIMULIA Co-Simulation Engine (CSE) controller. Typically, you are +not required to invoke the CSE controller process; +it is invoked automatically when you run the +Abaqus co-simulation procedure (“Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD co-simulation +execution,” Section 3.2.4). +If you are unable to use the Abaqus co-simulation procedure and are required to submit +the co-simulation analyses separately using the Abaqus execution procedure (“Abaqus/Standard, +Abaqus/Explicit, and Abaqus/CFD execution,” Section 3.2.2), you must invoke the CSE controller as +described in this section. +Command summary +abaqus cse +Command line options +job +job=cosim-job-name +listenerport=listener port-number +remoteconnections=comma-separated list of remote connection +hosts: port-numbers +[interactive] +[timeout=timeout value in seconds] +The value of this option specifies the name of the co-simulation summary log file generated during the +run. If this option is omitted from the command line, you will be prompted for its value. +listenerport +This option is used to specify the TCP/UDP port number for co-simulation inbound messages to the +controller. Set listenerport equal to the port number used for the connection. +remoteconnections +This option is used to specify the remote connections for co-simulation outbound messages between the +controller and the participating processes. One entry for each process is required, and the entries are +separated by commas. The remote connection entry consists of a host name and the listener TCP/UDP +port number separated by a colon (e.g., earth:30000,mars:40000 indicates that one process is +running on machine “earth” and using a listener port of “30000”, and another process is running on +machine “mars” and using a listener port of “40000”). +interactive +This option causes the controller to run interactively. +timeout +This option is used to specify a timeout value in seconds for the co-simulation controller connection. +The controller terminates if it does not receive any communication from the coupled analysis program +during the time specified. The default value is 3600 seconds. +Example +The following example illustrates the different functions and capabilities of the co-simulation controller +execution procedure when you are required to submit the co-simulation analyses separately. +Running an Abaqus/Standard to Abaqus/Explicit co-simulation +Use the following command for the first Abaqus analysis, running on machine “earth,” to receive +communication via port 55555: +abaqus job=explicit listenerport=55555 +remoteconnections=mercury:44444,venus:66666 +Use the following command for the second Abaqus analysis, running on machine “venus,” to receive +communication via port 66666: +abaqus job=standard listenerport=66666 +remoteconnections=mercury:44444,earth:55555 +Use the following command for the co-simulation controller running on machine “mercury,” to receive +communication via port 44444: +abaqus cse job=cosim listenerport=44444 +remoteconnections=venus:66666,earth:55555 +Abaqus/Standard, Abaqus/Explicit, AND Abaqus/CFD CO-SIMULATION +EXECUTION +CO-SIMULATION EXECUTION +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +Co-simulation between Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD can be executed by +running the Abaqus co-simulation procedure. Several parameters can be set either on the command line +or in the environment file . +A co-simulation analysis executes two “child” analyses and directs the communication of the +two processes. The co-simulation execution procedure allows you to enter a single command to +run the co-simulation and should be used whenever possible . +If you are +unable to use the Abaqus co-simulation procedure, you are required to submit the co-simulation +analyses separately using the Abaqus execution procedure (“Abaqus/Standard, Abaqus/Explicit, and +Abaqus/CFD execution,” Section 3.2.2) and to invoke the SIMULIA Co-Simulation Engine (CSE) +controller (“SIMULIA Co-Simulation Engine controller execution,” Section 3.2.3). +The co-simulation execution procedure supports a subset of the options that are available for the +Abaqus execution procedure; these options are included in the command summary below. +Allocating CPUs for parallel processing +Three methods are available for allocating CPUs to child analysis jobs for parallel processing: +specifying the number of CPUs for each job, distributing CPUs between analysis jobs, and distributing +CPUs between analysis products. +Specifying the number of CPUs for each job +The most direct method of allocating CPUs is to specify the number of CPUs to be used for each child +analysis. You provide a comma-separated pair of values using the cpus parameter. +Distributing CPUs between analysis jobs +You can specify the total number of CPUs to be used for your co-simulation analysis and weighting +factors that determine the distribution of the CPUs between the two child analyses. This method enables +you to specify a CPU count that relates directly to your resource limits and to describe the relative +computational needs of the two child analyses. You provide one value for the number of CPUs to +allocate for the co-simulation using the cpus parameter, and you define weight factors using the cpuratio +parameter. +Weight factors are floating point numbers and are considered in a normalized sense. For example, +if you wish to specify that the CPU allocation for the first child job is four times that of the second job, +you can provide any of the following pairings: +cpuratio=4.0,1.0 +cpuratio=16,4 +cpuratio=0.8,0.2 +Distributing CPUs between analysis products +You can specify the total number of CPUs to be used for your co-simulation analysis and weighting +factors that determine the distribution of the CPUs between the analysis products involved in the +co-simulation. This method enables you to specify a CPU count that relates directly to your resource +limits and to describe the relative computational needs of the two child analyses based on the analysis +product used (Abaqus/Standard, Abaqus/Explicit, or Abaqus/CFD). You provide one value for the +number of CPUs to allocate for the co-simulation using the cpus parameter, and you define weight +factors in the environment file using the cpus_weight_std, cpus_weight_xpl, and cpus_weight_cfd +environment variable parameters . +Weight factors are interpreted in a normalized sense. For example, if you wish to specify that the +CPU allocation for the Abaqus/CFD analysis is twice that of the Abaqus/Explicit analysis, you define +the parameters in the environment file as follows: +cpus_weight_xpl=1 +cpus_weight_cfd=2 +Rounding considerations for distributing CPUs +In cases where the distribution of the CPUs between analysis jobs or analysis products does not result +in whole numbers, Abaqus rounds down the CPU allocation for the first job listed in the job parameter +and rounds up the allocation for the second job listed. For example, if 8 CPUs are allocated and the CPU +allocation for the Abaqus/CFD analysis is twice that of the Abaqus/Explicit analysis, the distribution +between Abaqus/Explicit and Abaqus/CFD is 2/6 if the Abaqus/Explicit job is listed first and is 3/5 if the +Abaqus/CFD job is listed first. +Specifying options for child analyses +Command line options that pertain to the child analyses require you to enter a comma-separated pair +of values. The order of entries in the pairing must be consistent for all child analysis options to obtain +the desired co-simulation execution behavior. For example, in an Abaqus/Standard to Abaqus/Explicit +co-simulation, if you specify the job name for the Abaqus/Standard analysis as the first entry for the job +parameter, the first entry for the remainder of the child analysis options will apply to the Abaqus/Standard +analysis. +If an option is relevant for only one of the child analyses, you can enter a value of NONE for the +analysis in which the option is not relevant. In cases where you wish to use the default settings for an +option for both child analyses or wish to use environment settings to control the behavior, you need not +provide that option in the command line. +Limitations +The following limitations apply to the co-simulation execution procedure: +• Only co-simulation between two analyses is supported. +• The analyses can be run only on a single machine or a compute cluster where the head node can be +shared by both child analysis jobs. +• Co-simulation with third-party applications is not supported with this execution procedure; for +information on Abaqus job execution for co-simulation with third-party applications, consult the +third-party program documentation. +Command summary +abaqus cosimulation +cosimjob=cosim-job-name +job=comma-separated pair of job names +[cpus={number-of-cpus | comma-separated pair of number-of-cpus}] +[cpuratio=comma-separated pair of weight factors specifying cpu +allocation to child analyses] +[interactive | background | queue=[queue-name] [after=time] ] +[timeout=co-simulation timeout value in seconds] +[portpool=colon-separated pair of socket port numbers] +[input=comma-separated pair of input-file names] +[user=comma-separated pair of {source-file | object-file} names] +[globalmodel=comma-separated pair of {results file | output database +file} names] +[memory=comma-separated pair of memory-sizes] +[oldjob=comma-separated pair of oldjob-names] +[double=comma-separated pair of double precision executable +settings] +[scratch=comma-separated pair of scratch-dir names] +[output_precision=comma-separated pair of {single | full}] +[field=comma-separated pair of field output format settings] +[history=comma-separated pair of history output format settings] +Command line options +Required global option +cosimjob +This option specifies the name of the co-simulation summary log file generated during the run. If this +option is omitted from the command line, you will be prompted for its value. +Required option for child analyses +job +The comma-separated values of this option specify the names of all child analysis files generated during +the run. If this option is omitted from the command line, you will be prompted for its value. +Parallel processing options +cpus +This option is used to specify how CPUs are allocated for the co-simulation during parallel processing. +The default value for this parameter is 2 and can be changed to a value greater than 2 in the environment +file . +If this option is set equal to a single value, that value specifies the total number of processors +allocated for the co-simulation, which can be distributed between child analyses or between analysis +products. The distribution of the CPUs between child analyses is split evenly by default and may be +further controlled either by using the cpuratio parameter or by defining the distribution of the CPUs +between analysis products by setting the cpus_weight_std, cpus_weight_xpl, and cpus_weight_cfd +environment file parameters . +If this option is set equal to a comma-separated pair of values, these values specify the number of +processors to be used for each child analysis. +cpuratio +The comma-separated values of this option specify the relative weighting of the distribution of processors +allocated to each child analysis. This option is valid only when the cpus option is set to a single value. +Additional global options available +interactive +This option causes the co-simulation job to run interactively. A summary log file will be output to the +screen, and the child analysis summary output will be written to their separate log files. +background +This option submits the co-simulation job to run in the background, which is the default. Log file output +is saved for the co-simulation job in the file cosim-job-name.log and in the child analysis files job- +name.log in the current directory. +queue +This option submits the co-simulation job to a batch queue. If the option appears with no value, the +job is submitted to the system default queue. Quoted strings are allowed. The available queues are site +specific. Contact your site administrator to find out more about local queuing capabilities. +after +This option is used in conjunction with the queue option to specify the time at which the job will start +in the selected batch queue. This capability is supported for each individual site through the Abaqus +environment file. +timeout +This option is used to specify a timeout value in seconds for the co-simulation connection. Abaqus +terminates if it does not receive any communication between the child analysis processes during the time +specified. The default value is 3600 seconds. The default timeout value that Abaqus uses can be set +with the cosimulation_timeout parameter in the environment file . +portpool +This option is used to specify a colon-separated pair of TCP/UDP port numbers that represent the start +and end value of port numbers to be used when establishing connections between the child processes. +The default range is 51000:52000. The default range that Abaqus uses can be set with the portpool +parameter in the environment file . +Additional options for child analyses +input +The comma-separated values of this option specify the child analysis input file names, which may +be given with or without the .inp extension (if the extension is not supplied, Abaqus appends it +automatically). For each child analysis, if this option is not supplied, the procedure looks for an input +file called job-name.inp in the current directory. If job-name.inp cannot be found, the procedure +prompts for the input file name. +user +The comma-separated values of this option specify the names of FORTRAN source or object files that +contain any user subroutines to be used in the analysis. The names of the user routines may contain a path +name and may be given with or without a file extension. This option is not applicable for Abaqus/CFD. +globalmodel +The comma-separated values of this option specify the names of the global model’s results (.fil) file +or output database (.odb) file from which the results are to be interpolated to drive a submodel analysis. +This option is required whenever a submodel analysis or submodel boundary condition reads data from +the global model’s results. The file extension is optional. If both a results file and an output database file +exist for the global model and no extension is given, the results file is used. This option is not applicable +for Abaqus/CFD. +memory +The comma-separated values of this option specify the maximum amount of memory or maximum +percentage of the physical memory that can be allocated during the input file preprocessing and during +the Abaqus/Standard analysis phase . +This option is not applicable for Abaqus/CFD. +oldjob +The comma-separated values of this option specify the names of the files from a previous run from which +a restart run is to be started or from which results are to be imported. A path or file extension is not +allowed. This option is required when a restart or import analysis reads data from the restart file. The +oldjob-names must be different from the current job-names. +double +This option is applicable only for an Abaqus/Explicit analysis. +The comma-separated values of this option specify the double precision executable settings to be +used; the value for the Abaqus/Standard or Abaqus/CFD analysis is always NONE. The possible values +for the Abaqus/Explicit analysis are both, constraint, explicit, and off. This capability is +also supported through the Abaqus environment file with the environment variable double_precision +. +If the double option is omitted for an Abaqus/Standard to Abaqus/Explicit co-simulation, the +Abaqus/Explicit packager and analysis will be run in double precision. If the double option is omitted +for an Abaqus/CFD to Abaqus/Explicit co-simulation, the Abaqus/Explicit packager and analysis will +be run in single precision. +If double=both, both the Abaqus/Explicit packager and analysis will run in double precision. +If double=constraint, the constraint packaging and constraint solver in Abaqus/Explicit will +run in double precision, while the Abaqus/Explicit packager and Abaqus/Explicit analysis continue to +run in single precision. +If double=explicit or the double option is specified without a value, the Abaqus/Explicit +analysis will run in double precision, while the packager will still run in single precision. +If double=off, +the environment file setting is overridden if necessary to invoke both the +Abaqus/Explicit packager and Abaqus/Explicit analysis in single precision. For a discussion of when to +use the double precision executable, see “Defining an analysis,” Section 6.1.2. +scratch +The comma-separated values of this option specify the names of the directories used for scratch files. +On UNIX platforms the default value is the value of the $TMPDIR environment variable or /tmp +if $TMPDIR is not defined. On Windows platforms the default value is the value of the %TEMP% +environment variable or \TEMP if this variable is not defined. During the analysis a subdirectory will +be created under this directory to hold the analysis scratch files. +output_precision +The comma-separated values of this option specify the precision of the nodal field output written to +the output database files (job-name.odb). Using output_precision=full results in double precision +field output for Abaqus/Standard analyses. To obtain double precision field output for Abaqus/Explicit +analyses, use the double option in addition to using output_precision=full. Nodal history output is +available only in single precision. This option is not applicable for Abaqus/CFD. +field +This option is applicable only for an Abaqus/CFD analysis. +The comma-separated values of this option specify the format of the field output; the value for the +Abaqus/Standard or Abaqus/Explicit analysis is always NONE. The possible values for the Abaqus/CFD +analysis are odb, exodus, and nemesis. +If field=odb, field output is written to the output database file. If field=exodus, the field output +is written to files in EXODUS-II format, one file per processor. To obtain a single file for parallel +execution, use field=nemesis; the file is written in EXODUS-II format using the NEMESIS library. +The default value is odb. For more information, see “Alternate output formats in Abaqus/CFD” in +“Output,” Section 4.1.1. +history +This option is applicable only for an Abaqus/CFD analysis. +The comma-separated values of this option specify the format of the history output; the value for the +Abaqus/Standard or Abaqus/Explicit analysis is always NONE. The possible values for the Abaqus/CFD +analysis are odb and csv. +If history=odb, history output is written to the output database file. If history=csv, history +output is written to a file in comma-separated values format. +The default value depends on the setting for the field option. When field=odb, the default +is history=odb. When field=exodus or nemesis, the default is history=csv. For more +information, see “Alternate output formats in Abaqus/CFD” in “Output,” Section 4.1.1. +Examples +The following examples illustrate the different functions and capabilities of the abaqus cosimulation +execution procedure. +Running an Abaqus/Standard to Abaqus/CFD co-simulation interactively +Use the following command to run a co-simulation between a heat transfer analysis called “solid_heat” +and a fluids analysis called “fluid”, interactively: +abaqus cosimulation cosimjob=cosim_cht +job=solid_heat,fluid interactive +Allocating CPUs in an Abaqus/Explicit to Abaqus/CFD co-simulation +Use the following command to run a co-simulation between an Abaqus/Explicit analysis called “beam” +and an Abaqus/CFD analysis called “fluid” and to allocate 8 cores to the Abaqus/Explicit job and 16 +cores to the Abaqus/CFD job: +abaqus cosimulation cosimjob=beam_fluid job=beam,fluid cpus=8,16 +Equivalent results would be obtained using the following command: +abaqus cosimulation cosimjob=beam_fluid job=beam,fluid +cpus=24 cpuratio=1,2 +Alternatively, you can specify settings for co-simulation environment variable parameters in the +environment file and run the co-simulation execution procedure. Use the following combination of +environment file settings: +ask_delete=OFF +# The following parameters set the CPU +# allocation by analysis product +cpus_weight_xpl=1 +cpus_weight_std=1 +cpus_weight_cfd=2 +Use the following command: +abaqus cosimulation cosimjob=beam_fluid job=beam,fluid cpus=24 +Submitting an Abaqus/Standard to Abaqus/Explicit co-simulation to a batch queue +Use the following command to submit a co-simulation for an Abaqus/Explicit analysis called “beam” +and an Abaqus/Standard analysis called “beam2” to a batch queue named “long” and to allocate 8 cores +to the Abaqus/Explicit analysis and 4 cores to the Abaqus/Standard analysis: +abaqus cosimulation cosimjob=beam job=beam,beam2 +cpus=8,4 queue=long +3.2.5 +Abaqus/CAE EXECUTION +Product: Abaqus/CAE +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +Abaqus/CAE, an interactive environment for creating, submitting, monitoring, and evaluating results +from Abaqus simulations, is executed by running the Abaqus execution procedure and specifying the +cae parameter. +Command summary +abaqus cae +Command line options +database +[database=database-file] [replay=replay-file] [recover=journal-file] +[startup=startup-file] [script=script-file] [noGUI=[noGUI-file] ] +[noenvstartup] [noSavedOptions] [noSavedGuiOptions] +[noStartupDialog] [custom=script-file] [guiTester=[GUI-script] ] +[guiRecord] [guiNoRecord] +This option specifies the name of the model database file or output database file to open. To specify +a model database file, include either the .cae file extension or no file extension in the file name. To +specify an output database file, include the .odb file extension in the file name. +replay +This option specifies the name of the file from which Abaqus/CAE commands are to be replayed. The +commands in replay-file will execute immediately upon startup of Abaqus/CAE. If no file extension is +given, the default extension is .rpy. You cannot use the replay option to execute a script with control +flow statements. +recover +This option specifies the name of the file from which a model database is to be rebuilt. The commands +in journal-file will execute immediately upon startup of Abaqus/CAE. If no file extension is given, the +default extension is .jnl. +startup +This option specifies the name of the file containing Python configuration commands to be run at +application startup. Commands in this file are run after any configuration commands that have been +set in the environment file. Abaqus/CAE does not echo the commands to the replay file when they are +executed. +script +This option specifies the name of the file containing Python configuration commands to be run at +application startup. Commands in this file are run after any configuration commands that have been set +in the environment file. +Arguments can be passed into the file by entering -- on the command line, followed by the +arguments separated by one or more spaces. These arguments will be ignored by the Abaqus/CAE +execution procedure, but they will be accessible within the script. +noGUI +This option specifies that Abaqus/CAE is to be run without the graphical user interface (GUI). If no file +name is specified, an Abaqus/CAE license is checked out and the Python interpreter is initialized to allow +interactive entry of Python or Abaqus Scripting Interface commands. +If a file name is specified, Abaqus/CAE runs the commands in the file and exits upon their +If no file extension is given, the default extension is .py. This option is useful for +completion. +automating pre- or post-analysis processing tasks without the added expense of running a display. Since +no interface is provided, the scripts cannot include any user interaction. If you use the noGUI option, +Abaqus/CAE ignores any other command line options that you provide. +Arguments can be passed into the file by entering -- on the command line, followed by the +arguments separated by one or more spaces. These arguments will be ignored by the Abaqus/CAE +execution procedure, but they will be accessible within the Python script. If you are using the noGUI +option, you can use an argument to pass in a variable that would otherwise be provided by a command +line option. For example, you can pass in the name of a file that would otherwise be specified by the +script option. +noenvstartup +This option specifies that all configuration commands in the environment files should not be run at +application startup. This option can be used in conjunction with the script command to suppress all +configuration commands except those in the script file. +noSavedOptions +This option specifies that Abaqus/CAE should not apply the display options settings stored in +abaqus_v6.12.gpr (for example, the render style and the display of datum planes). For more +information, see “Saving your display options settings,” Section 76.16 of the Abaqus/CAE User’s +Manual. +noSavedGuiOptions +This option specifies +stored in +abaqus_v6.12.gpr (for example, the size and location of the Abaqus/CAE main window or its +dialog boxes). +that Abaqus/CAE should not +apply the GUI +settings +noStartupDialog +This option specifies that the Start Session dialog box for Abaqus/CAE should not be displayed. +custom +This option specifies the name of the file containing Abaqus GUI Toolkit commands. This option +executes an application that is a customized version of Abaqus/CAE. For more information, see +Chapter 1, “Introduction,” of the Abaqus GUI Toolkit User’s Manual. +guiTester +This option starts a separate user interface containing the Abaqus Python development environment +along with Abaqus/CAE. The Abaqus Python development environment allows you to create, edit, step +through, and debug Python scripts. For more information, see Part III, “The Abaqus Python development +environment,” of the Abaqus Scripting User’s Manual. +You can specify a script as the argument for this option, which prompts Abaqus/CAE to run a GUI +script. Abaqus/CAE closes when the end of the script is reached. +guiRecord +This option enables you to record your actions in the Abaqus/CAE user interface in a file named +abaqus.guiLog. You can also set this option at startup by using the environment variable +ABQ_CAE_GUIRECORD. The guiRecord option cannot be used with the guiTester option. +guiNoRecord +This option enables you to disable user +ABQ_CAE_GUIRECORD is set. +Examples +interface recording when the environment variable +The following examples illustrate the command line options of the cae execution procedure and how +arguments are passed to Abaqus/CAE. +Opening a model database +The following command will execute Abaqus/CAE and load the model database file called “beam”: +abaqus cae database=beam +Passing arguments to a script +The following command will run the Python script in a file named “try.py” at application startup and +pass “argument1” to the script: +abaqus cae script=try.py -- argument1 +The above command will print argument1 if “try.py” is defined as +import sys +print sys.argv[-1] +Running Abaqus/CAE without the graphical user interface +The following command will run the Python script in a file named “checkPartValidity.py” and pass +arguments to the script specifying the model database, the model, and the part. The script is executed by +Abaqus/CAE; however, the graphical user interface is never displayed. +abaqus cae noGui=checkPartValidity.py -- test.cae Model-1 Part-1 +The above command will print Part-1 is valid if “checkPartValidity.py” is defined as +import sys +import os +myMdb= sys.argv[-3] +myModel = sys.argv[-2] +myPart = sys.argv[-1] +mdb = openMdb(myMdb) +model = mdb.models[myModel] +part = model.parts[myPart] +if part.geometryValidity: +sys.__stderr__.write('%s is valid\n' % myPart) +else: +sys.__stderr__.write('%s is invalid\n' % myPart) +3.2.5 +Abaqus/CAE EXECUTION +This Abaqus functionality is not applicable to V6. +3.2.6 +Abaqus/Viewer EXECUTION +Product: Abaqus/Viewer +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +Abaqus/Viewer, a subset of Abaqus/CAE that contains only the postprocessing capabilities of the +Visualization module, is executed by running the Abaqus execution procedure and specifying the +viewer parameter. +Command summary +abaqus viewer +Command line options +database +[replay=replay-file] +[database=database-file] +[script=script-file] [noGUI=[noGUI-file] ] [noenvstartup] +[noSavedOptions] [noSavedGuiOptions] [noStartupDialog] +[custom=script-file] [guiTester=[GUI-script] ] [guiRecord] +[guiNoRecord] +[startup=startup-file] +This option specifies the name of the output database file to use if it is different from job-name. The +procedure searches for database-file as entered on the command line with the .odb file extension. +replay +This option specifies the name of the file from which Abaqus/Viewer commands are read. The commands +in replay-file will execute immediately upon startup of Abaqus/Viewer. If no file extension is given, the +default extension is .rpy. You cannot use the replay option to execute a script with control flow +statements. +startup +This option specifies the name of the file containing the Python configuration commands to be run at +application startup. Commands in this file are run after any configuration commands that have been set +in the environment file. Abaqus/Viewer does not echo the commands to the replay file when they are +executed. +script +This option specifies the name of the file containing Python configuration commands to be run at +application startup. Commands in this file are run after any configuration commands that have been set +in the environment file. +noGUI +This option specifies that Abaqus/Viewer is to be run without the graphical user interface (GUI). If no +file name is specified, an Abaqus/Viewer license is checked out and the Python interpreter is initialized +to allow interactive entry of Python or Abaqus Scripting Interface commands. +If a file name is specified, Abaqus/Viewer runs the commands in the file and exits upon their +If no file extension is given, the default extension is .py. This option is useful for +completion. +automating post-analysis processing tasks without the added expense of running a display. Since no +interface is provided, the scripts cannot include any user interaction. +noenvstartup +This option specifies that all configuration commands in the environment files should not be run at +application startup. This option can be used in conjunction with the script command to suppress all +configuration commands except those in the script file. +noSavedOptions +This option specifies that Abaqus/Viewer should not apply the display options settings stored in +abaqus_v6.12.gpr (for example, the render style and the display of boundary conditions). For +more information, see “Saving your display options settings,” Section 76.16 of the Abaqus/CAE User’s +Manual. +noSavedGuiOptions +stored in +This option specifies +abaqus_v6.12.gpr (for example, the size and location of the Abaqus/CAE main window or its +dialog boxes). +should not apply the GUI +that Abaqus/Viewer +settings +noStartupDialog +This option specifies that the Start Session dialog box for Abaqus/Viewer should not be displayed. +custom +This option specifies the name of the file containing Abaqus GUI Toolkit commands. This option +executes an application that is a customized version of Abaqus/Viewer. For more information, see +Chapter 1, “Introduction,” of the Abaqus GUI Toolkit User’s Manual. +guiTester +This option starts a separate user interface containing the Python development environment along +with Abaqus/Viewer. The Python development environment allows you to create, edit, step through, +and debug Python scripts. For more information, see Part III, “The Abaqus Python development +environment,” of the Abaqus Scripting User’s Manual. +You can specify a script as the argument for this option, which prompts Abaqus/Viewer to run a +GUI script. Abaqus/Viewer closes when the end of the script is reached. +guiRecord +This option enables you to record your actions in the Abaqus/Viewer user interface in a file named +abaqus.guiLog. You can also set this option at startup by using the environment variable +ABQ_CAE_GUIRECORD. The guiRecord option cannot be used with the guiTester option. +guiNoRecord +This option enables you to disable user +ABQ_CAE_GUIRECORD is set. +interface recording when the environment variable +3.2.6 +Abaqus/Viewer EXECUTION +This Abaqus functionality is not applicable to V6. +3.2.7 +Python EXECUTION +Products: Abaqus/Standard Abaqus/Explicit +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +The Python language is used throughout Abaqus: +in the Abaqus Scripting Interface, in the Abaqus +environment file (abaqus_v6.env), and to perform parametric studies. The abaqus python facility +is used to access the Python interpreter. +Command summary +abaqus python +[script-file] +Command line option +script-file +The Python interpreter executes the instructions in the specified script-file. If this option is omitted from +the command line, the Python interpreter is started in interactive mode. +3.2.8 +PARAMETRIC STUDIES +Products: Abaqus/Standard Abaqus/Explicit +References +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +• “Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD execution,” Section 3.2.2 +Overview +The abaqus script facility indicates that a parametric study is to be done . Each analysis involved in the design can be executed using the execute +command . You can add any +necessary Abaqus execution options (refer to “Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD +execution,” Section 3.2.2) to the execution command for each of the analyses by specifying them on the +execOptions option of the execute command. If the script file contains references to other input files, +these files must be located in the same directory as the script file. The files created by the execution of +the script file are placed in the directory from which the Abaqus execution procedure is run. +Command summary +abaqus script +Command line options +script-file +[=script-file] +[startup=startup file-name ] +[noenvstartup] +When a script file name is specified, the parametric study module is imported and the instructions in the +parametric study script file are executed. If the script file name is omitted from the command line, the +Python interpreter is initialized by importing the parametric study module. +startup +This option specifies the name of the file containing Python configuration commands to be run at +application startup. Commands in this file are run after any configuration commands that have been set +in the environment file. +noenvstartup +This option specifies that all configuration commands in the environment files should not be run at +application startup. This option can be used in conjunction with the startup command to suppress all +configuration commands except those in the startup file. +Examples +Use the following command to execute the Python script in a file named “parstudy.psf”: +abaqus script=parstudy +The following command will initiate a Python scripting session: +abaqus script +In a Python scripting session the following command will execute the Python script in a file named “scriptfile”: +script("scriptfile") +3.2.9 +Abaqus DOCUMENTATION +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +• “Getting help,” Section 2.6 of the Abaqus/CAE User’s Manual +Overview +Abaqus documentation is installed separately from the product and is viewed through a web browser or +PDF reader. See Chapter 2, “Installing Abaqus,” of the Abaqus Installation and Licensing Guide, for +information on installing the Abaqus documentation. +The documentation consists of the following books: +• Abaqus Analysis User’s Manual +• Abaqus/CAE User’s Manual +• Abaqus Keywords Reference Manual +• Abaqus Theory Manual +• Abaqus User Subroutines Reference Manual +• Abaqus Glossary +• Abaqus Example Problems Manual +• Abaqus Benchmarks Manual +• Abaqus Verification Manual +• Abaqus Release Notes +• Abaqus Installation and Licensing Guide +• Getting Started with Abaqus: Interactive Edition +• Getting Started with Abaqus: Keywords Edition +• Abaqus Scripting User’s Manual +• Abaqus Scripting Reference Manual +• Abaqus GUI Toolkit User’s Manual +• Abaqus GUI Toolkit Reference Manual +• Abaqus Interface for MSC.ADAMS User’s Manual +• Abaqus Interface for Moldflow User’s Manual +• Using Abaqus Online Documentation +Using Abaqus documentation +To view the documentation: +1. Type abaqus doc. +The documentation collection page (index.html or index.pdf file) opens in either a web +browser or Adobe Acrobat Reader, depending on which formats of documentation were installed +and configured by your system administrator. See “Information to enter during product installation,” +Section 2.4.2 of the Abaqus Installation and Licensing Guide, and “Configuration of documentation +application” below. The documentation collection page lists the book titles grouped by category. +2. Click the title of a book to display it. +In the HTML documentation, each book opens in a new browser window or tab. The book window +contains four HTML frames: the navigation frame (top frame), the expand/collapse frame (upper +left frame), the table of contents frame (lower left frame), and the text frame (right frame). +3. Navigate and search the book’s content. +• In the HTML documentation, use any of the following methods: +– Use the buttons in the expand/collapse frame to vary the level of detail displayed in the +table of contents frame. +– Use the back and forward arrows in the text frame to navigate sequentially through the +text. You can also use the web browser functions to return to recently viewed pages. +– Expand the topic headings in the table of contents by clicking the book icon to the left of +the heading. To jump directly to a section whose title is displayed in the table of contents, +click that title. +– Use the search panel located in the navigation frame to search for specific words or +phrases. +• In the PDF documentation, use the standard controls in Adobe Acrobat Reader to navigate and +search the books. +For more detailed information on viewing and searching the HTML or PDF documentation, refer to +Using Abaqus Online Documentation. +Configuration of documentation application +The abaqus doc command locates a web browser executable or the Adobe Acrobat Reader executable +depending on which documentation format was installed and configured by your system administrator. +Configuration of web browser +If the HTML documentation was installed and configured by your system administrator, the abaqus doc +command will locate a web browser executable as follows: +• Windows platforms: The abaqus doc command uses your default web browser. +• UNIX and Linux platforms: The abaqus doc command searches the system path for Firefox. If +the help system cannot find Firefox, an error is displayed. +The browser_type and browser_path variables can be set in the Abaqus environment file +to modify the behavior of this command. For more information, see “System customization +parameters,” Section 4.1.4 of the Abaqus Installation and Licensing Guide. +Configuration of PDF reader executable +If the PDF documentation was installed and configured by your system administrator, the abaqus doc +command will locate the Adobe Acrobat Reader executable as follows: +• Windows platforms: The abaqus doc command uses the default installed Acrobat Reader. +• UNIX and Linux platforms: The abaqus doc command searches the system path for the +acroread executable. You can also set the doc_resource variable (in the Abaqus environment +file) to the path of the acroread executable. For more information, see “System customization +parameters,” Section 4.1.4 of the Abaqus Installation and Licensing Guide. +Command summary +abaqus doc +3.2.10 +LICENSING UTILITIES +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +The abaqus licensing utilities provide management and monitoring tools for both types of Abaqus +licensing: FLEXnet and Dassault Systèmes licensing. Executing the abaqus licensing command without +additional arguments displays a command usage summary of all available utilities. +For a detailed description of all of the FLEXnet Licensing utilities, refer to the FLEXnet Licensing +End User Guide Version 11.6.1. You can download this document from the Licensing section of +the Support page at www.simulia.com. Several of the most useful licensing utilities are listed in the +command summary below. +For more information, see Chapter 3, “Abaqus licensing,” of the Abaqus Installation and Licensing +Guide. +Command summary +abaqus licensing +[lmstat | lmdiag | lmpath | lmtools | dslsstat] +Command line options +lmstat +This option displays information about the location and features served by the FLEXnet Licensing servers +used to serve the Abaqus license. Additional arguments may be used with this command to generate more +license usage information. +lmdiag +This option displays information relating to the various FLEXnet Licensing features and indicates +whether or not the feature may be checked out. +lmpath +This option can be used to control where Abaqus looks for licenses. Additional arguments are used to +print, set, or add license location information. Running the command without arguments will display the +command summary for each action. +lmtools +This option starts the FLEXnet Licensing toolchest on Windows platforms. This application can be used +to invoke most FLEXnet Licensing administration tool functions. +dslsstat +This option displays information about the location and features served by the Dassault Systèmes license +server (DSLS). See “Using the dslsstat utility for the Dassault Systèmes license server,” Section 3.9 +of the Abaqus Installation and Licensing Guide, for more information. +3.2.11 +ASCII TRANSLATION OF RESULTS (.FIL) FILES +Products: Abaqus/Standard Abaqus/Explicit +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +The abaqus ascfil translation facility: +• is provided to convert results (.fil) files (produced by an Abaqus analysis) to ASCII format for +porting between dissimilar operating systems; +• permits the movement of results data to a different system for postprocessing; and +• can also be used to convert a results file in ASCII format to binary format to save disk space. +Command summary +abaqus ascfil +Command line options +job +job=job-name +[input=input-file] +This option specifies the input and output file names to use during results file translation. The job-name +value is used as the default input file name. The translated output file will have the name job-name.fin. +If the input file is in binary format (default), this utility will create the job-name.fin file in ASCII +format. To transfer the results file back to binary format after porting to a dissimilar operating system, +rename the job-name.fin file to job-name.fil, and use this utility again; the resulting job-name.fin +file will be in binary format. +If this option is omitted from the command line, you will be prompted for this value. +input +This option specifies the name of the input file if it is different from job-name. +Example +To convert the results file c4.fil from binary to ASCII format, use the following command: +abaqus ascfil job=c4 +The translated file will have the name c4.fin. +3.2.12 +JOINING RESULTS (.FIL) FILES +Products: Abaqus/Standard Abaqus/Explicit +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +The abaqus append postprocessing facility: +• is provided to join results (.fil) files into a single file; +• permits two results files that may be either ASCII or binary files, or a combination of ASCII and +binary, to be joined for further postprocessing; and +• will write a results file in the same format as the file specified with the oldjob option. +A similar utility, abaqus restartjoin, is used to join output database (.odb) files. See “Joining +output database (.odb) files from restarted analyses,” Section 3.2.18, for details. +Command summary +abaqus append +Command line options +job +job=job-name +oldjob=oldjob-name +input=input-file +This option specifies the output file name to use during execution. The job-name value is used as the +output file name. The joined output file will have the name job-name.fil. +If this option is omitted from the command line, you will be prompted for this value. +oldjob +This option specifies the name of the first results file to use during execution. The oldjob-name value is +used as the results file name. +If this option is omitted from the command line, you will be prompted for this value. +input +This option specifies the name of the second results file to use during execution. The input-file results +file will be appended to the oldjob-name results file. +If this option is omitted from the command line, you will be prompted for this value. +Example +The following command will append the history contents of the fjoin003.fil results file to the end of +the fjoin002.fil results file and create the file fjoin001.fil: +abaqus append job=fjoin001 oldjob=fjoin002 input=fjoin003 +3.2.13 +QUERYING THE KEYWORD/PROBLEM DATABASE +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +The abaqus findkeyword utility queries a keyword/problem database that contains information +on Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD example problems, verification problems, +problems used in training seminars, problems shown in the Abaqus technology briefs, benchmark timing +problems, and those in the tutorial book Getting Started with Abaqus: Keywords Edition. You specify +which keywords, parameters, and values are of interest; and this utility will list the input files that +contain those keywords, parameters, and values. You can specify multiple keywords, which causes the +findkeyword utility to list those input files that contain all of the specified keywords. You can then use +the abaqus fetch utility to fetch the input files . The +output is grouped into problem sets; e.g., Abaqus Example Problems or Abaqus/Standard Technology +Brief Problems. +Command summary +abaqus findkeyword +keyword data lines +Command line options +job +[job=job-name] +[maximum=maximum-output] +This option is used to specify the output file name for the output listing. If this option is omitted from +the command line, the output will be printed to the standard output device. +maximum +This option is used to limit the number of sample problems that are listed for each set. If this option is +omitted, a maximum of 100 sample problems are listed for each set. +keyword data lines +The keyword data lines specify which Abaqus keywords, parameters, and values are of interest to the user. +The names of sample problems that contain the specified keywords, parameters, and values are printed +to the standard output device or to the file indicated by the job command line parameter. The keyword +is required, but parameters and values are optional. If a keyword is specified without a parameter or a +value, all sample problems that use that keyword (with or without parameters and values) will be listed. +If a parameter is specified without a value, all sample problems that use that parameter with any value +will be listed. Parameter values that are user-specified data (e.g., numeric data, set names, orientation +names, etc.) are ignored. The end of the keyword data lines is indicated by an empty line or an end of +file. +Examples +The following examples illustrate the different types of search criteria utilized by the findkeyword execution +procedure. +Querying for keywords and parameters +To list the sample problems that use the *RESTART option with the WRITE parameter, type the following +command and data lines: +abaqus findkeyword +*RESTART,WRITE +To generate a list of sample problems that contain two keyword lines in the same file, both keywords are +included as data lines. For example, +abaqus findkeyword +*RESTART,WRITE +*NGEN +To list all sample problems that use a keyword and parameter with a value, the value must be included +on the data line. For example, +abaqus findkeyword job=beam +*BEAM SECTION,SECTION=ARBITRARY +The output is written to the file beam.dat. +Querying for user-specified parameter values +User-specified parameter values (e.g., numeric data, set names, orientation names, etc.) are ignored. The +following two examples are equivalent because the value MYSET is an element set name. +abaqus findkeyword +*ELSET,ELSET=MYSET +abaqus findkeyword +*ELSET,ELSET +3.2.14 +FETCHING SAMPLE INPUT FILES +Products: Abaqus/Standard Abaqus/Explicit +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +The abaqus fetch utility is used to extract sample Abaqus input files, user subroutine files, journal files, +parametric study script files, or postprocessing programs from the compressed archive files provided with +the release (for problems in the Abaqus Example Problems Manual, the Abaqus Benchmarks Manual, +and the Abaqus Verification Manual). File names are specified in the manuals. If no file extension is +specified, all files corresponding to the name given will be extracted. +Wildcard expressions can be used when specifying the file names and include the following: +• An asterisk (*) matches a sequence of zero or more characters. +• A question mark (?) matches exactly one character. +• A bracketed item [...] matches any single character found inside the brackets; ranges are specified +by a beginning character, a hyphen, and an ending character. If an exclamation point (!) or a caret +(^) follow the left bracket, the range of characters within the brackets is complemented; that is, +anything except the characters inside the brackets is considered a match. +Any character that might otherwise be interpreted or modified by the operating system, particularly on +UNIX platforms, should be placed inside quotation marks. If no matches are found using the wildcard +expressions, the abaqus fetch utility attempts to extract a file with the name specified. +Command summary +abaqus fetch +Command line options +job +job=job-name +[input=input-file] +This option is used to specify the output file name for the fetched input file or files. It is also the default +name of the input file to fetch. +If this option is omitted from the command line, you will be prompted for this value. +input +This option is used to specify the name of the input file or files to fetch if it is different from the job-name. +Examples +To fetch the example input file c2.inp from the archive files, use the following command: +abaqus fetch job=c2.inp +To fetch all files associated with job c8 from the archive files, do not specify a file extension. The following +command will extract both the input file (c8.inp) and the user subroutine file (c8.f): +abaqus fetch job=c8 +To fetch the sample parametric study scripting file parstudy.psf from the archive files, use the following +command: +abaqus fetch job=parstudy.psf +3.2.15 +MAKING USER-DEFINED EXECUTABLES AND SUBROUTINES +Products: Abaqus/Standard Abaqus/Explicit +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +The abaqus make utility is used to create user postprocessing executables and user-defined libraries +of Abaqus user subroutines. The commands used to compile and link a user-supplied program or user +subroutine source file can be changed using the appropriate Abaqus environment file parameters; i.e., +compile_cpp, compile_fortran, link_exe, and link_sl. You can skip the compilation step by providing +a precompiled object as input for postprocessing programs. +Postprocessing executables created using this procedure must be run using the Abaqus execution +procedure. This is necessary to set the operating system environment variables for finding the Abaqus +utility libraries. To run a user postprocessing program, use the following command: +abaqus job-name +User subroutine shared libraries created using this procedure are used by specifying the +usub_lib_dir variable in the Abaqus environment file. The advantage of doing this is that an analysis +using user subroutines can execute without having to compile or link the user subroutine. +Command summary +abaqus make +Command line options +job +{job=job-name | library=source-file} +[user={source-file | object-file}] +[directory=library-dir] +[object_type={fortran | c | cpp}] +This option is used to create a user-supplied postprocessing program. The value of the option specifies +the name of the executable created by this procedure. It is also used as the default source file name. +If no option is given on the command line, you will be prompted for this value. +library +This option is used to create user subroutine object files and shared libraries. The value of the option +specifies the name of the user subroutine source file to be compiled and linked. The resulting object +and shared library files are placed in the directory given by the command line directory option. If the +directory option is not used, the files are placed in the current working directory. +The object file or files created have a suffix indicating if the user subroutine is for Abaqus/Standard +or Abaqus/Explicit. The Abaqus/Standard object file suffix is —std. Abaqus/Explicit has single and +double precision object files; the object file suffixes are —xpl and —xplD. The Abaqus/Standard user +subroutine shared library that is created is called standardU, and the Abaqus/Explicit shared libraries +are called explicitU and explicitU-D. If the directory option is used and it contains object files +with the appropriate suffix for the shared library that is being created, those files are linked to the shared +library. +user +This option is valid only when used in conjunction with the job option. It is used to specify the name of +the source or object file containing your program if it is different from job-name. If a file extension is +not provided, the option value with a FORTRAN source file extension is sought. If a file by this name +is not found, the option value with an object file extension is sought. +directory +This option is valid only when used in conjunction with the library option. It is used to specify the +destination of the user subroutine object and shared library files that will be created by the procedure. +It is also used to specify the location of additional object files that are to be linked to the shared library +or libraries being created. If the option is omitted, the files created by the procedure are placed in the +current working directory. +object_type +This option is valid only when used in conjunction with the job option. It is used to specify the type of +object file, either FORTRAN, C, or C++, given by the job or user option. +Example +To create an executable called “pprocess” given a FORTRAN source file of the same name, use the following +command: +abaqus make job=pprocess +This program can then be run using the command +abaqus pprocess +INPUT FILE AND OUTPUT DATABASE UPGRADE UTILITY +UPGRADE UTILITY +Products: Abaqus/Standard Abaqus/Explicit +References +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +• “Fixed format conversion utility,” Section 3.2.23 +Overview +The abaqus upgrade utility will convert an input file or output database file from earlier releases of +Abaqus to the current release. Input files based on the syntax of Abaqus 5.8 or later can be upgraded; +output database files from Abaqus 6.1 or later can be upgraded. The abaqus upgrade utility will generate +a log file (job-name.log) that contains error, warning, diagnostic, and informational messages. You +should carefully review the conversion log file to ensure that changes made to the older release input file +or output database file are appropriate. If no conversions are necessary, a message will be issued to the +log file as well as to the screen. +Abaqus does not allow the use of dots (".") in set, surface, or rebar names in an input file except +as delimiters between a part instance name and a set, surface, or rebar name. The abaqus upgrade +utility will change dots to underscores ("_") for dots not used as delimiters. Manual conversion of dots +to underscores will improve performance for very large input or include files. +The abaqus upgrade utility expects input files to be in free format; you can use the abaqus free +utility to convert fixed format data to free format. See “Fixed format conversion utility,” Section 3.2.23. +job=job-name +[input=old-input-file-name | odb=old-odb-file-name] +[fromversion=release] [previousdefaults] +Command summary +abaqus upgrade +Command line options +Required option +job +This option is used to specify the name of the upgraded input file or output database file to be output by +the utility. +Mutually exclusive options +input +This option is used to specify the name of the input file to be upgraded. +odb +This option is used to specify the name of the output database file to be upgraded. +Additional options +fromversion +This option is relevant for input file upgrades only. By default, the upgrade utility converts the input +file from Abaqus 6.11 to the current release. This option is used to upgrade an input file from an earlier +release. For the release number, specify the general release number (two numbers separated by a period, +such as 6.8). +previousdefaults +This option is relevant for input file upgrades only. This option is used to minimize modeling differences +between the old input file and the upgraded input file. +3.2.17 +GENERATING OUTPUT DATABASE REPORTS +Products: Abaqus/Standard Abaqus/Explicit +References +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +• “Object model for the output database,” Section 10.5 of the Abaqus Scripting User’s Manual +Overview +The output database report utility prints information from an Abaqus output database (.odb) file to a +formatted report. By default, the report is printed in plain text format; however, you can also create +reports in HTML and CSV (comma-separated values) formats. +Output database structure +Every output database consists of two main sections: model data and results data. The database is further +broken down into a hierarchical structure of containers, as indicated in Figure 3.2.17–1. +odb +mesh +sets +Model Data +steps +frames +fieldOutputs +historyRegions +invariants +components +orientation +historyOutputs +Results Data +Figure 3.2.17–1 Structure of an output database +The data that can appear in a report reside in the containers at the far right of each branch. These +containers can be used to classify the four main branches of the output database: +• The mesh branch terminates in a container holding nodal coordinates and element connectivity +information for the model. +• The sets branch terminates in a container holding the names and node or element labels of the sets +and surfaces in the model. +• The fieldOutputs branch terminates in a container holding the values of field output variables from +the analysis. These values are further broken down into their vector or tensor attributes: invariants, +components, and orientation. +• The historyOutputs branch terminates in a container holding the values of history output variables +from the analysis. +The containers in the model data section of the tree are singular containers: each model has one container +for mesh information and one container for sets information. The containers in the results section of the +tree, however, represent aggregates of multiple containers. For a multistep analysis, the output database +will have a separate step container for each step of the analysis. Within each step container will be +multiple frames and historyRegions containers. Within each individual frames container will be +multiple fieldOutputs containers, and so on. The output database assigns names or values to these +individual containers to help distinguish and identify them. +For a more detailed discussion of the output database structure, see “Object model for the output +database,” Section 10.5 of the Abaqus Scripting User’s Manual. +Generating summary reports +If you generate a report using only the required and file formatting command line options, the report will +be a brief summary of the output database. This summary contains a listing of the following information: +• Part instance names +• Number of nodes and elements in the model +• Names of sets and surfaces +• Names of steps and load cases +• Numbers of frames in the steps +• Names of field and history output variables +The information contained in this summary can help you determine the names and values of containers +in the output database. +Adding information to a report +You can create more comprehensive reports using additional command line options. Most of these +options correspond to a container in the output database structure outlined in Figure 3.2.17–1. Using +these options to specify the name or value of a container instructs the utility to extract the data found in +that container and to add it to the generated report. Container names and values are not always unique, and +may appear more than once in an output database. For example, a container corresponding to frame 1 will +likely appear in every individual step container for a multistep analysis; similarly, a container holding +a specific field output variable usually appears inside every frame of the step. The utility will add all +instances of these containers to the report. +To refine the container selection, you can combine options. When more than one container from the +same branch is indicated on the command line, the utility only reports the data that are common to both +containers. For example, if two options specify the container for Step 1 and the container for frame 3, +the utility will add results data only from the third frame of the first step to the report. If you specify +containers from different branches, the data from each container are added to the report. For example, if +the two options specify the sets container and a history region container, both sets data and history output +data are added to the report. +You identify specific containers by setting the associated option equal to the name or value of that +container. To include multiple containers of the same type, set the option equal to a comma-separated +list. The names are case-sensitive. If the names include spaces, you must enclose the entire value in +double quotation marks ("container name"). +Additional options +The output database report utility offers some additional options for controlling the organization and +details of a report. These options will have no effect unless they are invoked in conjunction with other +“container” options. +Command summary +abaqus odbreport +Command line options +Required options +[job=job-name] [odb=output-database-file] [mode={HTML | CSV}] +[all] [mesh] [sets] [results] [step={step-name | _LAST_}] +[frame={number | load-case-name | description | _LAST_}] +[framevalue={time | mode | frequency}] +[field=[field-variable] ] [components] [invariants] [orientation] +[histregion=region-name] [history=[history-variable] ] +[instance={instance-name | _NONE_}] [blocked] [extrema] +You must include at least one of the following options when executing abaqus odbreport. They +tell the utility where to find the output database and where to print the report. Use both options together +to make the report’s file name unique from the output database name. +job +This option is used to specify the file name of the generated report. If you omit this option, the utility +prints the report to the standard output device. +odb +This option is used to specify the output database (.odb) file from which the report is generated. If you +omit this option, the utility looks for an output database called job-name.odb in the current directory. +File formatting option +mode +This option specifies the file format of the generated report. If you omit this option, the report is in +plain text format with the file extension .rep. If mode=HTML, the report is in HTML format with +the file extension .htm. If mode=CSV, the report is in comma-separated values format with the file +extension .csv. +Option to generate a full output database report +all +This option is used to report all available model information and results information from every step in +the analysis; data from the base state of each step (frame zero) is not included in the report. The report +will be very long for large output databases. +Options to report model data +The following options extract information from the model data section of the output database. +mesh +This option is used to report the nodal coordinates and element connectivity associated with the model’s +mesh. +sets +This option is used to report the names and contents of all sets and surfaces associated with the model. +Options to report results data +The following options extract information from the results data section of the output database. +results +This option is used to report all field and history output variable values from the output database. If you +include any other options corresponding to specific results containers, this option is ignored. +step +This option is used to report the field and history output variable values for the specified steps. When +invoking this option, you must set it equal to at least one step name. If step=_LAST_, the report includes +results from only the last step of the analysis. +The steps container is common to both the fieldOutputs and historyOutputs branches of the +output database. If you combine the step option with a field output variable option, only field output +variable data appear in the report. Similarly, if you combine the step option with a history output variable +option, only history output variable data appear in the report. If you combine the step option with both +field and history output variable options, both types of variable data appear in the report. +Options to report field output variables +The following options extract information from containers in the fieldOutputs branch of the output +database. +frame +This option is used to report field output variable values for the specified frames. When invoking this +option, you must set it equal to at least one frame number, load case name, or frame description. The +initial (or “zero increment”) frame can be identified only by setting frame=0. If frame=_LAST_, the +report includes results from only the last frame of each included step. +framevalue +This option is used to report field output variable values for the specified frame values. Each frame can +be identified by a frame value that may be unique from the frame number. The frame value is either the +time, eigenmode number, or frequency point associated with a frame. +This option can be used as an alternative or complement to the frame option. When invoking this +option, you must set it equal to at least one frame value. The values you provide do not need to be exact; +the utility will find the frame with the closest frame value. +field +This option is used to report the specified field output variable values. If you invoke this option without +setting it equal to any variable names, all field variable containers are included in the report. +Options to report different field variable attributes +If none of the following options is invoked, the utility automatically reports components and (if +applicable) orientations for each field variable. Otherwise, the utility reports only the attributes specified +by these options. These options will have an effect only if used in conjunction with other field output +variable options. Invariants and orientations are not available for all field variables. +components +This option is used to report components for all field output variables. +invariants +This option is used to report invariant values for all field output variables. +orientation +This option is used to report the local coordinate system for each field output variable. +Options to report history output variables +The following options extract information from containers in the historyOutputs branch of the output +database. +histregion +This option is used to report history output variable values for the specified history region. When +invoking this option, you must set it equal to at least one history region name. +history +This option is used to report the specified history output variable values. If you invoke this option without +setting it equal to any variable names, all history variable containers are included in the report. +Additional options +The following options add an additional level of control and detail to a report. They are not associated +directly with the output database structure and will not add database information to a report. They must +be used in conjunction with the previously described options. +instance +This option is used to limit reported model and results data to a specific part or assembly instance in the +model. It is not directly associated with any output database containers and will not add any data to a +report. +When invoking this option, you must set it equal to at least one instance name. If instance=_NONE_, +the report includes data for the whole assembly and model. +blocked +This option is used to subdivide tables of field output variables into blocks according to part instance, +element type, and section point. It is useful if you are interested in separating output from different areas +of a large model. By default, the tables are organized according to variable name and frame. +This option instructs the report utility to access the output database using the field bulk data API. For +details about how the field bulk data API operates, see “Using bulk data access to an output database,” +Section 10.10.7 of the Abaqus Scripting User’s Manual. An additional benefit of this option is enhanced +performance of the utility when dealing with large volumes of field variables, leading to faster report +generation. The option has no effect if there are no field output variables in a report, or when the +invariants option is also specified. +extrema +This option is used to report maximum and minimum values at the end of each table of nodal coordinates +and field output variables. By default, these extrema do not appear in a report. The option will have no +effect if there are no nodal coordinates or field output variables in a report. +Examples +The following examples illustrate the capabilities of the odbreport execution procedure and the effects of +different option combinations. +File naming and formatting +The following command generates a brief summary of the output database beam.odb in a plain text +file named beam.rep: +abaqus odbreport job=beam +To create the same report in HTML format and with the name beamreport.htm, execute the following +command: +abaqus odbreport job=beamreport odb=beam mode=html +Adding information to a report +Use additional command line options to add data from specified containers to a report. The following +command creates a report listing nodal coordinates and element connectivity from the model and all +output variable values associated with the step named Apply weight: +abaqus odbreport job=beam mesh step="Apply weight" +You can refine the results data listed by using combinations of options. +In the following example, +the utility reports only history output variable values that were output from the history region named +Node350 in the Apply weight step: +abaqus odbreport job=beam step="Apply weight" +histregion=Node350 +If a container is identified by a name or value that is not unique, the generated report will include all +occurrences of that container. The following command creates a report listing the values for field variable +RF that were output in the third frame of every individual step: +abaqus odbreport job=beam frame=3 field=RF +To report the magnitude of RF instead of its components, use the invariants option: +abaqus odbreport job=beam frame=3 field=RF invariants +To add multiple containers of the same type to a report, you can set an option equal to a comma-separated +list. The following command reports all values of field output variables U and S that were output during +the steps Apply weight and Side load: +abaqus odbreport job=beam step="Apply weight","Side load" +field=U,S +Additional options +Use the instance option to limit reported information to a particular section of your model. The following +command reports set names and nodes, and values of S in the last frame of every step from the database +motor.odb. However, only information related to part instance pistonA appears in the report: +abaqus odbreport job=motor sets frame=_LAST_ field=S +instance=pistonA +Selecting frames +The frame and framevalue options can accept a wide variety of value types, making them powerful +report-building options. Because of this variety, it is sometimes necessary to invoke both options to +specify a particular frame. For example, consider the output database plate.odb, the results of a +steady-state dynamic analysis. The analysis investigated the response of a plate over a range of 20 +different frequencies under three different load cases. The output database, therefore, includes results +for the three different load cases at each frequency. You are interested in the response at 45 Hz under the +load case named lc2. Setting frame=lc2 will report field variables for load case lc2 at every frequency +(a total of 20 frames). Setting framevalue=45 will report field variables for every load case associated +with the 45 Hz frequency (a total of three frames). To limit the report to the single frame of interest, you +must invoke both options together: +abaqus odbreport job=plate frame=lc2 framevalue=45 +3.2.18 +JOINING OUTPUT DATABASE (.ODB) FILES FROM RESTARTED ANALYSES +Products: Abaqus/Standard Abaqus/Explicit +References +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +• “Continuation of output upon restart” in “Restarting an analysis,” Section 9.1.1 +Overview +The abaqus restartjoin utility appends an output database (.odb) file produced by a restart analysis of +a model to the output database produced by the original analysis of that model. Combining the original +and restart output database files into a single file enables you to examine all of the output data for the +analysis in Abaqus/CAE. +A similar utility, abaqus append, is used to join results (.fil) files. See “Joining results (.fil) +files,” Section 3.2.12, for details. +Appending data when the analysis restarts between steps versus midstep +You can append output database files from analyses that restart between steps and from analyses that +restart in the middle of a step. While the required syntax is the same for these two types of analyses, +Abaqus appends data differently, as follows: +• For an analysis that stops and restarts between steps, Abaqus simply appends the output from the +new steps to the output from the existing steps of the original analysis. +• For an analysis that stops and restarts in the middle of a step, the original and restart analyses overlap +because the restart analysis resumes at the beginning of the interrupted step. In this case the abaqus +restartjoin utility retains the results for any completed steps in the original analysis but replaces +the results for the interrupted step with the output data produced by the restart analysis. +Customizing the combined output database file +By default, Abaqus appends the output data produced by the restart analysis directly to the original output +database file. If you prefer to retain the original output database file, you can create a copy of it and +append the restart analysis output data to the copy instead. Abaqus names this copy using the format +Restart_original-odb-filename; for example, a copy of the original output database file job–1.odb +would be named Restart_job-1.odb. +Abaqus omits history data when you combine original and restart output databases; however, you +can override this default. You can also control whether Abaqus compresses the combined output database +file. +Command summary +abaqus restartjoin +Command line options +originalodb +originalodb=odb-file-name +restartodb=odb-file-name +[copyoriginal] [history] [compressresult] +This option specifies the output database file produced by the original analysis. +If you omit the +copyoriginal option, Abaqus appends the output data from the restart output database file directly to +the original output database file. +If you omit this option from the command line, Abaqus will prompt you for its value. +restartodb +This option specifies the output database file produced by the restart analysis. You can specify only one +restart analysis output database file at a time. +If you omit this option from the command line, Abaqus will prompt you for its value. +copyoriginal +If this option is specified, Abaqus creates a copy of the output database file specified by the originalodb +option and appends the contents of the restartodb output database file to that copy instead of to the +original file. When this option is omitted, Abaqus appends the output data from the restart analysis +directly to the original output database file. +Abaqus names the copied output database file by adding the prefix Restart_ to the name of the +original output database file; for example, a copy of the original output database file original.odb +would be named Restart_original.odb. +history +If this option is specified, Abaqus copies history data from the restart output database to the original +output database or its copy. Abaqus omits history data in the joined output database file unless you +specify this option. +compressresult +If this option is specified, Abaqus compresses the resulting output database file. +Examples +If your model produced an initial output database file named Job-1.odb and a restart output database file +named Job-1_res.odb, issue the following command to append the contents of the restart database to the +initial output database file: +abaqus restartjoin originalodb=Job-1.odb restartodb=Job-1_res.odb +If you prefer to retain the original output database file, you can create a copy of this original file and append +the contents of the restart output database file to the copy instead. Abaqus creates the name of the copied +output database file by adding the prefix Restart_ to the name of the original file; in the preceding example +the copy of the original file Job-1.odb would be named Restart_Job-1.odb. To perform the restart +join operation using a copy of the original file, issue the following command: +abaqus restartjoin originalodb=Job-1.odb restartodb=Job-1_res.odb +copyoriginal +By default, Abaqus does not copy history data to the combined output database. To include history data, issue +the following command: +abaqus restartjoin originalodb=Job-1.odb restartodb=Job-1_res.odb +history +3.2.19 +COMBINING OUTPUT FROM SUBSTRUCTURES +Products: Abaqus/Standard Abaqus/Explicit +References +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +• “Obtaining output of results within a substructure” in “Using substructures,” Section 10.1.1 +Overview +The abaqus substructurecombine utility combines the model and results data produced by two of +a model’s substructures into a single output database (.odb) file. By combining all of a model’s +substructure analysis output database files, you can display all of the data produced by a substructure +analysis in Abaqus/CAE. +Abaqus combines output data by adding the contents of the second file you specify (the copy output +database) directly into the first file you specify (the base output database). Because this process changes +the base output database, consider backing up your data before using this utility. +Combining data for models with more than two substructures +Because the abaqus substructurecombine utility combines data from only two output databases at a +time, you must run the utility multiple times to create a single output database from an analysis with +more than two substructures. Combine data from two of the substructures first, then repeat the operation +to combine the resulting output database file with data from each remaining substructure. +Customizing the combined output database +You can customize the substructure combine operation by adding only a subset of the data from the copy +output database into the base output database. Abaqus enables you to add output data to the base output +database from a single step or frame in the copy output database. You can also include only output data +from the copy output database that relates to a particular variable; for example, you can copy output data +related to Mises stress. +Command summary +abaqus substructurecombine +baseodb=odb-file-name +copyodb=odb-file-name +[all] [step=step-name] +[frame=frame-number] [variable=variable-key] +Command line options +baseodb +This option specifies the name of the base output database, to which Abaqus adds the contents of the +copy output database. +If you omit this option from the command line, Abaqus will prompt you for its value. +copyodb +This option specifies the name of the copy output database, which Abaqus adds to the contents of the +base output database. You can specify only one file at a time for this option. +If you omit this option from the command line, Abaqus will prompt you for its value. +all +step +This option indicates that data for all variables within all steps and frames of output should be copied +to the combined output database. When you specify this option, Abaqus ignores the step, frame, and +variable options. +This option indicates the name of the step from which Abaqus will copy results data. You can specify +only one step; if you omit this option, Abaqus copies data from the last step in the output database. +Abaqus ignores this option if you specify the all option. +frame +This option indicates the number of the frame from which Abaqus will copy results data. You can specify +only one frame; if you omit this option, Abaqus uses the last frame in the step specified by the step option. +Abaqus ignores this option if you specify the all option. +variable +This option indicates the variable key for the variable from which Abaqus will copy results data. If you +omit this option, Abaqus copies data for all variables in the output database. Abaqus ignores this option +if you specify the all option. +Only output variable keys that are valid for output database file output are available for use with +abaqus substructurecombine. In general, if a key corresponds to a collective output variable, rather +than an individual component, it can be used with this execution procedure. The collective output +variable keys are distinguished from their individual components by the fact that they have a bullet ( ) +in one of the .odb columns in the tables in “Abaqus/Standard output variable identifiers,” Section 4.2.1. +Examples +The following examples illustrate different methods of combining substructures using the abaqus +substructurecombine execution procedure. +Combining two substructures +If your model contains two substructures that produce output database files named subst1.odb and +subst2.odb, issue the following command to overwrite subst1.odb with the combined contents +of the two files: +abaqus substructureCombine baseodb=subst1.odb copyodb=subst2.odb +Combining more than two substructures +If your model contains more than two substructures, you must first combine the output database files from +two of the substructures, then combine the combined output database with each of the other substructures’ +output databases in turn. In this example the substructure analysis produces four output database files +named subst1.odb, subst2.odb, subst3.odb and subst4.odb, so you must issue the abaqus +substructure command a total of three times to combine all four files into a single output database, as +shown in the following example: +abaqus substructureCombine baseodb=subst1.odb copyodb=subst2.odb +abaqus substructureCombine baseodb=subst1.odb copyodb=subst3.odb +abaqus substructureCombine baseodb=subst1.odb copyodb=subst4.odb +Combining specific elements of the substructures +If you want to include only the output data from the step Step-1 in the combined output database, issue +the following command: +abaqus substructureCombine baseodb=subst1.odb copyodb=subst2.odb +step="Step-1" +If you want to include only the output data from the Mises variable in the combined output database, +issue the following command: +abaqus substructureCombine baseodb=subst1.odb copyodb=subst2.odb +variable="Mises" +COMBINING DATA FROM MULTIPLE OUTPUT DATABASES +COMBINING OUTPUT DATABASES +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD +References +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +• “Joining output database (.odb) files from restarted analyses,” Section 3.2.18 +• “Combining data from multiple output databases,” Section 82.13 of the Abaqus/CAE User’s +Manual, in the online HTML version of this manual +Overview +The abaqus odbcombine utility combines the results data in two or more Abaqus output database files +(.odb) into a single output database (.odb) file. The abaqus odbcombine utility is intended for the +combination of output databases containing different results. If you want to combine output databases +from the same analysis before and after a restart, use the abaqus restartjoin execution procedure instead. +For more information, see “Joining output database (.odb) files from restarted analyses,” Section 3.2.18. +Abaqus includes all model data from the selected output databases in the combined output database; +however, for results data you can choose to include a subset of the data from the output databases that +you specify. Abaqus/CAE determines which results data are included in the combined output database +based on two factors: the filtering options you specify and your selection of master output database. +Filters +You can filter the data that the utility includes in the combined output database to include results only +from selected steps or frames, from selected output variables, or from a combination of these options. +For example, a filter can enable you to include results data only from the last step and the last frame of +the specified output databases, and the same filter can dictate that only Mises stress results are included +in the combined output database. You can also establish multiple filters if you want to set up different +filtering conditions for the first step than in the second step. +The abaqus odbcombine utility also provides two levels of filtering: output database–specific +filters, which filter results from only a single output database; and default filters, which apply to the +entire job. The output database–specific filters take precedence over the default filters, so Abaqus/CAE +employs the settings in the default filters only when the default filter you define does not conflict with +filters for one of the individual output databases. +The filtering syntax is flexible enough to allow you to specify multiple steps, frame, or output +variable values. You can specify multiple step names in a comma-separated list, such as Step-1, +Step-2, Step-4. For frames you can include ranges or individual values; for example, entering 1, +3, 5, 7:9 returns frames 1, 3, 5, 7, 8, and 9 to the combined output database. +You can also use the symbolic constants ’ALL’, ’FIRST’, and ’LAST’ as shortcuts to specify +the data you want to include. These options enable you to include results data from all steps or frames +and data from all output variables rather than one or more selected variables. +Master output database +One output database in every combine operation is designated as the master output database. The utility +first transfers all field output data, subject to filtering selections, from the master output database to the +combined output database. The utility then locates results data from matching steps and frames in the +subsequent output databases and copies only those data into the combined output database. This strategy +provides a more coherent structure for the combined results data. +Configuration file usage +The abaqus odbcombine utility uses data in configuration files to determine which output databases to +combine, the file to designate as the master output database, and the filtering options to enforce by default +and for each output database. The configuration file must be in .xml format, and it can have three types +of elements in the following order: +• The element specifies one or more default filtering definitions. This section +is optional, but you must include it if you want to set up default filtering for your combine operation. +• The element specifies the location of the master output database and, if desired, +one or more filtering definitions for the data in that output database. This section is required. +• One element is required for each additional output database that you want to include in the +combine operation. +You can then specify default filters for output database–specific filters by embedding +elements within the element or within one of the output database elements. +Configuration file template +The following example illustrates the structure of the configuration file for the abaqus odbcombine +utility. + +Your XML file declaration may differ from this one. + + +The default filtering element is optional. If you include this element in the configuration file, +you must include at least one element within this section. Filter elements can +use the Steps or Frames attributes to refer to symbolic constants or the StepName or +FrameIndex attributes to refer to individual steps or frames, as shown in the following examples: + + + + +Filtering elements for the master output database are optional. If you want to filter +the data from this output database, include a element within this section +for each filtering option you want to define. + + +Filtering elements for the output database are optional. If you want to filter +the data from this output database, include a element within this section +for each filtering option you want to define. + +Append an element for each additional output database you want to include. + +Data not included in combined output databases +The following types of output data are not included when you combine output database files: +• History output. +• Surface data. +• Data from analytical rigid part instances. +• Local coordinate systems associated with field output data. +Command summary +abaqus odbcombine +Command line options +job +{job=job-name} +[input=configuration-file-name] [verbose=level] +This option specifies the name of the resulting combined output database and the name of the log file. +Abaqus also searches for a configuration file by this name. +If you omit this option from the command line, Abaqus will prompt you for its value. +input +This option specifies the name of the configuration file that specifies the output databases you want to +combine and the steps, frames, and output variables to be included in the combination. The configuration +file must be in .xml format. +verbose +This option specifies the level of detail for the messages that Abaqus writes to the log file. Possible values +are 1 or 2. If you specify 1, Abaqus writes only errors and warnings to the log file; if you specify 2, +Abaqus also records the filtering options you select and lists the model data and field output data that +were successfully copied to the combined output database. +3.2.21 +NETWORK OUTPUT DATABASE FILE CONNECTOR +Products: Abaqus/CAE Abaqus/Viewer +References +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +• “Accessing an output database on a remote computer,” Section 9.3 of the Abaqus/CAE User’s +Manual +Overview +A network ODB connector creates a connection to a network ODB server that can be used to access +a remote output database. The abaqus networkDBConnector command is used to start the network +ODB server. A network ODB connector can be created from any platform—Windows, UNIX, or Linux; +however, the network ODB server must reside on a UNIX or Linux platform. +Abaqus uses password files to authenticate the connection between the client and the server. The +password on the network ODB server must be stored in a file called .abaqus_net_passwd in your +home directory on the remote system. You must update this file after 30 days, and the password must be +at least 8 characters long. +In addition, your home directory on the local client machine can contain either of the following: +• A file called .abaqus_hostname_passwd. This file allows you to connect to the remote server +on the machine called hostname. +• A file called .abaqus_net_passwd. This file allows you to connect to the network ODB server +on any machine. +The contents of the password file on both the server and the client must be identical. In addition, Abaqus +checks that you are the only user with permission to read from or to write to the password files. If neither +file exists, Abaqus tries to use remote and secure shell commands to read the password from the network +ODB server. However, the security configuration at your site may prevent Abaqus from reading the +password. +Command summary +abaqus networkDBConnector port={serverPortNumber | auto_assigned} +[timeout=time out value in seconds] +[host=hostname] +[stop] +[ping] +Command line options +port +This option specifies the port number on the network ODB server. If port=auto_assigned, Abaqus +automatically assigns the port number. +timeout +This option specifies the timeout period in seconds for the network ODB server. The server exits if it +does not receive any communication from the client during the time specified. A timeout value of zero +indicates that the server will run until it is terminated explicitly using the stop option. +host +stop +ping +This option specifies the name of the machine that is hosting the network ODB server. This option is +used with the stop and ping options. If this option is not provided, Abaqus uses the name of the machine +from which the execution procedure was issued. +This option specifies that Abaqus should stop the network ODB server that was established using the +specified host name and port number. +This option queries the network ODB file server that was established using the specified host name and +port number. Use this option to confirm that the network ODB server exists and that communications +have been established. +3.2.22 +MAPPING THERMAL AND MAGNETIC LOADS +Product: Abaqus/Standard +References +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +• “Eddy current analysis,” Section 6.7.5 +• “Predefined loads for sequential coupling,” Section 16.1.3 +• *CFLUX +• *CLOAD +Overview +The abaqus emloads utility converts results output from a time-harmonic eddy current analysis for use as +loads in a subsequent heat transfer, coupled temperature-displacement, or stress/displacement analysis. +For example, magnetic body force intensity output is converted to point loads. You specify the names +of the time-harmonic eddy current analysis results output database (.odb) file and the input file for the +subsequent analysis on the command line. The utility creates an output database file containing a mesh +that matches the mesh in your subsequent analysis and steady-state concentrated nodal fields consistent +with the time-harmonic eddy current analysis results. Your time-harmonic eddy current and subsequent +analysis meshes can be dissimilar, and results transfer ensures global conservation of the flux quantities +when your model domains match; i.e., the model boundaries are the same. You can then use this new +output database file to apply concentrated loads and concentrated heat fluxes in the subsequent analysis. +Results conversion +The utility converts whole element output quantities from a time-harmonic eddy current analysis to nodal +results. You use the options listed in Table 3.2.22–1 in the subsequent analysis to specify the output +database file (and optionally the step and increment) from which the data are to be read. +Utility execution +The utility executes in two phases. Abaqus writes progress information and, if appropriate, error +messages to the screen during each phase. +In the first phase a datacheck analysis is performed on your subsequent analysis input file to create an +output database representation of a “target” mesh. This phase requires that your input file be sufficiently +complete to successfully run abaqus datacheck, with the exception that you can have *CFLUX and +*CLOAD options that include the FILE parameter to refer to files that are not available. If this phase is +successful, the utility proceeds to the second phase; otherwise, an error message is issued. +In the second phase time-harmonic eddy current analysis load data are mapped from the source to +the target output database. In this phase all steps and increments found in the original analysis are defined +Electromagnetic +analysis output +variable +Rate of Joule heat +dissipation +EMJH +Magnetic body force +intensity +EMBF +Table 3.2.22–1 Supported results conversion. +Converted +output variable +Input file option +Concentrated +heat flux +CFL11 +Point load +components +CF +*CFLUX, FILE=odb-name, STEP=step-number, INC=inc +*CLOAD, FILE=odb-name, STEP=step-number, INC=inc +in the target output database. This phase requires that your target model domain lie within the source +model domain. If it does not, an appropriate error message is issued. +Command summary +abaqus emloads +Command line options +job +job=target-odb-name +input=subsequent analysis input-file-name +sourceodb=time-harmonic eddy current analysis odb-file-name +This option specifies the name of the resulting “target” output database file. +input +This option specifies the name of the subsequent analysis Abaqus input file. This file must be sufficiently +complete to successfully run, as described above. +sourceodb +This option specifies the name of the time-harmonic eddy current analysis output database file. +3.2.23 +FIXED FORMAT CONVERSION UTILITY +Products: Abaqus/Standard Abaqus/Explicit +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +The abaqus free utility will convert the fixed format input files used with Abaqus 5.8 to the free format +input files used with subsequent Abaqus releases. +Command summary +abaqus free +Command line options +job +job=job-name +input=input-file +This option is used to specify the name of the free format input file to be output by the utility. +input +This option is used to specify the name of the fixed format input file to be converted. +3.2.24 +TRANSLATING NASTRAN BULK DATA FILES TO Abaqus INPUT FILES +Products: Abaqus/Standard Abaqus/Explicit +References +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +• “Translating Abaqus files to Nastran bulk data files,” Section 3.2.25 +• “Importing a model from a Nastran input file,” Section 10.5.4 of the Abaqus/CAE User’s Manual +Overview +The translator from Nastran to Abaqus converts certain entities in a Nastran input file into their equivalent +in Abaqus. +Using the translator +The Nastran data must be in a file with the extension .bdf, .dat, .nas, .nastran, .blk, or .bulk. +The Nastran data entries that are translated are listed in the tables below. Other valid Nastran data are +skipped over and noted in the log file. +The translator is designed to translate a complete Nastran input file. If only bulk data are present, +the first two lines in the file should be the terminators for the executive control and case control sections, +namely: +CEND +BEGIN BULK +For normal termination, end the Nastran input data with the line +ENDDATA +Nastran solution sequences are translated to the Abaqus procedures listed in Table 3.2.24–1. The +translator attempts to create a history section based on the contents of the case control data in the +Nastran file. +Summary of Nastran entities translated +Table 3.2.24–1 Executive control data. +Nastran Statement +Abaqus Equivalent +SOL +Nastran Statement +Abaqus Equivalent +(STATICS1) +*STATIC +24 +(STATICS) +101 +(SESTATIC) +106 +(NLSTATIC) +(MODES) +*FREQUENCY +25 +(OLDMODES) +103 +(SEMODES) +(BUCKLING) +*BUCKLE +105 +(SEBUCKL) +26 +(DFREQ) +*STEADY STATE DYNAMICS, DIRECT +108 +(SEDFREQ) +27 +(DTRAN) +*DYNAMIC +109 +(SEDTRAN) +107 +(SEDCEIG) +*COMPLEX FREQUENCY +110 +(SEMCEIG) +30 +(DFREQ) +111 +(SEMFREQ) +*FREQUENCY and *STEADY STATE +DYNAMICS +31 +(MTRAN) +*FREQUENCY and *MODAL DYNAMIC +112 +(SEMTRAN) +Table 3.2.24–2 Case control data. +Nastran Command +Comment +SPC +LOAD +METHOD +SUBCASE +Selects SPC sets alone or in combinations +Selects individual loads and load combinations +Selects EIGRL, EIGR, or EIGB from bulk data for +eigenfrequency extraction and eigenvalue buckling +prediction procedures +Delimiter for steps or load cases; optional if there +is only one step +Nastran Command +Comment +TITLE +SUBTITLE +LABEL +DLOAD +LOADSET +FREQUENCY +MPC +Echoed as comment at top of input file and for each +step +Echoed as comment for the step to which it applies +Used as text following the *STEP option +Selects dynamic loads from bulk data +Selects forcing frequencies from bulk data +Selects MPCADD and MPC from bulk data if +referenced in the first SUBCASE +SUPORT1 +Selects SUPORT1 from bulk data +Selects TSTEP from bulk data +Selects DMIG from bulk data using the matrix +name from the first SUBCASE +TSTEP +K2GG +K2PP +M2GG +M2PP +B2GG +B2PP +K42GG +TEMPERATURE +Selects nodal temperatures from bulk data +SET +Selects nodal quantities for output +DISPLACEMENT +VELOCITY +ACCELERATION +SPCFORCES +PRESSURE +Table 3.2.24–3 Bulk data. +Nastran Data Entry +Comment +PARAM +CDAMP1 +CDAMP2 +PDAMP +PDAMPT +CELAS1 +CELAS2 +PELAS +PELAST +CMASS2 +CBUSH +PBUSH +PBUSHT +CWELD +PWELD +CONM1 +CONM2 +Ignored except for: +1. WTMASS, which can be used to modify density, +mass, and rotary inertia values if the wtmass_fixup +command line parameter is used +2. INREL, which if equal to −1 or −2 will create +inertia relief loads +3. G, which is translated to *GLOBAL DAMPING, +STRUCTURAL, FIELD=MECHANICAL +4. GFL, which is translated to *GLOBAL DAMPING, +STRUCTURAL, FIELD=ACOUSTIC +DASHPOT1/DASHPOT2 and *DASHPOT +SPRING1/SPRING2 and *SPRING +(CELAS2 at SPOINTs are translated to *MATRIX +INPUT, stiffness, and/or structural damping terms.) +*MATRIX INPUT mass terms +CONN3D2 and *CONNECTOR SECTION +*FASTENER and *FASTENER PROPERTY +MASS and/or ROTARY INERTIA and/or UEL +MASS and/or ROTARY INERTIA +Nastran Data Entry +Comment +CHEXA +CPENTA +CTETRA +PSOLID +PLSOLID +CQUAD4 +CTRIA3 +CQUAD8 +CTRIA6 +CQUADR +CTRIAR +PSHELL +PCOMP +PCOMPG +CSHEAR +PSHEAR +CBAR +CBEAM +PBAR +PBARL +PBEAM +PBEAML +CROD +CONROD +PROD +CGAP +PGAP +RBAR +C3D8I/C3D20R/C3D6/C3D15/C3D4/C3D10 and +*SOLID SECTION +S4/S3R/S8R/STRI65, and *SHELL SECTION, +*SHELL GENERAL SECTION, or *MEMBRANE +SECTION. +M3D4 and *MEMBRANE SECTION; T3D2 and +*SOLID SECTION +B31 and *BEAM SECTION or *BEAM GENERAL +SECTION +T3D2 and *SOLID SECTION +GAPUNI and *GAP +*COUPLING or *MPC, type BEAM +Nastran Data Entry +Comment +MAT1 +MAT2 +MAT8 +MAT9 +MAT10 +ACMODL +NSM +NSM1 +NSML +NSML1 +NSMADD +GRID +*ELASTIC, TYPE=ISO; *EXPANSION, TYPE=ISO; +*DENSITY; and *DAMPING (G is used only for +*BEAM GENERAL SECTION) +When used alone in a PSHELL, MAT2 is translated +to *ELASTIC, TYPE=LAMINA or *ELASTIC, +TYPE=ANISOTROPIC. When used in combination +with other materials, the coefficients relating +midsurface strains and curvatures to section forces +and moments are computed and entered following the +*SHELL GENERAL SECTION option. +*ELASTIC, TYPE=LAMINA; *EXPANSION, +TYPE=ORTHO; *DENSITY; and *DAMPING +*ELASTIC, TYPE=ANISOTROPIC unless the +data are found to be orthotropic, in which case +the data are analyzed to create *ELASTIC, +TYPE=ENGINEERING CONSTANTS. Also +*DENSITY; *EXPANSION, TYPE=ANISO or +ORTHO; and *DAMPING. +*ACOUSTIC MEDIUM and *DENSITY +*TIE between a *SURFACE, TYPE=ELEMENT +defining the exterior surfaces of all acoustic solid +elements and a *SURFACE, TYPE=NODE defined by +the SET1 referenced by the SSID. +*NONSTRUCTURAL MASS +*NODE and *SYSTEM +Nastran Data Entry +Comment +*SYSTEM for nodes; *TRANSFORM if referred to +on GRID; *ORIENTATION for some elements +*COUPLING and *KINEMATIC; or *KINEMATIC +COUPLING +(If the RBE2 has only two nodes and neither node has +rotational stiffness, the RBE2 is translated to *MPC, +type LINK) +*COUPLING and *DISTRIBUTING; or DCOUP3D +and *DISTRIBUTING COUPLING +Used to combine SPC/SPC1/SPCD data into a new set +*BOUNDARY +Used to combine FORCE, MOMENT, etc. data into +a new set +*CLOAD +*DLOAD +3.2.24–7 +CORD1R +CORD1C +CORD1S +CORD2R +CORD2C +CORD2S +RBE2 +RBE3 +SPCADD +SPC +SPC1 +SPCD +LOAD +FORCE +FORCE1 +FORCE2 +MOMENT +MOMENT1 +MOMENT2 +PLOAD +PLOAD1 +PLOAD2 +PLOAD4 +Nastran Data Entry +Comment +DLOAD +DAREA +LSEQ +RLOAD1 +RLOAD2 +TLOAD1 +TABLED1 +TABLED2 +TABLED4 +DELAY +DPHASE +TEMP +TEMPD +TSTEP +EIGB +EIGR +EIGRL +EIGC +TABDMP1 +FREQ +FREQ1 +FREQ2 +FREQ3 +FREQ4 +FREQ5 +MPCADD +MPC +Dynamic loads as functions of time or frequency +*INITIAL CONDITIONS, TYPE=TEMPERATURE +and *TEMPERATURE +Time step size for dynamic and modal dynamic +procedures +*BUCKLE +*FREQUENCY +*COMPLEX FREQUENCY +*MODAL DAMPING +Forcing frequencies for steady-state dynamic +procedures +*EQUATION +Nastran Data Entry +Comment +SUPORT +SUPORT1 +DMIG +GENEL +*INERTIA RELIEF and *BOUNDARY +*MATRIX INPUT and *MATRIX ASSEMBLE +*USER ELEMENT, LINEAR and *MATRIX, +TYPE=STIFFNESS +PLOTEL +Ignored unless the command line option plotel=ON. +Command summary +abaqus fromnastran +Command line options +job +job=job-name [input=input-file] +[wtmass_fixup={OFF | ON}] [loadcases={OFF | ON}] +[pbar_zero_reset=[small-real-number] ] +[distribution={OFF | preservePID | ON}] +[surface_based_coupling={OFF | ON}] +[beam_offset_coupling={OFF | ON}] +[beam_orientation_vector={OFF | ON}] +[cbar=2-node-beam-element] [cquad4=4-node-shell-element] +[chexa=8-node-brick-element] +[ctetra=10-node-tetrahedron-element] +[plotel={OFF | ON}] [cdh_weld={OFF | RIGID | COMPLIANT}] +This option is used to specify the name of the Abaqus input file to be output by the translator. It is also +the default name of the file containing the Nastran data. Diagnostics created by the translator will be +written to a file named job-name.log. +input +This option is used to specify the name of the file containing the Nastran data if it is different from +job-name. +wtmass_fixup +If wtmass_fixup=ON, the value on the Nastran data line PARAM, WTMASS, value is used as a +multiplier for all density, mass, and rotary inertia values created in the Abaqus input file. +This option can be defined in the Abaqus environment file as follows: +fromnastran_wtmass_fixup={OFF | ON} +loadcases +By default, each SUBCASE is translated to a *STEP option in Abaqus. If loadcases=ON, this behavior +is altered for linear static analyses: each SUBCASE is translated to a *LOAD CASE option, and all such +*LOAD CASE options are grouped in a single *STEP option. +This option can be defined in the Abaqus environment file as follows: +fromnastran_loadcases={OFF | ON} +pbar_zero_reset +Nastran allows beams to have zero values for cross-sectional area or moments of inertia; Abaqus does +not. Set this option equal to a small real number to reset any zero values for A, +, or J to the specified +small real number. If this option is omitted or present without a value, the default value of 1.0 × 10−20 is +used in place of the zeros. To retain the zeros in the translated Abaqus input file, set pbar_zero_reset=0. +, +This option can be defined in the Abaqus environment file as follows: +fromnastran_pbar_zero_reset=small-real-number +distribution +This option determines how shell and membrane sections in Nastran data are translated to Abaqus. If +distribution=OFF, a separate section is created for each combination of orientation, material offset, +and/or thickness. If distribution=preservePID or ON, element orientations and offsets are written +If distribution=preservePID, an Abaqus section is created +using the *DISTRIBUTION option. +corresponding to each PSHELL or PCOMP property ID. If distribution=ON, a single Abaqus section is +created for all homogeneous elements referencing the same material. +This option can be defined in the Abaqus environment file as follows: +fromnastran_distribution={OFF | preservePID | ON} +surface_based_coupling +rigid +If +Certain Nastran +one +elements +surface_based_coupling=ON, RBE2 and RBE3 elements +to *COUPLING with +the appropriate parameters. Otherwise, RBE2 elements translate to *KINEMATIC COUPLING and +RBE3 elements translate to *DISTRIBUTING COUPLING. This translation behavior also applies to +“implied” RBE2-type rigid elements used for offsets on CBAR, CBEAM, and CONM2 elements. +equivalent +translate +in Abaqus. +have more +than +For input files created with surface_based_coupling=ON, the translated elements can be visualized +and manipulated in Abaqus/CAE. However, large numbers of these elements may cause slower +performance. +This option can be defined in the Abaqus environment file as follows: +fromnastran_surface_based_coupling={OFF | ON} +beam_offset_coupling +If beam_offset_coupling=ON, beam element offsets are translated by creating new nodes at the offset +locations, changing the beam connectivity to the new nodes, and rigidly coupling the new and original +nodes. +If beam_offset_coupling=OFF, beam element offsets are translated to the *CENTROID and +*SHEAR CENTER options, which are suboptions of the *BEAM GENERAL SECTION option. +The setting for this parameter is ignored if the beam element references a PBARL or PBEAML +property or if the beam offset has a significant component in the direction of the beam axis. In these +situations the beam offsets are always translated as if beam_offset_coupling=ON. +This option can be defined in the Abaqus environment file as follows: +fromnastran_beam_offset_coupling={OFF | ON} +beam_orientation_vector +If beam_orientation_vector=OFF, beam cross-section orientations are translated by creating new nodes +at the tips of vectors defining the first principal direction of the cross-section and changing the beam +connectivity to the new nodes. +If beam_orientation_vector=ON, beam cross-sections are translated by defining vectors on the +*BEAM SECTION and *BEAM GENERAL SECTION options. +This option can be defined in the Abaqus environment file as follows: +fromnastran_beam_orientation_vector={OFF | ON} +cbar +This option is used to define the 2-node beam that is created from CBAR and CBEAM elements. The +default is B31. +This option can be defined in the Abaqus environment file as follows: +fromnastran_cbar=2-node-beam-element +cquad4 +This option is used to define the 4-node shell that is created from CQUAD4 elements. The default is S4R. +If a reduced-integration element is chosen, the enhanced hourglass formulation is applied automatically. +This option can be defined in the Abaqus environment file as follows: +fromnastran_cquad4=4-node-shell-element +chexa +This option is used to define the 8-node brick that is created from CHEXA elements. The default +is C3D8I. If a reduced-integration element is chosen, the enhanced hourglass formulation is applied +automatically. +This option can be defined in the Abaqus environment file as follows: +fromnastran_chexa=8-node-brick-element +ctetra +This option is used to define the 10-node tetrahedron that is created from CTETRA elements. The default +is C3D10. +This option can be defined in the Abaqus environment file as follows: +fromnastran_ctetra=10-node-tetrahedron-element +plotel +By default, PLOTEL elements are not translated. If plotel=ON, PLOTEL elements are translated to T3D2 +truss elements in an element set named PLOTEL_TRUSSES. The cross-sectional area of the trusses is +the value entered for pbar_zero_reset, and the material has a Young’s modulus, E, equal to 1.0. +cdh_weld +By default, CHEXA elements with RBE3 elements at all eight corner nodes are translated to the type of +8-node element specified in the chexa parameter. If cdh_weld=RIGID, CHEXA elements with RBE3 +elements at all eight corner nodes are translated to rigid fasteners in Abaqus. If cdh_weld=COMPLIANT, +CHEXA elements with RBE3 elements at all eight corner nodes are translated to compliant fasteners in +Abaqus. +3.2.25 +TRANSLATING Abaqus FILES TO NASTRAN BULK DATA FILES +Products: Abaqus/Standard Abaqus/Explicit +References +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +• “Translating Nastran bulk data files to Abaqus input files,” Section 3.2.24 +Overview +The translator from Abaqus to Nastran converts certain entities in an Abaqus file into equivalent entities +in Nastran. Only “flat” Abaqus files can be translated; i.e., the Abaqus file cannot contain parts and +assemblies. +Using the translator +The Abaqus input data must be in a file with the extension .inp or .sim. If you specify an .inp +file, the execution procedure translates selected keywords and creates a Nastran bulk data file with the +extension .bdf. If you use the substructure option and specify a .sim file, the execution procedure +translates the substructure data and creates a Nastran bulk data file with the extension .bdf. +Summary of Abaqus keywords translated +In the *ELEMENT usages listed below, an italicized x indicates that all Abaqus elements beginning with +the preceding label will be mapped to the Nastran entity shown. For example, the statement *ELEMENT, +C3D4x indicates that the selected Abaqus-to-Nastran translation applies to the Abaqus elements C3D4, +C3D4H, and C3D4T. +Table 3.2.25–1 Abaqus keyword–to–Nastran mapping. +Abaqus Keyword +Nastran Complement +*BEAM GENERAL SECTION, +SECTION=GENERAL +*BOUNDARY +*CLOAD +*COUPLING, DISTRIBUTING +*COUPLING, KINEMATIC +*ELEMENT, B31 +PBAR +SPC +FORCE +RBE3 +RBE2 +CBAR (for *BEAM GENERAL SECTION, +SECTION=GENERAL) +Abaqus Keyword +*ELEMENT, B33 +Nastran Complement +CBAR (for *BEAM GENERAL SECTION, +SECTION=GENERAL) +CQUAD4 +CQUAD8 +CTETRA +CTETRA +CPENTA +CPENTA +CHEXA +CHEXA +CONM2 +CONM2 +CTRIA3 +*ELEMENT, C3D4x +*ELEMENT, C3D10x +*ELEMENT, C3D6x +*ELEMENT, C3D15x +*ELEMENT, C3D8x +*ELEMENT, C3D20x +*ELEMENT, MASS +*ELEMENT, ROTARYI +*ELEMENT, S3x +*ELEMENT, S4x +*ELEMENT, S8x +*ELEMENT, SPRING1 or SPRING2 +*ELEMENT, SPRINGA +*ELEMENT, STRI65 +*ELEMENT, T3D2 +*FREQUENCY +*HEADING +*MATERIAL, DENSITY +*MATERIAL, ELASTIC, TYPE=ISO +*MATERIAL, ELASTIC, TYPE=LAMINA +*MATERIAL, EXPANSION, TYPE=ISO +*MATERIAL, EXPANSION, TYPE=ORTHO MAT8 +*NODE +GRID +*ORIENTATION, +DEFINITION=COORDINATES +MAT1 +MAT1 +MAT8 +MAT1 +CELAS +CROD +CTRIA6 +CROD +SOL 103 +TITLE +CORD2R, CORD2C, or CORD2S +Abaqus Keyword +Nastran Complement +*SHELL GENERAL SECTION +(Non-composite) +*SHELL SECTION (Non-composite) +*SHELL SECTION (Composite) +*SHELL GENERAL SECTION (Composite) +*SOLID SECTION +*SOLID SECTION (Trusses) +*STATIC +*SYSTEM +*TRANSFORM +PSHELL +PCOMP +PSOLID +PROD +SOL 101 +CORD2R, CORD2C, or CORD2S +Command summary +abaqus tonastran +job=job-name [input=input-file] [substructure] +Command line options +job +This option is used to specify the name of the Nastran bulk data file to be output by the translator. It is +also the default name of the Abaqus file. Diagnostics created by the translator are written to a file named +job-name.log. +input +This option is used to specify the name of the file containing the Abaqus data if it is different from +job-name. +substructure +This option is used to translate a substructure within an Abaqus .sim file into Nastran bulk data file +(.bdf) format. +3.2.26 +TRANSLATING ANSYS INPUT FILES TO Abaqus INPUT FILES +Products: Abaqus/Standard Abaqus/Explicit +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +The translator from ANSYS to Abaqus converts certain entities in an ANSYS blocked coded database +file into their equivalent in an Abaqus input file. +Using the translator +The abaqus fromansys translator can convert ANSYS blocked coded database files (.cdb) into a “flat” +Abaqus input file; that is, an Abaqus input file that is not written in terms of parts and assemblies. The +.cdb file must be created in ANSYS using the following command: +CDWRITE , , , cdb +The second field of the CDWRITE command may contain ALL or DB. The eighth field may contain +BLOCKED. Any other use of the CDWRITE command will create problems for the translator. +Summary of ANSYS entities translated +The translator from ANSYS to Abaqus supports the mappings shown in the tables below. +Table 3.2.26–1 Nodal data mapping for ANSYS commands. +ANSYS +command +NBLOCK +Abaqus equivalent +*NODE +*TRANSFORM +Table 3.2.26–2 Element data mapping for ANSYS structural lines. +ANSYS +command +LINK1 +LINK8 +LINK10 +Abaqus equivalent +*ELEMENT, TYPE=T2D2 +*ELEMENT, TYPE=T3D2 +*ELEMENT, TYPE=T3D2 +ANSYS +command +LINK11 +LINK180 +Abaqus equivalent +*ELEMENT, TYPE=T3D2 +*ELEMENT, TYPE=T3D2 +Table 3.2.26–3 Element data mapping for ANSYS structural beams. +ANSYS +command +BEAM3 +BEAM4 +BEAM23 +BEAM24 +BEAM188 +BEAM189 +Abaqus equivalent +*ELEMENT, TYPE=B21 +*ELEMENT, TYPE=B31 +*ELEMENT, TYPE=B21 +*ELEMENT, TYPE=B31 +*ELEMENT, TYPE=B31 or B32 +*ELEMENT, TYPE=B32 +Table 3.2.26–4 Element data mapping for ANSYS structural shells. +ANSYS +command +SHELL43 +SHELL63 +SHELL93 +SHELL181 +Abaqus equivalent +*ELEMENT, TYPE=S4 or S3 +*ELEMENT, TYPE=S4, S3, M3D4, or M3D3 +*ELEMENT, TYPE=S8R or STRI65 +*ELEMENT, TYPE=S4R or S3R +Table 3.2.26–5 Element data mapping for ANSYS structural pipes. +ANSYS +command +PIPE16 +PIPE20 +PIPE59 +Abaqus equivalent +*ELEMENT, TYPE=PIPE32 +*ELEMENT, TYPE=PIPE31 +*ELEMENT, TYPE=PIPE31 +Table 3.2.26–6 Element data mapping for ANSYS planar elements. +Abaqus equivalent +*ELEMENT, TYPE=CPSn, CAXn, or CPEn +ANSYS +command +PLANE42 +PLANE82 +PLANE182 +PLANE183 +Table 3.2.26–7 Element data mapping for ANSYS solid elements. +ANSYS +command +SOLID45 +SOLID65 +SOLID92 +SOLID95 +SOLID147 +SOLID148 +SOLID185 +SOLID186 +SOLID187 +Abaqus equivalent +*ELEMENT, TYPE=C3D8I, C3D4, or C3D6 +*ELEMENT, TYPE=C3D8I, C3D4, or C3D6 +*ELEMENT, TYPE=C3D10 +*ELEMENT, TYPE=C3D20, C3D10, or C3D15 +*ELEMENT, TYPE=C3D20, C3D10, or C3D15 +*ELEMENT, TYPE=C3D10 +*ELEMENT, TYPE=C3D8, C3D4, or C3D6 +*ELEMENT, TYPE=C3D20R, C3D10, or C3D15 +*ELEMENT, TYPE=C3D10 +Table 3.2.26–8 Load and boundary condition data mapping. +ANSYS command +SFE, ELEM, LKEY, PRES, KVAL, VAL1, VAL2, +VAL3, VAL4, +where VAL1=VAL2=VAL3=VAL4=n +SFE, ELEM, LKEY, HFLU, KVAL, VAL1, VAL2, +VAL3, VAL4, +where VAL1=VAL2=VAL3=VAL4=n +BF, NODE, TEMP, VAL1, VAL2, VAL3, VAL4 +Abaqus equivalent +*SURFACE and *DSLOAD +*SURFACE and *DSFLUX +*TEMPERATURE and +*CFLUX +ANSYS command +Abaqus equivalent +BFE, NODE, HGEN, STLOCVAL1, VAL2, VAL3, +VAL4 +ACEL, 1-component, 2-component, 3-component +F, NODE, Lab, VALUE, VALUE2, NEND, NINC, +where Lab=FX, FY, or FZ +*DFLUX +*DLOAD +*CLOAD +D, NODE, Lab, VALUE, VALUE2, NEND, NINC, +where Lab=UX ,UY, UZ, ROTX, ROTY, or ROTZ +*BOUNDARY +Table 3.2.26–9 Material data mapping. +ANSYS command +Abaqus equivalent +MPTEMP, … +MPDATA, … , EX +MPDATA, … , NUXY or PRXY +MPTEMP, …. +MPDATA, … , EX +MPDATA, … , EY +MPDATA, … , EZ +MPDATA, … , NUXY or PRXY +MPDATA, … , NUXZ or PRXZ +MPDATA, … , NUYZ or PRYZ +MPDATA, … , GXY +MPDATA, … , GXZ +MPDATA, … , GYZ +MPTEMP, … +MPDATA, … , KXX +MPTEMP, … +MPDATA, … , DENS +MPTEMP, … +MPDATA, … , C +*MATERIAL and *ELASTIC +Minor Poisson’s ratios (such as NUXY), +if present, are automatically converted to +major Poisson’s ratios (such as PRXY). +*MATERIAL and *ELASTIC, +TYPE=ENGINEERING CONSTANTS +Minor Poisson’s ratios (such as NUXY), +if present, are automatically converted to +major Poisson’s ratios (such as PRXY). +*MATERIAL and *CONDUCTIVITY +*DENSITY +*SPECIFIC HEAT +MPTEMP, … +MPDATA, … , CTEX or ALPX +*EXPANSION +Command summary +abaqus fromansys +job=job-name [input=input-file] +Command line options +job +This option is used to specify the name of the Abaqus input file to be output by the translator. It is also +the default name of the input file containing the ANSYS data. Diagnostics created by the translator will +be written to a file named job-name.log. +input +This option is used to specify the name of the file containing the ANSYS data if it is different from +job-name. +TRANSLATING PAM-CRASH INPUT FILES TO PARTIAL Abaqus INPUT FILES +TRANSLATION FROM PAM-CRASH +Product: Abaqus/Explicit +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +The translator from PAM-CRASH to Abaqus converts certain keywords in a PAM-CRASH input file +into their equivalent in Abaqus/Explicit. +Using the translator +The translator requires an input file created by PAM-CRASH Version 2002 or later. The input file can +have any name and extension. +The PAM-CRASH data entries that are translated are listed in the tables below. Other PAM-CRASH +keywords and data are skipped over and noted in the log file. +The translator creates a partial Abaqus input file that contains only the model data. You must provide +history data (including output data) to complete the input. +Element numbering and grouping +All elements must have unique element numbers. Elements that are assigned the same PART +identification number are grouped together in an element set. +Except for connector elements that result from the translation of SPRING and KJOIN, section +properties need to be entered in the PART section rather than individually in the element section. +Elements that have different material or section properties should be given different PART identification +numbers; that is, the same material and section properties must be applicable to all elements grouped in +the same element set. +If elements that result from the translation of SPRING and KJOIN have different element data (such +as frame numbers used to define local directions), and they are assigned the same PART identification +number, the translator automatically separates them into different element sets. +Material models +The translator supports only the material models shown in Table 3.2.27–3. All unsupported material +models between Types 1 and 99 are translated as bilinear elastic-plastic, and all other material types +are translated as linear elastic if a stress-strain law definition is required. In these cases the translator +provides nominal values for the material properties. +History section data +The translator creates a history section based partially on keywords (except TITLE) from the control +section of the PAM-CRASH file as shown in Table 3.2.27–1. Other control data are unsupported. +Summary of PAM-CRASH entities translated +Table 3.2.27–1 Control section data. +PAM-CRASH keyword +Abaqus equivalent +TITLE +RUNEND +TCTRL / DYNA_MASS_SCALE +ECTRL / RATEFILTER +*HEADING +*DYNAMIC, EXPLICIT time period +*VARIABLE MASS SCALING +*MATERIAL, SRATE FACTOR +Table 3.2.27–2 Part section data. +PAM-CRASH keyword +Abaqus equivalent +PART / BAR +PART / BEAM +PART / SPRING +PART / KJOIN +PART / SOLID +PART / SHELL +PART / MEMBR +PART / TIED +PART / PLINK +Truss element properties and grouping data +Beam element properties and grouping data +Connector behavior and grouping data +Connector type, behavior, and grouping data +Solid element properties and grouping data +Shell element properties and grouping data +Membrane element properties and grouping data +Mesh tie constraint data and parameters +Mesh-independent fastener data and parameters +Table 3.2.27–3 Material section data. +PAM-CRASH keyword +Abaqus equivalent +MATER / Types 1, 16, 41, 99 +C3D4/C3D6/C3D8R; solid material model data +MATER / Types 100, 101, 102, 103, 105 +S3RS/S4RS; shell material model data +MATER / Types 150, 151 +MATER / Types 200, 201, 202 +M3D3/M3D4/M3D4R and *USER MATERIAL +T3D2/B31; beam and truss material model data +PAM-CRASH keyword +Abaqus equivalent +MATER / Types 203, 204, 205, 230 +CONN3D2; connector behavior data +MATER / Types 212, 213 +B31; beam material model data +MATER / Type 3021 +CONN3D2; connector behavior data +1 Material type 302 supports the use of a rupture model . +Table 3.2.27–4 Node section data. +PAM-CRASH keyword +Abaqus equivalent +FRAME +NODE +MASS +NSMAS +INVEL +BOUNC +DIS3D +VEL3D +DAMP +TRSFM +*ORIENTATION and *TRANSFORM +*NODE +*MASS and *ROTARY INERTIA +*NONSTRUCTURAL MASS +*INITIAL CONDITIONS, TYPE=VELOCITY or +ROTATING VELOCITY +*BOUNDARY +*BOUNDARY and *AMPLITUDE +*BOUNDARY and *AMPLITUDE +*DLOAD and *AMPLITUDE +*NODE with transformed coordinates +Table 3.2.27–5 Element section data. +PAM-CRASH keyword +Abaqus equivalent +C3D4/C3D6/C3D8R and *SOLID SECTION +C3D4 and *SOLID SECTION +S3RS/S4RS and *SHELL SECTION +M3D3/M3D4R and *MEMBRANE SECTION +B31 and *BEAM SECTION, SECTION=CIRC +For MATER / Types 203 and 204: CONN3D2 +and *CONNECTOR SECTION [AXIAL] +For all other MATER / Types: T3D2 and *SOLID +SECTION +3.2.27–3 +SOLID +TETR4 +SHELL +MEMBR +BEAM +PAM-CRASH keyword +Abaqus equivalent +SPRING +KJOIN +PLINK +CONN3D2 and *CONNECTOR SECTION [CARTESIAN ++ CARDAN] +CONN3D2 and *CONNECTOR SECTION +*FASTENER and *FASTENER PROPERTY; CONN3D2 +and *CONNECTOR SECTION +Table 3.2.27–6 Constraint section data. +PAM-CRASH keyword +Abaqus equivalent +RWALL +(Stationary, segmented finite rigid wall) +Velocity flag=0 +Wall description=20 +*RIGID BODY and *CONTACT +RBODY +Types 0, 3 +RBODY +Type 1 +CNTAC +Sliding interface types: +33, 34, 36, 37, 46 +*RIGID BODY and/or *MPC (type BEAM) +To define a group of elements as a rigid body, enter the part +identification number of that element group as the PART +entity1. +To define an element as a rigid body, enter the element +number as the ELE entity or enter all the element node +numbers as the NOD entity2 . +CONN3D2, *CONNECTOR SECTION [PROJECTION +CARTESIAN + PROJECTION FLEXION-TORSION], +*CONNECTOR DAMAGE INITIATION, and +*CONNECTOR DAMAGE EVOLUTION +*CONTACT, *CONTACT INCLUSIONS, *CONTACT +EXCLUSIONS, *CONTACT PROPERTY ASSIGNMENT, +*CONTACT FORMULATION, *SURFACE +INTERACTION, and *SURFACE PROPERTY +ASSIGNMENT +TIED +*TIE +1 If PART entities are used to define a rigid body, RBODY is translated as *RIGID BODY. +2 If the ELE and NOD entities constitute all elements in a part, RBODY is translated as *RIGID BODY. +If the ELE and NOD entities do not constitute all elements in a part (i.e., if the part consists of both rigid +and deformable elements), RBODY is translated as *MPC (MPC type BEAM), a beam-type multi-point +constraint for the set of nodes that consists of all input NOD entities and nodes extracted from all ELE +entities. +Table 3.2.27–7 Nodes/faces/elements entity selection data. +PAM-CRASH keyword +Abaqus equivalent +ELE +PART +NOD +ELE>NOD +PART>NOD +DELELE +DELPART +DELNOD +GRP +*ELSET; data for elements to be grouped in a set using +*ELSET +Data for selecting element sets (*ELSET) already defined +Data for nodes to be grouped in a set using *NSET +Same procedure as ELE +Same procedure as PART +*ELSET and *NSET +*ELSET and *NSET +*ELSET and *NSET +Named set of entities defined in GROUP +Table 3.2.27–8 Airbag data. +PAM-CRASH keyword +Abaqus equivalent +*FLUID BEHAVIOR, *MOLECULAR WEIGHT, and +*CAPACITY +*PHYSICAL CONSTANTS and *FLUID CAVITY +*INITIAL CONDITIONS +*FLUID CAVITY, BEHAVIOR or MIXTURE +*NODE, NSET=ref_node_name; *SURFACE, +TYPE=ELEMENT; and *FLUID CAVITY +M3D3/M3D4 and *SURFACE, TYPE=ELEMENT +*FLUID EXCHANGE, *FLUID EXCHANGE +ACTIVATION, and *FLUID EXCHANGE PROPERTY +*FLUID EXCHANGE, *FLUID EXCHANGE +ACTIVATION, and *FLUID EXCHANGE PROPERTY +*FLUID EXCHANGE, *FLUID EXCHANGE +ACTIVATION, and *FLUID EXCHANGE PROPERTY +3.2.27–5 +GASPEC +BAGIN +GEN_INI_COND +GAS +CHAMBER +EXT_SKIN +WALL_OPENING +WALL_FABRIC +PAM-CRASH keyword +Abaqus equivalent +INI_COND +INFLATOR +*INITIAL CONDITIONS +*FLUID INFLATOR, *FLUID INFLATOR ACTIVATION, +*FLUID INFLATOR MIXTURE, and *FLUID INFLATOR +PROPERTY +Table 3.2.27–9 Seat belt data. +PAM-CRASH keyword +Abaqus equivalent +SLIPR +RETRA +*ELEMENT, TYPE=CONN3D2; *CONNECTOR +SECTION; and *BOUNDARY +*ELEMENT, TYPE=CONN3D2; *CONNECTOR +SECTION; and *BOUNDARY +Table 3.2.27–10 Miscellaneous data. +PAM-CRASH keyword +Abaqus equivalent +GROUP +METRIC +SENSOR +FUNCT +RUPMO +THELE +THNOD +Convert entities to Abaqus equivalents +*INITIAL CONDITIONS, TYPE=REF COORDINATE +Type-1: use activation time in *AMPLITUDE +Type-4: use belt feed rate in *CONNECTOR LOCK +Data for material properties and time-dependent parameters, +such as *AMPLITUDE, *CONNECTOR ELASTICITY, +*PLASTIC, and *FLUID EXCHANGE PROPERTY +Data for connector behavior, such as *CONNECTOR +DAMAGE INITIATION, *CONNECTOR DAMAGE +EVOLUTION, *CONNECTOR POTENTIAL, and +*CONNECTOR HARDENING +Element sets defined as *ELSET; output quantities are not +specified for the element set +Node sets defined as *NSET; output quantities are not +specified for the node set +Command summary +abaqus frompamcrash +Command line options +job +job=job-name +input=input-file +[pLinkConnectors={OFF | ON}] +[splitAirbagElements={OFF | ON}] +[autoKJoinStops={OFF | ON}] +This option is used to specify the name of the Abaqus input file to be output by the translator. The name +of the Abaqus input file must be given without the .inp extension. Diagnostics created by the translator +are written to a file named job-name_frompam.log. +input +This option is used to specify the name of the file containing the PAM-CRASH data. The name of the +file must be given with the file extension. +pLinkConnectors +This option is used to specify the inclusion of connector elements in the PLINK translation. The default +value is ON. +splitAirbagElements +This option is used to specify the splitting of 4-node airbag membrane elements into two 3-node airbag +membrane elements. The default value is ON. Airbag membrane elements result from the translation of +MEMBR and MATER / Types 150 and 151. This option is valid only if the keyword BAGIN is specified +in the PAM-CRASH input file. +autoKJoinStops +This option is used to add connector stops to the behavior of all KJOIN connector elements. +If the +stiffness interpolated at an endpoint on the force-displacement curve exceeds the stiffness interpolated +at an adjacent point by a factor of 10, a connector stop is defined at the point adjacent to the endpoint. +The default value is OFF. +TRANSLATING RADIOSS INPUT FILES TO PARTIAL Abaqus INPUT FILES +TRANSLATION FROM RADIOSS +Product: Abaqus/Explicit +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +The translator from RADIOSS to Abaqus converts certain keywords in a RADIOSS input file into their +equivalent in Abaqus/Explicit. +Using the translator +The translator requires an input file in block format created by RADIOSS Version 4.4 or 5.1. The input +file can have any name and an optional extension. +The RADIOSS data entries that are translated are listed in the tables below. Other RADIOSS +keywords and data are skipped over and noted in the log file. +The translator creates a partial Abaqus input file that contains only the model data and time history +output data. You can provide additional output data to complete the input. +Element numbering and grouping +All elements in the generated Abaqus input file will have unique element numbers. New element numbers +will be assigned automatically to elements with non-unique element numbers in the RADIOSS input. +Elements that are assigned the same PART identification number are grouped together in an element set. +Elements that have different material or properties must be given different PART identification +numbers; that is, the same material and properties must be applicable to all elements grouped in the same +element set. +If elements that result from the translation of SPRING have different element properties (such as +skew systems used to define local directions) and are assigned the same PART identification number, the +translator automatically separates them into different element sets. +Material models +The translator supports only the material models shown in Table 3.2.28–1. All unsupported material +models are translated as linear elastic if a stress-strain law definition is required. +In these cases the +translator provides nominal values for the material properties. +Summary of RADIOSS entities translated +RADIOSS keyword +MAT / LAW01 (ELAST) +MAT / LAW02 (PLAS_JOHN) +MAT / LAW03 (HYDPLA) +MAT / LAW19 (FABRI) +MAT / LAW22 (DAMA) +MAT / LAW35 (FOAM_VISC) +MAT / LAW36 (PLAS_TAB) +Table 3.2.28–1 Material data. +Abaqus equivalent +*ELASTIC +*PLASTIC, HARDENING=JOHNSON COOK +*EOS, *TENSILE FAILURE, *DAMAGE INITIATION, +and *DAMAGE EVOLUTION +*USER MATERIAL +*PLASTIC, HARDENING=JOHNSON COOK; *RATE +DEPENDENT, TYPE=JOHNSON COOK; *DAMAGE +INITIATION; and *DAMAGE EVOLUTION +*HYPERFOAM and *VISCOELASTIC +*PLASTIC, HARDENING=ISOTROPIC +Table 3.2.28–2 Property data. +RADIOSS keyword +Abaqus equivalent +PROP / TRUS +PROP / BEAM +PROP / SPRING +PROP / SPR_BEAM +PROP / SPR_GENE +PROP / SOLID +PROP / SOL_ORTH +PROP / SHELL +PROP / SH_ORTH +Truss element properties and grouping data +Beam element properties and grouping data +Connector behavior and grouping data +Connector behavior and grouping data +Connector behavior and grouping data +Solid element properties and grouping data +Solid element properties and grouping data +Shell element properties and grouping data +Shell element properties and grouping data +Table 3.2.28–3 Nodal data. +RADIOSS keyword +Abaqus equivalent +NODE +ADMAS +*NODE +*MASS and *ROTARY INERTIA +Abaqus equivalent +TRANSLATION FROM RADIOSS +BCS +IMPDISP +IMPVEL +INIVEL +CLOAD +GRAV +SKEW +FRAME +*BOUNDARY +*BOUNDARY and *AMPLITUDE +*BOUNDARY and *AMPLITUDE +*INITIAL CONDITIONS, TYPE=VELOCITY or +ROTATING VELOCITY +*CLOAD and *AMPLITUDE +*DLOAD and *AMPLITUDE +*ORIENTATION and *TRANSFORM +*ORIENTATION and *TRANSFORM +Table 3.2.28–4 Element data. +RADIOSS keyword +Abaqus equivalent +BRICK +SHELL1 +SH3N1 +BEAM +TRUSS +SPRING +C3D4/C3D6/C3D8R and *SOLID SECTION +S3RS/S4RS and *SHELL SECTION; or +M3D3/M3D4/M3D4R and *MEMBRANE SECTION +S3RS and *SHELL SECTION; or M3D3 and *MEMBRANE +SECTION +B31 and *BEAM SECTION, SECTION=CIRC +T3D2 and *SOLID SECTION +CONN3D2 and *CONNECTOR SECTION +1 Shell elements with one integration point through the thickness are translated as membrane elements. +Table 3.2.28–5 Constraint data. +RADIOSS keyword +Abaqus equivalent +*RIGID BODY and *CONTACT +*RIGID BODY and/or *MPC (type BEAM) +To define an element as a rigid body, enter all the element +node numbers in the node group associated with the rigid +body. +3.2.28–3 +RWALL +RADIOSS keyword +INTER / Type 2 +INTER / Types 7, 10, 11 +CYL_JOINT +Abaqus equivalent +*TIE and *FASTENER +*CONTACT, *CONTACT CONTROLS ASSIGNMENT, +*CONTACT FORMULATION, *CONTACT INCLUSIONS, +*CONTACT EXCLUSIONS, *CONTACT PROPERTY +ASSIGNMENT, *SURFACE INTERACTION, and +*SURFACE PROPERTY ASSIGNMENT +CONN3D2 and *CONNECTOR SECTION +Table 3.2.28–6 Group data. +RADIOSS keyword +Abaqus equivalent +*ELSET; data for elements to be grouped in a set using +*ELSET +*ELSET; data for elements to be grouped in a set using +*ELSET +*ELSET; data for elements to be grouped in a set using +*ELSET +*ELSET; data for elements to be grouped in a set using +*ELSET +*NSET; data for elements to be grouped in a set using *NSET +*ELSET; data for elements to be grouped in a set using +*ELSET +*ELSET; data for elements to be grouped in a set using +*ELSET +*NSET; data for elements to be grouped in a set using *NSET +*ELSET; data for elements to be grouped in a set using +*ELSET +*ELSET; data for elements to be grouped in a set using +*ELSET +*ELSET; data for elements to be grouped in a set using +*ELSET +*NSET; data for elements to be grouped in a set using *NSET +3.2.28–4 +SUBSET +PART +MAT +PROP +NODE +SH3N +SHEL +GRNOD +GRSH3N +GRSHEL +GRSPRI +Abaqus equivalent +TRANSLATION FROM RADIOSS +*ELSET; data for elements to be grouped in a set using +*ELSET +*ELSET and *NSET +Table 3.2.28–7 Monitored volume and seat belt data. +SEG +SURF +RADIOSS keyword +MONVOL / GAS +MONVOL / AIRBAG +Abaqus equivalent +*FLUID BEHAVIOR, *FLUID CAVITY, *FLUID +EXCHANGE, *FLUID EXCHANGE ACTIVATION, +*FLUID EXCHANGE PROPERTY, *FLUID INFLATOR, +*FLUID INFLATOR ACTIVATION, *FLUID INFLATOR +MIXTURE, *FLUID INFLATOR PROPERTY, +*MOLECULAR WEIGHT, *CAPACITY, and *PHYSICAL +CONSTANTS +*ELEMENT, TYPE=CONN3D2; *CONNECTOR +SECTION; and *BOUNDARY +SPRING with property SPR_PUL +Table 3.2.28–8 Miscellaneous data. +RADIOSS keyword +Abaqus equivalent +*HEADING +CONN3D2 and connector type ACCELEROMETER +Data for material properties and time-dependent parameters, +such as *AMPLITUDE, *CONNECTOR ELASTICITY, +*PLASTIC, and *FLUID EXCHANGE PROPERTY +*INTEGRATED OUTPUT SECTION +Use activation time in *AMPLITUDE +Data for time history output, such as *OUTPUT, HISTORY; +*NODE OUTPUT; *ELEMENT OUTPUT; and *ENERGY +OUTPUT +job=job-name input=input-file +[splitAirbagElements={OFF | ON}] +[readAbaqusDat=data-file] +[userDefaultMass=real-number] +[userDefaultInertia=real-number] [userHistoryTime=real-number] +3.2.28–5 +TITLE +ACCEL +FUNCT +SECT +SENSOR / Type 0 +TH +Command summary +Command line options +job +This option is used to specify the name of the Abaqus input file to be output by the translator. The name +of the Abaqus input file must be given without the .inp extension. Diagnostics created by the translator +are written to a file named job-name_fromradioss.log. +input +This option is used to specify the name of the file containing the RADIOSS data. The file extension is +optional. +splitAirbagElements +This option is used to specify the splitting of 4-node airbag membrane elements into two 3-node airbag +membrane elements. The default value is ON. Airbag membrane elements result from the translation +of SHELL or SH3N with one integration point through the thickness. This option is valid only if the +keyword MONVOL/AIRBAG is specified in the RADIOSS input file. +readAbaqusDat +This option enables the use of an Abaqus data (.dat) file from a previous Abaqus analysis to reformulate +spot weld definitions. The data file should identify spot welds that could not be formed. Using this option, +the attachment points for the identified spot welds are translated using distributed coupling constraints. +userDefaultMass +This option is used to specify the nodal mass that is assigned to additional nodes generated during the +translation that require nonzero mass. This value should be small (typically 10−6 times the mass for the +entire model). If this option is omitted, the default mass is set to 10−4. +userDefaultInertia +This option is used to specify the rotary inertia that is assigned to additional nodes generated during the +translation that require nonzero rotary inertia. This value should be small (typically 10−6 times the inertia +for the entire model). If this option is omitted, the default rotary inertia is set to 10−3. +userHistoryTime +This option is used to specify the time interval used for time history output. If this option is omitted, the +time history interval is set to 10−5 . +3.2.29 +TRANSLATING Abaqus OUTPUT DATABASE FILES TO NASTRAN OUTPUT2 +RESULTS FILES +Product: Abaqus/Standard +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +The translator converts certain results from an Abaqus output database (.odb) file to the Nastran +Output2 file format. +Using the translator +The toOutput2 translator can only be used to translate Abaqus output database of a *STATIC or +*FREQUENCY procedure. Results from an Abaqus analysis are written to the Abaqus output database +by using the *OUTPUT option. The following options should be included in the Abaqus input file to +ensure that the results to be translated are available in the Abaqus output database: +*OUTPUT, FIELD +*NODE OUTPUT +U, +RF, +CF, +*ELEMENT OUTPUT +S, +E, +SF, +NFORC, +Results in the Abaqus output database other than those specified above are skipped during translation. +Only results from spring elements and three-dimensional continuum, shell, membrane, beam, and truss +elements are translated. +For shell elements, the translator treats stresses and strains at the lowest numbered section point as +being at the bottom surface and stresses and strains at the highest numbered section point as being at the +top surface. Midsurface stresses and strains translated to the Output2 file are computed as the averages +of the stresses and strains at the bottom and top surfaces. +Nodal results are always in global coordinates. Element tensor results are in the Abaqus element +coordinate system. +Model data from the output database (nodal coordinates, element topology, material properties, and +element properties) are written to the Output2 file when applicable records exist. +Command summary +abaqus toOutput2 +Command line options +job=job-name +[odb=odb-name] [step=step-number] +[increment=increment-number] [slim] [quad4corner] +job +odb +step +This option specifies the name of the Nastran Output2 file to be created by the translator. It is also the +default name for the Abaqus output database. +This option specifies the name of the Abaqus output database if it is different from job-name. +This option specifies the step number of the Abaqus output database for the translator to translate. If the +specified step contains multiple load cases, all of the load cases are translated. The default value is the +last step of the analysis. +increment +This option is valid only when used in conjunction with the step option. It is used to specify the increment +number of the step in the Abaqus output database for the translator to translate. The default value is the +last increment of the specified step. +slim +This option is used to include data blocks required for postprocessing in the SLIM/VISION software +(available from Third Millennium Productions, Inc.) in the Output2 file. +quad4corner +This option is used to request shell output at corner nodes instead of at the centroid. This option is +relevant for stress, strain, and section force output. +TRANSLATING LS-DYNA DATA FILES TO Abaqus INPUT FILES +TRANSLATION FROM LS-DYNA +Product: Abaqus/Explicit +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +The translator from LS-DYNA to Abaqus converts a set of supported keywords in an LS-DYNA input +file into their equivalent in Abaqus. +Using the translator +The translator supports translation of input files created by LS-DYNA Version 971 Rev 5 or earlier. The +input file can have any name and an optional extension. +The LS-DYNA keywords that are supported are listed in the tables below. Other LS-DYNA +keywords and data are skipped over and noted in the log file. +The translator creates an Abaqus input file that contains both the model data and history data. +However, the translator does not create exact Abaqus equivalents for specific output quantities for +nodal output, element output, and contact output; it uses preselected variables instead. You can provide +additional output entities to complete the requests. +Element numbering and grouping +All elements in the generated Abaqus input file have unique element numbers. New element numbers +are assigned automatically to elements with non-unique element numbers in the LS-DYNA input; all +element number reassignments are noted in the log file. +Elements that are assigned the same PART identification number are grouped together in an element +set. Elements that have different material or properties must be given different PART identification +numbers; that is, the same material and properties must be applicable to all elements grouped in the same +element set. +When a PART references a rigid material, the part is considered rigid. The element set that +corresponds to the part is used in the rigid body definition. +Material models +The translator supports only the material models shown in Table 3.2.30–1. All unsupported material +models are translated as linear elastic if a stress-strain law definition is required. +In these cases the +translator provides nominal values for the material properties. +Mapping LS-DYNA elements that end in _ID or _TITLE +Many LS-DYNA keywords include the options _ID, _TITLE, or both of these options. Unless the +LS-DYNA keyword with _ID or _TITLE is specified in the mapping tables in this document, the +translator maps data from these options to the same Abaqus keywords specified for the main LS-DYNA +keyword. +Summary of LS-DYNA entities translated +The translator from LS-DYNA to Abaqus supports the mappings shown in the tables below. +Table 3.2.30–1 Material data. +LS-DYNA Keyword +Abaqus Equivalent +*MAT_BLATZ-KO_RUBBER +*MAT_CABLE_DISCRETE_BEAM +*MAT_DAMPER_NONLINEAR +_VISCOUS +*MAT_DAMPER_VISCOUS +*MAT_ELASTIC +*MAT_ELASTIC_PLASTIC +_THERMAL +*MAT_FU_CHANG_FOAM +*MAT_HONEYCOMB +*MAT_JOHNSON_COOK +*MAT_LINEAR_ELASTIC +_DISCRETE_BEAM +*MAT_LOW_DENSITY_FOAM +*HYPERELASTIC, NEO HOOKE +*ELASTIC +*CONNECTOR DAMPING, NONLINEAR +*CONNECTOR DAMPING +*ELASTIC +*ELASTIC +*PLASTIC +*EXPANSION +*LOW DENSITY FOAM and +*UNIAXIAL TEST DATA +Built-in VUMAT user material model +ABQ_HONEYCOMB1 +*PLASTIC, HARDENING=JOHNSON COOK +*RATE DEPENDENT, TYPE=JOHNSON COOK +*SHEAR FAILURE, TYPE=JOHNSON COOK +*TENSILE FAILURE, TYPE=JOHNSON COOK +*CONNECTOR ELASTICITY and +*CONNECTOR DAMPING +*HYPERFOAM and *UNIAXIAL TEST DATA +LS-DYNA Keyword +Abaqus Equivalent +*MAT_NULL +*MAT_OGDEN_RUBBER +*MAT_PIECEWISE_LINEAR +_PLASTICITY +*MAT_PLASTIC_KINEMATIC +*MAT_RIGID +*MAT_SEATBELT +*MAT_SPOTWELD +*MAT_SPRING_ELASTIC +*MAT_SPRING_NONLINEAR +_ELASTIC +*ELASTIC +Shell elements that reference a null material are +translated as surface elements +*HYPERELASTIC, OGDEN +*PLASTIC +*PLASTIC, HARDENING=KINEMATIC +*ELASTIC +*RIGID BODY (for LS-DYNA parts that refer to a +rigid material) +*CONNECTOR ELASTICITY, NONLINEAR +*CONNECTOR ELASTICITY, RIGID +*CONNECTOR ELASTICITY +*CONNECTOR ELASTICITY, NONLINEAR +*MAT_VISCOELASTIC +*VISCOELASTIC, TIME=PRONY +1 For more information about using ABQ_HONEYCOMB, refer to “Abaqus/Explicit +honeycomb material model,” which is available in the Dassault Systèmes Knowledge Base +at www.3ds.com/support/knowledge-base or the SIMULIA Online Support System, which is +accessible through the My Support page at www.simulia.com. +Table 3.2.30–2 Part data. +LS-DYNA Keyword +Abaqus Equivalent +*PART +*PART_PRINT +*PART_CONTACT +*PART_INERTIA +*ELSET and the corresponding type of element section +*SURFACE INTERACTION properties +*ELEMENT, TYPE=MASS +*ELEMENT, TYPE=ROTARYI +Table 3.2.30–3 Auxiliary data. +LS-DYNA Keyword +Abaqus Equivalent +*DEFINE_COORDINATE_NODES +*DEFINE_COORDINATE +_SYSTEM +*DEFINE_COORDINATE +_VECTOR +*DEFINE_CURVE +*DEFINE_SD_ORIENTATION +*DEFINE_TABLE +*ORIENTATION, +DEFINITION=NODES +*ORIENTATION, +DEFINITION=COORDINATES +*ORIENTATION, +DEFINITION=COORDINATES +Data from a single curve used in the following +keywords: +*AMPLITUDE +*CONNECTOR DAMPING (nonlinear) +*CONNECTOR ELASTICITY (nonlinear) +*SURFACE BEHAVIOR +*UNIAXIAL TEST DATA +*ORIENTATION +Multi-curve data used in conjunction with +*PLASTIC and *LOW DENSITY FOAM in which +the stress-strain relationship is defined for various +strain rates +LS-DYNA Keyword +*SECTION_BEAM +*SECTION_DISCRETE +*SECTION_SEATBELT +*SECTION_SHELL +Table 3.2.30–4 Section data. +Abaqus Equivalent +Beam elements: *BEAM SECTION or +*BEAM GENERAL SECTION +Truss elements: *SOLID SECTION +*CONNECTOR SECTION +*CONNECTOR SECTION +Shell elements: *SHELL SECTION +Membrane elements: *MEMBRANE SECTION +Surface elements: *SURFACE SECTION +LS-DYNA Keyword +*SECTION_SOLID +*SECTION_TSHELL +Abaqus Equivalent +*SOLID SECTION +*SHELL SECTION +Table 3.2.30–5 Nodal data. +LS-DYNA Keyword +Abaqus Equivalent +*NODE +*NODE +Table 3.2.30–6 Output options data. +LS-DYNA Keyword +Abaqus Equivalent +*DATABASE_BINARY_D3PLOT +*DATABASE_BINARY_D3THDT +*DATABASE_DEFORC +*DATABASE_ELOUT +*DATABASE_NODOUT +*DATABASE_HISTORY_BEAM +*DATABASE_HISTORY_BEAM_ID +*DATABASE_HISTORY_BEAM_SET +*DATABASE_HISTORY_NODE +*DATABASE_HISTORY_NODE_ID +*DATABASE_HISTORY_NODE_SET +*DATABASE_HISTORY_SHELL +*DATABASE_HISTORY_SHELL_ID +*DATABASE_HISTORY_SHELL_SET +*DATABASE_HISTORY_SOLID +*DATABASE_HISTORY_SOLID_ID +*DATABASE_HISTORY_SOLID_SET +*OUTPUT, FIELD and +*ELEMENT OUTPUT +*OUTPUT, FIELD and +*ELEMENT OUTPUT +*OUTPUT, FIELD and +*ELEMENT OUTPUT +*OUTPUT, FIELD and +*ELEMENT OUTPUT +*OUTPUT, FIELD and *NODE OUTPUT +*OUTPUT, HISTORY and +*ENERGY OUTPUT +*OUTPUT, HISTORY and +*ENERGY OUTPUT +*OUTPUT, HISTORY and +*ENERGY OUTPUT +*OUTPUT, HISTORY and +*ENERGY OUTPUT +Table 3.2.30–7 Element data. +LS-DYNA Keyword +Abaqus Equivalent +*ELEMENT_BEAM +*ELEMENT_BEAM_PID +*ELEMENT_DISCRETE +*ELEMENT_MASS +*ELEMENT_SEATBELT +*ELEMENT_SHELL +Beam elements: *ELEMENT, TYPE=B31 +Truss elements: *ELEMENT, TYPE=T3D2 +*ELEMENT, TYPE=CONN3D2 and *FASTENER +*ELEMENT, TYPE=CONN3D2 +*ELEMENT, TYPE=MASS and *MASS +*ELEMENT, TYPE=CONN3D2 +Shell elements: *ELEMENT, TYPE=S3R or S4R +Membrane elements: *ELEMENT, TYPE=M3D3 or +M3D4R +Surface elements (with *MAT_NULL): *ELEMENT, +TYPE=SFM3D3 or SFM3D4R +*ELEMENT_SOLID +*ELEMENT, +TYPE=C3D4, C3D6, C3D8R, or C3D10M +*ELEMENT_TSHELL +*ELEMENT, TYPE=SC6R or SC8R +Table 3.2.30–8 Prescribed conditions data. +LS-DYNA Keyword +Abaqus Equivalent +*BOUNDARY_PRESCRIBED +_MOTION_NODE +*BOUNDARY_PRESCRIBED +_MOTION_SET +*BOUNDARY, +TYPE=DISPLACEMENT, +VELOCITY, or ACCELERATION +*BOUNDARY, +TYPE=DISPLACEMENT, +VELOCITY, or ACCELERATION +*BOUNDARY_PRESCRIBED +_MOTION_RIGID +*BOUNDARY for reference node of rigid +body +*BOUNDARY_PRESCRIBED +_MOTION_RIGID_LOCAL +*BOUNDARY for reference node of rigid +body +*BOUNDARY_SPC_NODE +*BOUNDARY_SPC_SET +*BOUNDARY +*BOUNDARY +LS-DYNA Keyword +Abaqus Equivalent +*INITIAL_VELOCITY +_GENERATION +*INITIAL_VELOCITY_NODE +*INITIAL CONDITIONS, +TYPE=ROTATING VELOCITY +*INITIAL CONDITIONS, +TYPE=VELOCITY +Table 3.2.30–9 Miscellaneous constraints data. +LS-DYNA Keyword +Abaqus Equivalent +*CONSTRAINED_NODE_SET +*CONSTRAINED_NODAL_RIGID +_BODY +*CONSTRAINED_EXTRA_NODES +_NODE +*CONSTRAINED_EXTRA_NODES +_SET +*CONSTRAINED_JOINT +_CYLINDRICAL +*CONSTRAINED_JOINT +_REVOLUTE +*CONSTRAINED_JOINT +_SPHERICAL +*CONSTRAINED_JOINT +_STIFFNESS_GENERALIZED +*CONSTRAINED_JOINT +_TRANSLATIONAL +*CONSTRAINED_JOINT +_UNIVERSAL +*EQUATION +*MPC type BEAM +Node set used as TIE NSET in the +definition of *RIGID BODY +Node set used as TIE NSET in the +definition of *RIGID BODY +*ELEMENT, TYPE=CONN3D2 +*ELEMENT, TYPE=CONN3D2 +*ELEMENT, TYPE=CONN3D2 +*ELEMENT, TYPE=CONN3D2 +*CONNECTOR SECTION, BEHAVIOR +*ELEMENT, TYPE=CONN3D2 +*ELEMENT, TYPE=CONN3D2 +*CONSTRAINED_RIGID_BODIES +*CONSTRAINED_SPOTWELD +Merged element set used in the definition +of *RIGID BODY +*MPC type BEAM +Table 3.2.30–10 Load data. +LS-DYNA Keyword +Abaqus Equivalent +*LOAD_BODY_PARTS *ELSET for *DLOAD +*LOAD_BODY_X +*LOAD_BODY_Y +*LOAD_BODY_Z +*DLOAD +*DLOAD +*DLOAD +*LOAD_NODE_POINT *CLOAD with node data +*LOAD_NODE_SET +*CLOAD with node set data +Table 3.2.30–11 Set data. +LS-DYNA Keyword +*SET_NODE_LIST +*SET_NODE_LIST_GENERATE +*SET_PART +*SET_PART_LIST +*SET_PART_LIST_GENERATE +*SET_SEGMENT +*SET_SHELL_LIST +*SET_SHELL_LIST_GENERATE +*SET_SOLID_LIST +Abaqus Equivalent +*NSET with node data +*NSET with node data +*ELSET with element set data +*ELSET with element set data +*ELSET with element set data +*ELSET with element data +*ELSET with element data +*ELSET with element data +*ELSET with element data +Table 3.2.30–12 Contact data. +LS-DYNA Keyword +Abaqus Equivalent +*CONTACT_AUTOMATIC_GENERAL +*CONTACT +*CONTACT INCLUSION +*CONTACT PROPERTY ASSIGNMENT +*SURFACE INTERACTION +*SURFACE PROPERTY ASSIGNMENT +Abaqus Equivalent +TRANSLATION FROM LS-DYNA +*CONTACT_AUTOMATIC +_NODES_TO_SURFACE +*CONTACT_AUTOMATIC +_SINGLE_SURFACE +*CONTACT_AUTOMATIC +_SURFACE_TO_SURFACE +*CONTACT_NODES_TO_SURFACE +*CONTACT_RIGID_NODES_TO +_RIGID_BODY +*CONTACT_SINGLE_SURFACE +*CONTACT +*CONTACT INCLUSION +*CONTACT PROPERTY ASSIGNMENT +*SURFACE INTERACTION +*SURFACE PROPERTY ASSIGNMENT +*CONTACT +*CONTACT INCLUSION +*CONTACT PROPERTY ASSIGNMENT +*SURFACE INTERACTION +*SURFACE PROPERTY ASSIGNMENT +*CONTACT +*CONTACT INCLUSION +*CONTACT PROPERTY ASSIGNMENT +*SURFACE INTERACTION +*SURFACE PROPERTY ASSIGNMENT +*CONTACT +*CONTACT INCLUSION +*CONTACT PROPERTY ASSIGNMENT +*SURFACE INTERACTION +*SURFACE PROPERTY ASSIGNMENT +*CONTACT +*CONTACT INCLUSION +*CONTACT PROPERTY ASSIGNMENT +*SURFACE INTERACTION +*SURFACE PROPERTY ASSIGNMENT +*CONTACT +*CONTACT INCLUSION +*CONTACT PROPERTY ASSIGNMENT +*SURFACE INTERACTION +*SURFACE PROPERTY ASSIGNMENT +LS-DYNA Keyword +Abaqus Equivalent +*CONTACT_SURFACE_TO_SURFACE +*CONTACT_TIED_NODES +_TO_SURFACE +*CONTACT_TIED_SURFACE +_TO_SURFACE +*CONTACT +*CONTACT INCLUSION +*CONTACT PROPERTY ASSIGNMENT +*SURFACE INTERACTION +*SURFACE PROPERTY ASSIGNMENT +*TIE +*TIE +Table 3.2.30–13 Miscellaneous data. +LS-DYNA Keyword +Abaqus Equivalent +*CONTROL +_TERMINATION +*END +*KEYWORD +*TITLE +*INCLUDE +Time period entered in *DYNAMIC, EXPLICIT +*END +None +*HEADING +Process multiple LS-DYNA files +Command summary +abaqus fromdyna +Command line options +job +job=job-name +input=dyna-input-file +[splitFile={OFF | ON}] +This option is used to specify the name of the Abaqus input file to be output by the translator. The name +of the Abaqus input file must be given without the .inp extension. Diagnostics created by the translator +are written to a file named job-name.log. +input +This option is used to specify the name of the file containing the LS-DYNA keyword data. The +LS-DYNA input file can have an extension. +splitFile +This option specifies whether the Abaqus input file is to be split into multiple files. If splitFile=ON, the +following files are output: +• job-name_nodes.inc: include file that contains the nodal data +• job-name_elements.inc: include file that contains the element data +• job-name_model.inc: include file that contains the remaining model data +• job-name.inp: Abaqus input file that includes all of the above include files and the history data +3.2.31 +EXCHANGING Abaqus DATA WITH ZAERO +Product: Abaqus/Standard +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +The abaqus tozaero interface enables you to exchange aeroelastic data between the Abaqus and ZAERO +analysis products. By using this interface between the applications, you can perform structural modal +analysis on a model in Abaqus, transfer the model to ZAERO for aeroelastic analysis, then transfer it +back to Abaqus for stress analysis. +Universal file +The universal file is the means of data exchange between Abaqus and ZAERO. It consists of four data +sets: 2411, which describes node and coordinate data; 2414, which describes mass-normalized mode +shapes; 2420, which describes the global coordinate system; and 2453, which describes the mass matrix +in text format, or 2453b, which describes the mass matrix in binary format. +You can specify the universal file’s output format by using the mode parameter. Choosing text +format enables you to modify the universal file in a text editor but increases the file size to over twice that +of similar files in binary format. Text is the default format and the only format supported by ZAERO. +Table 3.2.31–1 and Table 3.2.31–2 describe the mass matrix data set text format and binary format, +respectively. +Table 3.2.31–1 Format for data set 2453 (text). +Record +Field +Format +(I10) +Description +Matrix Identifier +1: DOF +131: Mass +139: Stiffness +147: Back-expansion +Record +Field +Format +(6I10) +Description +Matrix Data Type +1: Integer +2: Real +4: Double Precision +5: Complex +6: Complex Double +Precision +Matrix Form +3: General Rectangular +Number of rows +Number of columns +Storage Key +1: Row +2: Column +11: Sparse (not supported for +IMAT=1) +Matrix Size Parameter +For IMAT=1 this is the +number of dynamic modes. +For sparse this is the number +of matrix entries. +Otherwise, 0. +3 for storage +keys 1 and 2 +N/A +Matrix Data +For data type 1: +(8 I10) +For data type 2: +(4 E20.12) +For data type 4: +(4 D20.12) +For data type 5: +(2 (2 E20.12)) +For data type 6: +(2 (2 D20.12)) +Field +Description +Format +TRANSLATION TO ZAERO +3 for storage +key 11 +Row +Column +Value at cell +For data type 1: +(2 (2I10 1I10)) +For data type 2: +(2 (2I10 1E20.12)) +For data type 4: +(2 (2I10 1D20.12)) +For data type 5: +(1 (2I10 2E20.12)) +For data type 6: +(1 (2I10 2D20.12)) +Table 3.2.31–2 Format for data set 2453b (binary). +Field +Description +Format +Record +Header +2453 +Lowercase b +Byte Ordering Method +1: Little Endian (Windows +and DOS) +2: Big Endian (most UNIX) +Floating Point Format +1: DEC VMS +2: IEEE 754 (UNIX) +3: IBM 5/370 +Number of ASCII lines +following +2 for data set 2453b +(I6) +(IA1) +(I6) +(I6) +(I12) +Number of bytes following +ASCII lines +(I12) +Not used (fill with zeros) +(I10) +Matrix Identifier +1: DOF +131: Mass +139: Stiffness +147: Back-expansion +3.2.31–3 +7–10 +Record +Field +Format +(6I10) +Description +Matrix Data Type +1: Integer +2: Real +4: Double Precision +5: Complex +6: Complex Double +Precision +Matrix Form +3: General Rectangular +Number of rows +Number of columns +Storage Key +1: Row +2: Column +11: Sparse (not supported for +IMAT=1) +Matrix Size Parameter +For IMAT=1 this is the +number of dynamic modes. +For sparse this is the number +of matrix entries. +Otherwise, 0. +3 (Binary +Matrix Data) +1 (4 bytes) +Row +2 (4 bytes) +Column +Value at cell +For data type 1: +(2 Int32 1 Int32) +For data type 2: +(2 Int32 1 Flt32) +For data type 4: +(2 Int32 1 Dbl64) +For data type 5: +(2 Int32 2 Flt32) +For data type 6: +(2 Int32 2 Dbl64) +Preparing the Abaqus analysis input file +Before the interface can create the universal file, you must make the following additions to your Abaqus +input (.inp) file, then run Abaqus: +• Normalize the eigenvectors in the eigenfrequency extraction analysis with respect to the structure’s +mass matrix. This normalization is necessary because the translator assumes the mode shapes are +mass normalized; if you skip this step before the Abaqus run, the modes translated will be incorrect +and will give incorrect results with no warnings or errors. For more information, see “Natural +frequency extraction,” Section 6.3.5. +• Include the following line in the analysis step: +*ELEMENT MATRIX OUTPUT, ELSET=allelements, MASS=YES, +OUTPUT FILE=USER DEFINED, FILE NAME=mtx-file-name +where allelements is a defined element set containing all the elements that should be included +in the global mass matrix. The matrix output will be placed into the file mtx-file-name.mtx; you +should not specify the .mtx extension since Abaqus adds it automatically. +Workflow +This section describes the input and output of the three main steps in the workflow between Abaqus and +ZAERO. +Modal analysis in Abaqus +The Abaqus modal analysis uses an Abaqus input file and outputs the following data to an output database +(.odb) file and matrix (.mtx) file: structural model nodes, coordinate systems, mode frequencies, +generalized mass, mode shapes, and the mass matrix. +Aeroelastic analysis in ZAERO +Aeroelastic analysis requires a ZAERO input file and the universal file created by toZAERO. ZAERO +outputs force and moment data on structural nodes due to aeroelastic forces to the universal file. +Stress analysis in Abaqus +The forces and moments output from ZAERO can then be used in a static (linear or nonlinear) Abaqus +analysis to calculate deflections, stresses, and loads. +job=job-name +[unvfile=unv-file-name] +[odbfile=odb-file-name] +[mtxfile=mtx-file-name] +[step=step-number] +[mode={text | binary}] +3.2.31–5 +Command summary +Command line options +job +This option is used to specify the name of the Abaqus input file. It is also the default name for the +universal output database and mass matrix files. +unvfile +This option is used to specify the name of the universal file if it is different from job-name. If the .unv +extension is not supplied, Abaqus adds it automatically. +odbname +This option is used to specify the name of the Abaqus output database file if it is different from job-name. +If the .odb extension is not supplied, Abaqus adds it automatically. +mtxfile +This option is used to specify the file containing the element mass matrices generated by Abaqus. If the +.mtx extension is not supplied, Abaqus adds it automatically. +step +This option specifies the step number containing the eigenfrequency extraction results from Abaqus. The +default value is 1. +Note: You must normalize the eigenvectors in the eigenfrequency extraction analysis with respect to +the structure’s mass matrix. For more information, see “Natural frequency extraction,” Section 6.3.5. +mode +This option specifies the output format of the universal file. If this option is set equal to binary, Abaqus +writes a portion of the universal file in binary format to save space. If this option is set equal to text, +Abaqus writes the entire file in all text format. The default value is text, which is the only mode +currently supported by ZAERO. +3.2.32 +ENCRYPTING AND DECRYPTING Abaqus INPUT DATA +Products: Abaqus/Standard Abaqus/Explicit +References +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +• “Including an encrypted data file” in “Defining a model in Abaqus,” Section 1.3.1 +• *INCLUDE +Overview +You can use the abaqus encrypt utility to prevent the unauthorized use of Abaqus input data. The +utility converts a data file into an encrypted, password-protected format that only authorized Abaqus +input parties can access. The utility is intended for the encryption of data that you include by reference +in input (.inp) files or in other data files. For example, you could encrypt a file that contains all of +the proprietary material data for your model, then include the encrypted data file by reference in an +unencrypted Abaqus input file. See “Including an encrypted data file” in “Defining a model in Abaqus,” +Section 1.3.1, for information on how to include an encrypted data file in an Abaqus input file. +You can encrypt any input file. However, Abaqus cannot run an encrypted Abaqus input file directly; +the encrypted file must be included in an unencrypted file. +Specifying additional access levels and controls +You can customize your encryption so that only users with a license for a particular Abaqus feature +or from a particular site can include or decrypt the file. For example, you can specify that only +Abaqus/Standard users can access the file. You can also prevent decryption of an encrypted file by +any user, regardless of their license and site; end users can still use the encrypted data in an analysis +by including it by reference in an unencrypted Abaqus input file, provided that the users know the +encrypted file’s password. +Security and support considerations +The primary intent of the Abaqus encryption implementation is to prevent unauthorized use of encrypted +input data, not to prevent disclosure of encrypted data to authorized users. Running an Abaqus analysis +input using encrypted data may produce output files that are not encrypted. Only material and connector +behavior information contained within an encrypted input file is prevented from being visible in the +output. This approach means that recipients of encrypted data who satisfy the access criteria, such as +the password, license feature, or SiteID, will be able to reconstruct some input in an unencrypted form. +Providers of encrypted data should consider establishing contractual agreements to protect proprietary +data. Users of encrypted data must accept responsibility for security of files produced from encrypted +input and should consider restricting access to resulting analysis files. +Abaqus technical support cannot retrieve lost passwords for encrypted data files. Users receiving +encrypted data should contact the data provider for any technical support issues. +Adding comments to the header of an encrypted file +When you encrypt a file, Abaqus adds the following unencrypted comment line to the beginning of the +file: +** encrypted input +Do not modify or delete this header comment. You can, however, insert additional comment lines +between this header comment and the first line of encrypted data. These post-encryption comment +lines can describe the encrypted file’s contents, provide release numbers, or display copyright and legal +information about the encrypted data. For more information about comment line syntax, see “Input +syntax rules,” Section 1.2.1. +You should not, however, add post-encryption comment lines within the lines of encrypted data. If +you want to edit or amend the comment lines within the data itself, you must first decrypt the data. +Command summary +abaqus {encrypt | decrypt} +Command line options +input +input=input-file-name +output=output-file-name +password=password +[license=feature_list] +[expiration=expiration_date] +[siteid=site-id_list] +[include_only] +This option specifies the name of the data file that you want to encrypt or decrypt. +If you omit this option from the command line, Abaqus will prompt you for its value. +output +This option specifies the name of the data file after encryption or decryption. +If you omit this option from the command line, Abaqus will prompt you for its value. +password +This option specifies the password for this encryption or decryption. Passwords are case-sensitive. +If you omit this option from the command line while encrypting data, Abaqus will prompt you for +its value. If you enter the password incorrectly or omit it from the command line while decrypting data, +Abaqus reports that the input file is either corrupted or the password is incorrect. +license +This option applies only to file encryption. +This option specifies the Abaqus feature or features for which end users must be licensed if they +want to include or decrypt this encrypted data file. You can use a comma-separated list to allow access +to the file by licensees of any one of a series of Abaqus features. +Any feature name that appears in an Abaqus license file is valid. These might include the +following features: foundation, standard, explicit, design, aqua, ams, cae, viewer, +cae_nogui, adams, cmold, moldflow, safe, cadporter_catia, cadporter_catiav5, +cadporter_ideas, cadporter_parasolid, cadporter_proe, afcv5_structural, +and afcv5_thermal. +siteid +This option applies only to file encryption. +This option specifies the Abaqus Site ID or IDs where end users can include or decrypt this encrypted +data file. You can use a comma-separated list to allow multiple sites access to the file. You can use this +option only when you also use the license option. +To determine your Abaqus Site ID, run abaqus whereami from a command prompt. +include_only +This option applies only to file encryption. +This option specifies that encrypted input data cannot be decrypted using the abaqus decrypt +execution procedure; such data can only be included in an Abaqus input file. +If you attempt to decrypt a file that was encrypted with the include_only option, Abaqus issues an +error message stating that the input file can be included in an analysis but is not eligible for decryption. +expiration +This option applies only to file encryption. +This option specifies the date after which the end users can no longer decrypt or include the +encrypted data file. The date must be provided in the formYYYY-MM-DD. +Examples +The following examples illustrate the different encryption methods that are possible using the encrypt +execution procedure. +Creating encrypted files +In the simplest encryption scenario an Abaqus user creates an encrypted copy of a file named +material_data.inp, which contains all of the material data for a model, before sending the +encrypted version to an authorized end user. Encryption prevents unauthorized users from accessing the +encrypted file during its transmission. To create an encrypted copy of material_data.inp named +material_data_enc.inp, issue the following command: +abaqus encrypt input=material_data.inp +output=material_data_enc.inp password=e1No9c2z +Upon receiving the file, the end user can run the abaqus decrypt execution procedure to create a copy of +the original, non-encrypted material data file. Because of the encryption options selected in this example, +the end user requires only the encrypted file’s password to decrypt it. To decrypt the encrypted data file +material_data_enc.inp, producing the non-encrypted file material_data.inp, issue the +following command: +abaqus decrypt input=material_data_enc.inp +output=material_data.inp password=e1No9c2z +Alternatively, the end user can skip the decryption and run an analysis that includes the encrypted data by +reference. To include the encrypted file by reference in an Abaqus input file, add the following statement +to the input file: +*INCLUDE, INPUT=material_data_enc.inp, PASSWORD=e1No9c2z +Limiting access to decrypted files by license feature or site ID +You can specify that end users cannot access the file unless they have a valid license for a particular +Abaqus feature, run Abaqus at a particular site, or satisfy both of these criteria. To encrypt a data file +that can be accessed only by users who have an Abaqus/Explicit license and who run the software at site +09YYY, issue the following command: +abaqus encrypt input=material_data.inp +output=material_data_enc.inp password=e1No9c2z +license=explicit siteid=09YYY +An end user can attempt to access the file material_data_enc.inp using the same decryption +or inclusion syntax specified in the previous example. For this encrypted file, Abaqus would validate +that the end user has an Abaqus/Explicit license and is running Abaqus at site 09YYY before providing +access to the file. If the end user’s license or site settings do not match those specified during encryption, +Abaqus issues an error message that lists the licenses or sites that are required to access the file. +Creating encrypted files that must be included to be used by Abaqus +You can use the include_only option to prevent end users from decrypting the file directly using abaqus +decrypt. Authorized users can access a file encrypted with the include_only option by including the file +by reference in an Abaqus input file. Material and connector behavior definitions within an encrypted +input file are not written to the output database. +In addition, all material and connector behavior +definitions output to the data file are suppressed if an encrypted file is used as input for any portion of +the model. To create an encrypted file that is available only for inclusion by reference in other input +files, issue the following command: +abaqus encrypt input=material_data.inp +output=material_data_enc.inp password=e1No9c2z include_only +The resulting encrypted file can be included by reference in an Abaqus input file using the same syntax +as in the previous example. If you attempt to decrypt a file that was encrypted with the include_only +option, Abaqus returns an error message. +3.2.33 +JOB EXECUTION CONTROL +Products: Abaqus/Standard Abaqus/Explicit +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +The execution procedures for job execution control include abaqus suspend, abaqus resume, and +abaqus terminate. These utilities are used to suspend, resume, and terminate Abaqus analysis jobs. +Suspending an analysis job will stop its execution and release its license tokens to the free-token pool. +Resuming an analysis will reactivate a suspended job and check out license tokens for that job if they +are available. The job will be placed in the license queue if license tokens are not available. Terminating +an analysis job will stop the executable for the analysis and release its license tokens. A terminated +analysis job cannot be resumed. +Command summary +abaqus {suspend | resume | terminate} job=job-name +Command line options +Required option +job +This option is used to specify the name of the analysis job to suspend, resume, or terminate. +3.3 +Environment file settings +• “Using the Abaqus environment settings,” Section 3.3.1 +3.3.1 +USING THE Abaqus ENVIRONMENT SETTINGS +Products: Abaqus/Standard Abaqus/Explicit +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +The Abaqus environment settings allow you to control various aspects of an Abaqus job’s execution. For +example, you can +• “Tune” Abaqus to improve its performance by changing memory-related parameters. +• Control where and how scratch files are written. +• Provide default values for job parameters that would otherwise have to be given on the command +line. +Many other aspects of a job’s execution can be configured through the environment settings. Some of +these are discussed in this section; others, which are mainly of interest to the Abaqus site manager, are +discussed in detail in the Abaqus Installation and Licensing Guide. +Environment settings hierarchy +Abaqus environment settings are processed in the following order: +1. The host-level environment settings. These settings are applied to all Abaqus jobs run on the +designated computer. +2. The user-level environment settings. These settings are applied to all Abaqus jobs run in your +account. +For Abaqus to locate the environment file in your home directory on Windows platforms, +the full path to your home directory must be specified using the HOME environment variable or +a combination of the HOMEDRIVE and HOMEPATH environment variables. +3. The job-level environment settings. These settings are applied to only the designated Abaqus job. +Environment settings can be specified more than once. The last value processed will be the one +used for the setting if it is defined at more than one level or if it is given twice at the same level. +Abaqus environment settings are set using special files in specific directories. The host-level settings +are set in the site directory in the abaqus account directory. You can change these settings by creating +an environment file, abaqus_v6.env, in your home directory and/or the current directory. Settings in +the home directory file will be applied to all jobs that you run. Settings in the current directory file will +be applied only to jobs run from the current directory. +Syntax +The entries given in the environment file must be given using Python language syntax. Entries take the +form: +parameter=value +The following is a brief overview of the Python syntax rules: +• The parameter must always have a value. The value can be any valid Python constant or expression. +• A string value must be enclosed in a pair of double or single quotes. +• Comments are preceded by a number sign (#). All characters following a number sign on a line are +ignored. Number signs within a quoted string are part of the string, not the beginning of a comment. +• Blank lines are ignored. +• Embedded single quotes do not require special handling if they are placed within a double quoted +string. For example, "my value’s" is translated as my value’s. The same holds true for +double quotes embedded in a single quoted string. Quotes of the same type as the enclosing quotes +can be embedded if they are prefixed by the backslash (\) character. +• Triple quoted (""") strings can span more than one line, and no special treatment of quotes within +the string is necessary. Entries take the form: +parameter=""" +multi-line +value +""" +• Lists must be enclosed in parentheses (( )) or square brackets ([ ]). Individual items in the list are +separated by commas. If the list is enclosed in parentheses and contains only one value, a comma +has to follow the value. String list items must be enclosed in quotes. Entries take the form: +parameter=(value1, value2, value3) +Troubleshooting +Problems caused by faulty environment settings can be diagnosed by using the command +abaqus information=environment +This command prints all of the current environment settings. +Command line default parameters +The following parameters provide default values for various settings that would otherwise have to be +specified on the command line . Values given on the command line override values specified in the environment files. +cpus +Number of processors to use if parallel processing is available. The default is 2 for the co-simulation +execution procedure; otherwise, the default is 1. +domains +If the value is greater than 1, the domain +The number of parallel domains in Abaqus/Explicit. +decomposition will be performed regardless of the values of the parallel and cpus parameters. +However, if parallel=domain, the value of cpus must be evenly divisible into the value of +domains. If this parameter is not set, the number of domains defaults to the number of processors +used during the analysis run if parallel=domain or to 1 if parallel=loop. +double_precision +The default precision version of Abaqus/Explicit to run if you do not specify the precision version +on the abaqus command line. Possible values are EXPLICIT (only the Abaqus/Explicit analysis is +run in double precision), BOTH (both the Abaqus/Explicit packager and analysis are run in double +precision), CONSTRAINT (the constraint packager and constraint solver in Abaqus/Explicit are +run in double precision, while the Abaqus/Explicit packager and analysis continue to run in single +precision), or OFF (both the Abaqus/Explicit packager and analysis are run in single precision). The +default is OFF. +parallel +The default parallel method in Abaqus/Explicit if you do not specify the parallel method on the +abaqus command line. Possible values are DOMAIN or LOOP; the default value is DOMAIN. +run_mode +Default run mode (interactive, background, or batch) if you do not specify the run mode on the +abaqus command line. The default for abaqus analysis is "background", while the default for +abaqus viewer is "interactive". +scratch +Directory to be used for scratch files. This directory must exist (i.e., it will not be created by Abaqus) +and must have write permission assigned. On UNIX platforms the default value is the value of the +$TMPDIR environment variable or /tmp if $TMPDIR is not defined. On Windows platforms the +default value is the value of the %TEMP% environment variable or \TEMP if this variable is not +defined. During the analysis a subdirectory will be created under this directory to hold the analysis +scratch files. The name of the subdirectory is constructed from your user name, the job id, and +the job’s process identifier. The subdirectory and its contents are deleted upon completion of the +analysis. +standard_parallel +The default parallel execution mode in Abaqus/Standard if you do not specify the parallel mode on +the abaqus command line. If this parameter is set equal to ALL, both the element operations and +the solver will run in parallel. If this parameter is set equal to SOLVER, only the solver will run in +parallel. The default parallel execution mode is ALL. +gpus +The GPGPU direct solver acceleration setting in Abaqus/Standard if you do not specify the +GPGPU solver acceleration option on the abaqus command line. By default, GPGPU solver +acceleration is not activated. The value of this parameter is the number of GPGPUs to be used in +an Abaqus/Standard analysis. In an MPI-based analysis, this is the number of GPGPUs to be used +on each host. +unconnected_regions +If this variable is set to ON, Abaqus/Standard will create element and node sets in the output database +for unconnected regions in the model during a datacheck analysis. Element and node sets created +with this option are named MESH COMPONENT N, where N is the component number. The default +value is OFF. +order_parallel +The ordering mode for the direct sparse solver in Abaqus/Standard if you do not specify the ordering +mode on the abaqus command line. If this parameter is set equal to OFF, the ordering procedure +will not run in parallel. If this parameter is set equal to ON, the ordering procedure will run in +parallel. The default ordering mode is ON. +System resource parameters +The following environment file variable can be set after the code has been installed to change the +resources used by Abaqus and, therefore, to improve system performance. By default, Abaqus detects +the physical memory on a machine (or on each compute node in a cluster) and allocates a percentage +of the available memory based on the machine platform (for details, refer to the Dassault Systèmes +Knowledge Base at www.3ds.com/support/knowledge-base or the SIMULIA Online Support System, +which is accessible through the My Support page at www.simulia.com). You can override the default +percentage by specifying a number followed by the percentage sign. The variable can also be defined +as the number of megabytes or the number of gigabytes. More detailed information about changing the +system resources used by Abaqus is given in “Managing memory and disk use in Abaqus,” Section 3.4.1. +memory +Maximum amount of memory or maximum percentage of the physical memory that can be allocated +during the input file preprocessing and during the Abaqus/Standard analysis phase. For parallel +execution on computer clusters, this memory limit specifies the maximum amount of memory that +can be allocated on each process. +System customization parameters +The following is a discussion of some additional environment file parameters that are commonly used. +A complete listing of parameters can be found in the Abaqus Installation and Licensing Guide. +ask_delete +If this parameter is set equal to OFF, you will not be asked whether old job files of the same file +name should be deleted; the files will be deleted automatically. The default value is ON. +auto_calculate +If this parameter is set equal to ON, the postprocessing calculator will be launched automatically +at the end of an analysis if the execution procedure detects that output database file conversion is +necessary. If this parameter is set to OFF, the postprocessing calculator will not run at the end of an +analysis even if the execution procedure detects that it is necessary. The default value is ON. +auto_convert +If this parameter is set equal to ON and an Abaqus/Explicit analysis is run in parallel with +parallel=domain, the convert=select, convert=state, and convert=odb options will be +run automatically at the end of the analysis. The default value is ON. +average_by_section +If this parameter is set equal to +This parameter is used only for an Abaqus/Standard analysis. +OFF, the averaging regions for output written to the data (.dat) file and results (.fil) file are +based on the structure of the elements. If this parameter is set equal to ON, the averaging regions +also take into account underlying values of element properties and material constants. In problems +with many section and/or material definitions the default value of OFF will, in general, give much +better performance than the nondefault value of ON. See “Output to the data and results files,” +Section 4.1.2, for further details on the averaging scheme. +mp_host_list +List of host machine names to be used for an MPI-based parallel Abaqus analysis, including the +number of processors to be used on each machine; for example, +mp_host_list=[['maple',1],['pine',1],['oak',2]] +indicates that, if the number of cpus specified for the analysis is 4, the analysis will use one processor +on a machine called maple, one processor on a machine called pine, and two processors on a +machine called oak. The total number of processors defined in the host list has to be greater than +or equal to the number of cpus specified for the analysis. If the host list is not defined, Abaqus will +run on the local system. When using a supported queuing system, this parameter does not need to +be defined. If it is defined, it will get overridden by the queuing environment. +mp_mode +Set this variable equal to MPI to indicate that the MPI components are available on the system. +Set mp_mode=THREADS to use the thread-based parallelization method. The default value is MPI +where applicable. +odb_output_by_default +If this parameter is set equal to ON, output database output will be generated automatically. If this +parameter is set equal to OFF, output database request keywords must be placed in an input file to +obtain output database output. The default value is ON. +onCaeStartup +Optional function to be executed before Abaqus/CAE begins. See “Customizing Abaqus/CAE +startup,” Section 4.3.3 of the Abaqus Installation and Licensing Guide, for examples of this function. +Co-simulation parameters +The following environment file variables provide default settings for co-simulation between solvers +using the direct coupling interface. This includes Abaqus/Standard to Abaqus/Explicit co-simulation +and co-simulation between Abaqus and certain third-party analysis programs. +cosimulation_port +Set cosimulation_port equal to the port number used for the connection. The default value is +48000. +cosimulation_timeout +Set cosimulation_timeout equal to the timeout period in seconds. Abaqus terminates if it does +not receive any communication from the coupled analysis program during the time specified. The +default value is 3600 seconds. +The following environment file variables provide settings that allow you to allocate CPUs +This includes +and Abaqus/CFD +and Abaqus/CFD +for co-simulation jobs submitted using the co-simulation execution procedure. +Abaqus/Standard to Abaqus/Explicit, Abaqus/Standard to Abaqus/CFD, +to Abaqus/Explicit co-simulation . +cpus_weight_std +This option controls the allocation of CPUs to Abaqus/Standard analyses. The actual CPU allocation +for Abaqus/Standard analyses is made in proportion to this value and considering the settings of +cpus_weight_xpl, cpus_weight_cfd, and cpus. +cpus_weight_xpl +This option controls the allocation of CPUs to Abaqus/Explicit analyses. The actual CPU allocation +for Abaqus/Explicit analyses is made in proportion to this value and considering the settings of +cpus_weight_std, cpus_weight_cfd, and cpus. +cpus_weight_cfd +This option controls the allocation of CPUs to Abaqus/CFD analyses. The actual CPU allocation +for Abaqus/CFD analyses is made in proportion to this value and considering the settings of +cpus_weight_std, cpus_weight_xpl, and cpus. +portpool +Set this variable equal to a colon-separated pair of TCP/UDP port numbers that represents the +start and end value of port numbers to be used by the co-simulation execution procedure when +establishing connections between the child processes. +Environment file examples +Example environment files that use some of the previously discussed parameters are shown below. A +sample environment file, named abaqusinc.env, is included in the site subdirectory of the release +to show the options used at SIMULIA. +UNIX environment file: +ask_delete=OFF +# The following parameter causes the scratch files to +# be written to /tmp. +scratch="/tmp" +Windows environment file: +ask_delete=OFF +# The following parameter causes the scratch files to +# be written to the tmp directory on c:. +scratch="c:/tmp" +3.4 +Managing memory and disk resources +• “Managing memory and disk use in Abaqus,” Section 3.4.1 +3.4.1 +MANAGING MEMORY AND DISK USE IN Abaqus +Products: Abaqus/Standard Abaqus/Explicit +References +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +• “Using the Abaqus environment settings,” Section 3.3.1 +Overview +For small analyses management of computer resources is generally of secondary concern, but with +large models intelligent use of disk and memory resources is a critical part of the analysis process. For +moderate to large analyses you will find it necessary to modify resource management settings. +Understanding resource use +For Abaqus disk and memory are effectively two similar means of storing data. Data that will be required +after an analysis completes must eventually be written to disk; but during an analysis, disk and memory +provide functionally equivalent storage mechanisms. Typically disk is a more abundant resource, while +memory provides faster access to stored data. Management of Abaqus resources hinges on this simple +trade-off. +Abaqus data +There are effectively two types of data generated by an Abaqus analysis. The first is “output” data that +must persist after an analysis is complete. Output data are typically either results that you require for +postprocessing or data that are necessary to restart an analysis. As mentioned above, these data must be +stored on disk before an analysis completes. +In addition, an analysis generates a considerable amount of “scratch” or temporary data. These +are data that are needed only while an analysis is running. The scratch data can be subdivided into two +groups: performance-critical data and generic data. The performance-critical data are always stored in +memory, while the generic data can be stored either in memory or on disk. +Requirements and considerations +To run an analysis, the following requirements must be satisfied: +• There must be sufficient disk space available to hold the requested output data. +• There must be sufficient memory available to hold all performance-critical data. +• There must be sufficient disk space or memory resource available to hold all generic scratch data. +If the above requirements are satisfied, an analysis can be completed; however, for Abaqus/Standard +you may find that allowing Abaqus to use additional memory will often improve performance. With the +increased availability of computer clusters, dedicated shared memory computers, and most importantly +job queuing systems that allocate processors and memory for analyses, it makes most sense to be able to +use all the memory resources to improve performance. +Typically Abaqus/Standard allocates a large portion of the available system memory on a machine +during the analysis phase, but you can manually specify a limit for memory usage with the memory +parameter . No scratch data are written to disk during +the Abaqus/Explicit analysis phase, since the majority of scratch data are performance critical. +Resource management parameters +into two classes: memory management and disk +Abaqus resource management parameters fall +management. Each can be adjusted through one environment file parameter. The following sections +explain how to best make use of this parameter. For information about the environment file, see “Using +the Abaqus environment settings,” Section 3.3.1. +Memory management parameters +The memory parameter is used to limit the amount of memory that can be used during the analysis +phase of Abaqus/Standard and during the input file processing phase, which is executed before both +Abaqus/Standard and Abaqus/Explicit analyses. +If you do not define the memory parameter, Abaqus automatically detects the physical memory +on the machine and allocates a percentage of this available memory. The default percentages are +platform specific, but they typically represent a large portion of the available physical memory. For +details on the default memory allocation settings, refer to the Dassault Systèmes Knowledge Base at +www.3ds.com/support/knowledge-base or the SIMULIA Online Support System, which is accessible +through the My Support page at www.simulia.com. +You can override the default memory allocation by specifying the percent of physical memory or +by specifying an absolute limit in units of megabytes or gigabytes. Percentages are indicated by a “%” +sign following the specified limit. Units of megabytes and gigabytes are indicated by “mb” or “gb” +following the specified limit. If no units are specified, megabytes are assumed. For example, with any +of the following settings: +memory="2048 mb" +memory="2 gb" +memory="25 %" +Abaqus uses up to 2 gigabytes of memory on a machine with 8 gigabytes physical memory. The memory +setting value must be surrounded by quotes. The values specified for memory must be reasonable for +the machine being used. Abaqus/Standard does not check the validity of the numerical values. To be +consistent with operating system memory measurement tools, a megabyte is defined by Abaqus to be +1,048,576 bytes, not 1,000,000 bytes. A similar rule applies to the unit of gigabyte. +There are no memory management parameters for the Abaqus/Explicit analysis phase, since no +scratch data are written to disk during this phase. +Environment file parameters can be set for a host, for a user, or for a particular job . Because a default memory setting +that works well for one machine with a large amount of memory may not be ideal for another machine +that has less memory, it may be useful to vary the default memory settings by machine. +Disk management parameters +Management of output data is discussed in detail in “Output,” Section 4.1.1. Output data are written to +files in the directory from which you launched the job. +Abaqus/Standard scratch files are written to a separate scratch directory. You can control the +directory used to hold the scratch files with the scratch environment file parameter. Due to the frequent +access of the scratch data throughout the analysis phase, ensuring high I/O speed of the scratch disks +is essential to the analysis performance. +As explained above, no scratch data are written to disk for Abaqus/Explicit, so you have to be +concerned only with proper management of output data. +Input file processing and data check +In general, the amount of memory required during input file processing is not large. The amount of +memory and disk space needed for the analysis phase of a job is more likely to be a concern. +It is +not possible for Abaqus to estimate the amount of memory that will be required to complete input file +processing. A data check run can be performed by using the datacheck parameter in the command for +running Abaqus +to obtain an estimate of the required memory for completing the analysis phase. General guidelines for +setting the memory parameter for performing the data check (which includes the input file processing +phase) are given below. +Guidelines for memory settings +You will usually not have to change the default memory setting. If a job fails as a result of insufficient +memory with the default setting, you will need to find a machine with more memory to run the job. If you +need to override the default behavior by specifying a value for the memory environment file parameter, +Table 3.4.1–1 lists some typical data check memory settings for problems of various sizes. The actual +values required for memory may vary considerably from problem to problem depending on the features +used in a model. +Table 3.4.1–1 Typical memory settings for performing the data check analysis. +Degrees of freedom +Memory +250,000 +1 million +2.5 million +5 million +250 megabytes +750 megabytes +1200 megabytes +2000 megabytes +Abaqus/Standard analysis +Depending on the execution environment and typical job sizes run on the machine, memory can be set +by machine or by job. More detailed guidelines are provided in the following section. When setting +memory by job is needed, you are advised to run a data check analysis and set memory based on the +memory estimates. These estimates are written to the printed output (.dat) file in a table under the +heading “MEMORY ESTIMATE.” Two columns in this table are relevant to memory use. The first +relevant column is labeled “MINIMUM MEMORY REQUIRED” and specifies the memory setting that +is needed to hold critical scratch data in memory. An attempt to run the analysis with memory set below +this value will result in a warning, and the job is not likely to run to completion due to the insufficient +memory. The second relevant column is labeled “MEMORY TO MINIMIZE I/O” and specifies the +memory that is required to hold all scratch data, both critical and generic, in memory. If the memory +specified by memory is larger than the “MINIMUM MEMORY REQUIRED,” Abaqus/Standard +automatically uses the additional memory up to the memory limit to improve speed of access to generic +scratch data that would otherwise be written to disk. When the memory is not enough to hold all the +generic scratch data in memory, Abaqus/Standard decides which data should be written to disk and +which should be kept in memory based on their relative importance with respect to their effect on the +analysis performance. Therefore, the actual disk space used by the scratch data can vary from very +close to zero to the “MEMORY TO MINIMIZE I/O” depending on the memory setting. The memory +setting can be changed in an analysis continued from a data check without the need of rerunning the +analysis input file processor. +Guidelines for memory settings +The memory parameter allows you to specify the memory limit that can be used by Abaqus during the +input file processing and analysis phases. You can specify the setting that should generally be available +to Abaqus on a particular machine in the host environment file. Settings can be modified as necessary for +individual jobs in job-specific environment files. Reasonable settings for a particular machine depend +on the size of the problems being run and how the machine is being used in addition to the physical +memory available on the machine. You should be aware of the difference between physical and virtual +memory. When virtual memory is used, a machine’s operating system simply uses disk for additional +memory. While this can be useful, memory access may require I/O operations that add a considerable +performance penalty. Therefore, the guidelines below for managing memory in Abaqus/Standard are +always given relative to the physical memory on a machine. Virtual memory should be used only when +necessary and with awareness of the associated performance penalty. +Setting memory on single-user machines +For a single-user machine that is dedicated to running Abaqus/Standard, using the default setting of +memory is sensible. If the estimates indicate that the job requires more than this value, the job is too +large to run efficiently on this machine. At this point you are urged to move the analysis to another +machine with more memory resources. +For a single-user machine that is used to run both Abaqus/Standard and other applications +If an analysis requires more than the +simultaneously, setting a lower memory limit makes sense. +specified value, you can decide to increase memory and continue the job. However, Abaqus/Standard +will have to contend with the other applications for memory, which will impair the efficiency of both +Abaqus/Standard and the other applications. If the other applications are interactive, the performance +degradation could be problematic. In such a case you might decide to delay continuing the analysis +until the machine can be dedicated to running Abaqus/Standard alone. +Setting memory on multi-user machines +The guidelines for setting memory on a multi-user machine are very similar to those for single-user +machines, except that a judgement must be made as to the amount of memory that each user on the +machine can expect to have for a single analysis. A reasonable approach might be to divide the machine’s +physical memory by the number of expected simultaneous jobs. Another sensible approach is to divide +the machine’s physical memory by the total number of CPUs and then multiply by the number of CPUs +used for the current job. If the memory requirement among the simultaneous jobs is not even, you might +want to divide the machine’s physical memory in an uneven way accordingly. In general, to ensure +acceptable performance, users on multi-user machines need to coordinate with each other to properly set +the memory limit. +Setting memory when using queues +Often queues have an associated memory limit, and determining the appropriate queue for a job requires +some judgement. You are advised to run a data check analysis and select a queue based on the estimates +provided in the printed output file. However, for large analyses even a data check analysis can require +a large amount of memory. Choosing an appropriate queue for a data check analysis requires some +experience with particular classes of problems. You may want to submit data check runs initially to +queues with very large memory limits to get the necessary estimates. An appropriate queue can then +be chosen to actually run the job. If the jobs are to be submitted to shared memory machines, it makes +sense to set memory to about 90% of the memory limit for the queue. If the jobs are to be submitted to +computer clusters, it is reasonable to use the default memory setting. +3.5 +Parallel execution +• “Parallel execution: overview,” Section 3.5.1 +• “Parallel execution in Abaqus/Standard,” Section 3.5.2 +• “Parallel execution in Abaqus/Explicit,” Section 3.5.3 +• “Parallel execution in Abaqus/CFD,” Section 3.5.4 +3.5.1 +PARALLEL EXECUTION: OVERVIEW +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD +References +• “Obtaining information,” Section 3.2.1 +• “Using the Abaqus environment settings,” Section 3.3.1 +• “Parallel execution in Abaqus/Standard,” Section 3.5.2 +• “Parallel execution in Abaqus/Explicit,” Section 3.5.3 +• “Parallel execution in Abaqus/CFD,” Section 3.5.4 +Overview +Parallel execution of Abaqus is implemented using two different schemes: +threads and message +passing. Threads are lightweight processes that can perform different tasks simultaneously within +the same application. Threads can communicate relatively easily by sharing the same memory pool. +Thread-based parallelization is readily available on all shared memory platforms. +Parallelization with message passing uses multiple analysis processes that communicate with each +other via the Message Passing Interface (MPI). This requires MPI components to be installed. On the +command line you can set mp_mode=mpi to indicate that MPI components are available on the system. +Alternatively, set mp_mode=MPI in the environment file . The MPI-based implementation is the default on all platforms where it is supported. +Abaqus/CFD is implemented using only the MPI mode and does not support threads. The parallel +linear solvers used in Abaqus/CFD require that MPI components be installed even for single-processor +calculations. +Output the local installation notes for your system to learn about local multiprocessing capabilities +. From the Support page at www.simulia.com, refer to +the System Information page for the current release of Abaqus for complete information about parallel +processing support on various platforms, including information about MPI requirements and availability. +Parallel processing support for Abaqus features +The following Abaqus/Standard features can be executed in parallel: +the direct sparse solver, the +iterative solver, and element operations. The analysis input preprocessing is not executed in parallel. For +Abaqus/Explicit all of the computations other than those involving the analysis input preprocessor and +the packager can be executed in parallel. Each of the features that are available for parallel execution +has certain limitations, which are documented in detail; see “Parallel execution in Abaqus/Standard,” +Section 3.5.2, and “Parallel execution in Abaqus/Explicit,” Section 3.5.3. All features in Abaqus/CFD +are available for parallel execution without restrictions. +Parallel execution on shared memory computers +Abaqus/Standard and Abaqus/Explicit can be executed in parallel on shared memory computers by using +threads or the MPI. When the MPI is available, Abaqus runs all available parallel features with MPI- +based parallelization and activates thread-based parallel implementations for cases where an equivalent +MPI-based implementation does not exist (e.g., direct sparse solver). Abaqus/CFD can also be executed +on shared memory computers but only with the MPI. +Parallel execution on computer clusters +Abaqus can be executed in parallel on computer clusters by using MPI-based parallelization. For parallel +execution on computer clusters, the list of machines or hosts is given with the mp_host_list environment +file parameter. This parameter also defines the number of processors to be used on each host. +Parallel execution using GPGPU hardware +The direct solver in Abaqus/Standard can be executed in parallel on computers equipped with compute- +capable GPGPU cards. +Use with user subroutines +User subroutines can be used when running jobs in parallel. However, user subroutines and any +subroutines called by them must be thread safe. This precludes the use of common blocks, data +statements, and save statements. Calling subroutines that are not thread safe will result in unpredictable +behavior of the executable. +3.5.2 +PARALLEL EXECUTION IN Abaqus/Standard +Products: Abaqus/Standard Abaqus/CAE +References +• “Obtaining information,” Section 3.2.1 +• “Using the Abaqus environment settings,” Section 3.3.1 +• “Controlling job parallel execution,” Section 19.8.8 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +Parallel execution in Abaqus/Standard: +• reduces run time for large analyses; +• is available for shared memory computers and computer clusters for the element operations, direct +sparse solver, and iterative linear equation solver; and +• can use compute-capable GPGPU hardware on shared memory computers for the direct sparse +solver. +Parallel equation solution with the default direct sparse solver +The direct sparse solver (“Direct linear equation solver,” Section 6.1.5) supports both shared memory +computers and computer clusters for parallelization. On shared memory computers or a single node of a +computer cluster, thread-based parallelization is used for the direct sparse solver, and high-end graphics +cards that support general processing (GPGPUs) can be used to accelerate the solution. On multiple +compute nodes of a computer cluster, a hybrid MPI and thread-based parallelization is used. +The direct sparse solver cannot be used on multiple compute nodes of a computer cluster if: +• the analysis also includes an eigenvalue extraction procedure, or +• the analysis requires features for which MPI-based parallel execution of element operations is not +supported. +In addition, the direct sparse solver cannot be used on multiple nodes of a computer cluster for analyses +that include any of the following: +• multiple load cases with changing boundary conditions (“Multiple load case analysis,” +Section 6.1.4), and +• the quasi-Newton nonlinear solution technique (“Convergence criteria for nonlinear problems,” +Section 7.2.3). +To execute the parallel direct sparse solver on computer clusters, +the environment variable +mp_host_list must be set to a list of host machines . MPI-based parallelization is used between the machines in the host list. Thread-based +parallelization is used within a host machine if more than one processor is available on that machine +in the host list and if the model does not contain cavity radiation using parallel decomposition . For example, if the +environment file has the following: +cpus=8 +mp_host_list=[['maple',4],['pine',4]] +Abaqus/Standard will use four processors on each host through thread-based parallelization. A total of +two MPI processes (equal to the number of hosts) will be run across the host machines so that all eight +processors are used by the parallel direct sparse solver. +Models containing parallel cavity decomposition use only MPI-based parallelization. Therefore, +MPI is used on both shared memory parallel computers and distributed memory compute clusters. +The number of processes is equal to the number of CPUs requested during job submission. Element +operations are executed in parallel using MPI-based parallelization when parallel cavity decomposition +is enabled. +Input File Usage: +Use the following option in conjunction with the command line input to execute +the parallel direct sparse solver: +*STEP +Enter the following input on the command line: +abaqus job=job-name cpus=n +For example, the following input will run the job “beam” on two processors: +abaqus job=beam cpus=2 +Abaqus/CAE Usage: +Step module: step editor: Other: Method: Direct +Job module: job editor: Parallelization: toggle on Use multiple +processors, and specify the number of processors, n +GPGPU acceleration of the direct sparse solver +The direct sparse solver supports GPGPU acceleration for the symmetric solver; GPGPU acceleration +cannot be used with the unsymmetric solver. +Input File Usage: +Enter the following input on the command line to activate GPGPU direct sparse +solver acceleration: +Abaqus/CAE Usage: +Step module: step editor: Other: Method: Direct +abaqus job=job-name gpus=n +Job module: job editor: Parallelization: toggle on Use GPGPU +acceleration, and specify the number GPGPUs +Memory requirements for the parallel direct sparse solver +The parallel direct sparse solver processes multiple fronts in parallel in addition to parallelizing the +solution of individual fronts. Therefore, the direct parallel solver requires more memory than the serial +solver. The memory requirements are not predictable exactly in advance since it is not determined a +priori which fronts will actually be processed simultaneously. +Equation ordering for minimum solve time +Direct sparse solvers require the system of equations to be ordered for minimum floating point operation +count. The ordering procedure is performed in parallel when multiple host machines are used on +a computer cluster. +In a shared memory configuration the ordering procedure is not performed in +parallel. The parallel ordering procedure will compute different orders when run on different number +of host machines, which will affect the floating point operation count for the direct solver. Parallel +ordering can offer performance improvements, particularly for large models using many host machines +by significantly reducing the time to compute the order. Parallel ordering may cause performance +degradation if the order determined results in a higher floating point operation count for the direct solver. +The serial ordering procedure can be used in cases where the variability in the ordering inherent in +the parallel ordering procedure is not acceptable. You can deactivate parallel solver ordering from the +command line or by using the order_parallel environment file parameter . +Input File Usage: +Abaqus/CAE Usage: +Enter the following input on the command line to deactivate parallel solver +ordering: +abaqus job=job-name order_parallel=OFF +Deactivation of parallel solver ordering is not supported in Abaqus/CAE. +Parallel equation solution with the iterative solver +The iterative solver +(“Iterative linear equation solver,” Section 6.1.6) uses only MPI-based +parallelization. Therefore, MPI is used on both shared memory parallel computers and distributed +memory compute clusters. To execute the parallel iterative solver, specify the number of CPUs for +the job. The number of processes is equal to the number of CPUs requested during job submission. +Element operations are executed in parallel using MPI-based parallelization when the parallel iterative +solver is used. +Input File Usage: +Use the following option in conjunction with the command line input to execute +the parallel iterative solver: +*STEP, SOLVER=ITERATIVE +Enter the following input on the command line: +abaqus job=job-name cpus=n +For example, the following input will run the job “cube” on four processors +with the iterative solver: +abaqus job=cube cpus=4 +Abaqus/CAE Usage: +Step module: step editor: Other: Method: Iterative +Job module: job editor: Parallelization: toggle on Use multiple +processors, and specify the number of processors, n +Parallel execution of the element operations in Abaqus/Standard +Parallel execution of the element operations is the default on all supported platforms. The command +line and environment variable standard_parallel can be used to control the parallel execution of the +element operations . +operations is used, the solvers also run in parallel automatically. For analysis using the direct sparse +solver and not containing parallel cavity decomposition, thread-based parallelization of the element +operations is used on shared memory computers and a hybrid MPI and thread parallel scheme is used on +computer clusters. For analyses using the iterative solver or if parallel cavity decomposition is enabled, +only MPI-based parallelization of element operations is supported. +When MPI-based parallelization of element operations is used, element sets are created for each +domain and can be inspected in Abaqus/CAE. The sets are named STD_PARTITION_n, where n is the +domain number. +Parallel execution of the element operations (thread or MPI-based parallelization) is not supported +for the following procedures: +• eigenvalue buckling prediction (“Eigenvalue buckling prediction,” Section 6.2.3), +• natural frequency extraction (“Natural frequency extraction,” Section 6.3.5) that does not use the +SIM architecture, +• response spectrum analysis (“Response spectrum analysis,” Section 6.3.10), +• random response analysis (“Random response analysis,” Section 6.3.11), and +• mode-based linear dynamics (“Transient modal dynamic analysis,” Section 6.3.7; “Mode-based +steady-state dynamic analysis,” Section 6.3.8; “Subspace-based steady-state dynamic analysis,” +Section 6.3.9; and “Complex eigenvalue extraction,” Section 6.3.6) that do not use the SIM +architecture. +Parallel execution of element operations is available only through MPI-based parallelization for +analyses that include any of the following: +• static linear perturbation (“General and linear perturbation procedures,” Section 6.1.3), +• direct cyclic analysis (“Direct cyclic analysis,” Section 6.2.6), +• direct-solution +Section 6.3.4), +(“Direct-solution +steady-state +steady-state +dynamics +dynamic +analysis,” +• steady-state transport (“Steady-state transport analysis,” Section 6.4.1), +• coupled temperature-displacement (“Fully coupled thermal-stress analysis,” Section 6.5.3), +• coupled thermal-electrical-structural +(“Fully coupled thermal-electrical-structural analysis,” +Section 6.7.4), +• coupled pore fluid diffusion and stress (“Coupled pore fluid diffusion and stress analysis,” +Section 6.8.1), +• crack propagation analysis (“Crack propagation analysis,” Section 11.4.3), and +• pressure penetration loading (“Pressure penetration loading,” Section 36.1.7). +Analyses using the direct sparse solver and any of the procedures above that support only MPI-based +parallelization of element operations can be run on computer clusters. However, only one processor per +compute node is used for the element operations since thread-based parallelization is not supported. +Parallel execution of element operations is available only through thread-based parallelization for: +• cavity radiation analyses where parallel decomposition of the cavity is not allowed and writing of +restart data is requested (“Cavity radiation,” Section 40.1.1), and +• heat transfer analyses where average-temperature radiation conditions are specified (“Thermal +loads,” Section 33.4.4). +Finally, parallel execution of the element operations is not supported for analyses that include any of the +following: +• element matrix output requests (“Element matrix output +Section 4.1.1), +in Abaqus/Standard” in “Output,” +• alternative +solution +techniques +(“Approximate +quasi-Newton method +except +implementation” in “Fully coupled thermal-stress analysis,” Section 6.5.3; +“Approximate +implementation” in “Coupled thermal-electrical analysis,” Section 6.7.3; and “Specifying the +separated method” in “Convergence criteria for nonlinear problems,” Section 7.2.3), +the +for +• continuation of output upon restart (“Continuation of output upon restart” in “Restarting an +analysis,” Section 9.1.1), +• import from Abaqus/Explicit (“Transferring results between Abaqus analyses: +Section 9.2.1), +overview,” +• substructures (“Substructuring,” Section 10.1), and +• adaptive meshing (“Defining ALE adaptive mesh domains in Abaqus/Standard,” Section 12.2.6). +Input File Usage: +Enter the following input on the command line: +Abaqus/CAE Usage: +abaqus job=job-name standard_parallel=all cpus=n +Control of the parallel execution of the element operations is not supported in +Abaqus/CAE. +Memory management with parallel execution of the element operations +When running parallel execution of the element operations in Abaqus/Standard, specifying the upper +limit of the memory that can be used specifies the maximum amount of memory that can be allocated by each +process. +Transverse shear stress output for stacked continuum shells +The output variables CTSHR13 and CTSHR23 are currently not available when running parallel +execution of the element operations in Abaqus/Standard. See “Continuum shell element library,” +Section 29.6.8. +Consistency of results +Some physical systems (systems that, for example, undergo buckling, material failure, or delamination) +can be highly sensitive to small perturbations. For example, it is well known that the experimentally +measured buckling loads and final configurations of a set of seemingly identical cylindrical shells can +show significant scatter due to small differences in boundary conditions, loads, initial geometries, etc. +When simulating such systems, the physical sensitivities seen in an experiment can be manifested as +sensitivities to small numerical differences caused by finite precision effects. Finite precision effects can +lead to small numerical differences when running jobs on different numbers of processors. Therefore, +when simulating physically sensitive systems, you may see differences in the numerical results (reflecting +the differences seen in experiments) between jobs run on different numbers of processors. To obtain +consistent simulation results from run to run, the number of processors should be constant. +3.5.3 +PARALLEL EXECUTION IN Abaqus/Explicit +Products: Abaqus/Explicit Abaqus/CAE +References +• “Obtaining information,” Section 3.2.1 +• “Using the Abaqus environment settings,” Section 3.3.1 +• “Controlling job parallel execution,” Section 19.8.8 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +Parallel execution in Abaqus/Explicit: +• reduces run time for analyses that require a large number of increments; +• reduces run time for analyses that contain a large number of nodes and elements; +• produces analysis results that are independent of the number of processors used for the analysis; +• is available for shared memory computers using a thread-based loop level or thread-based domain +decomposition implementation; and +• is available for both shared memory computers and computer clusters using an MPI-based domain +decomposition parallel implementation. +Invoking parallel processing +Parallelization in Abaqus/Explicit is implemented in two ways: domain level and loop level. The +domain-level method breaks the model up into topological domains and assigns each domain to a +processor. The domain-level method is the default. The loop-level method parallelizes low-level loops +that are responsible for most of the computational cost. The element, node, and contact pair operations +account for the majority of the low-level parallelized routines. +Parallelization can be invoked by specifying the number of processors to be used. +Input File Usage: +Enter the following input on the command line: +abaqus job=job-name cpus=n +For example, the following input will run the job “beam” on two processors: +abaqus job=beam cpus=2 +Abaqus/CAE Usage: +Job module: job editor: Parallelization: toggle on Use multiple +processors, and specify the number of processors, n +Domain-level parallelization +The domain-level method splits the model into a number of topological domains. These domains are +referred to as parallel domains to distinguish them from other domains associated with the analysis. +The domains are distributed evenly among the available processors. The analysis is then carried out +independently in each domain. However, information must be passed between the domains in each +increment because the domains share common boundaries. Both MPI and thread-based parallelization +modes are supported with the domain-level method. +During initialization, the domain-level method divides the model so that the resulting domains +take approximately the same amount of computational expense. The load balance is defined as the +ratio of the computational expense of all domains in the most expensive process to that of all domains +in the least expensive process. For cases exhibiting significant load imbalance, either because the +initial load balancing is not adequate (static imbalance) or because imbalance develops over time +(dynamic imbalance), the dynamic load balancing technique may be applied . Dynamic load balancing is based +on over-decomposition: +the user selects a number of domains that is a multiple of the number of +processors. During the calculation, Abaqus/Explicit will regularly measure the computational expense +and redistribute the domains over the processors so as to minimize the load imbalance. The following +functionality is not supported with dynamic load balancing: +• Selective subcycling (“Selective subcycling,” Section 11.7.1) +• Co-simulation (“Co-simulation,” Section 17.1) +• Predefined fields using a results file (“Predefined fields,” Section 33.6.1) +The efficiency of the dynamic load balancing scheme depends on the load imbalance inherent to the +problem, on the degree of overdecomposition, and on the efficiency of the hardware. Most imbalanced +problems will see optimal performance improvement when the number of domains is two to four times the +number of processors. The efficiency may be significantly reduced on systems with a slow interconnect, +such as Gigabit Ethernet clusters. Best results are obtained when an external interconnect is not needed, +such as within a multicore node of a cluster, or on a shared-memory system. Applications most likely +to benefit from dynamic load balancing are problems with a strongly time-dependent and/or spatially +varying computational load. Examples are models containing airbags, where contact-impact activity is +highly localized and time dependent; and coupled Lagrangean-Eulerian problems, where constitutive +activity follows the material as it moves through empty space. +Element and node sets are created for each domain and can be inspected in Abaqus/CAE. The sets +are named domain_n, where n is the domain number. +During the analysis, separate state (job-name.abq) and selected results (job-name.sel) files +are created. There will be one state and one selected results file for each processor. The naming +convention is to append the processor number to the file name. For example, the state files are named +job-name.abq.n, where n is the processor number. At the completion of the analysis the individual +files are merged automatically into a single file (for example, job-name.abq), and the individual files +are deleted. +Input File Usage: +Enter the following input on the command line: +abaqus +job=job-name +dynamic_load_balancing +cpus=n +parallel=domain +domains=m +For example, the following input will run the job “beam” on two processors +with the domain-level parallelization method: +abaqus job=beam cpus=2 parallel=domain domains=2 +The domain-level parallelization method can also be set in the environment file +using the environment file parameters parallel=DOMAIN and domains. +Job module: job editor: Parallelization: toggle on Use multiple processors +and specify the number of processors, n; Number of domains: m; +toggle on Activate dynamic load balancing; Parallelization method: +Domain +You can activate dynamic load balancing when the number of domains is a +multiple of the number of processors. +Abaqus/CAE Usage: +Consistency of results +The analysis results are independent of the number of processors used for the analysis. However, the +results do depend on the number of parallel domains used during the domain decomposition. Except +for cases in which the single- and multiple-domain models are different due to features that are not +yet available with multiple parallel domains (discussed below), these differences should be triggered +only by finite precision effects. For example, the order of the nodal force assembly may depend on +the number of parallel domains, which can result in differences in trailing digits in the computed force. +Some physical systems are highly sensitive to small perturbations, so a tiny difference in the force applied +in one increment can result in noticeable differences in results in subsequent increments. Simulations +involving buckling and other bifurcations tend to be sensitive to small perturbations. +To obtain consistent analysis results from run to run, the number of domains used in the domain +decomposition should be constant. Increasing the number of domains increases the computational cost +slightly; therefore, unless dynamic load balancing is being applied, it is recommended that the number +of domains be set equal to the maximum number of processors used for analysis execution for optimal +performance. +If you do not specify the number of domains, the number defaults to the number of +processors. +Features that do not allow domain-level parallelization +The use of the domain-level parallelization method is not allowed with the following features: +• Extreme value output. +• Steady-state detection. +If these features are included, an error message will be issued. +Features that cannot be split across domains +Certain features cannot be split across domains. The domain decomposition algorithm automatically +takes this into account and forces these features to be contained entirely within one domain. If fewer +domains than requested processors are created, Abaqus/Explicit issues an error message. Even if the +algorithm succeeds in creating the requested number of domains, the load may be balanced unevenly. If +this behavior is not acceptable, the job should be run with the loop-level parallelization method. +Adaptive smoothing domains cannot span parallel domain boundaries. The nodes on the boundary +between an adaptive smoothing domain and a nonadaptive domain as well as the adaptive nodes on the +surface of the adaptive smoothing domain cannot be shared with another parallel domain. To enforce +this in a consistent manner when parallel domains are specified, all nodes shared by adjacent adaptive +smoothing domains will be set as nonadaptive. In this case the analysis results may be significantly +different from that of a serial run with no parallel domains. Set the number of parallel domains to 1, +and switch to the loop-level parallelization method if this behavior is undesirable. See “Defining ALE +adaptive mesh domains in Abaqus/Explicit,” Section 12.2.2, for details. +A contact pair cannot be split across parallel domains, but separate contact pairs are not restricted to +be in the same parallel domain. A contact pair that uses the kinematic contact algorithm requires that all +of the nodes associated with the involved surfaces be within a single parallel domain and not be shared +with any other parallel domains. A contact pair that uses the penalty contact algorithm requires that the +associated nodes be part of a single parallel domain, but these nodes may also be part of other parallel +domains. Analyses in which a large percentage of nodes are involved in contact may not scale well if +contact pairs are used, especially with kinematic enforcement of contact constraints. General contact +does not limit the domain decomposition boundaries. +Nodes involved in kinematic constraints (“Kinematic constraints: overview,” Section 34.1.1) will +be within a single parallel domain, and they will not be shared with another parallel domain. However, +two kinematic constraints that do not share nodes can be placed within different parallel domains. +In some cases beam elements that share a node may be forced into the same parallel domain. This +happens only for beams whose center of mass does not coincide with the location of the beam node or for +beams with additional inertia . +Restart +There are certain restrictions for restart when using domain-level parallelization. To ensure that optimal +parallel speedup is achieved, the number of processors used for the restart analysis must be chosen so +that the number of parallel domains used during the original analysis can be distributed evenly among +the processors. Because the domain decomposition is based only on the features specified in the original +analysis and steps defined therein, features that affect domain decomposition are restricted from being +defined in restart steps only if they would invalidate the original domain decomposition. Because the +newly added features will be added to existing domains, there is a potential for load imbalance and a +corresponding degradation of parallel performance. +The restart analysis requires that the separate state and selected results files created during the +original analysis be converted into single files, as described in “Abaqus/Standard, Abaqus/Explicit, and +Abaqus/CFD execution,” Section 3.2.2. This should be done automatically at the conclusion of the +original analysis. If the original analysis fails to complete successfully, you must convert the state and +selected results files prior to restart. An Abaqus/Explicit analysis packaged to run with a domain-level +parallelization technique cannot be restarted or continued with a loop-level parallelization technique. +Co-simulation +The co-simulation technique (“Co-simulation: overview,” Section 17.1.1) for run-time coupling +of Abaqus/Explicit +to Abaqus/Standard or to third-party analysis programs can be used with +Abaqus/Explicit running either in serial or parallel. +Loop-level parallelization +The loop-level method parallelizes low-level loops in the code that are responsible for most of the +computational cost. The speedup factor using loop-level parallelization may be significantly less than +what can be achieved with domain-level parallelization. The speedup factor will vary depending on the +features included in the analysis since not all features utilize parallel loops. Examples are the general +contact algorithm and kinematic constraints. The loop-level method may scale poorly for more than +four processors depending on the analysis. Using multiple parallel domains with this method will +degrade parallel performance and, hence, is not recommended. The loop-level method is not supported +on the Windows platform. +Analysis results for this method do not depend on the number of processors used. +Input File Usage: +Enter the following input on the command line: +abaqus job=job-name cpus=n parallel=loop +The loop-level parallelization method can also be set in the environment file +using the environment file parameter parallel=LOOP. +Job module: job editor: Parallelization: toggle on Use multiple processors, +and specify the number of processors, n; Parallelization method: Loop +Abaqus/CAE Usage: +Restart +There are no restrictions on features that can be included in steps defined in a restart analysis when using +loop-level parallelization. For performance reasons the number of processors used when restarting must +be a factor of the number of processors used in the original analysis. The most common case would +be restarting with the same number of processors as used in the original analysis. An Abaqus/Explicit +analysis packaged to run with a loop-level parallelization technique cannot be restarted or continued with +a domain-level parallelization technique. +Measuring parallel performance +Parallel performance is measured by comparing the total time required to run on a single processor +(serial run) to the total time required to run on multiple processors (parallel run). This ratio is referred +to as the speedup factor. The speedup factor will equal the number of processors used for the parallel +run in the case of perfect parallelization. Scaling refers to the behavior of the speedup factor as the +number of processors is increased. Perfect scaling indicates that the speedup factor increases linearly +with the number of processors. For both parallelization methods the speedup factors and scaling behavior +are heavily problem dependent. In general, the domain-level method will scale to a larger number of +processors and offer the higher speedup factor. +Output +There are no output restrictions. +3.5.4 +PARALLEL EXECUTION IN Abaqus/CFD +Products: Abaqus/CFD Abaqus/CAE +References +• “Obtaining information,” Section 3.2.1 +• “Using the Abaqus environment settings,” Section 3.3.1 +• “Controlling job parallel execution,” Section 19.8.8 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +Parallel execution in Abaqus/CFD: +• reduces run time for analyses that require a large number of increments; +• reduces run time for analyses that contain a large number of nodes and elements; +• produces analysis results that are independent of the number of processors used for the analysis; and +• is available for both shared memory computers and computer clusters using an MPI-based domain +decomposition parallel implementation. +Invoking parallel processing +Abaqus/CFD uses domain-based parallelism implemented with explicit message passing for both +shared memory and distributed memory computers. All procedures provided by Abaqus/CFD and their +associated features are fully parallel (“Parallel execution: overview,” Section 3.5.1). Parallel execution +is invoked by specifying the number of processors to be used. +Input File Usage: +Enter the following input on the command line: +abaqus job=job-name cpus=n +For example, the following input will run the job “manifold” on two processors: +abaqus job=manifold cpus=2 +Abaqus/CAE Usage: +Job module: job editor: Parallelization: toggle on Use multiple +processors, and specify the number of processors, n +Domain-based parallelism +Abaqus/CFD uses a domain-decomposition message passing paradigm for its parallel implementation. +An element-based decomposition strategy is used that minimizes the number of communications +required between subdomains while providing a nearly uniform computational work distribution among +the processors. The number of domains maps exactly to the number of user-specified processors +for a given calculation. The load-balancing procedures are implemented in parallel as well, so that +you can avoid time consuming serial load-balancing procedures at the start of a calculation. Every +attempt has been made to ensure that Abaqus/CFD provides scalable parallel solutions for a broad +range of applications. All procedures and features in Abaqus/CFD are provided with a fully parallel +implementation. All output is serialized automatically for the user so that there is no translation between +parallel domains and the original user input. In addition, this permits Abaqus/CFD to restart seamlessly +on any number of processors, regardless of how many were used for the original computation. +Co-simulation +The co-simulation technique (“Co-simulation: overview,” Section 17.1.1) for run-time coupling of +Abaqus/CFD to Abaqus/Standard or to Abaqus/Explicit can be used with Abaqus/CFD running either +in serial or parallel. +Restart +There are no restrictions on features that can be included in steps defined in a restart analysis. The number +of processors used for the restart analysis is not required to be the same as the number of processors used +in the original analysis. +Output +There are no output restrictions. +3.6 +File extension definitions +• “File extensions used by Abaqus,” Section 3.6.1 +3.6.1 +FILE EXTENSIONS USED BY Abaqus +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +The abaqus procedure generates several files. Some of these files contain analysis, postprocessing, and +translation results and are retained for use by other analysis options, restarting, or postprocessing. This +section describes the files that are created and retained by Abaqus. +Other files exist only while Abaqus is executing and are deleted when a run completes. These +temporary files are generated in the scratch directory. The number and types of temporary files generated +depend on the analysis procedures, memory management parameters, and environment settings. +Certain file extensions used by Abaqus are also used by other software applications. You must +handle any file extension conflicts with other applications. +File extensions +abq +axi +bsp +c++ +cpp +State file, only used by Abaqus/Explicit. It is written by the analysis, continue, and recover options. +It is read by the convert and recover options. This file is required for restart. +Symmetric model data file, only used by Abaqus/Standard. It is written during symmetric model +generation by the datacheck and analysis options. +Text file containing beam cross-section properties for meshed section profiles. +Abaqus/Standard during meshed beam cross-section generation. +It is written by +User subroutine or other special-purpose C file. +User subroutine or other special-purpose C++ file. +User subroutine or other special-purpose C++ file. +cid +com +dat +fil +fin +inp +ipm +lck +log +Auto-release file, which contains information needed for license recovery and suspension. +Command file, created by the Abaqus execution procedure. +Printed output file. +options. Abaqus/Explicit and Abaqus/CFD do not write analysis results to this file. +It is written by the analysis, datacheck, parametercheck, and continue +User subroutine or other special-purpose FORTRAN file. +Results file. +convert=select and convert=all options in Abaqus/Explicit. +It is written by the analysis and continue options in Abaqus/Standard and by the +Results file created when changing the format of the .fil file using the abaqus ascfil command. + files,” +It can be in either ASCII or binary format. +Section 3.2.11.) The ASCII format is convenient for data transfer between machines that do not +have compatible binary data formats. +Analysis input file. +selected. +It is read when the analysis, datacheck, and parametercheck options are +Interprocess message file. It is written when an analysis is run from Abaqus/CAE, and it contains a +log of all messages sent from Abaqus/Standard, Abaqus/Explicit, or Abaqus/CFD to Abaqus/CAE. +Lock file for the output database. This file is written whenever an output database file is opened +with write access; it prevents you from having simultaneous write permission to the output database +from multiple sources. It is deleted automatically when the output database file is closed or when +the analysis that creates it ends. The ask_delete environment file parameter setting will not affect +the lock file. +Log file, which contains start and end times for modules run by the current Abaqus execution +procedure. +mdl +msg +nck +odb +pac +par +pes +pmg +prt +Model file, used by Abaqus/Standard and Abaqus/Explicit. It is written by the datacheck option. +It is read and can be written by the analysis and continue options in Abaqus/Standard. It is read +by the analysis and continue options in Abaqus/Explicit. Multiple model files may exist if the +element operations are executed in parallel in an Abaqus/Standard analysis. In such a case a process +identifier is attached to the file name. This file is required for restart. +Message file. It is written by the analysis, datacheck, and continue options in Abaqus/Standard +and Abaqus/Explicit. Multiple message files may exist if the element operations are executed in +parallel in an Abaqus/Standard analysis. In such a case a process identifier is attached to the file +name. +Nickname file used by Abaqus/Standard. It stores a set of internal identifiers for the degrees of +freedom in a model. +Output database. +Abaqus/Explicit, and Abaqus/CFD. +(Abaqus/Viewer) and by the convert=odb option. This file is required for restart. +It is written by the analysis and continue options in Abaqus/Standard, +It is read by the Visualization module in Abaqus/CAE +Package file, which contains model information and is used by Abaqus/Explicit only. It is written +by the analysis and datacheck options. It is read by the analysis, continue, and recover options. +This file is required for restart. +Modified version of original parametrized input file showing input parameters and their values. +Modified version of original parametrized input file showing input free of parameter information +(after input parameter evaluation and substitution has been performed). +Parameter evaluation and substitution message file. It is written when the input file is parametrized. +Part file, used by Abaqus/Standard and Abaqus/Explicit. This file is used to store part and assembly +information and is created even if the input file does not contain an assembly definition. The part +file is required for restart, import, sequentially coupled thermal-stress analysis, symmetric model +generation, and underwater shock analysis, even if the model is not defined in terms of an assembly +of part instances. This file may also be needed for submodeling analysis. +psf +res +sel +sim +sta +stt +sup +var +023 +Python scripting file. You must create this type of file to define a parametric study. +Restart file, which contains information necessary to continue a previous analysis and is used by +Abaqus/Standard and Abaqus/Explicit. The restart file is written by the analysis, datacheck, and +continue options. It is read by any restarted analysis. +Selected results file, used by Abaqus/Explicit. It is written by the analysis, continue, and recover +options and is read by the convert=select option. This file is required for restart. +Linear dynamics data file, used by Abaqus/Standard. It is written during the frequency extraction +procedure in SIM-based linear dynamics analyses and is used to store eigenvectors, substructure matrices, and other modal system +information. This file is required for restart. +Model file, used by Abaqus/CFD. It is written by the datacheck option. It is read and can be +written by the analysis and continue options. This file is required for restart. +Status file. Abaqus writes increment summaries to this file in the analysis, continue, and recover +options. +State file. It is written by the datacheck option in Abaqus/Standard and Abaqus/Explicit. It is +read and can be written by the analysis and continue options in Abaqus/Standard. It is read by +the analysis and continue options in Abaqus/Explicit. Multiple state files may exist if the element +operations are executed in parallel in an Abaqus/Standard analysis. In such a case a process identifier +is attached to the file name. This file is required for restart. +Substructure file, used by Abaqus/Standard. +File containing information about the input file variations generated by a parametric study. +Communications file, used by Abaqus/Standard and Abaqus/Explicit. It is written by the analysis +and datacheck options and is read by the analysis and continue options. +3.7 +FORTRAN unit numbers +• “FORTRAN unit numbers used by Abaqus,” Section 3.7.1 +3.7.1 +FORTRAN UNIT NUMBERS USED BY Abaqus +Products: Abaqus/Standard Abaqus/Explicit +Reference +• “Execution procedure for Abaqus: overview,” Section 3.1.1 +Overview +Abaqus uses the FORTRAN unit numbers outlined in the table below. Unless noted otherwise, you +should not try to write to these FORTRAN units from user subroutines. +For Abaqus/Standard, you should specify unit numbers 15–18 or unit numbers greater than 100 . +For Abaqus/Explicit, specify units 16–18 or unit numbers greater than 100 ending in 5 to 9, e.g. +105, 268, etc. You cannot write to the.sta file. +FORTRAN unit numbers +Code +Unit Number +Description +Abaqus/Standard +10 +12 +19–30 +73 +Internal database +Solver file +Printed output (.dat) file (You can write output +to this file.) +Message (.msg) file (You can write output to this +file.) +Results (.fil) file +Internal database +Restart (.res) file +Internal databases (scratch files). Unit numbers 21 +and 22 are always written to disk. +Text file containing meshed beam cross-section +properties (.bsp) +Code +Unit Number +Description +Abaqus/Explicit +If domain-parallel +12 +13 +15 +23 +60 +61 +62 +63 +64 +65 +67 +68 +69 +70 +71 +73 +80 +81 +83 +... +Printed output (.log) . +Restart (.res) file +Old restart (.res) file, if applicable +Analysis Preprocessor (.dat or .pre) file +Communications (.023) file +Global package (.pac) file +Global state (.abq) file +Temporary file +Global selected results (.sel) file +Message (.msg) file +Output database (.odb) file +Old package (.pac) file, if import from +Abaqus/Explicit +Old state (.abq) file, if import from +Abaqus/Explicit +Internal database; temporary file +Local package (.pac.1) file for CPU #1 +Local state (.abq.1) file for CPU #1 +Local selected results (.sel.1) file for CPU #1 +Local package (.pac.2) file for CPU #2 +Local state (.abq.2) file for CPU #2 +Local selected results (.sel.2) file for CPU #2 +Add three files, incrementing units by 10, for each +additional CPU +• Chapter 4, “Output” +Output +Output +Output variables +The postprocessing calculator +OUTPUT +4.1 +4.2 +4.1 +Output +• “Output,” Section 4.1.1 +• “Output to the data and results files,” Section 4.1.2 +• “Output to the output database,” Section 4.1.3 +• “Error indicator output,” Section 4.1.4 +4.1.1 +OUTPUT +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD Abaqus/CAE +References +• “Output to the data and results files,” Section 4.1.2 +• “Output to the output database,” Section 4.1.3 +• “Abaqus/Standard output variable identifiers,” Section 4.2.1 +• “Abaqus/Explicit output variable identifiers,” Section 4.2.2 +• “Abaqus/CFD output variable identifiers,” Section 4.2.3 +• “Diagnostic printing,” Section 14.5.3 of the Abaqus/CAE User’s Manual +• “Degree of freedom monitor requests,” Section 14.5.4 of the Abaqus/CAE User’s Manual +Overview +Abaqus can create the following output files during an analysis: +• a data file containing printed output of the model and history definition generated by the analysis +input file processor and, in Abaqus/Standard, printed output of results written during the analysis +run; +• an output database file containing results for postprocessing with the Visualization module of +Abaqus/CAE (Abaqus/Viewer) and, in Abaqus/Standard, diagnostic information; +• a selected results file in Abaqus/Explicit; +• a results file containing results for postprocessing with external software in Abaqus/Standard and +Abaqus/Explicit (in Abaqus/Explicit this file is generated by converting the selected results file); +• a message file containing diagnostic messages about +Abaqus/Explicit; +the solution in Abaqus/Standard and +• a status file containing information about the status of the analysis and, in Abaqus/Explicit, +diagnostic messages and information about the stable time increment; and +• output files in Abaqus/CFD using alternate file formats. +In +Abaqus can create files for restarting an analysis—see “Restarting an analysis,” Section 9.1.1. +Abaqus/Standard these files can also be used to extract results output not requested during an analysis. +The data file +The data file (job-name.dat) is a text file that contains information about the model definition (generated +by the analysis input file processor) and, in Abaqus/Standard, tabular output of results. The analysis input +file processor information includes the model definition, the history definition, and messages identifying +any error and warning conditions that were detected while processing the input data. +Controlling the amount of analysis input file processor information written to the data file +You can control the amount of information written to the data file by the analysis input file processor in +Abaqus/Standard and Abaqus/Explicit. +Input File Usage: +Use the following option in the model definition section of the input file: +Abaqus/CAE Usage: +*PREPRINT +Job module: job editor: General: Preprocessor Printout +Input file echo +By default, the input file will not be echoed to the data file. You can choose to activate this printout. If +the input file is defined in terms of an assembly of part instances, the echo to the data file will be that of +the flattened input file (i.e., one that does not use parts and assemblies). +Input File Usage: +Abaqus/CAE Usage: +*PREPRINT, ECHO=YES or NO +Job module: job editor: General: Preprocessor Printout: +Print an echo of the input data +Input parameter information +For parametrized input files, information about input parameters and their values can be printed in the +data file. By default, the modified version of the original input file showing this information will not be +printed in the data file. You can choose to activate this printout. +Input File Usage: +Abaqus/CAE Usage: +*PREPRINT, PARVALUES=YES or NO +Parametrized input files are not supported in Abaqus/CAE. +Parameter-free input file information +For parametrized input files, a parameter-free version (after parameter evaluation and substitution) of the +original input file can be printed in the data file. By default, this modified version of the input file will +not be printed in the data file. You can choose to activate this printout. +Input File Usage: +Abaqus/CAE Usage: +*PREPRINT, PARSUBSTITUTION=YES or NO +Parametrized input files are not supported in Abaqus/CAE. +Model and history definition summaries +By default, the options defining the model and history data will not be summarized in the data file. You +can choose to activate this printout. +For an Abaqus/Explicit analysis the model summary data, when requested, includes the mass, +center of mass, and the rotary inertia information for the element sets in the model and for the whole +model. However, for two-dimensional models the reported rotary inertia includes the +component +corresponding to the only active rotation degree of freedom; the remaining components are not included. +Input File Usage: +*PREPRINT, MODEL=YES or NO, HISTORY=YES or NO +Abaqus/CAE Usage: +Job module: job editor: General: Preprocessor Printout: Print +model definition data and Print history data +Contact constraint information +In Abaqus/Standard you can choose to activate printout of detailed information about the contact +constraints generated by the contact pair definition data. +Input File Usage: +Abaqus/CAE Usage: +*PREPRINT, CONTACT=YES or NO +Job module: job editor: General: Preprocessor Printout: +Print contact constraint data +Mass information +In Abaqus/Explicit you can choose to activate printout of detailed information about the mass property +of each user-defined element set. +Input File Usage: +Abaqus/CAE Usage: +*PREPRINT, MASS PROPERTY=YES or NO +This parameter is not supported by Abaqus/CAE. +Requesting printed results +In Abaqus/Standard the values of output variables can be printed to the data file in tabular format +throughout the analysis. You can control the following types of printed output during the analysis run: +element output, node output, contact surface output, energy output, fastener interaction output, modal +output, section output, and radiation output—see “Output to the data and results files,” Section 4.1.2, +and “Cavity radiation,” Section 40.1.1. You specify the variables to be printed in each output table +and, for element variables, the locations at which they are to be printed (at the integration points, at the +element centroid, at the nodes, or averaged at the nodes). Nodal variables at nodes with transformations +can be written in either the global or the local coordinate system . The list of available variables is given in “Abaqus/Standard output variable identifiers,” +Section 4.2.1. Output of results to the data file is requested as part of a step definition. +Viewing part and assembly information in the data file +An Abaqus model can be defined in terms of an assembly of part instances . In such a model node and element numbers can be repeated within the definitions of +different parts. These local numbers are converted internally by Abaqus to unique global numbers, and +the output written to the data file is given in terms of those internal numbers. A map between user-defined +numbers and internal numbers is printed to the data file (after the step data) if any output that includes +node and element numbers is requested in the data file. +Set and surface names that appear in the data file are prefixed by the assembly and part instance +names, separated by underscores (Assembly_Part1–1_setname, for example). +Local coordinate systems defined within a part or part instance are translated and rotated according +to the positioning data given in the part instance definition. +The output database +The Abaqus output database (job-name.odb) is a neutral binary file used to store model information +and analysis results in terms of an assembly of part instances. The Visualization module of Abaqus/CAE +(Abaqus/Viewer) uses the output database for postprocessing analysis results and viewing diagnostic +information. +Requesting output to the output database +You choose the variables to be written to the output database from the lists in “Abaqus/Standard +output variable identifiers,” Section 4.2.1, “Abaqus/Explicit output variable identifiers,” Section 4.2.2, +and ���Abaqus/CFD output variable identifiers,” Section 4.2.3. The following types of output are +available: element output, node output, contact surface output, energy output, integrated output, +time incrementation output, fastener interaction output, modal output, and radiation output. +In +addition, a subset of the diagnostic information that is written to the message file in Abaqus/Standard +and Abaqus/Explicit and to the +Abaqus/Explicit status file is included in the output database. See “Output to the +output database,” Section 4.1.3, for a detailed explanation of how to generate output database requests. +Three types of information are stored in the output database: “field” output, “history” output, and +diagnostic information. Field output is intended to be relatively infrequent output for a large portion of +the model. Abaqus/CAE uses field output to generate contour plots, displaced shape plots, symbol plots, +and X–Y plots in the Visualization module. History output is intended to be output for a small portion of +the model requested at a fairly high frequency. Abaqus/CAE uses history output to generate X–Y plots in +the Visualization module. See “Output to the output database,” Section 4.1.3, for detailed descriptions of +field and history output. Diagnostic information is intended to provide convergence information for use +in Abaqus/CAE; for more information, see Chapter 41, “Viewing diagnostic output,” of the Abaqus/CAE +User’s Manual. +Format of the output database +The output database is a neutral binary, platform-independent file. Unlike the restart or binary results +files, it can be copied directly from one computing platform to another without translation. +By default, floating point data are written to the output database file in single precision. You can +choose to write floating point nodal field output data to the output database file in double precision; see +“Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD execution,” Section 3.2.2, for details. +You can open an output database file from an older release of Abaqus in Abaqus/CAE, with the +exception that Abaqus 5.8 output database files cannot be opened in Version 6. Output database files +from previous releases of Abaqus must be converted to the current release when they are opened. If you +are using an older release of Abaqus/CAE, you cannot open an output database file created from a newer +release of Abaqus. +The selected results file +The Abaqus/Explicit selected results file (job-name.sel) stores user-selected results, which are +converted into the results file (job-name.fil) for postprocessing by other commercial postprocessing +packages. +Element output, node output, and energy output can be requested ; the variables available for output are listed in “Abaqus/Explicit output +variable identifiers,” Section 4.2.2. You can write a user-selected subset of the results for a given node +set or element set at more frequent intervals than the restart intervals. You specify the output requests +within a step definition, which allows you to be selective about the amount of data written to the selected +results file to avoid using excessive disk storage. For example, when dealing with a very large model, +you may choose to write only the current displacements and the equivalent plastic strain for the entire +model 20 times in the step and to write the acceleration history at one node 200 times in the step. +The results file +The Abaqus results file in Abaqus/Standard and Abaqus/Explicit (job-name.fil) can be read by +external postprocessors to produce X–Y plots or printed tabular output. Most commercial finite element +results-display packages provide translators that use the Abaqus results file as their input. The results +file can also be used as a convenient medium for importing analysis results into your own postprocessing +program. “Accessing the results file information,” Section 5.1.3, provides details on how to read this +file. +Results file output of temperature from a heat transfer, thermal-electrical, or thermal-electrical- +structural analysis can be used as input to a stress analysis of the same mesh . +Obtaining results file output in Abaqus/Standard +In Abaqus/Standard you choose the variables to be written to the results file from the lists in +“Abaqus/Standard output variable identifiers,” Section 4.2.1, in a manner similar to that for output +printed to the data file. You must specifically request that values be written to the results file or none +will be provided. Element output, node output, contact surface output, energy output, modal output, +and radiation output are available—see “Output to the data and results files,” Section 4.1.2, and “Cavity +radiation,” Section 40.1.1, for details. +Obtaining results at the beginning of a step +You can request that the solution state at the beginning of a step (the zero increment) be written to the +Abaqus/Standard results file. Zero-increment file output is available only for steps in which the concept of +time governs the incrementation scheme of the selected procedure and, hence, the following procedures +are excluded: +• Linear static perturbation analysis (“Static stress analysis,” Section 6.2.2) +• “Eigenvalue buckling prediction,” Section 6.2.3 +• “Natural frequency extraction,” Section 6.3.5 +• “Mode-based steady-state dynamic analysis,” Section 6.3.8 +• “Response spectrum analysis,” Section 6.3.10 +• “Random response analysis,” Section 6.3.11 +If you request zero-increment results file output, it will be generated for all valid procedures in a given +analysis. +You must request zero-increment results file output to generate a zero-increment results file in a data +check analysis . It +is strongly recommended that you request zero-increment results file output if the results file is used to +drive a submodel; see “Node-based submodeling,” Section 10.2.2, for further discussion. +*FILE FORMAT, ZERO INCREMENT +Input File Usage: +The *FILE FORMAT option can be given as model data or as history data, but +it can appear only once in the input file. +Abaqus/CAE Usage: +Results file output cannot be requested in Abaqus/CAE. +Obtaining results file output in Abaqus/Explicit +The Abaqus/Explicit results file is a sequential access file generated from the selected results file . The results file +contains the requested results in the format described in “Results file output format,” Section 5.1.2. +Input File Usage: +Use either of the following command line options to convert a selected results +file to a results file: +abaqus job=job-name convert=select +Abaqus/CAE Usage: +abaqus job=job-name convert=all +The selected results file cannot be converted in Abaqus/CAE. +Part and assembly information +An Abaqus model can be defined in terms of an assembly of part instances . However, the results file does not contain part and assembly records. +In a model defined in terms of an assembly of part instances, node and element numbers can be +repeated within the definitions of different parts. These local numbers are converted internally by Abaqus +to unique global numbers, and the output written to the results file is given in terms of the global (internal) +numbers. A map between user-defined numbers and internal numbers is printed to the data file if any +results file output that includes node and element numbers is requested. +Set and surface names that appear in the results file are prefixed by the assembly and part instance +names, separated by underscores (Assembly_Part1–1_setname, for example). +Local coordinate systems defined within a part or part instance are translated and rotated according +to the positioning data given in the part instance definition. +Format of the results file +The Abaqus results file in Abaqus/Standard or Abaqus/Explicit is organized as a sequential file, in binary +or in ASCII format. ASCII format is necessary if the file is to be read on a computer system that is +different from the one on which the file was written. ASCII format allows the results file to be transferred +between different computer systems without having to translate binary data. ASCII format is not needed +if the file will always be used on the same system or on systems that use the same binary format. If the +results file output will always reside on the same computer, the default binary format is usually the most +efficient way of storing the file. For large problems a file in ASCII format will be significantly larger +than the same file in binary format. +Controlling the format of the results file in Abaqus/Standard +Abaqus/Standard can write the results file in either binary or ASCII format. The default format is binary. +The results file output must be written in the same format for the entire analysis. The format cannot +be changed upon restarting the problem. +The format of the Abaqus/Standard results file can also be controlled in the Abaqus/Standard +environment file . The format specified in +an analysis supersedes the value defined in the enviroment file. +In addition, +the ascfil facility in the Abaqus execution procedure (“ASCII translation of +results (.fil) files,” Section 3.2.11) can be used to convert a binary Abaqus/Standard results file +(job-name.fil) to ASCII format (job-name.fin) after the analysis completes. +Input File Usage: +*FILE FORMAT, ASCII +The *FILE FORMAT option can be given as model data or as history data, but +it can appear only once in the input file. +Abaqus/CAE Usage: +Results file output cannot be requested in Abaqus/CAE. +Controlling the format of the results file in Abaqus/Explicit +Abaqus/Explicit always writes the results file output in binary format during file conversion, but the +binary Abaqus/Explicit results file can be converted to ASCII format using the ascfil facility (“ASCII +translation of results (.fil) files,” Section 3.2.11). +ASCII format +“Results file output format,” Section 5.1.2, defines the contents of the records that are written to the +results file; these descriptions also hold if the results file is written in ASCII format. All the data items +in these files are either integers, floating point numbers, or character strings. When ASCII format is +requested, each data item is translated into an equivalent character string before it is written to the file. +These strings are written in 80-character logical records in the order described in the record definitions. +Each 80-character logical record is completely filled before the next one is started, so that any data +item can be split, with some of the characters that define the item in one logical record and the remainder +in the next. Each data item usually follows immediately behind its predecessor. The exception is that +for results file record key 2001 Abaqus will fill out the logical record with blank characters, so that the +record can be written immediately to the physical storage medium. Abaqus then inserts a logical record +consisting of 80 blanks, which allows the end-of-file to be handled correctly. +The beginning of each “record” is indicated by an asterisk (*). Each floating point number begins +with the character D, followed by the number in the format E22.15 or D22.15, depending on whether the +release of Abaqus that wrote the results file used single precision or double precision. Each character +string begins with the character A, followed by eight characters (if the character string has fewer than +eight characters, the right part of the string is blank; character strings longer than eight characters are +written eight characters at a time). Each integer begins with the character I, followed by a two digit +integer giving the number of decimal digits in the integer, followed by the integer itself (written as +decimal digits). +For example, record key 1900 for an S4R element with element number 5 and nodes 195, 198, 205, +and 204 would be written +*I 18I 41900I 15AS4R +I 3195I 3198I 3205I 3204 +and record key 101 for node 135 and 6 degrees of freedom would be written +*I 19I 3101I 3135D1.280271914214298E-10D1.500000000000036E+00 +D-1.074629835784448E-46D 6.983222716550941E-12 +D-4.084928798492785E-13D-1.072688441364597E-10 +Precision of floating point data in the results file +The precision of floating point data written to the results file depends on the precision of the executable +thus, floating point data +that generates the data. Abaqus/Standard always uses double precision; +are always written to the Abaqus/Standard results file in double precision. Abaqus/Explicit can be +run in single or double precision on most machines; see “Defining an analysis,” Section 6.1.2, for +details on the precision level of the Abaqus/Explicit executable. If the double precision executable for +Abaqus/Explicit is used, floating point data are written to the Abaqus/Explicit results file in double +precision; likewise, if the single precision executable for Abaqus/Explicit is used, floating point data are +written to the Abaqus/Explicit results file in single precision. +Maximizing the efficiency of the results file +In Abaqus/Standard each element output request (a collection of identifying keys entered on a single +line) is preceded by an “element header” record . Hence, +the size of the results file can be minimized by entering all element output variables of the same “type” +(element integration point variable, element section variable, whole element variable, etc.) on a single +line. Consolidating output variable entries is encouraged, since it will reduce the size of the results +file. +Example +For example, the following output requests can be used to request output of element variables in the +results file in a stress/displacement analysis: +*EL FILE +S, SINV, E, PE, CE, EE, ENER, TEMP, FV, COORD +SF, SE +LOADS, ELEN, EVOL +*EL FILE, REBAR +S, SINV, E, PE, CE, EE, RBFOR, RBANG +SF, SE +LOADS, ELEN +(The output requests for rebar quantities need not be the same as the underlying element output requests.) +The message file in Abaqus/Standard and Abaqus/Explicit +The message file (job-name.msg) is a text file that contains diagnostic messages about the progress of +the solution. +The Abaqus/Standard message file +In Abaqus/Standard the message file contains diagnostic or informative messages about the progress +If any of these messages describe errors or warnings, the number of such errors or +of the solution. +warnings is also given at the end of the data file. The message file is written automatically during an +Abaqus/Standard analysis. +The Abaqus/Standard message file contains information about the increment number, step time, +fraction of a step completed, equilibrium iterations, severe discontinuity (contact) iterations, plasticity +algorithms, adaptive mesh smoothing, the load proportionality factor in a Riks analysis, etc. A portion of +the diagnostic information in the message file is also written to the output database for use in Abaqus/CAE +(for more information, see “Requesting diagnostic information in Abaqus/Standard and Abaqus/Explicit” +in “Output to the output database,” Section 4.1.3). +You can control the amount of information written to the message file for each step. This feature +is sometimes helpful in difficult analyses since it allows detailed diagnostic information to be written +about certain events (such as contact) during a nonlinear solution; this information can often be useful +in developing a strategy for the solution of highly nonlinear problems. +Input File Usage: +*PRINT +The *PRINT option can appear only once within a step definition. +Abaqus/CAE Usage: +Step module: Output→Diagnostic Print +Controlling the frequency of output to the message file +You can control the frequency at which information is printed to the message file by specifying the desired +output frequency in increments. The default output frequency is 1 (or 10 in a direct cyclic or a low-cycle +fatigue analysis). The output will always be printed at the last increment of each step unless you specify +a frequency of zero to suppress the output. +Input File Usage: +Abaqus/CAE Usage: +*PRINT, FREQUENCY=N +Step module: Output→Diagnostic Print: Frequency N +Requesting detailed contact printout +You can obtain a detailed printout of contact conditions during iteration. This information about which +points are contacting or separating in interface and gap problems is useful in tracking the development of +the solution in difficult contact problems. The details are written for every severe discontinuity iteration. +By default, the detailed contact output is suppressed. +Input File Usage: +Abaqus/CAE Usage: +*PRINT, CONTACT=YES or NO +Step module: Output→Diagnostic Print: toggle on Contact +Requesting detailed model change printout +You can obtain a detailed printout of model change operations (removal and reactivation) at the start of a +step. This information includes the new original coordinates and normals of elements being reactivated +strain free in a large-displacement analysis. By default, the detailed model change output is suppressed. +See “Element and contact pair removal and reactivation,” Section 11.2.1, for details on model change +operations. +Input File Usage: +Abaqus/CAE Usage: +*PRINT, MODEL CHANGE=YES or NO +Step module: Output→Diagnostic Print: toggle on Model Change +Requesting detailed printout of problems with the plasticity algorithms +You can activate printout of element and integration point numbers for which the plasticity algorithms +have failed to converge during an iteration. This information is useful for finding the place in the mesh +and/or the plasticity model at which Abaqus is encountering material model difficulties. Modeling +problems and material parameter specification problems can be identified using this detailed printout. +By default, this printout is suppressed. +Input File Usage: +Abaqus/CAE Usage: +*PRINT, PLASTICITY=YES or NO +Step module: Output→Diagnostic Print: toggle on Plasticity +Requesting output of equilibrium residuals +By default, equilibrium residuals during equilibrium iterations are output. You can choose to suppress +this output entirely, but it is not recommended; without the output of equilibrium residuals, you cannot +see the accuracy of the iteration process. +Input File Usage: +Abaqus/CAE Usage: +*PRINT, RESIDUAL=YES or NO +Step module: Output→Diagnostic Print: toggle on Residual +Requesting solver information +By default, information about the number of equations being solved and the required memory for each +iteration is output. You can request that output be suppressed. +Input File Usage: +Abaqus/CAE Usage: +*PRINT, SOLVE=YES or NO +Step module: Output→Diagnostic Print: toggle on Solve +Requesting detailed adaptive mesh smoothing printout +You can activate detailed printout of adaptive mesh smoothing in Abaqus/Standard. The output includes +information about the magnitude of the maximum displacement and the node and degree of freedom +where the maximum displacement increment occurs during each mesh sweep. It also provides the node +numbers at which geometric feature changes occur. By default, only a summary is output. +Input File Usage: +Abaqus/CAE Usage: +*PRINT, ADAPTIVE MESH=YES or NO +Adaptive mesh output to the message file is not supported in Abaqus/CAE. +Monitoring a degree of freedom in the message file +You can write the current value of a specified point and degree of freedom to the message file. This +information can be used to monitor the progress of the solution. The information will also be written in +the status file . You can control the frequency at which the value is printed in the message +file. The default frequency is 1 (or 10 in a direct cyclic analysis). +Degree of freedom monitoring does not apply to eigenvalue buckling prediction, eigenfrequency +extraction, or response spectrum procedures. For other linear perturbation procedures output for the +monitored degree of freedom is the base state value. +Input File Usage: +*MONITOR, NODE=node_number, DOF=dof, FREQUENCY=N +Abaqus/CAE Usage: +The node and degree of freedom being monitored can be changed from step +to step by repeating the *MONITOR option. The node and degree of freedom +specified in the last occurrence of this option in a step will be used for that step. +Step module: Output→DOF Monitor: Monitor a degree of freedom +throughout the analysis, click Edit to select the point, Degree of +freedom: dof, Print to the message file every N increments +In Abaqus/CAE only one point and degree of freedom can be monitored for an +analysis; you cannot change the monitor request from step to step. +The Abaqus/Explicit message file +In Abaqus/Explicit the message file contains messages if potential problems are detected during an +analysis. You can control the output of diagnostic messages for each step . A +portion of the diagnostic information in the message file is also written to the output database for use in +Abaqus/CAE (for more information, see “Requesting diagnostic information in Abaqus/Standard and +Abaqus/Explicit” in “Output to the output database,” Section 4.1.3). +The status file +The status file (job-name.sta) is a text file that contains information about the progress of an analysis. +The Abaqus/Standard or Abaqus/CFD status file +The Abaqus/Standard or Abaqus/CFD status file contains a single 80-character record for each increment +and is updated upon completion of each increment of an analysis. This record is written directly to +secondary storage immediately at the completion of the increment. Therefore, the status file can be +examined as the analysis job is executing, thus providing a monitor of the progress of the analysis. Other +than specifying that a degree-of-freedom variable be monitored in the status file in Abaqus/Standard (as +described below), the information written to the Abaqus/Standard or Abaqus/CFD status file cannot be +controlled. +The Abaqus/Explicit status file +In Abaqus/Explicit the status file (job-name.sta) contains, by default, mass and inertial properties for +the model, initial stable time increment information, a synopsis of the progress of the analysis including +total accumulated CPU usage and the current time increment size, and an estimate of the memory required +to process each step. You can control additional output including the total kinetic energy, the energy +balance, the identifiers of the elements with the smallest stable time increments, and the percent change +in total mass of the model due to mass scaling. +The frequency at which summary increments are written to the Abaqus/Explicit status file depends +on the duration of the analysis in CPU minutes and the amount of output specified in the analysis. The +following list provides general guidelines for when a summary increment will be written to the status +file. +Summary information will generally be written: +• Each time restart information, field output to the output database, or results file output is written. +• Once per increment if the problem requires fewer than 20 increments. +• 20 times during the step for a short analysis (less than 40 CPU minutes). +• Every 2 CPU minutes for an analysis longer than 40 CPU minutes. +A degree-of-freedom variable can be monitored in the status file while the analysis is running. +You can also write additional diagnostic information to the status file . +A portion of the diagnostic information in the status file, including information for each summary +increment, is also written to the output database for use in Abaqus/CAE (for more information, see +“Requesting diagnostic information in Abaqus/Standard and Abaqus/Explicit” in “Output to the output +database,” Section 4.1.3). +Errors that can be detected only while packaging the data for Abaqus/Explicit or during analysis are +also written to the status file. +Input File Usage: +*PRINT +Abaqus/CAE Usage: +The *PRINT option can appear only once within a step definition. +Step module: Output→Diagnostic Print +Requesting kinetic energy output +By default, the kinetic energy for the model is written to the status file. This output is written periodically +throughout the step. You can choose to include or exclude the kinetic energy output for each step. +Input File Usage: +Abaqus/CAE Usage: +*PRINT, ALLKE=YES or NO +Step module: Output→Diagnostic Print: toggle on Allke +Requesting total energy output +By default, the energy balance is written periodically throughout the step. You can choose to include or +exclude the energy balance output for each step. +Input File Usage: +Abaqus/CAE Usage: +*PRINT, ETOTAL=YES or NO +Step module: Output→Diagnostic Print: toggle on Etotal +Requesting output of the critical element +By default, the number of the element with the current minimum stable time increment and its value +are output to the status file. This output is written periodically throughout the step. You can choose to +include or exclude the critical element output for each step. +Input File Usage: +Abaqus/CAE Usage: +*PRINT, CRITICAL ELEMENT=YES or NO +Step module: Output→Diagnostic Print: toggle on Crit. Elem. +Requesting output of the change in the total mass +You can write the percent change in total mass of the model due to mass scaling to the status file for each +step. This output is written periodically throughout the step. The percent change in total mass is printed +by default only if mass scaling is present in the model. +Input File Usage: +Abaqus/CAE Usage: +*PRINT, DMASS=YES or NO +Step module: Output→Diagnostic Print: toggle on Dmass +Monitoring a degree of freedom in the status file +You can write the current value of a specified point and degree of freedom to the Abaqus/Standard status +file. The value of the point and degree of freedom being monitored will appear in the status file for every +increment written during the analysis. +When a degree of freedom is monitored in the Abaqus/Standard status file, the same information +is written to the message file , but the specified frequency has no effect on the output to the +status file. +Degree of freedom monitoring does not apply to eigenvalue buckling prediction, eigenfrequency +extraction, or response spectrum procedures. For other linear perturbation procedures output for the +monitored degree of freedom is the base state value. +Input File Usage: +*MONITOR, NODE=node_number, DOF=dof +The node and degree of freedom being monitored can be changed from step +to step by repeating the *MONITOR option. The node and degree of freedom +specified in the last occurrence of this option in a step will be used for that step. +Abaqus/CAE Usage: +Step module: Output→DOF Monitor: Monitor a degree of +freedom throughout the analysis, click Edit to select the +point, Degree of freedom: dof +In Abaqus/CAE only one point and degree of freedom can be monitored for an +analysis; you cannot change the monitor request from step to step. +Alternate output formats in Abaqus/CFD +By default, when you request output in Abaqus/CFD, the output is sent to the output database file. +However, you have the option of selecting alternate file formats for field and history output. Field output +can be sent to files in EXODUS-II format; history output can be sent to files in comma-separated values +(CSV) format. +You request the field and history output in the same manner as described in “Requesting output to +the output database.” To select an alternate output format, you set the field and history options on the +command line when you run an Abaqus/CFD analysis. For more information, see “Abaqus/Standard, +Abaqus/Explicit, and Abaqus/CFD execution,” Section 3.2.2. +Field output in EXODUS-II format +The EXODUS-II format is widely supported by third-party postprocessors for both computational solid +mechanics and computational fluid dynamics. This format is binary, machine independent, and well +suited for transient simulation results on unstructured grids. +The EXODUS-II +format and associated EXODUS-II/NEMESIS programming API +for +reading and writing were developed at Sandia National Laboratories. This open source software +is available under the BSD License. +The source code and documentation can be found at +http://sourceforge.net/projects/exodusii. +The EXODUS-II format cannot natively represent all of the Abaqus/CFD output features. The +features listed in Table 4.1.1–1 cannot be represented directly and are either omitted or modified. +Table 4.1.1–1 Abaqus/CFD output feature representation in EXODUS-II format. +Feature +Comment +Parts and assemblies +Element sets +Amplitudes +Node and element numbers do not include the part instance +name and are numbered sequentially +General element sets are not supported and are omitted +Not supported +The EXODUS-II format uses file extension exo. For parallel processing of an analysis run, +EXODUS-II output is directed to multiple files (one file per processor is created), which is useful for +some third-party postprocessors. The files are named job.exo.rank, where rank is a number ranging +from 0 to one less than the number of CPUs. In contrast, you can write field output for parallel execution +to a single file (job.exo); the file is written in EXODUS-II format using the NEMESIS library. +Input File Usage: +Abaqus/CAE Usage: +Use the following command line option in Abaqus/CFD to write field output in +EXODUS-II format to one file per processor: +abaqus job=job-name field=exodus +Use the following command line option in Abaqus/CFD to write field output in +EXODUS-II format to a single file for parallel execution: +abaqus job=job-name field=nemesis +You cannot select an alternate format for field output in Abaqus/CAE. +History output in CSV format +The comma-separated values (CSV) format is a text-based output format. The format of the CSV text +file consists of one or more comment lines followed by one line of comma-separated data per history +output frame. Comments in the CSV file begin with the character #. Each column in the CSV file has a +comment that describes the mesh location, the part instance, and the output request label. Possible values +for mesh locations are node, element, or surface. Vector output requests also include the component; i.e., +1, 2, or 3. +This format uses file extension csv. History output in the CSV format creates one file per output +request label per step. Additional files are created if the job is run in parallel and the set associated +with the history output request is split between processors due to the domain decomposition. In this +case there will be one file per processor on which the set is present. The files are named job_output- +request_rank_step-number.csv, where rank is a number ranging from 0 to one less than the number +of CPUs. +Input File Usage: +Abaqus/CAE Usage: +Use the following command line option to write history output to an alternate +file format in Abaqus/CFD: +abaqus job=job-name history=csv +You cannot select an alternate format for history output in Abaqus/CAE. +Requesting output in multiple steps +In general, output requests apply to the step in which they are given and to all subsequent steps until +they are respecified. However, output specifications for linear perturbation steps (available only in +Abaqus/Standard; see below and “General and linear perturbation procedures,” Section 6.1.3) are +treated independently of output requests for general analysis steps and apply only to a continuous +sequence of linear perturbation steps. +Database output, printed output, and results file output are independent output modes in Abaqus; +therefore, changing the specification for one form of output does not affect the other forms. +General analysis steps +The default output requests are used in the first general analysis step of an analysis unless you redefine +them. For subsequent general analysis steps, the definition of each form of output from the previous +general step is maintained unless you redefine it. +Linear perturbation steps +The default output requests are used in the first of any sequence of linear perturbation steps unless they are +redefined in that step. If a subsequent linear perturbation step is defined without an intermediate general +analysis step, the definition of each mode of output from the previous perturbation step is maintained +unless you redefine it. If an intermediate general step is defined, the default output requests are again +used in the linear perturbation step unless they are redefined in that step. +Element matrix output in Abaqus/Standard +In Abaqus/Standard you can write element stiffness matrices and, if available, mass matrices for each +step to a file. For heat transfer elements the operator matrices are written if stiffness matrix output is +requested. +Element matrix output is available only for elements without internal nodes (unless those nodes +have no active degrees of freedom) and with no acoustic or internal degrees of freedom. Examples +of elements for which element matrix output is prohibited include acoustic, pipe, elbow, frame, gap, +and interface elements as well as axisymmetric elements with Fourier modes. Element matrix output +is not available for elements with coupled fields such as coupled temperature-displacement elements +and pore pressure elements. For incompatible mode and hybrid elements, stiffness matrix output is +prohibited while mass matrix output is available. A substructure matrix output request is used to write +a substructure’s reduced stiffness matrix, mass matrix, and load case vectors to a file . +Element matrix output cannot be requested in a mode-based dynamic analysis (response spectrum, +steady-state dynamic, modal dynamic, or random response). However, it can be requested in the +eigenfrequency extraction analysis that precedes the mode-based dynamic analysis to output the mass +and stiffness matrices. +The element matrices are written without the effects of nodal conditions; therefore, boundary +conditions, concentrated loads, and the effects of multi-point constraints are not included in this +output. The degrees of freedom are always in the global directions, even if a local coordinate system +(“Transformed coordinate systems,” Section 2.1.5) has been defined at nodes associated with the +element. +You must select the element set for which output is requested. For models defined in terms of +an assembly of part instances (“Defining an assembly,” Section 2.10.1), element numbers written with +element matrix output are internal numbers generated by Abaqus/Standard. A map between internal +numbers and the original element numbers and part instance names is provided in the data file. +Writing the element matrices to the results file +By default, element matrix output records are written to the Abaqus/Standard results file. The record +formats for the results file are described in “Results file output format,” Section 5.1.2. The file can be +written in binary or ASCII format based on the file format you specify . +Input File Usage: +Abaqus/CAE Usage: +*ELEMENT MATRIX OUTPUT, ELSET=element_set, +OUTPUT FILE=RESULTS FILE +Element matrix output is not supported in Abaqus/CAE. +Writing the element matrices to a user-defined file +You can write the element matrices to a user-defined file. The file name should not include an extension; +the extension .mtx will be added. + +The format of the output file is compatible with the linear user element . +Input File Usage: +*ELEMENT MATRIX OUTPUT, ELSET=elset, +OUTPUT FILE=USER DEFINED, FILE NAME=output_file_name +Abaqus/CAE Usage: +Element matrix output is not supported in Abaqus/CAE. +Writing the element matrices to the data file +You can write the element matrix records to the Abaqus/Standard data file. +*ELEMENT MATRIX OUTPUT, ELSET=elset, +OUTPUT FILE=USER DEFINED +Input File Usage: +Abaqus/CAE Usage: +Element matrix output is not supported in Abaqus/CAE. +Including distributed loads +You can choose to write the load vector from distributed loads on the elements. By default, the load +vector is not written. +Input File Usage: +Abaqus/CAE Usage: +*ELEMENT MATRIX OUTPUT, ELSET=elset, DLOAD=YES or NO +Element matrix output is not supported in Abaqus/CAE. +Controlling the frequency of element matrix output +You can control the frequency at which element matrix output will be written by specifying an output +frequency in increments. By default, the element matrices will be output every increment (equivalent to +an output frequency of 1). Specify an output frequency of 0 to suppress output of the element matrices. +Unless the output is suppressed, the matrices will always be written at the last increment of a step. +Input File Usage: +Abaqus/CAE Usage: +*ELEMENT MATRIX OUTPUT, ELSET=elset, FREQUENCY=N +Element matrix output is not supported in Abaqus/CAE. +Writing the stiffness or operator matrix +You can choose to output the stiffness matrix (or operator matrix in heat transfer elements). By default, +the stiffness (operator) matrix is not output. +Input File Usage: +Abaqus/CAE Usage: +*ELEMENT MATRIX OUTPUT, ELSET=elset, STIFFNESS=YES or NO +Element matrix output is not supported in Abaqus/CAE. +Writing the mass matrix +You can choose to output the mass matrix. By default, element mass matrices are not output. +Input File Usage: +Abaqus/CAE Usage: +*ELEMENT MATRIX OUTPUT, ELSET=elset, MASS=YES or NO +Element matrix output is not supported in Abaqus/CAE. +User-defined output variables in Abaqus/Standard +In Abaqus/Standard output quantities can be defined as functions of any element integration point +variable listed in “Abaqus/Standard output variable identifiers,” Section 4.2.1, by using user subroutine +UVARM. Then, output variable UVARMn can be requested for output to the data file, the results file, +or the output database. +User-defined state variables in Abaqus/Standard +In Abaqus/Standard you can allocate solution-dependent state variables and define them in user +subroutines defining material behavior, as well as user subroutines FRIC, UEL, and UINTER . Output variable SDVn can be requested for output of these +state variables to the data file, the results file, or the output database. For user-defined elements output +variable SDVn cannot be requested for output to the output database. +Postprocessing with Abaqus/CAE +Abaqus/CAE provides interactive graphical postprocessing from the Abaqus output database file in +the Visualization module (also licensed separately as Abaqus/Viewer). Capabilities include model and +deformed shape plotting, contour plotting, vector plotting, X–Y plotting, and animation. +Recovering additional results output from restart data in Abaqus/Standard +Data needed for restart in Abaqus/Standard are contained in several files that are generated when you +request that restart data be written for an analysis: the restart (.res), analysis database (.mdl and +.stt), part (.prt), and output database (.odb) files. “Restarting an analysis,” Section 9.1.1, describes +the writing of restart data in more detail. +In Abaqus/Standard you can extract output from the restart data and write it to new data (.dat), +results (.fil), and output database (.odb) files using a postprocessing analysis procedure. +If +the original analysis included user subroutines, the postprocessing analysis procedure requires the +specification of the user subroutines. The data, results, and output database file output requests are +defined as described in “Output to the data and results files,” Section 4.1.2, and “Output to the output +database,” Section 4.1.3. The output requests should be defined exactly as they would be in an analysis, +except that: +1. The output frequency specification has no meaning and is, therefore, ignored (unless you are +recovering additional output from a previous direct cyclic or low-cycle fatigue analysis). Instead, +you specify each increment at which output is to be generated in the postprocessing procedure +definition. +2. No default output is provided to the output database. Furthermore, model information, such as +boundary conditions, is not written to the output database. +3. Element set energy information cannot be recovered since it is not written to the restart file. +4. Output is not available for procedures that do not support restart; for example, linear perturbation +procedures. +The element sets and node sets that are defined for the analysis can be used for defining output sets during +the postprocessing procedure. Additional sets can also be defined for the postprocessing procedure. You +specify the step number in the restart file from which output is required. You cannot obtain results at the +beginning of a step . +Input File Usage: +*POST OUTPUT, STEP=step_number +When the *POST OUTPUT option is used, it must appear as the first option +in the input file. No data lines from the analysis input file are required. This +option can be repeated as often as necessary to obtain further output. Since +*POST OUTPUT is a purely postprocessing procedure, analysis options must +not appear in the input file. +Abaqus/CAE Usage: +Postprocessing of restart data is not supported in Abaqus/CAE. +Recovering additional output from a direct cyclic analysis +If you use this postprocessing technique to recover additional output from a previous direct cyclic analysis +, you must specify the iteration number in the restart file from +which output is required instead of the increment. If temperatures (or predefined field variables) are read +from a results (.fil) file in the original direct cyclic analysis, the same temperatures (or predefined field +variables) must be read into the postprocessing analysis. This specification is needed to recover thermal +strains at each time increment in the original direct cyclic analysis since the results file is not stored in +the restart analysis database. +Input File Usage: +*POST OUTPUT, STEP=step_number, ITERATION=iteration_number +There are no data lines associated with this option if the ITERATION parameter +is specified. +Abaqus/CAE Usage: +Postprocessing of restart data is not supported in Abaqus/CAE. +Recovering additional output from a low-cycle fatigue analysis +If you use this postprocessing technique to recover additional output from a previous low-cycle fatigue +analysis , you must +specify the cycle number in the restart file from which output is required instead of the increment. +If temperatures (or predefined field variables) are read from a results (.fil) file in the original +low-cycle fatigue analysis, the same temperatures (or predefined field variables) must be read into the +postprocessing analysis. This specification is needed to recover thermal strains at each time increment in +the original low-cycle fatigue analysis since the results file is not stored in the restart analysis database. +Input File Usage: +*POST OUTPUT, STEP=step_number, CYCLE=cycle_number +There are no data lines associated with this option if the CYCLE parameter is +specified. +Abaqus/CAE Usage: +Postprocessing of restart data is not supported in Abaqus/CAE. +Example +A job can be submitted using the following input file. The analysis for which restart data were written +must be specified when you submit the job (using the oldjob parameter of the Abaqus execution +procedure). This example creates a new data (.dat) file containing tabular data. The first two tables +will contain data from increments 5 and 10 of Step 1 and will give the reaction forces of the nodes in +the set CLAMP, which was defined when the analysis was run. The next table will contain data from +increment 3 of Step 2 and will give displacements from the new node set TIP that is defined in this +postprocessing analysis. +*HEADING +*POST OUTPUT, STEP=1 +5, 10 +*NODE PRINT, NSET=CLAMP +RF, +*POST OUTPUT, STEP=2 +3, +*NSET, NSET=TIP +1200, 1203, 1205 +*NODE PRINT, NSET=TIP +U, +The following example input file recovers additional output from a previous direct cyclic analysis +and creates a new output database (.odb) file, which contains the stress and strain for the elements in +the set ELIST from each increment in Iteration 5 of Step 1, followed by data from each increment in +Iteration 10 of Step 1: +*HEADING +*POST OUTPUT, STEP=1, ITERATION=5 +*OUTPUT, HISTORY +*ELEMENT OUTPUT, ELSET=ELIST +S,E +*POST OUTPUT, STEP=1, ITERATION=10 +*OUTPUT, HISTORY +*ELEMENT OUTPUT, ELSET=ELIST +S,E +The following example input file recovers additional output from a previous low-cycle fatigue +analysis and creates a new output database (.odb) file, which contains the stress and strain for the +elements in the set ELIST from each increment in Cycle 5 of Step 1, followed by data from each +increment in Cycle 10 of Step 1: +*HEADING +*POST OUTPUT, STEP=1, CYCLE=5 +*OUTPUT, HISTORY +*ELEMENT OUTPUT, ELSET=ELIST +S,E +*POST OUTPUT, STEP=1, CYCLE=10 +*OUTPUT, HISTORY +*ELEMENT OUTPUT, ELSET=ELIST +S,E +4.1.2 +OUTPUT TO THE DATA AND RESULTS FILES +Products: Abaqus/Standard Abaqus/Explicit +References +• “Output,” Section 4.1.1 +• *CONTACT FILE +• *CONTACT PRINT +• *EL FILE +• *EL PRINT +• *ENERGY FILE +• *ENERGY PRINT +• *FILE OUTPUT +• *MODAL FILE +• *MODAL PRINT +• *NODE FILE +• *NODE PRINT +• *RADIATION FILE +• *RADIATION PRINT +• *SECTION PRINT +• *SECTION FILE +Overview +Output variables are available for: +• element integration points, element section points, whole elements, and element sets; +�� nodes; +• the whole model; +• modes in mode-based dynamics procedures; +• surfaces in Abaqus/Standard; and +• sections in Abaqus/Standard. +All of the output variables are defined in “Abaqus/Standard output variable identifiers,” Section 4.2.1, +and “Abaqus/Explicit output variable identifiers,” Section 4.2.2. Output quantities from the elements, +nodes, and whole model can be written to the data and results files in Abaqus/Standard and to the selected +results file in Abaqus/Explicit. In Abaqus/Standard output quantities from eigenmodes, surfaces, and +sections can also be written to the data and results files. +For Abaqus models defined in terms of an assembly of part instances , output in the data and results files is given in terms of node, element, set, and surface +labels generated internally by Abaqus. See “Output,” Section 4.1.1, for details on how to relate the +internally generated numbers and names to those you specified. +Requesting output to the data and results files +The following sections discuss the input file syntax for requesting output to the data and results files. +Abaqus/CAE automatically requests that a data file containing the default printed output for the current +analysis procedure at the end of each step be generated; you cannot control the contents of the data file +from within Abaqus/CAE. An analysis from Abaqus/CAE does not create a results file. +Output to the Abaqus/Standard data file +Abaqus/Standard analysis results can be written to the data (.dat) file. Element output, nodal output, +contact surface output, energy output, modal output, and section output are available. +Input File Usage: +Use any of the following options to request output to the Abaqus/Standard data +file: +*CONTACT PRINT +*EL PRINT +*ENERGY PRINT +*MODAL PRINT +*NODE PRINT +*SECTION PRINT +These options are discussed in detail below. +Output to the Abaqus/Standard results file +Abaqus/Standard analysis results can be written to the results (.fil) file. Element output, nodal output, +contact surface output, energy output, modal output, and section output are available. +Input File Usage: +Use any of the following options to request output to the Abaqus/Standard +results file: +*CONTACT FILE +*EL FILE +*ENERGY FILE +*MODAL FILE +*NODE FILE +*SECTION FILE +These options are discussed in detail below. +Output to the Abaqus/Explicit results file +You can write Abaqus/Explicit analysis results to the selected results (.sel) file by specifying a results +file output request in conjunction with element output, nodal output, and/or energy output requests, as +explained below. A results file output request can appear only once per step but remains in effect in +subsequent steps unless it is redefined. +You can convert the selected results file (job-name.sel) into the results (job-name.fil) file +using the convert utility described in “Obtaining results file output in Abaqus/Explicit” in “Output,” +Section 4.1.1, and “Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD execution,” Section 3.2.2. +Input File Usage: +Use the first option in conjunction with one or more of the subsequent options +to request output to the Abaqus/Explicit selected results file: +*FILE OUTPUT +*EL FILE +*ENERGY FILE +*NODE FILE +Output frequency +You can control the frequency of all Abaqus/Explicit results file output for a particular step by specifying +the number of intervals during the step at which file output will be written, n. The data are always written +at the start and end of each step in which a results file output request is active. The times at which the +results are written are referred to as time marks. +If the specified number of intervals is 10, Abaqus/Explicit will write results 11 times: the values +at the beginning of the step and at the end of 10 equal time intervals throughout the step. The specified +number of intervals must be a positive integer. +By default, results will be written at the increment ending immediately after each time mark. +Alternatively, you can choose to have the time increment size adjusted so that an increment will end +exactly at each of the time marks calculated by dividing the step into n equal intervals. +Input File Usage: +Use the following option to request +immediately after each time interval: +results at +the increments ending +*FILE OUTPUT, NUMBER INTERVAL=n, TIME MARKS=NO +Use the following option to request results at the exact time intervals: +*FILE OUTPUT, NUMBER INTERVAL=n, TIME MARKS=YES +Requesting output in multiple steps +Output requests apply to the step in which they are defined and to all subsequent steps until they are +respecified. +One exception occurs when the step type changes from general to linear perturbation (available +only in Abaqus/Standard). Output requests defined in general steps apply only to subsequent general +steps; output requests defined in linear perturbation steps apply only to subsequent consecutive linear +perturbation steps. In other words, output defined in a general step is independent of output defined in a +linear perturbation step. Propagation between linear perturbation steps occurs only for consecutive linear +perturbation steps. If a general analysis step occurs between perturbation steps, output defined in the first +perturbation step will not propagate to the next perturbation step. In addition, section output requests are +not propagated among linear perturbation steps in Abaqus/Standard. +Element output +You can output element variables (stresses, strains, section forces, element energies, etc.) +for a +particular step to the Abaqus/Standard data (.dat) file, the Abaqus/Standard results (.fil) file, or the +Abaqus/Explicit selected results (.sel) file. The output requests can be repeated as often as necessary +within a step to define output for different types of element variables, different element sets, etc. The +same element (or element set) can appear in several output requests. +In general, element output requests remain in effect for subsequent steps unless they are redefined; +the appearance of a single element output request in a step removes all element output requests from +a previous step. See “Output,” Section 4.1.1, for a discussion of requesting output in multiple general +analysis steps or linear perturbation steps. +In Abaqus/Explicit the element output is written to the selected results (.sel) file, which must be +converted to the results (.fil) file as explained above. +Input File Usage: +Use the following option to output element variables to the Abaqus/Standard +data file: +*EL PRINT +Use the following option to output element variables to the Abaqus/Standard +results file or the Abaqus/Explicit selected results file: +*EL FILE +Selecting the element output variables +The following types of element variables are recognized for the purpose of defining output: +• “Element integration point” variables are associated with the integration points at which the material +calculations are performed (for example, components of stress and strain). For beams and pipes +defined in Abaqus/Standard with a general beam section, integration point variables are available +only if the output section points were specified for the section . For first-order heat transfer elements the integration +points are located at the corners of the element in heat capacitance calculations. +• “Element section point” variables are associated with the cross-section of a beam, pipe, or a shell +(for example, bending moments and membrane forces on the section). +• “Whole element” variables are attributes of an entire element (for example, the total energy content +of the element). +• “Whole element set” variables are attributes of an entire element set (for example, the current +coordinates of the center of mass); these variables are available only in Abaqus/Standard. +The element variables that can be written to the data and results files are defined in “Abaqus/Standard +output variable identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” +Section 4.2.2. +Abaqus/Standard allows only complete sets of basic variables (for example, all of the stress or strain +components) to be written to the results file. Individual variables (such as a particular stress component) +cannot be selected and must be obtained by postprocessing. Abaqus/Standard element variables can be +written to the data and results files at the integration points, at the centroid, averaged at the nodes, or +extrapolated to the nodes. +In Abaqus/Explicit the complete stress or strain tensors can be written to the selected results file, +or individual scalar variables such as equivalent plastic strain can be written. Abaqus/Explicit writes +element variables to the results file only at the integration points where they are calculated. +Selecting the elements for which output is required +You can specify the element set for which output is being requested. If you do not specify an element +set, the output will be printed for all elements and, in Abaqus/Explicit, for all rebars in the model. In +Abaqus/Standard output requests for rebars are governed separately, as discussed below. +Input File Usage: +Use either of the following options: +*EL PRINT, ELSET=element_set_name +*EL FILE, ELSET=element_set_name +Specifying the section point in beams, pipes, shells, and layered solid elements +For beams, pipes, shells, or layered solid elements in Abaqus/Standard output is provided at the default +section points listed in Part VI, “Elements.” You can specify nondefault output points. +In Abaqus/Explicit output is always provided at all section points for beam, pipe, and shell element +output requests. +Input File Usage: +Use either of the following options in Abaqus/Standard: +*EL PRINT +list of output points +*EL FILE +list of output points +Requesting output for rebars in a reinforced model +In Abaqus/Standard you can request output for rebars (“Defining reinforcement,” Section 2.2.3). If you +do not explicitly request rebar output in an Abaqus/Standard model with rebars, the element output +requests govern the output for the matrix material only (except for section forces, where the forces in +the rebar are included in the force calculation). You can request output for a particular rebar. If you do +not specify the name of a rebar, output will be given for all rebars in the specified element set (or in the +whole model, if you have not specified an element set). +In beam and continuum elements in Abaqus/Standard rebar output can be obtained at the integration +points only. In shell, membrane, and surface elements rebar output is available at the integration points +and at the element’s centroid. +In Abaqus/Explicit output for the rebars in the specified element set (or the whole model, if you +have not specified an element set) is always included for element output requests. +Input File Usage: +Use either of the following options in Abaqus/Standard: +*EL PRINT, REBAR=rebar_name +*EL FILE, REBAR=rebar_name +Selecting the position of element integration and section point output in Abaqus/Standard +In Abaqus/Standard integration point variables and section variables can be written to the data and results +files in four different positions. By default, output is provided at the integration points. +Obtaining element output at the integration points +By default, the variables are output at the integration points where they are calculated. (You can obtain +the position of the integration points by using output variable COORD—see “Abaqus/Standard output +variable identifiers,” Section 4.2.1.) +Input File Usage: +Use either of the following options: +*EL PRINT, POSITION=INTEGRATION POINTS +*EL FILE, POSITION=INTEGRATION POINTS +Obtaining element output at the centroid of each element +You can choose to output the variables at the centroid of each element (the centroid of the reference +surface of a shell element or the midpoint between the end nodes of a beam or a pipe element). Centroidal +values are obtained by interpolation of the integration point values if the integration scheme for the +element does not include a centroidal integration point. +Input File Usage: +Use either of the following options: +*EL PRINT, POSITION=CENTROIDAL +*EL FILE, POSITION=CENTROIDAL +Obtaining element output averaged at the nodes +You can choose to extrapolate the variables to the nodes, then average them over all of the elements in the +set that contribute to each node. For derived variables, such as the principal stress, Abaqus/Standard will +first average the extrapolated tensor components over all of the elements connected to the node to obtain +unique components at each node, then calculate the derived value based on the averaged components. +By default, Abaqus/Standard partitions the elements in the model into averaging regions. The +partitioning is based upon the structure of the elements: element type, number of section points, type of +material, single layer or composite, etc. Partitioning is not based upon the values of element properties +(such as thickness), material orientations, or material constants. Averaging will occur only over elements +that contribute to a node and belong to the same averaging region. +In some situations you may want the averaging regions to take into account the values of element +properties. For example, since variables may be discontinuous between elements with different material +constants, you may not want elements with different property definitions included in the same averaging +region. In such cases you can force Abaqus/Standard to take into account values of element properties +by setting the Abaqus environment parameter average_by_section to ON. However, in problems with +many section and/or material definitions the default value of OFF will, in general, give much better +performance than the nondefault value of ON. +Input File Usage: +Use either of the following options: +*EL PRINT, POSITION=AVERAGED AT NODES +*EL FILE, POSITION=AVERAGED AT NODES +Obtaining element output extrapolated to the nodes +You can choose to extrapolate the element integration point variables to the nodes of each element +independently, without averaging the results from adjoining elements. +Input File Usage: +Use either of the following options: +*EL PRINT, POSITION=NODES +*EL FILE, POSITION=NODES +Extrapolation and interpolation of element output variables +The shape functions of the element are used for purposes of extrapolation and interpolation of output +variables. Extrapolated values are generally not as accurate as the values calculated at the integration +points in the areas of high stress gradients, particularly in the case of modified triangles and tetrahedra. +Therefore, adequately detailed meshing is necessary around nodes where accurate nodal values of such +element results are needed. If a cylindrical or spherical coordinate system is defined for the element +, the orientation at each integration point may be different. When +the values at the integration points are extrapolated to the nodes, the difference in the orientation is not +taken into account; therefore, if the orientation varies significantly over the elements connected to a +node, the extrapolated values will not be very accurate. If the material orientation undergoes significant +spatial variation in a region of the model where the material behavior is truly anisotropic, a finer mesh +is required to obtain accurate results even at the integration points. In that situation once the overall +solution has converged with respect to the mesh density, the interpolation or extrapolation away from +the integration points can also be assumed to be reasonably accurate. Element output for second-order +elements with one collapsed side in two dimensions or one collapsed face in three dimensions should +not be extrapolated to the nodes. +In a coupled temperature-displacement and a coupled thermal-electrical-structural analysis nodal +temperatures (variable NT11) are more accurate than temperatures at the integration point (variable +TEMP) extrapolated to the nodes. +For derived variables, such as the Mises equivalent stress, the components are first extrapolated +or interpolated, then the derived value is calculated from the extrapolated or interpolated components. +However, in linear mode-based dynamic analysis procedures where values are obtained as nonlinear +combinations of modal response magnitudes (“Random response analysis,” Section 6.3.11, and +“Response spectrum analysis,” Section 6.3.10), the nonlinear combinations are first calculated at the +integration points. These derived values are extrapolated to the nodes or interpolated to the centroid. +Requesting summaries in the Abaqus/Standard data file +By default in Abaqus/Standard, summaries of element variables are printed in the data file. A summary of +the maximum and minimum values is printed at the end of each column in an output table. The locations +of the maximum and minimum values are also printed. You can choose to suppress this summary. +Input File Usage: +*EL PRINT, SUMMARY=YES or NO +Requesting totals in the Abaqus/Standard data file +In Abaqus/Standard you can print the sum (total) of each column in an output table to the data file. Totals +can be used, for example, to obtain a sum of all the energies in a set of elements. By default, these totals +are suppressed. +Input File Usage: +*EL PRINT, TOTALS=YES or NO +Controlling the frequency of output +In Abaqus/Standard you can control the frequency of element output by specifying the output frequency +in increments. Unless a frequency of zero is specified to suppress output, the variables will always be +output at the last increment of the step. +In Abaqus/Explicit the frequency of element output is controlled as described in “Output frequency” +above. +Input File Usage: +Use either of the following options in Abaqus/Standard: +*EL PRINT, FREQUENCY=n +*EL FILE, FREQUENCY=n +Specifying the directions for element output +For components of stress, strain, and similar material variables, 1, 2, and 3 refer to the directions in +an orthogonal coordinate system. If a local orientation is not defined for the element, the stress/strain +components are in the default directions defined by the convention given in “Conventions,” Section 1.2.2: +global directions for solid elements; surface directions for shell, membrane, and gasket elements; and +axial and transverse directions for beam and pipe elements. +If a local orientation is associated with the element, the element output variable components are in +the local directions defined by the orientation . In Abaqus/Standard +you can request that the local directions be written to the results file if component output is requested +for any variable . +In Abaqus/Explicit the +local directions will always be written to the results file when tensor output is requested for any +element variable. The local directions are written automatically to the output database file from both +Abaqus/Standard and Abaqus/Explicit. +In large-displacement problems the local directions defined in the reference configuration are rotated +into the current configuration by the average material rotation. See “State storage,” Section 1.5.4 of the +Abaqus Theory Manual, for details. +Controlling the output during eigenvalue extraction +You can control element output during natural frequency extraction (“Natural frequency extraction,” +Section 6.3.5), complex eigenvalue extraction (“Complex eigenvalue extraction,” Section 6.3.6), and +eigenvalue buckling analysis (“Eigenvalue buckling prediction,” Section 6.2.3) by specifying the first +and last mode numbers for which output is required. By default, the first mode number is 1 and the last +mode number is N, where N is the number of modes extracted. If you specify the first mode number, the +default value for the last mode number is M, where M is the value specified for the first mode number. +Input File Usage: +Use either of the following options: +*EL PRINT, MODE=m, LAST MODE=n +*EL FILE, MODE=m, LAST MODE=n +Abaqus/Standard data file format +In Abaqus/Standard the printed output of variables is arranged in tables in the data file. For element +variables, each row of a table corresponds to a particular location: an element, a node, a section point +within an element, or an integration point. The rows that will appear in a particular table are defined by +choosing an element set and, possibly, locations within each element in the set. +Each table is defined by a data line of the element output request, which specifies the variables to +appear in that table. There is no limit to the number of tables that can be defined. The first columns +of a table define the location—the element or node number, integration point number, etc. You choose +which data will appear in the remaining columns; up to 9 variables (columns) can appear in a table. +For example, output variables S and E cannot be requested on the same data line in a three-dimensional +analysis because that would produce 12 columns of output. If all of the entries in a row are zero, the row +is not printed. +Each table can contain only one type of output variable (whole element, section, or integration +point); one type of element; and only one type of section definition. If an element output request to the +data file includes more than one type of output variable, element, or section definition, Abaqus/Standard +will split the output automatically into the necessary number of individual tables. All of the tables defined +by the first data line of the output request will be printed, then all of the tables defined by the second data +line, etc. +Results file format +An element header record (the type 1 record described in “Results file output format,” Section 5.1.2) is +created for each line of requests for each integration point and section point in an element. In addition to +the element header record, a direction record (record type 85) can be written in Abaqus/Standard when +complete stress or strain tensor output is requested . In Abaqus/Explicit a direction record is +always written when complete stress or strain tensor output is requested. +For Abaqus/Standard file output requests with multiple variables, it is advantageous to specify as +many variables as possible on each data line of the element output request (up to 16). By keeping the +number of lines of requests to a minimum, extra type 1 and type 85 records are avoided and the size of +the results file may be reduced substantially. This is not an issue in Abaqus/Explicit. Element variables +must be of the same “type” (element integration point variable; element section variable; whole element +variable; etc.) to be entered on a single line—see “Output,” Section 4.1.1. In Abaqus/Standard if all +results in a file output record are zero, the record is not written to the results file. +Output of local directions to the results file +By default, in Abaqus/Standard the local coordinate directions are not written to the results file. +If +component output is requested, you can write the local coordinate directions to the results file. A direction +record of type 85 will be written following the type 1 record. +In Abaqus/Explicit the local coordinate directions are always written to the selected results file as a +direction record of type 85 when complete stress or strain tensor output is requested. +Tensor component output is given in the local coordinate system, which may be inherent to the +element (as is the case in shells and membranes) or user-defined (“Orientations,” Section 2.2.5). +For shell elements a direction record is written for every material point in the section for which +component output is requested, and a separate direction record is written for section forces and section +strains. For geometrically nonlinear analysis in Abaqus/Standard the record contains the current, updated +directions, except for small-strain shells and gasket elements, for which the original directions are given. +For three-dimensional beams, direction output is written only if section output has been requested. +Direction output is not provided for trusses, two-dimensional beams, two-dimensional gasket +elements, axisymmetric shells, axisymmetric membranes, axisymmetric gasket elements, or for values +averaged at nodes. +In addition, it is not provided for GKxxN-type gasket elements, which have no +membrane or transverse shear deformation. +Input File Usage: +Use the following option in Abaqus/Standard: +*EL FILE, DIRECTIONS=YES +Default element output +If you do not specify an element output request to the results file in a step (or in any previous step of the +analysis), no element output will be written to the results file; similarly, if you do not specify an element +output request to the data file (available only in Abaqus/Standard) in a step (or in any previous step of +the analysis), no element output will be written to the data file. +Node output +You can output nodal variables (displacements, reaction forces, etc.) +for a particular step to the +Abaqus/Standard data (.dat) file, the Abaqus/Standard results (.fil) file, or the Abaqus/Explicit +selected results (.sel) file. The output requests can be repeated as often as necessary within a step to +define output for different node sets. The same node (or node set) can appear in several output requests. +In general, nodal output requests remain in effect for subsequent steps unless they are redefined; the +appearance of a single nodal output request in a step removes all nodal output requests from a previous +step. See “Output,” Section 4.1.1, for a discussion of requesting output in multiple general analysis steps +or linear perturbation steps. +In Abaqus/Explicit the nodal output is written to the selected results (.sel) file, which must be +converted to the results (.fil) file as explained above. +Input File Usage: +Use the following option to output nodal variables to the Abaqus/Standard data +file: +*NODE PRINT +Use the following option to output nodal variables to the Abaqus/Standard +results file or the Abaqus/Explicit selected results file: +*NODE FILE +Selecting the nodal output variables +The nodal variables that can be written to the data and results files are defined in the “Nodal variables” +portion of “Abaqus/Standard output variable identifiers,” Section 4.2.1, and “Abaqus/Explicit output +variable identifiers,” Section 4.2.2. +Abaqus allows only complete sets of basic variables (for example, all of the displacement +components) to be written to the results file. Individual variables (such as a particular displacement +component) cannot be selected and must be obtained by postprocessing. +Selecting the nodes for which output is required +You can specify the node set for which output is being requested. If you do not specify a node set, the +output will be printed for all nodes in the model. +Input File Usage: +Use either of the following options: +*NODE PRINT, NSET=node_set_name +*NODE FILE, NSET=node_set_name +Requesting summaries in the Abaqus/Standard data file +By default in Abaqus/Standard, summaries of nodal variables are printed in the data file. A summary of +the maximum and minimum values is printed at the end of each column in an output table. The locations +of the maximum and minimum values are also printed. You can choose to suppress this summary. +*NODE PRINT, SUMMARY=YES or NO +Input File Usage: +Requesting totals in the Abaqus/Standard data file +In Abaqus/Standard you can print the sum (total) of each column in an output table to the data file. Totals +can be used, for example, to sum reaction forces at the nodes. By default, these totals are suppressed. +Input File Usage: +*NODE PRINT, TOTALS=YES or NO +Controlling the frequency of output +In Abaqus/Standard you can control the frequency of nodal output by specifying the output frequency +in increments. Unless a frequency of zero is specified to suppress output, the variables will always be +output at the last increment of the step. +In Abaqus/Explicit the frequency of nodal output is controlled as described in “Output frequency” +above. +Input File Usage: +Use either of the following options in Abaqus/Standard: +*NODE PRINT, FREQUENCY=n +*NODE FILE, FREQUENCY=n +Specifying the directions for nodal output +For nodal variables 1, 2, and 3 refer to the global directions X, Y, and Z, respectively. For axisymmetric +elements 1 and 2 refer to the global directions r and z. +In Abaqus/Standard components of nodal variables such as reaction forces are output in the global +directions unless a local coordinate system has been defined at a node . +In this case you can specify whether output is desired in global or local +directions. The local directions defined by the nodal transformation cannot be written to the results file. +The data in the Abaqus/Explicit selected results file are always output in the global directions, even +if a local coordinate system has been defined at a node. +Obtaining nodal output in the global directions +In Abaqus/Standard you can request vector-valued nodal variables in the global directions, which is the +default for nodal output requests to the results file since most postprocessors assume that components +are given in the global system. +Input File Usage: +Use either of the following options: +*NODE PRINT, GLOBAL=YES +*NODE FILE, GLOBAL=YES +Obtaining nodal output in the local directions defined by nodal transformations +In Abaqus/Standard you can request vector-valued nodal variables in the local directions defined by nodal +transformations, which is the default for nodal output requests to the data file. +Input File Usage: +Use either of the following options: +*NODE PRINT, GLOBAL=NO +*NODE FILE, GLOBAL=NO +Controlling the output during eigenvalue extraction +You can control nodal output during natural frequency extraction, complex eigenvalue extraction, and +eigenvalue buckling analysis by specifying the first and last mode numbers for which output is required, +as described above for element output. +Input File Usage: +Use either of the following options: +*NODE PRINT, MODE=m, LAST MODE=n +*NODE FILE, MODE=m, LAST MODE=n +Abaqus/Standard data file format +In Abaqus/Standard the printed output of variables is arranged in tables by node set in the data file. For +nodal variables each row of a table corresponds to an individual node. +Each table is defined by a data line of the nodal output request, which specifies the variables to +appear in that table. There is no limit to the number of tables that can be defined. The first column of +each table is the node number. You choose the variables to appear in the remaining columns; up to nine +variables (columns) can appear in a table. If all of the entries in a row are zero, the row is not printed. +Displacement, velocity, and acceleration components less than a relative tolerance (equal to 100 times +the machine precision times the current maximum value in the model) are treated as zero. +Results file format +There is no header or direction record for nodes, so it makes little difference whether items are requested +on a single line or multiple lines. In Abaqus/Standard if all results in a record are zero, the record is not +written to the results file. +Default nodal output +If you do not specify a nodal output request to the results file in a step (or in any previous step of the +analysis), no nodal output will be written to the results file; similarly if you do not specify a nodal output +request to the data file (available only in Abaqus/Standard) in a step (or in any previous step of the +analysis), no nodal output will be written to the data file. +Total energy output +You can output summaries of the energy content of the model to the Abaqus/Standard data (.dat) file, +the Abaqus/Standard results (.fil) file, or the Abaqus/Explicit selected results (.sel) file. Energy +output requests are not available for the following procedures: +• “Eigenvalue buckling prediction,” Section 6.2.3 +• “Natural frequency extraction,” Section 6.3.5 +• “Complex eigenvalue extraction,” Section 6.3.6 +Energy output requests remain in effect for subsequent steps. Detailed energy density output is +available by using element output requests . +In Abaqus/Explicit the energy output is written to the selected results (.sel) file, which must be +converted to the results (.fil) file as explained above. +Input File Usage: +Use the following option to output summaries of the energy content to the +Abaqus/Standard data file: +*ENERGY PRINT +Use the following option to output summaries of the energy content to the +Abaqus/Standard results file or the Abaqus/Explicit selected results file: +*ENERGY FILE +External work calculation due to concentrated follower forces +Abaqus/Standard may generate inaccurate external work (ALLWK) in the presence of a concentrated +follower load that rotates with time . This problem may occur in both static and implicit dynamic analyses and may +result in an inaccurate total energy (ETOTAL) history output. Other results (displacements, stresses, +strains, etc.) are not affected. The inaccuracy is due to the fact that the increment of work is calculated +using the direction of the concentrated load at the end of the increment instead of using an average load +over the increment. +Selecting the energy output variables +When energy output is requested, all of the total energy quantities listed in “Abaqus/Standard output +variable identifiers,” Section 4.2.1, or “Abaqus/Explicit output variable identifiers,” Section 4.2.2, are +output; the variables cannot be selected individually. +Selecting the element set for which total energy output is required +In Abaqus/Standard you can specify the element set for which total energy output is being requested. In +this case the energies are summed for all the elements in the specified set. You cannot specify an element +set for the following procedures: +• “Transient modal dynamic analysis,” Section 6.3.7 +• “Mode-based steady-state dynamic analysis,” Section 6.3.8 +• “Response spectrum analysis,” Section 6.3.10 +• “Random response analysis,” Section 6.3.11 +If you do not specify an element set, the total energies for the whole model will be output. If total energy +output for both the whole model and for different element sets is desired, the energy output requests must +be repeated; once without a specified element set to request energy output for the whole model and once +for each specified element set. +In Abaqus/Explicit you cannot specify selected element sets for an energy output request; the total +energies for the whole model will always be output. +Input File Usage: +Use one of the following options in Abaqus/Standard: +*ENERGY PRINT, ELSET=element_set_name +*ENERGY FILE, ELSET=element_set_name +Controlling the frequency of output +In Abaqus/Standard you can control the frequency of energy output by specifying the output frequency +in increments. Unless a frequency of zero is specified to suppress output, the variables will always be +output at the last increment of the step. +In Abaqus/Explicit the frequency of energy output is controlled as described in “Output frequency” +above. +Input File Usage: +Use either of the following options in Abaqus/Standard: +*ENERGY PRINT, FREQUENCY=n +*ENERGY FILE, FREQUENCY=n +Default energy output +Energy output requests must be included for total energy output to be written to the data and results files; +no default output is provided. +Modal output from Abaqus/Standard +You can output generalized coordinate (modal amplitude and phase) values during modal dynamic +procedures to the data (.dat) file or results (.fil) file. +You can also request that eigenvalues be written to the results file during “Eigenvalue buckling +prediction,” Section 6.2.3, or “Natural frequency extraction,” Section 6.3.5. The eigenvalues are always +written to the results file when element or nodal output to the results file is requested; however, modal +output requests allow you to write the eigenvalues to the results file without requesting any additional +output. +Input File Usage: +Use the following option to output modal variables to the Abaqus/Standard data +file: +*MODAL PRINT +Use the following option to output modal variables to the Abaqus/Standard +results file: +*MODAL FILE +Selecting the modal output variables +The modal variables that can be written to the data and results files are defined in the “Modal variables” +portion of “Abaqus/Standard output variable identifiers,” Section 4.2.1. +Controlling the frequency of output +You can control the frequency of modal output by specifying the output frequency in increments. Unless +a frequency of zero is specified to suppress output, the variables will always be output at the last increment +of the step. +Input File Usage: +Use either of the following options: +*MODAL PRINT, FREQUENCY=n +*MODAL FILE, FREQUENCY=n +Default modal output +Modal output requests must be included for modal results to be written to the data and results files; no +default output is provided. +Surface output from Abaqus/Standard +In Abaqus/Standard you can write variables associated with surfaces in contact, coupled temperature- +displacement, coupled thermal-electrical-structural, coupled thermal-electrical, and crack propagation +problems to the data and results files. The output requests can be repeated as often as necessary within +a step to define output for different contact pairs and different types of surface variables. +See “Cavity radiation,” Section 40.1.1, for information on requesting output of surface variables +associated with cavity radiation. +Use element output requests to obtain data and results file output for contact +elements (such as slide line elements; see “Slide line contact elements,” Section 39.4.1). +Selecting the surface output variables +The following types of surface variables are recognized for the purpose of defining output: +• “Slave node” variables are associated with the integration points at which the material calculations +are performed (for example, the contact stress). +• “Whole surface” variables are attributes of an entire slave surface (for example, the total force due +to contact pressure). +The surface variables that can be written to the data and results files are listed in the “Surface variables” +portion of “Abaqus/Standard output variable identifiers,” Section 4.2.1. +Selecting the contact pairs for which output is required +You can select the master and slave surfaces for which output is required, and you can specify a subset +of slave nodes for output in addition to the master and slave surfaces or independently. If no surfaces +or slave nodes are specified, surface variables are written for all the contact pairs in the model. If you +specify the slave surface but not the master surface, output is given for all contact pairs that involve the +specified slave surface. +Input File Usage: +Use either of the following options: +*CONTACT PRINT, MASTER=master, SLAVE=slave, NSET=node_set +*CONTACT FILE, MASTER=master, SLAVE=slave, NSET=node_set +Requesting summaries in the data file +By default, summaries of surface variables are printed in the data file. A summary of the maximum and +minimum values is printed at the end of each column in an output table. The locations of the maximum +and minimum values are also printed. You can choose to suppress this summary. +Input File Usage: +*CONTACT PRINT, SUMMARY=YES or NO +Requesting totals in the data file +You can print the sum (total) of each column in an output table to the data file. By default, these totals +are suppressed. +Input File Usage: +*CONTACT PRINT, TOTALS=YES or NO +Controlling the frequency of output +You can control the frequency of surface output by specifying the output frequency in increments. Unless +a frequency of zero is specified to suppress output, the variables will always be output at the last increment +of the step. +Input File Usage: +Use either of the following options: +*CONTACT PRINT, FREQUENCY=n +*CONTACT FILE, FREQUENCY=n +Default surface output +Surface output requests must be included for surface variables associated with contact pairs to be written +to the data and results files; no default output is provided. +If a surface output request is defined without any specified output variables, the following variables +will be written to the data and results files by default: +• For contact analysis, contact pressure (CPRESS), frictional shear stresses (CSHEAR), contact +opening (COPEN), and relative tangential motions (CSLIP); see “Defining contact pairs in +Abaqus/Standard,” Section 35.3.1. +• For heat transfer analysis, heat flux per unit area (HFL), heat flux (HFLA), time integrated HFL +(HTL), and time integrated HFLA (HTLA); see “Thermal contact properties,” Section 36.2.1. +• For coupled thermal-electrical analysis, HFL, HFLA, HTL, HTLA, electrical current per unit +area (ECD), electrical current (ECDA), time integrated ECD (ECDT), and time integrated ECDA +(ECDTA); see “Electrical contact properties,” Section 36.3.1. +• For coupled pore fluid-mechanical analysis, CPRESS, CSHEAR, COPEN, CSLIP, pore fluid +volume flux per unit area (PFL), pore fluid volume flux (PFLA), time integrated PFL (PTL), and +time integrated PFLA (PTLA); see “Pore fluid contact properties,” Section 36.4.1. +• For crack propagation analysis, there are no default output quantities; bond failure quantities must +be requested explicitly; see “Crack propagation analysis,” Section 11.4.3. +Data file format +Printed output of variables is arranged in tables. Each table is defined by a data line of the surface output +request, which specifies the variables to appear in that table. Each table can contain only one type of +output variable (slave node or whole surface). For example, output variables CSTRESS and CFN cannot +be requested on the same data line. For the slave node type of output, each row of a table corresponds +to a node on the slave surface. The rows that will appear in a particular table will be limited to the +node set specified in the output request. The first column of each table defines the location (the node +number). The remaining columns contain variables such as contact pressure, frictional shear stresses, +contact opening, and relative tangential (slip) motions. For the whole surface type of output, each row +of a table corresponds to an entire slave surface. If all of the variables in a row of a table are zero, the +row is not printed. +If a contact output request refers to more than one contact pair, a separate table will be generated +for each contact pair. All of the tables defined by the first data line of the output request will be printed, +then all of the tables defined by the second line, etc. +Results file format +A contact output request record (the type 1503 record described in “Results file output format,” +Section 5.1.2) is created for each output request. For the slave node type of output, this record is +followed by several node header records, each of which contains a node on the slave surface. Each node +header record is followed by records that contain output variables. The output will be limited to the +node set specified in the output request. For the whole surface type of output, the type 1503 record is +followed by only one type 1504 node header record with a node number zero. The node header record +is followed by records containing the requested output variables. +If a contact output request refers to more than one contact pair, a separate contact output request +record is generated for each contact pair. +Section output from Abaqus/Standard +In Abaqus/Standard you can output accumulated quantities associated with user-defined sections for a particular step to the data or results +file. This facility provides “free body diagram” output, allowing analyses of force flow through a +redundant structure. The output requests can be repeated as often as necessary within a step to define +output for different sections and different section output variables. You can assign a label to each +output request that will be used to identify the output for the section. Section output is not available +for eigenfrequency extraction, eigenvalue buckling prediction, complex eigenfrequency extraction, or +linear dynamics procedures or in procedures using multiple load cases. +Defining the surface section +Section output requests are available only for sections defined using element-based surfaces . Consequently, the sections must be defined using +faces of continuum elements although other types of elements (beams, membranes, shells, springs, +dashpots, etc.) can be attached to the section. +Calculation of accumulated quantities on the section (such as the total force) involves nodal +quantities associated with elements on one side of the section only. Therefore, the surface definition +should use elements only from one side of the section (the “base elements,” as defined in “Prescribed +assembly loads,” Section 33.5.1), thus precisely identifying the side from which accumulated quantities +are computed. +Since the section usually cuts through the mesh in a typical section output request, automatic +generation of the surface cannot be used. Specifying the element faces gives exact control over which +element faces form the surface, which is essential when defining a cross-section through a solid body. +You must specify the name of the surface for which output is being requested. +Surfaces that are defined in a restart analysis can be used only for section output requests. The +newly defined surface cannot be used for any other purpose (such as a contact pair or pre-tension section +definition). +Input File Usage: +Use either of the following options: +*SECTION PRINT, NAME=section_name, SURFACE=surface_name +*SECTION FILE, NAME=section_name, SURFACE=surface_name +Example +For example, the following input illustrates a typical section output request to the data file: +*HEADING +Section print example +… +*SURFACE, NAME=surface_name +Data lines that specify the elements and their associated faces to define the +surface section +… +*STEP +… +*SECTION PRINT, NAME=section_name, +SURFACE=surface_name, … +… +*END STEP +Alternatively, if additional section output requests are needed after the analysis is completed, a restart +analysis can be performed to request more output as shown in the following input: +*RESTART, READ, … +… +*SURFACE, NAME=surface_name +Data lines that specify the elements and their associated faces to define the +surface section +… +*STEP +… +*SECTION PRINT, NAME=section_name, +SURFACE=surface_name, … +… +*END STEP +Selecting the coordinate system in which output is desired +You can specify the choice of coordinate system in which the section output is desired. By default, the +components of vector quantities associated with the section are obtained with respect to the global system +of coordinates. Alternatively, you can specify that output is desired in a local system as defined below. +Input File Usage: +Use either of the following options: +*SECTION PRINT, NAME=section_name, SURFACE=surface_name, +AXES=GLOBAL or LOCAL +*SECTION FILE, NAME=section_name, SURFACE=surface_name, +AXES=GLOBAL or LOCAL +Defining a coordinate system local to the surface section +You can allow Abaqus/Standard to define the local system, or you can specify it directly. +Default local system +The default local system is particularly useful when the section is flat or almost flat. While it can also be +used in the case when the defined surface is curved, the default local system may be irrelevant for such +problems. +The default system is defined by a straight line in two-dimensional and axisymmetric cases or by +a plane in three-dimensional cases, fitted (in a least square sense) through the nodes belonging to the +section. The anchor point (origin) of the local system is the centroid of the projection of the surface +on the fitted line or plane. The local directions are given by the normal (1-direction) and the tangent +direction (the 2-direction in two-dimensional and axisymmetric cases) or the tangent directions (the 2- +and 3-directions in three-dimensional cases) to the fitted line or plane. When several straight lines or +planes can be fit equally well between the nodes defining the section (for example, a closed circular or +spherical surface), the original local directions will be parallel to the global axes. +The positive local 1-direction is selected such that it will form an acute angle with the average +normal direction to the section, computed by averaging the positive normals to the element faces defining +the section. If the average normal direction is zero (a closed surface), the 1-direction will form an acute +angle with the global x-axis. If in two-dimensional or axisymmetric cases the 1-direction is within 0.1° of +being normal to the global x-axis, it will form an acute angle with the global y-axis. In three-dimensional +cases if the 1-direction is within 0.1° of being normal to the global X–Y plane, it will form an acute angle +with the global z-axis. +In two-dimensional and axisymmetric cases the local 2-direction is obtained by rotating the local +1-direction counterclockwise by 90° about the anchor point. For three-dimensional situations the tangent +directions of the surface are defined using the Abaqus conventions for local directions on surfaces in +space . +Input File Usage: +Use either of the following options to use the default local coordinate system: +*SECTION PRINT, NAME=section_name, SURFACE=surface_name, +AXES=LOCAL +*SECTION FILE, NAME=section_name, SURFACE=surface_name, +AXES=LOCAL +User-specified local system +A user-specified local system is defined by specifying the origin and the directions of the axes. You can +specify the origin (anchor point) by giving a node number or by specifying the coordinates of the anchor +point. +In two-dimensional and axisymmetric cases the local 2-direction is defined by specifying either +a predefined node number or the coordinates of a point (point a) on the local 2-direction. The local +1-direction is then obtained by rotating the local 2-axis clockwise by 90° about the anchor point . If node numbers are used to define the anchor point or the local directions, they must +be connected to the mesh. +In three-dimensional cases either two predefined nodes or the coordinates of two points can be used +to specify the local directions. A rectangular Cartesian coordinate system is then defined by its origin +(the anchor point) and these two points. The first point (point a) must lie on the local 2-direction, and +anchor point +.DAT AND .FIL OUTPUT +anchor point +elements used to +define the section +defined section +2-D and axisymmetric +3-D +Figure 4.1.2–1 User-defined local coordinate system. +the second (point b) must be in the local 2–3 plane on the side of the local 3-direction. Although it is +not necessary, it is intuitive to select the second point such that it is on or near the local 3-direction . +If you do not specify the anchor point of the local system, it is taken to be the centroid of the +projection of the surface on the fitted line or plane. If you do not specify the directions of the axes, the +local system will be anchored at the specified anchor point and its axes will be parallel to the default +axes of the projected surface. If neither the anchor point nor the directions are defined, the default local +system will be used. +In large-deformation analyses the surface section may rotate significantly during the deformation. +By default, when output is requested in a local coordinate system, the system rotates with the average +rigid body motion of the elements used to define the surface section (i.e., the local system and the output +are updated during the analysis). The anchor point and local directions must then be specified relative +to the undeformed configuration. You can choose to obtain vector output in the original local coordinate +system instead. This choice is irrelevant in steps in which geometric nonlinearities are not considered. +Input File Usage: +Use either of the following options to specify the local coordinate system +directly: +*SECTION PRINT, NAME=section_name, SURFACE=surface_name, +AXES=LOCAL, UPDATE=YES or NO +anchor point definition +axes definition +*SECTION FILE, NAME=section_name, SURFACE=surface_name, +AXES=LOCAL, UPDATE=YES or NO +anchor point definition +axes definition +Controlling the frequency of output +You can control the frequency of section output by specifying the output frequency in increments. Unless +a frequency of zero is specified to suppress output, the variables will always be output at the last increment +of the step. +Input File Usage: +Use either of the following options: +*SECTION PRINT, NAME=section_name, SURFACE=surface_name, +FREQUENCY=n +*SECTION FILE, NAME=section_name, SURFACE=surface_name, +FREQUENCY=n +Data file format +Printed output is arranged in tables. The first line of the table contains the name of the requested output +variable , and the second line contains +the corresponding value. If a section output request is defined without any specified output variables, all +appropriate variables associated with the current analysis type are output. +If several section output requests to the data file are encountered in one particular step, separate +tables will be created for each request. Each table has a header denoting the name of the section and the +name of the surface used. In addition, if the output is requested in a local coordinate system, the global +coordinates of the anchor point and the cosine directions of the local axes are output. +Results file format +Several section output records (record numbers 1580–1591 in “Results file output format,” Section 5.1.2) +are output for each section output request to the results file. The actual collection of records to be written +to the results file depends on the number of valid output requests. If a section output request is defined +without any specified output variables, all records relevant to the current analysis type are stored in the +results file. +Vector output in the section +Vector output associated with section output requests consists of the total force (SOF), the total moment +(SOM), and the center of forces (SOCF). Output variable SOF is computed as a vector sum of the stress- +based (internal) nodal forces of the nodes in the surface. +Output variable SOM is computed with respect to the origin of the coordinate system considered. +Thus, if the output is requested in the global coordinate system, the total moment is computed about the +global origin; if the output is requested in a local coordinate system, the moment is computed about the +current anchor point of the local system. The coordinates of the current anchor point may change during +the analysis if the local coordinate system is updated. Output variables SOF and SOM are both reported +in the coordinate system considered. +The center of forces SOCF is computed as the closest point to the centroid of the section through +which the total force SOF acts. SOCF is always reported in the global coordinate system. If the total +force vector is equal to zero, the centroid of the section is reported as the center of forces SOCF. +The total moment vector, SOM, will not necessarily equal the cross product of the center of force +vector, SOCF, and total force vector, SOF. Forces acting on two different points of the section may have +components acting in opposite directions, such that these force components generate a net moment but +not a net force; therefore, the total moment may not arise entirely from the resultant force. +Scalar output in the section +Scalar output associated with a section output request consists of the area of the defined section +(SOAREA), the total heat flux (SOH) in heat transfer analysis, the total current (SOE) in electrical +analysis, the total mass flow (SOD) in mass diffusion analysis, and the total pore fluid volume flux +(SOP) in couple pore fluid diffusion-stress analysis. These output variables are computed as the +algebraic sum of the scalar internal nodal fluxes (work-conjugate to the associated primary solution +variables) of the nodes in the surface. For example, in heat transfer analysis the total heat flux (SOH) is +the sum of the NFLUX values at the nodes on the surfaces. +Limitations when using section output requests +Section output requests are subject to the following limitations: +• Section output requests are available only for sections defined by an element-based surface. Thus, +they can be used only for sections along faces of continuum elements. +• When defining the section, elements on only one side of the section must be used. Abaqus/Standard +identifies all elements attached to the surface on this side and computes the section output variables +as in a free-body diagram. +• The defined section must cut completely through the mesh, form a closed surface, or be on the +exterior of the body. Figure 4.1.2–2 presents some typical cases of valid surfaces. If the section cuts +only partially through the mesh, a valid free-body diagram cannot be isolated +and incorrect answers may be computed. Abaqus/Standard will attempt to identify the invalid cases +and will issue error or warning messages. +• Elements attached to the section can be on either side of the surface but must not cross the +defined section. Figure 4.1.2–3 presents a few invalid cases. In most cases Abaqus/Standard will +successfully identify elements that cross the surface, and warning messages will be issued. The +elements will then not be considered in the calculation of the section variables. +• For section output purposes, Abaqus/Standard will ignore the elements attached to the section for +which it cannot establish whether they belong to one side or the other of the section (e.g., SPRING1 +elements). +• Section output requests cannot be specified within a substructure. +• Section output requests cannot be specified in random response analyses. +• The total force and the total moment in the section are computed based only on the stresses (internal +forces) in the identified elements. Thus, inaccurate results may be obtained if distributed body +spring A +pressure load +beam +spring A +defined section +elements used to define the section +Figure 4.1.2–2 Valid section definitions. +beam +incomplete cut +defining elements on +both sides +beam crossing the +section +defined section +elements used to define the section +Figure 4.1.2–3 Invalid section definitions. +loads are present in these elements since their effect on the total force in the section is not included. +Common examples are the inertial loading in dynamic analyses, gravity loads, distributed body +forces, and centrifugal loads. In these cases the total force in the section may depend on the choice +of elements used to define the section as illustrated in Figure 4.1.2–4(a). Assuming that gravity +loading is the only active load, the element stresses will be different in the two elements. Hence, +if the same section is defined first using element 1 and then using element 2, different answers for +the total force will be obtained. In a similar way the effects of any distributed body fluxes (heat, +electrical, etc.) prescribed in the identified elements are not included. +surface defined +using element 1 +concentrated +loads +distributed +body loads +(a) +surface defined +using element 2 +(b) +Figure 4.1.2–4 Total force in the section. +• Depending on which side of the surface is used to define the section, different answers will be +obtained in analyses similar to the case illustrated in Figure 4.1.2–4(b). Assuming a static analysis +with the concentrated loads shown in the figure being the only active loads, a zero total force is +reported if the section is defined using element 1 and a nonzero force equal to the sum of the +concentrated loads is obtained if the section is defined using element 2. +4.1.3 +OUTPUT TO THE OUTPUT DATABASE +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD Abaqus/CAE +References +• “Element-based surface definition,” Section 2.3.2 +• “Integrated output section definition,” Section 2.5.1 +• “Output,” Section 4.1.1 +• “The postprocessing calculator,” Section 4.3.1 +• *OUTPUT +• *FILTER +• *CONTACT OUTPUT +• *ELEMENT OUTPUT +• *ENERGY OUTPUT +• *INTEGRATED OUTPUT +• *INCREMENTATION OUTPUT +• *MODAL OUTPUT +• *NODE OUTPUT +• *RADIATION OUTPUT +• *SURFACE OUTPUT +• “Understanding output requests,” Section 14.4 of the Abaqus/CAE User’s Manual +Overview +Output variables are available for: +• element integration points, element section points, whole elements, and element sets; +• surfaces in Abaqus/Explicit and Abaqus/CFD; +• integrated output sections in Abaqus/Explicit; +• nodes; and +• the whole model. +All the output variables are defined in “Abaqus/Standard output variable identifiers,” Section 4.2.1, +“Abaqus/Explicit output variable identifiers,” Section 4.2.2, and “Abaqus/CFD output variable +identifiers,” Section 4.2.3. +Model information and analysis results are stored in terms of an assembly of part instances . +See the Abaqus Scripting User’s Manual for a description of how to use the Abaqus Scripting +Interface or C++ to access an output database. +Requesting output to the output database +Three types of information are stored in the output database in Abaqus/Standard and Abaqus/Explicit: +“field” output, “history” output, and diagnostic information. In Abaqus/CFD four types of information +are stored in the output database: nodal field output, surface field output, element history output, and +surface history output. Field output and history output are controlled by output database requests as +described in this section. A subset of the diagnostic information that is written to the message file for +Abaqus/Standard analyses and to the status and message files for Abaqus/Explicit analyses is included +in the output database. +• Field output is intended for infrequent requests for a large portion of the model and can be +used to generate contour plots, animations, symbol plots, X–Y plots, and displaced shape plots +in Abaqus/CAE. Only complete sets of basic variables (for example, all the stress or strain +components) can be requested as field output. +• History output is intended for relatively frequent output requests for small portions of the model +and is displayed in X–Y data plots in Abaqus/CAE. Individual variables (such as a particular stress +component) can be requested. +• Diagnostic information in Abaqus/Standard and Abaqus/Explicit is intended to provide analysis +warning and/or error information as well as convergence information for use in Abaqus/CAE. +Output database requests can be repeated as often as necessary within a step to produce both field +and history output at multiple frequencies. +Requesting field output +Contact surface output, element output, nodal output, and radiation output are available as field output in +Abaqus/Standard and Abaqus/Explicit. Nodal, element, and surface output are available as field output +in Abaqus/CFD. +Input File Usage: +Use the first option in conjunction with one or more of the subsequent options +to request field output to the output database: +*OUTPUT, FIELD +*CONTACT OUTPUT +*ELEMENT OUTPUT +*NODE OUTPUT +*RADIATION OUTPUT +*SURFACE OUTPUT +These options are discussed in detail below. +Abaqus/CAE Usage: +Step module: field output request editor +Requesting history output +Contact surface output, element output, energy output, integrated output, time incrementation output, +modal output, nodal output, and radiation output are available as history output in Abaqus/Standard and +Abaqus/Explicit. Both element output and surface output are available as history output in Abaqus/CFD. +Requesting large amounts of history output (more than 1000 output requests) may cause +performance to degrade in Abaqus/Standard and will cause performance to degrade in Abaqus/Explicit +and Abaqus/CFD. For vector- or tensor-valued output variables each component is considered to be +a single request. In the case of element variables history output will be generated at each integration +point. For example, requesting history output of the tensor variable S (stress) for a C3D10M element +will generate 24 history output requests: (6 components) × (4 integration points). When requesting +history output of vector- and tensor-valued variables, it is recommended that individual components +be selected where available. +Input File Usage: +Use the first option in conjunction with one or more of the subsequent options +to request history output to the output database: +*OUTPUT, HISTORY +*CONTACT OUTPUT +*ELEMENT OUTPUT +*ENERGY OUTPUT +*INTEGRATED OUTPUT +*INCREMENTATION OUTPUT +*MODAL OUTPUT +*NODE OUTPUT +*RADIATION OUTPUT +*SURFACE OUTPUT +These options are discussed in detail below. +Abaqus/CAE Usage: +Step module: history output request editor +Requesting diagnostic information in Abaqus/Standard and Abaqus/Explicit +By default, a subset of the diagnostic information that is written to the message file for Abaqus/Standard +analyses and to the status and message files for Abaqus/Explicit analyses is also written to the output +database. You can use the Visualization module of Abaqus/CAE to view this diagnostic information +interactively, highlighting problematic areas on a view of the model and using them to resolve errors +and warnings in the analysis. For more information, see “The message file in Abaqus/Standard and +Abaqus/Explicit” in “Output,” Section 4.1.1, and Chapter 41, “Viewing diagnostic output,” of the +Abaqus/CAE User’s Manual. +Input File Usage: +Use the following option to write diagnostic information to the output database: +Abaqus/CAE Usage: +*OUTPUT, DIAGNOSTICS=YES +Use the following option to exclude diagnostic information: +*OUTPUT, DIAGNOSTICS=NO +You cannot exclude diagnostic information from the output database from +within Abaqus/CAE. Use the following option to view the saved diagnostic +information: +Visualization module: Tools→Job Diagnostics +Controlling the output frequency +The frequency of output +to the output database is controlled differently in Abaqus/Standard, +Abaqus/Explicit, and Abaqus/CFD. Control of the output frequency in Abaqus/Explicit depends upon +whether field or history output was selected. +Controlling the output frequency in Abaqus/Standard +Abaqus/Standard provides several options for controlling the output frequency, depending on whether +the analysis is in the time domain (e.g., general statics), frequency domain (e.g., steady state dynamics), +or mode domain (e.g., natural frequency extraction). These options can be used to reduce the amount of +output written and hence improve performance and disk space use as compared to the default output. +History output in Abaqus/Standard is buffered and is written to disk only after every 10 increments +of history data output or when a step has completed. Therefore, history results may not be available +immediately for postprocessing. +Default output frequency +If you do not specify the output frequency, field and history output will be written at every increment of +the analysis for all procedure types except dynamic and modal dynamic analyses for which output will +be written every 10 increments. +Controlling output frequency in a frequency domain analysis +In frequency domain procedures, you only can control the frequency of output by specifying the +frequency of output in increments. The data will be written at this frequency as well as at the end of +each step of the analysis. Specify an output frequency of zero to suppress output. +*OUTPUT, FREQUENCY=n +Input File Usage: +Abaqus/CAE Usage: +Step module: field or history output request editor: Frequency: +Every n increments: n +Controlling output frequency in a mode domain analysis +In an eigenvalue extraction or eigenvalue buckling analysis, you can select the modes at which output is +desired. If you do not specify a list of modes, output is produced for all of the modes. +*OUTPUT, FIELD, MODE LIST +Step module: field output request editor: Frequency: Specify +modes: list of modes +Abaqus/CAE Usage: +Input File Usage: +Controlling output frequency in a time domain analysis +In time domain analyses, you can control the frequency of output by specifying the output frequency in +terms of increments, the number of intervals during the step, the size of regular time intervals throughout +the step, or time points throughout the step. The different options are described in more detail below. +Whichever option is chosen, the output will always be written at the zero-increment and last +increment of the analysis and, for a low-cycle fatigue analysis, at the end of each cycle. The +zero-increment output represents the initial conditions for the current analysis step and is essential for +sequential thermal-stress analyses and analyses involving submodeling, for which a complete solution +history (including the solution state at the beginning of the step) is needed to ensure proper interpolation +in time. The zero-increment state is written at the beginning of the step, before the solution of the +incremental nonlinear finite-element equations for the step commences, and is therefore in general not +an equilibrium solution. Particular examples where the solution is not in equilibrium include the first +step of an analysis in which an initial stress state is defined and when loads or boundary condition +changes are discontinuous between steps. +Usually, the zero-increment output in any step corresponds to the base state, which is the state of +the model at the end of the last general step. The exception to this is modal transient dynamic analysis, +where the zero-increment output represents the linear perturbation response at time zero. +Time domain analysis: specifying output frequency in increments +You can specify how frequently you want output in terms of increments. Specify an output frequency of +zero to suppress output. +Input File Usage: +Abaqus/CAE Usage: +*OUTPUT, FREQUENCY=n +Step module: field or history output request editor: Frequency: +Every n increments: n +Time domain analysis: specifying output frequency in number of intervals +You can specify the output frequency in number of intervals, n. The specified number of intervals must +be a positive integer. +By default, Abaqus/Standard adjusts the time increment (in some cases Abaqus/Standard might +violate the minimum time increment specified) to ensure that data are written at the exact times +calculated by dividing the step into n equal intervals. Alternatively, you can specify that the data be +written immediately after each time mark. In this case no adjustment of the time increment is necessary. +Input File Usage: +Use the following option to request results at the exact time intervals: +*OUTPUT, NUMBER INTERVAL=n, TIME MARKS=YES +Use the following option to request +immediately after each time interval: +results at +the increments ending +Abaqus/CAE Usage: +*OUTPUT, NUMBER INTERVAL=n, TIME MARKS=NO +Use the following option to request results at the exact time intervals: +Step module: field or history output request editor: Frequency: Evenly +spaced time intervals, Interval: n, Timing: Output at exact times +Use the following option to request +immediately after each time interval: +results at +the increments ending +Step module: field or history output request editor: Frequency: Evenly +spaced time intervals, Interval: n, Timing: Output at approximate times +Time domain analysis: specifying output frequency in regular time interval size +You can write the results at specified regular intervals throughout the step as well as at the end of the step. +By default, Abaqus/Standard will adjust the time increment (in some cases Abaqus/Standard might +violate the minimum time increment specified) to ensure that data will be written at the exact times, as +defined by multiples of the time interval, t. Alternatively, the data can be written immediately after each +time mark. In this case no adjustment of the time increment is necessary. +Input File Usage: +Use the following option to request results at the exact time intervals: +*OUTPUT, TIME INTERVAL=t , TIME MARKS=YES +Use the following option to request +immediately after each time interval: +results at +the increments ending +Abaqus/CAE Usage: +*OUTPUT, TIME INTERVAL=t , TIME MARKS=NO +Use the following option to request results at the exact time intervals: +Step module: field or history output request editor: Frequency: Every +x units of time: t, Timing: Output at exact times +Use the following option to request +immediately after each time interval: +results at +the increments ending +Step module: field or history output request editor: Frequency: Every +x units of time: t, Timing: Output at approximate times +Time domain analysis: specifying output frequency in time points +You can write the results at specified time points throughout the step. +By default, Abaqus/Standard adjusts the time increment (in some cases Abaqus/Standard might +violate the minimum time increment specified) to ensure that data are written at the exact time points +specified. Alternatively, you can specify that the data be written immediately after each time point. In +this case no adjustment of the time increment is necessary. +Input File Usage: +Use the following options to request results at the exact time points: +*TIME POINTS, NAME=time points name +*OUTPUT, TIME POINTS=time points name, TIME MARKS=YES +Use the following options to request results at +immediately after each time point: +the increments ending +*TIME POINTS, NAME=time points name +*OUTPUT, TIME POINTS=time points name, TIME MARKS=NO +Use the following option to request results at the exact time points: +Step module: field or history output request editor: From time points, +Name: time points name, Timing: Output at exact times +Abaqus/CAE Usage: +Use the following option to request +immediately after each time point: +results at +the increments ending +Step module: field or history output request editor: From time points, +Name: time points name, Timing: Output at approximate times +Time domain analysis: time incrementation +If the output frequency is specified at exact times and in terms of the number of intervals, in regular time +intervals, or in time points, Abaqus/Standard adjusts the time increments to ensure that data are written +at the exact time points. In some cases Abaqus may use a time increment smaller than the minimum time +increment allowed in the step in the increment directly before a time point. However, Abaqus will not +violate the minimum time increment allowed for consolidation, transient mass diffusion, transient heat +transfer, transient couple thermal-electrical, transient coupled temperature-displacement, and transient +coupled thermal-electrical-structural analyses. For these procedures if a time increment smaller than the +minimum time increment is required, Abaqus will use the minimum time increment allowed in the step +and will write output data at the first increment after the time point. +When the output frequency is specified at exact times and in terms of the number of intervals, in +regular time intervals, or in time points, the number of increments necessary to complete the analysis +might increase, which might adversely affect performance. +Controlling the output frequency for field output in Abaqus/Explicit +Field output data are always written at the start and end of each step in which the output request is active. +In addition, you can specify the output frequency in terms of the number of intervals during the step, the +size of regular time intervals throughout the step, or time points throughout the step. The times at which +the results are written are referred to as time marks. +Specifying field output frequency in number of intervals +You can specify the output frequency in number of intervals, n. The specified number of intervals must +be a positive integer. For example, if the specified number of intervals is 10, Abaqus/Explicit will write +field data 11 times: the values at the beginning of the step and at the end of 10 equal time intervals +throughout the step. +By default, field data will be written at the increment ending immediately after each time mark. +Alternatively, when you specify the output frequency in number of intervals, you can choose to have the +time increment size adjusted so that an increment will end exactly at each of the time marks calculated +by dividing the step into n equal intervals. +Input File Usage: +Use the following option to request +immediately after each time interval: +results at +the increments ending +*OUTPUT, FIELD, NUMBER INTERVAL=n, TIME MARKS=NO +Use the following option to request results at the exact time intervals: +*OUTPUT, FIELD, NUMBER INTERVAL=n, TIME MARKS=YES +Abaqus/CAE Usage: +Use the following option to request +immediately after each time interval: +results at +the increments ending +Step module: field output request editor: Frequency: Evenly spaced time +intervals, Interval: n, Timing: Output at approximate times +Use the following option to request results at the exact time intervals: +Step module: field output request editor: Frequency: Evenly spaced +time intervals, Interval: n, Timing: Output at exact times +Specifying field output frequency in regular time interval size +Alternatively, you can write the results at specified regular intervals throughout the step as well as at the +beginning and end of the step. The time increment size will not be adjusted to meet the specified time +marks; results will be written at the increment ending immediately after each time mark, as defined by +multiples of the time interval, t. +Input File Usage: +Abaqus/CAE Usage: +*OUTPUT, FIELD, TIME INTERVAL=t +Step module: field output request editor: Frequency: Every x units of time: t +Specifying field output frequency in time points +You can write the results at specified time points throughout the step. Regular time intervals between +time points are not required; you can specify any desired time points at which the field output is to be +written. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to request results at the exact time points: +*TIME POINTS, NAME=time points name +*OUTPUT, FIELD, TIME POINTS=time points name, TIME MARKS=YES +the increments ending +Use the following option to request +immediately after each time point: +*TIME POINTS, NAME=time points name +*OUTPUT, FIELD, TIME POINTS=time points name, TIME MARKS=NO +Use the following option to request results at the exact time points: +results at +Step module: field output request editor: Frequency: From time points, +Name: time points name, Timing: Output at exact times +Use the following option to request +immediately after each time point: +results at +the increments ending +Step module: field output request editor: Frequency: From time points, +Name: time points name, Timing: Output at approximate times +Default field output +If you do not specify the output frequency (in either number of intervals, time interval size, or time +points), field output will be written at 20 equally spaced intervals throughout the step. +Controlling the output frequency for history output in Abaqus/Explicit +If history output is selected, you can specify the output frequency in terms of either increments or regular +intervals throughout the step. +Specifying history output frequency in increments +You can specify the output frequency in increments. The data will be written at this frequency as well as +at the end of each step of the analysis. +Input File Usage: +Abaqus/CAE Usage: +*OUTPUT, HISTORY, FREQUENCY=n +Step module: history output request editor: Frequency: Every +n time increments: n +Specifying history output frequency in regular time interval size +Alternatively, you can write the results at specified regular intervals throughout the step as well as at the +end of the step. The time increment size will not be adjusted to meet the specified time marks; results +will be written at the increment ending immediately after each time mark, as defined by multiples of the +time interval, t. +Input File Usage: +Abaqus/CAE Usage: +*OUTPUT, HISTORY, TIME INTERVAL=t +Step module: history output request editor: Frequency: Every +x units of time: t +Default history output +If you do not specify the output frequency (in either increments or time interval size), history output will +be written at 200 equally spaced intervals throughout the step. +Controlling the output frequency for field output in Abaqus/CFD +Field output data are always written at the start and end of each step in which the output request is active. +In addition, you can specify the output frequency in terms of increments, the number of intervals during +the step, or the size of regular time intervals throughout the step. By default, field output will be written +at 20 equally spaced intervals throughout the step. +Specifying field output frequency in increments +You can specify the output frequency in increments. The data will be written at this frequency as well as +at the beginning and end of each step of the analysis. +Input File Usage: +Abaqus/CAE Usage: +*OUTPUT, FIELD, FREQUENCY=n +Step module: field output request editor: Frequency: Every +n time increments: n +Specifying field output frequency in number of intervals +You can specify the output frequency in number of intervals, n. The specified number of intervals must +be a positive integer. For example, if the specified number of intervals is 10, Abaqus/CFD will write field +data 11 times: the values at the beginning of the step and at the end of 10 equal time intervals throughout +the step. +Input File Usage: +Abaqus/CAE Usage: +*OUTPUT, FIELD, NUMBER INTERVAL=n +Step module: field output request editor: Frequency: Evenly +spaced time intervals, Interval: n +Specifying field output frequency in regular time interval size +Alternatively, you can write the results at specified regular intervals throughout the step as well as at the +beginning and end of the step. The time increment size will not be adjusted to meet the specified time +marks; results will be written at the increment ending immediately after each time mark, as defined by +multiples of the time interval, t. +Input File Usage: +Abaqus/CAE Usage: +*OUTPUT, FIELD, TIME INTERVAL=t +Step module: field output request editor: Frequency: Every x units of time: t +Controlling the output frequency for history output in Abaqus/CFD +You can specify the output frequency in terms of increments, the number of intervals during the step, or +regular intervals throughout the step. By default, no history output is automatically written to the output +database. +Specifying history output frequency in increments +You can specify the output frequency in increments. The data will be written at this frequency as well as +at the beginning and end of each step of the analysis. +Input File Usage: +Abaqus/CAE Usage: +*OUTPUT, HISTORY, FREQUENCY=n +Step module: history output request editor: Frequency: Every +n time increments: n +Specifying history output frequency in number of intervals +You can specify the output frequency in number of intervals, n. The specified number of intervals must +be a positive integer. For example, if the specified number of intervals is 10, Abaqus/CFD will write +history data 11 times: the values at the beginning of the step and at the end of 10 equal time intervals +throughout the step. +Input File Usage: +Abaqus/CAE Usage: +*OUTPUT, HISTORY, NUMBER INTERVAL=n +Step module: history output request editor: Frequency: Evenly +spaced time intervals, Interval: n +Specifying history output frequency in regular time interval size +Alternatively, you can write the results at specified regular intervals throughout the step as well as at the +end of the step. The time increment size will not be adjusted to meet the specified time marks; results +will be written at the increment ending immediately after each time mark, as defined by multiples of the +time interval, t. +Input File Usage: +Abaqus/CAE Usage: +*OUTPUT, HISTORY, TIME INTERVAL=n +Step module: history output request editor: Frequency: Every +x units of time: t +Requesting output in multiple steps +Output requests apply to the step in which they are defined and to all subsequent steps until they are +respecified. +The only exception occurs when the step type changes from general to linear perturbation (available +only in Abaqus/Standard). Output requests defined in general steps apply only to subsequent general +steps; output requests defined in linear perturbation steps apply only to subsequent consecutive linear +perturbation steps. In other words, output defined in a general step is independent of output defined in +a linear perturbation step. Propagation between linear perturbation steps occurs only for consecutive +linear perturbation steps. If a general analysis step occurs between perturbation steps, output defined in +the first perturbation step will not propagate to the next perturbation step. +In any given step you can add or selectively replace the output requests that are continued from +previous steps. Alternatively, you can discontinue all requests from previous steps and request a +completely new set of output. The preselected field variables and preselected history output variables + are requested by default for the first step of an analysis; you +can modify this request as in any other step. +Specifying new output requests +By default, all output requests defined in previous steps are removed when new requests are defined, +regardless of the type of output request being defined. In other words, a new field output request in a +step removes all field and history output requests defined in previous steps. +Because all existing output requests are removed when a new request is defined in a step, all output +requests within the same step are treated as new (i.e., additional output requests or replacement output +requests are treated as equivalent to new output requests). +Input File Usage: +Use one of the following options to remove all existing output requests and to +specify new requests: +Abaqus/CAE Usage: +*OUTPUT, FIELD, OP=NEW +*OUTPUT, HISTORY, OP=NEW +Step module: Create Field Output Request or Create +History Output Request +Abaqus/CAE automatically respecifies all previously defined output requests +when you create a new request. +Specifying additional output requests +Alternatively, you can specify additional output requests without removing all default and previously +defined output requests. +Input File Usage: +Use one of the following options to specify additional output requests without +removing all default and previously defined output requests: +Abaqus/CAE Usage: +*OUTPUT, FIELD, OP=ADD +*OUTPUT, HISTORY, OP=ADD +Step module: Create Field Output Request or Create +History Output Request +Abaqus/CAE automatically respecifies all previously defined output requests +when you create a new request. +Replacing or removing an output request +You can replace an output request of the same type (e.g., field or history) and frequency with a new +request. No other previously defined requests will be affected. +You cannot replace an output request to change its frequency. If no matching request is found, the +request specified is simply added to the step. +To remove a previously defined request, you can replace the output request without specifying any +new output variables. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options to replace an output request with a new +request: +*OUTPUT, FIELD, OP=REPLACE +*OUTPUT, HISTORY, OP=REPLACE +Step module: Field Output Requests Manager or History Output +Requests Manager: Edit or Delete +Suppressing output requests defined in previous steps +To suppress completely all output requests that have been defined in previous steps, you can specify an +output frequency of 0. +Preselected output requests +There are two ways to define output variable requests quickly and easily. Both methods are available +for field and history output requests and for the individual output requests used for requesting specific +variable types (e.g., nodal, element). There are no preselected output variables for surface output requests +in Abaqus/CFD. The use of these methods with individual output requests for specific variable types is +explained in detail later in this section. +Requesting procedure-specific preselected output requests +You can activate a procedure-specific set of commonly requested output variables. See Table 4.1.3–1 +for a list of procedure types and their accompanying preselected variables. The variables written to the +output database may change if the procedure type changes between steps. +If you request preselected field or history output and request additional output variables using +individual output requests for specific variable types, the variables requested will be appended to the +variables contained in the preselected list. +For geometrically nonlinear analysis in Abaqus/Standard, E is not available for output and +LE is output by default. +For linear perturbation analyses and geometrically linear analyses in +Abaqus/Standard, LE and NE strain output requests yield the same output as E. For geometrically linear +analysis in Abaqus/Explicit, LE is output. +Abaqus may omit some preselected variables from the analysis results. Abaqus omits preselected +output variables if they are not applicable for the element type used to mesh the model or if other factors +make the variables unsuitable for the analysis. No preselected variables are available for surface output +in an Abaqus/CFD analysis. +Input File Usage: +Use one of the following options: +Abaqus/CAE Usage: +*OUTPUT, FIELD, VARIABLE=PRESELECT +*OUTPUT, HISTORY, VARIABLE=PRESELECT +Step module: field or history output request editor: Preselected defaults +Table 4.1.3–1 List of preselected variables for various procedure types. +Procedure type +Preselected +element variables +(field; history for +Abaqus/CFD) +Preselected nodal +and surface +variables (field) +Preselected energy +variables (history) +Annealing +Complex frequency +extraction +Coupled pore fluid +diffusion/stress +none +none +none +none +none +S, E, VOIDR, SAT, +POR +U, RF, CF, PFL, PFLA, +PTL, PTLA, TPFL, +TPTL +ALLAE, ALLCD, +ALLFD, ALLIE, +ALLKE, ALLPD, +ALLSE, ALLVD, +ALLDMD, ALLWK, +ALLKL, ALLQB, +ALLEE, ALLJD, +ALLSD, ETOTAL +Procedure type +Preselected +element variables +(field; history for +Abaqus/CFD) +Preselected nodal +and surface +variables (field) +Preselected energy +variables (history) +Coupled thermal-electric HFL, EPG +NT, RFL, EPOT +Direct cyclic +S, E, PE, PEEQ, +PEMAG +U, RF, CF +Direct-integration +implicit dynamic (with an +output frequency of 10) +S, E, PE, PEEQ, +PEMAG +U, V, A, RF, CF, +CSTRESS, CDISP +Direct-solution +steady-state dynamic +Eigenfrequency +extraction +Eigenvalue buckling +prediction +S, E +none +none +U, V, A, RF, CF +ALLAE, ALLCD, +ALLFD, ALLIE, +ALLKE, ALLPD, +ALLSE, ALLVD, +ALLDMD, ALLWK, +ALLKL, ALLQB, +ALLEE, ALLJD, +ALLSD, ETOTAL +ALLAE, ALLCD, +ALLFD, ALLIE, +ALLKE, ALLPD, +ALLSE, ALLVD, +ALLDMD, ALLWK, +ALLKL, ALLQB, +ALLEE, ALLJD, +ALLSD, ETOTAL +ALLAE, ALLCD, +ALLFD, ALLIE, +ALLKE, ALLPD, +ALLSE, ALLVD, +ALLDMD, ALLWK, +ALLKL, ALLQB, +ALLEE, ALLJD, +ALLSD, ETOTAL +ALLKE, ALLSE, +ALLVD, ALLWK +none +none +Procedure type +Explicit dynamic +Preselected +element variables +(field; history for +Abaqus/CFD) +S, LE, PE, +PEEQ, EVF, +SVAVG, PEVAVG, +PEEQVAVG +Preselected nodal +and surface +variables (field) +Preselected energy +variables (history) +U, V, A, RF, CSTRESS ALLKE, ALLSE, +ALLWK, ALLPD, +ALLCD, ALLVD, +ALLDMD, ALLAE, +ALLIE, ALLFD, +ETOTAL +Fully coupled thermal- +electrical-structural in +Abaqus/Standard +S, E, PE, PEEQ, +PEMAG, HFL, EPG +U, RF, CF, NT, RFL, +CSTRESS, CDISP, +EPOT +Fully coupled +thermal-stress in +Abaqus/Standard +S, E, PE, PEEQ, +PEMAG, HFL +U, RF, CF, NT, RFL, +CSTRESS, CDISP +Fully coupled +thermal-stress in +Abaqus/Explicit +S, LE, PE, PEEQ, HFL U, V, A, RF, +CSTRESS, NT, RFL +ALLAE, ALLCD, +ALLFD, ALLIE, +ALLKE, ALLPD, +ALLSE, ALLVD, +ALLDMD, ALLWK, +ALLKL, ALLQB, +ALLEE, ALLJD, +ALLSD, ETOTAL +ALLAE, ALLCD, +ALLFD, ALLIE, +ALLKE, ALLPD, +ALLSE, ALLVD, +ALLDMD, ALLWK, +ALLKL, ALLQB, +ALLEE, ALLJD, +ALLSD, ETOTAL +ALLKE, ALLSE, +ALLWK, ALLPD, +ALLCD, ALLVD, +ALLDMD, ALLAE, +ALLIE, ALLFD, +ALLIHE, ALLHF, +ETOTAL +Procedure type +Preselected +element variables +(field; history for +Abaqus/CFD) +Preselected nodal +and surface +variables (field) +Preselected energy +variables (history) +Geostatic stress field +S, E, POR, SAT, +VOIDR +U, RF, CF, CSTRESS, +CDISP +Heat transfer +HFL +NT, RFL +Incompressible fluid +dynamics in Abaqus/CFD +V, PRESSURE, +TEMP, TURBNU +U, V, PRESSURE, +TEMP, TURBNU +Linear static perturbation +S, E +U, RF, CF +ALLAE, ALLCD, +ALLFD, ALLIE, +ALLKE, ALLPD, +ALLSE, ALLVD, +ALLDMD, ALLWK, +ALLKL, ALLQB, +ALLEE, ALLJD, +ALLSD, ETOTAL +none +none +ALLAE, ALLCD, +ALLFD, ALLIE, +ALLKE, ALLPD, +ALLSE, ALLVD, +ALLDMD, ALLWK, +ALLKL, ALLQB, +ALLEE, ALLJD, +ALLSD, ETOTAL +Mass diffusion +CONC, MFL +NNC, RFL +none +Modal dynamic (with an +output frequency of 10) +S, E +U, V, A, RF, CF +ALLAE, ALLCD, +ALLFD, ALLIE, +ALLKE, ALLPD, +ALLSE, ALLVD, +ALLDMD, ALLWK, +ALLKL, ALLQB, +ALLEE, ALLJD, +ALLSD, ETOTAL +SIM-based modal +dynamic +none +none +none +Quasi-static +Preselected +element variables +(field; history for +Abaqus/CFD) +S, E, PE, PEEQ, +PEMAG, CE, CEEQ, +CEMAG +.ODB OUTPUT +Preselected nodal +and surface +variables (field) +Preselected energy +variables (history) +U, RF, CF, CSTRESS, +CDISP +ALLAE, ALLCD, +ALLFD, ALLIE, +ALLKE, ALLPD, +ALLSE, ALLVD, +ALLDMD, ALLWK, +ALLKL, ALLQB, +ALLEE, ALLJD, +ALLSD, ETOTAL +none +ALLKE, ALLSE, +ALLWK +ALLAE, ALLCD, +ALLFD, ALLIE, +ALLKE, ALLPD, +ALLSE, ALLVD, +ALLDMD, ALLWK, +ALLKL, ALLQB, +ALLEE, ALLJD, +ALLSD, ETOTAL +ALLKE, ALLSE, +ALLWK +ALLAE, ALLCD, +ALLFD, ALLIE, +ALLKE, ALLPD, +ALLSE, ALLVD, +ALLDMD, ALLWK, +ALLKL, ALLQB, +ALLEE, ALLJD, +ALLSD, ETOTAL +ALLKE, ALLSE, +ALLVD, ALLWK +Random response +Response spectrum +S, E +S, E +U, V, A +U, RF, CF +Static +S, E, PE, PEEQ, +PEMAG +U, RF, CF, CSTRESS, +CDISP +Steady-state dynamic +S, E +U, V, A, RF, CF +SIM-based steady-state +dynamic +none +Steady-state transport +S, E +none +none +U, RF, CF, CSTRESS, +CDISP +Subspace-based +steady-state dynamic +S, E +U, V, A, RF, CF +Requesting all variables applicable to the current procedure and material type in +Abaqus/Standard and Abaqus/Explicit +You can request all variables applicable to the current procedure and material type. Any individual output +requests for specific variable types are ignored in this case. +Input File Usage: +Use one of the following options: +*OUTPUT, FIELD, VARIABLE=ALL +*OUTPUT, HISTORY, VARIABLE=ALL +Step module: field or history output request editor: All +Abaqus/CAE Usage: +Default output +In Abaqus/Standard and Abaqus/Explicit, if no output database requests are specified, the preselected +field and history output variables are written automatically to the output database. In Abaqus/Standard +the default variables are written at every increment for both field and history output for all procedure +types except dynamic and modal dynamic analyses; the default frequency for field and history output for +these procedure types is every 10 increments. In Abaqus/Explicit the default variables are written at 20 +intervals for field output and 200 intervals for history output. In Abaqus/CFD the default variables are +written at 20 intervals for field output. +You can turn these defaults off for an analysis in Abaqus/Standard and Abaqus/Explicit by using +the odb_output_by_default environment file parameter; see “Using the Abaqus environment settings,” +Section 3.3.1, for details. Furthermore, specifying new output database requests in a step overrides the default field and history output requests for that step. For large +models the default output to the output database may increase the solution time and required disk space +considerably. In such cases you are encouraged to review carefully the relevance of the default output +variables for the proposed analysis. A C++ program is available that creates a smaller copy of a large +output database by copying data from only selected frames; for more information, see “Decreasing the +amount of data in an output database by retaining data at specific frames,” Section 10.15.4 of the Abaqus +Scripting User’s Manual. +The odb_output_by_default environment file parameter is ignored in a restart analysis. If no output +requests are defined in a restart analysis, the output requests are those that propagate from the original +analysis. +Abaqus/Explicit output as a result of analysis termination +When an Abaqus/Explicit analysis encounters a fatal error in an increment, the preselected variables +applicable to the current procedure are written automatically to the output database as field data. The +analysis will go through an additional increment with a zero time increment size before writing these +data. +Element output +You can request that element variables (stresses, strains, section forces, element energies, etc.) be written +to the output database. The output request can be repeated as often as necessary to define output for +different types of element variables, different element sets, etc. The same element (or element set) +can appear in several output requests. Element output to the output database is not supported for user +elements. +Selecting the element output variables +The following types of element variables are recognized for the purpose of defining output: +• “Element integration point” variables are associated with the integration points at which material +calculations are performed (for example, components of stress and strain). +• “Element section point” variables are associated with the cross-section of a beam, pipe, or a shell (for +example, bending moments and membrane forces on the section); these variables are not available +in Abaqus/CFD. +• “Element face” variables are associated with the faces of a shell or a solid (for example, uniformly +distributed pressure load on the face). +• “Whole element” variables are attributes of an entire element (for example, the total energy content +of the element). +• “Whole element set” variables are attributes of an entire element set (for example, the current +these variables are available in Abaqus/Standard and +coordinates of the center of mass); +Abaqus/Explicit. +The element variables that can be written to the output database are defined in “Abaqus/Standard output +variable identifiers,” Section 4.2.1, “Abaqus/Explicit output variable identifiers,” Section 4.2.2, and +“Abaqus/CFD output variable identifiers,” Section 4.2.3. +Input File Usage: +*ELEMENT OUTPUT +list of output variables +Abaqus/CAE Usage: +Step module: field or history output request editor: Select from list below +Selecting elements for which output is required +For history output you must specify the element set (or, in Abaqus/Explicit, the tracer set) for which +output is being requested. For field output specifying the element set or tracer set is optional; if you do +not specify an element set or tracer set, the output will be written for all the elements in the model. +Input File Usage: +Abaqus/CAE Usage: +*ELEMENT OUTPUT, ELSET=element_set_name +Step module: field or history output request editor: Domain: Set: set_name +Requesting field output for the exterior elements in the model in Abaqus/Standard and Abaqus/Explicit +You can select output on the element set consisting of all the exterior three-dimensional elements in the +model. This element set is generated internally by Abaqus. +Input File Usage: +Abaqus/CAE Usage: +*ELEMENT OUTPUT, EXTERIOR +Step module: field output request editor: Domain: Whole +model; toggle on Exterior only +Specifying the section point in beam, pipe, shell, and layered solid elements in Abaqus/Standard and +Abaqus/Explicit +For beams, pipes, shells, or layered solids output is provided at the default section points. You can specify +nondefault output points. +Input File Usage: +*ELEMENT OUTPUT +list of output points +list of output variables +Abaqus/CAE Usage: +Step module: field or history output request editor: Output at shell, beam, +and layered section points: Specify: list of output points +Requesting output for rebars in a reinforced model in Abaqus/Standard and Abaqus/Explicit +You can request output for rebars (“Defining reinforcement,” Section 2.2.3). If you do not explicitly +request rebar output in a model with rebars, the element output requests govern the output for the +matrix material only (except for section forces, where the forces in the rebar are included in the force +calculation). You can request output for a particular rebar. If you do not specify the name of a rebar, +output will be given for all rebars in the specified element set (or in the whole model, if you have not +specified an element set). +Rebar output is available only in membrane, shell, or surface elements at the integration points and +at the centroid of the element. +Input File Usage: +Use the following options: +Abaqus/CAE Usage: +*OUTPUT, FIELD +*ELEMENT OUTPUT, REBAR=rebar_name, ELSET=element_set_name +*OUTPUT, HISTORY +*ELEMENT OUTPUT, REBAR=rebar_name, ELSET=element_set_name +Use the following option to request output for rebar in addition to output for +the matrix material: +Step module: field or history output request editor: Output for rebar: Include +Use the following option to request output only for rebar: +Step module: field or history output request editor: Output for rebar: Only +You cannot request output for a particular rebar in Abaqus/CAE; if you request +rebar output, it is given for all rebars in the specified output domain. +Selecting the position of element integration point and section point output +Integration point variables and section variables in Abaqus/Standard and Abaqus/Explicit can be written +as field output to the output database in three different positions: the integration points, the centroid, or +the nodes. By default, output is provided at the integration points. +In most cases Abaqus writes only integration point data to the output database. Transferring of +results from the integration points to the user-specified position in Abaqus/Standard and Abaqus/Explicit +is done by the postprocessing calculator. See “The postprocessing calculator,” Section 4.3.1, for details. +In Abaqus/Standard an alternative procedure is available for three commonly requested output +variables: stress components, Mises equivalent stress, and equivalent pressure stress. To activate +this alternate procedure for Mises equivalent stress and equivalent pressure stress, output variables +MISESONLY and PRESSONLY, respectively, must be requested. +If output variables, MISES and +PRESS, are used instead, the old procedure is invoked. +If output at the nodes or at the centroid is +requested for any of these variables, the interpolation and extrapolation are performed during the +analysis as soon as stresses are available at the integration points. This eliminates the need to store +stress components at the integration points and reduces the size of the output database. This procedure +is invoked automatically when output is requested for any of the supported variables. +Element history output to the output database is always provided at the integration points. +Obtaining output at the integration points in Abaqus/Standard and Abaqus/Explicit +the variables are output at +By default, +In +Abaqus/Standard you can obtain the position of the integration points by using output variable COORD +. +the integration points where they are calculated. +Input File Usage: +Abaqus/CAE Usage: +*ELEMENT OUTPUT, POSITION=INTEGRATION POINTS +You cannot select the position of element output in Abaqus/CAE; it is always +given at the integration points. +Obtaining output at the centroid of each element in Abaqus/Standard and Abaqus/Explicit +You can choose to output the variables at the centroid of each element (the midpoint between the +end nodes of a beam or a pipe element). Centroidal values are obtained through the postprocessing +calculator by interpolation of the integration point values if the integration scheme for the element +does not include a centroidal integration point. Element output of the element centroidal values is not +available for recovering results within substructures; for more information, see “Using substructures,” +Section 10.1.1. +Input File Usage: +Abaqus/CAE Usage: +*ELEMENT OUTPUT, POSITION=CENTROIDAL +You cannot select the position of element output in Abaqus/CAE; it is always +given at the integration points. +Obtaining element output extrapolated to the nodes in Abaqus/Standard and Abaqus/Explicit +You can choose to extrapolate the element integration point variables to the nodes of each element +independently, without averaging the results from adjoining elements. Element output at the element +nodes is not available for recovering results within substructures; for more information, see “Using +substructures,” Section 10.1.1. +Input File Usage: +Abaqus/CAE Usage: +*ELEMENT OUTPUT, POSITION=NODES +You cannot select the position of element output in Abaqus/CAE; it is always +given at the integration points. +Extrapolation and interpolation of element output variables in Abaqus/Standard and Abaqus/Explicit +The shape functions of the element are used by the postprocessing calculator for purposes of +extrapolation and interpolation of output variables. Extrapolated values are generally not as accurate as +the values calculated at the integration points in the areas of high stress gradients, particularly in the +case of modified triangles and tetrahedra. Therefore, adequately detailed meshing is necessary around +nodes where accurate nodal values of such element results are needed. +If a cylindrical or spherical +coordinate system is defined for the element , the orientation at each +integration point may be different. When the values at the integration points are extrapolated to the +nodes, the difference in the orientation is not taken into account; therefore, if the orientation varies +significantly over the elements connected to a node, the extrapolated values are not very accurate. If the +material orientation undergoes significant spatial variation in a region of the model where the material +behavior is truly anisotropic, a finer mesh is required to obtain accurate results even at the integration +points. In that situation once the overall solution has converged with respect to the mesh density, the +interpolation or extrapolation away from the integration points can also be assumed to be reasonably +accurate. You should also be particularly careful when interpreting output variables extrapolated to the +nodes for second-order elements with midside nodes outside the quarter-point region, such as when one +edge is collapsed in two dimensions or one face is collapsed in three dimensions. +For derived variables, such as Mises equivalent stress, the components are first extrapolated or +interpolated. The derived value is then calculated from the extrapolated or interpolated components. +However, in linear mode-based dynamic analysis procedures where derived values are obtained as +nonlinear combinations of modal response magnitudes (“Random response analysis,” Section 6.3.11, +and “Response spectrum analysis,” Section 6.3.10), the nonlinear combinations are first calculated at +the integration points. These derived values are then extrapolated to the nodes or interpolated to the +centroid. +Controlling the output frequency +The frequency of element output is controlled as described above in “Controlling the output frequency.” +Requesting preselected output +You can request the preselected, procedure-specific element output variables described in Table 4.1.3–1. +In this case you can specify additional variables as part of the output request. +Alternatively, you can request all element variables applicable to the current procedure and material +type. In this case any additional variables you specify are ignored. +Input File Usage: +Use the following option to request the preselected element output variables: +*ELEMENT OUTPUT, VARIABLE=PRESELECT +Use the following option to request all applicable element output variables: +Abaqus/CAE Usage: +*ELEMENT OUTPUT, VARIABLE=ALL +Step module: field or history output request editor: +Preselected defaults or All +Specifying the directions for element output in Abaqus/Standard and Abaqus/Explicit +For components of stress, strain, and similar material variables 1, 2, and 3 refer to the directions for +an orthogonal coordinate system. If a local orientation is not defined for the element, the stress/strain +components are in the default directions defined by the convention given in “Orientations,” Section 2.2.5: +global directions for solid elements, surface directions for shell and membrane elements, and axial and +transverse directions for beam and pipe elements. +By default, the element material directions for element field output are written to the output database. +If a local orientation is associated with the element, by default the results displayed in Abaqus/CAE are +in the directions defined by the local orientation. These directions can be visualized in Abaqus/CAE by +selecting Plot→Material Orientations in the Visualization module. You can choose to suppress the +direction output to the output database. +Input File Usage: +Use the following option to indicate that the element material directions should +not be written to the output database: +Abaqus/CAE Usage: +*ELEMENT OUTPUT, DIRECTIONS=NO +Step module: field output request editor: toggle off Include local +coordinate directions when available +Node output +You can output nodal variables (displacements, reaction forces, etc.) to the output database. The output +request can be repeated as often as necessary to define output for different node sets. The same node (or +node set) can appear in several output requests. +Selecting the nodal output variables +The nodal variables that can be written to the output database are defined in the “Nodal variables” +section of “Abaqus/Standard output variable identifiers,” Section 4.2.1, “Abaqus/Explicit output variable +identifiers,” Section 4.2.2, and “Abaqus/CFD output variable identifiers,” Section 4.2.3. +Input File Usage: +*NODE OUTPUT +list of output variables +Abaqus/CAE Usage: +Step module: field or history output request editor: Select from list below +Selecting the nodes for which output is required +For history output you must specify the node set (or, in Abaqus/Explicit, the tracer set) for which output +is being requested. For field output the specification of the node set or tracer set is optional; if you do +not specify a node set or tracer set, the output will be written for all the nodes in the model. +Input File Usage: +Abaqus/CAE Usage: +*NODE OUTPUT, NSET=node_set_name +Step module: field or history output request editor: Domain: Set: set_name +Requesting field output for the exterior nodes in the model in Abaqus/Standard and Abaqus/Explicit +You can select output on the node set consisting of all the exterior nodes in the model. This node set is +generated internally by Abaqus and includes all the nodes that belong to the exterior three-dimensional +elements. +Input File Usage: +Abaqus/CAE Usage: +*NODE OUTPUT, EXTERIOR +Step module: field output request editor: Domain: Whole +model; toggle on Exterior only +Controlling the output frequency +The frequency of nodal output is controlled as described above in “Controlling the output frequency.” +Controlling the precision in Abaqus/Standard and Abaqus/Explicit +You can control the precision of nodal output for an analysis. +Input File Usage: +Use the following command line option to request single-precision nodal +output: +abaqus job=job-name output_precision=single +Use the following command line option to request double-precision nodal +output: +Abaqus/CAE Usage: +abaqus job=job-name output_precision=full +Job module: job editor: Precision: Nodal output precision: Single or Full +Requesting preselected output +You can request the preselected, procedure-specific nodal output variables described in Table 4.1.3–1. +In this case you can specify additional variables as part of the output request. +Alternatively, you can request all nodal variables applicable to the current procedure type. In this +case any additional variables you specify are ignored. +Input File Usage: +Use the following option to request the preselected nodal output variables: +*NODE OUTPUT, VARIABLE=PRESELECT +Use the following option to request all applicable nodal output variables: +Abaqus/CAE Usage: +*NODE OUTPUT, VARIABLE=ALL +Step module: field or history output request editor: +Preselected defaults or All +Specifying the directions for nodal field output in Abaqus/Standard and Abaqus/Explicit +For nodal variables 1, 2, and 3 refer to the global directions X, Y, and Z, respectively. For axisymmetric +elements 1 and 2 refer to the global directions r and z. Nodal field results are written to the output +database in the global directions. If a local coordinate system is defined at a node , the local nodal transformations are written to the output database as +well. You can apply these transformations to the results in the Visualization module of Abaqus/CAE to +view components in the local systems. +Specifying the directions for nodal history output in Abaqus/Standard and Abaqus/Explicit +For nodal variables 1, 2, and 3 refer to the global directions X, Y, and Z, respectively. For axisymmetric +elements 1 and 2 refer to the global directions r and z. Nodal history results are written to the output +database in the global directions unless a local coordinate system has been defined at a node . +desired in global or local directions. +Obtaining nodal history output in the global directions +You can request vector-valued nodal variables in the global directions, which is the default for nodal +history output requests to the output database since most postprocessors assume that components are +given in the global system. +Input File Usage: +Abaqus/CAE Usage: +*NODE OUTPUT, GLOBAL=YES +Step module: history output request editor: Domain: Set: +global directions for vector-valued output +toggle on Use +Obtaining nodal history output in the local directions defined by nodal transformations +You can request vector-valued nodal variables in the local directions defined by nodal transformations. +Input File Usage: +Abaqus/CAE Usage: +*NODE OUTPUT, GLOBAL=NO +Step module: history output request editor: Domain: Set: +global directions for vector-valued output +toggle off Use +Visualizing boundary conditions +Boundary conditions can be visualized in the Visualization module of Abaqus/CAE by selecting +View→ODB Display Options. Click the Entity Display tab in the dialog box that appears. +In an Abaqus/Standard analysis boundary condition information is written to the output database +only when some nodal output variables are requested as field output. +Tracer particle output from Abaqus/Explicit +In Abaqus/Explicit tracer particles can be used to obtain output at specific material points that may +not correspond to a fixed location in the mesh if adaptive meshing is used. Tracer particles follow the +material motion throughout an analysis regardless of the mesh motion, which makes them ideal for use +with adaptive meshing . +Both nodal and element output can be obtained at tracer particles. +Defining tracer particles +You define the initial location of each tracer particle to be coincident with a node, called the “parent +node.” These parent nodes are grouped into a tracer set; you must assign a name to the tracer set when +you define the tracer particles. +Input File Usage: +*TRACER PARTICLE, TRACER SET=tracer_set_name +list of parent nodes (either node numbers or node set labels) +Abaqus/CAE Usage: +Tracer particles are not supported in Abaqus/CAE. +Particle birth stages +Sets of tracer particles can be released from the current locations of the parent nodes at multiple times +during a step. Each release of tracer particles is referred to as a “particle birth.” After particle birth the +tracer particles follow the motion of the associated material regardless of the motion of the mesh. You +can indicate the number of particle birth stages in a step, n. One particle birth will occur at the beginning +of the step, and the rest of the stages will be evenly spaced throughout the step. If you do not specify a +number of particle birth stages, a single particle birth will occur at the beginning of the step. +Input File Usage: +*TRACER PARTICLE, TRACER SET=tracer_set_name, +PARTICLE BIRTH STAGES=n +Abaqus/CAE Usage: +Tracer particles are not supported in Abaqus/CAE. +Tracer particles in the output database +Tracer sets will appear as both node and element sets in the output database. If a tracer set has multiple +birth stages, additional node and element sets will be created that group all the tracer particles associated +with a given birth stage. These subsets are named by appending the birth stage number to the tracer +set name. For example, if a tracer set with the name INLET is defined with two particle birth stages, +three node sets and three element sets will be created in the output database: INLET Stage 1, +INLET Stage 2, and INLET (which contains all the nodes/elements from both INLET Stage 1 +and INLET Stage 2). +Internal field output requests are generated automatically for the requested output variables for all +the elements or nodes in the domain that completely defines the space of possible tracer particle locations. +This region is determined by Abaqus/Explicit and typically corresponds to the elements attached to the +parent nodes and any intersecting adaptive mesh domains. The postprocessing calculator will compute the value of any requested output quantity at a +tracer particle by interpolating the results from the element that encompasses the particle at the time of +output. +Requesting output at tracer particles +You can request element or nodal output for a particular tracer set. Output will be given for all tracer +particles that are associated with the specified tracer set name. +Input File Usage: +Use one of the following options: +Abaqus/CAE Usage: +*NODE OUTPUT, TRACER SET=tracer_set_name +*ELEMENT OUTPUT, TRACER SET=tracer_set_name +Tracer particle output is not supported in Abaqus/CAE. +Field output at tracer particles +Displacement is the only valid field request for tracer particles. You can obtain the positions of the +tracer particles in a specific tracer set by requesting displacements as nodal field output. Tracer particle +displacements are output automatically if displacement output is requested for the entire model. You can +use the node and element sets created for tracer particles in the output database to control the display of +tracer particles in the Visualization module of Abaqus/CAE. +Input File Usage: +Use both of the following options: +*OUTPUT, FIELD +*NODE OUTPUT, TRACER SET=tracer_set_name +Abaqus/CAE Usage: +Tracer particle output is not supported in Abaqus/CAE. +History output at tracer particles +Requesting history output for tracer particles is similar to requesting history output for elements and +nodes. Any valid element integration point variable can be requested. U, V, A, and COORD are the +only valid nodal requests. Whole element variables and element section variables cannot be requested. +History data are available for a tracer particle only after its birth. +A tracer particle history output request triggers an internal field output request for the desired +variables for all the elements or nodes in the domain that completely defines the space of possible tracer +particle locations. +Input File Usage: +Use the following options: +*OUTPUT, HISTORY +*NODE OUTPUT, TRACER SET=tracer_set_name +*ELEMENT OUTPUT, TRACER SET=tracer_set_name +Tracer particle output is not supported in Abaqus/CAE. +Abaqus/CAE Usage: +Tracer particle propagation in multiple steps +Once defined, all tracer particles remain active in subsequent steps. However, no further particle births +occur in the steps that follow the tracer set definition. You can define new tracer particles in subsequent +steps by specifying a new tracer set name. The same tracer set name cannot be used more than once +within an analysis. +Tracer particle deactivation +Individual tracer particles are deactivated if they flow out of the mesh across an Eulerian boundary or are +currently tracking material points inside a failed element that has been deleted from the mesh. History +data for tracer particles are zero at all times after deactivation. +Controlling the output frequency at tracer particles +The frequency of tracer particle output is controlled as described above in “Controlling the output +frequency.” +WARNING: Requesting tracer set history output at a high frequency may cause +the output database (.odb) to become large. The disk space required to store the +field data is directly proportional to the size of the adaptive mesh domain and +the number of tracer sets. The disk space usage is independent of the number of +tracer particles in a tracer set. The output database file size is reduced after the +postanalysis calculation is performed. +Integrated output in Abaqus/Explicit +Integrated output can be requested either over a surface or over an element set. An integrated output +request is used to write the time history of variables such as the total force transmitted across a surface, +the total mass of an element set, or the percentage change of the total mass of an element set. +Selecting the integrated output variables +The integrated variables that can be written to the output database are defined in the “Integrated variables” +section of “Abaqus/Explicit output variable identifiers,” Section 4.2.2. +Input File Usage: +*INTEGRATED OUTPUT +list of output variables +Abaqus/CAE Usage: +Step module: history output request editor: Select from list below +Selecting the surface over which integrated output is required +You can specify the surface directly for an integrated output request. Alternatively, you can associate +an integrated output section that identifies the surface with the integrated output request. +Integrated output can be requested for a surface that includes facets, edges, or ends of various +types of deformable elements. The surface can include facets of three-dimensional solid elements and +continuum shell elements; edges of two-dimensional solid elements, membrane elements, conventional +shell, and surface elements; and ends of beam elements, pipe elements, and truss elements. +Specifying the surface for integrated output directly +If you specify the surface for an integrated output request directly, any vector output variables are given +with respect to a fixed global coordinate system and the total moment transmitted across the surface, +SOM, is computed about the fixed global origin. See “Element-based surface definition,” Section 2.3.2, +for information on defining element-based surfaces. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options: +*SURFACE, NAME=surface_name, TYPE=ELEMENT +*INTEGRATED OUTPUT, SURFACE=surface_name +You cannot specify the surface for an integrated output request directly in +Abaqus/CAE; you must create an integrated output section as described below. +Specifying the surface through an integrated output section definition +If you associate an integrated output section definition with an integrated output request, the integrated +output variables can be obtained in a local coordinate system that can translate and/or rotate with the +deformation . In addition, the total moment transmitted across the surface, SOM, +can be computed about a moving location. +defined section +anchor point +anchor point +elements used to +define the section +defined section +2-D +3-D +Figure 4.1.3–1 A user-defined local coordinate system. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options: +*INTEGRATED OUTPUT SECTION, NAME=section_name, +SURFACE=surface_name +*INTEGRATED OUTPUT, SECTION=section_name +Step module: +Output→Integrated Output Sections→Create: Name: section_name: +select regions for the surface +History output request editor: Domain: Integrated output section: +section_name +Requesting integrated output for “force-flow” studies +To study the “force-flow” through various paths in a model, you must create interior surfaces that cut +through one or more regions (similar to a cross-section) so that you can request integrated output of +the total force transmitted across these surfaces. You can create such interior surfaces over the element +facets, edges, or ends by simply cutting through one or more regions of the model with a plane; see +“Creating interior cross-section surfaces” in “Element-based surface definition,” Section 2.3.2, for more +information. +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*SURFACE, NAME=surface_name, TYPE=CUTTING SURFACE +*INTEGRATED OUTPUT, SURFACE=surface_name +You cannot specify the surface for an integrated output request directly in +Abaqus/CAE; you must create an integrated output section as described above. +Requesting integrated output over an element set +You can request integrated output over an element set to output its total mass, the percentage change of +its total mass, its average rigid body motion or any combination of these variables. The element set must +have been defined previously, and it can include any type of elements. +Input File Usage: +Use the following option to request integrated output over an element set: +Abaqus/CAE Usage: +*INTEGRATED OUTPUT, ELSET=element set name +Requesting integrated output over an element set +Abaqus/CAE. +is not supported in +Controlling the output frequency +The frequency of integrated output is controlled as described above in “Controlling the output frequency +for history output in Abaqus/Explicit.” +Requesting preselected output +Preselected output variables are available only when the integrated output is requested over a surface. If +integrated output is requested over an element set, you must specify the variables on the data line. +If the integrated output is requested over a surface, you can request the preselected integrated output +variables SOF and SOM. In this case you can also specify additional variables as part of the output +request. Alternatively, you can request all integrated variables applicable to the current procedure type. +In this case any additional variables that you specify are ignored. If you do not request the preselected +variables or all variables, you must specify the variables individually. +Input File Usage: +Use the following option to request the preselected integrated output variables: +*INTEGRATED OUTPUT, VARIABLE=PRESELECT +optional additional variables +Use the following option to request all integrated output variables relevant to +the current procedure type: +*INTEGRATED OUTPUT, VARIABLE=ALL +Use the following option to specify individual integrated output variables: +*INTEGRATED OUTPUT +individual variables +Abaqus/CAE Usage: +Step module: history output request editor: Preselected defaults or All +Limitations when using integrated output requests +Integrated output requests over a surface are subject to the following limitations: +• Integrated output can be requested over a surface that includes facets, edges, or ends of various +types of deformable elements. The surface can include facets of three-dimensional solid elements +and continuum shell elements; edges of two-dimensional solid elements, membrane elements, +conventional shell, and surface elements; and ends of beam elements, pipe elements, and truss +elements. The surface should not contain facets of axisymmetric elements or facets of rigid +elements. +• When defining the surface, elements on only one side of the surface must be used. Abaqus/Explicit +computes the integrated output variables using the stresses and hourglass-mode forces in elements +underlying the surface as in a free-body diagram. +• The defined surface must cut completely through the mesh, form a closed surface, or be on the +exterior of the body. Figure 4.1.3–2 presents some typical cases of valid surfaces. If the surface cuts +only partially through the mesh, a valid free-body diagram cannot be isolated +and incorrect answers may be computed. +spring A +pressure load +beam +spring A +defined section +elements used to define the section +Figure 4.1.3–2 Valid section definitions. +beam +incomplete cut +defining elements on +both sides +beam crossing the +section +defined section +elements used to define the section +Figure 4.1.3–3 Invalid section definitions. +• Elements attached to the surface can be on either side of the surface but must not cross the defined +surface. Figure 4.1.3–3 presents a few invalid cases. +• The total force and the total moment in the section are computed based only on the stresses (internal +forces) in the identified elements. Thus, inaccurate results may be obtained if distributed body +loads are present in these elements since their effect on the total force in the section is not included. +Common examples are the inertial loading in dynamic analyses, gravity loads, distributed body +forces, and centrifugal loads. In these cases the total force in the section may depend on the choice +of elements used to define the section as illustrated in Figure 4.1.3–4(a). Assuming that gravity +loading is the only active load, the element stresses will be different in the two elements. Hence, +if the same surface is defined first using element 1 and then using element 2, different answers for +the total force will be obtained. In a similar way the effects of any distributed body fluxes (heat, +electrical, etc.) prescribed in the identified elements are not included. +• Depending on which side of the surface is used to define the section, different answers will be +obtained in analyses similar to the case illustrated in Figure 4.1.3–4(b). Assuming a quasi-static +analysis with the concentrated loads shown in the figure being the only active loads, a zero total +force is reported if the surface is defined using element 1 and a nonzero force equal to the sum of +the concentrated loads is obtained if the surface is defined using element 2. +Total energy output +You can output the total energy of the model or of a specific element set to the output database. Energy +output is available only as history output. Energy output requests are not available for the following +procedures: +• “Eigenvalue buckling prediction,” Section 6.2.3 +surface defined +using element 1 +concentrated +loads +distributed +body loads +(a) +surface defined +using element 2 +(b) +Figure 4.1.3–4 Total force in the section. +• “Natural frequency extraction,” Section 6.3.5 +• “Complex eigenvalue extraction,” Section 6.3.6 +Selecting the energy output variables +The energy variables that can be written to the output database are defined in the “Total energy output +quantities” section of “Abaqus/Standard output variable identifiers,” Section 4.2.1; “Abaqus/Explicit +output variable identifiers,” Section 4.2.2; and “Abaqus/CFD output variable identifiers,” Section 4.2.3. +Input File Usage: +*ENERGY OUTPUT +list of output variables +Abaqus/CAE Usage: +Step module: history output request editor: Select from list below +Selecting the element set for which total energy output is required +You can specify the element set for which total energy output is being requested. In this case the energies +are summed for all the elements in the specified set. You cannot specify an element set for the following +procedures: +• “Transient modal dynamic analysis,” Section 6.3.7 +• “Mode-based steady-state dynamic analysis,” Section 6.3.8 +• “Response spectrum analysis,” Section 6.3.10 +• “Random response analysis,” Section 6.3.11 +The following energies are not available as element set quantities: ALLWK, ALLFD, ALLQB, +ALLKL, ALLFC, and ETOTAL. +If +If you do not specify an element set, the total energies for the whole model will be output. +total energy output for both the whole model and for different element sets is desired, the energy output +requests must be repeated: once without a specified element set to request energy output for the whole +model and once for each specified element set. +Input File Usage: +Abaqus/CAE Usage: +*ENERGY OUTPUT, ELSET=element_set_name +Step module: history output request editor: Domain: Set: set_name +Controlling the output frequency +The frequency of energy output is controlled as described above in “Controlling the output frequency.” +Requesting preselected output +You can request the preselected, procedure-specific energy output variables described in Table 4.1.3–1. +In this case you can specify additional variables as part of the output request. +Alternatively, you can request all energy variables applicable to the current procedure and material +type. In this case any additional variables you specify are ignored. +Input File Usage: +Use the following option to request the preselected energy output variables: +*ENERGY OUTPUT, VARIABLE=PRESELECT +Use the following option to request all applicable energy output variables: +Abaqus/CAE Usage: +*ENERGY OUTPUT, VARIABLE=ALL +Step module: history output request editor: Preselected defaults or All +Sensor definition in Abaqus/Standard and Abaqus/Explicit +For nodal and connector element output variables, history output requests can be used to define sensors. +Sensors are named entities that are intended to be used to model physical sensors such as the total force +or displacement of a hydraulic piston, the motion of a given point on a structure, or the acceleration as +measured by an accelerometer. Sensor values can be fed back into the model to produce actuation that +is a function of the sensed quantity thus allowing for modeling of control engineering aspects of your +system. +You can use sensors in user subroutine UAMP or VUAMP to define a customized amplitude that is a +function of sensor values at the end of the previous increment as shown in “VUAMP,” Section 1.2.7 of +the Abaqus User Subroutines Reference Manual, and illustrated in the example in “Crank mechanism,” +Section 4.1.2 of the Abaqus Example Problems Manual. The amplitude function can be used to actuate +any Abaqus feature that can reference an amplitude, such as concentrated loads, boundary conditions, +connector motion/load, distributed pressure, and material properties via field variables. +A sensor must be uniquely associated with a particular scalar output variable (U1, CTF3, etc.) and +can be defined using history output requests by following some simple rules. The sensor name is specified +in the history output definition, and one and only one nodal output or element output request can be +specified for each sensor definition. Since the named sensor must point to a unique real number at a +given time, the node set or element set used in the definition must contain only one member. Moreover, +regardless of the user-specified output frequency, sensors are computed at every increment during the +analysis. However, they are written to the output database according to the user-specified frequency. +Input File Usage: +Use the following options to specify a sensor definition using element output: +*OUTPUT, HISTORY, SENSOR, NAME=name +*ELEMENT OUTPUT +element output variable +Use the following options to specify a sensor definition using nodal output: +*OUTPUT, HISTORY, SENSOR, NAME=name +*NODE OUTPUT +nodal output variable +Abaqus/CAE Usage: +Step module: history output request editor: Domain: Set: name, +toggle on Include sensor when available +Filtering output and operating on output in Abaqus/Explicit +You can pre-filter element and nodal field output and element, nodal, contact, integrated, and fastener +interaction history output before it is written to the output database. You can also operate on filtered +or unfiltered (raw) output data to extract the maximum, minimum, or absolute maximum of the output +variables over time. In addition, you can set a limit value for the output variables, and you can stop the +analysis at the time this limit is reached. For field output the time at which the maximum, minimum, and +absolute maximum were reached or the time when the limit was reached is output by default for each +output variable. +If you filter a field output request that includes many output variables and applies to the entire +model, the memory requirements and the running time will both increase. For common output requests +consisting of a few element output variables and a few nodal output variables the memory requirements +and the running time will not increase substantially. +Defining a low-pass Infinite Impulse Response digital filter +You can define three types of low-pass Infinite Impulse Response filters as part of the model definition. +Typical magnitude curves for analog type filters are presented in Figure 4.1.3–5, where +represents +the normalized cutoff frequency, which is the ratio of the cutoff frequency to the sampling frequency +(the sampling frequency is the inverse of the time increment). The Butterworth filter is very common; its +response in the pass band is known as maximally flat. The Type I Chebyshev filter has a sharper transition +between the pass band and the stop band, but it has a ripple in the pass band. The Type II Chebyshev +filter also has a sharper transition between the pass band and the stop band than a Butterworth filter +of the same order, but it has a ripple in the stop band. The higher the order of the filter, the narrower +the transition band. However, the computational cost increases as the order increases. In addition, for +high-order filters the phase lag, which is the time delay between the filtered and unfiltered signal, may +become significant. For most applications filter orders of two or four are sufficiently accurate. +To define a Butterworth filter, you must specify the cutoff frequency, +, and the filter order, N. +Since the implementation of the filters is done using cascades of second-order sections, Abaqus expects +an even number for the filter order. If you specify an odd number for the order, the order will be increased +internally to the next even number. The default value for the order is two, and the highest order that can +be prescribed is twenty. For the Chebyshev filters you must also specify an additional parameter, the +ripple factor. The ripple factor is equal to for a Type I Chebyshev filter and is equal to +for a Type +II Chebyshev filter . + +⏐ +⏐ (magnitude gain) +Butterworth +Type I Chebyshev +Type II Chebyshev +passband +stopband +1+ε2 + c +transition band +(frequency) +Figure 4.1.3–5 Typical magnitude curves for low-pass filters. +No checks are performed to ensure that the cutoff frequency is appropriate; for example, Abaqus +does not check that only the noise of the signal is eliminated. You need to know the range of the physical +frequencies that are expected in the solution, and you must prescribe a cutoff frequency greater than these +frequencies. In addition, the cutoff frequency should be less than half the sampling frequency; otherwise, +no filtering is performed. Abaqus internally remaps (using a quadratic interpolation) the output raw data +so that the filtering can satisfy the constant time-increment (sampling) requirement. +You must assign each filter definition a name that can be used to refer to the filter from an output +request. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options to define a filter: +*FILTER, NAME=filter_name, TYPE=BUTTERWORTH +*FILTER, NAME=filter_name, TYPE=CHEBYS1 +*FILTER, NAME=filter_name, TYPE=CHEBYS2 +Step module: Tools→Filter→Create: Name: filter_name; Butterworth, +Type I Chebyshev, or Type II Chebyshev +Start-up conditions for the filter +By default, the values of the variables at time zero (zero increment) are used as the initial conditions (or +start-up conditions); however, you can change this initial value. +Input File Usage: +Use the following option to use the default initial conditions: +*FILTER, NAME=filter_name, TYPE=filter_type, START CONDITION=DC +Use the following option to specify the initial variable values: +*FILTER, NAME=filter_name, TYPE=filter_type, +START CONDITION=USER DEFINED +Abaqus/CAE Usage: +You cannot specify the initial variable values in Abaqus/CAE. +Filtering using the low-pass Infinite Impulse Response filters +To pre-filter element, nodal, contact, or integrated history output or element and nodal field output based +on one of the low-pass Infinite Impulse Response filters that you defined, you refer to this filter by name +from the output request. +Input File Usage: +Use the following option to apply a filter to an output request: +Abaqus/CAE Usage: +*OUTPUT, FILTER=filter_name +Step module: field or history output request editor: Apply filter: filter_name +Filtering the output based on the time interval +For history output you can request that Abaqus/Explicit create an anti-aliasing filter that is internally +based on the time interval specified in the output request. The cutoff frequency is set internally to one- +sixth of the time frequency (the time frequency is the inverse of the time interval, t, used for history +output). If no time intervals are specified, the default number of history output intervals is used to create +the cutoff frequency of the filter. You can also use anti-aliasing filters for a field output request, but +in this case the cutoff frequency is set to one-sixth of a time frequency corresponding to two hundred +time intervals per step if less than two hundred field frames are requested. If more than two hundred +field frames are requested, the cutoff frequency is set to one-sixth of the requested time frequency. The +anti-aliasing filter is a second-order Butterworth type and a filter definition is not required. +Abaqus/Explicit does not check whether the specified time interval for history output provides an +appropriate cutoff frequency to build the internal filter. You should know approximately how many data +points are required to describe your history curve (or signal) accurately, and Abaqus/Explicit will give +you the most physical (un-aliased) representation of the signal for that number of points. Similarly for +field output Abaqus/Explicit does not check whether the cutoff corresponding to two hundred sampling +intervals or more (if you request more than two hundred frames) is appropriate for your analysis. If a +lower (or higher) cutoff frequency is needed, you should define the filter in the model data. +Filtering field output or history output written at time intervals +You can apply a filter to a field output request or a history output request written at intervals of time in +your analysis. +Input File Usage: +Use one of the following options: +Abaqus/CAE Usage: +*OUTPUT, FIELD, FILTER=ANTIALIASING, TIME INTERVAL=t +*OUTPUT, HISTORY, FILTER=ANTIALIASING, TIME INTERVAL=t +Step module: field or history output request editor: Frequency: Every +x units of time: t, Apply filter: Antialiasing +Filtering field output written at evenly spaced intervals of time +Input File Usage: +You can apply a filter to a field output request written at evenly spaced time intervals in your analysis. +*OUTPUT, FIELD, FILTER=ANTIALIASING, NUMBER INTERVAL=n +Step module: field output request editor: Frequency: Evenly spaced +time intervals, Interval: n, Apply filter: Antialiasing +Abaqus/CAE Usage: +Requesting maximum, minimum, or absolute maximum values for an output request +You can apply a filter to a field output request or a history output request to obtain the maximum, +minimum, or absolute maximum values for each variable in the output request. The absolute maximum +option enables you to obtain the largest absolute value, negative or positive, for each variable in the output +request. Abaqus evaluates maximum, minimum, or absolute maximum values at every increment during +the analysis and reports these values at the time given by the output interval specified in the output request. +For field output requests the last output frame will contain the maximum (or absolute maximum) value +and minimum value over the entire step; the intermediate frames will show the maximum, minimum, or +absolute maximum value up to the frame time. An additional output variable containing the time when +the maximum, minimum, or absolute maximum occurred is output automatically for each output variable +requested. This time output is written by default (and it cannot be suppressed). +For field output requests Abaqus filters by default each component of tensor and vector quantities of +output variable independently and provides separate maximum, minimum, or absolute maximum values +for each component of the variable. You can, however, request the maximum or minimum value or apply +a limit value to an invariant such as Mises stress for element output or magnitude for nodal output . +Requesting maximum, minimum, or absolute maximum values for filtered output +You can define a low-pass digital filter that returns the maximum, minimum, or absolute maximum value +for output requests to which it is applied. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options: +*FILTER, TYPE=filter_type, OPERATOR=MAX +*FILTER, TYPE=filter_type, OPERATOR=MIN +*FILTER, TYPE=filter_type, OPERATOR=ABSMAX +Step module: Tools→Filter→Create: Butterworth, Type I Chebyshev, or +Type II Chebyshev: Determine bounding value: Maximum, Minimum, +or Absolute maximum +Requesting maximum, minimum, or absolute maximum values for unfiltered output +You can define a filter that returns the maximum, minimum, or absolute maximum value for output +requests to which it is applied without performing any digital filtering of the data. +Input File Usage: +Use one of the following options: +*FILTER, OPERATOR=MAX +Abaqus/CAE Usage: +*FILTER, OPERATOR=MIN +*FILTER, OPERATOR=ABSMAX +Step module: Tools→Filter→Create: Type: Operator: Determine +bounding value: Maximum, Minimum, or Absolute maximum +Setting an upper or lower limit on variables in an output request +You can apply a filter to a field output request or a history output request to prescribe a bounding value +for the variables in the output request. If any of the variables in the output request reach a value higher +than the maximum limit, lower than the minimum limit, or greater than the absolute maximum limit, +Abaqus returns the limiting value. The time at which the limit was reached is output separately for each +requested variable. This time output is written by default (and it cannot be suppressed). +Setting an upper limit or a lower limit for filtered output +You can define a low-pass digital filter that enforces an upper or lower bound for the variables in the +output requests to which it is applied. +Input File Usage: +Abaqus/CAE Usage: +*FILTER, TYPE=filter_type, OPERATOR=operator_type, LIMIT=value +Type: Butterworth, Type I +Step module: +Chebyshev, or Type II Chebyshev: Determine bounding value: +Maximum, Minimum, or Absolute maximum: toggle on Bounding value +limit: value +Tools→Filter→Create: +Setting an upper limit or a lower limit for unfiltered output +You can define a filter that enforces an upper or lower bound for the variables in the output requests to +which it is applied but that does not perform any Butterworth or Chebyshev filtering of the data. +Input File Usage: +Abaqus/CAE Usage: +*FILTER, OPERATOR=operator_type, LIMIT=value +Step module: Tools→Filter→Create: Type: Operator: Determine +bounding value: Maximum, Minimum, or Absolute maximum: toggle on +Bounding value limit: value +Stopping an analysis when an output variable reaches a prescribed limit +You can apply a filter to a field output request or a history output request that stops the analysis when the +value of any variable in the output request reaches a specified upper bound or lower bound. +Stopping an analysis of filtered output when a variable reaches a prescribed limit +You can define a low-pass digital filter that stops the analysis if any of the variables in the output requests +to which it is applied reach a prescribed limit. +Input File Usage: +*FILTER, TYPE=filter_type, OPERATOR=operator_type, +LIMIT=value, HALT +Abaqus/CAE Usage: +Step module: Tools→Filter→Create: Butterworth, Type I Chebyshev, or +Type II Chebyshev: Determine bounding value: Maximum, Minimum, +or Absolute maximum: toggle on Bounding value limit: value: toggle on +Stop analysis upon reaching limit +Stopping an analysis of unfiltered output when a variable reaches a prescribed limit +You can define a filter that does not perform any Butterworth or Chebyshev filtering of your output data +and stops the analysis if any of the variables in the output requests to which it is applied reach a prescribed +limit. +Input File Usage: +Abaqus/CAE Usage: +*FILTER, OPERATOR=operator_type, LIMIT=value, HALT +Step module: Tools→Filter→Create: Type: Operator: Determine +bounding value: Maximum, Minimum, or Absolute maximum: +toggle +on Bounding value limit: value: toggle on Stop analysis upon reaching +limit +Applying bounding values to invariants +By default, each component of a tensor or vector quantity is filtered individually and the maximum, +minimum, or absolute maximum value and the limiting values are reported separately for each +component. You can, however, apply a filter directly to an invariant. In this case Abaqus internally +monitors the invariant you specified. Abaqus still writes the components to the output database, +but these components correspond to the maximum, minimum, or limiting values of the invariant. +Table 4.1.3–2 shows which invariants are available for output variable categories. +Table 4.1.3–2 Invariants available for output variable categories. +Category +First invariant +Second invariant +All nodal vector +output +Magnitude +Stress element output +Mises +– +Press +Applying bounding values to invariants of filtered output +You can define a low-pass digital filter that filters the invariant. +Input File Usage: +*FILTER, TYPE=filter_type, OPERATOR=operator_type, LIMIT=value, +INVARIANT=FIRST or SECOND +Abaqus/CAE Usage: +Tools→Filter→Create: +Step module: +Chebyshev, or Type II Chebyshev; +value: Invariant: First or Second +Type: Butterworth, Type I +toggle on Bounding value limit: +Applying bounding values to invariants of unfiltered output +You can define a filter that does not perform any Butterworth or Chebyshev filtering of your output data +and filters the invariant. +Input File Usage: +*FILTER, OPERATOR=operator_type, LIMIT=value, INVARIANT= +FIRST or SECOND +Abaqus/CAE Usage: +Step module: +Tools→Filter→Create: +Bounding value limit: value: Invariant: First or Second +Type: Operator; +toggle on +Output variables available for filtering +Low-pass Infinite Impulse Response filters such as Butterworth and Chebyshev filters are intended +for filtering of output variables susceptible to noise, such as accelerations and reaction forces or, to a +lesser degree, stress and strain. However, digital filtering is allowed for most element and nodal output +variables, and you can apply bounding values on unfiltered data for nearly all element and nodal output +variables. Table 4.1.3–3 shows the set of output variables that cannot be digitally filtered but to which +you can apply bounding values, and Table 4.1.3–4 shows the set of output variables for which neither +digital filtering nor application of bounding values are allowed. +Table 4.1.3–3 Output variables to which bounding values can be +applied but digital filtering cannot be applied. +Category +Output variables +Tensors and invariants +PEEQ +State and field variables +TEMP, FV +Energy densities +ENER, SENER, PENER, CENER, VENER, DMENER +Additional plasticity quantities +PEQC +Cracking model quantities +CKSTAT +Whole element variables +EDT, EMSF, ELEDEN, ESEDEN, EPDDEN, ECDDEN, EVDDEN, +EASEDEN, EIHEDEN, EDMDDEN, ECDDEN, ELEN, ELSE, +ELCD, ELPD, ELVD, ELASE, ELIHE, ELDMD, ELDC, STATUS +Nodal output variables +NT, COORD +Table 4.1.3–4 Output variables that cannot be digitally filtered +or modified with bounding values. +Category +Output variables +Cracking model quantities +CRACK +Element face variables +STAGP, TRNOR, TRSHR +Whole element variables +GRAV, BF, SBF, P +Nodal output variables +CF +Modal output from Abaqus/Standard +You can output generalized coordinate (modal amplitude and phase) values during modal dynamic +procedures to the output database. Modal output is available +only as history output. +Controlling the frequency of output +The frequency of modal output is controlled as described above in “Controlling the output frequency in +Abaqus/Standard.” +Requesting output +You can choose to request all modal variables applicable to the current procedure and material type. In +this case any additional variables you specify are ignored. +Input File Usage: +Abaqus/CAE Usage: +*MODAL OUTPUT, VARIABLE=ALL +Step module: history output request editor: All +Surface output in Abaqus/Standard and Abaqus/Explicit +You can write variables associated with surfaces in contact, coupled thermal-electrical-structural +(Abaqus/Standard only), +coupled +thermal-electrical, and crack propagation problems to the output database. Multiple output requests can +be used to customize requests among interactions, surfaces, or node sets. +For surface variables associated with cavity radiation, +coupled temperature-displacement +see “Cavity radiation output +(Abaqus/Standard only), +in +Abaqus/Standard” below. +Use element output requests to obtain database output for contact elements +(such as gap elements; see “Gap contact elements,” Section 39.2.1). +In Abaqus/Standard contact history output cannot be saved in a linear perturbation step with +frequency extraction. +Displacement nodal output is generated automatically in Abaqus/Explicit when requesting surface +output. +Selecting the surface output variables +The surface variables that can be written to the output database are listed in the “Surface variables” +section of “Abaqus/Standard output variable identifiers,” Section 4.2.1, and “Abaqus/Explicit output +variable identifiers,” Section 4.2.2. +Input File Usage: +*CONTACT OUTPUT +list of output variables +Abaqus/CAE Usage: +Step module: field or history output request editor: Select from list below +Limiting the extent of a surface output request in Abaqus/Standard +Output requests apply to general contact and all contact pair interactions in a model by default in +Abaqus/Standard. Options to limit an output request to certain interactions are discussed below. +Limiting output to a node set in Abaqus/Standard +You can limit a surface output request to apply to a subset of surface nodes involved in contact pairs or +general contact in Abaqus/Standard. +Input File Usage: +Abaqus/CAE Usage: +*CONTACT OUTPUT, NSET=node_set_name +Step module: field or history output request editor: Domain: +Interaction: contact_interaction_name +Limiting output for contact pairs based on slave and master surface names in Abaqus/Standard +You can limit output to certain contact pairs based on surface names. If you specify both the slave and +master surface names, the output request is limited to a specific contact pair. If you specify the slave +surface but not the master surface, output is written for all contact pairs that involve the specified slave +surface. If you also specify a node set, the applicability of an output request is further limited (i.e., the +output request will generate output only for certain nodes of a certain contact pair (or pairs). Output +requests with a specific slave and/or master surface role specified will not generate output for general +contact. +Input File Usage: +*CONTACT OUTPUT, MASTER=master, SLAVE=slave, +NSET=node_set_name +Abaqus/CAE Usage: +Step module: field or history output request editor: Domain: +Interaction: contact_interaction_name +Limiting the extent of a surface field output request in Abaqus/Explicit +Field output requests apply to general contact and all contact pair interactions in a model by default +in Abaqus/Explicit. Options to limit a surface field output request to certain interactions are discussed +below. +Limiting surface field output to a contact pair set in Abaqus/Explicit +In Abaqus/Explicit you can select the contact pairs for which surface field output is desired. Surface +output is contact pair-specific, so that contact output for a particular surface involved in a selected contact +pair will include only the contributions from that contact pair if the surface is involved in multiple contact +pairs. Surface output is available only for discrete (node-based or element-based) surfaces; it is not +available for any analytical surfaces within a contact pair. +Input File Usage: +Use the following option to request surface field output for a particular contact +pair set: +*CONTACT OUTPUT, CPSET=contact_pair_set_name +Abaqus/CAE Usage: +Step module: field output request editor: Domain: Interaction: +contact_interaction_name +Limiting surface field output to general contact in Abaqus/Explicit +You can limit surface field output requests to apply only to general contact in Abaqus/Explicit, but you +cannot further limit this output to a subset of the general contact domain. +*CONTACT OUTPUT, GENERAL CONTACT +You cannot limit surface field output to general contact in Abaqus/CAE. +Abaqus/CAE Usage: +Input File Usage: +Limiting surface field output to a single surface in Abaqus/Explicit +You can limit surface field output requests to a single surface in the general contact domain in +Abaqus/Explicit. The contact output for the specified surface will include all the contributions from +other contact surfaces interacting with the surface. +Input File Usage: +Abaqus/CAE Usage: +*CONTACT OUTPUT, SURFACE=surface_name +You cannot limit a single surface output to general contact in Abaqus/CAE. +Limiting surface field output to pairwise surfaces in Abaqus/Explicit +You can specify a pair of surfaces in the general contact domain in Abaqus/Explicit for which the +interactions on one surface due to the contact with another surface will be output. This type of output +cannot be used for surfaces involving Eulerian regions. +Input File Usage: +*CONTACT OUTPUT, SURFACE=first_surface_name, +SECOND SURFACE=second_surface_name +Abaqus/CAE Usage: +You cannot limit pairwise surface output to general contact in Abaqus/CAE. +Specifying surface history output regions in Abaqus/Explicit +You must specify an interaction to which a surface history output request applies with one of the methods +discussed below. +Specifying surface history output by contact pair set in Abaqus/Explicit +In Abaqus/Explicit you can select the contact pairs for which surface history output is desired. Surface +output is contact pair-specific, so that contact output for a particular surface involved in a selected contact +pair will include only the contributions from that contact pair if the surface is involved in multiple contact +pairs. Surface output is available only for discrete (node-based or element-based) surfaces; it is not +available for any analytical surfaces within a contact pair. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to request surface history output for a particular +contact pair: +*CONTACT OUTPUT, CPSET=contact_pair_set_name +Step module: history output request editor: Domain: Interaction: +contact_interaction_name +Specifying whole surface history output in Abaqus/Explicit +You can specify a surface in the general contact domain for which whole surface contact force resultants +will be output. Whole surface contact force resultants for a surface in the general contact domain are +available only as history output. +Input File Usage: +Abaqus/CAE Usage: +*CONTACT OUTPUT, SURFACE=surface_name +Step module: history output request editor: Domain: General +contact surface: surface_name +Specifying pairwise surface history output in Abaqus/Explicit +You can specify a pair of surfaces in the general contact domain for which the resultant contact forces +on one surface due to the contact with another surface will be output. The contact force resultants in +this case consider only the contact interactions between the two specified surfaces. This type of output +cannot be requested for surfaces involving Eulerian regions. +Input File Usage: +*CONTACT OUTPUT, SURFACE=first_surface_name, +SECOND SURFACE=second_surface_name +Abaqus/CAE Usage: +You cannot request surface history output for a pair of surfaces in Abaqus/CAE. +Specifying surface history output by fastened node set in Abaqus/Explicit +You can select a fastened node set for which bond history output is desired: +Input File Usage: +Use the following option to request surface history output for a particular +fastened node set: +Abaqus/CAE Usage: +*CONTACT OUTPUT, NSET=node_set_name +You cannot request surface history output for a particular fastened node set in +Abaqus/CAE. +Controlling the output frequency +The frequency of surface output is controlled as described above in “Controlling the output frequency.” +Requesting preselected output +You can request the preselected, procedure-specific surface output variables described in Table 4.1.3–1. +In this case you can specify additional variables as part of the output request. +Alternatively, you can request all surface variables applicable to the current procedure. In this case +any additional variables you specify are ignored. +Input File Usage: +Use the following option to request the preselected surface output variables: +*CONTACT OUTPUT, VARIABLE=PRESELECT +Use the following option to request all applicable surface output variables: +*CONTACT OUTPUT, VARIABLE=ALL +Abaqus/CAE Usage: +Step module: field or history output request editor: +Preselected defaults or All +Surface output in Abaqus/CFD +You can write field and history output variables associated with surfaces in an Abaqus/CFD analysis to +the output database. +Selecting the surface output variables +The surface variables that can be written to the output database are listed in the “Surface variables” +section of “Abaqus/CFD output variable identifiers,” Section 4.2.3. +Input File Usage: +*SURFACE OUTPUT, SURFACE=surface_set_name +list of output variables +Abaqus/CAE Usage: +You cannot request surface output in Abaqus/CAE. +Controlling the output frequency +The frequency of surface output is controlled as described above in “Controlling the output frequency.” +Time incrementation output in Abaqus/Explicit +You can output incrementation variables for an Abaqus/Explicit analysis to the output database. +Incrementation output is available only as history output. +Selecting the incrementation output variables +The available incrementation output variables are the Abaqus/Explicit time increment size, DT; the +percent change in mass of the model due to mass scaling, DMASS; and the steady-state detection +variables SSPEEQ, SSSPRD, SSFORC, and SSTORQ. +Input File Usage: +*INCREMENTATION OUTPUT +list of output variables +Abaqus/CAE Usage: +Step module: history output request editor: Select from list below +Controlling the output frequency +The frequency of incrementation output is controlled as described above in “Controlling the output +frequency for history output in Abaqus/Explicit.” +Requesting preselected output +You can request the preselected, procedure-specific incrementation output variables. In this case you can +specify additional variables as part of the output request. +Alternatively, you can request all incrementation variables applicable to the current procedure type. +In this case any additional variables you specify are ignored. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to request the preselected incrementation output +variables: +*INCREMENTATION OUTPUT, VARIABLE=PRESELECT +Use the following option to request all applicable incrementation output +variables: +*INCREMENTATION OUTPUT, VARIABLE=ALL +Step module: history output request editor: Preselected defaults or All +Cavity radiation output in Abaqus/Standard +You can request that cavity-, element-, or surface-based output such as radiation fluxes, viewfactor totals +for a facet, and facet temperatures from an Abaqus/Standard analysis be written to the output database. +The output request can be repeated as often as necessary to define output for different variables, different +cavities, different element sets, different surfaces, etc. +Selecting the radiation output variables +The radiation output variables that can be written to the output database are listed in the “Cavity radiation +variables” section of “Abaqus/Standard output variable identifiers,” Section 4.2.1. +Input File Usage: +*RADIATION OUTPUT +list of output variables +Abaqus/CAE Usage: +Cavity radiation output requests are not supported in Abaqus/CAE. +Selecting the region of the model for which radiation output is required +You can specify the cavity, element set, or surface for which radiation output is required. Each radiation +output request can apply to only one type of region. If you do not specify a region of the model, radiation +variables are output for all the cavities in the model. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options: +*RADIATION OUTPUT, CAVITY=cavity_name +*RADIATION OUTPUT, ELSET=element_set_name +*RADIATION OUTPUT, SURFACE=surface_name +Cavity radiation output requests are not supported in Abaqus/CAE. +Controlling the output frequency +The frequency of radiation output is controlled as described above in “Controlling the output frequency.” +Requesting output +You can request all radiation variables applicable to the current procedure. In this case any additional +variables you specify are ignored. +Input File Usage: +Abaqus/CAE Usage: +*RADIATION OUTPUT, VARIABLE=ALL +Cavity radiation output requests are not supported in Abaqus/CAE. +Examples +The examples that follow illustrate how to request multiple types of output over multiple steps in both +Abaqus/Standard and Abaqus/Explicit. +Abaqus/Standard example +The input listing below will produce both field and history output for Step 1. Field output will be written +every 2 increments. This field output request consists of preselected element variables for the whole +model, as well as the variable PEQC. In addition, plastic strains will be written out for element set +SMALL, and the nodal variables U and RF will be written to the output database for node set NSMALL. +History output will be written every increment. The variables ALLKE, ALLSE, and ALLWK will be +written for the whole model. In addition, ALLPD will be written for element set SMALL. +In Step 2 the history output request defined in Step 1 is replaced by a request for the energy variables +ALLKE, ALLPD, and ALLSE for element set SMALL. The history output request defined in Step 1 is +removed. The field output request defined in Step 1 is passed into Step 2 unchanged, but another field +output request for element energies at every increment is added. +*STEP +*STATIC +... +... +*OUTPUT, FIELD, FREQUENCY=2 +*ELEMENT OUTPUT, VARIABLE=PRESELECT +PEQC, +*ELEMENT OUTPUT, ELSET=SMALL +PE, +*NODE OUTPUT, NSET=NSMALL +U, RF +*OUTPUT, HISTORY, FREQUENCY=1 +*ENERGY OUTPUT +ALLKE, ALLSE, ALLWK +*ENERGY OUTPUT, ELSET=SMALL +ALLPD +*END STEP +*STEP +*STATIC +... +... +*OUTPUT, HISTORY, OP=REPLACE, FREQUENCY=1 +*ENERGY OUTPUT, ELSET=SMALL +ALLKE, ALLPD, ALLSE +*OUTPUT, FIELD, OP=ADD, FREQUENCY=1 +*ELEMENT OUTPUT +ELEN +*END STEP +Abaqus/Explicit example +The input listing below will produce both field and history output for Step 1. Field output will be written +at 5 equally spaced intervals, and the time marks will be hit exactly. This field output request consists +of preselected element variables for the whole model, as well as the variable PEQC. In addition, plastic +strains will be written out for element set SMALL, and the nodal variables U and RF will be written to +the output database for node set NSMALL. History output will be written at a time interval of 0.005. +The Abaqus/Explicit time step, DT, will be written, along with the variables ALLKE, ALLSE, and +ALLWK for the whole model. The output variables SOAREA and SOF integrated over the surface +CROSS_SECTION1 will be written. The preselected variables SOF and SOM integrated over the surface +CROSS_SECTION2 defined by the integrated output section SECTION1 will be written in the local +coordinate system LOCALSYSTEM. In addition, ALLPD will be written for element set SMALL. +In Step 2 the history output request defined in Step 1 is replaced by a request for the energy variables +ALLKE, ALLPD, and ALLSE for element set SMALL. The history output request defined in Step 1 is +removed. The field output request defined in Step 1 is passed into Step 2 unchanged, but another field +output request for element energies at 10 equally spaced intervals is added. +*STEP +*DYNAMIC, EXPLICIT,.1... +... +*OUTPUT, FIELD, NUMBER INTERVAL=5, TIME MARKS=YES +*ELEMENT OUTPUT, VARIABLE=PRESELECT +PEQC, +*ELEMENT OUTPUT, ELSET=SMALL +PE, +*NODE OUTPUT, NSET=NSMALL +U, RF +*OUTPUT, HISTORY, TIME INTERVAL=0.005 +*INCREMENTATION OUTPUT +DT +*ENERGY OUTPUT +ALLKE, ALLSE, ALLWK +*ENERGY OUTPUT, ELSET=SMALL +ALLPD +*INTEGRATED OUTPUT, SURFACE=CROSS_SECTION1 +SOF, SOAREA +*INTEGRATED OUTPUT SECTION, NAME=SECTION1, +SURFACE=CROSS_SECTION2, ORIENTATION=LOCALSYSTEM +*INTEGRATED OUTPUT, SECTION=SECTION1, VARIABLE=PRESELECT +*END STEP +*STEP +*DYNAMIC, EXPLICIT,.1... +... +*OUTPUT, HISTORY, OP=REPLACE, TIME INTERVAL=0.005 +*ENERGY OUTPUT, ELSET=SMALL +ALLKE, ALLPD, ALLSE +*OUTPUT, FIELD, OP=ADD, NUMBER INTERVAL=10 +*ELEMENT OUTPUT +ELEN +*END STEP +4.1.4 +ERROR INDICATOR OUTPUT +Products: Abaqus/Standard Abaqus/CAE +WARNING: Error indicator output variables are approximate and do not represent +an accurate or conservative estimate of your solution error. The quality of an error +indicator can be particularly poor if your mesh is coarse. The error indicator +quality improves as you refine the mesh; however, you should never interpret these +variables as indicating what the value of a solution variable would be upon further +refinement of the mesh. +References +• “Abaqus/Standard output variable identifiers,” Section 4.2.1 +• “Adaptive remeshing: overview,” Section 12.3.1 +• “Selection of error indicators influencing adaptive remeshing,” Section 12.3.2 +• *CONTACT OUTPUT +• *ELEMENT OUTPUT +Overview +Error indicator output variables: +• indicate discretization error in a solution quantity (the base solution) and have units of the base +solution; +• can be requested with element output or contact output options or as part of an adaptive remeshing +rule; +• can be normalized by forms of the base solution to obtain nondimensional, such as percentage, +indicators of error; +• can increase your analysis solution time significantly in some cases; and +• are available in Abaqus/Standard but not Abaqus/Explicit. +Solution accuracy +The ability of a finite element analysis to make useful predictions of physical behavior depends on many +factors, including: +• representation of geometry, material behavior, load history, and various other modeling aspects +associated with describing the problem posed; +• spatial and temporal discretization (mesh refinement and incrementation); and +• convergence tolerances. +The primary focus of this section is spacial discretization error. Discussion to help understand and +control other potential sources of error appears in “Convergence criteria for nonlinear problems,” +Section 7.2.3, “Time integration accuracy in transient problems,” Section 7.2.4, “Evaluating hyperelastic +and viscoelastic material behavior,” Section 12.4.7 of the Abaqus/CAE User’s Manual, and other +portions of the Abaqus documentation. You should perform a detailed study of your analysis methods +and assumptions as part of any error assessment. +Spatial discretization error +The finite element discretization of a model domain results in an approximation to the exact solution for +all but trivial analyses. To aid you in understanding the extent and spatial distribution of the discretization +error in a finite element solution, Abaqus/Standard provides a set of error indicator output variables. +Ideally, error indicator output variables should be supplemented by other techniques, such as a mesh +refinement study, to gain confidence that discretization error is not significantly degrading the ability +of the finite element analysis to make useful predictions. In fact, error indicators can help automate a +mesh refinement study through the adaptive remeshing functionality of Abaqus/CAE; error indicators +variables are used by this functionality to determine where to refine or coarsen a mesh . +Error indicator and base solution variables available in Abaqus/Standard +Abaqus error indicator variables provide a measure of the local error resulting from mesh discretization. +Each error indicator, +. For +example, the Mises stress error indicator, MISESERI, provides an indicator of error in the Mises stress +variable MISESAVG. Table 4.1.4–1 shows the available error indicator variables and the corresponding +base solution variables. +, provides an indication of error in a particular base solution variable, +Table 4.1.4–1 Error indicator variables and their corresponding base solution variables. +Solution Quantity +Error indicator +Element energy density +Mises stress +Contact pressure +Contact shear stress +Equivalent plastic strain +Plastic strain +Creep strain +Heat flux +Electric flux +Electric potential gradient +variable ( +) +ENDENERI +MISESERI +CPRESSERI +CSHEARERI +PEEQERI +PEERI +CEERI +HFLERI +EFLERI +EPGERI +4.1.4–2 +Base solution +variable ( +) +ENDEN +MISESAVG +CPRESS +CSHEAR +PEEQAVG +PEAVG +CEAVG +HFLAVG +EFLAVG +The algorithms used by Abaqus/CAE to modify mesh seed sizes for the adaptive remeshing +capability consider error indicator values and corresponding base solution values together. When you +create a remeshing rule and request a particular error indicator, Abaqus automatically writes the error +indicator and corresponding base solution variable to the output database. +Input File Usage: +Abaqus/CAE Usage: +*OUTPUT, FIELD, ELSET=ElsetName +*ELEMENT OUTPUT +*CONTACT OUTPUT +Step module: Output→Field Output Request +Or, if you use the following option to specify an adaptive remeshing rule, the +associated error indicator and base solution output will occur by default: +Mesh module: Create Remeshing Rule: Step and Indicator +Effect of error indicator output requests on solution time +Abaqus/Standard determines error indicator variables based on the difference between a smoothed and +unsmoothed distribution of the base solution, using a smoothing technique such as the patch recovery +technique of Zienkiewicz and Zhu, (1987). The smoothing calculations occasionally noticeably increase +analysis time. If you find that adding an error indicator output request significantly increases analysis +time, strategies for reducing this effect include reducing the output frequency and limiting the output +request to a particular region of interest. Computations for most error indicator variables only occur +just prior to writing the error indicator variable to the output database, so reducing the output frequency +will tend to reduce the computation time; however this is not the case for the element energy density +error indicator, because contributions to this error indicator are accumulated each increment regardless +of whether this error indicator is output for a given increment. +Additional considerations for extent of output requests for element error indicator variables +When you request element error indicator output, the request should only apply to elements supported +for error indicator output. +The patch recovery technique used to compute element error indicator variables assumes that the +solution should be continuous over the element set specified. Abaqus/Standard confirms that your error +indicator output specification is consistent with this assumption by checking section property references +within the error indicator domain and issues a warning message if the elements in the provided element +set refer to distinct section definitions. You can safely ignore this warning if the sections are identical in +their properties. +Interpreting error indicator output +When interpreting error indicator output, you should remember that the error indicators are approximate +measures of the local error in the base solution and are, themselves, subject to discretization error. The +accuracy of the error estimates tends to improve as the mesh is refined. Each error indicator variable +has the same units has the corresponding base solution variable, which facilitates comparison of local +estimates of the error magnitude with local estimates of the base solution. +Regions of interest of a base solution and corresponding error indicator +Viewing contour plots of a base solution variable and corresponding error indicator variable side-by-side +can provide a useful perspective on the solution accuracy. For example, if the base solution is expressed +in units of stress, the corresponding error indicator is also expressed in units of stress. Figure 4.1.4–1 +shows contour plots of CPRESS and CPRESSERI for an analysis of a sphere pressed into a rigid plate. +These plots can be interpreted as follows: +• The contact pressure solution is quite accurate near the center of the active contact region, where +the contact pressure is largest, because the error indicator is a small fraction of the base solution in +that region. +• The contact pressure solution is less accurate near the perimeter of the active contact region, where +local variations in the contact pressure solution are largest (but the contact pressure is significantly +less than the maximum value), because the error indicator is quite large compared to the base +solution in that region. +The analyst may judge that the level of mesh refinement is adequate if the maximum contact pressure +is of primary interest in such a case. Local mesh refinement would be needed to accurately predict +the maximum contact pressure if the active contact region was significantly smaller than that shown in +Figure 4.1.4–1. +CPRESS +CPRESSERI ++6.1e+04 ++5.4e+04 ++4.8e+04 ++4.2e+04 ++3.6e+04 ++3.0e+04 ++2.4e+04 ++1.8e+04 ++1.2e+04 ++6.1e+03 ++0.0e+00 ++1.6e+04 ++1.4e+04 ++1.3e+04 ++1.1e+04 ++9.7e+03 ++8.0e+03 ++6.4e+03 ++4.8e+03 ++3.2e+03 ++1.6e+03 ++0.0e+00 +Figure 4.1.4–1 Contour plots of CPRESS and CPRESSERI for +contact between a deformable sphere and a rigid plate. +An error indicator tends to give a crude, non-conservative approximation of the deviation from +the exact solution if the mesh is coarse relative to local solution variations or the exact solution to the +problem posed involves a stress singularity. The following qualitative interpretations of error indicator +results exceeding approximately 10% of base solution results are often appropriate: +• “Significant potential for solution inaccuracy exists in this region.” +• “The mesh may be too coarse to give a good estimate of solution error in this region.” +• “Perhaps a stress singularity exists at this corner.” +Calculating normalized measures of solution error +You can use corresponding error indicator and base solution variables, +a field of local, normalized error indicators: +and +, respectively, to compute +where +is a normalized error measure. For example, +provides a percentage form of the Mises stress-based error indicator; however this normalized error +measure may not be particularly useful, because it: +• will tend to draw attention to regions where base solution values are small, which typically are not +critical regions of a design; and +• will have divide-by-zero issues where the base solution value is zero. +Other normalization approaches, such as normalizing based on a global norm of the base solution variable +or a constant value that you choose (such as the maximum value of the base solution allowed in a design), +may be more effective. +Normalized forms of an error indicator are not available directly through the error indicator +output variables; however, you can calculate normalized measures using the Visualization module of +Abaqus/CAE (Abaqus/Viewer) to operate on field output data. For more information, see “Building +valid field output expressions,” Section 42.7.1 of the Abaqus/CAE User’s Manual. Alternatively, you +can use the Abaqus Scripting Interface to read the error indicator and the base solution from the output +database and calculate normalized forms. For more information, see Chapter 9, “Using the Abaqus +Scripting Interface to access an output database,” of the Abaqus Scripting User’s Manual. +Limitations +Only the following element types are supported for error indicator computations: +• Planar continuum triangles and quadrilaterals +• Shell triangles and quadrilaterals +• Tetrahedrals +• Hexahedrals +Elements with variable nodes are not supported. +Additional reference +• Zienkiewicz, O. C., and J. Z. Zhu, “A Simple Error Estimator and Adaptive Procedure for +Practical Engineering Analysis,” International Journal for Numerical Methods in Engineering, +vol. 24, pp. 337–357, 1987. +4.2 +Output variables +• “Abaqus/Standard output variable identifiers,” Section 4.2.1 +• “Abaqus/Explicit output variable identifiers,” Section 4.2.2 +• “Abaqus/CFD output variable identifiers,” Section 4.2.3 +4.2.1 +Abaqus/Standard OUTPUT VARIABLE IDENTIFIERS +Product: Abaqus/Standard +References +• “Output,” Section 4.1.1 +• “Output to the data and results files,” Section 4.1.2 +• “Output to the output database,” Section 4.1.3 +Overview +The tables in this section list all of the output variables that are available in Abaqus/Standard. These +output variables can be requested for output to the data (.dat) and results (.fil) files or as either field- or history-type output to the output database +(.odb) file . As noted specifically in the tables, a +few of the output variables are written only to the output database and restart (.res) files (they are not +available for output to the data or results files). These variables can be accessed only in the Visualization +module of Abaqus/CAE (Abaqus/Viewer). Each table contains one variable type: +• Element integration point variables +• Element centroidal variables +• Element section variables +• Whole element variables +• Whole element energy density variables +• Nodal variables +• Modal variables +• Surface variables +• Cavity radiation variables +• Section variables +• Whole and partial model variables +• Solution-dependent amplitude variables +• Structural optimization variables +Symbols used in the tables +The availability of the various output variable identifiers is defined by a +under the following headings: +in the columns of the table, +.dat +means that the identifier can be used as a data file output selection. +.fil +means that the identifier can be used as a results file output selection. +.odb Field +means that the identifier can be used as a field-type output selection to the output database. +.odb History +means that the identifier can be used as a history-type output selection to the output database. +The appearance of a +in the .dat, .fil, or .odb columns indicates that the variable cannot be requested +by name but that it will be written to the data, results, or output database file according to the conditions +specified in the table for that particular variable type. +Requesting output of components +Variable identifiers of the form ABCn can be used with +highest value of n is determined by the type of variable. Similarly, variable identifiers of the form DEF +can be used for the ranges of i and j indicated (DEF11, DEF12, +(ABC1, ABC2, …), where the +). +Individual components cannot be requested in the results (.fil) file. For postprocessing of a +particular component of a variable, request file output for all components of the variable. Output for +individual variables can be requested during postprocessing. +Individual components of variables can be requested as history-type output in the output database +for X–Y plotting in Abaqus/CAE. Individual component requests to the output database are not available +for field-type output, with the exception of state, field, and user-defined variables (SDVn, FVn, and +UVARMn). If a particular component is desired for contouring in Abaqus/CAE, request field output of +the generic variable (e.g., S for stress). Output for individual components of field output can be requested +within the Visualization module of Abaqus/CAE. +Direction definitions +The direction definitions depend on the variable type. +Direction definitions for element variables +For components of stress, strain, and other tensor quantities 1, 2, and 3 refer to the directions in +an orthogonal coordinate system. These directions are global directions for solid elements, surface +directions for shell and membrane elements, and axial and transverse directions for beam elements. For +finite-membrane-strain shell elements, membrane elements, and continuum elements associated with a +local orientation , the local output directions rotate with the average +rotation of the element (integral with respect to time of the spin—see “Stress rates,” Section 1.5.3 of the +Abaqus Theory Manual). Tensor components in these cases are output in the rotating local directions. +In some cases the local output directions may differ from one integration point to the next within an +element. Abaqus/Standard does not take this variation into account when extrapolating output variables +to the nodes, which affects output such as element quantities averaged at the nodes or contour plots of +individual tensor components. Invariant quantities at the integration points will not be influenced by the +local output directions. +You can control writing the local directions to the output database file or to the results file . By default, the local directions are written to the output database for +all frames that include element field output. The local (material) directions (averaged at the nodes) can +be visualized in Abaqus/CAE by selecting Plot→Material Orientations in the Visualization module. +The directions can be printed to the data file by using user subroutine UVARM. +Direction definitions for equivalent rigid body variables +For all equivalent rigid body variables 1, 2, and 3 refer to global directions. +Direction definitions for nodal variables +For nodal variables 1, 2, and 3 are global directions (1=X, 2=Y, and 3=Z; or for axisymmetric elements, +1=r and 2=z). If a local coordinate system is defined at a node , you can specify whether output to the data or results file of vector-valued quantities at +these nodes is in the local or global system . By default, nodal output is written to the data file in the +local system, whereas it is written to the results file in the global system (since this is more convenient +for postprocessing). +If nodal field output is requested for a node that has a local coordinate system defined, a quaternion +representing the rotation from the global directions is written to the output database. Abaqus/CAE +automatically uses this quaternion to transform the nodal results into the local directions. Nodal history +data written to the output database are always stored in the global directions. +Direction definitions for integrated variables +For components of total force, total moment, and similar variables obtained through integration over a +surface, the directions 1, 2, and 3 refer to directions in an orthogonal coordinate system. A fixed global +coordinate system is used if the surface is specified directly for the integrated output request. If the +surface is identified by an integrated output section definition that is associated with the integrated output request, a local coordinate system in the initial +configuration can be specified and can translate or rotate with the deformation. +Distributed load output +You need to be aware of limitations that may be encountered when distributed load output is requested. +Distributed load output and user subroutines +Output can be requested for many of the distributed loads discussed in “Loads,” Section 33.4. However, +contributions to these loads defined through user subroutines (see “Abaqus/Standard subroutines,” +Section 1.1 of the Abaqus User Subroutines Reference Manual) are not displayed, except for the +variables FILMCOEF and SINKTEMP. +Distributed load output with modal procedures +For modal procedures only the magnitude of the load is written to the output database. +Strain output +The total strain E is composed of the elastic strain EE, the inelastic strain IE, and the thermal strain THE. +The inelastic strain IE consists of the plastic strain PE and the creep strain CE. +For geometrically nonlinear analysis Abaqus/Standard makes it possible to output different strain +measures as well as elastic and various inelastic strains. The various total strain measures (integrated +strain measure E, nominal strain measure NE, and logarithmic strain measure LE) are described in +“Conventions,” Section 1.2.2. The default strain measure for output to the data (.dat) and results +(.fil) files is E. However, for geometrically nonlinear analysis using element formulations that +support finite strains, E is not available for output to the output database (.odb) file, and LE is the +default strain measure. +Temperature output +In Abaqus temperature can either be a field variable (stress analysis, mass diffusion, …) or a degree of +freedom (heat transfer analysis, fully coupled temperature-displacement analysis, …). For any analysis +that involves temperature, you can request the temperature either at nodes (variable NT) or in elements +(variable TEMP). If element temperature output is requested at the nodes, the integration point values +are extrapolated and, if requested, averaged. These extrapolated values are generally not as accurate +as the nodal temperatures themselves. An exception to this is adiabatic analysis, in which the element +temperatures change due to plastic heat generation but the nodal temperatures are not updated. In that +case the current nodal temperatures are obtained only if element temperature output is requested at the +nodes. +For continuum elements there is only one temperature value per node (NT11). For shells and beams +more than one temperature is available for each node (NT11, NT12, …) since a temperature gradient +can exist through the thickness of a shell or across the cross-section of a beam. In general, variables +NT12, NT13, etc. contain temperature values. However, when temperature is defined by specifying +temperature gradients, nodal temperatures for a given section point can be obtained only by using the +variable TEMP. See “Specifying temperature and field variables” in “Using a beam section integrated +during the analysis to define the section behavior,” Section 29.3.6, and “Specifying temperature and +field variables” in “Using a shell section integrated during the analysis to define the section behavior,” +Section 29.6.5, for discussions on specifying temperatures in beams and shells. +Principal value output +Output of the principal values can be requested for stresses, strains, and other material tensors. Either +all principal values or the minimum, maximum, or intermediate values can be obtained. All principal +values of tensor ABC are obtained with the request ABCP. The minimum, intermediate, and maximum +principal values are obtained with the requests ABCP1, ABCP2, and ABCP3. +For three-dimensional, (generalized) plane strain, and axisymmetric elements all three principal +values are obtained. For plane stress, membrane, and shell elements, the out-of-plane principal value +cannot be requested for history-type output. For field-type output, Abaqus/CAE always reports the out- +of-plane principal value as zero. Principal values cannot be obtained for truss elements or for any beam +elements other than the three-dimensional beam elements with torsional shear stresses. +If a principal value or an invariant is requested for field-type output, the output request is replaced +with an output request for the components of the corresponding tensor. Abaqus/CAE calculates all +principal values and invariants from these components. If a principal value is desired as history-type +output, it must be explicitly requested since Abaqus/CAE does no calculations on history data. +Tensor output +Tensor variables that are written to the output database as field-type output are written as components +in either the default directions defined by the convention given in “Orientations,” Section 2.2.5 (global +directions for solid elements, surface directions for shell and membrane elements, and axial and +transverse directions for beam elements), or the user-defined local system. Abaqus/CAE calculates all +principal values and invariants from these components. See “Writing field output data,” Section 9.6.4 +of the Abaqus Scripting User’s Manual, for a description of the different types of tensor variables. +For plane stress, membrane, and shell elements, only the in-plane tensor components (11, 22, and +12 components) are stored by Abaqus/Standard. The out-of-plane direct component for stress (S33) is +reported as zero to the output database as expected, and the out-of-plane component of strain (E33) is +reported as zero even though it is not. This is because the thickness direction is computed based on +section properties rather than at the material level. The out-of-plane components can be requested for +field-type output and cannot be requested for history-type output. The out-of-plane stress components +are not reported to the data (.dat) file or to the results (.fil) file. +For three-dimensional beam elements with torsional shear stresses, only the axial and the torsional +components (the 11 and 12 components) are stored by Abaqus/Standard. The other direct component +(the 22 component) is reported as zero for field-type output and cannot be requested for history-type +output. +The components for tensor variables are written to the output database in single precision. +Therefore, a small amount of precision roundoff error may occur when calculating the variables’ +principal values. Such roundoff error may be observed, for example, when analytically zero values are +calculated as relatively small nonzero values. +Element integration point variables +You can request element integration point variable output to the data, results, or output database file . +Identifier +.dat +.fil +.odb +Field History +Description +Tensors and associated principal values and invariants +• +• +All stress components. +• +• +• +• +• +• +Sij +SP +SPn +SINV +MISES +MISESMAX +MISESONLY +• +• +• +• +• +• +• +• +• +• +-component of stress ( +). +All principal stresses. +Minimum, +stresses (SP1 +SP2 +SP3). +intermediate, and maximum principal +• +• +All stress invariant components (MISES, TRESC, +PRESS, INV3). For field output SINV is converted to +a request for the generic variable S. +Mises equivalent stress, defined as +where +is the deviatoric stress tensor, defined as +where +is the stress, p is the equivalent +pressure stress (defined below), and is a unit matrix. +In index notation +where +Kronecker delta. +, +, and +is the +Maximum Mises stress among all of the section +points. For a shell element it represents the maximum +Mises value among all the section points in the layer, +for a beam element it is the maximum Mises stress +among all the section points in the cross-section, and +for a solid element it represents the Mises stress at the +integration points. +Mises equivalent stress. When MISESONLY is used +the stress components are not +instead of MISES, +written to the output database; consequently, the size +of the database is reduced. +Identifier +.dat +.fil +.odb +Field History +Description +Tresca equivalent stress, defined as the maximum +difference between principal stresses. +Equivalent pressure stress, defined as +Equivalent pressure stress. When PRESSONLY is +used instead of PRESS, the stress components are not +written to the output database; consequently, the size +of the database is reduced. +Third stress invariant, defined as +where +of Mises equivalent stress, above. +is the deviatoric stress defined in the context +Stress triaxiality, +All total kinematic hardening shift tensor components. +. +-component of the total shift tensor ( +). +All +( +kinematic hardening shift tensor components +). +kinematic hardening shift +-component of the +and +). +tensor ( +All tensor components of all the kinematic hardening +shift tensors, except the total shift tensor, ALPHA. +All principal values of the total shift tensor. +Minimum, +values of +ALPHAP2 ALPHAP3). +All strain components. For geometrically nonlinear +analysis using element formulations that support finite +strains, E is not available for output to the output +database (.odb) file. +intermediate, and maximum principal +tensor +the total +(ALPHAP1 +shift +-component of strain ( +). +All principal strains. +Minimum, +strains (EP1 +All nominal strain components. +EP3). +EP2 +intermediate, and maximum principal +-component of nominal strain ( +). +4.2.1–7 +TRESC +PRESS +PRESSONLY +INV3 +TRIAX +ALPHA +ALPHAij +ALPHAk +ALPHAk_ij +ALPHAN +ALPHAP +ALPHAPn +Eij +EP +EPn +NE +NEij +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Identifier +.dat +.fil +.odb +Field History +Description +intermediate, and maximum principal +All principal nominal strains. +Minimum, +nominal strains (NEP1 NEP2 NEP3). +All logarithmic strain components. For geometrically +nonlinear analysis using element formulations that +support finite strains, LE is the default strain measure +for output to the output database (.odb) file. +-component of logarithmic strain ( +). +All principal logarithmic strains. +Minimum, +logarithmic strains (LEP1 +All mechanical strain rate components. +LEP2 +LEP3). +intermediate, and maximum principal +-component of strain rate ( +). +ERP2 +ERP3). +intermediate, and maximum principal +All principal mechanical strain rates. +Minimum, +mechanical strain rates (ERP1 +All components of the total deformation gradient. +hyperfoam, +Available +and material models defined in user subroutine +UMAT. For fully integrated first-order quadrilaterals +and hexahedra, +the selectively reduced integration +technique is used. A modified deformation gradient is +output for these elements. +hyperelasticity, +only +for +-component of the total deformation gradient ( +). +Principal stretches. +Minimum, +principal stretches (DGP1 DGP2 DGP3). +All elastic strain components. +intermediate, and maximum values of +-component of elastic strain ( +). +All principal elastic strains. +Minimum, +elastic strains (EEP1 +All inelastic strain components. +EEP2 +EEP3). +intermediate, and maximum principal +-component of inelastic strain ( +). +All principal inelastic strains. +4.2.1–8 +NEP +NEPn +LE +LEij +LEP +LEPn +ER +ERij +ERP +ERPn +DG +DGij +DGP +DGPn +EE +EEij +EEP +EEPn +IE +IEij +IEP +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Identifier +.dat +.fil +.odb +Field History +Description +Minimum, +inelastic strains (IEP1 +IEP2 +IEP3). +intermediate, and maximum principal +All thermal strain components. +-component of thermal strain ( +). +All principal thermal strains. +Minimum, +thermal strains (THEP1 +intermediate, and maximum principal +THEP2 +THEP3). +All plastic strain components. This identifier also +provides PEEQ, a yes/no flag telling if the material +is currently yielding or not (AC YIELD: “actively +yielding”; that is, the plastic strain changed during the +increment), and PEMAG when PE is requested for the +data or results files. When PE is requested for field +output to the output database, PEEQ is also provided. +-component of plastic strain ( +). +Equivalent plastic strain. This identifier also provides +a yes/no flag (1/0 on the output database) telling if +the material is currently yielding or not (AC YIELD: +“actively yielding”; that is, the plastic strain changed +during the increment). +The equivalent plastic strain is defined as +, where +is the initial equivalent plastic +strain. +The definition of +model. +For classical metal +depends on the material +(Mises) plasticity +. For other plasticity models, +see the appropriate section in Part V, “Materials.” +When plasticity occurs in the thickness direction to a +gasket element whose plastic behavior is specified as +part of a gasket behavior definition, PEEQ is PE11. +Maximum equivalent plastic strain, PEEQ, among all +of the section points. For a shell element it represents +the maximumPEEQ value among all the section points +in the layer, for a beam element it is the maximum +PEEQ among all the section points in the cross-section, +4.2.1–9 +• +• +• +• +• +• +• +• +• +• +• +• +• +IEPn +THE +THEij +THEP +THEPn +PE +PEij +PEEQ +• +• +• +• +• +• +• +• +• +• +• +Identifier +.dat +.fil +.odb +Field History +Description +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +and for a solid element it represents thePEEQ at the +integration points. +Equivalent plastic strain in uniaxial tension for cast +iron, Mohr-Coulomb tension cutoff, and concrete +damaged plasticity, which is defined as +. This +identifier also provides a yes/no flag (1/0 on the output +database) telling if the material is currently yielding +or not (AC YIELDT: “actively yielding”; that is, the +plastic strain changed during the increment). +Plastic strain magnitude, defined as +. +For most materials, PEEQ and PEMAG are equal only +for proportional loading. When plasticity occurs in the +thickness direction to a gasket element whose plastic +behavior is specified as part of a gasket behavior +definition, PEMAG is PE11. +All principal plastic strains. +Minimum, +plastic strains (PEP1 +PEP2 +PEP3). +intermediate, and maximum principal +All creep strain components. This identifier also +provides CEEQ, CESW, and CEMAG when CE is +requested for the data or results files. +-component of creep strain ( +Equivalent creep strain, defined as +). +. +The definition of +depends on the material model. +For classical metal (Mises) creep +. +For other creep models, see the appropriate section in +Part V, “Materials.” +When creep occurs in the thickness direction to a +gasket element whose creep behavior is specified as +part of a gasket behavior definition, CEEQ is CE11. +• +• +Magnitude of swelling strain. +For cap creep CESW gives the equivalent creep strain +produced by the consolidation creep mechanism, +is the equivalent creep +defined as +pressure, +, where +4.2.1–10 +PEEQT +PEMAG +PEP +PEPn +CE +CEij +CEEQ +CESW +• +• +• +• +• +• +• +Identifier +.dat +.fil +.odb +Field History +Description +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Magnitude of creep strain (defined by the same +formula given above for PEMAG, applied to the creep +strains). +All principal creep strains. +Minimum, +creep strains (CEP1 CEP2 CEP3). +intermediate, and maximum principal +for +contact pressure +Average +link and three- +dimensional line gasket elements. Available only +if the gasket contact area is specified; see “Defining +the contact area for average contact pressure output” +in “Defining the gasket behavior directly using a +gasket behavior model,” Section 32.6.6. +All transverse shear stress components. Available only +for thick shell elements such as S3R, S4R, S8R, and +S8RT. Contouring of this variable is supported in the +Visualization module of Abaqus/CAE. +-component of transverse shear stress ( +). +Available only for thick shell elements such as S3R, +S4R, S8R, and S8RT. +stress components +stacked +for +Transverse shear +Available only for +continuum shell elements. +SC6R and SC8R elements. +Contouring of this +variable is supported in the Visualization module of +Abaqus/CAE. +-component of transverse shear stress ( +Available only for SC6R and SC8R elements. +). +All substresses. Available only for ITS elements. +nth substress ( +elements. +). Available only for ITS +Vibration intensity. Available only for the steady-state +dynamics procedure. +real-only steady-state +For +dynamics analyses, the intensity is a pure imaginary +vector, but it is stored as real on the output database. +4.2.1–11 +CEMAG +CEP +CEPn +• +• +• +• +Additional element stresses +• +CS11 +• +TSHR +TSHRi3 +CTSHR +CTSHRi3 +SS +SSn +• +• +• +• +• +• +• +• +Vibration and acoustic quantities +Identifier +.dat +.fil +.odb +Field History +Description +Available for structural, solid, and acoustic elements +and for rebar. +Acoustic particle velocity. Available only if the +steady-state dynamic procedure is used, and available +only for acoustic finite elements. +Component n of the acoustic particle velocity vector (n += 1, 2, 3). Available only if the steady-state dynamic +procedure is used, and available only for acoustic finite +elements. +Acoustic pressure gradient. Available only if the +steady-state dynamic procedure is used, and available +only for acoustic finite elements. +All energy densities. None of the energy densities +are available in mode-based procedures; a limited +number of them are available for direct-solution +steady-state dynamic and subspace-based steady-state +dynamic analyses. In steady-state dynamics all energy +quantities are net per-cycle values, unless otherwise +noted . +Elastic strain energy density (with respect to current +volume). When the Mullins effect is modeled with +hyperelastic materials, this quantity represents only +the recoverable part of energy per unit volume. This +is the only energy density available in the data file +for eigenvalue extraction procedures; to obtain this +quantity for eigenvalue extraction procedures in the +results file or as field output in the output database, +request ENER. In steady-state dynamic analysis this +is the cyclic mean value. +Energy dissipated by rate-independent and rate- +dependent plasticity, per unit volume. Not available +for steady-state dynamic analysis. +dissipated +Energy +and +viscoelasticity, per unit volume. Not available for +steady-state dynamic analysis. +swelling, +creep, +by +4.2.1–12 +• +• +• +• +• +• +• +• +• +• +• +• +• +ACV +ACVn +GRADP +Energy densities +ENER +• +• +SENER +PENER +CENER +• +• +Identifier +.dat +.fil +.odb +Field History +Description +VENER +EENER +JENER +DMENER +• +• +• +• +• +• +• +• +• +• +• +• +Energy dissipated by viscous effects (except those +from viscoelasticity and static dissipation), per unit +volume. +Electrostatic energy density. Not available for steady- +state dynamic analysis. +Electrical energy dissipated as a result of the flow of +current, per unit volume. Not available for steady-state +dynamic analysis. +Energy dissipated by damage, per unit volume. Not +available for steady-state dynamic analysis. +State, field, and user-defined output variables +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Solution-dependent state variables. +Solution-dependent state variable n. +Temperature. +Predefined field variables, including those imported +using the FVi co-simulation field ID. +Predefined field variable n. +Predefined mass flow rates. +Component +( +User-defined output variables. +User-defined output variable n. +predefined mass flow rate +of +). +All failure measure components. +Maximum stress theory failure measure. +Tsai-Hill theory failure measure. +Tsai-Wu theory failure measure. +Azzi-Tsai-Hill theory failure measure. +Maximum strain theory failure measure. +Current value of the mass flow rate. +Current value of the total mass flow. +4.2.1–13 +SDV +SDVn +TEMP +FV +FVn +MFR +MFRn +UVARM +UVARMn +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Composite failure measures +• +CFAILURE +MSTRS +TSAIH +TSAIW +AZZIT +MSTRN +• +• +• +• +• +• +Fluid link quantities +• +• +MFL +MFLT +• +Identifier +.dat +.fil +.odb +Field History +Description +Fracture mechanics quantities +JK +• +• +• +• +J-integral, stress intensity factors. Available only for +line spring elements. Output is in the following order +for LS3S elements: J, K, +. Output is in +the following order for LS6 elements: J, +, +, and +, +, +, and +. +Concrete cracking and additional plasticity +CRACK +CONF +PEQC +PEQCn +• +• +• +• +• +• +• +Unit normal to cracks in concrete. +Number of cracks at a concrete material point. +• +• +• +All equivalent plastic strains when the model has more +than one yield/failure surface. +nth equivalent plastic strain ( +). +For jointed materials: PEQC provides equivalent +plastic strains for all four possible systems (three +joints - PEQC1, PEQC2, PEQC3, and bulk material +- PEQC4). This identifier also provides a yes/no flag +(1/0 on the output database) telling if each individual +system is currently yielding or not (AC YIELD: +“actively yielding”; that is, the plastic strain changed +during the increment). +For cap plasticity: PEQC provides equivalent plastic +three possible yield/failure surfaces +strains for all +(Drucker-Prager failure surface - PEQC1, cap surface +- PEQC2, and transition surface - PEQC3) and the total +volumetric inelastic strain (PEQC4). All identifiers +also provide a yes/no flag (1/0 on the output database) +telling whether the yield surface is currently active +or not (AC YIELD: “actively yielding”, that is, the +plastic strain changed during the increment). +When PEQC is requested as output to the output +database, the active yield flags for each component +are named AC YIELD1, AC YIELD2, etc. and take +the value 1 or 0. +Identifier +.dat +.fil +.odb +Field History +Description +Concrete damaged plasticity +DAMAGEC +DAMAGET +SDEG +PEEQ +Rebar quantities +RBFOR +RBANG +RBROT +• +• +• +• +• +• +• +Heat transfer analysis +HFL +HFLM +HFLn +• +• +• +Mass diffusion analysis +CONC +ISOL +MFL +MFLM +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +. +. +Compressive damage variable, +Tensile damage variable, +Scalar stiffness degradation variable, d. +Equivalent plastic strain in uniaxial compression, +This identifier also +which is defined as +provides a yes/no flag (1/0 on the output database) +telling if +is currently undergoing +compressive failure or not (AC YIELD: “actively +yielding”; that is, the plastic strain changed during the +increment). +the material +. +Force in rebar. +Angle in degrees between rebar and the user-specified +isoparametric direction. Available only for shell, +membrane, and surface elements. +Change in angle in degrees between rebar and the user- +specified isoparametric direction. Available only for +shell, membrane, and surface elements. +Current magnitude and components of the heat flux per +unit area vector. The integration points for these values +are located at the Gauss points. +Current magnitude of heat flux per unit area vector. +Component n of the heat flux vector ( +). +Mass concentration. +Amount of solute at an integration point, calculated as +the product of the mass concentration (CONC) and the +integration point volume (IVOL). +Current magnitude +concentration flux vector. +Current magnitude of the concentration flux vector. +components +and +the +of +Identifier +.dat +.fil +MFLn +• +.odb +Field History +• +Description +Component n of the concentration flux vector ( +). +Elements with electrical potential degrees of freedom +• +EPG +• +• +• +Current magnitude and components of the electrical +potential gradient vector. +Current magnitude of the electrical potential gradient +vector. +Component n of the electrical potential gradient vector +( +). +Current magnitude and components of the electrical +flux vector. +Current magnitude of the electrical flux vector. +Component n of the electrical flux vector ( +). +Current magnitude and components of the electrical +current density. +Current magnitude of the electrical current density. +Component n of the electrical current density vector +( +). +Maximum nominal stress damage initiation criterion. +Maximum nominal strain damage initiation criterion. +Quadratic nominal stress damage initiation criterion. +Quadratic nominal strain damage initiation criterion. +All active components of the damage initiation criteria. +Overall scalar stiffness degradation. +Status of the element (the status of an element is 1.0 if +the element is active, 0.0 if the element is not). +Number of cycles to initialize the damage at +material point. +the +4.2.1–16 +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +EPGM +EPGn +• +• +Piezoelectric analysis +EFLX +EFLXM +EFLXn +• +• +• +• +• +Coupled thermal-electrical elements +• +ECD +• +• +ECDM +ECDn +• +• +Cohesive elements +• +MAXSCRT +• +MAXECRT +• +QUADSCRT +QUADECRT • +• +DMICRT +• +SDEG +• +STATUS +• +• +• +Low-cycle fatigue analysis +CYCLEINI +• +• +• +• +• +• +• +Identifier +.dat +.fil +.odb +Field History +Description +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +SDEG +STATUS +• +• +Pore pressure analysis +VOIDR +POR +SAT +GELVR +FLUVR +FLVEL +FLVELM +FLVELn +• +• +• +• +• +• +• +• +Pore pressure cohesive elements +• +• +• +• +• +• +• +GFVR +• +PFOPEN +• +LEAKVRT +• +LEAKVRB +• +ALEAKVRT +ALEAKVRB • +• +• +• +• +• +• +Porous metal plasticity quantities +• +• +• +• +RD +VVF +VVFG +VVFN +• +• +• +• +• +• +• +• +Two-layer viscoplasticity quantities +• +• +VS +VSij +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Overall scalar stiffness degradation. +Status of the element (the status of an element is 1.0 if +the element is active, 0.0 if the element is not). +Void ratio. +Pore pressure. +Saturation. +Gel volume ratio. +Total fluid volume ratio. +Current magnitude and components of the pore fluid +effective velocity vector. +Current magnitude of the pore fluid effective velocity +vector. +Component n of the pore fluid effective velocity vector +( +). +Gap flow volume rate. +Pore pressure fracture opening. +Leak-off flow rate at the top of the element. +Leak-off flow rate at the bottom of the element. +Accumulated leak-off volume at the top of the element. +Accumulated leak-off volume at the bottom of the +element. +Relative density. +Void volume fraction. +Void volume fraction due to void growth. +Void volume fraction due to void nucleation. +Stress in the elastic-viscous network. +-component of stress in the elastic-viscous network +( +). +Identifier +.dat +.fil +.odb +Field History +Description +PS +PSij +VE +VEij +PE +PEij +VEEQ +PEEQ +• +• +• +• +• +• +• +• +Geometric quantities +• +COORD +IVOL +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +LOCALDIRn +Accuracy indicators +• +SJP +• +Random response analysis +Stress in the elastic-plastic network. +-component of stress in the elastic-plastic network +( +Viscous strain in the elastic-viscous network. +). +-component of viscous strain in the elastic-viscous +network ( +). +Plastic strain in the elastic-plastic network. +-component of plastic strain in the elastic-plastic +). +network ( +Equivalent viscous +network, defined as +Equivalent plastic strain in the elastic-plastic network, +defined as +strain in the elastic-viscous +. +. +Coordinates of the integration point for solid elements +and rebar. These are the current coordinates if the +large-displacement formulation is being used. +Section point volume +Integration point volume. +in the case of beams and shells. +(Not available +for eigenfrequency extraction, eigenvalue buckling +prediction, complex eigenfrequency extraction, or +linear dynamics procedures. +Available only for +continuum and structural elements not using general +beam or shell section definitions.) +Direction cosines of the local material directions +for an anisotropic hyperelastic material model. This +variable is output automatically if any other element +field output is requested for an anisotropic hyperelastic +material . +Strain jumps at nodes. +The following variables (beginning with R) are available only for random response dynamic analysis: +Identifier +.dat +.fil +.odb +Field History +Description +• +• +• +RS +RSij +RMISES +RE +REij +RCTF +RCTFn +RCTMn +RCEF +RCEFn +RCEMn +RCVF +RCVFn +RCVMn +RCRF +RCRFn +RCRMn +RCSF +RCSFn +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Root mean square of all stress components. +Root mean square of +-component of stress ( +). +Root mean square of Mises equivalent stress. +Root mean square of all strain components. +Root mean square of +-component of strain ( +). +RMS values of all components of connector total +forces and moments. +RMS value of connector total force component n ( +). +RMS value of connector total moment component n +( +). +RMS values of all components of connector elastic +forces and moments. +RMS value of connector elastic force component n +( +). +RMS value of connector elastic moment component n +( +). +RMS values of all components of connector viscous +forces and moments. +RMS value of connector viscous force component n +( +). +RMS value of connector viscous moment component +n ( +). +RMS values of all components of connector reaction +forces and moments. +RMS value of connector reaction force component n +( +). +RMS value of connector reaction moment component +n ( +). +RMS values of all components of connector friction +forces and moments. +RMS value of connector friction force component n +( +). +Identifier +.dat +.fil +.odb +Field History +Description +RCSMn +RCSFC +RCU +RCUn +RCURn +RCCU +RCCUn +RCCURn +RCNF +RCNFn +RCNMn +RCNFC +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +). +). +). +all +RMS value of connector friction moment component +n ( +RMS value of connector friction force in the direction +of the instantaneous slip direction. Available only if +friction is defined in the slip direction. +RMS values of all components of connector relative +displacements and rotations. +RMS value of connector relative displacement in the +n-direction ( +RMS value of connector relative rotation in the +n-direction ( +RMS values of +components of +constitutive displacements and rotations. +RMS value of connector constitutive displacement in +the n-direction ( +). +RMS value of connector constitutive rotation in the +n-direction ( +RMS values of all components of connector friction- +generating contact forces and moments. +RMS value of connector friction-generating contact +force component n ( +RMS value of connector friction-generating contact +moment component n ( +RMS values of connector friction-generating contact +force components in the instantaneous slip direction. +Available only if friction is defined in the slip direction. +connector +). +). +). +Steady-state dynamic analysis +The following variables (beginning with P) are available only for steady-state (frequency domain) +dynamic analysis. These variables include both the magnitude and phase angle for all components. +Phase angles are given in degrees. In the data file there are two lines of output for each request. The +first line contains the magnitude, and the second line (indicated by the SSD footnote) contains the phase +angle. In the results file the magnitudes of all components are first, followed by the phase angles of all +components. +PHS +PHSij +• +• +• +Magnitude and phase angle of all stress components. +Magnitude and phase angle of +-component of stress +( +). +Identifier +.dat +.fil +.odb +Field History +Description +PHE +PHEij +PHEPG +PHEPGn +PHEFL +PHEFLn +PHMFL +PHMFT +PHCTF +PHCTFn +PHCTMn +PHCEF +PHCEFn +PHCEMn +PHCVF +PHCVFn +PHCVMn +PHCRF +PHCRFn +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +). +). +). +total mass flow. +Magnitude and phase angle of all strain components. +Magnitude and phase angle of +-component of strain +( +Magnitude and phase angles of the electrical potential +gradient vector. +Magnitude and phase angle of component n of the +electrical potential gradient ( +Magnitude and phase angles of the electrical flux +vector. +Magnitude and phase angle of component n of the +electrical flux vector ( +Magnitude and phase angle of mass flow rate. +Available only for fluid link elements. +Magnitude and phase angle of +Available only for fluid link elements. +Magnitude and phase of all components of connector +total forces and moments. +Magnitude and phase of connector +component n ( +). +Magnitude and phase of connector total moment +component n ( +). +Magnitude and phase of all components of connector +elastic forces and moments. +Magnitude and phase of connector elastic force +component n ( +). +Magnitude and phase of connector elastic moment +component n ( +). +Magnitude and phase of all components of connector +viscous forces and moments. +Magnitude and phase of connector viscous force +component n ( +). +Magnitude and phase of connector viscous moment +component n ( +). +Magnitude and phase of all components of connector +reaction forces and moments. +Magnitude and phase of connector reaction force +component n ( +). +force +total +Identifier +.dat +.fil +.odb +Field History +Description +PHCRMn +PHCSF +PHCSFn +PHCSMn +PHCSFC +PHCU +PHCUn +PHCURn +PHCCU +PHCCUn +PHCCURn +PHCV +PHCVn +PHCVRn +PHCA +PHCAn +PHCARn +PHCNF +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +). +of +phase +relative +connector +Magnitude and phase of connector reaction moment +component n ( +). +Magnitude and phase of all components of connector +friction forces and moments. +Magnitude and phase of connector friction force +component n ( +). +Magnitude and phase of connector friction moment +component n ( +). +Magnitude and phase of connector friction force in the +direction of the instantaneous slip direction. Available +only if friction is defined in the slip direction. +Magnitude and phase of all components of connector +relative displacements and rotations. +Magnitude +and +displacement in the n-direction ( +Magnitude and phase of connector relative rotation in +the n-direction ( +). +Magnitude and phase of all components of connector +constitutive displacements and rotations. +Magnitude and phase of connector constitutive +displacement in the n-direction ( +Magnitude and phase of connector constitutive +rotation in the n-direction ( +Magnitude and phase of all components of connector +relative velocities. +Magnitude and phase of connector relative velocity in +the n-direction ( +). +Magnitude and phase of connector relative angular +velocity in the n-direction ( +Magnitude and phase of all components of connector +relative accelerations. +Magnitude +of +and +acceleration in the n-direction ( +Magnitude and phase of connector relative angular +acceleration in the n-direction ( +Magnitude and phase of all components of connector +friction-generating contact forces and moments. +connector +). +relative +phase +). +). +). +). +Identifier +.dat +.fil +.odb +Field History +Description +). +Magnitude and phase of connector friction-generating +contact force component n ( +Magnitude and phase of connector friction-generating +contact moment component n ( +Magnitude and phase of connector friction-generating +contact force in the instantaneous slip direction. +Available only if friction is defined in the slip direction. +Magnitude and phase of connector +instantaneous +velocity in the slip direction. Available only if friction +is defined in the slip direction. +). +Scalar stiffness degradation variable. +All active components of the damage initiation criteria. +Ductile damage initiation criterion. +Shear damage initiation criterion. +Forming limit diagram (FLD) damage initiation +criterion. +Forming limit +initiation criterion. +Müschenborn-Sonne forming limit stress diagram +(MSFLD) damage initiation criterion. +Ratio of principal strain rates, +damage initiation criterion. +Shear stress ratio, +shear damage initiation criterion. +stress diagram (FLSD) damage +, used for the MSFLD +, used for the +Hashin’s fiber tensile damage initiation criterion. +Hashin’s fiber compressive damage initiation criterion. +Hashin’s matrix tensile damage initiation criterion. +Hashin’s matrix compressive damage +criterion. +All active components of the damage initiation criteria. +Fiber tensile damage variable. +Fiber compressive damage variable. +initiation +4.2.1–23 +PHCNFn +PHCNMn +PHCNFC +PHCIVC +• +• +• +• +• +Failure with progressive damage +SDEG +DMICRT +DUCTCRT +SHRCRT +FLDCRT +FLSDCRT +MSFLDCRT +ERPRATIO +SHRRATIO +• +• +• +• +Fiber-reinforced materials damage +• +• +• +• +• +HSNFTCRT +• +HSNFCCRT +HSNMTCRT • +HSNMCCRT • +• +DMICRT +DAMAGEFT • +DAMAGEFC • +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Identifier +.dat +.fil +.odb +Field History +Description +DAMAGEMT • +DAMAGEMC • +DAMAGESHR • +• +STATUS +• +• +• +• +• +• +• +• +• +• +• +• +Matrix tensile damage variable. +Matrix compressive damage variable. +Shear damage variable. +Status of the element (the status of an element is 1.0 if +the element is active, 0.0 if the element is not). +Element centroidal variables +For electromagnetic elements, the element output is at the centroid of the element instead of at the +integration points. These variables are defined for electromagnetic elements in the element descriptions +in Part VI, “Elements,” and “Eddy current analysis,” Section 6.7.5. +Identifier +.dat +.fil +.odb +Field History +Description +EMB +EMH +EME +EMCD +EMJH +EMBF +EMBFC +• +• +• +• +• +• +• +• +• +• +• +• +• +• +All components of the magnetic flux density vector. +All components of the magnetic field vector. +All components of the electric field vector. +All components of +conducting regions. +the eddy current vector +in +Rate of Joule heat dissipation (amount of heat +dissipated per unit volume per unit time) in conductor +regions. +Magnetic body force intensity (force per unit volume) +vector in conductor regions. +Complex magnetic body force intensity (force +per unit volume) vector in conductor regions in a +time-harmonic eddy current analysis. +Element section variables +You can request element section variable output to the data, results, or output database file . These variables are available only for beam and shell elements with +the exception of STH, which is also available for membrane elements. They are defined for particular +elements in the element descriptions in Part VI, “Elements.” +Identifier +.dat +.fil +.odb +Field History +Description +SF +SFn +SMn +BIMOM +ESF1 +SSAVG +SSAVGn +SE +SEn +SKn +BICURV +MAXSS +COORD +STH +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +for +for continuum +All section force and moment components. +Section force component n ( +conventional shells; +shells; +for beams). +Section moment component n ( +Bimoment of beam cross-section. Available only for +open-section beam elements. +Effective axial force for beams and pipes subjected to +pressure loading. Available for all stress/displacement +procedure types except response spectrum and random +response. +All average shell section stress components. +Average shell section stress component n ( +). +). +). +for +stress on the section. +All section strain, curvature change, and twist +components. +Section strain component n ( +shells; +for beams). +Section curvature change or twist n ( +Bicurvature of beam cross-section. Available only for +open-section beam elements. +(This +Maximum axial +variable can be used with the following types of +general beam section definitions: +standard library +cross-sections, +linear generalized cross-sections, or +meshed cross-sections with specified output section +points. If the output section points are specified, the +MAXSS output will be the maximum of the stresses +at the user-specified points.) +Coordinates of the section point. These are the current +coordinates if the large-displacement formulation is +being used. +Section thickness (current thickness for SAX1, SAX2, +SAX2T, S3/S3R, S4, S4R, SAXA1N, SAXA2N, +and all membrane elements if the large-displacement +formulation is used; +initial thickness for all other +cases). +Identifier +.dat +.fil +.odb +Field History +Description +SVOL +SPE +SPEn +SEPE +SEPEn +Frame elements +SEE +SEE1 +SKEn +SEP +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +(Not available for +Integrated section volume. +eigenfrequency +buckling +extraction, +prediction, complex eigenfrequency extraction, or +Available only for +linear dynamics procedures. +continuum and structural elements not using general +beam or shell section definitions.) +eigenvalue +All generalized plastic strain components. Available +only for inelastic nonlinear response in a general beam +section. +Generalized plastic strain component n ( +). Representing axial plastic strain, curvature +change about the local 1-axis, curvature change about +the local 2-axis, and twist of the beam. Available only +for inelastic nonlinear response in a general beam +section. +All equivalent plastic strains. Available only for +inelastic nonlinear response in a general beam section. +Equivalent plastic strain component n ( +). +Representing axial plastic strain, curvature change +about the local 1-axis, curvature change about the +local 2-axis, and twist of the beam. Available only for +inelastic nonlinear response in a general beam section. +All elastic section axial, curvature, and twist strain +components. +Elastic axial strain component. +Elastic section curvature or twist strain component +( +). +All plastic axial displacements and rotations at the +element’s ends. This identifier also provides a yes/no +flag telling if the frame element’s end section is +currently yielding or not +(AC YIELD: “actively +yielding”; that is, the plastic strain changed during +the increment) and a yes/no/na flag telling if buckling +occurred in the strut response (AC BUCKL) or is +not applicable. AC YIELD and AC BUCKL are not +available in the output database. +Identifier +.dat +.fil +.odb +Field History +Description +SEP1 +SKPn +SALPHA +SALPHAn +• +• +• +• +• +• +• +• +• +• +Plastic axial displacement at the element’s ends. +Plastic rotations, either bending or twisting, at the +element’s ends ( +). +All generalized backstress +element’s ends. +ends +Generalized +( +is the +axial section backstress, followed by two bending +backstress components and the twist backstress +component. +element’s +The first component +backstress +). +components +the +the +at +at +Whole element variables +You can request whole element variable output to the data, results, or output database file . +Identifier +.dat +.fil +.odb +Field History +Description +LOADS +FOUND +FLUXS +CHRGS +ECURS +ELEN +ELKE +ELSE +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Current values of distributed loads (not available for +nonuniform loads). +Current values of foundation pressures. +Current values of distributed (heat or concentration) +fluxes (not available for nonuniform fluxes), including +those imported using the HFL co-simulation field ID. +Current values of distributed electrical charges. +Current values of distributed electrical currents. +None +All energy magnitudes in the element. +of +in mode-based +are +procedures; a limited number of them are available +and +for +subspace-based steady-state dynamic analyses. +In +steady-state dynamics all energy quantities are net +per-cycle values, unless otherwise noted. +Total kinetic energy in the element. +dynamic analysis this is the cyclic mean value. +Total elastic strain energy in the element. When the +Mullins effect is modeled with hyperelastic materials, +In steady-state +direct-solution +steady-state +available +dynamic +energies +the +Identifier +.dat +.fil +.odb +Field History +Description +ELPD +ELCD +ELVD +ELSD +ELCTE +ELJD +ELASE +ELDMD +NFORC +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +in the output database, +this quantity represents only the recoverable part of +energy in the element. This is the only energy request +available in the data file for eigenvalue extraction +to obtain this quantity for eigenvalue +procedures; +extraction procedures in the results file or as field +output +request ELEN. In +steady-state dynamic analysis this is the cyclic mean +value. +Total energy dissipated in the element by rate- +independent and rate-dependent plastic deformation. +Not available for steady-state dynamic analysis. +Total energy dissipated in the element by creep, +swelling, and viscoelasticity. +Not available for +steady-state dynamic analysis. +Total energy dissipated in the element by viscous +effects, not +including energy dissipated by static +stabilization or viscoelasticity. +Total energy dissipated in the element resulting from +automatic static stabilization. Not available for steady- +state dynamic analysis. +Total electrostatic energy in the element. Not available +for steady-state dynamic analysis. +Total electrical energy dissipated due to flow of +current. +Not available for steady-state dynamic +analysis. +Total “artificial” strain energy in the element (energy +associated with constraints used to remove singular +modes, such as hourglass control, and with constraints +used to make the drill rotation follow the in-plane +rotation of the shell element). Not available for +steady-state dynamic analysis. +Total energy dissipated in the element by damage. Not +available for steady-state dynamic analysis. +Forces at the nodes of an element from both the +hourglass and the regular deformation modes of that +element (internal forces in the global coordinate +system). The specified position in data and results file +requests is ignored. +Identifier +.dat +.fil +.odb +Field History +Description +Forces at the nodes of a beam element caused by the +stress resultants in the element (internal forces in the +beam section orientation coordinate system). +Uniformly distributed gravity load. +Uniformly distributed body force. +Magnitude of Coriolis load. +Magnitude of rotary acceleration load. +is the mass density per unit volume and +load (measured as +Magnitude of centrifugal +where +the angular velocity). +, +is +Magnitude of centrifugal load (measured as +, where +is the angular velocity). +Heat body flux. +Fluxes at the nodes of the element caused by the heat +conduction or mass diffusion in the element (internal +fluxes). +(The specified position for data and output +database file requests is ignored.) +Flux n at the nodes of the element ( +) +caused by the heat conduction or mass diffusion in the +element (internal fluxes). (The specified position for +data and output database file requests is ignored.) +Electrical current at +conduction in the element. +the nodes due to electrical +Current values of film conditions (not available for +nonuniform films). +Current values of radiation conditions. +(Not available for +Current element volume. +buckling +extraction, +eigenfrequency +prediction, complex eigenfrequency extraction, or +linear dynamics procedures. +Available only for +continuum and structural elements not using general +beam or shell section definitions.) +eigenvalue +Amount of solute in an element, calculated as the sum +of ISOL (amount of solute at an integration point) over +all the integration points in the element. +4.2.1–29 +NFORCSO +GRAV +BF +CORIOMAG +ROTAMAG +CENTMAG +CENTRIFMAG +HBF +NFLUX +NFLn +NCURS +FILM +RAD +EVOL +ESOL +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Identifier +.dat +.fil +.odb +Field History +Description +Enriched elements +STATUSXFEM +• +• +Status of the enriched element. +(The status of an +enriched element is 1.0 if the element is completely +cracked; 0.0 if the element is not. +If the element is +partially cracked, the value lies between 1.0 and 0.0.) +Enriched elements when the XFEM-based LEFM approach is used +• +ENRRTXFEM +• +All components of strain energy release rate. +Enriched elements in low-cycle fatigue analysis +• +• +• +• +• +• +• +• +• +• +CYCLEINIXFEM +Connector elements +• +CTF +CTFn +CTMn +CEF +CEFn +CEMn +CUE +CUEn +CUREn +CUP +CUPn +CURPn +CUPEQ +CUPEQn +CURPEQn +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Number of cycles to initialize the crack at the enriched +element. +). +). +total +forces and +All components of connector +moments. +Connector total force component n ( +Connector total moment component n ( +All components of connector elastic forces and +moments. +Connector elastic force component n ( +Connector elastic moment component n ( +Elastic displacements and rotations in all directions. +Elastic displacement in the n-direction ( +). +Elastic rotation in the n-direction ( +Plastic relative displacements and rotations in all +directions. +Plastic relative displacement in the n-direction ( +). +). +). +). +Plastic relative rotation in the n-direction ( +). +Equivalent plastic relative displacements and rotations +in all directions. +Equivalent plastic relative displacement +n-direction ( +Equivalent plastic relative rotation in the n-direction +( +in the +). +). +Identifier +.dat +.fil +.odb +Field History +Description +Equivalent plastic relative motion for a coupled +plasticity definition. +All components of connector kinematic hardening +shift forces and moments. +Connector kinematic hardening shift force component +n ( +). +Connector +component n ( +kinematic +hardening +). +shift moment +All components of connector viscous forces and +moments. +Connector viscous force component n ( +Connector viscous moment component n ( +). +). +All components of connector friction forces and +moments. +Connector friction force component n ( +Connector friction moment component n ( +). +). +Connector friction force in the instantaneous slip +direction. Available only if friction is defined in the +slip direction. +All components of connector +contact forces and moments. +friction-generating +Connector +component n ( +Connector +component n ( +friction-generating +friction-generating +contact +force +contact moment +). +). +Connector friction-generating contact force in the +instantaneous slip direction. Available only if friction +is defined in the slip direction. +All components of the overall damage variable. +Overall damage variable component n ( +Overall damage variable component n ( +Components +initiation criterion in all directions. +connector +of +force-based +). +). +damage +Connector force-based damage initiation criterion in +the n-translation direction ( +). +4.2.1–31 +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +CUPEQC +CALPHAF +CALPHAFn +CALPHAMn +CVF +CVFn +CVMn +CSF +CSFn +CSMn +CSFC +CNF +CNFn +CNMn +CNFC +CDMG +CDMGn +CDMGRn +CDIF +CDIFn +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Identifier +.dat +.fil +.odb +Field History +Description +CDIFRn +CDIFC +CDIM +CDIMn +CDIMRn +CDIMC +CDIP +CDIPn +CDIPRn +CDIPC +CSLST +CSLSTi +CASU +CASUn +CASURn +CASUC +CIVC +CRF +CRFn +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +). +). +). +Connector force-based damage initiation criterion in +the n-rotation direction ( +Connector force-based damage initiation criterion in +the instantaneous slip direction. +Components of connector motion-based damage +initiation criterion in all directions. +Connector motion-based damage initiation criterion in +the n-translation direction ( +Connector motion-based damage initiation criterion in +the n-rotation direction ( +Connector motion-based damage initiation criterion in +the instantaneous slip direction. +Components of +damage initiation criterion in all directions. +Connector plastic motion-based damage initiation +criterion in the n-translation direction ( +Connector plastic motion-based damage initiation +criterion in the n-rotation direction ( +Connector plastic motion-based damage initiation +criterion in the instantaneous slip direction. +All flags for connector stop and connector lock status. +Flag for connector stop and connector lock status in +the i-direction ( +). +Components of accumulated slip in all directions. +Connector accumulated slip in the n-direction ( +connector plastic motion-based +). +). +). +). +Connector angular accumulated slip in the n-direction +( +Connector accumulated slip in the instantaneous slip +direction. Available only if friction is defined in the +slip direction. +Connector instantaneous velocity in the slip direction. +Available only if friction is defined in the slip direction. +All components of connector reaction forces and +moments. +Connector reaction force component n ( +). +Identifier +.dat +.fil +.odb +Field History +Description +• +CRMn +CCF +CCFn +CCMn +CP +CPn +CPRn +CU +CUn +CURn +CCU +CCUn +CCURn +CV +CVn +CVRn +CA +CAn +CARn +CFAILST +CFAILSTi +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Connector reaction moment component n ( +). +All components of connector concentrated forces and +moments. +Connector concentrated force component n ( +). +Connector concentrated moment component n ( +). +in +the +position +angular +). +). +in all +). +n-direction +Relative positions in all directions. +Relative position in the n-direction ( +Relative +( +Relative displacements and rotations in all directions. +). +Relative displacement in the n-direction ( +Relative rotation in the n-direction ( +Constitutive displacements and rotations +directions. +Constitutive +( +Constitutive rotation in the n-direction ( +Relative velocities in all directions. +Relative velocity in the n-direction ( +Relative +( +Relative accelerations in all directions. +Relative acceleration in the n-direction ( +Relative angular acceleration in the n-direction ( +). +n-direction +angular +). +displacement +n-direction +velocity +the +the +in +in +). +). +). +). +All flags for connector failure status. +Flag for connector failure status in the i-direction ( +). +Element face variables +You can request element face variable output to the output database . These variables are available only for shell, membrane, and solid +elements. +Identifier +.dat +.fil +.odb +Field History +Description +HP +TRNOR +TRSHR +FLUXS +FILMCOEF +SINKTEMP +• +• +• +• +• +• +• +Uniformly distributed pressure load on element +faces, +including those imported using the PRESS +co-simulation field ID. When the pressure is defined +using *DLOAD, +the variable name is changed +automatically to PDLOAD. When the pressure +is defined using *DLOAD on shell or membrane +elements, Abaqus changes the sign of its value to +make it consistent with the pressure defined using +*DSLOAD. +Hydrostatic pressure load on element faces. When +the pressure is defined using *DLOAD, the variable +name is changed automatically to HPDLOAD. When +the pressure is defined using *DLOAD on shell or +membrane elements, Abaqus changes the sign of its +value to make it consistent with the pressure defined +using *DSLOAD. +Normal component (component along face normal) of +traction load on element faces. +Shear component (component along face tangent) of +traction load on element faces. +Uniformly distributed heat fluxes on element faces. +Reference film coefficient value on element faces. +Reference sink temperature on element faces. +Whole element energy density variables +The following energy density output variables are written to the restart (.res) file and the output +database (.odb) file : +Identifier +.dat +.fil +ELEDEN +.odb +Field History +• +Description +All energy density components. None of the energies +are available in mode-based procedures; a limited +number of them are available for direct-solution +steady-state dynamic and subspace-based steady-state +dynamic analyses. In steady-state dynamics all energy +quantities are net per-cycle values, unless otherwise +noted. +Identifier +.dat +.fil +.odb +Field History +Description +EKEDEN +ESEDEN +EPDDEN +ECDDEN +EVDDEN +ESDDEN +ECTEDEN +EASEDEN +EDMDDEN +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Kinetic energy density in the element. In steady-state +dynamic analysis this is the cyclic mean value. +Total elastic strain energy density in the element. +When the Mullins effect is modeled with hyperelastic +materials, this quantity represents only the recoverable +part of energy density in the element. This variable is +not available in eigenvalue extraction procedures. In +steady-state dynamic analysis this is the cyclic mean +value. +Total energy dissipated per unit volume in the +element by rate-independent and rate-dependent +plastic deformation. Not available for steady-state +dynamic analysis. +Total energy dissipated per unit volume in the element +by creep, swelling, and viscoelasticity. Not available +for steady-state dynamic analysis. +Total energy dissipated per unit volume in the element +by viscous effects, not inclusive of energy dissipated +through static stabilization or viscoelasticity. +Total energy dissipated per unit volume in the element +resulting from static stabilization. Not available for +steady-state dynamic analysis. +Total electrostatic energy density in the element. Not +available for steady-state dynamic analysis. +Total “artificial” strain energy density in the element +(energy associated with constraints used to remove +singular modes, such as hourglass control, and with +constraints used to make the drill rotation follow the +in-plane rotation of the shell element). Not available +for steady-state dynamic analysis. +Total energy dissipated per unit volume in the element +by damage. Not available for steady-state dynamic +analysis. +Whole element error indicator variables +You can request that the following error indicator variables and element average variables be output only +to the output database (.odb) file . +Identifier +.dat +.fil +.odb +Field History +Description +ENDEN +ENDENERI +MISESAVG +MISESERI +PEEQAVG +PEEQERI +PEAVG +PEERI +CEAVG +CEERI +HFLAVG +HFLERI +EFLAVG +EFLERI +EPGAVG +EPGERI +Nodal variables +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Element energy density, including plastic dissipation +and creep dissipation if present. +including +Element energy density error indicator, +plastic dissipation error and creep dissipation error if +present. +Element average Mises equivalent stress. +Element Mises equivalent stress error indicator. +Element average equivalent plastic strain. +Element equivalent plastic strain error indicator. +Element average plastic strain. +Element plastic strain error indicator. +Element average creep strain. +Element creep strain error indicator. +Element average heat flux. +Element heat flux error indicator. +Element average electric flux. +Element electric flux error indicator. +Element average electric potential gradient. +Element electric potential gradient error indicator. +You can request nodal variable output to the data, results, or output database file . +Identifier +.dat +.fil +.odb +Field History +Description +UT +UR +Un +URn +• +• +• +• +• +• +• +• +• +• +• +• +including +All physical displacement components, +rotations at nodes with rotational degrees of freedom +(for output to the output database, only field-type +output includes the rotations). +All translational displacement components. +All rotational displacement components. +displacement component ( +rotation component ( +). +). +Identifier +.dat +.fil +.odb +Field History +Description +WARP +VT +VR +Vn +VRn +AT +AR +An +ARn +POR +CFF +NT +NTn +EPOT +NNC +NNCn +RF +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +velocity +components, +Warping magnitude. Available only for open-section +beam elements. +rotational +All +velocities at nodes with rotational degrees of freedom +(for output to the output database, only field-type +output includes the rotational velocities). +All translational velocity components. +All rotational velocity components. +including +velocity component ( +rotational velocity component ( +). +). +including rotational +All acceleration components, +accelerations at nodes with rotational degrees of +freedom (for output +to the output database, only +field-type output includes the rotational accelerations). +All translational acceleration components. +All rotational acceleration components. +acceleration component ( +rotational acceleration component ( +). +). +Pore or acoustic pressure at a node. +Concentrated fluid flow at a node, including those +imported using the CFLOW co-simulation field ID. +including those +All temperature values at a node, +imported using the TEMP co-simulation field ID. +These will be the temperatures defined as degrees of +freedom if heat transfer elements are connected to +the node, or predefined temperatures if the node is +connected only to stress or mass diffusion elements +without temperature degrees of freedom. +Temperature degree of +( +All electrical potential degrees of freedom at a node. +All normalized concentration values at a node. +Normalized concentration degree of freedom n at a +node ( +including +All +components of +reaction moments at nodes with +rotational degrees of freedom (conjugate to prescribed +). +components of +freedom n at a node +reaction forces, +). +Identifier +.dat +.fil +.odb +Field History +Description +) +). +For output +) (conjugate +loads and concentrated +including loads imported using the CF +displacements and rotations). +to the +output database, only the field-type output includes +the components of reaction moments at nodes with +rotational degrees of freedom. +All reaction force components. +All reaction moment components. +Reaction force component n ( +to prescribed displacement +Reaction moment component n ( +(conjugate to prescribed rotation +). +Reaction bimoment in degree of freedom 7, conjugate +to prescribed warping amplitude. Available only for +open-section beam elements. +All components of point +moments, +co-simulation field ID. +Point load component n ( +Point moment component n ( +Load component in degree of freedom 7. Available +only for open-section beam elements. +All components of total forces, including components +of total moments at nodes with rotational degrees of +freedom. Total force is the sum of the reaction force +and point loads. For output to the output database, only +the field-type output includes the components of total +moments at nodes with rotational degrees of freedom. +Total force component n ( +Total moment component n ( +All components of viscous forces and moments due to +static stabilization. +Stabilization viscous force component n ( +Stabilization viscous moment component n ( +). +). +). +). +). +). +These are the current +Coordinates of the node. +coordinates if the large-displacement formulation is +being used. +Coordinate n ( +). +4.2.1–38 +• +• +• +• +• +• +• +• +• +• +RT +RM +RFn +RMn +RWM +CF +CFn +CMn +CW +TF +TFn +TMn +VF +VFn +VMn +COORD +COORn +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Identifier +.dat +.fil +.odb +Field History +Description +Strain-free adjustments to initial nodal positions +(adjusted position minus unadjusted position; only +written to the output database (.odb) file for the +original field output frame at zero time). +Reactive +prescribed electrical potential). +electrical nodal +charge +Concentrated electrical nodal charge. +Reactive electrical nodal current +prescribed electrical potential). +Concentrated electrical nodal current. +(conjugate +to +(conjugate to +Hydrostatic fluid gauge pressure (total pressure = +ambient pressure + hydrostatic fluid gauge pressure). +Hydrostatic fluid cavity volume. +All components of motion in cavity radiation heat +transfer analysis. +motion component ( +) in cavity radiation +heat transfer analysis. +Acoustic pressure. +Acoustic infinite element “radius,” used in the +coordinate map for these elements. Available only +if the steady-state dynamic procedure is used, and +available only for nodes attached to acoustic infinite +elements. +Acoustic infinite element “cosine,” used in the +coordinate map for these elements. Available only +if the steady-state dynamic procedure is used, and +available only for nodes attached to acoustic infinite +elements. +Acoustic infinite element normal vector. Available +only if the steady-state dynamic procedure is used, and +available only for nodes attached to acoustic infinite +elements. +Acoustic pressure coefficients for the higher-order +basis functions in acoustic infinite elements. Available +4.2.1–39 +STRAINFREE +RCHG +CECHG +RECUR +CECUR +PCAV +CVOL +MOT +MOTn +• +• +• +• +• +• +• +• +Acoustic quantities +• +POR +INFR +• +• +• +• +• +• +• +• +INFC +INFN +PINF +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Identifier +.dat +.fil +.odb +Field History +Description +SPL +Enriched element quantities +PHILSM +PSILSM +• +• +• +• +• +• +Heat or mass flux +only if the steady-state dynamic procedure is used, +and available only for acoustic infinite elements. +Acoustic sound pressure level at a node. +Signed distance function to describe the crack surface. +Signed distance function to describe the initial crack +front. +The following variables correspond to heat flux in temperature analyses or concentration volumetric flux +in mass diffusion analysis: +• +RFL +• +• +• +• +• +• +• +RFLn +CFL +CFLn +RFLE +RFLEn +• +• +• +• +• +• +• +• +• +• +All reaction flux values (conjugate to prescribed +temperature or normalized concentration). +Reaction flux value n at a node ( +) +(conjugate to prescribed temperature or normalized +concentration). +All concentrated flux values, including those imported +using the CFL co-simulation field ID. +Concentrated flux values n at a node ( +). +The total flux at the node (including flux convected +through the node in convection elements), excluding +external fluxes (due to concentrated fluxes, distributed +fluxes, film conditions, +radiation conditions, and +radiation viewfactors). The value of RFLE is, thus, +equal and opposite to the sum of all applied fluxes. +Flux value n excluding externally applied flux loads at +a node ( +). +Steady-state dynamic analysis +The following variables are available only for steady-state (frequency domain) dynamic analyses (modal +and direct). These variables include both magnitude and phase angle for all components. Phase angles +are given in degrees. In the data file there are two lines of output for each request. The first line contains +the magnitude, and the second line (indicated by the SSD footnote) contains the phase angle. In the +results file, the magnitudes of all components are first, followed by the phase angles of all components. +PU +• +• +Magnitude and phase angle of all displacement +components at the node and magnitude and phase +Identifier +.dat +.fil +.odb +Field History +Description +PUn +PURn +PPOR +PHPOT +PRF +PRFn +PRMn +PHCHG +• +• +• +• +• +• +• +• +• +• +• +• +). +angle of the rotations at nodes with rotational degrees +of freedom. +Magnitude and phase angle of component n of the +displacement ( +). +Magnitude and phase angle of component n of the +rotation ( +Magnitude and phase angle of the fluid, pore, or +acoustic pressure at the node. +Magnitude and phase angle of the electrical potential +at the node. +Magnitude and phase angle of the reaction forces at +the node and of the reaction moments at nodes with +rotational degrees of freedom. +Magnitude and phase angle of component n of the +reaction force ( +). +Magnitude and phase angle of component n of the +reaction moment ( +Magnitude and phase angle of the reactive charge at +the node. +). +Modal dynamic, steady-state, and random response analysis +The following variables are available only for modal dynamic, steady-state (frequency domain), and +random response analyses. “Relative” values are measured relative to the motion of the primary base +and are obtained with the identifiers U, V, and A; “Total” values include the motion of the primary base. +For steady-state dynamic output printed to the data file, there are two lines printed for each request; +the first line contains the real part of the variable, and the second line (indicated by the SSD footnote) +contains the imaginary part. +• +• +• +• +TU +TUn +TURn +TV +TVn +TVRn +• +• +• +• +• +• +• +• +• +• +• +• +All components of the total displacements at the node +and of the total rotations at nodes with rotational +degrees of freedom. +Component n of the total displacement ( +Component n of the total rotation ( +All components of the total velocity at the node, +including rotational velocities at nodes with rotational +degrees of freedom. +Component n of the total velocity ( +Component n of the total rate of rotation ( +). +). +). +). +Identifier +.dat +.fil +.odb +Field History +Description +• +• +TA +TAn +TARn +• +• +• +• +• +• +All components of the total acceleration at the node, +including rotational accelerations at nodes with +rotational degrees of freedom. +Component n of the total acceleration ( +Component n of the total rotational acceleration ( +). +). +Mode-based steady-state dynamic analysis +The following variables are available only for steady-state (frequency domain) dynamic analysis based +on modal superposition. “Total” values include the base motion. +PTU +PTUn +PTURn +• +• +• +• +Pore pressure analysis +Magnitude and phase angle of the total displacement +components at the node and magnitude and phase +angle of the total rotations at nodes with rotational +degrees of freedom. +Magnitude and phase angle of component n of the total +displacement ( +). +Magnitude and phase angle of component n of the total +rotation ( +). +The following variables correspond to fluid volume flux in pore pressure analyses. +• +RVF +• +• +• +Reaction fluid volume flux due to prescribed pressure. +This flux is the rate at which fluid volume is entering +or leaving the model through the node to maintain the +prescribed pressure boundary condition. A positive +value of RVF indicates fluid is entering the model. +Reaction total fluid volume (computed only in a +transient coupled pore fluid diffusion/stress analysis). +This value is the time integrated value of RVF. +RVT +• +• +• +• +Random response analysis +The following variables are available only for random response dynamic analysis. “Relative” values are +measured relative to the base motion; “Total” values include the base motion. +RU +• +• +• +• +Root mean square values of all components of +the relative displacement at +the node and of the +components of +rotation at nodes with rotational +degrees of freedom. +Identifier +.dat +.fil +.odb +Field History +Description +RUn +RURn +RTU +RTUn +RTURn +RV +RVn +RVRn +RTV +RTVn +RTVRn +RA +RAn +RARn +RTA +• +• +• +• +• +• +• +• +�� +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +). +). +). +Root mean square value of component n of the relative +displacement ( +). +Root mean square value of component n of the relative +rotation ( +Root mean square values of all components of the +total displacement at the node and of the components +of total rotation at nodes with rotational degrees of +freedom. +Root mean square value of component n of the total +displacement ( +). +Root mean square value of component n of the total +rotation ( +Root mean square values of all components of the +relative velocity at the node and of the components of +the rate of rotation at nodes with rotational degrees of +freedom. +Root mean square value of component n of the relative +velocity ( +Root mean square value of component n of the relative +rate of rotation ( +Root mean square values of all components of the total +velocity at the node and of the components of total +rotation at nodes with rotational degrees of freedom. +Root mean square value of component n of the total +velocity ( +Root mean square value of component n of the total +rate of rotation ( +Root mean square values of all components of the +relative acceleration at the node and of the components +of rotational acceleration at nodes with rotational +degrees of freedom. +Root mean square value of component n of the relative +acceleration ( +Root mean square value of component n of the relative +rotational acceleration ( +Root mean square values of all components of the +total acceleration at the node and of the components of +). +). +). +). +). +Identifier +.dat +.fil +.odb +Field History +Description +• +• +RTAn +RTARn +RRF +RRFn +RRMn +• +• +• +• +• +Modal variables +rotational acceleration at nodes with rotational degrees +of freedom. +Root mean square value of component n of the total +value of acceleration ( +). +Root mean square value of component n of the total +rotational acceleration ( +). +Root mean square values of all components of the +reaction forces and of reaction moments at nodes with +rotational degrees of freedom. +Root mean square value of component n of the reaction +force ( +). +Root mean square value of component n of the reaction +moment ( +). +• +• +• +• +• +You can request modal variable output to the data, results, or output database file . +etc. provide the amplitude of the mode. +Identifier +.dat +.fil +.odb +Field History +Description +GU +GUn +GV +GVn +GA +GAn +GPU +GPUn +GPV +GPVn +GPA +GPAn +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Generalized displacements for all modes. +Generalized displacement for mode n. +Generalized velocities for all modes. +Generalized velocity for mode n. +Generalized acceleration for all modes. +Generalized acceleration for mode n. +Phase angle of generalized displacements for all +modes. +Phase angle of generalized displacement for mode n. +Phase angle of generalized velocities for all modes. +Phase angle of generalized velocity for mode n. +Phase angle of generalized acceleration for all modes. +Phase angle of generalized acceleration for mode n. +Identifier +.dat +.fil +.odb +Field History +Description +SNE +SNEn +KE +KEn +Tn +BM +• +• +• +• +• +• +• +• +• +• +• +Surface variables +• +• +• +• +• +• +• +Elastic strain energy for the entire model per each +mode (not available for random response analysis). +Elastic strain energy for the entire model for mode n +(not available for random response analysis). +Kinetic energy for the entire model per each mode (not +available for random response analysis). +Kinetic energy for the entire model for mode n (not +available for random response analysis). +External work for the entire model per each mode (not +available for random response analysis). +External work for the entire model for mode n (not +available for random response analysis). +Base motion (not available for random response or +response spectrum analyses). +You can request surface variable output to the data, results, or output database file . +Additional information on these variables is provided in “Defining contact pairs in Abaqus/Standard,” +Section 35.3.1, and Chapter 36, “Contact Property Models.” The letter “M” at the end of an output +variable identifier designates the magnitude of the variable. Those variables that are output on both +master and slave surfaces in a single master-slave contact pair are designated below. For exceptions to +output on the master surface, see “Defining contact pairs in Abaqus/Standard,” Section 35.3.1. +Identifier +.dat +.fil +.odb +Field History +Description +• +Contact pressure (CPRESS) and frictional shear +stresses (CSHEAR). Output is also available on the +master surface to the .odb file in a single master-slave +setting. +Contact pressure (CPRESSETOS) and frictional shear +stresses (CSHEARETOS) due to edge-to-surface +contact constraints. Output is also available on the +4.2.1–45 +Mechanical analysis–nodal quantities +• +CSTRESS +• +• +CSTRESSETOS +Identifier +.dat +.fil +.odb +Field History +Description +master surface to the .odb file in a single master-slave +setting. +Error indicators for the contact pressure (CPRESSERI) +and frictional shear stresses (CSHEARERI). Output is +also available on the master surface to the .odb file in +a single master-slave setting. +Viscous pressure (CDPRESS) and viscous shear +stresses (CDSHEAR). Output is also available on the +master surface to the .odb file in a single master-slave +setting. +Contact opening (COPEN) and relative tangential +motions (CSLIP). +opening +Contact +relative +tangential motions (CSLIPETOS) for edge-to-surface +contact constraints. +(COPENETOS) +and +Contact normal force (CNORMF) and frictional shear +force (CSHEARF). Output is also available on the +master surface to the .odb file in a single master-slave +setting. +Contact nodal area. Output is also available on the +master surface to the .odb file in a single master-slave +setting. +Contact status. Output is also available on the master +surface to the .odb file in a single master-slave +setting. +Maximum stress-based damage initiation criterion for +cohesive surfaces. +Quadratic stress-based damage initiation criterion for +cohesive surfaces. +Maximum separation-based +criterion for cohesive surfaces. +damage +initiation +Quadratic separation-based damage initiation criterion +for cohesive surfaces. +Damage variable for cohesive surfaces. +Fluid pressure for pressure penetration analysis. +Solution-dependent state variables. +4.2.1–46 +• +• +• +• +CSTRESSERI +CDSTRESS +CDISP +CDISPETOS +CFORCE +CNAREA +CSTATUS +CSMAXSCRT +CSQUADSCRT +CSMAXUCRT +CSQUADUCRT +CSDMG +PPRESS +SDV +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Identifier +.dat +.fil +.odb +Field History +Description +Mechanical analysis–whole surface quantities +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Total force due to contact pressure (CFNn, n = 1, 2, 3). +Magnitude of total force due to contact pressure. +Total force due to frictional stress (CFSn, n = 1, 2, 3). +Magnitude of total force due to frictional stress. +Total force due to contact pressure and frictional stress +(CFTn, n = 1, 2, 3). +Magnitude of total force due to contact pressure and +frictional stress. +Total moment about the origin due to contact pressure +(CMNn, n = 1, 2, 3). +Magnitude of total moment about origin due to contact +pressure. +Total moment about the origin due to frictional stress +(CMSn, n = 1, 2, 3). +Magnitude of total moment about the origin due to +frictional stress. +Total moment about the origin due to contact pressure +and frictional stress (CMTn, n = 1, 2, 3). +Magnitude of total moment about the origin due to +contact pressure and frictional stress. +Total area in contact. +Maximum torque that can be transmitted about the +z-axis by a contact surface in an axisymmetric analysis +with a friction coefficient of unity. +Center of the total force due to contact pressure (XNn, +n = 1, 2, 3). +Center of the total force due to frictional stress (XSn, +n = 1, 2, 3). +Center of the total force due to contact pressure and +frictional stress (XTn, n = 1, 2, 3). +Heat flux per unit area leaving the slave surface. +HFL multiplied by the nodal area. +4.2.1–47 +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +CFN +CFNM +CFS +CFSM +CFT +CFTM +CMN +CMNM +CMS +CMSM +CMT +CMTM +CAREA +CTRQ +XN +XS +XT +• +• +• +• +• +• +• +• +• +• +• +Heat transfer analysis +HFL +HFLA +• +Identifier +.dat +.fil +.odb +Field History +Description +HTL +HTLA +• +• +• +• +• +• +Coupled thermal-electrical analysis +• +• +• +• +• +• +• +• +• +• +• +• +• +ECD +ECDA +ECDT +ECDTA +HFL +HFLA +HTL +HTLA +SJD +SJDA +SJDT +SJDTA +WEIGHT +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Time integrated HFL. +Time integrated HFLA. +Electrical current per unit area. +ECD multiplied by the nodal area. +Time integrated ECD. +Time integrated ECDA. +Heat flux per unit area leaving the slave surface. +HFL multiplied by the nodal area. +Time integrated HFL. +Time integrated HFLA. +Heat flux per unit area due to electrical current. +SJD multiplied by the nodal area. +Time integrated SJD. +Time integrated SJDA. +Weighting factor for heat distribution between the +interface surfaces. +Fully coupled temperature-displacement analysis +HFL +HFLA +HTL +HTLA +SFDR +SFDRA +SFDRT +SFDRTA +WEIGHT +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Heat flux per unit area leaving the slave surface. +HFL multiplied by the nodal area. +Time integrated HFL. +Time integrated HFLA. +Heat flux per unit area due to frictional dissipation. +SFDR multiplied by the nodal area. +Time integrated SFDR. +Time integrated SFDRA. +Weighting factor for heat distribution between the +interface surfaces. +Fully coupled thermal-electrical-structural analysis +• +• +• +ECD +ECDA +ECDT +• +• +• +• +• +• +• +• +• +Electrical current per unit area. +ECD multiplied by the nodal area. +Time integrated ECD. +Identifier +.dat +.fil +.odb +Field History +Description +ECDTA +HFL +HFLA +HTL +HTLA +SFDR +SFDRA +SFDRT +SFDRTA +SJD +SJDA +SJDT +SJDTA +WEIGHT +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Time integrated ECDA. +Heat flux per unit area leaving the slave surface. +HFL multiplied by the nodal area. +Time integrated HFL. +Time integrated HFLA. +Heat flux per unit area due to frictional dissipation. +SFDR multiplied by the nodal area. +Time integrated SFDR. +Time integrated SFDRA. +Heat flux per unit area due to electrical current. +SJD multiplied by the nodal area. +Time integrated SJD. +Time integrated SJDA. +Weighting factor for heat distribution between the +interface surfaces. +Coupled pore fluid-mechanical analysis–nodal quantities +PFL +PFLA +PTL +PTLA +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Pore fluid volume flux per unit area leaving the slave +surface. +PFL multiplied by the nodal area. +Time integrated PFL. +Time integrated PFLA. +Coupled pore fluid-mechanical analysis–whole surface quantities +TPFL +TPTL +• +• +Bond failure quantities +DBT +DBS +DBSF +BDSTAT +CSDMG +OPENBC +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Total pore fluid volume flux leaving the slave surface. +Time integrated TPFL. +• +• +• +• +• +• +• +• +• +• +• +• +Time when bond failure occurs. +All components of remaining stress in the failed bond. +Fraction of stress that remains at bond failure. +Bond state (varies from 1.0 to 0.0). +Damage variable. +Relative displacement behind crack when fracture +criterion is met. +Identifier +.dat +.fil +.odb +Field History +Description +CRSTS +ENRRT +EFENRRTR +• +• +• +• +• +• +• +• +• +• +• +• +All components of critical stress at failure. +All components of strain energy release rate. +Effective energy release rate ratio. +Cavity radiation variables +The following variables are associated with facets (sides of elements) composing cavities in radiation heat +transfer and include contributions due to exchanges with the ambient. You can request cavity radiation +variable output to the data, results, or output database file . +Identifier +.dat +.fil +.odb +Field History +Description +RADFL +RADFLA +RADTL +RADTLA +VFTOT +FTEMP +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Radiation flux per unit area. +Radiation flux over the facet. +Time integrated radiation per unit area. +Time integrated radiation over the facet. +Total viewfactor for the facet (sum of viewfactor +values in the row of viewfactor matrix corresponding +to the facet). +Facet temperature. +Section variables +You can request section variable output +to the data or results file . By default, all components of +forces and moments are given with respect to the global system. If a local coordinate system is defined +for the section output request, all components are given with respect to the local system. +Different output variables are available depending on the type of analysis. For coupled analyses +the appropriate combination of variables can be requested. For example, in a coupled thermal-electrical +analysis both SOH and SOE are valid output requests. Section output variables are not available for +random response analysis. +Identifier +.dat +.fil +.odb +Field History +Description +All analysis types +SOAREA +• +• +Area of the defined section. +Identifier +.dat +.fil +.odb +Field History +Description +Stress/displacement analysis +SOF +SOM +SOCF +• +• +• +Heat transfer analysis +SOH +Electrical analysis +SOE +• +• +Mass diffusion analysis +SOD +• +• +• +• +• +• +• +Total force in the section. +Total moment in the section. +Center of the total force in the section. +Total heat flux associated with the section. +Total current associated with the section. +Total mass flow associated with the section. +Coupled pore fluid diffusion-stress analysis +SOP +• +• +Whole and partial model variables +Total pore fluid volume flux associated with the +section. +The output variables listed below are available for part of the model as well as the whole model. +Identifier +.dat +.fil +.odb +Field History +Description +Adaptive mesh domains +The following variable is available only for adaptive domains . +• +VOLC +Change in area or change in volume of an element set +solely due to adaptive meshing. +• +• +Equivalent rigid body motion variables +You can request equivalent rigid body motion whole element set variable output to the data, results, or +output database file . The variables listed are available +only for implicit dynamic analyses using direct integration except where indicated. +Identifier +.dat +.fil +.odb +Field History +Description +XC +XCn +UC +UCn +URCn +VC +VCn +VRCn +HC +HCn +HO +HOn +RI +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +). +extraction, +eigenvalue +Current coordinates of the center of mass for the +entire set or the entire model. Not available for +buckling +eigenfrequency +prediction, complex eigenfrequency extraction, or +linear dynamics procedures. Available also for static +analyses but only from the output database. +Coordinate n of the center of mass for the entire set or +the entire model ( +Current displacement of the center of mass for the +entire set or the entire model. Available also for static +analyses but only from the output database. +Displacement component n of the center of mass for +the entire set or the entire model ( +Rotation component n of the center of mass for the +entire set or the entire model ( +Equivalent rigid body velocity components summed +over the entire set or the entire model. +Component n of the equivalent rigid body velocity +summed over the entire set or the entire model ( +). +). +). +). +). +Component n of the equivalent rigid body angular +velocity summed over the entire set or the entire +model ( +Current angular momentum about the center of mass +for the entire set or the entire model. +Component n of the angular momentum about the +center of mass for the entire set or the entire model +( +Current angular momentum about the origin for the +entire set or the entire model. +Component n of +the angular momentum about +the origin for the entire set or the entire model +( +Current rotary inertia about the origin of the entire set +or the entire model. Not available for eigenfrequency +extraction, eigenvalue buckling prediction, complex +dynamics +eigenfrequency +extraction, +linear +or +). +Identifier +.dat +.fil +.odb +Field History +Description +RIij +MASS +VOL +• +• +• +• +• +• +• +• +procedures. Available also for static analyses but +only from the output database. +-component of the rotary inertia about the origin of +the entire set or the entire model ( +). +Current mass of the entire set or the entire model. +Available also for static analyses but only from the +output database. +Current volume of the entire set or the entire model. +Available also for static analyses but only from the +output database. +(Available only for continuum and +structural elements that do not use general beam or +shell section definitions.) +Inertia relief output variables +You can request inertia relief whole model variable output to the data or output database file . Since these variables have unique values for the entire model, the +variable output is independent of the specified region. The variables listed are available only for those +analyses that include inertia relief loading . +Current coordinates of the reference point. +Coordinate n of the reference point ( +). +Equivalent rigid body acceleration components. +Component n of the equivalent rigid body acceleration +( +). +Component n of the equivalent rigid body angular +to the reference point +acceleration with respect +( +). +Inertia relief load corresponding to the equivalent rigid +body acceleration. +Component n of the inertia relief load corresponding +to the equivalent rigid body acceleration ( +). +of +the +Component +relief moment +corresponding to the equivalent rigid body angular +acceleration with respect +to the reference point +( +). +inertia +Rotary inertia about the reference point. +4.2.1–53 +• +• +• +• +• +• +• +• +• +IRX +IRXn +IRA +IRAn +IRARn +IRF +IRFn +IRMn +IRRI +• +• +• +• +• +• +• +• +Identifier +.dat +.fil +.odb +Field History +Description +IRRIij +IRMASS +• +• +Mass diffusion analysis +• +• +-component of the rotary inertia about the reference +point ( +). +Whole model mass. +You can request variable output from a mass diffusion analysis (“Mass diffusion analysis,” Section 6.9.1) +to the data, results, or output database file . If you specify an +output region, the variable is calculated over the user-specified region. If you do not specify an output +region, the variable is calculated as the total over the entire model. +SOL +• +• +• +Amount of solute in an element set, calculated as the +sum of ESOL (amount of solute in each element) over +all the elements in the set. +Analyses with time-dependent material behavior +CRPTIME +• +Creep time, which is equal +time in +procedures with time-dependent material behavior +. +to the total +Eigenvalue extraction +The following variables are output automatically during a frequency extraction analysis (“Natural +frequency extraction,” Section 6.3.5). +EIGVAL +EIGFREQ +GM +CD +PFn +EMn +Eigenvalues. +Eigenfrequencies. +Generalized masses. +Composite damping factors. +Modal participation factors 1–7 ( +corresponding to displacements, +the rotations, and +Modal +effective masses 1–7 ( +corresponding to displacements, +for the rotations, and +for acoustic pressure). +for +for acoustic pressure). +Complex eigenvalue extraction +The following variables are output automatically during a complex frequency extraction analysis +(“Complex eigenvalue extraction,” Section 6.3.6). +Identifier +.dat +.fil +.odb +Field History +Description +EIGREAL +EIGIMAG +EIGFREQ +DAMPRATIO +Total energy output quantities +Real parts of the eigenvalues. +Imaginary parts of the eigenvalues. +Eigenfrequencies. +Damping ratios. +If the following whole model variables are relevant for a particular analysis, you can request them as +output to the data, results, or output database file . +If you do not specify an output region, whole model variables are calculated. When you specify an output +region, the relevant energy totals are calculated over the user-specified region. +These variables are not available for eigenvalue buckling prediction, eigenfrequency extraction, or +complex frequency extraction analysis. You cannot specify an output region for modal dynamic, +random response, response spectrum, or steady-state dynamic analysis. +See “Energy balance,” Section 1.5.5 of the Abaqus Theory Manual, for details of the energy definitions. +ALLAE +ALLCD +ALLEE +ALLFD +ALLIE +ALLJD +ALLKE +ALLKL +ALLPD +ALLQB +• +• +• +• +• +• +• +• +• +• +by +and +creep, +swelling, +dissipated +“Artificial” strain energy associated with constraints +used to remove singular modes (such as hourglass +control), and with constraints used to make the drill +rotation follow the in-plane rotation of the shell +elements. +Energy +viscoelasticity. +Electrostatic energy. +Total energy dissipated through frictional effects. +(Available only for the whole model.) +Total strain energy. (ALLIE = ALLSE + ALLPD + +ALLCD + ALLAE + ALLQB + ALLEE + ALLDMD.) +Electrical energy dissipated due to flow of electrical +current. +Kinetic energy. +Loss of kinetic energy at impact. (Available only for +the whole model.) +Energy dissipated by rate-independent and rate- +dependent plastic deformation. +Energy dissipated through quiet boundaries (infinite +elements). (Available only for the whole model.) +Identifier +.dat +.fil +.odb +Field History +Description +ALLSD +ALLSE +ALLVD +ALLDMD +ALLWK +ETOTAL +• +• +• +• +• +• +Energy dissipated by automatic stabilization. This +includes both volumetric static stabilization and +automatic approach of contact pairs (the latter part +included only for the whole model). +Recoverable strain energy. +Energy dissipated by viscous effects including viscous +regularization, not inclusive of energy dissipated by +automatic stabilization and viscoelasticity. +Energy dissipated by damage. +External work. (Available only for the whole model.) +Total energy balance (available only for the whole +model). (ETOTAL = ALLKE + ALLIE + ALLVD + +ALLSD + ALLKL + ALLFD + ALLJD − ALLWK.) +Solution-dependent amplitude variables +Solution-dependent amplitude variables are given automatically with any file output or output database +request. +Identifier +.dat +.fil +.odb +Field History +Description +LPF +AMPCU +RATIO +Load proportionality factor in a static Riks analysis. +Current value of the solution-dependent amplitude. +Current maximum ratio of creep strain rate and target +creep strain rate. +Structural optimization variables +Structural optimization output variables are requested by the Abaqus Topology Optimization Module +during each design cycle. For more information, see Chapter 13, “Optimization Techniques.” +Identifier +.dat +.fil +.odb +Field History +Description +Toplogy optimization +The following variable is output automatically during topology optimization . +MAT_PROP_NORMALIZED +Element-based normalized material value. +Identifier +.dat +.fil +.odb +Field History +Description +Shape optimization +The following variables are output automatically during shape optimization . +CTRL_INPUT(OPT) +DISP_OPT_VAL +DISP_OPT +Material scaling coefficient. +The value of the optimization displacement. +A vector representing the optimization displacement. +4.2.2 +Abaqus/Explicit OUTPUT VARIABLE IDENTIFIERS +Product: Abaqus/Explicit +References +• “Output,” Section 4.1.1 +• “Output to the data and results files,” Section 4.1.2 +• “Output to the output database,” Section 4.1.3 +Overview +Except for the information in the status file, results can be obtained from Abaqus/Explicit only by +postprocessing. +The tables in this section list all of the output variables that are available in Abaqus/Explicit. These +output variables can be requested for output to the results (.fil) file or as either field- or history-type output to the output database (.odb) file . When the output variables are requested for output to +the results file, Abaqus/Explicit will first output these variables to the selected results (.sel) file and +will then convert the selected results file to the results file after the analysis completes. +Symbols used in the tables +The availability of the various output variable identifiers is defined by a +under the following headings: +in the columns of the table, +.fil +means that the identifier can be used as a results file output selection. +.odb Field +means that the identifier can be used as a field-type output selection to the output database. +.odb History +means that the identifier can be used as a history-type output selection to the output database. +Direction definitions +The direction definitions depend on the variable type. +Direction definitions for element variables +For components of stress, strain, and similar material variables, 1, 2, and 3 refer to the directions in an +orthogonal coordinate system. These are global directions for solid elements, surface directions for shell +and membrane elements, and axial and transverse directions for beam and pipe elements. However, if a +local orientation (“Orientations,” Section 2.2.5) is associated with the elements for which output is being +requested, 1, 2, and 3 are local directions. +Direction definitions for nodal variables +For nodal variables, 1, 2, and 3 refer to the global directions (1=X, 2=Y, 3=Z except for axisymmetric +elements, in which case 1=R, 2=Z). Even if a local coordinate system has been defined at a node +(“Transformed coordinate systems,” Section 2.1.5), the data in the results file and the selected results +file are still output in the global directions. +If nodal field output is requested for a node that has a local coordinate system defined, a quaternion +representing the rotation from the global directions is written to the output database. Abaqus/CAE +automatically uses this quaternion to transform the nodal results into the local directions. Nodal history +data written to the output database are always stored in the global directions. +Direction definitions for integrated variables +For components of total force, total moment, and similar variables obtained through integration over a +surface, the directions 1, 2, and 3 refer to directions in an orthogonal coordinate system. A fixed global +coordinate system is used if the surface is specified directly for the integrated output request. If the +surface is identified by an integrated output section definition that is associated with the integrated output request, a local coordinate system in the initial +configuration can be specified and can translate or rotate with the deformation. +Distributed load output and user subroutines +Output can be requested for many of the distributed loads discussed in “Loads,” Section 33.4. However, +contributions to these loads defined through user subroutines are not displayed. +Principal value output +Output of the principal values can be requested for stresses, logarithmic strains, and nominal strains. +Either all principal values or the minimum, intermediate, or maximum values can be obtained. All +principal values of tensor ABC are obtained with the request ABCP, and the minimum, intermediate, and +maximum principal values are obtained with the requests ABCP1, ABCP2, and ABCP3, respectively. For +three-dimensional, plane strain, and axisymmetric elements all three principal values are obtained. For +plane stress, membrane, and shell elements only the in-plane principal values are obtained for history- +type output, and the out-of-plane principal value cannot be requested. For field-type output, all three +principal values are obtained through Abaqus/CAE. Principal values cannot be obtained for beam, pipe, +and truss elements, and principal values of plastic strains cannot be requested. +If a principal value or an invariant is requested for field-type output, the output request is replaced +with an output request for the components of the corresponding tensor. Abaqus/CAE calculates all +principal values and invariants from these components. If a principal value is desired as history-type +output, it must be requested explicitly since Abaqus/CAE does no calculations on history data. +Tensor output +Tensor variables that are written to the output database as field-type output are written as components +in either the default directions defined by the convention given in “Orientations,” Section 2.2.5 (global +directions for solid elements, surface directions for shell and membrane elements, and axial and +transverse directions for beam and pipe elements), or the user-defined local system. Abaqus/CAE +calculates all principal values and invariants from these components. See “Writing field output data,” +Section 9.6.4 of the Abaqus Scripting User’s Manual, for a description of the different types of tensor +variables. +The components for tensor variables are written to the output database in single precision. +Therefore, a small amount of precision roundoff error may occur when calculating the variables’ +principal values. Such roundoff error may be observed, for example, when analytically zero values are +calculated as relatively small yet nonzero values. +Requesting output of components +Individual components of variables can be requested as history-type output in the output database for +X–Y plotting in Abaqus/CAE. Individual component requests are not available for field-type output. +If a particular component is desired for contouring in Abaqus/CAE, request field output of the generic +variable (e.g., S for stress). Output for individual components of this field output can be requested within +the Visualization module of Abaqus/CAE. +Element integration point variables +You can request element integration point variable output to the results or output database file . +Identifier +.fil +.odb +Field History +Description +Tensors and invariants +MISESMAX +• +• +• +Sij +SP +• +• +• +• +• +All stress components. +Maximum Mises stress among all of the section points. +For a shell element it represents the maximum Mises +value among all the section points in the layer, for a +beam or pipe element it is the maximum Mises stress +among all the section points in the cross-section, and +for a solid element it represents the Mises stress at the +integration points. +-component of stress ( +). +All principal stress components. +Identifier +.fil +.odb +Field History +Description +intermediate, and maximum principal +Minimum, +stress components (SP1 +All infinitesimal strain components for geometrically +linear analysis. +SP3). +SP2 +-component of infinitesimal strain ( +All logarithmic strain components. +-component of logarithmic strain ( +). +). +intermediate, and maximum principal +All principal logarithmic strain components. +Minimum, +logarithmic strain components (LEP1 +LEP3). +All logarithmic strain rate components. +-component of logarithmic strain rate( +LEP2 +). +All principal logarithmic strain rate components. +Minimum, +strain rate components (ERP1 +All nominal strain components. +intermediate, and maximum principal +ERP3). +ERP2 +-component of nominal strain ( +). +All principal nominal strain components. +Minimum, +intermediate, and maximum principal +nominal strain components (NEP1 NEP2 NEP3). +All plastic strain components. +-component of plastic strain ( +). +All principal plastic strains. +Minimum, +plastic strains. +Volumetric strain rate. +intermediate, and maximum principal +Mises equivalent stress, defined as +where +is the deviatoric stress tensor, defined as +, where +is the stress and +, +is +the equivalent pressure stress. +Equivalent pressure stress, +Stress triaxiality, +All total kinematic hardening shift tensor components. +. +. +-component of the total shift tensor ( +). +4.2.2–4 +SPn +Eij +LE +LEij +LEP +LEPn +ER +ERij +ERP +ERPn +NE +NEij +NEP +NEPn +PE +PEij +PEP +PEPn +ERV +MISES +PRESS +TRIAX +ALPHA +ALPHAij +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Identifier +.fil +.odb +Field History +Description +All +( +kinematic hardening shift tensor components +). +-component of the +and +tensor ( +kinematic hardening shift +). +All tensor components of all the kinematic hardening +shift tensors, except the total shift tensor, ALPHA. +All principal values of the total shift tensor. +Minimum, +values of +ALPHAP2 ALPHAP3). +intermediate, and maximum principal +tensor +the total +(ALPHAP1 +shift +Equivalent plastic strain. +For porous metal plasticity PEEQ is the equivalent +plastic strain in the matrix material defined as +. +For cap plasticity PEEQ gives +(the cap position). +crushable +For +foam plasticity with volumetric +hardening PEEQ gives the volumetric compacting +plastic strain defined as +. +For crushable foam plasticity with isotropic hardening +PEEQ gives the equivalent plastic strain defined as +is the uniaxial compression yield +, where +stress. +Equivalent plastic strain in uniaxial tension for cast +iron, Mohr-Coulomb tension cutoff, and concrete +damaged plasticity, which is defined as +. +Maximum equivalent plastic strain, PEEQ, among all +of the section points. For a shell element it represents +the maximum PEEQ value among all the section points +in the layer, for a beam or a pipe element it is the +maximum PEEQ among all the section points in the +cross-section, and for a solid element it represents the +PEEQ at the integration points. +4.2.2–5 +ALPHAk +ALPHAk_ij +ALPHAN +ALPHAP +ALPHAPn +PEEQ +• +• +PEEQT +PEEQMAX +• +• +• +• +• +• +• +• +• +• +• +• +Identifier +.fil +.odb +Field History +DMICRTMAX +• +Description +Maximum damage initiation among all of the section +points and all of the damage initiation criteria. +This output variable generates three output quantities +as follows: +DMICRTMAXVAL outputs the maximum damage +initiation value. +DMICRTPOS outputs the section point in the layer in +which the maximum damage initiation value occurred. +For solid elements, the output value is one. +DMICRTTYPE outputs a value that represents the +damage initiation criteria type that +reached the +maximum value in the element as follows: +For elements that have failure with progressive +1-DUCTCRT, 2-SHRCRT, 3-JCCRT, +damage: +4-FLDCRT, +and +7-MKCRT. +5-MSFLDCRT, +6-FLSDCRT, +For elements that have fiber-reinforced material +damage: +11-HSNFTCRT, 12-HSNFCCRT, 13- +HSNMTCRT, and 14-HSNMCCRT. +cohesive +For +behavior: +QUADSCRT, and 24-QUADECRT. +elements with traction-separation +23- +22-MAXECRT, +21-MAXSCRT, +Geometric quantities +COORD +• +• +The maximum damage initiation output values are +retained across the requested output frames until a +higher maximum damage initiation value is computed. +solid +Coordinates of +elements. These are the current coordinates if the +large-displacement formulation is being used. +the integration point +for +Identifier +.fil +.odb +Field History +Description +Direction cosines of the local material directions for +an anisotropic hyperelastic material model, or yarn +direction cosines for a fabric material model. This +variable is output automatically if any other element +field output is requested for anisotropic hyperelastic +or fabric material . +transverse shear stress components for three- +All +dimensional conventional shell elements. +-component of transverse shear stress. +-component of transverse shear stress. +All energy densities. +Elastic strain energy density, per unit volume. +Energy dissipated by rate-independent and rate- +dependent plasticity, per unit volume. +Energy dissipated by viscoelasticity, per unit volume +(not +supported for hyperelastic and hyperfoam +material models). +Energy dissipated by viscous effects, per unit volume. +Energy dissipated by damage, per unit volume. +Solution-dependent state variables. +Solution-dependent state variable n. +Temperature. +Material density. +Field variables. +Field variable n. +All failure measure components. +Maximum stress theory failure measure. +4.2.2–7 +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +LOCALDIRn +Additional element stresses +• +TSHR +• +• +• +TSHR13 +TSHR23 +Energy densities +ENER +SENER +PENER +CENER +VENER +DMENER +State and field variables +SDV +SDVn +TEMP +DENSITY +FV +FVn +• +• +• +• +• +• +• +Composite failure measures +• +CFAILURE +Identifier +.fil +.odb +Field History +Description +TSAIH +TSAIW +AZZIT +MSTRN +Tsai-Hill theory failure measure. +Tsai-Wu theory failure measure. +Azzi-Tsai-Hill theory failure measure. +Maximum strain theory failure measure. +All equivalent plastic strains, when the model has more +than one yield/failure surface. +nth equivalent plastic strain ( +). +For cap plasticity: PEQC provides equivalent plastic +strains for all +three possible yield/failure surfaces +(Drucker-Prager failure surface - PEQC1, cap surface +- PEQC2, and transition surface - PEQC3) and the +total volumetric plastic strain (PEQC4). All identifiers +also provide a yes/no flag (1/0 in the output database), +telling whether the yield surface is currently active or +not (AC YIELD: “actively yielding”). +When PEQC is requested as output to the output +database, the active yield flags for each component +are named AC YIELD1, AC YIELD2, etc. +Void volume fraction (porous metal plasticity). +Void volume fraction due to growth (porous metal +plasticity). +Void volume fraction due to nucleation (porous metal +plasticity). +Compressive damage variable, +. +Tensile damage variable, +. +Scalar stiffness degradation variable, d. +Equivalent plastic strain in uniaxial compression, +. +which is defined as +4.2.2–8 +Additional plasticity quantities +PEQC +PEQCn +• +• +• +• +Porous metal plasticity quantities +• +• +VVFG +VVF +• +• +• +• +VVFN +• +• +DAMAGEC +Concrete damaged plasticity +• +• +• +• +DAMAGET +SDEG +PEEQ +• +• +• +• +Identifier +.fil +.odb +Field History +Description +Cracking model quantities +All cracking strain components. +-component of cracking strain. +All cracking strain components in local crack axes. +-component of cracking strain in local crack axes. +Cracking strain magnitude, defined as +. +All stress components in local crack axes. +-component of stress in local crack axes. +Crack orientations. +Crack status of each crack. CKSTAT can have the +following values for each crack: +0.0=uncracked, +1.0=closed crack, 2.0=actively cracking, 3.0=crack +closing/reopening. +stress diagram (FLSD) damage +All active components of the damage initiation criteria. +Ductile damage initiation criterion. +Johnson-Cook damage initiation criterion. +Shear damage initiation criterion. +Forming limit diagram (FLD) damage initiation +criterion. +Forming limit +initiation criterion. +Müschenborn-Sonne forming limit stress diagram +(MSFLD) damage initiation criterion. +Marciniak-Kuczynski +criterion. +Overall scalar stiffness degradation. +Ratio of principal strain rates, +damage initiation criterion. +Shear stress ratio, +shear damage initiation criterion. +, used for the MSFLD +, used for the +initiation +damage +(M-K) +All active components of the damage initiation criteria. +4.2.2–9 +CKE +CKEij +CKLE +CKLEij +CKEMAG +CKLS +CKLSij +CRACK +CKSTAT +• +• +• +• +• +• +Failure with progressive damage +DMICRT +DUCTCRT +JCCRT +SHRCRT +FLDCRT +FLSDCRT +MSFLDCRT +MKCRT +SDEG +ERPRATIO +SHRRATIO +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Fiber-reinforced materials damage +• +DMICRT +Identifier +.fil +.odb +Field History +Description +HSNFTCRT +HSNFCCRT +HSNMTCRT +HSNMCCRT +DAMAGEFT +DAMAGEFC +DAMAGEMT +DAMAGEMC +DAMAGESHR +Fabric material +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Hashin’s fiber tensile damage initiation criterion. +Hashin’s fiber compressive damage initiation criterion. +Hashin’s matrix tensile damage initiation criterion. +Hashin’s matrix compressive damage +criterion. +Fiber tensile damage variable. +Fiber compressive damage variable. +Matrix tensile damage variable. +Matrix compressive damage variable. +Shear damage variable. +initiation +Output variable LOCALDIR (described above) is output automatically for fabric materials. +All fabric stress components. +All fabric strain components. +-component of fabric stress ( +-component of fabric strain ( +). +). +Burn fraction of the ignition and growth material. +Reaction rate of the ignition and growth material. +Density of the unreacted explosive in the ignition and +growth material. +Density of the reacted gas product in the ignition and +growth material. +Distension, +Minimum value, +during plastic compaction of the +material. +, of the distension attained +porous +porous material. +, of the +Force in rebar. +Angle, +in degrees, between rebar and the user- +specified isoparametric direction. Available only for +shell and membrane elements. +4.2.2–10 +SFABRIC +EFABRIC +SFABRICij +EFABRICij +Equation of state +BURNF +DBURNF +RHOE +RHOP +PALPH +PALPHMIN +Rebar quantities +RBFOR +RBANG +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Identifier +.fil +.odb +Field History +Description +Change in angle, in degrees, between rebar and the +user-specified isoparametric direction. Available only +for shell and membrane elements. +Coordinates of element integration point. +Current magnitude and components of the heat flux per +unit area vector. +Current magnitude of the heat flux per unit area vector. +Component n of the heat flux vector ( +). +Maximum nominal stress damage initiation criterion. +Maximum nominal strain damage initiation criterion. +Quadratic nominal stress damage initiation criterion. +Quadratic nominal strain damage initiation criterion. +All active components of the damage initiation criteria. +Overall scalar stiffness degradation. +Status of the element (the status of an element is 1.0 if +the element is active, 0.0 if the element is not). +Eulerian volume fraction. Output includes volume +fraction data for each material defined in the Eulerian +section, plus the volume fraction of void. +Density, computed as a volume fraction weighted +average of all materials in the element. +Mises stress, computed as a volume fraction weighted +average of all materials in the element. +Plastic strain components, computed as a volume +fraction weighted average of all materials in the +element. +Equivalent plastic strain, computed as a volume +fraction weighted average of all materials in the +element. +4.2.2–11 +• +• +• +• +• +• +• +• +• +• +• +• +• +RBROT +• +• +Integration point coordinates +COORD +• +Coupled thermal-stress elements +• +• +HFL +HFLM +HFLn +Cohesive elements +MAXSCRT +MAXECRT +QUADSCRT +QUADECRT +DMICRT +SDEG +STATUS +Eulerian elements +EVF +DENSITYVAVG +MISESVAVG +PEVAVG +PEEQVAVG +• +• +• +• +• +• +• +Identifier +.fil +.odb +Field History +Description +PRESSVAVG +SVAVG +TEMPMAVG +• +• +• +Element section variables +Equivalent pressure stress, computed as a volume +fraction weighted average of all materials in the +element. +Stress components, computed as a volume fraction +weighted average of all materials in the element. +Temperature, computed as a mass fraction weighted +average of all materials in the element. +You can request element section variable output to the results or output database file . These variables are available only for beam, pipe, and shell elements +with the exception of STH, which is also available for membrane elements. They are defined for +particular elements in the element descriptions in Part VI, “Elements.” +.odb +Field History +• +• +• +• +• +• +• +• +• +• +• +• +Description +Section thickness (shell and membrane elements only). +All section resultant components, both translational +(forces) and rotational (moments). +Section force component n, +conventional shells; +shells; +for beams and pipes. +for +for continuum +Section moment component n, +. +All section nominal strains, both translational and +rotational (e.g., midplane strain and curvature in +shells). +Section +nominal +strain +for shells; +component +n, +for +beams and pipes. +Section curvature change or twist n, +. +All average membrane and transverse shear stress +components (shell elements only). +transverse +shear +stress +(shell elements +Average membrane or +component n, +only). +4.2.2–12 +Identifier +.fil +• +• +• +• +STH +SF +SFn +SMn +SE +SEn +SKn +SSAVG +Whole element variables +You can request whole element variable output to the results or output database file . +.odb +Field History +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Description +All energy magnitudes in the element. +Total elastic strain energy in the element (includes +energy in transverse shear deformation in shells). +Total energy dissipated in the element by viscoelastic +(Not supported for hyperelastic and +deformation. +hyperfoam material models.) +Total energy dissipated in the element by rate- +independent and rate-dependent plastic deformation. +Total energy dissipated in the element by viscous +effects. This includes bulk viscosity and material +damping. +Total “artificial” strain energy in the element. This +includes hourglass energy and drilling stiffness energy +in shells. +Internal heat energy in the element. +Total energy dissipated in the element by damage. +Total energy dissipated in the element by distortion +control. +All element energy density components. +Total elastic strain energy density in the element. +Total energy dissipated per unit volume in the +element by rate-independent and rate-dependent +plastic deformation. +Total energy dissipated per unit volume in the element +by viscoelasticity. +Total energy dissipated per unit volume in the element +by viscous effects. +Total “artificial” strain energy density in the element +(energy associated with constraints used to remove +singular modes, such as hourglass control). +Internal heat energy density in the element. +4.2.2–13 +Identifier +.fil +• +ELEN +ELSE +ELCD +ELPD +ELVD +ELASE +ELIHE +ELDMD +ELDC +ELEDEN +ESEDEN +EPDDEN +ECDDEN +EVDDEN +EASEDEN +Identifier +.fil +.odb +Field History +Description +EDMDDEN +EDCDEN +EDT +EMSF +STATUS +• +• +• +EVOL +NFORC +GRAV +SBF +BF +EDMICRTMAX +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Total energy dissipated per unit volume in the element +by damage. +Total energy dissipated per unit volume in the element +by distortion control. +Element stable time increment. +Element mass scaling factor. +Status of element (material failure with progressive +damage, shear failure model, tensile failure model, +porous failure criterion, brittle failure model, Johnson- +Cook plasticity model, and VUMAT). The status of an +element is 1.0 if the element is active, 0.0 if the element +is not. +Current element volume. +(Only available for +continuum and structural elements not using general +beam or shell section definitions.) +Forces at the nodes of an element from both the +hourglass and the regular deformation modes of that +element (internal forces in the global coordinate +system). +Uniformly distributed gravity load. +Stagnation body force. +Uniformly distributed body force, including viscous +body force. +Whole shell element maximum damage initiation +output among all of the layers, all of the damage +initiation criteria, and for fully integrated elements +across all of the integration points. +This output variable is the same as DMICRTMAX +output for solid and beam elements but complements +the DMICRTMAX output variable for composite shell +elements because it extracts the maximum damage +initiation across all of the layers. +This output variable generates four element output +quantities as follows: +Identifier +.fil +.odb +Field History +Description +EDMICRTMAXVAL outputs the maximum damage +initiation value in the entire element. +EDMICRTLAYER outputs the layer number in which +the maximum damage initiation value occurred. +EDMICRTTYPE outputs a value that +represents +the damage initiation criteria type that reached the +maximum value in the element, as described in the +DMICRTMAX output variable description. +EDMICRTINTP outputs the integration point number +for which the maximum damage value occurred. For +reduced-integration elements, the output value is one. +The maximum damage initiation output values are +retained across the requested output frames until a +higher maximum damage initiation value is computed. +). +). +total +forces and +All components of connector +moments. +Connector total force component n ( +Connector total moment component n ( +All components of connector elastic forces and +moments. +Connector elastic force component n ( +Connector elastic moment component n ( +Elastic displacements and rotations in all directions. +Elastic displacement in the n-direction ( +). +Elastic rotation in the n-direction ( +Plastic relative displacements and rotations in all +directions. +Plastic relative displacement in the n-direction ( +). +). +). +). +). +Plastic relative rotation in the n-direction ( +Equivalent plastic relative displacements and rotations +in all directions, and equivalent plastic relative motion +for a coupled plasticity definition. +4.2.2–15 +Connector elements +• +CTF +CTFn +CTMn +CEF +CEFn +CEMn +CUE +CUEn +CUREn +CUP +CUPn +CURPn +CUPEQ +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Identifier +.fil +.odb +Field History +Description +CUPEQn +CURPEQn +CUPEQC +CALPHAF +CALPHAFn +CALPHAMn +CVF +CVFn +CVMn +CUF +CUFn +CUMn +CSF +CSFn +CSMn +CSFC +CNF +CNFn +CNMn +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Equivalent plastic relative displacement +n-direction ( +). +in the +Equivalent plastic relative rotation in the n-direction +( +). +Equivalent plastic relative motion for a coupled +plasticity definition. +All components of connector kinematic hardening +shift forces and moments. +Connector kinematic hardening shift force component +n ( +). +Connector +component n ( +kinematic +hardening +). +shift moment +All components of connector viscous forces and +moments. +Connector viscous force component n ( +Connector viscous moment component n ( +). +). +All components of connector uniaxial forces and +moments. +Connector uniaxial force component n ( +). +Connector uniaxial moment component n ( +). +All components of connector friction forces and +moments. +Connector friction force component n ( +Connector friction moment component n ( +). +). +Connector friction force in the instantaneous slip +direction. Available only if friction is defined in the +slip direction. +All components of connector +contact forces and moments. +Connector +component n (n = 1, 2, 3). +friction-generating +Connector +component n (n = 1, 2, 3). +friction-generating +friction-generating +contact +force +contact moment +Identifier +.fil +.odb +Field History +Description +Connector friction-generating contact force in the +instantaneous slip direction. Available only if friction +is defined in the slip direction. +All components of the overall damage variable. +Overall damage variable component n ( +Overall damage variable component n ( +Components +initiation criterion in all directions. +connector +of +force-based +). +). +damage +Connector force-based damage initiation criterion in +the n-translation direction ( +). +Connector force-based damage initiation criterion in +the n-rotation direction ( +). +Connector force-based damage initiation criterion in +the instantaneous slip direction. +Components of connector motion-based damage +initiation criterion in all directions. +Connector motion-based damage initiation criterion in +the n-translation direction ( +). +Connector motion-based damage initiation criterion in +the n-rotation direction ( +). +Connector motion-based damage initiation criterion in +the instantaneous slip direction. +Components of +connector plastic motion-based +damage initiation criterion in all directions (including +the instantaneous slip direction). +Connector plastic motion-based damage initiation +criterion in the n-translation direction ( +). +Connector plastic motion-based damage initiation +criterion in the n-rotation direction ( +). +Connector plastic motion-based damage initiation +criterion in the instantaneous slip direction. +All flags for connector stop and connector lock status. +Flag for connector stop and connector lock status in +the i-direction ( +). +Components of accumulated slip in all directions. +4.2.2–17 +CNFC +CDMG +CDMGn +CDMGRn +CDIF +CDIFn +CDIFRn +CDIFC +CDIM +CDIMn +CDIMRn +CDIMC +CDIP +CDIPn +CDIPRn +CDIPC +CSLST +CSLSTi +CASU +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Identifier +.fil +.odb +Field History +Description +CASUn +CASURn +CASUC +CIVC +CRF +CRFn +CRMn +CCF +CCFn +CCMn +CP +CPn +CPRn +CU +CUn +CURn +CCU +CCUn +CCURn +CV +CVn +CVRn +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Connector accumulated slip in the n-direction (n = 1, +2, 3). +Connector angular accumulated slip in the n-direction +(n = 1, 2, 3). +Connector accumulated slip in the instantaneous slip +direction. Available only if friction is defined in the +slip direction. +Connector instantaneous velocity in the slip direction. +Available only if friction is defined in the slip direction. +All components of connector reaction forces and +moments. +Connector reaction force component n ( +Connector reaction moment component n ( +). +). +All components of connector concentrated forces and +moments. +Connector concentrated force component n ( +). +Connector concentrated moment component n ( +). +in +the +position +angular +). +). +n-direction +Relative positions in all directions. +Relative position in the n-direction ( +Relative +( +Relative displacements and rotations in all directions. +). +Relative displacement in the n-direction ( +Relative rotation in the n-direction ( +Constitutive displacements and rotations +directions. +Constitutive +( +Constitutive rotation in the n-direction ( +Relative velocities in all directions. +Relative velocity in the n-direction ( +Relative +( +). +n-direction +). +in all +angular +). +displacement +n-direction +velocity +the +the +in +in +). +). +Identifier +.fil +.odb +Field History +Description +• +• +CA +CAn +CARn +CFAILST +CFAILSTi +CDERU +CDERF +• +• +• +• +• +• +• +• +• +• +• +Element face variables +Relative accelerations in all directions. +Relative acceleration in the n-direction ( +). +Relative angular acceleration in the n-direction ( +). +All flags for connector failure status. +Flag for connector failure status in the i-direction ( +). +Connector derived displacement. +Connector derived force. +You can request element face variable output to the output database file . These variables are available only for shell, membrane, and solid +elements. +Identifier +.fil +.odb +Field History +• +• +• +• +• +• +STAGP +VP +IWCONWEP +TRNOR +TRSHR +Nodal variables +Description +Uniformly distributed pressure load on element faces. +When the pressure is defined using *DLOAD, the +variable name is changed automatically to PDLOAD. +Stagnation pressure load on element faces. +Viscous pressure load on element faces. +Air blast pressure load from the CONWEP model on +element faces. +Normal component (component along face normal) of +traction load on element faces. +Shear component (component along face tangent) of +traction load on element faces. +You can request nodal variable output to the results or output database file . +.odb +Field History +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Description +Coordinates of the node. +These are the current +coordinates if the large-displacement formulation is +being used. +Coordinate n ( +). +Displacement components. +Results file and field-type output: both translation and +rotation. +History-type output: translation only. Rotation results +should be requested by components. +Translational displacement components. +Rotational displacement components. +displacement component ( +rotation component ( +). +). +Velocity components (both translation and rotation). +Results file and field-type output: both translation and +rotation. +History-type output: translation only. Rotation results +should be requested by components. +Translational velocity components. +Rotational velocity components. +velocity component ( +rotational velocity component ( +). +). +Acceleration components +rotation). +(both translation and +Results file and field-type output: both translation and +rotation. +History-type output: translation only. Rotation results +should be requested by components. +Translational acceleration components. +Rotational acceleration components. +acceleration component ( +rotational acceleration component ( +). +). +Acoustic pressure at a node. +4.2.2–20 +Identifier +.fil +COORD +COORn +UT +UR +Un +URn +VT +VR +Vn +VRn +AT +AR +An +ARn +POR +• +• +• +• +Identifier +.fil +.odb +Field History +Description +Acoustic absolute pressure at a node. +All temperature values at a node. Available only for +coupled thermal-stress analysis. +Temperature degree of freedom n at a node ( +Available only for coupled thermal-stress analysis. +Reaction force and moment components. +). +Results file and field-type output: both translation and +rotation. +History-type output: translation only. Rotation results +should be requested by components. +). +) (conjugate +). Available +Reaction force components. +Reaction moment components. +Reaction force component n ( +to prescribed displacement +All reaction flux values. Available only for coupled +thermal-stress analysis. +Reaction flux value n at a node ( +only for coupled thermal-stress analysis. +Reaction moment component n ( +(conjugate to prescribed rotation +). +All components of point +moments. +Point load component n ( +Point moment component n ( +Nodal volume fraction. +Status of the tied slave nodes (the status of a slave node +is 2 if the slave node is not tied, 1 if the slave node is +tied, and 0 for nodes that do not participate in a tie +constraint). +Position adjustment vector components of the tied +slave nodes. +loads and concentrated +). +). +) +Fluid cavity gauge pressure. +Fluid cavity volume. +4.2.2–21 +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +PABS +NT +NTn +RF +RT +RM +RFn +RFL +RFLn +RMn +CF +CFn +CMn +NVF +TIEDSTATUS +TIEADJUST +Fluid cavity variables +• +• +PCAV +Identifier +.fil +.odb +Field History +Description +CTEMP +CSAREA +CLAREA +CBLARAT +CMASS +APCAV +TCVOL +ACTEMP +TCSAREA +TCMASS +CMF +CMFL +CMFLT +CEFL +CEFLT +MINFL +MINFLT +TINFL +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Fluid cavity temperature for an ideal gas model used +under adiabatic conditions. +Fluid cavity surface area. +Fluid cavity unblocked leakage area. +Ratio of the blocked leakage area to the unblocked +leakage area. +Mass of the fluid contained in a fluid cavity. +Average gauge pressures for multiple fluid cavities. +Total volume of multiple fluid cavities. +Average fluid cavity temperature for an ideal gas +model used under adiabatic conditions for multiple +fluid cavities. +Total surface area of multiple fluid cavities. +Total mass of the fluid contained in the multiple fluid +cavities. +Molecular mass fraction of fluid species contained in +a fluid cavity. +Mass flow rate out of a fluid cavity. +Accumulated mass flow out of a fluid cavity. +Heat energy flow rate out of a fluid cavity. +Accumulated heat energy flow out of a fluid cavity. +Inflator mass flow rate into a fluid cavity. +Accumulated inflator mass flow into a fluid cavity. +Inflator temperature. +Surface variables +You can request surface variable output +in +Abaqus/Standard and Abaqus/Explicit” in “Output to the output database,” Section 4.1.3); additional +information on these variables is provided in “Defining general contact interactions in Abaqus/Explicit,” +Section 35.4.1; “Defining contact pairs in Abaqus/Explicit,” Section 35.5.1; and “Thermal contact +properties,” Section 36.2.1. +to the output database file (see “Surface output +Identifier +.fil +.odb +Field History +Description +Mechanical analysis–nodal quantities +damage +initiation +Contact normal force (CNORMF) and frictional shear +force (CSHEARF). +Contact pressure (CPRESS) and frictional shear stress +(CSHEAR). CSHEAR is not available for general +contact analyses. +Contact thickness in general contact or contact pairs. +Maximum stress-based damage initiation criterion for +cohesive surfaces in general contact. +Quadratic stress-based damage initiation criterion for +cohesive surfaces in general contact. +Maximum separation-based +criterion for cohesive surfaces in general contact. +Quadratic separation-based damage initiation criterion +for cohesive surfaces in general contact. +Damage variable for cohesive surfaces in general +contact. +Length of contact slip path at slave nodes during +contact (FSLIPEQ) and in some cases +tangent +components of net contact slip in local +directions (FSLIP1 and FSLIP2). These variables +remain constant while a slave node is not in contact. +Magnitude of contact slip rate at slave nodes during +contact (FSLIPR) and in some cases +components of contact slip rate in local +tangent +directions (FSLIPR1 and FSLIPR2). These variables +are set to zero while a slave node is not in contact. +Spot weld bond status. +Spot weld bond load. +Time when bond failure occurs. +All components of remaining stress in the failed bond. +Fraction of stress that remains at bond failure. +4.2.2–23 +CFORCE +CSTRESS +CTHICK +CSMAXSCRT +CSQUADSCRT +CSMAXUCRT +CSQUADUCRT +CSDMG +FSLIP +FSLIPR +• +• +• +• +• +• +• +• +• +• +BONDSTAT +BONDLOAD +• +• +Crack bond failure quantities +DBT +DBS +DBSF +• +• +Identifier +.fil +.odb +Field History +Description +BDSTAT +OPENBC +CRSTS +ENRRT +EFENRRTR +• +• +• +• +• +Mechanical analysis–whole surface quantities +CFN +CFNM +CFS +CFSM +CFT +CFTM +CMN +CMNM +CMS +CMSM +CMT +CMTM +CAREA +XN +XS +XT +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Bond state (the state is 1.0 if bonded, 0.0 if unbonded). +Relative displacement behind crack when fracture +criterion is met. +All components of critical stress at failure. +All components of strain energy release rate. +Effective energy release rate ratio. +Total force due to contact pressure (CFNn, n = 1, 2, 3). +Magnitude of total force due to contact pressure. +Total force due to frictional stress (CFSn, n = 1, 2, 3). +Magnitude of total force due to frictional stress. +Total force due to contact pressure and frictional stress +(CFTn, n = 1, 2, 3). +Magnitude of total force due to contact pressure and +frictional stress. +Total moment about the origin due to contact pressure +(CMNn, n = 1, 2, 3). +Magnitude of total moment about the origin due to +contact pressure. +Total moment about the origin due to frictional stress +(CMSn, n = 1, 2, 3). +Magnitude of total moment about the origin due to +frictional stress. +Total moment about the origin due to contact pressure +and frictional stress (CMTn, n = 1, 2, 3). +Magnitude of total moment about the origin due to +contact pressure and frictional stress. +Total area in contact. +Center of the total force due to contact pressure (XNn, +n = 1, 2, 3). +Center of the total force due to frictional stress (XSn, +n = 1, 2, 3). +Center of the total force due to contact pressure and +frictional stress (XTn, n = 1, 2, 3). +Identifier +.fil +.odb +Field History +Description +Fully coupled temperature-displacement analysis +HFL +HFLA +HTL +HTLA +SFDR +SFDRA +SFDRT +SFDRTA +Integrated variables +• +• +• +• +• +• +• +• +Heat flux per unit area leaving the surface. +HFL multiplied by the nodal area. +Time integrated HFL. +HTL multiplied by the nodal area. +Heat flux per unit area due to frictional dissipation. +SFDR multiplied by the nodal area. +Time integrated SFDR. +SFDRT multiplied by the nodal area. +integrated variable output +You can request +in +Abaqus/Explicit” in “Output to the output database,” Section 4.1.3). The output quantity is computed +by integration over a surface or an element set that is specified either directly in the integrated +output request or by associating an integrated output section definition or an element set definition with the integrated output request. +to the output database (see “Integrated output +The components of the vector output variables are given with respect to a global coordinate system +when no integrated output section definition is associated with the integrated output request. When an +integrated output section is associated with the integrated output request and a local coordinate system is +defined for the integrated output section, the components are given in the local system. The local system +will rotate with the deformation if a reference node with rotation degrees of freedom is associated with +the section definition. +Identifier +.fil +SOAREA +SOF +SOM +.odb +Field History +• +• +• +Description +Area of the surface as projected onto a plane normal to +the average surface normal. +Total force transmitted through the surface. +Total moment transmitted through the surface. The +moment of the forces transmitted through the surface +is taken about the current location of the reference +node if one is specified on an integrated output section +and is associated with the integrated output request. +The moment is taken about the global origin either if +no section definition is associated with the integrated +output request or if there is no reference node defined +in the associated section definition. +Identifier +.fil +.odb +Field History +Description +MASS +DMASS +UCOM +VCOM +ACOM +COORDCOM +MASSEUL +VOLEUL +Total energy output +• +• +• +• +• +• +• +• +Total mass of the element set. +Total mass change in percentage of the element set due +to mass scaling. +Equivalent rigid-body translational displacement of +the element set. +Equivalent rigid-body translational velocity of the +element set. +Equivalent rigid-body translational acceleration of the +element set. +Coordinates of the center of mass of the element set. +Total mass of each Eulerian material instance in the +element set. +Total volume of each Eulerian material instance in the +element set. +You can request total energy variable output to the results or output database file . All of these variables are written when total energy output is +requested. Energy history totals can be requested to the output database for part of the model as well as +the whole model. +Identifier +.fil +ALLAE +ALLCD +ALLFD +ALLIE +ALLKE +• +• +• +• +• +.odb +Field History +• +• +• +• +• +Description +“Artificial” strain energy associated with constraints +used to remove singular modes (such as hourglass +control) and with constraints used to make the drill +rotation follow the in-plane rotation of the shell +elements. +Energy dissipated by viscoelasticity. (Not supported +for hyperelastic and hyperfoam material models). +Total energy dissipated through frictional effects. +(Available only for the whole model). +Total strain energy. +(ALLIE=ALLSE + ALLPD + +ALLCD + ALLAE + ALLDMD+ ALLDC+ ALLFC.) +Kinetic energy. +Identifier +.fil +.odb +Field History +Description +• +• +• +• +• +• +• +• +ALLPD +ALLSE +ALLVD +ALLWK +ALLIHE +ALLHF +ALLDMD +ALLDC +ALLFC +ALLPW +ALLCW +ALLMW +ETOTAL +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Energy dissipated by rate-independent and rate- +dependent plastic deformation. +Recoverable strain energy. +Energy dissipated by viscous effects. +External work. (Available only for the whole model). +Internal heat energy. +External heat energy through external fluxes. +Energy dissipated by damage. +Energy dissipated by distortion control. +Fluid cavity energy, defined as the negative of the work +done by all fluid cavities. (Available only for the whole +model.) +Work done by contact penalties, +penalty/kinematic +contact +(Available only for the whole model.) +Work done by constraint penalties. (Available only for +the whole model.) +Work done in propelling mass added in mass scaling. +(Available only for the whole model.) +Energy balance defined as: ALLKE + ALLIE + +ALLVD + ALLFD + ALLIHE − ALLWK − ALLPW +− ALLCW − ALLMW − ALLHF. (Available only for +the whole model.) +including general +pairs. +contact +and +Time increment and mass output +The DT and DMASS variables are always written when any results file output is requested . You can request +output of the time increment and the steady-state detection variables SSPEEQ, SSSPRD, SSFORC, and +SSTORQ to the output database . +Identifier +.fil +• +• +DT +DMASS +SSPEEQ +.odb +Field History +• +• +• +Description +Time increment. +Percent change in mass of the model due to mass +scaling. +Steady-state equivalent plastic strain norms. +Identifier +.fil +.odb +Field History +Description +SSPEEQn +SSSPRD +SSSPRDn +SSFORC +SSFORCn +SSTORQ +SSTORQn +• +• +• +• +• +• +• +Steady-state equivalent plastic strain norm n. +Steady-state spread strain norms. +Steady-state spread norm n. +Steady-state force norms. +Steady-state force norm n. +Steady-state torque norms. +Steady-state torque norm n. +4.2.3 +Abaqus/CFD OUTPUT VARIABLE IDENTIFIERS +Products: Abaqus/CFD Abaqus/CAE +References +• “Output,” Section 4.1.1 +• “Output to the data and results files,” Section 4.1.2 +• “Output to the output database,” Section 4.1.3 +Overview +Results can be obtained from Abaqus/CFD only by postprocessing. +The tables in this section list all of the output variables that are available in Abaqus/CFD. The +output variables can be requested for either field- or history-type output to the output database (.odb) +file . The field type variables can be requested at the +nodes, elements, or element faces attached to a surface. +Symbols used in the tables +The availability of the various output variable identifiers is defined by a +under the following headings: +in the columns of the table, +.odb Field +means that the identifier can be used as a field-type output selection to the output database. +.odb History +means that the identifier can be used as a history-type output selection to the output database. +Direction definitions +The direction definitions depend on the variable type. +Direction definitions for element variables +For element variables, 1, 2, and 3 refer to the global directions (1=X, 2=Y, and 3=Z). Even if a local +coordinate system has been defined at a node (“Transformed coordinate systems,” Section 2.1.5), the +data are still output in the global directions. +Direction definitions for nodal variables +For nodal variables, 1, 2, and 3 refer to the global directions (1=X, 2=Y, and 3=Z). Even if a local +coordinate system has been defined at a node (“Transformed coordinate systems,” Section 2.1.5), the +data are still output in the global directions. +Requesting output of components +Individual components of variables can be requested as history-type output in the output database for +X–Y plotting in Abaqus/CAE. Individual component requests are not available for field-type output. +If a particular component is desired for contouring in Abaqus/CAE, request field output of the generic +variable (e.g., V for velocity). Output for individual components of this field output can then be requested +within the Visualization module of Abaqus/CAE. +Element variables +You can request element variable output to the output database file . +Identifier +.odb +Description +Field History +Coordinates of the element centroid for solid elements. +These are the current coordinates if the mesh has +moved. +Element volume. +Fluid density. +Divergence of the fluid velocity. +Enstrophy per unit mass. +Dot product of vorticity and velocity. +Fluid pressure. +Fluid temperature. +Fluid velocity. +Second +(symmetric part of the velocity gradient tensor). +Curl of the velocity vector. +Element molecular viscosity. +Shear rate computed using the second invariant of the +rate-of-strain tensor. +rate-of-strain +invariant +tensor +the +of +Wall-normal distance. +Energy dissipation rate. +4.2.3–2 +Geometric quantities +COORD +EVOL +State and field variables +DENSITY +DIV +ENSTROPHY +HELICITY +PRESSURE +TEMP +VGINV2 +VORTICITY +VISCOSITY +SHEARRATE +Turbulence variables +DIST +TURBEPS +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Identifier +.odb +Description +TURBKE +TURBNU +Nodal variables +Field History +• +• +• +• +Turbulent kinetic energy. +Turbulent eddy viscosity. +You can request nodal variable output to the output database file . +Identifier +.odb +Description +Field History +Coordinates of the node. +coordinates if the mesh has moved. +Coordinate n ( +). +These are the current +Fluid density at a node. +Divergence of the fluid velocity at a node. +Enstrophy per unit mass at a node. +Helicity at a node. +Fluid pressure at a node. +Fluid temperature at a node. +Fluid displacement components at a node. +fluid displacement component ( +Fluid velocity components at a node. +fluid velocity component ( +the +invariant +of +tensor +rate-of-strain +Second +(symmetric part of the velocity gradient tensor). +Vorticity components at a node. +Vorticity vorticity component ( +Shear rate at the nodes computed using the second +invariant of the rate-of-strain tensor. +). +). +). +Wall-normal distance. +Energy dissipation rate. +4.2.3–3 +Geometric quantities +COORD +COORn +State and field variables +DENSITY +DIV +ENSTROPHY +HELICITY +PRESSURE +TEMP +Un +Vn +VGINV2 +VORTICITY +VORTICITYn +SHEARRATE +Turbulence variables +DIST +TURBEPS +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Identifier +.odb +Description +Field History +TURBKE +TURBNU +• +• +Surface variables +Turbulent kinetic energy. +Turbulent eddy viscosity at a node. +You can request surface variable output to the output database file . The field output corresponds to the element faces +attached to a surface. +Identifier +.odb +Description +Field History +Area of a surface. For deforming meshes, it is the +surface area in the current configuration. +Area-averaged surface pressure. +Area-averaged surface temperature. +Area-averaged surface velocity vector. +Total fluid force components on the surface. +Integrated normal heat flux on a given surface. Heat +flow is considered positive if heat is added to the +system and negative otherwise. +Heat flux vector on a surface. +Normal heat flux on a surface. +Integrated mass flow rate across a given surface. +Fluid normal traction on a surface. +Fluid pressure force on a given surface. +Fluid surface (or shear) traction on a surface. +Fluid total traction on a surface. This is equal to the +sum of the normal traction (NTRACTION) and the +shear traction (STRACTION). +Fluid viscous force on a given surface. +Integrated volume flow rate across a given surface. +Fluid shear stress magnitude on a surface. +It is the +magnitude of the shear traction (STRACTION) vector. +4.2.3–4 +Geometric quantities +SURFAREA +State and field variables +AVGPRESS +AVGTEMP +AVGVEL +FORCE +HEATFLOW +HFL +HFLN +MASSFLOW +NTRACTION +PRESSFORCE +STRACTION +TRACTION +VISCFORCE +VOLFLOW +WALLSHEAR +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +Identifier +.odb +Description +Field History +Turbulence variables +YPLUS +YSTAR +• +• +Wall-normal distance measured in viscous lengths or +wall units. A default value of 0 is output for surfaces +that are not attached to a wall boundary. +Wall-normal distance scaled using turbulent kinetic +energy and viscosity. YSTAR output is available only +when TYPE=RNG KEPSILON is specified. A default +value of 0 is output for surfaces that are not attached +to a wall boundary. +Whole and partial model variables +The output variables listed below are available for part of the model as well as the whole model. +Identifier +.odb +Description +Field History +Geometric quantities +VOL +• +Total energy output quantities +Current volume of the entire set or the entire model. +If the following whole model variables are relevant for a particular analysis, you can request them +as output to the output database file . If you do not specify an output region, whole model variables are calculated. When +you specify an output region, the relevant energy totals are calculated over the user-specified region. +ALLKE +• +Kinetic energy. +4.3 +The postprocessing calculator +• “The postprocessing calculator,” Section 4.3.1 +4.3.1 +THE POSTPROCESSING CALCULATOR +Products: Abaqus/Standard Abaqus/Explicit +References +• “Output to the output database,” Section 4.1.3 +• “Abaqus/Standard output variable identifiers,” Section 4.2.1 +• “Abaqus/Explicit output variable identifiers,” Section 4.2.2 +• “Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD execution,” Section 3.2.2 +Overview +The postprocessing calculator can perform operations on output quantities written to the output database +(job-name.odb) by Abaqus. It then expands the output database by writing these new output quantities +to the output database. Once this expansion is done, it is not possible to convert the output database +back to its original form. The postprocessing calculator is for use only with the Visualization module of +Abaqus/CAE (Abaqus/Viewer). +Functionality of the calculator +The postprocessing calculator performs the following calculations on data written to the output database: +• Extrapolation of integration point quantities to the nodes or interpolation of integration point +quantities to the centroid of an element, according to the user-specified position for element output; +see “Selecting the position of element integration point and section point output” in “Output to the +output database,” Section 4.1.3, for details. +• Calculation of history output at tracer particles; see “Tracer particle output from Abaqus/Explicit” +in “Output to the output database,” Section 4.1.3. +Running the calculator +By default, the postprocessing calculator will run automatically upon the completion of an analysis. +During the execution of the analysis, Abaqus will determine if there are keywords in the input file +that require the use of the calculator and will initiate the calculator upon completion if it is required. +You can override this default behavior by using the environment variable auto_calculate in the Abaqus +environment file. See “Using the Abaqus environment settings,” Section 3.3.1, for details. +You can run the postprocessing calculator manually by using the convert=odb option on the abaqus +execution procedure. +To see the postprocessed results before an analysis is complete, you can run the postprocessing +calculator manually while the analysis is still running, using the oldjob option in conjunction with the +convert=odb option on the abaqus execution procedure. The postprocessing calculator will write a +new output database using the value of the job parameter as the file name. Due to the fact that the +analysis is writing to the output database at the same time the postprocessing calculator is attempting +to read it, the output database may be in an inconsistent state that makes reading it impossible. If this +problem occurs, the postprocessing calculator will stop attempting to read the output database and exit. A +warning message explaining what has happened will be output to the screen. You can then attempt to run +the postprocessing calculator again. If the inconsistent state has cleared, the postprocessing calculator +will run normally. +If the postprocessing calculator is run during an analysis without the oldjob option, Abaqus will ask +you to confirm that the existing output database can be overwritten. You should make sure the analysis +is complete before running the postprocessing calculator manually without the oldjob option. If the +analysis is still running when the postprocessing calculator is run without using the oldjob option, the +output database will be corrupted. +For a detailed description of the procedure for running the postprocessing calculator manually, see +“Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD execution,” Section 3.2.2. +If an analysis aborts because available CPU time has expired and you restart the analysis, the +postprocessing calculator will not automatically expand the output database from the original, aborted +run. You must manually run the postprocessing calculator to expand the original output database using +the procedure outlined above. +5. +File Output Format +Accessing the results file +5.1 +Accessing the results file +• “Accessing the results file: overview,” Section 5.1.1 +• “Results file output format,” Section 5.1.2 +• “Accessing the results file information,” Section 5.1.3 +• “Utility routines for accessing the results file,” Section 5.1.4 +5.1.1 +ACCESSING THE RESULTS FILE: OVERVIEW +Writing information to the results file +The Abaqus results file is the medium through which analysis results can be carried over into other +software, such as postprocessing programs. The following types of output can be written to the results +file: +• element output, nodal output, energy output, modal output, contact surface output, and section +output +• element matrix output +• substructure matrix output +• cavity radiation viewfactor matrices +“Output,” Section 4.1.1, describes the general format of the results file. +An Abaqus model can be defined in terms of an assembly of part instances . However, the results file is not organized by part; it contains internal node and +element numbers . A map between the original numbers and part instance +names and the internal numbers is written to the data file. +Accessing information in the results file +This chapter contains technical descriptions of the results file and is intended to be read by users or +programmers who need to write programs that use the results file. +• “Results file output format,” Section 5.1.2, describes the format of the individual records in the +results file. +• “Accessing the results file information,” Section 5.1.3, describes the subroutine calls required to +read the file output, contains an example of a program written to use the Abaqus results file, and +shows how you can write (or modify) a results file using the Abaqus file format. +• “Utility routines for accessing the results file,” Section 5.1.4, describes the utility subroutines that +can be used to access the results file. +5.1.2 +RESULTS FILE OUTPUT FORMAT +Products: Abaqus/Standard Abaqus/Explicit +References +• “Accessing the results file: overview,” Section 5.1.1 +• “Abaqus/Standard output variable identifiers,” Section 4.2.1 +• “Abaqus/Explicit output variable identifiers,” Section 4.2.2 +Overview +This section describes the format of the individual records in the Abaqus results file. Where applicable, +the output variable identifier used in writing a given value to the file is printed below the corresponding +record type description. Records that are available only in Abaqus/Standard are designated with an +(S) ; records that are available only in Abaqus/Explicit are designated with an (E) . The record key for a +particular record may differ between Abaqus/Standard and Abaqus/Explicit. +Record format +The results file is written as a sequential file. Each record has the following format: +Location +Length +Description +3, 4... +( +) +) +Record length ( +Record type key +Attributes +All words in the results file are of the same length, whether they contain integer, floating point +number, or character string data. The word length is that of a double precision floating point number +(8 bytes). +The attributes in a given record may depend on the element type being considered. For example, +(in local +, and +the stress components associated with three-dimensional shell elements are +directions), while those associated with three-dimensional solids are +(in global directions if no local orientation is specified). Thus, care must be used in interpreting the data +when postprocessing the file output. Refer to Part VI, “Elements,” for a definition of the ordering of +element-dependent attributes. +, and +, +, +, +, +, +In steady-state dynamic analyses, complex values are stored as the real components followed by +the imaginary components. For example, the stress components associated with three-dimensional shell +elements are +followed by +, and +, and +, +. +, +In models that are defined in terms of an assembly of part instances, the results file contains internal +(global) node and element numbers, as explained in “Output,” Section 4.1.1. Part and assembly records +are not included in the results file. +Local coordinate system +If the components of an element quantity are in local directions, a record of type 85 defining these +directions is generated for each point at which component output is requested if the local coordinate +directions were requested in Abaqus/Standard and automatically in Abaqus/Explicit. The local +coordinate system may be inherent to the element, as is the case in shells and membranes, or may have +been defined by a local orientation . +For shell elements a direction record is written for every material point in the section for which +component output is requested, and a separate direction record is written for section forces and section +strains. For geometrically nonlinear analysis in Abaqus/Standard the record contains the current, updated +directions, except for small-strain shells, in which case the original directions are given. Direction output +is not provided for trusses, two-dimensional beams, axisymmetric shells or membranes, or for values +averaged at nodes. +Label record +Some record types include labels, such as element and node set names, written in A8 format. If a label +exceeds 8 characters, an integer identifier will be written instead. This identifier can then be used to +cross-reference the actual label stored in 10A8 format on record type 1940. +Records written for any file output request +Record Record type +key +1900 +Element definitions +1990(S) +Element definition continuation +Attributes +1. Element number. +2. Element +justified). +type (characters, A8 format, +left +3. First node on the element. +4. Second node on the element. +5. Etc. +1. Node on the element in the previous 1900 record. +2. Etc. +In Abaqus/Explicit quadrilateral/brick elements that are degenerate (i.e., possessing identical nodes) are +written out in record 1900 as corresponding triangular/tetrahedral/wedge elements. For example, a CPE4R +element with two identical nodes is written as a CPE3 element, and a C3D8R element with identical third +and fourth nodes and identical seventh and eighth nodes is written as a C3D6 element. +1901 +Node definitions +1. Node number. +2. First coordinate. +3. Second coordinate. +4. Etc. +Record Record type +key +Attributes +Record key 1902 (below) defines the location of each active degree of freedom. For example, if the model +contains only two-dimensional beam elements, the only active degrees of freedom are 1, 2, and 6. Therefore, +this record would have the attributes (1, 2, 0, 0, 0, 3), meaning that degree of freedom 1 ( +) is the first active +variable at each node; degree of freedom 2 ( +) is the second active variable at each node; degrees of freedom +3, 4, and 5 are not active in the model; and degree of freedom 6 is the third active variable at each node. +1902 +Active degrees of freedom +1. Location in nodal arrays of degree of freedom 1 +(0 if dof 1 is not active in the model). +2. Location in nodal arrays of degree of freedom 2 +(0 if dof 2 is not active in the model). +3. Etc. +1910(S) +Substructure path +1. 0 substructure enter record; 1 substructure leave +record. +2. Element number on usage level. +3. Substructure type identifier (Zn). +4. Element number at the previous level if it is not +the usage level. +5. Etc. +1. Flag for element-based output (0), nodal output +(1), modal output (2), or element set energy output +(3). +2. Set name (node or element set) used in the request +(A8 format). This attribute is blank if no set was +specified. +3. Element +format). +type (only for element output, A8 +1. Abaqus release number (A8 format). +2. Date (2A8 format). +3. Date cont’d. +4. Time (A8 format). +5. Number of elements in the model. +6. Number of nodes in the model. +7. Typical element length in the model. +1. Attributes 1–10. The heading entered as the first +data line of the *HEADING option (A8 format). +Equivalent to the job description in Abaqus/CAE. +5.1.2–3 +1911 +Output request definition +1921 +Abaqus release, etc. +1922 +Record Record type +key +1931 +Node set +Attributes +1. Node set name (A8 format). In Abaqus/Explicit +only node sets defined as part of the model +definition are written. +2. First node in the node set. +3. Second node in the node set. +4. Etc. +1932 +Node set continuation +1. Node number in the node set of the previous 1931 +1933 +Element set +1. Element +set +name +(A8 +record. +2. Etc. +Abaqus/Explicit only element +as part of the model definition are written. +format). +In +sets defined +2. First element in the element set. +3. Second element in the element set. +4. Etc. +1934 +Element set continuation +1. Element number in the element set of the previous +1940 +Label cross-reference +1933 record. +2. Etc. +1. Integer reference. +2. Label (10A8 format). +Record written once per eigenvalue in natural frequency extraction +Record Record type +key +1980(S) Modal +Attributes +1. Eigenvalue number. +2. Eigenvalue. +3. Generalized mass. +4. Composite damping. +5. Participation factor for degree of freedom 1. +6. Effective mass for degree of freedom 1. +7. Participation factor for degree of freedom 2. +8. Effective mass for degree of freedom 2. +9. Etc. +Any nodal or element data after this record refer to the eigenvector, until a new record key 1980 or a record +key 2001 is encountered. Eigenvalue output for substructures also uses these records to divide up elemental and nodal results. This record is written if +Record Record type +key +Attributes +there are any results file output requests for an eigenvalue buckling prediction or eigenfrequency extraction +step. The generalized mass, etc. are not written for an eigenvalue buckling prediction step. This record is not +written for a complex eigenfrequency extraction step. +Records written once per increment +Record Record type +key +2000 +Increment start record +Attributes +1. Total time. +2. Step time. +3. Maximum creep strain-rate ratio (control of +solution-dependent amplitude) in +Abaqus/Standard; currently not used in +Abaqus/Explicit. +4. Solution-dependent amplitude in +Abaqus/Standard; currently not used in +Abaqus/Explicit. +5. Procedure type: gives a key to the step type. See +Table 5.1.2–1 at the end of this section. +6. Step number. +7. Increment number. +8. Linear perturbation flag in Abaqus/Standard: +0 if general step, 1 if linear perturbation step; +currently not used in Abaqus/Explicit. +9. Load proportionality factor: nonzero only in static +Riks steps; currently not used in Abaqus/Explicit. +10. Frequency (cycles/time) in a steady-state dynamic +response analysis or steady-state transport angular +velocity (rad/time) in a steady-state transport +analysis; currently not used in Abaqus/Explicit. +11. Time increment. +12. Attributes 12–21. The step subheading entered +as the first data line of +the *STEP option +(A8 format). Equivalent to the step description in +Abaqus/CAE. +The following record is written once per increment, after all data records have been written for that increment. +2001 +Increment end record +1. No attributes. +Record Record type +key +Attributes +Note: When binary format is used, the results file is written in blocks of 512 words for each +increment. If there are fewer than 512 words in the last block of the current increment, record 2001 +has zeros appended to it so that the total length of the block is 512. Hence, the length of record +2001 is 2 + the number of zeros appended. For an ASCII format results file record 2001 is extended +to complete an 80 character logical record, and a logical record of 80 blank characters is added +after this record. See “Accessing the results file information,” Section 5.1.3. +Records written for any element file output request +These records contain data about element variables at integration points within the elements, at the centroid +of elements, or at the nodes of an element. +Attributes +1. Element number or the node number if the +averaged +contain nodal +records +subsequent +element values. +2. Integration point number if the subsequent records +contain integration point data. Node number +the +if the subsequent records contain data at +nodes of the element. Integration plane number +if +records contain centroidal +values for CAXA and SAXA elements. 0 if the +subsequent records contain centroidal values or +nodal averaged values. +the subsequent +3. Section point number if this is a shell, beam, +or layered solid element and the subsequent +records contain data at a section point through +the thickness. 0 for continuum elements and for +section values in beams and shell elements. +4. Location identification. +0 if the subsequent +records contain data at an integration point; 1 +if the subsequent records contain values at the +centroid of the element; 2 if the subsequent +records contain data at the nodes of the element; 3 +if the subsequent records contain data associated +with rebar within an element; 4 if the subsequent +records contain nodal averaged values; 5 if the +subsequent records contain values associated with +the whole element. +5.1.2–6 +Record Record type +key +key +Attributes +FILE OUTPUT FORMAT +5. Rebar name if the subsequent records contain +values associated with a named rebar. +6. Number of direct stresses at a point (NDI). +7. Number of shear stresses at a point (NSHR). +8. 0, +currently not used in Abaqus/Standard; +number of directions in which displacement +or temperature gradients are computed in the +element (NDIR) in Abaqus/Explicit. +9. Number of +section force or +section strain +components (NSFC). +1. Temperature. +1. Load type. +2. Magnitude. +1. Flux type. +2. Magnitude. +1. State variable 1. +2. State variable 2. +3. Etc. The record can have up to 80 words in ASCII +format or 512 words in binary format. Repeat this +record as often as necessary to output all active +state variables in the model. +Temperature +Output variable: TEMP +Distributed load +Output variable: LOADS +Distributed flux +Output variable: FLUXS +Solution-dependent state variables +Output variable: SDV +Void ratio +Output variable: VOIDR +Foundation pressure +Output variable: FOUND +Coordinates +Output variable: COORD +Field variables +Output variable: FV +Nodal flux caused by heat +Output variable: NFLUX +1. Void ratio. +1. Foundation type. +2. Magnitude. +1. First coordinate. +2. Etc. +1. First field variable. +2. Etc. +1. Node number. +2. First flux component. +3. Etc. +Stresses +Output variable: S +1. First stress component. +2. Second stress component. +5.1.2–7 +3(S) +4(S) +6(S) +7(S) +8(S) +9(S) +10(S) +Record Record type +key +Attributes +3. Etc. + +1. Magnitude (available only when the gasket +contact area is specified; +see “Defining the +contact area for average contact pressure output” +in “Defining the gasket behavior directly using a +gasket behavior model,” Section 32.6.6). +1. Mises stress. +2. Tresca stress. +3. Hydrostatic pressure. +4. Currently not used. +5. Currently not used. +6. Currently not used. +7. Third stress invariant. +1. First section force. +2. Second section force. +3. Etc. +1. Effective axial section force for beams and pipes +subjected to pressure loading. +1. Strain energy. Elastic strain energy is the only +energy density request available in eigenvalue +extractions. None of the energy densities are +available in modal procedures or direct-solution +steady-state dynamics analyses. +2. Plastic dissipation. +3. Creep dissipation. +4. Viscous dissipation. +5. Electrostatic energy. +6. Energy dissipated due to electrical conduction. +7. Damage dissipation. +1. Elastic strain energy. +2. Plastic dissipation. +3. Viscoelastic dissipation (not +supported for +hyperelastic and hyperfoam material models). +5.1.2–8 +475(S) +Average contact pressure (for +link and three-dimensional line +gasket elements) +Output variable: CS11 +12(S) +Stress invariants +Output variable: SINV +13 +Section forces and moments +Output variable: SF +449(S) +14(S) +Effective axial section force +Output variable: ESF1 +Energy densities +Output variable: ENER +14(E) +Energy densities +Record Record type +key +Attributes +15(S) +Nodal forces caused by stress +Output variable: NFORC +4. Viscous dissipation. +5. Currently not used. +6. Currently not used. +7. Damage dissipation. +1. Node number. +2. First force component. +3. Etc. +16(S) +Maximum section stresses +1. Maximum stress on section. +The order of the data and the number of data items for record 17 depends on the element type. For LS3S +elements: +17(S) +Js, K for LS3S line springs +Output variable: JK +For LS6 elements: +17(S) +Js, Ks for LS6 line springs +Output variable: JK +18(S) +19(S) +Pore or acoustic pressure +Output variable: POR +Energy summed over element +Output variable: ELEN +1. J (J-integral). +2. K (stress intensity). +3. +4. +(elastic part of J-integral). +(plastic part of J-integral). +1. J (J-integral). +2. +3. +4. +5. +6. +(elastic part of J-integral). +(plastic part of J-integral). +(Mode I stress intensity factor). +(Mode II stress intensity factor). +(Mode III stress intensity factor). +1. Liquid pressure. +1. Kinetic energy. +2. Strain energy. Elastic strain energy is the only +whole element energy request available in +eigenvalue extractions. None of the element +energies are available in modal procedures or +direct-solution steady-state dynamics analyses. +3. Plastic dissipation. +4. Creep dissipation. +5. Viscous dissipation, not including dissipation due +to stabilization. +6. Static dissipation (due to stabilization). +7. Artificial strain energy. +Record Record type +key +Attributes +19(E) +Energy summed over element +Output variable: ELEN +21 +22 +Total strain in Abaqus/Standard; +infinitesimal strain in +Abaqus/Explicit +Output variable: E +Plastic strains +Output variable: PE +8. Electrostatic energy. +9. Electrical energy dissipated in a conductor. +10. Damage dissipation. +1. Currently not used. +2. Strain energy. +3. Plastic dissipation. +4. Viscoelastic dissipation (not +supported for +hyperelastic and hyperfoam material models). +5. Viscous dissipation. +6. Artificial strain energy. +7. Distortion control dissipation. +8. Currently not used. +9. Internal heat energy. +10. Damage dissipation. +1. First strain component. +2. Second strain component. +3. Etc. +1. First plastic strain component. +2. Second plastic strain component. +3. Etc; +by +followed +equivalent +plastic +the +strain, actively yielding flag (yes or no, A8 +format), and magnitude of plastic strain in +Abaqus/Standard; followed by “0.0, UNUSED, +0.0” in Abaqus/Explicit for consistency with +the length of the Abaqus/Standard record. + +23(S) +Creep strains (including swelling) +Output variable: CE +24(S) +Total inelastic strains +Output variable: IE +1. First creep strain component. +2. Second creep strain component. +3. Etc; +followed by the equivalent creep strain, +volumetric swelling strain, and magnitude of +creep strain. +1. First inelastic strain component. +2. Second inelastic strain component. +3. Etc. +key +25(S) +Total elastic strains +Output variable: EE +26 +Unit normal to crack in concrete +Output variable: CRACK +27 +28 +29 +Section thickness +Output variable: STH +Heat flux vector +Output variable: HFL +Section strains and curvatures +Output variable: SE +30(S) +Deformation gradient +Output variable: DG +FILE OUTPUT FORMAT +Attributes +1. First elastic strain component. +2. Second elastic strain component. +3. Etc. + +1. 11-component (if a 1-D, 2-D, or 3-D analysis). +2. 12-component (if a 2-D or 3-D analysis). +3. 13-component (if a 3-D analysis). +4. 21-component (if a 2-D or 3-D analysis). +5. 22-component (if a 2-D or 3-D analysis). +6. 23-component (if a 3-D analysis). +7. 31-component (if a 3-D analysis). +8. 32-component (if a 3-D analysis). +9. 33-component (if a 3-D analysis). +1. Current section thickness for membranes and +finite-strain shells in Abaqus/Standard and for +membranes and all shells in Abaqus/Explicit. +1. Magnitude. +2. First component. +3. Second component. +4. Etc. +1. First section strain. +2. Second section strain. +3. Etc. + +1. +. +2. Etc. +, +, +, +The record will have NDI diagonal +then NSHR above diagonal +components of +), then NSHR below +components ( +), where NDI +diagonal components ( +and NSHR are given in the element header record +(record key 1). Available only for hyperelasticity, +hyperfoam, and material models defined in user +subroutine UMAT. +, +, +Record Record type +key +Attributes +31(S) +32(S) +33(S) +34(S) +35(S) +36(S) +38(S) +446(S) +447(S) +448(S) +Concrete failure +Output variable: CONF +Strain jumps at nodes +Output variable: SJP +Film +Output variable: FILM +Radiation +Output variable: RAD +Saturation (pore pressure analysis) +Output variable: SAT +Substresses (for ITT elements) +Output variable: SS +Mass concentration (mass +diffusion analysis) +Output variable: CONC +Amount of solute at the integration +point (mass diffusion analysis) +Output variable: ISOL +Amount of solute in the current +element (mass diffusion analysis) +Output variable: ESOL +Amount of solute in the element set +or model (mass diffusion analysis) +Output variable: SOL +1. Summary of the state of a concrete material point. +This is the number of cracks or −1 if the concrete +has crushed. +1. First strain jump component. +2. Second strain jump component. +3. Etc. + +1. Type. +2. Sink temperature. +3. Film coefficient. +1. Type. +2. Sink temperature. +3. Radiation constant. +1. Saturation. +1. First substress. +2. Second substress. +1. Concentration. +1. Amount of solute. +1. Amount of solute. +1. Amount of solute. +The number of data items for record 39 depends on the element type. For pore pressure elements and mass +diffusion analysis: +39(S) +Mass concentration flux vector +Output variable: MFL +1. Magnitude. +2. First component. +Attributes +3. Second component. +4. Etc. +1. Current flow rate. +1. Gel volume ratio. +1. Total fluid volume ratio. +1. Status of element (shear failure model, tensile +failure model, porous failure criterion, brittle +failure model, Johnson-Cook plasticity model, +and VUMAT). The status of an element is 1.0 if the +element is active, 0.0 if the element is not. +1. Equivalent plastic strain. For crushable foam +plasticity with volumetric hardening, +it is the +volumetric compacting plastic strain. For cap +plasticity it is +(the cap position). +1. Mean pressure stress. +1. Mises stress. +1. Current maximum ratio of creep strain rate and +target creep strain rate. +1. Volumetric strain rate. +1. Current +value +of +the +solution-dependent +amplitude. +1. First section stress. +2. Second section stress. +3. Etc. +5.1.2–13 +Record Record type +key +For fluid link elements: +39(S) +40(S) +43(S) +61(E) +73(E) +74(E) +75(E) +79(S) +79(E) +80(S) +83(S) +Mass flow rate +Output variable: MFL +Gel (pore pressure analysis) +Output variable: GELVR +Total fluid volume ratio +Output variable: FLUVR +Element status +Output variable: STATUS +Equivalent plastic strain +Output variable: PEEQ +Mean pressure stress +Output variable: PRESS +Mises equivalent stress +Output variable: MISES +Creep strain rate ratio +Output variable: RATIO +Volumetric strain rate +Output variable: ERV +Solution-dependent +amplitude value +Output variable: AMPCU +Average shell section stresses +Record Record type +key +Attributes +The following record is generated in Abaqus/Standard when the local coordinate directions are requested, +component output is requested for a material or section point, and the components are given in a local +coordinate system ; it is generated automatically in Abaqus/Explicit when component output is requested for a +material or a section point and the components are given in a local coordinate system. Only the first two +directions are given; if needed, the third direction can be obtained as the cross product of the first two. The +direction record is not generated for trusses, two-dimensional beams, axisymmetric shells or membranes, or +for values averaged at nodes. +85 +Local coordinate directions +1. First component of the first direction. +2. Second component of the first direction. +3. Third component of the first direction. +4. First component of the second direction. +5. Second component of the second direction. +6. Third component of the second direction. +86 +87(S) +88(S) +89 +90 +Backstress for kinematic +hardening plasticity +Output variable: ALPHA +component. +component. +1. First +2. Second +3. Etc. (The number of components is equal to the +number of stress components; see the element +description in Part VI, “Elements.”) +User-defined output variables +Output variable: UVARM +1. Output variable 1. +2. Output variable 2. +3. Etc. +Thermal strains +Output variable: THE +Logarithmic strains +Output variable: LE +1. First thermal strain component. +2. Second thermal strain component. +3. Etc. + +1. First logarithmic strain component. +2. Second logarithmic strain component. +3. Etc. + +Nominal strains +Output variable: NE +1. First nominal strain component. +2. Second nominal strain component. +key +Attributes +FILE OUTPUT FORMAT +91(S) +Mechanical strain rates +Output variable: ER +96(S) +97(S) +476(E) +477(E) +Total mass flow through fluid link +Output variable: MFLT +Pore fluid effective velocity vector +Output variable: FLVEL +Scaling factor +Output variable: EMSF +Element time increment +Output variable: EDT +Principal value records +3. Etc. + +1. First strain rate component. +2. Second strain rate component. +3. Etc. + +1. Magnitude. +1. Magnitude. +2. First component. +3. Second component. +4. Etc. +1. Element mass scaling factor. +1. Element stable time increment. +For all principal values, the number of components equals NDI unless NDI equals 1, in which case the number +of components equals NDI plus NSHR, where NDI and NSHR are given on the element header record. In the +cases where NDI equals 2, only the in-plane values are given. +401 +402 +403 +404 +405 +Principal stresses +Output variable: SP +Principal values of backstress tensor +for kinematic hardening plasticity +Output variable: ALPHAP +1. Minimum principal stress. +2. Etc. +1. Minimum principal value. +2. Etc. +Principal strains +Output variable: EP +1. Minimum principal strain. +2. Etc. +Principal nominal strains +Output variable: NEP +Principal logarithmic strains +Output variable: LEP +1. Minimum principal nominal strain. +2. Etc. +1. Minimum principal logarithmic strain. +2. Etc. +Record Record type +key +Attributes +406(S) +407(S) +408(S) +409(S) +410(S) +411(S) +412(S) +Principal mechanical strain rates +Output variable: ERP +1. Minimum principal strain rate. +2. Etc. +Principal values of deformation +gradient +Output variable: DGP +1. Minimum principal value. +2. Etc. +Principal elastic strains +Output variable: EEP +Principal inelastic strains +Output variable: IEP +Principal thermal strains +Output variable: THEP +Principal plastic strains +Output variable: PEP +Principal creep strains +Output variable: CEP +1. Minimum principal elastic strain. +2. Etc. +1. Minimum principal inelastic strain. +2. Etc. +1. Minimum principal thermal strain. +2. Etc. +1. Minimum principal plastic strain. +2. Etc. +1. Minimum principal creep strain. +2. Etc. +1. f. +1. +1. +1. +. +. +1. First cracking strain component. +2. Second cracking strain component. +3. Etc. +1. First strain component in local crack directions. +2. Second strain component in local crack directions. +5.1.2–16 +Records for porous metal plasticity +413 +414 +415 +Void volume fraction +Output variable: VVF +Void volume fraction (growth) +Output variable: VVFG +Void volume fraction (nucleation) +Output variable: VVFN +416(S) +Relative density +Output variable: RD +Records for brittle cracking +421(E) +Cracking strains +Output variable: CKE +422(E) +Local cracking strains +key +Attributes +FILE OUTPUT FORMAT +423(E) +Local cracking stresses +Output variable: CKLS +424(E) +Status of cracks +Output variable: CKSTAT +3. Etc. +1. First stress component in local crack directions. +2. Second stress component in local crack directions. +3. Etc. +1. Status of first crack (if a 1-D, 2-D, or +CKSTAT can have +the +0.0=uncracked, 1.0=closed +3.0=crack +3-D analysis). +following values: +crack, +closing/reopening. +2.0=actively +cracking, +441(E) +Cracking strain magnitude +Output variable: CKEMAG +2. Status of second crack (if a 2-D or 3-D analysis). +3. Status of third crack (if a 3-D analysis). +1. Magnitude of cracking strain. +Records for inelastic nonlinear response in a beam general section +42(S) +Plastic strain components +Output variable: SPE +47(S) +Equivalent plastic strains +Output variable: SEPE +1. Axial plastic strain. +2. Curvature change about the local 1-axis. +3. Curvature change about the local 2-axis (available +only for 3-D beams). +4. Twist of the beam (available only for 3-D beams). +1. Axial equivalent plastic strain. +2. Curvature change about the local 1-axis. +3. Curvature change about the local 2-axis (available +only for 3-D beams). +4. Twist of the beam (available only for 3-D beams). +Records for elastic-plastic response in frame elements +462(S) +Elastic section strain components +Output variable: SEE +1. Elastic axial strain. +2. Elastic curvature change about the local 1-axis. +3. Elastic curvature change about the local 2-axis +(available only for 3-D frame elements). +4. Elastic twist of the beam (available only for 3-D +frame elements). +Record Record type +key +Attributes +1. Plastic axial displacement. +2. Plastic rotation about the local 1-axis. +3. Plastic rotation about the local 2-axis (available +only for 3-D frame elements). +4. Plastic rotation about the element axis (available +only for 3-D frame elements). +5. Actively yielding flag (yes or no, A8 format) for +frame element’s end sections. +6. Buckling flag (yes, no, or na; A8 format) for frame +element’s end sections. +1. Axial backstress component. +2. Bending backstress about the local 1-axis. +3. Bending backstress +about +the +local 2-axis +(available only for 3-D frame elements). +4. Twist backstress of the beam (available only for +3-D frame elements). +1. First component of total force. +2. Second component of total force. +3. Etc. +1. First component of elastic force. +2. Second component of elastic force. +3. Etc. +1. First component of viscous force. +2. Second component of viscous force. +3. Etc. +1. First component of friction force. +2. Second component of friction force. +3. Etc. +1. Flag in the 1-direction. +2. Flag in the 2-direction. +3. Etc. +1. First component of reaction force. +2. Second component of reaction force. +3. Etc. +5.1.2–18 +463(S) +Plastic displacements at frame +element’s ends +Output variable: SEP +464(S) +Generalized backstress components +Output variable: SALPHA +Records for connector elements +495 +496 +497 +498 +499 +500 +Connector total force +Output variable: CTF +Connector elastic force +Output variable: CEF +Connector viscous force +Output variable: CVF +Connector friction force +Output variable: CSF +Connector lock and connector +stop status flags +Output variable: CSLST +Connector reaction force +Record Record type +key +Attributes +501 +502 +503 +504 +505 +506 +Connector concentrated force +Output variable: CCF +Connector relative position +Output variable: CP +Connector relative displacement +Output variable: CU +Connector constitutive +displacement +Output variable: CCU +Connector relative velocity +Output variable: CV +Connector relative acceleration +Output variable: CA +1. First component of concentrated force. +2. Second component of concentrated force. +3. Etc. +1. First component of relative position. +2. Second component of relative position. +3. Etc. +1. First component of relative displacement. +2. Second component of relative displacement. +3. Etc. +1. First component of constitutive displacement. +2. Second component of constitutive displacement. +3. Etc. +1. First component of relative velocity. +2. Second component of relative velocity. +3. Etc. +1. First component of relative acceleration. +2. Second component of relative acceleration. +3. Etc. +507(E) +Connector failure status flags +Output variable: CFAILST +1. Flag in the 1-direction. +2. Flag in the 2-direction. +3. Etc. +1. First component of friction-generating force. +2. Second component of friction-generating force. +3. Etc. +1. Relative velocity in the direction of instantaneous +slip. +1. First component of accumulated frictional slip. +2. Second component of accumulated frictional slip. +3. Etc. +1. First component of elastic displacement. +2. Second component of elastic displacement. +3. Etc. +1. First component of plastic relative displacement. +relative +2. Second +component +plastic +of +displacement. +5.1.2–19 +542 +546 +548 +556 +557 +Connector friction-generating +contact force +Output variable: CNF +Connector relative velocity in the +direction of instantaneous slip +Output variable: CIVC +Accumulated frictional slip +Output variable: CASU +Connector elastic displacement +Output variable: CUE +Connector plastic relative +displacement +Record Record type +key +Attributes +3. Etc. +558 +Connector equivalent plastic +relative displacement +Output variable: CUPEQ +1. First component of equivalent plastic relative +displacement. +2. Second component of equivalent plastic relative +displacement. +3. Etc. +Connector overall damage variable +Output variable: CDMG +1. First component of overall damage variable. +2. Second component of overall damage variable. +3. Etc. +Connector force-based damage +initiation criterion +Output variable: CDIF +1. First component of connector force-based damage +initiation criterion. +2. Second component of connector +force-based +damage initiation criterion. +3. Etc. +Connector motion-based damage +initiation criterion +Output variable: CDIM +1. First component of connector motion-based +damage initiation criterion. +2. Second component of connector motion-based +559(E) +560(E) +561(E) +562(E) +Connector plastic motion-based +damage initiation criterion +Output variable: CDIP +563 +Connector kinematic hardening +shift force +Output variable: CALPHAF +damage initiation criterion. +3. Etc. +1. First component of connector plastic motion- +based damage initiation criterion. +2. Second component of connector plastic motion- +based damage initiation criterion. +3. Etc. +1. First +component +of +connector +kinematic +hardening shift force. +2. Second component of +hardening shift force. +3. Etc. +connector kinematic +Record for plane stress orthotropic failure measures +44(S) +Failure measures +Output variable: CFAILURE +1. Maximum stress theory. +2. Tsai-Hill theory. +3. Tsai-Wu theory. +4. Azzi-Tsai-Hill theory. +5. Maximum strain theory. +Record for equivalent plastic strain components for cap plasticity +key +45 +Equivalent plastic strain +components +Output variable: PEQC +FILE OUTPUT FORMAT +Attributes +1. Equivalent plastic strain for Drucker-Prager +failure surface. +2. Actively yielding flag (yes or no, A8 format) for +Drucker-Prager failure surface. +3. Equivalent plastic strain for cap surface. +4. Actively yielding flag (yes or no, A8 format) for +cap surface. +5. Equivalent plastic strain for transition surface. +6. Actively yielding flag (yes or no, A8 format) for +transition surface. +7. Total volumetric inelastic strain. +8. Actively yielding flag (yes or no, A8 format). +Record for equivalent plastic strain components for jointed materials +45(S) +Equivalent plastic strain +components +Output variable: PEQC +1. Equivalent plastic strain for joint 1. +2. Actively yielding flag (yes or no, A8 format) for +joint 1. +3. Equivalent plastic strain for joint 2. +4. Actively yielding flag (yes or no, A8 format) for +joint 2. +5. Equivalent plastic strain for joint 3. +6. Actively yielding flag (yes or no, A8 format) for +joint 3. +7. Equivalent plastic strain for bulk material. +8. Actively yielding flag (yes or no, A8 format) for +bulk material. +Record for equivalent plastic strain in uniaxial tension for cast iron plasticity +473(S) +Equivalent plastic strain in +uniaxial tension +Output variable: PEEQT +Records for two-layer viscoplasticity +22(S) +Plastic strains in the elastic- +plastic network +Output variable: PE +1. Equivalent plastic strain in uniaxial tension for +cast iron plasticity model. +2. Actively yielding flag (yes or no, A8 format). +1. First plastic strain component. +2. Second plastic strain component. +3. Etc.; followed by the equivalent plastic strain, +actively yielding flag (yes or no, A8 format), +and magnitude of plastic strain. +Record Record type +key +Attributes +524(S) +525(S) +526(S) +Stresses in the elastic-viscous +network +Output variable: VS +Stresses in the elastic-plastic +network +Output variable: PS +1. First stress component. +2. Second stress component. +3. Etc. + +1. First stress component. +2. Second stress component. +3. Etc. + +Viscous strains in the elastic- +viscous network +Output variable: VE +1. First viscous strain component. +2. Second viscous strain component. +3. Etc.; followed by the equivalent viscous strain. +Record for elements with electric potential degrees of freedom +50(S) +Electrical potential gradients +Output variable: EPG +Records for rebar quantities +442 +443 +444 +Force in rebar +Output variable: RBFOR +Rebar angle +Output variable: RBANG +Change in rebar angle +Output variable: RBROT +1. Magnitude. +2. First potential gradient. +3. Etc. + +1. Magnitude. +1. Angle in degrees between the reinforcing and the +user-specified isoparametric direction. Available +only for membrane, shell, and surface elements. +1. Change +in angle +in degrees between the +reinforcing and the user-specified isoparametric +direction. Available only for membrane, shell, +and surface elements. +Record for forced convection/diffusion heat transfer elements +445(S) +Mass flow rates +Output variable: MFR +1. First mass flow rate. +2. Etc. +Records for piezoelectric materials +key +Attributes +FILE OUTPUT FORMAT +46(S) +Magnitudes and phases of potential +gradients (linear dynamics only) +Output variable: PHEPG +49(S) +Magnitudes and phases of +electrical charge fluxes (linear +dynamics only) +Output variable: PHEFL +51(S) +Electrical charge fluxes +Output variable: EFLX +1. Magnitude of first electrical potential gradient. +2. Magnitude of second electrical potential gradient. + +4. Phase angle of first electrical potential gradient. +5. Phase +second electrical potential +angle of +gradient. +6. Etc. +1. Magnitude of first charge flux. +2. Magnitude of second charge flux. +3. Etc. + +4. Phase angle of first charge flux. +5. Phase angle of second charge flux. +6. Etc. +1. Magnitude. +2. First charge flux. +3. Etc. + +60(S) +Distributed electrical charges +Output variable: CHRGS +1. Charge type. +2. Magnitude. +Records for coupled thermal-electric elements +425(S) +Electrical current density +Output variable: ECD +1. Magnitude. +2. First current density. +3. Etc. + +426(S) +427(S) +Distributed electrical current +density +Output variable: ECURS +Nodal current due to electric +conduction +Output variable: NCURS +1. Electrical current type. +2. Magnitude. +1. Node number. +2. Magnitude. +Record Record type +key +Records for cohesive elements +252(S) +All active components of the +damage initiation criteria +Output variable: DMICRT +235(S) +61(S) +Overall scalar stiffness degradation +Output variable: SDEG +Element status +Output variable: STATUS +Attributes +1. MAXSCRT, maximum nominal stress damage +initiation criterion. +2. MAXECRT, maximum nominal strain damage +initiation criterion. +3. QUADSCRT, quadratic nominal stress damage +initiation criterion. +4. QUADECRT, quadratic nominal strain damage +initiation criterion. +1. Magnitude. +1. Status of the element (the status of an element is +1.0 if the element is active, 0.0 if the element is +not). +Records for equivalent rigid body variables in direct-integration implicit dynamic analyses +Records 52–59 provide values summed over an element set. These variables are available only in direct- +integration implicit dynamic analyses . +52(S) +53(S) +54(S) +55(S) +56(S) +Current coordinates of +center of mass +Output variable: XC +Displacement of the center of mass +Output variable: UC +Equivalent rigid body velocity +Output variable: VC +Angular momentum about +center of mass +Output variable: HC +1. Coordinate 1. +2. Coordinate 2. +3. Etc. (The number of components depends upon +the overall dimensionality of the element set.) +1. Displacement 1. +2. Displacement 2. +3. Etc. (The number of components depends upon +the overall dimensionality of the element set.) +1. Component 1. +2. Component 2. +3. Etc. (The number of components depends upon +the overall dimensionality of the element set.) +1. Component 1. +2. Component 2. +3. Etc. (The number of components depends upon +the overall dimensionality of the element set.) +Angular momentum about origin +Output variable: HO +1. Component 1. +2. Component 2. +Record Record type +key +Attributes +57(S) +58(S) +59(S) +Rotary inertia about the origin +Output variable: RI +Current mass of element set +Output variable: MASS +Current volume of element set +Output variable: VOL +3. Etc. (The number of components depends upon +the overall dimensionality of the element set.) +1. Component 11. +2. Component 22. +3. Etc. (The number of components depends upon +the overall dimensionality of the element set.) +1. Mass. +1. Volume. +(Only available for continuum and +structural elements not using general beam or +shell section definitions.) +Record for transverse shear stress in thick shell elements such as S3R, S4R, S8R, and S8RT +48 +Transverse shear stresses in +13 and 23 planes +Output variable: TSHR +Records for linear dynamics +1. Component 13. +2. Component 23. +Magnitude and phase angle of +stress components +Output variable: PHS +1. Magnitude of first stress component. +2. Magnutude of second stress component. +3. Etc. +4. Phase angle of first stress component. +5. Phase angle of second stress component. +6. Etc. +RMS values of stress components +Output variable: RS +1. First component of stress. +2. Second component of stress. +3. Etc. +62(S) +63(S) +65(S) +Magnitude and phase angle of +strain components +Output variable: PHE +1. Magnitude of first strain component. +2. Magnitude of second strain component. +3. Etc. +4. Phase angle of first strain component. +5. Phase angle of second strain component. +6. Etc. +1. First component of strain. +2. Second component of strain. +3. Etc. +66(S) +RMS values of strain components +Output variable: RE +Records for connector elements (available only for linear dynamics) +Record Record type +key +Attributes +508(S) +Magnitude and phase angle of +connector total forces +Output variable: PHCTF +509(S) +Magnitude and phase angle of +connector elastic forces +Output variable: PHCEF +510(S) +Magnitude and phase angle of +connector viscous forces +Output variable: PHCVF +511(S) +Magnitude and phase angle of +connector reaction forces +Output variable: PHCRF +520(S) +Magnitude and phase angle of +connector friction forces +Output variable: PHCSF +512(S) +Magnitude and phase angle of +connector relative displacements +Output variable: PHCU +1. Magnitude of the first component. +2. Magnitude of the second component. +3. Etc. +4. Phase angle of the first component. +5. Phase angle of the second component. +6. Etc. +1. Magnitude of the first component. +2. Magnitude of the second component. +3. Etc. +4. Phase angle of the first component. +5. Phase angle of the second component. +6. Etc. +1. Magnitude of the first component. +2. Magnitude of the second component. +3. Etc. +4. Phase angle of the first component. +5. Phase angle of the second component. +6. Etc. +1. Magnitude of the first component. +2. Magnitude of the second component. +3. Etc. +4. Phase angle of the first component. +5. Phase angle of the second component. +6. Etc. +1. Magnitude of the first component. +2. Magnitude of the second component. +3. Etc. +4. Phase angle of the first component. +5. Phase angle of the second component. +6. Etc. +1. Magnitude of the first component. +2. Magnitude of the second component. +3. Etc. +4. Phase angle of the first component. +5. Phase angle of the second component. +6. Etc. +key +513(S) +Magnitude and phase angle +of connector constitutive +displacements +Output variable: PHCCU +522(S) +Magnitude and phase angle of +connector relative velocities +Output variable: PHCV +523(S) +Magnitude and phase angle of +connector relative accelerations +Output variable: PHCA +543(S) +Magnitude and phase angle of +friction-generating connector force +Output variable: PHCNF +FILE OUTPUT FORMAT +Attributes +1. Magnitude of the first component. +2. Magnitude of the second component. +3. Etc. +4. Phase angle of the first component. +5. Phase angle of the second component. +6. Etc. +1. Magnitude of the first component. +2. Magnitude of the second component. +3. Etc. +4. Phase angle of the first component. +5. Phase angle of the second component. +6. Etc. +1. Magnitude of the first component. +2. Magnitude of the second component. +3. Etc. +4. Phase angle of the first component. +5. Phase angle of the second component. +6. Etc. +1. Magnitude of the first component of friction- +generating connector force. +2. Magnitude of the second component of friction- +generating connector force. +3. Etc. +4. Phase angle of the first component of friction- +generating connector force. +5. Phase angle of the second component of friction- +generating connector force. +6. Etc. +547(S) +514(S) +Magnitude and phase angle of +connector relative velocity in the +direction of instantaneous slip +Output variable: PHCIVSL +1. Magnitude of connector relative velocity in the +direction of instantaneous slip. +2. Phase angle of connector relative velocity in the +direction of instantaneous slip. +RMS values of connector +total forces +Output variable: RCTF +1. First component of force. +2. Second component of force. +3. Etc. +Record Record type +key +Attributes +515(S) +516(S) +517(S) +521(S) +518(S) +519(S) +544(S) +RMS values of connector +elastic forces +Output variable: RCEF +RMS values of connector +viscous forces +Output variable: RCVF +RMS values of connector +reaction forces +Output variable: RCRF +RMS values of connector +friction forces +Output variable: RCSF +1. First component of force. +2. Second component of force. +3. Etc. +1. First component of force. +2. Second component of force. +3. Etc. +1. First component of force. +2. Second component of force. +3. Etc. +1. First component of force. +2. Second component of force. +3. Etc. +RMS values of connector relative +displacements +Output variable: RCU +1. First component of relative displacements. +2. Second component of relative displacements. +3. Etc. +RMS values of connector +constitutive displacements +Output variable: RCCU +1. First component of constitutive displacements. +2. Second component of constitutive displacements. +3. Etc. +RMS values of connector force +generating friction +Output variable: RCNF +1. RMS values of first component of +friction- +generating connector force. +2. RMS values of second component of friction- +generating connector force. +3. Etc. +Records for fluid link elements (available only for linear dynamics) +94(S) +95(S) +Magnitude and phase angle of +mass flow rate +Output variable: PHMFL +Magnitude and phase angle of +total mass flow +Output variable: PHMFT +Records for output of element volumes +1. Magnitude. +2. Phase angle. +1. Magnitude. +2. Phase angle. +The following three variables are not available for eigenfrequency extraction, complex eigenfrequency +extraction, eigenvalue buckling prediction, or linear dynamics procedures. They are available only for +continuum and structural elements not using general beam or shell section definitions. +key +76(S) +77(S) +78(S) +Integration point volume +Output variable: IVOL +Section volume +Output variable: SVOL +Whole element volume +Output variable: EVOL +FILE OUTPUT FORMAT +Attributes +1. Current integration point volume. Section point +volume in the case of beams and shells. +1. Current section volume. +1. Current element volume. +Record for solid elements in an adaptive mesh domain in Abaqus/Standard +264(S) +Change in volume. +Output variable: VOLC +1. Change in area or volume of an element set solely +due to adaptive meshing. +Records written for any node file output request +Record Record type +key +Attributes +101 +102 +103 +104 +Displacements +Output variable: U +Velocities +Output variable: V +Accelerations +Output variable: A +Reaction forces +Output variable: RF +105(S) +106(S) +Electrical potential +Output variable: EPOT +Point loads, moments, fluxes +Output variable: CF +1. Node number. +2. First component of displacement. +3. Second component of displacement. +4. Etc. +1. Node number. +2. First component of velocity. +3. Second component of velocity. +4. Etc. +1. Node number. +2. First component of acceleration. +3. Second component of acceleration. +4. Etc. +1. Node number. +2. First component of reaction force. +3. Second component of reaction force. +4. Etc. +1. Node number. +2. Magnitude. +1. Node number. +2. First component of load or flux. +3. Second component of load or flux. +4. Etc. +Record Record type +key +107 +Coordinates +Output variable: COORD +108 +109(S) +110(S) +119(S) +120(S) +136 +137 +138(S) +139(S) +145(S) +Pore or acoustic pressure +Output variable: POR +Reactive fluid volume flux +Output variable: RVF +Reactive fluid total volume +Output variable: RVT +Electrical reaction charges +Output variable: RCHG +Concentrated electrical +nodal charges +Output variable: CECHG +Fluid cavity pressure +Output variable: PCAV +Fluid cavity volume +Output variable: CVOL +Electrical reaction current +Output variable: RECUR +Concentrated electrical +nodal current +Output variable: CECUR +Viscous forces due to static +stabilization +Output variable: VF +146(S) +Total forces +Output variable: TF +Attributes +1. Node number. +2. First coordinate. +3. Second coordinate. +4. Etc. +1. Node number. +2. Pressure. +1. Node number. +2. Reaction fluid volume flux. +1. Node number. +2. Reaction fluid total volume. +1. Node number. +2. Charge scalar value. +1. Node number. +2. Current scalar value. +1. Fluid cavity reference node number. +2. Pressure. +1. Fluid cavity reference node number. +2. Volume. +1. Node number. +2. Electrical current. +1. Node number. +2. Electrical current. +1. Node number. +2. First component of viscous force. +3. Second component of viscous force. +4. Etc. +1. Node number. +2. First component of total force. +3. Second component of total force. +4. Etc. +151(E) +Acoustic absolute pressure +Output variable: PABS +1. Node number. +2. Absolute pressure. +Record Record type +key +201 +Temperatures +Output variable: NT +204(S) +204(E) +206(S) +214(S) +221(S) +237(S) +Residual fluxes +Output variable: RFL +Reaction fluxes +Output variable: RFL +Concentrated fluxes +Output variable: CFL +Internal fluxes +Output variable: RFLE +Normalized concentration (mass +diffusion analysis) +Output variable: NNC +Motions (in cavity radiation +analysis) +Output variable: MOT +Attributes +1. Node number. +2. Temperature. +3. Etc. (for heat shells) +1. Node number. +2. Residual flux. +3. Etc. (for heat shells) +1. Node number. +2. First component of reaction flux. +3. Second component of reaction flux. +4. Etc. +1. Node number. +2. Concentrated flux. +3. Etc. (for heat shells) +1. Node number. +2. Flux, excluding external flux. +3. Etc. (for heat shells) +1. Node number. +2. Concentration. +1. Node number. +2. First component of motion. +3. Second component of motion. +4. Etc. +320(S) +Concentrated fluid flow +Output variable: CFF +1. Node number. +2. Magnitude of fluid flow. +Records for linear dynamics +111(S) +Magnitude and phase angle of +relative displacement +Output variable: PU +1. Node number. +2. Magnitude of first displacement component. +3. Magnitude of second displacement component. +4. Etc. +5. Phase angle of first displacement component. +6. Phase angle of second displacement component. +7. Etc. +Record Record type +key +Attributes +112(S) +Magnitude and phase angle of +total displacement +Output variable: PTU +113(S) +Total displacement +Output variable: TU +114(S) +Total velocity +Output variable: TV +115(S) +Total acceleration +Output variable: TA +116(S) +117(S) +118(S) +123(S) +Magnitude and phase angle of +acoustic or fluid cavity pressure +Output variable: PPOR +Magnitude and phase angle of +electrical potential +Output variable: PHPOT +Magnitude and phase angle of +reactive charge (piezoelectric +analysis) +Output variable: PHCHG +RMS values of relative +displacement +Output variable: RU +124(S) +RMS values of total displacement +Output variable: RTU +1. Node number. +2. Magnitude of first displacement component. +3. Magnitude of second displacement component. +4. Etc. +5. Phase angle of first displacement component. +6. Phase angle of second displacement component. +7. Etc. +1. Node number. +2. First component of displacement. +3. Second component of displacement. +4. Etc. +1. Node number. +2. First component of velocity. +3. Second component of velocity. +4. Etc. +1. Node number. +2. First component of acceleration. +3. Second component of acceleration. +4. Etc. +1. Node number. +2. Magnitude of pressure. +3. Phase angle of pressure. +1. Node number. +2. Magnitude of potential. +3. Phase angle of potential. +1. Node number. +2. Magnitude of charge. +3. Phase angle of charge. +1. Node number. +2. First component of displacement. +3. Second component of displacement. +4. Etc. +1. Node number. +2. First component of displacement. +3. Second component of displacement. +key +127(S) +RMS values of relative velocity +Output variable: RV +128(S) +RMS values of total velocity +Output variable: RTV +131(S) +RMS values of relative acceleration +Output variable: RA +132(S) +RMS values of total acceleration +Output variable: RTA +134(S) +RMS values of reaction forces +Output variable: RRF +135(S) +Magnitude and phase angle +of reaction force +Output variable: PRF +FILE OUTPUT FORMAT +Attributes +4. Etc. +1. Node number. +2. First component of velocity. +3. Second component of velocity. +4. Etc. +1. Node number. +2. First component of velocity. +3. Second component of velocity. +4. Etc. +1. Node number. +2. First component of acceleration. +3. Second component of acceleration. +4. Etc. +1. Node number. +2. First component of acceleration. +3. Second component of acceleration. +4. Etc. +1. Node number. +2. First component of reaction force. +3. Second component of reaction force. +4. Etc. +1. Node number. +2. Magnitude of first component of reaction force. +3. Magnitude of second component of +reaction +force. +4. Etc. +5. Phase angle of first component of reaction force. +6. Phase angle of second component of reaction +force. +7. Etc. +Records written for any modal file output request during mode-based dynamic analysis +Record Record type +key +Attributes +301(S) +Generalized displacements +Output variable: GU +1. First generalized displacement. +2. Second generalized displacement. +Record Record type +key +Generalized velocities +Output variable: GV +Generalized accelerations +Output variable: GA +Base motions +Output variable: BM +Attributes +3. Etc. +1. First generalized velocity. +2. Second generalized velocity. +3. Etc. +1. First generalized acceleration. +2. Second generalized acceleration. +3. Etc. +1. 1 if displacement, 2 if velocity, 3 if acceleration. +2. x-direction component. +3. y-direction component. +4. z-direction component. +5. x-rotation component. +6. y-rotation component. +7. z-rotation component. +8. Base name. +Phase angle of generalized +displacement +Output variable: GPU +1. Phase angle of generalized displacement for first +mode. +2. Phase angle of generalized displacement +for +second mode. +3. Etc. +Phase angle of generalized velocity +Output variable: GPV +1. Phase angle of generalized velocity for first mode. +2. Phase angle of generalized velocity for second +mode. +3. Etc. +Phase angle of generalized +acceleration +Output variable: GPA +1. Phase angle of generalized acceleration for first +mode. +2. Phase angle of generalized acceleration for second +Strain energy per mode +Output variable: SNE +Kinetic energy per mode +Output variable: KE +mode. +3. Etc. +1. Strain energy for first mode. +2. Strain energy for second mode. +3. Etc. +1. Kinetic energy for first mode. +2. Kinetic energy for second mode. +3. Etc. +5.1.2–34 +302(S) +303(S) +304(S) +305(S) +306(S) +307(S) +308(S) +Record Record type +key +310(S) +External work per mode +Output variable: T +Attributes +1. External work for first mode. +2. External work for second mode. +3. Etc. +Records written for any element matrix or substructure matrix file output request +The ordering of variables on element matrices is the same as that used for user elements : first the variables at the element’s first node, then those at its second node, etc. +Abaqus allows elements to have repeated nodes. +Record Record type +key +1001(S) +Element matrix header record +1002(S) +Element or substructure recovery +matrix nodal dof +1003(S) +Element or substructure recovery +matrix nodal dof change +1004(S) +Element matrix record size +Attributes +1. Element number (zero if this is a substructure). +2. Element or substructure type in A8 format. +3. Number of nodes on the element. +4. Node number of the element’s first node. +5. Node number of the element’s second node. +6. Etc. +1. First dof at +the element’s or at +the recovery +matrix’s first retained node. +2. Second dof at the element’s or at the recovery +matrix’s first retained node. +3. Etc. +1. Node where the dof’s change. +2. First dof at this node. +3. Second dof at this node. +4. Etc. +1. Maximum record length (including the record +length and record key words) for element matrix +and load vector records that follow. The matrix +or load vector records will be subdivided into +multiple records as needed to fit within this +maximum length. +The record key for any +continuation record will be the same as for +the first record. +1005(S) +Element matrix header (continued) +1. Element node number continued from record +1001 (if necessary). +Record Record type +key +1011(S) +Symmetric element stiffness matrix +Attributes +2. Etc. +1. (1, 1) stiffness. +2. (1, 2) stiffness. +3. (2, 2) stiffness. +4. Etc., stored in columns, from the first row to the +diagonal term of each column. +1012(S) +Nonsymmetric element +stiffness matrix +1. (1, 1) stiffness. +2. (2, 1) stiffness. +3. (3, 1) stiffness. +4. Etc., stored in columns. +1021(S) +Symmetric element mass matrix +1. (1, 1) mass. +2. (1, 2) mass. +3. (2, 2) mass. +4. Etc., stored in columns, from the first row to the +diagonal term of each column. +1022(S) +Nonsymmetric element mass matrix +1031(S) +Load vector +1032(S) +Substructure load case vector +1041(S) +Substructure recovery matrix +header record +1. (1, 1) mass. +2. (2, 1) mass. +3. (3, 1) mass. +4. Etc., stored in columns. +1. Load case. +2. Load on first dof. +3. Load on second dof. +4. Etc. +1. Load case name (A8 format). +2. Load on first dof. +3. Load on second dof. +4. Etc. +1. Zero. +2. Element or substructure type in A8 format. +3. Number of eliminated nodes. +4. Node number of the first eliminated node. +5. Node number of the second eliminated node. +6. Etc. +Record Record type +key +Attributes +1042(S) +Substructure recovery matrix +1. Column number corresponding to the retained +1043(S) +Substructure recovery matrix +header (continued) +dofs list. +2. Coefficient of first eliminated dof. +3. Coefficient of second eliminated dof. +4. Etc. +1. Node number continued from record 1041 (if +necessary). +2. Etc. +Record written for any energy file output request +When you do not specify an element set for which energy output is being requested in Abaqus/Standard, +record 1999 provides values summed over the entire model; when you specify an element set for energy +output, record 1999 provides values summed over all the elements in the specified element set. You can +distinguish between a whole model 1999 energy record and an element set 1999 energy record by searching +for a 1911 output request definition record containing the element set name; this 1911 record will be written +just before the element set 1999 energy record. This 1911 record also has the first attribute set to 3 to indicate +element set output. In Abaqus/Explicit you cannot specify selected element sets for an energy output request; +record 1999 provides the total energies for the whole model. +Record Record type +key +1999(S) +Total energies record +Attributes +1. Total kinetic energy (ALLKE). +2. Total recoverable (elastic) strain energy (ALLSE). +3. Total external work (ALLWK, available only for +the whole model.) +4. Total plastic dissipation (ALLPD). +5. Total creep dissipation (ALLCD). +6. Total +dissipation, +viscous +not +including +dissipation due to stabilization (ALLVD). +7. Total loss of kinetic energy at impacts (ALLKL, +available only for the whole model). +8. Total artificial strain energy (ALLAE). +9. Total energy dissipated through quiet boundaries +(ALLQB, available only for the whole model). +10. Total electrostatic energy (ALLEE). +11. Total strain energy (ALLIE). +12. Total energy balance (ETOTAL, available only for +the whole model). +Record Record type +key +Attributes +1999(E) +Total energies record +13. Total energy dissipated through frictional effects +(ALLFD, available only for the whole model). +14. Total +electrical +energy +dissipated +in +conductors (ALLJD). +15. Total static dissipation (due to stabilization, +ALLSD). +16. Total damage dissipation (ALLDMD). +17. Currently not used. +18. Currently not used. +1. Total kinetic energy (ALLKE). +2. Total recoverable (elastic) strain energy (ALLSE). +3. Total external work (ALLWK). +4. Total plastic dissipation (ALLPD). +5. Total viscoelastic dissipation (ALLCD). +6. Total viscous dissipation (ALLVD, not supported +for hyperelastic and hyperfoam material models). +7. Currently not used. +8. Total artificial strain energy (ALLAE). +dissipation +9. Total +distortion +control +energy +(ALLDC). +10. Currently not used. +11. Total strain energy (ALLIE). +12. Total energy balance (ETOTAL). +13. Total energy dissipated through frictional effects +(ALLFD). +14. Currently not used. +15. Percent change in mass (DMASS). +16. Total damage dissipation (ALLDMD). +17. Internal heat energy (ALLIHE). +18. External heat energy (ALLHF). +Records written for contour integrals +Calculations of the J-integral and the C -integral, the stress intensity factors, the crack propagation direction, +and the T-stress can be requested. The record is written for each crack, one record per crack front location. +See record key 17 for J-integral values for line spring elements. +key +1991(S) +J-integral values +1992(S) +C -integral values +1995(S) +Stress intensity factors +FILE OUTPUT FORMAT +Attributes +1. Crack number. +2. Node set (A8 format). +3. Number of contours. +4. J-integral value estimated by first contour. +5. J-integral value estimated by second contour. +6. Etc. +1. Crack number. +2. Node set (A8 format). +3. Number of contours. +4. C -integral value estimated by first contour. +5. C -integral value estimated by second contour. +6. Etc. +1. Crack number. +2. Node set (A8 format). +3. Number of contours. +4. +(Mode I stress intensity factor) estimated by +5. +6. +first contour. +(Mode II stress intensity factor) estimated by +first contour. +7. Crack +(Mode III stress intensity factor) estimated +by first contour (available only for 3-D elements). +degrees) +estimated by first contour (available only for +homogeneous, isotropic elastic materials). +propagation +direction +(in +8. J-integral value estimated from stress intensity +factors of first contour. +9. +(Mode I stress intensity factor) estimated by +second contour. +10. +11. +(Mode II stress intensity factor) estimated by +second contour. +(Mode III stress intensity factor) estimated +(available only for 3-D +by second contour +elements). +12. Crack +direction +propagation +estimated by second contour +for homogeneous, isotropic elastic materials). +13. J-integral value estimated from stress intensity +degrees) +(available only +(in +factors of second contour. +14. Etc. +Record Record type +key +1996(S) +T-stress values +Attributes +1. Crack number. +2. Node set (A8 format). +3. Number of contours. +4. T-stress value estimated by first contour. +5. T-stress value estimated by second contour. +6. Etc. +Record written for crack propagation analysis +The following record is written for each crack that is identified in the crack propagation analysis: +Record Record type +key +1993(S) +Crack tip location and associated +quantities +Attributes +1. Crack number. +2. Slave surface (A8 format). +3. Master surface (A8 format). +4. Initial crack-tip node number. +5. Current crack-tip node number. +6. Flag to indicate crack propagation criterion. 1 +for crack length criterion. 2 for critical stress +criterion. +3 for crack opening displacement +criterion. 5 for VCCT criterion. +7. Cumulative incremental crack length. +8. Value of +stress criterion is +used. Current value of critical crack opening +displacement +if crack opening displacement +criterion is used. +if critical +Records written once for any file output request when surfaces are defined in Abaqus/Standard +The number of data items for the following record depends on the type of surface being defined. +9. Value of +if critical stress criterion is used. +Record Record type +key +Rigid surfaces +1501(S) +Surface definition header +Attributes +1. Surface name. +2. Dimension key (1-1D, 2-2D, 3-3D, +4-Axisymmetric). +3. Type key (1-Deformable, 2-Rigid). +key +Attributes +FILE OUTPUT FORMAT +Deformable surfaces +1501(S) +Surface definition header +1502(S) +Surface facet +4. Number of facets making up the surface. +5. Reference node label. +1. Surface name. +2. Dimension key (1-1D, 2-2D, 3-3D, +4-Axisymmetric). +3. Type key (1-Deformable, 2-Rigid). +4. Number of facets making up the surface. +5. Number of contact master surfaces associated +with this surface through contact pairing (0 if this +surface is a master surface). +6. First master surface name. +7. Second master surface name. +8. Etc. +1. Underlying element number. +2. Element face key (1–S1, 2–S2, 3–S3, 4–S4, 5–S5, +6–S6, 7–SPOS, 8–SNEG). +3. Number of nodes in facet. +4. Node number of the facet’s first node. +5. Node number of the facet’s second node. +6. Etc. +Records written for any contact surface file output request +Record Record type +key +Attributes +5(S) +Solution-dependent state variables +Output variable: SDV +1503(S) +Output request definition +1. State variable 1. +2. State variable 2. +3. Etc. The record can have up to 80 words in ASCII +format or 512 words in binary format. Repeat this +record as often as necessary to output all active +state variables in the model. +1. Contact file output (0). +2. Slave surface name. +3. Master surface name. +4. Node set containing a subset of the nodes making +up the slave surface. +Record Record type +key +1504(S) +Node header +1511(S) +Contact tractions +Output variable: CSTRESS +1512(S) +Viscous tractions +Output variable: CDSTRESS +1521(S) +Contact clearances +Output variable: CDISP +1522(S) +Total force due to contact pressure +Output variable: CFN +1523(S) +Total force due to frictional stress +Output variable: CFS +1575(S) +Total force due to contact pressure +and frictional stress +Output variable: CFT +Attributes +1. Node number. +2. Number of traction components (2 for 2-D or +axisymmetric cases, 3 for 3-D cases). +1. Contact pressure between the node on the slave +surface and the master surface with which it +interacts. +2. Frictional shear traction component in the local +1-direction on the master surface. +3. Frictional shear traction component in the local +2-direction on the master surface for 3-D. +1. Viscous pressure between the node on the slave +surface and the master surface with which it +interacts. +2. Viscous shear traction component in the local 1- +direction on the master surface. +3. Viscous shear traction component in the local 2- +direction on the master surface for 3-D. +1. Separation of the surfaces in the direction of the +normal to the master surface. +2. Accumulated relative tangential displacement of +the surfaces in the local 1-direction on the master +surface. +3. Accumulated relative tangential displacement of +the surfaces in the local 2-direction on the master +surface for 3-D. +1. Magnitude. +2. Force component in the global 1-direction. +3. Force component in the global 2-direction. +4. Force component in the global 3-direction. +1. Magnitude. +2. Force component in the global 1-direction. +3. Force component in the global 2-direction. +4. Force component in the global 3-direction. +1. Magnitude. +2. Force component in the global 1-direction. +3. Force component in the global 2-direction. +4. Force component in the global 3-direction. +Attributes +1. Magnitude. +1. Magnitude. +2. Moment component about the global 1-axis. +3. Moment component about the global 2-axis. +4. Moment component about the global 3-axis. +1. Magnitude. +2. Moment component about the global 1-axis. +3. Moment component about the global 2-axis. +4. Moment component about the global 3-axis. +1. Magnitude. +2. Moment component about the global 1-axis. +3. Moment component about the global 2-axis. +4. Moment component about the global 3-axis. +1. Magnitude. +1. Coordinate in the global 1-direction. +2. Coordinate in the global 2-direction. +3. Coordinate in the global 3-direction. +1. Coordinate in the global 1-direction. +2. Coordinate in the global 2-direction. +3. Coordinate in the global 3-direction. +1. Coordinate in the global 1-direction. +2. Coordinate in the global 2-direction. +3. Coordinate in the global 3-direction. +1. Magnitude. +1. Magnitude. +5.1.2–43 +Record Record type +key +1524(S) +1526(S) +1527(S) +1576(S) +Total area in contact +Output variable: CAREA +Total moment about the origin +due to contact pressure +Output variable: CMN +Total moment about the origin +due to frictional stress +Output variable: CMS +Total moment about the origin +due to contact pressure and +frictional stress +Output variable: CMT +1578(S) Maximum torque that can be +transmitted about the z-axis +by a contact surface in an +axisymmetric analysis with a +friction coefficient of unity +Output variable: CTRQ +1573(S) +1574(S) +1577(S) +1528(S) +1529(S) +Coordinates of the center of the +force due to contact pressure +Output variable: XN +Coordinates of the center of the +force due to frictional stress +Output variable: XS +Coordinates of the center of the +force due to contact pressure +and frictional stress +Output variable: XT +Heat flux density +Output variable: HFL +HFL multiplied by the nodal area +Record Record type +key +Attributes +1530(S) +1531(S) +1532(S) +1533(S) +1534(S) +1535(S) +Time integrated HFL +Output variable: HTL +Time integrated HFLA +Output variable: HTLA +Heat flux density due to frictional +dissipation +Output variable: SFDR +SFDR multiplied by the nodal area +Output variable: SFDRA +Time integrated SFDR +Output variable: SFDRT +Time integrated SFDRA +Output variable: SFDRTA +1536(S) Weighting factor +Output variable: WEIGHT +1537(S) +1538(S) +1539(S) +1540(S) +1541(S) +1542(S) +1543(S) +1544(S) +Heat flux density due to +electrical current +Output variable: SJD +SJD multiplied by the nodal area +Output variable: SJDA +Time integrated SJD +Output variable: SJDT +Time integrated SJDA +Output variable: SJDTA +Electrical current density +Output variable: ECD +ECD multiplied by area +Output variable: ECDA +Time integrated ECD +Output variable: ECDT +Time integrated ECDA +Output variable: ECDTA +1. Magnitude. +1. Magnitude. +1. Magnitude. +1. Magnitude. +1. Magnitude. +1. Magnitude. +1. Magnitude. +1. Magnitude. +1. Magnitude. +1. Magnitude. +1. Magnitude. +1. Magnitude. +1. Magnitude. +1. Magnitude. +1. Magnitude. +Record Record type +key +Attributes +1545(S) +1546(S) +1547(S) +1548(S) +1549(S) +Pore fluid volume flux per unit area +Output variable: PFL +PFL multiplied by the nodal area +Output variable: PFLA +Time integrated PFL +Output variable: PTL +Time integrated PFLA +Output variable: PTLA +Total pore fluid volume flux +leaving the slave surface +Output variable: TPFL +1550(S) +Time integrated TPFL +Output variable: TPTL +1. Magnitude. +1. Magnitude. +1. Magnitude. +1. Magnitude. +1. Magnitude. +1. Magnitude. +Records for bond failure quantities from crack propagation analysis +1570(S) +1571(S) +1572(S) +290(S) +293(S) +294(S) +235(S) +295(S) +Time when bond failure occurs +Output variable: DBT +Fraction of stress that remains +at bond failure +Output variable: DBSF +1. Magnitude. +1. Magnitude. +Remaining stress in the failed bond +Output variable: DBS +1. 11-component of debond stress. +2. 12-component of debond stress. +Relative displacement behind crack +when fracture criterion is met +Output variable: OPENBC +Effective energy release rate ratio +Output variable: EFENRRTR +Bond state (varies from 1.0 to 0.0) +Output variable: BDSTAT +Damage variable +Output variable: CSDMG +Critical stress at failure +Output variable: CRSTS +1. Magnitude. +1. Magnitude. +1. Magnitude. +1. Magnitude. +1. 11-component of critical stress. +2. 12-component of critical stress. +Record Record type +key +Attributes +296(S) +Strain energy release rate +Output variable: ENRRT +3. 13-component of critical stress (only available to +three-dimensional models). +1. 11-component of strain energy release rate. +2. 12-component of strain energy release rate. +3. 13-component of strain energy release rate (only +available to three-dimensional models). +Record for surface-based pressure penetration analysis +1592(S) +Fluid pressure for surface-based +pressure penetration analysis +Output variable: PPRESS +1. Magnitude. +Records for surface-based cohesive behavior with damage +253(S) +345(S) +346(S) +347(S) +348(S) +Overall value of the scalar +damage variable +Output variable: CSDMG +Maximum contact stress damage +initiation criterion +Output variable: CSMAXSCRT +Maximum separation damage +initiation criterion +Output variable: CSMAXUCRT +Quadratic contact stress damage +initiation criterion +Output variable: CSQUADSCRT +Quadratic separation damage +initiation criterion +Output variable: CSQUADUCRT +1. Magnitude. +1. Magnitude. +1. Magnitude. +1. Magnitude. +1. Magnitude. +Records written once for any file output request when cavities are defined +Record Record type +key +1601(S) +Cavity definition header +Attributes +1. Number of surfaces making up the cavity. +2. Cavity name. +3. Name of cavity’s first surface. +4. Name of cavity’s second surface. +5. Etc. +key +1610(S) +Facet order record size +1602(S) +Cavity facet order +FILE OUTPUT FORMAT +Attributes +1. Maximum record length (including the record +length and record key words) for cavity facet +order records that follow. The cavity facet order +data will be subdivided into multiple records as +needed to fit within this maximum length. The +record key for any continuation record will be the +same as for the first record. +1. Number of facets making up the cavity. +2. Cavity name. +3. Cavity’s first (underlying) element number. +4. First element face key (1-S1, 2–S2, 3–S3, 4–S4, +5–S5, 6–S6, 7–SPOS, 8–SNEG) +5. Cavity’s second (underlying) element number. +6. Second element face key (1–S1, 2–S2, 3–S3, +4–S4, 5–S5, 6–S6, 7–SPOS, 8–SNEG) +7. Etc. +Records written for any viewfactor matrix output request +The ordering of the facets (each facet corresponds to one row of the viewfactor matrix) is that appearing in +the cavity facet order record 1602. +Record Record type +key +1608(S) +Output request definition +1605(S) +Viewfactor matrix header +1609(S) +Viewfactor matrix record size +1606(S) +Nonsymmetric viewfactor matrix +Attributes +1. Viewfactor output (0). +2. Cavity name. +1. Number of facets in the cavity. +2. Cavity name. +1. Maximum record length (including the record +length and record key words) for viewfactor +matrix and facet area records that follow. The +matrix or facet area records will be subdivided +into multiple records as needed to fit within +this maximum length. The record key for any +continuation record will be the same as for the +first record. +1. (1, 1) dimensionless viewfactor. +2. (1, 2) dimensionless viewfactor. +Record Record type +key +Attributes +1607(S) +Facet areas +3. (1, 3) dimensionless viewfactor. +4. Etc., stored in rows. +1. Area of first facet. +2. Area of second facet. +3. Area of third facet. +4. Etc. +Records written for any radiation file output request +Record Record type +key +1603(S) +Output request definition +Attributes +1. Radiation file output (1). +2. Cavity name. +3. Surface name. +4. Element set name. +1604(S) +Facet header record +1. (Underlying) user element number. +2. Element face key (1–S1, 2–S2, 3–S3, 4–S4, 5–S5, +6–S6, 7–SPOS, 8–SNEG) +231(S) +232(S) +233(S) +234(S) +235(S) +Radiation flux density +Radiation flux +Time integrated radiation +flux density +Time integrated radiation flux +Total viewfactor (sum of viewfactor +matrix row) +3. Facet area. +1. Magnitude. +1. Magnitude. +1. Magnitude. +1. Magnitude. +1. Magnitude. +236(S) +Facet temperature +1. Magnitude. +Records written for any section file output request +The output variables described below are not available for random response analysis. +Record Record type +key +1580(S) +Output request definition +Attributes +1. Surface section output (1). +2. Section name. +key +1581(S) +Section output header record +FILE OUTPUT FORMAT +Attributes +1. Surface name. +2. System of coordinates used for output (1–Global, +2–Local). +3. Flag to indicate whether or not +the local +coordinate system and the output are updated +during the analysis (1–Yes, 2–No). +For all analysis types +The following two records are generated only when section output is requested in a local coordinate system. +In that case all components of forces and moments are given with respect to the local system. Only the first +two directions of the local coordinate system are given; if needed, the third direction can be calculated as the +cross product of the first two. +1582(S) +1583(S) +Global coordinates of the +anchor point +Direction cosines of the local +coordinate system +1584(S) +Area of the defined section +Output variable: SOAREA +For stress/displacement analyses +1585(S) +1586(S) +1587(S) +Total force in the section in +the selected system +Output variable: SOF +Total moment in the section about +the origin of the selected system +Output variable: SOM +Global coordinates of the center of +the total force in the section +Output variable: SOCF +For heat transfer analyses +1. First coordinate. +2. Etc. +1. First component of the first direction. +2. Second component of the first direction. +3. Third component of the first direction. +4. First component of the second direction. +5. Second component of the second direction. +6. Third component of the second direction. +1. Magnitude. +1. Magnitude. +2. First force component. +3. Etc. +1. Magnitude. +2. First moment component. +3. Etc. +1. First coordinate. +2. Etc. +1588(S) +Total heat flux across the section +Output variable: SOH +1. Magnitude. +Record Record type +key +For electrical analyses +Attributes +1589(S) +Total current across the section +Output variable: SOE +1. Magnitude. +For mass diffusion analyses +1590(S) +Total mass flow across the section +Output variable: SOD +1. Magnitude. +For coupled pore fluid diffusion-stress analyses +1591(S) +Total pore fluid volume flux +across the section +Output variable: SOP +1. Magnitude. +For coupled analyses the appropriate combination of records is available. For example, in a thermal-electrical +analysis both SOH and SOE are valid output requests. +Procedure type keys +Key +Description +Table 5.1.2–1 Keys to procedure types. +11 +12 +13 +17 +21 +22 +31 +32 +33 +Static, automatic incrementation +Static, direct incrementation +Direct cyclic, automatic time incrementation +Direct cyclic, fixed time incrementation +Implicit dynamic, half-increment residual tolerance given +Implicit dynamic, fixed time increments +Implicit dynamic, subspace projection +Explicit dynamic +Quasi-static, explicit time integration +Quasi-static, implicit integration +Heat transfer, steady-state +Heat transfer, transient, fixed time increments +Heat transfer, transient, maximum allowable nodal temperature change given +Description +FILE OUTPUT FORMAT +34 +35 +36 +41 +42 +51 +61 +62 +63 +64 +65 +71 +72 +73 +74 +75 +76 +77 +85 +86 +91 +92 +93 +94 +95 +98 +Mass diffusion, steady-state +Mass diffusion, transient, fixed time increments +Mass diffusion, transient, maximum allowable normalized concentration change given +Eigenvalue frequency extraction +Eigenvalue buckling prediction +Substructure generation +Geostatic stress field +Coupled pore fluid diffusion/stress, steady-state, fixed time incrementation +Coupled pore fluid diffusion/stress, steady-state, automatic time incrementation +Coupled pore fluid diffusion/stress, transient, fixed time incrementation +Coupled pore fluid diffusion/stress, transient, automatic time incrementation +Coupled thermal-stress, steady-state +Coupled thermal-stress, transient, fixed time increments +Coupled thermal-stress, transient, maximum allowable nodal temperature change and/or +accuracy tolerance parameter given +Explicit dynamic coupled thermal-stress +Coupled thermal-electrical, steady-state +Coupled thermal-electrical, transient analysis, fixed time increments +Coupled thermal-electrical, transient analysis, maximum allowable nodal temperature +change given +Steady-state transport, automatic incrementation +Steady-state transport, direct incrementation +Response spectrum +Modal dynamic +Steady-state dynamic +Random response +Direct-solution steady-state dynamic +Annealing +5.1.3 +ACCESSING THE RESULTS FILE INFORMATION +Products: Abaqus/Standard Abaqus/Explicit +References +• “Accessing the results file: overview,” Section 5.1.1 +• “Results file output format,” Section 5.1.2 +• “Utility routines for accessing the results file,” Section 5.1.4 +Overview +The Abaqus results (.fil) file is written using internal data management routines to minimize I/O cost. +A postprocessing program must use these same Abaqus data management routines to read the results +file. The following utility routines must be called to obtain data from the Abaqus results file: +• INITPF +• DBRNU +• DBFILE +• POSFIL +You can also write a file in the format of the Abaqus results file by using the following utility subroutines: +• INITPF +• DBFILW +The syntax of these utility subroutines is described in “Utility routines for accessing the results file,” +Section 5.1.4. +Reading floating point and integer variables +To read both floating point and integer variables in the records, the following coding can be used in the +postprocessing program: +INCLUDE 'aba_param.inc' +DIMENSION ARRAY(513), JRRAY(NPRECD,513) +EQUIVALENCE (ARRAY(1),JRRAY(1,1)) +With this technique, for example, the record key is available after each call to DBFILE with LOP=0 as +KEY = +JRRAY (1,2) +The use of aba_param.inc eliminates the need to have different versions of the code for single and +double precision. The file aba_param.inc defines an appropriate IMPLICIT REAL statement and +sets the value of NPRECD to 1 or 2, depending upon whether the machine uses single or double precision. +The file aba_param.inc is referenced from the site subdirectory of the Abaqus installation when +the postprocessing program is compiled and linked using the abaqus make utility (explained below). +Linking the postprocessing program +The postprocessing program must be linked using the make parameter when running the Abaqus +execution procedure . To link +properly, the postprocessing program cannot contain a FORTRAN PROGRAM statement. Instead, the +program must begin with a FORTRAN SUBROUTINE with the name ABQMAIN. +Compiling, linking, and running a postprocessing program consists of two steps. For example, if +the name of the postprocessing program is postproc.f, use the following command to compile and +link postproc.f: +abaqus make job=postproc +The program must then be run using the command: +abaqus postproc +Calling the utility subroutines for reading the results file +Subroutine INITPF must be called before any results file is accessed. This subroutine contains +FORTRAN OPEN statements for all FORTRAN units assigned to results files through the call to +INITPF; therefore, your code must not contain any OPEN statements for these units. Abaqus +constructs a file name for a given unit based on information supplied as LRUNIT(1,K1) and FNAME, +as discussed in “Utility routines for accessing the results file,” Section 5.1.4. +Subroutine DBRNU must also be called before reading the first results file and then again each time +you need to change to reading another results file. This subroutine simply establishes the FORTRAN +unit number of the results file being read; no information is returned. DBRNU can be called before or +after INITPF but must be called before DBFILE. +Subroutine DBFILE is used to read each record from the results file. This subroutine will return +one record at a time in the format described in “Results file output format,” Section 5.1.2. +Example +The following program reads all the von Mises stresses in the results file and obtains the maximum value. +Then, it prints this value along with the element, section point, and integration point numbers where it +occurred. +In this example FORTRAN unit 8 is used to read the results file, and the name of the results file is +assumed to be TEST.fil. The results file is assumed to be a binary file, and only one results file will +be read. Thus, LRUNIT is dimensioned as LRUNIT(2,1); and in the call to the INITPF routine NRU +is set to 1, LRUNIT(1,1) is set to 8, and LRUNIT(2,1) is set to 2. A new results file will not be +written, so LOUTF is set to zero. +ACCESSING THE FILE INFORMATION +SUBROUTINE ABQMAIN +Calculate the maximum von Mises stress and its location +INCLUDE 'aba_param.inc' +CHARACTER*80 FNAME +DIMENSION ARRAY(513),JRRAY(NPRECD,513),LRUNIT(2,1) +EQUIVALENCE (ARRAY(1),JRRAY(1,1)) +File initialization +FNAME='TEST' +NRU=1 +LRUNIT(1,1)=8 +LRUNIT(2,1)=2 +LOUTF=0 +CALL INITPF(FNAME,NRU,LRUNIT,LOUTF) +JUNIT=8 +CALL DBRNU(JUNIT) +Loop on all records in results file +STRESS=0. +DO 100 K1=1,99999 +CALL DBFILE(0,ARRAY,JRCD) +IF(JRCD.NE.0)GO TO 110 +KEY=JRRAY(1,2) +IF(KEY.EQ.1) THEN +Element header record: +extract element, sec pt, int pt numbers +JEL=JRRAY(1,3) +JPNT=JRRAY(1,4) +JSPNT=JRRAY(1,5) +Stress invariant record for Abaqus/Standard +ELSE IF(KEY.EQ.12)THEN +Stress invariant record for Abaqus/Explicit +ELSE IF(KEY.EQ.75)THEN +Extract von Mises stress +IF(ARRAY(3).GT.STRESS)THEN +STRESS=ARRAY(3) +KEL=JEL +KPNT=JPNT +KSPNT=JSPNT +END IF +END IF +100 +110 +CONTINUE +CONTINUE +WRITE(6,120) KEL,KPNT,KSPNT,STRESS +FORMAT(5X,'ELEMENT',I5,5X,'POINT',I4,5X,'SECTION POINT', +120 +1 I4,5X,'STRESS',1PG12.3) +STOP +END +See Chapter 14, “Postprocessing of Abaqus Results Files,” of the Abaqus Example Problems Manual for +additional examples. +Writing a file in the results file format +Subroutine DBFILW can be used to write a file in the format of the Abaqus results file to modify the file +information or to add additional information before postprocessing. Subroutine INITPF must be called +before DBFILW. +The file will be written to FORTRAN unit 9 with the extension .fin. Unit 9 is opened by Abaqus +when DBFILW is first called; your coding must not open or redefine unit 9, but you must ensure that +FORTRAN unit 9 is saved following the job. +“Joining data from multiple results files and converting file format: FJOIN,” Section 14.1.2 of the +Abaqus Example Problems Manual, contains an example of the use of subroutine DBFILW to merge +specific records of discontinuous results files. Continuous results files are required for postprocessing +purposes; if you have written a results file during an analysis and a new results file on the restart of +the analysis without making the files continuous, they must be made continuous before postprocessing. +“Analysis of a cantilever subject to earthquake motion,” Section 1.4.13 of the Abaqus Benchmarks +Manual, also shows the use of DBFILW for merging results files. Alternatively, results files can be +merged using the abaqus append utility as described in “Joining results (.fil) files,” Section 3.2.12. +The DBFILW subroutine can also be used to convert the Abaqus results file from binary to ASCII +format to transfer it from one computer system to another. Alternatively, this conversion can be done +automatically by using the abaqus ascfil execution procedure, as described in “ASCII translation of +results (.fil) files,” Section 3.2.11. +5.1.4 +UTILITY ROUTINES FOR ACCESSING THE RESULTS FILE +Products: Abaqus/Standard Abaqus/Explicit +References +• “Accessing the results file information,” Section 5.1.3 +• “URDFIL,” Section 1.1.48 of the Abaqus User Subroutines Reference Manual +• “Joining data from multiple results files and converting file format: FJOIN,” Section 14.1.2 of the +Abaqus Example Problems Manual +• “Calculation of principal stresses and strains and their directions: FPRIN,” Section 14.1.3 of the +Abaqus Example Problems Manual +• “Creation of a perturbed mesh from original coordinate data and eigenvectors: FPERT,” +Section 14.1.4 of the Abaqus Example Problems Manual +Overview +The Abaqus results (.fil) file can be accessed with the utility routines described in this section. Access +is subsequent to an analysis by a user-written postprocessing program or, in Abaqus/Standard, from +within an analysis by user subroutine URDFIL. +The following utility subroutines are available: +• DBFILE (read from a file) +• DBFILW (write to a file) +• DBRNU (set a unit number for a file) +• INITPF (initialize a file) +• POSFIL (determine position in a file; available only in Abaqus/Standard) +These utility subroutines are described below in alphabetical order. +Only the subroutines DBFILE and POSFIL can be called from user subroutine URDFIL. +DBFILE (read from a file) +Interface +CALL DBFILE(LOP,ARRAY,JRCD) +Variable to be provided to the utility routine +LOP +A flag, which you must set before calling DBFILE, indicating the operation. Set LOP=0 to read the +next record in the file; set LOP=2 to rewind the file currently being read (for example, if it is necessary +to read the file more than once, it must be rewound since it is a sequential file). If LOP=2 is used, the +file must first be read to the end, and it should be rewound only when the end-of-file is reached. +Variables returned from the utility routine +ARRAY +The array containing one record from the file, in the format described in “Results file output format,” +Section 5.1.2. When LOP=0, this array will be filled by the data management routines with the +contents of the next record in the file as each call to DBFILE is executed. ARRAY must be dimensioned +adequately in your routines to contain the largest record in the file. For almost all cases 500 words is +sufficient. The exceptions arise if the problem definition includes user elements or user materials that +use more than this many state variables or if substructures with a large number of retained degrees of +freedom are used . +When the results file has been written on a system on which Abaqus runs in double precision, ARRAY +must be declared double precision in your routine. +JRCD +Returned as nonzero if an end-of-file marker is read when DBFILE is called with LOP=0. +DBFILW (write to a file) +Interface +CALL DBFILW(LOP,ARRAY,JRCD) +Variables to be provided to the utility routine +ARRAY +The array containing one record to be written to the file, in the format described in “Results file output +format,” Section 5.1.2. +JRCD +LOP +Return code (0 – record written successfully, 1 – record not written). +Not currently used. +DBRNU (set a unit number for a file) +Interface +CALL DBRNU(JUNIT) +Variable to be provided to the utility routine +JUNIT +The FORTRAN unit number of the results file to be read. Valid unit numbers are 8 to read the .fil +file, 15–18, or numbers greater than 100. +INITPF (initialize a file) +Interface +CALL INITPF(FNAME,NRU,LRUNIT,LOUTF) +Variables to be provided to the utility routine +FNAME +A character string defining the root file name (that is, the name without an extension) of the files +being read or written. FNAME must be declared as CHARACTER*80 and can include the directory +specification as well as the root file name. The extension of each individual file is defined by the +LRUNIT array below. See the discussion below for file naming conventions. +NRU +An integer giving the number of results files that the postprocessing program will read. Normally only +one results file is read, but sometimes it is necessary to read several results files—for example, to merge +them into a single file. +LRUNIT +An integer array that must be dimensioned LRUNIT(2,NRU) in the postprocessing program and must +contain the following data before INITPF is called: +LRUNIT(1,K1) is the FORTRAN unit number on which the K1th results file will be read. Valid +unit numbers are 8 to read the .fil file, 15–18, or numbers greater than 100. All other units are +reserved by Abaqus. See below for naming conventions based on the unit numbers. +LRUNIT(2,K1) is an integer that must be set to 2 if the K1th results file was written as a binary +file or set to 1 if the K1th results file was written in ASCII format. +LOUTF +Needs to be defined only if the program that is making the call to INITPF will also write an output file +in the Abaqus results file format (for example, if results files are being merged into a single results file +or if a results file is being converted from binary to ASCII format). In that case LOUTF should be set to +2 if the output file is to be written as a binary file or set to 1 if the output file is to be written as an ASCII +file. This results file will be written with the file name extension .fin. See “Accessing the results file +information,” Section 5.1.3, for a discussion of writing results files; see below for information on the +naming of this file. +File naming conventions +The file extension is derived from the value of LRUNIT(1,K1). If LRUNIT(1,K1) is 8, the file name +will be constructed with the extension fil. Any other unit number will result in a file extension of 0nn, +where nn is the number assigned to LRUNIT(1,K1). For example, if LRUNIT(1,K1) is 15, the file +extension is .015. If an output file has been indicated by a nonzero value of LOUTF, its extension will +be .fin. +For example, to read a file xxxx.fil, set LRUNIT(1,K1) to 8 and the character variable FNAME +to xxxx using assignment or data statements. If desired, FNAME can include a directory specification, +device name, or path. Operating system environment and shell variables will not be translated properly +and, therefore, should not be used. +All error messages generated by Abaqus are written to FORTRAN unit 6. On most machines error +messages will be printed by default directly to the screen if the program is run interactively. You can +include an open statement for unit 6 in the main program to redirect messages to a file. If you wish to +read or write to units other than those units specified in LRUNIT, OPEN statements for those units may +have to be included in the program (depending upon the computer being used). Unit numbers of such +auxiliary files should be greater than 100 to avoid any conflict with Abaqus internal files. +POSFIL (determine position in a file) +The POSFIL utility routine is available only in Abaqus/Standard. +Interface +CALL POSFIL(NSTEP,NINC,ARRAY,JRCD) +Variables to be provided to the utility routine +NSTEP +Desired step. If this variable is set to 0, the first available step will be read. +NINC +Desired increment. If this variable is set to 0, the first available increment of the specified step will be +read. +Variables returned from the utility routine +ARRAY +Real array containing the values of record 2000 from the results file for the requested step and +increment. +JRCD +Return code (0 – specified increment found, 1 – specified increment not found). +If the step and +increment requested are not found in the results file, POSFIL will return an error and leave you +positioned at the end of the results file. +Positioning with POSFIL +You may find it convenient to call POSFIL with both NSTEP and NINC set to 0 to skip over the +information that is written to the results file at the beginning of an analysis and, thus, start reading from the first increment written to the file. +POSFIL cannot be used to move backward in the results file: you cannot use POSFIL to find a +given increment in the file and then make a second call to POSFIL later to read an increment earlier +than the first one found. If this is attempted, POSFIL will return an error indicating that the requested +increment was not found. +OI.1 +Abaqus/Standard OUTPUT VARIABLE INDEX +This index provides a reference to all of the output variables that are available in Abaqus/Standard. Output +variables are listed in alphabetical order. +Variable +Page +Variable +Page +Variable +Page +BF . . . . . . . . . . . 4.2.1–29 +BICURV . . . . . . . 4.2.1–25 +BIMOM . . . . . . . 4.2.1–25 +BM. . . . . . . . . . . 4.2.1–45 +CA . . . . . . . . . . . 4.2.1–33 +CALPHAF . . . . . 4.2.1–31 +CALPHAFn. . . . . 4.2.1–31 +CALPHAMn . . . . 4.2.1–31 +CAn . . . . . . . . . . 4.2.1–33 +CAREA . . . . . . . 4.2.1–47 +CARn . . . . . . . . . 4.2.1–33 +CASU. . . . . . . . . 4.2.1–32 +CASUC . . . . . . . 4.2.1–32 +CASUn . . . . . . . . 4.2.1–32 +CASURn. . . . . . . 4.2.1–32 +CCF . . . . . . . . . . 4.2.1–33 +CCFn . . . . . . . . . 4.2.1–33 +CCMn. . . . . . . . . 4.2.1–33 +CCU . . . . . . . . . . 4.2.1–33 +CCUn . . . . . . . . . 4.2.1–33 +CCURn . . . . . . . . 4.2.1–33 +CD . . . . . . . . . . . 4.2.1–54 +CDIF . . . . . . . . . 4.2.1–31 +CDIFC . . . . . . . . 4.2.1–32 +CDIFn . . . . . . . . 4.2.1–31 +CDIFRn . . . . . . . 4.2.1–32 +CDIM . . . . . . . . . 4.2.1–32 +CDIMC. . . . . . . . 4.2.1–32 +CDIMn . . . . . . . . 4.2.1–32 +CDIMRn . . . . . . . 4.2.1–32 +CDIP . . . . . . . . . 4.2.1–32 +CDIPC . . . . . . . . 4.2.1–32 +CDIPn . . . . . . . . 4.2.1–32 +CDIPRn . . . . . . . 4.2.1–32 +OI.1–1 +CDISP . . . . . . . . 4.2.1–46 +CDISPETOS . . . . 4.2.1–46 +CDMG . . . . . . . . 4.2.1–31 +CDMGn . . . . . . . 4.2.1–31 +CDMGRn . . . . . . 4.2.1–31 +CDSTRESS . . . . . 4.2.1–46 +CE . . . . . . . . . . . 4.2.1–10 +CEAVG. . . . . . . . 4.2.1–36 +CECHG . . . . . . . 4.2.1–39 +CECUR . . . . . . . 4.2.1–39 +CEEQ . . . . . . . . . 4.2.1–10 +CEERI . . . . . . . . 4.2.1–36 +CEF . . . . . . . . . . 4.2.1–30 +CEFn . . . . . . . . . 4.2.1–30 +CEij . . . . . . . . . . 4.2.1–10 +CEMAG . . . . . . . 4.2.1–11 +CEMn. . . . . . . . . 4.2.1–30 +CENER. . . . . . . . 4.2.1–12 +CENTMAG . . . . . 4.2.1–29 +CENTRIFMAG . . 4.2.1–29 +CEP . . . . . . . . . . 4.2.1–11 +CEPn . . . . . . . . . 4.2.1–11 +CESW . . . . . . . . 4.2.1–10 +CF . . . . . . . . . . . 4.2.1–38 +CFAILST . . . . . . 4.2.1–33 +CFAILSTi . . . . . . 4.2.1–33 +CFAILURE . . . . . 4.2.1–13 +CFF . . . . . . . . . . 4.2.1–37 +CFL . . . . . . . . . . 4.2.1–40 +CFLn . . . . . . . . . 4.2.1–40 +CFn . . . . . . . . . . 4.2.1–38 +CFN . . . . . . . . . . 4.2.1–47 +CFNM . . . . . . . . 4.2.1–47 +CFORCE. . . . . . . 4.2.1–46 +A . . . . . . . . . . . . 4.2.1–37 +ACV. . . . . . . . . . 4.2.1–12 +ACVn . . . . . . . . . 4.2.1–12 +ALEAKVRB . . . . 4.2.1–17 +ALEAKVRT . . . . 4.2.1–17 +ALLAE. . . . . . . . 4.2.1–55 +ALLCD. . . . . . . . 4.2.1–55 +ALLDMD . . . . . . 4.2.1–56 +ALLEE . . . . . . . . 4.2.1–55 +ALLFD . . . . . . . . 4.2.1–55 +ALLIE . . . . . . . . 4.2.1–55 +ALLJD . . . . . . . . 4.2.1–55 +ALLKE. . . . . . . . 4.2.1–55 +ALLKL. . . . . . . . 4.2.1–55 +ALLPD . . . . . . . . 4.2.1–55 +ALLQB. . . . . . . . 4.2.1–55 +ALLSD . . . . . . . . 4.2.1–56 +ALLSE . . . . . . . . 4.2.1–56 +ALLVD. . . . . . . . 4.2.1–56 +ALLWK . . . . . . . 4.2.1–56 +ALPHA. . . . . . . . 4.2.1–7 +ALPHAij. . . . . . . 4.2.1–7 +ALPHAk . . . . . . . 4.2.1–7 +ALPHAk_ij . . . . . 4.2.1–7 +ALPHAN . . . . . . 4.2.1–7 +ALPHAP. . . . . . . 4.2.1–7 +ALPHAPn . . . . . . 4.2.1–7 +AMPCU . . . . . . . 4.2.1–56 +An . . . . . . . . . . . 4.2.1–37 +AR . . . . . . . . . . . 4.2.1–37 +ARn . . . . . . . . . . 4.2.1–37 +AT . . . . . . . . . . . 4.2.1–37 +AZZIT . . . . . . . . 4.2.1–13 +Variable +Page +Variable +Page +Variable +Page +CSFn . . . . . . . . . 4.2.1–31 +CSLST . . . . . . . . 4.2.1–32 +CSLSTi. . . . . . . . 4.2.1–32 +CSMAXSCRT . . . 4.2.1–46 +CSMAXUCRT. . . 4.2.1–46 +CSMn . . . . . . . . . 4.2.1–31 +CSQUADSCRT . . 4.2.1–46 +CSQUADUCRT . . 4.2.1–46 +CSTATUS . . . . . . 4.2.1–46 +CSTRESS . . . . . . 4.2.1–45 +CSTRESSERI . . . 4.2.1–46 +CSTRESSETOS . . 4.2.1–45 +CTF . . . . . . . . . . 4.2.1–30 +CTFn . . . . . . . . . 4.2.1–30 +CTMn. . . . . . . . . 4.2.1–30 +CTRL_INPUT(OPT) 4.2.1–57 +CTRQ. . . . . . . . . 4.2.1–47 +CTSHR . . . . . . . . 4.2.1–11 +CTSHRi3 . . . . . . 4.2.1–11 +CU . . . . . . . . . . . 4.2.1–33 +CUE . . . . . . . . . . 4.2.1–30 +CUEn . . . . . . . . . 4.2.1–30 +CUn . . . . . . . . . . 4.2.1–33 +CUP . . . . . . . . . . 4.2.1–30 +CUPEQ. . . . . . . . 4.2.1–30 +CUPEQC . . . . . . 4.2.1–31 +CUPEQn . . . . . . . 4.2.1–30 +CUPn . . . . . . . . . 4.2.1–30 +CUREn . . . . . . . . 4.2.1–30 +CURn . . . . . . . . . 4.2.1–33 +CURPEQn. . . . . . 4.2.1–30 +CURPn . . . . . . . . 4.2.1–30 +CV . . . . . . . . . . . 4.2.1–33 +CVF . . . . . . . . . . 4.2.1–31 +CVFn . . . . . . . . . 4.2.1–31 +CVMn . . . . . . . . 4.2.1–31 +CVn . . . . . . . . . . 4.2.1–33 +CVOL. . . . . . . . . 4.2.1–39 +CVRn . . . . . . . . . 4.2.1–33 +OI.1–2 +CW . . . . . . . . . . 4.2.1–38 +CYCLEINI . . . . . 4.2.1–16 +CYCLEINIXFEM 4.2.1–30 +DAMAGEC. . . . . 4.2.1–15 +DAMAGEFC. . . . 4.2.1–23 +DAMAGEFT . . . . 4.2.1–23 +DAMAGEMC . . . 4.2.1–24 +DAMAGEMT . . . 4.2.1–24 +DAMAGESHR . . 4.2.1–24 +DAMAGET. . . . . 4.2.1–15 +DAMPRATIO . . . 4.2.1–55 +DBS . . . . . . . . . . 4.2.1–49 +DBSF . . . . . . . . . 4.2.1–49 +DBT . . . . . . . . . . 4.2.1–49 +DG . . . . . . . . . . . 4.2.1–8 +DGij . . . . . . . . . . 4.2.1–8 +DGP . . . . . . . . . . 4.2.1–8 +DGPn . . . . . . . . . 4.2.1–8 +DISP_OPT . . . . . 4.2.1–57 +DISP_OPT_VAL . 4.2.1–57 +DMENER . . . . . . 4.2.1–13 +DMICRT. . . . . . . 4.2.1–16 +4.2.1–23 +DUCTCRT . . . . . 4.2.1–23 +E . . . . . . . . . . . . 4.2.1–7 +EASEDEN . . . . . 4.2.1–35 +ECD . . . . . . . . . . 4.2.1–16 +4.2.1–48 +ECDA. . . . . . . . . 4.2.1–48 +ECDDEN . . . . . . 4.2.1–35 +ECDM . . . . . . . . 4.2.1–16 +ECDn . . . . . . . . . 4.2.1–16 +ECDT . . . . . . . . . 4.2.1–48 +ECDTA. . . . . . . . 4.2.1–48 +4.2.1–49 +ECTEDEN . . . . . 4.2.1–35 +ECURS . . . . . . . . 4.2.1–27 +EDMDDEN. . . . . 4.2.1–35 +EE . . . . . . . . . . . 4.2.1–8 +CFS . . . . . . . . . . 4.2.1–47 +CFSM. . . . . . . . . 4.2.1–47 +CFT . . . . . . . . . . 4.2.1–47 +CFTM. . . . . . . . . 4.2.1–47 +CHRGS . . . . . . . 4.2.1–27 +CIVC . . . . . . . . . 4.2.1–32 +CMn . . . . . . . . . . 4.2.1–38 +CMN . . . . . . . . . 4.2.1–47 +CMNM . . . . . . . . 4.2.1–47 +CMS. . . . . . . . . . 4.2.1–47 +CMSM . . . . . . . . 4.2.1–47 +CMT . . . . . . . . . 4.2.1–47 +CMTM . . . . . . . . 4.2.1–47 +CNAREA . . . . . . 4.2.1–46 +CNF . . . . . . . . . . 4.2.1–31 +CNFC . . . . . . . . . 4.2.1–31 +CNFn . . . . . . . . . 4.2.1–31 +CNMn . . . . . . . . 4.2.1–31 +CONC . . . . . . . . 4.2.1–15 +CONF. . . . . . . . . 4.2.1–14 +COORD . . . . . . . 4.2.1–18 +4.2.1–25 +4.2.1–38 +COORn. . . . . . . . 4.2.1–38 +CORIOMAG . . . . 4.2.1–29 +CP . . . . . . . . . . . 4.2.1–33 +CPn . . . . . . . . . . 4.2.1–33 +CPRn . . . . . . . . . 4.2.1–33 +CRACK . . . . . . . 4.2.1–14 +CRF . . . . . . . . . . 4.2.1–32 +CRFn . . . . . . . . . 4.2.1–32 +CRMn. . . . . . . . . 4.2.1–33 +CRPTIME . . . . . . 4.2.1–54 +CRSTS . . . . . . . . 4.2.1–50 +CS11 . . . . . . . . . 4.2.1–11 +CSDMG . . . . . . . 4.2.1–46 +4.2.1–49 +CSF . . . . . . . . . . 4.2.1–31 +Variable +Page +Variable +Page +Variable +Page +ENER . . . . . . . . . 4.2.1–12 +ENRRT . . . . . . . . 4.2.1–50 +ENRRTXFEM . . . 4.2.1–30 +EP . . . . . . . . . . . 4.2.1–7 +EPDDEN . . . . . . 4.2.1–35 +EPG . . . . . . . . . . 4.2.1–16 +EPGAVG . . . . . . 4.2.1–36 +EPGERI . . . . . . . 4.2.1–36 +EPGM . . . . . . . . 4.2.1–16 +EPGn . . . . . . . . . 4.2.1–16 +EPn . . . . . . . . . . 4.2.1–7 +EPOT . . . . . . . . . 4.2.1–37 +ER . . . . . . . . . . . 4.2.1–8 +ERij . . . . . . . . . . 4.2.1–8 +ERP . . . . . . . . . . 4.2.1–8 +ERPn . . . . . . . . . 4.2.1–8 +ERPRATIO . . . . . 4.2.1–23 +ESDDEN . . . . . . 4.2.1–35 +ESEDEN. . . . . . . 4.2.1–35 +ESF1 . . . . . . . . . 4.2.1–25 +ESOL . . . . . . . . . 4.2.1–29 +ETOTAL . . . . . . . 4.2.1–56 +EVDDEN . . . . . . 4.2.1–35 +EVOL. . . . . . . . . 4.2.1–29 +FILM . . . . . . . . . 4.2.1–29 +FILMCOEF . . . . . 4.2.1–34 +FLDCRT . . . . . . . 4.2.1–23 +FLSDCRT . . . . . . 4.2.1–23 +FLUVR. . . . . . . . 4.2.1–17 +FLUXS . . . . . . . . 4.2.1–27 +4.2.1–34 +FLVEL . . . . . . . . 4.2.1–17 +FLVELM. . . . . . . 4.2.1–17 +FLVELn . . . . . . . 4.2.1–17 +FOUND . . . . . . . 4.2.1–27 +FTEMP . . . . . . . . 4.2.1–50 +FV . . . . . . . . . . . 4.2.1–13 +FVn . . . . . . . . . . 4.2.1–13 +GA . . . . . . . . . . . 4.2.1–44 +OI.1–3 +GAn . . . . . . . . . . 4.2.1–44 +GELVR. . . . . . . . 4.2.1–17 +GFVR. . . . . . . . . 4.2.1–17 +GM . . . . . . . . . . 4.2.1–54 +GPA . . . . . . . . . . 4.2.1–44 +GPAn . . . . . . . . . 4.2.1–44 +GPU . . . . . . . . . . 4.2.1–44 +GPUn . . . . . . . . . 4.2.1–44 +GPV . . . . . . . . . . 4.2.1–44 +GPVn . . . . . . . . . 4.2.1–44 +GRADP . . . . . . . 4.2.1–12 +GRAV. . . . . . . . . 4.2.1–29 +GU . . . . . . . . . . . 4.2.1–44 +GUn . . . . . . . . . . 4.2.1–44 +GV . . . . . . . . . . . 4.2.1–44 +GVn . . . . . . . . . . 4.2.1–44 +HBF . . . . . . . . . . 4.2.1–29 +HC . . . . . . . . . . . 4.2.1–52 +HCn . . . . . . . . . . 4.2.1–52 +HFL . . . . . . . . . . 4.2.1–15 +4.2.1–47 +4.2.1–48 +4.2.1–49 +HFLA . . . . . . . . . 4.2.1–47 +4.2.1–48 +4.2.1–49 +HFLAVG . . . . . . 4.2.1–36 +HFLERI . . . . . . . 4.2.1–36 +HFLM . . . . . . . . 4.2.1–15 +HFLn . . . . . . . . . 4.2.1–15 +HO . . . . . . . . . . . 4.2.1–52 +HOn . . . . . . . . . . 4.2.1–52 +HP . . . . . . . . . . . 4.2.1–34 +HSNFCCRT . . . . 4.2.1–23 +HSNFTCRT. . . . . 4.2.1–23 +HSNMCCRT . . . . 4.2.1–23 +HSNMTCRT . . . . 4.2.1–23 +HTL . . . . . . . . . . 4.2.1–48 +4.2.1–49 +EEij . . . . . . . . . . 4.2.1–8 +EENER . . . . . . . . 4.2.1–13 +EEP . . . . . . . . . . 4.2.1–8 +EEPn . . . . . . . . . 4.2.1–8 +EFENRRTR. . . . . 4.2.1–50 +EFLAVG . . . . . . . 4.2.1–36 +EFLERI . . . . . . . 4.2.1–36 +EFLX . . . . . . . . . 4.2.1–16 +EFLXM . . . . . . . 4.2.1–16 +EFLXn . . . . . . . . 4.2.1–16 +EIGFREQ . . . . . . 4.2.1–54 +4.2.1–55 +EIGIMAG . . . . . . 4.2.1–55 +EIGREAL . . . . . . 4.2.1–55 +EIGVAL . . . . . . . 4.2.1–54 +Eij . . . . . . . . . . . 4.2.1–7 +EKEDEN . . . . . . 4.2.1–35 +ELASE . . . . . . . . 4.2.1–28 +ELCD . . . . . . . . . 4.2.1–28 +ELCTE . . . . . . . . 4.2.1–28 +ELDMD . . . . . . . 4.2.1–28 +ELEDEN. . . . . . . 4.2.1–34 +ELEN . . . . . . . . . 4.2.1–27 +ELJD . . . . . . . . . 4.2.1–28 +ELKE . . . . . . . . . 4.2.1–27 +ELPD . . . . . . . . . 4.2.1–28 +ELSD . . . . . . . . . 4.2.1–28 +ELSE . . . . . . . . . 4.2.1–27 +ELVD . . . . . . . . . 4.2.1–28 +EMB . . . . . . . . . 4.2.1–24 +EMBF. . . . . . . . . 4.2.1–24 +EMBFC . . . . . . . 4.2.1–24 +EMCD . . . . . . . . 4.2.1–24 +EME. . . . . . . . . . 4.2.1–24 +EMH . . . . . . . . . 4.2.1–24 +EMJH . . . . . . . . . 4.2.1–24 +EMn . . . . . . . . . . 4.2.1–54 +ENDEN . . . . . . . 4.2.1–36 +Variable +Page +Variable +Page +Variable +Page +PEEQ . . . . . . . . . 4.2.1–9 +4.2.1–15 +4.2.1–18 +PEEQAVG . . . . . 4.2.1–36 +PEEQERI . . . . . . 4.2.1–36 +PEEQMAX . . . . . 4.2.1–9 +PEEQT . . . . . . . . 4.2.1–10 +PEERI . . . . . . . . 4.2.1–36 +PEij . . . . . . . . . . 4.2.1–9 +4.2.1–18 +PEMAG . . . . . . . 4.2.1–10 +PENER . . . . . . . . 4.2.1–12 +PEP . . . . . . . . . . 4.2.1–10 +PEPn . . . . . . . . . 4.2.1–10 +PEQC . . . . . . . . . 4.2.1–14 +PEQCn . . . . . . . . 4.2.1–14 +PFL . . . . . . . . . . 4.2.1–49 +PFLA . . . . . . . . . 4.2.1–49 +PFn . . . . . . . . . . 4.2.1–54 +PFOPEN . . . . . . . 4.2.1–17 +PHCA. . . . . . . . . 4.2.1–22 +PHCAn . . . . . . . . 4.2.1–22 +PHCARn. . . . . . . 4.2.1–22 +PHCCU . . . . . . . 4.2.1–22 +PHCCUn. . . . . . . 4.2.1–22 +PHCCURn . . . . . 4.2.1–22 +PHCEF . . . . . . . . 4.2.1–21 +PHCEFn . . . . . . . 4.2.1–21 +PHCEMn . . . . . . 4.2.1–21 +PHCHG . . . . . . . 4.2.1–41 +PHCIVC . . . . . . . 4.2.1–23 +PHCNF . . . . . . . . 4.2.1–22 +PHCNFC. . . . . . . 4.2.1–23 +PHCNFn . . . . . . . 4.2.1–23 +PHCNMn . . . . . . 4.2.1–23 +PHCRF . . . . . . . . 4.2.1–21 +PHCRFn . . . . . . . 4.2.1–21 +PHCRMn . . . . . . 4.2.1–22 +PHCSF . . . . . . . . 4.2.1–22 +HTLA. . . . . . . . . 4.2.1–48 +4.2.1–49 +IE. . . . . . . . . . . . 4.2.1–8 +IEij. . . . . . . . . . . 4.2.1–8 +IEP. . . . . . . . . . . 4.2.1–8 +IEPn . . . . . . . . . . 4.2.1–9 +INFC . . . . . . . . . 4.2.1–39 +INFN . . . . . . . . . 4.2.1–39 +INFR . . . . . . . . . 4.2.1–39 +INTEN . . . . . . . . 4.2.1–11 +INV3 . . . . . . . . . 4.2.1–7 +IRA . . . . . . . . . . 4.2.1–53 +IRAn . . . . . . . . . 4.2.1–53 +IRARn . . . . . . . . 4.2.1–53 +IRF. . . . . . . . . . . 4.2.1–53 +IRFn . . . . . . . . . . 4.2.1–53 +IRMASS . . . . . . . 4.2.1–54 +IRMn . . . . . . . . . 4.2.1–53 +IRRI . . . . . . . . . . 4.2.1–53 +IRRIij . . . . . . . . . 4.2.1–54 +IRX . . . . . . . . . . 4.2.1–53 +IRXn . . . . . . . . . 4.2.1–53 +ISOL . . . . . . . . . 4.2.1–15 +IVOL . . . . . . . . . 4.2.1–18 +JENER . . . . . . . . 4.2.1–13 +JK . . . . . . . . . . . 4.2.1–14 +KE . . . . . . . . . . . 4.2.1–45 +KEn . . . . . . . . . . 4.2.1–45 +LE . . . . . . . . . . . 4.2.1–8 +LEAKVRB . . . . . 4.2.1–17 +LEAKVRT . . . . . 4.2.1–17 +LEij . . . . . . . . . . 4.2.1–8 +LEP . . . . . . . . . . 4.2.1–8 +LEPn . . . . . . . . . 4.2.1–8 +LOADS. . . . . . . . 4.2.1–27 +LOCALDIRn . . . . 4.2.1–18 +LPF . . . . . . . . . . 4.2.1–56 +MASS. . . . . . . . . 4.2.1–53 +MAT_PROP_NORMALIZED 4.2.1–56 +MAXECRT . . . . . 4.2.1–16 +MAXSCRT . . . . . 4.2.1–16 +MAXSS . . . . . . . 4.2.1–25 +MFL . . . . . . . . . . 4.2.1–13 +4.2.1–15 +MFLM . . . . . . . . 4.2.1–15 +MFLn . . . . . . . . . 4.2.1–16 +MFLT . . . . . . . . . 4.2.1–13 +MFR. . . . . . . . . . 4.2.1–13 +MFRn . . . . . . . . . 4.2.1–13 +MISES . . . . . . . . 4.2.1–6 +MISESAVG . . . . . 4.2.1–36 +MISESERI . . . . . 4.2.1–36 +MISESMAX . . . . 4.2.1–6 +MISESONLY. . . . 4.2.1–6 +MOT . . . . . . . . . 4.2.1–39 +MOTn. . . . . . . . . 4.2.1–39 +MSFLDCRT . . . . 4.2.1–23 +MSTRN . . . . . . . 4.2.1–13 +MSTRS. . . . . . . . 4.2.1–13 +NCURS . . . . . . . 4.2.1–29 +NE . . . . . . . . . . . 4.2.1–7 +NEij . . . . . . . . . . 4.2.1–7 +NEP . . . . . . . . . . 4.2.1–8 +NEPn . . . . . . . . . 4.2.1–8 +NFLn . . . . . . . . . 4.2.1–29 +NFLUX. . . . . . . . 4.2.1–29 +NFORC . . . . . . . 4.2.1–28 +NFORCSO . . . . . 4.2.1–29 +NNC. . . . . . . . . . 4.2.1–37 +NNCn . . . . . . . . . 4.2.1–37 +NT . . . . . . . . . . . 4.2.1–37 +NTn . . . . . . . . . . 4.2.1–37 +OPENBC . . . . . . 4.2.1–49 +P . . . . . . . . . . . . 4.2.1–34 +PCAV . . . . . . . . . 4.2.1–39 +PE . . . . . . . . . . . 4.2.1–9 +4.2.1–18 +PEAVG . . . . . . . . 4.2.1–36 +Variable +Page +Variable +Page +Variable +Page +PSij . . . . . . . . . . 4.2.1–18 +PSILSM . . . . . . . 4.2.1–40 +PTL . . . . . . . . . . 4.2.1–49 +PTLA . . . . . . . . . 4.2.1–49 +PTU . . . . . . . . . . 4.2.1–42 +PTUn . . . . . . . . . 4.2.1–42 +PTURn . . . . . . . . 4.2.1–42 +PU . . . . . . . . . . . 4.2.1–40 +PUn . . . . . . . . . . 4.2.1–41 +PURn . . . . . . . . . 4.2.1–41 +QUADECRT . . . . 4.2.1–16 +QUADSCRT . . . . 4.2.1–16 +RA . . . . . . . . . . . 4.2.1–43 +RAD. . . . . . . . . . 4.2.1–29 +RADFL. . . . . . . . 4.2.1–50 +RADFLA . . . . . . 4.2.1–50 +RADTL. . . . . . . . 4.2.1–50 +RADTLA . . . . . . 4.2.1–50 +RAn . . . . . . . . . . 4.2.1–43 +RARn . . . . . . . . . 4.2.1–43 +RATIO . . . . . . . . 4.2.1–56 +RBANG . . . . . . . 4.2.1–15 +RBFOR. . . . . . . . 4.2.1–15 +RBROT . . . . . . . 4.2.1–15 +RCCU. . . . . . . . . 4.2.1–20 +RCCUn . . . . . . . . 4.2.1–20 +RCCURn. . . . . . . 4.2.1–20 +RCEF . . . . . . . . . 4.2.1–19 +RCEFn . . . . . . . . 4.2.1–19 +RCEMn . . . . . . . 4.2.1–19 +RCHG . . . . . . . . 4.2.1–39 +RCNF . . . . . . . . . 4.2.1–20 +RCNFC. . . . . . . . 4.2.1–20 +RCNFn . . . . . . . . 4.2.1–20 +RCNMn . . . . . . . 4.2.1–20 +RCRF . . . . . . . . . 4.2.1–19 +RCRFn . . . . . . . . 4.2.1–19 +RCRMn . . . . . . . 4.2.1–19 +RCSF . . . . . . . . . 4.2.1–19 +OI.1–5 +RCSFC . . . . . . . . 4.2.1–20 +RCSFn . . . . . . . . 4.2.1–19 +RCSMn. . . . . . . . 4.2.1–20 +RCTF . . . . . . . . . 4.2.1–19 +RCTFn . . . . . . . . 4.2.1–19 +RCTMn . . . . . . . 4.2.1–19 +RCU . . . . . . . . . . 4.2.1–20 +RCUn . . . . . . . . . 4.2.1–20 +RCURn . . . . . . . . 4.2.1–20 +RCVF . . . . . . . . . 4.2.1–19 +RCVFn . . . . . . . . 4.2.1–19 +RCVMn . . . . . . . 4.2.1–19 +RD . . . . . . . . . . . 4.2.1–17 +RE . . . . . . . . . . . 4.2.1–19 +RECUR . . . . . . . 4.2.1–39 +REij . . . . . . . . . . 4.2.1–19 +RF . . . . . . . . . . . 4.2.1–37 +RFL . . . . . . . . . . 4.2.1–40 +RFLE . . . . . . . . . 4.2.1–40 +RFLEn . . . . . . . . 4.2.1–40 +RFLn . . . . . . . . . 4.2.1–40 +RFn . . . . . . . . . . 4.2.1–38 +RI. . . . . . . . . . . . 4.2.1–52 +RIij. . . . . . . . . . . 4.2.1–53 +RM. . . . . . . . . . . 4.2.1–38 +RMISES . . . . . . . 4.2.1–19 +RMn . . . . . . . . . . 4.2.1–38 +ROTAMAG . . . . . 4.2.1–29 +RRF . . . . . . . . . . 4.2.1–44 +RRFn . . . . . . . . . 4.2.1–44 +RRMn. . . . . . . . . 4.2.1–44 +RS . . . . . . . . . . . 4.2.1–19 +RSij . . . . . . . . . . 4.2.1–19 +RT . . . . . . . . . . . 4.2.1–38 +RTA . . . . . . . . . . 4.2.1–43 +RTAn . . . . . . . . . 4.2.1–44 +RTARn . . . . . . . . 4.2.1–44 +RTU . . . . . . . . . . 4.2.1–43 +RTUn . . . . . . . . . 4.2.1–43 +PHCSFC . . . . . . . 4.2.1–22 +PHCSFn . . . . . . . 4.2.1–22 +PHCSMn. . . . . . . 4.2.1–22 +PHCTF . . . . . . . . 4.2.1–21 +PHCTFn . . . . . . . 4.2.1–21 +PHCTMn . . . . . . 4.2.1–21 +PHCU. . . . . . . . . 4.2.1–22 +PHCUn . . . . . . . . 4.2.1–22 +PHCURn. . . . . . . 4.2.1–22 +PHCV. . . . . . . . . 4.2.1–22 +PHCVF . . . . . . . . 4.2.1–21 +PHCVFn . . . . . . . 4.2.1–21 +PHCVMn . . . . . . 4.2.1–21 +PHCVn . . . . . . . . 4.2.1–22 +PHCVRn. . . . . . . 4.2.1–22 +PHE . . . . . . . . . . 4.2.1–21 +PHEFL . . . . . . . . 4.2.1–21 +PHEFLn . . . . . . . 4.2.1–21 +PHEij . . . . . . . . . 4.2.1–21 +PHEPG . . . . . . . . 4.2.1–21 +PHEPGn . . . . . . . 4.2.1–21 +PHILSM . . . . . . . 4.2.1–40 +PHMFL . . . . . . . 4.2.1–21 +PHMFT . . . . . . . 4.2.1–21 +PHPOT . . . . . . . . 4.2.1–41 +PHS . . . . . . . . . . 4.2.1–20 +PHSij . . . . . . . . . 4.2.1–20 +PINF . . . . . . . . . 4.2.1–39 +POR . . . . . . . . . . 4.2.1–17 +4.2.1–37 +4.2.1–39 +PPOR . . . . . . . . . 4.2.1–41 +PPRESS . . . . . . . 4.2.1–46 +PRESS . . . . . . . . 4.2.1–7 +PRESSONLY. . . . 4.2.1–7 +PRF . . . . . . . . . . 4.2.1–41 +PRFn . . . . . . . . . 4.2.1–41 +PRMn . . . . . . . . . 4.2.1–41 +Variable +Page +Variable +Page +Variable +Page +SFDRT . . . . . . . . 4.2.1–48 +4.2.1–49 +SFDRTA . . . . . . . 4.2.1–48 +4.2.1–49 +SFn . . . . . . . . . . 4.2.1–25 +SHRCRT. . . . . . . 4.2.1–23 +SHRRATIO . . . . . 4.2.1–23 +Sij . . . . . . . . . . . 4.2.1–6 +SINKTEMP. . . . . 4.2.1–34 +SINV . . . . . . . . . 4.2.1–6 +SJD . . . . . . . . . . 4.2.1–48 +4.2.1–49 +SJDA . . . . . . . . . 4.2.1–48 +4.2.1–49 +SJDT . . . . . . . . . 4.2.1–48 +4.2.1–49 +SJDTA . . . . . . . . 4.2.1–48 +4.2.1–49 +SJP. . . . . . . . . . . 4.2.1–18 +SKEn . . . . . . . . . 4.2.1–26 +SKn . . . . . . . . . . 4.2.1–25 +SKPn . . . . . . . . . 4.2.1–27 +SMn . . . . . . . . . . 4.2.1–25 +SNE . . . . . . . . . . 4.2.1–45 +SNEn . . . . . . . . . 4.2.1–45 +SOAREA . . . . . . 4.2.1–50 +SOCF . . . . . . . . . 4.2.1–51 +SOD . . . . . . . . . . 4.2.1–51 +SOE . . . . . . . . . . 4.2.1–51 +SOF . . . . . . . . . . 4.2.1–51 +SOH . . . . . . . . . . 4.2.1–51 +SOL . . . . . . . . . . 4.2.1–54 +SOM . . . . . . . . . 4.2.1–51 +SOP . . . . . . . . . . 4.2.1–51 +SP . . . . . . . . . . . 4.2.1–6 +SPE . . . . . . . . . . 4.2.1–26 +SPEn . . . . . . . . . 4.2.1–26 +SPL . . . . . . . . . . 4.2.1–40 +SPn . . . . . . . . . . 4.2.1–6 +OI.1–6 +SS . . . . . . . . . . . 4.2.1–11 +SSAVG . . . . . . . . 4.2.1–25 +SSAVGn . . . . . . . 4.2.1–25 +SSn . . . . . . . . . . 4.2.1–11 +STATUS . . . . . . . 4.2.1–16 +4.2.1–17 +4.2.1–24 +STATUSXFEM . . 4.2.1–30 +STH . . . . . . . . . . 4.2.1–25 +STRAINFREE . . . 4.2.1–39 +SVOL . . . . . . . . . 4.2.1–26 +T . . . . . . . . . . . . 4.2.1–45 +TA . . . . . . . . . . . 4.2.1–42 +TAn . . . . . . . . . . 4.2.1–42 +TARn . . . . . . . . . 4.2.1–42 +TEMP. . . . . . . . . 4.2.1–13 +TF . . . . . . . . . . . 4.2.1–38 +TFn . . . . . . . . . . 4.2.1–38 +THE . . . . . . . . . . 4.2.1–9 +THEij . . . . . . . . . 4.2.1–9 +THEP . . . . . . . . . 4.2.1–9 +THEPn . . . . . . . . 4.2.1–9 +TMn . . . . . . . . . . 4.2.1–38 +Tn . . . . . . . . . . . 4.2.1–45 +TPFL . . . . . . . . . 4.2.1–49 +TPTL . . . . . . . . . 4.2.1–49 +TRESC . . . . . . . . 4.2.1–7 +TRIAX . . . . . . . . 4.2.1–7 +TRNOR . . . . . . . 4.2.1–34 +TRSHR . . . . . . . . 4.2.1–34 +TSAIH . . . . . . . . 4.2.1–13 +TSAIW . . . . . . . . 4.2.1–13 +TSHR . . . . . . . . . 4.2.1–11 +TSHRi3 . . . . . . . 4.2.1–11 +TU . . . . . . . . . . . 4.2.1–41 +TUn . . . . . . . . . . 4.2.1–41 +TURn . . . . . . . . . 4.2.1–41 +TV . . . . . . . . . . . 4.2.1–41 +TVn . . . . . . . . . . 4.2.1–41 +RTURn . . . . . . . . 4.2.1–43 +RTV . . . . . . . . . . 4.2.1–43 +RTVn . . . . . . . . . 4.2.1–43 +RTVRn . . . . . . . . 4.2.1–43 +RU . . . . . . . . . . . 4.2.1–42 +RUn . . . . . . . . . . 4.2.1–43 +RURn . . . . . . . . . 4.2.1–43 +RV . . . . . . . . . . . 4.2.1–43 +RVF . . . . . . . . . . 4.2.1–42 +RVn . . . . . . . . . . 4.2.1–43 +RVRn . . . . . . . . . 4.2.1–43 +RVT . . . . . . . . . . 4.2.1–42 +RWM . . . . . . . . . 4.2.1–38 +S . . . . . . . . . . . . 4.2.1–6 +SALPHA. . . . . . . 4.2.1–27 +SALPHAn . . . . . . 4.2.1–27 +SAT . . . . . . . . . . 4.2.1–17 +SDEG . . . . . . . . . 4.2.1–15 +4.2.1–16 +4.2.1–17 +4.2.1–23 +SDV . . . . . . . . . . 4.2.1–13 +4.2.1–46 +SDVn . . . . . . . . . 4.2.1–13 +SE . . . . . . . . . . . 4.2.1–25 +SEE . . . . . . . . . . 4.2.1–26 +SEE1 . . . . . . . . . 4.2.1–26 +SEn . . . . . . . . . . 4.2.1–25 +SENER . . . . . . . . 4.2.1–12 +SEP . . . . . . . . . . 4.2.1–26 +SEP1 . . . . . . . . . 4.2.1–27 +SEPE . . . . . . . . . 4.2.1–26 +SEPEn . . . . . . . . 4.2.1–26 +SF . . . . . . . . . . . 4.2.1–25 +SFDR . . . . . . . . . 4.2.1–48 +4.2.1–49 +SFDRA . . . . . . . . 4.2.1–48 +Variable +Page +Variable +Page +Variable +Page +TVRn . . . . . . . . . 4.2.1–41 +U . . . . . . . . . . . . 4.2.1–36 +UC . . . . . . . . . . . 4.2.1–52 +UCn . . . . . . . . . . 4.2.1–52 +Un . . . . . . . . . . . 4.2.1–36 +UR . . . . . . . . . . . 4.2.1–36 +URCn . . . . . . . . . 4.2.1–52 +URn . . . . . . . . . . 4.2.1–36 +UT . . . . . . . . . . . 4.2.1–36 +UVARM . . . . . . . 4.2.1–13 +UVARMn . . . . . . 4.2.1–13 +V . . . . . . . . . . . . 4.2.1–37 +VC . . . . . . . . . . . 4.2.1–52 +VCn . . . . . . . . . . 4.2.1–52 +VE . . . . . . . . . . . 4.2.1–18 +VEEQ. . . . . . . . . 4.2.1–18 +VEij . . . . . . . . . . 4.2.1–18 +VENER. . . . . . . . 4.2.1–13 +VF . . . . . . . . . . . 4.2.1–38 +VFn . . . . . . . . . . 4.2.1–38 +VFTOT . . . . . . . . 4.2.1–50 +VMn. . . . . . . . . . 4.2.1–38 +Vn . . . . . . . . . . . 4.2.1–37 +VOIDR . . . . . . . . 4.2.1–17 +VOL . . . . . . . . . . 4.2.1–53 +VOLC. . . . . . . . . 4.2.1–51 +VR . . . . . . . . . . . 4.2.1–37 +VRCn . . . . . . . . . 4.2.1–52 +VRn . . . . . . . . . . 4.2.1–37 +VS . . . . . . . . . . . 4.2.1–17 +VSij . . . . . . . . . . 4.2.1–17 +VT . . . . . . . . . . . 4.2.1–37 +VVF . . . . . . . . . . 4.2.1–17 +VVFG. . . . . . . . . 4.2.1–17 +VVFN. . . . . . . . . 4.2.1–17 +WARP . . . . . . . . 4.2.1–37 +WEIGHT . . . . . . 4.2.1–48 +4.2.1–49 +XC . . . . . . . . . . . 4.2.1–52 +XCn . . . . . . . . . . 4.2.1–52 +XN . . . . . . . . . . . 4.2.1–47 +XS . . . . . . . . . . . 4.2.1–47 +XT . . . . . . . . . . . 4.2.1–47 +OI.2 +Abaqus/Explicit OUTPUT VARIABLE INDEX +This index provides a reference to all of the output variables that are available in Abaqus/Explicit. Output +variables are listed in alphabetical order. +Variable +Page +Variable +Page +Variable +Page +BF . . . . . . . . . . . 4.2.2–14 +BONDLOAD. . . . 4.2.2–23 +BONDSTAT . . . . 4.2.2–23 +BURNF . . . . . . . 4.2.2–10 +CA . . . . . . . . . . . 4.2.2–19 +CALPHAF . . . . . 4.2.2–16 +CALPHAFn. . . . . 4.2.2–16 +CALPHAMn . . . . 4.2.2–16 +CAn . . . . . . . . . . 4.2.2–19 +CAREA . . . . . . . 4.2.2–24 +CARn . . . . . . . . . 4.2.2–19 +CASU. . . . . . . . . 4.2.2–17 +CASUC . . . . . . . 4.2.2–18 +CASUn . . . . . . . . 4.2.2–18 +CASURn. . . . . . . 4.2.2–18 +CBLARAT . . . . . 4.2.2–22 +CCF . . . . . . . . . . 4.2.2–18 +CCFn . . . . . . . . . 4.2.2–18 +CCMn. . . . . . . . . 4.2.2–18 +CCU . . . . . . . . . . 4.2.2–18 +CCUn . . . . . . . . . 4.2.2–18 +CCURn . . . . . . . . 4.2.2–18 +CDERF . . . . . . . . 4.2.2–19 +CDERU . . . . . . . 4.2.2–19 +CDIF . . . . . . . . . 4.2.2–17 +CDIFC . . . . . . . . 4.2.2–17 +CDIFn . . . . . . . . 4.2.2–17 +CDIFRn . . . . . . . 4.2.2–17 +CDIM . . . . . . . . . 4.2.2–17 +CDIMC. . . . . . . . 4.2.2–17 +CDIMn . . . . . . . . 4.2.2–17 +CDIMRn . . . . . . . 4.2.2–17 +CDIP . . . . . . . . . 4.2.2–17 +CDIPC . . . . . . . . 4.2.2–17 +OI.2–1 +CDIPn . . . . . . . . 4.2.2–17 +CDIPRn . . . . . . . 4.2.2–17 +CDMG . . . . . . . . 4.2.2–17 +CDMGn . . . . . . . 4.2.2–17 +CDMGRn . . . . . . 4.2.2–17 +CEF . . . . . . . . . . 4.2.2–15 +CEFL . . . . . . . . . 4.2.2–22 +CEFLT . . . . . . . . 4.2.2–22 +CEFn . . . . . . . . . 4.2.2–15 +CEMn. . . . . . . . . 4.2.2–15 +CENER. . . . . . . . 4.2.2–7 +CF . . . . . . . . . . . 4.2.2–21 +CFAILST . . . . . . 4.2.2–19 +CFAILSTi . . . . . . 4.2.2–19 +CFAILURE . . . . . 4.2.2–7 +CFn . . . . . . . . . . 4.2.2–21 +CFN . . . . . . . . . . 4.2.2–24 +CFNM . . . . . . . . 4.2.2–24 +CFORCE. . . . . . . 4.2.2–23 +CFS . . . . . . . . . . 4.2.2–24 +CFSM. . . . . . . . . 4.2.2–24 +CFT . . . . . . . . . . 4.2.2–24 +CFTM. . . . . . . . . 4.2.2–24 +CIVC . . . . . . . . . 4.2.2–18 +CKE . . . . . . . . . . 4.2.2–9 +CKEij . . . . . . . . . 4.2.2–9 +CKEMAG . . . . . . 4.2.2–9 +CKLE . . . . . . . . . 4.2.2–9 +CKLEij . . . . . . . . 4.2.2–9 +CKLS . . . . . . . . . 4.2.2–9 +CKLSij . . . . . . . . 4.2.2–9 +CKSTAT . . . . . . . 4.2.2–9 +CLAREA . . . . . . 4.2.2–22 +CMASS . . . . . . . 4.2.2–22 +A . . . . . . . . . . . . 4.2.2–20 +ACOM . . . . . . . . 4.2.2–26 +ACTEMP . . . . . . 4.2.2–22 +ALLAE. . . . . . . . 4.2.2–26 +ALLCD. . . . . . . . 4.2.2–26 +ALLCW . . . . . . . 4.2.2–27 +ALLDC. . . . . . . . 4.2.2–27 +ALLDMD . . . . . . 4.2.2–27 +ALLFC . . . . . . . . 4.2.2–27 +ALLFD . . . . . . . . 4.2.2–26 +ALLHF . . . . . . . . 4.2.2–27 +ALLIE . . . . . . . . 4.2.2–26 +ALLIHE . . . . . . . 4.2.2–27 +ALLKE. . . . . . . . 4.2.2–26 +ALLMW . . . . . . . 4.2.2–27 +ALLPD . . . . . . . . 4.2.2–27 +ALLPW . . . . . . . 4.2.2–27 +ALLSE . . . . . . . . 4.2.2���27 +ALLVD. . . . . . . . 4.2.2–27 +ALLWK . . . . . . . 4.2.2–27 +ALPHA. . . . . . . . 4.2.2–4 +ALPHAij. . . . . . . 4.2.2–4 +ALPHAk . . . . . . . 4.2.2–5 +ALPHAk_ij . . . . . 4.2.2–5 +ALPHAN . . . . . . 4.2.2–5 +ALPHAP. . . . . . . 4.2.2–5 +ALPHAPn . . . . . . 4.2.2–5 +An . . . . . . . . . . . 4.2.2–20 +APCAV. . . . . . . . 4.2.2–22 +AR . . . . . . . . . . . 4.2.2–20 +ARn . . . . . . . . . . 4.2.2–20 +AT . . . . . . . . . . . 4.2.2–20 +AZZIT . . . . . . . . 4.2.2–8 +Variable +Page +Variable +Page +Variable +Page +CSTRESS . . . . . . 4.2.2–23 +CTEMP . . . . . . . 4.2.2–22 +CTF . . . . . . . . . . 4.2.2–15 +CTFn . . . . . . . . . 4.2.2–15 +CTHICK . . . . . . . 4.2.2–23 +CTMn. . . . . . . . . 4.2.2–15 +CU . . . . . . . . . . . 4.2.2–18 +CUE . . . . . . . . . . 4.2.2–15 +CUEn . . . . . . . . . 4.2.2–15 +CUF . . . . . . . . . . 4.2.2–16 +CUFn . . . . . . . . . 4.2.2–16 +CUMn . . . . . . . . 4.2.2–16 +CUn . . . . . . . . . . 4.2.2–18 +CUP . . . . . . . . . . 4.2.2–15 +CUPEQ. . . . . . . . 4.2.2–15 +CUPEQC . . . . . . 4.2.2–16 +CUPEQn . . . . . . . 4.2.2–16 +CUPn . . . . . . . . . 4.2.2–15 +CUREn . . . . . . . . 4.2.2–15 +CURn . . . . . . . . . 4.2.2–18 +CURPEQn. . . . . . 4.2.2–16 +CURPn . . . . . . . . 4.2.2–15 +CV . . . . . . . . . . . 4.2.2–18 +CVF . . . . . . . . . . 4.2.2–16 +CVFn . . . . . . . . . 4.2.2–16 +CVMn . . . . . . . . 4.2.2–16 +CVn . . . . . . . . . . 4.2.2–18 +CVOL. . . . . . . . . 4.2.2–21 +CVRn . . . . . . . . . 4.2.2–18 +DAMAGEC. . . . . 4.2.2–8 +DAMAGEFC. . . . 4.2.2–10 +DAMAGEFT . . . . 4.2.2–10 +DAMAGEMC . . . 4.2.2–10 +DAMAGEMT . . . 4.2.2–10 +DAMAGESHR . . 4.2.2–10 +DAMAGET. . . . . 4.2.2–8 +DBS . . . . . . . . . . 4.2.2–23 +DBSF . . . . . . . . . 4.2.2–23 +DBT . . . . . . . . . . 4.2.2–23 +OI.2–2 +DBURNF . . . . . . 4.2.2–10 +DENSITY . . . . . . 4.2.2–7 +DENSITYVAVG . 4.2.2–11 +DMASS . . . . . . . 4.2.2–26 +4.2.2–27 +DMENER . . . . . . 4.2.2–7 +DMICRT. . . . . . . 4.2.2–9 +4.2.2–11 +DMICRTMAX. . . 4.2.2–6 +DT . . . . . . . . . . . 4.2.2–27 +DUCTCRT . . . . . 4.2.2–9 +E . . . . . . . . . . . . 4.2.2–4 +EASEDEN . . . . . 4.2.2–13 +ECDDEN . . . . . . 4.2.2–13 +EDCDEN . . . . . . 4.2.2–14 +EDMDDEN. . . . . 4.2.2–14 +EDMICRTMAX. . 4.2.2–14 +EDT . . . . . . . . . . 4.2.2–14 +EFABRIC . . . . . . 4.2.2–10 +EFABRICij . . . . . 4.2.2–10 +EFENRRTR. . . . . 4.2.2–24 +EIHEDEN . . . . . . 4.2.2–13 +Eij . . . . . . . . . . . 4.2.2–4 +ELASE . . . . . . . . 4.2.2–13 +ELCD . . . . . . . . . 4.2.2–13 +ELDC . . . . . . . . . 4.2.2–13 +ELDMD . . . . . . . 4.2.2–13 +ELEDEN. . . . . . . 4.2.2–13 +ELEN . . . . . . . . . 4.2.2–13 +ELIHE . . . . . . . . 4.2.2–13 +ELPD . . . . . . . . . 4.2.2–13 +ELSE . . . . . . . . . 4.2.2–13 +ELVD . . . . . . . . . 4.2.2–13 +EMSF . . . . . . . . . 4.2.2–14 +ENER . . . . . . . . . 4.2.2–7 +ENRRT . . . . . . . . 4.2.2–24 +EPDDEN . . . . . . 4.2.2–13 +ER . . . . . . . . . . . 4.2.2–4 +ERij . . . . . . . . . . 4.2.2–4 +CMF. . . . . . . . . . 4.2.2–22 +CMFL. . . . . . . . . 4.2.2–22 +CMFLT. . . . . . . . 4.2.2–22 +CMn . . . . . . . . . . 4.2.2–21 +CMN . . . . . . . . . 4.2.2–24 +CMNM . . . . . . . . 4.2.2–24 +CMS. . . . . . . . . . 4.2.2–24 +CMSM . . . . . . . . 4.2.2–24 +CMT . . . . . . . . . 4.2.2–24 +CMTM . . . . . . . . 4.2.2–24 +CNF . . . . . . . . . . 4.2.2–16 +CNFC . . . . . . . . . 4.2.2–17 +CNFn . . . . . . . . . 4.2.2–16 +CNMn . . . . . . . . 4.2.2–16 +COORD . . . . . . . 4.2.2–6 +4.2.2–11 +4.2.2–20 +COORDCOM . . . 4.2.2–26 +COORn. . . . . . . . 4.2.2–20 +CP . . . . . . . . . . . 4.2.2–18 +CPn . . . . . . . . . . 4.2.2–18 +CPRn . . . . . . . . . 4.2.2–18 +CRACK . . . . . . . 4.2.2–9 +CRF . . . . . . . . . . 4.2.2–18 +CRFn . . . . . . . . . 4.2.2–18 +CRMn. . . . . . . . . 4.2.2–18 +CRSTS . . . . . . . . 4.2.2–24 +CSAREA . . . . . . 4.2.2–22 +CSDMG . . . . . . . 4.2.2–23 +CSF . . . . . . . . . . 4.2.2–16 +CSFC . . . . . . . . . 4.2.2–16 +CSFn . . . . . . . . . 4.2.2–16 +CSLST . . . . . . . . 4.2.2–17 +CSLSTi. . . . . . . . 4.2.2–17 +CSMAXSCRT . . . 4.2.2–23 +CSMAXUCRT. . . 4.2.2–23 +CSMn . . . . . . . . . 4.2.2–16 +CSQUADSCRT . . 4.2.2–23 +Variable +Page +Variable +Page +Variable +Page +MINFLT . . . . . . . 4.2.2–22 +MISES . . . . . . . . 4.2.2–4 +MISESMAX . . . . 4.2.2–3 +MISESVAVG. . . . 4.2.2–11 +MKCRT . . . . . . . 4.2.2–9 +MSFLDCRT . . . . 4.2.2–9 +MSTRN . . . . . . . 4.2.2–8 +MSTRS. . . . . . . . 4.2.2–7 +NE . . . . . . . . . . . 4.2.2–4 +NEij . . . . . . . . . . 4.2.2–4 +NEP . . . . . . . . . . 4.2.2–4 +NEPn . . . . . . . . . 4.2.2–4 +NFORC . . . . . . . 4.2.2–14 +NT . . . . . . . . . . . 4.2.2–21 +NTn . . . . . . . . . . 4.2.2–21 +NVF . . . . . . . . . . 4.2.2–21 +OPENBC . . . . . . 4.2.2–24 +P . . . . . . . . . . . . 4.2.2–19 +PABS . . . . . . . . . 4.2.2–21 +PALPH . . . . . . . . 4.2.2–10 +PALPHMIN. . . . . 4.2.2–10 +PCAV . . . . . . . . . 4.2.2–21 +PE . . . . . . . . . . . 4.2.2–4 +PEEQ . . . . . . . . . 4.2.2–5 +4.2.2–8 +PEEQMAX . . . . . 4.2.2–5 +PEEQT . . . . . . . . 4.2.2–5 +PEEQVAVG . . . . 4.2.2–11 +PEij . . . . . . . . . . 4.2.2–4 +PENER . . . . . . . . 4.2.2–7 +PEP . . . . . . . . . . 4.2.2–4 +PEPn . . . . . . . . . 4.2.2–4 +PEQC . . . . . . . . . 4.2.2–8 +PEQCn . . . . . . . . 4.2.2–8 +PEVAVG . . . . . . . 4.2.2–11 +POR . . . . . . . . . . 4.2.2–20 +PRESS . . . . . . . . 4.2.2–4 +PRESSVAVG. . . . 4.2.2–12 +QUADECRT . . . . 4.2.2–11 +OI.2–3 +QUADSCRT . . . . 4.2.2–11 +RBANG . . . . . . . 4.2.2–10 +RBFOR. . . . . . . . 4.2.2–10 +RBROT . . . . . . . 4.2.2–11 +RF . . . . . . . . . . . 4.2.2–21 +RFL . . . . . . . . . . 4.2.2–21 +RFLn . . . . . . . . . 4.2.2–21 +RFn . . . . . . . . . . 4.2.2–21 +RHOE. . . . . . . . . 4.2.2–10 +RHOP. . . . . . . . . 4.2.2–10 +RM. . . . . . . . . . . 4.2.2–21 +RMn . . . . . . . . . . 4.2.2–21 +RT . . . . . . . . . . . 4.2.2–21 +S . . . . . . . . . . . . 4.2.2–3 +SBF . . . . . . . . . . 4.2.2–14 +SDEG . . . . . . . . . 4.2.2–8 +4.2.2–9 +4.2.2–11 +SDV . . . . . . . . . . 4.2.2–7 +SDVn . . . . . . . . . 4.2.2–7 +SE . . . . . . . . . . . 4.2.2–12 +SEn . . . . . . . . . . 4.2.2–12 +SENER . . . . . . . . 4.2.2–7 +SF . . . . . . . . . . . 4.2.2–12 +SFABRIC . . . . . . 4.2.2–10 +SFABRICij . . . . . 4.2.2–10 +SFDR . . . . . . . . . 4.2.2–25 +SFDRA . . . . . . . . 4.2.2–25 +SFDRT . . . . . . . . 4.2.2–25 +SFDRTA . . . . . . . 4.2.2–25 +SFn . . . . . . . . . . 4.2.2–12 +SHRCRT. . . . . . . 4.2.2–9 +SHRRATIO . . . . . 4.2.2–9 +Sij . . . . . . . . . . . 4.2.2–3 +SKn . . . . . . . . . . 4.2.2–12 +SMn . . . . . . . . . . 4.2.2–12 +SOAREA . . . . . . 4.2.2–25 +SOF . . . . . . . . . . 4.2.2–25 +SOM . . . . . . . . . 4.2.2–25 +ERP . . . . . . . . . . 4.2.2–4 +ERPn . . . . . . . . . 4.2.2–4 +ERPRATIO . . . . . 4.2.2–9 +ERV . . . . . . . . . . 4.2.2–4 +ESEDEN. . . . . . . 4.2.2–13 +ETOTAL . . . . . . . 4.2.2–27 +EVDDEN . . . . . . 4.2.2–13 +EVF . . . . . . . . . . 4.2.2–11 +EVOL. . . . . . . . . 4.2.2–14 +FLDCRT . . . . . . . 4.2.2–9 +FLSDCRT . . . . . . 4.2.2–9 +FSLIP . . . . . . . . . 4.2.2–23 +FSLIPR. . . . . . . . 4.2.2–23 +FV . . . . . . . . . . . 4.2.2–7 +FVn . . . . . . . . . . 4.2.2–7 +GRAV. . . . . . . . . 4.2.2–14 +HFL . . . . . . . . . . 4.2.2–11 +4.2.2–25 +HFLA . . . . . . . . . 4.2.2–25 +HFLM . . . . . . . . 4.2.2–11 +HFLn . . . . . . . . . 4.2.2–11 +HSNFCCRT . . . . 4.2.2–10 +HSNFTCRT. . . . . 4.2.2–10 +HSNMCCRT . . . . 4.2.2–10 +HSNMTCRT . . . . 4.2.2–10 +HTL . . . . . . . . . . 4.2.2–25 +HTLA. . . . . . . . . 4.2.2–25 +IWCONWEP . . . . 4.2.2–19 +JCCRT . . . . . . . . 4.2.2–9 +LE . . . . . . . . . . . 4.2.2–4 +LEij . . . . . . . . . . 4.2.2–4 +LEP . . . . . . . . . . 4.2.2–4 +LEPn . . . . . . . . . 4.2.2–4 +LOCALDIRn . . . . 4.2.2–7 +MASS. . . . . . . . . 4.2.2–26 +MASSEUL . . . . . 4.2.2–26 +MAXECRT . . . . . 4.2.2–11 +MAXSCRT . . . . . 4.2.2–11 +Variable +Page +Variable +Page +Variable +Page +SP . . . . . . . . . . . 4.2.2–3 +SPn . . . . . . . . . . 4.2.2–4 +SSAVG . . . . . . . . 4.2.2–12 +SSAVGn . . . . . . . 4.2.2–12 +SSFORC . . . . . . . 4.2.2–28 +SSFORCn . . . . . . 4.2.2–28 +SSPEEQ . . . . . . . 4.2.2–27 +SSPEEQn . . . . . . 4.2.2–28 +SSSPRD . . . . . . . 4.2.2–28 +SSSPRDn . . . . . . 4.2.2–28 +SSTORQ . . . . . . . 4.2.2–28 +SSTORQn . . . . . . 4.2.2–28 +STAGP . . . . . . . . 4.2.2–19 +STATUS . . . . . . . 4.2.2–11 +4.2.2–14 +STH . . . . . . . . . . 4.2.2–12 +SVAVG . . . . . . . . 4.2.2–12 +TCMASS . . . . . . 4.2.2–22 +TCSAREA . . . . . 4.2.2–22 +TCVOL. . . . . . . . 4.2.2–22 +TEMP. . . . . . . . . 4.2.2–7 +TEMPMAVG. . . . 4.2.2–12 +TIEADJUST . . . . 4.2.2–21 +TIEDSTATUS . . . 4.2.2–21 +TINFL . . . . . . . . 4.2.2–22 +TRIAX . . . . . . . . 4.2.2–4 +TRNOR . . . . . . . 4.2.2–19 +TRSHR . . . . . . . . 4.2.2–19 +TSAIH . . . . . . . . 4.2.2–8 +TSAIW . . . . . . . . 4.2.2–8 +TSHR . . . . . . . . . 4.2.2–7 +TSHR13 . . . . . . . 4.2.2–7 +TSHR23 . . . . . . . 4.2.2–7 +U . . . . . . . . . . . . 4.2.2–20 +UCOM . . . . . . . . 4.2.2–26 +Un . . . . . . . . . . . 4.2.2–20 +UR . . . . . . . . . . . 4.2.2–20 +URn . . . . . . . . . . 4.2.2–20 +UT . . . . . . . . . . . 4.2.2–20 +V . . . . . . . . . . . . 4.2.2–20 +VCOM . . . . . . . . 4.2.2–26 +VENER. . . . . . . . 4.2.2–7 +Vn . . . . . . . . . . . 4.2.2–20 +VOLEUL . . . . . . 4.2.2–26 +VP . . . . . . . . . . . 4.2.2–19 +VR . . . . . . . . . . . 4.2.2–20 +VRn . . . . . . . . . . 4.2.2–20 +VT . . . . . . . . . . . 4.2.2–20 +VVF . . . . . . . . . . 4.2.2–8 +VVFG. . . . . . . . . 4.2.2–8 +VVFN. . . . . . . . . 4.2.2–8 +XN . . . . . . . . . . . 4.2.2–24 +XS . . . . . . . . . . . 4.2.2–24 +XT . . . . . . . . . . . 4.2.2–24 +OI.3 +Abaqus/CFD OUTPUT VARIABLE INDEX +This index provides a reference to all of the output variables that are available in Abaqus/CFD. Output +variables are listed in alphabetical order. +Variable +Page +Variable +Page +Variable +Page +ALLKE. . . . . . . . 4.2.3–5 +AVGPRESS . . . . . 4.2.3–4 +AVGTEMP . . . . . 4.2.3–4 +AVGVEL . . . . . . 4.2.3–4 +COORD . . . . . . . 4.2.3–2 +4.2.3–3 +COORn. . . . . . . . 4.2.3–3 +DENSITY . . . . . . 4.2.3–2 +4.2.3–3 +DIST . . . . . . . . . 4.2.3–2 +4.2.3–3 +DIV . . . . . . . . . . 4.2.3–2 +4.2.3–3 +ENSTROPHY . . . 4.2.3–2 +4.2.3–3 +EVOL. . . . . . . . . 4.2.3–2 +FORCE . . . . . . . . 4.2.3–4 +HEATFLOW . . . . 4.2.3–4 +HELICITY . . . . . 4.2.3–2 +4.2.3–3 +HFL . . . . . . . . . . 4.2.3–4 +HFLN . . . . . . . . . 4.2.3–4 +MASSFLOW . . . . 4.2.3–4 +NTRACTION . . . 4.2.3–4 +PRESSFORCE. . . 4.2.3–4 +PRESSURE . . . . . 4.2.3–2 +4.2.3–3 +SHEARRATE . . . 4.2.3–2 +4.2.3–3 +STRACTION. . . . 4.2.3–4 +SURFAREA . . . . 4.2.3–4 +TEMP. . . . . . . . . 4.2.3–2 +4.2.3–3 +TRACTION. . . . . 4.2.3–4 +TURBEPS . . . . . . 4.2.3–2 +4.2.3–3 +TURBKE . . . . . . 4.2.3–3 +4.2.3–4 +TURBNU . . . . . . 4.2.3–3 +4.2.3–4 +U . . . . . . . . . . . . 4.2.3–3 +Un . . . . . . . . . . . 4.2.3–3 +V . . . . . . . . . . . . 4.2.3–2 +4.2.3–3 +VGINV2 . . . . . . . 4.2.3–2 +4.2.3–3 +VISCFORCE . . . . 4.2.3–4 +VISCOSITY . . . . 4.2.3–2 +Vn . . . . . . . . . . . 4.2.3–3 +VOL . . . . . . . . . . 4.2.3–5 +VOLFLOW . . . . . 4.2.3–4 +VORTICITY . . . . 4.2.3–2 +4.2.3–3 +VORTICITYn . . . 4.2.3–3 +WALLSHEAR . . . 4.2.3–4 +YPLUS . . . . . . . . 4.2.3–5 +YSTAR . . . . . . . . 4.2.3–5 +SIMULIA is the Dassault Systèmes brand that delivers a scalable portfolio of +Realistic Simulation solutions including the Abaqus product suite for Unified Finite +Element Analysis; multiphysics solutions for insight into challenging engineering +problems; and lifecycle management solutions for managing simulation data, +processes, and intellectual property. By building on established technology, +respected quality, and superior customer service, SIMULIA makes realistic +simulation an integral business practice that improves product performance, +reduces physical prototypes, and drives innovation. Headquartered in Providence, +RI, USA, with R&D centers in Providence and in Vélizy, France, SIMULIA provides +sales, services, and support through a global network of regional offices and +distributors. For more information, visit www.simulia.com. +About Dassault Systèmes +As a world leader in 3D and Product Lifecycle Management (PLM) solutions, +Dassault Systèmes brings value to more than 100,000 customers in 80 countries. +A pioneer in the 3D software market since 1981, Dassault Systèmes develops and +markets PLM application software and services that support industrial processes +and provide a 3D vision of the entire lifecycle of products from conception to +maintenance to recycling. The Dassault Systèmes portfolio consists of CATIA for +designing the virtual product, SolidWorks for 3D mechanical design, DELMIA for +virtual production, SIMULIA for virtual testing, ENOVIA for global collaborative +lifecycle management, and 3DVIA for online 3D lifelike experiences. Dassault +Systèmes’ shares are listed on Euronext Paris (#13065, DSY.PA), and Dassault +Systèmes’ ADRs may be traded on the US Over-The-Counter (OTC) market (DASTY). +For more information, visit www.3ds.com. +fi +, +, +, +, +, +, +, +, +. +. +, +© +. +, +, +. +/ + +User’s Manual +CAUTION: This documentation is intended for qualified users who will exercise sound engineering judgment and expertise in the use of the Abaqus +Software. The Abaqus Software is inherently complex, and the examples and procedures in this documentation are not intended to be exhaustive or to apply +to any particular situation. Users are cautioned to satisfy themselves as to the accuracy and results of their analyses. +Dassault Systèmes and its subsidiaries, including Dassault Systèmes Simulia Corp., shall not be responsible for the accuracy or usefulness of any analysis +performed using the Abaqus Software or the procedures, examples, or explanations in this documentation. Dassault Systèmes and its subsidiaries shall not +be responsible for the consequences of any errors or omissions that may appear in this documentation. +The Abaqus Software is available only under license from Dassault Systèmes or its subsidiary and may be used or reproduced only in accordance with the +terms of such license. 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Bhd., Kuala Lumpur, Tel: +603 2039 9000, abaqus.my@worleyparsons.com +Kimeca.NET SA de CV, Mexico, Tel: +52 55 2459 2635 +Matrix Applied Computing Ltd., Auckland, Tel: +64 9 623 1223, abaqus-tech@matrix.co.nz +BudSoft Sp. z o.o., Poznań, Tel: +48 61 8508 466, info@budsoft.com.pl +TESIS Ltd., Moscow, Tel: +7 495 612 44 22, info@tesis.com.ru +WorleyParsons Pte Ltd., Singapore, Tel: +65 6735 8444, abaqus.sg@worleyparsons.com +Finite Element Analysis Services (Pty) Ltd., Parklands, Tel: +27 21 556 6462, feas@feas.co.za +Thailand +Turkey +Simutech Solution Corporation, Taipei, R.O.C., Tel: +886 2 2507 9550, camilla@simutech.com.tw +WorleyParsons Pte Ltd., Singapore, Tel: +65 6735 8444, abaqus.sg@worleyparsons.com +A-Ztech Ltd., Istanbul, Tel: +90 216 361 8850, info@a-ztech.com.tr +Preface +Support +Both technical engineering support (for problems with creating a model or performing an analysis) and +systems support (for installation, licensing, and hardware-related problems) for Abaqus are offered through +a network of local support offices. Regional contact information is listed in the front of each Abaqus manual +and is accessible from the Locations page at www.simulia.com. +Support for SIMULIA products +SIMULIA provides a knowledge database of answers and solutions to questions that we have answered, +as well as guidelines on how to use Abaqus, SIMULIA Scenario Definition, Isight, and other SIMULIA +products. You can also submit new requests for support. All support incidents are tracked. If you contact +us by means outside the system to discuss an existing support problem and you know the incident or support +request number, please mention it so that we can query the database to see what the latest action has been. +Many questions about Abaqus can also be answered by visiting the Products page and the Support +page at www.simulia.com. +Anonymous ftp site +To facilitate data transfer with SIMULIA, an anonymous ftp account is available at ftp.simulia.com. +Login as user anonymous, and type your e-mail address as your password. Contact support before placing +files on the site. +Training +All offices and representatives offer regularly scheduled public training classes. The courses are offered in +a traditional classroom form and via the Web. We also provide training seminars at customer sites. All +training classes and seminars include workshops to provide as much practical experience with Abaqus as +possible. For a schedule and descriptions of available classes, see www.simulia.com or call your local office +or representative. +Feedback +We welcome any suggestions for improvements to Abaqus software, the support program, or documentation. +We will ensure that any enhancement requests you make are considered for future releases. If you wish to +make a suggestion about the service or products, refer to www.simulia.com. Complaints should be made by +contacting your local office or through www.simulia.com by visiting the Quality Assurance section of the +1.1.1 +1.2.1 +1.2.2 +1.3.1 +1.4.1 +2.1.1 +2.1.2 +2.1.3 +2.1.4 +2.1.5 +2.1.6 +2.2.1 +2.2.2 +2.2.3 +2.2.4 +2.2.5 +2.3.1 +2.3.2 +2.3.3 +2.3.4 +Contents +Volume I +PART I +INTRODUCTION, SPATIAL MODELING, AND EXECUTION +1. +Introduction +Introduction: general +Abaqus syntax and conventions +Input syntax rules +Conventions +Abaqus model definition +Defining a model in Abaqus +Parametric modeling +Parametric input +2. Spatial Modeling +Node definition +Node definition +Parametric shape variation +Nodal thicknesses +Normal definitions at nodes +Transformed coordinate systems +Adjusting nodal coordinates +Element definition +Element definition +Element foundations +Defining reinforcement +Defining rebar as an element property +Orientations +Surface definition +Surfaces: overview +Element-based surface definition +Node-based surface definition +Analytical rigid surface definition +Eulerian surface definition +Operating on surfaces +Rigid body definition +Rigid body definition +Integrated output section definition +Integrated output section definition +Mass adjustment +Adjust and/or redistribute mass of an element set +Nonstructural mass definition +Nonstructural mass definition +Distribution definition +Distribution definition +Display body definition +Display body definition +Assembly definition +Defining an assembly +Matrix definition +Defining matrices +3. Job Execution +Execution procedures: overview +Execution procedure for Abaqus: overview +Execution procedures +Obtaining information +Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD execution +SIMULIA Co-Simulation Engine controller execution +Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD co-simulation execution +Abaqus/CAE execution +Abaqus/Viewer execution +Python execution +Parametric studies +Abaqus documentation +Licensing utilities +ASCII translation of results (.fil) files +Joining results (.fil) files +Querying the keyword/problem database +ii +Abaqus ID:usb-toc +Printed on: Fri February 3 -- 18:01:12 2012 +2.3.5 +2.3.6 +2.4.1 +2.5.1 +2.6.1 +2.7.1 +2.8.1 +2.9.1 +2.10.1 +2.11.1 +3.1.1 +3.2.1 +3.2.2 +3.2.3 +3.2.4 +3.2.5 +3.2.6 +3.2.7 +3.2.8 +3.2.9 +3.2.10 +Making user-defined executables and subroutines +Input file and output database upgrade utility +Generating output database reports +Joining output database (.odb) files from restarted analyses +Combining output from substructures +Combining data from multiple output databases +Network output database file connector +Mapping thermal and magnetic loads +Fixed format conversion utility +Translating Nastran bulk data files to Abaqus input files +Translating Abaqus files to Nastran bulk data files +Translating ANSYS input files to Abaqus input files +Translating PAM-CRASH input files to partial Abaqus input files +Translating RADIOSS input files to partial Abaqus input files +Translating Abaqus output database files to Nastran Output2 results files +Translating LS-DYNA data files to Abaqus input files +Exchanging Abaqus data with ZAERO +Encrypting and decrypting Abaqus input data +Job execution control +Environment file settings +Using the Abaqus environment settings +Managing memory and disk resources +Managing memory and disk use in Abaqus +Parallel execution +Parallel execution: overview +Parallel execution in Abaqus/Standard +Parallel execution in Abaqus/Explicit +Parallel execution in Abaqus/CFD +File extension definitions +File extensions used by Abaqus +FORTRAN unit numbers +FORTRAN unit numbers used by Abaqus +CONTENTS +3.2.14 +3.2.15 +3.2.16 +3.2.17 +3.2.18 +3.2.19 +3.2.20 +3.2.21 +3.2.22 +3.2.23 +3.2.24 +3.2.25 +3.2.26 +3.2.27 +3.2.28 +3.2.29 +3.2.30 +3.2.31 +3.2.32 +3.2.33 +3.3.1 +3.4.1 +3.5.1 +3.5.2 +3.5.3 +3.5.4 +3.6.1 +3.7.1 +4.1.2 +4.1.3 +4.1.4 +4.2.1 +4.2.2 +4.2.3 +4.3.1 +5.1.1 +5.1.2 +5.1.3 +5.1.4 +CONTENTS +4. Output +PART II +OUTPUT +Output +Output to the data and results files +Output to the output database +Error indicator output +Output variables +Abaqus/Standard output variable identifiers +Abaqus/Explicit output variable identifiers +Abaqus/CFD output variable identifiers +The postprocessing calculator +The postprocessing calculator +5. File Output Format +Accessing the results file +Accessing the results file: overview +Results file output format +Accessing the results file information +Utility routines for accessing the results file +OI.1 Abaqus/Standard Output Variable Index +OI.2 Abaqus/Explicit Output Variable Index +OI.3 Abaqus/CFD Output Variable Index +6.1.1 +6.1.2 +6.1.3 +6.1.4 +6.1.5 +6.1.6 +6.2.1 +6.2.2 +6.2.3 +6.2.4 +6.2.5 +6.2.6 +6.2.7 +6.3.1 +6.3.2 +6.3.3 +6.3.4 +6.3.5 +6.3.6 +6.3.7 +6.3.8 +6.3.9 +6.3.10 +6.3.11 +6.4.1 +6.5.1 +6.5.2 +Volume II +PART III +ANALYSIS PROCEDURES, SOLUTION, AND CONTROL +6. Analysis Procedures +Introduction +Solving analysis problems: overview +Defining an analysis +General and linear perturbation procedures +Multiple load case analysis +Direct linear equation solver +Iterative linear equation solver +Static stress/displacement analysis +Static stress analysis procedures: overview +Static stress analysis +Eigenvalue buckling prediction +Unstable collapse and postbuckling analysis +Quasi-static analysis +Direct cyclic analysis +Low-cycle fatigue analysis using the direct cyclic approach +Dynamic stress/displacement analysis +Dynamic analysis procedures: overview +Implicit dynamic analysis using direct integration +Explicit dynamic analysis +Direct-solution steady-state dynamic analysis +Natural frequency extraction +Complex eigenvalue extraction +Transient modal dynamic analysis +Mode-based steady-state dynamic analysis +Subspace-based steady-state dynamic analysis +Response spectrum analysis +Random response analysis +Steady-state transport analysis +Steady-state transport analysis +Heat transfer and thermal-stress analysis +Heat transfer analysis procedures: overview +Uncoupled heat transfer analysis +6.5.4 +6.6.1 +6.6.2 +6.7.1 +6.7.2 +6.7.3 +6.7.4 +6.7.5 +6.7.6 +6.8.1 +6.8.2 +6.9.1 +6.10.1 +6.11.1 +6.12.1 +7.1.1 +7.2.1 +7.2.2 +7.2.3 +7.2.4 +CONTENTS +Fully coupled thermal-stress analysis +Adiabatic analysis +Fluid dynamic analysis +Fluid dynamic analysis procedures: overview +Incompressible fluid dynamic analysis +Electromagnetic analysis +Electromagnetic analysis procedures +Piezoelectric analysis +Coupled thermal-electrical analysis +Fully coupled thermal-electrical-structural analysis +Eddy current analysis +Magnetostatic analysis +Coupled pore fluid flow and stress analysis +Coupled pore fluid diffusion and stress analysis +Geostatic stress state +Mass diffusion analysis +Mass diffusion analysis +Acoustic and shock analysis +Acoustic, shock, and coupled acoustic-structural analysis +Abaqus/Aqua analysis +Abaqus/Aqua analysis +Annealing +Annealing procedure +7. Analysis Solution and Control +Solving nonlinear problems +Solving nonlinear problems +Analysis convergence controls +Convergence and time integration criteria: overview +Commonly used control parameters +Convergence criteria for nonlinear problems +Time integration accuracy in transient problems +ANALYSIS TECHNIQUES +8. Analysis Techniques: Introduction +Analysis techniques: overview +9. Analysis Continuation Techniques +Restarting an analysis +Restarting an analysis +Importing and transferring results +Transferring results between Abaqus analyses: overview +Transferring results between Abaqus/Explicit and Abaqus/Standard +Transferring results from one Abaqus/Standard analysis to another +Transferring results from one Abaqus/Explicit analysis to another +10. Modeling Abstractions +Substructuring +Using substructures +Defining substructures +Submodeling +Submodeling: overview +Node-based submodeling +Surface-based submodeling +Generating global matrices +Generating matrices +CONTENTS +8.1.1 +9.1.1 +9.2.1 +9.2.2 +9.2.3 +9.2.4 +10.1.1 +10.1.2 +10.2.1 +10.2.2 +10.2.3 +10.3.1 +Symmetric model generation, results transfer, and analysis of cyclic symmetry models +Symmetric model generation +Transferring results from a symmetric mesh or a partial three-dimensional mesh to +a full three-dimensional mesh +Analysis of models that exhibit cyclic symmetry +Periodic media analysis +Periodic media analysis +Meshed beam cross-sections +Meshed beam cross-sections +vii +10.4.1 +10.4.2 +10.4.3 +10.5.1 +Modeling discontinuities as an enriched feature using the extended finite element method +Modeling discontinuities as an enriched feature using the extended finite element +10.7.1 +11.1.1 +11.2.1 +11.3.1 +11.4.1 +11.4.2 +11.4.3 +11.5.1 +11.5.2 +11.5.3 +11.5.4 +11.6.1 +11.7.1 +11.8.1 +12.1.1 +12.2.1 +12.2.2 +12.2.3 +12.2.4 +method +11. Special-Purpose Techniques +Inertia relief +Inertia relief +Mesh modification or replacement +Element and contact pair removal and reactivation +Geometric imperfections +Introducing a geometric imperfection into a model +Fracture mechanics +Fracture mechanics: overview +Contour integral evaluation +Crack propagation analysis +Surface-based fluid modeling +Surface-based fluid cavities: overview +Fluid cavity definition +Fluid exchange definition +Inflator definition +Mass scaling +Mass scaling +Selective subcycling +Selective subcycling +Steady-state detection +Steady-state detection +12. Adaptivity Techniques +Adaptivity techniques: overview +Adaptivity techniques +ALE adaptive meshing +ALE adaptive meshing: overview +Defining ALE adaptive mesh domains in Abaqus/Explicit +ALE adaptive meshing and remapping in Abaqus/Explicit +Modeling techniques for Eulerian adaptive mesh domains in Abaqus/Explicit +12.2.5 +12.2.6 +12.2.7 +12.3.1 +12.3.2 +12.3.3 +12.4.1 +13.1.1 +13.2.1 +13.2.2 +13.2.3 +14.1.1 +14.1.2 +14.1.3 +14.1.4 +15.1.1 +15.1.2 +16.1.1 +16.1.2 +16.1.3 +17.1.1 +17.2.1 +Output and diagnostics for ALE adaptive meshing in Abaqus/Explicit +Defining ALE adaptive mesh domains in Abaqus/Standard +ALE adaptive meshing and remapping in Abaqus/Standard +Adaptive remeshing +Adaptive remeshing: overview +Selection of error indicators influencing adaptive remeshing +Solution-based mesh sizing +Analysis continuation after mesh replacement +Mesh-to-mesh solution mapping +13. Optimization Techniques +Structural optimization: overview +Structural optimization: overview +Optimization models +Design responses +Objectives and constraints +Creating Abaqus optimization models +14. Eulerian Analysis +Eulerian analysis +Defining Eulerian boundaries +Eulerian mesh motion +Defining adaptive mesh refinement in the Eulerian domain +15. Particle Methods +Smoothed particle hydrodynamic analyses +Smoothed particle hydrodynamic analysis +Finite element conversion to SPH particles +16. Sequentially Coupled Multiphysics Analyses +Predefined fields for sequential coupling +Sequentially coupled thermal-stress analysis +Predefined loads for sequential coupling +17. Co-simulation +Co-simulation: overview +Preparing an Abaqus analysis for co-simulation +Preparing an Abaqus analysis for co-simulation +Co-simulation between Abaqus solvers +Abaqus/Standard to Abaqus/Explicit co-simulation +Abaqus/CFD to Abaqus/Standard or to Abaqus/Explicit co-simulation +18. Extending Abaqus Analysis Functionality +User subroutines and utilities +User subroutines: overview +Available user subroutines +Available utility routines +19. Design Sensitivity Analysis +Design sensitivity analysis +20. Parametric Studies +Scripting parametric studies +Scripting parametric studies +Parametric studies: commands +aStudy.combine(): Combine parameter samples for parametric studies. +aStudy.constrain(): Constrain parameter value combinations in parametric studies. +aStudy.define(): Define parameters for parametric studies. +aStudy.execute(): Execute the analysis of parametric study designs. +aStudy.gather(): Gather the results of a parametric study. +aStudy.generate(): Generate the analysis job data for a parametric study. +aStudy.output(): Specify the source of parametric study results. +aStudy=ParStudy(): Create a parametric study. +aStudy.report(): Report parametric study results. +aStudy.sample(): Sample parameters for parametric studies. +17.3.1 +17.3.2 +18.1.1 +18.1.2 +18.1.3 +19.1.1 +20.1.1 +20.2.1 +20.2.2 +20.2.3 +20.2.4 +20.2.5 +20.2.6 +20.2.7 +20.2.8 +20.2.9 +20.2.10 +21.1.1 +21.1.2 +21.1.3 +21.2.1 +22.1.1 +22.2.1 +22.2.2 +22.2.3 +22.3.1 +22.4.1 +22.5.1 +22.5.2 +22.5.3 +22.6.1 +22.6.2 +22.7.1 +22.7.2 +Volume III +PART V MATERIALS +21. Materials: Introduction +Introduction +Material library: overview +Material data definition +Combining material behaviors +General properties +Density +22. Elastic Mechanical Properties +Overview +Elastic behavior: overview +Linear elasticity +Linear elastic behavior +No compression or no tension +Plane stress orthotropic failure measures +Porous elasticity +Elastic behavior of porous materials +Hypoelasticity +Hypoelastic behavior +Hyperelasticity +Hyperelastic behavior of rubberlike materials +Hyperelastic behavior in elastomeric foams +Anisotropic hyperelastic behavior +Stress softening in elastomers +Mullins effect +Energy dissipation in elastomeric foams +Viscoelasticity +Time domain viscoelasticity +Frequency domain viscoelasticity +Nonlinear viscoelasticity +Hysteresis in elastomers +Parallel network viscoelastic model +Rate sensitive elastomeric foams +Low-density foams +23. +Inelastic Mechanical Properties +Overview +Inelastic behavior +Metal plasticity +Classical metal plasticity +Models for metals subjected to cyclic loading +Rate-dependent yield +Rate-dependent plasticity: creep and swelling +Annealing or melting +Anisotropic yield/creep +Johnson-Cook plasticity +Dynamic failure models +Porous metal plasticity +Cast iron plasticity +Two-layer viscoplasticity +ORNL – Oak Ridge National Laboratory constitutive model +Deformation plasticity +Other plasticity models +Extended Drucker-Prager models +Modified Drucker-Prager/Cap model +Mohr-Coulomb plasticity +Critical state (clay) plasticity model +Crushable foam plasticity models +Fabric materials +Fabric material behavior +Jointed materials +Jointed material model +Concrete +Concrete smeared cracking +Cracking model for concrete +Concrete damaged plasticity +xii +Abaqus ID:usb-toc +Printed on: Fri February 3 -- 18:01:12 2012 +22.8.1 +22.8.2 +22.9.1 +23.1.1 +23.2.1 +23.2.2 +23.2.3 +23.2.4 +23.2.5 +23.2.6 +23.2.7 +23.2.8 +23.2.9 +23.2.10 +23.2.11 +23.2.12 +23.2.13 +23.3.1 +23.3.2 +23.3.3 +23.3.4 +23.3.5 +23.4.1 +23.5.1 +23.7.1 +24.1.1 +24.2.1 +24.2.2 +24.2.3 +24.3.1 +24.3.2 +24.3.3 +24.4.1 +24.4.2 +24.4.3 +25.1.1 +25.2.1 +26.1.1 +26.1.2 +26.1.3 +26.1.4 +26.2.1 +26.2.2 +26.2.3 +26.2.4 +Permanent set in rubberlike materials +Permanent set in rubberlike materials +24. Progressive Damage and Failure +Progressive damage and failure: overview +Progressive damage and failure +Damage and failure for ductile metals +Damage and failure for ductile metals: overview +Damage initiation for ductile metals +Damage evolution and element removal for ductile metals +Damage and failure for fiber-reinforced composites +Damage and failure for fiber-reinforced composites: overview +Damage initiation for fiber-reinforced composites +Damage evolution and element removal for fiber-reinforced composites +Damage and failure for ductile materials in low-cycle fatigue analysis +Damage and failure for ductile materials in low-cycle fatigue analysis: overview +Damage initiation for ductile materials in low-cycle fatigue +Damage evolution for ductile materials in low-cycle fatigue +25. Hydrodynamic Properties +Overview +Hydrodynamic behavior: overview +Equations of state +Equation of state +26. Other Material Properties +Mechanical properties +Material damping +Thermal expansion +Field expansion +Viscosity +Heat transfer properties +Thermal properties: overview +Conductivity +Specific heat +Latent heat +Acoustic properties +Acoustic medium +Mass diffusion properties +Diffusivity +Solubility +Electromagnetic properties +Electrical conductivity +Piezoelectric behavior +Magnetic permeability +Pore fluid flow properties +Pore fluid flow properties +Permeability +Porous bulk moduli +Sorption +Swelling gel +Moisture swelling +User materials +User-defined mechanical material behavior +User-defined thermal material behavior +26.3.1 +26.4.1 +26.4.2 +26.5.1 +26.5.2 +26.5.3 +26.6.1 +26.6.2 +26.6.3 +26.6.4 +26.6.5 +26.6.6 +26.7.1 +26.7.2 +27.1.1 +27.1.2 +27.1.3 +27.1.4 +28.1.1 +28.1.2 +28.1.3 +28.1.4 +28.1.5 +28.1.6 +28.1.7 +28.2.1 +28.2.2 +28.3.1 +28.3.2 +28.4.1 +28.4.2 +28.5.1 +28.5.2 +29.1.1 +29.1.2 +29.1.3 +Volume IV +PART VI +ELEMENTS +27. Elements: Introduction +Element library: overview +Choosing the element’s dimensionality +Choosing the appropriate element for an analysis type +Section controls +28. Continuum Elements +General-purpose continuum elements +Solid (continuum) elements +One-dimensional solid (link) element library +Two-dimensional solid element library +Three-dimensional solid element library +Cylindrical solid element library +Axisymmetric solid element library +Axisymmetric solid elements with nonlinear, asymmetric deformation +Fluid continuum elements +Fluid (continuum) elements +Fluid element library +Infinite elements +Infinite elements +Infinite element library +Warping elements +Warping elements +Warping element library +Particle elements +Particle elements +Particle element library +29. Structural Elements +Membrane elements +Membrane elements +General membrane element library +Cylindrical membrane element library +Axisymmetric membrane element library +Truss elements +Truss elements +Truss element library +Beam elements +Beam modeling: overview +Choosing a beam cross-section +Choosing a beam element +Beam element cross-section orientation +Beam section behavior +Using a beam section integrated during the analysis to define the section behavior +Using a general beam section to define the section behavior +Beam element library +Beam cross-section library +Frame elements +Frame elements +Frame section behavior +Frame element library +Elbow elements +Pipes and pipebends with deforming cross-sections: elbow elements +Elbow element library +Shell elements +Shell elements: overview +Choosing a shell element +Defining the initial geometry of conventional shell elements +Shell section behavior +Using a shell section integrated during the analysis to define the section behavior +Using a general shell section to define the section behavior +Three-dimensional conventional shell element library +Continuum shell element library +Axisymmetric shell element library +Axisymmetric shell elements with nonlinear, asymmetric deformation +29.1.4 +29.2.1 +29.2.2 +29.3.1 +29.3.2 +29.3.3 +29.3.4 +29.3.5 +29.3.6 +29.3.7 +29.3.8 +29.3.9 +29.4.1 +29.4.2 +29.4.3 +29.5.1 +29.5.2 +29.6.1 +29.6.2 +29.6.3 +29.6.4 +29.6.5 +29.6.6 +29.6.7 +29.6.8 +29.6.9 +29.6.10 +30.1.1 +30.1.2 +30.2.1 +30.2.2 +30.3.1 +30.3.2 +30.4.1 +30.4.2 +31.1.1 +31.1.2 +31.1.3 +31.1.4 +31.1.5 +31.2.1 +31.2.2 +31.2.3 +31.2.4 +31.2.5 +31.2.6 +31.2.7 +31.2.8 +31.2.9 +31.2.10 +32.1.1 +32.1.2 +30. +Inertial, Rigid, and Capacitance Elements +Point mass elements +Point masses +Mass element library +Rotary inertia elements +Rotary inertia +Rotary inertia element library +Rigid elements +Rigid elements +Rigid element library +Capacitance elements +Point capacitance +Capacitance element library +31. Connector Elements +Connector elements +Connectors: overview +Connector elements +Connector actuation +Connector element library +Connection-type library +Connector element behavior +Connector behavior +Connector elastic behavior +Connector damping behavior +Connector functions for coupled behavior +Connector friction behavior +Connector plastic behavior +Connector damage behavior +Connector stops and locks +Connector failure behavior +Connector uniaxial behavior +32. Special-Purpose Elements +Spring elements +Springs +Spring element library +Dashpot elements +Dashpots +Dashpot element library +Flexible joint elements +Flexible joint element +Flexible joint element library +Distributing coupling elements +Distributing coupling elements +Distributing coupling element library +Cohesive elements +Cohesive elements: overview +Choosing a cohesive element +Modeling with cohesive elements +Defining the cohesive element’s initial geometry +Defining the constitutive response of cohesive elements using a continuum approach +Defining the constitutive response of cohesive elements using a traction-separation +description +Defining the constitutive response of fluid within the cohesive element gap +Two-dimensional cohesive element library +Three-dimensional cohesive element library +Axisymmetric cohesive element library +Gasket elements +Gasket elements: overview +Choosing a gasket element +Including gasket elements in a model +Defining the gasket element’s initial geometry +Defining the gasket behavior using a material model +Defining the gasket behavior directly using a gasket behavior model +Two-dimensional gasket element library +Three-dimensional gasket element library +Axisymmetric gasket element library +Surface elements +Surface elements +General surface element library +Cylindrical surface element library +Axisymmetric surface element library +32.2.1 +32.2.2 +32.3.1 +32.3.2 +32.4.1 +32.4.2 +32.5.1 +32.5.2 +32.5.3 +32.5.4 +32.5.5 +32.5.6 +32.5.7 +32.5.8 +32.5.9 +32.5.10 +32.6.1 +32.6.2 +32.6.3 +32.6.4 +32.6.5 +32.6.6 +32.6.7 +32.6.8 +32.6.9 +32.7.1 +32.7.2 +32.7.3 +32.7.4 +32.8.1 +32.8.2 +32.9.1 +32.9.2 +32.10.1 +32.10.2 +32.11.1 +32.11.2 +32.12.1 +32.12.2 +32.13.1 +32.13.2 +32.14.1 +32.14.2 +32.15.1 +32.15.2 +Tube support elements +Tube support elements +Tube support element library +Line spring elements +Line spring elements for modeling part-through cracks in shells +Line spring element library +Elastic-plastic joints +Elastic-plastic joints +Elastic-plastic joint element library +Drag chain elements +Drag chains +Drag chain element library +Pipe-soil elements +Pipe-soil interaction elements +Pipe-soil interaction element library +Acoustic interface elements +Acoustic interface elements +Acoustic interface element library +Eulerian elements +Eulerian elements +Eulerian element library +User-defined elements +User-defined elements +User-defined element library +EI.1 Abaqus/Standard Element Index +EI.2 Abaqus/Explicit Element Index +EI.3 Abaqus/CFD Element Index +Volume V +PART VII +PRESCRIBED CONDITIONS +33. Prescribed Conditions +Overview +Prescribed conditions: overview +Amplitude curves +Initial conditions +Initial conditions in Abaqus/Standard and Abaqus/Explicit +Initial conditions in Abaqus/CFD +Boundary conditions +Boundary conditions in Abaqus/Standard and Abaqus/Explicit +Boundary conditions in Abaqus/CFD +Loads +Applying loads: overview +Concentrated loads +Distributed loads +Thermal loads +Electromagnetic loads +Acoustic and shock loads +Pore fluid flow +Prescribed assembly loads +Prescribed assembly loads +Predefined fields +Predefined fields +PART VIII +CONSTRAINTS +34. Constraints +Overview +Kinematic constraints: overview +Multi-point constraints +Linear constraint equations +xx +Abaqus ID:usb-toc +Printed on: Fri February 3 -- 18:01:12 2012 +33.1.1 +33.1.2 +33.2.1 +33.2.2 +33.3.1 +33.3.2 +33.4.1 +33.4.2 +33.4.3 +33.4.4 +33.4.5 +33.4.6 +33.4.7 +33.5.1 +34.2.2 +34.2.3 +34.3.1 +34.3.2 +34.3.3 +34.3.4 +34.4.1 +34.5.1 +34.6.1 +35.1.1 +35.2.1 +35.2.2 +35.2.3 +35.2.4 +35.2.5 +35.2.6 +35.3.1 +35.3.2 +35.3.3 +35.3.4 +35.3.5 +35.3.6 +35.3.7 +35.3.8 +General multi-point constraints +Kinematic coupling constraints +Surface-based constraints +Mesh tie constraints +Coupling constraints +Shell-to-solid coupling +Mesh-independent fasteners +Embedded elements +Embedded elements +Element end release +Element end release +Overconstraint checks +Overconstraint checks +PART IX +INTERACTIONS +35. Defining Contact Interactions +Overview +Contact interaction analysis: overview +Defining general contact in Abaqus/Standard +Defining general contact interactions in Abaqus/Standard +Surface properties for general contact in Abaqus/Standard +Contact properties for general contact in Abaqus/Standard +Controlling initial contact status in Abaqus/Standard +Stabilization for general contact in Abaqus/Standard +Numerical controls for general contact in Abaqus/Standard +Defining contact pairs in Abaqus/Standard +Defining contact pairs in Abaqus/Standard +Assigning surface properties for contact pairs in Abaqus/Standard +Assigning contact properties for contact pairs in Abaqus/Standard +Modeling contact interference fits in Abaqus/Standard +Adjusting initial surface positions and specifying initial clearances in Abaqus/Standard +contact pairs +Adjusting contact controls in Abaqus/Standard +Defining tied contact in Abaqus/Standard +Extending master surfaces and slide lines +Contact modeling if substructures are present +Contact modeling if asymmetric-axisymmetric elements are present +Defining general contact in Abaqus/Explicit +Defining general contact interactions in Abaqus/Explicit +Assigning surface properties for general contact in Abaqus/Explicit +Assigning contact properties for general contact in Abaqus/Explicit +Controlling initial contact status for general contact in Abaqus/Explicit +Contact controls for general contact in Abaqus/Explicit +Defining contact pairs in Abaqus/Explicit +Defining contact pairs in Abaqus/Explicit +Assigning surface properties for contact pairs in Abaqus/Explicit +Assigning contact properties for contact pairs in Abaqus/Explicit +Adjusting initial surface positions and specifying initial clearances for contact pairs +in Abaqus/Explicit +Contact controls for contact pairs in Abaqus/Explicit +36. Contact Property Models +Mechanical contact properties +Mechanical contact properties: overview +Contact pressure-overclosure relationships +Contact damping +Contact blockage +Frictional behavior +User-defined interfacial constitutive behavior +Pressure penetration loading +Interaction of debonded surfaces +Breakable bonds +Surface-based cohesive behavior +Thermal contact properties +Thermal contact properties +Electrical contact properties +Electrical contact properties +Pore fluid contact properties +Pore fluid contact properties +37. Contact Formulations and Numerical Methods +Contact formulations and numerical methods in Abaqus/Standard +Contact formulations in Abaqus/Standard +xxii +Abaqus ID:usb-toc +Printed on: Fri February 3 -- 18:01:12 2012 +35.3.9 +35.3.10 +35.4.1 +35.4.2 +35.4.3 +35.4.4 +35.4.5 +35.5.1 +35.5.2 +35.5.3 +35.5.4 +35.5.5 +36.1.1 +36.1.2 +36.1.3 +36.1.4 +36.1.5 +36.1.6 +36.1.7 +36.1.8 +36.1.9 +36.1.10 +36.2.1 +37.1.2 +37.1.3 +37.2.1 +37.2.2 +37.2.3 +38.1.1 +38.1.2 +38.2.1 +38.2.2 +39.1.1 +39.2.1 +39.2.2 +39.3.1 +39.3.2 +39.4.1 +39.4.2 +39.5.1 +39.5.2 +40.1.1 +Contact constraint enforcement methods in Abaqus/Standard +Smoothing contact surfaces in Abaqus/Standard +Contact formulations and numerical methods in Abaqus/Explicit +Contact formulation for general contact in Abaqus/Explicit +Contact formulations for contact pairs in Abaqus/Explicit +Contact constraint enforcement methods in Abaqus/Explicit +38. Contact Difficulties and Diagnostics +Resolving contact difficulties in Abaqus/Standard +Contact diagnostics in an Abaqus/Standard analysis +Common difficulties associated with contact modeling in Abaqus/Standard +Resolving contact difficulties in Abaqus/Explicit +Contact diagnostics in an Abaqus/Explicit analysis +Common difficulties associated with contact modeling using contact pairs in +Abaqus/Explicit +39. Contact Elements in Abaqus/Standard +Contact modeling with elements +Contact modeling with elements +Gap contact elements +Gap contact elements +Gap element library +Tube-to-tube contact elements +Tube-to-tube contact elements +Tube-to-tube contact element library +Slide line contact elements +Slide line contact elements +Axisymmetric slide line element library +Rigid surface contact elements +Rigid surface contact elements +Axisymmetric rigid surface contact element library +40. Defining Cavity Radiation in Abaqus/Standard +Cavity radiation +Printed on: + +Prescribed Conditions +Overview +Initial conditions +Boundary conditions +Loads +Prescribed assembly loads +Predefined fields +PRESCRIBED CONDITIONS +33.1 +33.2 +33.3 +33.4 +33.5 +33.1 +Overview +• “Prescribed conditions: overview,” Section 33.1.1 +• “Amplitude curves,” Section 33.1.2 +33.1.1 +PRESCRIBED CONDITIONS: OVERVIEW +The following types of external conditions can be prescribed in an Abaqus model: +• Initial conditions: Nonzero initial conditions can be defined for many variables, as described in +“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1, and “Initial conditions in +Abaqus/CFD,” Section 33.2.2. +• Boundary conditions: Boundary conditions are used to prescribe values of basic solution variables: +displacements and rotations in stress/displacement analysis, temperature in heat transfer or coupled +thermal-stress analysis, electrical potential in coupled thermal-electrical analysis, pore pressure in soils +analysis, acoustic pressure in acoustic analysis, etc. Boundary conditions can be defined as described +in “Boundary conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1, and “Boundary +conditions in Abaqus/CFD,” Section 33.3.2. +• Loads: Many types of loading are available, depending on the analysis procedure. “Applying loads: +overview,” Section 33.4.1, gives an overview of loading in Abaqus. Load types specific to one analysis +procedure are described in the appropriate procedure section in Part III, “Analysis Procedures, Solution, +and Control.” General loads, which can be applied in multiple analysis types, are described in: +– “Concentrated loads,” Section 33.4.2 +– “Distributed loads,” Section 33.4.3 +– “Thermal loads,” Section 33.4.4 +– “Electromagnetic loads,” Section 33.4.5 +– “Acoustic and shock loads,” Section 33.4.6 +– “Pore fluid flow,” Section 33.4.7 +• Prescribed assembly loads: Pre-tension sections can be defined in Abaqus/Standard to prescribe +assembly loads in bolts or any other type of fastener. Pre-tension sections are described in “Prescribed +assembly loads,” Section 33.5.1. +• Connector loads and motions: Connector elements can be used to define complex mechanical +connections between parts, including actuation with prescribed loads or motions. Connector elements +are described in “Connectors: overview,” Section 31.1.1. +• Predefined fields: Predefined fields are time-dependent, non-solution-dependent fields that exist over +the spatial domain of the model. Temperature is the most commonly defined field. Predefined fields are +described in “Predefined fields,” Section 33.6.1. +Amplitude variations +Complex time- or frequency-dependent boundary conditions, loads, and predefined fields can be specified +by referring to an amplitude curve in the prescribed condition definition. Amplitude curves are explained +in “Amplitude curves,” Section 33.1.2. +In Abaqus/Standard if no amplitude is referenced from the boundary condition, +loading, or +predefined field definition, the total magnitude can be applied instantaneously at the start of the step and +remain constant throughout the step (a “step” variation) or it can vary linearly over the step from the +value at the end of the previous step (or from zero at the start of the analysis) to the magnitude given +(a “ramp” variation). You choose the type of variation when you define the step; the default variation +depends on the procedure chosen, as shown in “Defining an analysis,” Section 6.1.2. +In Abaqus/Standard the variation of many prescribed conditions can be defined in user subroutines. +In this case the magnitude of the variable can vary in any way with position and time. The magnitude +variation for prescribing and removing conditions must be specified in the subroutine . +In Abaqus/Explicit if no amplitude is referenced from the boundary condition or loading definition, +the total value will be applied instantaneously at the start of the step and will remain constant throughout +the step (a “step” variation), although Abaqus/Explicit does not admit jumps in displacement . If no amplitude is +referenced from a predefined field definition, the total magnitude will vary linearly over the step from +the value at the end of the previous step (or from zero at the start of the analysis) to the magnitude given +(a “ramp” variation). +When boundary conditions are removed , +in stress/displacement analysis) is converted to an applied conjugate flux (force or moment +in +stress/displacement analysis) at the beginning of the step. This flux magnitude is set to zero with a +“step” or “ramp” variation depending on the procedure chosen, as discussed in “Defining an analysis,” +Section 6.1.2. Similarly, when loads and predefined fields are removed, the load is set to zero and the +predefined field is set to its initial value. +In Abaqus/CFD if no amplitude is referenced from the boundary or loading condition, the total +value is applied instantaneously at the start of the step and remains constant throughout the step. +Abaqus/CFD does admit jumps in the velocity, temperature, etc. from the end value of the previous step +to the magnitude given in the current step. However, jumps in velocity boundary conditions may result +in a divergence-free projection that adjusts the initial velocities to be consistent with the prescribed +boundary conditions in order to define a well-posed incompressible flow problem. +Applying boundary conditions and loads in a local coordinate system +You can define a local coordinate system at a node as described in “Transformed coordinate systems,” +Section 2.1.5. Then, all input data for concentrated force and moment loading and for displacement and +rotation boundary conditions are given in the local system. +Loads and predefined fields available for various procedures +Table 33.1.1–1 Available loads and predefined fields. +Loads and predefined fields +Procedures +Added mass (concentrated and +distributed) +Abaqus/Aqua eigenfrequency extraction analysis +(“Natural frequency extraction,” Section 6.3.5) +Base motion +Procedures based on eigenmodes: +“Transient modal dynamic analysis,” Section 6.3.7 +“Mode-based steady-state dynamic analysis,” Section 6.3.8 +“Response spectrum analysis,” Section 6.3.10 +“Random response analysis,” Section 6.3.11 +All procedures except those based on eigenmodes +All relevant procedures except modal extraction, buckling, +those based on eigenmodes, and direct steady-state +dynamics +Boundary condition with a nonzero +prescribed boundary +Connector motion +Connector load +Cross-correlation property +“Random response analysis,” Section 6.3.11 +Current density (concentrated and +distributed) +“Coupled thermal-electrical analysis,” Section 6.7.3 +“Fully coupled thermal-electrical-structural analysis,” +Section 6.7.4 +Current density vector +“Eddy current analysis,” Section 6.7.5 +Electric charge (concentrated and +distributed) +“Piezoelectric analysis,” Section 6.7.2 +Equivalent pressure stress +“Mass diffusion analysis,” Section 6.9.1 +Film coefficient and associated sink +temperature +All procedures involving temperature degrees of freedom +Fluid flux +Analysis involving hydrostatic fluid elements +Fluid mass flow rate +Analysis involving convective heat transfer elements +Flux (concentrated and distributed) All procedures involving temperature degrees of freedom +“Mass diffusion analysis,” Section 6.9.1 +Force and moment (concentrated +and distributed) +All procedures with displacement degrees of freedom +except response spectrum +Loads and predefined fields +Procedures +Incident wave loading +Direct-integration dynamic analysis (“Implicit dynamic +analysis using direct integration,” Section 6.3.2) involving +solid and/or fluid elements undergoing shock loading +Predefined field variable +All procedures except those based on eigenmodes +Seepage coefficient and associated +sink pore pressure +Distributed seepage flow +“Coupled pore fluid diffusion and stress analysis,” +Section 6.8.1 +Substructure load +All procedures involving the use of substructures +Temperature as a predefined field +All procedures except adiabatic analysis, mode-based +procedures, and procedures involving temperature degrees +of freedom +With the exception of concentrated added mass and distributed added mass, no loads can be applied in +eigenfrequency extraction analysis. +33.1.2 +AMPLITUDE CURVES +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD Abaqus/CAE +References +• “Prescribed conditions: overview,” Section 33.1.1 +• *AMPLITUDE +• Chapter 57, “The Amplitude toolset,” of the Abaqus/CAE User’s Manual +Overview +An amplitude curve: +• allows arbitrary time (or frequency) variations of load, displacement, and other prescribed variables +to be given throughout a step (using step time) or throughout the analysis (using total time); +• can be defined as a mathematical function (such as a sinusoidal variation), as a series of +values at points in time (such as a digitized acceleration-time record from an earthquake), as a +user-customized definition via user subroutines, or, in Abaqus/Standard, as values calculated based +on a solution-dependent variable (such as the maximum creep strain rate in a superplastic forming +problem); and +• can be referred to by name by any number of boundary conditions, loads, and predefined fields. +Amplitude curves +By default, the values of loads, boundary conditions, and predefined fields either change linearly with +time throughout the step (ramp function) or they are applied immediately and remain constant throughout +the step (step function)—see “Defining an analysis,” Section 6.1.2. Many problems require a more +elaborate definition, however. For example, different amplitude curves can be used to specify time +variations for different loadings. One common example is the combination of thermal and mechanical +load transients: usually the temperatures and mechanical loads have different time variations during the +step. Different amplitude curves can be used to specify each of these time variations. +Other examples include dynamic analysis under earthquake loading, where an amplitude curve can +be used to specify the variation of acceleration with time, and underwater shock analysis, where an +amplitude curve is used to specify the incident pressure profile. +Amplitudes are defined as model data (i.e., they are not step dependent). Each amplitude curve must +be named; this name is then referred to from the load, boundary condition, or predefined field definition +. +*AMPLITUDE, NAME=name +Load or Interaction module: Create Amplitude: Name: name +Abaqus/CAE Usage: +Input File Usage: +Defining the time period +Each amplitude curve is a function of time or frequency. Amplitudes defined as functions of frequency +are used in “Direct-solution steady-state dynamic analysis,” Section 6.3.4, “Mode-based steady-state +dynamic analysis,” Section 6.3.8, and “Eddy current analysis,” Section 6.7.5. +Amplitudes defined as functions of time can be given in terms of step time (default) or in terms of +total time. These time measures are defined in “Conventions,” Section 1.2.2. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options: +*AMPLITUDE, NAME=name, TIME=STEP TIME (default) +*AMPLITUDE, NAME=name, TIME=TOTAL TIME +Load or Interaction module: Create Amplitude: any type: Time +span: Step time or Total time +Continuation of an amplitude reference in subsequent steps +If a boundary condition, load, or predefined field refers to an amplitude curve and the prescribed condition +is not redefined in subsequent steps, the following rules apply: +• If the associated amplitude was given in terms of total time, the prescribed condition continues to +follow the amplitude definition. +• If no associated amplitude was given or if the amplitude was given in terms of step time, the +prescribed condition remains constant at the magnitude associated with the end of the previous +step. +Specifying relative or absolute data +You can choose between specifying relative or absolute magnitudes for an amplitude curve. +Relative data +By default, you give the amplitude magnitude as a multiple (fraction) of the reference magnitude given +in the prescribed condition definition. This method is especially useful when the same variation applies +to different load types. +Input File Usage: +Abaqus/CAE Usage: +*AMPLITUDE, NAME=name, VALUE=RELATIVE +Amplitude magnitudes are always relative in Abaqus/CAE. +Absolute data +Alternatively, you can give absolute magnitudes directly. When this method is used, the values given in +the prescribed condition definitions will be ignored. +Absolute amplitude values should generally not be used to define temperatures or predefined field +variables for nodes attached to beam or shell elements as values at the reference surface together with +the gradient or gradients across the section (default cross-section definition; see “Using a beam section +integrated during the analysis to define the section behavior,” Section 29.3.6, and “Using a shell section +integrated during the analysis to define the section behavior,” Section 29.6.5). Because the values given +in temperature fields and predefined fields are ignored, the absolute amplitude value will be used to define +both the temperature and the gradient and field and gradient, respectively. +Input File Usage: +Abaqus/CAE Usage: +*AMPLITUDE, NAME=name, VALUE=ABSOLUTE +Absolute amplitude magnitudes are not supported in Abaqus/CAE. +Defining the amplitude data +The variation of an amplitude with time can be specified in several ways. The variation of an amplitude +with frequency can be given only in tabular or equally spaced form. +Defining tabular data +Choose the tabular definition method (default) to define the amplitude curve as a table of values at +convenient points on the time scale. Abaqus interpolates linearly between these values, as needed. By +default in Abaqus/Standard, if the time derivatives of the function must be computed, some smoothing is +applied at the time points where the time derivatives are discontinuous. In contrast, in Abaqus/Explicit +no default smoothing is applied (other than the inherent smoothing associated with a finite time +increment). You can modify the default smoothing values (smoothing is discussed in more detail below, +under the heading “Using an amplitude definition with boundary conditions”); alternatively, a smooth +step amplitude curve can be defined . +If the amplitude varies rapidly—as with the ground acceleration in an earthquake, for example—you +must ensure that the time increment used in the analysis is small enough to pick up the amplitude variation +accurately since Abaqus will sample the amplitude definition only at the times corresponding to the +increments being used. +If the analysis time in a step is less than the earliest time for which data exist in the table, Abaqus +applies the earliest value in the table for all step times less than the earliest tabulated time. Similarly, +if the analysis continues for step times past the last time for which data are defined in the table, the last +value in the table is applied for all subsequent time. +Several examples of tabular input are shown in Figure 33.1.2–1. +Input File Usage: +Abaqus/CAE Usage: +*AMPLITUDE, NAME=name, DEFINITION=TABULAR +Load or Interaction module: Create Amplitude: Tabular +Defining equally spaced data +Choose the equally spaced definition method to give a list of amplitude values at fixed time intervals +beginning at a specified value of time. Abaqus interpolates linearly between each time interval. You +must specify the fixed time (or frequency) interval at which the amplitude data will be given, +. You +can also specify the time (or lowest frequency) at which the first amplitude is given, +; the default is +=0.0. +If the analysis time in a step is less than the earliest time for which data exist in the table, Abaqus +applies the earliest value in the table for all step times less than the earliest tabulated time. Similarly, +a. Uniformly increasing load +1.0 +Relative +load +magnitude +0.0 +Time period +1.0 +b. Uniformly decreasing load +1.0 +Relative +load +magnitude +0.0 +Time period +1.0 +c. Variable load +1.0 +Relative +load +magnitude + Amplitude Table: +Time +Relative +load +0.0 +1.0 +0.0 +1.0 +0.0 +0.4 +0.6 +0.8 +1.0 +0.0 +1.0 +1.0 +0.0 +0.0 +1.2 +0.5 +0.5 +0.0 +0.0 +Time period +1.0 +Figure 33.1.2–1 Tabular amplitude definition examples. +if the analysis continues for step times past the last time for which data are defined in the table, the last +value in the table is applied for all subsequent time. +Input File Usage: +Abaqus/CAE Usage: +*AMPLITUDE, NAME=name, DEFINITION=EQUALLY SPACED, +FIXED INTERVAL= +, BEGIN= +Load or Interaction module: Create Amplitude: Equally +spaced: Fixed interval: +The time (or lowest frequency) at which the first amplitude is given, +indicated in the first table cell. +, is +Defining periodic data +Choose the periodic definition method to define the amplitude, a, as a Fourier series: +for +for +, N, +where +input is shown in Figure 33.1.2–2. +, and +, +, +, +, are user-defined constants. An example of this form of +Input File Usage: +Abaqus/CAE Usage: +*AMPLITUDE, NAME=name, DEFINITION=PERIODIC +Load or Interaction module: Create Amplitude: Periodic +0.60 +0.40 +0.20 +0.00 +− 0.20 +− 0.40 +0.00 +0.10 +0.20 +0.30 +0.40 +0.50 +Time +p = 0.2s +a = A0 + Σ [An cos nω(t−t0) + Bn sin nω(t−t0)] for t ≥ t0 +n=1 +a = A0 for t < t0 +with +N = 2, ω = 31.416 rad/s, t0 = −0.1614 s +A0= 0, A1 = 0.227, B1 = 0.0, A2 = 0.413, B2 = 0.0 +Figure 33.1.2–2 Periodic amplitude definition example. +Defining modulated data +Choose the modulated definition method to define the amplitude, a, as +for +for +, and +are user-defined constants. An example of this form of input is shown in +*AMPLITUDE, NAME=name, DEFINITION=MODULATED +Load or Interaction module: Create Amplitude: Modulated +where +, +Figure 33.1.2–3. +, A, +Input File Usage: +Abaqus/CAE Usage: +-1 +Time +10 +( x 10-1) +a = A0 + A sin ω +1 (t−t0) sin ω +2 (t−t0) for t > t0 +a = A0 +with +for t ≤ t0 +A0= 1.0, A = 2.0, ω +1 = 10π, ω +2 = 20π, t0 = .2 +Figure 33.1.2–3 Modulated amplitude definition example. +Defining exponential decay +Choose the exponential decay definition method to define the amplitude, a, as +for +for +where +Figure 33.1.2–4. +, A, +, and +are user-defined constants. An example of this form of input is shown in +Input File Usage: +Abaqus/CAE Usage: +*AMPLITUDE, NAME=name, DEFINITION=DECAY +Load or Interaction module: Create Amplitude: Decay +Time +( x 10-1) +10 +a = A0 + A exp [−(t−t0) / td] for t ≥ t0 +a = A0 for t < t0 +with +A0 = 0.0, A = 5.0, t0 = 0.2, td = 0.2 +Figure 33.1.2–4 Exponential decay amplitude definition example. +Defining smooth step data +Abaqus/Standard and Abaqus/Explicit can calculate amplitudes based on smooth step data. Choose the +smooth step definition method to define the amplitude, a, between two consecutive data points +and +as +for +where +first and second derivatives of a are zero at +smoothly from one amplitude value to another. +The amplitude, a, is defined such that +. The above function is such that +and +, and the +. This definition is intended to ramp up or down +at +at +, +for +for +where +and +are the first and last data points, respectively. +Examples of this form of input are shown in Figure 33.1.2–5 and Figure 33.1.2–6. This definition +cannot be used to interpolate smoothly between a set of data points; i.e., this definition cannot be used +to do curve fitting. +Input File Usage: +Abaqus/CAE Usage: +*AMPLITUDE, NAME=name, DEFINITION=SMOOTH STEP +Load or Interaction module: Create Amplitude: Smooth step +Defining a solution-dependent amplitude for superplastic forming analysis +Abaqus/Standard can calculate amplitude values based on a solution-dependent variable. Choose the +solution-dependent definition method to create a solution-dependent amplitude curve. The data consist +of an initial value, a minimum value, and a maximum value. The amplitude starts with the initial value +and is then modified based on the progress of the solution, subject to the minimum and maximum values. +The maximum value is typically the controlling mechanism used to end the analysis. This method is used +with creep strain rate control for superplastic forming analysis . +Input File Usage: +Abaqus/CAE Usage: +*AMPLITUDE, NAME=name, DEFINITION=SOLUTION DEPENDENT +Load or Interaction module: Create Amplitude: Solution dependent +Defining the bubble load amplitude for an underwater explosion +Two interfaces are available in Abaqus for applying incident wave loads . For either interface bubble dynamics +can be described using a model internal to Abaqus. A description of this built-in mechanical model and +the parameters that define the bubble behavior are discussed in “Defining bubble loading for spherical +incident wave loading” in “Acoustic and shock loads,” Section 33.4.6. The related theoretical details are +described in “Loading due to an incident dilatational wave field,” Section 6.3.1 of the Abaqus Theory +Manual. +1.0 +0.1 +Time +t0 = 0.0 A0 = 0.0 t1 = 0.1 A1 = 1.0 +a = A0 for t ≤ t0 += A0 + (A1 − A0) ξ3 (10 − 15 ξ + 6 ξ2) for t0 +< t < t1 += A1 for t ≥ t1 +where ξ = t − t0 + t1 − t0 +Figure 33.1.2���5 Smooth step amplitude definition example with two data points. +The preferred interface for incident wave loading due to an underwater explosion specifies bubble +dynamics using the UNDEX charge property definition . The alternative interface +for incident wave loading uses the bubble definition described in this section to define bubble load +amplitude curves. +An example of the bubble amplitude definition with the following input data is shown in +Figure 33.1.2–7. +(t3, A3) +(t4, A4) +(t2, A2) +(t0, A0) +(t1, A1) +Time +(t5, A5) +(t6, A6) +t0 = 0.0 A0 = 0.1 t1 = 0.1 A1 = 0.1 t2 = 0.2 A2 = 0.3 t3 = 0.3 A3 = 0.5 +t4 = 0.4 A4 = 0.5 t5 = 0.5 A5 = 0.2 t6 = 0.8 A6 = 0.2 +a = A0 for t ≤ t0 + = A6 for t ≥ t6 +Amplitude, a, between any two consecutive data points +(ti, Ai) and (ti+1, Ai+1) is +a = Ai + (Ai+1 − Ai) ξ3 (10 − 15ξ + 6 ξ2) +where ξ = t − ti + ti+1 − ti +Figure 33.1.2–6 Smooth step amplitude definition example with multiple data points. +Input File Usage: +Abaqus/CAE Usage: +*AMPLITUDE, NAME=name, DEFINITION=BUBBLE +Bubble amplitudes are not supported in Abaqus/CAE. However, bubble +loading for an underwater explosion is supported in the Interaction module +using the UNDEX charge property definition. +(a) +(b) +Figure 33.1.2–7 Bubble amplitude definition example: (a) radius of bubble and (b) +depth of bubble center under fluid surface. +Defining an amplitude via a user subroutine +Choose the user definition method to define the amplitude curve via coding in user subroutine UAMP +(Abaqus/Standard) or VUAMP (Abaqus/Explicit). You define the value of the amplitude function in time +and, optionally, the values of the derivatives and integrals for the function sought to be implemented as +outlined in “UAMP,” Section 1.1.19 of the Abaqus User Subroutines Reference Manual, and “VUAMP,” +Section 1.2.7 of the Abaqus User Subroutines Reference Manual. +You can use an arbitrary number of properties to calculate the amplitude, and you can use an arbitrary +number of state variables that can be updated independently for each amplitude definition. +In Abaqus/Standard user-defined amplitudes are not supported for complex eigenvalue extraction +and for linear dynamic procedures, except for steady-state dynamic analysis with the response computed +directly in terms of the physical degrees of freedom. +Moreover, solution-dependent sensors can be used to define the user-customized amplitude. The +sensors can be identified via their name, and two utilities allow for the extraction of the current sensor +value inside the user subroutine . Simple control/logical models can be implemented using this feature +as illustrated in “Crank mechanism,” Section 4.1.2 of the Abaqus Example Problems Manual. +Input File Usage: +*AMPLITUDE, NAME=name, DEFINITION=USER, +PROPERTIES=m, VARIABLES=n +Abaqus/CAE Usage: +Load or Interaction module: Create Amplitude: User: +Number of variables: n +User-defined amplitude properties are not supported in Abaqus/CAE. +Using an amplitude definition with boundary conditions +When an amplitude curve is used to prescribe a variable of the model as a boundary condition (by +referring to the amplitude from the boundary condition definition), the first and second time derivatives +of the variable may also be needed. For example, the time history of a displacement can be defined for +a direct integration dynamic analysis step by an amplitude variation; in this case Abaqus must compute +the corresponding velocity and acceleration. +When the displacement time history is defined by a piecewise linear amplitude variation (tabular +or equally spaced amplitude definition), the corresponding velocity is piecewise constant and the +acceleration may be infinite at the end of each time interval given in the amplitude definition table, +as shown in Figure 33.1.2–8(a). This behavior is unreasonable. (In Abaqus/Explicit time derivatives +of amplitude curves are typically based on finite differences, such as +, so there is some +inherent smoothing associated with the time discretization.) +You can modify the piecewise linear displacement variation into a combination of piecewise linear +and piecewise quadratic variations through smoothing. Smoothing ensures that the velocity varies +continuously during the time period of the amplitude definition and that the acceleration no longer has +singularity points, as illustrated in Figure 33.1.2–8(b). +the +When the velocity time history is defined by a piecewise linear amplitude variation, +corresponding acceleration is piecewise constant. Smoothing can be used to modify the piecewise linear +velocity variation into a combination of piecewise linear and piecewise quadratic variations. Smoothing +ensures that the acceleration varies continuously during the time period of the amplitude definition. +You specify t, the fraction of the time interval before and after each time point during which the +piecewise linear time variation is to be replaced by a smooth quadratic time variation. The default in +Abaqus/Standard is t=0.25; the default in Abaqus/Explicit is t=0.0. The allowable range is 0.0 +0.5. +A value of 0.05 is suggested for amplitude definitions that contain large time intervals to avoid severe +deviation from the specified definition. +In Abaqus/Explicit if a displacement jump is specified using an amplitude curve (i.e., the beginning +displacement defined using the amplitude function does not correspond to the displacement at that +time), this displacement jump will be ignored. Displacement boundary conditions are enforced in +Abaqus/Explicit in an incremental manner using the slope of the amplitude curve. To avoid the “noisy” +solution that may result in Abaqus/Explicit when smoothing is not used, it is better to specify the velocity +history of a node rather than the displacement history . +When an amplitude definition is used with prescribed conditions that do not require the evaluation +of time derivatives (for example, concentrated loads, distributed loads, temperature fields, etc., or a static +analysis), the use of smoothing is ignored. +When the displacement time history is defined using a smooth-step amplitude curve, the velocity +and acceleration will be zero at every data point specified, although the average velocity and acceleration +τ = Smooth Value x Minimum (t1 ,t2) +t1 +t2 +time +time +time +time +time +time +(a) without smoothing +(b) with smoothing +Figure 33.1.2–8 Piecewise linear displacement definitions. +may well be nonzero. Hence, this amplitude definition should be used only to define a (smooth) step +function. +Input File Usage: +Use either of the following options: +*AMPLITUDE, NAME=name, DEFINITION=TABULAR, SMOOTH=t +*AMPLITUDE, NAME=name, DEFINITION=EQUALLY +SPACED, SMOOTH=t +Abaqus/CAE Usage: +Load or Interaction module: Create Amplitude: choose Tabular +or Equally spaced: Smoothing: Specify: t +Using an amplitude definition with secondary base motion in modal dynamics +When an amplitude curve is used to prescribe a variable of the model as a secondary base motion in +a modal dynamics procedure (by referring to the amplitude from the base motion definition during a +modal dynamic procedure), the first or second time derivatives of the variable may also be needed. +For example, the time history of a displacement can be defined for secondary base motion in a modal +dynamics procedure. In this case Abaqus must compute the corresponding acceleration. +The modal dynamics procedure uses an exact solution for the response to a piecewise linear force. +Accordingly, secondary base motion definitions are applied as piecewise linear acceleration histories. +When displacement-type or velocity-type base motions are used to define displacement or velocity +time histories and an amplitude variation using the tabular, equally spaced, periodic, modulated, or +exponential decay definitions is used, an algorithmic acceleration is computed based on the tabular data +(the amplitude data evaluated at the time values used in the modal dynamics procedure). At the end of +any time increment where the amplitude curve is linear over that increment, linear over the previous +increment, and the slopes of the amplitude variations over the two increments are equal, this algorithmic +acceleration reproduces the exact displacement and velocity for displacement time histories or the exact +velocity for velocity time histories. +When the displacement time history is defined using a smooth-step amplitude curve, the velocity +and acceleration will be zero at every data point specified, although the average velocity and acceleration +may well be nonzero. Hence, this amplitude definition should be used only to define a (smooth) step +function. +Defining multiple amplitude curves +You can define any number of amplitude curves and refer to them from any load, boundary condition, or +predefined field definition. For example, one amplitude curve can be used to specify the velocity of a set +of nodes, while another amplitude curve can be used to specify the magnitude of a pressure load on the +body. If the velocity and the pressure both follow the same time history, however, they can both refer +to the same amplitude curve. There is one exception in Abaqus/Standard: only one solution-dependent +amplitude (used for superplastic forming) can be active during each step. +Scaling and shifting amplitude curves +You can scale and shift both time and magnitude when defining an amplitude. This can be helpful for +example when your amplitude data need to be converted to a different unit system or when you reuse +existing amplitude data to define similar amplitude curves. If both scaling and shifting are applied at the +same time, the amplitude values are first scaled and then shifted. The amplitude shifting and scaling can +be applied to all amplitude definition types except for solution dependent, bubble, and user. +Input File Usage: +*AMPLITUDE, NAME=name, SHIFTX=shiftx_value, SHIFTY=shifty_value, +SCALEX=scalex_value, SCALEY=scaley_value +Abaqus/CAE Usage: +The scaling and shifting of amplitude curves is not supported in Abaqus/CAE. +Reading the data from an alternate file +The data for an amplitude curve can be contained in a separate file. +Input File Usage: +*AMPLITUDE, NAME=name, INPUT=file_name +If the INPUT parameter is omitted, it is assumed that the data lines follow the +keyword line. +Abaqus/CAE Usage: +Load or Interaction module: Create Amplitude: any type: click mouse +button 3 while holding the cursor over the data table, and select Read from File +Baseline correction in Abaqus/Standard +When an amplitude definition is used to define an acceleration history in the time domain (a seismic +record of an earthquake, for example), the integration of the acceleration record through time may result +in a relatively large displacement at the end of the event. This behavior typically occurs because of +instrumentation errors or a sampling frequency that is not sufficient to capture the actual acceleration +history. In Abaqus/Standard it is possible to compensate for it by using “baseline correction.” +The baseline correction method allows an acceleration history to be modified to minimize the overall +drift of the displacement obtained from the time integration of the given acceleration. It is relevant only +with tabular or equally spaced amplitude definitions. +Baseline correction can be defined only when the amplitude is referenced as an acceleration +boundary condition during a direct-integration dynamic analysis or as an acceleration base motion in +modal dynamics. +Input File Usage: +Use both of the following options to include baseline correction: +*AMPLITUDE, DEFINITION=TABULAR or EQUALLY SPACED +*BASELINE CORRECTION +The *BASELINE CORRECTION option must appear immediately following +the data lines of the *AMPLITUDE option. +Load or Interaction module: Create Amplitude: choose Tabular +or Equally spaced: Baseline Correction +Abaqus/CAE Usage: +Effects of baseline correction +The acceleration is modified by adding a quadratic variation of acceleration in time to the acceleration +definition. The quadratic variation is chosen to minimize the mean squared velocity during each +correction interval. Separate quadratic variations can be added for different correction intervals within +the amplitude definition by defining the correction intervals. Alternatively, the entire amplitude history +can be used as a single correction interval. +The use of more correction intervals provides tighter control over any “drift” in the displacement at +the expense of more modification of the given acceleration trace. In either case, the modification begins +with the start of the amplitude variation and with the assumption that the initial velocity at that time is +zero. +The baseline correction technique is described in detail in “Baseline correction of accelerograms,” +Section 6.1.2 of the Abaqus Theory Manual. +33.2 +Initial conditions +• “Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1 +• “Initial conditions in Abaqus/CFD,” Section 33.2.2 +33.2.1 +INITIAL CONDITIONS IN Abaqus/Standard AND Abaqus/Explicit +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Prescribed conditions: overview,” Section 33.1.1 +• *INITIAL CONDITIONS +• “Using the predefined field editors,” Section 16.11 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +Initial conditions are specified for particular nodes or elements, as appropriate. The data can be provided +directly; in an external input file; or, in some cases, by a user subroutine or by the results or output +database file from a previous Abaqus analysis. +If initial conditions are not specified, all initial conditions are zero except relative density in the +porous metal plasticity model, which will have the value 1.0. +Specifying the type of initial condition being defined +Various types of initial conditions can be specified, depending on the analysis to be performed. Each +type of initial condition is explained below, in alphabetical order. +Defining initial acoustic static pressure +In Abaqus/Explicit you can define initial acoustic static pressure values at the acoustic nodes. These +values should correspond to static equilibrium and cannot be changed during the analysis. You can +specify the initial acoustic static pressure at two reference locations in the model, and Abaqus/Explicit +interpolates these data linearly to the acoustic nodes in the specified node set. The linear interpolation +is based upon the projected position of each node onto the line defined by the two reference nodes. If +the value at only one reference location is given, the initial acoustic static pressure is assumed to be +uniform. The initial acoustic static pressure is used only in the evaluation of the cavitation condition when the acoustic medium is capable of undergoing cavitation. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=ACOUSTIC STATIC PRESSURE +Initial acoustic static pressure is not supported in Abaqus/CAE. +Defining initial normalized concentration +In Abaqus/Standard you can define initial normalized concentration values for use with diffusion +elements in mass diffusion analysis . +*INITIAL CONDITIONS, TYPE=CONCENTRATION +Initial normalized concentration is not supported in Abaqus/CAE. +Abaqus/CAE Usage: +Input File Usage: +Defining initially bonded contact surfaces +In Abaqus/Standard you can define initially bonded or partially bonded contact surfaces. This type +of initial condition is intended for use with the crack propagation capability . The surfaces specified have to be different; this type of initial condition +cannot be used with self-contact. +If the crack propagation capability is not activated, the bonded portion of the surfaces will not +separate. In this case defining initially bonded contact surfaces would have the same effect as defining +tied contact, which generates a permanent bond between two surfaces during the entire analysis +(“Defining tied contact in Abaqus/Standard,” Section 35.3.7). +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=CONTACT +Initially bonded surfaces are not supported in Abaqus/CAE. +Define the initial location of an enriched feature +You can specify the initial location of an enriched feature, such as a crack, in an Abaqus/Standard +analysis . Two signed distance functions per node are generally required to describe the crack +location, including the location of crack tips, in a cracked geometry. The first signed distance function +describes the crack surface, while the second is used to construct an orthogonal surface such that the +intersection of the two surfaces defines the crack front. The first signed distance function is assigned only +to nodes of elements intersected by the crack, while the second is assigned only to nodes of elements +containing the crack tips. No explicit representation of the crack is needed because the crack is entirely +described by the nodal data. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=ENRICHMENT +Interaction module: crack editor: Crack location: Specify: select region +Defining initial values of predefined field variables +You can define initial values of predefined field variables. The values can be changed during an analysis +. +You must specify the field variable number being defined, n. Any number of field variables can be +used; each must be numbered consecutively (1, 2, 3, etc.). Repeat the initial conditions definition, with +a different field variable number, to define initial conditions for multiple field variables. The default is +n=1. +The definition of initial field variable values must be compatible with the section definition and with +adjacent elements, as explained in “Predefined fields,” Section 33.6.1. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=FIELD, VARIABLE=n +Initial predefined field variables are not supported in Abaqus/CAE. +Initializing predefined field variables with nodal temperature records from a user-specified results file +You can define initial values of predefined field variables using nodal temperature records from a +particular step and increment of a results file from a previous Abaqus analysis or from a results file +you create . The previous analysis is most commonly an +Abaqus/Standard heat transfer analysis. The use of the .fil file extension is optional. +The part (.prt) file from the previous analysis is required to read the initial values of predefined +field variables from the results file (“Defining an assembly,” Section 2.10.1). Both the previous model +and the current model must be consistently defined in terms of an assembly of part instances. +Input File Usage: +*INITIAL CONDITIONS, TYPE=FIELD, VARIABLE=n, +FILE=file, STEP=step, INC=inc +Abaqus/CAE Usage: +Initial predefined field variables are not supported in Abaqus/CAE. +Defining initial predefined field variables using scalar nodal output from a user-specified output +database file +You can define initial values of predefined field variables using scalar nodal output variables from a +particular step and increment in the output database file of a previous Abaqus/Standard analysis. For +a list of scalar nodal output variables that can be used to initialize a predefined field, see “Predefined +fields,” Section 33.6.1. +The part (.prt) file from the previous analysis is required to read initial values from the output +database file . Both the previous model and the current +model must be defined consistently in terms of an assembly of part instances; node numbering must be +the same, and part instance naming must be the same. +The file extension is optional; however, only the output database file can be used for this option. +Input File Usage: +*INITIAL CONDITIONS, TYPE=FIELD, VARIABLE=n, FILE=file, +OUTPUT VARIABLE=scalar nodal output variable, STEP=step, INC=inc +Abaqus/CAE Usage: +Initial predefined field variables are not supported in Abaqus/CAE. +Defining initial predefined field variables by interpolating scalar nodal output variables for dissimilar +meshes from a user-specified output database file +When the mesh for one analysis is different from the mesh for the subsequent analysis, Abaqus can +interpolate scalar nodal output variables (using the undeformed mesh of the original analysis) to +predefined field variables that you choose. For a list of supported scalar nodal output variables that can +be used to define predefined field variables, see “Predefined fields,” Section 33.6.1. This technique can +also be used in cases where the meshes match but the node number or part instance naming differs +between the analyses. Abaqus looks for the .odb extension automatically. The part (.prt) file +from the previous analysis is required if that analysis model is defined in terms of an assembly of part +instances . +Input File Usage: +*INITIAL CONDITIONS, TYPE=FIELD, VARIABLE=n, +OUTPUT VARIABLE=scalar nodal output variable, +INTERPOLATE, FILE=file, STEP=step, INC=inc +Abaqus/CAE Usage: +Initial predefined field variables are not supported in Abaqus/CAE. +Defining initial fluid pressure in fluid-filled structures +You can prescribe initial pressure for fluid-filled structures . +Do not use this type of initial condition to define initial conditions in porous media in +Abaqus/Standard; use initial pore fluid pressures instead . +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=FLUID PRESSURE +Load module: Create Predefined Field: Step: Initial, choose Other for the +Category and Fluid cavity pressure for the Types for Selected Step; +select a fluid cavity interaction; Fluid cavity pressure: pressure +Defining initial values of state variables for plastic hardening +You can prescribe initial equivalent plastic strain and, if relevant, the initial backstress tensor for +elements that use one of the metal plasticity (“Inelastic behavior,” Section 23.1.1) or Drucker-Prager +(“Extended Drucker-Prager models,” Section 23.3.1) material models. These initial quantities are +intended for materials in a work hardened state; they can be defined directly or by user subroutine +HARDINI. You can also prescribe initial values for the volumetric compacting plastic strain, +, +for elements that use the crushable foam material model with volumetric hardening (“Crushable foam +plasticity models,” Section 23.3.5). +You can also specify multiple backstresses for the nonlinear kinematic hardening model. Optionally, +you can specify the kinematic shift tensor (backstress) using the full tensor format, regardless of the +element type to which the initial conditions are applied. +Input File Usage: +*INITIAL CONDITIONS, TYPE=HARDENING, NUMBER +BACKSTRESSES=n, FULL TENSOR +Abaqus/CAE Usage: +Load module: Create Predefined Field: Step: Initial, choose Mechanical +for the Category and Hardening for the Types for Selected Step; +select region; Number of backstresses: n +Defining hardening parameters for rebars +The hardening parameters can also be defined for rebars within elements. Rebars are discussed in +“Defining rebar as an element property,” Section 2.2.4. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=HARDENING, REBAR +Load module: Create Predefined Field: Step: Initial, choose +Mechanical for the Category and Hardening for the Types for +Selected Step; select region; Definition: Rebar +Defining hardening parameters in user subroutine HARDINI +For complicated cases in Abaqus/Standard user subroutine HARDINI can be used to define the initial +work hardening. In this case Abaqus/Standard will call the subroutine at the start of the analysis for +each material point in the model. You can then define the initial conditions at each point as a function of +coordinates, element number, etc. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=HARDENING, USER +Load module: Create Predefined Field: Step: Initial, choose +Mechanical for the Category and Hardening for the Types for +Selected Step; select region; Definition: User-defined +Defining elements initially open for tangential fluid flow +You can specify the pore pressure cohesive elements that are initially open for tangential fluid flow . +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=INITIAL GAP +Initial gap is not supported in Abaqus/CAE. +Defining initial mass flow rates in forced convection heat transfer elements +In Abaqus/Standard you can define the initial mass flow rate through forced convection heat transfer +elements. You can specify a predefined mass flow rate field to vary the value of the mass flow rate within +the analysis step . +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=MASS FLOW RATE +Initial mass flow rate is not supported in Abaqus/CAE. +Defining initial values of plastic strain +You can define an initial plastic strain field on elements that use one of the metal plasticity (“Inelastic +behavior,” Section 23.1.1) or Drucker-Prager (“Extended Drucker-Prager models,” Section 23.3.1) +material models. The specified plastic strain values will be applied uniformly over the element unless +they are defined at each section point through the thickness in shell elements. +If a local coordinate system was defined , the plastic strain +components must be given in the local system. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=PLASTIC STRAIN +Initial plastic strain conditions are not supported in Abaqus/CAE. +Defining initial plastic strains for rebars +Initial values of stress can also be defined for rebars within elements ( see “Defining rebar as an element +property,” Section 2.2.4). +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=PLASTIC STRAIN, REBAR +Initial plastic strain conditions are not supported in Abaqus/CAE. +Defining initial pore fluid pressures in a porous medium +In Abaqus/Standard you can define the initial pore pressure, +, for nodes in a coupled pore fluid +diffusion/stress analysis . The +initial pore pressure can be defined either directly as an elevation-dependent function or by user +subroutine UPOREP. +Elevation-dependent initial pore pressures +When an elevation-dependent pore pressure is prescribed for a particular node set, the pore pressure +in the vertical direction (assumed to be the z-direction in three-dimensional and axisymmetric models +and the y-direction in two-dimensional models) is assumed to vary linearly with this vertical coordinate. +You must give two pairs of pore pressure and elevation values to define the pore pressure distribution +throughout the node set. Enter only the first pore pressure value (omit the second pore pressure value +and the elevation values) to define a constant pore pressure distribution. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=PORE PRESSURE +Load module: Create Predefined Field: Step: Initial: choose Other for the +Category and Pore pressure for the Types for Selected Step; select +region; Point 1 distribution: Uniform or select an analytical field +Defining initial pore pressures in user subroutine UPOREP +For complicated cases initial pore pressure values can be defined by user subroutine UPOREP. In this +case Abaqus/Standard will make a call to subroutine UPOREP at the start of the analysis for all nodes +in the model. You can define the initial pore pressure at each node as a function of coordinates, node +number, etc. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=PORE PRESSURE, USER +Load module: Create Predefined Field: Step: Initial: choose Other +for the Category and Pore pressure for the Types for Selected Step; +select region; Point 1 distribution: User-defined +Defining initial pore pressure values using nodal pore pressure output from a user-specified output +database file +You can define initial pore pressure values using nodal pore pressure output variables from a particular +step and increment in the output database (.odb) file of a previous Abaqus/Standard analysis. The file +extension is optional; however, only the output database file can be used. +For the same mesh pore pressure mapping, both the previous model and the current model must be +defined consistently, including node numbering, which must be the same in both models. If the models +are defined in terms of an assembly of part instances, the part instance naming must be the same. +Input File Usage: +*INITIAL CONDITIONS, TYPE=PORE PRESSURE, FILE=file, +STEP=step, INC=inc +Abaqus/CAE Usage: +Load module: Create Predefined Field: Step: Initial: choose Other +for the Category and Pore pressure for the Types for Selected Step; +select region; Point 1 distribution: From output database file +Interpolating initial pore pressure values for dissimilar pore pressure mapping values in a user-specified +output database file +For dissimilar mesh pore pressure mapping, interpolation is required. You can also limit the interpolation +region by specifying the source region in the form of an element set from which pore pressure is to be +interpolated and the target region in the form of a node set onto which the pore pressure is mapped. +Input File Usage: +*INITIAL CONDITIONS, TYPE=PORE PRESSURE, FILE=file, +INTERPOLATE, STEP=step, INC=inc +*INITIAL CONDITIONS, TYPE=PORE PRESSURE, FILE=file, +INTERPOLATE, STEP=step, INC=inc, DRIVING ELSETS +Abaqus/CAE Usage: +You cannot specify the regions where pore pressure values are +to be interpolated in Abaqus/CAE. +Defining initial pressure stress in a mass diffusion analysis +In Abaqus/Standard you can specify the initial pressure stress, +diffusion analysis . +, at the nodes in a mass +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=PRESSURE STRESS +Initial pressure stress is not supported in Abaqus/CAE. +Defining initial pressure stress from a user-specified results file +You can define initial values of pressure stress as those values existing at a particular step and increment +in the results file of a previous Abaqus/Standard stress/displacement analysis . The use of the .fil file extension is optional. The initial values of pressure stress +cannot be read from the results file when the previous model or the current model is defined in terms of +an assembly of part instances (“Defining an assembly,” Section 2.10.1). +Input File Usage: +*INITIAL CONDITIONS, TYPE=PRESSURE STRESS, +FILE=file, STEP=step, INC=inc +Abaqus/CAE Usage: +Initial pressure stress is not supported in Abaqus/CAE. +Defining initial void ratios in a porous medium +In Abaqus/Standard you can specify the initial values of the void ratio, e, at the nodes of a porous +medium . The initial void ratio can +be defined either directly as an elevation-dependent function, by interpolation from a previous output +database file, or by user subroutine VOIDRI. +Elevation-dependent initial void ratio +When an elevation-dependent void ratio is prescribed for a particular node set, the void ratio in the +vertical direction (assumed to be the z-direction in three-dimensional and axisymmetric models and the +y-direction in two-dimensional models) is assumed to vary linearly with this vertical coordinate. When +the void ratio is specified for a region meshed with fully integrated first-order elements, the nodal values +of void ratio are interpolated to the centroid of the element and are assumed to be constant through the +element. You must provide two pairs of void ratio and elevation values to define the void ratio throughout +the node set. Enter only the first void ratio value (omit the second void ratio value and the elevation +values) to define a constant void ratio distribution. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=RATIO +Load module: Create Predefined Field: Step: Initial: choose Other for +the Category and Void ratio for the Types for Selected Step; select +region; Point 1 distribution: Uniform or select an analytical field +Defining void ratio from a user-specified output database +You can define initial void ratios from the output database (.odb) file of a previous Abaqus/Standard +soil analysis in which the void ratio is requested as output. +Input File Usage: +*INITIAL CONDITIONS, TYPE=RATIO, FILE=file, STEP=step, INC=inc +Abaqus/CAE Usage: +Load module: Create Predefined Field: Step: Initial: choose Other for +the Category and Void ratio for the Types for Selected Step; select +region; Point 1 distribution: From output database file +Interpolating initial void ratios from values in a user-specified output database +When you define initial void ratios from the output database (.odb) file of a previous Abaqus/Standard +soil analysis, you can also limit the interpolation region by specifying the source region in the form of +an element set from which void ratios are to be interpolated and the target region in the form of a node +set onto which the void ratios are mapped. +Input File Usage: +*INITIAL CONDITIONS, TYPE=RATIO, +INTERPOLATE, FILE=file, STEP=step, INC=inc, DRIVING ELSETS +Abaqus/CAE Usage: +You cannot specify the regions where void ratios are to be +interpolated in Abaqus/CAE. +Defining void ratios in user subroutine VOIDRI +For complicated cases initial values of the void ratios can be defined by user subroutine VOIDRI. In this +case Abaqus/Standard will make a call to subroutine VOIDRI at the start of the analysis for each material +integration point in the model. You can then define the initial void ratio at each point as a function of +coordinates, element number, etc. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=RATIO, USER +Load module: Create Predefined Field: Step: Initial: choose Other +for the Category and Void ratio for the Types for Selected Step; +select region; Point 1 distribution: User-defined +Defining a reference mesh for membrane elements +In Abaqus/Explicit you can specify a reference mesh (initial metric) for membrane elements. This is +typically useful in finite element airbag simulations to model the wrinkles that arise from the airbag +folding process. A flat mesh may be suitable for the unstressed reference configuration, but the +initial state may require a corresponding folded mesh defining the folded state. Defining a reference +configuration that is different from the initial configuration may result in nonzero stresses and strains in +the initial configuration based on the material definition. If a reference mesh is specified for an element, +any initial stress or strain conditions specified for the same element are ignored. +If rebar layers are defined in membrane elements, the angular orientation defined in the reference +configuration is updated to obtain the same orientation in the initial configuration. +You can define the reference mesh using either the element numbers and the coordinates of the +nodes in each element or the node numbers and the coordinates of the nodes. The coordinates of all of +the nodes in the element have to be specified for both methods to have a valid initial condition for that +element. The two alternatives are mutually exclusive. +Input File Usage: +Specifying the reference mesh using element numbers and coordinates of all of +the element’s nodes: +*INITIAL CONDITIONS, TYPE=REF COORDINATE +Specifying the reference mesh using node numbers and the coordinates of the +nodes: +*INITIAL CONDITIONS, TYPE=NODE REF COORDINATE +The specification of a reference mesh for membrane elements is not supported +in Abaqus/CAE. +Abaqus/CAE Usage: +Defining initial relative density +You can specify the initial values of the relative density field for a porous metal plasticity material +model or equations of state . +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=RELATIVE DENSITY +Initial relative density is not supported in Abaqus/CAE. +Defining initial angular and translational velocity +You can prescribe initial velocities in terms of an angular velocity and a translational velocity. This type +of initial condition is typically used to define the initial velocity of a component of a rotating machine, +such as a jet engine. The initial velocities are specified by giving the angular velocity, +; the axis of +rotation, defined from a point a at +. The initial +; and a translational velocity, +velocity of node N at +is then +to a point b at +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=ROTATING VELOCITY +Load module: Create Predefined Field: Step: Initial: choose Mechanical +for the Category and Velocity for the Types for Selected Step +Defining initial saturation for a porous medium +In Abaqus/Standard you can define the initial saturation, s, for elements in a coupled pore fluid +diffusion/stress analysis . +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=SATURATION +Load module: Create Predefined Field: Step: Initial: choose Other for +the Category and Saturation for the Types for Selected Step +Defining the initial values of solution-dependent state variables +You can define initial values of solution-dependent state variables . The initial values can be defined directly or, in Abaqus/Standard, by user subroutine +SDVINI. Values given directly will be applied uniformly over the element. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=SOLUTION +Initial solution-dependent variables are not supported in Abaqus/CAE. +Defining the initial values of solution-dependent state variables for rebars +The initial values of solution-dependent variables can also be defined for rebars within elements. Rebars +are discussed in “Defining rebar as an element property,” Section 2.2.4. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=SOLUTION, REBAR +Initial solution-dependent state variables are not supported in Abaqus/CAE. +Defining the initial values of solution-dependent state variables in user subroutine SDVINI +For complicated cases in Abaqus/Standard user subroutine SDVINI can be used to define the initial +values of solution-dependent state variables. In this case Abaqus/Standard will make a call to subroutine +SDVINI at the start of the analysis for each material integration point in the model. You can then define +all solution-dependent state variables at each point as functions of coordinates, element number, etc. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=SOLUTION, USER +User subroutine SDVINI is not supported in Abaqus/CAE. +Defining initial specific energy for equations of state +In Abaqus/Explicit you can specify the initial values of the specific energy for equations of state . +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=SPECIFIC ENERGY +Initial specific energy is not supported in Abaqus/CAE. +Defining spud can embedment or spud can preload +In Abaqus/Standard you can define an initial embedment of a spud can. Alternatively, you can define an +initial vertical preload of a spud can . +Input File Usage: +Use one of the following options: +*INITIAL CONDITIONS, TYPE=SPUD EMBEDMENT +*INITIAL CONDITIONS, TYPE=SPUD PRELOAD +Initial spud can embedment and preload are not supported in Abaqus/CAE. +Abaqus/CAE Usage: +Defining initial stresses +You can define an initial stress field. Initial stresses can be defined directly or, in Abaqus/Standard, by +user subroutine SIGINI. Stress values given directly will be applied uniformly over the element unless +they are defined at each section point through the thickness in shell elements. +If a local coordinate system was defined , stresses must be given +in the local system. +In soils (porous medium) problems the initial effective stress should be given; see “Coupled pore +fluid diffusion and stress analysis,” Section 6.8.1, for a discussion of defining initial conditions in porous +media. +If the section properties of beam elements or shell elements are defined by a general section, +the initial stress values are applied as initial section forces and moments. In the case of beams initial +conditions can be specified only for the axial force, the bending moments, and the twisting moment. +In the case of shells initial conditions can be specified only for the membrane forces, the bending +moments, and the twisting moment. In both shells and beams initial conditions cannot be prescribed for +the transverse shear forces. +Initial stress fields cannot be defined for spring elements. See “Springs,” Section 32.1.1, for a +discussion of defining initial forces in spring elements. +Initial stress fields cannot be defined for elements using a fabric material. However, an initial stress +and strain state can be introduced in a fabric material made of membrane elements by defining a reference +mesh . +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=STRESS +Load module: Create Predefined Field: Step: Initial: choose Mechanical +for the Category and Stress for the Types for Selected Step +Defining initial stresses for rebars +Initial values of stress can also be defined for rebars within elements . +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=STRESS, REBAR +Initial stress for rebars is not supported in Abaqus/CAE. +Defining initial stresses that vary through the thickness of shell elements +Initial values of stress can be defined at each section point through the thickness of shell elements. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=STRESS, SECTION POINTS +Definition of initial stress that varies through the thickness of shell elements is +not supported in Abaqus/CAE. +Defining initial stresses in user subroutine SIGINI +For complicated cases (such as elbow elements) in Abaqus/Standard the initial stress field can be defined +by user subroutine SIGINI. In this case Abaqus/Standard will make a call to subroutine SIGINI at the +start of the analysis for each material calculation point in the model. You can then define all active stress +components at each point as functions of coordinates, element number, etc. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=STRESS, USER +User subroutine SIGINI is not supported in Abaqus/CAE. +Defining initial stresses using stress output from a user-specified output database file +You can define initial stresses using stress output variables from a particular step and increment in the +output database (.odb) file of a previous Abaqus/Standard analysis. +In this case both the previous model and the current model must be defined consistently. The element +numbering and element types must be the same in both models. If the models are defined in terms of an +assembly of part instances, part instance naming must be the same. +The file extension is optional; however, only the output database file can be used. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=STRESS, FILE=file, STEP=step, INC=inc +Load module: Create Predefined Field: Step: Initial: choose Mechanical +for the Category and Stress for the Types for Selected Step; select +region; Specification: From output database file +Establishing equilibrium in Abaqus/Standard +When initial stresses are given in Abaqus/Standard (including prestressing in reinforced concrete or +interpolation of an old solution onto a new mesh), the initial stress state may not be an exact equilibrium +state for the finite element model. Therefore, an initial step should be included to allow Abaqus/Standard +to check for equilibrium and iterate, if necessary, to achieve equilibrium. +In a soils analysis (that is, for models containing elements that include pore fluid pressure as a +variable) the geostatic stress field procedure (“Geostatic stress state,” Section 6.8.2) should be used for +the equilibrating step. Any initial loading (such as geostatic gravity loads) that contributes to the initial +equilibrium should be included in this step definition. The initial time increment and the total time +specified in this step should be the same. The initial stresses are applied in full at time zero; and if +equilibrium can be achieved, this step will converge in one increment. Therefore, there is no benefit to +incrementing. +To achieve equilibrium for all other analyses, a first step using the static procedure (“Static stress +analysis,” Section 6.2.2) should be used. It is recommended that you specify the initial time increment to +be equal to the total time specified in this step so that Abaqus/Standard will attempt to find equilibrium +in one increment. By default, Abaqus/Standard ramps down the unbalanced stress over the first step. +This allows Abaqus/Standard to use automatic incrementation if equilibrium cannot be found in one +increment. This ramping is achieved in the following manner: +1. An additional set of artificial stresses is defined at each material point. These stresses are equal in +magnitude to the initial stresses but are of opposite sign. The sum of the material point stresses and +these artificial stresses creates zero internal forces at the beginning of the step. +2. The internal artificial stresses are ramped off linearly in time during the first step. Thus, at the end +of the step the artificial stresses have been removed completely and the remaining stresses in the +material will be the stress state in equilibrium. +You can force Abaqus/Standard to achieve equilibrium in one increment by using a step variation on the +initial condition to resolve the unbalanced stress instead of ramping the stress down over the entire step. +If Abaqus/Standard cannot achieve equilibrium in one increment, the analysis will terminate. +If the equilibrating step does not converge, it indicates that the initial stress state is so far from +equilibrium with the applied loads that significantly large deformations would be generated. This is +generally not the intention of an initial stress state; therefore, it suggests that you should recheck the +specified initial stresses and loads. +Input File Usage: +Use one of the following options to specify how the unbalanced stress should +be resolved: +*INITIAL CONDITIONS, TYPE=STRESS, +UNBALANCED STRESS=RAMP (default) +*INITIAL CONDITIONS, TYPE=STRESS, +UNBALANCED STRESS=STEP +Abaqus/CAE Usage: +Initial equilibrium stress is not supported in Abaqus/CAE. +Establishing equilibrium in Abaqus/Explicit +Abaqus/Explicit computes the initial acceleration at nodes taking into account the initial stresses, +the loads, and the boundary conditions in the initial configuration. For an initially static problem, +the specified boundary conditions, the initial stresses, and the initial loading should be consistent +with a static equilibrium. Otherwise, the solution is likely to be noisy. The noise may be reduced +by introducing a dummy step with a temporary viscous loading to attempt to reestablish a static +equilibrium. Alternatively, you can introduce an initial short step in which all degrees of freedom are +fixed with boundary conditions (all initial loads should be included in this initial step); in a second step, +release all but the actual boundary conditions. +Defining elevation-dependent (geostatic) initial stresses +You can define elevation-dependent initial stresses. When a geostatic stress state is prescribed +for a particular element set, the stress in the vertical direction (assumed to be the z-direction in +three-dimensional and axisymmetric models and the y-direction in two-dimensional models) is assumed +to vary (piecewise) linearly with this vertical coordinate. +For the vertical stress component, you must give two pairs of stress and elevation values to define the +stress throughout the element set. For material points lying between the two elevations given, Abaqus +will use linear interpolation to determine the initial stress; for points lying outside the two elevations +given, Abaqus will use linear extrapolation. In addition, horizontal (lateral) stress components are given +by entering one or two “coefficients of lateral stress,” which define the lateral direct stress components +as the vertical stress at the point multiplied by the value of the coefficient. In axisymmetric cases only +one value of the coefficient of lateral stress is used and, therefore, only one value need be entered. +Geostatic initial stresses are for use with continuum elements only. +In Abaqus/Standard +elevation-dependent initial stresses should be specified for beams and shells in user subroutine SIGINI, +as explained earlier. +In Abaqus/Explicit elevation-dependent initial stresses cannot be specified for +beams and shells. +The geostatic stress state specified initially should be in equilibrium with the applied loads (such +as gravity) and boundary conditions. An initial step should be included to allow Abaqus to check for +equilibrium after this interpolation has been done; see the discussion above on establishing equilibrium +when an initial stress field is applied. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=STRESS, GEOSTATIC +Load module: Create Predefined Field: Step: Initial: choose Mechanical +for the Category and Geostatic stress for the Types for Selected Step +Defining initial temperatures +You can define initial temperatures at the nodes of either heat transfer or stress/displacement elements. +The temperatures of stress/displacement elements can be changed during an analysis . +The definition of initial temperature values must be compatible with the section definition of the +element and with adjacent elements, as explained in “Predefined fields,” Section 33.6.1. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=TEMPERATURE +Load module: Create Predefined Field: Step: Initial: choose Other for +the Category and Temperature for the Types for Selected Step +Defining initial temperatures from a user-specified results or output database file +You can define initial temperatures as those values existing as nodal temperatures at a particular step and +increment in the results or output database file of a previous Abaqus/Standard heat transfer analysis . +The part (.prt) file from the previous analysis is required to read initial temperatures from the +results or output database file . Both the previous model and +the current model must be consistently defined in terms of an assembly of part instances; node numbering +must be the same, and part instance naming must be the same. +The file extension is optional; however, if both results and output database files exist, the results file +will be used. +Input File Usage: +*INITIAL CONDITIONS, TYPE=TEMPERATURE, FILE=file, +STEP=step, INC=inc +Abaqus/CAE Usage: +Load module: Create Predefined Field: Step: Initial: choose Other +for the Category and Temperature for the Types for Selected Step: +select region: Distribution: From results or output database file, +File name: file, Step: step, and Increment: inc +Interpolating initial temperatures for dissimilar meshes from a user-specified results or output database +file +When the mesh for the heat +transfer analysis is different from the mesh for the subsequent +stress/displacement analysis, Abaqus can interpolate the temperature values from the nodes in the +undeformed heat transfer model to the current nodal temperatures. This technique can also be used +in cases where the meshes match but the node number or part instance naming differs between the +analyses. Only temperatures from an output database file can be used for the interpolation; Abaqus will +look for the .odb extension automatically. The part (.prt) file from the previous analysis is required +if that analysis model is defined in terms of an assembly of part instances . +Input File Usage: +*INITIAL CONDITIONS, TYPE=TEMPERATURE, INTERPOLATE, +FILE=file, STEP=step, INC=inc +Abaqus/CAE Usage: +Load module: Create Predefined Field: Step: analysis_step: choose +Other for the Category and Temperature for the Types for Selected +Step: select region: Distribution: From results or output database +file, File name: file, Mesh compatibility: Incompatible +Interpolating initial temperatures for dissimilar meshes with user-specified regions +When regions of elements in the heat transfer analysis are close or touching, the dissimilar mesh +interpolation capability can result in an ambiguous temperature association. For example, consider a +node in the current model that lies on or close to a boundary between two adjacent parts in the heat +transfer model, and consider a case where temperatures in these parts are different. When interpolating, +Abaqus will identify a corresponding parent element at the boundary for this node from the heat transfer +analysis. This parent element identification is done using a tolerance-based search method. Hence, in +this example the parent element might be found in either of the adjacent parts, resulting in an ambiguous +temperature definition at the node. You can eliminate this ambiguity by specifying the source regions +from which temperatures are to be interpolated. The source region refers to the heat transfer analysis +and is specified by an element set. The target region refers to the current analysis and is specified by a +node set. +Input File Usage: +*INITIAL CONDITIONS, TYPE=TEMPERATURE, INTERPOLATE, +FILE=file, STEP=step, INC=inc, DRIVING ELSETS +Abaqus/CAE Usage: +You cannot specify the regions where temperatures are to be interpolated in +Abaqus/CAE. +Interpolating initial temperatures for meshes that differ only in element order from a user-specified +results or output database file +If the only difference in the meshes is the element order (first-order elements in the heat transfer model +and second-order elements in the stress/displacement model), in Abaqus/Standard you can indicate +that midside node temperatures in second-order elements are to be interpolated from corner node +temperatures read from the results or output database file of the previous heat transfer analysis using +first-order elements. You must ensure that the corner node temperatures are not defined using a mixture +of direct data input and reading from the results or output database file, since midside node temperatures +that give unrealistic temperature fields may result. In practice, the capability for calculating midside +node temperatures is most useful when temperatures generated by a heat transfer analysis are read from +the results or output database file for the whole mesh during the stress analysis. Once the midside +node capability is activated, the capability will remain active for the rest of the analysis, including for +any predefined temperature fields defined to change temperatures during the analysis. The general +interpolation and midside node capabilities are mutually exclusive. +Input File Usage: +*INITIAL CONDITIONS, TYPE=TEMPERATURE, MIDSIDE, +FILE=file, STEP=step, INC=inc +Abaqus/CAE Usage: +Load module: Create Predefined Field: Step: Initial: choose Other +for the Category and Temperature for the Types for Selected Step: +select region: Distribution: From results or output database file, +File name: file, Step: step, Increment: inc, Mesh compatibility: +Compatible, and toggle on Interpolate midside nodes +Defining initial velocities for specified degrees of freedom +You can define initial velocities for specified degrees of freedom. When initial velocities are given for +dynamic analysis, they should be consistent with all of the constraints on the model, especially time- +dependent boundary conditions. Abaqus will ensure that they are consistent with boundary conditions +and with multi-point and equation constraints but will not check for consistency with internal constraints +such as incompressibility of the material. In case of conflict, boundary conditions take precedence over +initial conditions. +Initial velocities must be defined in global directions, regardless of the use of local transformations +(“Transformed coordinate systems,” Section 2.1.5). +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=VELOCITY +Load module: Create Predefined Field: Step: Initial: choose Mechanical +for the Category and Velocity for the Types for Selected Step +Defining initial volume fractions for Eulerian elements +You can define initial volume fractions to create material within Eulerian elements in Abaqus/Explicit. +By default, +these elements are filled with void. See “Initial conditions” in “Eulerian analysis,” +Section 14.1.1, for a description of strategies for initializing Eulerian materials. +Input File Usage: +*INITIAL CONDITIONS, TYPE=VOLUME FRACTION +Abaqus/CAE Usage: +Load module: Create Predefined Field: Step: Initial: choose Other for the +Category and Material Assignment for the Types for Selected Step +Reading the input data from an external file +The input data for an initial conditions definition can be contained in a separate file. See “Input syntax +rules,” Section 1.2.1, for the syntax of such file names. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, INPUT=file_name +Initial conditions cannot be read from a separate file in Abaqus/CAE. +Consistency with kinematic constraints +Abaqus does not ensure that initial conditions are consistent with multi-point or equation constraints for +nodal quantities other than velocity . +Initial conditions on nodal quantities such as temperature in +heat transfer analysis, pore pressure in soils analysis, or acoustic pressure in acoustic analysis must +be prescribed to be consistent with any multi-point constraint or equation constraint governing these +quantities. +Spatial interpolation method +When you define initial conditions using a method that interpolates between dissimilar meshes, Abaqus +operates by interpolating results from nodes in the old mesh to nodes in the new mesh. For each node: +1. The element (in the old mesh) in which the node lies is found, and the node’s location in that element +is obtained. (This procedure assumes that all nodes in the new mesh lie within the bounds of the +old mesh: warning messages are issued if this is not so.) +2. The initial condition values are then interpolated from the nodes of the element (in the old mesh) +to the new node. +33.2.2 +INITIAL CONDITIONS IN Abaqus/CFD +Products: Abaqus/CFD Abaqus/CAE +References +• “Prescribed conditions: overview,” Section 33.1.1 +• “Using the predefined field editors,” Section 16.11 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +In Abaqus/CFD initial conditions for fluid flow simulation are specified using element sets. +Defining initial velocities +You can define the initial fluid flow velocity in elements; however, if such conditions are omitted, a +default value of zero is assumed. Initial velocities must be defined in global directions, regardless of the +use of local transformations . +For incompressible flow Abaqus/CFD automatically uses the user-defined boundary conditions and +tests the specified initial velocity to be sure that the initial velocity field is divergence-free and that the +velocity boundary conditions are compatible with the initial velocity field. If they are not, the initial +velocity is projected onto a divergence-free subspace, yielding initial conditions that define a well-posed +incompressible Navier-Stokes problem. Therefore, in some circumstances, the user-specified initial +velocity may be overridden with a velocity that is divergence-free and matches the velocity boundary +conditions. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=VELOCITY, ELEMENT AVERAGE +Load module: Create Predefined Field: Step: Initial: +Category: Fluid: Fluid velocity +Defining initial density +You can define the initial fluid density in elements. However, if the initial condition is omitted, the +material density definition is assumed as default . Similarly, if the initial +density is specified on an element set that does not include all fluid elements, the material density is +assumed as the default for those elements not contained in the element set. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=DENSITY, ELEMENT AVERAGE +Load module: Create Predefined Field: Step: Initial: +Category: Fluid: Fluid density +Initial pressure for incompressible fluid flow +For incompressible flows it is not necessary to prescribe the initial pressure condition since the initial +pressure field is computed automatically from the initial velocity field and boundary conditions. This is +done to ensure proper starting conditions for incompressible flows. +Defining initial temperature +If the energy equation is solved, the initial fluid temperature in elements must be defined. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=TEMPERATURE, ELEMENT AVERAGE +Load module: Create Predefined Field: Step: Initial: Category: +Fluid: Fluid thermal energy +Defining initial Spalart-Allmaras turbulent eddy viscosity for fluid flow +If the Spalart-Allmaras turbulence model is active, you must prescribe an initial value for the Spalart- +Allmaras turbulent eddy viscosity that is greater than zero and roughly three to five times the kinematic +viscosity. The kinematic viscosity is the ratio of the fluid viscosity and density ( +). For more +information, see “Viscosity,” Section 26.1.4. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=TURBNU, ELEMENT AVERAGE +Load module: Create Predefined Field: Step: Initial: Category: +Fluid: Fluid turbulence; Eddy viscosity: +Defining initial k and for fluid flow +If the RNG k– turbulence model is active, initial conditions need to be specified for both k and . The +k and +values must be greater than zero. A simple procedure to approximate the initial conditions can +be obtained from values of the turbulence intensity and an approximate initial turbulent eddy viscosity +as described below. +The turbulent kinetic energy is defined as +where +characteristic velocity scale of the flow ( +is the characteristic velocity scale or root mean square velocity that is usually related to the +) through the turbulence intensity, +Therefore, an estimation for the initial conditions for the turbulent kinetic energy, k, can be expressed +in terms of the characteristic velocity and turbulence intensity as +The initial value for the turbulent kinetic energy dissipation, +, can be obtained from a +known/proposed level of the turbulent eddy viscosity, +, as +where +is the k– turbulent viscosity model coefficient and +is the fluid kinematic viscosity. +Input File Usage: +Use the following option to specify the initial turbulent kinetic energy: +*INITIAL CONDITIONS, TYPE=TURBKE, ELEMENT AVERAGE +Use the following option to specify the initial +dissipation rate: +turbulent kinetic energy +*INITIAL CONDITIONS, TYPE=TURBEPS, ELEMENT AVERAGE +Load module: Create Predefined Field: Step: Initial: Category: Fluid: +Fluid turbulence; Turbulent kinetic energy: k, Dissipation rate: +Abaqus/CAE Usage: +33.3 +Boundary conditions +• “Boundary conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1 +• “Boundary conditions in Abaqus/CFD,” Section 33.3.2 +33.3.1 +BOUNDARY CONDITIONS IN Abaqus/Standard AND Abaqus/Explicit +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Defining a model in Abaqus,” Section 1.3.1 +• “Prescribed conditions: overview,” Section 33.1.1 +• “VDISP,” Section 1.2.1 of the Abaqus User Subroutines Reference Manual +• “DISP,” Section 1.1.4 of the Abaqus User Subroutines Reference Manual +• *BOUNDARY +• “Using the boundary condition editors,” Section 16.10 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +Boundary conditions: +• can be used to specify the values of all basic solution variables (displacements, rotations, +warping amplitude, fluid pressures, pore pressures, temperatures, electrical potentials, normalized +concentrations, acoustic pressures, or connector material flow) at nodes; +• can be given as “model” input data (within the initial step in Abaqus/CAE) to define zero-valued +boundary conditions; +• can be given as “history” input data (within an analysis step) to add, modify, or remove zero-valued +or nonzero boundary conditions; and +• can be defined by the user through subroutines DISP for Abaqus/Standard and VDISP for +Abaqus/Explicit. +Relative motions in connector elements can be prescribed similar to boundary conditions. +“Connector actuation,” Section 31.1.3, for more detailed information. +See +Prescribing boundary conditions as model data +Only zero-valued boundary conditions can be prescribed as model data (i.e., in the initial step in +Abaqus/CAE). You can specify the data using either “direct” or “type” format. As described below, +the “type” format is a way of conveniently specifying common types of boundary conditions in +stress/displacement analyses. “Direct” format must be used in all other analysis types. +For both “direct” and “type” format you specify the region of the model to which the boundary +conditions apply and the degrees of freedom to be restrained. +Boundary conditions prescribed as model data can be modified or removed during analysis steps. +Input File Usage: +Abaqus/CAE Usage: +Using the direct format +*BOUNDARY +Any number of data lines can be used to specify boundary conditions, and in +stress/displacement analyses both “direct” and “type” format can be specified +with a single use of the *BOUNDARY option. +Load module: Create Boundary Condition: Step: Initial +You can choose to enter the degrees of freedom to be constrained directly. +Input File Usage: +Either a single degree of freedom or the first and last of a range of degrees of +freedom can be specified. +*BOUNDARY +node or node set, degree of freedom +*BOUNDARY +node or node set, first degree of freedom, last degree of freedom +For example, +*BOUNDARY +EDGE, 1 +indicates that all nodes in node set EDGE are constrained in degree of freedom +1 ( +), while the data line +EDGE, 1, 4 +indicates that all nodes in node set EDGE are constrained in degrees of freedom +1–4 ( +). +, +, +, +Abaqus/CAE Usage: +Load module: Create Boundary Condition: Step: Initial +Use one of the following options: +Category: Mechanical; Displacement/Rotation, Velocity/Angular +velocity, or Acceleration/Angular acceleration; select regions +and toggle on the degree or degrees of freedom +Category: Electrical/Magnetic; Electric potential; select regions +Category: Other; Temperature, Pore pressure, Mass concentration, +Acoustic pressure, or Connector material flow; select regions +If you are specifying a temperature boundary condition for a shell region, you +can enter multiple degrees of freedom, from 11 to 31, inclusive. +Using the “type” format in stress/displacement analyses +The type of boundary condition can be specified instead of degrees of freedom. The following boundary +condition “types” are available in both Abaqus/Standard and Abaqus/Explicit: +XSYMM +Symmetry about a plane +(degrees of freedom +). +YSYMM +ZSYMM +ENCASTRE +PINNED +Symmetry about a plane +Symmetry about a plane +Fully built-in (degrees of freedom +Pinned (degrees of freedom +(degrees of freedom +(degrees of freedom +). +). +). +). +The following boundary condition types are available only in Abaqus/Standard: +XASYMM +YASYMM +ZASYMM +Antisymmetry about a plane with +Antisymmetry about a plane with +Antisymmetry about a plane with +(degrees of freedom 2, 3, 4 +(degrees of freedom 1, 3, 5 +(degrees of freedom 1, 2, 6 +). +). +). +Caution: When boundary conditions are prescribed at a node in an analysis involving +finite rotations, at least two rotation degrees of freedom should be constrained. Otherwise, +the prescribed rotation at the node may not be what you expect. Therefore, antisymmetry +boundary conditions should generally not be used in problems involving finite rotations. +NOWARP +NOOVAL +NODEFORM +Prevent warping of an elbow section at a node. +Prevent ovalization of an elbow section at a node. +Prevent all cross-sectional deformation (warping, ovalization, and uniform radial +expansion) at a node. +The NOWARP, NOOVAL, and NODEFORM types apply only to elbow elements (“Pipes and pipebends +with deforming cross-sections: elbow elements,” Section 29.5.1). +For example, applying a boundary condition of type XSYMM to node set EDGE indicates that the +node set lies on a plane of symmetry that is normal to the X-axis (which will be the global X-axis or +the local X-axis if a nodal transformation has been applied at these nodes). This boundary condition is +identical to applying a boundary condition using the direct format to degrees of freedom 1, 5, and 6 in +node set EDGE since symmetry about a plane X=constant implies +, and +. +, +Once a degree of freedom has been constrained using a “type” boundary condition as model data, the +constraint cannot be modified by using a boundary condition in “direct” format as model data; modifying +a constraint in such a way will only produce an error message in the data (.dat) file indicating that +conflicting boundary conditions exist in the model data. +Input File Usage: +*BOUNDARY +node or node set, boundary condition type +Abaqus/CAE Usage: +Load module: Create Boundary Condition: Step: Initial: +Symmetry/Antisymmetry/Encastre: select regions and toggle +on the boundary condition type +Prescribing boundary conditions at phantom nodes for enriched elements +For an enriched element , you can specify the boundary conditions at a phantom node that is +originally located coincident with the specified real node. +Input File Usage: +Use the following option to specify boundary conditions at a phantom node +originally located coincident with the specified real node: +*BOUNDARY, PHANTOM=NODE +node number, first degree of freedom, last degree of freedom +Abaqus/CAE Usage: +Prescribing boundary conditions at phantom nodes for enriched elements is not +supported in Abaqus/CAE. +Prescribing boundary conditions as history data +Boundary conditions can be prescribed within an analysis step using either “direct” or “type” format. As +with model data boundary conditions, the “type” format can be used only in stress/displacement analyses; +whereas, the “direct” format can be used in analysis types. +When using the “direct” format, boundary conditions can be defined as the total value of a variable +or, in a stress/displacement analysis, as the value of a variable’s velocity or acceleration. +As many boundary conditions as necessary can be defined in a step. +Input File Usage: +Abaqus/CAE Usage: +*BOUNDARY +Load module: Create Boundary Condition: Step: analysis_step +Using the direct format +Specify the region of the model to which the boundary conditions apply, the degree or degrees of freedom +to be specified , +and the magnitude of the boundary condition. If the magnitude is omitted, it is the same as specifying a +zero magnitude. +In stress/displacement analysis you can specify a velocity history or an acceleration history. The +default is a displacement history. +Input File Usage: +Use either of the following options to prescribe a displacement history: +*BOUNDARY or *BOUNDARY, TYPE=DISPLACEMENT +node or node set, degree of freedom, magnitude +node or node set, first degree of freedom, last degree of freedom, magnitude +Use the following option to prescribe a velocity history (the data lines are the +same as above): +*BOUNDARY, TYPE=VELOCITY +Use the following option to prescribe an acceleration history (the data lines are +the same as above): +*BOUNDARY, TYPE=ACCELERATION +For example, +*BOUNDARY, TYPE=VELOCITY +EDGE, 1, 1, 0.5 +indicates that all nodes in node set EDGE have a prescribed velocity magnitude +of 0.5 in degree of freedom 1 ( +). +Abaqus/CAE Usage: +Load module: Create Boundary Condition: Step: analysis_step: +Select one of the following categories and types: +Category: Mechanical; Displacement/Rotation; select regions; +Distribution: Uniform or select an analytical field or a discrete field; +toggle on the degree or degrees of freedom; magnitude +Category: Mechanical; Velocity/Angular velocity or +Acceleration/Angular acceleration; select regions; Distribution: +Uniform or select an analytical field; toggle on the degree or +degrees of freedom; magnitude +Category: Electrical/Magnetic; Electric potential; select regions; +Distribution: Uniform or select an analytical field; Method: +Specify magnitude; magnitude +Category: Other; Temperature, Pore pressure, Mass concentration, +Acoustic pressure, or Connector material flow; select regions; +Distribution: Uniform or select an analytical field; Method: +Specify magnitude; magnitude +If you are specifying a temperature boundary condition for a shell region, you +can enter multiple degrees of freedom, from 11 to 31, inclusive. +Prescribed displacement +In Abaqus/Standard you can prescribe jumps in displacements. For example, a displacement-type +boundary condition is used to apply a prescribed displacement magnitude of 0.5 in degree of freedom 1 +) to the nodes in node set EDGE. In a second step these nodes can be moved by another 0.5 length +( +units (to a total displacement of 1.0) by applying a prescribed displacement magnitude of 1.0 in degree +of freedom 1 to node set EDGE. Specifying a prescribed displacement magnitude of 0 (or omitting the +magnitude) in degree of freedom 1 in the next step would return the nodes in node set EDGE to their +original locations. +In contrast, Abaqus/Explicit does not admit jumps in displacements and rotations. Displacement +boundary conditions in displacement and rotation degrees of freedom are enforced in an incremental +manner using the slope of the amplitude curve . If no amplitude is specified, Abaqus/Explicit +will ignore the user-supplied displacement value and enforce a zero velocity boundary condition. +The displacement must remain continuous across steps. +If amplitude curves are specified, it is +possible, but not valid, to specify a jump in the displacement across a step boundary when using step +time for the amplitude definition. Abaqus/Explicit will ignore such jumps in displacement if they are +specified. +Using the “type” format in stress/displacement analyses +The type of boundary condition can be specified (as history data) instead of degrees of freedom in the +same manner as discussed above for model data. The boundary condition “types” that are available as +history data are the same as those available as model data. +Once a degree of freedom has been constrained using a “type” boundary condition as history data, +the constraint cannot be modified by using a boundary condition in “direct” format. The constraint can +be redefined only by using a boundary condition in “direct” format after all previously applied boundary +conditions specified using “type” format are removed. +Input File Usage: +*BOUNDARY +node or node set, boundary condition type +Abaqus/CAE Usage: +Load module: Create Boundary Condition: Step: analysis_step: +Symmetry/Antisymmetry/Encastre: select regions and toggle +on the boundary condition type +Prescribing boundary conditions at phantom nodes for enriched elements +You can specify boundary conditions at phantom nodes as history data in the same manner as discussed +above for model data . To specify nonzero +boundary conditions, enter the actual magnitude. +Input File Usage: +Use the following option to specify boundary conditions at a phantom node +originally located coincident with the specified real node: +*BOUNDARY, PHANTOM=NODE +node number, first degree of freedom, last degree of freedom, magnitude +Abaqus/CAE Usage: +Prescribing boundary conditions at phantom nodes for enriched elements is not +supported in Abaqus/CAE. +Defining boundary conditions that vary with time +The prescribed magnitude of a basic solution variable, a velocity, or an acceleration can vary with time +during a step according to an amplitude definition (“Amplitude curves,” Section 33.1.2). +When an amplitude definition is used with a boundary condition in a dynamic or modal dynamic +analysis, the first and second time derivatives of the constrained variable may be discontinuous. For +example, Abaqus will compute the corresponding velocity and acceleration from a given displacement +boundary condition. +By default, Abaqus/Standard will smooth the amplitude curve so that the derivatives of the specified +boundary condition will be finite. You must ensure that the applied values are correct after smoothing. +Abaqus/Explicit does not apply default smoothing to discontinuous amplitude curves. To avoid +the “noisy” solution that may result from discontinuities in Abaqus/Explicit, it is better to specify the +velocity history of a node. See “Amplitude curves,” Section 33.1.2. +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*AMPLITUDE, NAME=name +*BOUNDARY, AMPLITUDE=name +Load or Interaction module: Create Amplitude: Name: amplitude_name +Load module: Create Boundary Condition: Step: analysis_step: +boundary condition; Amplitude: amplitude_name +Defining boundary condition through user subroutines +If an amplitude based evolution of a boundary condition is not sufficient, you can define it yourself +For this purpose, Abaqus/Standard provides the routine DISP; whereas, +in a user subroutine. +Abaqus/Explicit provides the routine VDISP. The region to which the boundary conditions apply and +the constrained degrees of freedom are specified as part of the boundary condition definition. The actual +boundary condition is set within the user routine based on a number of variables made available in those +routines ( see “DISP,” Section 1.1.4 of the Abaqus User Subroutines Reference Manual for DISP and +“VDISP,” Section 1.2.1 of the Abaqus User Subroutines Reference Manual for VDISP ). +Abaqus/Standard allows for an amplitude and a reference magnitude definition for a user defined +boundary condition and you may overwrite the amplitude based boundary value within the DISP routine. +Whereas, Abaqus/Explicit ignores the reference magnitude, but passes in the amplitude value as an +argument to the user routine VDISP and you may define the boundary condition to a non-zero value. +Input File Usage: +Abaqus/CAE Usage: +*BOUNDARY, USER +Load module: Create Boundary Condition: Step: analysis_step; +boundary condition; Distribution: User-defined +Boundary condition propagation +By default, all boundary conditions defined in the previous general analysis step remain unchanged in the +subsequent general step or in subsequent consecutive linear perturbation steps. Boundary conditions do +not propagate between linear perturbation steps. You define the boundary conditions in effect for a given +step relative to the preexisting boundary conditions. At each new step the existing boundary conditions +can be modified and additional boundary conditions can be specified. Alternatively, you can release +all previously applied boundary conditions in a step and specify new ones. In this case any boundary +conditions that are to be retained must be respecified. +Modifying boundary conditions +When you modify an existing boundary condition, the node or node set must be specified in exactly the +same way as previously. For example, if a boundary condition is specified for a node set in one step and +for an individual node contained in the set in another step, Abaqus issues an error. You must remove the +boundary condition and respecify it to change the way the node or node set is specified. +Input File Usage: +Use either of the following options to modify an existing boundary condition +or to specify an additional boundary condition: +Abaqus/CAE Usage: +*BOUNDARY +*BOUNDARY, OP=MOD +Load module: Create Boundary Condition or Boundary +Condition Manager: Edit +Removing boundary conditions +If you choose to remove any boundary condition in a step, no boundary conditions will be propagated +from the previous general step. Therefore, all boundary conditions that are in effect during this step must +be respecified. The only exception to this rule is during an eigenvalue buckling prediction procedure, as +described in “Eigenvalue buckling prediction,” Section 6.2.3. +Setting a boundary condition to zero is not the same as removing it. +Input File Usage: +Use the following option to release all previously applied boundary conditions +and to specify new boundary conditions: +Abaqus/CAE Usage: +*BOUNDARY, OP=NEW +If the OP=NEW parameter is used on any *BOUNDARY option within a step, +it must be used on all *BOUNDARY options in the step. +Use the following option to remove a boundary condition within a step: +Load module: Boundary Condition Manager: Deactivate +Abaqus/CAE automatically respecifies any boundary conditions that should +remain in effect during this step. +Fixing degrees of freedom at a point in an Abaqus/Standard analysis +In Abaqus/Standard you can “freeze” specified degrees of freedom at their final values from the last +general analysis step. Specifying a zero velocity or zero acceleration boundary condition will have the +same effect as fixing the degrees of freedom for displacement or velocity, respectively. +Input File Usage: +Abaqus/CAE Usage: +*BOUNDARY, FIXED +The OP=NEW parameter must be used with the FIXED parameter if there are +any other *BOUNDARY options in the same step that have the OP=NEW +parameter. Any magnitudes given for the boundary condition are ignored. +Load module; Create Boundary Condition; Step: analysis_step; +boundary condition; Method: Fixed at Current Position (available +only if a previous general analysis step exists) +Prescribing boundary conditions in linear perturbation steps +In a linear perturbation step (“General and linear perturbation procedures,” Section 6.1.3) the magnitudes +of prescribed boundary conditions should be given as the magnitudes of the perturbations about the base +state. Boundary conditions given within the model definition are always regarded as part of the base +state, even if the first analysis step is a linear perturbation step. The boundary conditions given in a +linear perturbation step will not affect subsequent steps. +If a perturbation step does not contain a boundary condition definition, degrees of freedom that are +restrained/prescribed in the base state will be restrained in the perturbation step and will have perturbation +magnitudes of zero. To prescribe nonzero perturbation magnitudes, you have to modify the existing +boundary conditions. You can also fix and prescribe perturbation magnitudes of degrees of freedom that +are unrestrained in the base state. +If degrees of freedom that are restrained/prescribed in the base state are released, all restraints that +are to remain must be respecified, remembering that all magnitudes will be interpreted as perturbations. +Fixing the degrees of freedom at their final values from the last general analysis step has the same effect as modifying the existing boundary conditions to have zero perturbation +magnitudes for all specified degrees of freedom. +The antisymmetric buckling modes of a symmetric structure can be found in an eigenvalue buckling +prediction analysis by specifying the proper boundary conditions . +Prescribing real and imaginary values in boundary conditions +In steady-state dynamic and matrix generation procedures, a boundary condition can be prescribed using +either a real or an imaginary value . If the real value is prescribed for a degree of freedom (and +the imaginary value is not explicitly prescribed), the imaginary value is considered to be zero. Similarly, +if the imaginary value is prescribed (and the real value is not explicitly prescribed), the real value is +considered to be zero. +Prescribed motion in modal superposition procedures +In modal superposition procedures (“Dynamic analysis procedures: overview,” Section 6.3.1) prescribed +displacements cannot be defined directly using a boundary condition. Instead, the boundary conditions +are grouped into bases in a frequency extraction step. Then, the motion of each base is prescribed in +the modal superposition step. See “Natural frequency extraction,” Section 6.3.5, and “Transient modal +dynamic analysis,” Section 6.3.7, for details on this method. +Input File Usage: +Abaqus/CAE Usage: +*BOUNDARY, BASE NAME +*BASE MOTION +Load module; Create Boundary Condition; Step: modal_dynamic_step, +steady-state_dynamic_step, or random_response_step; Category: +Mechanical; Types for Selected Step: Displacement base motion +or Velocity base motion or Acceleration base motion +Submodeling +When using the submodeling technique, the magnitudes of the boundary conditions in the submodel can +be defined by interpolating the values of the prescribed degrees of freedom from the file output results +of the global model. See “Node-based submodeling,” Section 10.2.2, for details. +Prescribing large rotations +Sequential finite rotations about different axes of rotation are not additive, which can make direct +It is much simpler to apply finite-rotation boundary +specification of such rotations challenging. +conditions by specifying the rotational velocity versus time. For a discussion of the rotation degrees +of freedom and a multiple step finite rotation example that demonstrates why velocity-type boundary +conditions are preferred for specifying finite-rotation boundary conditions, see “Conventions,” +Section 1.2.2. +When velocity-type boundary conditions are used to prescribe rotations, the definition is given in +If the angular velocity is associated with +terms of the angular velocity instead of the total rotation. +a nondefault amplitude, Abaqus calculates the prescribed increment of rotation as the average of the +prescribed angular velocities at the beginning and the end of each increment, multiplied by the time +increment. +In Abaqus/Explicit displacement-type boundary conditions that refer to an amplitude curve are +effectively enforced as velocity boundary conditions using average velocities over time increments as +computed by finite differences of values from the amplitude curve. As with prescribed displacements +, Abaqus/Explicit does not admit jumps in rotations. +Displacement-type boundary conditions in Abaqus/Standard that constrain just one component of +rotation can have essentially no effect on the solution because the two unconstrained rotational degrees +of freedom can combine to override the constraint. +Example: Using velocity-type boundary conditions to prescribe rotations +For example, if a rotation of +about the z-axis is required in a static step, with no rotation about the x- +and y-axes, use a step time (specified as part of the static step definition) of 1.0, and define a velocity- +type boundary condition to specify zero velocity for degrees of freedom 4 and 5 and a constant angular +velocity of +for degree of freedom 6. Since the default variation for a velocity-type boundary condition +in a static procedure is a step, the velocity will be constant over the step. Alternatively, an amplitude +reference could be used to specify the desired variation over the step. +*BOUNDARY, TYPE=VELOCITY +NODE, 4 +NODE, 5 +NODE, 6, 6, 18.84955592 +If, in the next step, the same node should have an additional rotation of +radians about the global +x-axis, use another static step with a step time of 1.0 and again define a velocity-type boundary condition +to prescribe zero velocity for degrees of freedom 5 and 6 and a constant angular velocity of +for +degree of freedom 4. +*BOUNDARY, TYPE=VELOCITY +NODE, 4, 4, 1.570796327 +NODE, 5 +NODE, 6 +Prescribing radial motion on an axisymmetric model +The radial coordinate for any node in an axisymmetric model must be positive. Therefore, you must +make sure that any specified boundary condition does not violate this condition. +33.3.2 +BOUNDARY CONDITIONS IN Abaqus/CFD +Products: Abaqus/CFD Abaqus/CAE +References +• “Distribution definition,” Section 2.8.1 +• “Prescribed conditions: overview,” Section 33.1.1 +• “Conventions,” Section 1.2.2 +• *BOUNDARY +• *DISTRIBUTION +• *FLUID BOUNDARY +• “Using the boundary condition editors,” Section 16.10 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +Boundary conditions: +• are used to prescribe the values of all primitive variables involved in a fluid dynamics calculation +(e.g., velocities, temperatures, turbulence variables, wall-normal distance, etc.); +• can be given as “history” input data (within an analysis step) to add, modify, or remove zero-valued +or nonzero boundary conditions; and +• can be prescribed through the use of a co-simulation region for multiphysics problems. +Computational fluid dynamics problems typically require the prescription of multiple variables such +as pressure, temperature, and velocity for boundary conditions. In practice, boundary conditions tend +to appear together to collectively define a physical behavior; e.g., no-slip/no-penetration conditions at a +wall. In contrast, Neumann conditions (e.g., prescribed heat flux) are specified as loads . In the absence of a prescribed +boundary condition or load, the default behavior for Abaqus/CFD is to enforce a homogeneous (zero) +Neumann condition. For example, if the temperature is not specified at a wall, the default behavior is to +automatically specify a perfectly insulated boundary; i.e., zero normal heat flux. Similarly, if the velocity +is not prescribed, the normal derivative of the velocity is set to zero. +In Abaqus/CAE combinations of boundary conditions that represent an inflow, outflow, or wall +behavior are grouped collectively for ease of use (for more information, see “Using the boundary +condition editors,” Section 16.10 of the Abaqus/CAE User’s Manual). +Active degrees of freedom +In Abaqus/CFD the active fields (degrees of freedom) are determined by the analysis procedure and the +options specified, such as turbulence models and auxiliary transport equations. You specify a boundary +condition type to identify the degree of freedom for a fluid boundary condition. Element-based and +node-based degrees of freedom and the analysis procedure and additional options required for activation, +if any, are listed in Table 33.3.2–1 and Table 33.3.2–2, respectively. +Table 33.3.2–1 Element-based degrees of freedom and activation +options for fluid boundary conditions. +Boundary condition +type +Description +Incompressible flow +TEMP +TEMPn +TURBEPS +TURBEPSn +TURBKE +TURBKEn +TURBNU +TURBNUn +VELX +VELXn +VELY +VELYn +VELZ +VELZn +VELXNU +VELYNU +Energy equation +Energy equation +RNG - model +RNG - model +RNG - model +RNG - model +Spalart-Allmaras model +Spalart-Allmaras model +— +— +— +— +— +— +— +— +Fluid temperature +Fluid temperature on +face n +Turbulent energy +dissipation rate ( ) +Turbulent energy +dissipation rate ( ) +on face n +Turbulent kinetic energy +( ) +Turbulent kinetic energy +( ) on face n +Turbulent kinematic +eddy viscosity +Turbulent kinematic +eddy viscosity on face n +x-velocity +x-velocity on face n +y-velocity +y-velocity on face n +z-velocity +z-velocity on face n +x-velocity defined via +user subroutine +y-velocity defined via +user subroutine +Description +Incompressible flow +Boundary condition +type +VELZNU +z-velocity defined via +user subroutine +PASSIVEOUTFLOW +Passive outflow +PNU +Fluid pressure +Fluid pressure defined +via user subroutine +— +— +— +— +Table 33.3.2–2 Node-based degrees of freedom and activation +options for fluid boundary conditions. +Boundary condition +type +Description +Incompressible flow +PVDEP +DIST +Fluid pressure +Fluid pressure that +varies with the total +volume of fluid crossing +the boundary +Wall-distance normal +function +— +— +— +Prescribing inflow and outflow boundary conditions +You can specify boundary conditions to describe the flow behavior where fluid enters the analysis domain +and where the fluid leaves the analysis domain. +Input File Usage: +Use the following option to define inflow and outflow boundary conditions at +surfaces: +*FLUID BOUNDARY, TYPE=SURFACE +surface name, boundary condition type label, magnitude +where boundary condition type label is VELX, VELY, VELZ, VELXNU, +VELYNU, VELZNU, TEMP, TURBKE, TURBEPS, TURBNU, P, +PNU, or PASSIVEOUTFLOW. The value of magnitude is ignored for +PASSIVEOUTFLOW. +Use the following option to define distributed inflow and outflow boundary +conditions at element faces: +*FLUID BOUNDARY, TYPE=ELEMENT +element set label, boundary condition type label, magnitude +where boundary condition type label is VELXn, VELYn, VELZn, TEMPn, +TURBKEn, TURBEPSn, or TURBNUn. +Use the following option to define distributed inflow and outflow boundary +conditions at nodes: +*FLUID BOUNDARY, TYPE=NODE +node set label, P, magnitude +Abaqus/CAE Usage: +Use the following option to define the inflow and outflow boundary conditions +at surfaces: +Load module: Create Boundary Condition: Step: flow_step: Category: +Fluid: Fluid inlet/outlet: select inlet regions or outlet regions; and +specify momentum (pressure or velocity), thermal energy (temperature), +and turbulence conditions at the inlet or outlet +Defining distributed inflow and outflow boundary conditions at element faces +is supported in Abaqus/CAE only for velocity boundary conditions. +Use the following option: +Load module: Create Boundary Condition: Step: flow_step: +Category: Fluid: Fluid inlet/outlet: select inlet regions or outlet +regions; Momentum: toggle on Specify, and choose Velocity; +Distribution: select an analytical field +Defining distributed inflow and outflow boundary conditions at nodes is not +supported in Abaqus/CAE. +Inflow boundary conditions +An inflow boundary condition is used to describe the flow behavior at a surface where fluid enters the +analysis domain. For incompressible flows, inflow conditions can be prescribed for velocity or pressure, +temperature, and turbulence variables. If boundary conditions are not specified explicitly for a variable, a +homogeneous Neumann condition is assumed automatically. This corresponds to permitting the variable +(e.g., temperature) to vary at the inflow and the incoming fluid to correspond to that local variable. +Similarly, if pressure is not specified, its normal derivative at the inflow surface is automatically set to +zero. The velocity components can be prescribed independently. +Outflow boundary conditions +An outflow boundary corresponds to a surface where the fluid flow leaves the analysis domain. +In +Abaqus/CFD outflow conditions are most frequently associated with a specified pressure. However, +all other flow variables can be prescribed at an outflow boundary as well. Similar to an inflow boundary, +when a variable is not specified, its normal derivative is assumed to be zero. As such, convective outflows +carry their quantities out of the domain at a fixed level, resulting in essentially nonreflecting boundaries. +Prescribing wall boundary conditions +Wall boundary conditions are typically associated with the no-slip/no-penetration behavior at a solid +surface. However, the behavior at a solid wall may also require the prescription of temperature and, +optionally, turbulence variables depending on the flow conditions. In situations where a wall heat flux is +required, a heat flux loading must be prescribed in addition to the wall boundary conditions. +Depending on the physical properties of the wall, the wall boundary conditions can be modified to +achieve a variety of physical behaviors that include slip, no-slip, infiltration, symmetry, etc. +Input File Usage: +Use the following option to define wall boundary conditions at surfaces: +*FLUID BOUNDARY, TYPE=SURFACE +surface name, boundary condition type label, magnitude +where boundary condition type label is VELX, VELY, VELZ, VELXNU, +VELYNU, VELZNU, TEMP, TURBKE, TURBEPS, TURBNU, P, PNU or +DIST. +Use the following option to define distributed wall boundary conditions at +element faces: +*FLUID BOUNDARY, TYPE=ELEMENT +element set label, boundary condition type label, magnitude +where boundary condition type label is VELXn, VELYn, VELZn, TEMPn, +TURBKEn, TURBEPSn, or TURBNUn. +Use the following option to define distributed wall boundary conditions at +nodes: +*FLUID BOUNDARY, TYPE=NODE +node set label, P, magnitude +For example, use the following settings for a no-slip/no-penetration wall that +is not moving and with the Spalart-Allmaras turbulence model active (wall- +normal distance boundary condition and turbulent eddy viscosity set to zero at +the wall): +*FLUID BOUNDARY, TYPE=SURFACE +surface name, DIST, 0 +surface name, VELX, 0 +surface name, VELY, 0 +surface name, VELZ, 0 +surface name, TURBNU, 0 +Abaqus/CAE Usage: +Use the following option to define wall boundary conditions at surfaces: +Load module: Create Boundary Condition: Step: flow_step: +Category: Fluid: Fluid wall condition: select regions; select Condition: +No slip, Shear, or Infiltration; and specify velocity, thermal energy +(temperature), and turbulence conditions at the wall +Defining distributed wall boundary conditions at elements is supported in +Abaqus/CAE only for velocity boundary conditions at a slip wall or infiltration +wall. +Use the following option to define distributed wall boundary conditions at +elements: +Load module: Create Boundary Condition: Step: flow_step: +Category: Fluid: Fluid wall condition: select regions; Velocity: +Distribution: select an analytical field +Defining distributed wall boundary conditions at nodes is not supported in +Abaqus/CAE. +No-slip/no-penetration wall +A no-slip (and no-penetration) wall is a surface where the fluid adheres to the wall without penetrating +it. No-slip/no-penetration conditions are prescribed by setting all velocity components equal to the wall +velocity (zero if the wall is not moving). If a turbulence model is specified, the wall-normal distance +boundary condition must be set to zero at the wall. The boundary conditions for the different turbulence +variables depend on the model selected. For the Spalart-Allmaras model, the turbulent eddy viscosity, +, is set to zero at the wall. For the RNG k– model, the wall boundary conditions are automatically +are required +implemented by the solver using the wall-function approach; no user settings for k or +because they are prescribed automatically. +Slip wall +A slip wall is a surface where the fluid does not adhere to the wall but cannot penetrate it. This wall +condition is modeled by specifying the wall-normal fluid velocity equal to the wall velocity (zero if +the wall is not moving). This situation also represents a symmetry condition for fluid flow since the +in-plane velocities can vary, but the out-of-plane velocity is zero. In cases where a moving boundary +is being considered, an associated set of mesh displacement boundary conditions must be prescribed +in conjunction with the surface fluid velocity to achieve the proper behavior. If a turbulence model is +specified, the wall-normal distance boundary condition must be set to zero at the wall. +Infiltration wall +Infiltration at a surface permits the fluid to penetrate the surface while maintaining the no-slip condition. +This wall condition is modeled by specifying the wall-normal velocity equal to the velocity representing +the infiltration velocity, while the wall-tangent fluid velocity is equal to the wall velocity (zero if the wall +is not moving). In the special case when a turbulence model is implemented, the wall-normal distance +boundary condition must be set to zero at the wall. If the Spalart-Allmaras turbulence model is enabled, +you can specify the value of the Spalart-Allmaras turbulent eddy viscosity, +, that is allowed at the wall +due to infiltration. If the RNG k– model is implemented, you can prescribe values at the wall for the +turbulent kinetic energy, k, and the dissipation rate, +. +Prescribed temperature +Temperatures can be prescribed at a wall. By default, if no temperature is prescribed at a wall, a perfectly +insulated boundary is specified automatically. For multiphysics applications such as conjugate heat +transfer, a variable temperature condition is imposed automatically using a co-simulation region (for +more information, see “Preparing an Abaqus analysis for co-simulation,” Section 17.2.1). +Prescribed displacement +Abaqus/CFD provides the capability to perform both deforming-mesh and fluid-structure interaction +(FSI) simulations using an arbitrary Lagrangian-Eulerian (ALE) methodology for the fluid flow. For FSI +and deforming-mesh problems, typically some portion of the fluid domain is deformed consistent with a +boundary motion. To manage the mesh motion, you must prescribe displacement boundary conditions +on the mesh. For FSI problems, displacement boundary conditions are not permitted at the co-simulation +region because these conditions are prescribed automatically. +Input File Usage: +*BOUNDARY +node or node set, first degree of freedom, last degree of freedom, magnitude +Abaqus/CAE Usage: +freedom is 1 for the x-displacement, 2 for the +where first degree of +y-displacement, or 3 for the z-displacement. +Load module: Create Boundary Condition: Step: flow_step: +Category: Mechanical: Displacement/Rotation: select regions +and toggle on the degree or degrees of freedom +Defining pressure boundary conditions that vary with the total volume of fluid crossing a surface +Abaqus/CFD provides the capability to define pressure boundary conditions that vary with the total +volume of fluid crossing a surface. The total volume of fluid crossing the surface is automatically +calculated and used to determine the current amplitude of the applied pressure. +Input File Usage: +Use the following options: +*DISTRIBUTION TABLE, NAME=table name +*DISTRIBUTION, LOCATION=NONE, TABLE=table name, +NAME=distribution name +*FLUID BOUNDARY, TYPE=SURFACE, +DISTRIBUTION=distribution name +surface name, PVDEP, initial volume +Abaqus/CAE Usage: +Defining pressure boundary conditions that vary with the total volume of fluid +crossing a surface is not supported in Abaqus/CAE. +Defining boundary conditions that vary with time +The prescribed magnitude of the boundary conditions can vary with time during a step according to an +amplitude definition (“Amplitude curves,” Section 33.1.2). +Input File Usage: +Use both of the following options to define the prescribed displacement at a +moving boundary: +*AMPLITUDE, NAME=name +*BOUNDARY, AMPLITUDE=name +Use both of the following options to define inflow and outflow boundary +conditions and wall boundary conditions that vary with time: +*AMPLITUDE, NAME=name +*FLUID BOUNDARY, AMPLITUDE=name +Load or Interaction module: Create Amplitude: Name: amplitude_name +Load module: Create Boundary Condition: Step: flow_step: +boundary condition; Amplitude: amplitude_name +Abaqus/CAE Usage: +Boundary condition propagation +By default, all boundary conditions defined in the previous general analysis step remain unchanged in +the subsequent general step. You define the boundary conditions in effect for a given step relative to +the preexisting boundary conditions. At each new step the existing boundary conditions can be modified +and additional boundary conditions can be specified. Alternatively, you can release all previously applied +boundary conditions in a step and specify new ones. In this case any boundary conditions that are to be +retained must be respecified. +Modifying boundary conditions +When you modify an existing boundary condition, the node or node set must be specified in exactly the +same way as previously. For example, if a boundary condition is specified for a node set in one step and +for an individual node contained in the set in another step, Abaqus issues an error. You must remove the +boundary condition and respecify it to change the way the node or node set is specified. +Input File Usage: +Use one of the following options to modify an existing boundary condition or +to specify an additional boundary condition: +*BOUNDARY +*BOUNDARY, OP=MOD +*FLUID BOUNDARY +*FLUID BOUNDARY, OP=MOD +Load module: Create Boundary Condition or Boundary +Condition Manager: Edit +Abaqus/CAE Usage: +Removing boundary conditions +If you choose to remove any boundary condition in a step, no boundary conditions will be propagated +from the previous general step. Therefore, all boundary conditions that are in effect during this step must +be respecified. +Setting a boundary condition to zero is not the same as removing it. +Input File Usage: +Use one of the following options to release all previously applied boundary +conditions and to specify new boundary conditions: +*BOUNDARY, OP=NEW +If the OP=NEW parameter is used on any *BOUNDARY option within a step, +it must be used on all *BOUNDARY options in the step. +*FLUID BOUNDARY, OP=NEW +If the OP=NEW parameter is used on any *FLUID BOUNDARY option within +a step, it must be used on all *FLUID BOUNDARY options in the step. +Use the following option to remove a boundary condition within a step: +Load module: Boundary Condition Manager: Deactivate +Abaqus/CAE automatically respecifies any boundary conditions that should +remain in effect during this step. +Abaqus/CAE Usage: +33.4 +Loads +• “Applying loads: overview,” Section 33.4.1 +• “Concentrated loads,” Section 33.4.2 +• “Distributed loads,” Section 33.4.3 +• “Thermal loads,” Section 33.4.4 +• “Electromagnetic loads,” Section 33.4.5 +• “Acoustic and shock loads,” Section 33.4.6 +• “Pore fluid flow,” Section 33.4.7 +33.4.1 +APPLYING LOADS: OVERVIEW +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD Abaqus/CAE +References +• “General and linear perturbation procedures,” Section 6.1.3 +• “Prescribed conditions: overview,” Section 33.1.1 +• “Concentrated loads,” Section 33.4.2 +• “Distributed loads,” Section 33.4.3 +• “Thermal loads,” Section 33.4.4 +• “Electromagnetic loads,” Section 33.4.5 +• “Acoustic and shock loads,” Section 33.4.6 +• “Pore fluid flow,” Section 33.4.7 +• “Creating and modifying prescribed conditions,” Section 16.4 of the Abaqus/CAE User’s Manual +• “Using the load editors,” Section 16.9 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +External loading can be applied in the following forms: +• Concentrated or distributed tractions. +• Concentrated or distributed fluxes. +• Incident wave loads. +Many types of distributed loads are provided; they depend on the element type and are described in +Part VI, “Elements.” This section discusses general concepts that apply to all types of loading; see +“Prescribed conditions: overview,” Section 33.1.1, for general information that applies to all types of +prescribed conditions. +Concentrated and distributed tractions are discussed in “Concentrated loads,” Section 33.4.2, and +“Distributed loads,” Section 33.4.3, respectively. Thermal loading (heat flux) is discussed in “Thermal +loads,” Section 33.4.4. Electromagnetic loads are discussed in “Electromagnetic loads,” Section 33.4.5. +Loads due to incident wave fields such as due to sound sources or an underwater explosion are discussed +in “Acoustic and shock loads,” Section 33.4.6. Pore fluid flow is discussed in “Pore fluid flow,” +Section 33.4.7. All other load types, which are applicable to only a single type of analysis, are discussed +in the appropriate sections in Part III, “Analysis Procedures, Solution, and Control.” +In some situations, concentrated loads and some commonly used distributed loads (such as pressure +applied on a surface) may rotate during a geometrically nonlinear analysis. Such loads are known as +follower loads; further details on follower loads can be found in “Follower loads in large-displacement +analysis;” “Specifying concentrated follower forces” in “Concentrated loads,” Section 33.4.2; “Follower +surface loads” in “Distributed loads,” Section 33.4.3; and “Follower edge and line loads” in “Distributed +loads,” Section 33.4.3. Follower loads may also lead to an unsymmetric contribution to the stiffness +matrix, which is generally referred to as the load stiffness; some issues related to the load stiffness +contribution are discussed in “Improving the rate of convergence in large-displacement implicit analysis” +in “Concentrated loads,” Section 33.4.2, and “Improving the rate of convergence in large-displacement +implicit analysis” in “Distributed loads,” Section 33.4.3. +Element-based versus surface-based distributed loads +There are two ways of specifying distributed loads in Abaqus: element-based distributed loads and +surface-based distributed loads. Element-based distributed loads can be prescribed on element bodies, +element surfaces, or element edges. Surface-based distributed loads can be prescribed on geometric +surfaces or geometric edges. In Abaqus/CAE distributed surface and edge loads can be element-based +or surface-based, while distributed body loads are prescribed on geometric bodies or element bodies. +Element-based loads +Use element-based loads to define distributed loads on element surfaces, element edges, and element +bodies. With element-based loads you must provide the element number (or an element set name) and +the distributed load type label. The load type label identifies the type of load and the element face or +edge on which the load is prescribed . This method of specifying distributed loads is very general and can +be used for all distributed load types and elements. +Surface-based loads +Use surface-based loads to prescribe a distributed load on a geometric surface or geometric edge. With +surface-based loads you must specify the surface or edge name and the distributed load type. The surface +or edge, which contains the element and face information, is defined as described in “Element-based +surface definition,” Section 2.3.2. In Abaqus/CAE surfaces can be defined as collections of geometric +faces and edges or collections of element faces and edges.This method of prescribing a distributed load +facilitates user input for complex models. It can be used with most element types for which a valid +surface can be defined. You can specify in the surface definition how the distributed load is applied +to the boundary of an adaptive mesh domain in Abaqus/Explicit . +Varying the magnitude of a load +The magnitude of a load is usually defined by the input data. The variation of the load magnitude during a +step can be defined by the default amplitude variation for the step ; by a user-defined amplitude curve ; or, in some +cases, by user subroutine DLOAD, UDECURRENT, UDSECURRENT, UTRACLOAD, or VDLOAD. +Loading during general analysis steps +If the analysis consists of one step only, the loads are defined in that step. If there are several analysis +steps, the definition of loading in each analysis step depends on whether that step and the previous +steps are general analysis steps or linear perturbation steps. Loading during linear perturbation steps +is discussed below. +In general analysis steps, load magnitudes must always be given as total values, not as changes +in magnitude. Multiple definitions of the same load condition in the same step are applied additively. +Element-based and surface-based distributed loads are considered independently. For example, element- +based and surface-based pressures applied to an element face in the same step are added. A single +redefinition of that same load condition in a subsequent step, however, replaces all the like definitions +(same load option, same load type) given in previous steps according to the rules described in “Removing +loads” below. +Any combination of loads can be applied together during a step. For a linear step it is possible to +analyze several load cases based on the same stiffness. +Modifying loads +At each new step the loading can be either modified or completely redefined. To redefine a load, the +node, element, node set, element set, or surface name must be specified in exactly the same way and the +load type must be identical. For example, if a node is part of a loaded node set in one step and is loaded +as an individual node (by listing its node number) in another step, the loads will be added. +All loads defined in previous steps remain unchanged unless they are redefined. When a load is left +unchanged, the following rules apply: +• If the associated amplitude was specified in terms of total time, the load continues to follow the +amplitude definition. +• If no amplitude was associated with the load or if the amplitude was given in terms of step time, the +load remains constant at the magnitude associated with the end of the previous step. +Input File Usage: +Use either of the following options to modify an existing load or to specify an +additional load (*LOADING OPTION represents any load type): +*LOADING OPTION +*LOADING OPTION, OP=MOD +Abaqus/CAE Usage: +Load module: Create Load or Load Manager: Edit +Removing loads +If you choose to remove any load of a particular type (concentrated load, element-based distributed load, +surface-based distributed load, etc.) in a step, no loads of that type will be propagated from the previous +general step. All loads of that type that are in effect during this step must be respecified. To redefine +a load, the node, element, node set, element set, or surface name must be specified in exactly the same +way and the load type must be identical. Refer to “Prescribed conditions: overview,” Section 33.1.1, for +a discussion of amplitude variations when removing loads. +Input File Usage: +Use the following option to release all previously applied loads of a given type +and to specify new loads (*LOADING OPTION represents any load type): +*LOADING OPTION, OP=NEW +For example, *CLOAD, OP=NEW with no data lines will remove all +concentrated forces and moments from the model. +If the OP=NEW parameter is used on any loading option in a step, it must be +used on all loading options of the same type within the step. +Abaqus/CAE Usage: +Use the following option to remove a load within a step: +Load module: Load Manager: Deactivate +Abaqus/CAE automatically respecifies any loads that should remain in effect +during this step. +Example +In the history definition input file section shown below, the distributed load (type BX) applied to element +set A2 has a magnitude of 20.0 in the first step, which is changed to 50.0 in the second step. Both the +set identifier (or element or node number) and the load type must be identical in both steps for Abaqus +to identify a load for redefinition. +In Step 1 a concentrated load of magnitude 10.0 is applied to degree of freedom 3 of all nodes in +node set NLEFT. In Step 2 a concentrated load of magnitude 5.0 is applied to degree of freedom 3 of +node 1. If node 1 is in node set NLEFT, the total load applied in Step 2 at this node is 15.0: the loads add. +The two distributed loads of type P1 acting on element set E1 in Step 1 will be added to give a total +distributed load of 43.0. +The pressure loads on element sets B3 and E1 are active during both steps. +*STEP +Step 1 +*STATIC +*CLOAD +NLEFT, 3, 10. +*DLOAD +A2, BX, 20. +B3, P1, 5. +E1, P1, 21. +*DLOAD +E1, P1, 22. +*END STEP +** +*STEP +Step 2 +*STATIC +*CLOAD +1, 3, 5. +*DLOAD, OP=MOD +A2, BX, 50. +*END STEP +Follower loads in large-displacement analysis +In large-displacement analysis distributed loads will be treated as follower forces when appropriate. +For beam and shell elements point (concentrated) loads may be fixed in direction or they may rotate +with the structure depending on whether you specify follower forces for the load . Follower loads defined at a rigid body tie node rotate with the rigid body in +Abaqus/Explicit. +Loading during linear perturbation steps +In a linear perturbation step (available only in Abaqus/Standard) the state at the end of the previous +general analysis step is considered as the “base state.” If the linear perturbation step is the first step of +the analysis, the initial conditions of the model form the base state. Loading during a linear perturbation +step must be defined as the change in load from the base state (the perturbation of load), not the total of +the base state load plus the perturbation load. +In consecutive linear perturbation steps, the perturbation of load that applies to each step must +be defined completely within that step—the analysis within each such step always starts from the base +state (except when you specify that a modal dynamic step should use the initial conditions from the +immediately preceding step—see “Transient modal dynamic analysis,” Section 6.3.7). +In nonlinear steps that follow linear perturbation analysis steps, the analysis is continued from the +base state as if the intermediate linear perturbation steps did not exist. +Loading during linear (mode-based) dynamics procedures +If a user subroutine is used to define loading in a mode-based linear dynamics analysis, the subroutine +will be called only at the beginning of the step to obtain the magnitude of the load. The load magnitude +then remains constant in the step unless it is modified by an amplitude curve. +CONCENTRATED LOADS +CONCENTRATED LOADS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD Abaqus/CAE +References +• “Applying loads: overview,” Section 33.4.1 +• *CLOAD +• “Defining a concentrated force,” Section 16.9.1 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Defining a moment,” Section 16.9.2 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +• “Defining a generalized plane strain load,” Section 16.9.10 of the Abaqus/CAE User’s Manual, in +the online HTML version of this manual +• “Defining a fluid reference pressure,” Section 16.9.23 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +Concentrated loads: +• apply concentrated forces and moments to nodal degrees of freedom; and +• can be fixed in direction; or +• can rotate as the node rotates (referred to as follower forces), resulting in an additional, and possibly +unsymmetric, contribution to the load stiffness +In steady-state dynamic analysis both real and imaginary concentrated loads can be applied . +Multiple concentrated load cases can be defined in random response analysis . +Concentrated loads are also used to apply the pressure-conjugate at nodes with pressure degree of +freedom in acoustic analysis and to specify a fluid +reference pressure for incompressible flow . +Actuation loads in connector elements can be defined as connector loads, applied similarly to +concentrated loads. See “Connector actuation,” Section 31.1.3, for more detailed information. +The procedures in which these loads can be used are outlined in “Prescribed conditions: overview,” +Section 33.1.1. See “Applying loads: overview,” Section 33.4.1, for general information that applies to +all types of loading. +Concentrated loads +In Abaqus/Standard and Abaqus/Explicit analyses concentrated forces or moments can be applied at any +nodal degree of freedom. +You should not apply a moment load at the origin of a cylindrical coordinate system; doing so would +make the radial and tangential loads indeterminate. +Input File Usage: +*CLOAD +node number or node set, degree of freedom, magnitude +Abaqus/CAE Usage: +Load module: Create Load: choose Mechanical for the Category +and Concentrated force, Moment, or Generalized plane strain +for the Types for Selected Step +Specifying concentrated follower forces +You can specify that the direction of a concentrated force should rotate with the node to which it is +applied. This specification should be used only in large-displacement analysis and can be used only at +nodes with active rotational degrees of freedom (such as the nodes of beam and shell elements or, in +Abaqus/Explicit, tie nodes on a rigid body), excluding the reference node of generalized plane strain +elements. If you specify follower forces, the components of the concentrated force must be specified +with respect to the reference configuration. +Follower loads lead to an unsymmetric contribution to the stiffness matrix that is generally referred +to as the load stiffness. Some issues associated with the load stiffness contribution are discussed in +“Improving the rate of convergence in large-displacement implicit analysis.” +*CLOAD, FOLLOWER +Load module: Create Load: choose Mechanical for the Category +and Concentrated force or Moment for the Types for Selected +Step: Follow nodal rotation +Abaqus/CAE Usage: +Input File Usage: +Defining the values of concentrated nodal force from a user-specified file +You can define nodal force using nodal force output from a particular step and increment in the output +database (.odb) file of a previous Abaqus analysis. The part (.prt) file from the original analysis is also +required when reading data from the output database file. In this case both the previous model and the +current model must be defined consistently, including node numbering, which must be the same in both +models. If the models are defined in terms of an assembly of part instances, part instance naming must +be the same. +Input File Usage: +*CLOAD, FILE=file, STEP=step, INC=inc +Abaqus/CAE Usage: +Defining the values of concentrated nodal force from a user-specified file is not +supported in Abaqus/CAE. +Specifying a fluid reference pressure +For incompressible fluid dynamic analyses in Abaqus/CFD, when no other pressure condition is +prescribed, you must specify a fluid reference pressure at one node to set the hydrostatic pressure +level. Multiple reference pressures can be specified, but only the last specified hydrostatic pressure +load is applied. For more information, see “Incompressible fluid dynamic analysis,” Section 6.6.2, and +“Boundary conditions in Abaqus/CFD,” Section 33.3.2. +Input File Usage: +*CLOAD +node number or node set, HP, magnitude +Abaqus/CAE Usage: +Load module: Create Load: choose Fluid for the Category and Fluid +reference pressure for the Types for Selected Step +Defining time-dependent concentrated loads +The prescribed magnitude of a concentrated load can vary with time during a step according to an +amplitude definition, as described in “Prescribed conditions: overview,” Section 33.1.1. +If different +variations are needed for different loads, each load can refer to its own amplitude. +Modifying concentrated loads +Concentrated loads can be added, modified, or removed as described in “Applying loads: overview,” +Section 33.4.1. +Improving the rate of convergence in large-displacement implicit analysis +When concentrated follower forces are specified in a geometrically nonlinear static and dynamic +analysis, the unsymmetric matrix storage and solution scheme should normally be used. See “Defining +an analysis,” Section 6.1.2, for more information on the unsymmetric matrix storage and solution +scheme. +33.4.3 +DISTRIBUTED LOADS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD Abaqus/CAE +References +• “Applying loads: overview,” Section 33.4.1 +• *DLOAD +• *DSLOAD +• “Defining a pressure load,” Section 16.9.3 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +• “Defining a shell edge load,” Section 16.9.4 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +• “Defining a surface traction load,” Section 16.9.5 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Defining a pipe pressure load,” Section 16.9.6 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Defining a body force,” Section 16.9.7 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +• “Defining a line load,” Section 16.9.8 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +• “Defining a gravity load,” Section 16.9.9 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +• “Defining a rotational body force,” Section 16.9.11 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Defining a porous drag body force,” Section 16.9.24 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +Distributed loads: +• can be prescribed on element faces, element bodies, or element edges; +• can be prescribed over geometric surfaces or geometric edges; +• require that an appropriate distributed load type be specified—see Part VI, “Elements,” for +definitions of the distributed load types available for particular elements; and +• may be of follower type, which can rotate during a geometrically nonlinear analysis and result in +an additional (often unsymmetric) contribution to the stiffness matrix that is generally referred to +as the load stiffness. +The procedures in which these loads can be used are outlined in “Prescribed conditions: overview,” +Section 33.1.1. See “Applying loads: overview,” Section 33.4.1, for general information that applies to +all types of loading. +Follower loads are discussed further in “Follower surface loads” and “Follower edge and line loads.” +The contribution of follower loads to load stiffness is discussed in “Improving the rate of convergence +in large-displacement implicit analysis.” +In steady-state dynamic analysis both real and imaginary distributed loads can be applied . +Incident wave loading is used to apply distributed loads for the special case of loads associated +with a wave traveling through an acoustic medium. Inertia relief is used to apply inertia-based loading +in Abaqus/Standard. These load types are discussed in “Acoustic and shock loads,” Section 33.4.6, and +“Inertia relief,” Section 11.1.1, respectively. Abaqus/Aqua load types are discussed in “Abaqus/Aqua +analysis,” Section 6.11.1. +Defining time-dependent distributed loads +The prescribed magnitude of a distributed load can vary with time during a step according to an amplitude +definition, as described in “Prescribed conditions: overview,” Section 33.1.1. If different variations are +needed for different loads, each load can refer to its own amplitude definition. +Modifying distributed loads +Distributed loads can be added, modified, or removed as described in “Applying loads: overview,” +Section 33.4.1. +Improving the rate of convergence in large-displacement implicit analysis +In large-displacement analyses in Abaqus/Standard some distributed load types introduce unsymmetric +load stiffness matrix terms. Examples are hydrostatic pressure, pressure applied to surfaces with free +edges, Coriolis force, rotary acceleration force, and distributed edge loads and surface tractions modeled +In such cases using the unsymmetric matrix storage and solution scheme for the +as follower loads. +analysis step may improve the convergence rate of the equilibrium iterations. See “Defining an analysis,” +Section 6.1.2, for more information on the unsymmetric matrix storage and solution scheme. +Defining distributed loads in a user subroutine +Nonuniform distributed loads such as a nonuniform body force in the X-direction can be defined by means +of user subroutine DLOAD in Abaqus/Standard or VDLOAD in Abaqus/Explicit. When an amplitude +reference is used with a nonuniform load defined in user subroutine VDLOAD, the current value of the +amplitude function is passed to the user subroutine at each time increment in the analysis. DLOAD and +VDLOAD are not available for surface tractions, edge tractions, or edge moments. +In Abaqus/Standard nonuniform distributed surface tractions, edge tractions, and edge moments can +be defined by means of user subroutine UTRACLOAD. User subroutine UTRACLOAD allows you to define +a nonuniform magnitude for surface tractions, edge tractions, and edge moments, as well as nonuniform +loading directions for general surface tractions, shear tractions, and general edge tractions. +Nonuniform distributed surface tractions, edge tractions, and edge moments are not currently +supported in Abaqus/Explicit. +When the user subroutine is used, the external work is calculated based only on the current +magnitude of the distributed load since the incremental value for the distributed load is not defined. +Specifying the region to which a distributed load is applied +As discussed in “Applying loads: overview,” Section 33.4.1, distributed loads can be defined as element- +based or surface-based. Element-based distributed loads can be prescribed on element bodies, element +surfaces, or element edges. Surface-based distributed loads can be prescribed directly on geometric +surfaces or geometric edges. +Three types of distributed loads can be defined: body loads, surface loads, and edge loads. +Distributed body loads are always element-based. Distributed surface loads and distributed edge loads +can be element-based or surface-based. Table 33.4.3–1 summarizes the regions on which each load +type can be prescribed. In Abaqus/CAE distributed loads are specified by selecting the region in the +viewport or from a list of surfaces.In the Abaqus input file different options are used depending on the +type of region to which the load is applied, as illustrated in the following sections. +Table 33.4.3–1 Regions on which the different load types can be prescribed. +Load type +Load definition Input file region +Abaqus/CAE region +Body loads +Element-based +Element bodies +Volumetric bodies +Surface loads +Element-based +Element surfaces +Edge loads +(including beam +line loads) +Surface-based +Geometric element- +based surfaces +Element-based +Element edges +Surface-based +Geometric edge-based +surfaces +Surfaces defined as collections of +geometric faces or element faces +(excluding analytical rigid surfaces) +Surfaces defined as collections of +geometric edges or element edges +Body forces +Body loads, such as gravity, centrifugal, Coriolis, and rotary acceleration loads, are applied as element- +based loads. The units of a body force are force per unit volume. +Table 33.4.3–2 lists all of the distributed body load types that are available in Abaqus, along with +the corresponding load type labels. +Table 33.4.3–2 Distributed body load types. +Load description +Body force in global X-, Y-, and +Z-directions +Nonuniform body force in global +X-, Y-, and Z-directions +Body force in radial and axial +directions (only for axisymmetric +elements) +Nonuniform body force in radial +and axial directions (only for +axisymmetric elements) +Viscous body force in global X-, +Y-, and Z-directions (available only +in Abaqus/Explicit) +Stagnation body force in global X-, +Y-, and Z-directions (available only +in Abaqus/Explicit) +Gravity loading +Centrifugal load (magnitude is input +as +is the mass density +, where +per unit volume and +is the angular +velocity) +Centrifugal load (magnitude is +input as +, where +velocity) +is the angular +Coriolis force +Rotary acceleration load +Rotordynamic load +Porous drag load (input is porosity +of the medium) +Load type label for +element-based loads +Abaqus/CAE +load type +BX, BY, BZ +Body force +BXNU, BYNU, BZNU +Body force +BR, BZ +BRNU, BZNU +VBF +SBF +GRAV +CENT +CENTRIF +CORIO +ROTA +ROTDYNF +PDBF +33.4.3–4 +Not supported +Gravity +Not supported +Rotational body +force +Coriolis force +Rotational body +force +Not supported +Porous drag body +Specifying general body forces +You can specify body forces on any elements in the global X-, Y-, or Z-direction. You can specify body +forces on axisymmetric elements in the radial or axial direction. +Input File Usage: +Use the following option to define a body force in the global X-, Y-, or Z- +direction: +*DLOAD +element number or element set, load type label, magnitude +where load type label is BX, BY, BZ, BXNU, BYNU, or BZNU. +Use the following option to define a body force in the radial or axial direction +on axisymmetric elements: +*DLOAD +element number or element set, load type label, magnitude +where load type label is BR, BZ, BRNU, or BZNU. +Abaqus/CAE Usage: +Load module: Create Load: choose Mechanical for the Category +and Body force for the Types for Selected Step +Specifying viscous body force loads in Abaqus/Explicit +Viscous body force loads are defined by +where +is the viscous force applied to the body; +is the velocity of the point on the body where the force is being applied; +is the viscosity, given as the magnitude of the load; +is the velocity of the +reference node; and +is the element volume. +Viscous body force loading can be thought of as mass-proportional damping in the sense that it +gives a damping contribution proportional to the mass for an element if the coefficient +is chosen to +be a small value multiplied by the material density +. Viscous +body force loading provides an alternative way to define mass-proportional damping as a function of +relative velocities and a step-dependent damping coefficient. +Input File Usage: +Use the following option to define a viscous body force load: +*DLOAD, REF NODE=reference_node +element number or element set, VBF, magnitude +Abaqus/CAE Usage: +Viscous body force loads are not supported in Abaqus/CAE. +Specifying stagnation body force loads in Abaqus/Explicit +Stagnation body force loads are defined by +is the velocity of the point on the body where the body force is being applied; +is the stagnation body force applied to the body; +where +load; +of the reference node; and +is the element volume. The coefficient +excessive damping and a dramatic drop in the stable time increment. +is the factor, given as the magnitude of the +is the velocity +should be very small to avoid +Input File Usage: +Use the following option to define a stagnation body force load: +*DLOAD, REF NODE=reference_node +element number or element set, SBF, magnitude +Abaqus/CAE Usage: +Stagnation body force loads are not supported in Abaqus/CAE. +Specifying gravity loading +Gravity loading (uniform acceleration in a fixed direction) is specified by using the gravity distributed +load type and giving the gravity constant as the magnitude of the load. The direction of the gravity field +is specified by giving the components of the gravity vector in the distributed load definition. Abaqus +uses the user-specified material density , together with the magnitude and +direction, to calculate the loading. The magnitude of the gravity load can vary with time during a step +according to an amplitude definition, as described in “Prescribed conditions: overview,” Section 33.1.1. +However, the direction of the gravity field is always applied at the beginning of the step and remains +fixed during the step. +You need not specify an element or an element set as is customary for the specification of other +distributed loads. Abaqus/Standard and Abaqus/Explicit automatically collect all elements in the model +that have mass contributions (including point mass elements but excluding rigid elements) in an element +set called _Whole_Model_Gravity_Elset and apply the gravity loads to the elements in this +element set. Abaqus/CFD applies the gravity loading to all user-defined elements. +In Abaqus/CFD gravity loading defines the gravity vector used with a Boussinesq-type body force in +buoyancy driven flow. You must activate the energy equation for incompressible flow and define thermal +expansion to specify the thermal expansion coefficient . Gravity loading can be used only in conjunction +with the energy equation and will be ignored if used without the energy equation; general body forces +can be defined for incompressible flow without the energy equation. +When gravity loading is used with substructures, the density must be defined and unit gravity +load vectors must be calculated when the substructure is created . +Input File Usage: +Use the following option to define a gravity load: +*DLOAD +element number or element set, GRAV, gravity constant, comp1, comp2, comp3 +Abaqus/CAE Usage: +Load module: Create Load: choose Mechanical for the Category +and Gravity for the Types for Selected Step +Specifying loads due to rotation of the model in Abaqus/Standard +Centrifugal loads, Coriolis forces, rotary acceleration, and rotordynamic loads can be applied in +Abaqus/Standard by specifying the appropriate distributed load type in an element-based distributed +load definition. These loading options are primarily intended for replicating dynamic loads while +performing analyses other than implicit dynamics using direct integration (“Dynamic stress/displacement +analysis,” Section 6.3). +In an implicit dynamic procedure inertia loads due to rotations come about +naturally due to the equations of motion. Applying distributed centrifugal, Coriolis, rotary acceleration, +and rotordynamic loads in an implicit dynamic analysis may lead to non-physical loads and should be +used carefully. +Centrifugal loads +, where +, where +Centrifugal load magnitudes can be specified as +is the angular velocity in radians per +time. Abaqus/Standard uses the specified material density , together with +the load magnitude and the axis of rotation, to calculate the loading. Alternatively, a centrifugal load +magnitude can be given as +is the material density (mass per unit volume) for solid or shell +elements or the mass per unit length for beam elements and +is the angular velocity in radians per time. +This type of centrifugal load formulation does not account for large volume changes. The two centrifugal +load types will produce slightly different local results for first-order elements; +uses a consistent mass +matrix, and +uses a lumped mass matrix in calculating the load forces and load stiffnesses. +The magnitude of the centrifugal load can vary with time during a step according to an amplitude +definition, as described in “Prescribed conditions: overview,” Section 33.1.1. However, the position and +orientation of the axis around which the structure rotates, which is defined by giving a point on the axis +and the axis direction, are always applied at the beginning of the step and remain fixed during the step. +Input File Usage: +Use either of the following options to define a centrifugal load: +*DLOAD +element number or element set, CENTRIF, +comp2, comp3 +*DLOAD +element number or element set, CENT, +comp2, comp3 +, coord1, coord2, coord3, comp1, +, coord1, coord2, coord3, comp1, +Abaqus/CAE Usage: +Load module: Create Load: choose Mechanical for the Category +and Rotational body force for the Types for Selected +Step: Load effect: Centrifugal +Coriolis forces +, where +Coriolis force is defined by specifying the Coriolis distributed load type and giving the load magnitude +as +is the material density (mass per unit volume) for solid and shell elements or the mass +per unit length for beam elements and +is the angular velocity in radians per time. The magnitude of +the Coriolis load can vary with time during a step according to an amplitude definition, as described in +“Prescribed conditions: overview,” Section 33.1.1. However, the position and orientation of the axis +around which the structure rotates, which is defined by giving a point on the axis and the axis direction, +are always applied at the beginning of the step and remain fixed during the step. +In a static analysis Abaqus computes the translational velocity term in the Coriolis loading by +dividing the incremental displacement by the current time increment. +The Coriolis load formulation does not account for large volume changes. +Input File Usage: +Use the following option to define a Coriolis load: +*DLOAD +element number or element set, CORIO, +comp1, comp2, comp3 +, coord1, coord2, coord3, +Abaqus/CAE Usage: +Load module: Create Load: choose Mechanical for the Category +and Coriolis force for the Types for Selected Step +Rotary acceleration loads +Rotary acceleration loads are defined by specifying the rotary acceleration distributed load type and +, in radians/time2, which includes any precessional motion +giving the rotary acceleration magnitude, +effects. The axis of rotary acceleration must be defined by giving a point on the axis and the axis direction. +Abaqus/Standard uses the specified material density , together with the +rotary acceleration magnitude and axis of rotary acceleration, to calculate the loading. The magnitude of +the load can vary with time during a step according to an amplitude definition, as described in “Prescribed +conditions: overview,” Section 33.1.1. However, the position and orientation of the axis around which +the structure rotates are always applied at the beginning of the step and remain fixed during the step. +Rotary acceleration loads are not applicable to axisymmetric elements. +Input File Usage: +Use the following option to define a rotary acceleration load: +*DLOAD +element number or element set, ROTA, +comp1, comp2, comp3 +, coord1, coord2, coord3, +Abaqus/CAE Usage: +Load module: Create Load: choose Mechanical for the Category +and Rotational body force for the Types for Selected Step: +Load effect: Rotary acceleration +Specifying general rigid-body acceleration loading in Abaqus/Standard +General rigid-body acceleration loading can be specified in Abaqus/Standard by using a combination of +the gravity, centrifugal ( +), and rotary acceleration load types. +Rotordynamic loads in a fixed reference frame +Rotordynamic loads can be used to study the vibrational response of three-dimensional models of +axisymmetric structures, such as a flywheel in a hybrid energy storage system, that are spinning about +their axes of symmetry in a fixed reference frame . This is in contrast to the centrifugal +loads, Coriolis forces, and rotary acceleration loads discussed above, which are formulated in a rotating +frame. Rotordynamic loads are, therefore, not intended to be used in conjunction with these other +dynamic load types. +The intended workflow for rotordynamic loads is to define the load in a nonlinear static step to +establish the centrifugal load effects and load stiffness terms associated with a spinning body. The +nonlinear static step can then be followed by a sequence of linear dynamic analyses such as complex +eigenvalue extraction and/or a subspace or direct-solution steady-state dynamic analysis to study +complex dynamic behaviors (induced by gyroscopic moments) such as critical speeds, unbalanced +responses, and whirling phenomena in rotating structures. You do not need to redefine the rotordynamic +load in the linear dynamic analyses—the load definition is carried over from the nonlinear static step. +The contribution of the gyroscopic matrices in the linear dynamic steps is unsymmetric; therefore, you +must use unsymmetric matrix storage as described in “Defining an analysis,” Section 6.1.2, during +these steps. +Rotordynamic loads are intended only for three-dimensional models of axisymmetric bodies; +you must ensure that this modeling assumption is met. Rotordynamic loads are supported for all +three-dimensional continuum and cylindrical elements, shell elements, membrane elements, cylindrical +membrane elements, beam elements, and rotary inertia elements. The spinning axis defined as part of +the load must be the axis of symmetry for the structure. Therefore, beam elements must be aligned with +the symmetry axis. In addition, one of the principal directions of each loaded rotary inertia element +must be aligned with the symmetry axis, and the inertia components of the rotary inertia elements must +be symmetric about this axis. Multiple spinning structures spinning about different axes can be modeled +in the same step. The spinning structures can also be connected to non-axisymmetric, non-rotating +structures (such as bearings or support structures). +Rotordynamic loads are defined by specifying the angular velocity, +, in radians per time. The +magnitude of the rotordynamic load can vary with time during a step according to an amplitude definition, +as described in “Prescribed conditions: overview,” Section 33.1.1. However, the position and orientation +of the axis around which the structure rotates, which is defined by giving a point on the axis and the axis +direction, are always applied at the beginning of the step and remain fixed during the step. +Input File Usage: +Use the following option to define a rotordynamic load: +*DLOAD +element number or element set, ROTDYNF, +comp1, comp2, comp3 +, coord1, coord2, coord3, +Abaqus/CAE Usage: +Element-based rotordynamic loads are not supported in Abaqus/CAE. +Specifying porous drag body force load in Abaqus/CFD +In Abaqus/CFD porous drag loading defines the porous drag body forces (Darcy and inertial drag forces) +in flow through porous media . +If the +porous drag body forces are activated, permeability of the medium must be defined . +flow problems involving heat transfer, the properties of both the solid and fluid phases of the porous +medium must be defined using a fluid section definition. Porous drag loads are defined by specifying +the dimensionless porosity, +(ratio of the fluid to the total volume of the porous medium). +Input File Usage: +Use the following option to define a porous drag body force load: +*DLOAD +element number or element set, PDBF, porosity +Abaqus/CAE Usage: +Load module: Create Load: choose Fluid for the Category and Porous +drag body force for the Types for Selected Step +Surface tractions and pressure loads +General or shear surface tractions and pressure loads can be applied in Abaqus as element-based or +surface-based distributed loads. The units of these loads are force per unit area. +Table 33.4.3–3 lists all of the distributed surface load types that are available in Abaqus, along with +the corresponding load type labels. Part VI, “Elements,” lists the distributed surface load types that +are available for particular elements and the Abaqus/CAE load support for each load type. For some +element-based loads you must identify the face of the element upon which the load is prescribed in the +load type label (for example, Pn or PnNU for continuum elements). +Follower surface loads +With the exception of general surface tractions, all +By definition, the line of action of a follower surface load rotates with the surface in a geometrically +nonlinear analysis. This is in contrast to a non-follower load, which always acts in a fixed global direction. +the distributed surface loads listed in +Table 33.4.3–3 are modeled as follower loads. The hydrostatic and viscous pressures listed in +Table 33.4.3–3 always act normal to the surface in the current configuration, the shear tractions always +act tangent to the surface in the current configuration, and the internal and external pipe pressures follow +the motion of the pipe elements. +General surface tractions can be specified to be follower or non-follower loads. There is no +difference between a follower and a non-follower load in a geometrically linear analysis since the +configuration of the body remains fixed. The difference between a follower and non-follower general +surface traction is illustrated in the next section through an example. +Input File Usage: +Use one of the following options to define general surface tractions as follower +loads (the default): +*DLOAD, FOLLOWER=YES +*DSLOAD, FOLLOWER=YES +Use one of the following options to define general surface tractions as non- +follower loads: +*DLOAD, FOLLOWER=NO +*DSLOAD, FOLLOWER=NO +Load module: Create Load: choose Mechanical for the Category +and Surface traction for the Types for Selected Step: Traction: +General, toggle on or off Follow rotation +Abaqus/CAE Usage: +Table 33.4.3–3 Distributed surface load types. +Load description +Load type label +for element-based +loads +Load type label +for surface-based +loads +Abaqus/CAE +load type +General surface traction +TRVECn, TRVEC +TRVEC +Surface traction +Shear surface traction +TRSHRn, TRSHR +TRSHR +Nonuniform general surface +traction +Nonuniform shear surface +traction +Pressure +Nonuniform pressure +Hydrostatic pressure (available +only in Abaqus/Standard) +Viscous pressure (available +only in Abaqus/Explicit) +Stagnation pressure (available +only in Abaqus/Explicit) +Hydrostatic internal and +external pressure (only for PIPE +and ELBOW elements ) +Uniform internal and external +pressure (only for PIPE and +ELBOW elements ) +Nonuniform internal and +external pressure (only for PIPE +and ELBOW elements ) +TRVECnNU, +TRVECNU +TRSHRnNU, +TRSHRNU +Pn, P +PnNU, PNU +HPn, HP +VPn, VP +SPn, SP +HPI, HPE +PI, PE +TRVECNU +TRSHRNU +Surface traction +(surface-based +loads only) +Pressure +Pressure +(surface-based +loads only) +Pipe pressure +PNU +HP +VP +SP +N/A +N/A +PINU, PENU +N/A +Specifying general surface tractions +General surface tractions allow you to specify a surface traction, +load, +, is computed by integrating +over S: +, acting on a surface S. The resultant +where +specify both a load magnitude, +is the magnitude and is the direction of the load. To define a general surface traction, you must +, and the direction of the load with respect to the reference configuration, +. The magnitude and direction can also be specified in user subroutine UTRACLOAD. The specified +traction directions are normalized by Abaqus and, thus, do not contribute to the magnitude of the load: +Input File Usage: +Use one of the following options to define a general surface traction: +*DLOAD +element number or element set, load type label, magnitude, +direction components +where load type label is TRVECn, TRVEC, TRVECnNU, or TRVECNU. +*DSLOAD +surface name, TRVEC or TRVECNU, magnitude, direction components +Abaqus/CAE Usage: +Use the following input to define an element-based general surface traction: +Load module: Create Load: choose Mechanical for the Category +and Surface traction for the Types for Selected Step: Traction: +General, Distribution: select an analytical field +Use the following input to define a surface-based general surface traction: +Load module: Create Load: choose Mechanical for the Category +and Surface traction for the Types for Selected Step: Traction: +General, Distribution: Uniform or User-defined +Nonuniform element-based general surface traction is not supported in +Abaqus/CAE. +Defining the direction vector with respect to a local coordinate system +By default, the components of the traction vector are specified with respect to the global directions. You +can also refer to a local coordinate system for the direction components +of these tractions. See “Examples: using a local coordinate system to define shear directions” below for +an example of a traction load defined with respect to a local coordinate system. +Input File Usage: +Use one of the following options to specify a local coordinate system: +Abaqus/CAE Usage: +*DLOAD, ORIENTATION=name +*DSLOAD, ORIENTATION=name +Load module: Create Load: choose Mechanical for the Category and +Surface traction for the Types for Selected Step: select CSYS: Picked and +click Edit to pick a local coordinate system, or select CSYS: User-defined +to enter the name of a user subroutine that defines a local coordinate system +Rotation of the traction vector direction +The traction load acts in the fixed direction +in a geometrically linear analysis or if a non-follower +load is specified in a geometrically nonlinear analysis (which includes a perturbation step about a +geometrically nonlinear base state). +If a follower load is specified in a geometrically nonlinear analysis, the traction load rotates rigidly +, +with the surface using the following algorithm. The reference configuration traction vector, +is decomposed by Abaqus into two components: a normal component, +and a tangential component, +where +The applied traction in the current configuration is then computed as +is the unit reference surface normal and +is the unit projection of +onto the reference surface. +where +the current surface; i.e., +decomposition of the local two-dimensional surface deformation gradient +is the normal to the surface in the current configuration and +, where +rotated onto +is the standard rotation tensor obtained from the polar +is the image of +. +Examples: follower and non-follower tractions +The following two examples illustrate the difference between applying follower and non-follower +tractions in a geometrically nonlinear analysis. Both examples refer to a single 4-node plane strain +element (element 1). +In Step 1 of the first example a follower traction load is applied to face 1 of +element 1, and a non-follower traction load is applied to face 2 of element 1. The element is rotated +rigidly 90° counterclockwise in Step 1 and then another 90° in Step 2. As illustrated in Figure 33.4.3–1, +the follower traction rotates with face 1, while the non-follower traction on face 2 always acts in the +global x-direction. +*STEP, NLGEOM +Step 1 - Rotate square 90 degrees +... +*DLOAD, FOLLOWER=YES +1, TRVEC1, 1., 0., -1., 0. +*DLOAD, FOLLOWER=NO +1, TRVEC2, 1., 1., 0., 0. +*END STEP +*STEP, NLGEOM +(a) +(b) +(c) +follower traction +non-follower traction +Figure 33.4.3–1 Follower and non-follower traction loads in a +geometrically nonlinear analysis, load applied in Step 1: (a) beginning +of Step 1; (b) end of Step 1, beginning of Step 2; (c) end of Step 2. +Step 2 - Rotate square another 90 degrees +... +*END STEP +In the second example the element is rotated 90° counterclockwise with no load applied in Step 1. +In Step 2 a follower traction load is applied to face 1, and a non-follower traction load is applied to face 2. +The element is then rotated rigidly by another 90°. The direction of the follower load is specified with +respect to the original configuration. As illustrated in Figure 33.4.3–2, the follower traction rotates with +face 1, while the non-follower traction on face 2 always acts in the global x-direction. +*STEP, NLGEOM +Step 1 - Rotate square 90 degrees +... +*END STEP +*STEP, NLGEOM +Step 2 - Rotate square another 90 degrees +*DLOAD, FOLLOWER=YES +1, TRVEC1, 1., 0., -1., 0. +*DLOAD, FOLLOWER=NO +1, TRVEC2, 1., 1., 0., 0. +... +*END STEP +(a) +(b) +(c) +follower traction +non-follower traction +Figure 33.4.3–2 Follower and non-follower traction loads in a +geometrically nonlinear analysis, load applied in Step 2: (a) beginning +of Step 1; (b) end of Step 1, beginning of Step 2; (c) end of Step 2. +Specifying shear surface tractions +Shear surface tractions allow you to specify a surface force per unit area, +S. The resultant load, +, is computed by integrating +over S: +, that acts tangent to a surface +is the magnitude and +where +traction, you must provide both the magnitude, +and direction vector can also be specified in user subroutine UTRACLOAD. +is a unit vector along the direction of the load. To define a shear surface +, for the load. The magnitude +, and a direction, +Abaqus modifies the traction direction by first projecting the user-specified vector, +, onto the +surface in the reference configuration, +where +direction +is the reference surface normal. The specified traction is applied along the computed traction +tangential to the surface: +Consequently, a shear traction load is not applied at any point where +surface. +is normal to the reference +The shear traction load acts in the fixed direction +in a geometrically linear analysis. In +a geometrically nonlinear analysis (which includes a perturbation step about a geometrically nonlinear +base state), the shear traction vector will rotate rigidly; i.e., +is the standard rotation +tensor obtained from the polar decomposition of the local two-dimensional surface deformation gradient +, where +. +Input File Usage: +Use one of the following options to define a shear surface traction: +*DLOAD +element number or element set, load type label, magnitude, +direction components +where load type label is TRSHRn, TRSHR, TRSHRnNU, or TRSHRNU. +*DSLOAD +surface name, TRSHR or TRSHRNU, magnitude, direction components +Abaqus/CAE Usage: +Use the following input to define an element-based shear surface traction: +Load module: Create Load: choose Mechanical for the Category +and Surface traction for the Types for Selected Step: Traction: +Shear, Distribution: select an analytical field +Use the following input to define a surface-based general surface traction: +Load module: Create Load: choose Mechanical for the Category +and Surface traction for the Types for Selected Step: Traction: +Shear, Distribution: Uniform or User-defined +Nonuniform element-based shear surface traction is not supported in +Abaqus/CAE. +Defining the direction vector with respect to a local coordinate system +By default, the components of the shear traction vector are specified with respect to the global directions. +You can also refer to a local coordinate system for the direction +components of these tractions. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options to specify a local coordinate system: +*DLOAD, ORIENTATION=name +*DSLOAD, ORIENTATION=name +Load module: Create Load: choose Mechanical for the Category and +Surface traction for the Types for Selected Step: select CSYS: Picked and +click Edit to pick a local coordinate system, or select CSYS: User-defined +to enter the name of a user subroutine that defines a local coordinate system +Examples: using a local coordinate system to define shear directions +It is sometimes convenient to give shear and general traction directions with respect to a local coordinate +system. The following two examples illustrate the specification of the direction of a shear traction on a +cylinder using global coordinates in one case and a local cylindrical coordinate system in the other case. +defined on the outside of the cylinder. +DISTRIBUTED LOADS +In the first example the direction of the shear traction, +, is given in global +The sense of the resulting shear tractions using global coordinates is shown in +coordinates. +Figure 33.4.3–3(a). +(a) +(b) +Figure 33.4.3–3 Shear tractions specified using global coordinates +(a) and a local cylindrical coordinate system (b). +*STEP +Step 1 - Specify shear directions in global coordinates +... +*DSLOAD +SURFA, TRSHR, 1., 0., 1., 0. +... +*END STEP +In the second example the direction of the shear traction, +, is given with respect +to a local cylindrical coordinate system whose axis coincides with the axis of the cylinder. The sense of +the resulting shear tractions using the local cylindrical coordinate system is shown in Figure 33.4.3–3(b). +*ORIENTATION, NAME=CYLIN, SYSTEM=CYLINDRICAL +0., 0., 0., 0., 0., 1. +... +*STEP +Step 1 - Specify shear directions in local cylindrical coordinates +... +*DSLOAD, ORIENTATION=CYLIN +SURFA, TRSHR, 1., 0., 1., 0. +... +*END STEP +Resultant loads due to surface tractions +You can choose to integrate surface tractions over the current or the reference configuration by specifying +whether or not a constant resultant should be maintained. +In general, the constant resultant method is best suited for cases where the magnitude of the resultant +load should not vary with changes in the surface area. However, it is up to you to decide which approach +is best for your analysis. An example of an analysis using a constant resultant can be found in “Distributed +traction and edge loads,” Section 1.4.18 of the Abaqus Verification Manual. +Choosing not to have a constant resultant +If you choose not to have a constant resultant, the traction vector is integrated over the surface in the +current configuration, a surface that in general deforms in a geometrically nonlinear analysis. By default, +all surface tractions are integrated over the surface in the current configuration. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options: +*DLOAD, CONSTANT RESULTANT=NO +*DSLOAD, CONSTANT RESULTANT=NO +Load module: Create Load: choose Mechanical for the Category +and Surface traction for the Types for Selected Step: Traction +is defined per unit deformed area +Maintaining a constant resultant +If you choose to have a constant resultant, the traction vector is integrated over the surface in the reference +configuration and then held constant. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options: +*DLOAD, CONSTANT RESULTANT=YES +*DSLOAD, CONSTANT RESULTANT=YES +Load module: Create Load: choose Mechanical for the Category +and Surface traction for the Types for Selected Step: Traction +is defined per unit undeformed area +Example +The constant resultant method has certain advantages when a traction is used to model a distributed load +with a known constant resultant. Consider the case of modeling a uniform dead load, magnitude p, acting +on a flat plate whose normal is in the +-direction in a geometrically nonlinear analysis (Figure 33.4.3–4). +e 2 +e 1 +deformed configuration +Figure 33.4.3–4 Dead load on a flat plate. +Such a model might be used to simulate a snow load on a flat roof. The snow load could be modeled as +a distributed dead traction load +and S denote the total surface area of the plate in the +reference and current configurations, respectively. With no constant resultant, the total integrated load +on the plate, +. Let +, is +In this case a uniform traction leads to a resultant load that increases as the surface area of the plate +increases, which is not consistent with a fixed snow load. With the constant resultant method, the total +integrated load on the plate is +In this case a uniform traction leads to a resultant that is equal to the pressure times the surface area in +the reference configuration, which is more consistent with the problem at hand. +Specifying pressure loads +Distributed pressure loads can be specified on any two-dimensional, three-dimensional, or axisymmetric +elements. Hydrostatic pressure loads can be specified in Abaqus/Standard on two-dimensional, three- +dimensional, and axisymmetric elements. Viscous and stagnation pressure loads can be specified in +Abaqus/Explicit on any elements. +Distributed pressure loads +Distributed pressure loads can be specified on any elements. For beam elements, a positive applied +pressure results in a force vector acting along the particular local direction of the section or a global +direction, whichever is specified. For conventional shell elements, the force vector points along the +element SPOS normal. For continuum solid or a continuum shell elements with the distributed load on +an explicitly identified facet, the force vector acts against the outward normal of that facet. Distributed +pressure loads are not supported for pipe and elbow elements. +Distributed pressure loads can be specified on a surface formed over elements; a positive applied +pressure results in a force vector acting against the local surface normal. +Input File Usage: +Use one of the following options to define a pressure load: +*DLOAD +element number or element set, load type label, magnitude +where load type label is Pn, P, PnNU, or PNU. +*DSLOAD +surface name, P or PNU, magnitude +Abaqus/CAE Usage: +Use the following input to define an element-based pressure load: +Load module: Create Load: choose Mechanical for the Category +and Pressure for the Types for Selected Step: Distribution: +select an analytical field or a discrete field +Use the following input to define a surface-based pressure load: +Load module: Create Load: choose Mechanical for the Category and +Pressure for the Types for Selected Step: Uniform or User-defined +Nonuniform element-based pressure loads are not supported in Abaqus/CAE. +Hydrostatic pressure loads on two-dimensional, three-dimensional, and axisymmetric elements in +Abaqus/Standard +To define hydrostatic pressure in Abaqus/Standard, give the Z-coordinates of the zero pressure level +(point a in Figure 33.4.3–5) and the level at which the hydrostatic pressure is defined (point b in +Figure 33.4.3–5) in an element-based or surface-based distributed load definition. For levels above the +zero pressure level, the hydrostatic pressure is zero. +Figure 33.4.3–5 Hydrostatic pressure distribution. +In planar elements the hydrostatic head is in the Y-direction; for axisymmetric elements the +Z-direction is the second coordinate. +Input File Usage: +Use one of the following options to define a hydrostatic pressure load: +*DLOAD +element number or element set, HPn or HP, magnitude, Z-coordinate of point a, +Z-coordinate of point b +*DSLOAD +surface name, HP, magnitude, Z-coordinate of point a, +Z-coordinate of point b +Abaqus/CAE Usage: +Use the following input to define a surface-based hydrostatic pressure load: +Load module: Create Load: choose Mechanical for the Category and +Pressure for the Types for Selected Step: Distribution: Hydrostatic +Element-based hydrostatic pressure loads are not supported in Abaqus/CAE. +Viscous pressure loads in Abaqus/Explicit +Viscous pressure loads are defined by +where p is the pressure applied to the body; +the velocity of the point on the surface where the pressure is being applied; +reference node; and +is the unit outward normal to the element at the same point. +is the viscosity, given as the magnitude of the load; +is +is the velocity of the +Viscous pressure loading is most commonly applied in structural problems when you want to damp +out dynamic effects and, thus, reach static equilibrium in a minimal number of increments. A common +example is the determination of springback in a sheet metal product after forming, in which case a viscous +pressure would be applied to the faces of shell elements defining the sheet metal. An appropriate choice +for the value of +is important for using this technique effectively. +To compute +, consider the infinite continuum elements described in “Infinite elements,” +Section 28.3.1. In explicit dynamics those elements achieve an infinite boundary condition by applying +a viscous normal pressure where the coefficient +is the density of the material at +the surface, and +is the value of the dilatational wave speed in the material (the infinite continuum +elements also apply a viscous shear traction). For an isotropic, linear elastic material +is given by +; +and +are Lamé’s constants, E is Young’s modulus, and +where +is Poisson’s ratio. This choice of +the viscous pressure coefficient represents a level of damping in which pressure waves crossing the free +surface are absorbed with no reflection of energy back into the interior of the finite element mesh. +For typical structural problems it is not desirable to absorb all of the energy (as is the case in the +as an +coefficient should have a positive value. +infinite elements). Typically +effective way of minimizing ongoing dynamic effects. The +is set equal to a small percentage (perhaps 1 or 2 percent) of +Input File Usage: +Use one of the following options to define a viscous pressure load: +*DLOAD, REF NODE=reference_node +element number or element set, VPn or VP, magnitude +*DSLOAD, REF NODE=reference_node +surface name, VP, magnitude +Abaqus/CAE Usage: +Use the following input to define a surface-based viscous pressure load: +Load module: Create Load: choose Mechanical for the Category and +Pressure for the Types for Selected Step: Distribution: Viscous, +toggle on or off Determine velocity from reference point +Element-based viscous pressure loads are not supported in Abaqus/CAE. +Stagnation pressure loads in Abaqus/Explicit +Stagnation pressure loads are defined by +is the stagnation pressure applied to the body; +where +load; +normal to the element at the same point; and +is the factor, given as the magnitude of the +is the unit outward +is the velocity of the reference node. The coefficient +is the velocity of the point on the surface where the pressure is being applied; +should be very small to avoid excessive damping and a dramatic drop in the stable time increment. +Input File Usage: +Use one of the following options to define a stagnation pressure load: +*DLOAD, REF NODE=reference_node +element number or element set, SPn or SP, magnitude +*DSLOAD, REF NODE=reference_node +element number or element set, SP, magnitude +Abaqus/CAE Usage: +Use the following input to define a surface-based stagnation pressure load: +Load module: Create Load: choose Mechanical for the Category and +Pressure for the Types for Selected Step: Distribution: Stagnation, +toggle on or off Determine velocity from reference point +Element-based stagnation pressure loads are not supported in Abaqus/CAE. +Pressure on pipe and elbow elements +You can specify external pressure, internal pressure, external hydrostatic pressure, or internal hydrostatic +pressure on pipe or elbow elements. When pressure loads are applied, the effective outer or inner diameter +must be specified in the element-based distributed load definition. +The loads resulting from the pressure on the ends of the element are included: Abaqus assumes +a closed-end condition. Closed-end conditions correctly model the loading at pipe intersections, tight +bends, corners, and cross-section changes; in straight sections and smooth bends the end loads of adjacent +elements cancel each other precisely. If an open-end condition is to be modeled, a compensating point +load should be added at the open end. A case where such an end load must be applied occurs if a +pressurized pipe is modeled with a mixture of pipe and beam elements. In that case closed-end conditions +generate a physically non-existing force at the transition between pipe and beam elements. Such mixed +modeling of a pipe is not recommended. +For pipe elements subjected to pressure loading, the effective axial force due to the pressure loads +can be obtained by requesting output variable ESF1 . +DISTRIBUTED LOADS +Use the following option to define an external pressure load on pipe or elbow +elements: +*DLOAD +element number or element set, PE or PENU, magnitude, +effective outer diameter +Use the following option to define an internal pressure load on pipe or elbow +elements: +*DLOAD +element number or element set, PI or PINU, magnitude, effective inner diameter +Use the following option to define an external hydrostatic pressure load on pipe +or elbow elements: +*DLOAD +element number or element set, HPE, magnitude, effective outer diameter +Use the following option to define an internal hydrostatic pressure load on pipe +or elbow elements: +*DLOAD +element number or element set, HPI, magnitude, effective inner diameter +Abaqus/CAE Usage: +Use the following input to define an external or internal pressure load on pipe +or elbow elements: +Load module: Create Load: choose Mechanical for the Category and Pipe +pressure for the Types for Selected Step: Side: External or Internal, +Distribution: Uniform, User-defined, or select an analytical field +Use the following input to define an external or internal hydrostatic pressure +load on pipe or elbow elements: +Load module: Create Load: choose Mechanical for the Category +and Pipe pressure for the Types for Selected Step: Side: External +or Internal, Distribution: Hydrostatic +Defining distributed surface loads on plane stress elements +Plane stress theory assumes that the volume of a plane stress element remains constant in a large-strain +analysis. When a distributed surface load is applied to an edge of plane stress elements, the current length +and orientation of the edge are considered in the load distribution, but the current thickness is not; the +original thickness is used. +This limitation can be circumvented only by using three-dimensional elements at the edge so that +a change in thickness upon loading is recognized; suitable equation constraints (“Linear constraint +equations,” Section 34.2.1) would be required to make the in-plane displacements on the two faces of +these elements equal. Three-dimensional elements along an edge can be connected to interior shell +elements by using a shell-to-solid coupling constraint . +Edge tractions and moments on shell elements and line loads on beam elements +Distributed edge tractions (general, shear, normal, or transverse) and edge moments can be applied to +shell elements in Abaqus as element-based or surface-based distributed loads. The units of an edge +traction are force per unit length. The units of an edge moment are torque per unit length. References to +local coordinate systems are ignored for all edge tractions and moments except general edge tractions. +Distributed line loads can be applied to beam elements in Abaqus as element-based distributed +loads. The units of a line load are force per unit length. +Table 33.4.3–4 lists all of the distributed edge and line load types that are available in Abaqus, +along with the corresponding load type labels. Part VI, “Elements,” lists the distributed edge and line +load types that are available for particular elements and the Abaqus/CAE load support for each load type. +For element-based loads applied to shell elements, you must identify the edge of the element upon which +the load is prescribed in the load type label (for example, EDLDn or EDLDnNU). +Follower edge and line loads +By definition, the line of action of a follower edge or line load rotates with the edge or line in a +geometrically nonlinear analysis. This is in contrast to a non-follower load, which always acts in a fixed +global direction. +With the exception of general edge tractions on shell elements and the forces per unit length in the +global directions on beam elements, all the edge and line loads listed in Table 33.4.3–4 are modeled as +follower loads. The normal, shear, and transverse edge loads listed in Table 33.4.3–4 act in the normal, +shear, and transverse directions, respectively, in the current configuration . The +edge moment always acts about the shell edge in the current configuration. The forces per unit length in +the local beam directions rotate with the beam elements. +Table 33.4.3–4 Distributed edge load types. +Load description +General edge traction +Normal edge traction +Shear edge traction +Transverse edge traction +Edge moment +Load type label +for element-based +loads +Load type label +for surface-based +loads +Abaqus/CAE +load type +Shell edge +load +EDLDn +EDNORn +EDSHRn +EDTRAn +EDMOMn +EDLD +EDNOR +EDSHR +EDTRA +EDMOM +Load description +Load type label +for element-based +loads +Load type label +for surface-based +loads +Abaqus/CAE +load type +Nonuniform general edge traction +EDLDnNU +Nonuniform normal edge traction +EDNORnNU +Nonuniform shear edge traction +EDSHRnNU +Nonuniform transverse edge +traction +EDTRAnNU +EDLDNU +EDNORNU +EDSHRNU +EDTRANU +Nonuniform edge moment +EDMOMnNU +EDMOMNU +Shell +edge load +(surface-based +loads only) +PX, PY, PZ +N/A +Line load +Force per unit length in global +X-, Y-, and Z-directions (only for +beam elements) +Nonuniform force per unit length +in global X-, Y-, and Z-directions +(only for beam elements) +Force per unit length in beam local +1- and 2-directions (only for beam +elements) +P1, P2 +PXNU, PYNU, +PZNU +N/A +N/A +Nonuniform force per unit length +in beam local 1- and 2-directions +(only for beam elements) +P1NU, P2NU +N/A +The forces per unit length in the global directions on beam elements are always non-follower loads. +General edge tractions can be specified to be follower or non-follower loads. There is no difference +between a follower and a non-follower load in a geometrically linear analysis since the configuration of +the body remains fixed. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options to define general edge tractions as follower +loads (the default): +*DLOAD, FOLLOWER=YES +*DSLOAD, FOLLOWER=YES +Use one of the following options to define general edge tractions as +non-follower loads: +*DLOAD, FOLLOWER=NO +*DSLOAD, FOLLOWER=NO +Load module: Create Load: choose Mechanical for the Category +and Shell edge load for the Types for Selected Step: Traction: +General, toggle on or off Follow rotation +EDTRA +EDTRA +EDSHR +EDNOR +EDTRA +EDNOR +EDTRA +EDNOR +EDSHR +EDNOR +EDSHR +EDSHR +EDTRA +EDTRA +EDSHR +EDNOR +EDSHR +EDTRA +EDNOR +EDNOR +EDSHR +Figure 33.4.3–6 Positive edge loads. +Specifying general edge tractions +General edge tractions allow you to specify an edge load, +, is computed by integrating +over L: +, acting on a shell edge, L. The resultant load, +To define a general edge traction, you must provide both a magnitude, +, for +the load. The specified load directions are normalized by Abaqus; thus, they do not contribute to the +magnitude of the load. +, and direction, +If a nonuniform general edge traction is specified, the magnitude, +, and direction, +, must be +specified in user subroutine UTRACLOAD. +Input File Usage: +Use one of the following options to define a general edge traction: +*DLOAD +element number or element set, EDLDn or EDLDnNU, magnitude, +direction components +*DSLOAD +surface name, EDLD or EDLDNU, magnitude, direction components +Abaqus/CAE Usage: +Use the following input to define an element-based general edge traction: +Load module: Create Load: choose Mechanical for the Category +and Shell edge load for the Types for Selected Step: Traction: +General, Distribution: select an analytical field +Use the following input to define a surface-based general edge traction: +Load module: Create Load: choose Mechanical for the Category +and Shell edge load for the Types for Selected Step: Traction: +General, Distribution: Uniform or User-defined +Nonuniform element-based general edge traction is not supported in +Abaqus/CAE. +Rotation of the load vector +In a geometrically linear analysis the edge load, +, acts in the fixed direction defined by +If a non-follower load is specified in a geometrically nonlinear analysis (which includes a +, acts in the fixed direction +perturbation step about a geometrically nonlinear base state), the edge load, +defined by +If a follower load is specified in a geometrically nonlinear analysis (which includes a perturbation +step about a geometrically nonlinear base state), the components must be defined with respect to the +reference configuration. The reference edge traction is defined as +The applied edge traction, +, is computed by rigidly rotating +onto the current edge. +Defining the direction vector with respect to a local coordinate system +By default, the components of the edge traction vector are specified with respect to the global directions. +You can also refer to a local coordinate system for the direction +components of these tractions. +Input File Usage: +Use one of the following options to specify a local coordinate system: +Abaqus/CAE Usage: +*DLOAD, ORIENTATION=name +*DSLOAD, ORIENTATION=name +Load module: Create Load: choose Mechanical for the Category and Shell +edge load for the Types for Selected Step: select CSYS: Picked and click +Edit to pick a local coordinate system, or select CSYS: User-defined to +enter the name of a user subroutine that defines a local coordinate system +Specifying shear, normal, and transverse edge tractions +The loading directions of shear, normal, and transverse edge tractions are determined by the underlying +elements. A positive shear edge traction acts in the positive direction of the shell edge as determined +by the element connectivity. A positive normal edge traction acts in the plane of the shell in the inward +direction. A positive transverse edge traction acts in a sense opposite to the facet normal. The directions +of positive shear, normal, and transverse edge tractions are shown in Figure 33.4.3–6. +To define a shear, normal, or transverse edge traction, you must provide a magnitude, +If a nonuniform shear, normal, or transverse edge traction is specified, the magnitude, +for the load. +, must be +specified in user subroutine UTRACLOAD. +In a geometrically linear step, the shear, normal, and transverse edge tractions act in the tangential, +normal, and transverse directions of the shell, as shown in Figure 33.4.3–6. In a geometrically nonlinear +analysis the shear, normal, and transverse edge tractions rotate with the shell edge so they always act in +the tangential, normal, and transverse directions of the shell, as shown in Figure 33.4.3–6. +Input File Usage: +Use one of the following options to define a directed edge traction: +*DLOAD +element number or element set, directed edge traction label, magnitude +*DSLOAD +surface name, directed edge traction label, magnitude +For element-based loads the directed edge traction label can be EDSHRn or +EDSHRnNU for shear edge tractions, EDNORn or EDNORnNU for normal +edge tractions, or EDTRAn or EDTRAnNU for transverse edge tractions. +For surface-based loads the directed edge traction label can be EDSHR or +EDSHRNU for shear edge tractions, EDNOR or EDNORNU for normal edge +tractions, or EDTRA or EDTRANU for transverse edge tractions. +Abaqus/CAE Usage: +Use the following input to define an element-based directed edge traction: +Load module: Create Load; choose Mechanical for the Category and +Shell edge load for the Types for Selected Step; Traction: Normal, +Transverse, or Shear; Distribution: select an analytical field +Use the following input to define a surface-based directed edge traction: +Load module: Create Load; choose Mechanical for the Category and +Shell edge load for the Types for Selected Step; Traction: Normal, +Transverse, or Shear; Distribution: Uniform or User-defined +Nonuniform element-based directed edge traction is not supported in +Abaqus/CAE. +Specifying edge moments +An edge moment acts about the shell edge with the positive direction determined by the element +connectivity. The directions of positive edge moments are shown in Figure 33.4.3–7. +Figure 33.4.3–7 Positive edge moments. +To define a distributed edge moment, you must provide a magnitude, +If a nonuniform edge moment is specified, the magnitude, +, for the load. +, must be specified in user subroutine +UTRACLOAD. +An edge moment always acts about the current shell edge in both geometrically linear and nonlinear +analyses. +In a geometrically linear step an edge moment acts about the shell edge as shown in Figure 33.4.3–7. +In a geometrically nonlinear analysis an edge moment always acts about the shell edge as shown in +Figure 33.4.3–7. +Input File Usage: +Use one of the following options to define an edge moment: +*DLOAD +element number or element set, EDMOMn or EDMOMnNU, magnitude +*DSLOAD +surface name, EDMOM or EDMOMNU, magnitude +Abaqus/CAE Usage: +Use the following input to define an element-based edge moment: +Load module: Create Load: choose Mechanical for the Category +and Shell edge load for the Types for Selected Step: Traction: +Moment, Distribution: select an analytical field +Use the following input to define a surface-based edge moment: +Load module: Create Load: choose Mechanical for the Category +and Shell edge load for the Types for Selected Step: Traction: +General, Distribution: Uniform or User-defined +Nonuniform element-based edge moments are not supported in Abaqus/CAE. +Resultant loads due to edge tractions and moments +You can choose to integrate edge tractions and moments over the current or the reference configuration +by specifying whether or not a constant resultant should be maintained. In general, the constant resultant +method is best suited for cases where the magnitude of the resultant load should not vary with changes +in the edge length. However, it is up to you to decide which approach is best for your analysis. +Choosing not to have a constant resultant +If you choose not to have a constant resultant, an edge traction or moment is integrated over the edge in +the current configuration, an edge whose length changes during a geometrically nonlinear analysis. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options: +*DLOAD, CONSTANT RESULTANT=NO +*DSLOAD, CONSTANT RESULTANT=NO +Load module: Create Load: choose Mechanical for the Category +and Shell edge load for the Types for Selected Step: Traction +is defined per unit deformed area +Maintaining a constant resultant +If you choose to have a constant resultant, an edge traction or moment is integrated over the edge in the +reference configuration, whose length is constant. +Input File Usage: +Use one of the following options: +Abaqus/CAE Usage: +*DLOAD, CONSTANT RESULTANT=YES +*DSLOAD, CONSTANT RESULTANT=YES +Load module: Create Load: choose Mechanical for the Category +and Shell edge load for the Types for Selected Step: Traction +is defined per unit undeformed area +Specifying line loads on beam elements +You can specify line loads on beam elements in the global X-, Y-, or Z-direction. In addition, you can +specify line loads on beam elements in the beam local 1- or 2-direction. +Input File Usage: +Use the following option to define a force per unit length in the global X-, Y-, +or Z-direction on beam elements: +*DLOAD +element number or element set, load type label, magnitude +where load type label is PX, PY, PZ, PXNU, PYNU, or PZNU. +Use the following option to define a force per unit length in the beam local 1- +or 2-direction: +*DLOAD +element number or element set, load type label, magnitude +where load type label is P1, P2, P1NU, or P2NU. +Abaqus/CAE Usage: +Load module: Create Load: choose Mechanical for the Category +and Line load for the Types for Selected Step +Additional references +• Genta, G., Dynamics of Rotating Systems, Springer, 2005. +33.4.4 +THERMAL LOADS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD Abaqus/CAE +References +• “Applying loads: overview,” Section 33.4.1 +• *CFLUX +• *DFLUX +• *DSFLUX +• *CFILM +• *FILM +• *SFILM +• *FILM PROPERTY +• *CRADIATE +• *RADIATE +• *SRADIATE +• “Defining a concentrated heat flux,” Section 16.9.19 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Defining a body heat flux,” Section 16.9.18 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Defining a surface heat flux,” Section 16.9.17 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Defining a fluid wall boundary condition,” Section 16.10.12 of the Abaqus/CAE User’s Manual, +in the online HTML version of this manual +• “Defining a surface film condition interaction,” Section 15.13.22 of the Abaqus/CAE User’s +Manual, in the online HTML version of this manual +• “Defining a concentrated film condition interaction,” Section 15.13.23 of the Abaqus/CAE User’s +Manual, in the online HTML version of this manual +• “Defining a surface radiative interaction,” Section 15.13.24 of the Abaqus/CAE User’s Manual, in +the online HTML version of this manual +• “Defining a concentrated radiative interaction,” Section 15.13.25 of the Abaqus/CAE User’s +Manual, in the online HTML version of this manual +Overview +Thermal loads can be applied in heat transfer analysis, in fully coupled temperature-displacement +analysis, fully coupled thermal-electrical-structural analysis, and in coupled thermal-electrical analysis, +as outlined in “Prescribed conditions: overview,” Section 33.1.1. The following types of thermal loads +are available: +• Concentrated heat flux prescribed at nodes. +• Distributed heat flux prescribed on element faces or surfaces. +• Body heat flux per unit volume. +• Boundary convection defined at nodes, on element faces, or on surfaces. +• Boundary radiation defined at nodes, on element faces, or on surfaces. +See “Applying loads: overview,” Section 33.4.1, for general information that applies to all types of +loading. +Modeling thermal radiation +The following types of radiation heat exchange can be modeled using Abaqus: +• Exchange between a nonconcave surface and a nonreflecting environment. This type of radiation +is modeled using boundary radiation loads defined at nodes, on element faces, or on surfaces, as +described below. +• Exchange between two surfaces within close proximity of each other in which temperature gradients +along the surfaces are not large. This type of radiation is modeled using the gap radiation capability +described in “Thermal contact properties,” Section 36.2.1. +• Exchange between surfaces that constitute a cavity. This type of radiation is modeled using the +cavity radiation capability available in Abaqus/Standard and described in “Cavity radiation,” +Section 40.1.1, or through the average-temperature radiation condition described in “Specifying +average-temperature radiation conditions,” below. +Prescribing heat fluxes directly +Concentrated heat fluxes can be prescribed at nodes (or node sets). Distributed heat fluxes can be defined +on element faces or surfaces. +Specifying concentrated heat fluxes +By default, a concentrated heat flux is applied to degree of freedom 11. For shell heat transfer elements +concentrated heat fluxes can be prescribed through the thickness of the shell by specifying degree of +freedom 11, 12, 13, etc. Temperature variation through the thickness of shell elements is described in +“Choosing a shell element,” Section 29.6.2. +Input File Usage: +*CFLUX +node number or node set name, degree of freedom, heat flux magnitude +Abaqus/CAE Usage: +Load module: Create Load: choose Thermal for the Category +and Concentrated heat flux for the Types for Selected Step: +select region: Magnitude: heat flux magnitude +Defining the values of concentrated nodal flux from a user-specified file +You can define nodal flux using nodal flux output from a particular step and increment in the output +database (.odb) file of a previous Abaqus analysis. The part (.prt) file from the original analysis is also +required when reading data from the output database file. In this case both the previous model and the +current model must be defined consistently, including node numbering, which must be the same in both +models. If the models are defined in terms of an assembly of part instances, part instance naming must +be the same. +Input File Usage: +Abaqus/CAE Usage: +*CFLUX, FILE=file, STEP=step, INC=inc +Defining the values of concentrated nodal flux from a user-specified file is not +supported in Abaqus/CAE. +Specifying element-based distributed heat fluxes +You can specify element-based distributed surface fluxes (on element faces) or body fluxes (flux per +unit volume). For surface fluxes you must identify the face of the element upon which the flux is +prescribed in the flux label (for example, Sn or SnNU for continuum elements). The distributed flux +types available depend on the element type. Part VI, “Elements,” lists the distributed fluxes that are +available for particular elements. +Input File Usage: +*DFLUX +element number or element set name, load type label, flux magnitude +Abaqus/CAE Usage: +Use the following input to define a distributed surface flux: +where load type label is Sn, SPOS, SNEG, S1, S2, or BF +Load module: Create Load: choose Thermal for the Category and Surface +heat flux for the Types for Selected Step: select region: Distribution: +select an analytical field, Magnitude: flux magnitude +Use the following input to define a distributed body flux: +Load module: Create Load: choose Thermal for the Category and Body +heat flux for the Types for Selected Step: select region: Distribution: +Uniform or select an analytical field, Magnitude: flux magnitude +Specifying surface-based distributed heat fluxes +When you specify distributed surface fluxes on a surface, the surface that contains the element and +face information is defined as described in “Element-based surface definition,” Section 2.3.2. You must +specify the surface name, the heat flux label, and the heat flux magnitude. +Input File Usage: +*DSFLUX +surface name, S, flux magnitude +Abaqus/CAE Usage: +Use the following input to specify surface-based distributed heat fluxes: +Load module: Create Load: choose Thermal for the Category and +Surface heat flux for the Types for Selected Step: select region: +Distribution: Uniform, Magnitude: flux magnitude +Use the following input to specify surface-based distributed wall heat fluxes in +Abaqus/CFD: +Load module: Create Boundary Condition: Step: flow_step: +choose Fluid for the Category and Fluid wall condition for the +Types for Selected Step: select region: Thermal Energy: Specify: +Heat flux, Magnitude: flux magnitude +Modifying or removing heat fluxes +Heat fluxes can be added, modified, or removed as described in “Applying loads: overview,” +Section 33.4.1. +Specifying time-dependent heat fluxes +The magnitude of a concentrated or a distributed heat flux can be controlled by referring to an amplitude +curve. +If different magnitude variations are needed for different fluxes, the flux definitions can be +repeated, with each referring to its own amplitude curve. See “Prescribed conditions: overview,” +Section 33.1.1, and “Amplitude curves,” Section 33.1.2, for details. +Defining nonuniform distributed heat flux in a user subroutine +In Abaqus/Standard a nonuniform distributed flux (element-based or surface-based) can be defined in +user subroutine DFLUX. The specified reference magnitude will be passed into user subroutine DFLUX +as FLUX(1). If the magnitude is omitted, FLUX(1) will be passed in as zero. +Input File Usage: +Use the following option to define a nonuniform element-based heat flux: +*DFLUX +element number or element set name, load type label, flux magnitude +where load type label is SnNU, SPOSNU, SNEGNU, S1NU, S2NU, or BFNU. +Use the following option to define a nonuniform surface-based heat flux: +*DSFLUX +surface name, SNU, flux magnitude +For example, for general heat transfer shell elements (“Three-dimensional +conventional shell element library,” Section 29.6.7) a uniform surface flux of +10.0 per unit area on the top face (SPOS) of shell element 100 can be applied +by +*DFLUX +100, SPOS, 10.0 +When the variation of the (nonuniform) flux magnitude is defined by means of +user subroutine DFLUX, the distributed flux type label SPOSNU is used. +*DFLUX +100, SPOSNU, magnitude +Abaqus/CAE Usage: +Use the following input to define a nonuniform element-based body flux: +Load module: Create Load: choose Thermal for the Category and +Body heat flux for the Types for Selected Step: select region: +Distribution: User-defined, Magnitude: flux magnitude +Use the following input to define a nonuniform surface-based heat flux: +Load module: Create Load: choose Thermal for the Category and +Surface heat flux for the Types for Selected Step: select region: +Distribution: User-defined, Magnitude: flux magnitude +Nonuniform element-based distributed surface fluxes are not supported in +Abaqus/CAE. +Prescribing boundary convection +Heat flux on a surface due to convection is governed by +where +is the heat flux across the surface, +is a reference film coefficient, +is the temperature at this point on the surface, and +is a reference sink temperature value. +Heat flux due to convection can be defined on element faces, on surfaces, or at nodes. +Specifying element-based film conditions +You can define the sink temperature value, +, and the film coefficient, h, on element faces. The +convection is applied to element edges in two dimensions and to element faces in three dimensions. +The edge or face of the element upon which the film is placed is identified by a film load type label +and depends on the element type . You must specify the element number or +element set name, the film load type label, a sink temperature, and a film coefficient. +Input File Usage: +*FILM +element number or element set name, film load type label, +, h +Abaqus/CAE Usage: +Element-based film conditions are supported in Abaqus/CAE only for the film +coefficient. +Interaction module: Create Interaction: Surface film condition: select +region: Definition: select an analytical field: Film coefficient: h +Specifying surface-based film conditions +You can define the sink temperature value, +, and the film coefficient, h, on a surface. The surface that +contains the element and face information is defined as described in “Element-based surface definition,” +Section 2.3.2. You must specify the surface name, the film load type, a sink temperature, and a film +coefficient. +Input File Usage: +*SFILM +surface name, F or FNU, +, h +Abaqus/CAE Usage: +Interaction module: Create Interaction: Surface film condition: +select region: Definition: Embedded Coefficient or User-defined: +Film coefficient: h and Sink temperature: +Specifying node-based film conditions +A node-based film condition requires that you define the nodal area for a specified node number or node +set; the sink temperature value, +; and the film coefficient, h. The associated degree of freedom is +11. For shell type elements where the film is associated with a degree of freedom other than 11, you can +specify the concentrated film for a duplicate node that is constrained to the appropriate degree of freedom +of the shell node by using an equation constraint . +Input File Usage: +*CFILM +node number or node set name, nodal area, +, h +Abaqus/CAE Usage: +Interaction module: Create Interaction: Concentrated film condition: +select region: Definition: Embedded Coefficient, User-defined, +or select an analytical field: Associated nodal area: nodal area, +Film coefficient: h, Sink temperature: +Specifying temperature- and field-variable-dependent film conditions +If the film coefficient is a function of temperature, you can specify the film property data separately and +specify the name of the property table instead of the film coefficient in the film condition definition. +You can specify multiple film property tables to define different variations of the film coefficient, +h, as a function of surface temperature and/or field variables. Each film property table must be named. +This name is referred to by the film condition definitions. +A new film property table can be defined in a restart step. If a film property table with an existing +name is encountered, the second definition is ignored. +Input File Usage: +For element-based film conditions, use the following options: +*FILM PROPERTY, NAME=film property table name +*FILM +element number or element set name, film load type label, +, film property table name +For surface-based film conditions, use the following options: +*FILM PROPERTY, NAME=film property table name +*SFILM +surface name, F, +, film property table name +For node-based film conditions, use the following options: +*FILM PROPERTY, NAME=film property table name +*CFILM +node number or node set name, nodal area, +The *FILM PROPERTY option must appear in the model definition portion of +the input file. +, film property table name +Interaction module: +Create Interaction Property: Name: film property table name and Film +condition +Create Interaction: Surface film condition or Concentrated film +condition: select region: Definition: Property Reference and Film +interaction property: film property table name +Abaqus/CAE Usage: +Modifying or removing film conditions +Film conditions can be added, modified, or removed as described in “Applying loads: overview,” +Section 33.4.1. +Specifying time-dependent film conditions +For a uniform film both the sink temperature and the film coefficient can be varied with time by referring +to amplitude definitions. One amplitude curve defines the variation of the sink temperature, +, with +time. Another amplitude curve defines the variation of the film coefficient, h, with time. See “Prescribed +conditions: overview,” Section 33.1.1, and “Amplitude curves,” Section 33.1.2, for more information. +Input File Usage: +Abaqus/CAE Usage: +Use the following options to define time-dependent film conditions: +*AMPLITUDE, NAME=temp_amp +*AMPLITUDE, NAME=h_amp +*FILM, AMPLITUDE=temp_amp, FILM AMPLITUDE=h_amp +*SFILM, AMPLITUDE=temp_amp, FILM AMPLITUDE=h_amp +*CFILM, AMPLITUDE=temp_amp, FILM AMPLITUDE=h_amp +Use the following input to define time-dependent film conditions. If you select +an analytical field to define the interaction, the analytical field affects only the +film coefficient. +Interaction module: +Create Amplitude: Name: h_amp +Create Amplitude: Name: temp_amp +Create Interaction: Surface film condition or Concentrated +film condition: select region: Definition: Embedded Coefficient +or select an analytical field: Film coefficient amplitude: h_amp +and Sink amplitude: temp_amp +Examples +A uniform, time-dependent film condition can be defined for face 2 of element 3 by +*AMPLITUDE, NAME=sink +0.0, 0.5, 1.0, 0.9 +*AMPLITUDE, NAME=famp +0.0, 1.0, 1.0, 22.0 +… +*STEP +** For an Abaqus/Standard analysis: +*HEAT TRANSFER +** For an Abaqus/Explicit analysis: +*DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT +… +*FILM, AMPLITUDE=sink, FILM AMPLITUDE=famp +3, F2, 90.0, 2.0 +A uniform, temperature-dependent film coefficient and a time-dependent sink temperature can be +defined for face 2 of element 3 by +*AMPLITUDE, NAME=sink +0.0, 0.5, 1.0, 0.9 +*FILM PROPERTY, NAME=filmp +80.0 +2.0, +2.3, +90.0 +8.5, 180.0 +… +*STEP +** For an Abaqus/Standard analysis: +*HEAT TRANSFER +** For an Abaqus/Explicit analysis: +*DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT +… +*FILM, AMPLITUDE=sink +3, F2, 90.0, filmp +A uniform, temperature-dependent film coefficient and a time-dependent sink temperature can be +defined for node 2, where the nodal area is 50, by +*AMPLITUDE, NAME=sink +0.0, 0.5, 1.0, 0.9 +*FILM PROPERTY, NAME=filmp +2.0, +2.3, +80.0 +90.0 +8.5, 180.0 +… +*STEP +** For an Abaqus/Standard analysis: +*HEAT TRANSFER +** For an Abaqus/Explicit analysis: +*DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT +… +*CFILM, AMPLITUDE=sink, +2, 50, 90.0, filmp +Defining nonuniform film conditions in a user subroutine +In Abaqus/Standard a nonuniform film coefficient can be defined as a function of position, time, +temperature, etc. in user subroutine FILM for element-based, surface-based, as well as node-based film +conditions. Amplitude references are ignored if a nonuniform film is prescribed. +Input File Usage: +Use the following option to define a nonuniform film coefficient for an element- +based film condition: +*FILM +element number or element set name, FnNU +Use the following option to define a nonuniform film coefficient for a surface- +based film condition: +*SFILM +surface name, FNU +Use the following option to define a nonuniform film coefficient for a node- +based film condition: +*CFILM, USER +node number or node set name, nodal area +Element-based film conditions to define a nonuniform film coefficient are not +supported in Abaqus/CAE. However, similar functionality is available using +surface-based film conditions. Use the following option to define a nonuniform +film coefficient for a surface-based film condition: +Interaction module: Create Interaction: Surface film condition: +select region: Definition: User-defined +Use the following option to define a nonuniform film coefficient for a node- +based film condition: +Interaction module: Create Interaction: Concentrated film condition: +select region: Definition: User-defined +33.4.4–9 +Prescribing boundary radiation +Heat flux on a surface due to radiation to the environment is governed by +where +is the heat flux across the surface, +is the emissivity of the surface, +is the Stefan-Boltzmann constant, +is the temperature at this point on the surface, +is an ambient temperature value, and +is the value of absolute zero on the temperature scale being used. +Heat flux due to radiation can be defined on element faces, on surfaces, or at nodes. +Specifying element-based radiation +To specify element-based radiation within a heat transfer or coupled temperature-displacement step +definition, you must provide the ambient temperature value, +. +The radiation is applied to element edges in two dimensions and to element faces in three dimensions. +The edge or face of the element upon which the radiation occurs is identified by a radiation type label +depending on the element type . +, and the emissivity of the surface, +Input File Usage: +*RADIATE +element number or element set name, Rn, +, +Abaqus/CAE Usage: +Interaction module: Create Interaction: Surface radiation: select +region: Radiation type: To ambient, Emissivity distribution: select an +analytical field, Emissivity: +, and Ambient temperature: +Specifying surface-based radiation to ambient +You can apply the radiation to a surface rather than to individual element faces. The surface that +contains the element and face information is defined as described in “Element-based surface definition,” +Section 2.3.2. You must specify the surface name; the radiation load type label, R (or RPOS, RNEG in +the case of shells); the ambient temperature value, +; and the emissivity of the surface, +. +Input File Usage: +*SRADIATE +surface name, R, +, +Abaqus/CAE Usage: +Interaction module: Create Interaction: Surface radiation: select region: +Radiation type: To ambient, Emissivity distribution: Uniform, +Emissivity: +, and Ambient temperature: +Specifying node-based radiation to ambient +To specify node-based radiation within a heat transfer or coupled temperature-displacement step +definition, you must provide the nodal area for a specified node number or node set; the ambient +temperature value, +. The associated degree of freedom is 11. For +shell elements where the concentrated radiation is associated with a degree of freedom other than 11, +you can specify the required data for a duplicate node that is constrained to the appropriate degree of +freedom of the shell node by using an equation constraint. +; and the emissivity of the surface, +Input File Usage: +*CRADIATE +node number or node set name, nodal area, +, +Abaqus/CAE Usage: +Interaction module: Create Interaction: Concentrated radiation +to ambient: select region: Associated nodal area: Emissivity: +and Ambient temperature: +Specifying time-dependent radiation +The user-specified value of the ambient temperature, +, can be varied throughout the step by referring +to an amplitude definition. See “Applying loads: overview,” Section 33.4.1, and “Amplitude curves,” +Section 33.1.2, for details. +Specifying average-temperature radiation conditions +The average-temperature radiation condition is an approximation to the cavity radiation problem, where +the radiative flux per unit area into a facet is +with the average temperature for the surface +being calculated as +The average temperature in the cavity is computed at the beginning of each increment and +held constant over the increment. Therefore, the average-temperature radiation condition has some +dependency on the increment size, and you need to ensure that the increment size you use is appropriate +for your model. If you see large changes in temperature over an increment, you may need to reduce +the increment size. +Input File Usage: +Use the following option to define the average-temperature radiation condition +on a surface: +*SRADIATE +surface name, AVG, , +Abaqus/CAE Usage: +Interaction module: Create Interaction: Surface radiation: select the surface +region: Radiation type: Cavity approximation (3D only), Emissivity: +Specifying the value of absolute zero +You can specify the value of absolute zero, +this value as model data. By default, the value of absolute zero is 0.0. +, on the temperature scale being used; you must specify +Input File Usage: +Abaqus/CAE Usage: +*PHYSICAL CONSTANTS, ABSOLUTE ZERO= +Any module: Model→Edit Attributes→model_name: +Absolute zero temperature: +Specifying the value of the Stefan-Boltzmann constant +If boundary radiation is prescribed, you must specify the Stefan-Boltzmann constant, +be specified as model data. +; this value must +Input File Usage: +Abaqus/CAE Usage: +*PHYSICAL CONSTANTS, STEFAN BOLTZMANN= +Any module: Model→Edit Attributes→model_name: +Stefan-Boltzmann constant: +Modifying or removing boundary radiation +Boundary radiation conditions can be added, modified, or removed as described in “Applying loads: +overview,” Section 33.4.1. +33.4.5 +ELECTROMAGNETIC LOADS +Products: Abaqus/Standard Abaqus/CAE +References +• “Prescribed conditions: overview,” Section 33.1.1 +• “Applying loads: overview,” Section 33.4.1 +• *CECHARGE +• *CECURRENT +• *DECHARGE +• *DECURRENT +• *DSECHARGE +• *DSECURRENT +• “Defining a concentrated current,” Section 16.9.25 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Defining a surface current,” Section 16.9.26 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Defining a body current,” Section 16.9.27 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +• “Defining a surface current density,” Section 16.9.28 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Defining a body current density,” Section 16.9.29 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Defining a concentrated charge,” Section 16.9.30 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Defining a surface charge,” Section 16.9.31 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Defining a body charge,” Section 16.9.32 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +As outlined in “Prescribed conditions: overview,” Section 33.1.1, electromagnetic loads can be applied +in “Piezoelectric analysis,” Section 6.7.2; “Coupled thermal-electrical analysis,” Section 6.7.3; “Fully +coupled thermal-electrical-structural analysis,” Section 6.7.4; “Eddy current analysis,” Section 6.7.5; +and “Magnetostatic analysis,” Section 6.7.6. +The types of electromagnetic loads available depend on the analysis being performed, as described +in the sections below. See “Applying loads: overview,” Section 33.4.1, for general information that +applies to all types of loading. +Defining time-dependent electromagnetic loads +The prescribed magnitude of a concentrated or a distributed electromagnetic load can vary with time +during a step according to an amplitude definition, as described in “Prescribed conditions: overview,” +Section 33.1.1. +If different variations are needed for different loads, each load can refer to its own +amplitude definition. +In a time-harmonic eddy current analysis all loads are assumed to be time-harmonic. +Modifying electromagnetic loads +Concentrated or distributed electromagnetic loads can be added, modified, or removed as described in +“Applying loads: overview,” Section 33.4.1. +Prescribing electromagnetic loads for piezoelectric analyses +In a piezoelectric analysis a concentrated electric charge can be prescribed at nodes, a distributed electric +surface charge can be defined on element faces and surfaces, and a distributed electric body charge can +be defined on elements. +Specifying concentrated electric charge +To specify a concentrated electric charge, specify the node or node set and the magnitude of the charge. +Input File Usage: +*CECHARGE +node number or node set name, , charge magnitude +Abaqus/CAE Usage: +Load module: Create Load: choose Electrical/Magnetic for the +Category and Concentrated charge for the Types for Selected +Step; Magnitude: charge magnitude +Specifying element-based distributed electric charge +You can specify a distributed surface charge (on element faces) or a distributed body charge (charge per +unit volume). For an element-based surface charge you must identify the face of the element upon which +the charge is prescribed in the charge label. The distributed charge types available depend on the element +type. Part VI, “Elements,” lists the distributed charges that are available for particular elements. +Input File Usage: +*DECHARGE +element number or element set name, charge label, charge magnitude +Abaqus/CAE Usage: +Use the following input to define a distributed surface charge on element faces: +where charge label is ESn or EBF +Load module: Create Load: choose Electrical/Magnetic for the Category +and Surface charge for the Types for Selected Step; Distribution: +select an analytical field, Magnitude: charge magnitude +Use the following input to define a body charge: +Load module: Create Load: choose Electrical/Magnetic for the Category +and Body charge for the Types for Selected Step +Specifying surface-based distributed electric charge +When you specify a distributed electric charge on a surface, the element-based surface contains the element and face information. You must specify +the surface name, the electric charge label, and the electric charge magnitude. +Input File Usage: +*DSECHARGE +surface name, ES, charge magnitude +Abaqus/CAE Usage: +Load module: Create Load: choose Electrical/Magnetic for the +Category and Surface charge for the Types for Selected Step; +Distribution: Uniform, Magnitude: charge magnitude +Specifying electric charge in direct-solution steady-state dynamics analysis +In the direct-solution steady-state dynamics procedure, electric charges are given in terms of their real +and imaginary components. +Input File Usage: +Use the following options to define electric charges in direct-integration steady- +state dynamics analysis: +Abaqus/CAE Usage: +*CECHARGE, REAL or IMAGINARY (real or imaginary component) +*DECHARGE, REAL or IMAGINARY +*DSECHARGE, REAL or IMAGINARY +Load module: Create Load: choose Electrical/Magnetic for the Category +and Concentrated charge, Surface charge, or Body charge for the Types +for Selected Step; Magnitude: real component + imaginary component +Loading in mode-based and subspace-based procedures +Electrical charge loads should be used only in conjunction with residual modes in the eigenvalue +extraction step, due to the “massless” mode effect. Since the electrical potential degrees of freedom do +not have any associated mass, these degrees of freedom are essentially eliminated (similar to Guyan +reduction or mass condensation) during the eigenvalue extraction. The residual modes represent +the static response corresponding to the electrical charge loads, which will adequately represent the +potential degree of freedom in the eigenspace. +Prescribing electromagnetic loads for coupled thermal-electrical and fully coupled +thermal-electrical-structural analyses +In a coupled thermal-electrical analysis and fully coupled thermal-electrical-structural analysis a +concentrated current can be prescribed at nodes, distributed current densities can be defined on element +faces and surfaces, and distributed body currents can be defined on elements. +Specifying concentrated current density +To define concentrated currents, specify the node or node set and the magnitude of the current. +Input File Usage: +*CECURRENT +node number or node set name, , current magnitude +Abaqus/CAE Usage: +Load module: Create Load: choose Electrical/Magnetic for the +Category and Concentrated current for the Types for Selected +Step; Magnitude: current magnitude +Specifying element-based distributed current density +You can specify distributed surface current densities (on element faces) or distributed body current +densities (current per unit volume). For element-based surface current densities you must identify the +face of the element upon which the current is prescribed in the current label. The distributed current +types available depend on the element type. Part VI, “Elements,” lists the distributed current densities +that are available for particular elements. +*DECURRENT +element number or element set name, current density label, +current density magnitude +Input File Usage: +where current density label is CSn, CS1, CS2, or CBF +Abaqus/CAE Usage: +Use the following input to define a distributed surface current density on +element faces: +Load module: Create Load: choose Electrical/Magnetic for the Category +and Surface current for the Types for Selected Step; Distribution: +select an analytical field, Magnitude: current density magnitude +Use the following input to define a body current density: +Load module: Create Load: choose Electrical/Magnetic for the Category +and Body current for the Types for Selected Step +Specifying surface-based distributed current densities +When you specify distributed current densities on a surface, the element-based surface contains the element and face information. You must specify +the surface name, the current density label, and the current density magnitude. +Input File Usage: +*DSECURRENT +surface name, CS, current density magnitude +Abaqus/CAE Usage: +Load module: Create Load: choose Electrical/Magnetic for the Category +and Surface current for the Types for Selected Step: Distribution: +Uniform, Magnitude: current density magnitude +Prescribing electromagnetic loads for eddy current and/or magnetostatic analyses +In an eddy current analysis a distributed surface current density vector can be defined on surfaces and a +distributed volume current density vector can be defined on elements. +Specifying element-based distributed current density vectors +When you define a distributed volume current density vector, you must specify the element or element +set, the current density vector label, the magnitude of the current density vector, the vector components +of the current density, and an optional orientation name that defines the local coordinate system in which +the vector components are specified. By default, the vector components of the current density are defined +with respect to the global directions. +The specified current density vector direction components are normalized by Abaqus and, thus, do +not contribute to the magnitude of the load. +Input File Usage: +*DECURRENT +element number or element set name, CJ, current density vector magnitude, +current density vector direction components, orientation name +Abaqus/CAE Usage: +Load module: Create Load: choose Electrical/Magnetic for +the Category and Body current density for the Types for +Selected Step; Distribution: Uniform +Specifying surface-based distributed current density vectors +When you specify distributed current density vectors on a surface, the element-based surface contains the element and face information. You must +specify the surface name, the current density vector label, and the magnitude of the current density +vector, the vector components of the current density, and an optional orientation name that defines +the local coordinate system in which the surface current density is specified. By default, the vector +components of the current density are defined with respect to the global directions. +The specified current density vector direction components are normalized by Abaqus and, thus, do +Input File Usage: +not contribute to the magnitude of the load. +*DSECURRENT +surface name, CK, current density vector magnitude, current density +vector direction components, orientation name +Abaqus/CAE Usage: +Load module: Create Load: choose Electrical/Magnetic for +the Category and Surface current density for the Types for +Selected Step; Distribution: Uniform +Defining nonuniform current density vectors in a user subroutine +Nonuniform volume current density vectors can be defined with user subroutine UDECURRENT, and +nonuniform surface current density vectors can be defined with user subroutine UDSECURRENT. If the +magnitude and direction components are given, the values are passed into the user subroutine. +Input File Usage: +Use the following option to define nonuniform element-based current density +vectors: +*DECURRENT +element number or element set name, CJNU, current density vector magnitude, +current density vector direction components, orientation name +Use the following option to define nonuniform surface-based current density +vectors: +*DSECURRENT +surface name, CKNU, current density vector magnitude, current density +vector direction components, orientation name +Abaqus/CAE Usage: +Use the following option to define nonuniform volume current density: +Load module: Create Load: choose Electrical/Magnetic for the +Category and Body current density for the Types for Selected +Step; Distribution: User-defined +Use the following option to define nonuniform surface current density: +Load module: Create Load: choose Electrical/Magnetic for +the Category and Surface current density for the Types for +Selected Step; Distribution: User-defined +Specifying real and imaginary components of current density vectors in a time-harmonic eddy +current analysis +In a time-harmonic eddy current analysis, current density vectors are given in terms of their real (in- +phase) and imaginary (out-of-phase) components. +Input File Usage: +Use the following options to define current density vectors: +Abaqus/CAE Usage: +*DECURRENT, REAL or IMAGINARY +*DSECURRENT, REAL or IMAGINARY +Load module: Create Load: choose Electrical/Magnetic for the Category +and Body current density or Surface current density for the Types +for Selected Step; real components + imaginary components +33.4.6 +ACOUSTIC AND SHOCK LOADS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Applying loads: overview,” Section 33.4.1 +• “Acoustic, shock, and coupled acoustic-structural analysis,” Section 6.10.1 +• *AMPLITUDE +• *BOUNDARY +• *CLOAD +• *CONWEP CHARGE PROPERTY +• *IMPEDANCE +• *IMPEDANCE PROPERTY +• *INCIDENT WAVE +• *INCIDENT WAVE FLUID PROPERTY +• *INCIDENT WAVE INTERACTION +• *INCIDENT WAVE INTERACTION PROPERTY +• *INCIDENT WAVE PROPERTY +• *INCIDENT WAVE REFLECTION +• *SIMPEDANCE +• *UNDEX CHARGE PROPERTY +• “Defining acoustic impedance,” Section 15.13.17 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Defining incident waves,” Section 15.13.18 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Defining an acoustic impedance interaction property,” Section 15.14.6 of the Abaqus/CAE User’s +Manual, in the online HTML version of this manual +• “Defining an incident wave interaction property,” Section 15.14.7 of the Abaqus/CAE User’s +Manual, in the online HTML version of this manual +Overview +Acoustic loads can be applied only in transient or steady-state dynamic analysis procedures. The +following types of acoustic loads are available: +• Boundary impedance defined on element faces or on surfaces. +• Nonreflecting radiation boundaries in exterior problems such as a structure vibrating in an acoustic +medium of infinite extent. +• Concentrated pressure-conjugate loads prescribed at acoustic element nodes. +• Temporally and spatially varying pressure loading on acoustic and solid surfaces due to incident +waves traveling through the acoustic medium. +Specified boundary impedance +A boundary impedance specifies the relationship between the pressure of an acoustic medium and the +normal motion at the boundary. Such a condition is applied, for example, to include the effect of small- +amplitude “sloshing” in a gravity field or the effect of a compressible, possibly dissipative, lining (such +as a carpet) between an acoustic medium and a fixed, rigid wall or structure. +The impedance boundary condition at any point along the acoustic medium surface is governed by +where +is the acoustic particle velocity in the outward normal direction of the acoustic medium +surface, +is the acoustic pressure, +is the time rate of change of the acoustic pressure, +is the proportionality coefficient between the pressure and the displacement normal to the +surface, and +is the proportionality coefficient between the pressure and the velocity normal to the surface. +This model can be conceptualized as a spring and dashpot in series placed between the acoustic medium +and a rigid wall. The spring and dashpot parameters are +, respectively, defined per unit area +of the interface surface. These reactive acoustic boundaries can have a significant effect on the pressure +distribution in the acoustic medium, in particular if the coefficients +are chosen such that the +boundary is energy absorbing. If no impedance, loads, or fluid-solid coupling are specified on the surface +of an acoustic mesh, the acceleration of that surface is assumed to be zero. This is equivalent to the +presence of a rigid wall at that boundary. +and +and +Use of the subspace-based steady-state dynamics procedure is not recommended if reactive acoustic +boundaries with strong absorption characteristics are used. Since the effect of +is not taken into account +in an eigenfrequency extraction step, the eigenmodes may have shapes that are significantly different +from the exact solution. +Sloshing of a free surface +To model small-amplitude “sloshing” of a free surface in a gravity field, set +and +, where +is the density of the fluid and g is the gravitational acceleration (assumed to be directed +normal to the surface). This relation holds for small volumetric drag. +Acoustic-structural interface +The impedance boundary condition can also be placed at an acoustic-structural interface. In this case the +boundary condition can be conceptualized as a spring and dashpot in series placed between the acoustic +medium and the structure. The expression for the outward velocity still holds, with +now being the +relative outward velocity of the acoustic medium and the structure: +where +is the velocity of the structure, +is the outward normal to the acoustic medium. +is the velocity of the acoustic medium at the boundary, and +Steady-state dynamics +In a steady-state dynamics analysis the expression for the outward velocity can be written in complex +form as +where +is the circular frequency (radians/second) and we define +The term +is its complex impedance. Thus, +a required complex impedance or admittance value can be entered for a given frequency by specifying +the parameters +is the complex admittance of the boundary, and +and +. +Specifying impedance conditions +You specify impedance coefficient data in an impedance property table. You can describe an impedance +table in terms of the admittance parameters, +, or in terms of the real and imaginary parts +and +of the impedance. In the latter case Abaqus converts the user-defined table of impedance data to the +admittance parameter form for the analysis. +The parameters in the table can be specified over a range of frequencies. The required values are +interpolated from the table in steady-state harmonic response analysis only; for other analysis types, only +the first table entry is used. The name of the impedance property table is referred to from a surface-based +or element-based impedance definition. In Abaqus/CAE impedance conditions are always surface-based; +surfaces can be defined as collections of geometric faces and edges or collections of element faces and +edges. +In a steady-state dynamics analysis you cannot specify impedance conditions on a surface on which +incident wave loading is applied. +Input File Usage: +Use the following option to specify an impedance using a table of admittance +parameters (default): +*IMPEDANCE PROPERTY, NAME=impedance property table name, +DATA=ADMITTANCE +Use the following option to specify an impedance using a table of the real and +imaginary parts of the impedance: +*IMPEDANCE PROPERTY, NAME=impedance property table name, +DATA=IMPEDANCE +Abaqus/CAE Usage: +Use the following input to specify an impedance using a table of admittance +parameters: +Interaction module: Create Interaction Property: Name: impedance +property table name and Acoustic impedance: Data type: Admittance +Use the following input to specify an impedance using a table of the real and +imaginary parts of the impedance: +Interaction module: Create Interaction Property: Name: impedance +property table name and Acoustic impedance: Data type: Impedance +Specifying surface-based impedance conditions +You can define the impedance condition on a surface. The impedance is applied to element edges in two +dimensions and to element faces in three dimensions. The element-based surface contains the element and face information. +Input File Usage: +Abaqus/CAE Usage: +*SIMPEDANCE, PROPERTY=impedance property table name +surface name +Interaction module: Create Interaction: Acoustic impedance: +select surface: Definition: Tabular, Acoustic impedance +property: impedance property table name +Specifying element-based impedance conditions +Alternatively, you can define the impedance condition on element faces. The impedance is applied to +element edges in two dimensions and to element faces in three dimensions. The edge or face of the +element upon which the impedance is placed is identified by an impedance load type and depends on the +element type . +Input File Usage: +*IMPEDANCE, PROPERTY=impedance property table name +element number or set name, impedance load type label +Abaqus/CAE Usage: +Element-based impedance conditions are not supported in Abaqus/CAE. +However, similar functionality is available using surface-based impedance +conditions. +Modifying or removing impedance conditions +Impedance conditions can be added, modified, or removed as described in “Applying loads: overview,” +Section 33.4.1. +Radiation boundaries for exterior problems +An exterior problem such as a structure vibrating in an acoustic medium of infinite extent is often of +interest. Such a problem can be modeled by using acoustic elements to model the region between the +structure and a simple geometric surface (located away from the structure) and applying a radiating +(nonreflecting) boundary condition at that surface. The radiating boundary conditions are approximate, +so the error in an exterior acoustic analysis is controlled not only by the usual finite element discretization +error but also by the error in the approximate radiation condition. In Abaqus the radiation boundary +conditions converge to the exact condition in the limit as they become infinitely distant from the radiating +structure. In practice, these radiation conditions provide accurate results when the surface is at least +one-half wavelength away from the structure at the lowest frequency of interest. +Except in the case of a plane wave absorbing condition with zero volumetric drag, the impedance +parameters in Abaqus/Standard are frequency dependent. The frequency-dependent parameters are used +in the direct-solution and subspace-based steady-state dynamics procedures. In direct time integration +procedures the zero-drag values for the constants +are used. These values will give good +results when the drag is small. (Small volumetric drag here means +is the density +where +of the acoustic medium and +is the circular excitation frequency or sound wave frequency.) +and +A direct-solution steady-state dynamics procedure (“Direct-solution steady-state dynamic analysis,” +Section 6.3.4) must include both real and complex terms if nonreflecting (also called quiet) boundaries +are present, because nonreflecting boundaries represent a form of damping in the system. +Several radiating boundary conditions are implemented as special cases of the impedance boundary +condition. The details of the formulation are given in “Coupled acoustic-structural medium analysis,” +Section 2.9.1 of the Abaqus Theory Manual. +Element-based impedance conditions are not supported in Abaqus/CAE. However, similar +functionality is available using surface-based impedance conditions. +Planar nonreflecting boundary condition +The simplest nonreflecting boundary condition available in Abaqus assumes that the plane waves are +normally incident on the exterior surface. This planar boundary condition ignores the curvature of the +boundary and the possibility that waves in the simulation may impinge on the boundary at an arbitrary +angle. The planar nonreflecting condition provides an approximation: acoustic waves are transmitted +across such a boundary with little reflection of energy back into the acoustic medium. The amount of +energy reflected is small if the boundary is far away from major acoustic disturbances and is reasonably +orthogonal to the direction of dominant wave propagation. Thus, if an exterior (unbounded domain) +problem is to be solved, the nonreflecting boundary should be placed far enough away from the sound +source so that the assumption of normally impinging waves is sufficiently accurate. This condition would +be used, for example, on the exhaust end of a muffler. +Input File Usage: +Use either of the following options (default): +*SIMPEDANCE, NONREFLECTING=PLANAR +*IMPEDANCE, NONREFLECTING=PLANAR +Abaqus/CAE Usage: +Use the following input +boundary condition: +to specify a surface-based planar nonreflecting +Interaction module: Create Interaction: Acoustic impedance: select +surface: Definition: Nonreflecting, Nonreflecting type: Planar +Improved nonreflecting boundary condition for plane waves +For the planar nonreflecting boundary condition to be accurate, the plane waves must be normally +incident to a planar boundary. However, the angle of incidence is generally unknown in advance. +A radiating boundary condition that is exact for plane waves with arbitrary angles of incidence is +available in Abaqus. The radiating boundary can have any arbitrary shape. This boundary impedance is +implemented only for transient dynamics. +Input File Usage: +Use either of the following options: +Abaqus/CAE Usage: +*SIMPEDANCE, NONREFLECTING=IMPROVED +*IMPEDANCE, NONREFLECTING=IMPROVED +Use the following input +nonreflecting boundary condition: +to specify a surface-based improved planar +Interaction module: Create Interaction: Acoustic impedance: select +surface: Definition: Nonreflecting, Nonreflecting type: Improved planar +Geometry-based nonreflecting boundary conditions +Four other types of absorbing boundary conditions that take the geometry of the radiating boundary +into account are implemented in Abaqus: circular, spherical, elliptical, and prolate spheroidal. These +boundary conditions offer improved performance over the planar nonreflecting condition if the +nonreflecting surface has a simple, convex shape and is close to the acoustic sources. The various +types of absorbing boundaries are selected by defining the required geometric parameters for the +element-based or surface-based impedance definition. +The geometric parameters affect the nonreflecting surface impedance. To specify a nonreflecting +boundary that is circular in two dimensions or a right circular cylinder in three dimensions, you must +specify the radius of the circle. To specify a nonreflecting spherical boundary condition, you must specify +the radius of the sphere. To specify a nonreflecting boundary that is elliptical in two dimensions or a +right elliptical cylinder in three dimensions or to specify a prolate spheroid boundary condition, you +must specify the shape, location, and orientation of the radiating surface. The two parameters specifying +the shape of the surface are the semimajor axis and the eccentricity. The semimajor axis, a, of an ellipse +or prolate spheroid is analogous to the radius of a sphere: it is one-half the length of the longest line +segment connecting two points on the surface. The semiminor axis, b, is one-half the length of the +longest line segment that connects two points on the surface and is orthogonal to the semimajor axis line. +The eccentricity, +. +, is defined as +See “Acoustic radiation impedance of a sphere in breathing mode,” Section 1.11.3 of the Abaqus +Benchmarks Manual, and “Acoustic-structural interaction in an infinite acoustic medium,” Section 1.11.4 +of the Abaqus Benchmarks Manual, for benchmark problems showing the use of these conditions. +Input File Usage: +Use one of the following options: +Abaqus/CAE Usage: +*SIMPEDANCE, NONREFLECTING=CIRCULAR +*SIMPEDANCE, NONREFLECTING=SPHERICAL +*SIMPEDANCE, NONREFLECTING=ELLIPTICAL +*SIMPEDANCE, NONREFLECTING=PROLATE SPHEROIDAL +In each case, the *IMPEDANCE element-based option can be used instead of +*SIMPEDANCE. +Use the following input to specify surface-based geometric nonreflecting +boundary conditions: +Interaction module: Create Interaction: Acoustic impedance: select +surface: Definition: Nonreflecting, Nonreflecting type: Circular, +Spherical, Elliptical, or Prolate spheroidal +Combining different radiation conditions in the same problem +Since the radiation boundary conditions for the different shapes are spatially local and do not involve +discretization in the infinite exterior domain, an exterior boundary can consist of the combination of +several shapes. The appropriate boundary condition can then be applied to each part of the boundary. +For example, a circular cylinder can be terminated with hemispheres , or +an elliptical cylinder can be terminated with prolate spheroidal halves. This modeling technique is most +effective if the boundaries between surfaces are continuous in slope as well as displacement, although +this is not essential. +Concentrated pressure-conjugate load +Distributed “loads” on acoustic elements can be interpreted as normal pressure gradients per unit density +(dimensions of force per unit mass or acceleration). When used in Abaqus, the applied distributed loads +must be integrated over a surface area, yielding a quantity with dimensions of force times area per unit +mass (or volumetric acceleration). For analyses in the frequency domain and for transient dynamic +analyses where the volumetric drag is zero, this acoustic load is equal to the volumetric acceleration of +the fluid on the boundary. For example, a horizontal, flat rigid plate oscillating vertically imposes an +acceleration on the acoustic fluid and an acoustic “load” equal to this acceleration times the surface area +of the plate. For the transient dynamics formulation in the presence of volumetric drag, however, the +specified “load” is slightly different. It is also a force times area per unit mass; but this force effect is +partially lost to the volumetric drag, so the resulting volumetric acceleration of the fluid on the boundary +is reduced. Noting this distinction for the special case of volumetric drag and transient dynamics, it is +nevertheless convenient to refer to acoustic “loads” as volumetric accelerations in general. +An inward volumetric acceleration can be applied by a positive concentrated load on degree +of freedom 8 at a node of an acoustic element that is on the boundary of the acoustic medium. +In +Abaqus/Standard you can specify the in-phase (real) part of a load (default) and the out-of-phase +(imaginary) part of a load. Inward particle accelerations (force per unit mass in transient dynamics) on +the face of an acoustic element should be lumped to concentrated loads representing inward volumetric +accelerations on the nodes of the face in the same way that pressure on a face is lumped to nodal forces +on stress/displacement elements. +Input File Usage: +Use the following option to define the real part of the load: +*CLOAD, REAL +Use the following option to define the imaginary part of the load: +*CLOAD, IMAGINARY +Load module: Create Load: choose Acoustic for the Category and +Inward volume acceleration for the Types for Selected Step +Abaqus/CAE Usage: +Incident wave loading due to external sources +Abaqus provides a type of distributed load for loads due to external wave sources. Individual spherical +monopole or individual or diffuse planar sources can be defined, subjecting the fluid and solid region of +interest to an incident field of waves. Waves produced by an explosion or sound source propagate from +the source, impinging on and passing over the structure, producing a temporally and spatially varying +load on the structural surface. In the fluid the pressure field is affected by reflections and emissions from +the structure as well as by the incident field from the source itself. The incident wave loads on acoustic +and/or solid meshes depend on the location of the source node, the properties of the propagating fluid, +and the reference time history or frequency dependence specified at the reference (“standoff”) node as +indicated in Figure 33.4.6–1. +Several distinct modeling methods can be used in Abaqus with incident wave loading, requiring +different approaches to applying the incident wave loads. For problems involving solid and structural +elements only (for example, where the incident wave field is due to waves in air) the wave loading is +applied roughly like a distributed surface load. This might apply to an analysis of blast loads in air on +a vehicle or building . In +Abaqus/Explicit the CONWEP model can be used for air blast loading on solid and structural elements, +without the need to model the fluid medium. “Deformation of a sandwich plate under CONWEP blast +loading,” Section 9.1.8 of the Abaqus Example Problems Manual, is an example of a blast loading +problem. +Incident wave loads (with the exception of CONWEP loading) can be applied to beam structures as +well; this is a common modeling method for ship whipping analysis and for steel frame buildings subject +to blast loads. Incident wave loads can be applied to surfaces defined on two- or three-dimensional beam +elements. However, incident wave loads can be applied only to three-dimensional beams for transient +dynamic analysis where beam fluid inertia is defined. Incident wave loads cannot be defined on frame +elements, line spring elements, three-dimensional open-section beam elements, or three-dimensional +Euler-Bernoulli beams. +In underwater explosion analyses (for example, a ship or submerged vehicle subjected to an +underwater explosion loading as depicted in Figure 33.4.6–4 and Figure 33.4.6–5) the fluid is also +discretized using a finite element model to capture the effects of the fluid stiffness and inertia. For these +problems involving both solid and acoustic elements, two formulations of the acoustic pressure field +Specify speed of +sound and density +for propagating wave +acoustic mesh +exterior +surface +structural +mesh +fluid +surface +solid +surface +reference or "standoff" node +source node +(where explosion +charge occurs) +Figure 33.4.6–1 Incident wave loading model. +exist. First, the acoustic elements can be used to model the total pressure in the medium, including +the effects of the incident field and the overall system’s response. Alternatively, the acoustic elements +can be used to model only the response of the medium to the wave loads, not the wave pulse itself. +The former case will be referred to as the “total wave” formulation, the latter as the “scattered wave” +formulation. +Incident wave interactions are also used to model sound fields impinging on structures or acoustic +domains. The acoustic field scattered by a structure or the sound transmitted through the structure may +be of interest. Usually, sound scattering and transmission problems are modeled using the scattered +formulation with steady-state dynamic procedures. Transient procedures can also be used, in a manner +analogous to underwater explosion analysis problems. +Scattered and total wave formulations +The distinction between the total wave formulation and the scattered wave formulation is relevant only +when incident wave loads are applied. The total wave formulation is more closely analogous to structural +loading than the scattered wave formulation: the boundary of the acoustic medium is specified as a loaded +surface, and a time-varying load is applied there, which generates a response in the acoustic medium. +This response is equal to the total acoustic pressure in the medium. The scattered wave formulation +exploits the fact that when the acoustic medium is linear, the response in the medium can be decomposed +into a sum of the incident wave and the scattered field. The total wave formulation must be used when the +acoustic medium is nonlinear due to possible fluid cavitation . +Table 33.4.6–1 describes the procedure types for which each formulation is supported. +Table 33.4.6–1 +Supported procedures for scattered and total wave formulations. +Procedure +Scattered Total Wave +Steady-state dynamics +Transient +Yes +Yes +No +Yes +Scattered wave formulation +When the mechanics of a fluid can be described as linear, the observed total acoustic pressure can be +decomposed into two components: the known incident wave and the “scattered” wave that is produced +by the interaction of the incident wave with structures and/or fluid boundaries. When this superposition +is applicable, it is common practice to seek the “scattered” wave field solution directly. When using the +scattered wave formulation, the pressures at the acoustic nodes are defined to be only the scattered part of +the total pressure. Both acoustic and solid surfaces at the acoustic-structural interface should be loaded +in this case. +When using incident wave loads in steady-state dynamic procedures, the scattered wave formulation +must be used. +Input File Usage: +Use the following option to specify the scattered wave formulation (default): +Abaqus/CAE Usage: +*ACOUSTIC WAVE FORMULATION, TYPE=SCATTERED WAVE +Any module: Model→Edit Attributes→model_name. Toggle on Specify +acoustic wave formulation: select Scattered wave +Total wave formulation +The total wave formulation is particularly applicable when the acoustic medium is capable of cavitation, +rendering the fluid mechanical behavior nonlinear. It should also be used if the problem contains either +a curved or a finite extent boundary where the pressure history is prescribed. Only the outer acoustic +surfaces should be loaded with the incident wave in this case, and the incident wave source must be +located exterior to the fluid model. Any impedance or nonreflecting condition that may exist on this outer +acoustic boundary applies only on the part of the acoustic solution that does not include the prescribed +incident wave field (that is, only the scattered field is subject to the nonreflecting condition). Thus, +the applied incident wave loading will travel into the problem domain without being affected by the +nonreflecting conditions on the outer acoustic surface. +In the total wave formulation the acoustic pressure degree of freedom stands for the total dynamic +acoustic pressure, including contributions from incident and scattered waves and, in Abaqus/Explicit, the +dynamic effects of fluid cavitation. The pressure degree of freedom does not include the acoustic static +pressure, which can be specified as an initial condition . This acoustic static +pressure is used only in determining the cavitation status of the acoustic element nodes and does not +apply any static loads to the acoustic or structural mesh at their common wetted interface. It does not +apply to analyses using Abaqus/Standard. +Input File Usage: +Use the following option to specify the total wave formulation: +Abaqus/CAE Usage: +*ACOUSTIC WAVE FORMULATION, TYPE=TOTAL WAVE +Any module: Model→Edit Attributes→model_name. Toggle on +Specify acoustic wave formulation: select Total wave +Initialization of acoustic fields +For transient dynamics, when the total wave formulation is used with the incident wave standoff point +located inside the acoustic finite element domain, the acoustic solution is initialized to the values of the +incoming incident wave. This initialization is performed automatically, for pressure-based incident wave +amplitude definitions only, at the beginning of the first direct-integration dynamic step in an analysis; in +restarted analyses, steps are counted from the beginning of the initial analysis. This initialization not +only saves computational time but also applies the incident wave loading without significant numerical +dissipation or distortion. During the initialization phase all incident wave loading definitions in the first +dynamic analysis step are considered, and all acoustic element nodes are initialized to the incident wave +field at time zero. Incident wave loads specified with different source locations count as separate load +definitions for the purpose of initialization of the acoustic nodes. Any reflections of the incident wave +loads are also taken into account during the initialization phase. +Describing incident wave loading +To use incident wave loading, you must define the following: +• information that establishes the direction and other properties of the incident wave, +• the time history or frequency dependence of the source pulse at some reference (“standoff”) point, +• the fluid and/or solid surfaces to be loaded, and +• any reflection plane outside the problem domain, such as a seabed in an underwater explosion study, +that would reflect the incident wave onto the problem domain. +Two interfaces are available in Abaqus for applying incident wave loads: a preferred interface +that is supported in Abaqus/CAE and an alternative interface that has been available in previous +releases and is not supported in Abaqus/CAE. The preferred interface is conceptually the same as the +alternative interface and uses essentially the same data. The preferred interface options include the +term “interaction” to distinguish them from the incident wave and incident wave property options of +the alternative interface. Unless otherwise specified, the discussion in this section applies to both of +the interfaces. The usages for the preferred interface are included in the discussion; the usages for the +alternative interface are described in “Alternative incident wave loading interface,” below. Refer to the +example problems discussed at the end of this section to see how the incident wave loading is specified +using the preferred interface. +Prescribing geometric properties and the speed of the incident wave +You must refer to a property definition for each prescribed incident wave. Incident wave loads in Abaqus +may be either planar, spherical, or diffuse. You select a planar incident wave (default), spherical incident +wave, or a diffuse field in the incident wave property definition. +Planar incident waves maintain constant amplitude as they travel in space; consequently, the speed +and direction of travel are the critical parameters to define. The speed is defined in the incident wave +interaction property definition, and the direction is determined by the locations of the source and standoff +points you define as part of the incident wave interaction. +For spherical incident wave definitions, the wave reduces in amplitude as a function of space. By +default, the amplitude of a spherical wave is inversely proportional to the distance from the source; +this behavior is called “acoustic” propagation. For the preferred interface you can modify the default +propagation behavior to define spatial decay of the incident wave field. The dimensionless constants +, +between the source point +are used to define the spatial decay as a function of the distance +, and +and the loaded point and the distance +between the source point and the standoff point: +Refer to “Loading due to an incident dilatational wave field,” Section 6.3.1 of the Abaqus Theory Manual, +for details of the generalized spatial decay formulation. +In Abaqus incident wave interactions can be used to simulate diffuse incident fields. Diffuse fields +are characteristic of reverberant spaces or other situations in which waves from many directions strike +a surface. For example, reverberant chambers are constructed intentionally in acoustic test facilities +for sound transmission loss measurements. The diffuse field model used in Abaqus, as shown in +Figure 33.4.6–2, allows you to specify a seed number +deterministic incident plane waves travel +along vectors distributed over a hemisphere so that the incident power per solid angle approximates a +diffuse incident field. +; +The fluid and the solid surfaces where the incident loading acts are specified in the incident wave +loading definition. The incoming wave load is further described by the locations of its source point and of +a reference (“standoff”) point where the wave amplitude is specified. For information on how to specify +these surfaces and the standoff point, see “Identifying the fluid and the solid surfaces for incident wave +loading,” and “The standoff point” below. For a planar wave the specified locations of the source and +the standoff points are used to define the direction of wave propagation. +The speed of the incident wave is prescribed by giving the properties for the incident wave-bearing +acoustic medium. These specified properties should be consistent with the properties specified for the +fluid discretized using acoustic elements. +For the preferred interface you must define nodes corresponding to the source and standoff points +for the incident wave; the node numbers or set names must be specified for each incident wave definition. +“Source” +Unit hemisphere +oriented along +source-standoff vector +Plane wave along +one of N2 directions +Plane normal to +source-standoff +vector +N seed point +columns +“Standoff” +N seed point rows +FE surface +to be loaded +Figure 33.4.6–2 Diffuse loading model. +The node set names, if used, must contain only a single node. Neither the source node nor the standoff +node should be connected to any elements in the model. +Input File Usage: +*INCIDENT WAVE INTERACTION PROPERTY, +NAME=wave property name, TYPE=PLANE or SPHERE +speed of sound, fluid mass density, A, B, C +*INCIDENT WAVE INTERACTION, PROPERTY=wave property name +fluid surface name, source node, standoff node, reference magnitude +The constants A, B, and C apply only for spherical incident waves with +generalized spatial decay propagation. +*INCIDENT WAVE INTERACTION PROPERTY, +NAME=wave property name, TYPE=DIFFUSE +speed of sound, fluid mass density +*INCIDENT WAVE INTERACTION, PROPERTY=wave property name +fluid surface name, source node, standoff node, reference magnitude, N +Abaqus/CAE Usage: +The seed number N generates planar incident waves with directions distributed +on a hemisphere centered at the standoff point. +Interaction module: Create Interaction Property: Name: wave +property name and Incident wave, Speed of sound in fluid: speed +of sound, Fluid density: fluid mass density +Select one of the following definitions: +Definition: Planar +Definition: Spherical, Propagation model: Acoustic +Definition: Spherical, Propagation model: Generalized decay, +enter values for A, B, and C +Definition: Diffuse, Seed number: N +Create Interaction: Incident wave: select the source point, select +the standoff point, select the region: Wave property: wave property +name, Reference magnitude: reference magnitude +Identifying the fluid and the solid surfaces for incident wave loading +In the scattered wave formulation the incident wave loading must be specified on all fluid and solid +surfaces that reflect the incident wave with two exceptions: +• those fluid surfaces that have the pressure values directly prescribed using boundary conditions; and +• those fluid surfaces that have symmetry conditions (the symmetry must hold for both the loading +and the geometry). +In problems with a fluid-solid interface both surfaces must be specified in the incident wave loading +definition for the scattered formulation. See “Example: submarine close to the free surface,” shown in +Figure 33.4.6–4. +When the total pressure-based formulation is specified, the incident wave loading must be specified +only on the fluid surfaces that border the infinite region that is excluded from the model. Typically, these +surfaces have a nonreflecting radiation condition specified on them, and the implementation ensures that +the radiation condition is enforced only on the scattered response of the modeled domain and not on the +incident wave itself. See “Example: submarine close to the free surface,” and “Example: surface ship,” +shown in Figure 33.4.6–4 and Figure 33.4.6–5, respectively. +In certain problems, such as blast loads in air, you may decide that the blast wave loads on a structure +need to be modeled, but the surrounding fluid medium itself does not. In these problems the incident wave +loading is specified only on the solid surfaces since the fluid medium is not modeled. The distinction +between the scattered wave formulation and the total wave formulation for handling the incident wave +loading is not relevant in these problems since the wave propagation in the fluid medium is of no interest. +The standoff point +In transient analyses the standoff point is a reference point used to specify the pulse loading time history: +it is the point at which the user-defined pulse history is assumed to apply with no time delay, phase shift, +or spreading loss. In steady-state analyses using discrete planar or spherical sources, the standoff point +is the point at which the incident field has zero phase. +In transient analyses the standoff point should be defined so that it is closer to the source than any +point on the surfaces in the model that would reflect the incident wave. Doing so ensures that all the +points on these surfaces will be loaded with the specified time history of the source and that the analysis +begins before the wave overtakes any portion of these surfaces. To save analysis time, the standoff point +is typically on or near the solid surface where the incoming incident wave would be first deflected . However, the standoff point +is a fixed point in the analysis: if the loaded surfaces move before the incident wave loading begins, +due to previous analysis steps or geometric adjustments, the surfaces may envelop the specified standoff +point. Care should be taken to define a standoff point such that it remains closer to the incident wave +source point than any point on the loaded surfaces at the onset of the loading. +When the total wave formulation is used and the incident wave loading is specified in the first +step of the analysis in terms of pressure history, Abaqus automatically initializes the pressure and the +pressure rate at the acoustic nodes to values based on the incident wave loading. This allows the acoustic +analysis to start with the incident waves partially propagated into the problem domain at time zero and +assumes that this propagation had taken place with negligible effect of any volumetric dissipative sources +such as the fluid drag. When the incident wave loading is specified in terms of the pressure values, the +recommendations given above for selecting a standoff point are valid with the total wave formulation as +well. However, when the incident wave loading is specified in terms of acceleration values, the automatic +initialization is not done and the standoff point should be located near the exterior fluid boundary of the +model such that the standoff point is closer to the source than any point on the exterior boundary. See +“Example: submarine close to the free surface,” and “Example: surface ship,” shown in Figure 33.4.6–4 +and Figure 33.4.6–5, respectively. +In steady-state analyses the role of the standoff point is somewhat different. When the incident +wave interaction property is of planar or spherical type, you define the real and imaginary parts of the +magnitude at the standoff point. Separately, the specified real and imaginary incident waves are taken to +have zero phase at the standoff point (combined, these two waves could be equivalent to a single wave +with nonzero phase at the standoff). Every location on the loaded surface has a phase shift in the applied +pressure or acoustic traction, corresponding to the difference in propagation time between the loaded +point and the standoff. This means that an incident wave defined, for example, with a pure real value at +the standoff point generates both real and imaginary tractions at all the other points on the loaded surface. +When the incident wave is of diffuse type, the role of the standoff and source points is primarily +to orient the loaded surface with respect to the incoming reverberant field. The model used for +diffuse incident wave loading applies a set of deterministically defined plane waves, whose directions +are defined as vectors connecting the standoff point and an array of points on a hemisphere. This +hemisphere is centered at the standoff point, and its apex is the source point. The array of points is +set according to the specified seed, +points on the +hemisphere. The algorithm concentrates the points so that the incident waves in the diffuse field model +are concentrated at normal incidence, with fewer waves at oblique angles. The specified amplitude +value and reference magnitude are divided equally among the +incident waves. The orientation of +, and a deterministic algorithm that arranges +the hemisphere containing the incident waves in the diffuse model is the same for all of the points on +the loaded surface—it does not vary with the local normal vector on the surface. +Defining the amplitude of the source pulse +For transient analyses the time history to be specified by the user is that observed at the standoff point: +histories at a point on the loaded surface are computed from the wave type and the location of that point +relative to the standoff point. The time history of the acoustic source pulse can be defined either in terms +of the fluid pressure values or the fluid particle acceleration values. Pressure time histories can be used +for any type of element, such as acoustic, structural, or solid elements; acceleration time histories are +applicable only for acoustic elements. In either case a reference magnitude is specified for any given +incident-wave-loaded surface, and a reference to a time-history data table defined by an amplitude curve +is specified. The reference magnitude varies with time according to the amplitude definition. +For steady-state dynamic analyses the amplitude definition specified as part of the incident wave +interaction definition is interpreted as the frequency dependence of the wave at the standoff point. +Currently the source pulse description in terms of fluid particle acceleration history is limited to +planar incident waves acting on fluid surfaces in transient analyses. Further, if an impedance condition +is specified on the same fluid surface along with incident wave loading, the source pulse is restricted to +the pressure history type even for planar incident waves. The source pulse in terms of pressure history +can be used without these limitations; i.e., pressure-history-based incident wave loading can be used with +fluid or solid surfaces, with or without impedance, and for both planar and spherical incident waves. +When the source pulse is specified using pressure values and is applied on a fluid surface, the +pressure gradient is computed and applied as a pressure-conjugate load on these surfaces. Hence, it is +desirable to define the pulse amplitude to begin with a zero value, particularly when the cavitation in the +fluid is a concern. If the structural response is of primary concern and the scattered formulation is being +used, any initial jump in the pressure amplitude can be addressed by applying additional concentrated +loads on the structural nodes that are tied to the acoustic mesh, corresponding to the initial jump in the +incident wave pressure amplitude. Clearly, the additional load on any given structural node should be +active from the instance the incident wave first arrives at that structural node. However, the scattered +wave solution in the fluid still needs careful interpretation taking the initial jump into account. +Input File Usage: +Use the following option to define the time history in terms of fluid pressure +values: +*INCIDENT WAVE INTERACTION, PRESSURE AMPLITUDE=amplitude +data table name +solid or fluid surface name, source node, standoff node, reference magnitude +Use the following option to define the time history in terms of fluid particle +acceleration values: +*INCIDENT WAVE INTERACTION, ACCELERATION +AMPLITUDE=amplitude data table name +fluid surface name, source node, standoff node, reference magnitude +ACOUSTIC AND SHOCK LOADS +Use the following option to define the real part of the loading (default): +*INCIDENT WAVE INTERACTION, REAL +Use the following option to define the imaginary part of the loading: +*INCIDENT WAVE INTERACTION, IMAGINARY +Interaction module: Create Interaction: Incident wave: select the +source point, select the standoff point, select the region: Reference +magnitude: reference magnitude +Use the following options to define the time history in terms of fluid pressure +values or fluid particle acceleration values: +Definition: Pressure or Acceleration, Pressure amplitude or +Acceleration amplitude: amplitude data table name +Use the following options to define the real or imaginary part of the loading: +Toggle on Real amplitude and/or Imaginary amplitude: +amplitude data table name +Defining bubble loading for spherical incident wave loading +An underwater explosion forms a highly compressed gas bubble that interacts with the surrounding water, +generating an outward-propagating shock wave. The gas bubble floats upward as it generates these waves +changing the relative positions of the source and the loaded surfaces. The loading effects due to bubble +formation can be defined for spherical incident wave loading by using a bubble definition in conjunction +with the incident wave loading definition. +The bubble dynamics can be described using a model internal to Abaqus or by using tabulated data. +Abaqus has a built-in mechanical model of the bubble interacting with the surrounding fluid, which is +simulated numerically to generate a set of data prior to running the finite element analysis. You can +specify the explosive material parameters, ending time, and other parameters that affect the computation +of the bubble amplitude curve used, as shown in Table 33.4.6–2. +Table 33.4.6–2 Parameters that define the bubble behavior. +Name +Dimensions +Description +Default +FL−2 (LM−1/3 )1+A +Charge constant +T/(M LB ) +Charge constant +Dimensionless +Similitude spatial exponent +Dimensionless +Similitude temporal exponent +F/L2 +Charge constant +Dimensionless +Ratio of specific heats for +explosion gas +None +None +None +None +None +None +Name +Dimensions +Description +Default +None +None +None +None +None +None +None +None +1.0 +0.0 +2.0 +None +1500 +M/L3 +Dimensionless +Dimensionless +Dimensionless +L/T2 +F/L2 +Charge material density +Mass of charge +Initial charge depth +X-direction cosine of the free +surface normal +Y-direction cosine of the free +surface normal +Z-direction cosine of the free +surface normal +Acceleration due to gravity +Atmospheric pressure at free +surface +Dimensionless +Wave effect parameter +Dimensionless +Bubble drag coefficient +Dimensionless +Bubble drag exponent +Dimensionless +Dimensionless +Dimensionless +Dimensionless +M/L3 +L/T +Maximum allowable time in +bubble simulation +Maximum allowable number of +steps in bubble simulation +Relative error tolerance parameter +for bubble simulation +Absolute error tolerance +parameter for bubble simulation +1 × 10−11 +1 × 10−11 +Error control exponent for bubble +simulation +0.2 +Fluid mass density +Fluid speed of sound +None +None +All of the parameters specified affect only the bubble amplitude; other physical parameters in the +problem are independent. You can suppress the effects of wave loss in the bubble dynamics and +introduce empirical flow drag, if desired. Detailed information about the bubble mechanical model +is given in “Loading due to an incident dilatational wave field,” Section 6.3.1 of the Abaqus Theory +Manual. +In an underwater explosion event a bubble migrates upward toward, and possibly reaches, the free +water surface. If the bubble migration reaches the free water surface during the specified analysis time, +Abaqus applies loads of zero magnitude after this point. +Model data about +the bubble simulation are written to the data (.dat) file. During an +Abaqus/Standard analysis history data are written each increment to the output database (.odb) file. +The history data include the radius of the bubble and the bubble depth below the free water surface. For +reference, the pressure and acoustic load quantities at the standoff point are also written to the data file; +these load terms include the direct plane-wave term and the spherical spreading (“afterflow”) effect . +For the preferred interface the loading effects due to bubble formation can be defined for spherical +incident wave loading using the UNDEX charge property definition. Because the bubble simulation uses +spherical symmetry, the incident wave interaction property must define a spherical wave. +You can also specify incident wave loading due to bubble dynamics using tabulated data for the +pressure and source migration. For the preferred interface you specify independent amplitude curves +for the pressure at the standoff point and any source node location time histories. The source location +amplitude names are referred to from boundary condition definitions for the source node. +Input File Usage: +Use the following options to specify loading effects due to bubble formation +using the UNDEX charge property definition: +*INCIDENT WAVE INTERACTION PROPERTY, +NAME=wave property name, TYPE=SPHERE +*UNDEX CHARGE PROPERTY +data defining the UNDEX charge +*INCIDENT WAVE INTERACTION, PROPERTY=wave property name, +UNDEX +fluid surface name, source node, standoff node, reference magnitude +Use the following options to specify pressure at the standoff point using +tabulated data: +*AMPLITUDE, DEFINITION=TABULAR, NAME=pressure +*INCIDENT WAVE INTERACTION, PRESSURE AMPLITUDE=pressure +solid or fluid surface name, source node, standoff node, reference magnitude +Use the following options to specify source node location time histories using +tabulated data: +*AMPLITUDE, DEFINITION=TABULAR, NAME=name +*BOUNDARY, TYPE=DISPLACEMENT or VELOCITY, +AMPLITUDE=name +source node, degrees of freedom +Abaqus/CAE Usage: +Use the following input to specify loading effects due to bubble formation using +the UNDEX charge property definition: +Interaction module: Create Interaction Property: Name: wave property +name and Incident wave: Definition: Spherical, Propagation model: +UNDEX charge, enter data defining the UNDEX charge +Create Interaction: Incident wave: Definition: UNDEX, Wave property: +wave property name, enter data defining the UNDEX charge +Use the following input to specify pressure at the standoff point using tabulated +data: +Load or Interaction module: Create Amplitude: Name: pressure +and select Tabular +Interaction module: Create Interaction: Incident wave: select the standoff +point: Definition: Pressure, Pressure amplitude: pressure +Use the following input to specify source node location time histories using +tabulated data: +Load or Interaction module: Create Amplitude: Name: name +and select Tabular +Load module: Create Boundary Condition: select step: +Displacement/Rotation or Velocity/Angular velocity: select +the source node as the region and toggle on the degree or degrees +of freedom, Amplitude: name +Modeling incident wave loading on a moving structure +To model the effect of relative motion between a structure (such as a ship) and the wave source during +the analysis using the preferred interface, the source node may be assigned a velocity. It is assumed that +the entire fluid-solid model is moving at a velocity with respect to the source node during the loading and +that the speed of the model’s motion is low compared to the speed of propagation of the incident wave. +That is, the effect of the speed of the source is neglected in the computation of the loads, but the change +in position of the source is included. This is equivalent to assuming that the relative motion between +the source and the model is at a low Mach number. Relative motion can be specified only for transient +analyses. +In addition to prescribing boundary conditions at the source node, a small mass element must be +defined at the source node. +Input File Usage: +Use the following option to assign a velocity to the source node: +*BOUNDARY, TYPE=DISPLACEMENT or VELOCITY, +AMPLITUDE=name +source node, degrees of freedom +Abaqus/CAE Usage: +Load module: Create Boundary Condition: select step: Velocity/Angular +velocity or Displacement/Rotation: select regions and toggle on the +degree or degrees of freedom, Amplitude: name +Specifying the reflection effects +The waves emanating from the source may reflect off plane surfaces, such as seabeds or sea surfaces, +before reaching the specified standoff point. Thus, the incident wave loading consists of the waves +arriving from a direct path from the source, as well as those arriving from reflections off the planes. In +Abaqus an arbitrary number of these planes can be defined, each with its own location, orientation, and +reflection coefficient. +If no reflection coefficient is specified, the plane is assumed to be nonreflective; a zero reflected +If a reflection coefficient is specified, the magnitude of the reflected waves are +pressure is applied. +modified by the reflection coefficient +according to the formula: +Only real values for +are used. +The reflection planes are allowed only for incident waves that are defined in terms of fluid pressure +values. Only one reflection off each plane is considered. If the effect of many successive reflections +is important, these surfaces should be part of the finite element model. Reflection planes should not be +used at a boundary of the finite element model if the total wave formulation is used, since in that case +the incident wave will be reflected automatically by that boundary. +Input File Usage: +Use the following option in conjunction with the *INCIDENT WAVE +INTERACTION option to define an incident wave reflection plane: +Abaqus/CAE Usage: +*INCIDENT WAVE REFLECTION +Incident wave reflections are not supported in Abaqus/CAE. +Boundary with prescribed pressure +The acoustic pressure degree of freedom at nodes of acoustic elements can be prescribed using a boundary +condition. However, since you can use the nodal acoustic pressure in an Abaqus analysis to refer to +the total pressure at that point or to only the scattered component, care must be exercised in some +circumstances. +When the total wave formulation is used, a boundary condition alone is sufficient to specify a +prescribed total dynamic pressure on a boundary. +In an analysis without incident wave loading, the nodal degree of freedom is generally equal to the +total acoustic pressure at that point. Therefore, its value can be prescribed using a boundary condition in +a manner consistent with other boundary conditions in Abaqus. For example, you may set the acoustic +pressure at all of the nodes at a duct inlet to a prescribed amplitude to analyze the propagation of waves +along the duct. The free surface of a body of water can be modeled by setting the acoustic pressure to +zero at the surface. +When incident wave loading is used, the scattered wave formulation defines the nodal acoustic +degree of freedom to be equal to the scattered pressure. Consequently, a boundary condition definition +for this degree of freedom affects the scattered pressure only. The total acoustic pressure at a node is +not directly accessible in this formulation. Specification of the total pressure in a scattered formulation +analysis is nevertheless required in some instances (for example, when modeling a free surface of a body +of water). In this case, one of the following methods should be used. +If the fluid surface with prescribed total pressure is planar, unbroken, and of infinite extent, an +incident wave reflection plane and a boundary condition can be used together to model the fact that the +total pressure is zero on the free surface. A “soft” incident wave reflection plane coincident with the +free surface will make sure that the structure is subjected to the incident wave load reflected off the free +surface. A boundary condition setting the acoustic pressure in the surface equal to zero will make sure +that any scattered waves emitted by the structure are reflected properly. The scattered wave solution +in the fluid must be interpreted taking into consideration the fact that the incident field now includes a +reflection of the source as well. If the fluid surface with prescribed total pressure is planar but broken by +an object, such as a floating ship, this modeling technique may still be applied. However, the reflected +loads due to the incident wave are computed as if the reflection plane passes through the hull of the ship; +this approximation neglects some diffraction effects and may or may not be applicable in all situations +of interest. +Alternatively, the free surface condition of the fluid can be eliminated by modeling the top layer +of the fluid using structural elements, such as membrane elements, instead of acoustic elements. The +“structural fluid” surface and the “acoustic fluid” surface are then coupled using either a surface-based +mesh tie constraint (“Mesh tie constraints,” Section 34.3.1) or, in Abaqus/Standard, acoustic-structural +interface elements; and the incident wave loading must be applied on both the “structural fluid” and the +“acoustic fluid” surfaces. The material properties of the “structural fluid” elements should be similar to +those of the adjacent acoustic fluid. In Abaqus/Explicit the thickness of the “structural fluid” elements +must be such that the masses at nodes on either side of the coupling constraint are nearly equal. This +modeling technique allows the geometry of the surface on which total pressure is to be prescribed to +depart from an unbroken, in���nite plane. As a secondary benefit of this technique, you can obtain the +velocity profile on the free surface since the displacement degrees of freedom are now activated at the +If a nonzero pressure boundary condition is desired, it can be applied as a +“structural fluid” nodes. +distributed loading on the other side of the “structural fluid” elements. +Input File Usage: +Use the following options for the first modeling technique with the default +scattered wave formulation: +*BOUNDARY +*INCIDENT WAVE REFLECTION +Use the following option for the second modeling technique with the default +scattered wave formulation: +*TIE +*INCIDENT WAVE INTERACTION +Use the following option with the total wave formulation: +Abaqus/CAE Usage: +*BOUNDARY +Load module: Create BC: choose Other for the Category and Acoustic +pressure for the Types for Selected Step +Defining air blast loading for incident shock waves using the CONWEP model in Abaqus/Explicit +An explosion in air forms a highly compressed gas mass that interacts with the surrounding air, generating +an outward-propagating shock wave. The loading effects due to an explosion in air can be defined, for +spherical incident waves (air blast) or hemispherical incident waves (surface blast), by empirical data +provided by the CONWEP model in conjunction with the incident wave loading definition. +Unlike an acoustic wave, a blast wave corresponds to a shock wave with discontinuities in pressure, +density, etc. across the wave front. Figure 33.4.6–3 shows a typical pressure history of a blast wave. +Pressure +max +Exponential decay +Positive phase +atm +Time of +detonation +Time of +arrival +Negative phase +Time +Figure 33.4.6–3 Pressure history of a blast wave. +The CONWEP model uses a scaled distance based on the distance of the loading surface from the +source of the explosion and the amount of explosive detonated. For a given scaled distance, the model +provides the following empirical data: the maximum overpressure (above atmospheric), the arrival time, +the positive phase duration, and the exponential decay coefficient for both the incident pressure and +the reflected pressure. Using these parameters, the entire time history of both the incident pressure and +reflected pressure as shown in Figure 33.4.6–3 can be constructed. Use of a standoff point is not required. +, on a surface due to the blast wave is a function of the incident pressure, +, which is defined as +the angle between the normal of the loading surface and the vector that points from the surface to the +explosion source. The total pressure is defined as +, and the angle of incidence, +, the reflected pressure, +The total pressure, +The air blast loading due to the total pressure can be scaled using a magnitude scale factor. +A detonation time can be specified if the explosion does not occur at the start of the analysis. The +detonation time needs to be given in total time; see “Conventions,” Section 1.2.2, for a description of +the time convention. The arrival time at a location is defined as the elapsed time for the wave to arrive +at that location after detonation. +The CONWEP empirical data are given in a specific set of units, which must be converted to the +units used in the analysis. You will need to specify multiplying factors for conversion of these units to +SI units. For the specification of the mass of the explosive in TNT equivalence, you can choose any +convenient mass unit, which can be different from the mass unit used in the analysis. For computation +of the pressure loading, you will need to specify multiplying factors for conversion of length, time, and +pressure units used in the analysis to SI units. Some typical conversion multiplier values are given in +Table 33.4.6–3. +Table 33.4.6–3 Multipliers used in conjunction with the CONWEP +model for conversion to SI units. +Quantity +Unit +SI Unit +Multiplier for +conversion to SI +Mass +Mass +Length +Length +Time +Pressure +Pressure +Pressure +ton +lb +mm +ft +msec +MPa +psi +psf +kg +kg +sec +Pa +Pa +Pa +1000 +0.45359 +0.001 +0.3048 +0.001 +10−6 +6894.8 +47.88 +For any given amount of explosive, the CONWEP empirical data are valid only within a range +of distances from the source. The minimum distance at which the data are valid corresponds to the +charge radius. Thus, the analysis terminates if the distance of any part of the loading surface from the +source is less than the charge radius. For distances that are larger than the maximum valid range, linear +extrapolation is used up to an extended maximum range where the reflected pressure decreases to zero. +No loading is applied beyond the extended maximum range. +The CONWEP empirical data do not account for shadowing by intervening objects or for any effects +due to confinement. In the definition of incident wave interaction using the CONWEP model, you cannot +use incident wave reflection. +The CONWEP pressure load can be requested as element face variable output to the output database +file . +Input File Usage: +Use the following options to specify loading effects due to explosion in air using +the CONWEP charge property definition: +*INCIDENT WAVE INTERACTION PROPERTY, +NAME=wave property name, TYPE=AIR BLAST or SURFACE BLAST +*CONWEP CHARGE PROPERTY +data defining the CONWEP charge +*INCIDENT WAVE INTERACTION, PROPERTY=wave property name, +CONWEP +loading surface name, source node, detonation time, magnitude scale factor +Abaqus/CAE Usage: +Use the following options to specify loading effects due to explosion in air using +the CONWEP charge property definition: +Interaction module: Create Interaction Property: Name: wave +property name and Incident wave: Definition: Air blast or Surface +blast: enter data defining the CONWEP charge +Interaction module: Create Interaction: Name: incident wave name +and Incident wave: select the source point: CONWEP (Air/Surface +blast): select the region: CONWEP Data: enter data defining the +time of detonation and magnitude scale factor +Modifying or removing incident wave loads +Only the incident wave loads that are specified in a particular step are applied in that step; previous +definitions are removed automatically. Consequently, incident wave loads that are active during two +subsequent steps should be specified in each step. This is akin to the behavior that can be specified +for other types of loads by releasing any load of that type in a step . +Alternative incident wave loading interface +In general, the concepts of the alternative incident wave loading interface are the same as the preferred +interface; however, the syntax for specifying the incident wave loading is different. The preferred +incident wave loading interface is supported in Abaqus/CAE. The alternative interface is not supported +in Abaqus/CAE. For conceptual information, see “Incident wave loading due to external sources.” +Prescribing the geometric properties and the speed of the incident wave (alternative interface) +Conceptually, the alternative interface is the same as the preferred interface; however, the usages are +different. For conceptual information, see “Prescribing geometric properties and the speed of the incident +wave.” +Input File Usage: +Abaqus/CAE Usage: +*INCIDENT WAVE PROPERTY, NAME=wave property name, +TYPE=PLANE or SPHERE +data lines to specify the location of the acoustic source and the standoff point +*INCIDENT WAVE FLUID PROPERTY +bulk modulus, mass density +*INCIDENT WAVE, PROPERTY=wave property name +The alternative incident wave loading interface is not +Abaqus/CAE. +supported in +Defining the time history of the source pulse (alternative interface) +Conceptually, the alternative interface is the same as the preferred interface; however, the usages are +different. For conceptual information, see “Defining the amplitude of the source pulse.” +Input File Usage: +Use the following option to define the time history in terms of fluid pressure +values: +*INCIDENT WAVE, PRESSURE AMPLITUDE=amplitude data table name +solid or fluid surface name, reference magnitude +Use the following option to define the time history in terms of fluid particle +acceleration values: +*INCIDENT WAVE, ACCELERATION AMPLITUDE=amplitude data table +name +fluid surface name, reference magnitude +Abaqus/CAE Usage: +The alternative incident wave loading interface is not +Abaqus/CAE. +supported in +Defining bubble loading for spherical incident wave loading (alternative interface) +Conceptually, the alternative interface is the same as the preferred interface; however, the usages are +different. For conceptual information, see “Defining bubble loading for spherical incident wave loading.” +To define the bubble dynamics using a model internal to Abaqus, you can specify a bubble +amplitude. Use of the bubble loading amplitude is generally similar to the use of any other amplitude in +Abaqus. +Input File Usage: +Use the following options: +*AMPLITUDE, DEFINITION=BUBBLE, NAME=name +*INCIDENT WAVE PROPERTY, TYPE=SPHERE, +NAME=wave property name +*INCIDENT WAVE, PRESSURE AMPLITUDE=name +solid or fluid surface name, reference magnitude +Abaqus/CAE Usage: +The alternative incident wave loading interface is not +Abaqus/CAE. +supported in +To define the bubble dynamics using tabulated data for the pressure and source migration, you can +specify independent amplitude curves for the pressure at the standoff point and any source location time +histories. The source location amplitude names, or floating point data for source point coordinates that +remain fixed, are referred to in the incident wave property definition. The amplitude name for the pressure +amplitude is referred to in the incident wave loading definition in the usual manner. +Input File Usage: +Use the following options: +*AMPLITUDE, DEFINITION=TABULAR, NAME=Pressure +*AMPLITUDE, DEFINITION=TABULAR, NAME=X +*AMPLITUDE, DEFINITION=TABULAR, NAME=Y +*AMPLITUDE, DEFINITION=TABULAR, NAME=Z +*INCIDENT WAVE PROPERTY, TYPE=SPHERE, +NAME=wave property name +{standoff point data} +X, Y, Z +*INCIDENT WAVE, PRESSURE AMPLITUDE=Pressure +solid or fluid surface name, reference magnitude +Abaqus/CAE Usage: +The alternative incident wave loading interface is not +Abaqus/CAE. +supported in +Specifying the reflection effects (alternative interface) +Conceptually, the alternative interface is the same as the preferred interface; however, the usages are +different. For conceptual information, see “Specifying the reflection effects.” +Input File Usage: +Use the following option in conjunction with the *INCIDENT WAVE option +to define an incident wave reflection plane: +Abaqus/CAE Usage: +*INCIDENT WAVE REFLECTION +The alternative incident wave loading interface is not +Abaqus/CAE. +supported in +Modeling incident wave loading on a moving structure (alternative interface) +To model the effect of rigid motion of a structure such as a ship during the incident wave loading history, +the standoff point can have a specified velocity. It is assumed that the entire fluid-solid model is moving +at this velocity with respect to the source point during the loading and that the speed of the model’s +motion is low compared to the speed of propagation of the incident wave. +Input File Usage: +*INCIDENT WAVE PROPERTY, NAME=wave property name +data line to specify the velocity of the standoff point +Abaqus/CAE Usage: +The alternative incident wave loading interface is not +Abaqus/CAE. +supported in +Example: submarine close to the free surface +The problem shown in Figure 33.4.6–4 has the following features: a free surface +reflection plane, a wet solid surface +the boundary +of the underwater explosion loading is also shown. +as a +, and +of the finite modeled domain separating the infinite acoustic medium. The source S +, seabed +that is tied to the solid surface +, the fluid surface +Free surface A 0 +Acoustic medium +Source +Seabed A sb +Solid surface Asw +Fluid +surface Afw +inf +model boundary +Figure 33.4.6–4 Incident wave loading on a submarine lying near a free surface. +Scattered wave solution +Here the scattered wave response in the acoustic medium is of interest along with that of the structure +to the incident wave loading. Cavitation in the fluid is not considered in a scattered wave formulation. +Similarly, the initial hydrostatic pressure in the fluid is not modeled. +The zero dynamic acoustic pressure boundary condition on the free surface requires both a “soft” +and a zero scattered pressure boundary condition at +, and on +. The incident wave loading can be only of pressure amplitude type since the +reflection plane coinciding with the free surface +the nodes on this free surface. The incident wave loading is applied on the fluid surface, +the wet solid surface, +loading includes a solid surface. +A good location for the standoff node is marked as A in Figure 33.4.6–4. This node is in the fluid, +close to the structure, and closer to incident wave source S than any portion of the seabed or the free +surface. The standoff node’s offset from the loaded surfaces is exaggerated for emphasis in the figure. +The radiation condition is specified on the acoustic surface +such that the scattered wave +impinging on this boundary with the infinite medium does not reflect back into the computational +domain. The seabed is modeled with an incident wave reflection plane on surface +. The reflection +loss at this seabed surface is modeled using an impedance property. +If the response of the structure in the nonlinear regime is of interest, the initial stress state in the +structure should be established using Abaqus/Standard in a static analysis. The stress state in the structure +is then imported into Abaqus/Explicit, and the loading on the solid surfaces causing the initial stress state +is respecified in the acoustic analysis. +The following template schematically shows some of the Abaqus input file options that are used to +solve this problem using the scattered wave formulation: +*HEADING +… +*SURFACE, NAME= +Data lines to define the acoustic surface that is wetting the solid +*SURFACE, NAME= +Data lines to define the solid surface that is wetted by the fluid +*SURFACE, NAME= +Data lines to define the acoustic surface separating the modeled region from the infinite medium +*INCIDENT WAVE INTERACTION PROPERTY, NAME=IWPROP +*AMPLITUDE, DEFINITION=TABULAR, NAME=PRESSUREVTIME +*TIE, NAME=COUPLING +, +*STEP +** For an Abaqus/Standard analysis: +*DYNAMIC +** For an Abaqus/Explicit analysis: +*DYNAMIC, EXPLICIT +** Load the acoustic surface +*INCIDENT WAVE INTERACTION, PRESSURE AMPLITUDE=PRESSUREVTIME, +PROPERTY=IWPROP +, source node, standoff node, reference magnitude +*INCIDENT WAVE REFLECTION +Data lines for the reflection plane over the seabed +*INCIDENT WAVE REFLECTION +Data lines for a "soft" reflection plane over the free surface +** Load the solid surface +*INCIDENT WAVE INTERACTION, PRESSURE AMPLITUDE=PRESSUREVTIME, +PROPERTY=IWPROP +, seabed_Q +. +, source node, standoff node, reference magnitude +*INCIDENT WAVE REFLECTION +Data lines for the reflection plane over the seabed +*INCIDENT WAVE REFLECTION +, seabed_Q +Data lines for a "soft" reflection plane over the free surface +*BOUNDARY +** zero pressure boundary condition on the free surface +Set of nodes on the free surface +*SIMPEDANCE +, 8, 8, 0.0 +. +, +*END STEP +Total wave solution +Here the total wave response in the acoustic medium is of interest along with that of the structure to +the incident wave loading. Cavitation in the fluid may be included. Similarly, a linearly varying initial +hydrostatic pressure in the fluid can be specified. +The zero dynamic acoustic pressure boundary condition on the free surfaces requires only a +zero pressure boundary condition at the nodes on this free surface. A reflection plane should not be +included along the free surface. The incident wave loading is applied only on the fluid surface, +, +that separates the modeled region from the surrounding infinite acoustic medium. No incident wave +should be applied directly on the structure surfaces. +If the incident wave is considered planar, an +acceleration-type amplitude can be used with the incident wave loading. Otherwise, a pressure-type +amplitude must be used with the incident wave loading. +An ideal location for the standoff node depends on the type of amplitude used for the time history +of the incident wave loading. The location A shown in Figure 33.4.6–4 can be used if the incident wave +loading time history is of pressure amplitude type. Otherwise, the location B that is just on the boundary +and closer to the source S than any part of either the seabed or the free surface can be used. +The nonreflecting impedance condition is specified on the acoustic surface, +, such that the +scattered part of the total wave impinging on this boundary with the infinite medium does not reflect +back into the computational domain. The seabed is modeled with an incident wave reflection plane on +the surface +. +If the response of the structure in the nonlinear regime is of interest, the initial stress state in the +structure should be established using Abaqus/Standard in a static analysis. The stress state in the structure +is then imported into Abaqus/Explicit, and the loading on the solid surfaces causing the initial stress state +is respecified in the acoustic analysis. +The following template schematically shows some of the input file options that are used to solve +this problem using the total wave formulation: +*HEADING +… +*ACOUSTIC WAVE FORMULATION, TYPE=TOTAL WAVE +*MATERIAL, NAME=CAVITATING_FLUID +*ACOUSTIC MEDIUM, BULK MODULUS +Data lines to define the fluid bulk modulus +*ACOUSTIC MEDIUM, CAVITATION LIMIT +Data lines to define the fluid cavitation limit +… +*SURFACE, NAME= +Data lines to define the acoustic surface that is wetting the solid +*SURFACE, NAME= +Data lines to define the solid surface that is wetted by the fluid +*SURFACE, NAME= +Data lines to define the acoustic surface separating the modeled region from the infinite medium +*INCIDENT WAVE INTERACTION PROPERTY, NAME=IWPROP +*AMPLITUDE, DEFINITION=TABULAR, NAME=PRESSUREVTIME +Data lines to define the pressure-time history at the standoff point +*TIE, NAME=COUPLING +, +*INITIAL CONDITIONS, TYPE=ACOUSTIC STATIC PRESSURE +Data lines to define the initial linear hydrostatic pressure in the fluid +*STEP +*DYNAMIC, EXPLICIT +** Load the acoustic surface +*INCIDENT WAVE INTERACTION, PRESSURE AMPLITUDE=PRESSUREVTIME, +PROPERTY=IWPROP +, source node, standoff node, reference magnitude +*INCIDENT WAVE REFLECTION +Data lines for the reflection plane over the seabed +*BOUNDARY +** zero pressure boundary condition on the free surface +Set of nodes on the free surface +*SIMPEDANCE +, seabed_Q +, 8, 8, 0.0 +, +*END STEP +Example: submarine in deep water +This problem is similar to the previous example of a submarine close to the free surface except for the +following differences. There is no free surface in this problem; and the fluid surface, +, and the fluid +medium completely enclose the structure. If the structure is sufficiently deep in the water, hydrostatic +pressure may be considered uniform instead of varying linearly with depth. Under this assumption, +the initial stress state in the structure can be established with a uniform pressure loading all around it, +if desired. In addition, if the structure is sufficiently deep in the water, the hydrostatic pressure may +be significant compared to the incident wave loading; hence, the cavitation in the fluid may not be of +concern. +Example: surface ship +Here the effect of underwater explosion loading on a surface ship is of interest . +This problem is similar to the previous example of a submarine close to the free surface except for the +Free surface A 01 +Free surface A 02 +Wet solid +surface Asw +Fluid +surface Afw +Source +Seabed A sb +inf +model boundary +Figure 33.4.6–5 Modeling of incident wave loading on a surface ship. +following differences. The free surface of fluid is not continuous, and a part of the structure is exposed +to the atmosphere. A soft reflection plane coinciding with the free surface is not used in this problem +as in the submarine problems under the scattered wave formulation. To be able to use the scattered +wave formulation in this case, the modeling technique is used in which the free surface is replaced with +“structural fluid” elements. A layer of fluid at the free surface is modeled using non-acoustic elements +such as membrane elements. These elements are coupled to the underlying acoustic fluid using a mesh +tie constraint. The non-acoustic elements have properties similar to the fluid itself since these elements +are replacing the fluid medium near the free surface and should have a thickness similar to the height of +the adjacent acoustic elements. Incident wave loading with the scattered wave formulation must now be +applied on these newly created surfaces as well. This technique has the added advantage of providing +the deformed shape of the free surface under the loading. +The following template shows some of the Abaqus input file options used for this case: +*HEADING +… +*SURFACE, NAME=A01_structuralfluid +Data lines to define the "structural fluid" surface +*SURFACE, NAME=A01_acousticfluid +Data lines to define the adjacent acoustic fluid surface +*SURFACE, NAME=A02_structuralfluid +Data lines to define the "structural fluid" surface +*SURFACE, NAME=A02_acousticfluid +Data lines to define the adjacent acoustic fluid surface +*SURFACE, NAME=Asw_solid +Data lines to define the actual solid surface that is wetted by the fluid +*SURFACE, NAME=Asw_fluid +Data lines to define the actual acoustic surface that is adjacent to the structure +*SURFACE, NAME= +Data lines to define the acoustic surface separating the modeled region from the infinite medium +*INCIDENT WAVE INTERACTION PROPERTY, NAME=IWPROP +*AMPLITUDE, DEFINITION=TABULAR, NAME=PRESSUREVTIME +Data lines to define the pressure-time history at the standoff point +*TIE, NAME=COUPLING +Asw_fluid, Asw_solid +A01_acousticfluid, A01_structuralfluid +A02_acousticfluid, A02_structuralfluid +*STEP +** For an Abaqus/Standard analysis: +*DYNAMIC +** For an Abaqus/Explicit analysis: +*DYNAMIC, EXPLICIT +** Load the acoustic surfaces +*INCIDENT WAVE INTERACTION, PRESSURE AMPLITUDE=PRESSUREVTIME, +PROPERTY=IWPROP +A01_acousticfluid, source point, standoff point, reference magnitude +*INCIDENT WAVE REFLECTION +Data lines for the reflection plane over the seabed +*INCIDENT WAVE INTERACTION, PRESSURE AMPLITUDE=PRESSUREVTIME, +PROPERTY=IWPROP +A02_acousticfluid, source point, standoff point, reference magnitude +*INCIDENT WAVE REFLECTION +Data lines for the reflection plane over the seabed +*INCIDENT WAVE INTERACTION, PRESSURE AMPLITUDE=PRESSUREVTIME, +PROPERTY=IWPROP +Asw_fluid, source point, standoff point, reference magnitude +*INCIDENT WAVE REFLECTION +Data lines for the reflection plane over the seabed +** Load the solid surfaces +*INCIDENT WAVE INTERACTION, PRESSURE AMPLITUDE=PRESSUREVTIME, +PROPERTY=IWPROP +A01_structuralfluid, source point, standoff point, reference magnitude +*INCIDENT WAVE REFLECTION +Data lines for the reflection plane over the seabed +*INCIDENT WAVE INTERACTION, PRESSURE AMPLITUDE=PRESSUREVTIME, +, seabed_Q +, seabed_Q +, seabed_Q +, seabed_Q +PROPERTY=IWPROP +A02_structuralfluid, source point, standoff point, reference magnitude +*INCIDENT WAVE REFLECTION +Data lines for the reflection plane over the seabed +*INCIDENT WAVE INTERACTION, PRESSURE AMPLITUDE=PRESSUREVTIME, +PROPERTY=IWPROP +Asw_solid, source point, standoff point, reference magnitude +*INCIDENT WAVE REFLECTION +Data lines for the reflection plane over the seabed +*SIMPEDANCE +, seabed_Q +, seabed_Q +, +*END STEP +Compared to the total wave formulation analysis of a submarine close to the free surface, the +following differences are noteworthy. As shown in Figure 33.4.6–5, the free surface with zero dynamic +pressure boundary condition is now split into two parts: +. The fluid surface wetting the ship +( +), which are tied together, do not encircle the whole structure. +Besides these differences, the modeling considerations for the surface ship problem are similar to the +total wave analysis of the submarine near the free surface. +) and the wetted ship surface ( +and +Example: airblast loading on a structure +Here the effect of airblast (explosion in the air) loading on a structure is of interest . +Since the stiffness and inertia of the air medium are negligible, the acoustic medium is not modeled. +Rather the incident wave loading is applied directly on the structure itself. The solid surface +where +the incident wave loading is applied is shown in Figure 33.4.6–6. Since the acoustic medium is not +modeled, the total wave and the scattered wave formulations are identical. +Example: fluid cavitation without incident wave loading +You may be interested in modeling acoustic problems in Abaqus/Explicit where the loading is applied +through either prescribed pressure boundaries or specified pressure-conjugate concentrated loads. Choice +of the scattered or the total wave formulation is not relevant in these problems even when the acoustic +medium is capable of cavitation. +Outer solid surface A sw +Source +Standoff +point +Figure 33.4.6–6 Modeling of airblast loading on a structure. +33.4.7 +PORE FLUID FLOW +Products: Abaqus/Standard Abaqus/CAE +References +• “Applying loads: overview,” Section 33.4.1 +• *CFLOW +• *DFLOW +• *DSFLOW +• *FLOW +• *SFLOW +• “Defining a surface pore fluid flow,” Section 16.9.22 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Defining a concentrated pore fluid flow,” Section 16.9.21 of the Abaqus/CAE User’s Manual, in +the online HTML version of this manual +Overview +Pore fluid flow can be prescribed in coupled pore fluid diffusion/stress analysis and in the geostatic stress field procedure . Pore fluid flow can be prescribed by: +• defining seepage coefficients and sink pore pressures on element faces or surfaces; +• defining drainage-only seepage coefficients on element faces or surfaces that are applied only when +surface pore pressures are positive; or +• prescribing an outward normal flow velocity directly at nodes, on element faces, or on surfaces. +Defining pore fluid flow as a function of the current pore pressure in consolidation analysis +In consolidation analysis you can provide seepage coefficients and sink pore pressures on element faces +or surfaces to control normal pore fluid flow from the interior of the region modeled to the exterior of +the region. +The surface condition assumes that the pore fluid flows in proportion to the difference between the +current pore pressure on the surface, +, and some reference value of pore pressure, +: +where +is the component of the pore fluid velocity in the direction of the outward normal to the +surface; +is the seepage coefficient; +is the current pore pressure at this point on the surface; and +is a reference pore pressure value. +Specifying element-based pore fluid flow +To define element-based pore fluid flow, specify the element or element set name; the distributed load +type; the reference pore pressure, +. The face of the elements +upon which the normal flow is enforced is identified by a seepage distributed load type. The seepage +types available depend on the element type . +; and the reference seepage coefficient, +Input File Usage: +*FLOW +element number or element set name, Qn, +, +Abaqus/CAE Usage: +Pore fluid flow cannot be defined as a function of the current pore pressure in +Abaqus/CAE. +Specifying surface-based pore fluid flow +To define surface-based pore fluid flow, specify a surface name, the seepage flow type, the reference pore +pressure, and the reference seepage coefficient. The element-based surface contains the element and face information. +Input File Usage: +*SFLOW +surface name, Q, +, +Abaqus/CAE Usage: +Pore fluid flow cannot be defined as a function of the current pore pressure in +Abaqus/CAE. +Defining drainage-only flow +Drainage-only flow types can be specified for element-based or surface-based pore fluid flow to indicate +that normal pore fluid flow occurs only from the interior to the exterior region of the model. The drainage- +only flow surface condition assumes that the pore fluid flows in proportion to the magnitude of the current +pore pressure on the surface, +, when that pressure is positive: +where +is the component of the pore fluid velocity in the direction of the outward normal to the +surface; +is the seepage coefficient; and +is the current pore pressure at this point on the surface. +Figure 33.4.7–1 illustrates this pore pressure–velocity relationship. This surface condition is +designed for use with the total pore pressure formulation , mainly for cases where the phreatic surface intersects an exterior surface that +is free to drain. See “Calculation of phreatic surface in an earth dam,” Section 10.1.2 of the Abaqus +Example Problems Manual, for an example of this type of calculation. +, +ks +pore pressure, uw +Figure 33.4.7–1 Drainage-only pore pressure–velocity relationship. +When surface pore pressures are negative, the constraint will properly enforce the condition that no +fluid can enter the interior region. When surface pore pressures are positive, the constraint will permit +fluid flow from the interior to the exterior region of the model. When the seepage coefficient value, +, +is large, this flow will approximately enforce the requirement that the pore pressure should be zero on a +freely draining surface. To achieve this condition, it is necessary to choose the value of +to be much +larger than a characteristic seepage coefficient for the material in the underlying elements: +where +is the permeability of the underlying material; +is the fluid specific weight; and +is a characteristic length of the underlying elements. +Values of +could result +in poor conditioning of the model. In all cases the freely draining flow type represents discontinuously +nonlinear behavior, and its use may require appropriate solution controls . +will be adequate for most analyses. Larger values of +Input File Usage: +Use the following option to define element-based drainage-only flow: +*FLOW +element number or element set name, QnD, +Use the following option to define surface-based drainage-only flow: +*SFLOW +surface name, QD, +Abaqus/CAE Usage: +Pore fluid flow cannot be defined as a function of the current pore pressure in +Abaqus/CAE. +Modifying or removing seepage coefficients and reference pore pressures +Seepage coefficients and reference pore pressures can be added, modified, or removed as described in +“Applying loads: overview,” Section 33.4.1. +Specifying a time-dependent reference pore pressure +, can be controlled by referring to an amplitude curve. +The magnitude of the reference pore pressure, +If different variations are needed for different portions of the flow, repeat the flow definition with each +referring to its own amplitude curve. See “Applying loads: overview,” Section 33.4.1, and “Amplitude +curves,” Section 33.1.2, for details. +Defining nonuniform flow in a user subroutine +To define nonuniform flow, the variation of the reference pore pressure and the seepage coefficient as +functions of position, time, pore pressure, etc. can be defined in user subroutine FLOW. +Input File Usage: +Use the following option to define a nonuniform element-based flow: +*FLOW +element number or element set name, QnNU +Use the following option to define a nonuniform surface-based flow: +Abaqus/CAE Usage: +*SFLOW +surface name, QNU +User subroutine FLOW is not supported in Abaqus/CAE. +Prescribing seepage flow velocity and seepage flow directly in consolidation analysis +You can directly prescribe an outward normal flow velocity, +flow at a node in consolidation analysis. +, across a surface or an outward normal +Prescribing element-based seepage flow velocity +To prescribe an element-based seepage flow velocity, specify the element or element set name, the +seepage type, and the outward normal flow velocity. The face of the element for which the seepage flow +is being defined is identified by the seepage type. The seepage types available depend on the element +type . +Input File Usage: +*DFLOW +element number or element set name, Sn, +Abaqus/CAE Usage: +Load module: Create Load: choose Fluid for the Category and +Surface pore fluid for the Types for Selected Step: select region: +Distribution: select an analytical field, Magnitude: +Prescribing surface-based seepage flow velocity +To prescribe a surface-based seepage flow velocity, specify a surface name, the seepage flow type, and the +pore fluid velocity. The element-based surface +contains the element and face information. +Input File Usage: +*DSFLOW +surface name, S, +Abaqus/CAE Usage: +Load module: Create Load: choose Fluid for the Category and +Surface pore fluid for the Types for Selected Step: select region: +Distribution: Uniform, Magnitude: +Prescribing node-based seepage flow +To prescribe node-based seepage flow, specify the node or node set name and the magnitude of the flow +per unit time. +Input File Usage: +*CFLOW +node number or node set name, +, magnitude +Abaqus/CAE Usage: +Load module: Create Load: choose Fluid for the Category and +Concentrated pore fluid for the Types for Selected Step: +select region: Magnitude: magnitude +Modifying or removing seepage flow velocities and seepage flow +Seepage flow velocities can be added, modified, or removed as described in “Applying loads: overview,” +Section 33.4.1. +Specifying time-dependent flow velocity and flow +The magnitude of the seepage velocity, +, can be controlled by referring to an amplitude curve. To +specify different variations for different flows, repeat the seepage flow velocity or seepage flow definition +with each referring to its own amplitude curve. See “Applying loads: overview,” Section 33.4.1, and +“Amplitude curves,” Section 33.1.2, for details. +Defining nonuniform flow velocities in a user subroutine +To define nonuniform element-based or surface-based flow, the variation of the seepage magnitude as a +function of position, time, pore pressure, etc. can be defined in user subroutine DFLOW. If the optional +, is specified directly, this value is passed into user subroutine DFLOW in the variable +seepage velocity, +used to define the seepage magnitude. +Input File Usage: +Use the following option to define nonuniform element-based flow: +*DFLOW +element number or element set name, SnNU, +Use the following option to define nonuniform surface-based flow: +*DSFLOW +surface name, SNU, +Abaqus/CAE Usage: +Use the following input to define nonuniform surface-based flow: +Load module: Create Load: choose Fluid for the Category and +Surface pore fluid for the Types for Selected Step: select region: +Distribution: User-defined, Magnitude: +Nonuniform element-based flow is not supported in Abaqus/CAE. +33.5 +Prescribed assembly loads +• “Prescribed assembly loads,” Section 33.5.1 +33.5.1 +PRESCRIBED ASSEMBLY LOADS +Products: Abaqus/Standard Abaqus/CAE +References +• “Prescribed conditions: overview,” Section 33.1.1 +• *BOUNDARY +• *CLOAD +• *PRE-TENSION SECTION +• *SURFACE +• Chapter 22, “Bolt loads,” of the Abaqus/CAE User’s Manual +Overview +Assembly loads: +• can be used to simulate the loading of fasteners in a structure; +• are applied across user-defined pre-tension sections; +• are applied to pre-tension nodes that are associated with the pre-tension sections; and +• require the specification of pre-tension loads or tightening adjustments. +Concept of an assembly load +Figure 33.5.1–1 is a simple example that illustrates the concept of an assembly load. +pre-tension +section +gasket +(cid:0)(cid:0)(cid:0)(cid:0)(cid:0) +(cid:0)(cid:0)(cid:0)(cid:0)(cid:0) +bolt +Figure 33.5.1–1 Example of assembly load. +Container A is sealed by pre-tensioning the bolts that hold the lid, which places the gasket under pressure. +This pre-tensioning is simulated in Abaqus/Standard by adding a “cutting surface,” or pre-tension section, +in the bolt, as shown in Figure 33.5.1–1, and subjecting it to a tensile load. By modifying the elements on +one side of the surface, Abaqus/Standard can automatically adjust the length of the bolt at the pre-tension +section to achieve the prescribed amount of pre-tension. In later steps further length changes can be +prevented so that the bolt acts as a standard, deformable component responding to other loadings on the +assembly. +Modeling an assembly load +Abaqus/Standard allows you to prescribe assembly loads across fasteners that are modeled by continuum, +truss, or beam elements. The steps needed to model an assembly load vary slightly depending on the +type of elements used to model the fasteners. +Modeling a fastener with continuum elements +In continuum elements the pre-tension section is defined as a surface inside the fastener that “cuts” it +into two parts . The pre-tension section can be a group of surfaces for cases where +a fastener is composed of several segments. +pre-tension +section +elements chosen by +user to describe +the pre-tension section +Figure 33.5.1–2 Pre-tension section defined using continuum elements. +The element-based surface contains the element and face information . You must convert the surface into a pre-tension section across which pre- +tension loads can be applied and assign a controlling node to the pre-tension section. +Input File Usage: +Abaqus/CAE Usage: +Use the following options to model an assembly load across a fastener that is +modeled with continuum elements: +*SURFACE, TYPE=ELEMENT, NAME=surface_name +*PRE-TENSION SECTION, SURFACE=surface_name, NODE=n +Load module: Create Load: choose Mechanical for the Category +and Bolt load for the Types for Selected Step +Assigning a controlling node to the pre-tension section +The assembly load is transmitted across the pre-tension section by means of the pre-tension node. The +pre-tension node should not be attached to any element in the model. It has only one degree of freedom +(degree of freedom 1), which represents the relative displacement at the two sides of the cut in the +direction of the normal . The coordinates of this node are not important. +pre-tension +section +pre-tension +node +Figure 33.5.1–3 Normal to the pre-tension section; this normal +should face away from the underlying elements. +Defining the normal to the pre-tension section +Abaqus/Standard computes an average normal to the section—in the positive surface direction, facing +away from the continuum elements used to generate the surface—to determine the direction along which +the pre-tension is applied. You may also specify the normal directly (when the desired direction of +loading is different from the average normal to the pre-tension section). The normal is not updated when +performing large-displacement analysis. +Recognizing elements on either side of the pre-tension section +For all the elements that are connected to the pre-tension section by at least one node, Abaqus/Standard +must determine on which side of the pre-tension section each element is located. This process is crucial +for the prescribed assembly load to work properly. +The elements used to define the section are referred to as “base elements” in this discussion. All +elements on the same side of the section as the base elements are referred to as the “underlying elements.” +All elements connected to the section that share faces (or in two-dimensional problems, edges) with the +base elements are added to the list of underlying elements. This is a repetitive process that enables +Abaqus/Standard to find the underlying elements in almost all meshes—triangles; wedges; tetrahedra; +and embedded beams, trusses, shells, and membranes—that were not used in the definition of the surface +. +embedded +beam +element +pre-tension +section +region 1{ +region 2 +base elements +underlying elements +that share facets with the +base elements +Figure 33.5.1–4 The base elements are used to find the underlying elements. +In most cases this process will group all of the elements that are connected to the section into +two regions, as shown in the figure. +In rare instances this process may group the elements in more +than two regions, in particular if line elements cross over element boundaries. An example is shown +in Figure 33.5.1–5; it has three regions, where region 1 is the underlying region. For each region other +than region 1 an additional step is necessary to determine on which side of the section the region is +located. Abaqus/Standard computes an average normal, +, for all the nodes of the region that belong +to the section; it also computes an average position ( +) of all these nodes. In addition, it computes an +average position ( +and +) of the remaining nodes of the region. If the dot product between the normal +the vector +is negative, the region is assumed to be an underlying region and is added to region 1. +This additional step is illustrated in Figure 33.5.1–5 for regions 2 and 3. +This additional step produces an incorrect separation for the beam element shown in Figure 33.5.1–6 +since the beam is not found to be an underlying element. If the pre-tension section has an odd shape and +one or more line elements that cross over element boundaries are connected to it, consult the list of the +underlying elements given in the data (.dat) file to make sure that the underlying elements are listed +correctly. +pre-tension +section +region 1 +region 2 +beam element (region 3) +position of A, B, and n for region 2 +position of A, B, and n for region 3 +Figure 33.5.1–5 An additional underlying element is found. +pre-tension +section +beam element +region 1 +Figure 33.5.1–6 An additional underlying element is not found. +Elements that are connected only to the nodes on the pre-tension section, including single-node +elements (such as SPRING1, DASHPOT1, and MASS elements) are not included as underlying +elements: they are considered to be attached to the other side of the section. +Modeling a fastener with truss or beam elements +When a pre-tensioned component is modeled with truss or beam elements, the pre-tension section is +reduced to a point. The section is assumed to be located at the last node of the element as defined +by the element connectivity , with +its normal along the element directed from the first to the last node. As a result, the section is defined +entirely by just specifying the element to which an assembly load must be prescribed and associating it +with a pre-tension node. +Input File Usage: +Use the following option to model an assembly load across fasteners modeled +with beam or truss elements: +Abaqus/CAE Usage: +*PRE-TENSION SECTION, ELEMENT=element_number, NODE=n +Load module: Create Load: choose Mechanical for the Category +and Bolt load for the Types for Selected Step +As in the case of a surface-based pre-tension section, the node has only one degree of freedom +(degree of freedom 1), which represents the relative displacement on the two sides of the cut in the +direction of the normal . The coordinates of the node are not important. +pre-tension +node +pre-tension +section +beam or truss +element +Figure 33.5.1–7 Pre-tension section defined using a truss or beam element. +Defining the normal to the pre-tension section +Abaqus/Standard computes the normal as the vector from the first to the last node in the connectivity of +the underlying element. Alternatively, you can specify the normal to the section directly. This normal is +not updated during large-displacement analysis. +Defining multiple pre-tension sections +You can define multiple pre-tension sections by repeating the pre-tension section definition input. Each +pre-tension section should have its own pre-tension node. +Use with nodal transformations +A local coordinate system cannot be used at a +pre-tension node. It can be used at nodes located on pre-tension sections. +Applying the prescribed assembly load +The pre-tension load is transmitted across the pre-tension section by means of the pre-tension node. +Prescribing the pre-tension force +You can apply a concentrated load to the pre-tension node. This load is the self-equilibrating force carried +across the pre-tension section, acting in the direction of the normal on the part of the fastener underlying +the pre-tension section (the part that contains the elements that were used in the definition of the pre- +tension section; see Figure 33.5.1–8). +Input File Usage: +Abaqus/CAE Usage: +*CLOAD +Load module: Create Load: choose Mechanical for the Category +and Bolt load for the Types for Selected Step: select surface and +if, necessary, datum axis: Method: Apply force +pre-tension +node +underlying +part +Figure 33.5.1–8 The prescribed assembly load is given at the +pre-tension node and applied in direction . +Prescribing a tightening adjustment +You can prescribe a tightening adjustment of the pre-tension section by using a nonzero boundary +condition at the pre-tension node (which corresponds to a prescribed change in the length of the +component cut by the pre-tension section in the direction of the normal). +Input File Usage: +Abaqus/CAE Usage: +*BOUNDARY +Load module: Create Load: choose Mechanical for the Category +and Bolt load for the Types for Selected Step: select surface and +if, necessary, datum axis: Method: Adjust length +Controlling the pre-tension node during the analysis +You can maintain the initial adjustment of the pre-tension section by using a boundary condition fixing +the degrees of freedom at their current values at the start of the step once an initial pre-tension is applied +in the fastener; this technique enables the load across the pre-tension section to change according to the +externally applied loads to maintain equilibrium. If the initial adjustment of a section is not maintained, +the force in the fastener will remain constant. +When a pre-tension node is not controlled by a boundary condition, make sure that the components +of the structure are kinematically constrained; otherwise, the structure could fall apart due to the presence +of rigid body modes. Abaqus/Standard will issue a warning message if it does not find any boundary +condition or load on a pre-tension node during the first step of the analysis. +Display of results +Abaqus/Standard automatically adjusts the length of the component at the pre-tension section to achieve +the prescribed amount of pre-tension. This adjustment is done by moving the nodes of the underlying +elements that lie on the pre-tension section relative to the same nodes when they appear in the other +elements connected to the pre-tension section. As a result, the underlying elements will appear shrunk, +even though they carry tensile stresses when a pre-tension is applied. +Limitations when using assembly loads +Assembly loads are subject to the following limitations: +• An assembly load cannot be specified within a substructure. +• If a submodeling analysis is performed (“Submodeling: overview,” Section 10.2.1), any pre-tension +section should not cross regions where driven nodes are specified. In other words, a pre-tension +section should appear either entirely in the region of the global model that is not part of a submodel +or entirely in the region of the global model that is part of a submodel. In the latter case, a pre-tension +section must also appear in the submodel when the submodel analysis is performed. +• Nodes of a pre-tension section should not be connected to other parts of the body through multi-point +constraints (“General multi-point constraints,” Section 34.2.2). These nodes can be connected to +other parts of the body through equations (“Linear constraint equations,” Section 34.2.1). However, +an equation connecting a node on the pre-tension section to a node located on the underlying side +of the section introduces a constraint that spans across the pre-tension cut and, therefore, interacts +directly with the application of the pre-tension load. On the other hand, an equation connecting a +node on the pre-tension section to a node on the other side of the section does not influence the +application of the pre-tension load. +Procedures +Any of the Abaqus/Standard procedures that use element types with displacement degrees of freedom +can be used. Static analysis is the most likely procedure type to be used when prescribing the +initial pre-tension (“Static stress analysis,” Section 6.2.2). Other analysis types such as coupled +temperature-displacement (“Sequentially coupled thermal-stress analysis,” Section 16.1.2) or coupled +thermal-electrical-structural (“Fully coupled thermal-electrical-structural analysis,” Section 6.7.4) can +also be used. Once the initial pre-tension is applied, a static or dynamic analysis (“Dynamic analysis +procedures: overview,” Section 6.3.1) may, for instance, be used to apply additional loads while +maintaining the tightening adjustment. +Output +The total force across the pre-tension section is the sum of the reaction force at the pre-tension node plus +any concentrated load specified at that node. The total force across the pre-tension section is available +as output using the output variable identifier TF . The forces are along the normal direction. The shear force across the pre-tension section +is not available for output. +The tightening adjustment of the pre-tension section is available as the displacement of the pre- +tension node. The output of displacement is requested using output identifier U. Only the adjustment +normal to the pre-tension section is output since there is no adjustment in any other direction. +The stress distribution across the pre-tension section is not available directly; however, the stresses +in the underlying elements can be displayed readily. Alternatively, a tied contact pair can be inserted at +the location of the pre-tension section to enable stress distribution output by means of output identifiers +CPRESS and CSHEAR. See “Defining tied contact in Abaqus/Standard,” Section 35.3.7, for details on +defining tied contact. +Input file template +*HEADING +Prescribed assembly load; example using continuum elements +… +*NODE +Optionally define the pre-tension node +*SURFACE, NAME=name +Data lines that specify the elements and their associated faces to define the pre-tension section +*PRE-TENSION SECTION, SURFACE=name, NODE=pre-tension_node +** +*STEP +** Application of the pre-tension across the section +*STATIC +Data line to control time incrementation +*CLOAD +pre-tension_node, 1, pre-tension_value +or +*BOUNDARY,AMPLITUDE=amplitude +pre-tension_node, 1, 1, tightening adjustment +*END STEP +*STEP +** maintain the tightening adjustment and apply new loads +*STATIC or *DYNAMIC +Data line to control time incrementation +*BOUNDARY,FIXED +pre-tension_node, 1, 1 +*BOUNDARY +Data lines to prescribe other boundary conditions +*CLOAD or *DLOAD +Data lines to prescribe other loading conditions +… +*END STEP +33.6 +Predefined fields +• “Predefined fields,” Section 33.6.1 +33.6.1 +PREDEFINED FIELDS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Prescribed conditions: overview,” Section 33.1.1 +• *TEMPERATURE +• *FIELD +• *PRESSURE STRESS +• *MASS FLOW RATE +• “Defining a temperature field,” Section 16.11.9 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +This section describes how to specify the values of the following types of predefined fields during an +analysis: +• temperature, +• field variables, +• equivalent pressure stress, and +• mass flow rate. +The procedures in which these fields can be used are outlined in “Prescribed conditions: overview,” +Section 33.1.1. +Temperature, field variables, equivalent pressure stress, and mass flow rate are time-dependent, +predefined (not solution-dependent) fields that exist over the spatial domain of the model. They can be +defined: +• by entering the data directly, +• by reading an Abaqus results file generated during a previous analysis (usually an Abaqus/Standard +heat transfer analysis), or +• in an Abaqus/Standard user subroutine. +Temperature can also be defined by reading an Abaqus output database file generated during a previous +analysis. In Abaqus/Standard field variables can also be defined by reading an Abaqus output database +file generated during a previous analysis. +Field variables can also be made solution dependent, which allows you to introduce additional +nonlinearities in the Abaqus material models. +Predefined temperature +In stress/displacement analysis the temperature difference between a predefined temperature field and any +initial temperatures (“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1) will +create thermal strains if a thermal expansion coefficient is given for the material (“Thermal expansion,” +Section 26.1.2). The predefined temperature field also affects temperature-dependent material properties, +if any. In Abaqus/Explicit temperature-dependent material properties may cause longer run times than +constant properties. +You define the magnitude and time variation of temperature at the nodes, and Abaqus interpolates +the temperatures to the material points. +Input File Usage: +Use the following option to specify a predefined temperature field: +Abaqus/CAE Usage: +*TEMPERATURE +Load module: Create Predefined Field: Step: analysis_step: choose Other +for the Category and Temperature for the Types for Selected Step +Restrictions +Do not specify predefined temperature fields in a pure heat transfer analysis, a coupled thermal-electrical +analysis, a fully coupled temperature-displacement analysis, or a fully coupled thermal-electrical- +structural analysis; instead, specify a boundary condition (“Boundary conditions in Abaqus/Standard +and Abaqus/Explicit,” Section 33.3.1) to prescribe temperature degrees of freedom (11, 12, ...). +Predefined temperature fields cannot be specified in an adiabatic analysis step or in any mode-based +dynamic analysis step. +To specify a predefined temperature field in a restart analysis, the corresponding predefined field +must have been specified in the original analysis as either initial temperatures or a +predefined temperature field. +Predefined field variables +The usage and treatment of predefined field variables is exactly analogous to that of temperature. You +can prescribe the magnitude and time variation of the field at all of the nodes of the model, and Abaqus +will interpolate the values to the material points. +When prescribing field variable values, you must specify the field variable number being defined; +the default is field variable number 1. Field variables must be numbered consecutively starting from one. +Repeat the field variable definition to define more than one field variable. +The field variable can be a real field (such as an electromagnetic field) generated by a previous +simulation (Abaqus or another analysis code). It can also be an artificial field that you define to modify +certain material properties during the course of an analysis. For example, suppose that you wish to vary +Young’s modulus linearly between 30 × 106 and 35 × 106 during the response. The linear elastic material +definition shown in Table 33.6.1–1 could be used. +Table 33.6.1–1 Sample material definition. +Number of field variable dependencies: 1 +Young’s +modulus +30.E6 +35.E6 +Poisson’s +ratio +Value of field +variable 1 +0.3 +0.3 +1.0 +2.0 +Define an initial condition to specify the initial value of field variable 1 as 1.0 for a node set. Then, +define a predefined field variable in the analysis step to specify the value of field variable 1 as 2.0 for the +node set. Young’s modulus will vary smoothly over the course of the step as the field variable’s value is +ramped from 1.0 to 2.0 at all nodes in the node set. +Field variables can also be used to vary real properties in space by making the properties depend on +field variables, as above, and by assigning different field variable values to different nodes. +Making properties depend on field variables will increase the computer time required, since Abaqus +must perform the necessary table look-ups. +In an Abaqus/Standard stress/displacement analysis the difference between a predefined +field variable and its initial value (“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” +Section 33.2.1) will create volumetric strains analogous to thermal strains if a field expansion coefficient +(for the corresponding field variable) is given for the material (“Thermal expansion,” Section 26.1.2). +Input File Usage: +Use the following option to specify a predefined field variable: +Abaqus/CAE Usage: +*FIELD, VARIABLE=n +Predefined field variables are not supported in Abaqus/CAE. +Restrictions +To specify a predefined field variable in a restart analysis, the corresponding predefined field must +have been specified in the original analysis as either an initial field variable value or a predefined field variable. +Predefined pressure stress +You can apply equivalent pressure stress as a predefined field in a mass diffusion analysis. The usage +and treatment of pressure stresses is analogous to that of temperatures and field variables. In Abaqus +equivalent pressure stresses are positive when they are compressive. +Input File Usage: +Use the following option to specify a predefined equivalent pressure stress field: +Abaqus/CAE Usage: +*PRESSURE STRESS +Predefined equivalent pressure stress is not supported in Abaqus/CAE. +Restrictions +Predefined equivalent pressure stress fields can be specified only in a mass diffusion procedure . +To specify a predefined equivalent pressure stress field in a restart analysis, the corresponding +predefined field must have been specified in the original analysis as either initial pressure stresses or a predefined equivalent pressure stress field. +Predefined mass flow rate +You can specify the mass flow rate per unit area (or through the entire section for one-dimensional +elements) for forced convection/diffusion elements in a heat transfer analysis. The usage and treatment +of mass flow rate is analogous to that of temperatures and field variables. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to specify a predefined mass flow rate field: +*MASS FLOW RATE +Predefined mass flow rate is not supported in Abaqus/CAE. +Restrictions +A predefined mass flow rate field can be specified only with forced convection/diffusion elements in a +heat transfer procedure . +To specify a predefined mass flow rate field in a restart analysis, the corresponding predefined +field must have been specified in the original analysis by using either initial mass flow rates or a predefined mass flow rate field. +Reading initial values of a field from a user-specified results file +An Abaqus/Standard results file can be used to specify initial values of +• temperature ; +• field variables ; and +• pressure stress . +Field variable values must be read from the temperature record . The part (.prt) file from the original analysis is also required when +reading data from the results file. +If the zero increment results were requested as output to the Abaqus/Standard results file , you can define initial values +of prescribed fields as those existing at the beginning of a step (the zero increment) in the previous heat +transfer analysis (field variables and temperatures) or stress/displacement analysis (pressure stress). The +.fil file extension is optional. +Reading initial values of a temperature field from a user-specified output database file +An Abaqus/Standard output database file can be used to specify initial values of temperature . The part (.prt) file from the original analysis is also required when reading data from +the output database file. Temperature values can be read between dissimilar meshes, as described in +“Interpolating initial temperatures for dissimilar meshes from a user-specified results or output database +file” in “Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1. +Initializing predefined field variables from a user-specified output database file in +Abaqus/Standard +In Abaqus/Standard nodal values of temperature (NT), normalized concentrations (NNC), and electric +potential (EPOT) can be used to initialize predefined fields . The +part (.prt) file from the original analysis is also required when reading data from the output database +file. The scalar nodal values can be mapped between dissimilar meshes, as described in “Defining +initial predefined field variables by interpolating scalar nodal output variables for dissimilar meshes from +a user-specified output database file” in “Initial conditions in Abaqus/Standard and Abaqus/Explicit,” +Section 33.2.1. +Defining time-dependent fields +The prescribed magnitude of a field can vary with time during a step according to an amplitude function. +See “Prescribed conditions: overview,” Section 33.1.1, and “Amplitude curves,” Section 33.1.2, for +details. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options: +*TEMPERATURE, AMPLITUDE=amplitude_name +*FIELD, AMPLITUDE=amplitude_name +*PRESSURE STRESS, AMPLITUDE=amplitude_name +*MASS FLOW RATE, AMPLITUDE=amplitude_name +In Abaqus/CAE only predefined temperature fields are available. +Load module: Create Predefined Field: Step: analysis_step: choose +Other for the Category and Temperature for the Types for Selected +Step: select region: Distribution: Direct specification or select an +analytical field or a discrete field, Amplitude: amplitude_name +Field propagation +By default, all fields defined in the previous general analysis step remain unchanged in the subsequent +general step or in subsequent consecutive linear perturbation steps. Fields do not propagate between +linear perturbation steps. You define the fields in effect for a given step relative to the preexisting fields. +At each new step the existing fields can be modified and additional fields can be specified. If you specify +additional values for a field, the definition of the field will be extended to those nodes where it was +previously undefined. Alternatively, you can release all previously applied fields of a given type in a +step and specify new ones. In this case any fields of that type that are to be retained must be respecified. +Modifying fields +By default, when you modify existing temperatures, field variables, pressure stresses, or mass flow rates, +all existing values of the field remain. +Input File Usage: +Use one of the following options to modify an existing field or to specify an +additional field: +*TEMPERATURE, OP=MOD +*FIELD, OP=MOD +*PRESSURE STRESS, OP=MOD +*MASS FLOW RATE, OP=MOD +In Abaqus/CAE only predefined temperature fields are available. +Load module: Create Predefined Field or Predefined Field Manager: Edit +Abaqus/CAE Usage: +Removing fields +A field that is removed is reset to the value given as an initial condition or to zero if no initial condition was +defined. When fields are reset to their initial conditions, the amplitude referred to in the field definition +does not apply. In Abaqus/Standard the amplitude variation defined for the step governs the behavior; +in most Abaqus/Standard procedures the default is to ramp the fields back to their initial conditions . In Abaqus/Explicit the values are always ramped linearly over +the step back to their initial conditions. +If the temperatures, field variables, pressure stresses, or mass flow rates are reset to a new value +(not to their initial conditions), the amplitude referred to in the field definition applies. +If you choose to remove any field in a step, no fields of that type will be propagated from the previous +general step. All fields of the same type that are in effect during this step must be respecified. +Input File Usage: +Use one of the following options to release all previously applied fields of a +particular type and to specify new fields: +*TEMPERATURE, OP=NEW +*FIELD, OP=NEW +*PRESSURE STRESS, OP=NEW +*MASS FLOW RATE, OP=NEW +If the OP=NEW parameter is used on any field option in a step, it must be used +on all field options of the same type within the step. +Abaqus/CAE Usage: +Use the following option to reset a temperature field to the value prescribed in +the initial step (or to zero if no initial value was defined): +Load module: temperature field editor: Reset to initial +Reading the values of a field directly from an alternate input file +The data for predefined temperature, field variables, pressure stress, or mass flow rate can be contained +in a separate input file . +Input File Usage: +Use one of the following options: +*TEMPERATURE, INPUT=file_name +*FIELD, INPUT=file_name +*PRESSURE STRESS, INPUT=file_name +*MASS FLOW RATE, INPUT=file_name +If the INPUT parameter is omitted, it is assumed that the data lines follow the +keyword line. +Abaqus/CAE Usage: +You cannot read field data from a separate input file in Abaqus/CAE. +Reading the values of a field from a user-specified file +Nodal temperatures calculated during an Abaqus/Standard heat transfer or coupled thermal-electrical +analysis can be used to define temperatures in a subsequent analysis. The temperatures must have been +written to the results or output database file. +If nodal temperatures are written to the results file during an Abaqus/Standard heat transfer or +coupled thermal-electrical analysis, they can be used to define field variables in a subsequent analysis. +In Abaqus/Standard if nodal values of temperature (NT), normalized concentrations (NNC), or +electric potential (EPOT) are written to the output database file, they can be used to define field variables +in a subsequent Abaqus/Standard analysis. +In Abaqus/Standard equivalent pressure stresses calculated during a mechanical analysis can be used +in a subsequent mass diffusion analysis if the element output variable SINV was written to the results +file averaged at the nodes . +Once the data are available in a results file or output database file, they can be read into a subsequent +analysis as a predefined field. Data for field variables and pressure stress can be read from a previously +generated results file. In Abaqus/Standard data can also be read from a previously generated output +database file. Data for temperatures can be read from a previously generated results or output database +file. Data for temperatures (and field variables in Abaqus/Standard) to be interpolated between dissimilar +meshes can be read only from the output database file. The part (.prt) file from the original analysis is +also required when reading data from the results or output database file. +When the output file of an Abaqus analysis involving beam and/or shell elements is used to define +temperatures, you must ensure that the number of temperature points through the section defined for +corresponding elements is consistent between the two analyses. Inconsistent temperature point definition +will result in an incorrect transfer of prescribed field quantities. +Reading field values from a user-specified results file +To read field values from a user-specified results file, the data must have been written to the results file +as nodal output . Only nodal +quantities can be read from the results file. Since field variables can be written to the results file only as +element quantities (record key 9), they cannot be read directly into a subsequent analysis. In this case +you must generate a results file with the field data in the temperature record, even if the field variable in +the current analysis is the same as a field variable in the previous analysis. Multiple results files must be +generated for multiple field variables. +To generate the results file, you can write a program to create a results file (without running an +Abaqus analysis) according to the format described in Chapter 5, “File Output Format.” Examples of +such programs are shown in that chapter. If the values will be read in as temperatures or field variables, +the data must be written as nodal quantities with record key 201. If the values will be read in as a pressure +stress field, the data must be averaged at the nodes (as explained in “Output to the data and results files,” +Section 4.1.2) and written as record key 12. +Specifying the results file to be read +You must specify the name of the results file from which the data are to be read for a temperature, field +variable, or pressure stress. The .fil file extension is optional. If both .fil and .odb files exist for +a temperature field and no extension is specified, the results file will be used. +Input File Usage: +Abaqus/CAE Usage: +*TEMPERATURE, FILE=file +*FIELD, FILE=file +*PRESSURE STRESS, FILE=file +In Abaqus/CAE only predefined temperature fields are available. +Load module: Create Predefined Field: Step: analysis_step: choose Other +for the Category and Temperature for the Types for Selected Step: select +region: Distribution: From results or output database file, File name: file +Creating a cyclic temperature history +In a direct cyclic analysis in Abaqus/Standard the temperature values must be cyclic over the step: the +start value must be equal to the end value. To create a cyclic temperature history from a prior heat transfer +analysis that is not cyclic, you can set the starting time, f (measured relative to the total step time period, +), after which the temperatures read from the results file will be ramped back to their initial condition +, the temperature value is equal to +values. At any time point +where +obtained from the results file at time t, as illustrated in Figure 33.6.1–1. +is the initial condition value, and +, +is the interpolated value +Input File Usage: +Use the following option to set the starting time for a cyclic temperature history: +Abaqus/CAE Usage: +*TEMPERATURE, FILE=file, BTRAMP=f +Cyclic temperature histories are not supported in Abaqus/CAE. +Temp +ini +Temp +ft +Figure 33.6.1–1 Ramp temperatures to their initial condition +values after +to create a cyclic temperature history. +Reading temperature values from a user-specified output database file +To read temperature values from a user-specified output database file, the temperatures must have been +written to the output database file as nodal output . +Specifying the output database file to be read for a temperature field +You must specify the name of the output database file from which the data are to be read for a temperature +field. The .odb extension must be included if both results and output database files exist. Only the data +for the part instances that are common to both the analyses will be transferred. If the part instance names +differ, you must activate the general interpolation capability. +Input File Usage: +Abaqus/CAE Usage: +*TEMPERATURE, FILE=file +Load module: Create Predefined Field: Step: analysis_step: choose Other +for the Category and Temperature for the Types for Selected Step: select +region: Distribution: From results or output database file, File name: file +Defining fields using nodal scalar output values from a user-specified output database file +In Abaqus/Standard if nodal values of temperature (NT), normalized concentrations (NNC), or electric +potential (EPOT) are written to the output database file, they can be used to define field variables in a +subsequent Abaqus/Standard analysis. To read these values from a user-specified output database file, +they must have been written to the output database file as nodal output . +Specifying the output database file to be read for a field variable +You must specify the name of the output database file from which the data are to be read for a field +variable. The .odb extension must be included if both results and output database files exist. +Input File Usage: +Abaqus/CAE Usage: +*FIELD, FILE=file, OUTPUT VARIABLE=scalar nodal output variable, +Predefined field variables are not supported in Abaqus/CAE. +Interpolating data between meshes +Data can be mapped between the same meshes, between meshes that differ only in the element order +(first-order element in heat transfer analysis and second-order element in thermal-stress analysis), or +between dissimilar meshes of matching element dimensionality (solid element to solid element or shell +element to shell element). If data are mapped between the same meshes, no additional computations +are required. To transfer data between meshes that differ only in the element order, you must activate +the midside node capability. To map data between dissimilar meshes, you must activate the general +interpolation capability. The midside node capability is available only for temperatures. The midside +node capability and the general interpolation capability are mutually exclusive. +Using second-order stress elements with first-order heat transfer elements (the midside node capability) +In some cases it makes sense to perform an Abaqus/Standard heat transfer analysis using first-order +elements followed by a thermal-stress analysis using second-order elements (and an otherwise similar +mesh). For example, a heat transfer analysis including latent heat effects—for which first-order elements +are best suited—can be followed by a stress analysis using second-order elements, which generally +have superior deformation characteristics. In addition, the first-order temperature field calculated in the +heat transfer analysis is consistent with the first-order thermal strain field provided by the second-order +stress/displacement elements. +For the instances in which there is a change in the order of interpolation of element temperature +variables between the heat transfer analysis and the stress analysis, temperatures must be assigned to +the midside nodes of the stress/displacement elements based on the temperatures of the corner nodes of +the heat transfer elements. If you specify that the midside node temperatures are needed, Abaqus will +interpolate the temperatures of the midside nodes of the second-order stress/displacement elements from +the corner nodes using first-order interpolation. If the midside node capability is activated in cases where +both the heat transfer analysis and the stress analysis are performed with second-order elements, it is +ignored. One exception is that if variable-node second-order stress/displacement elements are used in the +stress analysis, activating the midside node capability will cause Abaqus to interpolate the temperatures +of the midface nodes in the variable node elements from the corner or midside nodes using first-order +interpolation. +Since it is assumed that the corner node temperatures have been generated in a previous heat transfer +analysis, the midside node capability can be used only when the temperature field values are read from +a user-specified results or output database file. You must ensure that the nodal temperatures calculated +during the heat transfer analysis are written to the results or output database file. Once the temperatures of +the corner nodes are read in the subsequent stress/displacement analysis, Abaqus interpolates the midside +node temperatures so that all nodes have temperatures assigned to them. +You must ensure that all temperatures of the corner nodes belonging to elements for which midside +node temperatures are to be interpolated are read from the heat transfer analysis results or output +database file. If the corner node temperatures are defined using a mixture of direct data input, reading +from the results file or output database file, and user subroutine UTEMP, midside node temperatures +that give unrealistic temperature fields may result. In practice, the capability for calculating midside +node temperatures is most useful when temperatures generated by a heat transfer analysis are read from +the results or output database file for the whole mesh during the stress analysis. Once the midside +node capability is activated in a step, the capability will remain active throughout the remainder of the +analysis. +Values of temperature for nodes that existed in the original analysis but do not exist in the current +analysis will be ignored. Similarly, if additional nodes (but not midside nodes) exist in the current +analysis, the values of fields at these nodes cannot be prescribed by reading the output files. +Input File Usage: +Use the following option to interpolate temperatures between meshes that differ +only in the element order: +Abaqus/CAE Usage: +*TEMPERATURE, FILE=file, MIDSIDE +Load module: Create Predefined Field: Step: analysis_step: +choose Other for the Category and Temperature for the Types for +Selected Step: select region: Distribution: From results or output +database file, File name: file, Mesh compatibility: Compatible, +and toggle on Interpolate midside nodes +Interpolating temperatures between dissimilar meshes (the general interpolation capability) +In some cases the model for a heat transfer analysis and the model for a thermal-stress analysis may +require different meshes; for example, you may want to model a smooth temperature distribution in the +heat transfer analysis and stress concentration regions in the thermal-stress analysis. Both meshes have to +be different and independent of each other in such cases. Abaqus offers a general interpolation capability +that allows for the use of dissimilar meshes for heat transfer and thermal-stress analyses. +The interpolation is always based on the initial (undeformed) configurations. +If the mesh for +which the temperature field is obtained is quite different from the initial (undeformed) configuration +for the thermal-stress analysis, the interpolation may not work properly even when using the tolerance +parameters discussed below. +Temperatures can be interpolated between dissimilar meshes only when the temperatures are read +from an output database file. If temperatures for nodes in the heat transfer analysis that are needed for +interpolation are not written to the output database file, the values at those nodes are assumed to be +zero, which may lead to incorrect results for the temperature values in the stress analysis. Similarly, +if additional nodes exist in the mesh for the stress analysis, the values of temperatures at these nodes +are assumed to be zero. Interpolation of temperatures can also be used for specifying temperature as a +field variable in a submodel thermal-stress analysis where the temperature values are read directly from +a global heat transfer analysis. +You can specify an interpolation tolerance for use in locating the nodes in the heat transfer analysis. +The tolerance can be specified as an absolute value or as a fraction of the average element size. In a +multistep thermal-stress analysis in which several steps read the temperature values from the same file, +Abaqus interpolates the temperature values only once. If different interpolation tolerance values are used +for each step, the interpolation is based on the largest specified tolerance value. If a restart analysis is +performed from a particular step in the thermal-stress analysis, the restart interpolation is based on the +tolerance value specified for that step. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to interpolate temperatures between dissimilar +meshes: +*TEMPERATURE, FILE=file.odb, INTERPOLATE +Use the following option to specify the interpolation tolerance as an absolute +value: +*TEMPERATURE, FILE=file.odb, INTERPOLATE, ABSOLUTE +EXTERIOR TOLERANCE=tolerance +Use the following option to specify the interpolation tolerance as a fraction of +the average element size: +*TEMPERATURE, FILE=file.odb, INTERPOLATE, EXTERIOR +TOLERANCE=tolerance +Load module: Create Predefined Field: Step: analysis_step: choose +Other for the Category and Temperature for the Types for Selected +Step: select region: Distribution: From results or output database +file, File name: file.odb, Mesh compatibility: Incompatible, +exterior tolerance: absolute or relative tolerance +Interpolating temperatures between dissimilar meshes with user-specified regions +When regions of elements in the heat transfer analysis are close or touching, the dissimilar mesh +interpolation capability can result in an ambiguous temperature association. For example, consider a +node in the current model that lies on or close to a boundary between two adjacent parts in the heat +transfer model, and consider a case where temperatures in these parts are different. When interpolating, +Abaqus will identify a corresponding parent element at the boundary for this node from the heat transfer +analysis. This parent element identification is done using a tolerance-based search method. Hence, in +this example the parent element might be found in either of the adjacent parts, resulting in an ambiguous +temperature definition at the node. You can eliminate this ambiguity by specifying the source regions +from which temperatures are to be interpolated. The source region refers to the heat transfer analysis +and is specified by an element set. The target region refers to the current analysis and is specified by a +node set. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to interpolate temperatures between dissimilar meshes +with user-specified regions: +*TEMPERATURE, FILE=file.odb, INTERPOLATE, DRIVING ELSETS +You cannot specify the regions where temperatures are to be interpolated in +Abaqus/CAE. +Interpolating scalar nodal output variables between dissimilar meshes (the general interpolation +capability) onto field variables in Abaqus/Standard +Abaqus/Standard offers a general interpolation capability that allows for nodal values of temperature, +normalized concentration, and electric potential from one analysis to be mapped onto field variables in +a subsequent analysis in the cases where the meshes in the two analyses are dissimilar. +The interpolation is always based on the initial (undeformed) configurations. If the mesh for which +the field variable is obtained is quite different from the initial (undeformed) configuration for the original +analysis, the interpolation may not work properly even when using the tolerance parameters discussed +below. +Temperatures, normalized concentrations, and electric potentials can be interpolated between +dissimilar meshes onto field variables only when they are read from an output database file. If scalar +values for nodes in the current analysis that are needed for interpolation are not written to the output +database file, the values at those nodes are assumed to be zero, which may lead to incorrect results for +the field variables. Similarly, if additional nodes exist in the mesh for the current analysis, the values of +the field variables at these nodes are assumed to be zero. +You can specify an interpolation tolerance for use in locating the nodes in the original analysis. +The tolerance can be specified as an absolute value or as a fraction of the average element size. In a +multistep analysis in which several steps read nodal output variables values from the same file, Abaqus +interpolates the nodal values only once. If different interpolation tolerance values are used for each step, +the interpolation is based on the largest specified tolerance value. If a restart analysis is performed from +a particular step in the original analysis, the restart interpolation is based on the tolerance value specified +for that step. +Input File Usage: +Use the following option to interpolate scalar nodal output variables between +dissimilar meshes: +*FIELD, FILE=file.odb, OUTPUT VARIABLE=scalar nodal +output variable, INTERPOLATE +Use the following option to specify the interpolation tolerance as an absolute +value: +*FIELD, FILE=file.odb, OUTPUT VARIABLE=scalar nodal +output variable, INTERPOLATE, ABSOLUTE EXTERIOR +TOLERANCE=tolerance +Use the following option to specify the interpolation tolerance as a fraction of +the average element size: +*FIELD, FILE=file.odb, OUTPUT VARIABLE=scalar nodal output +variable, INTERPOLATE, EXTERIOR TOLERANCE=tolerance +Abaqus/CAE Usage: +Predefined field variables are not supported in Abaqus/CAE. +Specifying the step and increment to be read from the file +You can specify the first and last step, respectively, from which results will be read. Similarly, you +can specify the first and last increment, respectively, from which results will be read. You can specify +any combination of these values. Any zero-increment file output that is present in the results file of an +Abaqus/Standard analysis (written only if the zero increment results are requested; see “Obtaining results +at the beginning of a step” in “Output,” Section 4.1.1) will be ignored. Results must have been written +to the results or output database file at the specified step and increment. +If you do not specify the first step from which to read, Abaqus will begin reading results from the +first step available in the results or output database file. +If you do not specify the first increment from which to read, Abaqus will begin reading results from +the first increment available in the first step from which results will be read (the first increment following +the zero increment if zero-increment file output is present in the results file). +If you do not specify the last step from which to read, the first step from which results will be read +will also be the last step. +If you do not specify the last increment from which to read, Abaqus will read the results or output +database file until it reaches the last available increment in the last step from which results will be read. +Input File Usage: +Use one of the following options: +*TEMPERATURE, FILE=file, BSTEP=bstep, BINC=binc, ESTEP=estep, +EINC=einc +*FIELD, FILE=file, BSTEP=bstep, BINC=binc, ESTEP=estep, EINC=einc +*PRESSURE STRESS, FILE=file, BSTEP=bstep, BINC=binc, ESTEP=estep, +EINC=einc +For example, the following input would read temperature data from output +database file heat.odb beginning at Step 2, increment 2, and ending at Step 3, +increment 5: +*TEMPERATURE, FILE=heat.odb, BSTEP=2, BINC=2, +ESTEP=3, EINC=5 +Abaqus/CAE Usage: +In Abaqus/CAE only predefined temperature fields are available. +Load module: Create Predefined Field: Step: analysis_step: choose +Other for the Category and Temperature for the Types for Selected +Step: select region: Distribution: From results or output database +file, File name: file, Begin step: bstep, Begin increment: binc, +End step: estep, and End increment: einc +Interpolation in time +When Abaqus reads temperature, field variable, or equivalent pressure stress data from a results file or +temperatures from an output database file, it must obtain values of the field at the time points used by the +analysis. Since data corresponding to these time points are usually not present in the results or output +database files, Abaqus will interpolate linearly in time between the time points stored in the file to obtain +values at the time points required by the analysis. Since the interpolation is linear, you must take care to +provide sufficient data in the results or output database file to make this interpolation meaningful. +For the purpose of such interpolation the time period of the results being read in is determined as +follows: +• The period starts at the time of the most recent increment written, of the relevant field, that precedes +the beginning increment (either user-specified or default). For example if your results file contains +temperature field data at increments 5, 10, and 15; and you specify a beginning increment number +of 10 when reading these results; the results period starts with the time associated with increment 5 +since that is the most recent increment that precedes the specified beginning increment of 10. You +can ensure that the results starting time matches the beginning time of the beginning increment you +specify by writing the results data with an increment frequency of 1. +• The period ends at the completion of the ending increment (either user-specified or default). +If the analysis requires data at a time point prior to the first increment for which data are available +in the either of files, Abaqus will interpolate between the given initial condition data and the data of the +first increment stored in the file. +Reading results for multiple fields +If data for multiple fields are being read in the same step and the time values corresponding to the +starting step and increment or to the ending step and increment are different for different fields, Abaqus +interpolates through the total time period from the earliest time point chosen in any file to the latest. For +example, suppose the starting increment in the starting step in the temperature file begins at 3 sec and +the ending increment in the ending step ends at 6 sec. During the same step we also read field variable +data, for which the starting increment in the starting step begins at 2 sec and the ending increment in the +ending step ends at 5 sec. In such a case the time period used for interpolation is from 2 sec to 6 sec. +Automatic adjustment of the time scale +It is convenient to set the period of the step equal to the time period of the files being read in. Otherwise, +Abaqus will automatically scale the time period from the results or output database file to match the time +period of the stress analysis. The scale factor is +is the time period of the stress analysis +and +is the total time period obtained from all results or output database files, as described above. +, where +Obtaining results at a particular point in time +In Abaqus/Standard it is sometimes desirable to carry out a calculation corresponding to the field values +at a particular point in time. For example, suppose that temperature data are available in the output file +for increment 10 at time +and that you wish to carry out a static +and increment 15 at time +and +to obtain the intermediate result at +. In this case Abaqus must interpolate linearly between +analysis based on temperature values at +the results at +. To accomplish this task, you +should specify an initial time increment of 4.5 and a time period of 5. for the static analysis step and read +the temperature values from the output file starting at Step 1, Increment 1 and ending at Step 1, Increment +15. Specifying a starting increment of 1 instead of 10 ensures that +is the entire time period stored in +the output file, not just the period between increments 10 and 15; hence, the scale factor between the +output file data and the static analysis is unity, and the initial time of 4.5 has the desired meaning. +Initial transients +To track initial transients accurately, Abaqus/Standard may automatically reduce the initial time +increment for the step. If the user-specified suggested initial time increment is greater than the scaled +value of the first time increment read from the Abaqus/Standard results file, Abaqus/Standard will use +that scaled value. +Restrictions +The following restrictions exist: +• Temperatures and field variables cannot be read from a user-specified file in a modified Riks static +analysis step (“Unstable collapse and postbuckling analysis,” Section 6.2.4). +• Temperature cannot be interpolated from a coupled thermal-electrical analysis. +• Equivalent pressure stress cannot be read from the results file if the model is defined in terms of an +assembly of part instances. +• In Abaqus/Explicit field variables cannot be read from the output database file. +• Pressure stress cannot be read from the output database file. +• Elements that do not support interpolation for temperature mapping include the complete libraries +of convective heat +transfer elements, axisymmetric elements with nonlinear axisymmetric +deformation, axisymmetric surface elements, hydrostatic fluid elements, solid infinite stress +elements, and coupled thermal/electrical elements. Other specific elements that are not supported +include: GKPS6, GKPE6, GKAX6, GK3D18, GK3D12M, GK3D4L, GK3D6L, GKPS4N, +GKAX6N, GK3D18N, GK3D12MN, GK3D4LN, and GK3D6LN. +Defining the values of a predefined field in a user subroutine +In Abaqus/Standard you can specify predefined temperatures, field variables, equivalent pressure +stresses, or mass flow rates at the nodes in a user subroutine. Temperature values can be defined in user +subroutine UTEMP; field variable values, in user subroutine UFIELD; equivalent pressure stress values, +in user subroutine UPRESS; and mass flow rates, in user subroutine UMASFL. +The user subroutine (UTEMP, UFIELD, UPRESS, or UMASFL) will be called for each specified +node. Field values entered directly will be ignored. If a results or output database file has been specified +in addition to the user subroutine, values read from the results or output database file will be passed into +the user subroutine for possible modification. +Input File Usage: +Use one of the following options: +Abaqus/CAE Usage: +*TEMPERATURE, USER +*FIELD, USER +*PRESSURE STRESS, USER +*MASS FLOW RATE, USER +In Abaqus/CAE only predefined temperature fields are available. +Load module: Create Predefined Field: Step: analysis_step: choose +Other for the Category and Temperature for the Types for Selected +Step: select region: Distribution: User-defined or From results +or output database file and user-defined +Updating multiple predefined field variables +If multiple field variables are predefined, only one field variable at a time can be redefined in user +subroutine UFIELD. There are situations in which the analysis requires a number of field variables that +are predefined with respect to the solution but depend on each other. You can specify the number of field +variables to be updated simultaneously at a point, n. Abaqus/Standard passes information about n field +variables at each specified node into UFIELD. +You can update all or part of the field variables used in the analysis but must remember that the +field variables are numbered consecutively from 1. If, for example, you have four field variables in the +analysis and want to update the second and third variables simultaneously in subroutine UFIELD, you +must specify n=3. In this case Abaqus/Standard passes information about the first three field variables +into subroutine UFIELD, and you update only the second and third variables. +Input File Usage: +Abaqus/CAE Usage: +*FIELD, USER, NUMBER=n +Predefined field variables are not supported in Abaqus/CAE. +Defining solution-dependent field variables +In Abaqus/Standard solution-dependent field variables can be defined in user subroutine USDFLD. The +values of predefined field variables or initial fields can be passed into user subroutine USDFLD and can +be changed in that routine—see “Material data definition,” Section 21.1.2. +Changes to the field variables in USDFLD are local to the material point and do not affect the nodal +values. +Data hierarchy +If both results or output database file input and direct data input are used in the same step, the direct data +input will take precedence if both define the field at the same node. If user subroutine input is specified, +the values given directly are ignored and the user subroutine modifies the values read from the results or +output database file. +Element type considerations +You can specify either one or several values of a predefined field at a node, depending on the element +type that is used. You should note the following considerations when choosing the form of predefined +field specification. +Use in a mass diffusion analysis +For solid elements only one value can be given at a node. Since only solid elements can be used in mass +diffusion analysis, this is the only way to define equivalent pressure stresses at a node. +Use with beam and shell elements +The following possibilities exist for temperatures and field variable specification in beam and shell +elements: +• For shell and beam elements with general cross-section definitions, the temperature and field +variable magnitude at points in the section is defined by the value at the reference surface. Any +gradient of these variables specified across the section is ignored. +• For shell and beam elements with cross-sections that require numerical integration, the temperature +and field variable magnitudes at points in the section can be defined either from the value at the +reference surface and the gradient or gradients across the section or by giving the values at a +number of points across the section. The choice between these two methods is made in the section +definition . +See Part VI, “Elements,” for the details of use with each element type. The default, if only one +value is given, is a constant magnitude across the section. +Temperature and field variable compatibility across elements +Abaqus assumes that the field definitions (including initial conditions) at all the nodes of any element are +compatible with the field definition method chosen for the element. Cases may arise where the definition +of a field changes from one element to the next (for example, when two adjacent shell elements have +a different number of section points through the thickness or when the temperature and field variable +magnitudes for one beam element are defined by giving the values at a number of points across the +section while those for the abutting beam element are defined from the value at the reference surface +and the gradient or gradients across the section). In these cases separate nodes should be used on the +interface between such elements and multi-point constraints should be applied to make the displacements +and rotations the same at corresponding nodes ; +otherwise, the fields on the nodes at the interface will be used for each adjacent element with the field +definition method chosen for the element. + +Constraints +Overview +Multi-point constraints +Surface-based constraints +Embedded elements +Element end release +Overconstraint checks +CONSTRAINTS +34.1 +34.2 +34.3 +34.4 +34.5 +34.1 +Overview +• “Kinematic constraints: overview,” Section 34.1.1 +34.1.1 +KINEMATIC CONSTRAINTS: OVERVIEW +The following types of kinematic constraints can be defined: +• Equations: Linear multi-point constraints can be given in the form of an equation . +• Multi-point constraints: Multi-point constraints (MPCs) specify linear or nonlinear constraints +between nodes. These relations between nodes can be the default types that are provided in Abaqus or, +in Abaqus/Standard, can be coded in the form of a user subroutine. “General multi-point constraints,” +Section 34.2.2, explains the use of MPCs and lists the available default constraints. +• Kinematic coupling: +In Abaqus/Standard a node or group of nodes can be constrained to a reference +node. Similar to multi-point constraints, the kinematic coupling constraint allows general node-by-node +specification of constrained degrees of freedom . +• Surface-based tie constraints: Two surfaces can be tied together. Each node on the first surface (the +slave surface) will have the same values for its degrees of freedom as the point on the second surface (the +master surface) to which it is closest . In the case of surface +elements tied to a beam surface, the offset distances between the surface elements and the beam are used +in the definition of constraints, which include the rotational degrees of freedom of the beam. +• Surface-based coupling constraints: A group of nodes located on a surface can be constrained +to a reference node. This constraint may be kinematic, in which the group of coupling nodes can be +constrained to the rigid body motion defined by the reference node, or distributing, in which the group of +coupling nodes can be constrained to the rigid body motion defined by the reference node in an average +sense . +• Surface-based shell-to-solid coupling: An edge-based surface on a three-dimensional shell +element mesh can be coupled to an element- or node-based surface on a three-dimensional solid mesh. +The coupling is enforced by the creation of an internal set of distributing coupling constraints . +• Mesh-independent spot welds: Two or more surfaces can be bonded together using fasteners such +as spot welds . Distributed coupling constraints are +created on each of the connected surfaces. The connection is modeled independent of the mesh. +• Embedded elements: An element or a group of elements can be embedded in a group of host +elements . Abaqus will search for the geometric relationships +between nodes on the embedded elements and the host elements. If a node on an embedded element lies +within a host element, the degrees of freedom at the node will be eliminated by constraining them to the +interpolated values of the degrees of freedom of the host element. Host elements cannot be embedded +themselves. +• Release: +In Abaqus/Standard a local rotational degree of freedom or a combination of local rotational +degrees of freedom can be released at one or both ends of a beam element . +Boundary conditions are also a type of kinematic constraint in stress analysis because they define the support +of the structure or give fixed displacements at nodal points. Specification of boundary conditions is discussed +in “Boundary conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1. +Connector elements can be used to impose element-based kinematic constraints for mechanism-type +analysis. See “Connectors: overview,” Section 31.1.1. +Contact interactions, described in Part IX, “Interactions,” can be used to enforce constraints between +bodies that come into contact. Contact interactions can be used in mechanical as well as coupled thermal- +mechanical, coupled thermal-electrical-structural, and coupled pore fluid-mechanical analysis. +“Overconstraint checks,” Section 34.6.1, describes the overconstraint checks and the automatic +resolution of some overconstraints performed in Abaqus/Standard. +Multiple kinematic constraints at a node +It is possible to use a single node in several multi-point constraints, kinematic coupling constraints, tie +constraints, and constraint equations. However, the constraint dependencies are handled differently in +Abaqus/Standard and Abaqus/Explicit. +Multiple constraints in Abaqus/Standard +In Abaqus/Standard kinematic constraints are usually imposed by eliminating degrees of freedom at the +dependent nodes. Once a variable has been eliminated, it cannot be referenced in any boundary condition +or in any subsequent multi-point constraint, kinematic coupling constraint, tie constraint, or constraint +equation. If you intend to use a variable that is eliminated in one constraint equation as the retained +variable in another constraint equation, you must order the input so that the constraint equation in which +the variable is eliminated follows the other constraint equations. MPC types BEAM, CYCLSYM, LINK, +PIN, REVOLUTE, TIE, and UNIVERSAL, as well as the kinematic coupling and tie constraints, are +sorted internally by Abaqus/Standard to obtain a proper elimination order when possible. +Excessive chaining of multi-point constraints, kinematic coupling constraints, and constraint +equations is not recommended and may result in a degradation in performance during analysis +preprocessing. Whenever possible, it is best to relate the behavior of several nodes (grouped into a node +set) to a single node by using one multi-point constraint, kinematic coupling constraint, or constraint +equation. +Multiple constraints in Abaqus/Explicit +Kinematic constraints in Abaqus/Explicit can be defined in any order without regard to constraint +dependencies. With the exception of constraints arising from kinematic contact pairs, Abaqus/Explicit +solves for all kinematic constraints simultaneously. Thus, nodes involved in a combination of +multi-point constraints, constraint equations, connector element kinematic constraints, rigid body +constraints, and constraints due to boundary conditions will simultaneously satisfy these constraints as +long as they are not conflicting. Redundant and closed loop constraints are acceptable. +Since the above constraints are enforced independent of contact constraints, the penalty contact +algorithm should be used for nodes involved in both kinematic constraints and contact pair definitions. +The penalty contact algorithm introduces numerical softening through the use of penalty springs and does +not interfere with kinematic constraints. If a node that participates in a kinematic constraint is used in a +kinematic contact pair, the contact constraint will most likely override the kinematic constraint. Except +for rigid bodies, Abaqus/Explicit will not prevent you from defining these conditions, but the results +cannot be guaranteed. If a kinematic constraint is defined for a node on a rigid body, the penalty contact +algorithm must be used for all contact pairs involving the rigid body. +To obtain accurate reaction force and moment output from Abaqus/Explicit at nodes that are +constrained by boundary conditions in addition to one or more of the kinematic constraints described +above, it may sometimes be necessary to run the analysis in double precision. +In such a situation +a double precision run will also yield a better estimate of the work done by the reaction forces and +moments, thereby providing a more accurate value of the energy due to the external work reported by +Abaqus/Explicit. +Abaqus/Explicit uses a penalty method to solve for constraints in certain situations. The penalties +are weighted based on the masses of nodes participating in the constraint and the stable time increment. +The penalty formulation attempts to satisfy the constraint approximately (i.e., a very small lack of +compliance exits after imposition of the constraint). One situation in which the penalty approach is used +to solve the constraint is when slave nodes of a tie constraint participate in other constraints such as +multi-point constraints, kinematic coupling constraints, constraint equations, connector elements, rigid +body constraints, or constraints due to boundary conditions. In this case the lack of compliance in the +tie constraint is not carried across step boundaries; therefore, noisy accelerations and energy imbalance +may be observed at step boundaries for certain problems. An alternative modeling approach (such as +simply reversing the master and slave surfaces in the tie constraint) may switch to a different solution +approach and thus resolve the above mentioned inaccuracies. +In Abaqus/Explicit when there are two or more overlapping distributed coupling constraints or +overlapping distributed coupling and tie constraints, and the elements underlying the participating +surfaces have very low densities, the lack of compliance may result in an inaccurate solution. Specifying +reasonable density values for underlying elements may reduce the lack of compliance and improve +solution accuracy. +Abaqus/Explicit always uses a geometrically nonlinear formulation for the enforcement of +kinematic constraints. This is the case even when you have designated a particular analysis step as +being geometrically linear. Consequently, results in these geometrically linear analyses could be +hard to interpret, particularly when the loading in the model is high (displacements are large) and a +geometrically nonlinear formulation should have been used. +Initial conditions at constrained nodes +You should not think of initial conditions as boundary conditions at the beginning of the analysis. When +you prescribe initial conditions at a set of nodes that are constrained kinematically, Abaqus processes +the prescribed values to determine an initial value that is then redistributed to the nodes involved in +the constraints in a kinematically consistent manner via a “mass” weighted averaging method: the initial +value prescribed at each node involved in the constraint is weighted with the corresponding “mass” at the +node. Consequently, the values of the initial conditions that you specified at the nodes are recomputed, +and in many cases the output of the prescribed quantity at these nodes at the beginning of the analysis will +be different from the values that you have specified. Correct modeling practices consist of specifying +initial conditions at all nodes involved in the constraints in a manner consistent with constraint itself. +This behavior is probably best understood via a simple example. Consider a model consisting of +two nodes each with a mass of 1.0 constrained by boundary conditions in global directions 2 and 3 and +allowed to move freely along the global 1-direction while their relative motions is also constrained via +a rigid connection such as a BEAM connector. Assume that you have specified an initial translational +velocity along the global 1-direction only at the first node of 10.0 units and you have not specified initial +conditions at the second node. Consequently, Abaqus will consider that the initial velocity is 0.0 at the +second node. This initial velocity field is inconsistent with the kinematic constraint enforced by the +BEAM connector because the constraint would be violated if the initial conditions were to be enforced +even for an infinitesimally short period of time. The outcome is that Abaqus will compute an initial +velocity field that would redistribute the momentum of the first node in a manner consistent with the +constraint. In this particular example, the net effect is that both nodes will end up with an initial velocity +of 5.0 units along the global 1-direction. Most likely, this is not what you intended. Correct modeling +practice in this case would be to specify an initial velocity of 10.0 units at both nodes involved in the +constraint. In this case Abaqus will still recompute the initial values, but the outcome would be an initial +velocity of 10.0 units at both nodes, as intended. +The same principle applies in more complicated modeling situations. For example, if you prescribe +initial translational velocities at the nodes of the kinematic constraint, an average translational velocity +of the constrained nodes is computed by calculating a mass weighted average of the velocities at the +individual nodes. Depending on the nature of the kinematic constraint, initial translational velocities +at the nodes of a constraint may also give rise to an average rotational velocity about the center of +mass of the constraint. The velocity of each individual node of the constraint is then recomputed +from the average translational and rotational velocities at the center of mass of the constraint. The +“mass”-type quantity used in the weighting varies depending on the nature of the prescribed quantity: +if the initial condition is prescribed on the rotational velocities, the rotary inertia at the nodes is used in +the weighting; if temperature initial conditions are prescribed, the thermal capacitance at the nodes is +used in the weighting; and so on. +In all cases, you should specify initial conditions at all nodes involved in the constraint that are +consistent with the constraint. This is typically accomplished by specifying the same initial conditions +at all nodes involved in the constraint. +34.2 +Multi-point constraints +• “Linear constraint equations,” Section 34.2.1 +• “General multi-point constraints,” Section 34.2.2 +• “Kinematic coupling constraints,” Section 34.2.3 +34.2.1 +LINEAR CONSTRAINT EQUATIONS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Kinematic constraints: overview,” Section 34.1.1 +• *EQUATION +• “Defining equation constraints,” Section 15.15.9 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +A linear multi-point constraint requires that a linear combination of nodal variables is equal to zero; that +is, +is a nodal variable at node P, degree of freedom i; and +the +are coefficients that define the relative motion of the nodes. +, where +In Abaqus/Explicit linear constraint equations can be used only to constrain mechanical degrees of +freedom. +Defining a linear constraint equation +A linear constraint equation is defined in Abaqus by specifying: +• the number of terms in the equation, N; +• the nodes, P, and the degrees of freedom, i, corresponding to the nodal variables +• the coefficients, +. +; and +For example, to impose the equation +you would first write the equation in the standard form, +There are three terms in this equation (N=3). P=5, i=3, +=1.0, Q=6, j=1, +=−1.0, R=1000, k=3, and +=1.0. +Input File Usage: +*EQUATION +P, i, +, Q, j, +, etc. +For example, the following input could be used to define the equation constraint +above: +*EQUATION +5, 3, 1.0, 6, 1, -1.0, 1000, 3, 1.0 +Either node sets or individual nodes can be specified as input. If node sets are +used, corresponding set entries will be matched to each other. If sorted node sets +are given as input, you must ensure that the nodes are numbered such that they +will match up with each other correctly once sorted. The nodes in an unsorted +node set will be used in the order that they are given in defining the set . +If the first entry is a single node, subsequent entries must be single nodes. If +the first entry is a node set, subsequent entries can be either node sets or single +nodes. The latter option is useful if a degree of freedom at each of a set of nodes +depends on a degree of freedom of a single node, such as may occur in certain +symmetry conditions or in the simulation of a rigid body. +Abaqus/CAE Usage: +Interaction module: Create Constraint: Equation +The nodes must be specified as sets. The first set can contain one or more points. +Subsequent sets must contain only a single point. +In Abaqus/Standard the first nodal variable specified ( +) will be eliminated +to impose the constraint (in the above equation constraint, degree of freedom 3 at node 5 will be +eliminated); therefore, it should not be used to apply boundary conditions, nor should it be used in any +subsequent multi-point constraint, kinematic coupling constraint, tie constraint, or equation constraint +. In addition, the coefficient +should not be +set to zero. These restrictions do not apply in Abaqus/Explicit. +corresponding to +In Abaqus/Standard a linear multi-point constraint cannot be used to connect two rigid bodies at +nodes other than the reference nodes, since multi-point constraints use degree-of-freedom elimination +and the other nodes on a rigid body do not have independent degrees of freedom. In Abaqus/Explicit a +rigid body reference node or any other node on a rigid body can be used in an equation constraint +definition. +Use with transformed coordinate systems +If a local coordinate system (“Transformed coordinate systems,” Section 2.1.5) is defined for any node +involved in the equation, the variables at that node appear in the equation in the local system. +Use within a part +If an equation constraint is defined at the part (or part instance) level, the nodal variables are transformed +initially according to the positioning data given for each instance of the part . +Note: Equation constraints cannot be defined at the part (or part instance) level in Abaqus/CAE. +Prescribing a nonhomogeneous constraint +It is sometimes necessary to impose a constraint in the form +where +as +is a prescribed value that may vary with time, t. This is easily done by rewriting the equation +to be +and introducing a node, Z, that is not attached to any element in the model. Choosing +some convenient degree of freedom m at node Z allows the prescribed value +to be imposed +through a boundary condition specification. If necessary, an amplitude reference can be provided to +give the variation with time ; such an amplitude reference is required in Abaqus/Explicit for prescribed displacements. +For example, assume that node 1000 in the example above is a “dummy” node that appears only +in this equation and is not attached to any other part of the model. Defining a boundary condition to +constrain degree of freedom 3 at node 1000 to −12.5 would impose the constraint +Constraint forces and global equilibrium +Linear constraint equations introduce constraint forces at all degrees of freedom appearing in the +equations. These forces are considered external, but they are not included in reaction force output. +Therefore, the totals provided at the end of the reaction force output tables may reflect an incomplete +measure of global equilibrium. +To illustrate this behavior, consider a spring-supported beam subjected to a concentrated load as +shown in Figure 34.2.1–1. The static reaction forces are +. In Figure 34.2.1–2 +and +, which constrains +the same structure is subjected to the additional linear constraint equation +, and the +the beam to remain horizontal. This introduces constraint forces +. These reaction forces produce a global force balance in the +new reaction forces are +Y-direction, but since the constraint forces are not included in reaction force output, the global moment +balance about point A cannot be verified. +and +P = 9 +y +2 + 1 +R = –3 +y +R = – 6 +y +Figure 34.2.1–1 Beam with no linear constraints. +F = 1.5 +y +R = – 4.5 +y +P = 9 +y +F = –1.5 +y +2 + 1 +R = – 4.5 +y +Figure 34.2.1–2 Beam with linear constraint +. +Constraint forces +and +are not included in reaction force output. +The global force balance can also be incomplete. This is demonstrated in Figure 34.2.1–3, where a +. +, are not included in the reaction force output, producing +pulley connection between nodes A and B is represented by the linear constraint equation +The constraint forces at the pulley, +incomplete global force balances in both the X- and Y-directions. +and +P = 9 +y +F = –9 +F = –9 +R = 9x +Figure 34.2.1–3 Pulley connection represented by the linear +constraint +. Constraint forces +and +are +not included in reaction force output. +Obtaining the constraint force +The linear constraint generates constraint forces at all the degrees of freedom involved in the equation. +For a given constraint equation these forces are proportional to their respective coefficients. To find +the constraint forces, introduce a node Z that is not attached to any element in the model; rewrite the +constraint equation as +and specify a zero displacement boundary condition at degree of freedom m of node Z. The reaction +force obtained at node Z will be equal to the constraint force acting at node P in degree of freedom i. +The constraint force in any term with coefficient +in the constraint equation is obtained by multiplying +the constraint force at node P in degree of freedom i with the ratio +. For example, if the equation +is +and the forces in the constraint are needed, the equation can be rewritten as +is the opposite of the coefficient +, the constraint force at node 5 is the same as the reaction force at node 1000. Since the coefficient +, the constraint force at node 6 is the opposite of the reaction +where node 1000 is the fixed “dummy” node. Since the coefficient of +of +of +force at node 1000. +is the same as the coefficient of +Defining a constraint in a deformed state +Sometimes we may wish to impose an equation starting at a certain point in the analysis: +where +represents the change in displacement after time +. The equation can be rewritten as +(which is assumed to +further changes +are restrained in Abaqus/Standard by applying a boundary condition fixing the degree of freedom +where, again, node Z is not attached to any element in the model. Prior to time +be at the end of a step), degree of freedom m of node Z is left unrestrained. After time +in +at its current values at the start of the step. +Reading the data from an alternate input file +Input File Usage: +The input for a linear constraint equation can be contained in a separate input file. +*EQUATION, INPUT=file_name +If the INPUT parameter is omitted, it is assumed that the data lines follow the +keyword line. +Abaqus/CAE Usage: +Interaction module: Create Constraint: Equation: click mouse button 3 +while holding the cursor over the data table, and select Read from File +34.2.2 +GENERAL MULTI-POINT CONSTRAINTS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Kinematic constraints: overview,” Section 34.1.1 +• *MPC +• “Defining MPC constraints,” Section 15.15.6 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• Chapter 24, “Connectors,” of the Abaqus/CAE User’s Manual, in the online HTML version of this +manual +Overview +Multi-point constraints (MPCs): +• allow constraints to be imposed between different degrees of freedom of the model; and +• can be quite general (nonlinear and nonhomogeneous). +The most commonly required constraints are available directly by choosing an MPC type and giving +the associated data. The available MPC types are described below; MPCs that are available only in +Abaqus/Standard are designated with an (S) . +In Abaqus/Standard the constraints can also be given by user subroutine MPC. +Linear constraints can be given directly by defining a linear constraint equation . +In Abaqus/Explicit some multi-point constraints can be modeled more effectively using rigid bodies +. +Several MPC types are also available with connector elements (“Connector elements,” +Section 31.1.2). Although the connector elements impose the same kinematic constraint, connectors do +not eliminate degrees of freedom. +MPC constraint forces are not available as output quantities. Therefore, to output the forces required +to enforce the constraint specified in an MPC, you should use an equivalent connector element. Connector +element force, moment, and kinematic output is readily available and is defined in “Connector element +library,” Section 31.1.4. +Identifying the nodes involved in the MPC +For any MPC type, either node sets or individual nodes can be given as input. If the first entry is a node, +subsequent entries must be nodes. If the first entry is a node set, subsequent entries can be either node +sets or single nodes. The latter option is useful if a degree of freedom at each of a set of nodes depends +on a degree of freedom of a single node, such as may occur in certain symmetry conditions or in the +simulation of a rigid body. +If node sets are used, corresponding set entries will be constrained to each other. If sorted node sets +are given as input, you must ensure that the nodes are numbered such that they will match up correctly +when sorted. The nodes in an unsorted node set will be used in +the order that they are given in defining the set. +In Abaqus/Standard multi-point constraints cannot be used to connect two rigid bodies at nodes +other than the reference nodes, since multi-point constraints use degree-of-freedom elimination and the +other nodes on a rigid body do not have independent degrees of freedom. In Abaqus/Explicit a rigid +body reference node or any other node on a rigid body can be used in a multi-point constraint definition. +Abaqus/CAE uses connectors to define multi-point constraints between two points and constraints +to define multi-point constraints between a point and slave nodes in a region. Set-to-set multi-point +constraints and unsorted node sets are not supported in Abaqus/CAE. +Input File Usage: +Abaqus/CAE Usage: +*MPC +Use the following options to define a multi-point constraint between two points: +Interaction module: +Connector→Geometry→Create Wire Feature +Connector→Section→Create: Connection Category: MPC, +MPC type: select type +Connector→Assignment→Create: select wires: Section: +select MPC connector section +Use the following options to define a multi-point constraint between a point and +slave nodes in a region: +Interaction module: +Constraint→Create: MPC Constraint: select control point +and region; MPC type: select type +Use with transformed coordinate systems +Local coordinate systems can be defined for any +nodes connected to MPCs. Some special considerations apply for user-defined MPCs, as described in +“MPC,” Section 1.1.14 of the Abaqus User Subroutines Reference Manual. +Defining multiple multi-point constraints at a point +See “Kinematic constraints: overview,” Section 34.1.1, for details on how multiple kinematic constraints +at a point are treated in Abaqus/Standard and Abaqus/Explicit. +In Abaqus/Standard MPCs are usually imposed by eliminating the degree of freedom at the first node +given (the dependent degree of freedom). MPC types BEAM, CYCLSYM, LINK, PIN, REVOLUTE, +TIE, and UNIVERSAL are sorted internally by Abaqus/Standard so that the MPC in which a node is used +as a dependent node is the last MPC that uses this node. Therefore, groups of these MPCs can be given +in any order. However, even for these MPCs, a node can be used only once as a dependent node. In other +cases dependent degrees of freedom should not be used subsequently to impose kinematic constraints; +this generally precludes the use of the first node in an MPC definition as an independent node in any +subsequent multi-point constraint, equation constraint, kinematic coupling constraint, or tie constraint +definition. +Using MPCs in implicit dynamic analysis +In implicit dynamic analysis Abaqus/Standard enforces MPCs rigorously for the displacements. The +velocities and accelerations are derived from the displacements with the relations defined by the +dynamic integration operator . For linear MPCs (such as PIN, TIE, and mesh refinement MPCs) and geometrically linear +analysis the velocities obtained in this way satisfy the constraint exactly. However, the accelerations +satisfy the constraint only approximately. If nonlinear MPCs (such as BEAM, LINK, and SLIDER) are +used in geometrically nonlinear analysis, both the velocities and accelerations satisfy the constraint only +approximately. In most cases the approximation is quite accurate, but in some cases high frequency +oscillations may occur in the accelerations of the nodes involved in the MPC. +Using nonlinear MPCs in geometrically linear Abaqus/Standard analysis +If a nonlinear MPC is used in a geometrically linear Abaqus/Standard analysis , the MPC is linearized. For example, if MPC LINK is used +in a geometrically nonlinear Abaqus/Standard analysis, the distance between the two nodes of the link +remains constant. If it is used in a geometrically linear Abaqus/Standard analysis, the distance between +the two nodes is held constant after projection onto the direction of the line between the original +positions of the nodes. The difference should be noticeable only if the magnitudes of the rotations and +displacements are not small. +Defining MPCs in a user subroutine +In Abaqus/Standard you can define multi-point constraints in user subroutine MPC. +Constraints defined in user subroutine MPC can only use degrees of freedom that also exist on an +element somewhere in the same model. For example, if a model contains no elements with rotational +degrees of freedom, user subroutine MPC cannot use degrees of freedom 4, 5, or 6. This limitation can +be overcome by adding a suitable element somewhere in the model to introduce the required degrees of +freedom. This element can be added so that it does not affect the response of the model. +Constraints defined in the user subroutine are applied to the transformed degrees of freedom. +A boundary nonlinearity occurs in Abaqus/Standard when MPCs are activated/deactivated in a user +subroutine. +Input File Usage: +Abaqus/CAE Usage: +*MPC, USER +Use one of the following options: +Interaction module: Create Connector Section: select MPC as the +Connection Category and User-defined as the MPC Type +Interaction module: Create Constraint: MPC Constraint; select +User-defined as the MPC Type +Specifying the version of user subroutine MPC +You must specify whether the user subroutine will be coded in degree of freedom mode or in nodal mode. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options: +*MPC, USER, MODE=DOF +*MPC, USER, MODE=NODE +Use one of the following options: +Interaction module: Create Connector Section: select MPC as +the Connection Category and User-defined as the MPC Type, +choose DOF-by-DOF or Node-by-Node +Interaction module: Create Constraint: MPC Constraint: select +User-defined as the MPC Type, choose DOF-by-DOF or Node-by-Node +Reading the data from an alternate input file +The input for an MPC definition can be contained in a separate input file. +Input File Usage: +*MPC, INPUT=file_name +If the INPUT parameter is omitted, it is assumed that the data lines follow the +keyword line. +Abaqus/CAE Usage: +Reading data from an alternate input file is not supported in Abaqus/CAE. +MPCs for mesh refinement +LINEAR +QUADRATIC(S) +BILINEAR(S) +C BIQUAD(S) +This MPC is a standard method for mesh refinement of first-order elements. +It +applies to all active degrees of freedom at the involved nodes including temperature, +pressure, and electrical potential. +In Abaqus/Explicit it might be preferable to use a surface-based tie constraint + for mesh refinement, particularly when +one or more of the meshes to be constrained involve shell elements with thickness. +This MPC is a standard method for mesh refinement of second-order elements. It +applies to all active degrees of freedom at the involved nodes with the exception of +temperature degrees of freedom in coupled temperature-displacement analysis and +coupled thermal-electrical-structural analysis and to pressure degrees of freedom in +coupled pore pressure analysis. For refinement using second-order pore pressure +or coupled-temperature displacement elements, the P LINEAR or T LINEAR MPC +must be used in conjunction with this MPC. +This MPC is a standard method for mesh refinement of first-order solid elements in +three dimensions. It applies to all active degrees of freedom at the involved nodes +including temperature, pressure, and electrical potential. +This MPC is a standard method for mesh refinement of second-order solid +It applies to all active degrees of freedom at the +elements in three dimensions. +involved nodes with the exception of temperature degrees of freedom in coupled +thermal-electrical-structural +and +temperature-displacement +analysis and to pressure degrees of freedom in coupled pore pressure analysis. +For refinement using pore pressure or coupled-temperature displacement elements +in three dimensions, the P BILINEAR or T BILINEAR MPC must be used in +conjunction with this MPC. +analysis +coupled +P LINEAR(S) +T LINEAR(S) +P BILINEAR(S) +T BILINEAR(S) +This MPC can be used in conjunction with the QUADRATIC MPC for mesh +refinement of second-order, fully coupled pore fluid flow-displacement elements. +It applies to pressure degrees of freedom only. For acoustic analysis it applies the +same constraint as the LINEAR MPC. +This MPC can be used in conjunction with the QUADRATIC MPC for mesh +refinement of second-order, fully coupled temperature-displacement and fully +coupled thermal-electrical-structural elements. +It applies to temperature degrees +of freedom only. For heat transfer analysis it applies the same constraint as the +LINEAR MPC. +This MPC can be used in conjunction with the C BIQUAD MPC for mesh refinement +of pore fluid flow-displacement elements in three dimensions. It applies to pressure +degrees of freedom only. For acoustic analysis it applies the same constraint as the +BILINEAR MPC. +fully coupled temperature-displacement +This MPC can be used in conjunction with the C BIQUAD MPC for mesh +refinement of +and fully coupled +thermal-electrical-structural elements in three dimensions. It applies to temperature +degrees of freedom only. For heat transfer analysis it applies the same constraint as +the BILINEAR MPC. +Using mesh refinement MPCs with shell or beam elements +The Abaqus/Standard shell elements S4R5, S8R5, S9R5, and STRI65 use a penalty method to enforce +transverse shear constraints on the edges of the element. The use of mesh refinement MPCs LINEAR +and QUADRATIC may, therefore, lead to overconstraining or “shear locking” of the bending behavior. +Graded meshes, using the triangular elements as necessary to create a transition zone, are recommended +for mesh refinement with these elements. +The shear flexible beam elements in Abaqus/Standard such as B31 or B32 will also “lock” if used +as stiffeners along a mesh line where the mesh refinement MPCs are used. +For shell elements in Abaqus/Explicit the rotational degrees of freedom are not constrained by the +LINEAR MPC; therefore, a hinge is formed along the line defined by the constrained nodes. +Using MPC type LINEAR +MPC type LINEAR is a standard method for mesh refinement of first-order elements. However, in +Abaqus/Explicit it might be preferable to use a surface-based tie constraint for mesh refinement, particularly when one or more of the meshes to be constrained +involve shell elements with thickness. +This MPC constrains each degree of freedom at node p to be interpolated linearly from the +corresponding degrees of freedom at nodes a and b . +Figure 34.2.2–1 LINEAR type MPC. +Input data +Give the nodes p, a, and b as shown in Figure 34.2.2–1. +*MPC +LINEAR, p, a, b +Input File Usage: +Abaqus/CAE Usage: Mesh refinement multi-point constraints are not supported in Abaqus/CAE. +Using MPC type QUADRATIC +MPC type QUADRATIC is a standard method for mesh refinement of second-order elements. This MPC +type is available only in Abaqus/Standard. +This MPC constrains each degree of freedom at node p (where p is either +) to be interpolated +quadratically from the corresponding degrees of freedom at nodes a, b, and c (Figure 34.2.2–2). For +coupled temperature-displacement, coupled thermal-electrical-structural, or pore pressure elements, only +the displacement degrees of freedom are constrained. +or +p2 +p1 +p2 +p1 +Figure 34.2.2–2 QUADRATIC type MPC. +Input data +Give the nodes p, a, b, and c as shown in Figure 34.2.2–2, where p is either +or +. +Input File Usage: +*MPC +QUADRATIC, p, a, b, c +Abaqus/CAE Usage: Mesh refinement multi-point constraints are not supported in Abaqus/CAE. +Using MPC type BILINEAR +MPC type BILINEAR is a standard method for mesh refinement of first-order solid elements in three +dimensions. This MPC type is available only in Abaqus/Standard. +This MPC constrains each degree of freedom at node p to be interpolated bilinearly from the +corresponding degrees of freedom at nodes a, b, c, and d (Figure 34.2.2–3). +Figure 34.2.2–3 BILINEAR type MPC. +Input data +Give the nodes p, a, b, c, and d as shown in Figure 34.2.2–3. +Input File Usage: +*MPC +BILINEAR, p, a, b, c, d +Abaqus/CAE Usage: Mesh refinement multi-point constraints are not supported in Abaqus/CAE. +Using MPC type C BIQUAD +MPC type C BIQUAD is a standard method for mesh refinement of second-order solid elements in three +dimensions. This MPC type is available only in Abaqus/Standard. +This MPC constrains each degree of freedom at node p to be interpolated by a constrained +biquadratic from the corresponding degrees of freedom at the eight nodes a, b, c, d, e, f, g, and h +(Figure 34.2.2–4). For coupled temperature-displacement, coupled thermal-electrical-structural, or pore +pressure elements, only the displacement degrees of freedom are constrained. +Figure 34.2.2–4 C BIQUAD type MPC. +Input data +Give the nodes p, a, b, c, d, e, f, g, and h as shown in Figure 34.2.2–4. +Input File Usage: +*MPC +C BIQUAD, p, a, b, c, d, e, f, g, h +Abaqus/CAE Usage: Mesh refinement multi-point constraints are not supported in Abaqus/CAE. +Using MPC types P LINEAR and T LINEAR +The P LINEAR MPC can be used in conjunction with the QUADRATIC MPC for mesh refinement of +second-order, fully coupled pore fluid flow-displacement elements. +The T LINEAR MPC can be used in conjunction with the QUADRATIC MPC for mesh refinement +of second-order, fully coupled temperature-displacement and fully coupled thermal-electrical-structural +elements. +These MPC types are available only in Abaqus/Standard. +These MPCs constrain the pore pressure (P LINEAR) or temperature (T LINEAR) degree +of freedom at node p to be interpolated linearly from the degrees of freedom at nodes a and b +(Figure 34.2.2–5). +Figure 34.2.2–5 P LINEAR and T LINEAR MPCs. +Input data +Give the nodes p, a, and b as shown in Figure 34.2.2–5. +Input File Usage: +Use the following option to define a P LINEAR MPC: +*MPC +P LINEAR, p, a, b +Use the following option to define a T LINEAR MPC: +*MPC +T LINEAR, p, a, b +Abaqus/CAE Usage: Mesh refinement multi-point constraints are not supported in Abaqus/CAE. +Using MPC types P BILINEAR and T BILINEAR +The P BILINEAR MPC can be used in conjunction with the C BIQUAD MPC for mesh refinement of +pore fluid flow-displacement elements in three dimensions. +The T BILINEAR MPC can be used in conjunction with the C BIQUAD MPC for mesh refinement +of fully coupled temperature-displacement and fully coupled thermal-electrical-structural elements in +three dimensions. +These MPC types are available only in Abaqus/Standard. +These MPCs constrain the pore pressure (P LINEAR) or temperature (T LINEAR) at node p to be +interpolated bilinearly from the pore pressure or temperature at nodes a, b, c, and d (Figure 34.2.2–6). +Figure 34.2.2–6 P BILINEAR and T BILINEAR MPCs. +Input data +Give the nodes p, a, b, c, and d as shown in Figure 34.2.2–6. +Input File Usage: +Use the following option to define a P BILINEAR MPC: +*MPC +P BILINEAR, p, a, b, c, d +Use the following option to define a T BILINEAR MPC: +*MPC +T BILINEAR, p, a, b, c, d +Abaqus/CAE Usage: Mesh refinement multi-point constraints are not supported in Abaqus/CAE. +MPCs for connections and joints +BEAM +CYCLSYM(S) +ELBOW(S) +LINK +PIN +REVOLUTE(S) +SLIDER +TIE +UNIVERSAL(S) +V LOCAL(S) +Provide a rigid beam between two nodes to constrain the displacement and rotation +at the first node to the displacement and rotation at the second node, corresponding +to the presence of a rigid beam between the two nodes. +Constrain nodes to impose cyclic symmetry in a model. +Constrain two nodes of ELBOW31 or ELBOW32 elements together, where the +cross-sectional direction, +, changes . +Provide a pinned rigid link between two nodes to keep the distance between the +two nodes constant. The displacements of the first node are modified to enforce this +constraint. The rotations at the nodes, if they exist, are not involved in this constraint. +Provide a pinned joint between two nodes. This MPC makes the displacements equal +but leaves the rotations, if they exist, independent of each other. +Provide a revolute joint. +Keep a node on a straight line defined by two other nodes, but allow the possibility +of moving along the line and allow the line to change length. +Make all active degrees of freedom equal at two nodes. +Provide a universal joint. +Allow the velocity at the constrained node to be expressed in terms of velocity +components at the third node defined in a local, body axis system. These local +velocity components can be constrained, +thus providing prescribed velocity +boundary conditions in a rotating, body axis system. +See “Connectors: overview,” Section 31.1.1, for element-based versions of several of these MPCs for +connections and joints. +Using MPC type BEAM +MPC type BEAM provides a rigid beam between two nodes to constrain the displacement and rotation +at the first node to the displacement and rotation at the second node, corresponding to the presence of a +rigid beam between the two nodes. +beam node +shell node +beam node +shell node +Figure 34.2.2–7 BEAM type MPC. +Input data +Give the nodes a and b as shown in Figure 34.2.2–7. +Input File Usage: +*MPC +BEAM, a, b +Abaqus/CAE Usage: +Use one of the following options: +Interaction module: Create Connector Section: select MPC as the +Connection Category and Beam as the MPC Type +Interaction module: Create Constraint: MPC Constraint; +select Beam as the MPC Type +Constraining a beam stiffener to a shell +The general method of using a beam as a stiffener on a shell is to define the beam and shell elements +with separate nodes. These nodes can then be constrained to each other using BEAM type MPCs. +A more economical way, when applicable, is to use the same node for the beam node and the shell +node and then define the offset of the center of the cross-section of the beam in the beam section data. +Figure 34.2.2–8 shows a T-shaped stiffener attached to a shell, using the I-beam cross-section. This is +done by setting l equal to the distance between the +node and the underside of the lower flange and setting the thickness of the top flange to zero. This +approach can be used with all beam elements that use TRAPEZOID, I, or ARBITRARY beam sections. +node +t1 +b = 0. +t = 0. +b1 +Figure 34.2.2–8 Stiffened shell. +Using MPC type CYCLSYM +MPC type CYCLSYM is used to enforce proper constraints on the radial faces bounding a segment of a +cyclic symmetric structure . This MPC type is available only in Abaqus/Standard. +MPC type CYCLSYM imposes the cyclic symmetry by equating radial, circumferential, and axial +displacement components (and rotations, if active) at the two nodes (a and b). The symmetry axis can +be defined by the original coordinates of two additional nodes (c and d) that do not need to be connected +to any element in the structure. Scalar degrees of freedom (such as temperature) are made equal. +original part intended +to be analyzed possessing +cyclic symmetry +axis of +cyclic symmetry +section +actually modeled +Figure 34.2.2–9 MPC type CYCLSYM. +Input data +Give the nodes a, b, and (optionally) node c and/or d that define the axis of symmetry as shown in +Figure 34.2.2–9. Node set names can be used instead of the nodes a and b. If neither c nor d is given, the +global z-axis is taken to be the axis of cyclic symmetry. If only node c is given, the symmetry axis passes +through c and is parallel to the global z-axis. Thus, node d is not needed in two-dimensional cases. +Input File Usage: +Abaqus/CAE Usage: +*MPC +CYCLSYM, a, b, c, d +Cyclic symmetry multi-point constraints are not supported in Abaqus/CAE. +Using MPC type ELBOW +MPC type ELBOW constrains two nodes of ELBOW31 or ELBOW32 elements together, where the +cross-sectional direction, +, changes . This MPC type is available only in Abaqus/Standard. +a2(0,1,0) +a2(0,0,1) +Figure 34.2.2–10 ELBOW type MPC. +Input data +Give the nodes a and b as shown in Figure 34.2.2–10. +Input File Usage: +Abaqus/CAE Usage: +*MPC +ELBOW, a, b +Use one of the following options: +Interaction module: Create Connector Section: select MPC as the +Connection Category and Elbow as the MPC Type +Interaction module: Create Constraint: MPC Constraint; +select Elbow as the MPC Type +Using MPC type LINK +MPC type LINK provides a pinned rigid link between two nodes to keep the distance between the nodes +constant, as shown in Figure 34.2.2–11. The displacements of the first node are modified to enforce this +constraint. The rotations at the nodes, if they exist, are not involved in this constraint. +Figure 34.2.2–11 MPC type LINK. +Input data +Give the nodes a and b as shown in Figure 34.2.2–11. +Input File Usage: +Abaqus/CAE Usage: +*MPC +LINK, a, b +Use one of the following options: +Interaction module: Create Connector Section: select MPC as the +Connection Category and Link as the MPC Type +Interaction module: Create Constraint: MPC Constraint; +select Link as the MPC Type +Using MPC type PIN +MPC type PIN provides a pinned joint between two nodes. This MPC makes the global displacements +equal but leaves the rotations, if they exist, independent of each other, as shown in Figure 34.2.2–12. +u a = u b +u a = u b +u a = u b +φ a ≠ φ b +φ a ≠ φ b +φ a ≠ φ b +ub +φb +ub +φb +ua +φa +ua +φa +φb +ub +Figure 34.2.2–12 MPC type PIN. +φa +ua +Input data +Give the nodes a and b as shown in Figure 34.2.2–12. +Input File Usage: +Abaqus/CAE Usage: +*MPC +PIN, a, b +Use one of the following options: +Interaction module: Create Connector Section: select MPC as the +Connection Category and Pin as the MPC Type +Interaction module: Create Constraint: MPC Constraint; +select Pin as the MPC Type +Using MPC type REVOLUTE +This MPC type is available only in Abaqus/Standard. +A revolute joint is a joint in which relative rotation is allowed between two nodes about an axis +that rotates during the motion . The axis of the joint is defined in the initial +configuration as the line from node b to node c. If these nodes are coincident, the axis is assumed to +be the global z-axis. The rotation of the joint axis is that of node b. +The relative rotation in the joint is a single variable and is stored as degree of freedom 6 at node c. +This degree of freedom can be used with other members in the model, but caution should be used because +of the nonstandard use of degree of freedom 6. For example, a SPRING1 element (a spring to ground) +might be attached to this degree of freedom. Since the degree of freedom measures a relative rotation, +this spring would then be a torsional spring between nodes a and b. +The displacements at node a are not constrained by the REVOLUTE MPC to be the same as the +displacements at node b. Thus, the joint definition must usually be completed either by using a PIN type +MPC between nodes a and b or by using suitable stiffness members between these two nodes. +An example of a revolute joint and application of the REVOLUTE MPC is provided in “Revolute +MPC verification: rotation of a crank,” Section 1.3.8 of the Abaqus Benchmarks Manual. See “Revolute +joint,” Section 6.6.3 of the Abaqus Theory Manual, for more details on revolute joints. +Figure 34.2.2–13 Revolute joint. +Input data +Give the nodes a, b, and c as shown in Figure 34.2.2–13. Degree of freedom 6 at node c defines the +relative rotation between nodes a and b; therefore, this degree of freedom does not obey the standard +convention for degrees of freedom in Abaqus. +Input File Usage: +Abaqus/CAE Usage: +*MPC +REVOLUTE, a, b, c +Revolute joint multi-point constraints are not supported in Abaqus/CAE. +Using MPC type SLIDER +MPC type SLIDER keeps a node on a straight line defined by two other nodes but allows the possibility +of moving along the line and allows the line to change length. +When transitioning from multiple layers of solid elements to shells, it is often desirable to constrain +the nodes on the free edge of the solid elements to remain in a straight line. (This constraint is consistent +with shell theory.) The SLIDER MPC can perform this function without restraining the “thinning” +behavior of the solid layers. The SS LINEAR MPC is then used to attach the shell element to this edge. +In Abaqus/Standard when a SLIDER MPC is used with one of the shell-solid MPCs—SS LINEAR, +SS BILINEAR, or SSF BILINEAR—it must be given following the shell-solid MPCs. +Input data +For each node p shown in Figure 34.2.2–14 and Figure 34.2.2–15, give the nodes p, a, and b for each +line of nodes that should remain straight. For each node q shown in Figure 34.2.2–14, give the nodes q, +c, and d, and so on for each line of nodes that should remain straight. +Input File Usage: +Abaqus/CAE Usage: +*MPC +SLIDER, p, a, b +SLIDER, q, c, d +Slider multi-point constraints are not supported in Abaqus/CAE. +edge node line +Solid elements +(8-node) +edge node line +p5 +p4 +p3 +p2 +p1 +q2 +q1 +Solid elements +(20-node) +midside node line +Figure 34.2.2–14 SLIDER type MPC used at a shell-solid intersection. +a, b are nodes on the outer pipe +p1, p2 are nodes on the inner pipe +p2 +p1 +Figure 34.2.2–15 SLIDER type MPC used to model a telescoping beam. +Using MPC type TIE +MPC type TIE makes the global displacements and rotations as well as all other active degrees of freedom +equal at two nodes. If there are different degrees of freedom active at the two nodes, only those in +common will be constrained. +MPC type TIE is usually used to join two parts of a mesh when corresponding nodes on the two +parts are to be fully connected (“zipping up” a mesh). For example, when a mesh is generated on a +cylindrical body, the solution at the nodes at 0° and those at 360° must be the same. This can be done +either by renumbering the nodes on one of the mesh extremes or by using this MPC for each pair of +corresponding nodes, as shown in Figure 34.2.2–16. +a1 +b1 +a2 +b2 +a3 +b3 +Figure 34.2.2–16 Example of use of TIE MPC. +Input data +Give the nodes a and b as shown in Figure 34.2.2–16. +Input File Usage: +Abaqus/CAE Usage: +*MPC +TIE, a, b +Use one of the following options: +Interaction module: Create Connector Section: select MPC as the +Connection Category and Tie as the MPC Type +Interaction module: Create Constraint: MPC Constraint; +select Tie as the MPC Type +Using MPC type UNIVERSAL +This MPC type is available only in Abaqus/Standard. +A universal joint is a joint in which relative rotation is allowed between two nodes, about two +axes that are connected rigidly, and each of which rotates with the rotation of one end of the joint . Such a joint might be used to couple two shafts that have an angular misalignment. +The first axis of the joint, which is attached to node b, is defined in the initial configuration as the line +from node b to node c. If these nodes are coincident, the axis is assumed to be the global z-axis. The +second axis of the joint is at right angles to the first axis and is in the plane defined by the first axis and +node d. +The relative rotations in the joint are stored as degree of freedom 6 at the nodes c and d. These +degrees of freedom can be used with other members in the model, but caution should be used because +of the nonstandard use of degree of freedom 6. For example, a SPRING1 element (a spring to ground) +might be attached to one of these degrees of freedom. Since the degree of freedom measures a relative +rotation, this spring would then be a torsional spring, restraining that component of relative rotation. +The displacements at node a are not constrained by the UNIVERSAL MPC to be the same as the +displacements at node b. Thus, the joint definition must usually be completed either by using a PIN type +MPC between nodes a and b or by using suitable stiffness members between these two nodes. +See “Universal joint,” Section 6.6.4 of the Abaqus Theory Manual, for more details on universal +joints. +Figure 34.2.2–17 Universal joint. +Input data +Give the nodes a, b, c, and d as shown in Figure 34.2.2–17. Degrees of freedom 6 at nodes c and d define +the relative rotation in the joint; therefore, these degrees of freedom do not obey the standard convention +for degrees of freedom in Abaqus. +Input File Usage: +Abaqus/CAE Usage: +*MPC +UNIVERSAL, a, b, c, d +Universal joint multi-point constraints are not supported in Abaqus/CAE. +Using MPC type V LOCAL +This MPC type is available only in Abaqus/Standard. +As shown in Figure 34.2.2–18, MPC type V LOCAL constrains the velocity components associated +with degrees of freedom 1, 2, and 3 at a first node (a) to be equal to the velocity components at a third +node (c) along local, rotating directions. These local directions rotate according to the rotation at a second +node (b). In the initial configuration the first local direction is from the second to the third node of the +MPC (from b to c, as indicated by the arrows in Figure 34.2.2–18), or it is the global z-axis if these +nodes coincide. The other local directions are then defined by the standard Abaqus convention for such +directions . In Figure 34.2.2–18 this MPC is applied to nodes d, e, +and f in the same manner. +MPC type V LOCAL can be useful for defining a complex motion within a model. For example, the +MPC can be used to model the steering of an automobile in a dynamic analysis for which the resulting +inertial effects are of interest. See “Local velocity constraint,” Section 6.6.5 of the Abaqus Theory +Manual, for more details on the local velocity constraint. +a,b +d,e +Figure 34.2.2–18 Local velocity constraint. +Input data +Give the node whose velocity components are constrained (node a or d in Figure 34.2.2–18), the node +whose rotation defines the rotation of the local directions (node b or e in Figure 34.2.2–18), and the node +whose velocity components are in these local directions (node c or f in Figure 34.2.2–18). Nodes a and +b (or d and e) can be the same. +*MPC +V LOCAL, a, b, c +V LOCAL, d, e, f +Local velocity component multi-point constraints are not supported in +Abaqus/CAE. +Abaqus/CAE Usage: +Input File Usage: +MPCs for transitions +SS LINEAR +SS BILINEAR(S) +SSF BILINEAR(S) +Constrain a shell node to a solid node line for linear elements (S4, +S4R, S4R5, C3D8, C3D8R, SAX1, CAX4, etc.). +Constrain a shell node to a solid node line for edge lines on +quadratic elements (S8R, S8R5, C3D20, C3D20R, SAX2, CAX8, +etc.). +Constrain a midside node of a quadratic shell element (S8R, S8R5) +to midface lines on 20-node bricks (C3D20, C3D20R, etc.). +Modeling a shell-to-solid element transition +The SLIDER, SS LINEAR, SS BILINEAR, and SSF BILINEAR MPCs allow for a transition from shell +element modeling to solid element modeling on a shell surface. This modeling technique can be used +to obtain solutions at shell-solid intersections or other discontinuities, where the local modeling should +use full three-dimensional theory but the other parts of the structure can be modeled as shells. The shell- +to-solid submodeling capability (“Submodeling: overview,” Section 10.2.1) and the surface-based shell- +to-solid coupling constraint (“Shell-to-solid coupling,” Section 34.3.3) can also be used to obtain more +accurate solutions in such cases, with considerably less modeling effort. +, +, …, b in Figure 34.2.2–14 and lines +In Abaqus/Standard the MPC usage assumes that the interface between the shell and solid elements +is a surface containing the normals to the shell along the line of intersection of the meshes, so that the lines +of nodes on the solid mesh side of the interface in the normal direction to the surface are straight lines. +(Line a, +in Figure 34.2.2–19 to Figure 34.2.2–20 +, +should be straight lines.) It also assumes that the nodes of the solid elements are spaced uniformly on the +interface surface as indicated in Figure 34.2.2–14 and Figure 34.2.2–19 to Figure 34.2.2–20. For each +shell node on the edge use MPC type SS LINEAR, SS BILINEAR, or SSF BILINEAR, as appropriate, +to constrain the shell node to the corresponding line or face of solid element nodes through the thickness. +Then, use a SLIDER MPC to constrain each interior node on the line through the thickness to remain +on the straight line defined by the bottom and top nodes of that line. For an example, see “*MPC,” +Section 5.1.17 of the Abaqus Verification Manual. +, …, +The SS BILINEAR and SSF BILINEAR MPCs are not intended for use with the variable node solid +elements (C3D27, C3D27H, C3D27R, and C3D27RH). +In Abaqus/Standard MPCs SS LINEAR, SS BILINEAR, and SSF BILINEAR eliminate all +displacement components and two of the rotation components at the shell node, and the SLIDER MPC +eliminates two displacement components at each interior solid element node in the interface. Therefore, +any boundary conditions needed at the interface (such as those required when the shell/solid interface +intersects a symmetry plane) should be applied only to the top and bottom nodes on the solid element +side of the interface. +Using MPC type SS LINEAR +MPC type SS LINEAR constrains a shell corner node to a line of edge nodes on solid elements for linear +elements (S4, S4R, or S4R5; C3D8, C3D8R; SAX1; CAX4; etc.). +The constrained nodes need not lie exactly on these lines, but it is suggested that they be in close +proximity to the lines for meaningful results. +pn +p2 +p1 +Figure 34.2.2–19 SS LINEAR type MPC. 4-node shells to 8-node bricks. +Input data +Give the shell node, S, then the list of nodes along the corresponding line through the thickness in the solid +element mesh. In Abaqus/Explicit only two solid nodes can be given. Referring to Figure 34.2.2–19, in +Abaqus/Standard give S, +. The shell +, …, +node number must be different from the solid mesh node numbers. +, and in Abaqus/Explicit give S, +, where +, +, +Input File Usage: +In Abaqus/Standard use the following option: +*MPC +SS LINEAR, S, +, +, …, +In Abaqus/Explicit use the following option: +*MPC +SS LINEAR, S, +, +Abaqus/CAE Usage: Multi-point constraints for transitions are not supported in Abaqus/CAE. +Using MPC type SS BILINEAR +MPC type SS BILINEAR constrains a corner node of a quadratic shell element (S8R, S8R5) to a line of +edge nodes on 20-node bricks. This MPC type is available only in Abaqus/Standard. +The constrained node need not lie exactly on the line, but it is suggested that it be in close proximity +to the line for meaningful results. +pn +p4 +p3 +p2 +p1 +Figure 34.2.2–20 SS BILINEAR type MPC. Corner of +8-node shell to edge of 20-node bricks. +Input data +Give the shell node, S, then the list of nodes along the corresponding line through the thickness in the +solid element mesh. Referring to Figure 34.2.2–20, give S, +. The shell node number must +be different from the solid mesh node numbers. +,…, +, +Input File Usage: +*MPC +SS BILINEAR, S, +, +, …, +Abaqus/CAE Usage: Multi-point constraints for transitions are not supported in Abaqus/CAE. +Using MPC type SSF BILINEAR +MPC type SSF BILINEAR constrains a midside node on a quadratic shell element (S8R, S8R5) to a line +of midface nodes on solid 20-node bricks. This MPC type is available only in Abaqus/Standard. +The constrained node need not lie exactly on the line, but it is suggested that it be in close proximity +to the line for meaningful results. +pn-2 +p6 +p4 +p1 +pn-1 +p7 +p2 +pn +p8 +p5 +p3 +Figure 34.2.2–21 SSF BILINEAR type MPC. Midside of +8-node shell to surface of 20-node bricks. +Input data +Give the shell node, S, then the list of nodes on the solid face, in the order +Figure 34.2.2–21. +, +,…, +as shown in +Input File Usage: +*MPC +SSF BILINEAR, S, +, +, …, +Abaqus/CAE Usage: Multi-point constraints for transitions are not supported in Abaqus/CAE. +34.2.3 +KINEMATIC COUPLING CONSTRAINTS +Product: Abaqus/Standard +References +• “Kinematic constraints: overview,” Section 34.1.1 +• *KINEMATIC COUPLING +Overview +Kinematic coupling constraints: +• limit the motion of a group of nodes to the rigid body motion defined by a reference node; +• can be applied only to specific user-specified degrees of freedom at the constrained nodes; +• can be specified with respect to local coordinate systems at the constrained nodes; and +• can be used in geometrically linear or nonlinear analysis. +The preferred method of providing a kinematic constraint of this type is described in “Coupling +constraints,” Section 34.3.2. +Typical applications +The kinematic coupling constraints are useful in cases where a large number of nodes (the “coupling” +nodes) are constrained to the rigid body motion of a single node and the degrees of freedom that +participate in the constraint are selected individually in a local coordinate system. In many such cases +MPCs either are not available or would have to be prescribed individually for each constrained node. A +typical example is shown in Figure 34.2.3–1, where a kinematic coupling constraint is used to prescribe +a twisting motion to a model without constraining radial motions. In other applications the kinematic +coupling constraint can be used to provide coupling between continuum and structural elements. +Defining the constraint +A kinematic coupling constraint requires the specification of a reference node, coupling nodes, and the +constrained degrees of freedom at these nodes. The reference node has both translational and rotational +degrees of freedom. +Kinematic constraints are imposed by eliminating degrees of freedom at the coupling nodes. +Once any combination of displacement degrees of freedom at a coupling node is constrained, +additional displacement constraints—such as MPCs, boundary conditions, or other kinematic coupling +definitions—cannot be applied to any coupling node involved in a kinematic coupling constraint. The +same limitation applies for rotational degrees of freedom. +Input File Usage: +To constrain all available degrees of freedom: +*KINEMATIC COUPLING, REF NODE=node +coupling node number or node set +reference node +(node 500) +constrained nodes that are +free to translate radially +(COUPLESET) +axis of cylindrical +coordinate system +(COUPLEAXIS) +Figure 34.2.3–1 A kinematic coupling constraint used to transmit +rotation to a structure while permitting radial motion. +To constrain a single degree of freedom: +*KINEMATIC COUPLING, REF NODE=node +coupling node number or node set, dof +To constrain a range of degrees of freedom: +*KINEMATIC COUPLING, REF NODE=node +coupling node number or node set, first dof, last dof +To specify non-contiguous lists of constrained degrees of freedom, repeat the +node numbers or node sets on subsequent data lines. For example, the following +input is used to constrain degrees of freedom 1, 2, 3, and 6 at node 10 to the +motion of reference node 5: +*KINEMATIC COUPLING, REF NODE=5 +10, 1, 3 +10, 6 +Translational degrees of freedom +Translational degrees of freedom are constrained by eliminating the specified degrees of freedom at the +coupling nodes. When all translational degrees of freedom are specified, the coupling nodes follow the +rigid body motion of the reference node. +Rotational degrees of freedom +All combinations of selected rotational degrees of freedom result in rotational behavior that is identical +to existing MPC types. Specifically: +• Selection of three rotational degrees of freedom along with three displacement degrees of freedom +is equivalent to MPC type BEAM. +• Selection of two rotational degrees of freedom is equivalent to MPC type REVOLUTE. +• Selection of one rotational degree of freedom is equivalent to MPC type UNIVERSAL. +Internal nodes are created by the kinematic coupling to enforce the constraints that are equivalent +to MPC types REVOLUTE and UNIVERSAL. These nodes have the same degrees of freedom as the +additional nodes used in these MPC types and are included in the residual check for nonlinear analysis. +Specifying a local coordinate system +The constrained degrees of freedom at the coupling nodes can be specified in a local coordinate system +instead of the (default) global coordinate system . Figure 34.2.3–1 +illustrates the use of a local coordinate system definition with a kinematic coupling constraint to constrain +all but the radial translation of a group of nodes to a reference node. In this example a local cylindrical +coordinate system is defined that has its axis coincident with the structure’s axis. The coupling node +constraints are then specified in this local coordinate system. In this example the constrained nodes are +attached to continuum elements; thus, only translational degrees of freedom need to be specified. +*KINEMATIC COUPLING, REF NODE=node, ORIENTATION=name +For example, the following input is used to specify the kinematic coupling +constraint shown in Figure 34.2.3–1: +Input File Usage: +*ORIENTATION, SYSTEM=CYLINDRICAL, NAME=COUPLEAXIS +0.0, -1.0, 0.0, 0.0, 1.0, 0.0 +*KINEMATIC COUPLING, REF NODE=500, +ORIENTATION=COUPLEAXIS +COUPLESET, 2, 3 +Constraint directions and finite rotations +In geometrically nonlinear analysis steps, the coordinate system in which the constrained degrees of +freedom are specified will rotate with the reference node regardless of whether the constrained degrees +of freedom are specified in the global coordinate system or in a local system. Thus, the constraint +shown in Figure 34.2.3–1 will enable free radial motion throughout arbitrary rotations of the structure. +Radial motion in this case is defined as motion normal to the structure’s axis (defined in the undeformed +configuration by points a and b in the figure), with this axis rotating with the reference node. Therefore, +the free radial expansion shown in Figure 34.2.3–1 will not refer to an axis parallel to the global y-axis +for general rotations of the reference node but will refer to an axis that rotates with the structure. Rotation +of the constraint directions is not affected by the selection of the constrained degrees of freedom. +34.3 +Surface-based constraints +• “Mesh tie constraints,” Section 34.3.1 +• “Coupling constraints,” Section 34.3.2 +• “Shell-to-solid coupling,” Section 34.3.3 +• “Mesh-independent fasteners,” Section 34.3.4 +34.3.1 +MESH TIE CONSTRAINTS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Surfaces: overview,” Section 2.3.1 +• *TIE +• “Defining tie constraints,” Section 15.15.1 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +• “Using contact and constraint detection,” Section 15.16 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +A surface-based tie constraint: +• ties two surfaces together for the duration of a simulation; +• can be used only with surface-based constraint definitions; +• can be used in mechanical, coupled temperature-displacement, coupled thermal-electrical- +pore +pressure-displacement, +coupled +structural, +pressure–displacement, coupled thermal-electrical, or heat transfer simulations; +pressure, +acoustic +acoustic +coupled +• can also be used to create a constraint on a surface so that it follows the motion of a three-dimensional +beam; +• is useful for mesh refinement purposes, especially for three-dimensional problems; +• allows for rapid transitions in mesh density within the model; +• constrains each of the nodes on the slave surface to have the same motion and the same value +of temperature, pore pressure, acoustic pressure, or electrical potential as the point on the master +surface to which it is closest; +• will take the initial thickness and offset of shell elements underlying the surface into account by +default; and +• eliminates the degrees of freedom of the slave surface nodes that are constrained, where possible. +Defining a tie constraint for a pair of surfaces +A surface-based tie constraint can be used to make the translational and rotational motion as well as all +other active degrees of freedom equal for a pair of surfaces. By default, as discussed below, nodes are +tied only where the surfaces are close to one another. One surface in the constraint is designated to be +the slave surface; the other surface is the master surface. A name must be assigned to this constraint and +may be used in postprocessing with Abaqus/CAE. +Input File Usage: +*TIE, NAME=name +slave_surface_name, master_surface_name +Abaqus/CAE Usage: +Interaction module: Create Constraint: Tie +Defining the surfaces to be constrained +Either element-based or node-based surfaces can be used as the slave surface. Any surface type (element- +based, node-based, or analytical) can be used as the master surface. You may need to take some surface +restrictions into consideration depending on which tie formulation is used and whether the analysis is +conducted in Abaqus/Standard or Abaqus/Explicit. Two tie formulations are available: the surface-to- +surface formulation, which is used by default in Abaqus/Standard, and the more traditional node-to- +surface formulation, which is used by default in Abaqus/Explicit; these formulations are discussed in +more detail later in this section. Table 34.3.1–1 and Table 34.3.1–2 provide comparisons of surface +restrictions for the different formulations and analysis codes. +Table 34.3.1–1 Comparison of characteristics for surface-based tie formulations. +Tie formulation +Optimized +stress +accuracy +Node-based +surfaces +allowed +Surface-to-surface +(Abaqus/Standard or +Abaqus/Explicit) +Node-to-surface in +Abaqus/Standard +Node-to-surface in +Abaqus/Explicit +Yes +No +No +Reverts +to node- +to-surface +formulation +Yes +Yes +Mixture of +rigid and +deformable +subregions +allowed +Treatment of +nodes/facets +shared between +master and slave +surfaces +No +No +Yes +Eliminated from +slave +Eliminated from +slave +Eliminated from +master +The surface-to-surface formulation generally avoids stress noise at tied interfaces. As indicated +in Table 34.3.1–1 and Table 34.3.1–2, only a few surface restrictions apply to the surface-to-surface +formulation: this formulation reverts to the node-to-surface formulation if a node-based or edge-based +surface is used. The surface-to-surface formulation does not allow for a mixture of rigid and deformable +portions of a surface, and the master surface must not contain T-intersections. Any nodes shared +between the slave and master surfaces will not be tied with the surface-to-surface formulation. The same +comments apply to both Abaqus/Standard and Abaqus/Explicit in these tables for the surface-to-surface +formulation. +With the more traditional node-to-surface formulation additional surface restrictions apply in +Abaqus/Standard but fewer restrictions apply in Abaqus/Explicit in comparison to the surface-to-surface +Table 34.3.1–2 Comparison of element-based surface characteristics allowed +for surface-based tie formulations. +Surface Characteristics (Yes=allowed, No=not allowed) +Double-sided Discontinuous T-intersection +Edge-based +Tie formulation +Surface-to-surface +(Abaqus/Standard or +Abaqus/Explicit) +Master: Yes +Slave: Yes +Master: Yes +Slave: Yes +Master: No +Slave: Yes +Node-to-surface in +Abaqus/Standard +Node-to-surface in +Abaqus/Explicit +Master: Yes +Slave: Yes +Master: Yes +Slave: Yes +Master: Yes +Slave: Yes +Master: Yes +Slave: Yes +Master: No +Slave: Yes +Master: Yes +Slave: Yes +Reverts to +node-to-surface +formulation if +either surface is +edge-based +Master: Yes +Slave: Yes +Master: Yes +Slave: Yes +formulation. Relatively stringent restrictions on master surface connectivity for the node-to-surface +tie formulation in Abaqus/Standard are indicated in Table 34.3.1–2: +the master surface must be +simply connected and must not contain complex intersections such as T-intersections . +Differences with the node-to-surface formulation in Abaqus/Explicit are apparent in Table 34.3.1–1: +partially rigid surfaces can be used and the treatment of shared portions of slave and master surfaces is +unique to this case. Nodes and faces that are shared between the master and slave surfaces are eliminated +automatically from the master surface in this case if the paired surfaces are either both element-based or +both node-based, enabling the possibility of tying multiple slave surfaces (defined over various regions +of the model) to a common master surface defined over the entire model. This is a convenient way to +define tie constraints in large models, as it eliminates the need for defining specialized master surfaces +for each surface pairing; however, you must still take care that slave surfaces do not include portions of +the opposing surface to which they should be tied (for example, no tie constraints will be generated if the +master and slave surfaces are identical). In the node-to-surface formulation in Abaqus/Explicit all facets +attached to nodes that are common between slave and master surfaces are excluded from being tied to +slave nodes. Sometimes when meshes are transitioned from one type of element to another type or from +one element size to another element size, common nodes may exist at the interface of the two regions. +Typically, a tie constraint is defined at the interface of the two zones to stitch the two meshes together. +In a situation like this common nodes may get tied to a neighboring facet on the interface and may cause +undesirable mesh distortion due to the tie adjustment. One possible way to avoid the undesirable mesh +distortion is to specify a very small position tolerance for the tie pair. Another situation that may arise +when common nodes occur between the slave and master surfaces at the interface of mesh transition +zones is that slave nodes in the vicinity of the common node may not get tied. This happens due to the +exclusion of master facets attached to the common nodes. Therefore, care must be taken to ensure that +elements in different mesh zones do not share common nodes at the interface. For all such common +nodes, duplicate nodes occupying the same physical location should be defined. +Input File Usage: +Use the *SURFACE option to define the slave and master surfaces used in the +constraint : +Abaqus/CAE Usage: +*SURFACE, NAME=slave_surface_name +*SURFACE, NAME=master_surface_name +In Abaqus/CAE you can select one or more faces directly in the viewport when +you are prompted to select a surface. In addition, you can define surfaces as +collections of faces and edges using the Surface toolset. +Specifying the subset of slave nodes to be constrained +By default, Abaqus uses a position tolerance criterion to determine the constrained nodes based on the +distance between the slave nodes and the master surface. Alternatively, you can specify a node set +containing the slave nodes to be constrained regardless of their distance to the master surface. +Using the position tolerance criterion +The default position tolerance criterion ensures that nodes are tied only where the slave and master +surfaces are close to one another in the initial configuration. For example, consider the case shown in +Figure 34.3.1–1. Surfaces Comp1_surf and Comp2_surf are defined to cover all exposed faces of +Component 1 and Component 2, respectively. These two surfaces can be used as the slave and master +surfaces in a tie constraint to tie the two components in the desired region, because only the nodes at the +initial interface between the two surfaces are tied. +desired tie region +Component 1 +Component 2 +Figure 34.3.1–1 Example of two components to be tied together. +The default value of the position tolerance, +, typically results in desired tie constraints with little +effort. Details regarding the calculation of distances between surfaces and default values of the position +tolerances are provided below. You can modify the position tolerance if desired. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to use the default position tolerance: +*TIE +Use the following option to specify a position tolerance: +*TIE, POSITION TOLERANCE=distance +Interaction module: Create Constraint: Tie: Position +Tolerance: Specify distance +Calculating the distance between surfaces +The following factors influence the calculation of the distance between surfaces for a particular slave +node: +• Shell thickness. By default, calculations of distances between surfaces account for shell thickness +and offset effects for element-based slave or master surfaces: the distance is measured from the +actual top or bottom side of the surface, whichever is closer to the other surface. Alternatively, you +can specify that surface thicknesses and offsets should be ignored, which also has implications for +nodal position adjustments for resolving initial gaps (discussed later). +Input File Usage: +Use the following option to ignore surface thicknesses and offsets +in the distance calculations: +Abaqus/CAE Usage: +*TIE, NO THICKNESS +Interaction module: Create Constraint: Tie: Exclude +shell element thickness +• Whether the surface-to-surface or node-to-surface constraint formulation (discussed below) is used. +If a position tolerance is in effect, a constraint is generated at a slave node for either formulation if the +distance between the surfaces, as calculated at the slave node, does not exceed +. Additional slave +nodes may be tied if the surface-to-surface constraint formulation is used along with an element- +based slave surface and a master surface that is not node-based, because the following addendum to +the position tolerance criterion applies in such cases: if the distance between the surfaces is within +over a significant portion of a slave face (or segment in two dimensions) that forms an angle +of less than 30° with the master surface, all slave nodes attached to such a face (or segment) are +considered to satisfy the position tolerance. +• The types of surfaces involved (element-based, node-based, or analytical). +Position tolerance for an element-based master surface +The default position tolerance for element-based master surfaces is 5% or 10% of the typical master +facet diagonal length for the node-to-surface and surface-to-surface tie formulations, respectively. When +using an element-based master surface, the distance between surfaces for a particular point on a slave +surface is based on the closest point on the master surface (which may be on the edge of the master +surface or within a facet). Figure 34.3.1–2 shows an example with no thickness: nodes 2–14 satisfy +the position tolerance criterion for the node-to-surface and surface-to-surface constraint formulations. +Significant portions of the end slave segments (that is, the segment connecting nodes 1 and 2 and the +slave surface +15 +14 +13 +10 +11 +12 +element-based master surface +position +tolerance +Figure 34.3.1–2 Tolerance region around an element-based master surface with no thickness. +segment connecting nodes 14 and 15) are within the position tolerance shown, so nodes 1 and 15 would +also satisfy the position tolerance criterion for the surface-to-surface constraint formulation except for +the fact that the angle between the slave and master surfaces is slightly greater than 30° at those locations. +Position tolerance for a node-based master surface +The default position tolerance for a node-based master surface is based on the average distance between +nodes in the master surface. The distance between the surfaces for a particular slave node is based on +If this distance is less than the position tolerance, Abaqus will create a tie +the closest master node. +constraint between the slave node, the closest master node, and other master nodes in similar proximity +to the slave node. For mismatched meshes across a tied interface, the distance between slave and master +nodes can be much larger than the “normal” distance between the surfaces, which can lead to confusion +when using a position tolerance criterion with a node-based master surface. Figure 34.3.1–3 shows how +the tolerance region is defined around a node-based master surface. The surface-to-surface constraint +formulation reverts to the node-to-surface constraint formulation for a node-based master surface. +slave surface +10 +11 +12 +position +tolerance +15 +14 +13 +node-based master surface +Figure 34.3.1–3 Tolerance region around a node-based master surface with no thickness. +Position tolerance for an analytical rigid master surface +The default position tolerance for tie constraints between an element-based slave surface and an analytical +rigid master surface is 5% or 10% of the typical slave facet diagonal length for the node-to-surface +and surface-to-surface tied formulations, respectively. The default position tolerance for tie constraints +between a node-based slave surface and an analytical rigid master surface is 5% of the typical distance +between slave nodes. When using an analytical rigid master surface, the distance between surfaces for a +particular point on the slave surface is based on the closest point on the master surface. +Specifying the constrained nodes directly +This method allows you direct control over which slave nodes are tied. +Input File Usage: +Abaqus/CAE Usage: +*TIE, TIED NSET=node_set_label +Specifying the constrained nodes directly is not supported in Abaqus/CAE. +Unconstrained nodes in tie constraint pairs +Abaqus does not constrain slave nodes to the master surface unless they are included in the tied node +set or within the tolerance distance from the master surface at the start of the analysis, as discussed +above. Any slave nodes not satisfying these criteria will remain unconstrained for the duration of the +simulation; they will never interact with the master surface as part of the tie constraint. In mechanical +simulations an unconstrained slave node can penetrate the master surface freely unless contact is defined +between the slave node and master surface. The general contact algorithm in Abaqus/Explicit will +generate contact exclusions automatically for slave node–master surface combinations corresponding to +constrained nodes of tie constraint pairs, but no such contact exclusions are generated for nodes outside +the position tolerance of the constraints. In a thermal, acoustic, electrical, or pore pressure simulation an +unconstrained slave node will not exchange heat, fluid pressure, electrical current, or pore fluid pressure +with the master surface. +Determining which slave nodes have been tied and which slave nodes have not been tied +For each tie constraint pair, Abaqus creates a node set comprising slave nodes that will be tied and a +node set comprising slave nodes that will be left unconstrained. These node sets are available for display +during postprocessing in Abaqus/CAE, where they are listed as internal node sets. +In addition, Abaqus prints a table in the data (.dat) file listing each slave node and the master +surface nodes to which it will be tied if model definition data are requested . If a +constraint cannot be formed for a given slave node, Abaqus/Standard issues a warning message in the +data file. +In Abaqus/Explicit you can also request two nodal field output variables: TIEDSTATUS will help +you identify the constrained and unconstrained slave nodes, and TIEADJUST will help you visualize the +adjustment performed at the nodes . A +tied node that participates in more than one tie definition as a slave as well as a master is shown as “tied” +regardless of whether it got tied as a slave node or as a master node. +When creating a model with surface-based tie constraints, it is important to use the information +provided by Abaqus to identify any unconstrained nodes and to make any necessary modifications to the +model to constrain them. +Constraining the rotational degrees of freedom +By default, Abaqus will constrain the rotational degrees of freedom when they exist on both slave and +master surfaces . You can specify that the rotational degrees of freedom should not +be tied. +Input File Usage: +Abaqus/CAE Usage: +*TIE, NO ROTATION +Interaction module: Create Constraint: Tie: toggle off Tie +rotational DOFs if applicable +Constraining the faces of a cyclic symmetric structure in Abaqus/Standard +You can enforce proper constraints on the faces bounding a repetitive sector of a cyclic symmetric +structure . This makes it +possible to define a single sector of the cyclic symmetry model together with its axis of cyclic symmetry +to define the behavior of the 360° model. Cyclic symmetry models can be used within the following +procedures: static; quasi-static; eigenfrequency extraction, based on the Lanczos solver technique; +steady-state dynamics, based on modal superposition; and heat transfer. If an eigenfrequency extraction +is performed on a cyclic symmetric model, the nodes involved in the cyclic symmetry constraint cannot +be used in any other constraint (e.g., multi-point constraints, equations, rigid bodies, couplings, or +kinematic couplings). +Input File Usage: +*TIE, CYCLIC SYMMETRY +This parameter can be used only with the *CYCLIC SYMMETRY MODEL +option. +Abaqus/CAE Usage: +Interaction module: Interaction→Create: Cyclic symmetry +The surface-based tie constraint formulation +Abaqus uses the criteria discussed above to determine which slave nodes will be tied to the master +surface. Abaqus then forms constraints between these slave nodes and the nodes on the master surface. +A key aspect in forming the constraint for each slave node is determining the tie coefficients. These +coefficients are used to interpolate quantities from the master nodes to the tie point. Abaqus can use one of +two approaches to generate the coefficients: the “surface-to-surface” approach or the “node-to-surface” +approach. +If an analysis carried out with Abaqus/Standard is imported into Abaqus/Explicit or vice-versa, +the tie constraints are not imported and must be redefined. +If the imported analysis is essentially a +continuation of the original analysis, it is important that the tie constraints are as similar as possible. +Hence, you should make sure that the same constraint type is used. If the default approach was used +in the original Abaqus/Standard analysis, the surface-to-surface approach should be specified in the +Abaqus/Explicit analysis. Similarly, if the default approach was used in the original Abaqus/Explicit +analysis, the node-to-surface approach should be specified in the Abaqus/Standard analysis. +slave surface defined +on shell structure +master surface defined +on shell structure +slave surface defined +on shell structure +Displacement and rotation degrees of freedom +are tied, unless you specify that the rotation +degrees of freedom should not be tied. +master surface defined +on shell structure +Displacement and rotation degrees of freedom +are tied, unless you specify that the rotation +degrees of freedom should not be tied. +slave surface defined +on shell structure +master surface defined +on solid structure +Only displacement degrees +of freedom are tied. +Figure 34.3.1–4 Surface-based tie algorithm. +The “surface-to-surface” approach +The “surface-to-surface” approach minimizes numerical noise for tied interfaces involving mismatched +meshes. The surface-to-surface approach enforces constraints in an average sense over a finite +region, rather at discrete points as in the traditional node-to-surface approach. The surface-to-surface +formulation for surface-based tie constraints is similar to the surface-to-surface contact formulation ; however, a fundamental difference is that +each surface-based tie constraint involves only one slave node (and multiple master nodes), whereas +each surface-to-surface contact constraint involves multiple slave nodes. +The surface-to-surface approach is used by default in Abaqus/Standard with exceptions noted +below, and it is optional in Abaqus/Explicit. For the case of infinite acoustic elements tied to shell +elements in Abaqus/Standard the added cost of the surface-to-surface approach can be quite significant; +therefore, the node-to-surface approach is used by default in this case. If the surface-to-surface approach +is “on by default” or explicitly specified, Abaqus automatically reverts to the node-to-surface approach +for individual tie constraints in the following circumstances: +• if either of the surfaces being tied is node-based; +• if the projection along the slave surface normal direction does not intersect the master surface; or +• if single-sided slave and master surfaces have surface normals in approximately the same direction. +Abaqus/Explicit may automatically add a small amount of artificial mass to the model to maintain +numerical stability if the surface-to-surface approach is specified. +The surface-to-surface approach generally involves more master nodes per constraint than the node- +to-surface approach, which tends to increase the solver bandwidth in Abaqus/Standard and, therefore, +can increase solution cost. In most applications the extra cost is fairly small, but the cost can become +significant in some cases. The following factors (especially in combination) can lead to the surface-to- +surface approach being quite costly: +• A large fraction of tied nodes (degrees of freedom) in the model +• The master surface being more refined than the slave surface +• Multiple layers of tied shells, such that the master surface of one tie constraint acts as the slave +surface of another tie constraint +Input File Usage: +Abaqus/CAE Usage: +*TIE, TYPE=SURFACE TO SURFACE +Interaction module: Create Constraint: Tie: Discretization +method: Surface to surface +The “node-to-surface” approach +The traditional “node-to-surface” approach (which is used by default in Abaqus/Explicit and is optional +in Abaqus/Standard) sets the coefficients equal to the interpolation functions at the point where the slave +node projects onto the master surface. This approach is somewhat more efficient and robust for complex +surfaces. +For the node-to-surface method of establishing the tie coefficients with an element-based master +surface, the point on the surface closest to each slave node is calculated and used to determine the master +nodes that are going to form the constraint . For example, nodes 202, 203, 302, and +303 are used to constrain node a; nodes 204 and 304 are used to constrain node b; and node 402 is used +to constrain node c. +Input File Usage: +Abaqus/CAE Usage: +*TIE, TYPE=NODE TO SURFACE +Interaction module: Create Constraint: Tie: Discretization +method: Node to surface +103 +104 +203 +102 +202 +302 +101 +201 +301 +slave surface nodes +204 +303 +304 +403 +404 +503 +504 +502 +402 +401 +501 +Figure 34.3.1–5 Searching for the points on an element-based +master surface that are closest to nodes a, b, and c. +Choosing the slave and master surfaces of a surface-based tie constraint +The choice of slave and master surfaces can have a significant effect on the accuracy of the solution, in +particular if the “node-to-surface” approach is used. The effect is much less (and the accuracy generally +better) for the “surface-to-surface” approach. In either case, if both surfaces in a constraint pair are +deformable surfaces, the master surface should be chosen as the surface with the coarser mesh for best +accuracy. +In Abaqus/Standard a rigid surface cannot act as a slave surface in a tie constraint. To comply with +this rule, the capability to automatically resolve overconstraints in Abaqus/Standard will modify tie constraint definitions in the following cases: +• Tie constraints between two surfaces of the same rigid body are removed. +• Tie constraints between two surfaces of two rigid bodies are replaced by a BEAM-type connector +between the respective rigid body reference nodes. +• Tie constraints specified with a purely rigid slave surface and a purely deformable master surface +are modified to reverse the master and slave assignments unless this is not possible due to other +modeling restrictions (in which case an error message is issued). +These methods are not applied if the slave surface that you specified is partially rigid and partially +deformable; Abaqus/Standard issues an error message in such cases. +In acoustic, structural-acoustic, and elastic wave propagation problems care should be exercised +when tying meshes of highly dissimilar refinement. If two media have different wave speeds, the optimal +meshes for each of the media will have different characteristic element lengths: the faster medium will +have larger elements. If surfaces of these meshes are used in a tie constraint, the surface of the finer +mesh (of the slower medium) should be designated as the slave. Nevertheless, in the region near the +tied surfaces, the physical wave phenomena in both fast and slow media will typically have length +scales characteristic of the slower medium; that is, of the shortest length scale in the physical problem. +Therefore, if these phenomena are important, the mesh of the faster medium should be refined to the +scale of the slower medium in the vicinity of the contact region. +Adjusting the surfaces and considering offsets +By default, with the exceptions mentioned below, Abaqus will automatically reposition the slave nodes +to be tied in the initial configuration without causing strain to resolve gaps such that the surfaces are +just touching, accounting for any shell thickness (unless you have specified that thickness should not be +accounted for, as discussed above in the context of the position tolerance criterion) but not accounting +for beam or membrane thickness. One exception is that no adjustments are made where tied surfaces +are closer together than the combined half-shell thickness. All adjustments are performed such that the +slave and master surfaces are never pushed apart; that is, the reference surfaces will only become closer +as a result of the adjustments. +It is recommended that you allow the automatic adjustments to occur, especially if neither surface +has rotations; in this case a constant offset vector is used, so incorrect behavior of the constraint under +rigid body rotation can occur when slave nodes are not lying exactly on the master surface. Adjustments +are not made if the slave surface belongs to a substructure or when either the slave or master surface +is a beam element-based surface; in the latter cases you should locate the beam element nodes with the +desired offset from the other surface. +Input File Usage: +Abaqus/CAE Usage: +*TIE, ADJUST=YES or NO +Interaction module: Create Constraint: Tie: toggle Adjust +slave node initial position +Criteria for adjustment +A slave node is considered for adjustment if both of the following conditions are met: +• The slave node satisfies whatever criterion is in effect for generating a constraint (either because +it satisfies the position tolerance criterion or belongs to the specified node set of constrained slave +nodes, as previously discussed). +• The slave node is more than the combined thickness of the slave and master surfaces away from its +projection point on the master reference surface, accounting for any offset of the element reference +surfaces from the respective element midsurfaces. +For an element-based master surface a slave node will be moved toward the closest point on the master +surface; for a node-based master surface a slave node will be moved toward the closest master node. The +corrected position of an adjusted slave node is determined from the combined effects of shell element +thickness and any specified reference surface offset relative to the shell midsurface of either slave or +master surfaces. Figure 34.3.1–6 shows the adjusted slave node position in an example with two shell +element-based surfaces tied together (in this example one of the element reference surfaces is offset from +the element midsurface). It is assumed that the surfaces were farther apart than shown in Figure 34.3.1–6 +prior to the adjustment; otherwise, the slave nodes would not have been adjusted. +slave reference +surface +slave shell +midsurface +master shell +reference and +midsurface +shell (s) – shell (m) +slave shell element has offset = 1/2 (SPOS) +Figure 34.3.1–6 Adjusted slave node position for two shell element-based surfaces tied +together. The slave shell element has an offset of 0.5. +Adjustments are made only for slave nodes that are included in the user-specified tied node set or +that meet the tolerance criteria described above. +Adjustments for overlapping constraints +Nodal adjustments for tie constraints are processed sequentially in the order of the constraint definitions +at the start of an analysis. If different constraint or contact definitions involve the same nodes, some +adjustments may cause lack of compliance for contact or constraint definitions that were previously +processed. These conflicts are less likely to occur in Abaqus/Explicit because the adjustments +in Abaqus/Explicit are automatically processed in the chaining order discussed in “Overlapping +constraints.” These conflicts can be avoided in Abaqus/Standard in some cases by changing the +processing order of constraint and contact definitions: nodes in common between different contact or +constraint definitions should be processed first as slave nodes and later as master nodes. +Input File Usage: +Abaqus/CAE Usage: +To change the processing order of constraint and contact definitions, change the +order of the definitions in the input file. Constraint and contact definitions are +processed in the order in which they appear. +To change the processing order of constraint and contact definitions, change +the names of the constraints and interactions in the model. Constraints and +interactions are processed alphabetically according to their name. +Accounting for an offset between tied surfaces +Abaqus allows a gap to exist between tied surfaces. Such gaps may exist if you prevent nodal adjustments +for tied surfaces. A gap between the reference surfaces may remain due to the presence of shell thickness +even if nodal adjustments are performed. Figure 34.3.1–7 shows some cases where an offset between +the reference surfaces may be desirable for tied surface pairs to account for shell or beam thickness. +solid (s) – solid (m) +shell (s) – solid (m) +solid (s) – shell (m) +shell (s) - shell (m) +solid (s) – beam (m) +shell (s) – beam (m) +beam (s) – solid (m) +beam (s) – shell (m) +beam (s) – beam (m) +Figure 34.3.1–7 Tie constraints being applied between surfaces based on various element +types (h = offset between slave and master surfaces). +Rigid body motion is properly accounted for when the nodes are separated by a finite distance when at +least one of the surfaces is based on shell or beam elements; when the master surface is an analytical +rigid surface; or, in the case of node-based surfaces, when the nodes on at least one surface have active +rotational degrees of freedom. +The nature of the constraint on translational motion between surfaces in Abaqus depends on whether +there is an offset between the surfaces and on which surfaces have rotational degrees of freedom, as +discussed below. +Neither surface has rotational degrees of freedom +If neither surface has rotational degrees of freedom, the global translational degrees of freedom of the +slave node and the closest point on the master surface are constrained to be the same. When an offset +exists, Abaqus will enforce the constraint through the fixed offset like a PIN-type MPC when the nodes +in the MPC are not coincident. Because the fixed offset does not rotate, the surface-based constraint +will not represent rigid body rotation correctly. The constraint will represent rigid body motion correctly +when the offset is zero. This behavior can be ensured by specifying that all tied slave nodes should be +moved onto the master surface. +Only one surface has rotational degrees of freedom +If the slave surface has rotational degrees of freedom and the master surface does not, the translational +motion is constrained at the closest point on the master reference surface. When the reference surfaces +are offset, a moment will be applied to each slave node based on the constraint force times the offset +distance. Similarly, if the master surface has rotational degrees of freedom and the slave surface does +not, the translational motion is constrained at each slave node and a moment will be applied to the relevant +nodes on the master surface if an offset exists. In either case the surface-based constraint will behave +correctly under rigid body rotation regardless of the amount of offset. +Both surfaces have rotational degrees of freedom +If both surfaces have rotational degrees of freedom, are not offset, and the rotations are tied, each slave +node is constrained to the master surface like a TIE-type MPC. If an offset exists between the surfaces, +the constraint acts like a BEAM-type MPC between the slave node and the closest point on the master +reference surface. +If the rotations are not tied, Abaqus allows you to choose the location of the translational constraint. +It can be enforced at the master reference surface, the slave reference surface, or anywhere in between. +The location of the translational constraint enforcement for surfaces where the rotations are not tied will +affect the distribution of moment to each of the surfaces. The most physically reasonable choice is to +locate the constraint at the point where the actual top or bottom sides of each surface meet. The constraint +then models a perfect adhesive between the surfaces, which transfers shear stress to each surface. Abaqus +will choose the location of the translational constraint as follows: +• If the master surface is shell element-based, the translational constraint is enforced on the top or +bottom side of the master surface. +• If the slave surface is shell element-based and the master surface is not, the translational constraint +is enforced at the top or bottom side of the slave surface. +• Otherwise, the translational constraint is enforced at the master reference surface. +To override these default locations, you can specify a constraint ratio for the tie constraint equal to +the fractional distance between the master reference surface and the slave node at which the translational +constraint should act. Figure 34.3.1–8 shows an example of the use of a constraint ratio to prescribe the +location of the translational constraint between two shell surfaces that are tied together with no rotational +constraints. The distance between the master reference surface and the slave reference surface is b. The +slave reference surface +pin +rigid beams +master reference surface +constraint ratio, r = a/b +Figure 34.3.1–8 Use of a constraint ratio to prescribe the location of the translational constraint. +prescribed constraint ratio, r, is then used to locate the translational constraint at a distance a from the +master reference surface. All distances are measured along the vector between the slave node and its +projection point onto the master reference surface. The constraint behavior is then similar to that of two +rigid beams pinned together, as shown. +Input File Usage: +Abaqus/CAE Usage: +*TIE, CONSTRAINT RATIO=value +Interaction module: Create Constraint: Tie: Constraint ratio +Constraining a surface to a three-dimensional beam +The master surface for a tie constraint can be based on three-dimensional beam elements. For this case +each slave node is projected onto the line formed by the nodes of the beam elements in the undeformed +configuration to find the projection point. During the subsequent analysis the motion of each slave node is +rigidly constrained to the motion (translation and rotation) of its projection point; i.e., each slave node and +its projection point are connected by a rigid beam. Constraining other elements to a beam element-based +master surface allows modeling of interactions between the surface of a (complex) beam section and its +surroundings, without having to model the beam with continuum and/or shell elements. This feature can +be particularly useful for modeling acoustic-structural interactions. +Note: Abaqus/CAE currently does not support master surfaces based on beam elements. +Use of tie constraints in non-mechanical simulations +The surface-based tie constraint capability can be used in models where the nodal degrees of freedom on +both the slave and master surfaces include electrical potential, pore pressure, acoustic pressure, and/or +temperature. Except for the type of nodal degree of freedom being constrained, Abaqus uses exactly +the same formulation for the tie constraint in nonmechanical simulations as it does for mechanical +simulations. In general, degrees of freedom common to both surfaces are tied, and any other degrees of +freedom are unconstrained. +The case of structural-acoustic constraints is the exception to this rule. Here, appropriate relations +between the acoustic pressure on the fluid surface and displacements on the solid surface are formed +internally . The +displacements and/or pressure degrees of freedom on the surfaces are the only ones affected; rotations +are ignored by the tie constraint in this case. +The internally computed structural-acoustic coupling conditions use surface areas and normal +directions associated with the slave surface elements. The slave surface for structural-acoustic tie +constraints cannot be a node-based surface. +In two-dimensional analyses the out-of-plane thickness +of the slave elements is required. Generally, this thickness is the thickness specified on the section +definition for the slave surface elements. However, when beam elements form the slave surface in a +tie constraint pair with acoustic elements, a unit thickness in the out-of-plane direction is assumed for +the beams. +In Abaqus/Standard you can define coupling between solid medium and acoustic medium infinite +elements along the surfaces that extend to infinity. These surfaces are defined using the edges of the +acoustic elements and sides numbered “2” and higher of the solid medium infinite elements. The infinite +surfaces of solid medium and acoustic infinite elements can be coupled only through the use of a surface- +based tie constraint. As shown in Figure 34.3.1–9, the acoustic infinite elements must be the slave +elements and the edges of the acoustic infinite elements should lie within the specified position tolerance +to the solid medium infinite element base facets. +position +tolerance +solid infinite element +master surface +slave surface +acoustic infinite element +Figure 34.3.1–9 Use of a surface-based tie constraint to prescribe the coupling between +solid medium and acoustic medium infinite elements. +If the base facets of acoustic infinite elements are to be coupled to solid medium finite elements, to solid +medium infinite elements, or to structural elements, either a surface-based tie constraint or acoustic- +structural interaction elements can be used. Surfaces defined on solid medium infinite elements cannot +be used in a surface-based tie constraint in Abaqus/Explicit. +Table 34.3.1–3 enumerates all possible cases. For other slave-master pairings not listed in this table, +an error message will be issued. +Table 34.3.1–3 Possible slave-master surface pairings. +Slave Surface +Master Surface +Degrees of Freedom Tied +Acoustic +Acoustic +Stress +Stress +Heat-Stress +Stress +Acoustic +Acoustic pressure +Stress +Translations +Acoustic +Acoustic pressure +Stress +Stress +Translations and/or rotations +Translations and/or rotations +Heat-Stress +Translations and/or rotations +Heat-Stress +Heat-Stress +Temperature, translations and/or rotations +The following surface pairings are available only in Abaqus/Standard: +Heat transfer +Heat transfer +Temperature +Electrical-Heat +Heat transfer +Temperature +Heat transfer +Electrical-Heat +Temperature +Electrical-Heat +Electrical-Heat +Temperature and electric potential +Pore-Stress +Pore-Stress +Stress +Pore-Stress +Pore pressure and translations +Stress +Translations +Pore-Stress +Translations +Tie constraints versus tied contact in Abaqus/Standard +There are the following advantages to using a surface-based tie constraint in Abaqus/Standard instead of +defining tied contact as discussed in “Defining tied contact in Abaqus/Standard,” Section 35.3.7: +• Degrees of freedom of the slave surface nodes will be eliminated. +• The tie constraint is more efficient in terms of the size of the fronts of the operator matrix because +fewer master surface nodes are associated with each slave node. +• Rotational degrees of freedom as well as translational degrees of freedom can be tied. +• Tie constraints are much more general since they allow the use of general surfaces. +• Surface offsets and shell thickness are taken into account. +Overlapping constraints +In a model with multiple tie constraint definitions it is possible that the slave and master surfaces of +different tie constraint definitions may intersect. +If two tie constraint definitions have part or all of +their master surfaces in common or if the surfaces tied are layered (i.e., the master surface of one tie +constraint definition acts as the slave surface of a subsequent tie constraint definition), Abaqus will +attempt to chain the constraint definitions together. This will reduce the number of degrees of freedom +and lower the computational expense, resulting in faster run times. However, in a model with multiple +tie constraint definitions if nodes on the slave surface of one tie constraint definition are part of the slave +surface of other tie constraint definitions, an overconstraint occurs. In most cases the overconstraint is +due to the existence of redundant constraints, and it is safe to eliminate this redundancy. However, the +overconstraint may also be due to conflicting constraints, in which case the problem is due to a modeling +error that you should correct. Simulation results will vary depending on which constraint is removed to +avoid an overconstraint if the overlapping constraints are not identical. It is recommended that, wherever +possible, you order the slave and master surfaces of the constraint definitions to avoid intersecting slave +surfaces. See “Adjustments for overlapping constraints” for a discussion of initial strain-free adjustments +for overlapping constraints. +Overconstrained slave nodes in Abaqus/Standard +If an overconstraint occurs, Abaqus/Standard issues an error message unless the constraints are +redundant or nearly redundant, as discussed below. As discussed previously, each tie constraint involves +a single slave node and a set of master nodes with nonzero tie coefficents. Abaqus/Standard considers tie +constraints involving the same slave node to be nearly redundant if at least one node is common among +the respective sets of master nodes with nonzero tie coefficients. In such cases, rather than issuing an +error message, Abaqus/Standard issues a warning message and only enforces one of the constraints. +The surface-based tie constraint is imposed in Abaqus/Standard by eliminating the degrees of +therefore, nodes on the slave surface should not be used to apply +freedom on the slave surface; +boundary conditions, nor should they be used in any subsequent tie, multi-point, equation, or kinematic +coupling constraint . +Overconstrained slave nodes in Abaqus/Explicit +In contrast, Abaqus/Explicit treats overconstraints with a penalty method, thus enforcing the constraints +in an average sense; the computational cost of the analysis may increase in these cases. +In addition, if the slave surface for a tie constraint definition in Abaqus/Explicit is part of a rigid +body while the master surface comprises a deformable element- or node-based surface and the master +surface acts as the slave surface in a subsequent tie constraint definition, the resolution of the resulting +constraints can prove to be computationally intensive. It is recommended that, wherever possible, you +order the slave and master surfaces of the constraint definitions to avoid such a situation. +Nullifying the tie constraint on slave nodes due to element deletion in Abaqus/Explicit +In Abaqus/Explicit tie constraints are nullified as underlying elements of tied surfaces are deleted due +to material point failure. The tie constraint between a slave node and its corresponding master nodes is +deleted when either all the elements attached to the slave node are deleted or the master element to which +the slave node is tied is deleted. +Limitations +The following limitations exist for tie constraints: +• Surface-based tie constraints cannot be used to connect gasket elements that model thickness- +direction behavior only. +• A rigid surface cannot act as a slave surface in a constraint pair in Abaqus/Standard. +• A slave node of a tie constraint cannot act as a slave node of another constraint in Abaqus/Standard. +• Tie constraints cannot be used to tie infinite elements to finite elements in Abaqus/Explicit. To +couple infinite and finite elements in Abaqus/Explicit, the elements must share nodes. +• The axisymmetric solid Fourier elements with nonlinear, asymmetric deformation cannot form +element-based surfaces; therefore, such surfaces cannot be used in tie constraints. +34.3.2 +COUPLING CONSTRAINTS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Surfaces: overview,” Section 2.3.1 +• *COUPLING +• *KINEMATIC +• *DISTRIBUTING +• “Defining coupling constraints,” Section 15.15.4 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +The surface-based coupling constraint: +• couples the motion of a collection of nodes on a surface to the motion of a reference node; +• is of type kinematic when the group of nodes is coupled to the rigid body motion defined by the +reference node; +• is of type distributing when the group of nodes can be constrained to the rigid body motion defined +by a reference node in an average sense by allowing control over the transmission of forces through +weight factors specified at the coupling nodes; +• automatically selects the coupling nodes located on a surface lying within a region of influence; +• can be used with two- or three-dimensional stress/displacement elements; and +• can be used in geometrically linear and nonlinear analysis. +Surface-based coupling definitions +The surface-based coupling constraint in Abaqus provides coupling between a reference node and a +group of nodes referred to as the “coupling nodes.” This option provides the same functionality as +the kinematic coupling constraint and the distributing coupling elements (DCOUP2D, DCOUP3D) in +Abaqus/Standard with a surface-based user interface. The coupling nodes are selected automatically by +specifying a surface and an optional influence region. The procedure used to define the coupling nodes +is discussed below. +For a distributing coupling constraint, the distributing weight factors are calculated automatically if +the surface is an element-based surface. In such a case the weight factors are based on the tributary area +at each coupling node, except for a surface along a shell edge, where the weight factors are based on the +tributary edge length. Furthermore, the distributing weight factors can be modified using one of several +weighting methods, which allow the forces transferred to the coupling nodes to vary inversely with the +radial distance from the reference node. +Typical applications +The coupling constraint is useful when a group of coupling nodes is constrained to the rigid body motion +of a single node. The coupling constraint can be employed effectively in the following applications: +• To apply loads or boundary conditions to a model. Figure 34.3.2–1 illustrates the use of a kinematic +coupling constraint to prescribe a twisting motion to a model without constraining the radial motion. +reference node +axis of cylindrical +coordinate system +constrained nodes that are +free to translate radially +surface that defines +the coupling nodes +Figure 34.3.2–1 Kinematic coupling constraint. +Figure 34.3.2–2 illustrates a distributing coupling constraint used to prescribe a displacement and +rotation condition on a boundary where relative motion between the nodes on the boundary is +required. In this example a twist is prescribed at the end of the structure that is expected to warp +and/or deform within the end surface. +• To distribute loads on a model, where the load distribution can be described with a moment-of-inertia +expression. Examples of such cases include the classic bolt-pattern and weld-pattern distribution +expressions. +• To apply dimensionality transitions between continuum and structural elements. For example, a +distributing coupling allows flexible coupling between structural and solid elements. +• To model end conditions. For example, modeling a rigid end plate or modeling plane sections of a +solid to remain planar can be done easily with a kinematic coupling definition. +• To simplify modeling of complex constraints. In a kinematic coupling definition the degrees of +freedom that participate in the constraint may be selected individually in a local coordinate system. +• To model interactions with other constraints, such as connector elements. For example, a hinged part +may be modeled more realistically by two distributing coupling definitions, whose reference nodes +warping is permitted +by the coupling element +reference node +prescribed +rotation +surface that +defines the +coupling nodes +coupling nodes +Figure 34.3.2–2 Distributing coupling constraint. +are connected by a hinge connector element. The load transfer then occurs between two “clouds” of +nodes, rather than between two single nodes. “Substructure analysis of a one-piston engine model,” +Section 4.1.10 of the Abaqus Example Problems Manual, illustrates this use of connector elements +in conjunction with coupling constraints to model a one-piston engine. +Defining the coupling constraint +Defining a coupling constraint requires the specification of the reference node (also called the constraint +control point), the coupling nodes, and the constraint type. The coupling constraint associates the +reference node with the coupling nodes. A name must be assigned to the constraint and may be used in +postprocessing with Abaqus/CAE. A node number or node set name may be specified for the reference +node. If a node set is specified, the node set must contain exactly one node. The reference node for a +kinematic coupling constraint has both translational and rotational degrees of freedom. The surface +on which the coupling nodes are located can be node-based; element-based; or, in Abaqus/Explicit, +a combination of both surface types. You can specify an optional radius of influence that limits the +coupling nodes to a specific region on the surface. Details on how coupling nodes are defined by +specifying an influence region are discussed below. +The constraint type can be either kinematic or distributing, as discussed below. +Input File Usage: +Abaqus/CAE Usage: +Use the following options: +*COUPLING, CONSTRAINT NAME=name, REF NODE=n, +SURFACE=surface +*KINEMATIC or *DISTRIBUTING +Interaction module: Create Constraint: Coupling: Coupling type: +Kinematic or Distributing +Specifying a region of influence +By default, coupling nodes belonging to the entire surface are selected for the coupling definition. You +can limit the coupling nodes to lie within a spherical region centered about the reference node by defining +a radius of influence. +The procedure by which coupling nodes are selected for the constraint definition depends on the +surface type: +• For a node-based surface, all the nodes defined by the surface definition that fall within the influence +region are selected for the coupling definitions. +• For an element-based surface, the surface facets that are either fully or partially inscribed by the +influence region are determined. All nodes belonging to these facets, whether or not these nodes +fall within the influence region, are selected for the coupling nodes. When the influence radius is +less than the distance to the closest coupling node, Abaqus selects all nodes belonging to the closest +facet. If the projection of the reference node on the surface falls on an edge or a vertex of multiple +facets, all nodes belonging to these facets adjoining the edge or vertex are included in the coupling +definition. In the case where the influence radius is less than the distance to the closest coupling +node, adjacent surface faces must have consistent normal directions; otherwise, Abaqus issues an +error message. +• A distributing coupling constraint must include at least two coupling nodes. +If fewer than two +coupling nodes are found, Abaqus issues an error message during input file preprocessing. +Input File Usage: +*COUPLING, CONSTRAINT NAME=name, REF NODE=n, +SURFACE=surface, INFLUENCE RADIUS=r +Abaqus/CAE Usage: +Interaction module: Create Constraint: Coupling: Influence +radius: Specify +Kinematic coupling constraints +Kinematic coupling constrains the motion of the coupling nodes to the rigid body motion of the reference +node. The constraint can be applied to user-specified degrees of freedom at the coupling nodes with +respect to the global or a local coordinate system. +Kinematic constraints are imposed by eliminating degrees of freedom at the coupling nodes. +In Abaqus/Standard once any combination of displacement degrees of freedom at a coupling node +is constrained, additional displacement constraints—such as MPCs, boundary conditions, or other +kinematic coupling definitions—cannot be applied to any coupling node involved in a kinematic +coupling constraint. The same limitation applies for rotational degrees of freedom. This restriction +does not apply in Abaqus/Explicit. See “Kinematic constraints: overview,” Section 34.1.1, for more +information. +Input File Usage: +Use both of the following options to define a kinematic coupling constraint: +*COUPLING +*KINEMATIC +first dof, last dof +For example, the following coupling constraint is used to constrain degrees of +freedom 1, 2, and 6 on surface surfA to reference node 1000: +*COUPLING, CONSTRAINT NAME=C1, REF NODE=1000, +SURFACE=surfA +*KINEMATIC +1, 2 +6, +Abaqus/CAE Usage: +Interaction module: Create Constraint: Coupling: Coupling type: +Kinematic: toggle on the degrees of freedom +Translational degrees of freedom +Translational degrees of freedom are constrained by eliminating the specified degrees of freedom at the +coupling nodes. When all translational degrees of freedom are specified, the coupling nodes follow the +rigid body motion of the reference node. +Rotational degrees of freedom +Rotational degrees of freedom are constrained by eliminating the specified degrees of freedom at the +coupling nodes. +All combinations of selected rotational degrees of freedom result in rotational behavior identical to +existing MPC types: +• Selection of three rotational degrees of freedom along with three displacement degrees of freedom +is equivalent to MPC type BEAM. +• Selection of two rotational degrees of freedom is equivalent to MPC type REVOLUTE in +Abaqus/Standard. +• Selection of one rotational degree of freedom is equivalent to MPC type UNIVERSAL in +Abaqus/Standard. +In Abaqus/Standard internal nodes are created by the kinematic coupling to enforce the constraints +that are equivalent to MPC types REVOLUTE and UNIVERSAL. These nodes have the same degrees +of freedom as the additional nodes used in these MPC types and are included in the residual check for +nonlinear analysis. +Specifying a local coordinate system +The kinematic coupling constraint can be specified with respect to a local coordinate system instead of +the global coordinate system . Figure 34.3.2–1 illustrates the use of +a local coordinate system to constrain all but the radial translation degrees of freedom of the coupling +nodes to the reference node. In this example a local cylindrical coordinate system is defined that has its +axis coincident with the structure’s axis. The coupling node constraints are then specified in this local +coordinate system. +Input File Usage: +*COUPLING, ORIENTATION=local +For example, the following input is used to specify the kinematic coupling +constraint shown in Figure 34.3.2–1: +*ORIENTATION, SYSTEM=CYLINDRICAL, NAME=COUPLEAXIS +0.0, -1.0, 0.0, 0.0, 1.0, 0.0 +*COUPLING, REF NODE=500, SURFACE=Endcap, +ORIENTATION=COUPLEAXIS +*KINEMATIC +2, 3 +Abaqus/CAE Usage: +Interaction module: Create Constraint: Coupling: Edit: +select local coordinate system +Constraint direction and finite rotation +In geometrically nonlinear analysis steps the coordinate system in which the constrained degrees of +freedom are specified will rotate with the reference node regardless of whether the constrained degrees +of freedom are specified in the global coordinate system or in a local coordinate system. +Distributing coupling constraints +Distributing coupling constrains the motion of the coupling nodes to the translation and rotation of the +reference node. This constraint is enforced in an average sense in a way that enables control of the +transmission of loads through weight factors at the coupling nodes. Forces and moments at the reference +node are distributed either as a coupling node-force distribution only (default) or as a coupling node-force +and moment distribution. The constraint distributes loads such that the resultants of the forces (and +moments) at the coupling nodes are equivalent to the forces and moments at the reference node. For cases +of more than a few coupling nodes, the distribution of forces/moments is not determined by equilibrium +alone, and distributing weight factors are used to define the force distribution. +The moment constraint between the rotation degrees of freedom at the reference node and the +average rotation of the cloud nodes can be released in one direction in a two-dimensional analysis and +one, two, or three directions in a three-dimensional analysis. In a three-dimensional analysis you can +specify the moment constraint directions in the global coordinate system or in a local coordinate system. +All available translational degrees of freedom at the reference node are always coupled to the average +translation of the coupling nodes. +In a three-dimensional Abaqus/Standard analysis if all three moment constraints are released +by specifying only degrees of freedom 1 through 3, only translation degrees of freedom will be +activated on the reference node. If only one or two rotation degrees of freedom have been released, +all three rotation degrees of freedom are activated at the reference node. In this case you must ensure +that proper constraints have been placed on the unconstrained rotation degrees of freedom to avoid +numerical singularities. Most often this is accomplished by using boundary conditions or by attaching +the reference node to an element such as a beam or shell that will provide rotational stiffness to the +unconstrained rotation degrees of freedom. +In Abaqus/Explicit releasing one or more of the moment constraints may lead to significant +computational performance degradation. This is also the case when other constraints intersect the cloud +of coupling nodes. +In these cases, the degradation in performance is particularly noticeable when a +large number of such distributed couplings are present in the model or when the size of the constrained +“cloud” is large. For that matter, when the modeling conditions mentioned above are encountered, +the size of the coupling nodes cloud is limited to 1000. To alleviate the released moment constraint +issue, the following modeling technique can be used (also available in Abaqus/Standard): constrain all +moments in the distributed coupling and use an appropriate connector element at the reference node +(such as REVOLUTE, HINGE, CARDAN or BUSHING) to model released moments at the coupling’s +reference node. This technique has also the advantage of being able to specify finite compliance such +as elasticity, plasticity or damage in the “released” rotational component. +Input File Usage: +*DISTRIBUTING +first dof, last dof +If no degrees of freedom are specified, all available degrees of freedom are +coupled. If you specify one or more rotation degrees of freedom but not all +available translation degrees of freedom, Abaqus issues a warning message and +adds all available translation degrees of freedom to the constraint. +For example, the following coupling constraint is used to constrain degrees of +freedom 1–5 on the reference node 1000 to the average translation and rotation +of surface surfA: +*COUPLING, CONSTRAINT NAME=C1, REF NODE=1000, +SURFACE=surfA +*DISTRIBUTING +1, 5 +In this example the moment constraint between the reference node and the +coupling nodes will be released in the 6-direction but will be enforced in +the 4- and 5-directions. This provides a “revolute-like” rotation connection +between the reference node and the coupling nodes . +Interaction module: Create Constraint: Coupling: Coupling type: +Distributing: toggle on the rotational degrees of freedom (Abaqus/CAE +automatically constrains the translational degrees of freedom) +Abaqus/CAE Usage: +Node-based surface +User-defined weight factors are used for node-based surfaces. The cross-sectional areas specified in the +surface definition are used as the weight factors . +Element-based surface +For element-based surfaces the weight factors are calculated by Abaqus. The default weight distribution +is based on the tributary surface area at each coupling node, except for a surface along a shell edge +where the weight distribution is based on the tributary edge length. The procedure used to calculate the +default weight factors is designed to ensure that if a radius of influence is prescribed, the default weight +distribution varies smoothly with the influence radius. +Calculating the default distributing weight factors +The procedure to calculate the distributing weight factors depends on whether or not an influence radius +is specified. +• If no influence radius is specified, the entire surface is used in the coupling definition. In this case +all nodes located on the surface are included in the coupling definition and the distributing weight +factor at each coupling node is equal to the tributary surface area. +• If an influence radius is specified, the default distributing weight factors at the coupling nodes are +calculated as follows: +1. A “participation factor” is calculated for each surface facet. The participation factor is defined +below. +2. The tributary nodal area (or tributary edge length along a shell edge) at each facet node is +computed and is multiplied by the facet participation factor. +3. The coupling node distributing weight factor is computed as the sum of the corresponding facet +nodal areas (calculated above) for all joining facets. +Calculating the facet participation factor +The participation factor defines the proportion of the facet’s area that contributes to the distributing weight +factors when an influence radius is specified. The participation factor varies between zero and one. +To define the participation factor, the distance of the facet node closest to the reference node, +, +and the distance of the facet node farthest from the reference node, +, are calculated. +• If +, where +and a participation factor of one is used. +is the influence radius, all facet nodes lie within the influence region; +• If +is set to zero. +, none of the facet nodes lie within the influence region; and the participation factor +• If +, the facet is partially inscribed in the influence region; and the facet is assigned a +participation factor equal to +. +If all coupling nodes fall outside the influence radius (i.e., +for all facets), Abaqus selects +all nodes belonging to the closest facets (as outlined under “Specifying a region of influence”) and uses +a participation factor equal to one. +Weighting methods +You can modify the default weight distribution defined above. Various weighting methods are provided +that monotonically decrease with radial distance from the reference node. For each case the default +weight distribution that is based on the tributary surface area (or tributary edge length along a shell edge) +is scaled by the weight factor +. If the weighting method is not specified, a uniform weighting method +is used in which all weight factors are equal to 1.0. +A linearly decreasing weighting scheme +COUPLING CONSTRAINTS +is the coupling node radial distance from the reference +where +node, and +is the weight factor at coupling node i, +is the distance to the furthest coupling node. +Input File Usage: +Abaqus/CAE Usage: +*DISTRIBUTING, WEIGHTING METHOD=LINEAR +Interaction module: Create Constraint: Coupling: Coupling type: +Distributing: Weighting method: Linear +Quadratic polynomial weight distribution +A quadratic polynomial weight distribution defined by +Input File Usage: +Abaqus/CAE Usage: +*DISTRIBUTING, WEIGHTING METHOD=QUADRATIC +Interaction module: Create Constraint: Coupling: Coupling type: +Distributing: Weighting method: Quadratic +Monotonically decreasing weight distribution +A monotonically decreasing weight distribution according to the cubic polynomial +Input File Usage: +Abaqus/CAE Usage: +*DISTRIBUTING, WEIGHTING METHOD=CUBIC +Interaction module: Create Constraint: Coupling: Coupling type: +Distributing: Weighting method: Cubic +Specifying a local coordinate system +The distributing coupling constraint can be specified with respect to a local coordinate system instead of +the global coordinate system . Figure 34.3.2–2 illustrates the use of a +local coordinate system to release the moment constraints between the reference node and the coupling +nodes in the local 4- and 6-directions, providing a “universal-like” rotation connection. In this example +a local rectangular coordinate system is defined that has its local y-axis coincident with the global z-axis. +The moment constraint is specified in this local coordinate system. +Input File Usage: +*COUPLING, ORIENTATION=local +For example, the following input is used to specify the distributing coupling +constraint shown in Figure 34.3.2–2: +*ORIENTATION, SYSTEM=RECTANGULAR, NAME=COUPLEAXIS +0.0, 1.0, 0.0, 0.0, 0.0, 1.0 +*COUPLING, REF NODE=500, SURFACE=Endcap, +ORIENTATION=COUPLEAXIS +*DISTRIBUTING +1, 3 +5, 5 +Abaqus/CAE Usage: +Interaction module: Create Constraint: Coupling: Edit: +select local coordinate system +Defining the surface coupling method +There are two methods available to couple the motion of the reference node to the average motion of +the coupling nodes: the continuum coupling method and the structural coupling method. The continuum +coupling method is used by default. +Continuum coupling method +The default continuum coupling method couples the translation and rotation of the reference node to +the average translation of the coupling nodes. The constraint distributes the forces and moments at the +reference node as a coupling nodes force distribution only. No moments are distributed at the coupling +nodes. The force distribution is equivalent to the classic bolt pattern force distribution when the weight +factors are interpreted as bolt cross-section areas. The constraint enforces a rigid beam connection +between the attachment point and a point located at the weighted center of position of the coupling +nodes. For further details, see “Distributing coupling elements,” Section 3.9.8 of the Abaqus Theory +Manual. +Input File Usage: +Abaqus/CAE Usage: +*DISTRIBUTING , COUPLING=CONTINUUM +Coupling the motion of the reference node to the average motion of the coupling +nodes is not supported in Abaqus/CAE. +Structural coupling method +The structural coupling method couples the translation and rotation of the reference node to the +translation and the rotation motion of the coupling nodes. The method is particularly suited for +bending-like applications of shells when the coupling constraint spans small patches of nodes and the +reference node is chosen to be on or very close to the constrained surface. The constraint distributes +forces and moments at the reference node as a coupling node-force and moment distribution. For this +coupling method to be active, all rotation degrees of freedom at all coupling nodes must be active (as +would be the case when the constraint is applied to a shell surface) and the constraints must be specified +in all degrees of freedom (default). In addition, for the constraint to be meaningful, the local (or global) +z-axis used in the constraint should be such that it is parallel to the average normal direction of the +constrained surface. +With respect to translations, the constraint enforces a rigid beam connection between the reference +node and a moving point that remains at all times in the vicinity of the constrained surface. The location +of this moving point is determined by the approximate current curvature of the surface, the current +location of the weighted center of position of the coupling nodes , and the z-axis used in the constraint. This choice avoids +unrealistic contact interactions if multiple pairs of distributed coupling constraints are used to fasten shell +surfaces . +With respect to rotations, the constraint is different along different local directions. Along the +z-axis (twist direction), the constraint is identical to the one enforced via the continuum coupling method +. By contrast, the +rotational constraint in the plane perpendicular to the z-axis relates the in-plane reference node rotations +to the in-plane rotations of the coupling nodes in the immediate vicinity of the reference node. This +choice provides a more realistic (compliant) response when the constrained surface is small and deforms +primarily in a bending mode. +Input File Usage: +Abaqus/CAE Usage: +*DISTRIBUTING, COUPLING=STRUCTURAL +Coupling the motion of the reference node to the average motion of the coupling +nodes is not supported in Abaqus/CAE. +Moment release and finite rotation +In geometrically nonlinear analysis steps the coordinate system of the degrees of freedom that define the +moment release rotates with the reference node regardless of whether the global coordinate system or a +local coordinate system is used. +Colinear coupling node arrangements +The distributing coupling constraint transmits moments at the reference node as a force distribution +among the coupling nodes, even if these nodes have rotational degrees of freedom. Thus, when the +coupling node arrangement is colinear, the constraint is not capable of transmitting all components of +a moment at the reference node. Specifically, the moment component that is parallel to the colinear +coupling node arrangement will not be transmitted. When this case arises, a warning message is issued +that identifies the axis about which the element will not transmit a moment. +Limitations +• A distributing coupling constraint cannot be used with axisymmetric elements with asymmetric +deformation. This element type is not compatible with the distributing coupling constraint. +• If a distributing coupling constraint is used with axisymmetric elements with twist, the constraint +It will involve only the +will not include the twist degree of freedom 5 in those elements. +displacement degrees of freedom 1 and 2. +• A distributing coupling definition with a large number of coupling nodes produces a large wavefront +in Abaqus/Standard. This may result in significant memory usage and a long solution time to solve +the finite element equilibrium equations. +• A distributing coupling constraint cannot involve more than 46,000 degrees of freedom in +Abaqus/Standard, which implies an upper limit of 23,000 nodes per constraint for two-dimensional +and axisymmetric cases and an upper limit of 15,333 nodes per constraint for three-dimensional +cases. +34.3.3 +SHELL-TO-SOLID COUPLING +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Coupling constraints,” Section 34.3.2 +• “Surfaces: overview,” Section 2.3.1 +• *SHELL TO SOLID COUPLING +• “Defining shell-to-solid coupling constraints,” Section 15.15.7 of the Abaqus/CAE User’s Manual, +in the online HTML version of this manual +Overview +Surface-based shell-to-solid coupling: +• allows for a transition from shell element modeling to solid element modeling; +• is most useful when local modeling should use a full three-dimensional analysis but other parts of +the structure can be modeled as shells; +• uses a set of internally defined distributing coupling constraints to couple the motion of a “line” of +nodes along the edge of a shell model to the motion of a set of nodes on a solid surface; +• automatically selects the coupling nodes located on a solid surface lying within a region of influence; +• can be used with three-dimensional stress/displacement shell and solid (continuum) elements; +• does not require any alignment between the solid and shell element meshes; and +• can be used in geometrically linear and nonlinear analysis. +Shell-to-solid coupling +Shell-to-solid coupling in Abaqus is a surface-based technique for coupling shell elements to solid +elements. +Figure 34.3.3–1 illustrates two examples taken from “Shell-to-solid submodeling and +shell-to-solid coupling of a pipe joint,” Section 1.1.10 of the Abaqus Example Problems Manual, and +“The pinched cylinder problem,” Section 2.3.2 of the Abaqus Benchmarks Manual. Shell-to-solid +coupling is intended to be used for mesh refinement studies where local modeling requires a relatively +fine through-the-thickness solid mesh coupled to the edge of a shell mesh, as shown in Figure 34.3.3–2. +In such a case Abaqus will assemble constraints that couple the displacement and rotation of each shell +node to the average displacement and rotation of the solid surface in the vicinity of the shell node. +As shown in Figure 34.3.3–2, the coupling occurs along a shell-to-solid interface defined by two +user-specified surfaces: an edge-based shell surface and an element- or node-based solid surface . The shell surface (Figure 34.3.3–3) is referred to as the “shell +shell elements +solid elements +solid elements +shell elements +Figure 34.3.3–1 Typical examples of shell-to-solid coupling. +refined solid mesh +shell-to-solid interface +shell mesh +Figure 34.3.3–2 Shell-to-solid interface. +edge.” The shell element edges that define the edge-based shell surface are referred to as “edge facets.” +The edge facets are either linear or parabolic segments depending if the underlying shell elements are +linear or quadratic. +solid +solid surface +shell +shell edge +Figure 34.3.3–3 Shell and solid surfaces. +The shell-to-solid coupling is enforced by the automatic creation of an internal set of distributing +coupling constraints between nodes on the shell edge and +nodes on the solid surface. Abaqus uses default or user-defined distance and tolerance parameters +(discussed below) to determine which nodes on the shell edge will be coupled to which nodes on the +solid surface. For each shell node involved in the coupling, a distinct internal distributing coupling +constraint is created with the shell node acting as the reference node and the associated solid nodes +acting as the coupling nodes. Each internal constraint distributes the forces and moments acting at its +shell node as forces acting on the related set of coupling surface nodes in a self-equilibrating manner. +The resulting line of constraints enforces the shell-to-solid coupling. +Defining shell-to-solid coupling +Defining a shell-to-solid coupling constraint requires the specification of a constraint name, an edge- +based shell surface, and an element- or node-based solid surface. +Input File Usage: +*SHELL TO SOLID COUPLING, CONSTRAINT NAME=name +shell_surface, solid_surface +Abaqus/CAE Usage: +Interaction module: Create Constraint: Shell-to-solid coupling +Abaqus automatically determines which nodes on the two surfaces participate in the coupling and +creates appropriate internal distributed coupling constraints. You can also control which nodes on the +two surfaces participate in the coupling by specifying a position tolerance and/or influence distance as +described below. +The resulting coupling constraint definitions are printed to the data file when model definition data +are requested . Abaqus will also create an internal node set that contains all the +solid nodes included in the coupling; the node set can be visualized using the Visualization module of +Abaqus/CAE. The name of the internal node set is the name assigned to the coupling constraint. +Controlling the shell nodes included in the coupling +A position tolerance determines the absolute distance from the solid surface within which all shell nodes +to be included in the coupling must lie. Shell nodes that lie outside this tolerance are not coupled to the +solid surface. +When using an element-based solid surface, the defined distance between a shell node and the solid +surface is the projected distance measured along a line extending from the shell node to the closest point +on the solid surface (which may be on the edge of the solid surface). The default position tolerance when +using an element-based solid surface is 5% of the length of a typical facet on the shell edge. +For a node-based solid surface the defined distance of a shell node to the surface is the distance +to the closest node on the solid surface. The default position tolerance when using a node-based solid +surface is based on the average distance between nodes on the solid surface. +You can specify a nondefault position tolerance for element- or node-based solid surfaces.. +Input File Usage: +Abaqus/CAE Usage: +*SHELL TO SOLID COUPLING, POSITION TOLERANCE=distance +Interaction module: Create Constraint: Shell-to-solid coupling: select +the surfaces: choose Specify distance for the Position Tolerance +Controlling the solid nodes included in the coupling +A geometric tolerance, which is referred to as the influence distance, is defined for each edge facet. For a +given node or element facet on the solid surface to be included in the coupling constraint, its perpendicular +distance from at least one edge facet must be less than or equal to the influence distance defined for that +edge facet. The default influence distance for an edge facet is half the thickness of the underlying shell +element. The default automatically accounts for any offset or nodal thickness included with the shell +element’s cross-section definition. You can specify a nondefault influence distance. +Input File Usage: +Abaqus/CAE Usage: +*SHELL TO SOLID COUPLING, INFLUENCE DISTANCE=distance +Interaction module: Create Constraint: Shell-to-solid coupling: select +the surfaces: choose Specify value for the Influence Distance +A user-defined influence distance is optional in all cases except when an edge facet involved in +the coupling is associated with a general arbitrary elastic shell section definition in which you specified +the general stiffness. In this case since the shell thickness is not defined directly, you must supply an +influence distance. +Computation of the internal coupling constraints +This section outlines the basic procedure used by Abaqus to compute the internal shell-to-solid coupling +constraints. +A single distinct internal distributing coupling constraint is created for each shell node that lies +within the position tolerance from the solid surface. Internal coupling constraints are not created for +shell nodes that lie outside this tolerance. The shell node acts as the reference node, and a set of nodes +on the solid surface act as the coupling nodes. Abaqus finds the coupling nodes on the solid surface and +computes the weight factors for the internal constraints by considering each shell edge facet separately. +The following procedure is carried out for each edge facet: +1. Abaqus finds all nodes on the solid element surface that lie within the region of influence (discussed +below) of the current edge facet. These nodes are included in the coupling constraint. +2. Abaqus then computes a set of weight factors for the solid nodes. A weight factor is a measure of +both the tributary area of the solid node contained within the region of influence and the relative +position of the solid node with respect to each shell node. The tributary areas for node-based surfaces +are the cross-sectional areas that you specified when you defined the surface. For element-based +surfaces the tributary areas are calculated by Abaqus. The sum of all the weight factors in each +coupling constraint is a measure of the total tributary area of the solid surface that is contained +within the region of influence. +3. The above procedure is carried out for all the shell edge facets contained within the shell surface. +If a shell node belongs to more than one edge facet, all the coupling nodes and weight factors are +combined into a single distributing constraint definition. The resulting line of constraints along the +shell edge enforces the shell-to-solid coupling. +There are two situations in which a shell node might satisfy the position tolerance but no coupling +constraint is defined. If a shell node lies within the position tolerance but is not connected by an edge +facet to at least one other shell node that also satisfies the tolerance, a coupling constraint is not created +for this shell node. In this case it may be necessary to increase the position tolerance. Alternatively, if +nonzero weight factors are not computed for at least two solid nodes associated with the shell node, a +coupling constraint is not created for this shell node. The most likely cause for zero weight factors is that +the influence distance is too small. In the case of a node-based surface, zero weights might also arise if +the default cross-sectional area is used. For shell-to-solid coupling the default area is zero. +The region of influence for an edge facet +The region of influence of an edge facet is defined by a cylindrical volume whose centerline is the edge +facet and whose radius is the edge facet’s influence distance. The ends of the cylindrical volume are +defined by two bounding planes whose normals are the shell tangents at the two ends of the edge facet +. In this example a region of influence is constructed for shell edge 2–3. For a +node-based solid surface only the nodes that lie within or on the boundary of the region of influence are +assigned to the current edge facet and included in the coupling definition. For an element-based solid +surface each solid facet node is associated with part of the facet surface. If the part of the facet assigned +to a given solid node falls within the region of influence, that node is included in the coupling definition. +Using the normal on an element-based solid surface to restrict solid nodes that are used in the +coupling +In the case of an element-based solid surface Abaqus will compare the normal of each solid facet within +the region of influence to the normal of the solid surface closest to the centerline of the cylindrical volume +. In general, if the normal of a surface facet is not within 20° of the normal at the +centerline, the nodes on the solid surface facet are not included in the coupling definition. For the case +illustrated in Figure 34.3.3–4 this check would prevent nodes on the top and bottom surface of the solid +solid +shell +region of influence for edge facet 2-3 +shell node +edge facet +Figure 34.3.3–4 Regions of influence for an edge facet. +mesh from being coupled to the shell nodes even if the influence distance was arbitrarily large and the +solid surface definition included all sides of the solid geometry. This check is not used if the centerline +is on or near a feature edge of the solid mesh where the normal is not well defined . +Comments, restrictions, and modeling recommendations for shell-to-solid coupling +• The shell-to-solid coupling formulation assumes that the interface surface between the shell and +solid elements is normal to the shell. Therefore, while the solid surface can be curved in a direction +tangent to the shell edge, it should be straight in the direction along the shell normals. This is an +assumption on the geometry of the surfaces, not on the mesh. It is not necessary for the nodes on +the solid surface to line up with each other or to line up with the shell nodes. +• The shell-to-solid coupling capability is designed for analyses where the solid mesh is fine with +respect to the shell thickness. It is recommended that at least two solid elements be included through +the thickness at a shell-to-solid interface. Along the shell-to-solid interface the length of a shell edge +facet should in general be of the same order as the characteristic surface dimension of a solid element +facet. +• An assumption used in the design of the shell-to-solid coupling algorithms is that the weight factors +are based upon accurate nodal tributary areas, such as those automatically computed by Abaqus +when an element-based surface is used. Therefore, it is generally recommended that an element- +based solid surface be used instead of a node-based solid surface. However, in cases where the +shell and solid meshes align with each other, it is sometimes advantageous to use a node-based +solid surface especially when a homogenous solution is expected. +• Figure 34.3.3–5 illustrates some recommended modeling practices for shell-to-solid coupling. If +the shell reference surface is not offset, the shell edge should be centrally located with respect to +the thickness direction of the solid (Figure 34.3.3–5(a)). The solid surface should include only the +portion needed for the coupling (the shaded region shown in Figure 34.3.3–5(a)). +solid +shell edge centrally located with +respect to the thickness direction +of the solid +solid surface only includes +portion of solid where +coupling is needed +(a) +shell mesh +solid +at least two shell elements +between feature angles +on the solid +shell mesh +(b) +Figure 34.3.3–5 Modeling recommendations for the shell-to-solid interface. +• The shell-to-solid interface can be defined around geometric feature angles (corners), +(Figure 34.3.3–5(b)). However, it is recommended that the feature angles satisfy 60° < +< 300°. +In addition, as illustrated in Figure 34.3.3–5(b), at least two shell element edges should be included +between each feature angle. +• If an offset is defined for the shell section and the reference shell edge is placed at or near a feature +edge on the solid surface (Figure 34.3.3–6), the solid surface should include only the side of the +solid that you want to be included in the coupling definition. +shell reference surface containing shell nodes +solid +offset +shell midsurface +In this example, it is recommended that the solid surface +definition only include the shaded region. +Figure 34.3.3–6 Modeling recommendations for the shell-to-solid interface with a shell offset. +For example, if the top of the solid in Figure 34.3.3–6 is included in the surface definition, Abaqus +includes nodes on the top of the surface in the coupling constraint, which is not what you intended. +You intended only that the shell be coupled to the shaded region of the solid in Figure 34.3.3–6. +Therefore, the solid surface definition should include only this region. +• Care must be taken in interpreting the local stress and strain fields in the immediate vicinity of +the shell-to-solid interface. This is especially true if the shell-to-solid interface includes corners or +edges. The interface should be placed at least a distance more than the shell thickness away from +the region in the solid mesh where the stress and strain fields are of interest. +• The shell-to-solid interface should be located in a region of the model where shell theory is a valid +modeling approximation. +• Corners or kinks may exist in models made of shell elements. At such corners or kinks the shell +elements only approximate the distribution of the material away from the midsurface of the shell. +While the global moments and forces between the shell and solid models are transferred correctly, +the local stress and displacement fields in the region of the shell-to-solid interface may be inaccurate. +• Only displacement degrees of freedom in the solid elements and displacement and rotation degrees +of freedom in the shell elements are coupled in shell-to-solid coupling. Shell-to-solid coupling does +not couple other degrees of freedom such as temperature, pressure, etc. +• Shell-to-solid coupling can be used to couple three-dimensional shells to all three-dimensional +library,” +solid element +(“Cylindrical +cylindrical +elements +except +continuum elements +Section 28.1.5). +34.3.4 +MESH-INDEPENDENT FASTENERS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Surfaces: overview,” Section 2.3.1 +• “Coupling constraints,” Section 34.3.2 +• “Connector elements,” Section 31.1.2 +• *FASTENER +• *FASTENER PROPERTY +• “About fasteners,” Section 29.1 of the Abaqus/CAE User’s Manual +Overview +The mesh-independent fastener capability: +• is a convenient method to define a point-to-point connection between two or more surfaces such as +a spot weld or rivet connection; +• uses spatial coordinates of fastener locations to define point-to-point connections independent of +underlying meshes; +• combines either connector elements or BEAM MPCs with distributing coupling constraints to +provide a connection that can be located anywhere between two or more surfaces regardless of the +mesh refinement or location of nodes on each surface; +• can be used to connect both deformable and rigid element-based surfaces; +• can model either rigid, elastic, or inelastic connections with failure by using the generality of +connector behavior definitions; and +• is available only in three dimensions. +Introduction +Many applications require modeling of point-to-point connections between parts. These connections +may be in the form of spot welds, rivets, screws, bolts, or other types of fastening mechanisms. There +may be hundreds or even thousands of these connections in a large system model such as an automobile +or airframe. +The fastener can be located anywhere between the parts that are to be connected regardless of the +mesh. In other words, the location of the fastener can be independent of the location of the nodes on the +surfaces to be connected. Instead, the attachment to each of the parts being connected is distributed to +several nodes in the surfaces to be connected in the neighborhood of the fastening points. Figure 34.3.4–1 +shows a typical one-layer and two-layer fastener configuration. Each layer connects two fastening points +using either a connector element or a BEAM MPC. Each fastening point is connected to the surface using +Number of layers = 2 +layer 1 +Radius +of influence +layer 2 +Fastening point +Number of layers = 1 +Fastening point +Figure 34.3.4–1 Typical one-layer and two-layer fastener configuration. +a distributing coupling constraint that couples the displacement and rotation of each fastening point to +the average displacement and rotation of the nearby nodes. +The mesh-independent fastener capability in Abaqus is designed to model these connections in a +convenient manner. The fastener automatically: +• determines the locations of nodes and orientations of connector elements or BEAM MPCs between +two or more surfaces; +• generates distributing coupling constraints to attach the connector elements or BEAM MPCs to each +surface in a mesh-independent manner; and +• calculates weights for the distributing coupling constraints that complete the mesh-independent +connection. +For an example of the use of mesh-independent fasteners, see “Buckling of a column with spot welds,” +Section 1.2.3 of the Abaqus Example Problems Manual. Mesh-independent fasteners are referred to as +point-based fasteners by Abaqus/CAE. For more information, see “About fasteners,” Section 29.1 of the +Abaqus/CAE User’s Manual. It is also possible to assemble fasteners in Abaqus/CAE using connector +elements, coupling constraints, etc. For further details, see “About assembled fasteners,” Section 29.1.3 +of the Abaqus/CAE User’s Manual. +Fastener interactions +Fasteners are defined in groups called interactions, which are assigned names. Each interaction defines +one or more fasteners. The number of individual fasteners is equal to the number of positioning points +used to locate the fasteners. Fastening points on each surface are found by considering the position of +the positioning point as discussed in subsequent sections. +Fasteners can be defined using connector elements or BEAM MPCs. BEAM MPCs allow modeling +of perfectly rigid connectors between components; while connector elements allow you to model much +more complex behavior, such as deformable connectors that include the effects of elasticity, damage, +plasticity, and friction. +Input File Usage: +Abaqus/CAE Usage: +*FASTENER, INTERACTION NAME=name +Interaction module: Special→Fasteners→Create: Name: name, +Type: Point-based +Defining fasteners using BEAM MPCs +For modeling perfectly rigid connections you need not define fasteners using connector elements. +Instead, Abaqus can internally generate BEAM MPCs connecting the fastening points of the fasteners. +In this approach you assign a reference node set containing a list of user-defined nodes to the fastener +interaction. The nodes in this reference node set will be used as positioning points to locate the +fasteners. If single-layer fasteners are to be modeled, Abaqus generates single BEAM MPCs with each +node in the reference node set becoming the first node of the BEAM MPC. The second node of each +BEAM MPC will be generated internally by Abaqus. If multi-layer fasteners are to be defined, Abaqus +generates linked sets of BEAM MPCs with each node in the reference node set becoming the first node +of the first BEAM MPC in each linked set. The subsequent nodes in each linked set will be generated +internally by Abaqus. For multi-layer fasteners each linked set contains as many BEAM MPCs as the +number of layers in the fastener. +Input File Usage: +Abaqus/CAE Usage: +Use the following options: +*FASTENER, INTERACTION NAME=name, +REFERENCE NODE SET=node set label +*NSET, NSET=node set label +Interaction module: Special→Fasteners→Create: Point-based: select +positioning points: Property: Section: Rigid MPC +Defining fasteners using connector elements +Using connector elements as the basis for a point-to-point connection allows for very complex behavior +to be modeled with fasteners. Like other uses of connector elements, the connection can be fully rigid +or may allow for unconstrained relative motion in local connector components. In addition, deformable +behavior can be specified using a connector behavior definition that can include the effects of elasticity, +damping, plasticity, damage, and friction. There are two methods to define fasteners that use connector +elements to model the behavior between fastening points. For both methods the fastener interaction refers +to an element set containing the connector elements. You must specify a connector section definition that +refers to this element set. You should be careful when specifying the connector orientation (if needed) +as discussed below in “Defining the fastener orientation.” +Defining the connector elements directly +The most controlled approach to specifying fasteners using connector elements is to define the connector +elements explicitly and associate them with an element set. The fastener interaction refers to the element +set. Each fastener in the fastener interaction corresponds to one or more connector elements depending +on the number of layers of the fastener . A single connector element is associated +with each layer, and the two nodes of the connector element correspond to the fastening points of the two +adjacent surfaces. When specifying a multi-layer fastener, the connector elements for each layer should +share nodes with the connector elements of adjacent layers. +200 +100 +single layer fastener modeled with connectors +200 +100 +201 +101 +nodes +connector elements +positioning point location specified by user +multi-layer fastener modeled with connectors +Figure 34.3.4–2 Single- and multi-layer fasteners modeled with connector elements. +For a single-layer fastener the positioning point used to locate the fastener and its fastening points +is taken as the nodal coordinates of the first node of the connector element. For a multi-layer fastener +the positioning point is taken as the first node of the first connector in a linked set of connectors with as +many members as layers. Examples of defining a single-layer and multi-layer fastener are included at +the end of this section. +Input File Usage: +Abaqus/CAE Usage: +Use the following options: +*FASTENER, INTERACTION NAME=name, ELSET=element set label +blank line +*ELEMENT, TYPE=CONN3D2, ELSET=element set label +*CONNECTOR SECTION, ELSET=element set label +For point-based fasteners in Abaqus/CAE, you cannot define the connector +elements directly; the connector elements are generated by Abaqus. +Connector elements generated by Abaqus +In this approach you do not need to explicitly define the connector elements that connect the fastening +points of the fastener. The fastener interaction refers to an empty element set. You must specify a +connector section definition that refers to this element set. In addition, you assign a reference node set +containing a list of user-defined nodes to the fastener interaction. The nodes in this reference node set +are used as positioning points to locate the fasteners. +If single-layer fasteners are to be modeled, Abaqus generates single connector elements with each +node in the reference node set becoming the first node of a connector element. The second node of each +connector element will be generated internally by Abaqus. If multi-layer fasteners are to be defined, +Abaqus generates linked sets of connector elements with each node in the reference node set becoming +the first node of the first connector element in each linked set. The subsequent nodes in each linked set will +be generated internally by Abaqus. For multi-layer fasteners each linked set contains as many connector +elements as the number of layers in the fastener. The connector elements are given internally generated +element numbers and assigned to the named user-specified element set. You can use this element set to +request output for these connector elements. However, this element set should not be included in another +element set definition. +Input File Usage: +Abaqus/CAE Usage: +Use the following options: +*FASTENER, INTERACTION NAME=name, ELSET=element set label, +REFERENCE NODE SET=node set label +blank line +*NSET, NSET=node set label +*CONNECTOR SECTION, ELSET=element set label +Interaction module: Special→Fasteners→Create: Point-based: +select positioning points: Property: Section: Connector +section: select connector section +Example: using connector elements to define single-layer fasteners directly +To define a single-layer fastener directly using connector elements: +• Define two connector elements with user element numbers 100 and 200 and user-defined node +numbers 1, 2 and 3, 4, respectively, and include them in an element set. Nodes 1 and 3 act as +the positioning points for the two fasteners . +• Refer to the element set in the fastener interaction and connector section definitions. +• Assign section properties to the fasteners. Suppose in this example that relative displacements +between the fastening points are to be allowed. Therefore, the fasteners must be assigned a section +that has available components of motion; for example, a CARTESIAN section can be used. +• The relative displacement between the fastening points gives rise to elastic deformations. Hence, +the material between the fasteners is modeled as linear elastic with a spring stiffness of 10000 using +connector elasticity. +The following input can be used: +*FASTENER, INTERACTION NAME=fastinter, ELSET=fastconn, PROPERTY=fastprop +blank line +surface1, surface2 +*ELEMENT, TYPE=CONN3D2, ELSET=fastconn +100, 1, 2 +200, 3, 4 +*CONNECTOR SECTION, ELSET=fastconn, BEHAVIOR=behav +CARTESIAN, +*CONNECTOR BEHAVIOR, NAME=behav +*CONNECTOR ELASTICITY, COMPONENT=1 +10000, +*CONNECTOR ELASTICITY, COMPONENT=2 +10000, +*CONNECTOR ELASTICITY, COMPONENT=3 +10000, +Example: using connector elements to define multi-layer fasteners directly +To define a multi-layer fastener directly using connector elements: +• Define two linked sets of connector elements with each linked set containing exactly two connectors. +The first linked set comprises element numbers 100 and 101, with node numbers 1, 2 and 2, 3, +respectively. The second linked set comprises element numbers 200 and 201, with node numbers +4, 5 and 5, 6, respectively. Include the connector elements in an element set. Nodes 1 and 4 act as +the positioning points for the two fasteners . +• Refer to the element set in the fastener interaction and connector section definitions +• Assign section properties to the fasteners. Suppose in this example that rigid beam-type behavior +between the fastening points is to be modeled; in that case the fasteners must be assigned a BEAM +section. +The following input can be used: +*FASTENER, INTERACTION NAME=fastinter, ELSET=fastconn, PROPERTY=fastprop +blank line +surface1, surface2, surface3 +*ELEMENT, TYPE=CONN3D2, ELSET=fastconn +100, 1, 2 +101, 2, 3 +200, 4, 5 +201, 5, 6 +*CONNECTOR SECTION, ELSET=fastconn +BEAM, +Specifying the positioning points, projection method, and fastening points +Each interaction defines one or more fasteners. The number of individual fasteners is equal to the number +of positioning points used to locate the fasteners. Positioning points are nodes defined at the fastener +locations and assigned as a reference node set to the interaction. +In general, a positioning point should be located as close to the surfaces being connected as possible. +The reference node specifying the positioning point can be one of the nodes on the connected surfaces +or can be defined separately. Abaqus determines the actual points where the fastener layers attach to +the surfaces that are being connected by first projecting the positioning point onto the closest surface. +Abaqus offers the following projection methods to find fastening points on the specified surfaces to form +fasteners: +• Face-to-face +• Face-to-edge +• Edge-to-face +• Edge-to-edge +The choice of method depends on how the surfaces are oriented relative to each other. +Fastening surfaces that are nearly parallel to each other +Most commonly the surfaces to be fastened together are nearly parallel to each other; in which case the +fastening points are located on element facets away from the periphery of the surfaces. The face-to-face +projection method is most appropriate for such situations. It is also the default projection method. +In the face-to-face projection method, Abaqus projects each positioning point onto the closest +surface along a directed line segment normal to the surface. Alternatively, you can specify the projection +direction. Specifying the direction may be useful when two-dimensional drawings are used to identify +the positioning point locations and those locations are known precisely in two dimensions but not in a +third. For this case the direction specified is typically the normal to the plane of the drawing. +Once the fastening point on the closest surface has been identified, Abaqus determines the points on +the other surface or surfaces to be connected by projecting the first fastening point onto the other surfaces +along the fastener normal direction, which is typically normal to the closest surface. Figure 34.3.4–3 +shows the two ways of locating the projection points. When surfaces to be fastened are not exactly +parallel, Abaqus sometimes sets attachment points to be at the closest facet edges or corner on the surface, +rather than along the fastener normal direction. +The location of the positioning point (a node in the reference node set) might not coincide with the +locations of the fastening points found by Abaqus. Hence, the coordinates of the node at the positioning +point may change from their user-prescribed values when the node is shifted to a fastening point. If +the node at the positioning point is part of the connectivity of a user-defined element, this can cause +the element whose connectivity includes that node to undergo unacceptable initial distortions. In such +situations it is recommended that you define the node at the positioning point separately. In general, you +should not specify this node to be one of the nodes of the connected surfaces. +Input File Usage: +Use the following option to allow Abaqus to define the projection direction: +*FASTENER, REFERENCE NODE SET=node set label, ATTACHMENT +METHOD=FACETOFACE (default) +blank line +Use the following option to define the projection direction directly: +*FASTENER, REFERENCE NODE SET=node set label, ATTACHMENT +METHOD=FACETOFACE (default) +x-component, y-component, z-component +Positioning +point +Projection direction +specified by user +Projection normal +for surface +Positioning point +First fastening +point +Second fastening +point +Figure 34.3.4–3 Directed and normal projection to locate the fastening points +for the face-to-face projection method. +Abaqus/CAE Usage: +Use the following input to allow Abaqus to define the projection direction: +Interaction module: Special→Fasteners→Create: Point-based: select +positioning points: Domain tabbed page: Direction vector: Default, +Criteria tabbed page: Attachment method: Face-to-Face +Use the following input to define the projection direction directly: +Interaction module: Special→Fasteners→Create: Point-based: select +positioning points: Domain tabbed page: Direction vector: Specify, +Criteria tabbed page: Attachment method: Face-to-Face +Fastening nearly perpendicular surfaces +When you need to fasten surfaces that are perpendicular or nearly perpendicular to each other; i.e., +forming a T-intersection, the face-to-edge or the edge-to-face projection methods are appropriate choices. +Figure 34.3.4–4 shows attachments for the face-to-edge and edge-to-face projection methods. +Creating the first fastening point on a face +In the face-to-edge projection method Abaqus projects the positioning point onto the closest surface along +a directed line segment normal to the surface. The subsequent fastening points are found by searching +for the closest points on the remaining specified surfaces. The closest fastening point may fall on the +edge or a corner of a surface. +Input File Usage: +*FASTENER, REFERENCE NODE SET=node set label, +ATTACHMENT METHOD=FACETOEDGE +blank line +First +fastening +point +Subsequent +fastening point +First +fastening +point +Positioning +point +Subsequent +fastening point +Positioning +point +Figure 34.3.4–4 Face-to-edge and edge-to-face projection methods to locate fastening +points for surfaces that form T-intersections. +Abaqus/CAE Usage: +Interaction module: Special→Fasteners→Create: Point-based: select +positioning points: Criteria: Attachment method: Face-to-Edge +Creating the first fastening point on an edge +In the edge-to-face projection method, the first fastening point is found by searching for the closest point +on the specified surface or surfaces. The closest point may be on the edge or corner of the surface. For +subsequent fastening points Abaqus projects the previous fastening point along a directed line segment +normal to the surface. +Input File Usage: +*FASTENER, REFERENCE NODE SET=node set label, +ATTACHMENT METHOD=EDGETOFACE +blank line +Abaqus/CAE Usage: +Interaction module: Special→Fasteners→Create: Point-based: select +positioning points: Criteria: Attachment method: Edge-to-Face +Fastening abutting surfaces +When it is desired to form fasteners between surfaces that are butting against each other, the edge-to-edge +projection method is appropriate. In this method the first as well as the subsequent fastening points are +located by searching for the closest point on the specified surface or surfaces. The fastening points in this +method may be located on the edge of a surface. Figure 34.3.4–5 shows attachments for the edge-to-edge +projection method. +Input File Usage: +*FASTENER, REFERENCE NODE SET=node set label, +ATTACHMENT METHOD=EDGETOEDGE +blank line +First fastening +point +Positioning +point +Subsequent +fastening point +Figure 34.3.4–5 Edge-to-edge projection method to locate fastening points for abutting surfaces. +Abaqus/CAE Usage: +Interaction module: Special→Fasteners→Create: Point-based: select +positioning points: Criteria: Attachment method: Edge-to-Edge +Specifying the surfaces to be fastened +Once the positioning points have been specified, the surfaces to be fastened can be specified using two +different approaches. In the first approach you directly specify the surfaces that are to be connected with +a fastener. In the second approach you specify a search zone, and Abaqus automatically identifies the +surfaces that are to be connected. However, in the second approach Abaqus does not distinguish between +coincident facets. Hence, if coincident facets are to be fastened, you should specify distinct surfaces +containing each of the coincident facets and use the first approach. Only element-based surfaces defined +on faces can be fastened together . +Forming fasteners on user-specified surfaces +If you specify multiple surfaces as part of the interaction definition, the surfaces to be fastened are +restricted to these surfaces. In general, specifying multiple surfaces is the preferred way of defining +fasteners; this method leads to a more precise fastener construct definition. The number of layers of each +fastener is one less than the number of surfaces specified. One fastening point is found on each surface. +Input File Usage: +*FASTENER +first data line +surface1, surface2, surface3, etc. +Abaqus/CAE Usage: +Interaction module: Special→Fasteners→Create: Point-based: Domain: +Approach: Fasten specified surfaces by proximity, select surfaces +When you select multiple surfaces for a single surface region, Abaqus/CAE +combines the multiple surfaces using the single-surface search method, as +described in “Forming fasteners on surfaces inside a user-specified search +zone” below. +Controlling connectivity of fasteners on user-specified surfaces +By default, the connectivity of the fastening points is determined by their relative position along the +fastener projection direction. For example, the default connectivity for the two-layer example shown in +Figure 34.3.4–1 connects fastening point A to point B (layer 1) and point B to point C (layer 2). +You can control the connectivity of the fastening points when the fasteners are formed on user- +specified surfaces. You can specify that the connectivity of the fastening points be defined by the order +in which you specified their associated surfaces. +Input File Usage: +*FASTENER, UNSORTED +first data line +surface1, surface2, surface3, etc. +If user-specified surfaces are not included on the data lines, the UNSORTED +parameter is ignored. +Abaqus/CAE Usage: +Interaction module: Special→Fasteners→Create: Point-based: Domain: +Approach: Fasten in specified order, select surfaces +Forming fasteners on surfaces inside a user-specified search zone +If you do not specify any surfaces as part of the interaction definition, Abaqus searches for fastening +points on all element facets that fall within a sphere of user-specified radius R with its center at the +positioning point. If you do not specify the search radius, Abaqus computes a default search radius +based on five times the facet thickness (for shell element facets) or the characteristic element length (for +other element types) in the vicinity of each positioning point. +To refine the search, you can specify a single surface definition that will limit the facet search to +element facets belonging to that surface. In this case you must define a collective surface that includes +at least each connected surface. A combined surface can also be used . +To refine the search further, you can specify a positive integer value, N, for the number of layers of +each fastener. Abaqus searches for the +fastening points closest to the positioning point. If BEAM +MPCs are used to model the fastener, a warning message is issued if the requisite number of fastening +points is not found. However, if connector elements are used to model the fastener and the requisite +number of fastening points is not found, Abaqus issues an error message. Thus, when specifying the +number of layers, you should ensure that the search radius has been specified such that +fastening +points can be found. +If multiple surfaces are listed as part of the fastener definition, the number of layers for each fastener +is ignored. If a user-specified search radius is used for the multiple surface case, Abaqus searches for +fastening points on all facets belonging to each of the listed surfaces that fall within a sphere of user- +specified radius R with its center at the positioning point. Facets of the listed multiple surfaces that +lie outside this sphere are not included in the search. A maximum of 15 layers can be specified for a +particular fastener definition. +Input File Usage: +*FASTENER, SEARCH RADIUS=R, NUMBER OF LAYERS=N +first data line +Abaqus/CAE Usage: +Interaction module: Special→Fasteners→Create: Point-based: Criteria: +Search radius: Specify: R, Maximum layers for projection: Specify: N +Defining the radius of influence +Each fastening point is associated with a group of nodes on the surface in the immediate neighborhood +of the fastening point called a region of influence. The motion of the fastening point is then coupled in +a weighted sense to the motion of the nodes in this region by a distributed coupling constraint. Several +weighting options are available and are discussed in the next section. +To define the region of influence, Abaqus computes an internal radius of influence based on +the geometric properties of the fastener, the characteristic length of the connected facets, and the +type of weighting function used. The default radius of influence is always chosen to be the largest +of the internally computed radius of influence, the physical fastener radius, and the distance of the +projection point to the closest node. You can also specify the desired radius of influence. However, +Abaqus overrides a user-specified radius of influence that is smaller than the computed default radius of +influence. In any case each region of influence will contain a minimum of three nodes. +Input File Usage: +*FASTENER, RADIUS OF INFLUENCE=distance +blank line +Abaqus/CAE Usage: +Interaction module: Special→Fasteners→Create: Point-based: +Adjust: Influence radius: Specify: distance +Defining the weighting method +The weighting methods available for the distributed coupling constraints created for a fastener +interaction are the same as those available for the surface-based coupling constraints in Abaqus . Besides an area-based uniform weighting scheme, various +weighting methods are provided that monotonically decrease with radial distance from the fastening +point: linear, quadratic, and cubic polynomial weight distributions. By default, Abaqus uses the uniform +weighting method. You can modify the default weighting distribution. +The default radius of influence calculated by Abaqus is larger for higher-order weighting methods +since the resulting weights for nodes away from the fastening point contribute comparatively little to the +motion of the fastening point. Hence, to ensure that there is a sufficient “smearing” effect, it becomes +necessary to increase the number of nodes in the region of influence by increasing the size of the default +radius of influence. +In comparison, for a uniform weighting scheme, surface nodes away from the +fastening point contribute significantly to the motion of the fastening point. For this case the default +radius of influence chosen can be comparatively small, since even with a small number of nodes in the +region of influence, the smearing effect is sufficiently strong. If fewer than three cloud nodes are found, +increasing the radius of influence may help in forming the fastener by including more nodes in the cloud +of coupling nodes. +Use the following option to specify a uniform weight distribution: +MESH-INDEPENDENT FASTENERS +*FASTENER, WEIGHTING METHOD=UNIFORM +blank line +Use the following option to specify a linear weight distribution: +*FASTENER, WEIGHTING METHOD=LINEAR +blank line +Use the following option to specify a quadratic polynomial weight distribution: +*FASTENER, WEIGHTING METHOD=QUADRATIC +blank line +Use the following option to specify a cubic polynomial weight distribution: +*FASTENER, WEIGHTING METHOD=CUBIC +blank line +Abaqus/CAE Usage: +Interaction module: Special→Fasteners→Create: Point-based: +Formulation: Weighting method: Uniform, Linear, Quadratic, or Cubic +Defining the fastener orientation +Each fastener is formulated in a local coordinate system that rotates with the motion of the fastener. By +default, Abaqus defines the local system by projecting the global coordinate system onto the surfaces +that are being fastened according to the usual convention for surfaces in space . Local directions specified in this manner are such that the local z-axis for each fastener +is normal to the surface that is closest to the reference node for the fastener. +You can override the default local system by specifying a local coordinate system for the fastener +interaction. Generally, the user-defined orientation should be such that the local z-axis of the orientation +is approximately normal to the surfaces that are being connected and the local x- and y-axes are +approximately tangent to the surfaces that are being connected. By default, Abaqus adjusts the +user-defined orientation such that the local z-axis for each fastener is normal to the surface that is closest +to the reference node for the fastener. In cases where you wish to define the local directions precisely, +you can specify that Abaqus should not adjust them. +Fasteners support only rectangular, cylindrical, and spherical orientation definitions. Additional +rotations defined as part of the orientation definition are ignored. +In geometrically nonlinear analysis steps the local directions rotate with the motion of the fastener +reference node. +Local coordinate system when connector elements are used +If a connector element is used to model a fastener, the local coordinate system defined on the connector +section, +, to determine the +final local coordinate system of the connector element, +, operates on the local coordinate system for the fastener, +. In other words, +and +In the above equations +are assumed to be orthogonal rotation matrices +with the local 1-, 2-, and 3-directions being the first, second, and third rows, respectively. The local +coordinate system for a connector element modeling a fastener should be specified with respect to +the local coordinate system of the fastener. The orientation displayed in the Visualization module of +Abaqus/CAE (Abaqus/Viewer) is +at all fastener locations unless you specify not to +write the orientations to the database; in this case, only +is displayed. If connector field output +is requested, field output for additional nodal rotation at the connector nodes is generated automatically +to ensure that the appropriate connector orientation directions are displayed as the analysis progresses. +Otherwise, the orientation +computed at the beginning of the analysis is displayed at all +times with the updated orientations used for computation purposes. +For example, suppose you use a HINGE connector and want the released rotational degree of +freedom, which is in the connector’s local 1-direction, to be normal to the surfaces that are being +fastenened. If the default local coordinate system is used for the fastener (local 3-direction normal to the +surface), the local 1-direction for the connector should be set to (0., 0., 1.); i.e., the local 3-direction of +the fastener. When compounded with the local coordinate system for the fastener, the local 1-direction +for the connector will be normal to the surface. See “Mesh-independent spot welds,” Section 5.1.16 of +the Abaqus Verification Manual, for an example of a compounded orientation. +Input File Usage: +*FASTENER, ORIENTATION=orientation name, +ADJUST ORIENTATION=NO +blank line +Abaqus/CAE Usage: +Interaction module: Special→Fasteners→Create: Point-based: Adjust: +Fastener CSYS: Edit: select local coordinate system, toggle off Adjust +CSYS to make local Z-axis normal to closest surface +Clarifications regarding the computation of +A few clarifications regarding the default definition of +are necessary for a precise +understanding of the behavior when connector elements are used to model fasteners. The positioning +point is always projected on the closest surface to be fastened. Therefore, the choice of coordinates +of the reference node relative to the stack of surfaces to be fastened determines which surface is used +to compute the local directions. Typically this choice does not matter much in realistic applications +because the surfaces to be fastened are more or less parallel to each other in the fastener area. +The projection of the reference node on the closest surface generates a fastening point for the +connector element. The local z-axis for each fastener ( +) is normal to the surface at this fastening +point. The fastening point generated on the closest surface is by default the first fastening point and, +therefore, the first connector node. The precise direction into which the local z-axis is pointing is chosen +such that the dot product with the unit vector pointing from the first node of the connector to the second +node of the connector is positive. As explained above, you can control the connectivity of the fastening +points in the connectors by specifying unsorted surfaces. Therefore, you can control the precise direction +the local z-axis is pointing along the surface normal by either selecting appropriate coordinates for the +reference node and/or by using unsorted surfaces. +The two tangential directions in +are computed by default according to the usual +convention for surfaces in space . The global X-axis is projected +onto the closest surface at the location of the fastening point to determine the local x-axis in +. +If the global X-axis is within 0.1 degrees of being normal to the surface, the local x-axis in +is +the projection of the global Z-axis on the closest surface. The local y-axis in +is then at right +angles to the local x-axis and z-axis so that the three local axes form a right-handed set. +In the rare cases when the default definition of +does not suit your application, you can +always specify the orientation directly. +Common modeling practices +In most applications the default choice for +at both connector nodes would result in a +combined with a choice of global system for +that is most suitable. The +connection type that you choose depends on several modeling considerations, but very often the +BUSHING connection type offers the best choice. To simplify the discussion, consider that only +two surfaces are being fastened, a very common situation as illustrated in the spot weld example in +“Connector functions for coupled behavior,” Section 31.2.4. For this common choice, +has the local z-axis normal to the closest surface and pointing from the first fastening point (first +connector node) toward the second fastening point (second connector node). This choice ensures that +for a fastener subjected to a tension load (fastened plates pulled apart) a positive force always develops +in the connector along the local z-axis (CTF3) regardless of the choice of coordinates for the positioning +point and/or use of unsorted surfaces. Conversely, if a compression load is applied (fastened plates +pressed against each other), a negative force develops in the connector. +In most cases, the behavior in the tangential plane defined by the local x- and local y-axes is isotropic; +therefore, the precise orientation of these two axes is of less interest to you. The spot weld example in +“Connector functions for coupled behavior,” Section 31.2.4, illustrates such a typical case where the +(isotropic) magnitude of two in-plane forces ( +) are used in the +kinetic behavior of the connector element. +) and of the two moments ( +If you need to specify anisotropic behavior in the tangential plane, you need to understand precisely +how the directions in +are defined. As explained above, the choice of coordinates for the +positioning point relative to the stack of surfaces to be fastened and/or use of unsorted surfaces determines +the precise direction of the default local axes. In most cases you have two common modeling choices. In +the first case you can specify the coordinates of the positioning points to be exactly on or very close to the +surface onto which the first fastening points (connector nodes) are to be placed and use the default sorted +surfaces. In this case you do not need to specify the surfaces to be fastened individually. However, in +many practical situations imprecise geometry for the surfaces to be fastened and/or inexact coordinates +of the fastener reference nodes make the consistent placement of the reference nodes in the vicinity of +one particular surface very hard to accomplish. The second modeling technique consists of using sorted +surfaces. The exact location of the reference node with respect to the surface stack to be fastened is not +that important because the first fastening point is always on the first specified surface. In this case you +do have to specify two or more individual surfaces to be fastened. In the rare cases when neither of these +modeling techniques suits your application, you can specify the fastener orientation directly to match +your needs exactly. +Defining the surface coupling method +There are two methods available to couple the motion of each fastening point to the motion of the +associated coupling nodes on the fastened surfaces: the continuum coupling method and the structural +coupling method. The continuum coupling method is used by default. +In many cases when the pair of fastened surfaces are close to each other, unrealistic contact +interactions may occur between the two surfaces if the continuum coupling method is used. This +is particularly the case in shell bending applications. Moreover, in many situations the continuum +coupling method can yield an overly stiff response if the two surfaces are pried apart, especially when +the fastener radius is small. The structural coupling method can be used to alleviate these issues. +Continuum coupling method +The default continuum coupling method couples the translation and rotation of each fastening point to +the average translation of the group of coupling nodes on each of the fastened surfaces. The constraint +distributes the forces and moments at the fastening point as a coupling node-force distribution only. The +force distribution is equivalent to the classic bolt pattern force distribution when the weight factors are +interpreted as bolt cross-section areas. For each pair of fastening point and group of coupling nodes, +the constraint enforces a rigid beam connection between the fastening point and a point located at the +weighted center of position of the coupling nodes. The formulation is discussed in detail in “Distributing +coupling elements,” Section 3.9.8 of the Abaqus Theory Manual. +Input File Usage: +*FASTENER, COUPLING=CONTINUUM +Abaqus/CAE Usage: +Interaction module: Special→Fasteners→Create: Point-based: +Formulation: Coupling type: Continuum distributing +Structural coupling method +The structural coupling method couples the translation and rotation of each fastening point to the +translation and the rotation motion of the group of coupling nodes on each of the fastened surfaces. The +constraint distributes forces and moments at the fastening point as coupling nodes forces and moments. +For this coupling method to be active, all rotation degrees of freedom at all coupling nodes must be +active (as would be the case when shells are fastened together) and all degrees of freedom must be +constrained (which is the default; see “Defining fastener properties” below). +With respect to translations, for each pair of fastening point and group of coupling nodes, the +constraint enforces a rigid beam connection between the fastening point and a moving point that remains +at all times in the vicinity of the fastened surface. The location of this moving point is determined by the +current curvature of the surface, the current location of the weighted center of position of the coupling +nodes, and the fastener projection direction. This choice avoids unrealistic contact interactions between +the fastened surfaces when the surfaces are close to each other (typically the case). +With respect to rotations, for each pair of fastening point and group of coupling nodes, the constraint +is different along different local directions. Along the projection direction (the twist direction), the +constraint is identical to the one enforced via the continuum coupling method . By contrast, the rotational constraint in the plane +perpendicular to the projection direction relates the in-plane fastening point rotations to the in-plane +rotations of the coupling nodes in the immediate vicinity of the fastening point. This choice provides a +more realistic response when the fastened surfaces are pried apart. +Input File Usage: +Abaqus/CAE Usage: +*FASTENER, COUPLING=STRUCTURAL +Interaction module: Special→Fasteners→Create: Point-based: +Formulation: Coupling type: Structural distributing +Defining fastener properties +Each fastener interaction definition must refer to a property, which defines the geometric section +properties of the fastener. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options: +*FASTENER, PROPERTY=fastener property name +*FASTENER PROPERTY, NAME=fastener property name +Interaction module: Special→Fasteners→Create: Point-based: Property +Geometric section quantities +Fasteners are assumed to have a circular projection onto the connected surfaces. You are required to +specify the radius of the fastener. +Input File Usage: +*FASTENER PROPERTY +Abaqus/CAE Usage: +Interaction module: Special→Fasteners→Create: Point-based: +Property: Physical radius: r +Mass +In many cases fasteners may add mass to the assembly. To model the added mass, specify an additional +mass that is assigned to each fastener and lumped to the fastening points. +*FASTENER PROPERTY, MASS=mass value +Interaction module: Special→Fasteners→Create: Point-based: +Property: Additional mass: mass value +Abaqus/CAE Usage: +Input File Usage: +Releasing degrees of freedom on fasteners using connector elements +For fasteners modeled with connector elements, translational as well as rotational degrees of freedom +can be released by prescribing connector section types that have unconstrained (available) degrees of +freedom. For example, a HINGE connector can be used to release the rotational degree of freedom in +the connector’s local 1-direction. +Releasing degrees of freedom on fasteners using BEAM MPCs +For fasteners modeled with BEAM MPCs, the moment constraint between the rotation degrees of +freedom at the fastening points and the average rotation of the coupling nodes can be released in one, +two, or three directions. You can specify the moment constraint directions in the default local coordinate +system or a user-defined local coordinate system. The three translational degrees of freedom at the +fastening points are always coupled to the average translation of the coupling nodes. You specify the +degrees of freedom of the fastening point to be coupled to the average motion of the coupling nodes +as part of the fastener property definition. +If no degrees of freedom are specified as part of the fastener property definition, all six degrees of +freedom are coupled. If you specify one or more degrees of freedom but not all available translation +degrees of freedom, Abaqus issues a warning message and adds all the available translation degrees of +freedom to the constraint. If a user-specified local orientation is specified for the fastener interaction, the +local degrees of freedom are with respect to the user-defined coordinate system. +*FASTENER PROPERTY +section properties +first dof, last dof +Input File Usage: +For example, if the default local coordinate system is used, the following +property definition would release the relative rotation constraint of the +connected parts about the surface normal: +*FASTENER PROPERTY +section properties +1, 5 +The above property definition might be used to approximate a riveted +connection. +Abaqus/CAE always constrains all translational degrees of freedom in a +fastener. Use the following input to remove constraints on the rotational +degrees of freedom: +Interaction module: Special→Fasteners→Create: Point-based: +Formulation: toggle off UR1, UR2, or UR3 +Abaqus/CAE Usage: +Overconstraints in fasteners modeled with BEAM MPCs +There are several instances in which a model with fasteners modeled with BEAM MPCs might be +overconstrained. Described below are two potential overconstraints that Abaqus automatically attempts +to detect and resolve during solver input file processing. +Fasteners and rigid bodies +Fasteners can be used to connect both deformable and rigid element-based surfaces. However, if the +fasteners are modeled with BEAM MPCs, potential overconstraints may arise if more than one rigid +surface is involved in a given fastener definition. Abaqus automatically attempts to remove these types +of overconstraints by allowing at most one rigid surface in any individual fastener definition. A warning +message is generated if an overconstraint of this type is detected. +For example, suppose surfaces A and C in Figure 34.3.4–1 are part of the same rigid body, and +surface B is deformable. Abaqus automatically removes either surface A or surface C from the fastener +definition and only forms the fastener between the deformable surface and the remaining rigid surface. If +surface A and surface C belong to two separate rigid bodies, their respective rigid body reference nodes +will be joined by an internally generated BEAM MPC. +In another example, suppose all three surfaces in Figure 34.3.4–1 are rigid. In this case no fastener +will be formed, and the unique rigid body reference nodes for surfaces A, B, and C will be joined +by beam MPCs. Unresolvable overconstraints may arise if inconsistent kinematic constraints (such as +displacement boundary conditions) are placed on rigid body reference nodes that have been joined by +BEAM MPCs. In this case you must modify the model to resolve the overconstraints. Possible courses of +action include removing some of the rigid surfaces from the fastener definitions or removing inconsistent +kinematic conditions on the rigid body reference nodes. +The above-described procedure to resolve overconstraints with fasteners and rigid bodies will +preserve the kinematics of the original model. In Abaqus/Standard you can bypass the overconstraint +checks and prevent automatic model modifications in the model preprocessor . +Overlapping fasteners +Potential overconstraints exist with rigid fasteners if all the coupling nodes of any associated distributing +coupling element are wholly contained within one or more other fastener definitions. This can happen if +the spacing between positioning points is small compared to the typical element size in a mesh (which is +often the case in automotive models). To avoid overconstraints in this situation, Abaqus uses a penalty +formulation for all fastener distributing coupling elements that satisfy the above criteria. The penalty +distributing coupling formulation relaxes, to a small degree, the constraint between the motion of the +distributing coupling element reference node and its coupling nodes. +Output +If fasteners are modeled using connector elements, connector element output variables can be used to +request output for fasteners . No fastener output is available +if the fasteners are modeled using BEAM MPCs. +34.4 +Embedded elements +• “Embedded elements,” Section 34.4.1 +34.4.1 +EMBEDDED ELEMENTS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Kinematic constraints: overview,” Section 34.1.1 +• *EMBEDDED ELEMENT +• “Defining embedded region constraints,” Section 15.15.8 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +The embedded element technique: +• is used to specify an element or a group of elements that lie embedded in a group of host elements +whose response will be used to constrain the translational degrees of freedom of the embedded +nodes (i.e., nodes of embedded elements); +• can be used in geometrically linear or nonlinear analysis; +• is not available for host elements with rotational degrees of freedom; +• can be used to model a set of rebar-reinforced membrane, shell, or surface elements that lie +embedded in a set of three-dimensional solid (continuum) elements; a set of truss or beam elements +that lie embedded in a set of solid elements; or a set of solid elements that lie embedded in another +set of solid elements; +• will not constrain rotational degrees of freedom of the embedded nodes when shell or beam elements +are embedded in solid elements; and +• can be imported from Abaqus/Standard into Abaqus/Explicit and vice versa. +Introduction +The embedded element technique is used to specify that an element or group of elements is embedded in +“host” elements. The embedded element technique can be used to model rebar reinforcement. Abaqus +searches for the geometric relationships between nodes of the embedded elements and the host elements. +If a node of an embedded element lies within a host element, the translational degrees of freedom at the +node are eliminated and the node becomes an “embedded node.” The translational degrees of freedom of +the embedded node are constrained to the interpolated values of the corresponding degrees of freedom +of the host element. Embedded elements are allowed to have rotational degrees of freedom, but these +rotations are not constrained by the embedding. Multiple embedded element definitions are allowed. +Available embedded element types +Different element types can be used in the element set containing embedded elements and the element +set containing the host elements. However, all the host elements can have only translational degrees of +freedom, and the number of translational degrees of freedom at a node on the embedded element must be +identical to the number of translational degrees of freedom at a node on the host element. The following +general types of “embedded elements-in-host elements” are provided: +• Two-dimensional models: +– Beam-in-solid +– Solid-in-solid +– Truss-in-solid +• Axisymmetric models: +– Membrane-in-solid (Abaqus/Standard only) +– Shell-in-solid +– Solid-in-solid +– Surface-in-solid (Abaqus/Standard only) +• Three-dimensional models: +– Beam-in-solid +– Membrane-in-solid +– Shell-in-solid +– Solid-in-solid +– Surface-in-solid +– Truss-in-solid +Specifying the host elements +By default, the elements in the vicinity of the embedded elements are searched for elements that contain +embedded nodes; the embedded nodes are then constrained by the response of these host elements. To +preclude certain elements from constraining the embedded nodes, you can define a host element set; +the search will be limited to this subset of the host elements in the model. This feature is strongly +recommended if the embedded nodes are close to discontinuities in the model (cracks, contact pairs, +etc.). +Input File Usage: +*EMBEDDED ELEMENT, HOST ELSET=name +The *EMBEDDED ELEMENT option must be included in the model +definition portion of the input file. Multiple *EMBEDDED ELEMENT +options are allowed. +Abaqus/CAE Usage: +Interaction module: Create Constraint: Embedded region: choose Select +Region from the prompt area when selecting the host region +Specifying the embedded elements +You must specify the embedded elements. Individual elements or element sets can be specified. +An embedded element may share some nodes with host elements. These nodes, however, will not +be considered to be embedded nodes. +Input File Usage: +*EMBEDDED ELEMENT +embedded elements +Abaqus/CAE Usage: +Interaction module: Create Constraint: Embedded region: +select the embedded region +Defining geometric tolerances +A geometric tolerance is used to define how far an embedded node can lie outside the regions of the host +elements in the model. By default, embedded nodes must lie within a distance calculated by multiplying +the average size of all non-embedded elements in the model by 0.05; however, you can change this +tolerance. +You can define the geometric tolerance as a fraction of the average size of all non-embedded +elements in the model. Alternatively, you can define the geometric tolerance as an absolute distance in +the length units chosen for the model. If you specify both exterior tolerances, Abaqus uses the tighter +tolerance of the two. The average size of all the non-embedded elements is calculated and multiplied +by the fractional exterior, which is then compared to the absolute exterior tolerance to determine the +tighter tolerance of the two. The exterior tolerance for embedded elements in host elements is indicated +by the shaded region in Figure 34.4.1–1. +Nodes on the host elements +Nodes on the embedded elements +Edges of the host elements +Edges of the embedded elements +Figure 34.4.1–1 The exterior tolerance for embedded elements. +If an embedded node is located inside the specified tolerance zone, the node is constrained to the host +elements. The position of this node will be adjusted to move the node precisely onto the host elements. +If an embedded node is located outside the specified tolerance zone, an error message will be issued. +Input File Usage: +Use the following option to define the tolerance as a fraction: +*EMBEDDED ELEMENT, EXTERIOR TOLERANCE=tolerance +Use the following option to define the tolerance as an absolute distance: +*EMBEDDED ELEMENT, +ABSOLUTE EXTERIOR TOLERANCE=tolerance +Abaqus/CAE Usage: +Interaction module: Create Constraint: Embedded region: Fractional +exterior tolerance or Absolute exterior tolerance +Adjusting the positions of embedded nodes +If an embedded node lies close to an element edge or an element face within a host element, it is +computationally efficient to make a small adjustment to the position of the embedded node so that the +node will lie precisely on the edge or face of the host element. A small tolerance, below which the +weight factors of the nodes on a host element associated with an embedded node will be zeroed out, +is defined. The small weight factors will be redistributed to the other nodes on the host element in +proportion to their initial weights, and the position of the embedded node will be adjusted based on the +new weight factors. This adjustment is performed only at the start of the analysis and does not create +any strain in the model. It is most useful for making small adjustments to make the embedded nodes +lie on the edge or face of a host element. If a large nondefault value of the roundoff tolerance is used +to make significant adjustments to the positions of the embedded nodes, you should carefully review +the mesh obtained after adjusting. +Input File Usage: +Abaqus/CAE Usage: +*EMBEDDED ELEMENT, ROUNDOFF TOLERANCE=tolerance +Interaction module: Create Constraint: Embedded region: +Weight factor roundoff tolerance +Use with other multiple kinematic constraints +If an embedded node is also tied by multi-point, equation, kinematic coupling, surface-based tie, or rigid +body constraints, an overconstraint is introduced and an error message will be issued. If a boundary +condition is applied to an embedded node, the embedded element definition always takes precedence. +The boundary condition will be neglected, and a warning message will be issued. +Defining surfaces on embedded elements +Embedded elements have no exterior (free) surface due to the embedding. Consequently, their faces are +not part of the all-inclusive surface defined automatically for interactions modeled with general contact. +In addition, any surface definitions based on these elements must have the face identifier specified +explicitly . +Limitations +The following limitations exist for the embedded element technique: +• Elements with rotational degrees of freedom (except axisymmetric elements with twist) cannot be +used as host elements. +• Rotational, +temperature, pore pressure, acoustic pressure, and electrical potential degrees of +freedom at an embedded node are not constrained. +• Host elements cannot be embedded themselves. +• The material defined for the host element is not replaced by the material defined for the embedded +element at the same location of the integration point. +• Additional mass and stiffness due to the embedded elements are added to the model. +• If modified tetrahedron elements are used as host elements, only the corner nodes are used to +constrain the appropriate embedded nodes. +Example +Consider the example in Figure 34.4.1–2. +1 3 +Nodes on the host elements +Nodes on the embedded elements +Edges of the host elements +Edges of the embedded elements +Figure 34.4.1–2 Elements lie embedded in host elements. +Elements 3 (truss) and 4 (membrane) lie embedded in elements 1 and 2. Element 1 is formed by nodes a, +b, c, d, e, f, g, and h; element 2 is formed by nodes e, f, g, h, i, j, k, and l; element 3 is formed by nodes A +and B; and element 4 is formed by nodes C, D, E, and F. If the host element set includes elements 1 and +2 and the embedded element sets contain elements 3 and 4, respectively, Abaqus will attempt to find if +there are any embedded nodes (A, B, C, D, E, and F) lying within host elements 1 or 2. If node A is found +to be lying close to the a-b-f-e face of element 1, all the degrees of freedom at node A are constrained to +nodes a, b, f, and e, with appropriate weight factors being determined based on the geometric location +of node A in element 1. Similarly, if node B is found to be lying inside element 1 and node E is found +to be lying close to the g–k edge of element 2, respectively, all the degrees of freedom at node B are +constrained to nodes a, b, c, d, e, f, g, and h, and all the degrees of freedom at node E are constrained +to nodes g and k, with appropriate weight factors being determined based on the geometric location of +node B in element 1 and the geometric location of node E on the g–k edge of element 2, respectively. +You should make sure that all the nodes on the embedded elements are properly constrained to nodes +on the host elements. This can be verified by performing a data check analysis . For each embedded node a list of nodes +that are used to constrain this node and the associated weight factors are output to the data file during the +data check analysis. An error message is issued if an embedded node is not constrained. +Template +*HEADING +… +*NODE +Data line to define the nodal coordinates +*ELEMENT, TYPE=C3D8, ELSET=SOLID3D +Data line to define the solid elements +*ELEMENT, TYPE=T3D2, ELSET=TRUSS +Data line to define the truss elements +*ELEMENT, TYPE=M3D4, ELSET=MEMB +Data line to define the membrane elements +*EMBEDDED ELEMENT, EXTERIOR TOLERANCE=tolerance, HOST ELSET=SOLID3D +TRUSS, MEMB +*STEP +*STATIC (or any other allowable procedure) +Data line to define step time and control incrementation +… +*END STEP +34.5 +Element end release +• “Element end release,” Section 34.5.1 +34.5.1 +ELEMENT END RELEASE +Product: Abaqus/Standard +References +• “Kinematic constraints: overview,” Section 34.1.1 +• *RELEASE +Overview +Element end release: +• allows a rotational degree of freedom or a combination of rotational degrees of freedom to be +released at one or both ends of an element or element set; +• can be used in geometrically linear or nonlinear analysis; and +• is available only for beam and pipe elements in Abaqus/Standard. +Introduction +Element end release is used to model hinged connections (hinged in one, two, or three orthogonal +directions) at one or both ends of the element. By releasing rotational degrees of freedom, an element +end is allowed to rotate freely relative to the node about the chosen degrees of freedom. Any rotational +degrees of freedom that are not released are shared with the node. You must be careful not to release +a given degree of freedom at a node for all elements that share that node; otherwise, the node has no +stiffness for that degree of freedom and Abaqus/Standard issues zero pivot warning messages. +Element end release operates on the element local degrees of freedom. See “Beam element cross- +, t) for beam-type elements. +-axis, the +-axis, and the rotation about the local t-axis for beams in space. For beams +-axis is active (which coincides with rotations about the +section orientation,” Section 29.3.4, for a definition of the local axes ( +The rotational degrees of freedom affected by the release are the rotation about the local +rotation about the local +in a plane, only the rotation about the local +negative global z-axis). +, +Equivalent MPCs +If only one rotational degree of freedom is released, the kinematic constraint is equivalent to MPC type +REVOLUTE plus MPC type PIN between two nodes. If two rotational degrees of freedom are released, +the kinematic constraint is equivalent to MPC type UNIVERSAL plus MPC type PIN. If all rotational +degrees of freedom are released, the kinematic constraint is equivalent to MPC type PIN. See “General +multi-point constraints,” Section 34.2.2, for details. +Identifying the element end involved in the release +Either element sets or individual elements can be specified for a release definition. Degrees of freedom +can be released at the first, second, or first and second ends of an element. The first end of the element, +S1, is node 1 on the element as defined by the element connectivity; the second end, S2, is the last node +(node 2 or 3, as appropriate) on the element. See “Beam element library,” Section 29.3.8, for a definition +of the node ordering for beam elements. +Identifying the local rotational degrees of freedom involved in the release +Rotation combination codes rather than degrees of freedom are specified to identify the rotational degrees +of freedom involved in the release. +M1 +M2 +refers to the rotation about the +refers to the rotation about the +-axis, +-axis, +M1-M2 refers to a combination of rotational degrees of freedom about the +-axis and the +-axis, +M1-T +M2-T +refers to the rotation about the t-axis, +refers to a combination of rotational degrees of freedom about the +refers to a combination of rotational degrees of freedom about the +-axis and the t-axis, +-axis and the t-axis, and +ALLM represents a combination of all the rotational degrees of freedom (i.e., M1, M2, and T). +Input File Usage: +*RELEASE +element number or element set, element end ID, release combination code +-axis at the +For example, to release the rotational degree of freedom about the +first end of element 10 and all the rotational degrees of freedom at the second +end of the element, use the following input: +*RELEASE +10, S1, M1 +10, S2, ALLM +Use with transformed coordinate systems +Transformations applied to released nodes (“Transformed coordinate systems,” Section 2.1.5) have no +influence on the release. The release operates on the local degrees of freedom for the element. +Reading the data from an alternate input file +The data for a release definition can be contained in a separate input file. +Input File Usage: +*RELEASE, INPUT=file_name +If the INPUT parameter is omitted, it is assumed that the data lines follow the +keyword line. +34.6 +Overconstraint checks +• “Overconstraint checks,” Section 34.6.1 +34.6.1 +OVERCONSTRAINT CHECKS +Product: Abaqus/Standard +References +• “Rigid body definition,” Section 2.4.1 +• “Connectors: overview,” Section 31.1.1 +• “Boundary conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1 +• “General multi-point constraints,” Section 34.2.2 +• “Mesh tie constraints,” Section 34.3.1 +• “Coupling constraints,” Section 34.3.2 +• “Mesh-independent fasteners,” Section 34.3.4 +• “Defining contact pairs in Abaqus/Standard,” Section 35.3.1 +• *BASE MOTION +• *CONSTRAINT CONTROLS +Overview +An overconstraint means applying multiple consistent or inconsistent kinematic constraints. Many +models have nodal degrees of freedom that are overconstrained. Such overconstraints may lead +to inaccurate solutions or nonconvergence. Common examples of situations that may lead to +overconstraints include (but are not limited to): +• contact slave nodes that are involved in boundary conditions or multi-point constraints; +• edges of surfaces involved in a surface-based tie constraint that are included in contact slave surfaces +or have symmetry boundary conditions; and +• boundary conditions applied to nodes already involved in coupling or rigid body constraints. +The overconstraint checks performed in Abaqus/Standard: +• check for overconstraints caused by combinations of the following: base motions, boundary +conditions, contact pairs, coupling constraints, linear constraint equations, mesh-independent spot +welds, multi-point constraints, rigid body constraints, and surface-based tie constraints; +• check for overconstraints resulting from kinematic constraints introduced through connector +elements, coupling elements, special-purpose contact elements, and elements with incompressible +material behavior; +• identify through detailed messages the constraints that cause overconstraints; +• automatically resolve a limited set of consistent overconstraints detected during model +preprocessing and during an Abaqus/Standard analysis; +• use the equation solver to detect overconstraints that cannot be resolved automatically; and +• can have the default behavior modified. +Overconstraints: general remarks +In general, the term overconstraint refers to multiple constraints acting on the same degree of freedom. +Overconstraints are then categorized as consistent (if all the constraints are compatible with each other) +or inconsistent (if the constraints are incompatible with each other). Consistent overconstraints are also +called redundant constraints, and inconsistent overconstraints are also called conflicting constraints. +In Abaqus/Standard the following types of constraints, in combination, may lead to overconstraints: +• boundary conditions or base motions, +• contact pairs, +• coupling constraints, +• mesh-independent spot welds, +• multi-point constraints or linear constraint equations, +• surface-based tie constraints, and +• rigid body constraints. +In addition to these constraints the following elements impose kinematic constraints and, when used in +combination with each other or with the above constraints, may lead to overconstraints: +• connector elements, +• special-purpose contact elements, and +• hybrid elements for incompressible material response. +An illustration of several consistent overconstraints is given in Figure 34.6.1–1. The upper block +is built from three separately meshed regions, which are connected together using a surface-based tie +constraint. This block is in contact with the lower rigid block, which is made rigid by specifying a rigid +body constraint. The rigid block’s reference node is fixed. Symmetry boundary conditions are used at +the left edge of the upper block, and rough friction is defined for the surface interaction between the +upper and lower blocks. The following redundant constraints can be identified: +• Intersecting tie constraints: At (A) three nodes share the same location, and their relative motions +are constrained by two surface-based tie constraints (one vertical and one horizontal). Only two +constraints (two dependent nodes and one independent node) are needed to fully constrain the +motion of the three nodes, but three constraints are generated internally (one for the horizontal tie +constraint and two for the vertical one). Therefore, one redundant constraint exists. +• Tie constraint and symmetry boundary condition: At (B) nodes 141 and 151 have their motion +constrained horizontally by the symmetry boundary condition, but their relative motion is also +constrained by the surface-based tie constraint. Therefore, one redundant constraint exists. +• Rough friction and symmetry boundary condition: At (C) node 101 is constrained horizontally by +the symmetry boundary condition. The rough friction contact acts in the same direction as the +boundary condition. Therefore, one redundant constraint exists. +reference node ++ +rigid punch +tie constraints +(A) +symmetry +boundary +conditions +(B) +(C) +141 +151 +101 +501 +625 +423 +801 +301 +rigid body reference +node for lower block ++ +rough friction +(D) +symmetry line +Figure 34.6.1–1 Model with redundant constraints. +• Tie constraint and contact interactions: At (D) nodes 801 and 301 are involved in the surface-based +tie constraint, but two contact constraints (one at each node) act in the vertical direction. Therefore, +one redundant constraint exists. +Even in this simple model the number of redundant constraints is surprisingly large. If not appropriately +accounted for, the redundant constraints can lead to convergence difficulties, even nonconvergence. +Moreover, in the cases when a solution is obtained (despite the convergence difficulties), the reported +reaction forces and contact pressures may be inaccurate. +Abaqus/Standard checks for the inappropriate use of combinations of constraints for the majority +of constraint and element types listed in this section. Depending on the complexity of the constraints +involved, Abaqus/Standard identifies three classes of consistent and inconsistent overconstraints. +Overconstraints detected in the model preprocessor +Many relatively simple overconstraints can be identified by inspecting the constraints defined +If a consistent overconstraint is detected, the unnecessary constraints are eliminated +at a node. +automatically and a warning message is generated. +If the overconstraints are inconsistent, the +analysis is stopped and an error message is generated. +Overconstraints detected and resolved in an Abaqus/Standard analysis +Some overconstraints involving contact interactions may become overconstrained only during an +analysis due to changes in contact status. Certain of these cases are detectable and eliminated +automatically by Abaqus/Standard. Appropriate messages are issued. +Overconstraints detected by the equation solver +Many overconstraints involve complex interactions between various constraint definitions and +element types. Automatic resolution of these situations may not be possible. In such cases the +equation solver will detect the overconstraint, and a detailed message listing potential causes of +the problem will be issued. +Overconstraints detected in the model preprocessor +In this section we consider overconstraints that involve two or more of the following: +• surface-based tie constraints, +• rigid body constraints, +• boundary conditions, and +• connector elements. +While the number of cases handled automatically in the model preprocessor is limited, many often- +encountered situations are corrected. The list of overconstraints to be resolved automatically in the +preprocessor is organized based on the constraint types involved. Each case is illustrated by examples. +Intersecting tie constraints +Examples of intersecting tie constraint definitions are shown in Figure 34.6.1–2. In both cases there is +at least one node that, if not properly treated, will be redundantly constrained. In the case on the left, the +three edges belonging to the three surfaces overlap (shown here in an exploded view for clarity). Each +of the three end nodes on either end occupy the same location. Therefore, one redundant tie constraint +exists. In the case shown on the right, four adjacent meshes are “glued” together using four tie constraints. +Only three constraints are needed to “glue” the center nodes together, but four are generated (one from +each tie constraint). Therefore, one constraint is not needed and in both cases one constraint is removed. +Tie constraint inside a rigid body constraint +An example of a tie constraint inside a rigid body constraint is shown in Figure 34.6.1–3(a). Two surfaces +are connected by a tie constraint, and the two element sets are included in the same rigid body. Since the +motion of all the nodes is constrained to the motion of the rigid body’s reference node, the tie constraint +is redundant. The tie constraint definition is removed from the model. +tie constraint between faces +AM–CD AB–HJ +CE–FG HI–FN +C J +tie constraint between faces +ABCD–IJKL +EFGH–KLNM +ABRS–EHPO +nodes B, H, K +are at the same +location +F N +(a) +nodes A, E, L +are at the same +location +(b) +Figure 34.6.1–2 Consistent overconstraints due to intersecting tie constraints. +rigid body includes +all elements +tie constraint +along this line +tie constraint +tie constraint +deformable +rigid +element set 2 +element set 1 +rigid body 1 +rigid body 2 +reference node 1 +reference node 2 ++ ++ +internally +generated +connector +element +(a) +(b) +(c) +Figure 34.6.1–3 Consistent overconstraints due to combinations of tie and rigid body constraints. +Tie constraint between two rigid bodies +An example of a tie constraint between two rigid bodies is shown in Figure 34.6.1–3(b). If the two +surfaces are connected by a tie constraint at more than two or three points (in two- or three-dimensional +analyses, respectively), the tie constraint definition is redundant. A connector type BEAM is placed +between the two reference nodes, and the tie constraint is removed. +Tie constraint between a deformable and a rigid body +An example of connecting a deformable body to a rigid body with a surface-based tie constraint is shown +in Figure 34.6.1–3(c). If the slave surface in the tie constraint definition belongs to the rigid body, the tie +and the rigid body constraints are redundant for the slave nodes. If possible, Abaqus/Standard will switch +the master and the slave surface in the tie constraint definition. If switching the master and the slave +surfaces is not possible due to other modeling restrictions, an error message is issued and the analysis is +stopped. +Intersecting rigid bodies +Figure 34.6.1–4(a) illustrates the case when two rigid bodies partially overlap and, thus, the union of the +two bodies behaves as one rigid body. However, the motion of the nodes in this region is governed by the +motion of the two rigid body reference nodes; hence, the model is overconstrained. In Figure 34.6.1–4(b) +several rigid bodies are included in a larger rigid body definition. The nodes belonging to the included +bodies will be overconstrained. +reference node 1 ++ +reference node 2 +rigid body 1 ++ +internally generated +connector element +(type BEAM) +rigid body 2 +overlapping +region +rigid body 1 +rigid body 2 +reference node 1 +reference node 2 ++ ++ +(a) +(b) +Figure 34.6.1–4 Rigid body including other rigid bodies. +In both cases the rigid body constraint will be enforced only once for the nodes that belong to several +rigid bodies. To enforce the rigid behavior of the ensemble, connector elements of type BEAM are +generated between the rigid body reference nodes to ensure a rigid connection between the intersecting +rigid body definitions. +Tie constraints and boundary conditions +There are numerous cases of overconstraints when a surface-based tie constraint and a boundary +condition are used together, as illustrated in Figure 34.6.1–5. +tie constraint +between faces +BJIE and AFHK +symmetry boundary conditions along +1-direction on the faces CDEB and AFGM +tie constraint +node a +node b +boundary condition of 0.1 at node a, dof 1 +boundary condition of 0.2 at node b, dof 1 +(a) +(b) +Figure 34.6.1–5 Overconstraints involving tie constraints and boundary conditions. +In the first case nodes A and B are constrained to move together by the tie constraint. The vertical +symmetry boundary conditions will constrain the motion of both nodes in the horizontal direction, +generating one redundant constraint. In the second case the two specified boundary conditions conflict, +thus generating a conflicting constraint. +For every tie-dependent node with a boundary condition, Abaqus/Standard first determines which +independent nodes are involved in the tie constraint . +If +only one independent node is involved, Abaqus/Standard will transfer the boundary conditions from +the dependent node to the independent node. +If conflicting boundary conditions are detected at the +independent node during the transferring process, the analysis is stopped and an error message is issued. +If several independent nodes are involved, Abaqus/Standard checks if the specified boundary conditions +at all the nodes involved in the constraint are identical. +If no conflicts are identified, the boundary +conditions at the independent node are redundant and, therefore, ignored. Otherwise, an error message +is issued, and the analysis is stopped. +Rigid body constraints and boundary conditions +Combinations of rigid body constraints and boundary conditions can lead to overconstrained models +when boundary conditions are specified at nodes other than the reference node (Figure 34.6.1–6). In +Figure 34.6.1–6(a) boundary conditions are specified at several nodes belonging to the rigid body. In +Figure 34.6.1–6(b) symmetry boundary conditions are specified on the flat surface of the rigid body, and +the body is spun around an axis perpendicular to the symmetry plane at the reference node. +boundary conditions +specified at +nodes a, b, and c +symmetry boundary +conditions +rigid body ++ +face +normal ++ +reference node +reference node +(a) +rigid +body +(b) +Figure 34.6.1–6 Overconstraints due to boundary conditions +applied at rigid body nodes. +In case (a) if the specified boundary conditions are not consistent with the rigid constraint, the model +will be inconsistently overconstrained. In case (b) if the reference node has the symmetry boundary +conditions, there is no need to have symmetry boundary conditions at the nodes of the flat surface. +Abaqus/Standard will attempt to remove all boundary conditions specified at the dependent nodes and +redefine them at the reference node. To do so, the consistency of the boundary conditions specified at +the dependent nodes is checked. If the boundary conditions are not identical, an error message is issued +and the analysis is stopped (since otherwise the solution of a nonlinear system of equations would be +required in the general case to assess whether the boundary conditions are consistent or not). Otherwise, +Abaqus/Standard will try to merge the boundary conditions at the dependent nodes with those at the +reference node by: +• checking the consistency of the overlapping boundary conditions; +• moving to the reference node any boundary conditions specified at the dependent nodes but not +specified at the reference node; and +• applying additional zero rotational boundary conditions at the reference node to compensate for the +removed displacement constraints from the dependent nodes. +To illustrate, refer to Figure 34.6.1–6(b): as the symmetry boundary conditions specified at the dependent +nodes are consistent with each other, they are removed from the dependent nodes and applied to the +reference node (boundary condition in the 2-direction). In addition, the symmetry constraints preclude +rotations about the 1- and 3-directions; therefore, zero rotational boundary conditions are applied to the +reference node about these axes. +Connector elements and rigid bodies +In most cases detection and automatic resolution of redundant constraints involving connector elements +cannot be done by simple inspection of the constraints involved. However, the examples shown in +Figure 34.6.1–7 are simple enough to be resolved automatically. It is assumed that the connector elements +are connected to nodes on the rigid body whose rotational degrees of freedom are dependent on the +rotation of the reference node. In Figure 34.6.1–7(a) the connector elements are assumed to enforce +some kinematic constraints. They are redundant since the rigid body definition constrains the motion of +all nodes to the motion of the rigid body’s reference node. Abaqus/Standard automatically removes the +connector elements from the model. +reference node +connector +rigid body +composed of +both ELSET1 +and ELSET2 ++ +connector +reference +node 1 ++ +ELSET 1 +ELSET 2 +rigid body 1 +rigid body 2 ++ +reference node 2 +connector +(a) +BEAM connector +(b) +Figure 34.6.1–7 Redundant constraints involving rigid +bodies and connector elements. +When connector elements are placed between two rigid bodies (as in Figure 34.6.1–7(b)), the model +may be redundantly constrained. As shown in Figure 34.6.1–7(b), if a connector element of type BEAM +(or WELD) is placed between two rigid bodies, the connection is rigid and any additional connector +elements between the two rigid bodies are redundant. Abaqus/Standard will automatically remove these +redundant connector elements. +When the ensemble of connector elements placed between two rigid bodies enforces more than +the necessary translational and rotational constraints between the two rigid bodies, but none of the +connectors is of type BEAM (or WELD), only warning messages are issued to signal the overconstraint +In these cases none of the connector elements can be eliminated automatically since the +situation. +connection between the two rigid bodies may become underconstrained. To illustrate this situation, +assume that in Figure 34.6.1–7(b) the two connectors were of type SLOT and TRANSLATOR. Thus, +four translational constraints (in three dimensions) are enforced between the two rigid bodies, rendering +the system overconstrained since only three translational constraints are needed to fully constrain the +relative translation between the two bodies. However, if the SLOT were eliminated from the model, the +model would become underconstrained and different from the original one. Only a warning message +is issued in this case. +Coupling constraints and rigid bodies +When all or some of the nodes involved in a kinematic coupling constraint belong to the same rigid body, +the coupling constraint becomes redundant. The situation is illustrated in Figure 34.6.1–8. Node 101 +is the reference node for the coupling constraint involving nodes 1001–1005. At the same time nodes +1001–1003 are included in the rigid body definition with reference node 102. +rigid body +102 +rigid body +reference node +1001 +1002 +1003 +1004 +101 x +coupling +reference node +1005 +Figure 34.6.1–8 Redundant constraints involving coupling constraints and rigid bodies. +If the coupling constraint was defined as kinematic, it will not be enforced at nodes 1001–1003 +to avoid overconstraining the model. The removed overconstraint may be inconsistent such as when +incompatible boundary conditions are prescribed at the two reference nodes. However, the constraint +will be enforced at nodes 1004 and 1005 since these nodes do not belong to the rigid body. +If a distributing coupling constraint was used instead, the model would not be overconstrained. +However, if node 101 was added to the rigid body definition and nodes 1004 and 1005 were not +included in the coupling constraint, the model would be overconstrained. Indeed, all nodes involved in +the coupling constraint would be already constrained by the rigid body definition, making the coupling +constraint redundant. To avoid the overconstraint, Abaqus/Standard will not enforce the coupling +constraint in this case. +Coupling constraints and boundary conditions +When boundary conditions are specified at all nodes involved in a distributing coupling constraint, the +model may become overconstrained. Abaqus/Standard will issue a warning message outlining the cause +of the potential overconstraint. +Spot welds and rigid bodies +Potential overconstraints that may arise when a rigid body is involved in a mesh-independent spot weld +definition are discussed in “Mesh-independent fasteners,” Section 34.3.4. +Overconstraints detected and resolved during analysis +There are numerous situations when contact interactions in combination with other constraint types may +lead to overconstraints. Since contact status typically changes during the analysis, it is not possible to +detect redundant constraints associated with contact in the model preprocessor. Instead, these checks +are performed during the analysis. Due to the complexities associated with contact interactions, only a +limited number of redundant constraint cases are resolved automatically. +Contact interactions and tie constraints +Redundant constraints are common in cases when slave nodes used in surface-based tie constraints +(“Mesh tie constraints,” Section 34.3.1) are also slave nodes in contact, as illustrated in Figure 34.6.1–9. +In Figure 34.6.1–9(a) nodes 5 and 9 are connected with a tie constraint, and both are in contact with a +master surface. Since the two nodes are tied together, one of the contact constraints is redundant. A +similar situation is presented in Figure 34.6.1–9(b): two mismatched solid meshes are connected with +a tie constraint, and contact is defined with a flat rigid surface. Node S is a dependent node in the tie +constraint, so its motion is determined by that of nodes B and C. Therefore, any contact constraint +applied at node S is redundant. Moreover, the contact constraints at nodes G and H are redundant, since +the motion of these nodes is determined by nodes B and C, respectively. To eliminate these redundancies +when all nodes involved in the tie constraint are in contact, Abaqus/Standard will automatically apply +a tie-type constraint between the Lagrange multipliers associated with the contact constraint. The +redundant contact constraint is eliminated. The contact pressure and the friction forces at the slave node +are recovered from the pressures and friction forces at the associated tie-independent nodes. +Deleting contact elements to remove overconstraints +Instead of letting Abaqus remove overconstraints by tying Lagrange multipliers, you can apply constraint +controls that delete the contact elements associated with tied slave nodes. If you use this technique, +contact-related output is not available for the tied slave nodes. +Input File Usage: +*CONSTRAINT CONTROLS, DELETE SLAVE +distributed load on these faces + 7 + 6 +4 +tie constraint +between +these surfaces +14 +1 +11 +(a) +D E +A F +C H +B G +(b) +master surface +completely fixed +13 +12 +tie constraint between +faces ABCD and FGHE +contact master +surface +Figure 34.6.1–9 Redundant constraints arising from contact interactions and tie constraints. +Contact interactions and prescribed boundary conditions +Contact +interactions and prescribed boundary conditions may lead to redundant constraints if +either normal contact with the default “hard contact” formulation (“Contact pressure-overclosure +relationships,” Section 36.1.2) or frictional contact with the Lagrange multiplier formulation is invoked. Abaqus/Standard attempts to resolve these types of +redundant constraints for contact pairs involving rigid surfaces. +Checks related to normal contact interactions +In Figure 34.6.1–10 the fixed analytical rigid master surface is in contact with a slave node that has a +���xed boundary condition specified in the direction normal to the contact surface. If during a particular +increment in the analysis the node is in contact, the contact constraint is redundant and will not be +enforced during that increment. +If the boundary condition at the slave node is in conflict with the +boundary conditions at the rigid surface’s reference node, an error message is issued and the analysis is +stopped. +distributed load +boundary condition in +direction normal to the +master surface ++ +rigid master surface +reference node +completely fixed +Figure 34.6.1–10 Overconstraints involving normal contact interactions and boundary conditions. +The contact and boundary conditions related to overconstraints are removed automatically only if +the master surface is defined as an analytical rigid surface. In all other cases, if an overconstraint occurs +during the analysis, a zero pivot message is issued by the equation solver and the chains of +constraints responsible for the overconstraint are clearly outlined. +Checks related to Lagrange friction +A common redundant constraint case is depicted in Figure 34.6.1–11. The symmetry boundary conditions +combined with the Lagrange friction are redundant. The slave node is in contact and the tangent to the +surface is in approximately the same direction as the specified boundary condition at the slave node. To +avoid redundancy, at this node Abaqus/Standard will switch from the Lagrange friction formulation to +the default penalty formulation (“Frictional behavior,” Section 36.1.5) if the motion of the master nodes +is prescribed in the tangent direction. +symmetry boundary +conditions on faces +BDEF and ACHJ +nodes A, G, and C +are overconstrained +Lagrange friction +Figure 34.6.1–11 Lagrange friction and boundary conditions. +Overconstraints detected in the equation solver +All overconstraints that cannot be identified and resolved during preprocessing or during the analysis +need to be detected by the equation solver. Examples include models with contact interactions where +slave nodes are driven by specified boundary conditions into partially fixed rigid surfaces; contact with +multiple master surfaces; closed-loop and multiple-loop mechanisms in which rigid bodies are connected +by connector elements; and many more. By default, equation solver overconstraint checks are performed +continuously during the analysis. +Abaqus/Standard will not resolve overconstraints detected by the equation solver. Instead, detailed +messages with information regarding the kinematic constraints involved in the overconstraint will +be issued. The message first identifies the nodes involved in either a consistent or an inconsistent +overconstraint by using zero pivot information from the Gauss elimination in the solver (“Direct linear +equation solver,” Section 6.1.5). A detailed message containing constraint information is then issued. +The 4-bar mechanism shown in Figure 34.6.1–12 illustrates this strategy. Four three-dimensional +rigid bodies are defined as follows: the rigid body with reference node 10001 includes nodes 2 and 101; +the rigid body with reference node 10002 includes nodes 3 and 102; the rigid body with reference node +10003 includes nodes 4 and 103; and the rigid body with reference node 10004 includes nodes 1 and 104. +The four rigid bodies are connected with four JOIN and REVOLUTE combination connector elements +defined as follows: element 20001 between nodes 1 and 101; element 20002 between nodes 2 and 102; +element 20003 between nodes 3 and 103; and element 20004 between nodes 4 and 104. Each connector +element enforces three translation and two rotation constraints (“Connectors: overview,” Section 31.1.1), +and all four revolute axis directions are parallel. The bottom rigid body (with reference node 10004) is +fixed. The motion of the bottom left REVOLUTE connector (element 20001) is prescribed to rotate the +mechanism. +When Abaqus/Standard attempts to find a solution for this model, three zero pivots are identified +in the first increment of the analysis suggesting that there are three constraints too many in the model. +element 20002 +102 +10002 +element 20003 +10001 +101 +connector +motion +103 +10003 +element 20001 +104 +10004 (fixed) +element 20004 +Figure 34.6.1–12 Hard-to-detect redundant constraints. +Eventually, one would have to remove three constraints to render the model properly constrained. In this +simple example a count of the degrees of freedom and constraints confirms the number of overconstraints, +as follows. There are four rigid bodies in the model, with a total of 24 degrees of freedom. The reference +node 10004 is completely fixed with a boundary condition, constraining six degrees of freedom; and +the prescribed connector motion enforces one rotational constraint, constraining one degree of freedom. +Hence, there are 17 degrees of freedom remaining. Each of the four connector elements enforces five +constraints, for a total of 20 constraints. Thus, there are three constraints too many in the model, which +matches the number of zero pivots identified by the equation solver. To help you identify the constraints +that should be removed, the following message is produced in the message (.msg) file outlining the +chains of constraints that generated the overconstraint: +***WARNING: SOLVER PROBLEM. ZERO PIVOT WHEN PROCESSING ELEMENT 20004 +INTERNAL NODE 1 D.O.F. 4 +An overconstraint was detected at one of the +OVERCONSTRAINT CHECKS: +Lagrange multipliers associated with element 20004. There are +multiple constraints applied directly or chained constraints that +are applied indirectly to this element. The following is a list of +nodes and chained constraints between these nodes that most likely +lead to the detected overconstraint. +LAGRANGE MULTIPLIER: 4 <-> 104: connector element 20004 type +JOIN REVOLUTE constraining 3 translations +and +2 rotations +..4 -> 10003: *RIGID BODY (or *COUPLING-KINEMATIC) +....10003 -> 103: *RIGID BODY (or *COUPLING-KINEMATIC) +......103 -> 3: connector element 20003 type JOIN REVOLUTE +constraining 3 translations +2 rotations +and +........3 -> 10002: *RIGID BODY (or *COUPLING-KINEMATIC) +..........10002 -> 102: *RIGID BODY (or *COUPLING-KINEMATIC) +............102 -> 2: connector element 20002 type JOIN REVOLUTE +constraining 3 translations and 2 rotations +..............2 -> 10001: *RIGID BODY (or *COUPLING-KINEMATIC) +................10001 -> 101: *RIGID BODY (or *COUPLING-KINEMATIC) +..................101 -> 1: connector element 20001 type +JOIN REVOLUTE constraining +translations +....................1 -> 10004: *RIGID BODY (or *COUPLING-KINEMATIC) +......................10004 -> *BOUNDARY in degrees of freedom +and 2 rotations +......................10004 -> 104: *RIGID BODY +....................1 -> 101: connector element 20001 with +*CONNECTOR MOTION in components +(or *COUPLING-KINEMATIC) +Please analyze these constraint loops and remove unnecessary +constraints. +First, the message identifies the user-defined or, in this case, the internally defined (Lagrange multiplier) +node at which a zero pivot was identified. A typical line in this output issues information related to one +constraint. For example, the first line in this output +LAGRANGE MULTIPLIER: 4 <-> 104: connector element 20004 type +JOIN REVOLUTE constraining 3 translations +and +2 rotations +informs you that the Lagrange multiplier on which the zero pivot occurs enforces one of the five +constraints (JOIN and REVOLUTE) associated with connector element 20004 between user-defined +nodes 4 and 104. Each of the subsequent lines conveys information related to one constraint in the +chains of constraints originating at the zero pivot node or in chains adjacent to them. For example, the +line +....10003 -> 103: *RIGID BODY (or *COUPLING - KINEMATIC) +informs you that there is a rigid body constraint between nodes 10003 and 103, while the line +.....................10004 -> *BOUNDARY in degrees of freedom +states that there is a boundary condition constraint fixing degrees of freedom 1 through 6 at node 10004. +Indentation levels (the dots in front of the node numbers) identify links in a chain of constraints. +Each time a constraint is found to link another node in a particular chain, the indentation is increased +by two dots and the constraint information is printed out. For example, starting from the top of the +message, the Lagrange multiplier is connected to node 4, node 4 is connected to node 10003, node 10003 +is connected to node 103, and so on. When the indentation on a certain line is less than or equal to the +indentation on the previous line, a chain of constraints has ended on the previous line. For example, a +chain has ended on the line +.....................10004 -> *BOUNDARY in degrees of freedom +since the next line has equal indentation. +Three chains of constraints (in correspondence with the three zero pivots that were found) that most +likely generated the overconstraint can be identified in the model above. Starting from the top, one can +first identify a chain of constraints that terminates in a boundary condition (ground): +Lagrange multiplier: 4 –> 10003 –> 103 –> 3 –> 10002 –> 2 –> +10001 –> 101 –> 1 –> 10004 –> *BOUNDARY +Since the indentation of the two lines starting with node 10004 is the same, one should expect another +chain of constraints to include the constraint output on the second of the two lines. Indeed, one can +identify a closed loop of constraints: +Lagrange multiplier : 4–> 10003 –> 103 –> 3 –> 10002 –> 2 –> +10001 –> 101 –> 1 –> 10004 –> 104 <-> 4 +Finally, since the two lines starting with node 1 have the same indentation, one expects that a separate +chain of constraints will include the last line in the output. A third (closed) loop +101 –> 1 –> 101 +is identified. +If the chains of constraints terminate in a free end (not ending in a constraint), the chain does not +have any contribution in generating the overconstraint. There are no such chains in this example. +Correcting an overconstrained model +A node set containing all the nodes in the chains of constraints associated with a particular zero pivot is +generated automatically and can be displayed in the Visualization module of Abaqus/CAE. +There is no unique way to remove the overconstraints in this model. For example, if one JOIN +and REVOLUTE (five constraints) combination is replaced with a SLOT connector element, which +enforces only the two translation constraints in the plane of the mechanism, there are no redundancies. +Alternatively, you could remove the REVOLUTE from one of the connector elements and also use a +SLOT connection instead of a JOIN in one of the other connector elements. +Another alternative is to relax some of the constraints. In the example outlined here, an elastic +body could replace one or more of the rigid bodies. You could also relax the Lagrange multiplier-based +constraints (e.g., JOIN or REVOLUTE) by using CARTESIAN and CARDAN connection types with +appropriate elastic stiffnesses . +After analyzing the chains of constraints, you have to decide which constraints have to be removed +to render the model properly constrained and also best fit the modeling goals. For this example the +three constraints cannot be removed randomly. Removing any three combinations of the six boundary +conditions, for example, would make the problem worse: the model is still overconstrained, and three +rigid body modes have been added to the model. Moreover, you should remove the constraints that do +not affect the kinematics of the model. For example, you cannot completely remove a JOIN connection +from any of the connector elements since the model would be different from that originally intended. +Controlling the overconstraint checks +By default, Abaqus/Standard will attempt to remove as many redundant constraints as possible, +as discussed in the sections above. When it is not possible to remove a redundant constraint or +an inconsistent overconstraint is detected, a detailed message is issued identifying the constraints +contributing to the overconstraint. You can modify this default behavior by prescribing constraint +controls for the model or the step. +Overconstraints may produce damaging and unpredictable behavior. Therefore, it is strongly +recommended that overconstraint checking be used in both the preprocessor and during the analysis +at least during the first running of a model. Furthermore, it is recommended that the original model +be changed to correct any overconstraints identified by Abaqus/Standard. Only after establishing +confidence that the model is free of overconstraints should constraint checks be turned off. The only +advantage of turning off the constraint checks is a minor speedup of the analysis. +Bypassing the overconstraint checks +The overconstraint checks performed during input file preprocessing and during the analysis can be +bypassed. Bypassing these checks is not recommended, as it may allow a model with overconstraints to +enter into the analysis code. Bypassing the overconstraint checks is not step dependent; i.e., the setting +is defined as model data and affects the entire analysis. +Input File Usage: +*CONSTRAINT CONTROLS, NO CHECKS +Preventing automatic redundant constraint resolution +Automatic model modifications in the model preprocessor can be prevented. +In this case +Abaqus/Standard will still perform overconstraint checks, but no automatic redundant constraint +resolution will be performed; only appropriate error messages will be issued. Preventing constraint +resolution is not step dependent; i.e., the setting is defined as model data and affects the entire analysis. +Input File Usage: +*CONSTRAINT CONTROLS, NO CHANGES +Changing the frequency of the overconstraint checks +By default, the overconstraint checks are performed at every increment during the analysis. You can +modify the frequency of these checks (in increments) for each step in the analysis. If the frequency +is set equal to zero, no overconstraint checks are performed during that analysis step. The frequency +specification is maintained in subsequent steps until the value is reset. +Input File Usage: +*CONSTRAINT CONTROLS, CHECK FREQUENCY=n +Stopping the analysis when overconstraints are detected +By default, the analysis continues even though an overconstraint is detected. This behavior can be +changed on a step-dependent basis. The analysis can be stopped the first time an overconstraint is detected +in a step, or it can be stopped only if a converged solution is obtained despite the fact that overconstraints +exist. This setting is maintained in subsequent steps until it is reset. +Input File Usage: +Use one of the following options: +*CONSTRAINT CONTROLS, TERMINATE ANALYSIS=FIRST +OCCURRENCE +*CONSTRAINT CONTROLS, TERMINATE ANALYSIS=CONVERGED +• Chapter 35, “Defining Contact Interactions” +• Chapter 36, “Contact Property Models” +• Chapter 37, “Contact Formulations and Numerical Methods” +• Chapter 38, “Contact Difficulties and Diagnostics” +• Chapter 39, “Contact Elements in Abaqus/Standard” +35. +Defining Contact Interactions +Overview +Defining general contact in Abaqus/Standard +Defining contact pairs in Abaqus/Standard +Defining general contact in Abaqus/Explicit +Defining contact pairs in Abaqus/Explicit +35.1 +35.2 +35.3 +35.4 +35.1 +Overview +• “Contact interaction analysis: overview,” Section 35.1.1 +35.1.1 +CONTACT INTERACTION ANALYSIS: OVERVIEW +This section presents an overview of the contact analysis capabilities in Abaqus. +Available contact algorithms in Abaqus +Abaqus provides more than one approach for defining contact. Abaqus/Standard includes the following +approaches for defining contact: +• general contact; +• contact pairs; and +• contact elements. +Abaqus/Explicit includes the following approaches for defining contact: +• general contact; and +• contact pairs. +Each approach has somewhat unique advantages and limitations. +The remainder of this section is organized as follows: +• first, discuss common aspects of the surface-based contact-definition approaches (i.e., contact pairs +and general contact); +• next, provide an overview of the contact definition approaches in Abaqus/Standard and the contact +definition approaches in Abaqus/Explicit; +• finally, discuss compatibility between the contact algorithms +Abaqus/Explicit. +in Abaqus/Standard and +Defining a surface-based contact simulation +A contact simulation using contact pairs or general contact is defined by specifying: +• surface definitions for the bodies that could potentially be in contact; +• the surfaces that interact with one another (the contact interactions); +• any nondefault surface properties to be considered in the contact interactions; +• the mechanical and thermal contact property models, such as the pressure-overclosure relationship, +the friction coefficient, or the contact conduction coefficient; +• any nondefault aspects of the contact formulation; and +• any algorithmic contact controls for the analysis. +In many cases you do not need to explicitly specify many of the aspects listed above because the default +settings are usually appropriate. +Surfaces +Surfaces can be defined at the beginning of a simulation or upon restart as part of the model definition +. Abaqus has four classifications of contact surfaces: +• element-based deformable and rigid surfaces (“Element-based surface definition,” Section 2.3.2); +• node-based deformable and rigid surfaces (“Node-based surface definition,” Section 2.3.3); +• analytical rigid surfaces (“Analytical rigid surface definition,” Section 2.3.4); and +• Eulerian material surfaces for Abaqus/Explicit (“Eulerian surface definition,” Section 2.3.5). +Surfaces of the same type can be combined to create new surfaces . However, with regard to contact a combined surface can be used only with general +contact in Abaqus/Explicit. +When the general contact algorithm is used, Abaqus also provides a default all-inclusive, +automatically defined surface that includes all element-based surface facets (in Abaqus/Standard and in +Abaqus/Explicit), all analytical rigid surfaces (in Abaqus/Explicit only), and all Eulerian materials (in +Abaqus/Explicit only) in the model. +Contact interactions +Contact interactions for contact pairs and general contact are defined by specifying surface pairings and +self-contact surfaces. General contact interactions typically are defined by specifying self-contact for the +default surface, which allows an easy, yet powerful, definition of contact. (Self-contact for a surface that +spans multiple bodies implies self-contact for each body as well as contact between the bodies.) +At least one surface in an interaction must be a non-node-based surface, and at least one surface in +an interaction must be a non-analytical rigid surface. Additional restrictions and guidelines for contact +surfaces are discussed for each contact definition approach. The definition of contact pairs is discussed +in detail in “Defining contact pairs in Abaqus/Standard,” Section 35.3.1, and “Defining contact pairs in +Abaqus/Explicit,” Section 35.5.1. The definition of general contact interactions is discussed in detail +in “Defining general contact interactions in Abaqus/Standard,” Section 35.2.1, and “Defining general +contact interactions in Abaqus/Explicit,” Section 35.4.1. +Surface properties +Nondefault surface properties (such as thickness and, in some cases, offset) can be defined for particular +surfaces in a contact model. In addition, you can control which edges of a surface will be included +in the general contact domain in Abaqus/Explicit. Surface properties for contact pairs are discussed +in “Assigning surface properties for contact pairs in Abaqus/Standard,” Section 35.3.2, and “Assigning +surface properties for contact pairs in Abaqus/Explicit,” Section 35.5.2. Surface properties for general +contact are discussed in “Surface properties for general contact in Abaqus/Standard,” Section 35.2.2, and +“Assigning surface properties for general contact in Abaqus/Explicit,” Section 35.4.2. +Contact properties +Contact interactions in a model can refer to a contact property definition, in much the same way that +elements refer to an element property definition. By default, the surfaces interact (have constraints) +only in the normal direction to resist penetration. The other mechanical contact interaction models +available depend on the contact algorithm and whether Abaqus/Standard or Abaqus/Explicit is used . Some of the available models are: +• softened contact (“Contact pressure-overclosure relationships,” Section 36.1.2, and “Frictional +behavior,” Section 36.1.5); +• contact damping (“Contact damping,” Section 36.1.3, and “Frictional behavior,” Section 36.1.5); +• friction (“Frictional behavior,” Section 36.1.5); +• a user-defined constitutive model for surface interactions (“User-defined interfacial constitutive +behavior,” Section 36.1.6); and +• spot welds bonding two surfaces together until the welds fail (“Breakable bonds,” Section 36.1.9). +The thermal, +thermal-electrical, and pore-fluid surface interaction models available in Abaqus +are discussed in “Thermal contact properties,” Section 36.2.1; “Electrical contact properties,” +Section 36.3.1; and “Pore fluid contact properties,” Section 36.4.1, respectively. +Contact interaction models are defined as model data except for contact pairs in Abaqus/Explicit, in +which case they are defined as history data. Information on assigning contact properties to contact pairs +can be found in “Assigning contact properties for contact pairs in Abaqus/Standard,” Section 35.3.3, +and “Assigning contact properties for contact pairs in Abaqus/Explicit,” Section 35.5.3. Information +on assigning contact properties to general contact interactions can be found in “Contact properties for +general contact in Abaqus/Standard,” Section 35.2.3, and “Assigning contact properties for general +contact in Abaqus/Explicit,” Section 35.4.3. +Numerical controls +The default algorithmic controls for contact analyses are usually sufficient, but you can adjust numerical +controls for some special cases. For example, depending on the contact algorithm used, the numerical +controls for the contact formulation, the master and slave roles for the contact surfaces, and the sliding +formulation are provided. +Information on contact formulations and numerical methods used by the +contact algorithms is provided in “Contact formulations in Abaqus/Standard,” Section 37.1.1, and +“Contact formulations for contact pairs in Abaqus/Explicit,” Section 37.2.2. The available numerical +controls for the various contact algorithms are discussed in “Numerical controls for general contact in +Abaqus/Standard,” Section 35.2.6; “Adjusting contact controls in Abaqus/Standard,” Section 35.3.6; +“Contact controls for general contact in Abaqus/Explicit,” Section 35.4.5; and “Contact controls for +contact pairs in Abaqus/Explicit,” Section 35.5.5. +Contact simulation capabilities in Abaqus/Standard +Abaqus/Standard provides the following approaches for defining contact interactions: general contact, +contact pairs, and contact elements. Contact pairs and general contact both use surfaces to define contact; +comparisons of these approaches are provided later in this section. Contact elements are provided for +certain interactions that cannot be modeled with either general contact or contact pairs; however, it is +generally recommended to use general contact or contact pairs if possible. +Capabilities of contact pairs and general contact in Abaqus/Standard +Contact pairs and general contact combine to provide the following capabilities in Abaqus/Standard: +• Contact between two deformable bodies. The structures can be either two- or three-dimensional, +and they can undergo either small or finite sliding. Examples of such problems include the assembly +of a cylinder head gasket and the slipping between the two components of a threaded connector. +• Contact between a rigid surface and a deformable body. The structures can be either two- or three- +dimensional, and they can undergo either small or finite sliding. Examples of such problems include +metal forming simulations and analyses of rubber seals being compressed between two components. +• Finite-sliding self-contact of a single deformable body. An example of such a problem is a complex +rubber seal that folds over on itself. +• Small-sliding or finite-sliding interaction between a set of points and a rigid surface. These models +can be either two- or three-dimensional. An example of this type of problem is the pull-in of an +underwater cable that is resting on the seabed, with the seabed modeled as a rigid surface. +• Contact between a set of points and a deformable surface. These models can be either two- or +three-dimensional. An example of this class of contact problem is the design of a bearing where +one of the bearing surfaces is modeled with substructures. +• Problems where two separate surfaces need to be “tied” together so that there is no relative motion +between them. This modeling technique allows for joining dissimilar meshes. +• Coupled thermal-mechanical interaction between deformable bodies with finite relative motion. +The analysis of a disc brake is an example of such a problem. +• Coupled thermal-electrical-structural interaction between deformable bodies with finite relative +motion. An example of this type of problem is the analysis of resistance spot welding. +• Coupled pore fluid-mechanical interaction between bodies. An example of this type of problem is +the analysis of the interfaces between layered soil material at a waste disposal site. +Coupled thermal-mechanical and coupled thermal-electrical-structural interactions can be included in +any of the above examples as long as both of the surfaces are deformable. +Choosing between general contact or contact pairs in Abaqus/Standard +For most contact problems you have a choice of whether to define contact interactions using general +contact or contact pairs. In Abaqus/Standard the distinction between general contact and contact pairs +lies primarily in the user interface, the default numerical settings, and the available options. The general +contact and contact pair implementations share many underlying algorithms. +The contact +interaction domain, contact properties, and surface attributes are specified +independently for general contact, offering a more flexible way to add detail incrementally to a model. +The simple interface for specifying general contact allows for a highly automated contact definition; +however, it is also possible to define contact with the general contact interface to mimic traditional +contact pairs. Conversely, specifying self-contact of a surface spanning multiple bodies with the contact +pair user interface (if the surface-to-surface formulation is used) mimics the highly automated approach +often used for general contact. +In Abaqus/Standard, traditional pairwise specifications of contact interactions will often result +in more efficient or robust analyses as compared to an all-inclusive self-contact approach to defining +contact. Therefore, there is often a trade-off between ease of defining contact and analysis performance. +Abaqus/CAE provides a contact detection tool that greatly simplifies the process of creating traditional +contact pairs for Abaqus/Standard . +Default settings for general contact and contact pairs +Differences in default settings for general contact and contact pairs in Abaqus/Standard include the +following: +• Contact formulation: General contact uses the finite-sliding, surface-to-surface formulation +supplemented by the finite-sliding, edge-to-surface formulation. +Contact pairs use the +finite-sliding, node-to-surface formulation by default except when the contact detection tool in +Abaqus/CAE is used to create the contact pairs, in which case the finite-sliding, surface-to-surface +formulation is used by default. See “Contact formulations in Abaqus/Standard,” Section 37.1.1, +for a discussion of contact formulations. +• Treatment of shell thickness and offset: General contact automatically accounts for thicknesses and +offsets associated with shell-like surfaces. Contact pairs that use the finite-sliding, node-to-surface +formulation do not account for shell thicknesses and offsets. See “Surface properties for general +contact in Abaqus/Standard,” Section 35.2.2, and “Assigning surface properties for contact +pairs in Abaqus/Standard,” Section 35.3.2, for discussions of surface properties for contact in +Abaqus/Standard. +• Contact constraint enforcement: General contact uses the penalty method to enforce the contact +constraints by default. Contact pairs that use the finite-sliding, node-to-surface formulation use a +Lagrange multiplier method to enforce contact constraints by default in most cases. See “Contact +constraint enforcement methods in Abaqus/Standard,” Section 37.1.2, for a discussion of contact +constraint enforcement methods. +• Treatment of initial overclosures: General contact eliminates initial overclosures with strain-free +adjustments by default. Contact pairs treat initial overclosures as interference fits to be resolved +in the first increment of the analysis by default. +See “Controlling initial contact status in +Abaqus/Standard,” Section 35.2.4; “Modeling contact interference fits in Abaqus/Standard,” +Section 35.3.4; and “Adjusting initial surface positions and specifying initial clearances in +Abaqus/Standard contact pairs,” Section 35.3.5; for more information on contact initialization in +Abaqus/Standard. +• Master-slave assignments: General contact automatically assigns pure master and slave roles for +most contact interactions and automatically assigns balanced master-slave roles to other contact +interactions. The user must assign master and slave roles for most contact pairs. See “Numerical +controls for general contact in Abaqus/Standard,” Section 35.2.6, and “Choosing the master +and slave roles in a two-surface contact pair” in “Contact formulations in Abaqus/Standard,” +Section 37.1.1, for discussions of master and slave roles for contacting surfaces. +The first three differences listed above disappear if you specify the finite-sliding, surface-to-surface +formulation for contact pairs. +Additional contact pair capabilities +The following capabilities are available only for contact pairs in Abaqus/Standard (they are not available +for general contact in Abaqus/Standard): +• Contact involving analytical rigid surfaces or rigid surfaces defined with user subroutine RSURFU +(however, element-based rigid surfaces can be included in either general contact or contact pairs). +• Contact involving node-based surfaces or surfaces on three-dimensional beam elements. +• Small-sliding contact and tied contact. +• The finite-sliding, node-to-surface contact formulation. +• Debonding and cohesive contact behavior. +• Surface interactions in analyses without displacement degrees of freedom, such as pure heat transfer. +• Pressure-penetration loading. +• Local definitions of some numerical contact controls. +• Symmetric model generation. +A single analysis can include general contact and contact pair definitions. For example, you may +choose to model contact interactions involving analytical rigid surfaces with contact pairs and other +contact interactions with general contact. General contact automatically avoids processing contact +interactions that are treated by contact pairs. +Contact simulations requiring contact elements +Surface-based contact methods associated with general contact and contact pairs cannot be used for +certain classes of problems. Abaqus/Standard provides a library of contact elements for these problems. +Examples of such problems are: +• Contact interaction between two pipelines or tubes modeled with pipe, beam, or truss elements +where one pipe lies inside the other (such as a J-tube pull in offshore piping installation) or the +pipes lie next to each other (available in both two and three dimensions; see “Tube-to-tube contact +elements,” Section 39.3.1). +• Contact between two nodes along a fixed direction in space. An example of such a problem is the +interaction of a piping system with its supports . +• Simulations using axisymmetric elements with asymmetric deformations, CAXAn and +SAXAn elements. See “Contact modeling if asymmetric-axisymmetric elements are present,” +Section 35.3.10, for details. +• Heat transfer analyses where the heat flow is one-dimensional. An example of such a problem is +the heat flow in a piping system that is discontinuous. The thermal interaction in this problem is +one-dimensional, so no surfaces can be defined . +Defining a contact simulation using contact elements +The steps required for defining a contact simulation using contact elements are similar to those needed +when defining a surface-based contact simulation: +• create the contact elements or slide lines; +• assign element section properties to the contact elements; +• associate sets of contact elements with the slide lines if applicable; and +• define the contact property models for the contact elements. +The first three steps are discussed in Chapter 39, “Contact Elements in Abaqus/Standard,” in the sections +for each type of contact element. The contact property models for contact elements are identical to those +used for surface-based contact. +Contact simulation capabilities in Abaqus/Explicit +Abaqus/Explicit provides two algorithms for modeling contact interactions. The general (“automatic”) +contact algorithm allows very simple definitions of contact with very few restrictions on the types +of surfaces involved . The contact +pair algorithm has more restrictions on the types of surfaces involved and often requires more careful +definition of contact; however, it allows for some interaction behaviors that currently are not available +with the general contact algorithm . The +general contact and contact pairs algoirthms in Abaqus/Explicit differ by more than the user interface; +in general they use completely separate implementations with many key differences in the designs of +the numerical algorithms. +The two contact algorithms combine to provide the following capabilities in Abaqus/Explicit: +• Contact between rigid and/or deformable bodies. +• Contact of a body with itself. +• Finite-sliding or small-sliding contact. +• Contact with eroding bodies (due to element failure). A node-based surface must be used to model +the eroding body if contact pairs are used. General contact allows element-based surfaces to be +defined on eroding bodies, so contact between any number of eroding bodies can be modeled. +• General constitutive models for the contact behavior, including user-defined models through user +subroutines, relating constraint pressure and shear traction to penetration distance and relative +tangential motion. +• Thermal interaction at the surface of a body; for example, conductive heat transfer. +• Contact between Eulerian material and Lagrangian bodies. +• A friction coefficient defined in terms of average surface temperature and/or field variables. +Choosing between general contact or contact pairs in Abaqus/Explicit +Contact definitions are not entirely automatic with the general contact algorithm but are greatly +simplified. The generality of this algorithm is primarily in the relaxed restrictions on the surfaces that +can be used in contact. The general contact algorithm in Abaqus/Explicit allows the following (none of +which are allowed with the contact pair algorithm in Abaqus/Explicit): +• A surface can span unattached bodies. +• More than two surface facets can share a common edge (allowing “T-intersections” in shells, for +example). +• A surface can include deformable and rigid regions; furthermore, the rigid regions need not be from +the same rigid body. +• A surface can have mixed parent element types; for example, adjacent surface facets can be on shell +and solid elements. +• A surface can be based on combinations of surfaces of the same type. +• An element-based surface can be defined on the interior of solid bodies for use in modeling erosion +due to element failure. +• A surface can be defined on the exterior of an Eulerian material instance . +Other benefits of the general contact algorithm in Abaqus/Explicit include the following: +• The general contact algorithm can enforce edge-to-edge contact for geometric feature edges, +perimeter edges of structural elements, and edges defined by beam and truss elements, unlike the +contact pair algorithm. +• The general contact algorithm is the only option for enforcing contact between Eulerian materials +and Lagrangian bodies . +• The general contact algorithm eliminates problematic, nonphysical “bull-nose” extensions that may +arise at shell surface perimeters in the contact pair algorithm. +• With the general contact algorithm each slave node can see contact with multiple facets per +increment; with the contact pair algorithm each slave node can see contact with only one facet +per increment unless multiple surface pairings are specified. Likewise, each contact edge can see +contact with multiple edges per increment when the general contact algorithm is used. +• The general contact algorithm has some built-in smoothing for element-based surfaces that can be +beneficial for modeling contact near corners. +• The general contact algorithm, unlike the contact pair algorithm, removes contact faces and contact +edges from the contact domain and, if an interior surface is defined, activates newly exposed surface +faces as elements fail. Thus, element-based surfaces can be used to describe eroding solids. This +allows contact between multiple eroding solids to be modeled since a node-based surface does not +need to be defined on the eroding solid. +• Contact state information (such as the proper contact normal orientation for double-sided surfaces) +is transferred across step boundaries in the general contact algorithm even if the contact domain +is modified; in the contact pair algorithm, contact state information is transferred across step +boundaries only for contact pairs with no modifications. +• The contact +interaction domain, contact properties, and surface attributes are specified +independently for the general contact algorithm, offering a more flexible way to add detail +incrementally to a model. +• The general contact algorithm does not place any restrictions on the domain decomposition for +domain level parallelization . +• The general contact algorithm in Abaqus/Explicit has been developed to minimize the need for +algorithmic controls. +See “Knee bolster impact with general contact,” Section 2.1.9 of the Abaqus Example Problems Manual; +“Crimp forming with general contact,” Section 2.1.10 of the Abaqus Example Problems Manual; and +“Collapse of a stack of blocks with general contact,” Section 2.1.11 of the Abaqus Example Problems +Manual, for example analyses that use the general contact algorithm. +Although the general contact algorithm is more powerful and allows for simpler contact definitions, +the contact pair algorithm must be used in certain cases where more specialized contact features are +desired. The following features are available in Abaqus/Explicit only when the contact pair algorithm is +used: +• Two-dimensional surfaces +• Kinematically enforced contact +• Small-sliding contact +Section 37.2.2) + +In addition, the general contact algorithm in Abaqus/Explicit places more restrictions on adaptive +meshing than the contact pair algorithm . +the speedup factor if loop-level +parallelization is used: the contact pair algorithm includes some loop-level parallelization, while the +general contact algorithm has no loop-level parallelization. Contact output is more complete for a +contact pair analysis. +The choice of contact algorithm may affect +The two contact algorithms can be used together in the same Abaqus/Explicit analysis. The +general contact algorithm automatically avoids processing interactions that are treated by the contact +pair algorithm. +Compatibility between Abaqus/Standard and Abaqus/Explicit +There are fundamental differences in the mechanical contact algorithms in Abaqus/Standard and +Abaqus/Explicit even though the input syntax is similar. The main differences are the following: +• Contact pair and general contact definitions in Abaqus/Standard are model definition data (although +contact pairs can be removed for a portion of the analysis and added back to the model in a later +step of the analysis, as discussed in “Removing and reactivating contact pairs” in “Defining contact +pairs in Abaqus/Standard,” Section 35.3.1). In the contact pair algorithm in Abaqus/Explicit contact +constraints are history definition data ; in the +general contact algorithm in Abaqus/Explicit contact definitions can be either model or history data. +• Abaqus/Standard typically uses a pure master-slave relationship for the contact constraints; +whereas Abaqus/Explicit typically uses balanced master-slave contact by default. This difference +is primarily due to overconstraint issues unique to Abaqus/Standard. +• The contact formulations in Abaqus/Standard and Abaqus/Explicit differ in many respects due to +different convergence, performance, and numerical requirements: +– Abaqus/Standard provides surface-to-surface and edge-to-surface formulations, which +Abaqus/Explicit does not; +– Abaqus/Explicit provides an edge-to-edge formulation, which Abaqus/Standard does not; +– Abaqus/Standard and Abaqus/Explicit both provide node-to-surface formulations, but some +details associated with surface smoothing, etc. differ in the respective implementations. +• The constraint enforcement methods in Abaqus/Standard and Abaqus/Explicit differ in some +respects. For example, both analysis codes provide penalty constraint methods, but the default +penalty stiffnesses differ (this is primarily due to the effect of the penalty stiffness on the stable +time increment for Abaqus/Explicit). +• The small-sliding contact capability in Abaqus/Standard transfers the load to the master nodes +according to the current position of the slave node, but the small-sliding contact capability in +Abaqus/Explicit always transfers the load through the anchor point due to a numerical limitation +associated with the implementation. +• Abaqus/Explicit can account for the thickness and midsurface offset of shells and membranes +in the contact penetration calculations (although in some cases changes in the thickness upon +deformation are not accounted for in the contact calculations). Abaqus/Standard cannot account +for the thickness and offset of shells and membranes when using the finite-sliding, node-to-surface +contact formulation (but can account for the original thickness and offset in all other contact +formulations). +As a result of these differences, contact definitions specified in an Abaqus/Standard analysis cannot +be imported into an Abaqus/Explicit analysis and vice versa . However, in many cases you can successfully +respecify a contact definition in an import analysis. +35.2 +Defining general contact in Abaqus/Standard +• “Defining general contact interactions in Abaqus/Standard,” Section 35.2.1 +• “Surface properties for general contact in Abaqus/Standard,” Section 35.2.2 +• “Contact properties for general contact in Abaqus/Standard,” Section 35.2.3 +• “Controlling initial contact status in Abaqus/Standard,” Section 35.2.4 +• “Stabilization for general contact in Abaqus/Standard,” Section 35.2.5 +• “Numerical controls for general contact in Abaqus/Standard,” Section 35.2.6 +35.2.1 +DEFINING GENERAL CONTACT INTERACTIONS IN Abaqus/Standard +Products: Abaqus/Standard Abaqus/CAE +References +• “Contact interaction analysis: overview,” Section 35.1.1 +• *CONTACT +• *CONTACT INCLUSIONS +• *CONTACT EXCLUSIONS +• “Defining general contact,” Section 15.13.1 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +Abaqus/Standard provides two algorithms for modeling contact and interaction problems: the general +contact algorithm and the contact pair algorithm. See “Contact interaction analysis: overview,” +Section 35.1.1, for a comparison of the two algorithms. This section describes how to include general +contact in an Abaqus/Standard analysis, how to specify the regions of the model that may be involved +in general contact interactions, and how to obtain output from a general contact analysis. +The general contact algorithm in Abaqus/Standard: +• is specified as part of the model definition; +• allows very simple definitions of contact with very few restrictions on the types of surfaces involved; +• uses sophisticated tracking algorithms to ensure that proper contact conditions are enforced +efficiently; +• can be used simultaneously with the contact pair algorithm (i.e., some interactions can be modeled +with the general contact algorithm, while others are modeled with the contact pair algorithm); +��� can be used with two- or three-dimensional surfaces; and +• uses the finite-sliding, surface-to-surface contact formulation. +Defining a general contact interaction +The definition of a general contact interaction consists of specifying: +• the general contact algorithm and defining the contact domain (i.e., the surfaces that interact with +one another), as described in this section; +• the contact surface properties (“Surface properties for general contact in Abaqus/Standard,” +Section 35.2.2); +• the mechanical contact property models +Abaqus/Standard,” Section 35.2.3); +(“Contact properties +for general +contact +in +• the controls associated with the initial contact state (“Controlling initial contact status in +Abaqus/Standard,” Section 35.2.4); and +• the algorithmic contact controls (“Numerical controls for general contact in Abaqus/Standard,” +Section 35.2.6). +An example of an analysis that uses general contact to define contact between the various +components of an assembly is described in “Impact analysis of a pawl-ratchet device,” Section 2.1.17 +of the Abaqus Example Problems Manual. +Surfaces used for general contact +The general contact algorithm in Abaqus/Standard allows for quite general characteristics in the surfaces +that it uses, as discussed in “Contact interaction analysis: overview,” Section 35.1.1. For detailed +information on defining surfaces in Abaqus/Standard for use with the general contact algorithm, see +“Element-based surface definition,” Section 2.3.2. +A convenient method of specifying the contact domain is using cropped surfaces. Such surfaces can +be used to perform “contact in a box” by using a contact domain that is enclosed in a specified rectangular +box in the original configuration. For more information, see “Operating on surfaces,” Section 2.3.6. +In addition, Abaqus/Standard automatically defines an all-inclusive surface that is convenient for +prescribing the contact domain, as discussed later in this section. The all-inclusive automatically defined +surface includes all element-based surface facets. +The general contact algorithm in Abaqus/Standard uses the surface-to-surface contact formulation +as the primary formulation and can use the edge-to-surface contact formulation as a supplementary +formulation. The general contact algorithm does not consider contact involving analytical surfaces or +node-based surfaces, although these surface types can be included in contact pairs in analyses that also +use general contact. +Considerations for edge-to-surface contact +The general contact algorithm can consider three-dimensional edge-to-surface contact, which is more +effective at resolving some interactions than the surface-to-surface contact formulation. The edge-to- +surface contact formulation is primarily intended to avoid localized penetration of a feature’s edge of one +surface into a relatively smooth portion of another surface when the normal directions of the respective +surface facets in the active contact region form an oblique angle. The model shown in Figure 35.2.1–1 +will benefit from supplementary edge-to-surface contact enforcement because the active contact zone +corresponds to a feature edge during some periods of the insertion loading. Supplementary edge-to- +surface contact enforcement is not necessary for the model shown in Figure 35.2.1–2 because the surface- +to-surface contact formulation is able to adequately resist the penetrations. +By default, when a surface is used in a general contact interaction, all applicable facets are included +in the contact definition along with edges of solid and shell elements with feature angles of at least 45°. +See “Feature edges” in “Surface properties for general contact in Abaqus/Standard,” Section 35.2.2 for a +discussion of controls related to which feature edges are considered for edge-to-surface contact. Edge-to- +surface contact constraints never participate in thermal, electrical, or pore pressure contact properties. For +example, in a coupled temperature-displacement analysis, surface-to-surface constraints can influence +Figure 35.2.1–1 Snap-fit example involving feature edge-to-surface contact with an +oblique angle between surface normals in the contact region. +Figure 35.2.1–2 Example with feature-edges at the perimeter of an active contact +region that has opposing surface normals. +mechanical and thermal interactions; but, if edge-to-surface constraints are included, they will only help +resist penetrations. +The contact area associated with a feature edge depends on the mesh size; therefore, contact +pressures (in units of force per area) associated with edge-to-surface contact are mesh dependent. +Both surface-to-surface and edge-to-surface contact constraints may be active at the same nodes. +To help avoid numerical overconstraint issues, edge-to-surface contact constraints are always enforced +with a penalty method. +Including general contact in an analysis +General contact in Abaqus/Standard is defined at the beginning of an analysis. Only one general contact +definition can be specified, and this definition is in effect for every step of the analysis. +Input File Usage: +Use the following option to indicate the beginning of a general contact +definition: +Abaqus/CAE Usage: +*CONTACT +This option can appear only once in the model definition. +Interaction module: Create Interaction: Step: Initial, +General contact (Standard) +Defining the general contact domain +You specify the regions of the model that can potentially come into contact with each other by defining +general contact inclusions and exclusions. Only one contact inclusions definition and one contact +exclusions definition are allowed in the model definition. +All contact inclusions in an analysis are applied first, then all contact exclusions are applied, +regardless of the order in which they are specified. The contact exclusions take precedence over the +contact inclusions. The general contact algorithm will consider only those interactions specified by the +contact inclusions definition and not specified by the contact exclusions definition. +General contact interactions typically are defined by specifying self-contact for the default +automatically generated surface provided by Abaqus/Standard. All surfaces used in the general contact +algorithm can span multiple unattached bodies, so self-contact in this algorithm is not limited to contact +of a single body with itself. For example, self-contact of a surface that spans two bodies implies contact +between the bodies as well as contact of each body with itself. +Specifying contact inclusions +Define contact inclusions to specify the regions of the model that should be considered for contact +purposes. +Specifying “automatic” contact for the entire model +You can specify self-contact for a default unnamed, all-inclusive surface defined automatically by +Abaqus/Standard. This default surface contains, with the exceptions noted below, all exterior element +faces. This is the simplest way to define the contact domain. +The default surface does not include faces that belong only to cohesive elements. In fact, the default +surface is generated as if cohesive elements were not present. See “Modeling with cohesive elements,” +Section 32.5.3, for further discussion of contact modeling issues related to cohesive elements. +Input File Usage: +Use both of the following options to specify “automatic” contact for the entire +model: +*CONTACT +*CONTACT INCLUSIONS, ALL EXTERIOR +The *CONTACT INCLUSIONS option should have no data lines when the +ALL EXTERIOR parameter is used. +Abaqus/CAE Usage: +Interaction module: Create Interaction: General contact (Standard): +Included surface pairs: All* with self +Specifying individual contact interactions +Alternatively, you can define the general contact domain directly by specifying the individual contact +surface pairings. Self-contact will be modeled only if the two surfaces specified in a pair overlap (or are +identical) and will be modeled only in the overlapping region. In some cases computational performance +and robustness can be improved by including only portions of surfaces in the general contact domain that +will experience contact during an analysis. +Multiple surface pairings can be included in the contact domain. All of the surfaces specified must +be element-based surfaces. +Input File Usage: +Use both of the following options to specify individual contact interactions: +*CONTACT +*CONTACT INCLUSIONS +surface_1, surface_2 +At least one data line must be specified when the ALL EXTERIOR parameter +is omitted. Either or both of the data line entries can be left blank, but each +data line must contain at least a comma; an error message will be issued for +empty data lines. If the first surface name is omitted, the default unnamed, +all-inclusive, automatically generated surface is assumed. If the second surface +name is omitted or is the same as the first surface name, contact between the first +surface and itself is assumed. Leaving both data line entries blank is equivalent +to using the ALL EXTERIOR parameter. +Interaction module: Create Interaction: General contact (Standard): +Included surface pairs: Selected surface pairs: Edit, select the +surfaces in the columns on the left, and click the arrows in the middle to +transfer them to the list of included pairs +Abaqus/CAE Usage: +Examples +The following input specifies that contact should be enforced between the default all-inclusive, +automatically generated surface and surface_2, including self-contact in any overlap regions: +*CONTACT +*CONTACT INCLUSIONS +, surface_2 +Either of the following methods can be used to define self-contact for surface_1: +or +*CONTACT +*CONTACT INCLUSIONS +surface_1, +*CONTACT +*CONTACT INCLUSIONS +surface_1, surface_1 +Specifying contact exclusions +You can refine the contact domain definition by specifying the regions of the model to exclude from +contact. Possible motivations for specifying contact exclusions include: +• avoiding physically unreasonable contact interactions; +• improving computational performance by excluding parts of the model that are not likely to interact. +Contact will be ignored for all the surface pairings specified, even if these interactions are specified +directly or indirectly in the contact inclusions definition. +Multiple surface pairings can be excluded from the contact domain. All of the surfaces specified +must be element-based surfaces. Keep in mind that surfaces can be defined to span multiple unattached +bodies, so self-contact exclusions are not limited to exclusions of single-body contact. +Input File Usage: +Use both of the following options to specify contact exclusions: +*CONTACT +*CONTACT EXCLUSIONS +surface_1, surface_2 +Either or both of the data line entries can be left blank. If the first surface name +is omitted, the default unnamed, all-inclusive, automatically generated surface +is assumed. If the second surface name is omitted or is the same as the first +surface name, contact between the first surface and itself is excluded from the +contact domain. +Interaction module: Create Interaction: General contact (Standard): +Excluded surface pairs: Edit, select the surfaces in the columns on the left, +and click the arrows in the middle to transfer them to the list of excluded pairs +Abaqus/CAE Usage: +Automatically generated contact exclusions +Abaqus/Standard automatically generates contact exclusions for general contact in some situations. +• Contact exclusions are generated automatically for interactions that are defined with the contact +pair algorithm or surface-based tie constraints to avoid redundant (and possibly inconsistent) +enforcement of these interaction constraints. +if a contact pair is defined for +surface_1 and surface_2 and “automatic” general contact is defined for the entire model, +Abaqus/Standard generates a contact exclusion for general contact between surface_1 and +For example, +surface_2 so that interactions between these surfaces are modeled only with the contact pair +algorithm. These automatically generated contact exclusions are in effect throughout the analysis. +• Abaqus/Standard automatically generates contact exclusions for self-contact of each rigid body in +the model, because it is not possible for a rigid body to contact itself. +• When you specify pure master-slave contact surface weighting for a particular general contact +surface pair, contact exclusions are generated automatically for the master-slave orientation +opposite to that specified . +• Abaqus/Standard assigns default pure master-slave roles for contact involving disconnected bodies +within the general contact domain, and contact exclusions are generated by default for the opposite +master-slave orientations. Options to override the default pure master-slave assignments with +alternative pure master-slave assignments or balanced master-slave assignments are discussed in +“Numerical controls for general contact in Abaqus/Standard,” Section 35.2.6. +• Contact exclusions are generated automatically for portions of surfaces that are severely overclosed +in the initial configuration of the model. See “Controlling initial contact status in Abaqus/Standard,” +Section 35.2.4, for more information. +Examples +The following input specifies that the contact domain is based on self-contact of an all-inclusive, +automatically generated surface but that contact (including self-contact in any overlap regions) should +be ignored between the all-inclusive, automatically generated surface and surface_2: +*CONTACT +*CONTACT INCLUSIONS, ALL EXTERIOR +*CONTACT EXCLUSIONS +, surface_2 +Either of the following methods can be used to exclude self-contact for surface_1 from the contact +domain: +*CONTACT EXCLUSIONS +surface_1, +or +Output +*CONTACT EXCLUSIONS +surface_1, surface_1 +nodal variables (sometimes +Output variables associated with contact fall +called constraint variables) and whole surface variables. +In addition, Abaqus outputs an array of +diagnostic information associated with contact interactions, as discussed in “Contact diagnostics in an +Abaqus/Standard analysis,” Section 38.1.1, and internal surfaces generated for general contact. +into two categories: +For more detailed discussions of variables associated with thermal, electrical, and pore fluid +analyses, see the sections on the related contact properties in Chapter 36, “Contact Property Models.” +General contact domain and component surfaces +the following internal +surfaces associated with general contact: +Abaqus/Standard generates +General_Contact_Faces, General_Contact_Edges, General_Contact_Faces_k, +and General_Contact_Edges_k, where k corresponds to an automatically assigned “component +number.” The two internal surfaces for general contact without a component number contain all surface +faces and all feature edges, respectively, included in the general contact domain. +Each feature edge component surface, General_Contact_Edges_k, has a subset of +face edges (satisfying the feature edge criteria) of the corresponding face component surface, +General_Contact_Faces_k. The face component surfaces have no nodes in common with +each other. A lowered-numbered face-based component surface will act as a master surface to a +higher-numbered face-based component surface for the surface-to-surface formulation by default. +Component numbers do not +is considered by the edge-to-surface formulation. +Component surfaces are referred to in diagnostic messages for both formulation types. +influence what +Internal surfaces can be viewed using display groups in the Visualization module of Abaqus/CAE. +Internal surface names generated by Abaqus/Standard should not be used in model definitions. +Nodal contact variables +Nodal contact variables can be contoured on contact surfaces in the Visualization module of +Abaqus/CAE. Nodal contact variables include contact pressure and force, frictional shear stress and +force, relative tangential motion (slip) of the surfaces during contact, clearance between surfaces, heat +or fluid flux per unit area, and fluid pressure. Many of the nodal contact variables written to the output +database (.odb) file are often available for all contact nodes, regardless of whether they act as slave or +master nodes. In such cases the nodal values are generally affected by more than one contact constraint. +Other nodal contact variables are available only at nodes acting as slave nodes. In these cases the value +at each slave node reflects a value associated with a particular contact constraint. Most contact output +to the data (.dat) and results (.fil) files is associated with individual constraints. +Contact pressure +The contact pressure distribution is of key interest in many Abaqus analyses. You can view the contact +pressure on all contact surfaces except for analytical rigid surfaces and discrete rigid surfaces based on +rigid-type elements (the latter restriction does not apply to general contact). You can view a contour plot +of the contact pressure error indicator next to a contour plot of the contact pressure to gain perspective +on local accuracy of the contact pressure solution in regions where the contact pressure solution is of +interest . +In some cases you may observe the contact pressure extending beyond the actual contact zone due +to the following factors: +• The contour plots are constructed by interpolating nodal values, which can cause nonzero values +to appear within portions of facets outside of the contact region. For example, this effect is often +noticeable at corners, such as when two same-sized, aligned blocks are in contact—if the contact +surfaces wrap around the corners, the contact pressure contours will extend slightly around the +corners. +• To minimize contact stress noise within a region of active contact, Abaqus/Standard computes nodal +contact stresses as weighted averages of values associated with active contact constraints in which a +node participates. Some filtering is applied to reduce the contact stress values reported for nodes on +the fringe of the active contact region (that only weakly participate in contact constraints), but this +filtering is not “perfect,” which can result in the contact zone size appearing somewhat exaggerated. +Similarly, contact status output will also be affected at nodes that lie on the fringe of the active +contact region. In such cases the contact status may be reported as closed at nodes in the exaggerated +region even though it is open. +Due to these factors, trying to infer the contact force distribution from the contact stress distribution +can be somewhat misleading. Instead, you can request nodal contact force output, which accurately +represents the contact force distribution present in the analysis. +Contact stresses due to edge-to-surface interactions +Contact stresses (CSTRESS) reported byAbaqus/Standard to the output database (.odb) file contain +contributions from both surface-to-surface and edge-to-surface constraints, if active. Contact stresses +(in units of force per area) solely due to edge-to-surface constraints can be output as a separate field +(CSTRESSETOS) for visualizing regions where the edge-to-surface contact constraints are active. The +edge-to-surface formulation computes contact pressures in units of force per area, by dividing contact +force per edge length by a representative surface facet length. Since the contact area depends on the +mesh size, edge-to-surface contact stresses are mesh dependent. In addition, because edges represent +a discontinuity in the surface smoothness, the true contact stress solution near an edge is commonly +characterized by a strong gradient. Error indicators output for contact stresses (CSTRESSERI) are +typically quite high for regions in which edge-to-surface constraints are significant. +Whole surface variables +Whole surface variables are only marginally supported for general contact in Abaqus/Standard because +these variable are associated with the overall general contact domain by default rather than individual +surfaces associated with general contact. The only way to limit whole surface variables to be affected +by a portion of the general contact domain is to specify a node set in the output request. Whole surface +variables are computed as sums over all nodes (or optionally limited to a particular node set) of general +contact while acting as slave nodes. For example, CFN is the total force acting on slave nodes due to +contact pressure. CFN and other whole surface variables for general contact are typically of little utility, +because contributions to the variable from different interactions within general contact will often cancel +one another and the net result will typically depend on internal assignments of master and slave roles. +Requesting output +Certain contact variables must be requested as a group. For example, to output the clearance between +surfaces (COPEN), you must request the variable CDISP (contact displacements). CDISP outputs both +COPEN and CSLIP (tangential motion of the surfaces during contact). A complete listing of available +contact variables and identifiers is given in “Abaqus/Standard output variable identifiers,” Section 4.2.1. +Output requests can be limited by specifying a node set containing a subset of the nodes acting +as slave nodes for some general contact interactions. Instructions on forming these output requests are +available in the following sections: +• To request output to the data (.dat) file, see “Surface output from Abaqus/Standard” in “Output +to the data and results files,” Section 4.1.2. +• To request output to the output database (.odb) file, see “Surface output in Abaqus/Standard and +Abaqus/Explicit” in “Output to the output database,” Section 4.1.3. +Output of tangential results +Abaqus reports the values of tangential variables (frictional shear stress, viscous shear stress, and +relative tangential motion) with respect to the slip directions defined on the surfaces. The definition +of slip directions is explained in “Local tangent directions on a surface” in “Contact formulations in +Abaqus/Standard,” Section 37.1.1. These directions do not always correspond to the global coordinate +system, and they rotate with the contact pair in a geometrically nonlinear analysis. +Abaqus/Standard calculates tangential results at each constraint point by taking the scalar product +, associated with the constraint point. The number +of the variable’s vector and a slip direction, +at the end of a variable’s name indicates whether the variable corresponds to the first or second slip +direction. For example, CSHEAR1 is the frictional shear stress component in the first slip direction, +while CSHEAR2 is the frictional shear stress component in the second slip direction. +or +Definition of accumulated incremental relative motion (slip) +Abaqus/Standard defines the incremental relative motion (also known as slip) as the scalar product of +the incremental relative nodal displacement vector and a slip direction. The incremental relative nodal +displacement vector measures the motion of a slave node relative to the motion of the master surface. +The incremental slip is accumulated only when the slave node is contacting the master surface. The sums +of all such incremental slips during the analysis are reported as CSLIP1 and CSLIP2. Details about the +calculation of this quantity can be found in “Small-sliding interaction between bodies,” Section 5.1.1 +of the Abaqus Theory Manual; “Finite-sliding interaction between deformable bodies,” Section 5.1.2 +of the Abaqus Theory Manual; and “Finite-sliding interaction between a deformable and a rigid body,” +Section 5.1.3 of the Abaqus Theory Manual. +Extending the range for which contact opening output is provided for gaps +To reduce computational costs, detailed computations to monitor potential points of interaction are +avoided by default where surfaces are separated by a distance greater than the minimum gap distance at +which contact forces (or thermal fluxes, etc.) may be transmitted. Therefore, contact opening (COPEN) +output is typically not provided where surfaces are opened by more than a small amount compared +to surface facet dimensions. You can extend the range for which Abaqus/Standard provides contact +opening output; COPEN will be provided up to gap distances equal to a specified “tracking thickness.” +Using this control may increase computational cost due to extra contact tracking computations, +especially if you specify a large tracking thickness value. +Input File Usage: +Abaqus/CAE Usage: +*SURFACE INTERACTION, TRACKING THICKNESS=value +You cannot adjust the default tracking thickness in Abaqus/CAE. +35.2.2 +SURFACE PROPERTIES FOR GENERAL CONTACT IN Abaqus/Standard +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining general contact interactions in Abaqus/Standard,” Section 35.2.1 +• *CONTACT +• *SURFACE PROPERTY ASSIGNMENT +• “Specifying surface property assignments for general contact,” Section 15.13.5 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +Surface property assignments: +• can be used to specify geometric corrections for regions of a surface; +• can be used to change the contact thickness used for regions of a surface based on structural elements +or to add a contact thickness for regions of a surface based on solid elements; +• can be used to specify surface offsets for regions of a surface based on shell, membrane, rigid, and +surface elements; +• can be applied selectively to particular regions within a general contact domain; and +• cannot be applied to analytical rigid surfaces. +Assigning surface properties +You can assign nondefault surface properties to surfaces involved in general contact interactions. These +properties are considered only when the surfaces are involved in general contact interactions; they are +not considered when the surfaces are involved in other interactions such as contact pairs. The general +contact algorithm does not consider surface properties specified as part of the surface definition. +Surface properties for general contact in Abaqus/Standard are assigned at the beginning of an +analysis and cannot be modified across steps. +The surface names used to specify the regions with nondefault surface properties do not have to +correspond to the surface names used to specify the general contact domain. In many cases the contact +interaction will be defined for a large domain, while nondefault surface properties will be assigned to a +subset of this domain. Any surface property assignments for regions that fall outside the general contact +domain will be ignored. The last assignment will take precedence if the specified regions overlap. +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY +This option must be used in conjunction with the *CONTACT option and +should appear at most once for each value of the PROPERTY parameter +discussed below; the data line can be repeated as often as necessary to assign +surface properties to different regions. +Abaqus/CAE Usage: +Interaction module: Create Interaction: General contact (Standard): +Surface Properties +Surface geometry correction +By default, contact calculations are based on unsmoothed, faceted representations of the finite element +surfaces in a general contact domain. An optional contact smoothing technique simulates a more realistic +representation of curved surfaces in the contact calculations, resulting in improved contact stress and +pressure accuracy. This contact smoothing technique is discussed in “Smoothing contact surfaces in +Abaqus/Standard,” Section 37.1.3. +Surface thickness +The default surface thickness is equal to the original parent element thickness. Alternatively, you can +specify a value for the surface thickness or a thickness scaling factor. A nonzero thickness can be assigned +to solid element surfaces; for example, to model the effect of a finite thickness surface coating. +Using the original parent element thickness +The default surface thickness is equal to the original parent element thickness. +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=THICKNESS +surface, ORIGINAL (default) +Abaqus/CAE Usage: +If the surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +Interaction module: Create Interaction: General contact (Standard): +Surface Properties: Surface thickness assignments: Edit: +Select surface, click the arrows to transfer surface to list of thickness +assignments, and enter ORIGINAL in the Thickness column. +Specifying a value for the surface thickness +You can specify the surface thickness value directly. +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=THICKNESS +surface, value +Abaqus/CAE Usage: +If the surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +Interaction module: Create Interaction: General contact (Standard): +Surface Properties: Surface thickness assignments: Edit: +Select surface, click the arrows to transfer surface to list of thickness +assignments, and enter a value for the surface thickness magnitude +in the Thickness column. +Applying a scale factor to the surface thickness +You can apply a scale factor to any value of the surface thickness. For example, if you specify that +the original parent element thickness should be used for surf1 and apply a scale factor of 0.5, a +value of one half the original parent element thickness will be used for surf1 when it is involved +in a general contact interaction (all other surfaces included in the general contact domain will use the +default original parent element thickness). Scaling the surface thickness in this way can be used to avoid +initial overclosures in some situations. Abaqus/Standard will automatically adjust surface positions to +resolve initial overclosures +associated with general contact. However, if nodal position adjustments are undesirable (for example, +if they would introduce an imperfection in an otherwise flat part, resulting in an unrealistic buckling +mode), you may prefer to reduce the surface thickness and avoid the overclosures entirely. +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=THICKNESS +surface, value or label, scale_factor +If the surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +Interaction module: Create Interaction: General contact (Standard): +Surface Properties: Surface thickness assignments: Edit: +Select surface, click the arrows to transfer surface to list of thickness +assignments, and enter a Scale Factor. +Abaqus/CAE Usage: +Surface offset +A surface offset is the distance between the midplane of a thin body and its reference plane (defined by the +nodal coordinates and element connectivities). It is computed by multiplying the offset fraction (specified +as a fraction of the surface thickness) by the surface thickness and the element facet normal. This defines +the position of the midsurface and, thus, the position of the body with respect to the reference surface; +the coordinates of the nodes on the reference surface are not modified. Surface offsets can be specified +only for surfaces defined on shell and similar elements (i.e., membrane, rigid, and surface elements). +Surface offsets specified for other elements (e.g., solid or beam elements) will be ignored. By default, +surface offsets specified in element section definitions will be used in the general contact algorithm. +You specify the surface offset as a fraction of the surface thickness. The surface offset fraction can +be set equal to the offset fraction used for the surface’s parent elements or to a specified value. Surface +offsets specified for general contact do not change the element integration. +Input File Usage: +Use the following option to use the surface offset fraction from the surface’s +parent elements (default): +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=OFFSET +FRACTION +surface, ORIGINAL +Abaqus/CAE Usage: +Use the following option to specify a value for the surface offset fraction: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=OFFSET +FRACTION +surface, offset +The offset can be specified as a value or a label (SPOS or SNEG). Specifying +SPOS is equivalent to specifying a value of 0.5; specifying SNEG is equivalent +to specifying a value of −0.5. +Interaction module: Create Interaction: General contact (Standard): +Surface Properties: Shell/Membrane offset assignments: Edit: +Select surface, and click the arrows to transfer surface to list of offset +assignments. +In the Offset Fraction column, enter ORIGINAL to use the surface +offset fraction from the surface's parent elements, enter SPOS to use a +surface offset fraction of 0.5, enter SNEG to use a surface offset fraction +of −0.5, or enter a value for the surface offset fraction. +Feature edges +General contact in Abaqus/Standard includes a supplementary edge-to-surface contact formulation +for feature edges of solid and shell bodies, as discussed in “Defining general contact interactions +in Abaqus/Standard,” Section 35.2.1. By default, the edge-to-surface contact formulation considers +perimeter edges and edges corresponding to initial geometric feature angles of 45° and higher. You can +control the feature edge criterion globally or locally. +Some aspects of the contact property assignment options apply only to the surface-to-surface +formulation . The edge-to-surface formulation always uses the +penalty enforcement method and only involves displacement degrees of freedom. For example, the +edge-to-surface formulation does not contribute to thermal gap conductance across a contact interface. +Specifying a cutoff feature angle +The feature angle is the angle formed between normals of two facets connected to an edge. The angles +between facets are based on the initial configuration. A negative angle results at concave meetings of +facets; therefore, these edges are never included in the contact domain. Figure 35.4.2–4 shows some +examples of how the feature angle is calculated for different edges.The feature angle for edge A is 90° +(the angle between +). +Edge C forms a T-intersection with three facets (shown in two dimensions in Figure 35.4.2–5); its feature +angles are 0°, −90°, and −90°. Perimeter edges (for example, edge D in Figure 35.4.2–4) can be thought +of as a special type of feature edge where the feature angle is 180°. +); the feature angle for edge B is −25° (the angle between +and +and +If a feature angle criterion is in effect (by default or because you specified it), geometric edges of +solid and shell bodies with feature angles greater than or equal to the specified angle are included in the +general contact domain. The contact inclusion and exclusion options (discussed in “Defining general +contact interactions in Abaqus/Standard,” Section 35.2.1) apply to both the surface-to-surface contact +n2 +n1 +n2 +n2 +n3 +( )_ +25o +n3 +n1 +SURFACE PROPERTIES FOR Abaqus/Standard GENERAL CONTACT +( )_ +n5 +n4 +n5 +n4 +n7 +D (perimeter edge) +n5 +(+) +180 +n7 +n6 +0o +n II n +Figure 35.2.2–1 Calculating the feature angle. +_ +90o +_ +90o +arrows are perpendicular +to surface facets +Figure 35.2.2–2 Feature angles for a T-intersection (for example, edge C in Figure 35.4.2–4). +formulation and the edge-to-surface contact formulation (and further control which portions of surfaces +may interact with either formulation). The sign of the feature angle is considered when determining +whether or not a geometric feature edge should be included in the general contact domain. For example, +if a cutoff feature angle of 20° were specified, edge A would be activated as a feature edge in the contact +model (because the feature angle of 90° is greater than the cutoff of 20°) but edges B and C would not +be activated (because the feature angle at edge B is −25° and the maximum feature angle at edge C is +0°, which are both less than the cutoff of 20°). The cutoff feature angle cannot be set to less than 0° or +more than 180°. Specifying a small cutoff feature angle (for example, less than 20°) may considerably +increase run time without a major impact on the results compared to a larger cutoff angle (> 20°). The +default feature angle cutoff is 45°. +Figure 35.4.2–6 illustrates further how the feature angle is used to determine which geometric +feature edges are activated in the general contact domain. The table to the right of the figure lists the +feature angle values for various edges in the model. Edges connected to shell facets, but not on the +shell perimeter, have more than one corresponding feature angle. The largest feature angle at an edge is +compared to the default or specified cutoff feature angle. For example, if the default cutoff feature angle +Thin solid lines +indicate feature edges. +Thick solid lines indicate +shell perimeter edges. +Edge +Largest feature +angle at edge +Other feature +angles at edge +Shells +Solid +Dashed lines indicate element +boundaries for which edge-to-edge +contact is not modeled. +approximately +105 +o +approximately 30 +_ +o +o +0 ++180 +o +o ++90 +o +0 +none +none +_ + 90 +o +none +_ +o +90 +_ _ +o o +90 , 90 +Figure 35.2.2–3 Feature edges activated in the general contact +domain for the default cutoff feature angle of 45°. +of 45° is in effect, edges A, D, and E would be considered for edge-to-surface contact, while edges B, C, +and F would be ignored for edge-to-surface contact. +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=FEATURE +EDGE CRITERIA +surface, feature_angle_value +Abaqus/CAE Usage: +If the surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +Interaction module: Create Interaction: General contact (Standard): +Surface Properties: Feature edge criteria assignments: Edit: +Select the surface, click the arrows to transfer the surface to the list of +feature assignments, and enter a numerical value for the cutoff feature +angle (in degrees) in the Feature Edge Criteria column. +Specifying that only perimeter edges should be activated +You can specify that only perimeter edges should be considered by the edge-to-surface formulation +globally or in a local region. Perimeter edges occur on “physical” perimeters of shell elements and +on “artificial” edges that occur when a subset of exposed facets on a body are included in the general +contact domain. The classification of an edge as being on the perimeter of the contact domain (or as a +geometric edge with a particular feature angle) is based on the contact inclusion and contact exclusion +definitions and the mesh characteristics. When structural elements share nodes with continuum elements, +the perimeter edges will not be activated on the structural elements because the criterion to designate them +as such is no longer satisfied. +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=FEATURE +EDGE CRITERIA +surface, PERIMETER EDGES +Abaqus/CAE Usage: +If the surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +Interaction module: Create Interaction: General contact (Standard): +Surface Properties: Feature edge criteria assignments: Edit: +Select the surface, click the arrows to transfer the surface to the list of feature +assignments, and enter PERIMETER in the Feature Edge Criteria column. +Specifying that feature edges should not be included +You can specify that no edges should be considered by the edge-to-surface formulation globally or in a +local region. +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=FEATURE +EDGE CRITERIA +surface, NO FEATURE EDGES +Abaqus/CAE Usage: +If the surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +Interaction module: Create Interaction: General contact (Standard): +Surface Properties: Feature edge criteria assignments: Edit: +Select the surface, click the arrows to transfer the surface to the list of feature +assignments, and enter NONE in the Feature Edge Criteria column. +35.2.3 +CONTACT PROPERTIES FOR GENERAL CONTACT IN Abaqus/Standard +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining general contact interactions in Abaqus/Standard,” Section 35.2.1 +• “Mechanical contact properties: overview,” Section 36.1.1 +• “Contact pressure-overclosure relationships,” Section 36.1.2 +• “Contact damping,” Section 36.1.3 +• “Frictional behavior,” Section 36.1.5 +• *CONTACT +• *CONTACT PROPERTY ASSIGNMENT +• *SURFACE INTERACTION +• “Specifying and modifying contact property assignments for general contact,” Section 15.13.2 of +the Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +Contact properties: +• define the surface interaction models that govern the behavior of surfaces when they are in contact; +and +• can be applied selectively to particular regions within a general contact domain. +Assigning contact properties +The default contact property model in Abaqus/Standard assumes “hard” contact in the normal direction, +no friction, no thermal interactions, etc. You can assign a nondefault contact property definition (surface +interaction) to specified regions of the general contact domain. +Contact properties for general contact in Abaqus/Standard are assigned at the beginning of the +analysis and cannot be modified across steps, with an exception for changes to the friction model, as +discussed below. +The surface names used to specify the regions where nondefault contact properties should be +assigned do not have to correspond to the surface names used to specify the general contact domain. +In many cases the contact interaction will be defined for a large domain, while nondefault contact +properties will be assigned to a subset of this domain. Any contact property assignments for regions +that fall outside of the general contact domain will be ignored. The last assignment will take precedence +if the specified regions overlap. +Input File Usage: +*CONTACT PROPERTY ASSIGNMENT +surface_1, surface_2, interaction_property_name +Abaqus/CAE Usage: +This option must be used in conjunction with the *CONTACT option and +should appear at most once; the data line can be repeated as often as necessary +to assign contact properties to different regions. +If the first surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +If the second surface name is omitted +or is the same as the first surface name, contact between the first surface +and itself is assumed. Surfaces can be defined to span multiple unattached +bodies, so self-contact is not limited to contact of a single body with itself. If +the interaction property name is omitted, the unnamed set of default contact +If an interaction property name +properties in Abaqus/Standard is assumed. +is specified, it must also appear as the value of the NAME parameter on a +*SURFACE INTERACTION option in the model portion of the input file. +Use the following options to assign a global contact property to the entire +general contact domain: +Interaction module: Create Interaction: General contact (Standard): +Contact Properties: Global property assignment: +interaction_property_name +Use the following options to assign contact properties to individual surface +pairs: +Interaction module: Create Interaction: General contact (Standard): +Contact Properties: Individual property assignments: Edit: select the +surfaces and the contact property in the columns on the left, and click the +arrows in the middle to transfer them to the list of contact property assignments +In Abaqus/CAE you must assign a global contact property; Abaqus/CAE does +not assume a default contact interaction property. Contact properties assigned +to individual surface pairs override the global assignment. +Changing friction properties during an analysis +The friction properties associated with a given named surface interaction definition can be modified in +any particular step of an Abaqus/Standard analysis, as discussed in “Changing friction properties during +an Abaqus/Standard analysis” in “Frictional behavior,” Section 36.1.5. +Example +The following contact property assignments are specified below as model data in a general contact +analysis: +• a global assignment of contProp1 to the entire general contact domain; +• a local assignment of contProp2 to self-contact for surf1; +• a local assignment of the default Abaqus contact property to contact between surf2 and surf3; +and +• a local assignment of contProp3 to contact between the entire contact domain and surf4. The +friction coefficient for contProp3 is reset from the initial value of 0.20 to 0.05 in the second step. +*SURFACE INTERACTION, NAME=contProp1 +*FRICTION +0.1 +*SURFACE INTERACTION, NAME=contProp2 +*FRICTION +0.15 +*SURFACE INTERACTION, NAME=contProp3 +*FRICTION +0.20 +*CONTACT +*CONTACT INCLUSIONS, ALL EXTERIOR +*CONTACT PROPERTY ASSIGNMENT +, , contProp1 +surf1, surf1, contProp2 +surf2, surf3, +, surf4, contProp3 +… +*STEP +Step1 +*STATIC +… +*END STEP +*STEP +Step2 +*STATIC +… +*CHANGE FRICTION, INTERACTION NAME=contProp3 +*FRICTION +0.05 +*END STEP +35.2.4 +CONTROLLING INITIAL CONTACT STATUS IN Abaqus/Standard +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining general contact interactions in Abaqus/Standard,” Section 35.2.1 +• *CONTACT INITIALIZATION ASSIGNMENT +• *CONTACT INITIALIZATION DATA +• “Creating contact initializations,” Section 15.12.4 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Specifying and modifying contact initialization assignments for general contact,” Section 15.13.3 +of the Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +Contact initialization controls for general contact in Abaqus/Standard: +• can be used to specify whether initial overclosures should be resolved without generating stresses +and strains or treated as interference fits that are gradually resolved over multiple increments; and +• can be used to specify nondefault search zones that determine which nodes are affected in the case +of strain-free adjustments or interference fits. +Abaqus/Standard initializes the contact state based on the gap or penetration state observed in the initial +geometry. Small initial contact overclosures are resolved by default using strain-free adjustments to the +positions of surface nodes. You can define alternative contact initialization methods and then assign them +to contact interactions. For example, you can choose to have initial overclosures for certain interactions +treated as interference fits. +Default contact initialization method +By default, +the general contact algorithm adjusts the initial positions of surface nodes during +preprocessing to remove small initial surface overclosures without generating strains or stresses in the +model, as shown in Figure 35.2.4–1. These adjustments are intended to correct only minor mismatches +associated with mesh generation. +General contact automatically assigns master and slave roles for contact interactions, as discussed +in “Numerical controls for general contact in Abaqus/Standard,” Section 35.2.6. Abaqus/Standard +calculates an overclosure tolerance based on the size of the underlying element facets on a slave +surface. Slave surfaces in a particular interaction are repositioned onto the associated master surface +(using strain-free adjustments) if the two surfaces are initially overclosed by a distance smaller than +the calculated tolerance. Initial gaps between surfaces remain unchanged by default adjustments. If +a portion of a slave surface is initially overclosed by a distance greater than the calculated tolerance, +Abaqus/Standard automatically generates a contact exclusion for this surface portion and its associated +Figure 35.2.4–1 Configuration of contact surfaces after strain-free adjustments to resolve overclosure. +master surface. Therefore, general contact does not create interactions between surfaces (or portions of +surfaces) that are severely overclosed in the initial configuration of the model, and these surfaces can +freely penetrate each other throughout the analysis. +General contact uses the finite-sliding, surface-to-surface contact formulation, so penetration/gap +calculations are computed as averages over finite regions; therefore, it is possible for penetrations and +gaps to be present at individual surface nodes after the adjustments. The default adjustments will +not resolve initial crossings of two reference surfaces associated with shells or membranes, although +techniques to resolve such cases are discussed in “Assigning contact initializations to shell surfaces.” +Defining alternative contact initialization methods +You can define alternative contact initialization methods if the default behavior is not desired. For +example, you may want to increase the tolerance for deep penetrations or specify that certain openings +should be adjusted to a “just touching” status. Furthermore, some analyses call for initial overclosures +to be treated as interference fits rather than resolved with strain-free adjustments. To modify the contact +initialization behavior, you must define one or more alternate contact initialization methods and then +identify which surface pairings are to use which methods. +You assign a name to each contact initialization method. This name is used in the assignment of a +contact initialization method to specific surface pairings . +Input File Usage: +*CONTACT INITIALIZATION DATA, +NAME=contact_initialization_method_name +Abaqus/CAE Usage: +Interaction module: Interaction→Contact Initialization→Create: +Name: contact_initialization_method_name +Increasing the search zones for strain-free adjustments +As discussed above in “Default contact initialization method,” initial gaps and large initial overclosures +between surfaces are not adjusted by the default contact initialization methods. You can optionally +specify nondefault search distances both above and below the surfaces in an interaction; slave surfaces +that lie within these search distances are repositioned directly onto their associated master surface using +strain-free nodal adjustments. Abaqus/Standard takes shell thickness into account when calculating these +search distances. +Specifying a search distance above a surface is used to close small initial gaps between surfaces. +Specifying a search distance below a surface is used to increase the default overclosure tolerance that +Abaqus/Standard uses when performing strain-free adjustments; if you specify a search distance smaller +than the default overclosure tolerance, Abaqus/Standard uses the default tolerance instead. As with the +default initialization behavior, contact exclusions are created for initial overclosures that are larger than +the specified search zone. +Increasing the extent of the search zones for strain-free adjustments can potentially increase the +computational cost of an analysis. It is not generally recommended that you specify a large search zone +since this may cause mesh distortion when nodes are repositioned over large distances. +Input File Usage: +*CONTACT INITIALIZATION DATA, SEARCH ABOVE=a, +SEARCH BELOW=b +Abaqus/CAE Usage: +Interaction module: Interaction→Contact Initialization→Create: +Resolve with strain-free adjustments: Ignore overclosures greater +than: b, Ignore initial openings greater than: a +Specifying an initial clearance distance +By default, the strain-free adjustments discussed above will adjust initial nodal positions such that +surfaces are “just-touching” (with zero penetration/separation). Alternatively, Abaqus/Standard can +make the adjustments to achieve an initial clearance distance that you specify. The adjustments will +occur only for regions that satisfy the search zone tolerances, as discussed above. Mesh distortion can +occur if large strain-free adjustments are necessary to achieve the specified initial clearance distance. +Input File Usage: +Abaqus/CAE Usage: +*CONTACT INITIALIZATION DATA, INITIAL CLEARANCE=h +Interaction module: Interaction→Contact Initialization→Create: +Specify clearance distance: h +Modeling interference fits +the general contact algorithm in Abaqus/Standard can treat +initial overclosures as +Optionally, +interference fits. The general contact algorithm uses a shrink-fit method to gradually resolve the +interference distance over the first step of the analysis (if multiple load increments are used for the +first step) as shown in Figure 35.2.4–2, such that the fraction of the interference resolved up to and +including a particular increment approximately corresponds to the fraction of the step completed. +Stresses and strains are generated as the interference is resolved. Gradually resolving interference over +several increments improves robustness (compared to always resolving the full interference in the first +increment, which is the default for contact pairs) for cases in which a nonlinear response occurs for +“interference-fit loading.” It is generally recommended that you do not apply other loads while the +interference fit is being resolved. +Because contact conditions are enforced in an average sense in a region around each constraint +location for the surface-to-surface contact formulation used by general contact in Abaqus/Standard, +BEGINNING OF STEP +MIDDLE OF STEP +END OF STEP +Figure 35.2.4–2 Gradual resolution of contact interference fit. +penetrations or gaps may be observed at slave nodes when surface-to-surface constraints are in a +zero-penetration state. +Input File Usage: +Abaqus/CAE Usage: +*CONTACT INITIALIZATION DATA, INTERFERENCE FIT +Interaction module: Interaction→Contact Initialization→Create: +Treat as interference fits +Increasing the tolerance for interference fits +Abaqus/Standard calculates an overclosure tolerance based on the size of the underlying element facets +on a slave surface . An interference fit between two +surfaces affects only those slave surfaces that are overclosed by a distance smaller than the calculated +tolerance; contact is ignored entirely for surfaces that are overclosed by a distance greater than the +calculated tolerance. +Optionally, you can redefine the overclosure tolerance to include larger overclosures in the +If you specify a tolerance that is smaller than the default calculated tolerance, +interference fit. +Abaqus/Standard uses the default calculated tolerance instead. +Input File Usage: +*CONTACT INITIALIZATION DATA, INTERFERENCE FIT, +SEARCH BELOW=b +Abaqus/CAE Usage: +Interaction module: Interaction→Contact Initialization→Create: +Treat as interference fits: Ignore overclosures greater than: b +Specifying the interference distance +By default, the interference distance is implied by the initial overclosure of the mesh; alternatively, you +can specify the interference distance. In this case Abaqus/Standard first makes strain-free adjustments +of nodal positions such that the initial overclosure in the adjusted configuration corresponds to the +specified interference distance and then invokes the shrink fit method discuss above, as depicted in +Figure 35.2.4–3. Mesh distortion can occur if large strain-free adjustments are necessary to achieve the +specified interference distance. +The search region for the strain-free adjustments and subsequent shrink fit resolution is at least at +large as the search region for the case discussed previously in which the interference distance is not +specified. The search region will include overclosures at least as large as the specified interference fit +and openings at least as large as the optionally specified search distance above a surface. +Input File Usage: +*CONTACT INITIALIZATION DATA, INTERFERENCE FIT=h, +SEARCH ABOVE=a, SEARCH BELOW=b +Abaqus/CAE Usage: +Interaction module: Interaction→Contact Initialization→Create: +Treat as interference fits: Specify interference distance: h: Ignore +overclosures greater than: b, Ignore initial openings greater than: a +Deactivating friction while resolving interference fits +The presence of a friction model can degrade the robustness of resolving interference fits. +It is +generally recommended that you temporarily deactivate friction models while Abaqus/Standard +resolves interference fits. You can deactivate the friction model in the first step while interference fits +are resolved using the “change friction” method discussed in “Changing friction properties during an +Abaqus/Standard analysis” in “Frictional behavior,” Section 36.1.5. +Cases in which interference fit resolution with contact pairs is preferred +Large interferences may be difficult to resolve with the finite-sliding, surface-to-surface formulation. +Using this formulation, overclosures tend to be resolved along the slave facet normal directions; using +the node-to-surface formulation, which is available only with the contact pair algorithm, overclosures +tend to be resolved along the master surface normal directions. Figure 35.2.4–4 illustrates a case where +differing normal directions lead to undesirable tangential motion during an interference fit. In some +cases it may be preferable to resolve large initial overclosures with node-to-surface discretization using +the contact pair algorithm . +Original mesh +geometry +After strain-free +adjustments +Middle of step +End of step +Figure 35.2.4–3 Treatment of a specified interference distance that +differs from the interference implied by the original mesh. +surface-to-surface +node-to-surface +master surface +overclosure resolution direction +Figure 35.2.4–4 Comparison of contact formulations in an example with a large interference fit. +Assigning contact initialization methods +You can assign contact initialization methods to selected surface pairings. +The surface names used in the assignment of contact initialization methods do not have to +correspond to the surface names used to specify the general contact domain. In many cases nondefault +contact initialization methods will be assigned to a subset of the overall general contact domain. Any +contact initialization assignments for regions that fall outside of the general contact domain are ignored. +The last assignment takes precedence if the specified interactions overlap. +Input File Usage: +Use the following option to assign contact inititialization methods: +*CONTACT INITIALIZATION ASSIGNMENT +surface_1, surface_2, contact_initialization_method_name +This option must be used in conjunction with the *CONTACT option. The +data line can be repeated as often as necessary to assign contact initialization +methods to different regions. +If the first surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. If the second surface name is omitted or is +the same as the first surface name, contact between the first surface and itself is +assumed. Keep in mind that surfaces can be defined to span multiple unattached +bodies, so self-contact is not limited to contact of a single body with itself. +If the contact initialization method name is omitted, +the default contact +initialization method in Abaqus/Standard is assumed. If a contact initialization +method name is specified, it must also appear as the value of the NAME +Abaqus/CAE Usage: +parameter on a *CONTACT INITIALIZATION DATA option in the model +portion of the input file. +Interaction module: Create Interaction: General contact (Standard): +Contact Properties: Initialization assignments: Edit: select the surfaces +and the initialization in the columns on the left, and click the arrows in the +middle to transfer them to the list of contact initialization assignments +Assigning contact initializations to shell surfaces +The surfaces in a contact initialization assignment can be either single- or double-sided. Single-sided +surfaces must have consistent surface normal orientations for adjacent faces. Strain-free adjustments +will not move surface nodes past the reference surface of the opposing surface if the assignment of a +contact initialization method is made with double-sided surfaces. +Using single-sided surfaces in the assignment of a contact initialization method for shells or +membranes provides enhanced control over contact initialization for cases in which shell or membrane +reference surfaces are initially crossed or are initially on the wrong side of each other. Figure 35.2.4–5 +shows examples of adjustments for nearby segments of shell surfaces. For the case shown on the left it +is assumed that single-sided surfaces with normal directions pointing away from each another are used +in the assignment of the contact initialization method. In this case nodes are moved across the opposing +reference surface during the strain-free adjustments. +For the case shown on the right in Figure 35.2.4–5 it is assumed that single-sided surfaces with +normal directions pointing toward each other are used in the assignment of the contact initialization +method. In this case an initial gap is observed between the single-sided surfaces (which is also the case +if double-sided surfaces are used in the contact initialization assignment). No strain-free adjustments will +be made by default for openings such as this; however, if a nondefault contact initialization method is +specified with an initial opening search tolerance set to a value exceeding the initial separation distance, +strain-free adjustments will close the gap as shown in the figure (without moving nodes past the opposing +reference surface). +Examples +The following contact initialization assignments are specified below as model data in a general contact +analysis: +• a global assignment of shrink_fit to the entire general contact domain; +• a local assignment of shrink_fit_local to contact between surfaces surface_A and +surface_B—the search zone is specified explicitly to increase the default overclosure tolerance; +• a local assignment of the default Abaqus contact +surface_C and surface_D; and +initialization method to contact between +• a local assignment of sfa_pickside to contact between double-sided surfaces surface_1 +each surface, surface_1_TOP and +side of +and surface_2 by specifying one +surface_2_BOTTOM, in the data lines . +Surface 1 +top +Overclosure +Gap +Surface 1 +bottom +Surface 2 +top +Surface 2 +bottom +Overclosure +resolution +Gap +resolution +Surface 2 +Surface 1 +Surface 1 +Surface 2 +Figure 35.2.4–5 Strain-free adjustments during contact initialization for single-sided shell surfaces. +*CONTACT INITIALIZATION DATA, NAME=shrink_fit, INTERFERENCE FIT +*CONTACT INITIALIZATION DATA, NAME=shrink_fit_local, +INTERFERENCE FIT, SEARCH BELOW = 15.0 +*CONTACT INITIALIZATION DATA, NAME=sfa_pickside, +SEARCH BELOW = 10.0 +… +*CONTACT +*CONTACT INCLUSIONS, ALL EXTERIOR +*CONTACT INITIALIZATION ASSIGNMENT +, , shrink_fit +surface_A, surface_B, shrink_fit_local +surface_C, surface_D, +surface_1_TOP, surface_2_BOTTOM, sfa_pickside +35.2.5 +STABILIZATION FOR GENERAL CONTACT IN Abaqus/Standard +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining general contact interactions in Abaqus/Standard,” Section 35.2.1 +• *CONTACT +• *CONTACT STABILIZATION +• “Creating contact stabilization definitions,” Section 15.12.5 of the Abaqus/CAE User’s Manual, in +the online HTML version of this manual +• “Specifying and modifying contact stabilization assignments for general contact,” Section 15.13.4 +of the Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +Contact stabilization for general contact in Abaqus/Standard: +• is often helpful in stabilizing unconstrained rigid body modes in static analyses; +• can be applied selectively to particular regions within a general contact domain; and +• can vary over time. +Stabilization based on viscous damping of relative motion between surfaces +Contact stabilization is based on viscous damping opposing incremental relative motion between nearby +surfaces, in the same manner as contact damping . The most +common purpose of contact stabilization is to stabilize otherwise unconstrained “rigid body motion” +before contact closure and friction restrain such motions. A goal of artificial stabilization, such as contact +stabilization, is to provide enough stabilization to enable a robust, efficient simulation without degrading +the accuracy of the results. In most cases contact stabilization is not activated by default (an exception +is discussed in “Contact at a single point” in “Common difficulties associated with contact modeling +in Abaqus/Standard,” Section 38.1.2), so you will generally need to activate contact stabilization if +convergence problems associated with unconstrained rigid body modes may be present in your analysis. +Once activated, contact stabilization is highly automated. +The following expressions for the normal pressure, +, associated with +contact stabilization involve many semi-automated factors to facilitate achieving the desired stabilization +characteristics: +, and shear stress, +where +and +is a damping coefficient; +are the relative normal and tangential velocities, respectively, between nearby +points on opposing contact surfaces; +is a constant scale factor; +is a time-dependent scale factor; +is a scale factor based on the increment number; +is a scale factor based on the separation distance; and +is a constant scale factor for tangential stabilization. +The damping coefficient and relative velocities are computed by Abaqus/Standard. The damping +coefficient is equal to a fixed, small fraction, +, times a representative stiffness of elements underlying +the contact surfaces, +. Relative velocities in a static +analysis are computed by dividing relative incremental displacements, +, by the time +increment size, +, times the time period of the step, +and +. +Therefore, the following contact stabilization expressions apply to statics: +where the portions within brackets can be thought of as stabilization stiffnesses (representing resistance to +relative motion between nearby surfaces). The stabilization stiffness is inversely proportional to the time +increment size, which is a desirable characteristic. Stabilization stiffness increases if the time increment +size is reduced, which happens automatically in Abaqus/Standard if convergence difficulties occur for a +particular time increment size. +Assigning stabilization to interactions +Contact stabilization assignments for specific interactions within general contact can be made globally +or locally and are specified as part of step definitions. In most cases you only need to specify which +interactions are eligible for contact stabilization without adjusting the scale factors discussed previously. +Input File Usage: +Use the following option to specify which interactions should use contact +stabilization: +*CONTACT STABILIZATION +surf_1, surf_2 +If the first surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +If the second surface name is omitted, +contact between the first surface and itself is assumed. +Abaqus/CAE Usage: +Use the following options to assign contact stabilization definitions to +individual surface pairs: +Interaction module: Create Interaction: General contact (Standard): +Contact Properties: Stabilization assignments: Edit: select the surfaces +and the stabilization name in the columns on the left, and click the arrows in +the middle to transfer them to the list of contact stabilization assignments +Specifying stabilization scale factors +In some cases you may want to adjust one or more scale factors associated with contact stabilization. You +can use multiple instances of this option to achieve different scale factor settings for different general +contact interactions. +Constant scale factors +The default setting of +As shown in the expressions above for the stabilization pressure and shear stress, the scale factor +applies to normal and tangential stabilization, whereas the scale factor +stabilization. The default setting of the constant scale factor +applies only to tangential +is unity for the specified interactions. +is zero such that no tangential stabilization stiffness exists by default +for the specified interactions. Normal-direction-only contact stabilization is adequate in many cases. +Other analyses can benefit from tangential stabilization stiffness; however, if you specify a nonzero +setting of +, keep in mind that tangential contact stabilization often absorbs significant energy if +large relative tangential motion occurs between nearby surfaces. Large energy absorbed by stabilization +is one indication that analysis results are likely to be significantly affected by the stabilization. Normal +contact stabilization is much less likely to absorb significant energy and, thus, tends to have less influence +on the results. +Input File Usage: +*CONTACT STABILIZATION, SCALE FACTOR= +TANGENT FRACTION= +, +Abaqus/CAE Usage: +Interaction module: Interaction→Contact Stabilization→Create: +Scale factor: +, Tangential factor: +Time-dependent scale factors +and +control time-dependence of the contact stabilization. By default, +is a per-increment reduction factor (equal to 0.1 by default) and +The scale factors +is equal to the fraction of the step remaining. The other factor varies according to +, +where +is the increment +number within a step. These defaults imply that the stabilization is reduced by more than an order +of magnitude in successive increments of the same size and that no stabilization is applied in the final +increment of a step. The defaults are appropriate for most cases in which contact stabilization is intended +to provide stabilization in initial increments while contact is being established. +amplitude curve that will govern +Two options are provided for adjusting the time-dependent scale factors: you can refer to an +(recall the expression +given previously). For example, if unstable modes remain after contact is established, +, and you can specify the value of +you may want +to remain equal to unity throughout a step for certain interactions, +which can be accomplished by referring to an amplitude with a constant value of one and setting the +per-increment reduction factor, +, equal to one. +and +Input File Usage: +*AMPLITUDE, NAME=name +*CONTACT STABILIZATION, AMPLITUDE=name, +REDUCTION PER INCREMENT= +Abaqus/CAE Usage: +Load or Interaction module: Create Amplitude: Name: name +Interaction module: Interaction→Contact Stabilization→Create: +Reduction factor: +, Amplitude: name +Resetting time-dependent scale factors in subsequent steps +Contact stabilization definitions do not affect subsequent steps unless an amplitude reference is +specified. If an amplitude based on the total time is specified, the same amplitude curve continues to +govern the variation of +in subsequent steps until a new contact stabilization definition is assigned +If an amplitude based on the step time is specified, the amplitude curve governs +to the interaction. +remains constant (at the ending value) in subsequent steps until a new +contact stabilization definition is assigned to the interaction. In both cases you can also reset the contact +stabilization definition to remove stabilization from a step. Resetting ensures that contact stabilization +options from prior steps do not affect the current step. +for a single step and +Input File Usage: +Abaqus/CAE Usage: +*CONTACT STABILIZATION, RESET +Load or Interaction module: Create Amplitude: Name: name +Interaction module: Interaction→Contact Stabilization→Create: +Reset values from previous steps +Gap-dependent scale factor +The scale factor +controls contact stabilization as a function of the local separation distance between +surfaces. By default, this factor is unity for zero gap distance and is zero when the gap distance is greater +than or equal to a characteristic surface dimension. You can control the gap distance at which +becomes zero. Specifying a large value for this threshold distance is not recommended because of the +tendency to increase solution cost per iteration (due to increased connectivity) as the threshold distance +increases. +Input File Usage: +Abaqus/CAE Usage: +*CONTACT STABILIZATION, RANGE=distance +Interaction module: Interaction→Contact Stabilization→Create: +Zero stabilization distance: Specify: distance +Hierarchy of contact stabilization definitions +The interface discussed above is the recommended method for specifying contact stabilization for general +contact; however, contact stabilization can be introduced for general contact interactions in two other +ways. The order of precedence in cases of overlap is as follows: +• First priority is given to the contact stabilization assignment options discussed in this section. +• Second priority is given to the contact stabilization assignment options discussed in “Automatic +stabilization of rigid body motions in contact problems” in “Adjusting contact controls in +Abaqus/Standard,” Section 35.3.6. +• Third priority is given to the default contact stabilization discussed in “Contact at a single point” in +“Common difficulties associated with contact modeling in Abaqus/Standard,” Section 38.1.2. +35.2.6 +NUMERICAL CONTROLS FOR GENERAL CONTACT IN Abaqus/Standard +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining general contact interactions in Abaqus/Standard,” Section 35.2.1 +• *CONTACT +• *CONTACT FORMULATION +• *CONTACT CONTROLS +• “Specifying master-slave assignments for general contact,” Section 15.13.6 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +Numerical controls associated with the general contact algorithm in Abaqus/Standard: +• should not be modified from their default settings for the majority of problems; +• can be used for problems where the default settings do not provide cost-effective solutions; +• can be used to control the master-slave roles and the sliding formulation; and +• in some cases can be applied selectively to particular regions within a general contact domain. +Contact formulation +The general contact algorithm uses the finite-sliding, surface-to-surface contact formulation, which is +discussed in “Contact formulations in Abaqus/Standard,” Section 37.1.1. Other contact formulations are +not available for general contact in Abaqus/Standard. +Constraint enforcement method +The general contact algorithm uses a penalty method to enforce active contact constraints by default. +Other constraint enforcement methods can be specified as part of the surface interaction (i.e., contact +property) definition, as discussed in “Contact constraint enforcement methods in Abaqus/Standard,” +Section 37.1.2. Assignment of contact properties to general contact interactions is discussed in “Contact +properties for general contact in Abaqus/Standard,” Section 35.2.3. +Numerical controls for friction +Numerical controls associated with friction are discussed in “Frictional behavior,” Section 36.1.5. +Master and slave roles +The surface-to-surface contact formulation used by general contact generates individual contact +constraints using a master-slave approach, as discussed in “Contact formulations in Abaqus/Standard,” +Section 37.1.1. Abaqus/Standard assigns default pure master-slave roles for contact +involving +disconnected bodies within the general contact domain. Internal surfaces are generated automatically +using the naming convention General_Contact_Faces_k, where k corresponds to an +automatically assigned component number. By default, the lowered-number component surfaces will +act as master surfaces to the higher-numbered component surfaces. You can determine the default pure +master-slave roles by viewing the automatically generated internal surfaces in the Visualization module +of Abaqus/CAE . Self-contact within a body is treated with balanced master-slave contact +by default, with each surface node acting as a master node in some constraints and as a slave node in +other constraints. +For example, if the general contact domain spans three disconnected bodies, the following three +internal “component-surfaces” for general contact are created automatically: +• General_Contact_Faces_1 +• General_Contact_Faces_2 +• General_Contact_Faces_3 +By default, the first surface listed acts as a master to the other two, and General_Contact_Faces_2 +acts as a master to General_Contact_Faces_3. Self-contact within each of these three surfaces +is modeled with balanced master-slave contact by default. +Specifying non-default master-slave roles +You can override the default master-slave roles by specifying pure master-slave roles or by specifying +that balanced master-slave contact should be used. The default master-slave treatment works well in most +cases. Keep the following points in mind when modifying the master-slave assignments, in addition to +other factors discussed in this section: +• Do not use the internally generated component surfaces when assigning alternative master-slave +roles (instead, use surface names that you define). +• The master-slave role assignments are part of the model definition and cannot be modified from step +to step. +• The guidelines for assigning pure master-slave roles for contact pairs discussed in “Defining contact +between two separate surfaces” in “Defining contact pairs in Abaqus/Standard,” Section 35.3.1, are +also applicable for situations in which you reassign pure master-slave roles for general contact. +• The limitations of balanced (symmetric) master-slave contact pairs discussed in “Using +symmetric master-slave contact pairs to improve contact modeling” in “Defining contact pairs in +Abaqus/Standard,” Section 35.3.1, are also applicable for situations in which you reassign balanced +master-slave contact for general contact. Balanced master-slave contact can result in reduced +robustness due to the increased number of constraints and the possibility of overconstraints. +Input File Usage: +Use the following option to indicate that the first surface should be considered +the slave surface: +*CONTACT FORMULATION, TYPE=MASTER SLAVE ROLES +surf_1, surf_2, SLAVE +Use the following option to indicate that the first surface should be considered +the master surface: +*CONTACT FORMULATION, TYPE=MASTER SLAVE ROLES +surf_1, surf_2, MASTER +If the first surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. The second surface name must be specified. +Use the following option to specify that balanced master-slave contact should +be used between two surfaces: +*CONTACT FORMULATION, TYPE=MASTER SLAVE ROLES +surf_1, surf_2, BALANCED +If the first surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +If the second surface name is omitted, +contact between the first surface and itself is assumed. +Interaction module: Create Interaction: General contact (Standard): +Contact Formulation: Master-slave assignments: Edit: +select the surfaces in the columns on the left, and click the arrows in the middle +to transfer them to the list of master-slave assignments. +In the First Surface Type column, enter SLAVE to indicate that the +first surface should be considered the slave surface, enter MASTER +to indicate that the first surface should be considered the master +surface, or enter BALANCED to specify that balanced master-slave +contact should be used between the two surfaces. +Abaqus/CAE Usage: +Automatically generated contact exclusions +Abaqus/Standard automatically generates contact exclusions for the master-slave roles opposite to +specified pure master-slave roles; therefore, self-contact is excluded for any regions of the two surfaces +that overlap. For example, specifying that the general contact interaction between surf_A and surf_B +should use pure master-slave contact with surf_A considered to be the slave surface would result in +exclusions being generated internally for master faces of surf_A contacting slave faces of surf_B; +self-contact would be excluded for the region of overlap between surf_A and surf_B. An error message +is issued if the second surface name is omitted or is the same as the first surface name since this input +would result in the exclusion of self-contact for the surface. +Smoothness of contact force redistribution upon sliding +You can control the smoothness of nodal contact force redistribution upon sliding. The default setting, +which is generally appropriate, results in the smoothness of the nodal force redistribution being of the +same order as the elements underlying the slave surface; that is, linear redistribution smoothness for linear +elements, and quadratic redistribution smoothness for second-order elements. Quadratic redistribution +smoothness usually tends to improve convergence behavior and improve resolution of contact stresses +within regions of rapidly varying contact stresses. However, quadratic redistribution smoothness tends +to increase the number of nodes involved in each constraint, which can increase the computational cost +of the equation solver. Linear redistribution smoothness tends to provide better resolution of contact +stresses near edges of active contact regions and, therefore, occasionally results in better convergence +behavior. +Input File Usage: +Use the following option to indicate that the smoothness of the contact force +redistribution upon sliding should be of the same order as the elements +underlying the slave surface: +*CONTACT FORMULATION, TYPE=SLIDING TRANSITION +surf_1, surf_2, ELEMENT ORDER SMOOTHING +If the first surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +If the second surface name is omitted, +contact between the first surface and itself is assumed. +Use the following option to indicate linear smoothness of the contact force +redistribution upon sliding: +*CONTACT FORMULATION, TYPE=SLIDING TRANSITION +surf_1, surf_2, LINEAR SMOOTHING +If the first surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +If the second surface name is omitted, +contact between the first surface and itself is assumed. +Use the following option to indicate quadratic smoothness of the contact force +redistribution upon sliding: +*CONTACT FORMULATION, TYPE=SLIDING TRANSITION +surf_1, surf_2, QUADRATIC SMOOTHING +If the first surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +If the second surface name is omitted, +contact between the first surface and itself is assumed. +Additional global numerical controls for general contact +Some additional numerical contact controls can be modified globally from step-to-step for general +contact; you cannot specify contact controls for individual surface pairings within the general contact +domain. You can apply contact stabilization to address rigid body modes that occur prior to the +establishment of contact in the model, and you can adjust the tolerances used by Abaqus/Standard to +determine contact penetrations and separations; both techniques are discussed in “Adjusting contact +controls in Abaqus/Standard,” Section 35.3.6. +35.3 +Defining contact pairs in Abaqus/Standard +• “Defining contact pairs in Abaqus/Standard,” Section 35.3.1 +• “Assigning surface properties for contact pairs in Abaqus/Standard,” Section 35.3.2 +• “Assigning contact properties for contact pairs in Abaqus/Standard,” Section 35.3.3 +• “Modeling contact interference fits in Abaqus/Standard,” Section 35.3.4 +• “Adjusting initial surface positions and specifying initial clearances in Abaqus/Standard contact +pairs,” Section 35.3.5 +• “Adjusting contact controls in Abaqus/Standard,” Section 35.3.6 +• “Defining tied contact in Abaqus/Standard,” Section 35.3.7 +• “Extending master surfaces and slide lines,” Section 35.3.8 +• “Contact modeling if substructures are present,” Section 35.3.9 +• “Contact modeling if asymmetric-axisymmetric elements are present,” Section 35.3.10 +35.3.1 +DEFINING CONTACT PAIRS IN Abaqus/Standard +Products: Abaqus/Standard Abaqus/CAE +References +• “Element-based surface definition,” Section 2.3.2 +• “Node-based surface definition,” Section 2.3.3 +• “Analytical rigid surface definition,” Section 2.3.4 +• “Contact interaction analysis: overview,” Section 35.1.1 +• *CONTACT PAIR +• *SURFACE +• *MODEL CHANGE +• “Defining surface-to-surface contact,” Section 15.13.7 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Defining self-contact,” Section 15.13.8 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +• “Using contact and constraint detection,” Section 15.16 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +Contact pairs in Abaqus/Standard: +• can be used to define interactions between bodies in mechanical, coupled temperature- +displacement, coupled thermal-electrical-structural, coupled pore pressure-displacement, coupled +thermal-electrical, and heat transfer simulations; +• are part of the model definition; +• can be formed using a pair of rigid or deformable surfaces or a single deformable surface; +• do not have to use surfaces with matching meshes; and +• cannot be formed with one two-dimensional surface and one three-dimensional surface. +You can define contact in Abaqus/Standard in terms of two surfaces that may interact with each +other as a “contact pair” or in terms of a single surface that may interact with itself in “self-contact.” +Abaqus/Standard enforces contact conditions by forming equations involving groups of nearby nodes +from the respective surfaces or, in the case of self-contact, from separate regions of the same surface. +This section describes various aspects of defining contact pairs and refers to other sections for additional +details. +Defining contact pairs +To define a contact pair, you must indicate which pairs of surfaces may interact with one another or which +surfaces may interact with themselves. Contact surfaces should extend far enough to include all regions +that may come into contact during an analysis; however, including additional surface nodes and faces +that never experience contact may result in significant extra computational cost (for example, extending a +slave surface such that it includes many nodes that remain separated from the master surface throughout +an analysis can significantly increase memory usage unless penalty contact enforcement is used). +Every contact pair is assigned a contact formulation (either explicitly or by default) and must +refer to an interaction property. Discussion of the various available contact formulations (based on +whether the tracking approach assumes finite- or small-sliding—and whether the contact discretization +is based on a node-to-surface or surface-to-surface approach) is provided in “Contact formulations in +Abaqus/Standard,” Section 37.1.1. Interaction property definitions are discussed in “Assigning contact +properties for contact pairs in Abaqus/Standard,” Section 35.3.3. +Defining contact between two separate surfaces +When a contact pair contains two surfaces, the two surfaces are not allowed to include any of the same +nodes and you must choose which surface will be the slave and which will be the master. The selection of +master and slave surfaces is discussed in detail in “Choosing the master and slave roles in a two-surface +contact pair” in “Contact formulations in Abaqus/Standard,” Section 37.1.1. For simple contact pairs +consisting of two deformable surfaces, the following basic guidelines can be used: +• The larger of the two surfaces should act as the master surface. +• If the surfaces are of comparable size, the surface on the stiffer body should act as the master surface. +• If the surfaces are of comparable size and stiffness, the surface with the coarser mesh should act as +the master surface. +Defining contact pairs using the finite-sliding, node-to-surface formulation +Abaqus/Standard uses a finite-sliding, node-to-surface formulation by default. +Input File Usage: +*CONTACT PAIR, INTERACTION=interaction_property_name +slave_surface_name, master_surface_name +Abaqus/CAE Usage: +You can also specify the contact discretization directly: +*CONTACT PAIR, INTERACTION=interaction_property_name, +TYPE=NODE TO SURFACE +slave_surface_name, master_surface_name +Interaction module: Create Interaction: Surface-to-surface +contact (Standard): select the master surface, click Surface or +Node Region, select the slave surface, +Interaction editor, Sliding formulation: Finite sliding, Discretization +method: Node to surface, Contact interaction property: +interaction_property_name +Defining contact pairs using the finite-sliding, surface-to-surface formulation +A node-based slave surface precludes the use of surface-to-surface discretization. Some contact +capabilities are not available with the finite-sliding, surface-to-surface formulation, including crack +propagation . +Input File Usage: +Use the following option to define contact constraints using the finite-sliding, +surface-to-surface formulation: +Abaqus/CAE Usage: +*CONTACT PAIR, INTERACTION=interaction_property_name, +TYPE=SURFACE TO SURFACE +slave_surface_name, master_surface_name +Interaction module: Create Interaction: Surface-to-surface contact +(Standard): select the master surface, click Surface, select the slave surface, +Interaction editor, Sliding formulation: Finite sliding, Discretization +method: Surface to surface, Contact interaction property: +interaction_property_name +Defining contact pairs using the small-sliding, node-to-surface formulation +The small-sliding tracking approach uses node-to-surface discretization by default. For an explanation +of when the small-sliding tracking approach is appropriate in an analysis, see “Using the small-sliding +tracking approach” in “Contact formulations in Abaqus/Standard,” Section 37.1.1. +Input File Usage: +Abaqus/CAE Usage: +*CONTACT PAIR, INTERACTION=interaction_property_name, +SMALL SLIDING +slave_surface_name, master_surface_name +You can also specify the contact discretization directly: +*CONTACT PAIR, INTERACTION=interaction_property_name, +SMALL SLIDING, TYPE=NODE TO SURFACE +slave_surface_name, master_surface_name +Interaction module: Create Interaction: Surface-to-surface +contact (Standard): select the master surface, click Surface or +Node Region, select the slave surface, +Interaction editor, Sliding formulation: Small sliding, Discretization +method: Node to surface, Contact interaction property: +interaction_property_name +Defining contact pairs using the small-sliding, surface-to-surface formulation +A node-based slave surface precludes the use of surface-to-surface discretization. +Input File Usage: +*CONTACT PAIR, INTERACTION=interaction_property_name, +SMALL SLIDING, TYPE=SURFACE TO SURFACE +slave_surface_name, master_surface_name +Abaqus/CAE Usage: +Interaction module: Create Interaction: Surface-to-surface contact +(Standard): select the master surface, click Surface, select the slave surface, +Interaction editor, Sliding formulation: Small sliding, Discretization +method: Surface to surface, Contact interaction property: +interaction_property_name +Using symmetric master-slave contact pairs to improve contact modeling +For node-to-surface contact it is possible for master surface nodes to penetrate the slave surface +without resistance with the strict master-slave algorithm used by Abaqus/Standard. This penetration +tends to occur if the master surface is more refined than the slave surface or a large contact pressure +develops between soft bodies. Refining the slave surface mesh often minimizes the penetration of +the master surface nodes. If the refinement technique does not work or is not practical, a symmetric +master-slave method can be used if both surfaces are element-based surfaces with deformable or +deformable-made-rigid parent elements. To use this method, define two contact pairs using the same two +surfaces, but switch the roles of master and slave surface for the two contact pairs. This method causes +Abaqus/Standard to treat each surface as a master surface and, thus, involves additional computational +expense because contact searches must be conducted twice for the same contact pair. The increased +accuracy provided by this method must be compared to the additional computational cost. +All of the contact formulations are available for symmetric master-slave contact pairs, and can be +applied using the same options discussed above. +Input File Usage: +Abaqus/CAE Usage: +*CONTACT PAIR, INTERACTION=interaction_property_name +surface_1, surface_2 +surface_2, surface_1 +Interaction module: Create Interaction: Surface-to-surface +contact (Standard): select the master surface, click Surface, +select the slave surface +Copy this interaction to a new interaction, and edit the new interaction. In the +interaction editor, click Switch to reverse the master and slave surfaces. +Limitations of symmetric master-slave contact pairs +Using symmetric master-slave contact pairs can lead to overconstraint problems when very stiff or “hard” +contact conditions are enforced. See “Contact constraint enforcement methods in Abaqus/Standard,” +Section 37.1.2, for a discussion of overconstraints and alternate constraint enforcement methods. +For softened contact conditions, use of symmetric master-slave contact pairs will cause deviations +from the specified pressure-versus-overclosure behavior, because both contact pairs contribute to the +overall interface stress without accounting for one another. For example, symmetric master-slave +contact pairs effectively double the overall contact stiffness if a linear pressure-overclosure relationship +is specified. +Likewise, use of symmetric master-slave contact pairs will cause deviations from the friction +model if an optional shear stress limit is specified , because the contact stresses observed by each contact pair will +be approximately one-half of the total interface stress. +Similarly, it can be difficult to interpret the results at the interface for symmetric master-slave contact +pairs. In this case both surfaces at the interface act as slave surfaces, so each has contact constraint values +associated with it. The constraint values that represent contact pressures are not independent of each +other. Therefore, the constraint values reported in the data (.dat) and results (.fil) files represent +only a part of the total interface pressure and have to be summed to obtain the total. +In the output database, mechanical contact variables are reported at the nodes on both the master and +slave surfaces per contact pair and not just the slave surface where constraints are formed. Consequently, +two result sets are available per surface of a symmetric master-slave contact pair; once when a surface +acts as a slave and once as a master. For nodal contact pressures the Visualization module of Abaqus/CAE +only reports the maximum of the two pressure values associated with a node when the surface containing +the node acts either as a master or as a slave surface. Even in this case, the contact pressures do not +represent the true interface pressure. +Apart from contact pressures, some contact output may be confusing with symmetric master-slave +contact pairs. For example, Abaqus/Standard may report a positive opening distance on one side of a +contact interface but zero opening distance (i.e., touching) on the opposite side of the interface. Typically +this is caused by the shape or relative mesh refinement of the two surfaces. +Defining self-contact +Define contact between a single surface and itself by specifying only a single surface or by specifying +the same surface twice. The small-sliding tracking approach cannot be used with self-contact. +Defining self-contact using node-to-surface discretization +Abaqus/Standard uses node-to-surface contact discretization by default for self-contact. +Input File Usage: +Use either of the following options: +Abaqus/CAE Usage: +*CONTACT PAIR, INTERACTION=interaction_property_name +surface_1, +*CONTACT PAIR, INTERACTION=interaction_property_name +surface_1, surface_1 +Interaction module: Create Interaction: +Self-contact (Standard): select the surface +Interaction editor, Discretization method: Node to surface, Contact +interaction property: interaction_property_name +or +Interaction module: Create Interaction: Surface-to-surface contact +(Standard): select the surface, click Surface, select the surface again +Interaction editor, Sliding formulation: Finite sliding, Discretization +method: Node to surface, Contact interaction property: +interaction_property_name +Defining self-contact using surface-to-surface discretization +Surface-to-surface discretization often leads to more accurate modeling of self-contact simulations. +However, because the self-contact surface is acting as both a master and a slave, surface-to-surface +discretization can sometimes significantly increase the solution cost. +Input File Usage: +Use either of the following options: +*CONTACT PAIR, INTERACTION=interaction_property_name, +TYPE=SURFACE TO SURFACE +surface_1, +*CONTACT PAIR, INTERACTION=interaction_property_name, +TYPE=SURFACE TO SURFACE +surface_1, surface_1 +Abaqus/CAE Usage: +Interaction module: Create Interaction: +Self-contact (Standard): select the surface +Interaction editor, Discretization method: Surface to surface, Contact +interaction property: interaction_property_name +or +Interaction module: Create Interaction: Surface-to-surface contact +(Standard): select the surface, click Surface, select the surface again +Interaction editor, Sliding formulation: Finite sliding, Discretization +method: Surface to surface, Contact interaction property: +interaction_property_name +Limitations of self-contact +Self-contact is valid only for mechanical surface interactions and is limited to finite sliding with element- +based surfaces. +A node of a self-contact surface can be both a slave node and a member of the master surface +for two-dimensional self-contact using the surface-to-surface formulation and for all three-dimensional +self-contact. In these cases the contact behavior is similar to symmetric master-slave contact pairs, and +the issues discussed in “Using symmetric master-slave contact pairs to improve contact modeling apply. +Abaqus/Standard automatically applies some numerical “softening” to contact conditions in these cases, +as discussed in “Contact constraint enforcement methods in Abaqus/Standard,” Section 37.1.2. +Direct enforcement of hard contact conditions is the default constraint enforcement method for two- +dimensional self-contact using the node-to-surface formulation. In this case, each node adjacent to a +vertex where a two-dimensional surface folds onto itself is automatically assigned a slave or master +role during the analysis. Since contact constraints directly resist penetrations at nodes that act as slave +nodes, there is some possibility of unresolved penetrations at nodes that only act as master nodes for +two-dimensional self-contact using the node-to-surface formulation. +Selecting surfaces used in contact pairs +Methods for creating surfaces are discussed in “Element-based surface definition,” Section 2.3.2; +“Node-based surface definition,” Section 2.3.3; and “Analytical rigid surface definition,” Section 2.3.4; +those sections discuss general restrictions for the various surface types. Considerations related to +surface characteristics for various contact formulations are discussed in “Contact formulations in +Abaqus/Standard,” Section 37.1.1. Additional considerations for surfaces used in contact definitions +are discussed below. +Orientation considerations for shell-like surfaces +Abaqus/Standard requires master contact surfaces to be single-sided for node-to-surface contact and +for some surface-to-surface contact formulations . This requires +that you consider the proper orientation for master surfaces defined on elements, such as shells and +membranes, that have positive and negative directions. For node-to-surface contact the orientation of +slave surface normals is irrelevant, but for surface-to-surface contact the orientation of single-sided +slave surfaces is taken into consideration. +Double-sided element-based surfaces are allowed for the default surface-to-surface contact +formulations, although they are not always appropriate for cases with deep initial penetrations. If the +master and slave surfaces are both double-sided, the positive or negative orientation of the contact +normal direction will be chosen such as to minimize (or avoid) penetrations for each contact constraint. +If either or both of the surfaces are single-sided, the positive or negative orientation of the contact +normal direction will be determined from the single-sided surface normals rather than the relative +positions of the surfaces. +When the orientation of a contact surface is relevant to the contact formulation, you must consider +the following aspects for surfaces on structural (beam and shell), membrane, truss, or rigid elements: +• Adjacent surface faces must have consistent normal directions. Abaqus/Standard will issue an +error message if adjacent surface faces have inconsistent normals on a single-sided surface whose +orientation is relevant to the contact formulation. +• Except +for +initial +interference fit problems , +the slave surface should be on the same side of the +master surface as the outward normal. If, in the initial configuration, the slave surface is on the +opposite side of the master surface as the outward normal, Abaqus/Standard will detect overclosure +of the surfaces and may have difficulty finding an initial solution if the overclosure is severe. An +improper specification of the outward normal will often cause an analysis to immediately fail to +converge. Figure 35.3.1–1 illustrates the proper and improper specification of a master surface’s +outward normal. +• Contact will be ignored with surface-to-surface discretization if single-sided slave and master +surfaces have normal directions that are in approximately the same direction (for example, contact +will not be enforced if the dot product of the slave and master surface normals is positive). +master +surface +outward normal +slave +surface +Incorrect master surface orientation +Correct master surface orientation +Figure 35.3.1–1 Example of proper and improper master surface orientation. +The following output from a data check analysis can be useful in identifying incorrectly oriented master +surfaces: +• Initial clearances can be displayed in Abaqus/CAE with a contour plot of the variable COPEN at +increment 0 of the first step; initial overclosures correspond to negative clearances. +• Abaqus/Standard provides a detailed printout of the model’s initial contact state. +Surface connectivity restrictions +Certain connectivity restrictions apply to contact surfaces depending on the type of contact formulation. +Surface connectivity restrictions for the various contact formulations are summarized in Table 35.3.1–1. +As indicated in this table, the connectivity restrictions are sometimes different for master and slave +surfaces. Self-contact surfaces act as both master and slave surfaces; therefore, if a restriction applies +to either a master or slave surface, it also applies to self-contact. The potential connectivity restrictions +referred to in Table 35.3.1–1 are described below: +• Discontinuous surfaces: Discontinuous contact surfaces are allowed in many cases, but the master +surface for finite-sliding, node-to-surface contact cannot be made up of two or more disconnected +regions (they must be continuous across element edges in three-dimensional models or across nodes +in two-dimensional models). Figure 35.3.1–2 shows examples of continuous surfaces, whereas +Figure 35.3.1–3 and Figure 35.3.1–4 show examples of discontinuous surfaces. Figure 35.3.1–5 +shows an automatically generated free surface resulting from the specification of an element set +consisting of two disjointed groups of elements. The resulting surface is not continuous since it +is composed of two disjoint open curves, so this surface would be invalid as a master surface for +finite-sliding, node-to-surface contact. +Table 35.3.1–1 Summary of which connectivity characteristics of element-based +surfaces are allowed for various contact formulations. +Connectivity characteristics +Contact +formulation +Discontinuous +(or 3-D faces joined +at only one node) +T-intersection +Finite-sliding, +node-to-surface +Master: Not allowed +Slave: Allowed +Master: Not allowed +Slave: Allowed +Small-sliding, +node-to-surface +Master: Allowed +Slave: Allowed +Master: Not allowed +Slave: Allowed +Finite-sliding, +surface-to-surface +Master: Allowed +Slave: Allowed +Master: Allowed +Slave: Allowed +Small-sliding, +surface-to-surface +Master: Allowed +Slave: Allowed +Master: Not allowed +Slave: Allowed +Closed 2-D surface +Closed 3-D surface +Open 2-D surface +Open 3-D surface +Figure 35.3.1–2 Examples of continuous surfaces. +Figure 35.3.1–3 Example of a discontinuous 2-D surface. +Figure 35.3.1–4 Example of a discontinuous 3-D surface. +user-specified element set +automatically generated free surface +Figure 35.3.1–5 Example of a discontinuous surface resulting from +automatic free surface generation with a disjoint element set. +• Portions of three-dimensional surfaces joined at only one node: The finite-sliding, node-to-surface +contact formulation also does not allow three-dimensional master surface faces to be joined at +a single node (they must be joined across a common element edge). Figure 35.3.1–6 shows an +example of a surface with two faces connected by a single node. +Figure 35.3.1–6 Example of a 3-D surface with two faces sharing a single node. +• Surfaces with T-intersections: In some cases a contact surface cannot have more than two surface +faces sharing a common master node in two dimensions or a common master edge in three +dimensions. For example, Figure 35.3.1–7 shows examples of surfaces with T-intersections, in +which three faces share a common node in two dimensions or a common edge in three dimensions. +While more than two surface faces can share a common slave node in two dimensions or a common +edge in three dimensions for node-to-surface formulations, the slave faces must be single-sided, +which precludes the most common T-intersection cases for node-to-surface formulations. +T-intersection in 2-D +T-intersection in 3-D +Figure 35.3.1–7 Examples of surfaces with T-intersections. +Analytical rigid surfaces +Analytical rigid surfaces are often effective for efficiently modeling curved, rigid geometries, as +discussed in “Analytical rigid surface definition,” Section 2.3.4. For rare cases in which a very +large number (thousands) of segments would be necessary to define an analytical rigid surface, +better performance can be achieved with an element-based rigid surface . +Three-dimensional beam and truss surfaces +Abaqus/Standard cannot use three-dimensional beams or trusses to form a master surface because the +elements do not have enough information to create unique surface normals. However, these elements can +be used to define a slave surface. Two-dimensional beams and trusses can be used to form both master +and slave surfaces. +Edge-based surfaces +Edge-based surfaces (“Element-based surface definition,” Section 2.3.2) on three-dimensional shell +elements cannot be used in a contact analysis in Abaqus/Standard. +Limitations of node-based surfaces +Use node-based surfaces with caution when the contact property definition includes user-defined softened +contact properties or thermal or electrical interactions because the contact constitutive behavior (which +relies on accurate calculation of contact pressure, heat flux, or electric current) will not be enforced +correctly unless the precise surface area is associated with each node. For details, see “Contact pressure- +overclosure relationships,” Section 36.1.2; “Thermal contact properties,” Section 36.2.1; or “Electrical +contact properties,” Section 36.3.1. +Removing and reactivating contact pairs +You can temporarily remove contact pairs from a simulation, which may result +in significant +computational savings by eliminating unnecessary contact searches and updates of surface orientations +during the simulation. Removal and reactivation of contact pairs is commonly used in complicated +forming processes where multiple tools need to interact with the workpiece at different stages in the +analysis. +You cannot remove tied contact pairs from a simulation . +Removing contact pairs +Removal of contact pairs is a useful technique for uncoupling components of an assembly until +they should be brought together (such as tooling in manufacturing process simulations). Significant +computational expense may be saved by removing a contact pair and introducing it at the proper time, +thus eliminating the need to monitor the contact conditions except when they are relevant. +Input File Usage: +*MODEL CHANGE, TYPE=CONTACT PAIR, REMOVE +slave_surface, master_surface +Abaqus/CAE Usage: +Use one of the following options: +Repeat the data line as needed. +Interaction module: Create Interaction: surface-to-surface contact or +self-contact interaction editor: toggle off Active in this step +Interaction module: interaction manager: select interaction, Deactivate +Removal of contact forces associated with closed contact pairs +If the surfaces are in contact when a contact pair is removed, Abaqus/Standard stores the corresponding +contact forces (or heat fluxes if thermal interactions are present, or electrical currents if it is a +coupled-thermal electrical analysis) for every node on each surface. Abaqus/Standard automatically +ramps these forces (or heat fluxes or electrical currents) linearly down to zero magnitude during +the removal step. Abaqus/Standard always removes the contact constraints for mechanical surface +interactions instantaneously. +Care must be taken in removing contact pairs in transient procedures. In transient heat transfer, fully +coupled temperature-displacement, or fully coupled thermal-electrical-structural analysis if the fluxes are +high and the step is long, this ramping down may have the effect of cooling down or heating up the rest of +the body. In dynamic analysis if the forces are high and the step is long, kinetic energy can be imparted +to the remaining portion of the model. This problem can be avoided by removing the contact pairs in a +very short transient step prior to the rest of the analysis. This step can be done in a single increment. +Using an allowable contact interference to deactivate contact pairs +A contact pair with mechanical contact interactions can be deactivated during an analysis by assigning a +very large allowable contact interference to the contact pairs . This method has the disadvantage of not reducing the computational +cost of the analysis because the contact algorithm will still calculate the contact conditions for the contact +pair in each increment. +Reactivating contact pairs +All contact pairs that will be used in a simulation must be created at the start of the analysis; they cannot +be created once the simulation has begun. However, contact pairs can be created, removed at the start of +the analysis in the first step, and then reactivated at a later point during the simulation. +In Abaqus/CAE you can create contact pairs in any step. +If a contact pair is created in a step +other than the initial step, Abaqus/CAE automatically deactivates the contact pair in the initial step and +reactivates it in the step in which you created it. +Input File Usage: +*MODEL CHANGE, TYPE=CONTACT PAIR, ADD +slave_surface, master_surface +Repeat the data line as needed. +Abaqus/CAE Usage: +Interaction module: Create Interaction: surface-to-surface contact or +self-contact interaction editor: toggle on Active in this step +Reactivating overclosed contact pairs +When a contact pair is reactivated, the contact constraint becomes active immediately. In mechanical +simulations it is possible for the surfaces of a contact pair to move such that they become overclosed +while the contact pair is inactive. If this overclosure is too severe when the contact pair is reactivated, +Abaqus/Standard may encounter convergence problems as it tries to enforce the suddenly activated +contact constraint. To avoid such problems, you can specify a permissible interference value, v, for +the contact pair that is larger than the overclosure for the contact pair. Abaqus/Standard will ramp v +down to zero during the step. For details on specifying allowable interferences, see “Modeling contact +interference fits in Abaqus/Standard,” Section 35.3.4. +Output +Output variables associated with the interaction of contact pairs fall into two categories: nodal variables +(sometimes called constraint variables) and whole surface variables. In addition, Abaqus outputs an array +of diagnostic information associated with contact interactions, as discussed in “Contact diagnostics in an +Abaqus/Standard analysis,” Section 38.1.1. +For more detailed discussions of variables associated with thermal, electrical, and pore fluid +analyses, see the sections on the related contact properties in Chapter 36, “Contact Property Models.” +Nodal contact variables +Nodal contact variables can be contoured on contact surfaces in the Visualization module of +Abaqus/CAE. Nodal contact variables include contact pressure and force, frictional shear stress and +force, relative tangential motion (slip) of the surfaces during contact, clearance between surfaces, heat +or fluid flux per unit area, fluid pressure, and electrical current per unit area. Many of the nodal contact +variables written to the output database (.odb) file are often available for all contact nodes, regardless +of whether they act as slave or master nodes. In such cases the nodal values are generally affected by +more than one contact constraint. Other nodal contact variables are available only at nodes acting as +slave nodes. In these cases the value at each slave node reflects a value associated with a particular +contact constraint. Most contact output to the data (.dat) and results (.fil) files is associated with +individual constraints. +The contact pressure distribution is of key interest in many Abaqus analyses. You can view the +contact pressure on all contact surfaces except for analytical rigid surfaces and discrete rigid surfaces +based on rigid-type elements (the latter restriction does not apply to general contact). You can view +a contour plot of the contact pressure error indicator next to a contour plot of the contact pressure to +gain perspective on local accuracy of the contact pressure solution in regions where the contact pressure +solution is of interest . +In some cases you may observe the contact pressure extending beyond the actual contact zone due +to the following factors: +• The contour plots are constructed by interpolating nodal values, which can cause nonzero values +to appear within portions of facets outside of the contact region. For example, this effect is often +noticeable at corners, such as when two same-sized, aligned blocks are in contact—if the contact +surfaces wrap around the corners, the contact pressure contours will extend slightly around the +corners. +• To minimize contact stress noise within a region of active contact, Abaqus/Standard computes nodal +contact stresses as weighted averages of values associated with active contact constraints in which a +node participates. Some filtering is applied to reduce the contact stress values reported for nodes on +the fringe of the active contact region (that only weakly participate in contact constraints), but this +filtering is not “perfect,” which can result in the contact zone size appearing somewhat exaggerated. +Similarly, contact status output will also be affected at nodes that lie on the fringe of the active +contact region. In such cases, the contact status may be reported as closed at nodes in the exaggerated +region even though it is open. +Due to these factors, trying to infer the contact force distribution from the contact stress distribution +can be somewhat misleading. Instead, you can request nodal contact force output, which accurately +represents the contact force distribution present in the analysis. +Whole surface variables +Whole surface variables are attributes of an entire slave surface. Available as history output, these +variables record the total force and moment due to contact pressure and frictional stress, the center of +pressure and frictional stress (defined as the point closest to the centroid of the surface that lies on the +line of action of the resultant force for which the resultant moment is minimal), and the total contact area +(defined as the sum of all the facets where there is contact force). The last letter of each variable name +(except the variable CAREA) denotes which contact force distribution on the surface is used to calculate +the resultant: +Normal contact forces are used to derive the resultant quantity. +Shear contact forces are used to derive the resultant quantity. +The sum of the normal and shear contact forces is used to derive the resultant quantity. +For example, CFN is the total force due to contact pressure, CFS is the total force due to frictional stress, +and CFT is the total force due to both contact pressure and frictional stress. +Each total moment output variable will not necessarily equal the cross product of the respective +center of force vector and resultant force vector. Forces acting on two different nodes of a surface may +have components acting in opposite directions, such that these nodal force components generate a net +moment but not a net force; therefore, the total moment may not arise entirely from the resultant force. +The center of force output variables tend to be most meaningful when the surface nodal forces act in +approximately the same direction. +Requesting output +Certain contact variables must be requested as a group. For example, to output the clearance between +surfaces (COPEN), you must request the variable CDISP (contact displacements). CDISP outputs +both COPEN and CSLIP (tangential motion of the surfaces during contact). A complete listing of +available contact pair variables and identifiers is given in “Abaqus/Standard output variable identifiers,” +Section 4.2.1. +Output requests can be limited to individual contact pairs or portions of a slave surface. You can: +• request output associated with a given contact pair; +• request output associated with a given slave surface, including contributions from all of the contact +pairs to which the slave surface belongs; and +• limit the output by specifying a node set containing a subset of the nodes on the slave surface. +Instructions on forming these output requests are available in the following sections: +• To request output to the data (.dat) file, see “Surface output from Abaqus/Standard” in “Output +to the data and results files,” Section 4.1.2. +• To request output to the output database (.odb) file, see “Surface output in Abaqus/Standard and +Abaqus/Explicit” in “Output to the output database,” Section 4.1.3. +Differences for small-sliding and finite-sliding contact +For small-sliding contact problems the contact area is calculated in the input file preprocessor from the +undeformed shape of the model; thus, it does not change throughout the analysis, and contact pressures +for small-sliding contact are calculated according to this invariant contact area. This behavior is different +from that in finite-sliding contact problems, where the contact area and contact pressures are calculated +according to the deformed shape of the model. +Output of tangential results +Abaqus reports the values of tangential variables (frictional shear stress, viscous shear stress, and +relative tangential motion) with respect to the slip directions defined on the surfaces. The definition +of slip directions is explained in “Local tangent directions on a surface” in “Contact formulations in +Abaqus/Standard,” Section 37.1.1. These directions do not always correspond to the global coordinate +system, and they rotate with the contact pair in a geometrically nonlinear analysis. +Abaqus/Standard calculates tangential results at each constraint point by taking the scalar product +of the variable’s vector and a slip direction, +, associated with the constraint point. The number +at the end of a variable’s name indicates whether the variable corresponds to the first or second slip +direction. For example, CSHEAR1 is the frictional shear stress component in the first slip direction, +while CSHEAR2 is the frictional shear stress component in the second slip direction. +or +Definition of accumulated incremental relative motion (slip) +Abaqus/Standard defines the incremental relative motion (also known as slip) as the scalar product of +the incremental relative nodal displacement vector and a slip direction. The incremental relative nodal +displacement vector measures the motion of a slave node relative to the motion of the master surface. +The incremental slip is accumulated only when the slave node is contacting the master surface. The sums +of all such incremental slips during the analysis are reported as CSLIP1 and CSLIP2. Details about the +calculation of this quantity can be found in “Small-sliding interaction between bodies,” Section 5.1.1 +of the Abaqus Theory Manual; “Finite-sliding interaction between deformable bodies,” Section 5.1.2 +of the Abaqus Theory Manual; and “Finite-sliding interaction between a deformable and a rigid body,” +Section 5.1.3 of the Abaqus Theory Manual. +Extending the range for which contact opening output is provided for gaps +To reduce computational costs, detailed computations to monitor potential points of interaction are +avoided by default where surfaces are separated by a distance greater than the minimum gap distance at +which contact forces (or thermal fluxes, etc.) may be transmitted. Therefore, contact opening (COPEN) +output is typically not provided for finite-sliding contact where surfaces are opened by more than a small +amount compared to surface facet dimensions. You can extend the range in which Abaqus/Standard +provides contact opening output; COPEN will be provided up to gap distances equal to a specified +“tracking thickness.” Using this control may increase computational cost due to extra contact tracking +computations, especially if you specify a large tracking thickness value. +Input File Usage: +Abaqus/CAE Usage: +*SURFACE INTERACTION, TRACKING THICKNESS=value +You cannot adjust the default tracking thickness in Abaqus/CAE. +Output for axisymmetric models +In an axisymmetric analysis the total forces and moments transmitted between the contacting bodies as a +result of contact pressure and frictional stress are computed in the same manner as in a two-dimensional +analysis. Therefore, the component of the total forces along the r-axis is nonzero, and the components +of the total moments include contributions from the total forces along the r-axis. +Obtaining the “maximum torque” that can be transmitted about the z-axis in an axisymmetric +analysis +When modeling surface-based contact with axisymmetric elements (element types CAX and CGAX), +Abaqus/Standard can calculate the maximum torque (output variable CTRQ) that can be transmitted +This capability is often of interest when modeling threaded connectors . The maximum torque, T, is defined as +where p is the pressure transmitted across the interface, r is the radius to a point on the interface, and s is +the current distance along the interface in the r–z plane. This definition of “torque” effectively assumes +a friction coefficient of unity. +35.3.2 +ASSIGNING SURFACE PROPERTIES FOR CONTACT PAIRS IN Abaqus/Standard +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining contact pairs in Abaqus/Standard,” Section 35.3.1 +• *CONTACT PAIR +• “Defining surface-to-surface contact,” Section 15.13.7 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Defining self-contact,” Section 15.13.8 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +This section describes how to modify the properties associated with surfaces in a contact pair definition. +Accounting for shell and membrane thickness +All of the contact formulations except the finite-sliding, node-to-surface formulation account for +initial shell and membrane thicknesses for element-based surfaces by default. The finite-sliding, +node-to-surface formulation will not account for surface thickness. Node-based surfaces have no +thickness, regardless of which element types are connected to the surface nodes. Accounting for +element thicknesses in contact calculations is generally desirable, but you can avoid having thickness +considered if it is not desired. +Input File Usage: +Abaqus/CAE Usage: +*CONTACT PAIR, NO THICKNESS +Interaction module: interaction editor: Sliding formulation: Small sliding +or Finite sliding, Discretization method: Surface to surface or Node +to surface, toggle on Exclude shell/membrane element thickness +Example +Consider the case of a shell pinched between two rigid surfaces, as shown in Figure 35.3.2–1. +In this example contact pairs using the small-sliding, node-to-surface formulation are defined +between the top surface of the shell and the top rigid surface and between the bottom surface of +the shell and the bottom rigid surface. Although the shell surfaces are defined at the shell reference +location, the contact interactions account for the thickness of the shell and are offset from the reference +surface. The penalty constraint enforcement method is used to avoid overconstraining slave nodes. The following input is used: +*SURFACE, NAME=TOP_RIG_SURF +TOP_RIG_ELS, +*SURFACE, NAME=SHELL_TOP_SURF +deformable shell +rigid solids +shell reference surface +shell thickness +contact interactions +Figure 35.3.2–1 Shell pinched between two rigid bodies. +SHELL_ELS,SPOS +*SURFACE, NAME=SHELL_BOT_SURF +SHELL_ELS,SNEG +*SURFACE, NAME=BOT_RIG_SURF +BOT_RIG_ELS, +*CONTACT PAIR, INTERACTION=INTER_AL, SMALL SLIDING +SHELL_TOP_SURF, TOP_RIG_SURF +SHELL_BOT_SURF, BOT_RIG_SURF +*SURFACE INTERACTION, NAME=INTER_AL +*SURFACE BEHAVIOR, PENALTY +Specifying surface geometry corrections +With the finite element method, curved geometric surfaces are naturally approximated as a faceted group +of connected element faces. The use of a faceted surface geometry rather than the true surface geometry +can significantly contribute to contact stress inaccuracy in contact pairs, especially when the magnitude +of the differences between the faceted and true surface is not small with respect to the deformation of +the components in contact. Methods for overcoming convergence and accuracy difficulties associated +with faceted surfaces in contact interactions are discussed in “Contact formulations in Abaqus/Standard,” +Section 37.1.1, and “Smoothing contact surfaces in Abaqus/Standard,” Section 37.1.3. +35.3.3 +ASSIGNING CONTACT PROPERTIES FOR CONTACT PAIRS IN Abaqus/Standard +Products: Abaqus/Standard Abaqus/CAE +References +• “Contact interaction analysis: overview,” Section 35.1.1 +• “Defining contact pairs in Abaqus/Standard,” Section 35.3.1 +• *CONTACT PAIR +• *SURFACE INTERACTION +• “Defining surface-to-surface contact,” Section 15.13.7 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Defining self-contact,” Section 15.13.8 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +• “Using contact and constraint detection,” Section 15.16 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +Contact properties: +• define the mechanical and thermal surface interaction models that govern the behavior of surfaces +when they are in contact; and +• are assigned to individual contact pairs. +Assigning a surface interaction definition to a contact pair +A surface interaction definition specifies the constitutive contact properties and the constraint +enforcement methods used by a contact pair. Every contact pair in a model must refer to a surface +interaction definition, even if the contact pair uses the default contact property models. See “Mechanical +contact properties: overview,” Section 36.1.1, for information on defining contact properties. A +non-default constraint enforcement method can be specified as part of a surface interaction definition, +as described in “Contact constraint enforcement methods in Abaqus/Standard,” Section 37.1.2. +Multiple contact pairs can refer to the same surface interaction definition. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options: +*CONTACT PAIR, INTERACTION=interaction_property_name +*SURFACE INTERACTION, NAME=interaction_property_name +Interaction module: +Create Interaction Property: Name: interaction_property_name, Contact +Interaction editor: Contact interaction property: interaction_property_name +Example +Figure 35.3.3–1 shows the mesh used in this example. For purposes of this example, the surface ASURF +is the slave surface of the contact pair. The property definition for the contact pair (GRATING) uses the +finite-sliding, node-to-surface formulation with a friction model with =0.4 and uses the default “hard” +contact model for the behavior normal to the surfaces. +ESETB +ESETA +502 +BSURF +201 +501 +202 +101 +102 +103 +ASURF +Figure 35.3.3–1 Mechanical surface interaction with friction and finite sliding. +*HEADING +… +*SURFACE, NAME=ASURF +ESETA, +*SURFACE, NAME=BSURF +ESETB, +*CONTACT PAIR, INTERACTION=GRATING +ASURF, BSURF +*SURFACE INTERACTION, NAME=GRATING +*FRICTION +0.4 +*NSET, NSET=SNODES +101, 102, 103 +*STEP, NLGEOM +… +*END STEP +35.3.4 +MODELING CONTACT INTERFERENCE FITS IN Abaqus/Standard +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining contact pairs in Abaqus/Standard,” Section 35.3.1 +• *CONTACT INTERFERENCE +• “Specifying interference fit options” in “Defining surface-to-surface contact,” Section 15.13.7 of +the Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +Interference fits in Abaqus/Standard: +• occur by default when the contact formulation computes overclosures between surfaces in the initial +configuration of a model; +• are resolved in the first increment of a step by default; +• can be gradually resolved over multiple increments; +• result in stresses and strains in a model as overclosures are resolved; +• can be specified for both surface-based contact pairs and contact elements; and +• cannot be specified for self-contact. +Abaqus/Standard offers alternative methods to resolve initial overclosures with strain-free adjustments +and to model specific overclosures or clearances different from those calculated from the initial +configuration. These methods are discussed in “Adjusting initial surface positions and specifying initial +clearances in Abaqus/Standard contact pairs,” Section 35.3.5. +Resolving excessive initial overclosures +If there are large overclosures in the initial configuration of model, Abaqus/Standard may not be able +to resolve the interference fit in a single increment. Abaqus/Standard provides alternative methods that +allow overclosures to be resolved gradually over multiple increments. +The default contact constraint imposed at each constraint location is that the current penetration +is positive. To alter this constraint, you can specify an allowable +is +interference, +, that will be ramped down over the course of a step. The specified allowable interference +modifies the contact constraint as follows: +. Penetration exists when +Thus, specifying a positive value for +causes Abaqus/Standard to ignore penetrations up to that +magnitude. Figure 35.3.4–1 illustrates a typical interference fit problem. If the penetration in the model +is +or request an automatic shrink fit. In either case Abaqus/Standard will +, you may declare +BEGINNING OF STEP +MIDDLE OF STEP +END OF STEP +Figure 35.3.4–1 Interference fit with contact surfaces. +consider the two bodies to be just in contact at the start of the simulation. As the allowable interference, +, is decreased during the step, Abaqus/Standard pushes the surfaces apart until there is no more allowable +penetration. +There are three different ways in which to specify the allowable interference, +. By default, in all +cases the value of the specified allowable interference is applied instantaneously at the start of the step +and then ramped down to zero linearly over the step, unless you specify an amplitude reference that +defines a particular allowable interference-time variation. It is recommended that you specify allowable +interferences in a step separate from the rest of the analysis; additional loads may adversely affect the +resolution of the interference fit and the response to loading with partially-resolved interferences may be +non-physical. Once the overclosures are resolved, you can continue the analysis in a new step. +When the contact interference is specified, output variable COPEN does not reflect the actual +overclosure value during the step; it reflects the actual value only at the end of the step. +You must specify the contact pairs or contact elements at which the allowable interference should +apply. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to define an allowable interference for contact pairs: +*CONTACT INTERFERENCE, TYPE=CONTACT PAIR +slave surface, master surface, +... +Use the following option to define an allowable interference for contact +elements: +*CONTACT INTERFERENCE, TYPE=ELEMENT +contact element set, +... +Interaction module: interaction editor: Interference Fit: Gradually +remove slave node overclosure during the step, Uniform allowable +interference, Magnitude at start of step: +Element-based contact is not supported in Abaqus/CAE. +Using a nondefault amplitude curve for the allowable interference +You can define a time-varying allowable contact interference by creating an amplitude curve and then referring to this curve from the contact +interference definition. The amplitude will be ignored, however, if the Riks method is used. +Input File Usage: +Abaqus/CAE Usage: +*CONTACT INTERFERENCE, AMPLITUDE=amplitude_curve_name +Interaction module: interaction editor: Interference Fit: Gradually +remove slave node overclosure during the step, Uniform allowable +interference, Amplitude: amplitude_curve_name +Removing or modifying the allowable contact interferences +By default, only the allowable contact interferences defined or redefined by a particular contact +interference definition will be modified. Alternatively, you can specify that all previously defined +allowable contact interferences should be removed from the model and only those defined with this +definition will remain. +Input File Usage: +Use the following option to add or modify an allowable contact interference +definition: +*CONTACT INTERFERENCE, OP=MOD +Use the following option to remove all previously defined allowable contact +interferences: +*CONTACT INTERFERENCE, OP=NEW +Abaqus/CAE Usage: +Contact interferences in Abaqus/CAE propagate along with the interaction for +which they are defined. You cannot remove all previously defined contact +interferences at once in Abaqus/CAE. +Specifying the same allowable contact interference for an entire surface +A single allowable interference +can be specified for every node on the slave surface or every slave +node in the specified set of contact elements. The concepts of slave nodes for the various families of +contact elements are discussed in their respective sections. The specified allowable contact interferences +are included in the current penetrations of the slave nodes reported in the message file when you request +detailed contact printout. Thus, any slave node that penetrates the master surface by less than the +allowable interference will be reported as being open. +Using the automatic “shrink” fit method +This method is applicable only during the first step of an analysis and requires no interference value. +With this method Abaqus/Standard assigns a different +to each slave node that is equal to that node’s +initial penetration (or zero if the point is initially open) except for the finite-sliding, surface-to-surface +formulation, in which case the same value of +, corresponding to the maximum penetration of the contact +pair, is assigned to all constraints that are initially closed. These automatically calculated allowable +contact interferences are not included in the current penetrations reported in the message file when +detailed contact printout is requested. +When the automatic “shrink” fit method is used, only the default amplitude curve, a linear ramp to +zero magnitude, can be used. +Input File Usage: +Abaqus/CAE Usage: +*CONTACT INTERFERENCE, SHRINK +Interaction module: interaction editor: Interference Fit: Gradually remove +slave node overclosure during the step, Automatic shrink fit +Applying an allowable contact interference with a shift vector +In this method you specify a uniform allowable interference +. The allowable +interference value, +is applied to the +, defines the magnitude of a shift vector. A relative shift +slave nodes before Abaqus/Standard determines the contact conditions. In certain applications, such +as contact simulations of threaded connectors, shifting the surfaces in a specified direction is more +effective than simply allowing an interference. +and a direction +Figure 35.3.4–2 illustrates the potential difference that can result when using an allowable contact +interference with a shift vector rather than using a uniform allowable contact interference. In case (a) a +shift direction +is defined as well as an allowable interference , while in case (b) the standard approach +is used, with an allowable interference . The magnitude of +is the same in both cases, but it is less +than the penetration in case (a) and more than the penetration in case (b). In case (a) contact is detected +immediately for slave node A, and the penetration is resolved with that node sliding along segment +because node A is shifted in the direction +Abaqus/Standard determines that node A is closest to segment +before Abaqus/Standard checks for contact. After the shift +and moves the node onto that segment. +S1 +S2 +a) +b) +Figure 35.3.4–2 Effect of direction definition on interference +accommodation: a) with direction, b) without direction. +In case (b) slave node A detects contact with segment +remains in its initial position. Thus, node A will slide along segment +because that is the closest segment when node A +if no shift direction is provided. +Input File Usage: +Abaqus/CAE Usage: +, Z-direction cosine of +, X-direction cosine of +*CONTACT INTERFERENCE +slave surface, master surface, +cosine of +... +Interaction module: interaction editor: Interference Fit: Gradually +remove slave node overclosure during the step, Uniform allowable +interference, Magnitude at start of step: +, Along direction: +, Y-direction +Interference fits for surface-to-surface discretization +Because contact conditions are enforced in an average sense in a region around each constraint location +for surface-to-surface contact, penetrations or gaps may be observed at slave nodes when surface-to- +surface constraints are in a zero-penetration state. +Large interferences may be difficult +surface-to-surface +formulation. Using this formulation, overclosures tend to be resolved along the slave facet normal +to resolve with the finite-sliding, +directions; using node-to-surface contact, overclosures tend to be resolved along the master surface +Figure 35.3.4–3 illustrates a case where differing normal directions lead to +normal directions. +undesirable tangential motion during an interference fit. In some cases it may be preferable to resolve +large initial overclosures with node-to-surface discretization. +surface-to-surface +node-to-surface +master surface +overclosure resolution direction +Figure 35.3.4–3 Comparison of contact formulations in an +example with a large interference fit. +Friction and contact interferences +Frequently, an actual assembly process is modeled as an interference fit problem. If frictional interface +properties are desired, they should usually be introduced after the initial interference has been resolved. +The initial interference problem should be modeled under frictionless conditions since the physical +assembly process is not typically modeled exactly. Friction can be introduced in subsequent steps +. +35.3.5 +ADJUSTING INITIAL SURFACE POSITIONS AND SPECIFYING INITIAL +CLEARANCES IN Abaqus/Standard CONTACT PAIRS +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining contact pairs in Abaqus/Standard,” Section 35.3.1 +• “Modeling contact interference fits in Abaqus/Standard,” Section 35.3.4 +• “Defining tied contact in Abaqus/Standard,” Section 35.3.7 +• “Contact formulations in Abaqus/Standard,” Section 37.1.1 +• *CLEARANCE +• *CONTACT PAIR +• “Defining surface-to-surface contact,” Section 15.13.7 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Using contact and constraint detection,” Section 15.16 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +Adjusting the position of surfaces in an Abaqus/Standard contact pair: +• can be performed only at the start of a simulation; +• causes Abaqus/Standard to move the nodes of the slave surface so that they precisely contact +the master surface (with some exceptions for surface-to-surface discretization and overlapping +interaction definitions); +• does not create any strain in the model; +• can eliminate small gaps or penetrations caused by numerical roundoff when a graphical +preprocessor such as Abaqus/CAE is used and, thus, prevent possible convergence problems; +• is required when two surfaces are tied together for the duration of the analysis; +• should not be used to correct gross errors in the mesh design; +• cannot be used with symmetric master-slave contact; and +• will account for shell and membrane thicknesses and shell offsets (these factors are accounted +for in the adjustment zone and in the adjustments) for contact formulations other than the default +finite-sliding, node-to-surface contact formulation . +In addition to adjusting two surfaces into precise contact, Abaqus/Standard offers various methods to +define the initial clearances between two surfaces precisely in both magnitude and direction. Responses +to negative clearances, or interference fits, are discussed in “Modeling contact interference fits in +Abaqus/Standard,” Section 35.3.4. +Adjusting the surfaces in a contact pair +You can have Abaqus/Standard adjust the position of the slave surface of a contact pair by specifying +either a floating point value a for the depth of an “adjustment zone” around the master surface or a node +set label. +Abaqus/Standard does not adjust the nodes on the slave surface by default for contact pairs; rather +initial overclosures are treated as interference fits by default for contact pairs. +Comments unique to surface-to-surface contact +The following points apply to contact pairs with surface-to-surface discretization : +for +• Strain-free adjustments to slave node positions may not result in exactly zero gap with respect to the +master surface as measured at a slave node. The adjustments are made to achieve zero gap between +the surfaces in an average sense in a region near each slave node within the adjustment zone. +• The magnitude of strain-free adjustments is limited to half the typical facet length. For instances of +initial overclosures exceeding this limit, an allowable penetration equal to the initial overclosure is +stored for the associated contact constraints such that penetrations deeper than the initial overclosure +are resisted during the analysis, but penetrations less than the initial overclosure are not resisted. +• Strain-free adjustments will occur for some slave nodes outside the adjustment zone if a significant +portion of a slave face (or segment in two dimensions) to which it is attached is within the adjustment +zone. +The discussion in the remainder of this section applies directly to node-to-surface contact discretizations +(for which contact is enforced at discrete points—slave nodes) but should be considered within the +context of the above points for surface-to-surface contact discretizations. +Using an “adjustment zone” when adjusting surfaces +When you specify a, the depth of the “adjustment zone,” Abaqus/Standard forms an adjustment zone +extending a distance a from the master surface. Abaqus/Standard measures the distance along the master +surface normals that pass through the nodes of the slave surface. Any nodes on the slave surface that are +within the “adjustment zone” in the initial geometry of the model are moved precisely onto the master +surface. The motion of these slave nodes does not create any strain in the model; it is treated as a change +in the model definition. An example of adjusting the surfaces of a contact pair is shown in Figure 35.3.5–1 +and Figure 35.3.5–2. If you specify a negative value for a, Abaqus/Standard will issue an error message. +Input File Usage: +Abaqus/CAE Usage: +*CONTACT PAIR, ADJUST=a +slave_surface, master_surface +... +Interaction module: contact interaction editor: Specify tolerance +for adjustment zone: a +adjust +Figure 35.3.5–1 Initial configuration of the contact surfaces showing +the “adjustment zone.” The slave surface is in bold. +Figure 35.3.5–2 Configuration of the contact surfaces after the adjustment. Nodes within +the adjustment zone and overclosed nodes have been moved. +Adjusting overclosed slave nodes using an adjustment zone +When you specify the depth of the adjustment zone, Abaqus/Standard moves any slave nodes +penetrating the master surface in the initial configuration so that they just contact the master surface. +Specifying a value of 0.0 for a causes Abaqus/Standard to adjust only those slave nodes that are +penetrating the master surface. Figure 35.3.5–3 shows the effect of specifying a=0.0 in the example +shown in Figure 35.3.5–1. If you do not have Abaqus/Standard adjust the position of the slave surface, +slave nodes that are overclosed in the initial configuration will remain overclosed at the start of the +simulation, which may cause convergence problems. +Using a node set label when adjusting surfaces +You can specify a node set label instead of an adjustment zone depth when only a subset of the slave +nodes should be adjusted and specifying a may cause the inappropriate adjustment of other slave nodes. +Abaqus/Standard adjusts only those nodes on the slave surface belonging to the node set. The node set +can contain nodes that are not on the slave surface at all: Abaqus/Standard will ignore them and adjust +only the nodes in the node set that are part of the slave surface. +Figure 35.3.5–3 Adjusted configuration of contact surfaces when a=0. +Abaqus/Standard moves any slave nodes in the specified node set regardless of how far they are from +the master surface. The adjustments of the nodes from their initial configurations do not create strains +in the elements forming the slave surface. If Abaqus/Standard adjusts slave nodes that are far from the +master surface, the elements may become poorly shaped, which can cause convergence difficulties. +*CONTACT PAIR, ADJUST=node_set_label +slave_surface, master_surface +... +Interaction module: contact interaction editor: Adjust slave +nodes in set: node_set_label +Abaqus/CAE Usage: +Input File Usage: +Adjusting overclosed slave nodes using a node set label +Because Abaqus/Standard adjusts only the slave nodes in the specified node set, any overclosed slave +nodes not in the specified node set remain overclosed at the start of the simulation. Using a node set +label may, therefore, cause convergence problems if severely overclosed slave nodes, which need to be +adjusted, are not included in the node set. This behavior is different from that seen if a is specified, in +which case Abaqus/Standard adjusts all of the overclosed nodes on the slave surface. +Adjustments for overlapping contact pairs +Nodal adjustment definitions are processed sequentially at the start of an analysis. If different constraint +or contact definitions involve the same nodes, some adjustments may cause lack of compliance for contact +or constraint definitions that were previously processed. These conflicts can be avoided in some cases by +changing the processing order of constraint and contact definitions: nodes in common between different +contact or constraint definitions should be processed first as slave nodes and later as master nodes. +Input File Usage: +Abaqus/CAE Usage: +To change the processing order of constraint and contact definitions, change the +order of the definitions in the input file. Constraint and contact definitions are +processed in the order in which they appear. +To change the processing order of constraint and contact definitions, change +the names of the constraints and interactions in the model. Constraints and +interactions are processed alphabetically according to their name. +When to adjust contact surface pairs +There are several instances when adjusting the surfaces in a contact pair is required or strongly +recommended: +• When tying two surfaces together for the duration of the analysis . +• When using small- or infinitesimal-sliding contact . +• When specifying a precise initial clearance or initial overclosure for the contact surfaces by defining +an allowable contact interference . +Defining a precise initial clearance or overclosure for small-sliding contact +You can define precise initial clearance or overclosure values and contact directions for the nodes on +the slave surface when they would not be computed accurately enough from the nodal coordinates; for +example, if the initial clearance is very small compared to the coordinate values. +The initial clearance or overclosure value calculated at every slave node (based on the coordinates +of the slave node and the master surface) is overwritten by the value that you specify. This procedure is +performed internally, and it does not affect the coordinates of the slave nodes. If you define a clearance, +Abaqus/Standard will treat the two surfaces as not being in contact, regardless of their nodal coordinates. +If you define an overclosure, Abaqus/Standard will treat the two surfaces as an interference fit and attempt +to resolve the overclosure in the first increment. If the defined overclosure is large, you may need to +specify an allowable interference that is ramped off over several increments. See “Modeling contact +interference fits in Abaqus/Standard,” Section 35.3.4, for further discussion of interference fits. +You can define initial clearance or overclosure values only for small-sliding contact (“Contact +formulations in Abaqus/Standard,” Section 37.1.1). For a technique that can be used to model clearances +or overclosures between finite-sliding contact pairs, see “Alternative methods for specifying precise +initial clearances or overclosures” below. +Specifying a uniform clearance or overclosure for the surfaces +You can specify a uniform clearance or overclosure for a contact pair by identifying the master and slave +surfaces of the contact pair and the desired initial clearance, +(positive for a clearance; negative for an +overclosure). No other data are needed. +Input File Usage: +*CLEARANCE, SLAVE=surface_name, MASTER=surface_name, +VALUE= +Abaqus/CAE Usage: +Interaction module: contact interaction editor: Clearance: Initial +clearance: Uniform value across slave surface: +Specifying spatially varying clearances or overclosures for the surfaces +Alternatively, you can specify spatially varying clearances or overclosures for a contact pair by +identifying the master and slave surfaces of the contact pair and providing a table of data specifying +the clearance at a single node or a set of nodes belonging to the slave surface. Any slave surface node +that is not identified will use the clearance that Abaqus/Standard calculates from the initial geometry of +the surfaces. +Input File Usage: +*CLEARANCE, SLAVE=surface_name, MASTER=surface_name, +TABULAR +node number or node set label, clearance value +Repeat the data line as often as necessary. +Abaqus/CAE Usage: +You cannot specify initial clearance or overclosure values using a table of data +in Abaqus/CAE. +Reading spatially varying clearances or overclosures from an external file +Abaqus/Standard can read the spatially varying clearances or overclosures for a contact pair from an +external file. +Input File Usage: +*CLEARANCE, SLAVE=surface_name, MASTER=surface_name, +TABULAR, INPUT=file_name +Abaqus/CAE Usage: +You cannot specify initial clearance or overclosure values using an external +input file in Abaqus/CAE. +Specifying the surface normal for the contact calculations +Normally Abaqus/Standard calculates the surface normal used for the contact calculations from the +geometry of the discretized surfaces, using the algorithms described in “Contact formulations in +Abaqus/Standard,” Section 37.1.1. When specifying spatially varying clearances or overclosures, you +can redefine the contact direction that Abaqus/Standard uses with each slave node by specifying the +components of this vector. The vector must be defined in the global Cartesian coordinate system, and it +should define the master surface’s desired outward normal direction. +Input File Usage: +*CLEARANCE, SLAVE=surface_name, MASTER=surface_name, +TABULAR +node number or node set label, clearance value, first normal component, +second normal component, third normal component +Repeat the data line as often as necessary. +Abaqus/CAE Usage: +You cannot redefine contact directions in Abaqus/CAE, except for threaded bolt +connections . +Generating the contact normal directions for a threaded bolt connection automatically +Alternatively, for a single-threaded bolt connection the contact normal directions for each slave node can +be generated automatically by specifying the thread geometry data and two points used to define a vector +on the axis of the bolt/bolt hole. Either the bolt or bolt hole can be a master or slave surface. However, +the vector defining the axis of the bolt or bolt hole must be chosen appropriately. +For example, when the bolt surface is chosen to be the master surface, the vector should be oriented +to point from the tip of the bolt to the head of the bolt if the bolt is in tension and from the head to the tip +if the bolt is in compression. If the bolt surface is chosen to be the slave surface and the bolt is in tension, +the bolt axis should be flipped (i.e., from the head to the tip) and a negative half-thread angle should be +specified. An incorrect bolt axis direction will not engage the contact interaction, and the surfaces will +be unconstrained. You should check the stresses in the bolt to make sure that the contact is engaged. +Input File Usage: +Abaqus/CAE Usage: +*CLEARANCE, SLAVE=surface_name, MASTER=surface_name, +TABULAR, BOLT +half-thread angle, pitch, major bolt diameter, mean bolt diameter +node number or node set label, clearance value, coordinates of +points a and b on the axis of the bolt/bolt hole +Repeat the second data line as often as necessary. +Interaction module: contact interaction editor: Clearance: Initial +clearance: Computed for single-threaded bolt or Specify for +single-threaded bolt: clearance value, +Clearance region on slave surface: Edit Region: select region, +Bolt direction vector: Edit: select axis, +Half-thread angle: half-thread angle, Pitch: pitch, +Bolt diameter: Major: major bolt diameter or Mean: mean bolt diameter +Visualizing the precise initial clearances or overclosures +Abaqus/Standard does not adjust the coordinates of the slave surface when precise initial clearances or +overclosures are specified. Therefore, the specified clearances or overclosures cannot be seen in the +model in Abaqus/CAE. Thus, depending on the initial geometry of the surfaces and the magnitude of +the clearances or overclosures, the surfaces may appear open or closed in Abaqus/CAE when they are +actually just in contact. However, the actual clearance can be displayed in Abaqus/CAE by plotting a +contour plot of the variable COPEN. +Alternative methods for specifying precise initial clearances or overclosures +Abaqus/Standard offers an alternative method of defining precise initial clearances or overclosures that is +applicable to both small-sliding and finite-sliding contact pairs. In this method you specify an adjustment +zone depth for the contact pair (as described above in “Adjusting the surfaces in a contact pair”) to move +the surfaces forming the contact pair exactly into contact at the start of the analysis. Then, in the first step +of the simulation you specify an allowable contact interference, +, for the contact pair . The contact interference definition must +refer to an amplitude curve; the form of the amplitude curve depends on whether a clearance or an +overclosure is being defined and is described below. The clearance or overclosure will be uniform across +the surfaces. +Input File Usage: +Use all of the following options: +*CONTACT PAIR, ADJUST=a +slave_surface, master_surface +*AMPLITUDE, NAME=amplitude_name +*CONTACT INTERFERENCE, AMPLITUDE=amplitude_name +slave_surface, master_surface, +Abaqus/CAE Usage: +Interaction module: contact interaction editor: Specify tolerance for +adjustment zone: a, Interference Fit: toggle on Uniform allowable +interference, Amplitude: amplitude_name, Magnitude at start of step: +Specifying a precise clearance by defining an allowable contact interference +To specify a precise clearance by defining an allowable contact interference, the amplitude curve should +have a constant magnitude for the duration of the step. A positive value should be given as the allowable +interference, +. When viewed in Abaqus/CAE, these surfaces will appear to penetrate each other when +they are in contact. The surfaces start the simulation with coordinates that have them exactly touching, +but the specified interference makes them behave as if they have a clearance between them. +Specifying a precise overclosure by defining an allowable contact interference +To specify a precise overclosure by defining an allowable contact interference, the amplitude curve +should ramp from zero to unity over the duration of the step to allow Abaqus/Standard to resolve the +overclosure gradually. A negative value should be given as the allowable interference, +. When viewed +in Abaqus/CAE, the surfaces start the simulation with coordinates that have them exactly touching, but +the specified interference makes them behave as if they are overclosed. As Abaqus/Standard resolves +the overclosure, these surfaces will appear to separate from each other. When the gap between the two +surfaces is equal to a distance of +, the surfaces will behave as if they are precisely in contact. +35.3.6 +ADJUSTING CONTACT CONTROLS IN Abaqus/Standard +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining contact pairs in Abaqus/Standard,” Section 35.3.1 +• *CONTACT CONTROLS +• *CONTACT PAIR +• “Defining surface-to-surface contact,” Section 15.13.7 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Defining self-contact,” Section 15.13.8 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +• “Specifying contact controls in an Abaqus/Standard analysis,” Section 15.13.9 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +Contact controls in Abaqus/Standard: +• should not be modified from the default settings for the majority of problems; +• can be used for problems where the standard contact controls do not provide cost-effective solutions; +• can be used for problems where the standard controls do not effectively establish the desired contact +conditions; and +• can be used in some situations to control whether supplementary contact constraints are created. +Problems that benefit from adjustments to the contact controls in Abaqus/Standard are generally large +models with complicated geometries and numerous contact interfaces. +Applying contact controls +You can apply contact controls on a step-by-step basis to all of the contact pairs and contact elements that +are active in the step or to individual contact pairs. This makes it possible to apply contact controls to +a specific contact pair to take the simulation through a difficult phase. Contact controls remain in effect +until they are either changed or reset to their default values. If in any given step the contact controls are +declared for both the entire model and for a specific contact pair, the controls for the specific contact pair +will override those for the entire model for that contact pair. +In addition, you can specify supplementary contact constraints on individual contact pairs as +described below in “Supplementary contact constraints.” +Input File Usage: +To apply contact controls to all contact pairs and contact elements: +*CONTACT CONTROLS +contact control options +To apply contact controls to a specific contact pair: +*CONTACT CONTROLS, SLAVE=slave surface, MASTER=master surface +contact control options +Repeat this option to apply contact controls to several contact pairs. +Abaqus/CAE Usage: +Contact controls in Abaqus/CAE can be applied only to specific contact pairs: +Interaction module: Interaction→Contact Controls→Create: +Abaqus/Standard contact controls +Contact interaction editor: Contact controls: contact controls name +Resetting contact controls +You can reset all contact controls to their default values, or you can reset the controls for a specific contact +pair. +Input File Usage: +To reset all contact controls: +*CONTACT CONTROLS, RESET +To reset the controls for a specific contact pair: +*CONTACT CONTROLS, SLAVE=slave surface, +MASTER=master surface, RESET +Abaqus/CAE Usage: +Interaction module: contact interaction editor: Contact controls: (Default) +You cannot reset all contact controls at once in Abaqus/CAE. +Automatic stabilization of rigid body motions in contact problems +Abaqus/Standard offers contact stabilization to help automatically control rigid body motion in static +problems before contact closure and friction restrain such motion. +It is recommended that you first try to stabilize rigid body motion through modeling techniques +(modifying geometry, imposing boundary conditions, etc.). The automatic stabilization capability is +meant to be used in cases in which it is clear that contact will be established, but the exact positioning +of multiple bodies is difficult during modeling. It is not meant to simulate general rigid body dynamics; +nor is it meant for contact chattering situations or to resolve initially tight clearances between mating +surfaces. +When automatic contact stabilization is used, Abaqus/Standard activates viscous damping for +relative motions of the contact pair at all slave nodes, in the same manner as contact damping . Unlike most contact controls, which carry over to subsequent +steps until they are modified or reset, automatic stabilization damping is applied only for the duration +of the step in which it is specified. In subsequent steps the stabilization is removed, even if contact was +not established or if rigid body motions appear later because of complete separation of the contact pair. +If needed, you should specify stabilization for subsequent steps as well. +By default, the damping coefficient: +• is calculated automatically for each contact constraint based on the stiffness of the underlying +elements and the step time, +• is applied to all contact pairs equally in the normal and tangential directions, +• is ramped down linearly over the step, +• is active only when the distance between the contact surfaces is smaller than a characteristic surface +dimension, and +• is zero for contact modeled with contact elements (such as gap contact elements, tube-to-tube contact +elements, etc.). +Although the automatically calculated damping coefficient typically provides enough damping to +eliminate the rigid body modes without having a major effect on the solution, there is no guarantee that the +value is optimal or even suitable. This is particularly true for thin shell models, in which the damping may +be too high. Hence, you may have to increase the damping if the convergence behavior is problematic +or decrease the damping if it distorts the solution. The first case is obvious, but the latter case requires a +post-analysis check. There are several ways to carry out such checks. The simplest method is to consider +the ratio between the energy dissipated by viscous damping and a more general energy measure for the +model, such as the elastic strain energy. These quantities can be obtained as output variables ALLSD +and ALLSE, respectively. More detailed information can be obtained by comparing the contact damping +stresses CDSTRESS (with the individual components CDPRESS, CDSHEAR1, and CDSHEAR2) to the +true contact stresses CSTRESS (with the individual components CPRESS, CSHEAR1, and CSHEAR2). +If the contact damping stresses are too high, you should decrease the damping. The comparison should +be made after contact is firmly established; the contact damping stresses will always be relatively high +when contact is not yet or only partially established. +The easiest way to increase or decrease the amount of damping is to specify a factor by which +the automatically calculated damping coefficient will be multiplied. Typically, you should initially +consider changing the default damping by (at least) an order of magnitude; if that addresses the problem +sufficiently, you can do some subsequent fine-tuning. In some cases a larger or smaller factor may be +needed; this is not a problem as long as a converged solution is obtained and the dissipated energy and +contact damping stresses are sufficiently small. +It is also possible to specify the damping coefficient directly. Direct specification of the damping +value is not easy and may require some trial and error. For efficiency reasons this may best be done on a +similar model of reduced size. If the damping coefficient is specified directly, any multiplication factor +specified for the default damping coefficient is ignored. +Input File Usage: +To use the default damping coefficient: +*CONTACT CONTROLS, STABILIZE +To specify a scale factor for the default damping coefficient: +*CONTACT CONTROLS, STABILIZE=factor +To specify the damping coefficient directly: +*CONTACT CONTROLS, STABILIZE +damping coefficient +Abaqus/CAE Usage: +Interaction module: Abaqus/Standard contact controls editor: Stabilization: +Automatic stabilization, Factor: factor or Stabilization coefficient: +damping coefficient +Specifying the stabilization ramp-down factor +You can specify the ramp-down factor at the end of the step. By default, this value is equal to zero, so that +the damping vanishes completely at the end of the step. Entering a nonzero value for this factor can be +useful in cases where the rigid body modes are not fully constrained at the end of the step; for example, if +the problem is frictionless and sliding motions can occur but there is no net force in the sliding direction. +In that case it is usually desirable to maintain the small damping in the next step by using the value used +for the ramp-down as the multiplication factor for the damping coefficient. If needed, you can maintain +this damping level by setting the ramp-down factor equal to one. +*CONTACT CONTROLS, STABILIZE +, ramp-down factor +Input File Usage: +Abaqus/CAE Usage: +Interaction module: Abaqus/Standard contact controls editor: Stabilization: +Automatic stabilization or Stabilization coefficient, Fraction +of damping at end of step: ramp-down factor +Specifying the damping range +By default, the opening distance over which the damping is applied (the damping range) is equal to the +characteristic slave surface facet dimension; if such a dimension is not available (for example, in the +case of a node-based surface), a characteristic element length obtained for the whole model is used. The +damping is 100% of the reference value for openings less than half the damping range and from there is +ramped to zero for an opening equal to the damping range. Alternatively, you can specify the damping +range directly, overriding the calculated value. This can be useful if the damping should work only for a +narrow gap, or if the damping should be in effect regardless of the opening distance. In the latter case a +large value should be entered. +Input File Usage: +*CONTACT CONTROLS, STABILIZE +, , damping range +Abaqus/CAE Usage: +Interaction module: Abaqus/Standard contact controls editor: Stabilization: +Automatic stabilization or Stabilization coefficient, Clearance at +which damping becomes zero: Specify: damping range +Specifying tangential damping +By default, the damping in the tangential direction is the same as the damping in the normal direction. +However, if a lower or higher value is desired, you can decrease or increase the tangential damping or +set it to zero. +Input File Usage: +*CONTACT CONTROLS, STABILIZE, TANGENT FRACTION=value +Abaqus/CAE Usage: +Interaction module: Abaqus/Standard contact controls editor: +Stabilization: Automatic stabilization or Stabilization coefficient, +Tangent fraction: value +Contact controls associated with normal contact constraints +These controls allow you to specify that nodes on the contact interfaces can violate “hard” contact +conditions. In addition, these controls can be used to modify the behavior of the “softened” pressure- +overclosure relationships and the augmented Lagrangian or penalty contact constraint enforcement. The +no separation pressure-overclosure relationships cannot be modified by the contact controls. +A node can violate the contact condition in one of two ways. First, Abaqus/Standard may consider +that there is no contact at that node, even though the node has penetrated the master surface by a small +distance. Second, Abaqus/Standard may consider that there is contact at a node, even though the normal +pressure transmitted between the contacting surfaces at the node is negative (that is, a tensile stress is +being transmitted). +Modifying the behavior of the augmented Lagrangian or penalty contact constraint enforcement +For augmented Lagrangian contact you can specify the allowable penetration (either directly or as a +fraction of a characteristic contact surface dimension) that is permitted to violate the impenetrability +condition. In addition, for augmented Lagrangian or penalty contact you can scale the default penalty +stiffness calculated by Abaqus/Standard. Controls for the augmented Lagrange and penalty constraint +enforcement methods are discussed in “Contact constraint enforcement methods in Abaqus/Standard,” +Section 37.1.2. +Modifying the tangential penalty stiffness in linear perturbation steps +The penalty stiffness used to enforce tangential constraints in linear perturbation steps generally +In perturbation steps +differs from the penalty stiffness used to enforce sticking in a general step. +Abaqus/Standard activates the tangential contact constraints when the corresponding normal constraint +is active in the base state and the contact property (surface interaction) definition includes a friction +model. By default, the tangential penalty stiffness is equal to the default normal penalty stiffness. +You can scale the tangential penalty stiffness to simulate sticking/slipping conditions on a step-by- +step basis. This scaling only affects the perturbation step in which it is specified; it will not carry over +to subsequent steps. If you want the same scale factor applied in a series of perturbation steps, you must +specify the scale factor explicitly in each step. +Some procedures that rely on a frequency analysis, such as complex frequency analysis and +subspace-based steady-state dynamic analysis, are influenced by the scaling of the tangential stiffness +that was in effect for the prior frequency analysis and the scaling of the tangential stiffness that is +in effect for these steps. In such cases consistent scaling is recommended for these steps. For other +mode-based procedures based on a frequency analysis, the scaling of the tangential stiffness is ignored +and only the effect of the previous frequency analysis is considered. +Input File Usage: +To modify the tangential penalty stiffness for all contact pairs in a linear +perturbation step: +*CONTACT CONTROLS, PERTURBATION TANGENT +SCALE FACTOR=factor +To modify the tangential penalty stiffness for a specific contact pair in a linear +perturbation step: +*CONTACT CONTROLS, PERTURBATION TANGENT SCALE +FACTOR=factor, SLAVE=slave surface, MASTER=master surface +Abaqus/CAE Usage: Modifying the tangential penalty stiffness in linear perturbation steps is not +supported in Abaqus/CAE. +Contact controls associated with second-order faces +Second-order elements not only provide higher accuracy but also capture stress concentrations more +effectively and are better for modeling geometric features than first-order elements. Surfaces based on +second-order element types work well with the surface-to-surface contact formulation but, in some cases, +do not work well with the node-to-surface formulation . +Some second-order element types are not well-suited for underlying the slave surface with the +combination of a node-to-surface contact formulation and strict enforcement of “hard” contact conditions +because of the distribution of equivalent nodal forces when a pressure acts on the face of the element. +As shown in Figure 35.3.6–1, a constant pressure applied to the face of a second-order element without +a midface node produces forces at the corner nodes acting in the opposite sense of the pressure. This +ambiguous nature of the nodal forces in second-order elements can cause Abaqus/Standard to alter its +internal contact logic inadequately. Slave surfaces based on second-order tetrahedral elements can also +be problematic for the node-to-surface contact formulation because the distribution of equivalent nodal +forces for a pressure acting on a face of these elements is such that the corner nodes have zero force. +Options available in Abaqus/Standard to make it easier to use node-to-surface contact pairs +involving second-order slave faces are discussed below. You can also avoid potential difficulties by +using the surface-to-surface contact formulation, which is generally preferable. +Manually or automatically adjusting element types +Modified 10-node tetrahedral elements (C3D10M, etc.) do not cause fundamental difficulties for +the node-to-surface contact formulation and often provide a viable option to 10-node second-order +tetrahedral elements (C3D10, C3D10I, etc.) for models with node-to-surface contact pairs. Trade-offs +in characteristics of modified 10-node tetrahedral elements versus second-order tetrahedral elements +are discussed in “Modified triangular and tetrahedral elements” in “Solid (continuum) elements,” +Section 28.1.1. +If desired, you must make this adjustment to the element type as it does not occur +automatically. +Abaqus/Standard automatically adds midface nodes to underlying (serendipity) elements of +most 8-node slave facets associated with node-to-surface contact pairs. For the three-dimensional +18-node gasket elements, the midface nodes are also generated automatically if they are not given in +the element connectivity. The presence of the midface node results in a distribution of nodal forces +that is not ambiguous for the contact algorithm. The element families C3D20(RH), C3D15(H), S8R5, +q = pA +r = pA +12 +Figure 35.3.6–1 Equivalent nodal loads produced by a constant +pressure on the second-order element face in “hard” contact simulations. +and M3D8 are converted to the families C3D27(RH), C3D15V(H), S9R5, and M3D9, respectively. +Since Abaqus/Standard does not convert second-order coupled temperature-displacement, coupled +thermal-electrical-structural, and coupled pore pressure–displacement elements, you should use +an alternative method to avoid problems with serendipity elements in the node-to-surface contact +formulation in those cases. Abaqus/Standard will interpolate nodal quantities, such as temperature and +field variables, at the automatically generated midface nodes when values are prescribed at any of the +user-defined nodes. +By default, Abaqus/Standard does not automatically add midface nodes to second-order serendipity +elements that form a slave surface for surface-to-surface contact pairs; however, an option is available +to enable the same algorithm for automatically adding midface nodes as used by node-to-surface contact +pairs. +Input File Usage: +*CONTACT PAIR, TYPE=SURFACE TO SURFACE, +MIDFACE NODES=YES +Abaqus/CAE Usage: +You cannot enable automatic conversion of serendipity elements underlying +slave surfaces of surface-to-surface contact pairs in Abaqus/CAE. +Supplementary contact constraints +Another approach to avoiding difficulties that certain element types present to the node-to-surface +contact formulation is to add supplementary contact constraints without changing the underlying element +formulation. This approach is applicable only to cases in which node-to-surface contact pairs use +penalty or augmented Lagrange constraint enforcement or a softened pressure-overclosure relationship, +because it would result in overconstrained conditions if strictly enforced “hard” contact conditions are +in effect. Supplementary contact constraints are sometimes helpful for improving convergence behavior +or for improving the smoothness and accuracy of the contact pressure and underlying element stress; +however, the extra constraints present some risk of degrading convergence behavior. Supplementary +constraints are used selectively by default for node-to-surface contact pairs with 6-node slave faces of +non-modified elements and 8-node slave faces unless strictly enforced “hard” contact conditions are +in effect. You can deactivate supplementary constraints or add activate supplementary constraints for +additional second-order element types underlying the slave surface. +Input File Usage: +*CONTACT PAIR, INTERACTION=interaction_property_name, +SUPPLEMENTARY CONSTRAINTS=SELECTIVE +slave_surface_name, master_surface_name +Use the following option to add supplementary contact constraints for +additional second-order element types: +*CONTACT PAIR, INTERACTION=interaction_property_name, +SUPPLEMENTARY CONSTRAINTS=YES +slave_surface_name, master_surface_name +Use the following option to forgo supplementary contact constraints: +*CONTACT PAIR, INTERACTION=interaction_property_name, +SUPPLEMENTARY CONSTRAINTS=NO +slave_surface_name, master_surface_name +Abaqus/CAE Usage: +For a node-to-surface contact formulation: +Interaction module: Create Interaction: Surface-to-surface contact +(Standard): select the master surface; click Surface; select the slave surface; +Interaction editor; Use supplementary contact points: +Selectively, Always, or Never; Contact interaction property: +interaction_property_name +Smoothness of contact force redistribution upon sliding for surface-to-surface contact pairs +You can control the smoothness of nodal contact force redistribution upon sliding for surface-to-surface +contact pairs. The default setting, which is generally appropriate, results in the smoothness of the nodal +force redistribution being of the same order as the elements underlying the slave surface; that is, linear +redistribution smoothness for linear elements, and quadratic redistribution smoothness for second-order +elements. Quadratic redistribution smoothness usually tends to improve convergence behavior and +improve resolution of contact stresses within regions of rapidly varying contact stresses. However, +quadratic redistribution smoothness tends to increase the number of nodes involved in each constraint, +which can increase the computational cost of the equation solver. Linear redistribution smoothness +tends to provide better resolution of contact stresses near edges of active contact regions and, therefore, +occasionally results in better convergence behavior. +Input File Usage: +Use the following option to indicate that the smoothness of the contact force +redistribution upon sliding should be of the same order as the elements +underlying the slave surface for surface-to-surface contact pairs: +*CONTACT PAIR, TYPE=SURFACE TO SURFACE, SLIDING +TRANSITION=ELEMENT ORDER SMOOTHING +slave_surface_name, master_surface_name +Use the following option to indicate linear smoothness of the contact force +redistribution upon sliding for surface-to-surface contact pairs: +*CONTACT PAIR, TYPE=SURFACE TO SURFACE, SLIDING +TRANSITION=LINEAR +slave_surface_name, master_surface_name +Use the following option to indicate quadratic smoothness of the contact force +redistribution upon sliding for surface-to-surface contact pairs: +*CONTACT PAIR, TYPE=SURFACE TO SURFACE, SLIDING +TRANSITION=QUADRATIC +slave_surface_name, master_surface_name +Abaqus/CAE Usage: +You cannot change the default contact force redistribution in Abaqus/CAE. +35.3.7 +DEFINING TIED CONTACT IN Abaqus/Standard +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining contact pairs in Abaqus/Standard,” Section 35.3.1 +• “Adjusting initial surface positions and specifying initial clearances in Abaqus/Standard contact +pairs,” Section 35.3.5 +• *CONTACT PAIR +• “Defining surface-to-surface contact,” Section 15.13.7 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Using contact and constraint detection,” Section 15.16 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +Tied contact in Abaqus/Standard: +• ties two surfaces forming a contact pair together for the duration of a simulation; +• can be used in mechanical, coupled temperature-displacement, coupled thermal-electrical- +transfer +structural, coupled pore pressure-displacement, coupled thermal-electrical, or heat +simulations; +• constrains each of the nodes on the slave surface to have the same value of displacement, +temperature, pore pressure, or electrical potential as the point on the master surface that it contacts; +• allows for rapid transitions in mesh density within the model; +• requires the adjustment of the contact pair surfaces; and +• cannot be used with self-contact or symmetric master-slave contact. +It is preferable to use the surface-based tie constraint capability instead of tied contact . +Defining tied contact for a contact pair +To “tie” the surfaces of a contact pair together for an analysis, you must also adjust the surfaces because, +as described below, it is very important that the tied surfaces be precisely in contact at the start of the +simulation. See “Adjusting initial surface positions and specifying initial clearances in Abaqus/Standard +contact pairs,” Section 35.3.5, for details on adjusting surfaces. As always, you must associate the contact +pair with a contact interaction property definition. +Input File Usage: +*CONTACT PAIR, TIED, ADJUST=a or node_set_label, +INTERACTION=name +Abaqus/CAE Usage: +Interaction module: Interaction→Create: select a Slave Node/Surface +Adjustment option: toggle on Tie adjusted surfaces +The tied contact formulation +When a contact pair uses the tied contact formulation, Abaqus/Standard uses the undeformed +configuration of the model to determine which slave nodes are within the adjustment zone , accounting for any shell or membrane +thickness by default. Abaqus/Standard then adjusts these slave nodes’ positions into a zero-penetration +state and forms constraints between these slave nodes and the surrounding nodes on the master surface. +The constraints are formed with either a “surface-to-surface” or a “node-to-surface” approach, similar +to small-sliding contact. The traditional node-to-surface approach is used by default for tied contact. +The user interface for selecting between the surface-to-surface and node-to-surface approaches and +to avoid consideration of shell and membrane thickness for tied contact is the same as for small-sliding +contact . +Use of tied contact in mechanical simulations +The tied contact formulation constrains only translational degrees of freedom in mechanical simulations. +Abaqus/Standard places no constraints on the rotational degrees of freedom of structural elements +involved in tied contact pairs. +Self-contact is not supported with tied contact. Self-contact is designed for finite-sliding situations +in which it is not obvious from the original geometry which parts of the surface will come into contact +during the deformation. +Mechanical constraints for tied contact are strictly enforced with a direct Lagrange multiplier +method by default. Alternatively, you can specify that these constraints should be enforced with a +penalty or augmented Lagrange constraint method . The constraint enforcement method specified will be applied to +the tangential constraints in addition to the normal constraints. Softened contact pressure-overclosure +linear—see “Contact pressure-overclosure relationships,” +relationships (exponential, +Section 36.1.2) are ignored for tied contact. +tabular, or +Use of tied contact in nonmechanical simulations +The tied contact capability can be used in models where the nodal degrees of freedom include +electrical potential and/or temperature. Except for the nodal degree of freedom being constrained, +Abaqus/Standard uses exactly the same formulation for tied contact in nonmechanical simulations as it +does for mechanical simulations. +Unconstrained nodes in tied contact pairs +Abaqus/Standard does not constrain slave nodes to the master surface unless they are precisely in contact +with the master surface at the start of the analysis. Any slave nodes not precisely in contact at the +start of the analysis—e.g., either open or overclosed—will remain unconstrained for the duration of the +simulation; they will never interact with the master surface. In mechanical simulations an unconstrained +slave node can penetrate the master surface freely. In a thermal, electrical, or pore pressure simulation an +unconstrained slave node will not exchange heat, electrical current, or pore fluid with the master surface. +To avoid such unconstrained nodes in tied contact pairs, use the capability for adjusting the surfaces +of a contact pair described in “Adjusting initial surface positions and specifying initial clearances in +Abaqus/Standard contact pairs,” Section 35.3.5. This capability moves slave nodes onto the master +surface before Abaqus/Standard checks for the initial contact state. It is intended only for nodes that are +close to the master surface and is not intended to correct large errors in the mesh geometry. +Checking that slave nodes are constrained +Abaqus/Standard prints a table in the data (.dat) file identifying the predominant slave node and other +nodes involved in each constraint. If Abaqus/Standard cannot form a constraint for a given slave node +acting as a predominant slave node, either because it is not in contact with the master surface or it cannot +“see” the master surface, it will issue a warning message in the data file. For an explanation of when a +slave node would not “see” a master surface and how to correct this problem, see “Contact formulations +in Abaqus/Standard,” Section 37.1.1. When creating a model with tied contact, it is important to use +this information provided by Abaqus/Standard to identify any unconstrained nodes and to make any +necessary modifications to the model to constrain them. +35.3.8 +EXTENDING MASTER SURFACES AND SLIDE LINES +Product: Abaqus/Standard +References +• “Defining contact pairs in Abaqus/Standard,” Section 35.3.1 +• “Common difficulties associated with contact modeling in Abaqus/Standard,” Section 38.1.2 +• *CONTACT PAIR +• *SLIDE LINE +Overview +Extending the master surface or a slide line: +• can prevent nodes from “falling off” or getting trapped behind the master surface (or slide line) in +finite-sliding problems; +• allows the slave node to find a master surface when the slave node has no intersection with the +master surface at the start of the analysis in small- and infinitesimal-sliding problems; +• can avoid numerical roundoff difficulties associated with contact modeling; +• should not be used in lieu of proper contact modeling techniques; +• should not be used to reduce the number of underlying elements of a contact surface; and +• applies only to contact pairs that use a node-to-surface discretization. +Extending the master surface for small-sliding, node-to-surface contact +If a slave node cannot find an intersection with the master surface at the start of the analysis, it will be +free to penetrate the master surface because no local tangent plane will be formed. This type of problem, +which typically occurs for node-to-surface contact when the slave node is aligned with the edge of the +master surface, is illustrated in Figure 35.3.8–1 and may be caused by numerical roundoff errors when a +preprocessor is used to generate the nodal coordinates. Cases such as that shown in Figure 35.3.8–1 are +not problematic for the small-sliding, surface-to-surface formulation because the constraint formulation +considers the region of the slave surface near a slave node. +Slave Node +Slave Node +Master Surface +Master Surface +No intersection (e = 0) +Intersection found (e > 0) +Figure 35.3.8–1 Slave node fails to find an intersection with the +master surface for small-sliding, node-to-surface contact if e=0. +For node-to-surface contact you can specify the size of the extension zone, e, as a fraction of the +end segment or facet edge length . If e is set to zero, Abaqus will not extend the +ends. The value given must lie between 0.0 and 0.2. The default value is 0.1 for node-to-surface contact; +surface extensions are not available for surface-to-surface contact. +Input File Usage: +*CONTACT PAIR, SMALL SLIDING, EXTENSION ZONE=e +Extending the master surface or slide line in finite-sliding, node-to-surface contact +To prevent slave nodes from “falling off” or getting trapped behind the master surface, an open surface +or slide line can be extended for finite-sliding, node-to-surface contact. +You can specify the size of the extension zone, e, as a fraction of the end segment or facet edge +length . The geometry in the extension zone is extrapolated from the end segment +or facet edge. +If e is set to zero, Abaqus/Standard will not extend the ends. The value given must +lie between 0.0 and 0.2. The default value is 0.1 for node-to-surface contact. Surface extensions are +not available for surface-to-surface contact; for finite-sliding, surface-to-surface contact, constraints are +located within slave faces, and “falling off” will not occur until nearly the entire slave facet slides off +the master surface. Extensions for finite-sliding, node-to-surface contact should be considered only if +other modeling techniques to prevent “falling off” are not feasible and when the slave node is expected +to travel in the extended zone for a short period of the solution phase or during nonconverged iterations. +Input File Usage: +Use either of the following options: +*CONTACT PAIR, EXTENSION ZONE=e +*SLIDE LINE, ELSET=element_set_name, EXTENSION ZONE=e +Master Surface +Extension Zone +Extension Zone +e × l1 +l 2 +e × l2 +e × l2 +l2 +Master Surface +l1 +e × l1 +Open 2-D Master Surface +Open Axisymmetric Surface +Extension Zone +Slave Node +2-D Slide Line +Slave Node +e × l3 +e × l1 +2l +Extension Zone +e × l2 +Open Slide Line +e × l4 +1l +4l +e × l1 +Master Surface +3l +2l +e × l2 +3-D Master Surface +Figure 35.3.8–2 Definition of size of extension zone. +CONTACT MODELING IF SUBSTRUCTURES ARE PRESENT +CONTACT WITH SUBSTRUCTURES +Product: Abaqus/Standard +References +• “Element-based surface definition,” Section 2.3.2 +• “Node-based surface definition,” Section 2.3.3 +• “Using substructures,” Section 10.1.1 +• “Membrane elements,” Section 29.1.1 +• “Surface elements,” Section 32.7.1 +• “Contact interaction analysis: overview,” Section 35.1.1 +• “Defining contact pairs in Abaqus/Standard,” Section 35.3.1 +Overview +Contact in Abaqus/Standard involving substructures: +• is not part of the substructure definition; +• requires retaining nodes on the exterior of the substructure; +• requires the definition of a contact surface on the retained nodes; and +• can be between the exterior of one substructure and another surface, the exterior of one substructure +and the exterior of another substructure, and the exterior of one substructure and itself. +Defining the contact surface of a substructure +Since a substructure consists only of a group of retained nodal degrees of freedom, it has no surface +geometry upon which Abaqus/Standard can define a contact surface. One of the following methods +must be used to define the surface geometry of the substructure: +• mesh the exterior of the substructure with surface elements, +• mesh the exterior of the substructure with structural elements, +• use a node-based surface, or +• use contact elements. +Meshing the surface of the substructure with surface or structural elements provides the most flexibility +in defining the contact conditions; the surface can be used as either a master or slave surface in the +simulation. Using a node-based surface is probably the easiest method to use, but the limitations inherent +to node-based surfaces (such as the inability to act as a master surface, the need to define nodal contact +areas for exact contact stress recovery, and the lack of visualization of contact stresses) may limit the +usefulness of this approach. Contact elements can be a useful method if the model uses matched meshes. +Meshing the surface of the substructure with surface elements +The surface geometry of the body being modeled with a substructure can be designated by defining +elements on the retained surface nodes of the substructure. The elements can be used to create an +element-based surface , which can then be used +as part of a contact pair. +Whenever possible, it is recommended that you use surface elements to mesh the exterior of a +substructure. Surface elements will accurately define the surface geometry of the substructure without +introducing any additional stiffness to the model; the stiffness of the underlying body is built into the +substructure. See “Surface elements,” Section 32.7.1, for more information about surface elements. +Figure 35.3.9–1 shows a simulation where both of the contacting bodies have been modeled with +substructures. The nodes retained in the model are indicated in the figure. If this were a three-dimensional +model, general surface elements would be used to reconstruct the appropriate surface geometries of the +original mesh. +⇒ +(a) critical model +(b) nodes retained +for contact resolution +Figure 35.3.9–1 Substructuring in a contact simulation. +Limitations of surface elements +Surface elements cannot be used to overlay substructures in planar models. +Surface elements also cannot be used to overlay a substructure that consists of second-order, +three-dimensional elements with midface nodes (C3D27(R)(H) or C3D15V(H)). Surface elements +with midface nodes are not currently available in Abaqus/Standard, and the 8-node surface element +(SFM3D8) is not well suited for contact modeling. +Meshing the surface of the substructure with structural elements +Although surface elements are generally preferable for use in substructure contact situations, you can +also use structural elements to define the surface geometry of a substructure. You can use membrane +elements in three-dimensional models and axisymmetric models, and trusses in planar models. Define +the elements to have very small thickness or area and define their material property to have a very small +elastic modulus so that their contribution to the stiffness of the model is negligible. +If the model in Figure 35.3.9–1 were a planar model, truss elements would be used to connect the +nodes and define the surface geometry. The truss elements would have a very small cross-sectional area +and refer to a material property with very low stiffness so that they do not add any significant stiffness +to the underlying bodies. +Limitations of structural elements +Membrane elements cannot be used to overlay a substructure that consists of second-order, +three-dimensional brick elements of type C3D20(R)(H) if the substructure will be used as a slave +surface. Normally, Abaqus/Standard automatically converts C3D20(R)(H) brick elements to elements +with midface nodes C3D27(R)(H) because this class of elements performs better in contact simulations. +that does +Abaqus/Standard also converts any second-order, +not have a midface node when it is used in a slave surface . Therefore, if second-order membrane +elements (type M3D8) are used to reconstruct the surface topology of a substructure consisting of +C3D20 elements, Abaqus/Standard will convert them to M3D9 elements when the surface is used as a +slave surface. The midface nodes that are generated automatically will not correspond to any retained +nodes and, thus, will have zero stiffness. The lack of stiffness at these nodes will cause numerical +problems during the analysis. Membrane elements can be used if elements of type C3D27(R)(H) have +been used on the surface of the substructure. +three-dimensional structural element +Using a node-based surface to define the substructure’s surface +If the retained nodes of the substructures are associated with the slave surface of a contact pair, +the retained nodes can be included in a node-based surface . In this case it is not necessary to overlay the surface of the substructure with elements. +Using contact elements to define the substructure’s surface +GAP elements (“Gap contact elements,” Section 39.2.1) can be used to define the contact interactions in +the model. These elements require that matching nodes be present on the opposite sides of the contact +surfaces and allow only for small relative sliding between the surfaces. This latter assumption is usually +consistent with the assumption of linear behavior that is built into a substructure. +CONTACT MODELING IF ASYMMETRIC-AXISYMMETRIC ELEMENTS ARE +PRESENT +ASYMM.-AXISYMM. CONTACT +Product: Abaqus/Standard +References +• “Slide line contact elements,” Section 39.4.1 +• “Rigid surface contact elements,” Section 39.5.1 +• *ASYMMETRIC-AXISYMMETRIC +Overview +Modeling contact in asymmetric-axisymmetric problems: +• requires the use of contact elements (ISL or IRS); +• requires independent contact elements on each circumferential plane; and +• can be done only on certain circumferential planes. +Modeling contact in asymmetric-axisymmetric problems +asymmetric +CAXA or SAXA elements are used to model problems where initially axisymmetric structures may +undergo asymmetric deformations. These asymmetric deformations may include asymmetric contact +conditions. The surface-based contact capability cannot be used to model such problems; contact +elements (ISL or IRS) must be used. +Independent sets of two-dimensional contact elements must be created for each circumferential +plane in the CAXA or SAXA elements. You must specify the angle, +, of the circumferential plane +with which each set of contact elements is associated and the number of Fourier modes, n, used with the +underlying CAXA or SAXA elements. +Input File Usage: +Use both of the following options: +*INTERFACE, ELSET=element_set_name +*ASYMMETRIC-AXISYMMETRIC, MODE=n, ANGLE= +where the ELSET parameter refers to a set of ISL- or IRS-type contact elements. +Limitations on contact in asymmetric-axisymmetric problems +If the circumferential planes in an asymmetric-axisymmetric problem rotate more than a few degrees, +Abaqus/Standard can model contact conditions correctly only on the =0 and 180 circumferential planes. +The asymmetric-axisymmetric elements have internal degrees of freedom for the rotation and out-of- +plane motion of the circumferential planes, but these degrees of freedom are not accounted for in the +contact elements. +Ignoring these degrees of freedom means that Abaqus/Standard keeps the contact +directions fixed in initial circumferential planes and the position of the nodes is projected back onto +these initial planes for contact calculations. If the rotation and motion of the nodes from these initial +planes are small, the errors caused by this approach are minimal. If they are large, the errors will become +very large, making the results unrealistic. +35.4 +Defining general contact in Abaqus/Explicit +• “Defining general contact interactions in Abaqus/Explicit,” Section 35.4.1 +• “Assigning surface properties for general contact in Abaqus/Explicit,” Section 35.4.2 +• “Assigning contact properties for general contact in Abaqus/Explicit,” Section 35.4.3 +• “Controlling initial contact status for general contact in Abaqus/Explicit,” Section 35.4.4 +• “Contact controls for general contact in Abaqus/Explicit,” Section 35.4.5 +35.4.1 +DEFINING GENERAL CONTACT INTERACTIONS IN Abaqus/Explicit +Products: Abaqus/Explicit Abaqus/CAE +References +• “Contact interaction analysis: overview,” Section 35.1.1 +• *CONTACT +• *CONTACT INCLUSIONS +• *CONTACT EXCLUSIONS +• “Defining general contact,” Section 15.13.1 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +Abaqus/Explicit provides two algorithms for modeling contact and interaction problems: the general +contact algorithm and the contact pair algorithm. See “Contact interaction analysis: overview,” +Section 35.1.1, for a comparison of the two algorithms. This section describes how to include general +contact in an Abaqus/Explicit analysis, how to specify the regions of the model that may be involved in +general contact interactions, and how to obtain output from a general contact analysis. +The general contact algorithm in Abaqus/Explicit: +• is specified as part of the model or history definition of the model; +• allows very simple definitions of contact with very few restrictions on the types of surfaces involved; +• uses sophisticated tracking algorithms to ensure that proper contact conditions are enforced +efficiently; +• can be used simultaneously with the contact pair algorithm (i.e., some interactions can be modeled +with the general contact algorithm, while others are modeled with the contact pair algorithm); +• can be used only with three-dimensional surfaces; +• can be used only in mechanical finite-sliding contact analyses; and +• does not support kinematic constraint enforcement (contact constraints are enforced with the penalty +method). +Defining a general contact interaction +The definition of a general contact interaction consists of specifying: +• the general contact algorithm and defining the contact domain (i.e., the surfaces that interact with +one another), as described in this section; +• the +contact +surface properties +Abaqus/Explicit,” Section 35.4.2); +(“Assigning surface properties +for general +contact +in +• the mechanical contact property models (“Assigning contact properties for general contact in +Abaqus/Explicit,” Section 35.4.3); +• the contact +Section 37.2.1); +formulation (“Contact +formulation for general contact +in Abaqus/Explicit,” +• the initial clearance between contact surfaces (“Controlling initial contact status for general contact +in Abaqus/Explicit,” Section 35.4.4); and +• the algorithmic contact controls (“Contact controls for general contact in Abaqus/Explicit,” +Section 35.4.5). +Surfaces used for general contact +The general contact algorithm allows for very general characteristics in the surfaces that it uses, as +discussed in “Contact interaction analysis: overview,” Section 35.1.1. For detailed information on +defining surfaces in Abaqus/Explicit for use with the general contact algorithm, see “Element-based +surface definition,” Section 2.3.2; “Node-based surface definition,” Section 2.3.3; “Analytical rigid +surface definition,” Section 2.3.4; “Eulerian surface definition,” Section 2.3.5; and “Operating on +surfaces,” Section 2.3.6. Two-dimensional surfaces cannot be used with the general contact algorithm. +A convenient method of specifying the contact domain is using cropped surfaces. Such surfaces can +be used to perform “contact in a box” by using a contact domain that is enclosed in a specified rectangular +box in the original configuration. For more information, see “Operating on surfaces,” Section 2.3.6. +In addition, Abaqus/Explicit automatically defines an all-inclusive surface that is convenient for +prescribing the contact domain, as discussed later in this section. The all-inclusive automatically defined +surface includes all element-based surface facets as well as all analytical rigid surfaces and surfaces on +all Eulerian materials. +The general contact algorithm generates contact forces to resist node-into-face, node-into-analytical +rigid surface, and edge-into-edge contact penetrations. The primary mechanism for enforcing contact is +node-to-face contact (the only mechanism used in the contact pair algorithm). If analytical rigid surfaces +are present in the contact domain, the general contact algorithm also enforces node-to-analytical rigid +surface contact. +Considerations for edge-to-edge contact +The general contact algorithm also considers edge-to-edge contact, which is very effective in enforcing +contact that cannot be detected as penetrations of nodes into faces. For example, contact between beam +segments and shell perimeter edges usually is detected only as edge-to-edge +contact. The terminology “contact edges” refers to feature edges of surface facets (on both shells and +solids) as well as to segments representing beam and truss elements. The contact edges representing +beam and truss elements have a circular cross-section, regardless of the actual cross-section of the +beam or truss element. The radius of a contact edge representing a truss element is derived from the +cross-sectional area specified on the truss section definition (it is equal to the radius of a solid circular +section with an equivalent cross-sectional area). For beams with circular cross-sections, the radius +of the contact edge is equivalent to the section radius. For beams with non-circular cross-sections, +the radius of the contact edge is equal to the radius of a circumscribed circle around the section. If +geometric feature edges, +which can optionally be included +in the contact domain. +Abaqus/Explicit GENERAL CONTACT +Thick solid lines indicate shell +perimeter edges and "contact +edges" corresponding to beams. +Beam +Solid +Shells +Dashed lines indicate element +boundaries for which edge-to-edge +contact is not modeled. +Figure 35.4.1–1 General contact domain, including edge-to-edge contact. +connected edges have different radii, a nodal radius is first computed as the minimum radius of the +adjacent contact edges, and the radius of the edge cross-section is interpolated linearly over the length +of the contact edge from the nodal values. Shell element edges reflect the shell thickness in the normal +direction and do not extend past the perimeter (similar to shell nodes and facets). Some numerical +rounding of features occurs for both node-to-facet and edge-to-edge contact. +To model contact between edges that are not cylindrical in shape, surface elements can be attached +to the edge nodes using surface-based tie constraints and node-to-face contact can be defined between +the surface elements . This technique is useful for modeling +geometric details important to the contact definition that are not modeled with the underlying element +geometry. Surface elements can also be defined around shell elements in which Abaqus has reduced +the contact thickness (i.e., if the thickness exceeds the surface facet edge lengths or diagonal lengths) so +that the true surface thickness can be modeled. However, using surface elements with general contact +requires a physically reasonable mass to be associated with the surface element nodes, and care must +be taken not to alter the bulk mass properties when transferring mass to the surface elements from the +underlying elements. +By default, when a surface is used in a general contact interaction, all applicable facets, analytical +rigid surfaces, nodes, perimeter edges, and beam and truss segments are included in the contact definition. +You can control which feature edges are considered for edge-to-edge contact, as discussed in “Assigning +surface properties for general contact in Abaqus/Explicit,” Section 35.4.2. Geometric feature edges and +perimeter edges do not have to be included explicitly in a surface definition (by using edge identifiers) +for them to be considered for edge-to-edge contact. +Eulerian-Lagrangian contact +The general contact algorithm also enforces contact between Eulerian materials and Lagrangian surfaces. +This algorithm automatically compensates for mesh size discrepancies to prevent penetration of Eulerian +material through the Lagrangian surface. The all-inclusive surface that is defined by Abaqus/Explicit +can be used to enforce contact between all Eulerian materials and all Lagrangian bodies in a model; you +can also specify individual Eulerian surfaces in the contact domain . Eulerian-Lagrangian contact is enforced only for Lagrangian surfaces defined on solid +and shell elements. Other surface types, such as beam edges and analytical rigid surfaces, are ignored. +Contact interactions between Eulerian materials and interactions due to Eulerian material self-contact +are handled naturally by the Eulerian formulation; these interactions do not require a general contact +definition. See “Interactions” in “Eulerian analysis,” Section 14.1.1, for more information. +Including general contact in an analysis +If a general contact definition does not appear in a step, any general contact definition active in the +previous step will be propagated to the current step. +For convenience, general contact can be defined as model data. A general contact definition +specified as model data is considered to be defined in the initial step, or “Step 0,” of the analysis; it can +be modified or removed in Step 1 or later steps. +Input File Usage: +Use the following option to indicate the beginning of a general contact +definition: +*CONTACT +This option can appear only once per step. +Abaqus/CAE Usage: +Interaction module: Create Interaction: General contact (Explicit) +Removing general contact definitions +You can remove the previously specified general contact definition and specify a new one. +Input File Usage: +Abaqus/CAE Usage: +*CONTACT, OP=NEW +Interaction module: interaction manager: select interaction, Deactivate +Modifying general contact definitions +Alternatively, you can make changes to an existing general contact definition. In this case the existing +general contact definition remains active and any additional information specified is appended to the +general contact definition. +Contact state information (such as the proper contact normal orientation for double-sided surfaces) +is transferred across step boundaries even if the contact domain is modified. +*CONTACT, OP=MOD +Input File Usage: +Abaqus/CAE Usage: +Interaction module: interaction manager: +select interaction, Edit +Example +Each part of a general contact definition is considered independently when it is modified. For example, +the following contact definition is specified in Step 1 (the individual options are discussed later in this +section): +*CONTACT +*CONTACT INCLUSIONS +surf_1, +*CONTACT EXCLUSIONS +surf_a, surf_b +This contact definition is then modified in Step 2 with the following input: +*CONTACT, OP=MOD +*CONTACT INCLUSIONS +surf_2, surf_3 +*CONTACT EXCLUSIONS +surf_a, surf_c +An equivalent contact definition for Step 2 could be specified as follows: +*CONTACT, OP=NEW +*CONTACT INCLUSIONS +surf_1, +surf_2, surf_3 +*CONTACT EXCLUSIONS +surf_a, surf_b +surf_a, surf_c +Defining the general contact domain +You specify the regions of the model that can potentially come into contact with each other by defining +general contact inclusions and exclusions. Only one contact inclusions definition and one contact +exclusions definition are allowed per step. +All contact inclusions in an analysis are applied first, then all contact exclusions are applied, +regardless of the order in which they are specified. The contact exclusions take precedence over the +contact inclusions. The general contact algorithm will consider only those interactions specified by the +contact inclusions definition and not specified by the contact exclusions definition. +General contact interactions typically are defined by specifying self-contact for the default +automatically generated surface provided by Abaqus/Explicit. All surfaces used in the general contact +algorithm can span multiple unattached bodies, so self-contact in this algorithm is not limited to contact +of a single body with itself. For example, self-contact of a surface that spans two bodies implies contact +between the bodies as well as contact of each body with itself. +Specifying contact inclusions +Define contact inclusions to specify the regions of the model that should be considered for contact +purposes. +Specifying “automatic” contact for the entire model +You can specify self-contact for a default unnamed, all-inclusive surface defined automatically by +Abaqus/Explicit. This default surface contains, with the exceptions noted below, all exterior element +faces, all analytical rigid surfaces and all edges based on beam and truss elements in the model, as well +as the nodes attached to these faces and edges; in addition, feature edges are included according to +the user-specified criteria . This is the simplest way to define the contact domain. With this approach contact is +modeled for all node-to-facet, node-to-analytical rigid surface, and edge-to-edge interactions of the +nodes, facets, analytical rigid surfaces, and contact edges of the default surface. This default surface +does not include the following: +• Nodes that cannot be part of an element-based surface; for example, nodes attached only to point +masses or connectors. +• Faces, edges, and nodes that belong only to cohesive elements. +In fact, this default surface is +generated as if cohesive elements were not present. See “Modeling with cohesive elements,” +Section 32.5.3, for further discussion of contact modeling issues related to cohesive elements. +Input File Usage: +Use both of the following options to specify “automatic” contact for the entire +model: +*CONTACT +*CONTACT INCLUSIONS, ALL EXTERIOR +The *CONTACT INCLUSIONS option should have no data lines when the +ALL EXTERIOR parameter is used. +Abaqus/CAE Usage: +Interaction module: Create Interaction: General contact (Explicit): +Included surface pairs: All* with self +Specifying individual contact interactions +Alternatively, you can define the general contact domain directly by specifying the individual contact +surface pairings. Self-contact will be modeled only if the two surfaces specified in a pair overlap (or are +identical) and will be modeled only in the overlapping region. +Multiple surface pairings can be included in the contact domain. At least one surface in each pair +must be either an element-based surface or an analytical rigid surface. +Input File Usage: +Use both of the following options to specify individual contact interactions: +*CONTACT +*CONTACT INCLUSIONS +surface_1, surface_2 +At least one data line must be speci���ed when the ALL EXTERIOR parameter +is omitted. Either or both of the data line entries can be left blank, but each +data line must contain at least a comma; an error message will be issued for +empty data lines. If the first surface name is omitted, the default unnamed, +all-inclusive, automatically generated surface is assumed. If the second surface +name is omitted or is the same as the first surface name, contact between the first +surface and itself is assumed. Leaving both data line entries blank is equivalent +to using the ALL EXTERIOR parameter. +Interaction module: Create Interaction: General contact (Explicit): +Included surface pairs: Selected surface pairs: Edit, select the +surfaces in the columns on the left, and click the arrows in the middle to +transfer them to the list of included pairs +Abaqus/CAE Usage: +Examples +The following input specifies that contact should be enforced between the default all-inclusive, +automatically generated surface and surface_2, including self-contact in any overlap regions: +*CONTACT +*CONTACT INCLUSIONS +, surface_2 +Either of the following methods can be used to define self-contact for surface_1: +or +*CONTACT +*CONTACT INCLUSIONS +surface_1, +*CONTACT +*CONTACT INCLUSIONS +surface_1, surface_1 +The following input can be used to introduce a node-based surface containing point masses to the contact +domain as well as specify self-contact for the default all-inclusive, automatically generated surface: +*CONTACT +*CONTACT INCLUSIONS +, +, node_based_surf +Specifying contact exclusions +You can refine the contact domain definition by specifying the regions of the model to exclude from +contact. +The primary motivation for specifying contact exclusions is to avoid physically unreasonable +contact interactions. For example, a finite element model may contain multiple forming tools, but not +all of the tools participate in the forming process simultaneously; you can specify contact exclusions to +prevent certain tools from participating in the contact model in certain steps. +You do not need to be concerned with specifying contact exclusions for parts of the model that +are not likely to interact, since these exclusions typically will have minimal effect on computational +performance. +Contact will be ignored for all the surface pairings specified, even if these interactions are specified +directly or indirectly in the contact inclusions definition. +Multiple surface pairings can be excluded from the contact domain. At least one surface in each pair +must be either an element-based surface or an analytical rigid surface. Keep in mind that surfaces can +be defined to span multiple unattached bodies, so self-contact exclusions are not limited to exclusions of +single-body contact. +You cannot exclude only one side of shell-like surfaces. If a side label (SPOS or SNEG) is used in +defining an element-based shell-like surface and that surface is excluded from contact, Abaqus/Explicit +will exclude all faces associated with these elements. +Input File Usage: +Use both of the following options to specify contact exclusions: +*CONTACT +*CONTACT EXCLUSIONS +surface_1, surface_2 +Either or both of the data line entries can be left blank. If the first surface name +is omitted, the default unnamed, all-inclusive, automatically generated surface +is assumed. If the second surface name is omitted or is the same as the first +surface name, contact between the first surface and itself is excluded from the +contact domain. +Interaction module: Create Interaction: General contact (Explicit): +Excluded surface pairs: Edit, select the surfaces in the columns on the left, +and click the arrows in the middle to transfer them to the list of excluded pairs +Abaqus/CAE Usage: +Automatically generated contact exclusions +Abaqus/Explicit automatically generates contact exclusions for general contact in some situations. +• Contact exclusions are generated automatically for interactions that are defined with the contact +pair algorithm or surface-based tie constraints to avoid redundant (and possibly inconsistent) +if a contact pair is defined for +enforcement of these interaction constraints. +surface_1 and surface_2 and “automatic” general contact is defined for the entire model, +Abaqus/Explicit would generate a contact exclusion for general contact between surface_1 and +surface_2, so that interactions between these surfaces would be modeled only with the contact +pair algorithm. These automatically generated contact exclusions are in effect only during the steps +in which the contact pair algorithm or surface-based tie constraint interactions are active. +For example, +• Abaqus/Explicit automatically generates contact exclusions for self-contact of each rigid body in +the model, because it is not possible for a rigid body to contact itself. +• When you specify pure master-slave contact surface weighting for a particular general contact +surface pair, contact exclusions are generated automatically for the master-slave orientation +opposite to that specified . +• The general contact algorithm, unlike the contact pair algorithm, activates and deactivates contact +faces and contact edges in the contact domain based on the failure status of the underlying elements. +See “Modeling surface erosion” below for details. +Examples +The following input specifies that the contact domain is based on self-contact of an all-inclusive, +automatically generated surface but that contact (including self-contact in any overlap regions) should +be ignored between the all-inclusive, automatically generated surface and surface_2: +*CONTACT +*CONTACT INCLUSIONS, ALL EXTERIOR +*CONTACT EXCLUSIONS +, surface_2 +Either of the following methods can be used to exclude self-contact for surface_1 from the contact +domain: +*CONTACT EXCLUSIONS +surface_1, +or +*CONTACT EXCLUSIONS +surface_1, surface_1 +Modeling surface erosion +General contact allows the use of element-based surfaces to model surface erosion for analyses. +If +an appropriate “interior” surface is defined, the surface topology will evolve to match the exterior of +elements that have not failed. Alternatively, if only one of the bodies can erode, a node-based surface can +be used to model surface erosion; this approach can be used with either the general contact or contact pair +algorithms. However, even if only one body can erode, it is recommended to define an element-based +surface for the eroding body to avoid the usual limitations of node-based surfaces . +The general contact algorithm modifies the list of contact faces and contact edges that are active in +the contact domain based on the failure status of the underlying elements (element failure is discussed +in “Dynamic failure models,” Section 23.2.8). General contact considers a face only if its underlying +element has not failed and it is not coincident with a face from an adjacent element that has not failed; +thus, exterior faces are initially active, and interior faces are initially inactive. Once an element fails, its +faces are removed from the contact domain, and any interior faces that have been exposed are activated. +A contact edge is removed when all the elements that contain the edge have failed. New contact edges +are not created as elements erode. Based on this algorithm, the active contact domain evolves during the +analysis as elements fail . +newly exposed +faces +surface topology before +the shaded elements +have failed +surface topology after failure +Figure 35.4.1–2 Topology of an eroding contact surface. +You can control whether contact nodes remain in the contact domain after all the surrounding +elements have failed. By default, these nodes remain in the contact domain and act as free-floating +point masses that can experience contact with faces that are still part of the contact domain. You can +specify that nodes of element-based surfaces should erode (i.e., be removed from the contact domain) +once all contact faces and contact edges to which they are attached have eroded. Further discussion of +this technique, including reasons for and against nodal erosion, can be found in “Contact controls for +general contact in Abaqus/Explicit,” Section 35.4.5. +Erosion of surfaces specified on solid elements +For a solid element mesh consisting of elements that may fail, every face that can potentially be involved +in contact (both exterior and interior faces) should be included in the contact domain. The general contact +algorithm will activate and deactivate faces as necessary when elements fail. +For example, you define an element set ELERODE that contains all the solid elements in the model +that refer to a material failure model. First, you must create a surface SURFERODE containing all of +the interior and exterior faces of these elements. You could define this surface using the automatic +free surface and interior surface generation methods in Abaqus/Explicit. Assuming all the elements +in ELERODE are of type C3D8R, you could alternatively define the surface by specifying the faces +S1 through S6 directly. See “Creating surfaces on solid, continuum shell, and cohesive elements” in +“Element-based surface definition,” Section 2.3.2, for a discussion of these three methods. +Next, you must construct the contact domain. Defining “automatic” general contact for the entire +model is not sufficient because the contact domain created when this method is used does not include any +interior faces. Therefore, you must define the pairwise interactions with the erodable surface explicitly +in the contact inclusions definition, as outlined in Table 35.4.1–1. +Alternatively, you could create a more concise definition of the same contact domain by first defining +a surface named SURFALL that includes all exterior faces in the entire model and all interior faces of +element set ELERODE. In this case, since all faces (exterior and interior) in the contact domain are +Table 35.4.1–1 Contact inclusions definitions. +Contact inclusions +Input file syntax Abaqus/CAE syntax +Self-contact for the default all-inclusive +surface specifies contact between every +exterior face in the model +, +Contact between the default +all-inclusive surface and SURFERODE +specifies contact between every exterior +face and SURFERODE +, SURFERODE +First Surface: (All*) +Second Surface: (Self) +First Surface: (All*) +Second Surface: +SURFERODE +Self-contact for SURFERODE specifies +self-contact between the eroding bodies +SURFERODE, +First Surface: SURFERODE +Second Surface: (Self) +defined in one surface, there is no need to define contact explicitly between the exterior and interior +faces. It would be adequate to specify only self-contact for SURFALL. +Abaqus/Explicit automatically computes a nonzero contact thickness associated with interior faces +based on element dimensions, and this default value cannot be changed via a surface property assignment. +Erosion of surfaces specified on structural elements +For structural elements, the general contact algorithm checks the underlying elements of the faces (or +“contact edges” on beam and truss elements) for failure. Once the underlying element fails, the face is +removed. As with solids, feature edges on structural elements are removed once all of the surrounding +faces have failed. A perimeter edge (e.g., on the perimeter of a shell element mesh) is removed once +the face it is connected to fails. New perimeter edges are not created to conform to the new perimeter +created by the removal of a face. +Memory use +The amount of contact data used to describe the surface topology is proportional to the number of faces +included in the contact domain. Including a large number of interior faces in the contact domain can +potentially increase memory use significantly compared to analyses in which the contact domain is +defined using only exterior faces. Consider creating a surface on a cubic mesh of C3D8R elements with +n elements per side. A surface including the exterior faces of the mesh (suitable for modeling contact +without element failure) would contain 6n2 element faces. A surface including both exterior and interior +faces of the mesh (suitable for modeling contact with element failure for every element in the mesh) +would contain 6n3 element faces. For large meshes the memory use can increase easily by an order of +magnitude when interior element faces are included in the contact domain to model erosion. Therefore, +it is recommended to include only those interior element faces in the contact domain that could possibly +participate in contact. +Output +The surfaces that compose the general contact domain are available as output in addition to the contact +analysis output variables. +General contact domain surfaces +defined: +the following internal +General_Contact_Edges_k, +General_Contact_Faces_k, +surfaces when a general contact domain +Abaqus/Explicit generates +is +and +General_Contact_Nodes_k, where k is the step number. General_Contact_Nodes_k +contains only nodes in the general contact domain that are not included in the other two surfaces. For +example, General_Contact_Faces_2 would contain all surface faces (interior and exterior) that +were initially included in the general contact domain for Step 2. These surfaces contain the contact +faces, edges, and nodes that were included in the contact domain at the beginning of the step and are +not modified to reflect surface erosion. These internal surfaces can be viewed using display groups in +the Visualization module of Abaqus/CAE . The internal surface +names used by Abaqus/Explicit should not appear in the input file. +General contact output variables +You can write the contact surface variables associated with general contact interactions to the Abaqus +output database (.odb) file . The available variables are contact pressure, +normal contact force, frictional force, and whole surface resultant quantities (i.e., force, moment, center +of pressure, and total area in contact). +Field output +The generic variables CSTRESS and CFORCE are valid field output requests for general contact in +Abaqus/Explicit. If CSTRESS is requested for the general contact domain, the variable CPRESS (contact +pressure) can be contoured in Abaqus/CAE. If CFORCE is requested for the general contact domain, +the variables CNORMF (normal contact force) and CSHEARF (shear contact force) can be plotted as +vectors in a symbol plot in Abaqus/CAE. +For general contact CPRESS is calculated as the magnitude of the net contact normal force (the +CNORMF vector) per unit area (it is an unsigned value). This convention for reporting contact pressure +is different from the convention used for contact pairs. The direction of action of the net contact pressure +for general contact can be determined by examining a plot of CNORMF. +CNORMF and CSHEARF are resultant force quantities. If a double-sided surface is contacted on +both sides, the resultant force is a vector sum of the force from each side of the surface (for example, +the contact normal force will be zero for a double-sided surface that is pinched with equal and opposite +forces on each side of the surface). +History output +Several whole surface contact force-derived variables are available as history output. You can specify +the surface from which the contact force resultants will be calculated. +Force distributions on the surface due to general contact are used to calculate the surface force +resultants; forces due to contact pair interactions are not included and must be output separately. The +contact state of a surface is output as a set of force (CFN, CFS, and CFT) and moment (CMN, CMS, +and CMT) resultants with respect to the origin. Additional variables give the center of force (XN, XS, +and XT) on the surface (defined as the point closest to the centroid of the surface that lies on the line of +action of the resultant force for which the resultant moment is minimal). The last letter of each variable +name denotes which contact force distribution on the surface is used to calculate the resultant: the letter +N denotes that the normal contact forces are used to derive the resultant quantity; the letter S denotes that +the shear contact forces are used to derive the resultant quantity; and the letter T denotes that the sum of +the normal and shear contact forces are used to derive the resultant quantity. +Each total moment output variable will not necessarily equal the cross product of the respective +center of force vector and resultant force vector. Forces acting on two different nodes of a surface may +have components acting in opposite directions, such that these nodal force components generate a net +moment but not a net force; therefore, the total moment may not arise entirely from the resultant force. +The center of force output variables tend to be most meaningful when the surface nodal forces act in +approximately the same direction. +The total area in contact at a given time can be requested using output variable CAREA, defined as +the sum of all the facets where there is contact force. The contact area reported by CAREA is generally +slightly larger than the true contact area for reasonably meshed contact surfaces; therefore, interpretation +of CAREA should be done with care. The discrepancy between the CAREA output and the true contact +area decreases as the mesh density increases. Using contact inclusions or exclusions to limit CAREA +output to smaller contact surfaces may also reduce the discrepancy in some cases. Since the CAREA +output is an approximation of the true contact area, deriving force or stress values using this output may +not yield accurate values; requesting contact force and stress directly is the most appropriate way to +obtain accurate results. +Requesting element output when modeling surface erosion +When modeling the erosion of surfaces, it is useful to request additional element field output of the +element status (output variable STATUS). Failed elements (with an element status of zero) can then be +excluded from the display group in the Visualization module of Abaqus/CAE so that the active contact +surface can be identified and contact results on the active contact surface can be viewed. +35.4.2 +ASSIGNING SURFACE PROPERTIES FOR GENERAL CONTACT IN Abaqus/Explicit +Products: Abaqus/Explicit Abaqus/CAE +References +• “Defining general contact interactions in Abaqus/Explicit,” Section 35.4.1 +• *CONTACT +• *SURFACE PROPERTY ASSIGNMENT +• “Specifying surface property assignments for general contact,” Section 15.13.5 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +Surface property assignments: +• can be used to change the contact thickness used for regions of a surface based on structural elements +or to add a contact thickness for regions of a surface based on solid elements; +• can be used to specify surface offsets for regions of a surface based on shell, membrane, rigid, and +surface elements; +• can be used to specify which edges of a model should be included in the general contact domain; +• can be used to specify geometric corrections for regions of a surface; +• can be applied selectively to particular regions within a general contact domain; and +• cannot be applied to analytical rigid surfaces. +Assigning surface properties +You can assign nondefault surface properties to surfaces involved in general contact interactions. These +properties are considered only when the surfaces are involved in general contact interactions; they are +not considered when the surfaces are involved in other interactions such as contact pairs. The general +contact algorithm does not consider surface properties specified as part of the surface definition. +Surface property assignments propagate through all analysis steps in which the general contact +interaction is active. +The surface names used to specify the regions with nondefault surface properties do not have to +correspond to the surface names used to specify the general contact domain. In many cases the contact +interaction will be defined for a large domain, while nondefault surface properties will be assigned to a +subset of this domain. Any surface property assignments for regions that fall outside the general contact +domain will be ignored. The last assignment will take precedence if the specified regions overlap. +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY +This option must be used in conjunction with the *CONTACT option. It should +appear at most once per step for each value of the PROPERTY parameter +discussed below; the data line can be repeated as often as necessary to assign +surface properties to different regions. +Abaqus/CAE Usage: +Interaction module: Create Interaction: General contact +(Explicit): Surface Properties +Surface thickness +The default calculation of the nodal surface thickness (described in detail below) is appropriate for most +analyses; one exception is sheet forming analysis, in which the thinning of a sheet significantly influences +contact. This case can be modeled by specifying that the decreasing parent element thickness should be +used. As a third alternative, you can specify a value for the surface thickness. A nonzero thickness can be +assigned to solid element surfaces, for example, to model the effect of a finite-thickness surface coating. +“Element-based surface definition,” Section 2.3.2, contains information on the spatial variation of the +surface thickness. +Specifying the original or decreasing thickness results in a zero thickness for node-based surfaces; +you can specify a nonzero thickness for a node-based surface used with the general contact algorithm +(the contact pair algorithm will not consider a nonzero thickness for such surfaces). +The general contact algorithm requires that the contact thickness does not exceed a certain fraction +of the surface facet edge lengths or diagonal lengths. This fraction generally varies from 20% to 60% +based on the geometry of the element. The general contact algorithm will scale back the contact thickness +automatically where necessary without affecting the thickness used in the element computations for the +underlying elements. Diagnostic information is provided in the status (.sta) file if such scaling is +performed. +To bypass this limitation on thickness, the contact surface can be modeled with surface elements +. The surface elements must be attached to the underlying +elements using a surface-based tie constraint , and a physically +reasonable mass must be associated with the surface elements. This requires a significant fraction of the +mass to be transferred to the surface elements from the underlying elements without appreciably altering +the bulk mass properties. Alternatively, contact controls settings can be used to limit the thickness +reduction checks . +The “bull-nose” effect that occurs at shell perimeters with the contact pair algorithm is avoided with the general +contact algorithm by default. Shell element edges, nodes, and facets reflect the shell thickness in the +normal direction only and do not extend past the perimeter. Contact controls settings can be used to +turn off the bull-nose prevention checks . +Using the original parent element thickness +By default, the nodal thickness for surfaces based on shell, membrane, or rigid elements equals the +minimum original thickness of the surrounding elements . +specified element thickness +(constant over element) +interpolated surface +thickness +nodal surface thickness +Figure 35.4.2–1 Continuous variation of surface thickness across facet boundaries. +Table 35.4.2–1 Thicknesses corresponding to Figure 35.4.2–1. +Node +Element +Specified element +thickness +Nodal surface +thickness (minimum +of adjacent element +thicknesses) +0.5 +0.5 +0.9 +0.9 +0.5 +0.5 +0.5 +0.9 +0.9 +The surface thickness within a facet is interpolated from the nodal values; the interpolated surface +thickness never extends past the specified element or nodal thickness, which may be significant with +respect to initial overclosures. The default nodal surface thickness is zero for regions of a surface based +on solid elements. If a spatially varying nodal thickness is defined for the underlying elements , the nodal surface thickness may not correspond exactly to the +specified nodal thickness . +element thickness +(constant over element) +nodal surface +thickness +specified +nodal thickness +interpolated surface +thickness +Figure 35.4.2–2 Small discrepancy between the nodal surface thickness and the specified nodal thickness. +Table 35.4.2–2 Thicknesses corresponding to Figure 35.4.2–2. +Node +Element +Specified +nodal +thickness +Element +thickness +(average of +specified nodal +thickness) +Nodal surface +thickness +(minimum of +adjacent element +thicknesses) +0.5 +0.5 +0.5 +0.9 +0.9 +0.9 +0.5 +0.5 +0.7 +0.9 +0.9 +35.4.2–4 +0.5 +0.5 +0.5 +0.7 +0.9 +The nodal surface thickness distribution will tend to be more diffuse than the specified nodal thickness +distribution (because the specified nodal thicknesses are averaged to compute the element thicknesses, +and the minimum of the surrounding element thicknesses is the nodal surface thickness). +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=THICKNESS +surface, ORIGINAL (default) +Abaqus/CAE Usage: +If the surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +Interaction module: Create Interaction: General contact (Explicit): +Surface Properties: Shell/Membrane thickness assignments: Edit: +Select surface, click the arrows to transfer surface to list of thickness +assignments, and enter ORIGINAL in the Thickness column. +Using the decreasing parent element thickness +If you specify that the decreasing parent element thickness should be used, only decreases in the parent +element thickness are reflected in the contact surface thickness; if the parent element thickness actually +increases during the analysis, the contact thickness will remain constant. +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=THICKNESS +surface, THINNING +Abaqus/CAE Usage: +If the surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +Interaction module: Create Interaction: General contact (Explicit): +Surface Properties: Shell/Membrane thickness assignments: Edit: +Select surface, click the arrows to transfer surface to list of thickness +assignments, and enter THINNING in the Thickness column. +Specifying a value for the surface thickness +You can directly specify the surface thickness value. +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=THICKNESS +surface, value +Abaqus/CAE Usage: +If the surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +Interaction module: Create Interaction: General contact (Explicit): +Surface Properties: Shell/Membrane thickness assignments: Edit: +Select surface, click the arrows to transfer surface to list of thickness +assignments, and enter a value for the surface thickness magnitude +in the Thickness column. +Applying a scale factor to the surface thickness +You can apply a scale factor to any value of the surface thickness. For example, if you specify that the +decreasing parent element thickness should be used for surf1 and apply a scale factor of 0.5, a value +of one half the decreasing parent element thickness will be used for surf1 when it is involved in a +general contact interaction (all other surfaces included in the general contact domain will use the default +original parent element thickness). Scaling the surface thickness in this way can be used to avoid initial +overclosures in some situations. Abaqus/Explicit will automatically adjust surface positions to resolve +initial overclosures . However, if nodal position adjustments are undesirable (for example, if they would +introduce an imperfection in an otherwise flat part, resulting in an unrealistic buckling mode), you may +prefer to reduce the surface thickness and avoid the overclosures entirely. +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=THICKNESS +surface, value or label, scale_factor +If the surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +Interaction module: Create Interaction: General contact (Explicit): +Surface Properties: Shell/Membrane thickness assignments: Edit: +Select surface, click the arrows to transfer surface to list of thickness +assignments, and enter a Scale Factor. +Abaqus/CAE Usage: +Surface offset +A surface offset is the distance between the midplane of a thin body and its reference plane (defined by the +nodal coordinates and element connectivities). It is computed by multiplying the offset fraction (specified +as a fraction of the surface thickness) by the surface thickness and the element facet normal. This defines +the position of the midsurface and, thus, the position of the body with respect to the reference surface; +the coordinates of the nodes on the reference surface are not modified. Surface offsets can be specified +only for surfaces defined on shell and similar elements (i.e., membrane, rigid, and surface elements). +Surface offsets specified for other elements (e.g., solid or beam elements) will be ignored. By default, +surface offsets specified in element section definitions will be used in the general contact algorithm. +The surface offset at each node is the average of the maximum and minimum offsets among the +faces connected to the node. The offset at a point within a facet is interpolated from the nodal values. +At complex intersections (edges connected to more than two faces) the surface offset is set to zero. +Figure 35.4.2–3 shows some examples of the positioning of the contact surface with respect to the +reference surface for various combinations of surface offsets. Surface offsets used in the general contact +algorithm are constrained to lie between −0.5 and 0.5 of the thickness. +You specify the surface offset as a fraction of the surface thickness. The surface offset fraction can +be set equal to the offset fraction used for the surface’s parent elements or to a specified value. Surface +offsets specified for general contact do not change the element integration. +midsurface = reference surface +thickness +offset fraction = 0.0 at the +horizontal and tilted surfaces +reference +surface +midsurface +reference +surface +midsurface +element normals +offset fraction = 0.5 at the +horizontal and tilted surfaces +offset fraction = 0.5 at the horizontal surface +offset fraction = 0.0 at the tilted surface +(assumed that linear elements are used) +Figure 35.4.2–3 Specifying surface offsets for general contact. +Input File Usage: +Use the following option to use the surface offset fraction from the surface’s +parent elements (default): +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=OFFSET +FRACTION +surface, ORIGINAL +Use the following option to specify a value for the surface offset fraction: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=OFFSET +FRACTION +surface, offset +The offset can be specified as a value or a label (SPOS or SNEG). Specifying +SPOS is equivalent to specifying a value of 0.5; specifying SNEG is equivalent +to specifying a value of −0.5. +Abaqus/CAE Usage: +Interaction module: Create Interaction: General contact (Explicit): +Surface Properties: Shell/Membrane offset assignments: Edit: +Select surface, and click the arrows to transfer surface to list of offset +assignments. +In the Offset Fraction column, enter ORIGINAL to use the surface +offset fraction from the surface's parent elements, enter SPOS to use a +surface offset fraction of 0.5, enter SNEG to use a surface offset fraction +of −0.5, or enter a value for the surface offset fraction. +Feature edges +Feature edges of a model are defined on beam and truss elements and edges of faces (perimeter and +otherwise) of solid and structural elements. By default, edge-to-edge contact in the general contact +algorithm in Abaqus/Explicit accounts for perimeter edges as well as “contact edges” of beam and truss +elements. +You can control which feature edges should be activated in the general contact domain by specifying +feature edge criteria. By default, only perimeter edges are activated. Feature edge criteria have no effect +on “edges” of beam and truss elements—they are activated by their inclusion in the contact domain. +The feature angle +The feature angle is the angle formed between the normals of the two facets connected to an edge. The +angles between facets are based on the initial configuration. A negative angle will result at concave +meetings of facets; therefore, these edges are never included in the contact domain. Figure 35.4.2–4 +shows some examples of how the feature angle is calculated for different edges. +(+) +n2 +n1 +n2 +n2 +n3 +( )_ +25o +n3 +n1 +( )_ +n5 +n4 +n5 +n4 +n7 +D (perimeter edge) +n5 +(+) +180 +n7 +n6 +0o +n II n +Figure 35.4.2–4 Calculating the feature angle. +The feature angle for edge A is 90° (the angle between +(the angle between +in Figure 35.4.2–5); its feature angles are 0°, −90°, and −90°. +); the feature angle for edge B is −25° +). Edge C forms a T-intersection with three facets (shown in two dimensions +and +and +_ +90o +_ +90o +arrows are perpendicular +to surface facets +Figure 35.4.2–5 Feature angles for a T-intersection (for example, edge C in Figure 35.4.2–4). +Perimeter edges (for example, edge D in Figure 35.4.2–4) can be thought of as a special type of feature +edge where the feature angle is 180°. +The sign of the feature angle is considered when determining whether or not a geometric feature +edge should be activated in the general contact domain. For example, if a cutoff feature angle of 20° +were specified, edge A would be activated as a feature edge in the contact model (90° > 20°) but edges B +and C would not be activated: −25° < 20° and 0° (the maximum feature angle for edge C) < 20°. +Figure 35.4.2–6 illustrates further how the feature angle is used to determine which geometric +feature edges should be activated in the general contact domain. +Thin solid lines +indicate feature edges. +Thick solid lines indicate +shell perimeter edges. +Edge +Largest feature +angle at edge +Other feature +angles at edge +Shells +Solid +Dashed lines indicate element +boundaries for which edge-to-edge +contact is not modeled. +approximately +105 +o +approximately 30 +_ +o +o +0 ++180 +o +o ++90 +o +0 +none +none +_ + 90 +o +none +_ +o +90 +_ _ +o o +90 , 90 +Figure 35.4.2–6 Feature edges activated in the general contact +domain for a cutoff feature angle of 20°. +The table to the right of the figure lists the feature angle values for various edges in the model. Edges +connected to more than two facets, as well as edges connected to two shell facets, have more than one +corresponding feature angle. The largest feature angle at an edge is compared to the specified cutoff +feature angle. For example, if a cutoff feature angle of 20° were specified, edges A, D, and E would be +considered feature edges, while edges B, C, and F would be ignored for edge-to-edge contact. +Specifying that only perimeter edges should be activated +By default, only perimeter edges are included in the general contact domain. Perimeter edges occur on +“physical” perimeters of shell elements and on “artificial” edges that occur when a subset of exposed +facets on a body are included in the general contact domain. When structural elements share nodes with +continuum elements, the perimeter edges will not be activated on the structural elements because the +criterion to designate them as such is no longer satisfied. +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=FEATURE +EDGE CRITERIA +surface, PERIMETER EDGES (default) +Abaqus/CAE Usage: +If the surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +Interaction module: Create Interaction: General contact (Explicit): +Surface Properties: Feature edge criteria assignments: Edit: +Select surface, click the arrows to transfer surface to list of feature +assignments, and enter PERIMETER in the Feature Edge Criteria column. +Specifying particular feature edges to be activated +You can choose particular feature edges on surface, structural, and rigid elements to be activated in +domain. A surface containing a list of element labels and edge identifiers is used to specify the edges to activate. +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=FEATURE +EDGE CRITERIA +surface, PICKED EDGES +Abaqus/CAE Usage: +Interaction module: Create Interaction: General contact (Explicit): +Surface Properties: Feature edge criteria assignments: Edit: +Select the surface, click the arrows to transfer the surface to the list of feature +assignments, and enter PICKED in the Feature Edge Criteria column. +Specifying that all feature edges should be activated +You can choose to activate all edges in a given surface in the general contact domain. This will activate +all edges of every face specified in the given surface. +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=FEATURE +EDGE CRITERIA +surface, ALL EDGES +Abaqus/CAE Usage: +Interaction module: Create Interaction: General contact (Explicit): +Surface Properties: Feature edge criteria assignments: Edit: +Select the surface, click the arrows to transfer the surface to the list of feature +assignments, and enter ALL in the Feature Edge Criteria column. +Specifying that all feature edges should be deactivated +You can choose to deactivate all feature edges (including perimeter edges) in the general contact domain. +This option does not deactivate “contact edges” associated with beam and truss elements. +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=FEATURE +EDGE CRITERIA +surface, NO FEATURE EDGES +Abaqus/CAE Usage: +If the surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +Interaction module: Create Interaction: General contact (Explicit): +Surface Properties: Feature edge criteria assignments: Edit: +Select the surface, click the arrows to transfer the surface to the list of feature +assignments, and enter NONE in the Feature Edge Criteria column. +Specifying a cutoff feature angle +If you specify a cutoff feature angle as the feature edge criteria, perimeter edges and geometric edges with +feature angles greater than or equal to the specified angle are activated in the general contact domain. As +described previously, you can activate additional feature edges if needed. +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=FEATURE +EDGE CRITERIA +surface, feature_angle_value +Abaqus/CAE Usage: +If the surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +Interaction module: Create Interaction: General contact (Explicit): +Surface Properties: Feature edge criteria assignments: Edit: +Select surface, click the arrows to transfer surface to list of feature +assignments, and enter a value for the cutoff feature angle (in degrees) +in the Feature Edge Criteria column. +Example: assigning different feature edge criteria to different regions +You can assign a different feature edge criteria to different regions of the general contact domain. For +example, the input shown in the following table could be used to specify that none of the feature edges +of surf1, only perimeter edges of surf2, and perimeter edges and feature edges of surf3 with a +feature angle greater than 30° should be considered for edge-to-edge contact: +Input File Syntax +Abaqus/CAE Syntax +surf1, NO FEATURE +EDGES +Surface: surf1, Feature Edge Criteria: NONE +surf2, PERIMETER EDGES +Surface: surf2, Feature Edge Criteria: PERIMETER +surf3, 30 +Surface: surf3, Feature Edge Criteria: 30 +Primary and secondary feature edges +To cut down on the computational cost in certain situations, it may be desirable to identify a limited +number of feature edges on a surface (presumably at locations where there are sharp gradients in the +surface normals) as “primary” feature edges. A more relaxed criterion can be used to denote certain other +edges on the surface as “secondary” feature edges. If secondary feature edges are specified in addition to +primary feature edges, Abaqus/Explicit enforces edge-to-edge contact between primary feature edges and +between primary feature edges and secondary feature edges only. Edge-to-edge contact is not enforced +between secondary feature edges. This ensures that interpenetrations are avoided at locations where there +are “true” edges in the model, without the need to activate primary feature edges at locations where the +gradients in the surface normals are only moderate. A judicious choice of criteria for selecting primary +and secondary feature edges can lead to significant savings in computational costs. +Secondary feature edges can be selected for a surface by specifying a secondary feature edge +criterion in addition to the criterion used to select the primary feature edges for that surface. +If the +secondary feature edge criterion is omitted, only primary feature edges are activated for the surface. +Allowable criteria for secondary feature edges are: +• all edges that have not been selected as primary feature edges; +• all picked edges that have not been selected as primary feature edges; +• all perimeter edges that have not been selected as primary feature edges; and +• all edges with a feature angle greater than a specified cutoff angle value that have not been selected +as primary feature edges. +The allowable values for the secondary feature edge criterion permit possible combinations of +criteria for primary feature edges and secondary feature edges, shown in Table 35.4.2–3. +Table 35.4.2–3 Valid combinations of primary feature edge +and secondary feature edge criteria. +Primary Feature Edge Criterion +Secondary Feature Edge Criterion +No feature edges +All edges +All remaining edges, picked edges, +perimeter edges, cutoff angle +Any criterion specified for secondary +feature edges will be ignored +Primary Feature Edge Criterion +Secondary Feature Edge Criterion +Picked edges +Perimeter edges +Cutoff angle +All remaining edges, perimeter edges, +cutoff angle +All remaining edges, picked edges, cutoff +angle +All remaining edges, picked edges, +perimeter edges, cutoff angle +Specifying all remaining edges as secondary feature edges +You can specify that all edges belonging to the surface that have not been selected as primary feature +edges become secondary feature edges. +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=FEATURE +EDGE CRITERIA +surface, primary feature edge criterion, ALL REMAINING EDGES +If the surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +Abaqus/CAE Usage: +Secondary feature edges are not supported in Abaqus/CAE. +Specifying picked edges as secondary feature edges +You can specify that all picked edges of the surface that have not already been selected as primary feature +edges become secondary feature edges. +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=FEATURE +EDGE CRITERIA +surface, primary feature edge criterion, PICKED EDGES +If the surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +Abaqus/CAE Usage: +Secondary feature edges are not supported in Abaqus/CAE. +Specifying perimeter edges as secondary feature edges +You can specify that all perimeter edges of the surface that have not already been selected as primary +feature edges become secondary feature edges. +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=FEATURE +EDGE CRITERIA +surface, primary feature edge criterion, PERIMETER EDGES +If the surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +Abaqus/CAE Usage: +Secondary feature edges are not supported in Abaqus/CAE. +Specifying a cutoff feature angle for secondary feature edges +You can specify that edges on the surface with a feature angle greater than the specified value that have +not been selected as primary feature edges become secondary feature edges. If an angle value has also +been specified for primary feature edges, the angle value specified for secondary feature edges must be +smaller than the value specified for primary edges. +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=FEATURE +EDGE CRITERIA +surface, primary feature edge criterion, feature_angle_value +If the surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +Abaqus/CAE Usage: +Secondary feature edges are not supported in Abaqus/CAE. +Specifying that edges are activated only as secondary feature edges +For a particular surface you may not want to activate any primary feature edges; instead, you might want +to activate all or some edges on the surface as secondary feature edges (to enforce contact between these +secondary feature edges and primary feature edges on another surface in the model). In that case you can +specify that no feature edges should be activated as the primary feature edge criterion for the surface, +while using any criterion of choice for the secondary feature edges. +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=FEATURE +EDGE CRITERIA +surface, NO FEATURE EDGES, secondary feature edge criterion +If the surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +Abaqus/CAE Usage: +Secondary feature edges are not supported in Abaqus/CAE. +Surface geometry correction +By default, contact calculations are based on unsmoothed, faceted representations of the finite element +surfaces in a general contact domain. Discrepancies between the true surface geometry and the faceted +surface geometry may result in significant noise in the solution. Optional contact smoothing techniques +simulate a more realistic representation of curved surfaces in the contact calculations. These techniques +allow a discretized surface with discontinuous surface normals to more closely approximate the behavior +of a smooth surface during an analysis. Improvements to results with the surface correction include more +accurate contact stresses and less solution noise upon relative sliding between contact surfaces. +Contact smoothing can be specified for surfaces in a general contact domain using a surface property +assignment. A single surface property assignment specifies all of the surfaces to be smoothed, as well as +the appropriate geometry correction method for each surface. Three geometry correction methods can +be employed: +• The circumferential smoothing method is applicable to surfaces approximating a portion of a surface +of revolution. +• The spherical smoothing method is applicable to surfaces approximating a portion of a sphere. +• The toroidal smoothing method is applicable to surfaces approximating a portion of a torus (i.e., a +circular arc revolved about an axis). +For each surface, you must specify the appropriate geometry correction method and either the +approximate axis of revolution (for circumferential or toroidal smoothing) or the approximate spherical +center (for spherical smoothing). For toroidal smoothing, you must also specify the distance of the center +of the circular arc from the axis of revolution, and the line joining point (Xa , Ya , Za ) and the center of +the circular arc should be perpendicular to the axis of revolution. +Input File Usage: +Use the following option to apply a geometric correction: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=GEOMETRIC +CORRECTION +data lines to define smoothing regions +Use the following data line to apply circumferential smoothing to a +surface with an axis of symmetry passing through points (Xa , Ya , Za ) +and (Xb , Yb, Zb ): +surface, CIRCUMFERENTIAL, Xa , Ya, Za , Xb , Yb , Zb +Use the following data line to apply spherical smoothing to a +surface with a spherical center at point (Xa , Ya , Za ): +surface, SPHERICAL, Xa, Ya , Za +Use the following data line to apply toroidal smoothing to a +surface with an axis of symmetry passing through points (Xa , Ya , Za ) +and (Xb , Yb, Zb ) with the center of the revolved circular arc +at a distance R from the axis of symmetry: +surface, TOROIDAL, Xa , Ya, Za , Xb , Yb , Zb, R +Repeat the data lines as many times as necessary to define the appropriate +geometry corrections for all surfaces in the contact domain. +Contact surface smoothing can be applied only to native geometry models in +Abaqus/CAE. Abaqus/CAE can automatically detect all circumferential and +spherical surfaces in the general contact domain that can be smoothed and apply +the appropriate smoothing. +Use the following option to enable automatic surface smoothing of a model: +Interaction module: Create Interaction: General contact (Explicit): +Surface Properties: Surface smoothing assignments: Edit: +toggle on Automatically assign smoothing for geometric faces +35.4.2–15 +Use the following option to manually apply smoothing to a surface: +Interaction module: Create Interaction: General contact (Explicit): +Surface Properties: Surface smoothing assignments: Edit: +Select the surface, click the arrows to transfer the surface to the list of smoothing +assignments. +In the Smoothing Option column, select REVOLUTION to apply +circumferential smoothing, select SPHERICAL to apply spherical smoothing, +or select NONE to prevent smoothing of the surface. +Toroidal surface smoothing cannot be defined in Abaqus/CAE. +Considerations for geometric correction +The contact smoothing technique assumes that the initial locations of the surface nodes lie on the true +initial surface geometry, with the exception of midedge nodes of C3D10M elements. This smoothing +technique remains effective even if the midedge nodes of C3D10M elements do not lie on the true initial +geometry (models meshed using Abaqus/CAE always have midedge nodes placed on the true initial +geometry, but this may not be the case with other meshing preprocessors). +The effects of contact smoothing tend to be most significant for analyses involving small +deformation, and the smoothing technique works well for cases involving large relative motion between +the surfaces. For analyses with large deformation this smoothing technique typically has an insignificant +effect on the solution. However, in some cases—especially where the underlying elements can fail—the +smoothing can degrade the solution accuracy after large deformation. +Effects of geometric correction +The impact of contact surface smoothing can be demonstrated by a simple model of contact between +concentric cylinders with a small clearance between them. With a matched mesh as shown in +Figure 35.4.2–7 there are no initial overclosures; +there are no initial strain-free initial +displacement adjustments. However, if the inner cylinder is rotated, the cylinders develop stresses as contact is detected due to the linear faceted representation of the master surface. +This behavior is improved when the circumferential smoothing technique is applied to the contacting +surfaces of the two cylinders. +therefore, +Figure 35.4.2–7 Concentric cylinders with matched mesh. +S, Mises +(Avg: 75%) ++8.165e+02 ++7.487e+02 ++6.809e+02 ++6.131e+02 ++5.453e+02 ++4.775e+02 ++4.097e+02 ++3.419e+02 ++2.741e+02 ++2.063e+02 ++1.385e+02 ++7.071e+01 ++2.905e+00 +Figure 35.4.2–8 Stesses as cylinder rotates. +35.4.3 +ASSIGNING CONTACT PROPERTIES FOR GENERAL CONTACT IN Abaqus/Explicit +Products: Abaqus/Explicit Abaqus/CAE +References +• “Defining general contact interactions in Abaqus/Explicit,” Section 35.4.1 +• “Mechanical contact properties: overview,” Section 36.1.1 +• “Contact pressure-overclosure relationships,” Section 36.1.2 +• “Contact damping,” Section 36.1.3 +• “Frictional behavior,” Section 36.1.5 +• *CONTACT +• *CONTACT PROPERTY ASSIGNMENT +• *SURFACE INTERACTION +• “Specifying and modifying contact property assignments for general contact,” Section 15.13.2 of +the Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +Contact properties: +• define the mechanical surface interaction models that govern the behavior of surfaces when they +are in contact; and +• can be applied selectively to particular regions within a general contact domain. +Assigning contact properties +The default contact property model in Abaqus/Explicit assumes “hard” contact in the normal direction, +no friction, no thermal interactions, etc. You can assign a nondefault contact property definition (surface +interaction) to specified regions of the general contact domain. +Contact property assignments propagate through all analysis steps in which the general contact +interaction is active. +The surface names used to specify the regions where nondefault contact properties should be +assigned do not have to correspond to the surface names used to specify the general contact domain. +In many cases the contact interaction will be defined for a large domain, while nondefault contact +properties will be assigned to a subset of this domain. Any contact property assignments for regions +that fall outside of the general contact domain will be ignored. The last assignment will take precedence +if the specified regions overlap. +Input File Usage: +*CONTACT PROPERTY ASSIGNMENT +surface_1, surface_2, interaction_property_name +This option must be used in conjunction with the *CONTACT option. It should +appear at most once per step; the data line can be repeated as often as necessary +to assign contact properties to different regions. +If the first surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. If the second surface name is omitted or +is the same as the first surface name, contact between the first surface and +itself is assumed. Keep in mind that surfaces can be defined to span multiple +unattached bodies, so self-contact is not limited to contact of a single body with +itself. If the interaction property name is omitted, the unnamed set of default +contact properties in Abaqus/Explicit is assumed. If an interaction property +name is specified, it must also appear as the value of the NAME parameter on +a *SURFACE INTERACTION option in the model portion of the input file. +Interaction module: Create Interaction: General contact (Explicit): +Contact Properties: +Individual property assignments: Edit: select the surfaces and the contact +property in the columns on the left, and click the arrows in the middle to transfer +them to the list of contact property assignments +or +Global property assignment: interaction_property_name +In Abaqus/CAE you must assign a contact property definition to every general +contact interaction; Abaqus/CAE does not assume a default contact interaction +property. +Abaqus/CAE Usage: +Example +The following contact property assignments are specified below for the first step in a general contact +analysis: +• a global assignment of contProp1 to the entire general contact domain; +• a local assignment of contProp2 to self-contact for surf1; +• a local assignment of the default Abaqus contact property to contact between surf2 and surf3; +and +• a local assignment of contProp3 to contact between the entire contact domain and surf4. +*SURFACE INTERACTION, NAME=contProp1 +*FRICTION +0.1 +*SURFACE INTERACTION, NAME=contProp2 +*FRICTION +0.15 +*SURFACE INTERACTION, NAME=contProp3 +*FRICTION +0.20 +*STEP +Step1 +*DYNAMIC, EXPLICIT +… +*CONTACT +*CONTACT INCLUSIONS, ALL EXTERIOR +*CONTACT PROPERTY ASSIGNMENT +, , contProp1 +surf1, surf1, contProp2 +surf2, surf3, +, surf4, contProp3 +Changing contact properties +Contact property models for general contact interactions are independent of the steps in which they are +used and cannot be modified from step to step. To change the contact properties used in a given step, +you must specify a new contact property assignment that refers to a different contact property model. +Example +For example, the following input could be used to change the friction coefficient used for contact between +the entire general contact domain and surf4 in the second step of the analysis started in the previous +example: +*STEP +Step2 +*DYNAMIC, EXPLICIT +… +*CONTACT +*CONTACT PROPERTY ASSIGNMENT +, surf4, contProp2 +35.4.4 +CONTROLLING INITIAL CONTACT STATUS FOR GENERAL CONTACT IN +Abaqus/Explicit +Products: Abaqus/Explicit Abaqus/CAE +References +• “Defining general contact interactions in Abaqus/Explicit,” Section 35.4.1 +• *CONTACT +• *CONTACT CLEARANCE +• *CONTACT CLEARANCE ASSIGNMENT +• “Producing a deformed shape plot,” Section 43.5 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +Initial clearances for surface interactions included in the general contact domain: +• are set to zero automatically for small initial overclosures (e.g., for small penetrations caused by +numerical roundoff when a graphical preprocessor such as Abaqus/CAE is used); +• can be specified to resolve large initial overclosures that are not resolved automatically; +• can be specified to separate entangled double-sided surfaces; +• can be specified to model an initial gap between surfaces; +• are enforced without creating any strains or momentum in the model; +• should not be specified to correct gross errors in the mesh design; and +• can be used to identify an initially bonded node set in crack propagation analyses. +Default adjustments for initial overclosures in the first step of the simulation +Abaqus/Explicit automatically adjusts the positions of surfaces to remove small initial overclosures that +exist in the general contact domain in the first step of a simulation. The adjustments are made with +strain-free initial displacements. This automatic adjustment of surface position is intended to correct +only minor mismatches associated with mesh generation and is done even when the interaction is defined +through user subroutine VUINTERACTION. +Conflicting adjustments from separate contacts, boundary conditions, tie constraints, coupling +constraints, and rigid body constraints can cause incomplete resolution of initial overclosures. This can +occur, for example, when a slave node is pinched between two master facets. Initial overclosures that +are not resolved by repositioning nodes are stored as temporary contact offsets to avoid large contact +forces at the beginning of an analysis. The penalty contact force is computed as +; +where k is the penalty stiffness, +is the current +penetration distance. If +is the initial unresolved penetration distance, and +ever decreases below , +is reset to +. +Because of the lack of a unique outward direction from double-sided facets, the resolution of large +initial penetrations for double-sided surfaces can be difficult. Initial penetration will be detected only +when a slave node lies within the thickness of the underlying element, and the initial penetration will be +resolved by moving the slave node to the nearest free surface as shown in Figure 35.4.4–1. +corrected position +of slave node +original position +of slave node +master surface thickness +master node +Figure 35.4.4–1 Correction of initial overclosure for contact +involving two double-sided surfaces. +Slave nodes that are trapped on opposite sides of a double-sided master surface will often lead to +serious problems, which may not become apparent until later in the analysis. Surfaces that are initially +crossed often indicate a modeling problem for single-sided surfaces as well, because the initial search for +slave nodes in the interior of solids is limited to a distance of about 15% of the facet dimensions; slave +nodes more deeply penetrated than this are ignored by the algorithm to adjust initial overclosures. +Initial overclosure information—including node adjustment data, contact offsets, crossed surfaces, +nodes that could not be corrected, and any warnings—is written to the status (.sta) file, the message +(.msg) file, and the output database (.odb) file. The default tolerance used to report gross initial +penetrations, which could indicate an error with your model definition, depends on the contact type. +Node-to-surface contact uses the characteristic length of the contact facet, edge-to-edge contact uses +the length of the tracked edge, and the typical element dimension is used for node-to-analytical rigid +surface contact. For more information on the overclosure warnings, see “Contact diagnostics in +an Abaqus/Explicit analysis,” Section 38.2.1, and Chapter 41, “Viewing diagnostic output,” of the +Abaqus/CAE User’s Manual. +Default adjustments of overclosed surfaces during subsequent steps in the simulation +Initial penetrations are stored as temporary contact offsets that do not generate contact forces in the +following cases: +• If the general contact domain is created in steps other than the first step (i.e., the contact definition +follows a step in which no contact was defined) or +• if an Abaqus/Standard analysis is imported into Abaqus/Explicit and the contact interaction is not +defined with user subroutine VUINTERACTION. +However, deep penetrations may not be treated correctly; they may be ignored or, in the case of +penetrations past the midsurface of shells, the wrong contact directions may be used. Initial overclosure +and crossed surface diagnostics can be requested to diagnose these problems . +If the general contact domain is extended after the first step, Abaqus/Explicit does not take any +special actions to gradually resolve initial penetrations for the newly introduced interactions: penalty +contact forces will be applied proportional to the penetration, or the penetration may be ignored. In +addition, initial overclosure and crossed surface diagnostics are not available for these new interactions. +Specifying initial clearances and controlling initial overclosure adjustments +In some cases the default algorithm will not correctly resolve initial overclosures, or a precise initial gap +(i.e., a positive clearance) between surfaces may need to be modeled. Specifically, deep penetrations +may be ignored, tangled double-sided surfaces may not be separated correctly , +and gaps between curved surfaces in the discretized model may be inconsistent with the non-discretized +model. To resolve these issues, you can define contact clearances and assign them to contact interactions. +Examples are given below. +Defining contact clearances +You must assign a name to each contact clearance definition that is used to associate the clearance +definition with a contact interaction. +Input File Usage: +Abaqus/CAE Usage: +*CONTACT CLEARANCE, NAME=clearance_name +Contact clearances for general contact are not supported in Abaqus/CAE. +Applying contact clearances by adjusting the nodal coordinates or by creating contact offsets +Clearances are applied to the model by adjusting the nodal coordinates or by creating contact offsets. +By default, contact clearances are resolved by adjusting the nodal coordinates without creating strain or +momentum in the model (this method can be used only in the first step of an analysis). Alternatively, +contact offsets can be created for clearance specifications. These offsets are permanent (as opposed to +temporary offsets created during the default initial overclosure resolution procedure) and are not ramped +to zero as the surfaces separate. Contact offsets will also be created for clearances specified via nodal +adjustments if the clearance violations cannot be resolved due to conflicting adjustments from separate +contacts, boundary conditions, tie constraints, coupling constraints or rigid body constraints. Clearances +can be applied via contact offsets in steps in which the whole contact domain is newly defined (i.e., no +contact was defined in the previous step) and in the first step of an import analysis. +Input File Usage: +Use the following option to apply contact clearances by adjusting the nodal +coordinates (default): +*CONTACT CLEARANCE, NAME=clearance_name, ADJUST=YES +Abaqus/CAE Usage: +Use the following option to apply contact clearances by creating contact offsets: +*CONTACT CLEARANCE, NAME=clearance_name, ADJUST=NO +Contact clearances for general contact are not supported in Abaqus/CAE. +Setting the value of the initial clearance +You can define the clearance as a single value for the whole interaction or as a nodal distribution to define +a clearance per slave node . If a distribution is defined and +the clearance is omitted for a slave node, the clearance value will be interpolated from the values at the +master nodes. The slave node will be ignored if clearance values are specified for neither the slave node +nor all of the nodes of the nearest master face. +The clearance values must be non-negative for slave nodes on solid element surfaces. The default +value is 0.0 if a value or distribution is not given. +Input File Usage: +*CONTACT CLEARANCE, NAME=clearance_name, +CLEARANCE=value or distribution_name +Abaqus/CAE Usage: +Contact clearances for general contact are not supported in Abaqus/CAE. +Defining search zones +You can specify search distances to define “zones” above and below the surfaces. Slave nodes that lie +within these zones will be given the specified clearance values with respect to their closest master faces +by pulling them closer or pushing them farther away, regardless of their initial positions (overclosure +or initial gap bigger than the clearance defined). Nodes whose closest point is a perimeter edge will be +excluded from the clearance specification. +The default value for each search distance for solid elements is approximately one-tenth of the +element size of the elements attached to the slave node. The default value for each search distance for +structural elements (e.g., shell elements) is the thickness associated with the slave node. +Input File Usage: +Abaqus/CAE Usage: +Defining a search node set +*CONTACT CLEARANCE, NAME=clearance_name, +SEARCH ABOVE=value, SEARCH BELOW=value +Contact clearances for general contact are not supported in Abaqus/CAE. +As an alternative to specifying search distances, you can specify a search node set, containing the slave +nodes for which clearance has been defined. Slave nodes that belong to this node set will be given the +specified clearance values with respect to their closest master faces by pulling them closer or pushing +them farther away, regardless of their initial positions (overclosure or initial gap bigger than the clearance +defined). If a search node set has been specified, no clearance will be applied to slave nodes that do not +belong to the specified search node set. +When a search node set is specified, there is a default search distance value associated with the +maximum element size for solid elements or the thickness for structural elements (e.g., shell elements) +associated with the nodes. The position of any node beyond the search distance is not adjusted. +Input File Usage: +*CONTACT CLEARANCE, NAME=clearance_name, +SEARCH NSET=node set name +Abaqus/CAE Usage: +Contact clearances for general contact are not supported in Abaqus/CAE. +Assigning contact clearances to contact interactions +You can assign initial clearance definitions to node-to-face interactions (except self-contact interactions) +in the general contact domain. Initial clearance definitions cannot be assigned to node-to-analytical rigid +surface interactions. For node-to-face interactions, the clearances defined between two surfaces apply to +the interaction between the slave nodes in each surface and the whole of the other surface. When nodal +adjustments are used to resolve clearance violations, the adjustments are made to satisfy the clearance +specification with respect to each slave node’s nearest master face in the initial configuration. Contact +offsets are set to the value of the clearance violation between each slave node and its nearest master face +in the initial configuration, and the slave nodes are then offset by that value with respect to the whole of +the other surface during the analysis. +The surfaces specified must be single-sided and cannot contain complex intersections of faces (i.e., +an edge cannot be connected to more than two faces) or discontinuous normals. Surfaces defined on solid +elements will satisfy these requirements automatically. These restrictions arise from the definition of a +clearance for surfaces on double-sided elements: a node has a positive (negative) clearance with respect +to a surface if it is above (below) the surface as defined by the surface normal . +A negative clearance of a node with respect to a surface on double-sided elements does not indicate a +state of penetration, but rather that the node has a gap with the other side of the elements underlying the +surface. +topsurf +negative clearance +with respect to +topsurf +botsurf +positive clearance +with respect to +botsurf +Figure 35.4.4–2 Contact clearance sign convention for double-sided elements. +By default, clearances are applied to all master-slave views of the surface pair that exist in the contact +domain. In addition, if clearances between two element-based surfaces are specified to be resolved via +nodal adjustments, the nodal adjustment procedure can be directed to perform the adjustments for one +master-slave view of the surface pair (this applies only to the nodal adjustment procedure and does not +apply to the contact formulation used between the surfaces during the analysis). +Input File Usage: +Use the following option to specify clearances for all master-slave views of the +given surface pair (default): +*CONTACT CLEARANCE ASSIGNMENT +surface_1, surface_2, clearance_name +Use the following option to specify clearances between the nodes of the second +surface and the faces of the first surface (the first surface is treated as the master +surface): +*CONTACT CLEARANCE ASSIGNMENT +surface_1, surface_2, clearance_name, MASTER +Use the following option to specify clearances between the nodes of the first +surface and the faces of the second surface (the first surface is treated as the +slave surface): +*CONTACT CLEARANCE ASSIGNMENT +surface_1, surface_2, clearance_name, SLAVE +Abaqus/CAE Usage: +Contact clearances for general contact are not supported in Abaqus/CAE. +Examples +The default algorithm to resolve initial overclosures does not detect penetrations of solid element +surfaces that are greater than approximately 15% of the dimension of facets attached to the slave node. +Figure 35.4.4–3 shows two solid elements with large initial penetrations that will not be detected during +the default initial overclosure resolution procedure. +initial overclosures +detected in this zone only +surf1 +surf2 +0.2 +Figure 35.4.4–3 Undetected large penetrations of solid elements. +A zero clearance can be defined explicitly for the overclosed portions of this model to resolve the +initial overclosures. Define the clearance definition as follows: +*CONTACT CLEARANCE, NAME=c1, ADJUST=YES, SEARCH BELOW=0.2 +SEARCH ABOVE=0.0 +and assign it to the interaction between surf1 and surf2: +*CONTACT +*CONTACT CLEARANCE ASSIGNMENT +surf1, surf2, c1 +The resulting adjustment is shown in Figure 35.4.4–4. Adjusting the nodal coordinates may degrade +the mesh geometry by creating imperfections that were not initially present, may reduce the element size +and correspondingly the stable time increment size, or may cause elements to invert and prevent the +analysis from continuing. In such cases it is preferable to bypass the nodal coordinate adjustments and +specify the storage of a contact offset. +initial position +adjusted position +Figure 35.4.4–4 Resolution of large penetrations of solid elements. +The initial overclosure adjustment algorithm must also be directed to separate entangled +double-sided surfaces. Figure 35.4.4–1 shows the default adjustments made for entangled shell surfaces +assuming the nodes of surf3 have fixed boundary conditions. Figure 35.4.4–5 shows the adjustments +made from the following clearance definition and assignment: +*CONTACT CLEARANCE, NAME=c2, ADJUST=YES, SEARCH BELOW=1.5, +SEARCH ABOVE=0.0 +... +*CONTACT +*CONTACT CLEARANCE ASSIGNMENT +surf3, surf4, c2 +If the nodes of surf3 are not fixed, the clearance interaction can be set to pure master-slave (with +surf3 defined as the master) to prevent the geometry of surf3 from being modified. +In cases where the geometry of the mesh is important or if nodal adjustments conflict, contact offsets +should be created. Conflicting nodal adjustments are a common problem when specifying clearances via +nodal adjustment for curved surfaces with a balanced master-slave interaction. Adjustments of nodes +tend to change the curvature of curved surfaces because the clearance “constraint” can be satisfied only +corrected position +of surf4 +single-sided +surface surf3 +(fixed) +thickness =1.0 +original position +of surf4 +Figure 35.4.4–5 Separation of tangled double-sided surfaces. +if the surface meshes are coincident (and a zero clearance is specified) or if the surfaces are flat . +Figure 35.4.4–6 Specifying a uniform initial gap between concentric circular surfaces. +Identifying potentially partially bonded surfaces +You can specify a search node set to identify which slave nodes will be tagged as initially bonded in a +VCCT crack propagation analysis. See “Crack propagation analysis,” Section 11.4.3, for more details. +Input File Usage: +Use the following options: +*CONTACT CLEARANCE, NAME=clearance_name, +SEARCH NSET=node set name +*CONTACT CLEARANCE ASSIGNMENT +surface_1, surface_2, clearance_name +35.4.5 +CONTACT CONTROLS FOR GENERAL CONTACT IN Abaqus/Explicit +Product: Abaqus/Explicit +References +• “Defining general contact interactions in Abaqus/Explicit,” Section 35.4.1 +• “Assigning surface properties for contact pairs in Abaqus/Explicit,” Section 35.5.2 +• *CONTACT +• *CONTACT CONTROLS ASSIGNMENT +Overview +Contact controls for the general contact algorithm: +• can be used to selectively scale the default penalty stiffness for particular regions within a general +contact domain; +• can be used to control whether nodes are removed from the general contact domain once all of the +faces and edges to which they are attached have eroded; +• can be used to activate a nondefault tracking algorithm for node-to-face contact in particular regions +within a general contact domain; +• can be used to control whether checks need to be performed to prevent folds in general contact +surfaces from inverting on themselves; +• can be used to modify the default initial overclosure resolution method for one or more pairs of +surfaces in the general contact domain; and +• can be used to modify the default contact thickness reduction checks. +Scaling default penalty stiffnesses +The general contact algorithm uses a penalty method to enforce the contact constraints . The +“spring” stiffness that relates the contact force to the penetration distance is chosen automatically by +Abaqus/Explicit, such that the effect on the time increment is minimal yet the allowed penetration is not +significant in most analyses. Significant penetrations may develop in an analysis if any of the following +factors are present: +• Displacement-controlled loading +• Materials at the contact interface that are purely elastic or stiffen with deformation +• Deformable elements (especially membrane and surface elements) that have relatively little mass of +their own and are constrained via methods other than boundary conditions (for example, connectors) +involved in contact +• Rigid bodies that have relatively little mass or rotary inertia of their own and are constrained via +methods other than boundary conditions (for example, connectors) involved in contact +See “The Hertz contact problem,” Section 1.1.11 of the Abaqus Benchmarks Manual, for an example in +which the first two of these factors combine such that the contact penetrations with the default penalty +stiffness are significant. +You can specify a scale factor by which to modify penalty stiffnesses for specified interactions +within the general contact domain. This scaling may affect the automatic time incrementation. Use of +a large scale factor is likely to increase the computational time required for an analysis because of the +reduction in the time increment that is necessary to maintain numerical stability . +The user-specified (variable) mass scaling does not take into account the effect of contact when it +computes the necessary increase of mass. In general, this effect is not significant as the default penalty +stiffness will decrease the stable time increment only by very small amounts. However, if high penalty +scale factors are specified, the stable time increment could be reduced significantly despite the specified +mass scaling. +The surface names used to specify the regions where nondefault penalty stiffness should be assigned +do not have to correspond to the surface names used to specify the general contact domain. In many cases +the contact interaction will be defined for a large domain, while a nondefault penalty stiffness will be +assigned to a subset of this domain. If the surfaces to which a nondefault penalty stiffness is assigned +fall outside the general contact domain, the controls assignment will be ignored. The last assignment +will take precedence if the specified regions overlap. +Input File Usage: +*CONTACT CONTROLS ASSIGNMENT, TYPE=SCALE PENALTY +surface_1, surface_2, scale_factor +This option must be used in conjunction with the *CONTACT option. It should +appear at most once per step; the data line can be repeated as often as necessary +to assign penalty stiffness scale factors to different regions. If the first surface +name is omitted, a default surface that encompasses the entire general contact +domain is assumed. If the second surface name is omitted or is the same as +the first surface name, the specified contact controls are assigned to contact +interactions between the first surface and itself. Keep in mind that surfaces can +be defined to span multiple unattached bodies, so self-contact is not limited to +contact of a single body with itself. +Control of nodal erosion +You can control whether contact nodes remain in the contact domain after all the surrounding faces and +edges have eroded due to element failure. By default, these nodes remain in the contact domain and +act as free-floating point masses that can experience contact with faces that are still part of the contact +domain. You can specify that nodes of element-based surfaces should erode (i.e., be removed from the +contact domain) once all contact faces and contact edges to which they are attached have eroded. Nodes +that you include in the contact domain only with node-based surfaces are never removed from the contact +domain. +Computational cost can increase as a result of free-flying nodes if nodal erosion is not specified, +particularly for analyses conducted in parallel. The increased computational cost is related to the +likelihood of free-flying nodes moving far away from the elements that remain active, which stretches +the volume of the contact domain and thereby tends to increase contact search costs as well as the cost +of communication between processors in parallel analysis. However, contact involving free-flying +nodes can contribute significant momentum transfer in some cases, which will not be accounted for if +nodal erosion is specified. +Input File Usage: +*CONTACT CONTROLS ASSIGNMENT, NODAL EROSION=NO +This option must be used in conjunction with the *CONTACT option. This +parameter setting applies to the entire general contact domain. +Activating the nondefault tracking algorithm for node-to-face contact +A nondefault contact tracking algorithm is available that utilizes more local topological and geometric +information in tracking contact between nodes and faces. This algorithm may lead to more robust contact +tracking in certain modeling situations, for instance during the inflation event of a folded air-bag. +The tracking algorithm is activated on a surface-by-surface basis. You must specify the surface +name for which the tracking algorithm needs to be activated. All contact interactions in the contact +domain in which nodes of the specified surface contact faces belonging to either the surface itself (self- +contact) or faces belonging to any other surface (for which node-to-face contact has not been excluded) +will be tracked using the nondefault node-to-face tracking scheme. +The surface names used to specify the regions where the nondefault tracking algorithm should be +used do not have to correspond to the surface names used to specify the general contact domain. In many +cases the contact interaction will be defined for a large domain, while the nondefault tracking algorithm +will be assigned to a subset of this domain. If the surfaces for which the nondefault tracking algorithm +needs to be activated fall outside the general contact domain, the controls assignment is ignored. +Input File Usage: +*CONTACT CONTROLS ASSIGNMENT, TYPE=FOLD TRACKING +surface_1 +This option must be used in conjunction with the *CONTACT option. It should +appear at most once per step; the data line can be repeated as often as necessary +to activate the nondefault tracking algorithm in different regions of the contact +domain. If the surface name is omitted, a default surface that encompasses the +entire general contact domain is assumed. +Activating the fold inversion check +If a general contact surface contains sharp folds, significant loading events (for example, +those +encountered during the inflation of a folded airbag) may cause one or more of the folds to invert. +Inversion is most likely to occur at a fold where edge-to-edge contact has not been activated on the +edges of the faces forming the fold. The presence of edge-to-edge constraints usually prevents a fold +from inverting. +Inversion of a fold, in the absence of edge-to-edge contact constraints, may induce +errors in the node-to-face contact tracking algorithm and may result in a node that was being tracked +on a face that forms part of an inverted fold getting “snagged” on the wrong side of the tracked face. +To avoid such situations, it may be desirable to activate the fold inversion check for models containing +sharp folds. The fold inversion check detects situations where a fold is about to invert and applies a +force field to the faces forming the fold to prevent the fold from inverting. +The fold inversion check is activated on a surface-by-surface basis. You must specify the surface +name for which the fold inversion check needs to be activated. If activated for a particular surface, the +fold inversion check applies to all folds within that surface. +The surface names used to specify the regions where the fold inversion check should be activated do +not have to correspond to the surface names used to specify the general contact domain. In many cases +the contact interaction will be defined for a large domain, while the fold inversion check will be activated +in a subset of this domain. If the surfaces for which the fold inversion check needs to be activated fall +outside the general contact domain, the controls assignment is ignored. +*CONTACT CONTROLS ASSIGNMENT, +TYPE=FOLD INVERSION CHECK +surface_1 +Input File Usage: +This option must be used in conjunction with the *CONTACT option. It should +appear at most once per step; the data line can be repeated as often as necessary +to activate the fold inversion check in different regions of the contact domain. +If the surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. +Activating the default tracking algorithm for edge-to-edge contact +The default contact tracking algorithm utilizes more local information than the alternative tracking +algorithm in tracking contact between edges and typically reduces the extent of global tracking required. +The use of this algorithm may lead to smaller computational times in analyses that have extensive +edge-to-edge contact defined (for example, during the inflation simulation of a folded airbag, where it +may be desirable to activate all feature edges on the airbag membrane surface to accurately enforce +contact during the inflation event). +The default tracking algorithm can be explicitly specified, though all edge-to-edge contact in the +contact domain will be enforced using the default tracking algorithm if contact controls are not specified +for the tracking algorithm. +Input File Usage: +*CONTACT CONTROLS ASSIGNMENT, TYPE=ENHANCED +EDGE TRACKING (default) +This option must be used in conjunction with the *CONTACT option. This +parameter setting applies to the entire general contact domain. +An alternative tracking algorithm for edge-to-edge contact +An alternative contact tracking algorithm is available that utilizes less local information than the default +tracking algorithm in tracking contact between edges. This algorithm typically increases the extent of +global tracking required and, hence, in most analyses the computational time. When the alternative edge +tracking algorithm is specified, all edge-to-edge contact in the contact domain is enforced using this +algorithm. +Input File Usage: +*CONTACT CONTROLS ASSIGNMENT, TYPE=EDGE TRACKING +If specified, this option must be used in conjunction with the *CONTACT +option. This parameter setting applies to the entire general contact domain. +Control of initial overclosure resolution +By default, Abaqus/Explicit automatically adjusts the positions of surfaces to remove small initial +overclosures that exist in the general contact domain in the first step of a simulation. Conflicting +adjustments from separate contact definitions, boundary conditions, tie constraints, and rigid body +constraints can cause incomplete resolution of initial overclosures. +Initial overclosures that are not +resolved by repositioning nodes are stored as initial contact offsets to avoid large contact forces at the +beginning of an analysis. +Alternatively, in certain situations it may be desirable to avoid nodal adjustments altogether between +a pair of surfaces and to treat all initial overclosures between the surfaces as temporary contact offsets. +You can then specify the surfaces for which the initial overclosures should not be resolved by nodal +adjustments and which should instead be stored as offsets. +Input File Usage: +*CONTACT CONTROLS ASSIGNMENT, AUTOMATIC +OVERCLOSURE RESOLUTION +surface_1, surface_2, STORE OFFSETS +This option must be used in conjunction with the *CONTACT option. It should +appear at most once per step; the data line can be repeated as often as necessary +to assign a nondefault overclosure resolution method to different regions. If +the first surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. If the second surface name is omitted or is +the same as the first surface name, the specified contact controls are assigned +to contact interactions between the first surface and itself. +Control of contact thickness reduction checks +By default, the general contact algorithm requires that the contact thickness does not exceed a certain +fraction of the surface facet edge lengths or diagonal lengths. This fraction generally varies from 20% +to 60% based on the geometry of the element and whether the element is near a shell perimeter. The +general contact algorithm will scale back the contact thickness automatically where necessary without +affecting the thickness used in the element computations for the underlying elements. +To check whether the thickness needs to be reduced in any particular region in the model, the contact +algorithm first assigns the full thickness to each contact node, represented by a sphere centered at the node +with a diameter equal to the thickness. Next, the thickness is reduced so that the spheres do not overlap +with any neighboring facets that are not attached directly to the node, preventing spurious self-contact +from developing. Then, the nodes on the perimeter of shells are moved a maximum of 50% of the facet +size in the plane of the facet away from the perimeter to eliminate the “bull-nose” effect that occurs +with the contact pair algorithm . If the thickness of the shell perimeter nodes is greater than twice the maximum perimeter +offset, a final thickness reduction is performed to eliminate the remainder of the “bull-nose.” +If the default thickness reductions are unacceptable in particular regions of the model, you can +exclude self-contact for those regions via contact exclusion definitions and activate a control for the contact thickness reduction +checks. +Input File Usage: +Use the following option to eliminate thickness reductions in regions of the +model that are excluded from self-contact, while still reducing thickness at +shell perimeters where perimeter offsets are insufficient to avoid the “bull-nose” +effect: +*CONTACT CONTROLS ASSIGNMENT, +CONTACT THICKNESS REDUCTION=SELF +Use the following option to eliminate thickness reductions in regions of the +model that are excluded from self-contact and at all shell perimeters (a “bull- +nose” will form at shell perimeter nodes if the thickness is greater than twice +the maximum perimeter offset): +*CONTACT CONTROLS ASSIGNMENT, +CONTACT THICKNESS REDUCTION=NOPERIMSELF +35.5 +Defining contact pairs in Abaqus/Explicit +• “Defining contact pairs in Abaqus/Explicit,” Section 35.5.1 +• “Assigning surface properties for contact pairs in Abaqus/Explicit,” Section 35.5.2 +• “Assigning contact properties for contact pairs in Abaqus/Explicit,” Section 35.5.3 +• “Adjusting initial surface positions and specifying initial clearances for contact pairs in +Abaqus/Explicit,” Section 35.5.4 +• “Contact controls for contact pairs in Abaqus/Explicit,” Section 35.5.5 +35.5.1 +DEFINING CONTACT PAIRS IN Abaqus/Explicit +Products: Abaqus/Explicit Abaqus/CAE +References +• “Element-based surface definition,” Section 2.3.2 +• “Node-based surface definition,” Section 2.3.3 +• “Analytical rigid surface definition,” Section 2.3.4 +• “Contact interaction analysis: overview,” Section 35.1.1 +• *CONTACT CONTROLS +• *CONTACT PAIR +• *SURFACE +• “Defining surface-to-surface contact,” Section 15.13.7 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Defining self-contact,” Section 15.13.8 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +Abaqus/Explicit provides two algorithms for modeling contact and interaction problems: the general +contact algorithm and the contact pair algorithm. See “Contact interaction analysis: overview,” +Section 35.1.1, for a comparison of the two algorithms. This section describes how to define contact +pairs with surfaces for contact simulations in Abaqus/Explicit. +Contact pairs in Abaqus/Explicit: +• are part of the history definition of the model and can be created, modified, and removed from step +to step (unlike Abaqus/Standard, where contact pairs are model data); +• use sophisticated tracking algorithms to ensure that proper contact conditions are enforced +efficiently; +• can be used simultaneously with the general contact algorithm (i.e., some interactions can be +modeled with contact pairs, while others are modeled with the general contact algorithm); +• can be formed using a pair of rigid or deformable surfaces or a single deformable surface; +• do not have to use surfaces with matching meshes; +• cannot be formed with one two-dimensional surface and one three-dimensional surface; and +• cannot be used for self-contact where the surface is composed of both first-order elements and +second-order elements. +Defining a contact pair interaction +The definition of a contact pair interaction in Abaqus/Explicit consists of specifying: +• the contact pair algorithm and the surfaces that interact with one another, as described in this section; +• the contact surface properties (“Assigning surface properties for contact pairs in Abaqus/Explicit,” +Section 35.5.2); +• the mechanical contact property models (“Assigning contact properties for contact pairs in +Abaqus/Explicit,” Section 35.5.3); +• the contact +Section 37.2.2); +formulation (“Contact +formulations +for contact pairs +in Abaqus/Explicit,” +• the contact constraint enforcement method (“Contact constraint enforcement methods in +Abaqus/Explicit,” Section 37.2.3); and +• the algorithmic contact controls (“Common difficulties associated with contact modeling using +contact pairs in Abaqus/Explicit,” Section 38.2.2). +Defining a contact pair containing two surfaces +To define a contact pair, you must indicate which pairs of surfaces will interact with each other. The order +in which the surfaces are specified is important only when a nondefault weighting factor is specified +. See “Element-based surface definition,” Section 2.3.2; “Node-based surface +definition,” Section 2.3.3; and “Analytical rigid surface definition,” Section 2.3.4, for information on +defining surfaces for use in contact pairs. +Input File Usage: +*CONTACT PAIR +surface_1_name, surface_2_name +Abaqus/CAE Usage: +Interaction module: Create Interaction: Surface-to-surface contact +(Explicit): select the first surface, click Surface, select the second surface +Defining self-contact +Define contact between a single surface and itself by specifying only a single surface or by specifying +the same surface twice. +Input File Usage: +Use either of the following options: +*CONTACT PAIR +surface_1, +*CONTACT PAIR +surface_1, surface_1 +Abaqus/CAE Usage: +Interaction module: Create Interaction: +Self-contact (Explicit): select the surface +or +Surface-to-surface contact (Explicit): select the surface, click +Surface, select the surface again +Limitations with self-contact +The following limitations are enforced for a contact pair with self-contact: +• The balanced master-slave contact algorithm will always be used for the contact pair (a nondefault +weighting factor cannot be specified for the contact pair). +• A contact thickness must be considered for self-contact surfaces on shell or membrane elements ; i.e., a zero surface thickness causes Abaqus/Explicit to issue an error message. By default, the contact thickness +is equal to the current thickness. +• The contact thickness for self-contact should not exceed the edge lengths or diagonal lengths of the +facets. You can reduce the contact thickness, if necessary; see “Controlling the effects of surface +thickness and offset in contact calculations” in “Assigning surface properties for contact pairs in +Abaqus/Explicit,” Section 35.5.2. +• A specialized finite-sliding tracking algorithm must be used. The use of the small-sliding contact +formulation is not supported and causes Abaqus/Explicit to issue an error message. +• Contact will be recognized between any node on a self-contact surface and any other point on +the same surface, including either side of shells or membranes (i.e., self-contact on shells and +membranes is independent of the face identifier specified in the surface definition). +Removing and adding contact pairs +Removal and addition of contact pairs: +• can be used to simulate complicated forming processes where multiple tools need to interact with +the workpiece at different stages; +• can be used to extend surfaces to prevent one surface from sliding off another; +• can result in significant computational savings by eliminating unnecessary contact searches; and +• can be used to change the definition of a contact pair. +Adding contact pairs +By default, the contact pairs specified are added to the list of active contact pairs in the model. +Initial penetrations should be avoided for contact pairs introduced after the first step, as large +nodal accelerations and severe element distortions can result . Redefining a +contact pair by deleting it and adding it in the same step can also lead to problems, because the “state” +information associated with the slave nodes in contact will be reinitialized. For example, a penalty +contact slave node with a penetration past the midsurface of a double-sided master surface would be +allowed to pass through the master surface if the contact state were reinitialized. +*CONTACT PAIR, OP=ADD +Interaction module: Create Interaction +Abaqus/CAE Usage: +Input File Usage: +Removing contact pairs +Removal of contact pairs is a useful technique for simulating complicated forming processes where +multiple tools will contact the same workpiece. Removing a contact pair once it is no longer needed +eliminates the need to monitor the contact conditions and reduces the cost of the simulation. +Input File Usage: +Abaqus/CAE Usage: +*CONTACT PAIR, OP=DELETE +Interaction module: interaction manager: Deactivate +General restrictions on surfaces used in contact pairs +The following general restrictions (in addition to those discussed in “Element-based surface definition,” +Section 2.3.2) apply to all surfaces used in contact pairs: +• The surface normals of a surface must point toward the other surface that it may contact except +when the surface is double-sided, as discussed below. +• Element-based surfaces should not be used in contact pairs if the underlying elements may fail . Use general contact (“Defining +general contact interactions in Abaqus/Explicit,” Section 35.4.1) or node-based surfaces (“Node- +based surface definition,” Section 2.3.3) in such cases. +• The surface must be continuous, as discussed below. +• Continuum and structural elements cannot be mixed in the same surface definition. +• Deformable elements cannot be combined with elements that are part of a rigid body to define a +single surface. +These restrictions do not apply to surfaces used with the general contact algorithm (“Defining general +contact interactions in Abaqus/Explicit,” Section 35.4.1). +The following restrictions apply to the surfaces forming a kinematic contact pair: +• Rigid surfaces must always be the master surface. +• Slave surfaces must be part of a deformable body. +• A node-based surface can be used only as a slave surface. +The following restrictions apply to the surfaces forming a penalty contact pair: +• Analytical rigid surfaces must always be the master surface. +• A node-based surface can be used only as a slave surface. +Orienting the surface’s normal +The orientation of a surface’s normal can be critical for the proper detection of contact between two +contacting surfaces. At the point of closest proximity the normals of a single-sided master surface +forming the contact pair should always point toward the slave surface. If, in the initial configuration of the +model, a single-sided master surface’s normal points away from its slave surface, Abaqus/Explicit will +detect that the slave surface penetrates the master surface. Abaqus/Explicit will attempt to resolve this +initial overclosure of the contact pair with strain-free displacements before the start of the simulation (see +“Adjusting initial surface positions and specifying initial clearances for contact pairs in Abaqus/Explicit,” +Section 35.5.4). Abaqus/Explicit may have difficulty with the simulation if the overclosure is too severe. +In most of these cases the analysis will terminate immediately, and an error message about severely +distorted elements will be issued. +You must give particular attention to checking that analytical rigid surfaces or single-sided +Surface +surfaces created on shell, membrane, or rigid elements have the proper orientation. +orientation errors can often be quickly and easily detected by running a data check analysis +(“Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD execution,” Section 3.2.2) and inspecting the +deformed configuration in Abaqus/CAE. If large displacements have occurred, they may be due to an +incorrect surface orientation. +The proper and improper orientation of a rigid and deformable surface is shown in Figure 35.5.1–1. +rigid +surface +outward normal +deformable +surface +Incorrect rigid surface orientation +Correct rigid surface orientation +Figure 35.5.1–1 Example of proper and improper surface orientation with a rigid surface. +It is not necessary for the normals of all of the underlying shell or membrane elements to have +if possible, Abaqus/Explicit will define +a consistent positive orientation for a double-sided surface: +the surface such that its facets have consistent normals, even if the underlying elements do not have +consistent normals. The facet normals will be the same as the element normals if the element normals +are all consistent; otherwise, an arbitrary positive orientation is chosen for the surface. For double-sided +surfaces the positive orientation is significant only with respect to the sign of the contact pressure output +variable, CPRESS, as discussed in “Element-based surface definition,” Section 2.3.2. +Defining a continuous surface +A contact pair surface cannot be made up of two or more disconnected regions. The definition of +analytical rigid surfaces automatically ensures that these surfaces are continuous. However, care must +be taken to define surfaces formed with elements so that they are continuous across element edges in +three-dimensional models or through nodes in two-dimensional models. This continuity requirement +has several implications for what constitutes a valid or invalid surface definition. In two dimensions +the surface must be either a simple, nonintersecting curve with two terminal ends or a closed loop. +Figure 35.5.1–2 shows examples of valid and invalid two-dimensional surfaces for use in contact pairs. +Valid Closed +Simply Connected +2D Surface +Valid Open +Simply Connected +2D Surface +Invalid 2D Surface +Figure 35.5.1–2 Valid and invalid 2-D surfaces. +In three dimensions an edge of an element face belonging to a valid surface may be either on the +perimeter of the surface or shared by one other face. Two element faces forming a contact pair surface +cannot be joined just at a shared node; they must be joined across a common element edge. An element +edge cannot be shared by more than two surface facets. Figure 35.5.1–3 illustrates valid and invalid +three-dimensional surfaces for use in contact pairs. +The continuity requirement applies to both automatically generated free surfaces and surfaces +defined with element +face identifiers . +Figure 35.5.1–4 shows an automatically generated free surface resulting from the specification of an +element set consisting of two disjointed groups of elements. The resulting surface is not continuous +since it is composed of two disjoint open curves. +Restrictions for two-dimensional contact simulations +The following restrictions apply when defining a contact simulation for two-dimensional (planar) or +axisymmetric problems: +• A contact pair cannot involve a planar surface and an axisymmetric surface. This restriction applies +only to deformable and element-based rigid surfaces. +• Defining a contact pair that contains two surfaces formed by planar elements of different sizes in +the out-of-plane direction (“depth”) is not recommended and will result in a warning message. In +such a case frictional stresses are calculated based on a weighted average depth, with the weighting +for the first surface equal to the user-specified contact surface weighting factor. The out-of-plane +Valid Simply Connected Surface +Invalid Surface +Invalid Surface +Figure 35.5.1–3 Valid and invalid 3-D surfaces. +user-specified element set +automatically generated free surface +Figure 35.5.1–4 Automatic free surface generation. +thickness for two-dimensional beam element-based surfaces is always assumed to be one. As a +result, the contact pressure acting on such a surface can be considered as a line force as well. +• When more than one contact pair involves contact between the same rigid surface formed by planar +elements and different planar deforming surfaces, the deforming surfaces must all have the same +depth; otherwise, a warning message will be issued. The depth value used for calculating contact +stresses will then be taken from one of these deforming surfaces, but this choice cannot be predicted. +Limitations in contact simulations with three-dimensional beam and truss elements +Element-based surfaces cannot be formed on three-dimensional beam or truss elements, so node-based +surfaces must be used to define a surface on these elements. Because a node-based surface must be +used, a surface on three-dimensional beam or truss elements must always form the slave surface in a +pure master-slave contact pair. Therefore, it is not possible to have two three-dimensional beam or truss +structures contact each other. +Output +You can write the contact surface variables associated with the interaction of contact pairs to the Abaqus +output database (.odb) file. The surface variables for a mechanical contact analysis include contact +pressure and force, frictional shear stress and force, relative tangential motion (slip) of the surfaces +during contact, whole surface resultant quantities (i.e., force, moment, center of pressure, and total +area in contact), the status of bonded nodes, and the maximum torque transmitted about the z-axis of +axisymmetric elements. +Additional discussion on requesting contact surface output can be found in “Surface output in +Abaqus/Standard and Abaqus/Explicit” in “Output to the output database,” Section 4.1.3. Output from +thermal interactions is discussed in “Thermal contact properties,” Section 36.2.1. +Field output +The generic variables CSTRESS, CFORCE, FSLIP, and FSLIPR are valid field output requests for +Abaqus/Explicit. If CSTRESS is requested for a contact pair, the variables CPRESS (contact pressure), +CSHEAR1 (contact traction in the local 1-direction), and, if the contact interaction is three-dimensional, +CSHEAR2 (contact traction in the local 2-direction) can be contoured in Abaqus/CAE for each discrete +(i.e., non-analytical) surface in a contact pair. +Contours of contact pressure (CPRESS) on surfaces used with the contact pair algorithm will be +displayed using the convention that a positive pressure represents compressive contact on the positive +side of the surface. The positive side of the surface can be determined by drawing the surface normals +in the Visualization module of Abaqus/CAE. Following this convention, the sign of CPRESS will be +reversed for contact on the negative (back) side of a double-sided surface, so negative values of CPRESS +may be seen if contact occurs on the back side of a double-sided surface. If contact from separate contact +pairs occurs on both sides of the double-sided surface at the same point, the value of CPRESS is given +for each contact pair separately. +If CFORCE is requested for a contact pair, the variables CNORMF (normal contact force) and +CSHEARF (shear contact force) can be plotted as vectors in a symbol plot in Abaqus/CAE for each +discrete (i.e., non-analytical) surface in a contact pair. +If FSLIPR is requested, FSLIPR (the magnitude of the slip rate for slave nodes in contact) can be +contoured in Abaqus/CAE for each slave surface in a contact pair. In addition, for three-dimensional +contact interactions involving an analytical rigid surface and for all two-dimensional contact interactions, +components of net slip rate based on local tangent directions (FSLIPR1 and, in three dimensions, +FSLIPR2) can also be contoured in Abaqus/CAE for each slave surface in a contact pair if FSLIPR is +requested. All of the slip rate variables associated with FSLIPR are zero whenever a slave node is not +in contact. +If FSLIP is requested, FSLIPEQ (the length of the overall slip path for a slave node while it is +in contact) can be contoured in Abaqus/CAE for each slave surface in a contact pair. In addition, for +three-dimensional contact interactions involving an analytical rigid surface and for all two-dimensional +contact interactions, components of net slip (FSLIP1 and, in three dimensions, FSLIP2) can also be +contoured in Abaqus/CAE for each slave surface in a contact pair if FSLIP is requested. These slip +variables are equivalent to the slip rate variables integrated over time: FSLIPEQ, FSLIP1, and FSLIP2 +are equivalent to FSLIPR, FSLIPR1, and FSLIPR2 integrated over time, respectively. Therefore, these +slip variables account only for relative motions that occur while slave nodes are in contact. +History output +Several whole surface contact variables are available as history output. These variables record the contact +state of a surface as a set of force (CFN, CFS, and CFT) and moment (CMN, CMS, and CMT) resultants +with respect to the origin. Additional variables give the center of pressure (XN, XS, and XT) on the +surface (defined as the point closest to the centroid of the surface that lies on the line of action of the +resultant force for which the resultant moment is minimal). The last letter of each variable name (except +the variable CAREA) denotes which contact force distribution on the surface is used to calculate the +resultant: the letter N denotes that the normal contact forces are used to derive the resultant quantity; +the letter S denotes that the shear contact forces are used to derive the resultant quantity; and the letter +T denotes that the sum of the normal and shear contact forces are used to derive the resultant quantity. +These history output variables will be written twice to the output database once for each surface involved +in the contact pair. +Each total moment output variable will not necessarily equal the cross product of the respective +center of force vector and resultant force vector. Forces acting on two different nodes of a surface may +have components acting in opposite directions, such that these nodal force components generate a net +moment but not a net force; therefore, the total moment may not arise entirely from the resultant force. +The center of force output variables tend to be most meaningful when the surface nodal forces act in +approximately the same direction. +The total area in contact at a given time can be requested using output variable CAREA, defined as +the sum of all the facets where there is contact force. The contact area reported by CAREA is generally +slightly larger than the true contact area for reasonably meshed contact surfaces; therefore, interpretation +of CAREA should be done with care. The discrepancy between the CAREA output and the true contact +area decreases as the mesh density increases. Using contact inclusions or exclusions to limit CAREA +output to smaller contact surfaces may also reduce the discrepancy in some cases. Since the CAREA +output is an approximation of the true contact area, deriving force or stress values using this output may +not yield accurate values; requesting contact force and stress directly is the most appropriate way to +obtain accurate results. +Detailed history output on the status of bonded surfaces is available from an Abaqus/Explicit +simulation. Details can be found in “Breakable bonds,” Section 36.1.9. +Obtaining the “maximum torque” that can be transmitted about the z-axis in an axisymmetric +analysis +When modeling surface-based contact with axisymmetric (CAX) elements, Abaqus/Explicit can +calculate the maximum torque (output variable CTRQ) that can be transmitted about the z-axis. The +maximum torque, T, is defined as +where p is the pressure transmitted across the interface, r is the radius to a point on the interface, and s is +the current distance along the interface in the r–z plane. This definition of “torque” effectively assumes +a friction coefficient of unity. +35.5.2 +ASSIGNING SURFACE PROPERTIES FOR CONTACT PAIRS IN Abaqus/Explicit +Products: Abaqus/Explicit Abaqus/CAE +References +• “Defining contact pairs in Abaqus/Explicit,” Section 35.5.1 +• *CONTACT PAIR +• *SURFACE +• “Specifying geometric properties for mechanical contact property options” in “Defining a contact +interaction property,” Section 15.14.1 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +This section describes how to modify the surface properties for contact interactions in Abaqus/Explicit +defined with the contact pair algorithm, including the surface thickness and offset. +Shell, membrane, or rigid element thickness and shell or rigid element offset +To define surfaces on shell, membrane, or rigid elements such that they are in contact at the start of the +analysis, the element thicknesses must be considered when defining the nodal coordinates; otherwise, +the surfaces in the contact pair will be overclosed. Surface thickness and surface offset are properties +that are inherited from underlying shell and membrane elements by default. For a surface based on rigid +elements, the default surface thickness and offset correspond to the thickness and offset defined for the +rigid body to which the elements belong . The surface thickness +and offset are zero for surfaces based on solid elements. +By default, the nodal thickness for surfaces based on shell, membrane, or rigid elements equals the +minimum thickness of the surrounding elements . The surface +thickness within a facet is interpolated from the nodal values; the interpolated surface thickness never +extends past the specified element or nodal thickness, which may be significant with respect to initial +overclosures. +If a spatially varying nodal +thickness is defined for the underlying elements , the nodal surface thickness may not correspond exactly to the specified +nodal thickness . The nodal surface thickness +distribution will tend to be more diffuse than the specified nodal thickness distribution (because the +specified nodal thicknesses are averaged to compute the element thicknesses, and the minimum of the +surrounding element thicknesses is the nodal surface thickness). +Effects of surface thickness and offsets, as well as methods for modifying the surface thickness and +for avoiding surface offsets, are discussed below. +specified element thickness +(constant over element) +interpolated surface +thickness +nodal surface thickness +Figure 35.5.2–1 Continuous variation of surface thickness across facet boundaries. +Table 35.5.2–1 Thicknesses corresponding to Figure 35.5.2–1. +node +element +specified element +thickness +nodal surface +thickness (minimum +of adjacent element +thicknesses) +0.5 +0.5 +0.5 +0.9 +0.9 +0.5 +0.5 +0.9 +0.9 +element thickness +(constant over element) +nodal surface +thickness +specified +nodal thickness +interpolated surface +thickness +Figure 35.5.2–2 Small discrepancy between the nodal surface thickness and the specified nodal thickness. +Table 35.5.2–2 Thicknesses corresponding to Figure 35.5.2–2. +node +element +specified +nodal +thickness +element +thickness +(average of +specified nodal +thickness) +nodal surface +thickness +(minimum of +adjacent element +thicknesses) +0.5 +0.5 +0.5 +0.9 +0.9 +0.9 +0.5 +0.5 +0.7 +0.9 +0.9 +35.5.2–3 +0.5 +0.5 +0.5 +0.7 +0.9 +Effects of surface thickness and offsets +Accounting for thickness in the contact pair algorithm will cause the surface to extend past the parent +element boundary in the plane of the element by an amount equal to one-half its thickness. For example, +this surface extension, which is semi-circular in shape, will cause contact to be established between the +edge of a shell and an opposing surface before the node on the shell boundary reaches the opposing +surface. The extension is present for both single-sided and double-sided surfaces. Figure 35.5.2–3 +demonstrates this concept. Such “bull-nose” extensions are avoided when the general contact algorithm +(“Defining general contact interactions in Abaqus/Explicit,” Section 35.4.1) is used. The effect of a shell +or rigid offset on a surface is shown in Figure 35.5.2–4. Poorly defined surfaces can result near corners if +large offsets are present, as shown in Figure 35.5.2–5. You should consider this when defining a model. +A warning message will be issued if the offset magnitude is greater than one-half of any of the parent +shell element edge lengths. However, at acute corners it is possible for an offset less than one-half of +the parent element size to result in a poorly defined contact surface (and in this case no warning will be +given). +contacting surface +surface extension +shell nodes +shell reference surface +contact established +Figure 35.5.2–3 Extension of contact surface for edge contact without zero surface thickness. +midsurface +t/2 +t/2 +offset +contact surface, +same as shell outer surface except at edges +reference surface +Figure 35.5.2–4 Extension of contact surface if a shell offset is present. +nodal +offset +adjusted +nodal +position +shell midsurface +reference surface +Figure 35.5.2–5 Example of a poorly defined surface near +a corner when a large shell offset is present. +Controlling the effects of surface thickness and offset in contact calculations +You can control the thickness and offset used in the contact calculations only; they do not affect surface- +based constraints. These settings are intended primarily for self-contact surfaces since you cannot force +zero thickness for these surfaces, as described below. +Self-contact surfaces should not contain facets that are thicker than their edge or diagonal lengths. +Extremely large thicknesses will cause nodes to appear to be penetrating nearby facets in even a flat +self-contact surface due to the algorithmic use of a semi-circular tube with a radius of half the contact +thickness around the edge of each facet . +outer boundary +of node +penetration +outer boundary +of overall surface +outer boundary +of facet +reference surface +Figure 35.5.2–6 Undesired penetration resulting from a +large thickness in a self-contact surface. +You can scale the effective thickness used for all of the facets on a surface by a single factor, f. +Alternatively, you can adjust only the thicknesses for surface facets in which the thickness to minimum +edge or diagonal length ratio exceeds a specified value, r; the amount by which a facet thickness is +adjusted may vary during an analysis because of changes in the facet size. If the thickness to element size +ratio exceeds 1.0 in the initial configuration for a self-contact surface, an error message recommending +that you adjust the thickness will be issued. +You should not specify extremely small values for f or r for double-sided surfaces or surfaces that +will be involved in self-contact since these surfaces must have a contact thickness that is significant +compared to the facet size. For surfaces involved only in two-surface contact it is acceptable to set +f=0.0; however, it is computationally more efficient to use the method described below to force a zero +surface thickness. It is also possible to enforce the offset but not the thickness in the surface model by +setting the scale factor, f, equal to zero. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to scale the surface thickness by a single factor: +*SURFACE, NAME=name, SCALE THICK=f +Use the following option to adjust the thickness to element size ratios: +*SURFACE, NAME=name, MAX RATIO=r +You cannot scale the thickness of a contact surface in Abaqus/CAE. +Forcing zero surface thickness and offset +You can force the surface thickness and offset to be zero, rather than inherit the thickness and offset of +underlying shell, membrane, or rigid elements. In this case the contact surface is taken as the reference +surface . +midsurface +t/2 +t/2 +shell surfaces +reference surface +and contact surface +Figure 35.5.2–7 Contact surface with zero thickness and offset. +You cannot ignore the thickness for a surface that is used as a contact surface for single-surface (self) +contact. If one of the surfaces in a contact pair is a double-sided surface, zero thickness can be forced on +only one of the two surfaces: at least one surface in a contact pair involving double-sided surfaces must +have a nonzero thickness. The ability to force zero surface thickness is useful for performing parameter +studies on the thickness or offset of a model since you can change the thickness and offset without also +having to move the mesh to control the initial separation between the surfaces. +Input File Usage: +Abaqus/CAE Usage: +*SURFACE, NAME=name, NO THICK +You cannot force a surface thickness to be zero in Abaqus/CAE. +Example +Contact calculations are generally most accurate with the default treatment of thickness and offset. +However, when a shell offset of half the original shell thickness has been specified, forcing zero surface +thickness will give an accurate representation of one side of the surface. This approach can be more +accurate near a corner (especially on the exterior side of a corner) than if the offset and thickness are +enforced for the surface, as shown in Figure 35.5.2–8. +default +surface +desired +midsurface +reference surface +Shell model with +offset equal to half +the thickness +surface if +zero +thickness +is forced +adjusted +nodal +position +midsurface +contact surfaces +contact surface +Figure 35.5.2–8 Forcing zero surface thickness when the shell offset is half the original shell thickness. +Forcing zero surface offset +For situations in which it is desirable to ignore the effect of the offset but when it is still necessary to +model the thickness in the contact calculations, you can force only the surface offset to be zero without +affecting the surface thickness. In this case the contact surface is the outside surface of an imaginary +shell, membrane, or rigid element whose midsurface is at the reference surface . +This method could be used for a self-contact surface that would be poorly defined if the offset were +enforced (thickness must be enforced for self-contact surfaces). +Input File Usage: +Abaqus/CAE Usage: +*SURFACE, NAME=name, NO OFFSET +You cannot force a surface offset to be zero in Abaqus/CAE. +midsurface +t/2 +t/2 +shell surfaces +contact surface +reference surface +Figure 35.5.2–9 Contact surface with zero offset. +Defining additional contact thicknesses for a contact pair interaction +You can specify a contact offset for a contact pair interaction in addition to any element thicknesses +or midsurface offsets already defined for the elements underlying the contact pair surfaces. For small +sliding this includes contact offsets defined by initial clearances . The specified offset value will be applied as an additional thickness +of a layer separating the two surfaces, not as an additional thickness for each surface in the contact pair. +This value can be positive or negative. This technique is often used in conjunction with softened behavior + to model the thickness of a thin layer +between two contacting surfaces. +Input File Usage: +Abaqus/CAE Usage: +*SURFACE INTERACTION, PAD THICKNESS=value +Interaction module: contact property editor: Mechanical→Geometric +Properties: toggle on Thickness of interfacial layer (Explicit): value +35.5.3 +ASSIGNING CONTACT PROPERTIES FOR CONTACT PAIRS IN Abaqus/Explicit +Products: Abaqus/Explicit Abaqus/CAE +References +• “Mechanical contact properties: overview,” Section 36.1.1 +• “Contact pressure-overclosure relationships,” Section 36.1.2 +• “Contact damping,” Section 36.1.3 +• “Frictional behavior,” Section 36.1.5 +• “User-defined interfacial constitutive behavior,” Section 36.1.6 +• “Breakable bonds,” Section 36.1.9 +• *CONTACT PAIR +• *SURFACE INTERACTION +• “Interaction property editors,” Section 15.9.3 of the Abaqus/CAE User’s Manual +Overview +Contact properties: +• define the mechanical and thermal surface interaction models that govern the behavior of surfaces +when they are in contact; and +• are assigned to individual contact pairs. +Assigning a contact property definition to a contact pair +If nondefault contact properties are desired, you can refer to a contact property definition that governs +the interaction of the two surfaces. +Multiple contact pairs can refer to the same contact property definition. +Input File Usage: +Use both of the following options: +*CONTACT PAIR, INTERACTION=interaction_property_name +surface_1, surface_2 +*SURFACE INTERACTION, NAME=interaction_property_name +Interaction module: +Abaqus/CAE Usage: +Create Interaction Property: Name: interaction_property_name, Contact +Interaction editor: Contact interaction property: interaction_property_name +Example +Figure 35.5.3–1 shows the mesh used in this example. For purposes of this example, a balanced master- +slave contact pair is used. The property definition for the contact pair (GRATING) uses a friction model +where =0.4. +ESETB +ESETA +502 +BSURF +201 +501 +202 +101 +102 +103 +ASURF +Figure 35.5.3–1 Surface interaction with friction. +*HEADING +… +*SURFACE, NAME=ASURF +ESETA, +*SURFACE, NAME=BSURF +ESETB, +… +*STEP +Step1 +*DYNAMIC, EXPLICIT +… +*CONTACT PAIR, INTERACTION=GRATING +ASURF, BSURF +*SURFACE INTERACTION, NAME=GRATING +*FRICTION +0.4 +Changing contact properties +Contact property models are defined as model or history data for a contact pair analysis. You can modify +the contact properties from step to step; however, the old contact pair should be deleted and redefined +using the new interaction. +Example +For example, the following input could be used to change the friction coefficient used for contact between +ASURF and BSURF in the second step of the analysis started in the previous example: +*STEP +Step2 +*DYNAMIC, EXPLICIT +… +*CONTACT PAIR, INTERACTION=GRATING,OP=DELETE +ASURF, BSURF +*SURFACE INTERACTION, NAME=GRATING_NEW +*FRICTION +0.5 +*CONTACT PAIR, INTERACTION=GRATING_NEW +ASURF, BSURF +35.5.4 +ADJUSTING INITIAL SURFACE POSITIONS AND SPECIFYING INITIAL +CLEARANCES FOR CONTACT PAIRS IN Abaqus/Explicit +Products: Abaqus/Explicit Abaqus/CAE +References +• “Defining contact pairs in Abaqus/Explicit,” Section 35.5.1 +• *CLEARANCE +• *CONTACT PAIR +• “Defining surface-to-surface contact,” Section 15.13.7 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +Adjustments to the positions of the slave nodes in an Abaqus/Explicit contact pair: +• are performed for all contact pairs that have slave nodes that are overclosed and that do not have +specified initial clearances, except when nodes of a rigid body act as slave nodes; +• can eliminate small gaps or penetrations caused by numerical roundoff when a graphical +preprocessor such as Abaqus/CAE is used; +• do not create any strains or momentum in the model during the first step of a simulation; +• do create strains and momentum in subsequent steps of a simulation; +• should not be used to correct gross errors in the mesh design; and +• should not be used to resolve initial overclosures involving a slave node that is pinched between +two master surfaces. +If the small-sliding contact formulation is used, an alternative to adjusting the position of the surfaces is to define the initial +clearances between the surfaces precisely in both magnitude and direction. +Adjustments of overclosed surfaces in the first step of the simulation +Abaqus/Explicit will automatically adjust the positions of surfaces to remove any initial overclosures that +exist when a contact pair is defined in the first step of a simulation, except when nodes of a rigid body act +as a slave nodes or user subroutine VUINTER is used. The adjustments are made with strain-free initial +displacements to the slave nodes on the surfaces. Therefore, when a balanced master-slave contact pair +is defined, nodes on both surfaces may be adjusted. This automatic adjustment of surface position is +intended to correct only minor mismatches associated with mesh generation. You can review the surface +adjustments in the status (.sta) file, the message (.msg) file, and the output database (.odb) file; see +“Contact diagnostics in an Abaqus/Explicit analysis,” Section 38.2.1, for more information. +Some softened contact models have nonzero contact pressure at zero overclosure . For these models some initial, nonequilibrated +contact pressure may be present at the beginning of an analysis, as the adjustments are made to satisfy +zero overclosure rather than zero contact pressure. Large initial contact pressures may cause excessive +distortion of elements near the contact surfaces. +Conflicting adjustments from separate contact pairs will cause incomplete resolution of initial +overclosures and will lead to a noisy solution or severe distortion of elements. This can occur when a +slave node is pinched between two master surfaces. +Because of the lack of a unique outward direction from double-sided facets, the resolution of large +initial penetrations for double-sided surfaces can be difficult. Initial penetration will be detected only +when a slave node lies within the thickness of the underlying element, and the initial penetration will be +resolved by moving the slave node to the nearest free surface as shown in Figure 35.5.4–1. +corrected position +of slave node +original position +of slave node +master surface thickness +master node +Figure 35.5.4–1 Correction of initial overclosure for a contact +pair involving two double-sided surfaces. +A warning message will be issued to the status (.sta) file if two adjacent slave nodes (connected by a +facet edge) are detected on opposite sides of a double-sided master surface involved in contact defined +with the contact pair algorithm. No such warning will be issued for node-based surface nodes on opposite +sides of a double-sided master surface, because adjacency cannot be determined among the node-based +surface nodes. If the master surface is a single-sided surface, initial overclosures will be resolved using +the surface normal of the master surface, as shown in Figure 35.5.4–2. +Having slave nodes trapped on opposite sides of a double-sided master surface will often lead +to serious problems, which may not became apparent until later in an analysis. Therefore, a data +check analysis is +recommended prior to running a large contact pair analysis so that you can check for warning messages +side of surface (SPOS or SNEG) +used in single-sided contact +corrected position +of slave node +original position +of slave node +master surface thickness +master node +Figure 35.5.4–2 Correction of initial overclosure for a contact +pair involving a single-sided and a double-sided surface. +in the status file (.sta) and check for mislocated adjacent slave nodes on opposite sides of the master +surface. +The adjustments affect only the nodes on the surfaces. Excessive distortion of neighboring elements +may result if this feature is used to correct for gross errors in the initial geometry, causing the analysis +to end with an error message. +Nodes on a rigid body can act as slave nodes only for penalty contact pairs. Initial penetrations +of slave nodes that are part of a rigid body are not resolved with strain-free corrections; i.e., the slave +nodes are not adjusted. These penetrations are likely to cause artificially large contact forces in the first +increments of an analysis and should, therefore, be avoided in the mesh definition. +Adjustments of overclosed surfaces during subsequent steps in the simulation +If contact pairs are defined in later steps with initially overclosed surfaces, Abaqus/Explicit does not take +any special actions to gradually resolve these initial penetrations: contact forces will be applied according +to whatever contact constraint enforcement method is being used. These contact forces may be very large, +causing large accelerations and velocities and possible distortion of elements. Initial penetrations have +the potential to cause problems for contact pairs introduced in any step if a VUINTER user subroutine is +used; but in that case you control the application of contact forces. +Minimizing the noise associated with adjustments of initially overclosed surfaces +When a balanced master-slave contact pair is used for situations where the initial overclosure +adjustments are not very small, non-negligible errors may persist in the adjusted geometry and can +lead to a noisy oscillation (or “ringing”) in the contact procedure. This problem can sometimes be +mitigated by modifying the contact pair to be a pure master-slave relationship using a weighting +factor; see “Contact surface weighting” in “Contact formulations for contact pairs in Abaqus/Explicit,” +Section 37.2.2, for details. +Specifying initial clearance values precisely +You can define initial clearances and contact directions precisely for the nodes on the slave surface +when they would not be computed accurately enough from the nodal coordinates; for example, if +Initial clearances and contact +the initial clearance is very small compared to the coordinate values. +directions can be defined only in small-sliding contact analyses (“Contact formulations for contact pairs +in Abaqus/Explicit,” Section 37.2.2). +The initial clearance value calculated at every slave node based on the coordinates of the slave node +and the master surface is overwritten by the value that you specify. This procedure does not alter the +coordinates of the slave nodes. +When the balanced-master slave contact algorithm is invoked for the contact pair, the initial +clearance values can be defined on one or both of the surfaces. Initial clearances defined on contact +surfaces that act only as master surfaces will be ignored. +Specifying a uniform clearance for the surfaces +You can specify a uniform clearance for a contact pair by identifying the contact pair and the desired +initial clearance, +Input File Usage: +Abaqus/CAE Usage: +(the value must be positive). No other data are needed. +*CLEARANCE, CPSET=cpset_name, VALUE= +Interaction module: contact interaction editor: Clearance: Initial +clearance: Uniform value across slave surface: +Specifying spatially varying clearances for the surfaces +Alternatively, you can specify spatially varying clearances for a contact pair by identifying the contact +pair and a table of data specifying the clearance at a single node or a set of nodes belonging to the +slave surface. Any slave surface node that is not identified will use the clearance that Abaqus/Explicit +calculates from the initial geometry of the surfaces. +Input File Usage: +Abaqus/CAE Usage: +*CLEARANCE, CPSET=cpset_name, TABULAR +You cannot specify initial clearance or overclosure values using a table of data +in Abaqus/CAE. +Reading spatially varying clearances from an external file +Input File Usage: +Abaqus/Explicit can read the spatially varying clearances for a contact pair from an external file. +*CLEARANCE, CPSET=cpset_name, TABULAR, INPUT=file_name +You cannot specify initial clearance or overclosure values using an external +input file in Abaqus/CAE. +Abaqus/CAE Usage: +Specifying the surface normal for the contact calculations +Normally Abaqus/Explicit calculates the surface normal used for the contact calculations from the +geometry of the discretized surfaces, using the algorithms described in “Contact formulations for +contact pairs in Abaqus/Explicit,” Section 37.2.2. When specifying spatially varying clearances, you +can redefine the contact direction that Abaqus/Explicit uses with each slave node by specifying the +components of this vector. The vector must define the global Cartesian components of the outward +normal to the master surface. +Input File Usage: +*CLEARANCE, SLAVE=surface_name, MASTER=surface_name, +TABULAR +node number or node set label, clearance value, first normal component, +second normal component, third normal component +Repeat the data line as often as necessary. +Abaqus/CAE Usage: +You cannot redefine contact directions in Abaqus/CAE, except for thread bolt +connections . +Generating the contact normal directions for a thread bolt connection automatically +Alternatively, for a single-threaded bolt connection the contact normal directions for each slave node can +be generated automatically by specifying the thread geometry data and two points used to define a vector +on the axis of the bolt/bolt hole. The axis vector should be oriented to point from the tip of the bolt to +the head of the bolt when in tension and from the head to the tip when in compression. +Input File Usage: +Abaqus/CAE Usage: +*CLEARANCE, CPSET=cpset_name, TABULAR, BOLT +half-thread angle, pitch, major bolt diameter, mean bolt diameter +node number or node set label, clearance value, coordinates of +points a and b on the axis of the bolt/bolt hole +Repeat the second data line as often as necessary. +Interaction module: contact interaction editor: Clearance: Initial +clearance: Computed for single-threaded bolt or Specify for +single-threaded bolt: clearance value, +Clearance region on slave surface: Edit Region: select region, +Bolt direction vector: Edit: select axis, +Half-thread angle: half-thread angle, Pitch: pitch, +Bolt diameter: Major: major bolt diameter or Mean: mean bolt diameter +35.5.5 +CONTACT CONTROLS FOR CONTACT PAIRS IN Abaqus/Explicit +Products: Abaqus/Explicit Abaqus/CAE +References +• “Defining contact pairs in Abaqus/Explicit,” Section 35.5.1 +• *CONTACT CONTROLS +• “Specifying contact controls in an Abaqus/Explicit analysis,” Section 15.13.10 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +Contact controls for Abaqus/Explicit contact pairs can be used +• to scale the stiffness used by penalty contact constraints, and +• to adjust the search algorithms that track the motions between two surfaces. +Scaling default penalty stiffnesses +If you use the penalty method to enforce contact constraints in a contact pair , Abaqus/Explicit resists penetrations +between surfaces by applying a “spring” stiffness to penetrating nodes. The “spring” stiffness that +relates the contact force to the penetration distance is chosen automatically by Abaqus/Explicit, such +that the effect on the time increment is minimal yet the allowed penetration is not significant in most +analyses. Significant penetrations may develop in an analysis if any of the following factors are present: +• Displacement-controlled loading +• Materials at the contact interface that are purely elastic or stiffen with deformation +• Deformable elements (especially membrane and surface elements) that have relatively little mass of +their own and are constrained via methods other than boundary conditions (for example, connectors) +involved in contact +• Rigid bodies that have relatively little mass or rotary inertia of their own and are constrained via +methods other than boundary conditions (for example, connectors) involved in contact +See “The Hertz contact problem,” Section 1.1.11 of the Abaqus Benchmarks Manual, for an example in +which the first two of these factors combine such that the contact penetrations with the default penalty +stiffness are significant. +You can specify a scale factor by which to modify penalty stiffnesses for specified contact pairs. +This scaling may affect the automatic time incrementation. Use of a large scale factor is likely to +increase the computational time required for an analysis because of the reduction in the time increment +that is necessary to maintain numerical stability . +Input File Usage: +Use both of the following options to scale the default penalty stiffnesses: +Abaqus/CAE Usage: +*CONTACT PAIR, MECHANICAL CONSTRAINT=PENALTY, +CPSET=contact_pair_set_name +surface_1, surface_2 +*CONTACT CONTROLS, CPSET=contact_pair_set_name, +SCALE PENALTY=factor +Interaction module: +Create Contact Controls: Name: contact_controls_name, +Abaqus/Explicit contact controls: Penalty stiffness scaling +factor: factor +Interaction editor: Mechanical constraint formulation: Penalty contact +method, Contact controls: contact_controls_name +Adjusting the finite-sliding contact tracking algorithm +In a finite-sliding contact pair, searches are conducted continually throughout an analysis to track the +relative motion between the two contacting surfaces. The contact tracking algorithm consists of an +expensive, periodic global search and a less expensive, regular local search; the search algorithms +are discussed in detail in “Contact tracking algorithms” in “Contact formulations for contact pairs in +Abaqus/Explicit,” Section 37.2.2. You can use contact controls to adjust the frequency and cost of these +searches. +Specifying more frequent global contact searches +By default for two-surface contact pairs, Abaqus/Explicit performs a more thorough search of the master +faces near each slave node every one hundred increments, which is sufficient for most analyses. However, +there are some valid contact situations where a global search needs to be used more or less often during +the step. Figure 35.5.5–1 illustrates a situation that might require more frequent global tracking. The +master surface is a valid surface, but it contains a hole. The slave node shown identifies the shaded +element facet as the closest master surface facet during an increment. The local contact search looks at +this master surface facet and its neighbors. +If the slave node displaces across the hole in relatively few increments, the potential contact between +the slave node and the master surface facets across the hole will not be detected because the local contact +search will still be checking the shaded facet. This same situation can occur when a slave node moves +rapidly across a deep valley in the master surface. The solution to this problem is to conduct global +contact searches more frequently. You can specify the number of increments between global searches, +n, for a given contact pair, if a value other than the default of 100 is desired. +Input File Usage: +Use both of the following options: +*CONTACT PAIR, CPSET=contact_pair_set_name +*CONTACT CONTROLS, CPSET=contact_pair_set_name, +GLOBTRKINC=n +master surface +slave node +previous nearest +master face +trajectory of slave node +Figure 35.5.5–1 Example where local search may fail. +Abaqus/CAE Usage: +Interaction module: +Create Contact Controls: Name: contact_controls_name, +Abaqus/Explicit contact controls: Specify max number of +increments: n +Interaction editor: Contact controls: contact_controls_name +Using a more conservative local contact search +The default local contact search used by Abaqus/Explicit uses techniques that allow it to use a minimum +amount of computational time. +If the local contact search has difficulty enforcing the appropriate +contact conditions, a more conservative local contact search may resolve the problem. The contact +search specified has no effect on contact pairs using self-contact. +Input File Usage: +Use both of the following options: +*CONTACT PAIR, CPSET=contact_pair_set_name +*CONTACT CONTROLS, CPSET=contact_pair_set_name, +FASTLOCALTRK=NO +Abaqus/CAE Usage: +Interaction module: +Create Contact Controls: Name: contact_controls_name, +Abaqus/Explicit contact controls: toggle off Fast local tracking +Interaction editor: Contact controls: contact_controls_name +Tracking contact with highly warped surfaces +Calculating the correct contact conditions along a surface that is highly warped is very difficult, especially +when the relative velocity of the contacting surfaces is very large. By default, Abaqus/Explicit monitors +the orientation of every deformable master surface formed by element faces every 20 increments to +check that the surface is not highly warped; rigid faceted surfaces are checked for large warping only +at the beginning of a step. If a surface becomes highly warped, a warning message is issued in the +status (.sta) file , and a more +accurate algorithm is used to calculate each slave node’s nearest point on the warped master surface. The +alternate algorithm provides a more accurate solution but uses slightly more computational time. +Redefining the criteria for a highly warped surface +By default, Abaqus/Explicit considers a surface to be highly warped when the angle between surface +normals at the nodes of a facet varies by more than 20°. The maximum variation of the surface normal +over a facet is called the out-of-plane warping angle. You can change the default value of the out-of-plane +warping angle cutoff from step to step for any contact pair in the model. +Input File Usage: +*CONTACT CONTROLS, CPSET=contact_pair_set_name, +WARP CUT OFF=angle +Abaqus/CAE Usage: +Interaction module: +Create Contact Controls: Name: contact_controls_name, +Abaqus/Explicit contact controls: Angle criteria for highly +warped facet (degrees): angle +Interaction editor: Contact controls: contact_controls_name +Modifying how frequently Abaqus/Explicit checks for warped surfaces +You can specify the frequency, in increments, at which Abaqus/Explicit checks for warped surfaces for +any contact pair in the model. The frequency can be changed from step to step. Checking for warped +surfaces more frequently (the default is every 20 increments) will cause a slight increase in computational +time for the analysis. +Input File Usage: +*CONTACT CONTROLS, CPSET=contact_pair_set_name, +WARP CHECK PERIOD=n +Abaqus/CAE Usage: +Interaction module: +Create Contact Controls: Name: contact_controls_name, +Abaqus/Explicit contact controls: Warp check increment: n +Interaction editor: Contact controls: contact_controls_name +36. +Contact Property Models +Mechanical contact properties +Thermal contact properties +Electrical contact properties +Pore fluid contact properties +36.1 +36.2 +36.3 +36.1 +Mechanical contact properties +• “Mechanical contact properties: overview,” Section 36.1.1 +• “Contact pressure-overclosure relationships,” Section 36.1.2 +• “Contact damping,” Section 36.1.3 +• “Contact blockage,” Section 36.1.4 +• “Frictional behavior,” Section 36.1.5 +• “User-defined interfacial constitutive behavior,” Section 36.1.6 +• “Pressure penetration loading,” Section 36.1.7 +• “Interaction of debonded surfaces,” Section 36.1.8 +• “Breakable bonds,” Section 36.1.9 +• “Surface-based cohesive behavior,” Section 36.1.10 +36.1.1 +MECHANICAL CONTACT PROPERTIES: OVERVIEW +References +• “Contact interaction analysis: overview,” Section 35.1.1 +• “Defining contact pairs in Abaqus/Standard,” Section 35.3.1 +• “Assigning contact properties for general contact in Abaqus/Explicit,” Section 35.4.3 +• “Assigning contact properties for contact pairs in Abaqus/Explicit,” Section 35.5.3 +• “Contact pressure-overclosure relationships,” Section 36.1.2 +• “Contact damping,” Section 36.1.3 +• “Contact blockage,” Section 36.1.4 +• “Frictional behavior,” Section 36.1.5 +• “User-defined interfacial constitutive behavior,” Section 36.1.6 +• “Pressure penetration loading,” Section 36.1.7 +• “Interaction of debonded surfaces,” Section 36.1.8 +• “Breakable bonds,” Section 36.1.9 +• “Surface-based cohesive behavior,” Section 36.1.10 +• *SURFACE INTERACTION +• “Understanding interaction properties,” Section 15.4 of the Abaqus/CAE User’s Manual +Overview +In a mechanical contact simulation the interaction between contacting bodies is defined by assigning +a contact property model to a contact interaction . +Mechanical contact property models: +• may include a constitutive model for the contact pressure-overclosure relationship that governs the +motion of the surfaces; +• may include a damping model that defines forces resisting the relative motions of the contacting +surfaces; +• may include a friction model that defines the force resisting the relative tangential motion of the +surfaces; +• may include a constitutive model in which you define the normal and tangential behavior in user +subroutine UINTER in Abaqus/Standard; +• may include a constitutive model in which you define the normal and tangential behavior in user +subroutine VUINTER in Abaqus/Explicit when using the contact pair algorithm; +• may include a constitutive model in which you define the normal and tangential behavior in user +subroutine VUINTERACTION in Abaqus/Explicit when using the general contact algorithm; +• in Abaqus/Standard may include a constitutive model for the penetration of fluid between two +contacting surfaces; +• in Abaqus/Standard may include a constitutive model for the interaction of debonded surfaces; +• in Abaqus/Explicit may include a constitutive model that simulates the failure of bonds connecting +the interacting bodies; and +• may include surface-based cohesive behavior that allows modeling of delamination of bonds or +“sticky” contact using progressive damage evolution models. +This section provides a general outline of how to define the components of a mechanical contact property +model. Specific details about the different components of the contact property models and the algorithms +used for the contact calculations are found in other sections of this chapter. +Defining the contact property model +There are different methods for defining the components of a mechanical contact property model. +Defining the contact pressure-overclosure relationship +The default contact pressure-overclosure relationship used by Abaqus is referred to as the “hard” contact +model. Hard contact implies that: +• the surfaces transmit no contact pressure unless the nodes of the slave surface contact the master +surface; +• no penetration is allowed at each constraint location (depending on the constraint enforcement +method used, this condition will either be strictly satisfied or approximated); +• there is no limit to the magnitude of contact pressure that can be transmitted when the surfaces are +in contact. +You can define a nondefault pressure-overclosure relationship for a surface interaction. The various +pressure-overclosure relationships available in Abaqus are discussed in “Contact pressure-overclosure +relationships,” Section 36.1.2, and the constraint methods available to enforce these relationships are +discussed in “Contact constraint enforcement methods in Abaqus/Standard,” Section 37.1.2. +Defining a surface interaction model with damping between the surfaces +You can define damping forces to oppose the relative motion between the interacting surfaces. +In Abaqus/Standard the specified contact damping affects the motion in the normal direction only, +whereas in Abaqus/Explicit contact damping can affect both the relative tangential motion and the motion +normal to the surfaces. +The details of the contact damping model are discussed in “Contact damping,” Section 36.1.3. +Defining contact blockage in Abaqus/Explicit +In Abaqus/Explicit you can control the combination of surfaces that can cause blockage of flow out +of a surface-based fluid cavity. The details of contact blockage are discussed in “Contact blockage,” +Section 36.1.4. +Defining a friction model +By default, Abaqus assumes that contact between surfaces is frictionless. You can include a friction +model as part of a surface interaction definition. +Details of the various friction models available in Abaqus are discussed in “Frictional behavior,��� +Section 36.1.5. +User-defined interfacial constitutive behavior +Instead of choosing one or some combination of the various interfacial behavior models that are available +in Abaqus, you can define any special or proprietary interfacial constitutive behavior through a user +subroutine. In Abaqus/Standard you can use the subroutine UINTER; whereas in Abaqus/Explicit you +can use VUINTER if you are using the contact pair algorithm and VUINTERACTION if you are using +the general contact algorithm. +In Abaqus/Explicit a penalty enforcement of the contact constraint must be used for interacting +surfaces whose interfacial behavior is governed by VUINTER or VUINTERACTION. +Details of the definition of a user-defined interfacial constitutive behavior are discussed in “User- +defined interfacial constitutive behavior,” Section 36.1.6. +Defining a pressure penetration load in Abaqus/Standard +You can define pressure penetration loads to simulate the penetration of fluid between two contacting +surfaces in Abaqus/Standard. The details of the pressure penetration model are discussed in “Pressure +penetration loading,” Section 36.1.7. +Defining the interaction of debonded surfaces in Abaqus/Standard +You can allow two initially bonded surfaces to debond in Abaqus/Standard, as discussed in “Crack +propagation analysis,” Section 11.4.3. The details of the contact interaction model after debonding are +discussed in “Interaction of debonded surfaces,” Section 36.1.8. +Defining breakable bonds in Abaqus/Explicit +In Abaqus/Explicit you can define breakable bonds that connect the interacting surfaces. The kinematic +contact pair algorithm must be used when defining breakable bonds. +The breakable bonds affect both the relative tangential motion and the motion normal to the surfaces. +Breakable bonds cannot be used with analytical rigid surfaces. The details of the breakable bond model, +known as the spot weld model, are discussed in “Breakable bonds,” Section 36.1.9. +Defining surface-based cohesive behavior +You can define surface-based cohesive behavior to model delamination of initially bonded surfaces or to +model “sticky” contact between parts that are initially separated but bond on coming into contact, with +the possibility that the bond may undergo progressive damage and fail. +Surface-based cohesive behavior +framework in +Abaqus/Explicit and within the contact pair framework in Abaqus/Standard. The details of the +surface-based cohesive behavior model are discussed in “Surface-based cohesive behavior,” +Section 36.1.10. +is modeled within the general contact +CONTACT PRESSURE-OVERCLOSURE RELATIONSHIPS +CONTACT PRESSURE-OVERCLOSURE +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Mechanical contact properties: overview,” Section 36.1.1 +• *CONTACT CONTROLS +• *SURFACE BEHAVIOR +• “Creating interaction properties,” Section 15.12.2 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Customizing contact controls,” Section 15.12.3 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +In Abaqus the following contact pressure-overclosure relationships can be used to define the contact +model: +• the “hard” contact relationship minimizes the penetration of the slave surface into the master surface +at the constraint locations and does not allow the transfer of tensile stress across the interface; +• a “softened” contact relationship in which the contact pressure is a linear function of the clearance +between the surfaces; +• a “softened” contact relationship in which the contact pressure is an exponential function of the +clearance between the surfaces (in Abaqus/Explicit this relationship is available only for the contact +pair algorithm); +• a “softened” contact relationship in which a tabular pressure-overclosure curve is constructed +by progressively scaling the default penalty stiffness (available only for general contact in +Abaqus/Explicit); +• a “softened” contact relationship in which the contact pressure is a piecewise linear (tabular) +function of the clearance between the surfaces; and +• a relationship in which there is no separation of the surfaces once they contact. +In addition, a viscous damping relationship can be defined that will affect the pressure-overclosure +relationship; see “Contact damping,” Section 36.1.3, for more information. +In Abaqus/Standard +pressure penetration loads can be applied to model fluid penetrating into the surface between two +contacting bodies; see “Pressure penetration loading,” Section 36.1.7. +Including a contact pressure-overclosure relationship in a contact property definition +By default, a “hard” contact pressure-overclosure relationship is used for both surface-based contact +and element-based contact. You can include a nondefault contact pressure-overclosure relationship in a +specific contact property definition. +Input File Usage: +Abaqus/CAE Usage: +the +Use both of the following options for surface-based contact: +*SURFACE INTERACTION, NAME=interaction_property_name +*SURFACE BEHAVIOR +Use both of +Abaqus/Standard: +*INTERFACE or *GAP, ELSET=name +*SURFACE BEHAVIOR +Interaction module: contact property editor: Mechanical→Normal +Behavior: Constraint enforcement method: Default +following options +for +element-based contact +in +Element-based contact is not supported in Abaqus/CAE. +Using the “hard” contact relationship +The most common contact pressure-overclosure relationship is shown in Figure 36.1.2–1, although +the zero-penetration condition may or may not be strictly enforced depending on the constraint +enforcement method used (the constraint enforcement methods are discussed in “Contact constraint +enforcement methods in Abaqus/Standard,” Section 37.1.2, and “Contact constraint enforcement +methods in Abaqus/Explicit,” Section 37.2.3). When surfaces are in contact, any contact pressure can +be transmitted between them. The surfaces separate if the contact pressure reduces to zero. Separated +surfaces come into contact when the clearance between them reduces to zero. +Input File Usage: +*SURFACE BEHAVIOR (omit +parameter to obtain the default “hard” pressure-overclosure relationship) +the PRESSURE-OVERCLOSURE +Abaqus/CAE Usage: +Interaction module: contact property editor: Mechanical→Normal +Behavior: Constraint enforcement method: Default: +Pressure-Overclosure: Hard Contact +Using a “softened” contact relationship +Three types of “softened” contact relationships are available in Abaqus. The pressure-overclosure +relationship can be prescribed by using a linear law, a tabular piecewise-linear law, or an exponential +law (in Abaqus/Explicit available only with the contact pair algorithm). +For contact involving element-based surfaces and for element-based contact (available only +in Abaqus/Standard), the “softened” contact relationships are specified in terms of overclosure (or +clearance) versus contact pressure. For contact involving a node-based surface or nodal contact +elements (such as GAP and ITT elements) for which an area or length dimension is not defined, softened +contact is specified in terms of overclosure (or clearance) versus contact force. For slave surfaces on +Contact +pressure +Any pressure possible when in contact +No pressure when no contact +Clearance +Figure 36.1.2–1 Default pressure-overclosure relationship. +beam-type elements in Abaqus/Standard and for the contact pair algorithm in Abaqus/Explicit, specify +pressure as force per unit length. If the general contact algorithm in Abaqus/Explicit is being used for +slave surfaces on beam-type elements, specify pressure as force per unit area. +When using softened contact relationships that have nonzero pressure at zero overclosure (not +allowed with the general contact algorithm) in Abaqus/Explicit, you should be aware that initial, +nonequilibrated contact pressures may be present in the analysis . +“Softened” contact versus “hard” contact +The “softened” contact pressure-overclosure relationships might be used to model a soft, thin layer on +one or both surfaces. In Abaqus/Standard they are also sometimes useful for numerical reasons because +they can make it easier to resolve the contact condition. +Using “softened” contact in implicit dynamic simulations +Use the softened contact relationship with caution in implicit dynamic impact simulations. +If this +relationship is used in such a simulation, Abaqus/Standard will not use the impact algorithm, which +destroys kinetic energy of the nodes on the surface when impact occurs, but will instead assume +a perfectly elastic collision. The consequence of this change is that the slave nodes bounce back +immediately after impact with the master surface; hence, extensive “chattering” may result, leading to +convergence problems and small time increments. +However, softened contact may work well in implicit dynamic calculations where impact effects +are not important; for example, if contact changes are primarily due to sliding motion along a curved +surface, such as may occur in low-speed metal forming applications. +Using “softened” contact in explicit dynamic simulations +In Abaqus/Explicit softened contact can be enforced with either the kinematic or the penalty constraint +enforcement method . With penalty enforcement the contact collisions are elastic except for the influence of contact +damping, whereas with softened kinematic contact some energy will be absorbed by the impact because +of algorithmic characteristics: the energy absorbed tends to increase as the contact stiffness increases. +Another consideration is the effect on the time increment: with kinematic enforcement the stable time +increment is independent of the contact stiffness, but with penalty contact the time increment decreases +as the contact stiffness increases. +“Softened” contact defined as a linear function +In a linear pressure-overclosure relationship the surfaces transmit contact pressure when the overclosure +between them, measured in the contact (normal) direction, is greater than zero. The linear pressure- +overclosure relationship is identical to a tabular relationship with two data points, where the first point +is located at the origin. +You specify the slope of the pressure-overclosure relationship, k. +Input File Usage: +Abaqus/CAE Usage: +*SURFACE BEHAVIOR, PRESSURE-OVERCLOSURE=LINEAR +Interaction module: contact property editor: Mechanical→Normal +Behavior: Constraint enforcement method: Default: +Pressure-Overclosure: Linear, Contact stiffness: k +“Softened” contact defined in tabular form +form, as shown in +To define a piecewise-linear pressure-overclosure relationship in tabular +Figure 36.1.2–2, you specify data pairs ( +) of pressure versus overclosure (where overclosure +corresponds to negative clearance). You must specify the data as an increasing function of pressure and +overclosure. In this relationship the surfaces transmit contact pressure when the overclosure between +them, measured in the contact (normal) direction, is greater than +is the overclosure at +zero pressure. For the general contact algorithm in Abaqus/Explicit +must be zero. For overclosures +greater than +the pressure-overclosure relationship is extrapolated based on the last slope computed +from the user-specified data . +, where +, +Input File Usage: +Abaqus/CAE Usage: +*SURFACE BEHAVIOR, PRESSURE-OVERCLOSURE=TABULAR +Interaction module: contact property editor: Mechanical→Normal +Behavior: Constraint enforcement method: Default: +Pressure-Overclosure: Tabular +“Softened” contact defined as a geometric scaling of the default contact stiffness +An alternative piecewise linear tabular pressure-overclosure relationship can be constructed by +geometrically scaling the default contact stiffness. This model provides a simple interface to increase +the default contact stiffness when a critical penetration is exceeded. A penetration measure, +, is +Pressure p +(pn,hn) +(p3,h3) +(p2,h2) +(0,h1) +Clearance c +Overclosure h +Figure 36.1.2–2 “Softened” pressure-overclosure relationship defined in tabular form. +defined either directly or as a fraction, +, in the contact region. +Each time the current penetration exceeds a multiple of this penetration measure, the contact stiffness +is scaled by a factor, +. The initial stiffness is set equal to the default contact +stiffness, +, of the minimum element length, +, multiplied by a factor, +. +Pressure +dflt +elem += segment number += default stiffness += element length += initial scale factor += geometric scale factor += overclosure factor += r L = overclosure measure +elem +segment i +Ki = s0 k dflt si-1 +1 +0 +(i -1) d +i d +Overclosure +Figure 36.1.2–3 “Softened” scale factor pressure-overclosure relationship. +This option is available only for the general contact algorithm in Abaqus/Explicit. +Input File Usage: +Abaqus/CAE Usage: +*SURFACE BEHAVIOR, PRESSURE-OVERCLOSURE=SCALE FACTOR +Interaction module: contact property editor: Mechanical→Normal Behavior: +Constraint enforcement method: Default: Pressure-Overclosure: +Scale Factor (General Contact) +“Softened” contact defined with an exponential law +In an exponential (soft) contact pressure-overclosure relationship the surfaces begin to transmit contact +pressure once the clearance between them, measured in the contact (normal) direction, reduces to +. +The contact pressure transmitted between the surfaces then increases exponentially as the clearance +continues to diminish. Figure 36.1.2–4 illustrates this behavior in Abaqus/Standard. In Abaqus/Explicit +this behavior is available only for the contact pair algorithm. +Contact +pressure +Exponential pressure-overclosure relationship +p 0 +Clearance +c 0 +Figure 36.1.2–4 Exponential “softened” pressure-overclosure relationship in Abaqus/Standard. +In Abaqus/Explicit you can specify an optional limit on the contact stiffness that the model can attain, +; this limit is useful for penalty contact to mitigate the effect that large +will be set to infinity for +stiffnesses have on reducing the stable time increment. By default, +kinematic contact and to the default penalty stiffness for penalty contact. +You specify +; the contact pressure at zero clearance, +; and, optionally in Abaqus/Explicit, +. +Input File Usage: +*SURFACE BEHAVIOR, PRESSURE-OVERCLOSURE=EXPONENTIAL +, +, +Interaction module: contact property editor: Mechanical→Normal Behavior: +Constraint enforcement method: Default: Pressure-Overclosure: +Exponential, Pressure +, Clearance +, Specify: +36.1.2–6 +Contact +pressure +Kmax +Exponential pressure-overclosure relationship +p0 +Clearance +c0 +Overclosure +Figure 36.1.2–5 Exponential “softened” pressure-overclosure relationship in Abaqus/Explicit. +Using the no separation relationship +You can indicate that Abaqus should use the contact pressure-overclosure relationship that prevents +surfaces from separating once they have come into contact. In Abaqus/Explicit this relationship can +be specified only for pure master-slave contact pairs and cannot be used with adaptive meshing or with +the general contact algorithm. +The no separation relationship is often used with the rough friction model to model nonintermittent, rough frictional contact. Using this combination of surface +interaction models causes surfaces to remain fully bonded together (no separation and no tangential +sliding) once they contact, even if the contact pressure between them is tensile. +Input File Usage: +Abaqus/CAE Usage: +*SURFACE BEHAVIOR, NO SEPARATION +Interaction module: contact property editor: Mechanical→Normal Behavior: +Constraint enforcement method: Default: Pressure-Overclosure: +Hard, toggle off Allow separation after contact +“Softened” contact with the no separation relationship in Abaqus/Explicit +In Abaqus/Explicit if a softened contact relationship is specified with the no separation relationship, the +pressure-overclosure relationship will include tensile behavior. The exponential relationship cannot be +used with no separation behavior. For the tabular relationship, a point must be specified on the zero +pressure axis, and the slope will continue into the tensile regime following the same slope as the first two +data points . The linear relationship will have a linear tensile pressure-overclosure +relationship with the same slope that is used for the compressive behavior. +pressure p +(compressive) +(pn,hn) +clearance c +(0,hi) +overclosure h +(p2,h2) +(p1,h1) +(tensile) +Figure 36.1.2–6 Piecewise linear “softened” pressure-overclosure +relationship with tensile behavior in Abaqus/Explicit. +Surface interaction output variables related to the contact pressure-overclosure +Abaqus/Standard provides both the clearance, COPEN, and the contact pressure, CPRESS, as output to +the data, results, and output database files. Output to these files is requested as described in “Output to +the data and results files,” Section 4.1.2, and “Output to the output database,” Section 4.1.3. +Abaqus/Explicit provides the contact pressure, CPRESS, as output to the output database file . +In the data, results, and output database files the output variable CPRESS gives the viscous damping +pressures for an open slave node. This variable also gives the contact pressure for a closed slave node. +In printed output a “VD” status indicates that the forces are for viscous damping. +Contours of the contact pressure on the slave surface can be plotted in Abaqus/CAE. +36.1.3 +CONTACT DAMPING +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Mechanical contact properties: overview,” Section 36.1.1 +• *CONTACT DAMPING +• “Creating interaction properties,” Section 15.12.2 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +Contact damping: +• can be defined to oppose the relative motion between the interacting surfaces (in addition +to the contact pressure-overclosure relationships discussed in “Contact pressure-overclosure +relationships,” Section 36.1.2, and the friction models discussed in “Frictional behavior,” +Section 36.1.5); +• can affect both the motion normal and tangential to the surfaces; +• in the normal direction is proportional to the relative velocity between the surfaces; +• in the tangential direction is proportional to the relative tangential velocity in Abaqus/Standard and +to the “elastic slip rate” associated with friction in Abaqus/Explicit—hence, in Abaqus/Explicit it does not resist the bulk +of tangential sliding; +• is not applicable for linear perturbation procedures; +• in Abaqus/Standard it contributes to the force and stiffness definition and should generally be used +only when it is otherwise impossible to obtain a solution—the best method for allowing a viscous +pressure and shear stress to be transmitted between the contact surfaces in Abaqus/Standard to +reduce convergence difficulties due to the sudden violation of contact constraints (common in some +snap-through and buckling problems involving contact) is to specify the damping on a step-by-step +basis using contact controls, as discussed in “Automatic stabilization of rigid body motions in +contact problems” in “Adjusting contact controls in Abaqus/Standard,” Section 35.3.6; and +• can be useful in Abaqus/Explicit to reduce solution noise—a small amount of viscous contact +damping is used by default for softened contact and penalty contact in Abaqus/Explicit, as +discussed below. +Defining viscous contact damping for relative motions of surfaces +In Abaqus/Standard the damping coefficient, +is a function of surface clearance, as shown in +, +Figure 36.1.3–1. The damping coefficient is defined as a proportionality constant with units of pressure +divided by velocity. +Damping +coefficient +Clearance +co +co +Figure 36.1.3–1 Damping coefficient-clearance relationship for viscous damping in Abaqus/Standard. +In Abaqus/Explicit the damping coefficient will remain at the specified constant value while the +surfaces are in contact and at zero otherwise. The damping coefficient can be defined as a proportionality +constant with units of pressure divided by velocity or as a unitless fraction of critical damping. +To define viscous damping, you must include it in a contact property definition. +Input File Usage: +Use both of the following options for surface-based contact: +*SURFACE INTERACTION, NAME=interaction_property_name +*CONTACT DAMPING +Use both of +Abaqus/Standard: +following options +the +for +element-based contact +in +Abaqus/CAE Usage: +*INTERFACE or *GAP, ELSET=name +*CONTACT DAMPING +Interaction module: contact property editor: Mechanical→Damping +Element-based contact is not supported in Abaqus/CAE. +Damping and pressure-overclosure relationships +In Abaqus/Standard the viscous damping relationship can be used with any contact relationship . +In Abaqus/Explicit contact damping is not available for hard kinematic contact. Softened kinematic +contact and all penalty contact will have default damping in the form of a critical damping fraction with += 0.03. +Specifying the damping coefficient such that the damping force is directly proportional to the +rate of relative motion between the surfaces +You can specify damping directly in terms of the damping coefficient with units of pressure per velocity +such that the damping forces will be calculated with +is the rate of relative motion between the two surfaces. +, where A is the nodal area and +For contact involving element-based surfaces and for element-based contact (available only +in Abaqus/Standard), the damping coefficient is specified in terms of contact pressure. For contact +involving a node-based surface or nodal contact elements (such as GAP elements and ITT elements) for +which an area or length dimension has not been defined, +must be specified as force per velocity. For +slave surfaces on beam-type elements, specify +as force per unit length per velocity. +Input File Usage: +Use the following syntax in Abaqus/Standard: +*CONTACT DAMPING, DEFINITION=DAMPING COEFFICIENT +, +, +Use the following syntax in Abaqus/Explicit: +*CONTACT DAMPING, DEFINITION=DAMPING COEFFICIENT +Abaqus/CAE Usage: +Use the following syntax in Abaqus/Standard: +Interaction module: contact property editor: Mechanical→Damping: +Definition: Damping coefficient, Linear or Bilinear, Damping Coeff. +, Clearance c and +( =0 for Linear and +for Bilinear) +Use the following syntax in Abaqus/Explicit: +Interaction module: contact property editor: Mechanical→Damping: +Definition: Damping coefficient, Step, Damping Coeff. +Specifying the damping coefficient as a fraction of critical damping in Abaqus/Explicit +In Abaqus/Explicit you can specify a unitless damping coefficient in terms of the fraction of critical +damping associated with the contact stiffness; this method is not available in Abaqus/Standard. The +damping forces will be calculated with +is the nodal +contact stiffness (in units of +is the rate of relative motion between the two surfaces. +, where m is the nodal mass, +), and +Input File Usage: +*CONTACT DAMPING, DEFINITION=CRITICAL DAMPING FRACTION +critical damping fraction +Abaqus/CAE Usage: +Interaction module: contact property editor: Mechanical→Damping: +Definition: Critical damping fraction, Crit. Damping +Fraction critical damping fraction +Specifying the tangential damping coefficient +You can specify the ratio of the tangential damping coefficient to the normal damping coefficient, also +called the tangent fraction. +The tangential damping uses the same form of damping as the normal damping. Tangential +If tangential damping is +damping can be specified only in conjunction with normal damping. +activated in Abaqus/Standard, the damping stress is proportional to the relative tangential velocity. In +Abaqus/Explicit tangential damping will be ignored if hard kinematic contact is used in the tangential +direction or if friction is not defined. As stated previously, damping in the tangential direction in +Abaqus/Explicit is proportional to the elastic slip rate rather +than the total rate of relative sliding. +For Abaqus/Standard the default value for the tangent fraction is 0.0; therefore, by default, the +damping coefficient for the tangential direction is zero. For Abaqus/Explicit the default value for the +tangent fraction is 1.0; therefore, by default, the damping coefficient for the tangential direction is equal +to the damping coefficient for the normal direction. Furthermore, in Abaqus/Explicit softened contact +and hard penalty contact have a default critical damping fraction of 0.03. +Input File Usage: +Abaqus/CAE Usage: +*CONTACT DAMPING, TANGENT FRACTION=value +Interaction module: contact property editor: Mechanical→Damping: +Tangent fraction: Specify value: value +Choosing the appropriate coefficients for viscous damping in Abaqus/Standard +In Abaqus/Standard the appropriate magnitude for the local contact damping factor, +, is problem- +dependent. In some cases a simple calculation can be used to determine the magnitude; in other cases a +reasonable value for must be determined by trial and error. A reasonable value is one that has minimal +impact on the solution prior to the unstable behavior in the model. A preliminary value can be found by +looking at the contact pressures and velocities in the model before damping is added, as described below. +It may be difficult to determine the nodal velocities prior to the unstable behavior if output was +not requested frequently. In such a situation the information in the message (.msg) file can be used to +estimate the peak nodal velocity. By default, Abaqus/Standard provides the peak nodal displacement +increment at every converged increment in this file. This displacement increment can be used along with +the time increment to calculate a peak nodal velocity for the model. Although this velocity may not be +very close to the actual relative velocity of the surfaces, it should be within an order of magnitude and is +a reasonable value to use in calculating an initial viscous damping coefficient. +The maximum contact pressure between the surfaces also needs to be estimated. The viscous +damping coefficient should then be set to a value that is a few orders of magnitude less than the ratio of +the estimated maximum contact pressure over the calculated nodal velocity. +If it is not feasible to obtain the pressure and velocities as discussed above, a high damping value +should be used initially and repeated analyses should be performed with smaller and smaller values. An +appropriate value for +is one that is large enough to enable the analysis to get past any unstable response +but not so large that the results at earlier or later times are affected significantly. “Snap-through buckling +analysis of circular arches,” Section 1.2.1 of the Abaqus Example Problems Manual, demonstrates how +the magnitude of the damping coefficient can be determined using the methods explained above. +The following example outlines how the value might be chosen for a typical case. Consider a simple +modification to the two-dimensional Euler column buckling problem: add rigid surfaces parallel and on +either side of the column so that the beam will contact the surfaces when it buckles. As the axial load is +of contact will lift off the surface and the beam will buckle into a higher mode. Figure 36.1.3–2 shows +this shape. +CONTACT DAMPING +Figure 36.1.3–2 Constrained Euler buckling example for viscous damping. +When the column first buckles, the contact force, F, that the column exerts on one of the rigid +surfaces can be approximated as +where h is the separation distance between the rigid surfaces, l is the beam length, P is the applied load, +and +is the buckling load. +The approximation of the contact force entails the assumption that a single point comes into contact +and that the shape of the buckled column does not change. The units of +are contact force per velocity, +assuming that a node-based surface is used in this model. The velocity of the column, v, at the point of +contact can be approximated as +where +value for the damping coefficient: +is the time increment. These estimates for the contact force and the column velocity give a +This value can be used as a starting value, but different values should be tested. +36.1.4 +CONTACT BLOCKAGE +Product: Abaqus/Explicit +References +• “Mechanical contact properties: overview,” Section 36.1.1 +• “Surface-based fluid cavities: overview,” Section 11.5.1 +• “Fluid exchange definition,” Section 11.5.3 +• *BLOCKAGE +• *FLUID EXCHANGE ACTIVATION +• *SURFACE INTERACTION +Overview +The blockage of flow out of a cavity due to an obstruction caused by contacting surfaces: +• can be defined selectively for particular surfaces that may fully or partially cause the blockage; and +• can be accounted for only when the surfaces are used with the general contact algorithm. +Surfaces used to account for contact blockage +To consider an obstruction by contacting surfaces as discussed in “Accounting for blockage due to +contacting boundary surfaces” in “Fluid exchange definition,” Section 11.5.3, you must define a surface +to represent the leakage area on the boundary of the fluid cavity. In addition, you must specify that the +contacting surfaces can potentially cause blockage. All the surfaces (the surface on the boundary of the +fluid cavity and the contacting surfaces) must be included in a general contact domain. To account for +contact blockage, the nodes on the surfaces must be in node-to-face contact. When the nodes on the +surface on the boundary of the fluid cavity come into contact with the contacting surfaces, the slave +nodes are marked as active nodes for contact blockage. The contact blockage is also considered in the +edge-to-edge contact . +Input File Usage: +Use the following options to specify that two contacting surfaces can cause +blockage: +*CONTACT PROPERTY ASSIGNMENT +surface_1, surface_2, property_name +*SURFACE INTERACTION, NAME=property_name +*BLOCKAGE +Determining the obstruction area +Abaqus/Explicit determines the obstruction area by calculating the area fraction of the surface on the +boundary of the fluid cavity that is not blocked by contacting surfaces. For each element face of this +surface representing the leakage area, the blocked area is calculated based on the active nodes for contact +blockage. The element blocked area is determined by +is the element area, +is the element blocked area, +is the total number of element nodes, +where +and +is the total number of active nodes for contact blockage in the element. The element is fully +blocked by the contacting surfaces when all element nodes are active for contact blockage. The total +obstruction area is the sum of all the element blocked areas. The leakage area used in the fluid exchange +calculation is obtained by subtracting the total obstruction area from the total area of the surface if the +effective area is not specified for the fluid exchange. If both the effective area and a surface are specified +, the leakage area used in the fluid exchange calculation +is obtained by using the ratio of the total obstruction area to the total area of the surface multiplied by the +effective area. In this case a node-based surface can be used, and the leakage area is obtained by using +the ratio of the total active contact blockage nodes to the total number of nodes defined in the surface. +36.1.5 +FRICTIONAL BEHAVIOR +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Mechanical contact properties: overview,” Section 36.1.1 +• “FRIC,” Section 1.1.8 of the Abaqus User Subroutines Reference Manual +• “FRIC_COEF,” Section 1.1.9 of the Abaqus User Subroutines Reference Manual +• “VFRIC,” Section 1.2.4 of the Abaqus User Subroutines Reference Manual +• “VFRIC_COEF,” Section 1.2.5 of the Abaqus User Subroutines Reference Manual +• “VFRICTION,” Section 1.2.6 of the Abaqus User Subroutines Reference Manual +• *FRICTION +• *CHANGE FRICTION +• “Creating interaction properties,” Section 15.12.2 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +When surfaces are in contact they usually transmit shear as well as normal forces across their interface. +There is generally a relationship between these two force components. The relationship, known as the +friction between the contacting bodies, is usually expressed in terms of the stresses at the interface of the +bodies. The friction models available in Abaqus: +• include the classical isotropic Coulomb friction model , which in Abaqus: +– in its general form allows the friction coefficient to be defined in terms of slip rate, contact +pressure, average surface temperature at the contact point, and field variables; and +– provides the option for you to define a static and a kinetic friction coefficient with a smooth +transition zone defined by an exponential curve; +• allow the introduction of a shear stress limit, +, which is the maximum value of shear stress that +can be carried by the interface before the surfaces begin to slide; +• include an anisotropic extension of the basic Coulomb friction model in Abaqus/Standard; +• include a model that eliminates frictional slip when surfaces are in contact; +• include a “softened” interface model for sticking friction in Abaqus/Explicit in which the shear +stress is a function of elastic slip; +• can be implemented with a stiffness (penalty) method, a kinematic method (in Abaqus/Explicit), or +a Lagrange multiplier method (in Abaqus/Standard), depending on the contact algorithm used; and +• can be defined in user subroutines FRIC or FRIC_COEF (in Abaqus/Standard) or VFRIC, +VFRICTION, or VFRIC_COEF (in Abaqus/Explicit). +In Abaqus/Standard tangential damping forces can be introduced proportional to the relative tangential +velocity, while in Abaqus/Explicit tangential damping forces can be introduced proportional to the rate +of relative elastic slip between the contacting surfaces . +Including friction properties in a contact property definition +Abaqus assumes by default that the interaction between contacting bodies is frictionless. You can include +a friction model in a contact property definition for both surface-based contact and element-based contact. +Input File Usage: +Abaqus/CAE Usage: +the +Use both of the following options for surface-based contact: +*SURFACE INTERACTION, NAME=interaction_property_name +*FRICTION +Use both of +Abaqus/Standard: +*INTERFACE or *GAP, ELSET=name +*FRICTION +Interaction module: contact property editor: Mechanical→Tangential +Behavior +following options +for +element-based contact +in +Changing friction properties during an analysis +Element-based contact is not supported in Abaqus/CAE. +The methods used to change friction properties during an analysis differ between Abaqus/Standard and +Abaqus/Explicit. +Changing friction properties during an Abaqus/Standard analysis +It is possible to remove, to modify, or to add a friction model that does not involve a user subroutine to +a contact property definition in any particular step of an Abaqus/Standard simulation. In some models, +such as shrink-fit contact interference problems, friction should not be added until after the first steps have +been completed. In other models friction might be removed or lowered to represent the introduction of +a lubricant between the bodies. +You must identify which contact property definition or contact element set is being changed. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options for surface-based contact: +*CHANGE FRICTION, INTERACTION=name +*FRICTION +Use both of the following options for element-based contact: +*CHANGE FRICTION, ELSET=name +*FRICTION +Define a contact property with a new friction definition. Then change the +contact property assigned to an interaction in a particular step. +Interaction module: +Contact property editor: Mechanical→Tangential Behavior +Interaction editor: Contact interaction property: +new_interaction_property_name +Element-based contact is not supported in Abaqus/CAE. +Specifying the time variation of the change in friction properties +You can specify an amplitude curve to define the time variation +of changes in friction coefficients and, if applicable, allowable elastic slip throughout the step. If you do not specify +an amplitude curve, changes in these friction properties are either applied immediately at the beginning +of the step or ramped up linearly over the step, depending on the default amplitude variation assigned +to the step , with some exceptions as described below. For +many step types the default transition type is a linear ramping from old to new values, which helps avoid +convergence problems that can occur upon sudden changes in friction properties. +Amplitude curves used to control variations in friction properties are subjected to the following +restrictions: +• a tabular or smooth step amplitude definition must be used, +• only amplitudes with monotonically increasing values between 0.0 and 1.0 are accepted, and +• the amplitude must be defined in terms of step time and using relative magnitudes. +The value of a friction coefficient or allowable elastic slip in effect at a given time is typically equal +to the value of the property at the start of the step plus the current amplitude value times the anticipated +change in property value over the step. Variations in friction properties must consider the following: +• Changes in the type of frictional constraint enforcement method (penalty or Lagrange multiplier +methods), changes between a “rough” friction model and a finite friction coefficient, and changes +to friction properties other than the friction coefficient or allowable elastic slip always occur at the +beginning of a step. +• If a friction coefficient is dependent on slip rate, contact pressure, average surface temperature at +the contact point, or field variables, the estimate of the final value of the friction coefficient for the +step (which is used in calculating the anticipated change in the friction coefficient over the step) +assumes that the current slip rate, contact pressure, etc. will remain in effect at the end of the step. +• If a friction coefficient is changed during the first step of an analysis, its value at the start of the step +is equal to zero for this calculation, regardless of the original friction definition in the model. +• Changes in allowable elastic slip always occur at the beginning of a step when an exponential-decay +friction model is used or when frictional properties are changed during the first general step or during +a steady-state transport step that is preceded by a step type other than steady-state transport. +Input File Usage: +Abaqus/CAE Usage: +*CHANGE FRICTION, AMPLITUDE=name +Time-dependent changes +Abaqus/CAE. +in friction properties are not +supported in +Resetting the frictional properties to their default values +You can reset the frictional properties of the specified contact property definition or element set to their +original values. +Input File Usage: +Abaqus/CAE Usage: +Use either of the following options: +*CHANGE FRICTION, RESET, INTERACTION=name +*CHANGE FRICTION, RESET, ELSET=name +In this case the *FRICTION option is not needed. +Interaction module: +Contact property editor: Mechanical→Tangential Behavior: +Friction formulation: Frictionless +Interaction editor: Contact interaction property: +default_interaction_property_name +Changing friction properties during an Abaqus/Explicit analysis +In Abaqus/Explicit the friction definition is specified as part of the model definition for a general contact +analysis and as part of the history definition for a contact pair analysis. See “Assigning contact properties +for general contact in Abaqus/Explicit,” Section 35.4.3, and “Assigning contact properties for contact +pairs in Abaqus/Explicit,” Section 35.5.3, for information on changing aspects of any contact property +definition during an Abaqus/Explicit analysis. +Using the basic Coulomb friction model +The basic concept of the Coulomb friction model is to relate the maximum allowable frictional (shear) +stress across an interface to the contact pressure between the contacting bodies. In the basic form of +the Coulomb friction model, two contacting surfaces can carry shear stresses up to a certain magnitude +across their interface before they start sliding relative to one another; this state is known as sticking. +The Coulomb friction model defines this critical shear stress, +, at which sliding of the surfaces starts +as a fraction of the contact pressure, p, between the surfaces ( +). The stick/slip calculations +determine when a point transitions from sticking to slipping or from slipping to sticking. The fraction, +, is known as the coefficient of friction. +For the case when the slave surface consists of a node-based surface, the contact pressure is equal to +the normal contact force divided by the cross-sectional area at the contact node. In Abaqus/Standard the +default cross-sectional area is 1.0; you can specify a cross-sectional area associated with every node in +the node-based surface when the surface is defined or, alternatively, assign the same area to every node +through the contact property definition. In Abaqus/Explicit the cross-sectional area is always 1.0, and +you cannot change it. +The basic friction model assumes that +is the same in all directions (isotropic friction). For a +three-dimensional simulation there are two orthogonal components of shear stress, +, along the +interface between the two bodies. These components act in the slip directions for the contact surfaces +or contact elements. The slip directions for contact surfaces are defined in “Contact formulations in +and +Abaqus/Standard,” Section 37.1.1, and those for contact elements are defined in the sections describing +contact modeling with those elements. +Abaqus combines the two shear stress components into an “equivalent shear stress,” +. +, for the +stick/slip calculations, where +In addition, Abaqus combines the two slip velocity +components into an equivalent slip rate, +. The stick/slip calculations define a surface + in the contact pressure–shear stress space +along which a point transitions from sticking to slipping. +equivalent +shear stress +critical shear stress +in default model +stick region +μ (constant friction coefficient) +contact pressure +Figure 36.1.5–1 Slip regions for the basic Coulomb friction model. +There are two ways to define the basic Coulomb friction model in Abaqus. In the default model the +friction coefficient is defined as a function of the equivalent slip rate and contact pressure. Alternatively, +you can specify the static and kinetic friction coefficients directly. +Using the default model +In the default model you define the coefficient of friction directly as +, +, +, and +is the equivalent slip rate, p is the contact pressure, +where +at the contact point, and +is the average temperature +at the contact point. +is the average predefined field variable +are the temperature and predefined field variables at points A and B on the surfaces. +Point A is a node on the slave surface, and point B corresponds to the nearest point on the opposing +master surface. The temperature and field variables are interpolated along the surface at location B. If +the master surface consists of a rigid body, the temperature and field variable at the reference node are +used. Dependence on +is not available with the general contact algorithm in Abaqus/Explicit. +and +The friction coefficient can depend on slip rate, contact pressure, temperature, and field variables. +By default, it is assumed that the friction coefficients do not depend on field variables. +The coefficient of friction can be set to any nonnegative value. A zero friction coefficient means +that no shear forces will develop and the contact surfaces are free to slide. You do not need to define a +friction model for such a case. +Input File Usage: +*FRICTION, DEPENDENCIES=n +, +, p, +, +Abaqus/CAE Usage: +Interaction module: contact property editor: Mechanical→Tangential +Behavior: Friction formulation: Penalty: Friction +If necessary, +toggle on Use slip-rate-dependent data, Use contact- +pressure-dependent data, and/or Use temperature-dependent data; +and/or specify the Number of field variable dependencies in addition to slip +rate, contact pressure, and temperature. +Specifying static and kinetic friction coefficients +Experimental data show that the friction coefficient that opposes the initiation of slipping from a +sticking condition is different from the friction coefficient that opposes established slipping. The former +is typically referred to as the “static” friction coefficient, and the latter is referred to as the “kinetic” +friction coefficient. Typically, the static friction coefficient is higher than the kinetic friction coefficient. +In the default model the static friction coefficient corresponds to the value given at zero slip rate, +and the kinetic friction coefficient corresponds to the value given at the highest slip rate. The transition +between static and kinetic friction is defined by the values given at intermediate slip rates. In this model +the static and kinetic friction coefficients can be functions of contact pressure, temperature, and field +variables. +Abaqus also provides a model to specify a static and a kinetic friction coefficient directly. In this +model it is assumed that the friction coefficient decays exponentially from the static value to the kinetic +value according to the formula: +is the kinetic friction coefficient, +where +is a user-defined decay +is the static friction coefficient, +coefficient, and +is the slip rate . This model can be used +only with isotropic friction and does not allow dependence on contact pressure, temperature, or field +variables. There are two ways of defining this model. +Providing the static, kinetic, and decay coefficients directly +You can provide the static friction coefficient, the kinetic friction coefficient, and the decay coefficient +directly . +μ = μ +k + (μ +s − μ +k) e−dc +eq +eq +Figure 36.1.5–2 Exponential decay friction model. +Input File Usage: +*FRICTION, EXPONENTIAL DECAY +, +, +Abaqus/CAE Usage: +Interaction module: contact property editor: Mechanical→Tangential +Behavior: Friction formulation: Static-Kinetic Exponential +Decay: Friction, Definition: Coefficients +Using test data to fit the exponential model +, +Alternatively, you can provide test data points to fit the exponential model. At least two data points must +be provided. The first point represents the static coefficient of friction specified at +, and the +second point, ( +) (shown in Figure 36.1.5–3), corresponds to an experimental measurement taken at +a reference slip rate +. An additional data point can be specified to characterize the exponential decay. +If this additional data point is omitted, Abaqus will automatically provide a third data point, ( +), +to model the assumed asymptotic value of the friction coefficient at infinite velocity. In such a case +is chosen such that +, +. +*FRICTION, EXPONENTIAL DECAY, TEST DATA +Input File Usage: +, +Abaqus/CAE Usage: +Interaction module: contact property editor: Mechanical→Tangential +Behavior: Friction formulation: Static-Kinetic Exponential +Decay: Friction, Definition: Test data +(γ += + 0, μ +1 = μ +s) +1 +(γ +2, μ +2) +∞ +(γ +3 = γ +∞, μ +3 = μ += +∞ +k) +1 = 0.0 +eq +Figure 36.1.5–3 Exponential decay friction model specified with test data points. +Using the optional shear stress limit +, so that, regardless of the magnitude of +You can specify an optional equivalent shear stress limit, +the contact pressure stress, sliding will occur if the magnitude of the equivalent shear stress reaches this +value . A value of zero is not allowed. +equivalent +shear stress +max +critical shear stress in +model with τ +max limit +μ (constant friction coefficient) +stick region +contact pressure +Figure 36.1.5–4 Slip regions for the friction model with a limit on the critical shear stress. +This shear stress limit is typically introduced in cases when the contact pressure stress may become +very large (as can happen in some manufacturing processes), causing the Coulomb theory to provide +a critical shear stress at the interface that exceeds the yield stress in the material beneath the contact +surface. A reasonable upper bound estimate for +is the Mises yield stress of +the material adjacent to the surface; however, empirical data are the best source for +. +, where +is +Input File Usage: +Abaqus/CAE Usage: +*FRICTION, TAUMAX= +Interaction module: contact property editor: Mechanical→Tangential +Behavior: Friction formulation: Penalty or Lagrange Multiplier: +Shear Stress, Shear stress limit: Specify: +Limitations with the shear stress limit +In Abaqus/Explicit a shear stress limit cannot be used when a contact pair uses a node-based surface as +one of the surfaces. +Using the anisotropic friction model in Abaqus/Standard +The anisotropic friction model available in Abaqus/Standard allows for different friction coefficients in +the two orthogonal directions on the contact surface. These orthogonal directions coincide with the slip +directions defined in “Contact formulations in Abaqus/Standard,” Section 37.1.1; and those for contact +elements are described in the sections defining contact modeling with those elements. The orientation of +the slip directions cannot be changed. +If you indicate that the anisotropic friction model should be used, you must specify two friction +is the coefficient of +is the coefficient of friction in the first slip direction and +coefficients, where +friction in the second slip direction. +The critical shear stress surface is an ellipse in +extreme points being +in contact pressure between the surfaces. The direction of slip, +stress surface. +and +space with the two +. The size of this ellipse will change with the change +, is orthogonal to the critical shear +– +The friction coefficients can depend on slip rate, contact pressure, temperature, and field variables. +By default, it is assumed that the friction coefficients do not depend on field variables. +Input File Usage: +*FRICTION, ANISOTROPIC, DEPENDENCIES=n +, +, +, p, +, +Abaqus/CAE Usage: +Interaction module: contact property editor: Mechanical→Tangential +Behavior: Friction formulation: Penalty: Friction, +Directionality: Anisotropic +toggle on Use slip-rate-dependent data, Use contact- +If necessary, +pressure-dependent data, and/or Use temperature-dependent data; +and/or specify the Number of field variable dependencies in addition to slip +rate, contact pressure, and temperature. +crit +2 = μ +2 P +stick region +crit +1 = μ +1 P +direction of slip dγ +Figure 36.1.5–5 Critical shear stress surface for the anisotropic friction model. +Preventing slipping regardless of contact pressure +Abaqus offers the option of specifying an infinite coefficient of friction ( +). This type of surface +interaction is called “rough” friction, and with it all relative sliding motion between two contacting +surfaces is prevented (except for the possibility of “elastic slip” associated with penalty enforcement) as +long as the corresponding normal-direction contact constraints are active. In most cases Abaqus/Standard +uses a penalty method to enforce these tangential constraints; however, a Lagrange multiplier method is +used during general (non-perturbation) analysis steps if the corresponding normal-direction constraints +have directly enforced “hard contact” or exponential pressure-overclosure behavior. Abaqus/Explicit +uses either a kinematic or penalty method, depending on the contact formulation chosen. +Rough friction is intended for nonintermittent contact; once surfaces close and undergo rough +friction, they should remain closed. Convergence difficulties may arise in Abaqus/Standard if a closed +contact interface with rough friction opens, especially if large shear stresses have developed. The rough +friction model is typically used in conjunction with the no separation contact pressure-overclosure +relationship for motions normal to the surfaces , which prohibits separation of the surfaces once +they are closed. +When rough friction is used with the no separation relationship for hard contact in Abaqus/Explicit +specified with the kinematic contact method, no relative motions of the surfaces will occur. For hard +contact in Abaqus/Explicit specified with the penalty contact method, relative motions will be limited +to the elastic slip and penetration corresponding to the inexact satisfaction of the contact constraints +by the applied penalty forces. When softened tangential behavior is specified in Abaqus/Explicit , the relative surface motions will be governed +by the specified softening behavior. +Input File Usage: +Abaqus/CAE Usage: +*FRICTION, ROUGH +Interaction module: contact property editor: Mechanical→Tangential +Behavior: Friction formulation: Rough +Shear stress versus elastic slip while sticking +In some cases some incremental slip may occur even though the friction model determines that the current +frictional state is “sticking.” In other words, the slope of the shear (frictional) stress versus total slip +relationship may be finite while in the “sticking” state, as shown in Figure 36.1.5–6. +shear stress +sticking friction +slipping friction +crit +total slip +Figure 36.1.5–6 Elastic slip versus shear traction relationship for sticking and slipping friction. +corresponds to Young’s modulus, and +The relationship shown in this figure is analogous to elastic-plastic material behavior without hardening: +corresponds to yield stress; sticking friction corresponds +to the elastic regime, and slipping friction corresponds to the plastic regime. A finite value of the +sticking stiffness may reflect a user-specified physical behavior or may be characteristic of the constraint +enforcement method. +Frictional constraints are enforced with a stiffness (penalty method) by default in Abaqus/Standard +and for the general contact algorithm in Abaqus/Explicit; in this case the sticking stiffness will have a +finite value. An infinite sticking stiffness, in which case the elastic slip is always zero, can be achieved +with the optional Lagrange multiplier method for imposing frictional constraints in Abaqus/Standard +In +or with the kinematic constraint method (available only for contact pairs) in Abaqus/Explicit. +Abaqus/Explicit some tangential contact damping acts on the elastic slip rate by default, as discussed +in “Contact damping,” Section 36.1.3. Tangential softening to reflect a physical behavior is available +only in Abaqus/Explicit. +Defining tangential softening in Abaqus/Explicit +To activate softened tangential behavior in Abaqus/Explicit, specify the slope of the shear stress versus +in Figure 36.1.5–6). User subroutine VFRIC cannot be used in conjunction +elastic slip relationship ( +with softened tangential behavior. +Input File Usage: +Abaqus/CAE Usage: +*FRICTION, SHEAR TRACTION SLOPE= +Interaction module: contact property editor: Mechanical→Tangential +Behavior: Friction formulation: Penalty or Static-Kinetic +Exponential Decay: Elastic Slip, Specify: +Stiffness method for imposing frictional constraints in Abaqus/Standard +The stiffness method used for friction in Abaqus/Standard is a penalty method that permits some relative +motion of the surfaces (an “elastic slip”) when they should be sticking (similar to the allowable elastic slip +defined with softened tangential behavior in Abaqus/Explicit). While the surfaces are sticking (i.e., +), the magnitude of sliding is limited to this elastic slip. Abaqus continually adjusts the magnitude +of the penalty constraint to enforce this condition. +The stiffness method in Abaqus/Standard requires the selection of an allowable elastic slip, +. +Using a large +in the simulation makes convergence of the solution more rapid at the expense of solution +accuracy (there is greater relative motion of the surfaces when they should be sticking). Behavior in +which no slip is permitted in the sticking state is approximated more accurately by allowing only a small +is chosen very small, convergence problems may occur; in that case, it may be better to use +the Lagrange multiplier method to apply the sticking constraint . +. If +The default value of allowable elastic slip used by Abaqus/Standard generally works very well, +providing a conservative balance between efficiency and accuracy. Abaqus/Standard calculates +as a +small fraction of the “characteristic contact surface length,” , and scans all of the facets of all the slave +surfaces when calculating . Abaqus/Standard reports the value of +used for each contact pair in the +data (.dat) file if you request detailed printout of contact constraint information . +The allowable elastic slip is given as +, where +is 0.005. +is the slip tolerance; the default value of +This method of calculating the allowable elastic slip is used for all analysis procedures +(“Steady-state transport analysis,” +. The +steady-state transport analysis +in Abaqus/Standard except +Section 6.4.1), in which the penalty constraint is based on a maximum allowable slip rate, +maximum slip rate is calculated as +where +is the angular spinning rate and R is the radius of the rolling structure. +Cases in which the default elastic slip value may not be suitable +In certain situations the default value for the allowable elastic slip may not be suitable. For example, +slave surfaces defined by node-based surfaces or some contact element types, such as GAPUNI +elements, have no physical dimensions and Abaqus/Standard cannot estimate a value of +. For models +containing only node-based surfaces or these types of contact elements, Abaqus/Standard first tries +to use the “characteristic contact surface length” of the other contact pairs in the model. If there are +none, it calculates +using all of the elements in the model and issues a warning message. If a model +contains no elements for which a characteristic length can be determined (for example, if it contains +only substructures), Abaqus/Standard has no information with which to calculate +. As a result, it uses +a value of 1.0 and issues a warning message. If the contact surface face dimensions vary greatly, the +average value of may be unreasonable for some contact surfaces. The elastic slip should then be +specified directly for the surfaces with a much smaller “characteristic face dimension.” +There are two methods for modifying the allowable elastic slip. One method is to specify +the other is to specify the slip tolerance, +steps . +. Some analyses call for nondefault +or +directly; +only in specific +Specifying the allowable elastic slip directly +You can provide the absolute magnitude of +directly. Specify a reasonable value for the relative +displacement that may occur before surfaces actually begin to slip. Typically, the allowable elastic +slip is set to a small fraction (10−2 –10−4 ) of a “characteristic contact surface face dimension.” In a +steady-state transport analysis you can define the maximum allowable viscous slip rate, +. +The specified allowable elastic slip will be used only for the contact pairs referencing the contact +property definition that contains the friction definition. For example, three surfaces ASURF, BSURF, and +CSURF form two contact pairs that each refer to their own contact property definition, as shown below. +Contact Pair +Contact Property +ASURF, BSURF +DEFAULT +CSURF, BSURF +NONDEF +0.1 +In the DEFAULT contact property definition no value for +for the friction interaction between ASURF and BSURF would be the default value +contact property definition a value of 0.1 is specified for +for the friction interaction between CSURF and BSURF. +*FRICTION, ELASTIC SLIP= +Interaction module: contact property editor: Mechanical→Tangential +Behavior: Friction formulation: Penalty or Static-Kinetic +Exponential Decay: Elastic Slip, Absolute distance: +is specified, so the allowable elastic slip used +. In the NONDEF +, which will be the allowable elastic slip used +Abaqus/CAE Usage: +Input File Usage: +Changing the default slip tolerance +You can alter the default value of the slip tolerance, +. This method of altering the default elastic slip +is convenient if the goal is to increase computational efficiency, in which case a value larger than the +default of 0.005 would be given, or if the goal is to increase accuracy, in which case a value smaller than +the default would be given. +Input File Usage: +Abaqus/CAE Usage: +*FRICTION, SLIP TOLERANCE= +Interaction module: contact property editor: Mechanical→Tangential +Behavior: Friction formulation: Penalty or Static-Kinetic +Exponential Decay: Elastic Slip, Fraction of characteristic +surface dimension: +Stiffness method for imposing frictional constraints in Abaqus/Explicit +The stiffness method used for friction with the general contact algorithm in Abaqus/Explicit and, +optionally, with the contact pair method in Abaqus/Explicit is a penalty method that permits some +relative motion of the surfaces (an “elastic slip”) when they should be sticking (similar to the allowable +elastic slip defined with softened tangential behavior in Abaqus/Explicit). While the surfaces are +sticking (i.e., +), the magnitude of sliding is limited to this elastic slip. Abaqus continually +adjusts the magnitude of the penalty constraint to enforce this condition. +In Abaqus/Explicit you can choose to have contact constraints for the contact pair algorithm +enforced with the penalty method; the general contact algorithm always uses a penalty method . +The default penalty stiffness for frictional constraints is chosen automatically by Abaqus/Explicit +and is the same as would be used for normal hard contact constraints. Softening in the normal direction +does not affect the penalty stiffness used to enforce stick conditions. If tangential softening is specified +, the penalty stiffness will be equal to +the value specified for the slope of the shear stress versus elastic slip relationship. You can specify +a scale factor to adjust the penalty stiffness, as discussed in “Contact controls for general contact +in Abaqus/Explicit,” Section 35.4.5, and “Contact controls for contact pairs in Abaqus/Explicit,” +Section 35.5.5. +Lagrange multiplier method for imposing frictional constraints in Abaqus/Standard +In Abaqus/Standard the sticking constraints at an interface between two surfaces can be enforced exactly +by using the Lagrange multiplier implementation. With this method there is no relative motion between +two closed surfaces until +. However, the Lagrange multipliers increase the computational +cost of the analysis by adding more degrees of freedom to the model and often by increasing the +number of iterations required to obtain a converged solution. The Lagrange multiplier formulation may +even prevent convergence of the solution, especially if many points are iterating between sticking and +slipping conditions. This effect can occur particularly if locally there is a strong interaction between +slipping/sticking conditions and contact stresses. +Because of the added cost of using the Lagrange friction formulation, it should be used only in +problems where the resolution of the stick/slip behavior is of utmost importance, such as modeling +fretting between two bodies. In typical metal forming applications or for contact of rubber components, +accurate resolution of the stick/slip behavior is not important enough to justify the added costs of the +Lagrange multiplier formulation. +Input File Usage: +Abaqus/CAE Usage: +*FRICTION, LAGRANGE +Interaction module: contact property editor: Mechanical→Tangential +Behavior: Friction formulation: Lagrange Multiplier +Kinematic method for imposing frictional constraints in Abaqus/Explicit +By default, the contact pair algorithm in Abaqus/Explicit uses a kinematic method for imposing frictional +constraints . The +kinematic method applies sticking constraints in a way similar to the optional Lagrange multiplier method +in Abaqus/Standard; however, the algorithm is quite different. The value of the force required to enforce +sticking at a node is first calculated using the mass associated with the node; the distance the node has +slipped; the time increment; and additionally for softened contact, the current value of the elastic slip and +the elastic slip versus shear stress slope. For hard contact this sticking force is that which is required to +maintain the node’s position on the opposite surface in the predicted configuration. For softened contact +this force is consistent with the user-specified value for the slope of the shear stress versus elastic slip +relationship. The sticking force for each node is calculated using the mass associated with the node, the +distance the node has slipped, the shear traction-elastic slip slope (if softened contact is specified in the +tangential direction), and the time increment. If the shear stress at the node calculated using this force is +less than +, the node is considered to be sticking and this force is applied to each surface in opposing +directions. If the shear stress exceeds +is applied. In either case the forces result in acceleration corrections tangential to the surface at the slave +node and either the nodes of the master surface facet or the points on the analytical rigid surface that it +contacts. +, the surfaces are slipping and the force corresponding to +User-defined friction model +You can define the shear stress between contacting surfaces through a user subroutine when the friction +behavior provided by Abaqus is not sufficient. The shear stress can be defined as a function of a number +of variables such as slip, slip rate, temperature, and field variables. You can also introduce a number of +solution-dependent state variables that you can update and use within the friction user subroutines. You +can declare a number of properties or constants associated with your friction model and use these values +in the user subroutine. +In addition to the friction user subroutines, subroutines are available for defining the complete +mechanical interaction between surfaces, including the interaction in the normal direction as well as +the frictional behavior in the tangential direction; see “User-defined interfacial constitutive behavior,” +Section 36.1.6, for more information. +Defining generic frictional behavior +You can define a generic frictional behavior between contacting surfaces using user subroutine FRIC in +Abaqus/Standard. In Abaqus/Explicit the generic frictional behavior for contact pairs is defined in user +subroutine VFRIC, while the generic frictional behavior for general contact is defined in user subroutine +VFRICTION. +Input File Usage: +Use the following option to define a frictional behavior with user subroutine +FRIC or VFRIC: +Abaqus/CAE Usage: +*FRICTION, USER, DEPVAR=n, PROPERTIES=p +Use the following option to define a frictional behavior with user subroutine +VFRICTION: +*FRICTION, USER=FRICTION, DEPVAR=n, PROPERTIES=p +Use the following options to define a frictional behavior with user subroutine +FRIC or VFRIC: +Interaction module: contact property editor: Mechanical→Tangential +Behavior: Friction formulation: User-defined, Number of +state-dependent variables: n, Friction Properties +User subroutine VFRICTION is not supported in Abaqus/CAE. +Defining complex isotropic friction +Abaqus provides a simple way to specify complex isotropic frictional behavior when the expression +for the friction coefficient can be defined explicitly. You need only to specify the friction coefficient, +and Abaqus will compute the resulting frictional forces. Abaqus/Standard provides user subroutine +FRIC_COEF and Abaqus/Explicit provides user subroutine VFRIC_COEF for +this purpose. +VFRIC_COEF can be used only with general contact. +Input File Usage: +Abaqus/CAE Usage: +*FRICTION, USER=COEFFICIENT, PROPERTIES=p +User subroutines FRIC_COEF and VFRIC_COEF are not supported in +Abaqus/CAE. +Improving Abaqus/Standard simulations that include friction in the surface interactions +Several features of the frictional interaction of surfaces can have a strong influence on the rate of +convergence in an Abaqus/Standard simulation. +Unsymmetric terms in the system of equations +Friction constraints produce unsymmetric terms when the surfaces are sliding relative to each other. +These terms have a strong effect on the convergence rate if frictional stresses have a substantial influence +on the overall displacement field and the magnitude of the frictional stresses is highly solution dependent. +Abaqus/Standard will automatically use the unsymmetric solution scheme if +is pressure- +or if +dependent. +solution scheme in Abaqus/Standard” in “Defining an analysis,” Section 6.1.2. +If desired, you can turn off the unsymmetric solution scheme; see “Matrix storage and +No slip occurs with rough friction; the contribution to the stiffness will be fully symmetric, and +Abaqus/Standard will use the symmetric solution scheme by default. +Heat generated by frictional interaction of surfaces +In fully coupled temperature-displacement analysis and fully coupled thermal-electrical-structural +analysis, all dissipated mechanical (frictional) energy is converted to heat and distributed equally +between the two surfaces by default. This behavior can be modified; for details about this and other +thermal surface interactions, see “Thermal contact properties,” Section 36.2.1. +Temperature and field-variable dependence of friction properties for structural elements +Temperature and field-variable distributions in beam and shell elements can generally include gradients +through the cross-section of the element. Contact between these elements occurs at the reference surface; +therefore, temperature and field-variable gradients in the element are not considered when determining +friction properties that depend on these variables. +Surface interaction variables related to friction +Abaqus provides output of the shear stresses at points on the slave surface that use a surface interaction +model containing frictional properties. The shear stresses, CSHEAR1 and CSHEAR2, are given in the +two orthogonal slip directions, which are constructed on the master surface . There is only one slip direction in two-dimensional problems. +Details about how to request contact surface variable output are given in “Defining contact pairs in +Abaqus/Standard,” Section 35.3.1, and “Defining contact pairs in Abaqus/Explicit,” Section 35.5.1. +Contour plots of these variables can also be plotted in Abaqus/CAE. +Additional reference +• Oden, J. T., and J. A. C. Martins, “Models and Computational Methods for Dynamic Friction +Phenomena,” Computer Methods in Applied Mechanics and Engineering, vol. 52, pp. 527–634, +1985. +36.1.6 +USER-DEFINED INTERFACIAL CONSTITUTIVE BEHAVIOR +Products: Abaqus/Standard Abaqus/Explicit +References +• “UINTER,” Section 1.1.38 of the Abaqus User Subroutines Reference Manual +• “VUINTER,” Section 1.2.15 of the Abaqus User Subroutines Reference Manual +• “VUINTERACTION,” Section 1.2.16 of the Abaqus User Subroutines Reference Manual +• *SURFACE INTERACTION +Overview +User-defined interfacial constitutive behavior: +• is provided so that any constitutive behavior across an interface can be added to the library of +existing models such as softened contact and Coulomb friction; +• requires that a constitutive model (or a library of models) for the interface be programmed in user +subroutine UINTER in Abaqus/Standard; +• requires that a constitutive model (or a library of models) for the interface be programmed in user +subroutine VUINTER in Abaqus/Explicit when using the contact pair algorithm; +• requires that a constitutive model (or a library of models) for the interface be programmed in user +subroutine VUINTERACTION in Abaqus/Explicit when using the general contact algorithm; +• is available only for surface-based contact definition involved in stress/displacement, coupled +temperature-displacement, coupled thermal-electrical-structural, or heat transfer analysis; and +• requires considerable effort and expertise: the feature is very general and powerful, but it is intended +for advanced users. +Purpose of user subroutines UINTER, VUINTER, and VUINTERACTION +User subroutines UINTER, VUINTER, and VUINTERACTION provide a very general interface for you +to define the constitutive behavior across the interface between two surfaces. These subroutines replace +all built-in interfacial constitutive behavior models; hence, no other contact property definitions (e.g., +friction, thermal conductance, etc.) can be specified in conjunction with them. +In a stress/displacement analysis you must define the stresses, both normal and tangential, +at the slave node (or points on the slave surface) at the current point in time. +In a coupled +temperature-displacement analysis and a coupled thermal-electrical-structural analysis you must also +define the heat flux across the interface. The constitutive calculation thus involves computing the +stresses and heat fluxes based on the increments in relative position of the slave node with respect to +the master surface (which act as strains in this context), temperature at the surface, and predefined field +variables. The calculations would typically involve solution-dependent state variables, which can be +updated inside these routines. If contact damping is to be included in the interfacial constitutive model, +you must include the damping contribution in the stress definition. +When a user subroutine is used to define the interfacial constitutive behavior, all decisions regarding +the contact status of a slave node must be made inside the subroutine based on the information provided. +You can make such decisions based on the values of the relative position of the point on the slave +surface with respect to the master surface and appropriately defined solution-dependent state variables. +Thus, usage of this feature involves not only developing a constitutive behavior of the interface but also +developing conditions under which contact is active at a given point on the slave surface. The interface +is always assumed to be massless. +User subroutine UINTER will be called for each contact constraint location of affected contact pairs +in each iteration of an Abaqus/Standard analysis. The input to this user subroutine includes the current +relative position of a particular constraint point on the slave surface with respect to the corresponding +closest point on the master surface, as well as the incremental relative motion between these two points. +Values of temperature and field variables at the constraint point on the slave surface and the corresponding +closest point on the master surface and several other variables are also provided as input. In addition to +defining the contact stress or heat flux, appropriate Jacobian terms must also be defined to ensure proper +convergence characteristics in Abaqus/Standard. +User subroutine VUINTER will be called multiple times for the affected contact pairs in each time +increment of an Abaqus/Explicit analysis. All slave nodes are processed in each call to VUINTER, +whereas only a single constraint is processed in each call to UINTER. Similar input is provided to +VUINTER as UINTER. +User subroutine VUINTERACTION will be called multiple times for each interacting surface in +each time increment of an Abaqus/Explicit analysis. Points of potential contact for a given interaction +are processed in blocks in calls to VUINTERACTION. Similar input is provided to VUINTERACTION +as VUINTER. +Interfacial constants +You must specify the number of interfacial constants that are needed in user subroutine UINTER, +VUINTER, or VUINTERACTION; and you must provide values for all these constants. All surface +constitutive behavior calculations and all decisions regarding the contact status at a slave node (or a +point on the slave surface in question) must be programmed in the user subroutine. Any other contact +property definitions included in the analysis are reported as an error. +Input File Usage: +For contact interactions defined through user subroutine UINTER or VUINTER: +*SURFACE INTERACTION, USER, +PROPERTIES=number_of_material_constants +For contact interactions defined through user subroutine VUINTERACTION: +*SURFACE INTERACTION, USER=INTERACTION, +PROPERTIES=number_of_material_constants +Tracking thickness when VUINTERACTION is used +A surface interaction is considered active if the interacting surfaces are within a separation distance +called the tracking thickness. Abaqus/Explicit uses an internal default value for the tracking thickness. +Alternatively, you can specify the tracking thickness in conjunction with a user-defined surface +In this case contacting surfaces whose proximity is within this thickness are +interaction model. +available for user-defined interactions. Use of a user-specified tracking thickness is supported only with +node-to-surface contact and not with edge-to-edge contact. +Input File Usage: +*SURFACE INTERACTION, USER=INTERACTION, +TRACKING THICKNESS=tracking_thickness +Interfacial state +Constitutive models used to define the interfacial behavior may require the storage of solution-dependent +state variables. You must allocate storage space for these variables by indicating the number of variables. +There is no restriction on the number of state variables associated with a user-defined constitutive +behavior for the interface. +User subroutine UINTER is called for points on the slave surface at each iteration of every +increment. User subroutine VUINTER is called in every time increment for each master-slave view of +each contact pair it affects, as discussed earlier. User subroutine VUINTERACTION is called in every +time increment for each pair of surfaces actively interacting, as discussed earlier. Each subroutine is +provided with the state of the slave node or potential contact point at the start of the increment (the state +includes stress, flux, solution-dependent state variables, temperature, and any predefined field variables) +and with the increments in temperature, predefined state variables, relative position, and time. +Input File Usage: +Use the following option to allocate storage space for solution-dependent state +variables: +*SURFACE INTERACTION, DEPVAR=number_of_state_variables +Use with the unsymmetric equation solver in Abaqus/Standard +If the constitutive Jacobian matrix, +equation solution capability in Abaqus/Standard . +, is not symmetric, you should invoke the unsymmetric +Input File Usage: +*SURFACE INTERACTION, USER, UNSYMM +Defining the contact status in Abaqus/Standard +In addition to defining the constitutive behavior, in Abaqus/Standard you may also update the flags +LOPENCLOSE, LSTATE, and LSDI. The flag LOPENCLOSE is useful when UINTER is used to model +standard contact between two surfaces (similar to the default hard contact in Abaqus). It should be set +to 0 to indicate an open status and to 1 to indicate a closed status. At the beginning of the analysis it is +set to −1 before UINTER is called. A change in this flag from one iteration to the next will have two +consequences. It will result in output related to the change in contact status if detailed contact output has +been requested to the message file , +and it will also trigger a severe discontinuity iteration. The flag LSTATE can be used to store the current +contact status of the points on the slave surface in non-standard situations where a simple open/close +status is not appropriate. An example of such a situation is debonding, where three different states can +be defined—fully bonded, partially bonded or debonding, and fully debonded. You can assign an integer +to each of these states and set LSTATE accordingly. At the beginning of the analysis LSTATE is set +to −1 before UINTER is called. When this flag is used and it changes from one iteration to the next, +you can output messages to the message file (unit 7) related to such a change in state directly from user +subroutine UINTER. The flag LPRINT is provided to allow you to output messages related to change +in contact status only when you request detailed contact output to the message file. In such a situation +the LSDI flag may be set to 1 to trigger a severe discontinuity iteration (this issue is discussed in detail +later). +An example of a situation where both the flags LOPENCLOSE and LSTATE can be used arises in the +modeling of debonding between two surfaces. When the surface is in a state of transition from bonded to +debonded, the flag LSTATE may be used, while the flag LOPENCLOSE may be left to its original value +of −1. However, once complete debonding has taken place, the contact between the two surfaces may +be modeled using standard hard contact. In that situation the LSTATE flag may be set to −1, and the +LOPENCLOSE flag used. Any time one of these two flags is set to −1, Abaqus/Standard assumes that it +is not being used. A change of these flags from some other value to −1 does not result in contact-status +related output or severe discontinuity iterations. Similarly, a change of these flags from −1 to some other +value will not result in contact-status related output or severe discontinuity iterations. +If these flags are not used, there will be no output related to change in contact status unless you +decide to output messages that are not based on these flags directly from UINTER. +Severe discontinuity iterations in Abaqus/Standard +Abaqus/Standard classifies iterations in which the contact state at the end of the iteration is different +from the state assumed for that iteration as severe discontinuity iterations. The treatment of severe +discontinuity iterations by Abaqus/Standard is discussed in “Severe discontinuities in Abaqus/Standard” +in “Defining an analysis,” Section 6.1.2. When you define the interfacial constitutive behavior through +user subroutine UINTER and do not use the LOPENCLOSE flag, it is your responsibility to provide +Abaqus/Standard with input on how an iteration should be treated. The flag LSDI is provided in user +subroutine UINTER for this purpose. It is set to 0 before each call to UINTER; you should set it to 1 to +treat the current iteration as a severe discontinuity iteration. If the LOPENCLOSE flag is used, the value +of this flag alone determines whether a severe discontinuity iteration is necessary or not, and the LSDI +flag is ignored. +Use with contact in Abaqus/Explicit +The penalty contact algorithm must be used with user subroutines VUINTER and VUINTERACTION; +see “Penalty contact algorithm” in “Contact constraint enforcement methods in Abaqus/Explicit,” +Section 37.2.3. +When VUINTER is used and balanced master-slave contact is specified (i.e., the contact pair +weighting factor is not equal to 0.0 or 1.0), VUINTER will be called for each surface in the contact pair +that can act as a slave surface. The forces and fluxes defined in VUINTER will be multiplied by the +weight value for the master-slave view before they are applied. +Effects on solution time in Abaqus/Explicit +Abaqus/Explicit accounts for the contact stiffness and conductance in the stable time increment +calculation. Specifying stresses and fluxes in the user subroutine that correspond to large contact +stiffness (e.g., large slope of contact pressure versus penetration) and large contact conductance will +cause a significant drop in the stable time increment and, therefore, an increase in the solution time. +Tangent stiffnesses and conductances are determined by Abaqus/Explicit using a finite difference +method. User subroutine VUINTER is called three times per increment for each master-slave +view of each two-dimensional contact pair that references it and four times per increment for each +three-dimensional contact pair that references it. User subroutine VUINTERACTION is called four times +per increment for each active surface interaction that references it. The user subroutines are called once +with the actual configuration and subsequently with perturbed configurations based on displacement +perturbations in the normal direction, the +tangential direction, and, in three-dimensional cases, +the +tangential direction, respectively . For example, each component of contact stiffness is computed as a difference +in contact stress divided by a difference in relative position. You do not have access to the computed +values of contact stiffness and conductance, but you can control the constitutive behavior of the model. +Estimated default penalty stiffness (and conductance) values are provided to the user subroutines for +comparison purposes. Contact stiffnesses or conductances that exceed the default penalty values can +significantly reduce the time increment size. The default penalty stiffnesses and conductances are based +on an assumption that all slave nodes are in contact. In the case of VUINTER, if only a fraction of the +slave nodes are in contact, higher penalties than are reported in VUINTER would be assigned in some +cases with the default penalty algorithm. +Any changes to state variables are ignored for the perturbation calls. +In the case of VUINTER there can be significant additional CPU expense associated with contact +tracking. Since the contact state is unknown on entry to VUINTER, all nodes on the slave surface must +be tracked in every increment. This can increase the cost of an analysis significantly compared to the +contact models in Abaqus/Explicit if a large proportion of the slave nodes are not involved in contact. +In the case of VUINTERACTION there can be significant additional CPU expense associated with +contact tracking only if the tracking thickness is large compared to the element facet size on contacting +surfaces. +Use with other subroutines +Any other user subroutine that does not deal with constitutive behavior across an interface can be used +in conjunction with UINTER, VUINTER, or VUINTERACTION. +For example, user subroutines UMAT and UMATHT can be used in conjunction with UINTER +to define the constitutive mechanical and thermal behaviors of the material underlying the contact +surfaces. User subroutine VUMAT can be used in conjunction with VUINTER to define the mechanical +constitutive behavior of the material underlying the contact surfaces. However, user subroutines FRIC, +GAPCON, and GAPELECTR—available in Abaqus/Standard for defining mechanical, thermal, and +electrical interactions between surfaces—can be used in conjunction with UINTER only if they are +referenced on separate surface interactions. The same restriction applies to user subroutine VFRIC +used in conjunction with VUINTER and to user subroutines VFRICTION or VFRIC_COEF used in +conjunction with VUINTERACTION. +Use with contact controls +In Abaqus/Standard contact controls will not have any effect when used at an interface whose constitutive +behavior is defined through user subroutine UINTER. +In Abaqus/Explicit contact controls can be specified for a contact pair referencing a user-defined +In the case of user subroutine VUINTERACTION the default penalty stiffness +surface interaction. +argument includes any scale factor specified; whereas with user subroutine VUINTER the scale factor +is ignored. +Output +Most of the standard output variables that are normally available in an analysis involving contact are +available with this capability. +Output for UINTER +The variables COPEN and CSLIP represent the relative positions normal and tangential to the interface, +respectively. The surface-based thermal interaction variable, SFDR, contains the heat flux due to the total +energy dissipated due to friction, and not some fraction of it. This is unlike using the built-in capability +in Abaqus/Standard, where SFDR may contain the heat flux due to only a fraction of the total frictional +dissipation, depending on the specified fraction of the dissipated energy that is converted into heat. In +addition, the surface-based thermal interaction variable WEIGHT, which represents the weighting factor +for heat flux (generated by frictional sliding) distribution between the surfaces, is not available with this +capability. +Additional user-defined output variables can be defined for UINTER by using the solution- +dependent state variables (SDV). +Output for VUINTER and VUINTERACTION +All contact output variables in Abaqus/Explicit will be available except output for spot welds +(BONDSTAT and BONDLOAD). +The following user subroutine variables will contribute to the associated total energy variables: the +variable sed will contribute to the energy output variable ALLSE; sfd will contribute to ALLFD; scd +will contribute to ALLCD; spd will contribute to ALLPD; and svd will contribute to ALLVD. +If SFDR is requested, sfd, scd, spd, and svd will also be used to calculate the heat generated +at the interface (for output purposes only; the generated heat will not be applied to the model). The +default values of the fraction of mechanical energy converted into heat and the weighting factor for the +distribution of heat between the two surfaces (1.0 and 0.5, respectively) are used. +User-defined, solution-dependent state variables associated with the user subroutine cannot be +output to the output database (.odb) file or results (.fil) file. +36.1.7 +PRESSURE PENETRATION LOADING +Products: Abaqus/Standard Abaqus/CAE +References +• *PRESSURE PENETRATION +• *SURFACE +• *CONTACT PAIR +• “Defining pressure penetration,” Section 15.13.16 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +Pressure penetration loads simulated with contact pairs: +• model the penetration of fluid between two contacting structures; and +• allow the fluid to penetrate from multiple locations on the surface. +Defining pressure penetration loads between contacting bodies +Distributed pressure penetration loads allow for the simulation of fluid penetrating into the surface +to the surfaces. +between two contacting bodies and application of the fluid pressure normal +Element-based contact surfaces are used to model the interactions between the bodies . The surfaces are modeled as slave and master contact +surfaces . +Any contact formulation can be used. +The bodies forming the joint may both be deformable, as would be the case with threaded +connectors; or one may be rigid, as would occur when a soft gasket is used as a seal between stiffer +structures. You specify the nodes exposed to the fluid pressure, the magnitude of the fluid pressure, and +the critical contact pressure below which fluid penetration starts to occur. See “Pressure penetration +loading with surface-based contact,” Section 6.4.1 of the Abaqus Theory Manual, for more details. +Input File Usage: +*PRESSURE PENETRATION, SLAVE=slave1, MASTER=master1 +slave surface node or node set, master surface node or node set, +magnitude, critical contact pressure +Abaqus/CAE Usage: +If a node set is specified, it can contain only one node in two dimensions; in +three dimensions it can contain any number of nodes. +Interaction module: +Create Interaction: Surface-to-surface contact (Standard), Name: +contact_interaction_name; select master and slave surfaces +Create Interaction: Pressure penetration; Contact interaction: +contact_interaction_name, Region on Master: select face, edge, or point, +Region on Slave: select face, edge, or point, Critical Contact Pressure: +critical contact pressure, Fluid Pressure: magnitude +Specifying a pressure penetration criterion +A single slave-node-based penetration criterion is used. Fluid will penetrate into the surface between the +contacting bodies from one or multiple locations, which are exposed to the fluid, until a point is reached +where the contact pressure is greater than the specified critical value, cutting off further penetration of +the fluid. +Specifying a penetration time for the fluid pressure +When the fluid pressure penetration criterion is satisfied, the fluid pressure is applied normal to the +surfaces. +If the full current fluid pressure is applied immediately, the resulting large changes in the +strains near the contact surfaces can cause convergence difficulties. For large-strain problems severe +mesh distortion can also occur. To ensure a smooth solution, the fluid pressure is ramped up linearly +over a time period from zero pressure penetration load to the full current magnitude. +You can specify the time period taken for the fluid pressure penetration load to reach the full +current magnitude on newly penetrated surface segments. If the accumulated increment size, measured +immediately after the penetration, is greater than the penetration time, the full current fluid pressure +penetration load will be applied; otherwise, the fluid pressure on the newly penetrated surface segments +is ramped up linearly to the current magnitude over the penetration time period, possibly over a number +of increments. When the penetration time is equal to 0, the current fluid pressure is applied immediately +once the fluid pressure penetration criterion is satisfied. The default penetration time is chosen to be +0.001 of the total step time. The penetration time is ignored in a linear perturbation analysis. +Input File Usage: +Abaqus/CAE Usage: +*PRESSURE PENETRATION, PENETRATION TIME=n +Interaction module: Create Interaction: Pressure penetration; +Penetration time: n +Specifying the nodes exposed to the fluid pressure +The fluid can penetrate from either one or multiple locations of the surface. You must identify a node or +node set on the slave surface of the contacting bodies that defines where the surface is exposed to the fluid +pressure. In two dimensions if the master surface is not an analytical rigid surface , you must also identify a node or node set on the master surface that +defines where the surface is exposed to the fluid pressure. You can specify multiple nodes or node sets if +multiple locations of the surface are exposed to the fluid. These nodes or node sets are always subjected +to the pressure penetration load if they are on the slave surface, regardless of their contact status. The +fluid then starts to penetrate into the surface between the two contacting bodies from these nodes or node +sets. +Specifying the applied fluid pressure +You must define the reference magnitude of the fluid pressure. You can define the variation of the fluid +pressure during a step by referring to an amplitude curve. By default, the reference magnitude is applied +immediately at the beginning of the step or ramped up linearly over the step, depending on the amplitude +variation assigned to the step . +The fluid pressure penetration load will be applied to the element surface based on the pressure +penetration criterion at the beginning of an increment and will remain constant over that increment even +if the fluid penetrates further during that increment. A nodal integration scheme is used to integrate the +distributed fluid pressure penetration load over an element in two dimensions, while in three dimensions +Gauss integration scheme is used; the variation of the distributed fluid pressure over an element will be +determined by the load magnitudes at the element’s nodes. +Input File Usage: +Use the following option to define the variation of the fluid pressure during a +step: +Abaqus/CAE Usage: +*PRESSURE PENETRATION, AMPLITUDE=name +Interaction module: Create Interaction: Pressure penetration; +Amplitude: name +Removing or modifying the pressure penetration loads +After pressure penetration loads are applied to the element surfaces, +they will not be removed +automatically even when contact between the surfaces is reestablished. At each new step the fluid +pressure penetration loading, however, can be modified or completely redefined in a manner similar to +the way that distributed loads can be defined . +Input File Usage: +Use the following option to modify the fluid pressure penetration loads that +were applied in previous steps: +*PRESSURE PENETRATION, OP=MOD (default) +In this case the slave nodes exposed to the fluid pressure must be specified on +the data lines. If the master surface is not an analytical rigid surface, the master +nodes exposed to the fluid pressure must also be specified on the data lines for +planar or axisymmetric models. +Use the following option to remove all fluid pressure penetration loads and, +optionally, to specify new fluid pressure penetration loads: +*PRESSURE PENETRATION, OP=NEW +When OP=NEW is used to remove all fluid pressure penetration loads, no +data line is needed. However, when OP=NEW is used to specify new fluid +pressure penetration loads, the nodes exposed to the fluid pressure must be +specified on the data lines. OP=NEW must be used when defining new exposed +nodes. In addition, when OP=NEW is used to re-specify a previously defined +pressure penetration load, the fluid pressure loading will revert to its last known +configuration first, even if the contact status has subsequently changed. +Abaqus/CAE Usage: +Use the following option to modify a fluid pressure penetration that was applied +in a previous step: +Interaction module: Interaction Manager: select interaction, Edit +Use the following option to remove a fluid pressure penetration that was applied +in a previous step: +Interaction module: Interaction Manager: select interaction, Deactivate +Specifying a critical mechanical contact pressure +To account for the asperities on the contacting surfaces, a critical contact pressure, below which fluid +penetration starts to occur, is introduced. The higher this value, the easier the fluid penetrates. The +default value of the critical contact pressure is zero, in which case fluid penetration occurs only if contact +is lost. +Use in linear perturbation analysis +Linear perturbation analyses can be performed from time to time during a fully nonlinear analysis by +including linear perturbation steps between the general analysis steps. Because contact conditions cannot +change during a linear perturbation analysis, the fluid will not penetrate further into the surface and it +remains as it was defined in the base state. The fluid pressure magnitude applied in the previous general +analysis step, however, can be modified during a linear perturbation analysis step. In matrix generation + and steady-state dynamic analyses (direct or modal—see +“Direct-solution steady-state dynamic analysis,” Section 6.3.4, and “Mode-based steady-state dynamic +analysis,” Section 6.3.8) you can specify both the real (in-phase) and imaginary (out-of-phase) parts of +the loading. +Input File Usage: +Use the following option to define the real (in-phase) part of the loading: +*PRESSURE PENETRATION, REAL (default) +Use the following option to define the imaginary (out-of-phase) part of the +loading: +*PRESSURE PENETRATION, IMAGINARY +The REAL or IMAGINARY parameters are ignored in all procedures other +than steady-state dynamics. +Abaqus/CAE Usage: +Use the following option to define the real (in-phase) part of the loading: +Interaction module: Create Interaction: Pressure penetration; +Fluid Pressure (Real) +Use the following option to define the imaginary (out-of-phase) part of the +loading: +Interaction module: Create Interaction: Pressure penetration; +Fluid Pressure (Imaginary) +Limitations with pressure penetration loads +Each slave surface subjected to pressure penetration loading must be continuous and cannot be a closed +loop. Pressure penetration loading cannot be used with a node-based slave surface. The pressure +penetration load applied at any increment is based on the contact status at the beginning of that +increment. You should, therefore, be careful in interpreting the results at the end of an increment during +which the contact status has changed. Small time increments are recommended to obtain accurate +results. +When pressure penetrates into contacting bodies between an analytical rigid surface and a +deformable surface, no pressure penetration load will be applied to the analytical rigid surface. The +reference node on the analytical rigid surface should, therefore, be constrained in all directions. To +account for the effect of fluid pressure penetration loads on the rigid surface, the analytical rigid surface +should be replaced with an element-based rigid surface. +When fluid with different pressure loads penetrates into an element simultaneously from multiple +locations on a surface, the maximum value of the fluid pressure loads is applied to the element. +In large-displacement analyses pressure penetration loads introduce unsymmetric load stiffness +matrix terms. Using the unsymmetric matrix storage and solution scheme for the analysis step may +improve the convergence rate of the equilibrium iterations. See “Defining an analysis,” Section 6.1.2, +for more information on the unsymmetric matrix storage and solution scheme. +Only solid, shell, cylindrical, and rigid elements are supported for three-dimensional pressure +penetration. +Output +You can request the fluid pressure load, PPRESS, at the nodes on the slave surface as surface output to +the data, results, and output database files . +36.1.8 +INTERACTION OF DEBONDED SURFACES +Product: Abaqus/Standard +References +• “Contact pressure-overclosure relationships,” Section 36.1.2 +• “Frictional behavior,” Section 36.1.5 +• “Thermal contact properties,” Section 36.2.1 +• “Pore fluid contact properties,” Section 36.4.1 +• *DEBOND +• *FRACTURE CRITERION +Overview +This section outlines briefly how initially bonded surfaces may interact once they have started to +debond. Details on defining a crack propagation analysis can be found in “Crack propagation analysis,” +Section 11.4.3. +When two initially bonded surfaces start to debond: +• the debonded slave surface nodes are released and can move freely; +• the tractions acting on the slave surface nodes at the instant of debonding are ramped down to zero +using a user-supplied amplitude curve; and +• the contact property models assigned to the contact pair formed by the two surfaces start to govern +the interaction of the surfaces. +Frictional interactions of debonding surfaces +Once the surfaces start to debond, +the friction model assigned to the surfaces will govern the +tangential motion of the debonded slave nodes. Friction generates forces tangential to the interface +when the surfaces are closed. The frictional forces are independent of the debonding tractions that +Abaqus/Standard applies and ramp off once a slave node debonds; the debonding tractions have no +influence on the frictional behavior of a surface. +Interaction models for behavior normal to the debonding surfaces +The crack propagation capability in Abaqus/Standard was designed for use in classical fracture +It is intended that the capability be used with the default “hard” contact +mechanics problems. +pressure-clearance model. +the nondefault +pressure-clearance models when the surfaces can debond. +Abaqus/Standard will prevent +the use of one of +Thermal interaction of bonded and debonding surfaces +Crack propagation simulations can be performed as coupled temperature-displacement analyses +in Abaqus/Standard. While bonded, the surfaces are treated as having complete continuity of the +temperature field across the interface. Once the surfaces start to debond, the thermal contact property +models assigned to the surfaces will govern the thermal interactions across the debonded portion of the +interface. +Pore fluid interaction of bonded and debonding surfaces +Crack propagation simulations can be performed in coupled pore pressure-displacement analyses. +Whether the surfaces are bonded or are debonding, they are treated as having complete continuity of +the pore pressure field across the interface. +36.1.9 +BREAKABLE BONDS +Product: Abaqus/Explicit +References +• “Contact formulations for contact pairs in Abaqus/Explicit,” Section 37.2.2 +• *BOND +• *SURFACE INTERACTION +• *CONTACT PAIR +Overview +Breakable bonds, such as spot welds, between surfaces: +• can be defined only at the nodes of the slave surface of a pure master-slave contact pair; +• can be defined only in the first step of a simulation; +• constrain the slave node to the master surface until the failure criterion of the bond is met; +• are designed to provide a simple simulation of spot weld failure under relatively monotonic +straining, such as occurs during an impact of a vehicle structure; +• do not constrain the rotational degrees of freedom at the node; +• use either a time to failure or a damaged failure model to simulate the postfailure response of the +bonds; +• use the default contact property model (“Mechanical contact properties: overview,” Section 36.1.1) +once the bonds have been broken; and +• can be used only between two deformable surfaces with the kinematic contact pair algorithm. +Specifying spot welds for a contact pair +A contact pair that contains spot welds must be a pure master-slave contact pair; therefore, spot welds +If the contact pair consists of two deformable surfaces, +cannot be used with single-surface contact. +Abaqus/Explicit would normally use a balanced master-slave contact pair. +In such situations you +must specify a weighting factor to define a pure master-slave contact pair. Contact pairs containing spot welds must be +defined in the first step of a simulation. The spot welds are located at the nodes of the slave surface of +the contact pair. +Spot welds can also be modeled more accurately using fasteners instead of breakable bonds. +Fasteners have the advantage of being mesh independent in their definition and are convenient for +defining point-to-point connections between two or more surfaces with the capability to model plasticity, +damage, and failure behavior. However, fasteners are intended to be used in three dimensions; therefore, +the fastener method cannot be used to specify spot welds for contact pairs in a two-dimensional case. +If non-breakable bonds (rigid spot welds) are to be modeled, it is recommended that you use the +mesh-independent spot weld feature (“Mesh-independent fasteners,” Section 34.3.4). +All of the slave nodes which are bonded to a master surface can be grouped together into a node set. +Input File Usage: +Use all of the following options: +*CONTACT PAIR, MECHANICAL CONSTRAINT=KINEMATIC, +INTERACTION=interaction_property_name +*SURFACE INTERACTION, NAME=interaction_property_name +*BOND +node_set_name, … +Adjustments to the initial positions of the bonded nodes +Nodes that are bonded to a master surface with spot welds should be defined so that they contact +If the bonded nodes are not in contact initially, +the surface in the model’s initial configuration. +Abaqus/Explicit will enforce the bonded constraint by prescribing strain-free displacements to those +nodes. The nodes will begin the simulation exactly in contact with the master surface. +If the spot +welds are defined incorrectly, this automatic adjustment of the nodes may cause the analysis to end +immediately as a result of excessive initial distortion of elements that are connected to the bonded nodes. +Forces carried by a spot weld +Abaqus assumes that a spot weld carries a force normal to the surface onto which the node is welded, +. The magnitude of the resultant +, and two orthogonal shear forces tangent to the surface, +, +shear force, +, is defined as +. The normal force is positive in tension. +A spot weld is assumed to be so small that it carries no moments or torque. As a result, spot welds +do not impose any constraints on rotational degrees of freedom. +Defining the failure criterion for the spot welds +The failure criterion for a spot weld is defined as +where +and +is the force required to cause failure in tension (Mode I loading), +is the force required to cause failure in pure shear (Mode II loading), and +are defined above. +A typical yield surface for spot welds is shown in Figure 36.1.9–1. By specifying a very large value for +either +, the yield criteria of the spot welds can be made independent of either shear forces or +normal forces, as shown in Figure 36.1.9–2. +or +sF +F f +yield surface +F f +F n +Figure 36.1.9–1 Typical yield surface for spot welds. +F = ∞ +sF +F f +yield surface +sF +F = ∞ +yield surface +nF +nF +F f +shear failure only +tensile failure only +Figure 36.1.9–2 Degenerate yield surfaces for spot welds. +Input File Usage: +*BOND +node_set_name, +, +Spot weld forces sometimes exhibit significant noise, which can cause the spot weld to reach its +failure criterion when a filtered solution of the spot weld forces would still be well within the strength +limits of the spot weld. This is characterized by a noisy time history of the BONDSTAT variable and can +correspond to an unrealistically early onset of failure of a spot weld. Two models for deterioration of a +spot weld after the onset of failure are discussed below: a time to failure model and a postfailure damage +model. With the time to failure model a single, spurious spike in the constraint force history that just +exceeds the spot weld strength will lead to complete failure of the spot weld. The postfailure damage +model may mitigate the effects of noise in the spot weld force. +Defining the postfailure behavior of the spot welds +Once the constraint forces on a spot weld exceed the failure criterion, the spot weld fails and deteriorates +until the weld is broken completely. The behavior of the spot weld during this deterioration process +can be simulated using either a damaged failure model or by linearly reducing the constraint forces to +zero over a specified time period. With either model, the applied constraint forces from a spot weld are +limited by the size of the yield surface as defined by the failure criterion. Deterioration of the spot weld +is modeled by shrinking the yield surface to zero while retaining its original shape. +If the predicted constraint forces exceed the yield surface, the applied forces are calculated using a +radial flow rule to return to the yield surface. +After complete failure, the node behaves like the rest of the slave nodes in the contact pair. The +node may recontact the master surface, but the weld plays no further role. +Defining the time to failure model +You specify the time to failure, +, which is the time required for the spot weld to fail completely after +the initial failure criterion has been exceeded. Once failure is detected, the weld constraint is relaxed +linearly over the time +. Abaqus/Explicit shrinks the yield surface to zero over the time period +: +where t is the time since Abaqus/Explicit detected initial failure of the weld. +Input File Usage: +*BOND +node_set_name, +, +, +, +Defining the postfailure damage model +As stated above, if the predicted constraint forces exceed the failure criterion, the forces carried by the +spot weld are calculated using a radial flow rule to return to the yield surface. Since the forces in the weld +in this case are less than the constraint forces required to constrain the welded node on the master surface, +the welded node will move relative to the master surface. The work expended during this relative motion +is used to determine how the yield surface degrades. +During failure the behavior of the weld is assumed to be such that any stretching of the weld in the +normal direction, or any shearing of the weld, dissipates energy. Abaqus/Explicit assumes a linear force- +displacement relationship after failure, thus resulting in the behaviors sketched in Figure 36.1.9–3 when +the weld is subjected to pure Mode I or pure Mode II loading. More general loadings create combinations +of these responses. +You define the amount of energy that the weld can dissipate in Mode I and Mode II by specifying +the breakage displacements in the normal and shear directions under pure Mode I and Mode II loading, +and +. +nF +F f +sF +F f +nu +u f +u f +su +Figure 36.1.9–3 Typical postfailure behavior in pure +tension/compression (Mode I) and in pure shear (Mode II). +Using these linear force-displacement relationships, the failure criterion for the damaged failure +model is +where +is the energy expended in Mode I; +is the energy expended in Mode II; +is the breakage energy in Mode I, which is calculated as +is the breakage energy in Mode II, which is calculated as +; and +. +Input File Usage: +*BOND +node_set_name, +, +, +, , +, +Post-yield surface interactions in spot welds +Any friction, contact damping, or softening defined at the spot weld will not affect the analysis until the +weld is broken completely; i.e., until the failure surface has shrunk to zero. +Bead size of the spot weld +The initial bead size of the spot weld, +, is taken into account by offsetting the slave surface node +associated with the spot weld from the master surface by an amount equal to the bead size during the +penetration calculations. A master or slave surface defined on shell or membrane elements is itself offset +from the midplane of the element by the half-thickness of the shell or membrane. +If the damaged failure model is chosen to characterize the postfailure behavior, the size of the spot +weld bead may grow due to tensile yielding of the spot weld. The size of the spot weld is equal to the +sum of +accumulated after the failure of the spot weld. After the weld has broken, the +and the +size of the bead at breakage is taken into account for subsequent contact between the weld node and the +master surface. +Available output for spot welds +You can examine the forces carried by spot welds in Abaqus/CAE by generating a vector plot of the +reaction forces on the surface (output variable CFORCE). Two output variables specifically related to spot +welds, the bond status and bond load, are available for use in Abaqus/CAE. These variables can be written +as history output to the output database (.odb) file. They can be used in X–Y plots in Abaqus/CAE. +Definition of bond status +The bond status (output variable BONDSTAT) is a measure of how close a spot weld is to complete +failure. The bond status varies between 0.0 and 1.0 and is defined to be +if the time to failure postfailure model is chosen or +if the damaged failure model is chosen. With either model, the bond status is equal to 1.0 before the spot +weld fails. +Definition of bond load +The bond load (output variable BONDLOAD) is a measure of how close the current constraint forces at +a spot weld are to its failure surface. The value of the bond load also varies between 0.0 and 1.0 and is +defined to be +if the damaged failure model is chosen. For the time to failure model, the bond load is defined to be +prior to failure. Then, the bond load is 1.0 from the moment of first yield until total failure, at which +point the bond load becomes 0.0. +Example: Spot welds and output requests +The spot-welded nodes in node set WELDS are a subset of the nodes on surface A, which is the slave +surface of the pure master-slave contact pair. +*NSET, NSET=WELDS +node set definition +*CONTACT PAIR, MECHANICAL CONSTRAINT=KINEMATIC, +INTERACTION=A TO B, WEIGHT=0. +slave surface A, master surface B +*SURFACE INTERACTION, NAME=A TO B +*BOND +WELDS, +*OUTPUT, HISTORY, TIME INTERVAL=0.001 +*CONTACT OUTPUT, NSET=WELDS +BONDSTAT, BONDLOAD +, +, +, +, +, +Here +damaged failure model is chosen. +must be specified if the time to failure model is used, or +and +must be specified if the +36.1.10 +SURFACE-BASED COHESIVE BEHAVIOR +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Progressive damage and failure,” Section 24.1.1 +• “De��ning the constitutive response of cohesive elements using a traction-separation description,” +Section 32.5.6 +• “Defining contact pairs in Abaqus/Standard,” Section 35.3.1 +• “Defining general contact interactions in Abaqus/Explicit,” Section 35.4.1 +• “Mechanical contact properties: overview,” Section 36.1.1 +• “Crack propagation analysis,” Section 11.4.3 +• *COHESIVE BEHAVIOR +• *SURFACE INTERACTION +• *DAMAGE INITIATION +• *DAMAGE EVOLUTION +• *DAMAGE STABILIZATION +• *FRACTURE CRITERION +• “Specifying cohesive behavior properties for mechanical contact property options” in “Defining +a contact interaction property,” Section 15.14.1 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Specifying cohesive damage properties for mechanical contact property options” in “Defining a +contact interaction property,” Section 15.14.1 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +The features described in this section allow the specification of generalized traction-separation behavior +for surfaces. This behavior offers capabilities that are very similar to cohesive elements that are defined +using a traction-separation law . However, surface-based cohesive behavior is typically +easier to define and allows simulation of a wider range of cohesive interactions, such as two “sticky” +surfaces coming into contact during an analysis. +Surface-based cohesive behavior is primarily intended for situations in which the interface thickness +is negligibly small. If the interface adhesive layer has a finite thickness and macroscopic properties (such +as stiffness and strength) of the adhesive material are available, it may be more appropriate to model +the response using conventional cohesive elements . +In Abaqus/Explicit the surface-based cohesive behavior framework can also be used to model crack +propagation in initially partially bonded surfaces via linear elastic fracture mechanics principles (LEFM) +as implemented using the Virtual Crack Closure Technique (VCCT). +Surface-based cohesive behavior: +• is defined as a surface interaction property; +• can be used to model the delamination at interfaces directly in terms of traction versus separation; +• can be used to model “sticky” contact (i.e., surfaces or parts of surfaces that are not initially in +contact may bond on coming into contact; subsequently the bond may damage and fail); +• can be restricted to surface regions that are initially in contact and, in Abaqus/Standard, to portions +of surface regions that are initially in contact; +• allows specification of cohesive data such as the fracture energy as a function of the ratio of normal +to shear displacements (mode mix) at the interface; +• assumes a linear elastic traction-separation law prior to damage; +• assumes that failure of the cohesive bond is characterized by progressive degradation of the +cohesive stiffness, which is driven by a damage process (in Abaqus/Explicit brittle fracture can +also be modeled using a VCCT fracture crierion); +• allows specification of post-failure cohesive behavior if failed nodes re-enter contact; +• is implemented within the general contact algorithmic framework in Abaqus/Explicit and within +the contact pair framework in Abaqus/Standard; +• can be used to enforce “rough friction” surface interactions, the “no separation” contact relationship, +or a combined “no separation and rough friction” behavior within the general contact framework in +Abaqus/Explicit; +• is enforced only for node-to-face contact interactions in Abaqus/Explicit and is not available for +edge-to-edge and node-to-analytical rigid surface contact interactions; +• cannot be used in a coupled Eulerian-Lagrangian analysis in Abaqus/Explicit; and +• can be used for all Abaqus/Standard contact formulations except the finite sliding, surface-to-surface +formulation. +Defining cohesive behavior in Abaqus/Explicit +Cohesive behavior in Abaqus/Explicit is defined as part of the surface interaction properties that are +assigned to the applicable surfaces. General contact must be defined for the model. +Input File Usage: +Use the following options to define cohesive behavior between two surfaces in +a general contact definition: +*SURFACE INTERACTION, NAME=name +*COHESIVE BEHAVIOR +*CONTACT +*CONTACT PROPERTY ASSIGNMENT +surface1, surface2, name +Abaqus/CAE Usage: +Use the following option to define cohesive behavior between two surfaces: +Interaction module: contact property editor: Mechanical→Cohesive +Behavior +Use the following option to define contact between two surfaces: +Interaction module: interaction editor: General contact (Explicit): +specify Contact interaction property +Contact formulation for cohesive behavior in Abaqus/Explicit +In Abaqus/Explicit overconstraints can arise in certain situations if the balanced master-slave formulation +is enforced in addition to the cohesive constraint. To prevent this from occurring, a pure master-slave +formulation is enforced for surfaces with cohesive behavior in Abaqus/Explicit. If cohesive behavior is +defined between two surfaces, the first surface defined in the contact property assignment is treated as a +slave surface and the second surface as its corresponding master surface. For contact interactions between +the cohesive surfaces and other parts of the general contact domain, the default contact formulation +(balanced master-slave) is applicable, unless a nondefault general contact formulation has been defined +. The surface-based +cohesive behavior is available only for node-to-face contact interactions; it is not available for edge- +to-edge interactions. Hence, it is not possible to define surface-based cohesion between edges of beam +and truss elements. +In addition, contact definitions related to thermal interactions are ignored when +surface-based cohesive behavior is defined. +Care should be exercised when cohesive behavior is used in conjunction with stacked conventional +shell elements. Depending on the load case, the specialized contact formulation may lead to approximate +normal contact forces, which in turn may induce approximate transverse shear behavior in the stacked +shells that affect the bending behavior of the stack. Continuum shells should be used instead of +conventional shells in such modeling scenarios. +Resolving initial overclosures and gaps in Abaqus/Explicit +In many debonding applications using cohesive surfaces, it may be desirable to begin the analysis with the +surfaces just touching each other. This requires the resolution of initial overclosures and gaps between the +surfaces at the start of the analysis to ensure that the slave nodes are precisely in contact with the master +surface. In Abaqus/Explicit small initial overclosures are set to zero by default. To resolve large initial +overclosures or to close initial gaps between the surfaces, an appropriate contact clearance specification +may be defined, as explained in “Controlling initial contact status for general contact in Abaqus/Explicit,” +Section 35.4.4. Since a pure-master slave formulation is enforced for cohesive surfaces, only nodes of +the slave surface will undergo strain-free corrections to resolve any initial overclosures or gaps with their +master facets; the nodes of the master facets will not be moved. +Defining cohesive behavior in Abaqus/Standard +Cohesive behavior in Abaqus/Standard is defined as part of the surface interaction properties that are +assigned to a contact pair. Cohesive behavior cannot be assigned to contact pairs using the finite sliding, +surface-to-surface formulation . +Input File Usage: +Use the following options to define cohesive behavior between the surfaces in +a contact pair: +*SURFACE INTERACTION, NAME=name +*COHESIVE BEHAVIOR +*CONTACT PAIR, INTERACTION=name +surface1, surface2 +Abaqus/CAE Usage: +Use the following option to define cohesive behavior between two surfaces: +Interaction module: contact property editor: Mechanical→Cohesive +Behavior +Use the following option to define surface-to-surface contact between two +surfaces: +Interaction module: interaction editor: Surface-to-surface contact +(Standard): Bonding tabbed page: specify Contact interaction property +Resolving initial overclosures and gaps in Abaqus/Standard +As discussed above, it is often desirable in debonding applications for the cohesive surfaces to begin +the analysis just touching each other. Abaqus/Standard offers some tools for adjusting slave nodes in a +contact pair so that they precisely contact the master surface, thereby eliminating initial overclosures and +gaps. If nodes are not adjusted, even an extremely small initial gap will cause the contact constraints to +be initialized to inactive and, thus, not cohered. These tools are described in “Adjusting initial surface +positions and specifying initial clearances in Abaqus/Standard contact pairs,” Section 35.3.5. +Controlling the set of cohered nodes +By default, cohesive constraint forces can potentially act on all nodes of the surfaces for which cohesive +behavior is defined. Slave nodes that are initially contacting the master surface can experience cohesive +forces at the start of the analysis, and slave nodes that are not initially contacting the master surface can +experience cohesive forces if they contact the master surface during the analysis. There may, however, +be situations where it is desirable to enforce cohesive behavior only for portions of surfaces that are +contacting at the start of the analysis. +Restricting cohesive behavior to initially contacting nodes +As part of the cohesive behavior definition, you can indicate that only those nodes that are in contact with +the master surface at the start of the step should experience cohesive forces. Any new contacts that occur +during the step will not experience cohesive constraint forces; they will be modeled only as compressive +contact. +Input File Usage: +*COHESIVE BEHAVIOR, ELIGIBILITY=ORIGINAL CONTACTS +Abaqus/CAE Usage: +Interaction module: contact property editor: Mechanical→Cohesive +Behavior: Only slave nodes initially in contact +Restricting cohesive behavior to specified nodes +In Abaqus/Standard you can specify a subset of initially slave nodes that should experience cohesive +forces. Strain-free adjustments will be made for those nodes initially not in contact but specified in the +node set. All slave nodes outside of this set (including those that are initially contacting the master +surface) will experience only compressive contact forces over the course of the analysis. This method is +particularly useful for modeling crack propagation along an existing fault line. +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=CONTACT +*COHESIVE BEHAVIOR, ELIGIBILITY=SPECIFIED CONTACTS +Interaction module: contact property editor: Mechanical→Cohesive +Behavior: Specify the bonding node set in the surface- +to-surface (Standard) interaction +Interaction module: interaction editor: Bonding tabbed page: Limit +bonding to slave nodes in sub-set +Interaction of traction-separation behavior with compressive and friction behavior +In the contact normal direction, the pressure overclosure relationship governing the compressive behavior +between the surfaces does not interact with the cohesive behavior, since they each describe the interaction +between the surfaces in a different contact regime. The pressure overclosure relationship governs the +behavior only when a slave node is “closed” (i.e., it is in contact with the master surface); the cohesive +behavior contributes to the contact normal stress only when a slave node is “open” (i.e., not in contact). +In the case of “sticky” cohesive behavior—where the two surfaces are not initially in contact—cohesive +effects are activated in the increment after the slave node status changes from open to closed. +In the shear direction, if the cohesive stiffness is undamaged, it is assumed that the cohesive model +is active and the friction model is dormant. Any tangential slip is assumed to be purely elastic in nature +and is resisted by the cohesive strength of the bond, resulting in shear forces. If damage has been defined, +the cohesive contribution to the shear stresses starts degrading with damage evolution. Once the cohesive +stiffness starts degrading, the friction model activates and begins contributing to the shear stresses. The +elastic stick stiffness of the friction model is ramped up in proportion to the degradation of the elastic +cohesive stiffness. Prior to the ultimate failure of the cohesive bond, and following the initiation of the +degradation of the cohesive bond, the shear stress is a combination of the cohesive contribution and +the contribution from the friction model. Once maximum degradation has been reached, the cohesive +contribution to the shear stresses is zero, and the only contribution to the shear stresses is from the friction +model. +Applying cohesive material concepts to surface-based cohesive behavior +The formulae and laws that govern cohesive surface behavior are very similar to those used for cohesive +elements with traction-separation constitutive behavior (“Defining the constitutive response of cohesive +elements using a traction-separation description,” Section 32.5.6). The similarities extend to the linear +elastic traction-separation model, damage initiation criteria, and damage evolution laws. +However, it is important to recognize that damage in surface-based cohesive behavior is an +interaction property, not a material property. Concepts of strain and displacement (used in behavior +model formulae for cohesive elements) are reinterpreted as contact separations; contact separations are +the relative displacements between the nodes on the slave surface and their corresponding projection +points on the master surface along the contact normal and shear directions. Stresses are defined for +surface-based cohesive behavior as the cohesive forces acting along the contact normal and shear +directions divided by the current area at each contact point. +The specifics of the surface-based cohesive behavior model are discussed in the sections that follow. +Linear elastic traction-separation behavior +The available traction-separation model in Abaqus assumes initially linear elastic behavior followed by the initiation and evolution of damage. The elastic behavior is +written in terms of an elastic constitutive matrix that relates the normal and shear stresses to the normal +and shear separations across the interface. +traction stress vector, +, +, consists of three components (two components in +two-dimensional problems): +, which represent the normal +(along the local 3-direction in three dimensions and along the local 2-direction in two dimensions) and +the two shear tractions (along the local 1- and 2-directions in three dimensions and along the local +1-direction in two dimensions), respectively. The corresponding separations are denoted by +, and +, and (in three-dimensional problems) +The nominal +, +. The elastic behavior can then be written as +Uncoupled traction-separation behavior +The simplest specification of cohesive behavior generates contact penalties that enforce the cohesive +constraint in both normal and tangential directions. By default, the normal and tangential stiffness +components will not be coupled: pure normal separation by itself does not give rise to cohesive forces in +the shear directions, and pure shear slip with zero normal separation does not give rise to any cohesive +forces in the normal direction. +For uncoupled traction-separation behavior, the terms +must be defined, as well +as any dependencies on temperature or field variables. If these terms are not defined, Abaqus uses default +contact penalties to model the traction-separation behavior. +, and +, +Input File Usage: +Abaqus/CAE Usage: +*COHESIVE BEHAVIOR, TYPE=UNCOUPLED (default) +Interaction module: contact property editor: Mechanical→Cohesive +Behavior: Specify stiffness coefficients: Uncoupled +Coupled traction-separation behavior +In its full generality, the elasticity matrix provides fully coupled behavior between all components of the +traction vector and separation vector and can depend on temperature and/or field variables. All terms in +the matrix must be defined for coupled traction-separation behavior. +Input File Usage: +Abaqus/CAE Usage: +*COHESIVE BEHAVIOR, TYPE=COUPLED +Interaction module: contact property editor: Mechanical→Cohesive +Behavior: Specify stiffness coefficients: Coupled +Cohesive behavior in the normal or shear direction only +To restrict the cohesive constraint to act along the contact normal direction only, define uncoupled +cohesive behavior and specify zero values for the shear stiffness components, +. +and +Alternatively, if only tangential cohesive constraints are to be enforced, the normal stiffness term, +, +can be set to zero, in which case the normal “separations” will not be constrained. Normal compressive +forces are resisted as per the usual contact behavior. +Damage modeling +Damage modeling allows you to simulate the degradation and eventual failure of the bond between two +cohesive surfaces. The failure mechanism consists of two ingredients: a damage initiation criterion and +a damage evolution law. The initial response is assumed to be linear as discussed above. However, once +a damage initiation criterion is met, damage can occur according to a user-defined damage evolution law. +Figure 36.1.10–1 shows a typical traction-separation response with a failure mechanism. If the damage +initiation criterion is specified without a corresponding damage evolution model, Abaqus evaluates the +damage initiation criterion for output purposes only; there is no effect on the response of the cohesive +surfaces (i.e., no damage will occur). Cohesive surfaces do not undergo damage under pure compression. +Damage of the traction-separation response for cohesive surfaces is defined within the same general +framework used for conventional materials , +except the damage behavior is specified as part of the interaction properties for the surfaces. Multiple +damage response mechanisms are not available for cohesive surfaces: cohesive surfaces can have only +one damage initiation criterion and only one damage evolution law. +Input File Usage: +Use the following options to define damage initiation and damage evolution for +cohesive surfaces: +*SURFACE INTERACTION, NAME=name +*COHESIVE BEHAVIOR +*DAMAGE INITIATION +*DAMAGE EVOLUTION +Interaction module: contact property editor: Mechanical→Damage: +Damage Initiation and Damage Evolution tabbed pages +Abaqus/CAE Usage: +traction +t (t , t ) +n s t +δ (δ ,δ ) +δ (δ ,δ ) +separation +Figure 36.1.10–1 Typical traction-separation response. +Damage initiation +Damage initiation refers to the beginning of degradation of the cohesive response at a contact point. The +process of degradation begins when the contact stresses and/or contact separations satisfy certain damage +initiation criteria that you specify. Several damage initiation criteria are available and are discussed +below. +Each damage initiation criterion also has an output variable associated with it to indicate whether +the criterion is met. A value of 1 or higher indicates that the initiation criterion has been met. Damage +initiation criteria that do not have an associated evolution law affect only output. Thus, you can use +these criteria to evaluate the propensity of the material to undergo damage without actually modeling the +damage process (i.e., without actually specifying damage evolution). +, +, and +In the discussion below, +represent the peak values of the contact stress when the +separation is either purely normal to the interface or purely in the first or the second shear direction, +respectively. Likewise, +represent the peak values of the contact separation, when the +separation is either purely along the contact normal or purely in the first or the second shear direction, +respectively. The symbol +used in the discussion below represents the Macaulay bracket with the usual +interpretation. The Macaulay brackets are used to signify that a purely compressive displacement (i.e., +a contact penetration) or a purely compressive stress state does not initiate damage. +, and +, +Maximum stress criterion +Damage is assumed to initiate when the maximum contact stress ratio (as defined in the expression below) +reaches a value of one. This criterion can be represented as +Input File Usage: +Abaqus/CAE Usage: +*DAMAGE INITIATION, CRITERION=MAXS +Interaction module: contact property editor: Mechanical→Damage: +Initiation tabbed page: Criterion: Maximum nominal stress +Maximum separation criterion +Damage is assumed to initiate when the maximum separation ratio (as defined in the expression below) +reaches a value of one. This criterion can be represented as +Input File Usage: +Abaqus/CAE Usage: +*DAMAGE INITIATION, CRITERION=MAXU +Interaction module: contact property editor: Mechanical→Damage: +Initiation tabbed page: Criterion: Maximum separation +Quadratic stress criterion +Damage is assumed to initiate when a quadratic interaction function involving the contact stress ratios +(as defined in the expression below) reaches a value of one. This criterion can be represented as +Input File Usage: +Abaqus/CAE Usage: +*DAMAGE INITIATION, CRITERION=QUADS +Interaction module: contact property editor: Mechanical→Damage: +Initiation tabbed page: Criterion: Quadratic traction +Quadratic separation criterion +Damage is assumed to initiate when a quadratic interaction function involving the separation ratios (as +defined in the expression below) reaches a value of one. This criterion can be represented as +Input File Usage: +Abaqus/CAE Usage: +*DAMAGE INITIATION, CRITERION=QUADU +Interaction module: contact property editor: Mechanical→Damage: +Initiation tabbed page: Criterion: Quadratic separation +Damage evolution +The damage evolution law describes the rate at which the cohesive stiffness is degraded once the +corresponding initiation criterion is reached. The general framework for describing the evolution of +damage in bulk materials (as opposed to interfaces modeled using cohesive surfaces) is described in +“Damage evolution and element removal for ductile metals,” Section 24.2.3. Conceptually, similar +ideas apply for describing damage evolution in cohesive surfaces. +A scalar damage variable, D, represents the overall damage at the contact point. It initially has a +value of 0. If damage evolution is modeled, D monotonically evolves from 0 to 1 upon further loading +after the initiation of damage. The contact stress components are affected by the damage according to +otherwise (no damage to compressive stiffness); +, +where +for the current separations without damage. +, and +are the contact stress components predicted by the elastic traction-separation behavior +To describe the evolution of damage under a combination of normal and shear separations across +the interface, it is useful to introduce an effective separation (Camanho and Davila, 2002) defined as +it can be +While this formula was originally applied to damage evolution in cohesive elements, +reinterpreted in terms of contact separations for cohesive surface behavior, as discussed above . +Mixed-mode definition +The relative proportions of normal and shear separations at a contact point define the mode mix at the +point. Abaqus uses two measures of mode mix, one based on energies and the other based on tractions. +You can choose one of these measures when you specify the mode dependence of the damage evolution +process. Denoting by +the work done by the tractions and their conjugate separations +in the normal, first, and second shear directions, respectively, and defining +, the +mode-mix definitions based on energies are as follows: +, and +, +Clearly, only two of the three quantities defined above are independent. It is also useful to define the +quantity +to denote the portion of the total work done by the shear traction and the +corresponding separation components. As discussed later, Abaqus requires that you specify material +properties related to damage evolution as functions of +) +and +(or, equivalently, +. +The corresponding definitions of the mode mix based on traction components are given by +where +definition (before they are normalized by the factor +is a measure of the effective shear traction. The angular measures used in the above +) are illustrated in Figure 36.1.10–2. +t~ +normal +t n +t t +Shear 2 +t s +Shear 1 +Figure 36.1.10–2 Mode-mix measures based on traction. +The mode-mix ratios defined in terms of energies and tractions can be quite different in general. The +following example illustrates this point. In terms of energies a separation in the purely normal direction +is one for which +, irrespective of the values of the normal and the shear +tractions. In particular, for coupled traction-separation behavior both the normal and shear tractions may +be nonzero for a purely normal separation. For this case the definition of mode mix based on energies +would indicate a purely normal separation, while the definition based on tractions would suggest a mix +of both normal and shear separation. +and +There are two components to the definition of damage evolution. The first component involves +specifying either the effective separation at complete failure, +, relative to the effective separation at +the initiation of damage, +. The +second component to the definition of damage evolution is the specification of the nature of the evolution +of the damage variable, D, between initiation of damage and final failure. This can be done by either +defining linear or exponential softening laws or specifying D directly as a tabular function of the effective +separation relative to the effective separation at damage initiation. The data described above will in +general be functions of the mode mix, temperature, and/or field variables. +; or the energy dissipated due to failure, +traction +δ o +δ f +separation +Figure 36.1.10–3 Linear damage evolution. +Figure 36.1.10–4 is a schematic representation of the dependence of damage initiation and evolution +on the mode mix for a traction-separation response with isotropic shear behavior. The figure shows the +traction on the vertical axis and the magnitudes of the normal and the shear separations along the two +horizontal axes. The unshaded triangles in the two vertical coordinate planes represent the response under +pure normal and pure shear separation, respectively. All intermediate vertical planes (that contain the +vertical axis) represent the damage response under mixed-mode conditions with different mode mixes. +The dependence of the damage evolution data on the mode mix can be defined either in tabular form or, +in the case of an energy-based definition, analytically. The manner in which the damage evolution data +are specified as a function of the mode mix is discussed later in this section. +Figure 36.1.10–4 Illustration of mixed-mode response in cohesive interactions. +Unloading subsequent to damage initiation is always assumed to occur linearly toward the origin +of the traction-separation plane, as shown in Figure 36.1.10–3. Reloading subsequent to unloading +also occurs along the same linear path until the softening envelope (line AB) is reached. Once the +softening envelope is reached, further reloading follows this envelope as indicated by the arrow in +Figure 36.1.10–3. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to use the mode-mix definition based on energies: +*DAMAGE EVOLUTION, MODE MIX RATIO=ENERGY +Use the following option to use the mode-mix definition based on tractions: +*DAMAGE EVOLUTION, MODE MIX RATIO=TRACTION +Interaction module: contact property editor: Mechanical→Damage: +Evolution tabbed page: toggle on Specify mixed-mode behavior: +Mode mix ratio: Energy or Traction +Evolution based on effective separation +You specify the quantity +the effective separation at damage initiation, +(i.e., the effective separation at complete failure, +, relative to +, as shown in Figure 36.1.10–3) as a tabular function +of the mode mix, temperature, and/or field variables. +In addition, you also choose either a linear +or an exponential softening law that defines the detailed evolution (between initiation and complete +failure) of the damage variable, D, as a function of the effective separation beyond damage initiation. +Alternatively, instead of using linear or exponential softening, you can specify the damage variable, D, +directly as a tabular function of the effective separation after the initiation of damage, +; mode +mix; temperature; and/or field variables. +Linear damage evolution +For linear softening Abaqus uses an evolution of the damage variable, D, that +reduces (in the case of damage evolution under a constant mode mix, temperature, and field variables) +to the following expression: +In the preceding expression and in all later references, +refers to the maximum value of the effective +separation attained during the loading history. The assumption of a constant mode mix at a contact point +between initiation of damage and final failure is customary for problems involving monotonic damage +(or monotonic fracture). +Input File Usage: +Use the following option to specify linear damage evolution: +*DAMAGE EVOLUTION, TYPE=DISPLACEMENT, +SOFTENING=LINEAR +Abaqus/CAE Usage: +Interaction module: contact property editor: Mechanical→Damage: +Evolution tabbed page: Type: Displacement: Softening: Linear +Exponential damage evolution +For exponential softening Abaqus uses an evolution of the damage variable, D, +that reduces (in the case of damage evolution under a constant mode mix, temperature, and field variables) +to +In the expression above +is a non-dimensional parameter that defines the rate of damage evolution and +is the exponential function. +Input File Usage: +Use the following option to specify exponential softening: +*DAMAGE EVOLUTION, TYPE=DISPLACEMENT, +SOFTENING=EXPONENTIAL +Abaqus/CAE Usage: +Interaction module: contact property editor: Mechanical→Damage: +Evolution tabbed page: Type: Displacement: Softening: Exponential +traction +δ o +δ f +separation +Figure 36.1.10–5 Exponential damage evolution. +Tabular damage evolution +For tabular softening you define the evolution of D directly in tabular form. D must be specified +as a function of the effective separation relative to the effective separation at initiation, mode mix, +temperature, and/or field variables. +Input File Usage: +Use the following option to define the damage variable directly in tabular form: +*DAMAGE EVOLUTION, TYPE=DISPLACEMENT, +SOFTENING=TABULAR +Abaqus/CAE Usage: +Interaction module: contact property editor: Mechanical→Damage: +Evolution tabbed page: Type: Displacement: Softening: Tabular +Evolution based on energy +Damage evolution can be defined based on the energy that is dissipated as a result of the damage process, +also called the fracture energy. The fracture energy is equal to the area under the traction-separation +curve . You specify the fracture energy as a property of the cohesive interaction +and choose either a linear or an exponential softening behavior. Abaqus ensures that the area under the +linear or the exponential damaged response is equal to the fracture energy. +The dependence of the fracture energy on the mode mix can be specified either directly in tabular +form or by using analytical forms as described below. When the analytical forms are used, the mode-mix +ratio is assumed to be defined in terms of energies. +Tabular form +The simplest way to define the dependence of the fracture energy is to specify it directly as a function of +the mode mix in tabular form. +Input File Usage: +Use the following option to specify fracture energy as a function of the mode +mix in tabular form: +*DAMAGE EVOLUTION, TYPE=ENERGY, +MIXED MODE BEHAVIOR=TABULAR +Abaqus/CAE Usage: +Interaction module: contact property editor: Contact: +Mechanical→Damage: Evolution tabbed page: Type: Energy: +toggle on Specify mixed mode behavior: Tabular +Power law form +The dependence of the fracture energy on the mode mix can be defined based on a power law fracture +criterion. The power law criterion states that failure under mixed-mode conditions is governed by a +power law interaction of the energies required to cause failure in the individual (normal and two shear) +modes. It is given by +The mixed-mode fracture energy +when the above condition is satisfied. In other words, +You specify the quantities +failure in the normal, the first, and the second shear directions, respectively. +, and +, +, which refer to the critical fracture energies required to cause +Input File Usage: +Use the following option to define the fracture energy as a function of the mode +mix using the analytical power law fracture criterion: +Abaqus/CAE Usage: +*DAMAGE EVOLUTION, TYPE=ENERGY, +MIXED MODE BEHAVIOR=POWER LAW, POWER= +Interaction module: contact property editor: Mechanical→Damage: +Evolution tabbed page: Type: Energy: toggle on Specify mixed +mode behavior: Power law: +Benzeggagh-Kenane (BK) form +The Benzeggagh-Kenane fracture criterion (Benzeggagh and Kenane, 1996) is particularly useful when +the critical fracture energies during separation purely along the first and the second shear directions are +the same; i.e., +. It is given by +where +and . +Input File Usage: +, +, and +is a cohesive property parameter. You specify +, +, +Use the following option to define the fracture energy as a function of the mode +mix using the analytical BK fracture criterion: +*DAMAGE EVOLUTION, TYPE=ENERGY, +MIXED MODE BEHAVIOR=BK, POWER= +Abaqus/CAE Usage: +Interaction module: contact property editor: Mechanical→Damage: +Evolution tabbed page: Type: Energy: toggle on Specify mixed +mode behavior: Benzeggagh-Kenane: +Linear damage evolution +For linear softening Abaqus uses an evolution of the damage variable, D, that +reduces to +where +maximum value of the effective separation attained during the loading history. +as the effective traction at damage initiation. +with +refers to the +Input File Usage: +Use the following option to specify linear damage evolution: +Abaqus/CAE Usage: +*DAMAGE EVOLUTION, TYPE=ENERGY, SOFTENING=LINEAR +Interaction module: contact property editor: Mechanical→Damage: +Evolution tabbed page: Type: Energy: Softening: Linear +Exponential damage evolution +For exponential softening Abaqus uses an evolution of the damage variable, D, that reduces to +In the expression above +is the elastic +energy at damage initiation. In this case the traction might not drop immediately after damage initiation, +which is different from what is seen in Figure 36.1.10–5. +and are the effective traction and separation, respectively. +Input File Usage: +Use the following option to specify exponential softening: +*DAMAGE EVOLUTION, TYPE=ENERGY, +SOFTENING=EXPONENTIAL +Abaqus/CAE Usage: +Interaction module: contact property editor: Mechanical→Damage: +Evolution tabbed page: Type: Energy: Softening: Exponential +Defining damage evolution data as a tabular function of mode mix +As discussed earlier, the data defining the evolution of damage at the cohesive interface can be tabular +functions of the mode mix. The manner in which this dependence must be defined in Abaqus is outlined +below for mode-mix definitions based on energy and traction, respectively. In the following discussion +it is assumed that the evolution is defined in terms of energy. Similar observations can also be made for +evolution definitions based on effective separation. +Mode mix based on energy +and +. The quantity +For an energy-based definition of mode mix, in the most general case of a three-dimensional state of +separation with anisotropic shear behavior the fracture energy, +, must be defined as a function of +is a measure of the fraction of the +total separation that is shear, while +is a measure of the fraction of the total +shear separation that is in the second shear direction. Figure 36.1.10–6 shows a schematic of the fracture +energy versus mode-mix behavior. The limiting cases of pure normal and pure shear separations in the +first and second shear directions are denoted in Figure 36.1.10–6 by +, respectively. The +lines labeled “Modes n-s,” “Modes n-t,” and “Modes s-t” show the transition in behavior between the +pure normal and the pure shear in the first direction, pure normal and pure shear in the second direction, +and pure shears in the first and second directions, respectively. In general, +must be specified as a +function of +. In the discussion that follows we +at various fixed values of +refer to a data set of +as a “data block.” +versus +The following guidelines are useful in defining the fracture energy as a function of the mode mix: +corresponding to a fixed +, and +, +• For a two-dimensional problem +only. The data column corresponding to +only one “data block” is needed. +needs to be defined as a function of +in this case) +must be left blank. Hence, essentially +( +• For a three-dimensional problem with isotropic shear response, the shear behavior is defined by the +. Therefore, in this case a single +) also suffices to define the fracture energy +and not by the individual values of +and +sum +“data block” (the “data block” for +as a function of the mode mix. +at a fixed value of +“data blocks” would be needed. As discussed earlier, each “data block” would contain +• In the most general case of three-dimensional problems with anisotropic shear behavior, several +versus +can vary between +0 and 1.0. The case +(the first data point in any “data block”), which corresponds to +a purely normal mode, can never be achieved when +(i.e., the only valid point +on line OB in Figure 36.1.10–6 is the point O, which corresponds to a purely normal separation). +However, in the tabular definition of the fracture energy as a function of mode mix, this point simply +serves to set a limit that ensures a continuous change in fracture energy as a purely normal state is +approached from various combinations of normal and shear separations. Hence, the fracture energy +. In each “data block” +Modes n-s +Modes s-t +Modes n-t +m + m = ( +2 3 +G s +G T +( +1.0 +1.0 +Figure 36.1.10–6 Fracture energy as a function of mode mix. + m + 3 +m + m = ( +2 3 +( +G t +GS +of the first data point in each “data block” must always be set equal to the fracture energy in a purely +normal separation ( +). +As an example of the anisotropic shear case, consider that you want to input three “data blocks” +corresponding to fixed values of +0., 0.2, and 1.0, respectively. For each of the +three “data blocks,” the first data point must be +for the reasons discussed above. The rest +of the data points in each “data block” define the variation of the fracture energy with increasing +proportions of shear separation. +Mode mix based on traction +at various fixed values of +needs to +The fracture energy needs to be specified in tabular form of +be specified as a function of +. A “data block” in this case corresponds to +a set of data for +may vary from 0 (purely +versus +normal separation) to 1 (purely shear separation). An important restriction is that each data block must +specify the same value of the fracture energy for +. This restriction ensures that the energy required +for fracture as the traction vector approaches the normal direction does not depend on the orientation of +the projection of the traction vector on the shear plane . +. In each “data block” +, at a fixed value of +. Thus, +versus +and +Viscous regularization in Abaqus/Standard +Models exhibiting various forms of softening behavior and stiffness degradation often lead to severe +convergence difficulties in Abaqus/Standard. Viscous regularization of the constitutive equations +defining surface-based cohesive behavior can be used to overcome some of these convergence +difficulties. This technique is also applicable to cohesive elements, fastener damage, and the concrete +material model in Abaqus/Standard. Viscous regularization damping causes the tangent stiffness matrix +that defines the contact stresses to be positive for sufficiently small time increments. +The approximate amount of energy associated with viscous regularization over the whole model is +available using output variable ALLVD. +Input File Usage: +Abaqus/CAE Usage: +*DAMAGE STABILIZATION +Interaction module: +Stabilization tabbed page: Viscosity coefficient +contact property editor: Mechanical→Damage: +Post-failure behavior +Two types of post-failure behavior can be specified to define the cohesive behavior at a node on the slave +surface after the maximum degradation value, +, has been reached at the node. +By default, once fully degraded, normal contact behavior is enforced at the node and no further +cohesive constraints are enforced. +If the slave node re-enters contact, penetrations will give rise to +compressive contact stresses, and frictional stresses will be applied in the shear directions according to +the prescribed friction model, if any. Separations can occur without giving rise to any cohesive stresses. +In some situations it may be desirable to enforce cohesive behavior again if a slave node re-enters +contact, even after maximum degradation has been reached. For cohesive behavior allowing repeated +contacts, the overall damage variable will be re-initialized to zero when a failed slave node re-enters +contact. Subsequently, normal separations may give rise to tensile cohesive stresses, and shear +separations may give rise to tangential cohesive stresses in accordance with the type of cohesive +behavior defined. Further loading can again cause the cohesive stresses to undergo progressive damage, +degrade, and fail. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to enforce cohesive behavior subsequent to maximum +degradation: +*COHESIVE BEHAVIOR, REPEATED CONTACTS +Interaction module: contact property editor: Mechanical→Cohesive +Behavior: Allow cohesive behavior during repeated +post-failure contacts +Virtual Crack Closure Technique in Abaqus/Explicit +In Abaqus/Explicit, the surface-based cohesive behavior framework can be used to model brittle crack +propagation problems based on linear elastic fracture mechanics principles. The Virtual Crack Closure +Technique (VCCT) fracture criterion can be used to model crack propagation in initially partially bonded +surfaces. A detailed discussion of this topic can be found in “Crack propagation analysis,” Section 11.4.3. +The VCCT fracture criterion cannot be combined with a damage-based surface behavior of +the traction-separation response. However, you can use a surface-based VCCT fracture criterion in +conjunction with cohesive elements. VCCT could model brittle failure/crack propagation while the +cohesive elements could model other aspects of the bonded interface such as stitches. +Input File Usage: +Use the following options to enforce cohesive behavior subsequent +maximum degradation: +*COHESIVE BEHAVIOR +*FRACTURE CRITERION, TYPE= VCCT +to +Cohesive surfaces versus cohesive elements +As described above, the formulation used for surface-based cohesive behavior is very similar to that for +cohesive elements with traction-separation response. However, certain differences exist. +Interface thickness effects are never considered for cohesive surfaces; in cohesive elements with +traction-separation response, thickness effects can be incorporated by either specifying a nonzero +thickness for the interface or by requiring the initial constitutive thickness to be determined from the +nodal coordinates of the cohesive elements. Since thickness effects are not considered for cohesive +surfaces, material properties used to describe the constitutive response for traction-separation cohesive +elements with thickness effects may not be directly reusable for cohesive surfaces. +For cohesive surfaces the cohesive constraint is enforced at each slave node; +in cohesive +elements the cohesive constraints are calculated at the material points (for the locations of material +points in cohesive elements, see “Two-dimensional cohesive element library,” Section 32.5.8, and +“Three-dimensional cohesive element library,” Section 32.5.9). Hence for cohesive surfaces, refining +the slave surface as compared to the master surface will likely lead to improved constraint satisfaction +and more accurate results. +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2), +the +following variables have special meaning for cohesive surfaces with traction-separation behavior: +CSDMG +CSMAXSCRT +CSMAXUCRT +Overall value of the scalar damage variable, D. +This variable indicates whether the maximum contact stress damage initiation +criterion has been satisfied at a contact point. It is evaluated as +. +This variable indicates whether the maximum separation damage initiation +criterion has been satisfied at a contact point. It is evaluated as +. +CSQUADSCRT +This variable indicates whether the quadratic contact stress damage initiation +criterion has been satisfied at a contact point. It is evaluated as +. +CSQUADUCRT +This variable indicates whether the quadratic separation damage initiation criterion +has been satisfied at a contact point. It is evaluated as +. +For the variables above that indicate whether a certain damage initiation criterion has been satisfied +or not, a value that is less than 1.0 indicates that the criterion has not been satisfied, while a value of +1.0 indicates that the criterion has been satisfied. If damage evolution is specified for this criterion, the +maximum value of this variable does not exceed 1.0. +Additional references +• Benzeggagh, M. L., and M. Kenane, “Measurement of Mixed-Mode Delamination Fracture +Toughness of Unidirectional Glass/Epoxy Composites with Mixed-Mode Bending Apparatus,” +Composites Science and Technology, vol. 56, pp. 439–449, 1996. +• Camanho, P. P., and C. G. Davila, “Mixed-Mode Decohesion Finite Elements for the Simulation +of Delamination in Composite Materials,” NASA/TM-2002–211737, pp. 1–37, 2002. +36.2 +Thermal contact properties +• “Thermal contact properties,” Section 36.2.1 +36.2.1 +THERMAL CONTACT PROPERTIES +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Contact interaction analysis: overview,” Section 35.1.1 +• “User-defined interfacial constitutive behavior,” Section 36.1.6 +• “GAPCON,” Section 1.1.10 of the Abaqus User Subroutines Reference Manual +• *GAP +• *GAP CONDUCTANCE +• *GAP HEAT GENERATION +• *GAP RADIATION +• *INTERFACE +• *SURFACE INTERACTION +• “Creating interaction properties,” Section 15.12.2 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +Thermal interaction at the surface of a body: +• can be included in heat transfer problems (“Uncoupled heat transfer analysis,” Section 6.5.2; +“Fully coupled thermal-stress analysis,” Section 6.5.3; “Fully coupled thermal-electrical-structural +analysis,” Section 6.7.4; and “Coupled thermal-electrical analysis,” Section 6.7.3); +• can involve conductive heat transfer between surfaces; +• can involve radiative heat transfer between surfaces when the surfaces are separated by a narrow +gap; +• in Abaqus/Standard can involve convective heat flow across the boundary layer between a solid +surface and a moving fluid; +• can involve heat generated by frictional work in fully coupled thermal-mechanical or fully coupled +thermal-electrical-structural simulations; and +• in Abaqus/Standard can involve heat generated by an electrical current (Joule heating) in fully +coupled thermal-electrical and fully coupled thermal-electrical-structural analyses. +General radiative heat transfer between surfaces is not discussed in this section. For information on +modeling these types of problems in Abaqus/Standard, see “Cavity radiation,” Section 40.1.1. The +thermal contact property models described here are for bodies in close proximity or in contact. For +these problems gap radiation may be more efficient and robust than cavity radiation. +Including thermal properties in a contact property definition +All of the thermal properties discussed in this section—gap conductance, gap radiation, and gap +heat generation—can be included in a contact property definition for both surface-based contact and +element-based contact. All three types of thermal properties can be included in the same contact +property definition. +The thermal contact property model between two surfaces can also be completely defined through +user subroutine UINTER, VUINTER, or VUINTERACTION . +Input File Usage: +Use the following options for surface-based contact: +*SURFACE INTERACTION, NAME=name +*GAP CONDUCTANCE +*GAP RADIATION +*GAP HEAT GENERATION +Use the following options for element-based contact in Abaqus/Standard: +*INTERFACE or *GAP, ELSET=name +*GAP CONDUCTANCE +*GAP RADIATION +*GAP HEAT GENERATION +Use the following option for user-defined, surface-based contact: +*SURFACE INTERACTION, USER +Interaction module: contact property editor: Thermal→Thermal +Conductance, Heat Generation, and/or Radiation +Element-based contact and user-defined surface-based contact are not +supported in Abaqus/CAE. +Abaqus/CAE Usage: +Thermal contact considerations in Abaqus/Explicit +Gap conductance and gap radiation are enforced in Abaqus/Explicit with an explicit algorithm analogous +to the penalty method for mechanical contact interaction. Therefore, gap conductance and gap radiation +can influence the stability condition; although in a fully coupled temperature-displacement analysis the +mechanical portion of the system usually governs the overall stability condition . Extremely large values of gap conductance or gap radiation +can result in a decrease in the stable time increment, which will be accounted for by the automatic time +incrementation algorithm in Abaqus/Explicit. +Gap heat generation is applied within whichever algorithm (kinematic or penalty) is used to enforce +the mechanical contact constraints. Gap heat generation has no effect on the stable time increment. +Thermal contact fluxes may be inaccurate during increments in which mesh adaptivity occurs +if the mechanical contact constraints are enforced kinematically, because mesh adjustments occur in +Abaqus/Explicit between the determination of the mechanical contact state for kinematic contact and +the calculation of thermal contact fluxes. For example, mesh adjustments for adaptivity may cause +for pressure-dependent gap conductance, the gap conduction +discontinuity in the contact pressure: +coefficient will be set based on the pressure determined by the kinematic contact algorithm prior to +the mesh adjustment, even though the thermal contact flux is applied after the mesh adjustment. The +significance of this inaccuracy on the solution will depend on the size and frequency of the mesh +adjustments and the degree of variation in the conduction coefficient. This inaccuracy can be avoided +by enforcing the mechanical contact constraints with the penalty method. +Thermal contact for general contact works analogously to thermal contact for contact pairs. Gap +conductance, gap radiation, and gap heat generation can all be specified and incorporated in general +contact definitions through contact property assignments. As discussed above, large values of gap +conductance or gap radiation can result in performance degradation, particularly since more surfaces +are typically involved in general contact than in contact pairs. Thermal contact properties cannot be +specified for general contact involving edge-to-edge contact or Eulerian elements. Thermal contact +properties are ignored when shell elements are used to define surfaces involved in a contact pair +definition. In these cases general contact should be used. +Modeling conductance between surfaces +The conductive heat transfer between the contact surfaces is assumed to be defined by +and +where q is the heat flux per unit area crossing the interface from point A on one surface to point B on +the other, +are the temperatures of the points on the surfaces, and k is the gap conductance. +Point A is a node on the slave surface; and point B is the location on the master surface contacting the +slave node or, if the surfaces are not in contact, the location on the master surface with a surface normal +that intersects the slave node. +You can define k directly or, in Abaqus/Standard, in user subroutine GAPCON. +Defining the gap conductance directly +When defining k directly, define it as +where +Abaqus Version 6.12 ID: +Printed on: +is the clearance between A and B, +is the contact pressure transmitted across the interface between +A and B, +is the average of the surface temperatures at A and B, +is the average of the magnitudes of the mass flow rates per unit +is the average of any predefined field variables at A and B, and +Defining gap conductance as a function of clearance +You can create a table of data defining the dependence of k on the variables listed above. The default in +Abaqus is to make k a function of the clearance d. When k is a function of gap clearance, d, the tabular +data must start at zero clearance (closed gap) and define k as d increases. At least two pairs of +points +must be given to define k as a function of the clearance. The value of k drops to zero immediately after the +last data point, so there is no heat conductance when the clearance is greater than the value corresponding +to the last data point. If gap conductance is not also defined as a function of contact pressure, k will remain +constant at the zero clearance value for all pressures, as shown in Figure 36.2.1–1(a). +Input File Usage: +*GAP CONDUCTANCE +, d, +Abaqus/CAE Usage: +Interaction module: contact property editor: Thermal→Thermal +Conductance: Definition: Tabular, Use only clearance- +dependency data +(a) +(b) +Figure 36.2.1–1 Examples of input data to define the gap +conductance as a function of clearance or contact pressure. +Defining gap conductance as a function of contact pressure +You can define k as a function of the contact pressure, p. When k is a function of contact pressure at the +interface, the tabular data must start at zero contact pressure (or, in the case of contact that can support +a tensile force, the data point with the most negative pressure) and define k as p increases. The value +of k remains constant for contact pressures outside of the interval defined by the data points. If gap +conductance is not also defined as a function of clearance, k is zero for all positive values of clearance +and discontinuous at zero clearance, as shown in Figure 36.2.1–1(b). +Input File Usage: +*GAP CONDUCTANCE, PRESSURE +, p, +Abaqus/CAE Usage: +Interaction module: contact property editor: Thermal→Thermal +Conductance: Definition: Tabular, Use only pressure-dependency data +Gap conductance as a function of both clearance and contact pressure +k can depend on both clearance and pressure. A discontinuity in k is allowed at +. At the +state of zero clearance and zero pressure the value of k corresponding to the zero pressure data point is +used, as shown in Figure 36.2.1–2(a). +and +dependence on pressure +for negative contact pressure +dclearance +(a) +pcontact +dclearance +pcontact +(b) +dependence on clearance +prior to contact +Figure 36.2.1–2 Examples of input data to define the gap +conductance as a function of both clearance and contact pressure. +In the case of no-separation contact, once contact occurs the conductance is always evaluated +based on the portion of the curve that defines the pressure dependence. The gap conductance, k, +remains constant for contact pressures outside of the interval defined by the data points, as shown in +Figure 36.2.1–2(b). The pressure dependence of k is extended into the negative pressure region even if +no data points with negative pressure are included. +*GAP CONDUCTANCE +Input File Usage: +for the zero clearance data +, d, +*GAP CONDUCTANCE, PRESSURE +, p, +for the zero pressure data point: +For example, the following input defines +point and +*SURFACE INTERACTION, NAME=name +*GAP CONDUCTANCE +20.0, 0.0 +10.0, 0.1 +… +*GAP CONDUCTANCE, PRESSURE +50.0, 0.0 +65.0, 100.0 +70.0, 250.0 +… +Abaqus/CAE Usage: +Interaction module: contact property editor: Thermal→Thermal +Conductance: Definition: Tabular, Use both clearance- +and pressure-dependency data +Using gap conductance to model convective heat transfer from a surface in Abaqus/Standard +Generally, mass flow rates are defined in Abaqus/Standard only for nodes associated with forced convection +elements. However, they can be defined for any node in a model. By using the dependence of k on the +average mass flow rate at the interface (in addition to other dependencies), it is possible for the contact +property definition to simulate convective heat transfer to the boundary layer between a solid and a +moving fluid. If mass flow rates are given only for nodes on one side of the interface, which is typically +the case when simulating convective heat transfer, the average mass flow rate +used to define k will +be half the magnitude specified. +Input File Usage: +Abaqus/CAE Usage: +, +*GAP CONDUCTANCE +k, d, +Interaction module: contact property editor: Thermal→Thermal +Conductance: Definition: Tabular, Clearance Dependency +and/or Pressure Dependency, toggle on Use mass flow +rate-dependent data (Standard only) +Defining gap conductance to be a function of predefined field variables +In addition to the dependencies mentioned previously, the gap conductance can be dependent on any +number of predefined field variables, +. To make the gap conductance depend on field variables, at +least two data points are required for each field variable value. +Input File Usage: +Abaqus/CAE Usage: +, +, +*GAP CONDUCTANCE, DEPENDENCIES=n +k, d, +Interaction module: contact property editor: Thermal→Thermal +Conductance: Definition: Tabular, Clearance Dependency and/or +Pressure Dependency, Number of field variables: n +Defining the gap conductance using user subroutine GAPCON +In Abaqus/Standard k can be defined in user subroutine GAPCON. In this case there is greater flexibility +in specifying the dependencies of k. It is no longer necessary to define k as a function of the average of +the two surface’s temperatures, mass flow rates, or field variables. +Input File Usage: +Abaqus/CAE Usage: +*GAP CONDUCTANCE, USER +Interaction module: contact property editor: Thermal→Thermal +Conductance: Definition: User-defined +Defining the gap conductance to be strongly dependent on temperature +If k depends strongly on temperature, the unsymmetric terms in the calculations start to become +increasingly important in Abaqus/Standard. Using the unsymmetric matrix storage and solution scheme +for the step may improve the convergence rate in the analysis . +Temperature and field-variable dependence of gap conductance for structural elements +Temperature and field-variable distributions in beam and shell elements can generally include gradients +through the cross-section of the element. Contact between these elements occurs at the reference surface; +therefore, temperature and field-variable gradients in the element are not considered when determining +gap conductance, even in cases where the properties are also clearance dependent. +Modeling radiation between surfaces when the gap is small +transfer between closely spaced contact surfaces occurs in +Abaqus assumes that radiative heat +the direction of the normal between the surfaces. +this +normal corresponds to the master surface normal . +connectivity defines the normal direction. +In models using surface-based contact +The gap radiation functionality in Abaqus is intended for modeling radiation between surfaces +across a narrow gap. A more general capability for modeling radiation is available in Abaqus/Standard +. +Radiative heat transfer is defined as a function of clearance between the surfaces through the +effective viewfactor. Abaqus maintains the radiative heat flux even when the surfaces are in contact. +This causes only a minor inaccuracy since normally the heat flux from conduction is much larger than +the radiative heat flux. +Abaqus defines the heat flow per unit surface area between corresponding points as +where q is the heat flux per unit surface area crossing the gap at this point from surface A to surface B, +and +used, and the coefficient C is given by +are the temperatures of the two surfaces, +is the absolute zero on the temperature scale being +is the Stefan-Boltzmann constant, +where +viewfactor, which corresponds to viewing the master surface from the slave surface. +are the surface emissivities, and F is the effective +and +The viewfactor F must be defined as a function of the clearance, d, and should have a value between +0.0 and 1.0. At least two pairs of +points are required to define the viewfactor, and the tabular data +must start at zero clearance (closed gap) and define the viewfactor as the clearance increases. The value +of F drops to zero immediately after the last data point, so there is no radiative heat transfer when the +clearance is greater than the value corresponding to the last data point . +1.0 +0.0 +Figure 36.2.1–3 Example of input data to define the viewfactor as a function of clearance. +Input File Usage: +*GAP RADIATION +, +, +, +Abaqus/CAE Usage: +… +Interaction module: contact property editor: Thermal→Radiation: +Emissivity of master surface: +, Viewfactor and Clearance +, Emissivity of slave surface: +Specifying the value of absolute zero +You must specify the value of +. +Input File Usage: +Abaqus/CAE Usage: +*PHYSICAL CONSTANTS, ABSOLUTE ZERO= +Any module: Model→Edit Attributes→model_name: +Absolute zero temperature: +Specifying the Stefan-Boltzmann constant +You must specify the Stefan-Boltzmann constant, +. +Input File Usage: +Abaqus/CAE Usage: +*PHYSICAL CONSTANTS, STEFAN BOLTZMANN= +Any module: Model→Edit Attributes→model_name: +Stefan-Boltzmann constant: +Improving convergence in Abaqus/Standard +Since the heat flux due to radiation is a strongly nonlinear function of the temperature, the radiation +equations are strongly nonsymmetric and using the unsymmetric matrix storage and solution scheme +for the step may improve the convergence rate in Abaqus/Standard . +Modeling heat generated by nonthermal surface interactions +In fully coupled temperature-displacement, fully coupled thermal-electrical-structural, or coupled +thermal-electrical simulations, Abaqus allows for heat generation due to the dissipation of energy +created by the mechanical or electrical interaction of contacting surfaces. The source of the heat in +a fully coupled temperature-displacement analysis and a fully coupled thermal-electrical-structural +analysis is frictional sliding; +the source in a coupled thermal-electrical and a fully coupled +thermal-electrical-structural analysis simulation is the flow of electrical current across the interface +surfaces. By default, Abaqus releases all of the dissipated energy as heat between the surfaces and +distributes it equally between the two interacting surfaces. +You can specify the fraction of dissipated energy converted into heat, +weighting factor, f (default is 0.5), for distribution of the heat between the interacting surfaces. +includes a factor to convert mechanical energy into thermal energy. +(default is 1.0), and the +often +f = 1.0 indicates that all of the generated heat flows into the first (slave) surface of the contact pair. +f = 0.0 indicates that all of the generated heat flows into the opposite (master) surface. Unless valid +experimental data suggest otherwise, it is best to assume the default value of f = 0.5 because this value +evenly distributes the generated heat between the surfaces. +If user subroutine UINTER, VUINTER, or VUINTERACTION is used to define the interfacial +constitutive behavior, all gap heat generation effects will be turned off; you must supply an additional +heat flux in the user subroutine to model these effects. +*GAP HEAT GENERATION +, f +Input File Usage: +Abaqus/CAE Usage: +Interaction module: contact property editor: Thermal→Heat +Generation: Specify: +and f +Heat generated due to frictional sliding +In coupled thermal-mechanical and coupled thermal-electrical-structural surface interactions, the rate of +frictional energy dissipation is given by +is the frictional stress and +where +surface is assumed to be +is the slip rate. The amount of this energy released as heat on each +and +and f are defined above. The heat flux into the slave surface is +, and the heat into the master +where +surface is +. +Heat generated due to flow of electrical current in Abaqus/Standard +In a coupled thermal-electrical analysis and +a fully coupled thermal-electrical-structural analysis , the rate of electrical energy dissipated by electric current flowing across the +interface is +where J is the electrical current density and +The amount of this energy released as heat on each of the interface surfaces is assumed to be +are the electrical potentials on the two surfaces. +and +and +where +surface is +and f are defined in the same way as for frictional dissipation. Again, the heat flux into the slave +. +, and the heat into the master surface is +Surface-based interaction variables for thermal contact property models +Abaqus provides many output variables related to the thermal interaction of surfaces. In Abaqus/Standard +the values of these variables are always given at the nodes of the slave surface. In Abaqus/Explicit these +variables can be output for master and slave surfaces, although they are not available for analytical +surfaces. The variables are available only for simulations that use surface-based contact definitions. +They can be requested as surface output to the data, results, or output database files . +Surface-based interaction variables for heat fluxes +The following variables are available for any simulation in which heat transfer can occur (fully coupled +temperature-displacement, fully coupled thermal-electrical-structural, coupled thermal-electrical, or +pure heat transfer analyses): +HFL +HFLA +HTL +HTLA +Heat flux per unit area leaving the surface. +HFL multiplied by the nodal area. +Time integrated HFL. +Time integrated HFLA. +Abaqus/Standard provides all of these variables by default whenever surface output is requested to the +data or results file and thermal surface interactions are present. +These variables can also be displayed in contour plots in the Visualization module of Abaqus/CAE +(Abaqus/Viewer). +Surface-based interaction variables for heat generated by frictional sliding +The following variables are available for fully coupled temperature-displacement simulations in which +there is frictional interaction between contacting surfaces or user subroutine UINTER, VUINTER, or +VUINTERACTION is used: +SFDR +SFDRA +SFDRT +SFDRTA +WEIGHT +Heat flux per unit area entering the surface due to frictional dissipation (includes +). When user subroutine UINTER, +heat flux to both surfaces, +and +VUINTER, or VUINTERACTION is used to define the interfacial +thermal +constitutive behavior, this quantity represents the heat flux resulting from the total +energy dissipation due to friction and other dissipative effects. The effects of gap +heat generation are turned off. +SFDR multiplied by the nodal area. +Time integrated SFDR. +Time integrated SFDRA. +Weighting factor, f, for heat flux distribution between the surfaces (available only +in Abaqus/Standard; not available when the constitutive behavior of the interface +is defined using user subroutine UINTER). +Abaqus/Standard does not provide these variables by default when surface output is requested to the data +or results file; you must specify the variable identifiers. +Contour plots of these variables can also be created in the Visualization module of Abaqus/CAE +(Abaqus/Viewer). +Surface-based interaction variables for heat generated by electrical currents +The following variables are available for any coupled thermal-electrical and any fully coupled thermal- +electrical-structural simulation: +SJD +SJDA +SJDT +SJDTA +Heat flux per unit area generated by the electrical current, includes heat flux to both +surfaces ( +and +). +SJD multiplied by area. +Time integrated SJD. +Time integrated SJDA. +WEIGHT +Weighting factor, f, for heat flux distribution between the surfaces. +Abaqus/Standard does not provide these variables by default when surface output is requested to the data +or results file; you must specify the variable identifiers. +Contour plots of these variables can also be plotted in the Visualization module of Abaqus/CAE +(Abaqus/Viewer). +Thermal interaction variables for thermal gap elements +Abaqus/Standard provides the heat flux per unit area across the thermal gap elements as output. Request +element output of the variable identifier HFL to the data, results, or output database file . The only nonzero component will be HFL1: there is no +heat flux tangential to the interface defined by the gap element. A positive value of HFL1 indicates +heat flowing in the direction of the normal to the master surface side of the element . +Contours of the heat flux across the thermal contact elements can be plotted using Abaqus/CAE. +Thermal interactions involving rigid bodies +Various factors to consider when modeling thermal interactions involving rigid bodies are discussed +in “Rigid body definition,” Section 2.4.1. For example, Abaqus/Standard does not allow modeling of +thermal interactions with analytical rigid surfaces. +Modeling thermal interactions with node-based surfaces +The following limitations apply to fully coupled thermal-electrical-structural and fully coupled thermal- +stress analyses in Abaqus/Standard: +• No heat flow will occur across a contact pair involving a node-based surface. +• No heat generation will occur for a contact pair involving a node-based surface. +These limitations do not apply to Abaqus/Explicit and do not apply to other analysis types involving +thermal +overview,” +Section 6.5.1). +interactions in Abaqus/Standard . +Thermal interactions between surfaces with nodes containing multiple temperature degrees +of freedom +When the surfaces involved in a thermal interaction are defined on shell elements that have multiple +temperature degrees of freedom at each node, the choice of the temperature degree of freedom at a given +node for the thermal interaction depends on how the surface is defined. For an element-based surface +the temperature degree of freedom closest to the surface is chosen; i.e., the first temperature degree of +freedom at the node for the bottom surface and the last temperature degree of freedom at the node for +the top surface. For a node-based surface the first temperature degree of freedom at the node is always +chosen for a thermal interaction. +36.3 +Electrical contact properties +• “Electrical contact properties,” Section 36.3.1 +36.3.1 +ELECTRICAL CONTACT PROPERTIES +Products: Abaqus/Standard Abaqus/CAE +References +• “Contact interaction analysis: overview,” Section 35.1.1 +• “Thermal contact properties,” Section 36.2.1 +• “GAPELECTR,” Section 1.1.11 of the Abaqus User Subroutines Reference Manual +• *GAP ELECTRICAL CONDUCTANCE +• *SURFACE INTERACTION +• “Specifying gap conductance for electrical contact property options” in “Defining a contact +interaction property,” Section 15.14.1 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +Electrical conduction between two bodies: +• is proportional to the difference in electric potentials across the interface; +• is a function of the clearance between the surfaces; +• can be a function of contact pressure; +• can be a function of surface temperatures and/or predefined field variables on the surfaces; and +• can generate heat at the interface. +See “Coupled thermal-electrical analysis,” Section 6.7.3, and “Fully coupled thermal-electrical-structural +analysis,” Section 6.7.4, for details on coupled thermal-electrical and coupled thermal-electrical- +structural analyses. +Including gap electrical conductance properties in a contact property definition +You can include electrical conductance properties in a contact property definition for surface-based +contact. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options: +*SURFACE INTERACTION, NAME=name +*GAP ELECTRICAL CONDUCTANCE +Interaction module: contact property editor: Electrical→Electrical +Conductance +Modeling electrical conductance between surfaces +Abaqus/Standard models the electrical current flowing between two surfaces as +where J is the electrical current density flowing across the interface from point A on one surface to +point B on the other, +is the gap electrical conductance. Point A corresponds to a node on the slave surface of the contact pair. +Point B is the point of the master surface in contact with point A. +are the electrical potentials on opposite points on the surfaces, and +and +You can provide the electrical conductance directly or in user subroutine GAPELECTR. +Defining σg directly +When the gap electrical conductance is defined directly, Abaqus/Standard assumes that +where +is the average of the surface temperatures at A and B, +is the clearance between A and B, +is the contact pressure transmitted across the interface between A and B, and +is the average of any predefined field variables at A and B. +Defining gap electrical conductance as a function of clearance +a function of the clearance, d. When +You can create a table of data defining the dependence of +in Abaqus is to make +tabular data must start at zero clearance (closed gap) and define +value of +electrical conductance is not also defined as a function of contact pressure, +the zero clearance value for all pressures, as shown in Figure 36.3.1–1(a). +on the variables listed above. The default +is a function of gap clearance, d, the +as a function of the clearance. The +remains constant for clearances outside of the interval defined by the data points. If gap +will remain constant at +Σg +Σg +(a) +(b) +Figure 36.3.1–1 Examples of defining the gap electrical conductance +as a function of clearance (a) or contact pressure (b). +Input File Usage: +*GAP ELECTRICAL CONDUCTANCE +, +, +Abaqus/CAE Usage: +Interaction module: contact property editor: Electrical→Electrical +Conductance; Definition: Tabular; Use only clearance- +dependency data +Defining gap electrical conductance as a function of contact pressure +as a function of the contact pressure, p. When +is a function of contact pressure +You can define +at the interface, the tabular data must start at zero contact pressure (or, in the case of contact that can +support a tensile force, the data point with the most negative pressure) and define +as p increases. The +value of +remains constant for contact pressures outside of the interval defined by the data points. If +gap electrical conductance is not also defined as a function of clearance, +is zero for all positive values +of clearance and discontinuous at zero clearance, as shown in Figure 36.3.1–1(b). +*GAP ELECTRICAL CONDUCTANCE, PRESSURE +Input File Usage: +, +, +Abaqus/CAE Usage: +Interaction module: contact property editor: Electrical→Electrical +Conductance; Definition: Tabular; Use only pressure-dependency data +Gap electrical conductance as a function of both clearance and contact pressure +to depend on both clearance and pressure. A discontinuity in +You can define +and +that defines the pressure dependence. The gap electrical conductance, +pressures outside of the interval defined by the data points. The pressure dependence of +into the negative pressure region even if no data points with negative pressure are included. +. Once contact occurs, the conductance is always evaluated based on the portion of the curve +, remains constant for contact +is extended +is allowed at +Input File Usage: +Use both of the following options: +*GAP ELECTRICAL CONDUCTANCE +, +, +*GAP ELECTRICAL CONDUCTANCE, PRESSURE +, +, +Abaqus/CAE Usage: +Interaction module: contact property editor: Electrical→Electrical +Conductance; Definition: Tabular; Use both clearance- +and pressure-dependency data +Defining gap electrical conductance to be a function of predefined field variables +. By +The gap electrical conductance can be dependent on any number of predefined field variables, +default, it is assumed that the electrical conductivity depends only on the surface separation and, possibly, +on the average interface temperature. +Input File Usage: +*GAP ELECTRICAL CONDUCTANCE, DEPENDENCIES=n +Abaqus/CAE Usage: +Interaction module: contact property editor: Electrical→Electrical +Conductance; Definition: Tabular, Clearance Dependency and/or +Pressure Dependency, Number of field variables: n +Defining σg using user subroutine GAPELECTR +When +dependencies of +define +is defined in user subroutine GAPELECTR, there is greater flexibility in specifying the +than there is using direct tabular input. For example, it is no longer necessary to +as a function of the average of the two surfaces’ temperatures or field variables: +Input File Usage: +Abaqus/CAE Usage: +*GAP ELECTRICAL CONDUCTANCE, USER +Interaction module: contact property editor: Electrical→Electrical +Conductance; Definition: User-defined +Modeling heat generated by electrical conduction between surfaces +Abaqus/Standard can include the effect of heat generated by electrical conduction between surfaces in +a coupled thermal-electrical and a fully coupled thermal-electrical-structural analysis. By default, all +dissipated electrical energy is converted to heat and distributed equally between the two surfaces. You +can modify the fraction of electrical energy that is released as heat and the distribution between the +two surfaces; see “Modeling heat generated by nonthermal surface interactions” in “Thermal contact +properties,” Section 36.2.1, for details. +Surface-based output variables for electrical contact property models +Abaqus/Standard provides the following output variables related to the electrical interaction of surfaces: +ECD +ECDA +ECDT +ECDTA +Electric current per unit area leaving slave surface. +ECD multiplied by the area associated with the slave node. +Time integrated ECD. +Time integrated ECDA. +The values of these variables are always given at the nodes of the slave surface. They can be requested as +surface output to the data, results, or output database files . +Contour plots of these variables can also be displayed in the Visualization module of Abaqus/CAE +(Abaqus/Viewer). +36.4 +Pore fluid contact properties +• “Pore fluid contact properties,” Section 36.4.1 +36.4.1 +PORE FLUID CONTACT PROPERTIES +Product: Abaqus/Standard +References +• “Contact interaction analysis: overview,” Section 35.1.1 +• *CONTACT PERMEABILITY +• *SURFACE +• *SURFACE INTERACTION +• *CONTACT PAIR +Overview +The pore fluid contact property models: +• are often used in geotechnical applications, where pore pressure continuity between material on +opposite sides of an interface must be maintained; +• govern pore fluid flow across a contact interface and into a gap region for nearby contact surfaces; +• are applicable when pore pressure degrees of freedom are present on both sides of a contact interface +(if pore pressure degrees of freedom are present on only one side of a contact interface, the surfaces +are treated as impermeable); +• affect the pore fluid flow normal to the contact surfaces; +• can apply to small- and finite-sliding contact formulations; and +• assume that there is no fluid flowing tangentially to the surface. +Contact in coupled pore fluid diffusion/stress analysis involves displacement constraints to resist +penetrations and pore fluid contact properties that influence the fluid flow. See “Coupled pore fluid +diffusion and stress analysis,” Section 6.8.1, for details on coupled pore fluid diffusion/stress analyses. +See “Defining the constitutive response of fluid within the cohesive element gap,” Section 32.5.7, for +details on the use of pore pressure cohesive elements as an alternative to using contact models and pore +fluid contact properties. +Contact pressure in pore fluid interactions +The pore fluid contact properties discussed in this section apply when pore pressure degrees of freedom +exist on both sides of a contact interface. In such cases the calculated contact pressure is effective; it +does not include the pore fluid pressure contribution. +If only one side of a contact interface includes pore pressure degrees of freedom, no fluid flow +into or across the contact interface occurs. In this case the reported contact pressure represents the total +pressure, including the effective structural and pore fluid pressure contributions; but only the effective +contact pressure is used for the computation of friction. +Including pore fluid properties in a contact property definition +Abaqus/Standard assumes that pore fluid flows in the normal direction at a contact interface and does not +flow tangentially along the interface. Two contributions to the fluid flow into each surface at a contact +interface are generally present, as shown in Figure 36.4.1–1. The fluid flow into the master and slave +surface at corresponding points on the interface are +, respectively. +and +• One contribution ( +) is associated with flow across the interface. A positive value of +corresponds to flow out from the master surface and into the slave surface. +• The other contribution ( +for the slave surface and +for the master surface) is associated +with removing or adding fluid from the region between the surfaces while the gap distance is +changing. The sign convention is such that +are positive when these contributions +flow into the respective surfaces (while the gap width decreases). The sum of +(which is the same as the sum of +) is equal to negative one times the rate of change of +and +the gap width up to the threshold distance discussed in “Controlling the distance within which pore +fluid contact properties are active.” +and +and +In steady-state analyses the rate of separation of the surfaces is zero, so the fluid flow contributions +and +are zero; all fluid flowing out of one surface flows into the other in steady-state analyses. +Slave surface +d1 +qS1= qgap S1 + qacross1 +qM1= qgap M1 – qacross1 +d2 +Master surface +Figure 36.4.1–1 Flow patterns in the interface contact element. +Pore fluid flow at a contact interface typically occurs even if contact permeability characteristics are +not explicitly specified in the contact property definition. Alternatively, you can directly specify contact +permeability characteristics for enhanced control over the flow of fluid across a contact interface. +Input File Usage: +*SURFACE INTERACTION, NAME=interaction_name +*CONTACT PERMEABILITY +Controlling the distance within which pore fluid contact properties are active +The models governing fluid flow across a contact interface are most appropriate for two surfaces in +contact or separated by a relatively small gap distance. By default, Abaqus assumes no fluid flow +occurs once the surfaces have separated by a distance larger than the characteristic element length of +the underlying surfaces. Alternatively, you can directly specify a cutoff gap distance beyond which no +fluid flow occurs. Separate controls are provided for the contribution of fluid flow across the interface +( +) and the contribution of fluid flow into the interface ( +). +Input File Usage: +) for the +Use the following option to specify a cutoff distance ( +contribution of fluid flow across the contact interface ( +*CONTACT PERMEABILITY, CUTOFF FLOW ACROSS= +Use the following option to specify a cutoff distance ( +of fluid flow into the contact interface ( +*CONTACT PERMEABILITY, CUTOFF GAP FILL= +): +): +) for the contribution +Controlling contact permeability associated with fluid flow across a contact interface +If you do not specify contact permeability characteristics, the default model ensures continuity of the pore +pressures on opposite sides of a contact interface while the contact separation is less than the threshold +distance discussed in “Controlling the distance within which pore fluid contact properties are active”: +where +that contact permeability across the interface is infinite. +and +are pore pressures at points on opposite sides of the interface. This relationship implies +Alternatively, you can specify a contact permeability, k, such that fluid flow across a contact +, discussed above in “Including pore fluid properties in a contact property definition”) +interface ( +is proportional to the difference in pore pressure magnitudes across the interface: +When defining k directly, define it as +where +is the contact pressure transmitted across the interface between +A and B, +is the average of the pore pressures at A and B, +is the average of the surface temperatures at A and B, and +is the average of any predefined field variables at A and B. +Figure 36.4.1–2 shows an example of k depending on the contact pressure. Use tabular data to +specify the value of k at one or more contact pressures as p increases. The value of k remains constant +for contact pressures outside of the interval defined by the data points. Once the surfaces have separated, +k remains at a constant value until the separation between the surfaces exceeds the specified flow cutoff +distance , at which +point k drops to zero. +specified data points +dclearance +dacross_cutoff +pcontact +Figure 36.4.1–2 Contact-pressure-dependent contact permeability. +Input File Usage: +*CONTACT PERMEABILITY +, +, +, +Defining gap permeability to be a function of predefined field variables +In addition to the dependencies mentioned previously, the gap permeability can be dependent on any +number of predefined field variables, +. To make the gap permeability depend on field variables, at +least two data points are required for each field variable value. +Input File Usage: +*CONTACT PERMEABILITY, DEPENDENCIES=n +, +, +, +, +Coupled heat transfer–pore fluid contact properties +Heat transfer can be considered simultaneously with pore fluid flow, in which case heat flow across +the contact interface can occur in conjunction with fluid flow. These various contact property aspects +are defined with separate options as part of a single contact property definition that you assign to the +contact interaction; see “Thermal contact properties,” Section 36.2.1, for details on defining heat transfer +properties. +Output +You can write the contact surface variables associated with the interaction of contact pairs to the +Abaqus/Standard data (.dat), results (.fil), and output database (.odb) files. +In addition to the +surface variables associated with the mechanical contact analysis (shear stresses, contact pressures, +etc.) several pore fluid-related variables (such as pore fluid volume flux per unit area) on the contact +interface can be reported. A detailed discussion of these output requests can be found in “Surface output +from Abaqus/Standard” in “Output to the data and results files,” Section 4.1.2, and “Surface output in +Abaqus/Standard and Abaqus/Explicit” in “Output to the output database,” Section 4.1.3. +Abaqus/Standard provides the following output variables related to the pore fluid interaction of +surfaces: +PFL +PFLA +PTL +PTLA +TPFL +TPTL +Pore volume flux per unit area leaving the slave surface. +PFL multiplied by the area associated with the slave node. +Time integrated PFL. +Time integrated PFLA. +Total pore volume flux leaving the slave surface. +Time integrated TPFL. +37. +Contact Formulations and Numerical Methods +Contact formulations and numerical methods in Abaqus/Standard +Contact formulations and numerical methods in Abaqus/Explicit +37.1 +37.1 +Contact formulations and numerical methods in Abaqus/Standard +• “Contact formulations in Abaqus/Standard,” Section 37.1.1 +• “Contact constraint enforcement methods in Abaqus/Standard,” Section 37.1.2 +• “Smoothing contact surfaces in Abaqus/Standard,” Section 37.1.3 +37.1.1 +CONTACT FORMULATIONS IN Abaqus/Standard +Products: Abaqus/Standard Abaqus/CAE +References +• “Surfaces: overview,” Section 2.3.1 +• “Defining general contact interactions in Abaqus/Standard,” Section 35.2.1 +• “Defining contact pairs in Abaqus/Standard,” Section 35.3.1 +• *CONTACT +• *CONTACT PAIR +• “Defining general contact,” Section 15.13.1 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +• “Defining surface-to-surface contact,” Section 15.13.7 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Defining self-contact,” Section 15.13.8 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +• “Using contact and constraint detection,” Section 15.16 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +Abaqus/Standard provides several contact fomulations. Each formulation is based on a choice of +a contact discretization, a tracking approach, and assignment of “master” and “slave” roles to the +contact surfaces. For general contact interactions, the discretization, tracking approach, and surface +role assignments are selected automatically by Abaqus/Standard; for contact pairs, you can specify +these aspects of the contact formulation using the interface described in “Defining contact pairs in +Abaqus/Standard,” Section 35.3.1. The default contact formulation is applicable in most situations, but +you may find it desirable to choose another formulation in some cases. This section discusses in detail +the formulations that Abaqus/Standard uses in contact simulations. +Your choice of a tracking approach will have a considerable impact on how contact surfaces +interact. In Abaqus/Standard there are two tracking approaches to account for the relative motion of +two interacting surfaces in mechanical contact simulations: +• finite sliding, which is the most general and allows any arbitrary motion of the surfaces ; and +• small sliding, which assumes that although two bodies may undergo large motions, there will +be relatively little sliding of one surface along the other . +You can choose between node-to-surface contact discretization and true surface-to-surface contact +discretization for each of the above tracking approaches. +Formulations for general contact +in Abaqus/Standard always uses the finite-sliding, +surface-to-surface contact +General contact +formulation. This formulation can also be used for contact pairs, but it is not the default. The +discussions in this section of finite-sliding, surface-to-surface contact apply equally to general contact +and to contact pairs. +In a general contact domain the master and slave roles are assigned to surfaces automatically, +although it is possible to override these default assignments. The behavior of master surfaces and slave +surfaces is consistent across general contact and contact pair interactions. The specification of master +and slave surfaces in a general contact domain is covered in detail in “Numerical controls for general +contact in Abaqus/Standard,” Section 35.2.6. +Discretization of contact pair surfaces +Abaqus/Standard applies conditional constraints at various locations on interacting surfaces to simulate +contact conditions. The locations and conditions of these constraints depend on the contact discretization +used in the overall contact formulation. Abaqus/Standard offers two contact discretization options: a +traditional “node-to-surface” discretization and a true “surface-to-surface” discretization. +Node-to-surface contact discretization +With traditional node-to-surface discretization the contact conditions are established such that each +“slave” node on one side of a contact interface effectively interacts with a point of projection on the +“master” surface on the opposite side of the contact interface . Thus, each contact +condition involves a single slave node and a group of nearby master nodes from which values are +interpolated to the projection point. +Traditional node-to-surface discretization has the following characteristics: +• The slave nodes are constrained not to penetrate into the master surface; however, the nodes of the +master surface can, in principle, penetrate into the slave surface (for example, see the case on the +upper-right of Figure 37.1.1–2). +• The contact direction is based on the normal of the master surface. +• The only information needed for the slave surface is the location and surface area associated with +each node; the direction of the slave surface normal and slave surface curvature are not relevant. +Thus, the slave surface can be defined as a group of nodes—a node-based surface. +• Node-to-surface discretization is available even if a node-based surface is not used in a contact pair +definition. +Surface-to-surface contact discretization +Surface-to-surface discretization considers the shape of both the slave and master surfaces in the region +of contact constraints. Surface-to-surface discretization has the following key characteristics: +master surface +slave surface +closest point +to A +closest point +to B +Figure 37.1.1–1 Node-to-surface contact discretization. +Node-to-Surface Contact +Node-to-Surface Contact +slave +master +master +slave +Surface-to-Surface Contact +Surface-to-Surface Contact +slave +master +master +slave +Figure 37.1.1–2 Comparison of contact enforcement for different master-slave assignments +with node-to-surface and surface-to-surface contact discretizations. +• The surface-to-surface formulation enforces contact conditions in an average sense over regions +nearby slave nodes rather than only at individual slave nodes. The averaging regions are +approximately centered on slave nodes, so each contact constraint will predominantly consider +one slave node but will also consider adjacent slave nodes. Some penetration may be observed +at individual nodes; however, +large, undetected penetrations of master nodes into the slave +surface do not occur with this discretization. Figure 37.1.1–2 compares contact enforcement for +node-to-surface and surface-to-surface contact for an example with dissimilar mesh refinement on +the contacting bodies. +• The contact direction is based on an average normal of the slave surface in the region surrounding +a slave node. +• Surface-to-surface discretization is not applicable if a node-based surface is used in the contact pair +definition. +Choosing a contact discretization +In general, surface-to-surface discretization provides more accurate stress and pressure results than node- +to-surface discretization if the surface geometry is reasonably well represented by the contact surfaces. +Figure 37.1.1–3 shows an example of improved contact pressure accuracy with surface-to-surface contact +compared to node-to-surface contact. +Figure 37.1.1–3 Comparison of contact pressure accuracy for +node-to-surface and surface-to-surface contact discretizations. +Since node-to-surface discretization simply resists penetrations of slave nodes into the master surface, +forces tend to concentrate at these slave nodes. This concentration leads to spikes and valleys in the +distribution of pressure across the surface. Surface-to-surface discretization resists penetrations in an +average sense over finite regions of the slave surface, which has a smoothing effect. As the mesh is +refined, the discrepancies between the discretizations lessen, but for a given mesh refinement the surface- +to-surface approach tends to provide more accurate stresses. +Contact using surface-to-surface discretization is also less sensitive to master and slave surface +designations than node-to-surface contact . Figure 37.1.1–4 shows a simple model involving two blocks with dissimilar mesh +densities. +uniform pressure +Figure 37.1.1–4 Test model for comparison of different +master and slave surface designations. +The bottom block is fixed to the ground, and a uniform pressure of 100 Pa is applied to the top face of +the top block. Analytically, the top block should exert a uniform pressure of 100 Pa on the bottom block +across the entire contact interface. Table 37.1.1–1 compares the Abaqus analysis results for different +contact discretizations and slave surface designations. +Table 37.1.1–1 Error (from analytical results) for various +discretization/slave surface combinations. +Contact discretization +Slave Surface +Maximum error in CPRESS +Node-to-surface +Surface-to-surface +Top block +Bottom block +Top block +Bottom block +13% +31% +~1% +~1% +If the surface geometry is not well-represented due to the use of a coarse mesh, significant +inaccuracies can exist regardless of whether surface-to-surface contact or node-to-surface contact +In some cases surface smoothing techniques available for surface-to-surface contact can +is used. +significantly improve solutions obtained with a coarse mesh. See “Smoothing contact surfaces in +Abaqus/Standard,” Section 37.1.3, for a discussion of surface smoothing options for surface-to-surface +contact. +Surface-to-surface discretization generally involves more nodes per constraint and can, +therefore, increase solution cost. In most applications the extra cost is fairly small, but the cost can +become significant in some cases. The following factors (especially in combination) can lead to +surface-to-surface contact being costly: +• A large fraction of the model is involved in contact. +• The master surface is more refined than the slave surface. +• Multiple layers of shells are involved in contact, such that the master surface of one contact pair +acts as the slave surface of another contact pair. +The surface-to-surface formulation is primarily intended for common situations in which normal +directions of contacting surfaces are approximately opposite. The node-to-surface contact formulation +is often preferable for treating contact involving feature edges or corners if the respective slave and +master facet normal directions are not approximately opposite in the active contact region. +Contact tracking approaches +In Abaqus/Standard there are two tracking approaches to account for the relative motion of two +interacting surfaces in mechanical contact simulations. +The finite-sliding tracking approach +Finite-sliding contact is the most general tracking approach and allows for arbitrary relative separation, +sliding, and rotation of the contacting surfaces. For finite-sliding contact the connectivity of the +currently active contact constraints changes upon relative tangential motion of the contacting surfaces. +For a detailed description of how Abaqus/Standard calculates finite-sliding contact, see “Using the +finite-sliding tracking approach” later in this section. +The small-sliding tracking approach +Small-sliding contact assumes that there will be relatively little sliding of one surface along the +other and is based on linearized approximations of the master surface per constraint. The groups of +nodes involved with individual contact constraints are fixed throughout the analysis for small-sliding +contact, although the active/inactive status of these constraints typically can change during the analysis. +You should consider using small-sliding contact when the approximations are reasonable, due to +computational savings and added robustness. For a detailed description of how Abaqus/Standard +calculates small-sliding contact, see “Using the small-sliding tracking approach” later in this section. +Choosing the master and slave roles in a two-surface contact pair +Abaqus/Standard enforces the following rules related to the assignment of the master and slave roles for +contact surfaces: +• Analytical rigid surfaces and rigid-element-based surfaces must always be the master surface. +• A node-based surface can act only as a slave surface and always uses node-to-surface contact. +• Slave surfaces must always be attached to deformable bodies or deformable bodies defined as rigid. +• Both surfaces in a contact pair cannot be rigid surfaces with the exception of deformable surfaces +defined as rigid . +When both surfaces in a contact pair are element-based and attached to either deformable bodies or +deformable bodies defined as rigid, you have to choose which surface will be the slave surface and which +will be the master surface. This choice is particularly important for node-to-surface contact. Generally, +if a smaller surface contacts a larger surface, it is best to choose the smaller surface as the slave surface. +If that distinction cannot be made, the master surface should be chosen as the surface of the stiffer body +or as the surface with the coarser mesh if the two surfaces are on structures with comparable stiffnesses. +The stiffness of the structure and not just the material should be considered when choosing the master +and slave surface. For example, a thin sheet of metal may be less stiff than a larger block of rubber even +though the steel has a larger modulus than the rubber material. If the stiffness and mesh density are the +same on both surfaces, the preferred choice is not always obvious. +The choice of master and slave roles typically has much less effect on the results with a surface-to- +surface contact formulation than with a node-to-surface contact formulation. However, the assignment +of master and slave roles can have a significant effect on performance with surface-to-surface contact if +the two surfaces have dissimilar mesh refinement; the solution can become quite expensive if the slave +surface is much coarser than the master surface. +Fundamental choices affecting the contact formulation +Your choice of contact discretization and tracking approach have considerable impact on an analysis. +In addition to the qualities already discussed, certain combinations of discretizations and tracking +approaches have their own characteristics and limitations associated with them. These characteristics +are summarized in Table 37.1.1–2. You should also consider the solution costs associated with the +various contact formulations. +Accounting for shell thickness +Most contact formulations will account for the surface thickness of a shell when calculating contact +constraints. However, +the finite-sliding, node-to-surface formulation will not account for shell +thicknesses. These calculations are discussed in more detail in “Accounting for shell and membrane +thickness” in “Assigning surface properties for contact pairs in Abaqus/Standard,” Section 35.3.2. +Allowing for self-contact +Self-contact is typically the result of large deformation in a model. It is often difficult to predict which +regions will be involved in the contact or how they will move relative to each other. Therefore, self- +contact cannot use the small-sliding tracking approach. +Table 37.1.1–2 Comparison of contact formulation characteristics. +Contact formulation +Characteristic +Node-to-surface +Surface-to-surface +Finite-sliding +Small-sliding +Finite-sliding +Small-sliding +Account for shell +thickness by default +Allow self-contact +Allow double-sided +surfaces +No +Yes +Yes +No +Slave surface only Slave surface only +Surface smoothing +by default +Some smoothing +of master surface +Yes for anchor +points; each +constraint uses +flat approximation +of master surface +Yes +Yes +Yes1 +No +Yes +No +Yes +No for anchor +points; each +constraint uses +flat approximation +of master surface +Augmented +Lagrange +method for 3-D +self-contact; +otherwise, direct +method +Direct method +Penalty method +Direct method +No +No +Yes +Yes +Default constraint +enforcement method +Ensure moment +equilibrium for +offset reference +surfaces with friction +1 Double-sided master surfaces are allowed with the finite-sliding, surface-to-surface formulation only +if the path-based tracking algorithm is used . +Double-sided slave surfaces are allowed with both tracking algorithms if the master surface is not user +defined. +Allowing double-sided surfaces +Doubled-sided contact surfaces based on shell-like elements are allowed to act as slave and/or master +surfaces for the surface-to-surface contact formulation by default and are allowed to act as the slave +surface for the node-to-surface contact formulation. For a shell-like surface to act as the master surface +for the surface-to-surface formulation with the optional state-based tracking algorithm or for the node-to-surface contact formulation, the +surface must be defined as single-sided (see “Defining single-sided surfaces” in “Element-based surface +definition,” Section 2.3.2, and “Orientation considerations for shell-like surfaces” in “Defining contact +pairs in Abaqus/Standard,” Section 35.3.1, for more information). +Surface smoothing +When using node-to-surface discretization, corners or small protrusions of a jagged master surface are +allowed to penetrate the spaces between nodes in the node-based surface. It is sometimes possible for +a slave node sliding along the master surface to snag on these corners. Therefore, Abaqus/Standard +automatically smooths the master surface for contact calculations utilizing node-to-surface discretization +to minimize this phenomenon. The details are discussed further in “Smoothing master surfaces for the +finite-sliding, node-to-surface formulation” later in this section. +No surface smoothing occurs by default when using surface-to-surface discretization. +Surface-to-surface discretization considers contact conditions in an average sense over a finite region, +which tends to alleviate problems associated with small protrusions of the master surface penetrating the +slave surface and introduces some inherent smoothing characteristics at the constraint level. However, +this inherent smoothing typically does not significantly mitigate errors associated with poor geometric +representations of curved surfaces when a relatively coarse mesh is used. +In some cases nondefault +circumferential or spherical surface smoothing methods available for surface-to-surface contact can +significantly improve solutions obtained with a coarse mesh . +Constraint enforcement methods +In many cases Abaqus/Standard strictly enforces the contact constraints discussed previously by +default. However, strict enforcement of contact constraints can sometimes lead to overconstraint +issues (for example, see “Overconstraint checks,” Section 34.6.1) or convergence difficulty. To +address these issues and allow for decreased solution cost with typically minimal sacrifice to solution +accuracy, Abaqus/Standard also provides penalty-based constraint enforcement methods. The numerical +constraint enforcement methods (and defaults) are discussed in detail in “Contact constraint enforcement +methods in Abaqus/Standard,” Section 37.1.2. +Moment equilibrium +Based on Newton’s third law of motion, contact forces should be self-equilibrating; that is, the net +contact forces acting on the respective surfaces for each active contact constraint should be equal and +opposite and effectively act through a common point. Contact constraints based on surface-to-surface +contact discretization always exhibit this characteristic. Contact constraints based on node-to-surface +discretization always generate zero net force, but under certain circumstances can generate a net moment +in the numerical solution. Frictional forces associated with node-to-surface contact constraints will +generate net moment if an offset exists between the respective reference surfaces. The following factors +can contribute to a normal-direction offset between nodes of respective contact surfaces while contact +constraints are active: +• The presence of a softened pressure-versus-overclosure behavior (due to a user-specified, softened +pressure-overclosure model or use of a constraint enforcement method, such as the penalty method, +that exhibits numerical softening. +• Contact calculations accounting for shell or membrane thicknesses (which is not allowed with the +finite-sliding, node-to-surface formulation). +• User-specified initial contact clearances . +• Various usages of special-purpose contact elements, such as tube-to-tube contact elements +, result in some normal distance between nodes that interact with each other. +While undesirable, the net moment that sometimes occurs with node-to-surface contact constraints is +typically not significantly detrimental to the analysis results. +Effect of the contact discretization method on solution cost +There is no easy way to predict which contact discretization method will result in lower overall solution +cost. Basic trends include: +• Node-to-surface contact discretization tends to be less costly per iteration than surface-to-surface +contact discretization (because surface-to-surface contact discretization generally involves more +nodes per constraint). +• Contact conditions with finite-sliding contact tend to converge in fewer iterations with surface-to- +surface contact discretization than with node-to-surface contact discretization (because surface-to- +surface contact discretization has more continuous behavior upon sliding). +Using the finite-sliding tracking approach +The finite-sliding tracking approach allows for arbitrary separation, sliding, and rotation of the surfaces. +Abaqus/Standard contact pairs use a finite-sliding, node-to-surface contact formulation by default. +General contact in Abaqus/Standard always uses a finite-sliding, surface-to-surface contact formulation. +Example +Consider the case shown in Figure 37.1.1–5, with surface ASURF acting as the slave surface to surface +BSURF in a finite-sliding, node-to-surface contact pair. +In this example slave node 101 may come into contact anywhere along the master surface BSURF. +While in contact, it is constrained to slide along BSURF, irrespective of the orientation and deformation of +this surface. This behavior is possible because Abaqus/Standard tracks the position of node 101 relative +to the master surface BSURF as the bodies deform. Figure 37.1.1–6 shows the possible evolution of the +contact between node 101 and its master surface BSURF. Node 101 is in contact with the element face +with end nodes 201 and 202 at time +. The load transfer at this time occurs between node 101 and nodes +201 and 202 only. Later on, at time +, node 101 may find itself in contact with the element face with +end nodes 501 and 502. Then the load transfer will occur between node 101 and nodes 501 and 502. +ESETB +ESETA +502 +BSURF +201 +501 +202 +101 +102 +103 +ASURF +Figure 37.1.1–5 Contacting bodies. +BSURF +201 +t = t 1 +202 +501 +502 +t = t 2 +101 +t = 0 +Figure 37.1.1–6 Trajectory of node 101 in finite-sliding contact. +Path-based versus state-based tracking algorithms +Brief descriptions of the tracking algorithms available in Abaqus/Standard are provided below so that +you can be aware of their characteristics and available options. +Path-based tracking algorithm +The “path-based” tracking algorithm carefully considers the relative paths of points on the slave surface +with respect to the master surface within each increment and allows for double-sided shell and membrane +master surfaces. The path-based tracking algorithm is available only for finite-sliding, surface-to-surface +contact interactions involving element-based master surfaces and is the default for those interactions. The +path-based algorithm is sometimes more effective than the state-based algorithm for analyses involving +self-contact or large incremental relative motion. +Input File Usage: +Use the following option to specify use of the path-based tracking algorithm: +Abaqus/CAE Usage: +*CONTACT PAIR, INTERACTION=interaction_property_name, +TYPE=SURFACE TO SURFACE, TRACKING=PATH +Interaction module: surface-to-surface contact or self-contact interaction +editor: Discretization method: Surface to surface, Contact +tracking: Two configurations (path) +State-based tracking algorithm +The “state-based” tracking algorithm updates the tracking state based on the tracking state associated +with the beginning of the increment together with geometric information associated with the predicted +configuration. This algorithm is well-suited for most finite-sliding analyses but requires the use of single- +sided surfaces and occasionally has difficulty tracking large incremental motion. State-based tracking +may miss detecting contact if the incremental relative motion exceeds the dimensions of the master +surface or if the incremental motion cuts across corners of the master surface; specifying an upper bound +for the increment size helps avoid these problems. The state-based tracking algorithm is: +• the only tracking algorithm available for finite-sliding, node-to-surface contact pairs; +• the only tracking algorithm available for finite-sliding contact interactions involving an analytical +rigid master surface; +• a non-default option for finite-sliding, surface-to-surface contact pairs involving an element-based +master surface. +Input File Usage: +Use the following option to specify use of the state-based tracking algorithm: +Abaqus/CAE Usage: +*CONTACT PAIR, INTERACTION=interaction_property_name, +TYPE=SURFACE TO SURFACE, TRACKING=STATE +Interaction module: surface-to-surface contact or self-contact interaction +editor: Discretization method: Surface to surface, Contact +tracking: Single configuration (state) +Smoothing master surfaces for the finite-sliding, node-to-surface formulation +The finite-sliding, node-to-surface contact formulation requires that master surfaces have continuous +surface normals at all points. Convergence problems can result if master surfaces that do not have +continuous surface normals are used in finite-sliding, node-to-surface contact analyses; slave nodes +tend to get “stuck” at points where the master surface normals are discontinuous. Abaqus/Standard +automatically smooths the surface normals of element-based master surfaces used in finite-sliding, +node-to-surface contact simulations, including those modeled with slide lines. You are expected to +create smooth analytical rigid surfaces . No such +smoothing of master surface normals is needed with the finite-sliding, surface-to-surface formulation. +Smoothing deformable master surfaces and rigid surfaces defined with rigid elements +For finite-sliding, node-to-surface contact simulations with planar or axisymmetric deformable +master surfaces, Abaqus/Standard will smooth any discontinuous transitions between two first-order +element faces with parabolic curves. Discontinuous transitions between two second-order element +faces are smoothed with cubic curves connecting two points located on the element’s faces. This +smoothing is shown in Figure 37.1.1–7 for first-order elements (linear segments) and in Figure 37.1.1–8 +for second-order elements (parabolic segments). +For finite-sliding, node-to-surface simulations +with three-dimensional deformable master surfaces and rigid master surfaces using rigid elements, +Abaqus/Standard will smooth any discontinuous surface normal transitions between the master surface +facets. +master surface linear segments +smooth transition +l 1 +l 2 +a 1 +a 2 +Figure 37.1.1–7 Smoothing between linear segments. +master surface + quadratic segments +smooth transition +l 1 +l 2 +a 1 +a 2 +Figure 37.1.1–8 Smoothing between quadratic segments. +You can control the degree of smoothing of the master surface in node-to-surface contact simulations +or in analyses using slide lines and contact elements by specifying a fraction f. The default value of f is +0.2. +are +For planar or axisymmetric deformable master surfaces, +the lengths of the element facets that join at the surface node and +. Abaqus/Standard will construct either a parabolic or a cubic segment between two +points at distances +from the node at which the discontinuity exists; this smoothed segment +will be used in the contact calculations. Thus, the contact surface will differ from the faceted element +geometry. Smoothing affects only segments where the normal to the deformable master surface is +discontinuous at the node joining two elements: +it does not affect the two segments adjacent to the +midside nodes on second-order element faces. +, where +and +and +For three-dimensional, element-based master surfaces, f is defined as a fraction of the dimension of a +facet as shown in Figure 37.1.1–9. The normal vector of a point within the region bounded by the dashed +lines is computed to be normal to the facet. Outside this region the normal is smoothed with respect to the +adjacent facets, using a generalization of the two-dimensional approach shown in Figure 37.1.1–7 and +Figure 37.1.1–8. The physical geometry of a three-dimensional facet is not smoothed; only the surface +normal definitions associated with the facet are affected by the smoothing operation. The implementation +of the normal-direction smoothing algorithm is slightly different for surfaces based on rigid type elements + than other element types. This difference typically has minimal +effect on the convergence behavior or solution results; however, for example, different solution behavior +may occasionally be observed between otherwise identical analyses in which a rigid body is modeled +with R3D4 elements in one case and S4R elements assigned to a rigid body in another case. +fl2 +fl2 +l2 +l3 +fl3 +fl3 +fl2 +l2 +fl2 +fl1 +fl1 +fl1 +fl1 +l1 +l1 +Figure 37.1.1–9 Smoothing of a three-dimensional master surface. +Input File Usage: +Use the following option for node-to-surface contact simulations: +*CONTACT PAIR, INTERACTION=interaction_property_name, +SMOOTH=f +Use the following option when using slide lines and contact elements: +*SLIDE LINE, ELSET=name, SMOOTH=f +Abaqus/CAE Usage: +Interaction module: Interaction→Create: Surface-to-surface +contact (Standard) or Self-contact (Standard): Degree of +smoothing for master surface: f +Smoothing a deformable master surface along symmetry edges +When a two-dimensional or axisymmetric deformable master surface ends at a symmetry plane and +node-to-surface discretization is used, Abaqus/Standard will smooth and calculate the proper surface +normals and tangent planes of the end segment if the boundary condition at the symmetry end is specified +with the symmetry “type” boundary XSYMM or YSYMM. This smoothing procedure is accomplished +by reflecting the end segment about the symmetry plane and constructing either a parabolic or a cubic +segment between the end segment and the reflected segment. Thus, the contact surface may differ +from the faceted element geometry near the end. Abaqus/Standard will automatically adjust the surface +normal and tangent planes at +of an axisymmetric master surface regardless of whether a symmetry +boundary condition is defined. The finite-sliding, surface-to-surface formulation has no special treatment +for surfaces ending at a symmetry plane. See “Modifying the master surface normals” in “Contact +formulations in Abaqus/Standard,” Section 37.1.1, for a discussion of how the small-sliding, node-to- +surface formulation treats master surfaces ending at a symmetry plane. See “Small-sliding, surface-to- +surface contact” in “Contact formulations in Abaqus/Standard,” Section 37.1.1, for a discussion of how +the small-sliding, node-to-surface formulation treats slave surfaces ending at a symmetry plane. +Overriding the default smoothing behavior for finite-sliding, node-to-surface contact +To model a master surface with corners in two dimensions (fold lines in three dimensions), break the +surface into multiple surfaces. This technique prevents Abaqus/Standard from smoothing out the corners +or fold lines and allows Abaqus/Standard to introduce constraints associated with each surface if a slave +node is in contact with an interior corner or fold in the master surface. +To accurately model the master surface with a corner shown in Figure 37.1.1–10, you must define +two contact pairs: the first contact pair has ASURF as the slave surface and BSURFA as the master surface; +the second contact pair has ASURF as the slave surface and BSURFB as the master surface. +Finite sliding in a geometrically linear analysis +Finite-sliding simulations usually include nonlinear geometric effects because such simulations +generally involve large deformations and large rotations. However, it is also possible to use the +finite-sliding tracking approach in a geometrically linear analysis . The load transfer paths between the +surfaces and the contact direction are updated in finite-sliding, geometrically linear analyses. This +capability is useful for analyzing finite sliding between two stiff bodies that do not undergo large +rotations. +Unsymmetric terms in finite-sliding contact simulations +Normal contact constraints due to node-to-surface discretization produce unsymmetric terms in the +system of equations when three-dimensional faceted surfaces come in contact. These terms have a +BSURFA +ASURF +BSURFB +corner +Figure 37.1.1–10 Master surface with a corner. +strong effect on the convergence rate in regions on the master surfaces with large differences in surface +normals between facets. +Normal contact constraints due to surface-to-surface discretization produce unsymmetric terms in +both two- and three-dimensional cases. These terms have a strong effect on the convergence rate in +regions where the master and slave surfaces are not parallel to each other. +In both cases you should use the unsymmetric solution scheme for the step to improve the +convergence rate of the simulation . +Contact simulations that involve strong frictional effects can also produce unsymmetric terms. See +“Unsymmetric terms in the system of equations” in “Frictional behavior,” Section 36.1.5, for details. +Using the small-sliding tracking approach +For a large class of contact problems the general tracking of the finite-sliding approach is unnecessary, +even though geometric nonlinearity may need to be considered. Abaqus/Standard provides a small- +sliding tracking approach for such problems. For geometrically nonlinear analyses this formulation +assumes that the surfaces may undergo arbitrarily large rotations but that a slave node will interact with +the same local area of the master surface throughout the analysis. For geometrically linear analyses the +small-sliding approach reduces to an infinitesimal-sliding and rotation approach, in which it is assumed +that both the relative motion of the surfaces and the absolute motion of the contacting bodies are small. +Abaqus/Standard attempts to associate a planar approximation of the master surface with each slave +node of a small-sliding contact pair. Contact interactions are considered between a given slave node (or +region nearby a given slave node for the surface-to-surface formulation) and the associated local tangent +plane. An example for the small-sliding, node-to-surface formulation is shown in Figure 37.1.1–11 (for +example, the slave node is typically constrained not to penetrate this local tangent plane). Each local +tangent plane, which is a line in two dimensions, is defined by an anchor point, +, on the master surface +and an orientation vector at the anchor point . +103 +slave surface +102 +N(X0) +104 +N3 +X0 +N2 +local tangent plane +master surface +N4 +Figure 37.1.1–11 Definition of the anchor point and local tangent plane used by the +small-sliding, node-to-surface formulation for node 103. +The algorithm used to define anchor points is described below. If an anchor point cannot be determined +for a particular slave node, no contact constraint will be enforced for that slave node. +Having a local tangent plane for each slave node means that for the small-sliding tracking approach +Abaqus/Standard does not have to monitor slave nodes for possible contact along the entire master +surface. Therefore, small-sliding contact is generally less expensive computationally than finite-sliding +contact. The cost savings are often most dramatic in three-dimensional contact problems. +Small-sliding, node-to-surface contact +For node-to-surface contact Abaqus/Standard chooses the anchor point of a slave node’s local tangent +plane such that the vector from the anchor point to the slave node coincides with a smoothly varying +normal vector on the master surface. The anchor point is chosen before the analysis starts using the +initial configuration of the model. +Smoothly varying master surface normals +is +The algorithm requires that the master surface have a smoothly varying normal vector +any point on the master surface. The first step in defining +is to construct the unit normal vectors at +each node of the master surface. Abaqus/Standard forms these nodal normals by averaging the normals +of the element faces making up the master surface; only the element faces in the surface definition will +contribute to the nodal normals and, thus, to +. Abaqus/Standard uses the initial nodal coordinates +to compute these normals. +, where +Figure 37.1.1–11 shows the nodal unit normals for a master surface, the anchor point +local tangent plane associated with slave node 103. Abaqus/Standard uses the nodal unit normals +, along with the shape functions of the element containing the two nodes, to construct +, and the +and +on the +2–3 element face. Abaqus/Standard chooses the anchor point +of the local tangent plane for node 103 +so that +is the contact direction for slave node 103 and defines +the orientation of the local tangent plane. In this example, as in many cases, the local tangent plane is +only an approximation of the actual mesh geometry. +passes through node 103. +Modifying the master surface normals +Defining user-specified nodal normals on the master surface will improve the local tangent planes calculated for the small-sliding, node-to-surface +formulation in some cases. For example, a default nodal normal corresponding to an average normal +among adjacent facets can cause significant deviation from the true surface normal direction at perimeter +nodes, as shown in Figure 37.1.1–12. The nodal normal +does not point along the symmetry plane, +which means that slave node 100 will never intersect the master surface. In a small-sliding problem if a +slave node fails to intersect the master surface at the start of the analysis, it will be free to penetrate the +master surface because no local tangent plane will be formed. +master surface CSURF +slave surface DSURF +N1 +100 +symmetry plane +Figure 37.1.1–12 Master surface normal at node 1 in a small-sliding model of concentric +cylinders. With the default +slave node 100 will never contact CSURF. +Defining a user-specified normal (1.00E+00, 0.00E+00, 0.00E+00) at node 1 on the master surface +CSURF will correct the problem, as shown in Figure 37.1.1–13. This method allows slave node 100 to +see the master surface, and the correct contact normal direction will be used. Master surface normals at +perimeter nodes are adjusted automatically to lie along the symmetry plane if boundary conditions are +specified at these nodes in symmetry “type” format (XSYMM, YSYMM, or ZSYMM—see “Boundary +conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1). +master surface CSURF +slave surface DSURF +100 +N1 +tangent plane +Figure 37.1.1–13 The modified master surface normal at node 1 +of CSURF now allows slave node 100 to contact CSURF. +Small-sliding, surface-to-surface contact +A key difference with the surface-to-surface approach is that more than one slave node is involved +in each contact constraint (except when the slave surface is based on gasket elements, as discussed +below). This is related to the fact that the surface-to-surface formulation enforces contact conditions in an +average sense over regions nearby slave nodes rather than only at individual slave nodes . The small-sliding, surface-to-surface contact formulation is +a limit case of the finite-sliding, surface-to-surface formulation, using a planar approximation of the +master surface per averaging region of the slave surface. The constraint participation factors for the slave +nodes remain constant for small-sliding contact. The effective center-of-action on the slave surface per +contact constraint may differ slightly from the location of the predominant slave node associated with +the constraint. +A special version of the small-sliding, surface-to-surface formulation is used if the slave surface +is based on gasket elements to avoid a tendency to trigger unstable deformation modes in the gasket +elements. This special formulation has only one slave node per contact constraint and preserves the +accuracy advantages of the surface-to-surface formulation, but it is not well-suited for extension to +finite-sliding and is otherwise not as generally applicable as the regular small-sliding, surface-to-surface +formulation. (The finite-sliding, surface-to-surface formulation always uses multiple slave nodes per +constraint and is not recommended for contact involving gasket elements.) +The small-sliding, surface-to-surface contact formulation determines master anchor points and +normal directions in a manner similar to that used by the small-sliding, node-to-surface contact +formulation; however, there are some differences. For the surface-to-surface approach the anchor point +approximately corresponds to the center of the zone on the master surface where the averaging region +of the slave projects onto the master surface. This projection occurs along the slave surface normal +direction. This method does not make use of smoothed master surface nodal normals. The anchor +point location typically does not depend significantly on whether node-to-surface or surface-to-surface +discretization is used, unless the surfaces are significantly separated and non-parallel in the initial +configuration (in which case small-sliding contact may not be appropriate). +Abaqus/Standard automatically reverts to the node-to-surface approach for individual small-sliding +contact constraints in the following circumstances, even if you have specified use of the surface-to- +surface approach: +• if the slave surface is a node-based surface; +• if the projection along the slave surface normal direction does not intersect the master surface (but +an anchor point can be found using the interpolated master surface normal direction algorithm +discussed above for the small-sliding, node-to-surface formulation); or +• if single-sided slave and master surfaces have surface normals in approximately the same direction. +For constraints based on surface-to-surface discretization it is not necessary that the constraint +associated with a node on a symmetry plane is parallel to the symmetry plane. Hence, there is usually +no need to specify specific normal directions. As in the case of node-to-surface contact, the contact +direction points from the anchor point to the slave node, and the tangent plane is normal to this direction. +The contact normal for the small-sliding, surface-to-surface formulation is adjusted automatically to +lie along the symmetry plane for each slave node that has a boundary condition specified in symmetry +“type” format (XSYMM, YSYMM, or ZSYMM—see “Boundary conditions in Abaqus/Standard and +Abaqus/Explicit,” Section 33.3.1). +Orientation of local tangent planes +The local tangent plane is by definition orthogonal to the contact direction. You can override the default +contact direction to specify a direction with a spatially varying clearance or overclosure definition . +Once the contact direction is defined, the orientation of the local tangent plane with respect to +the master surface facet remains fixed. Because small-sliding contact considers nonlinear geometric +effects, Abaqus/Standard continuously updates the orientation of the local tangent plane to account for +the rotation and, assuming that the master surface is deformable, the deformation of the master surface. +The position of the anchor point relative to the surrounding nodes on the master surface facet does not +change as the master surface deforms. +Load transfer +In a small-sliding analysis each constraint can transfer load only to a limited number of nodes on the +master surface. These nodes on the master surface are chosen based on their initial proximity to the +anchor point. The magnitude of load transferred to each master surface node is based on proximity in the +current, deformed configuration to the center-of-action on the slave surface (which corresponds to a slave +node for the node-to-surface formulation). For example, in Figure 37.1.1–11 node 103 transmits load to +both nodes 2 and 3 on the master surface if node-to-surface discretization is used (if surface-to-surface +discretization is used, load may be transmitted to additional nearby master nodes). Thus, if node 103 +contacts the local tangent plane, a larger share of the force would be transmitted to the master surface +node, 2 or 3, closer to the slave node. +When the anchor point +corresponds to a node on the master surface, as is the case with slave +node 104 and master surface node 3 in Figure 37.1.1–11, the transmitted load for node-to-surface contact +is shared by the node at +and all of the master surface nodes that share an adjacent surface facet with +that node (additional master nodes may take part in the load transfer for surface-to-surface contact). In +Figure 37.1.1–11 the three master surface nodes sharing the force transmitted by slave node 104 are +nodes 2, 3, and 4. +As the center-of-action on the slave surface for a constraint slides along its local tangent plane, +Abaqus/Standard updates the distribution among the master surface nodes. However, no additional +master surface nodes are ever added to the original list of nodes associated with a given small-sliding +constraint. The constraint will continue to transmit load to the original list of master surface nodes, +regardless of the sliding distance. Figure 37.1.1–14 shows the potential problem that arises if small +sliding is used but the relative tangential motion of the surfaces is not “small.” It shows the possible +evolution of contact between slave node 101 in Figure 37.1.1–5 and its master surface BSURF. Using the +unit normal vectors +is found for slave node 101; for the purposes +of this example, assume that it lies at the midpoint of the 201–202 face. With this location of +the +local tangent plane for node 101 is parallel with the 201–202 face. The load transfer always occurs +between node 101 and nodes 201 and 202, no matter how far node 101 slides along the local tangent +plane. Therefore, if node 101 moves as shown in Figure 37.1.1–14, it will continue to transmit load to +nodes 201 and 202 when, in fact, it really slid off the mesh forming the master surface BSURF. +, the anchor point +and +201 +X0 +202 +BSURF +N201 +101 +t = 0 +N202 +101 +t > 0 +Figure 37.1.1–14 Excessive sliding in a small-sliding contact analysis. +What can be considered small sliding +A contact pair in a small-sliding contact simulation should not grossly violate any of the assumptions or +limitations outlined above. Adhere to the following guidelines: +• Slave nodes should slide less than an element length from their corresponding anchor point and +still be contacting their local tangent plane. If the master surface is highly curved, the slave nodes +should slide only a fraction of an element length. The accumulated slip at a slave node (CSLIP) can +provide a good estimate of how far a slave node has moved. +• The local tangent planes formed by Abaqus/Standard should be a good approximation of the +if necessary, define a user-specified normal (“Normal definitions at nodes,” +mesh geometry; +Section 2.1.4) to improve the smoothly varying master surface normal, +. +• The rotation and deformation of the master surface should not cause the local tangent planes to +become a poor representation of the master surface during the course of the analysis. +Choosing the master and slave surfaces in small-sliding problems +The basic guidelines given in “Defining contact pairs in Abaqus/Standard,” Section 35.3.1, should still +be followed in a small-sliding simulation—the slave surface should be the more refined surface or the +surface on the more deformable body. However, in a small-sliding simulation more thought must be +given when defining the master surface. With small-sliding contact each slave node views the master +surface as a flat surface, which can be significantly different than the true shape of the surface, even +in the local region near the anchor point. In some cases the local tangent planes provide a good local +approximation to the master surface in the initial configuration, but deformation and rotation of the master +surface can reorient the local tangent planes such that they become a poor representation of the master +surface. Figure 37.1.1–15 shows an example where distortion of the master surface results in such a +situation. This problem can be minimized to some extent by using a more refined mesh on the master +surface, thus providing more element faces to control the motion of the tangent planes. Excessive mesh +refinement should not be necessary since only small sliding should occur. +Infinitesimal sliding +As was mentioned before, the small-sliding tracking approach reduces to an infinitesimal-sliding tracking +approach for geometrically linear analyses. Infinitesimal sliding assumes that both the relative motions +of the surfaces and the absolute motions of the model remain small. The orientations of the local tangent +planes are not updated, and the load transfer paths and the weightings assigned to each master surface +node remain constant during an infinitesimal-sliding simulation. +As in the case of small sliding, you can choose between node-to-surface and surface-to-surface +discretizations with the infinitesimal-sliding tracking approach. The same user interface applies, and the +default is node-to-surface discretization. +Local tangent directions on a surface +Local tangent directions on a contact surface (sometimes called “slip directions”) are a reference +orientation by which Abaqus calculates tangential behavior in a contact interaction. Abaqus/Standard +calculates the initial orientation of the two local tangent directions by default. The local tangent +directions rotate with the contact surface in a geometrically nonlinear analysis. +initial +configuration +local tangent +plane +master +surface +slave +surface +large +deformation +Figure 37.1.1–15 Master surface deformation in a small-sliding +contact analysis can cause problems with the local tangent planes. +Calculating the initial local tangent directions for a two-dimensional surface +Two-dimensional and standard axisymmetric models have only one local +. +Abaqus/Standard defines the orientation of this direction by the cross product of the vector into the +plane of the model (0., 0., 1.0) and the contact normal vector. +tangent direction, +Models consisting of generalized axisymmetric bodies have a second local tangent direction, +, to +account for the component of slip associated with relative differences in circumferential twist between +contacting bodies. The first local tangent direction at any point on the surface is always tangent to the +master surface in the local r–z plane. The second local tangent direction is orthogonal to this plane +in the local circumferential direction. For more information about generalized axisymmetric models, +see “Generalized axisymmetric stress/displacement elements with twist” in “Choosing the element’s +dimensionality,” Section 27.1.2. +Calculating the initial local tangent directions for a three-dimensional surface +By default, Abaqus/Standard determines the initial orientation of the two local tangent directions, +and +, using the following conventions: +• Finite-sliding, surface-to-surface formulation: The default initial orientations of the two +local tangent directions are based on the slave surface normal, using the standard convention +for calculating surface tangents with the assumption that the +contact normal corresponds to the negative normal to the slave surface. +• Finite-sliding, node-to-surface formulation: For contact involving a slave surface based on +three-dimensional beam-type elements, the first and second local tangent directions are defined +along the length of the beam and transverse to the beam, respectively. For contact involving +an analytical rigid surface and a slave surface that is not based on three-dimensional beam-type +elements, the first local tangent direction is tangential to the cross-section used to generate the +analytical rigid surface, and the second local tangent direction is orthogonal to the plane of the +cross-section in which the contact occurs. +In other cases, default initial orientations of the two local tangent directions are calculated +by first computing tentative +directions. For element-based slave surfaces the tentative +directions are based on the slave surface using the standard convention for calculating surface +tangents. For node-based slave surfaces the tentative +directions are set at each node to +coincide with the global x- and y-axes, respectively. Abaqus constructs an orthogonal triad of +, +becomes aligned with the master +), then rotates this triad such that +(where +, and +and +and +surface normal at the tracked point on the master surface. +• Small-sliding, surface-to-surface formulation: The default initial orientations of the two +local tangent directions are based on the slave surface normal, using the standard convention for +calculating surface tangents, except for contact involving analytical rigid surfaces, in which case +the local tangent directions are based on the master surface normal. +• Small-sliding, node-to-surface formulation: The default initial orientations of the two local +tangent directions are calculated at each point on the master surface based on the master surface +normal, using the standard convention for calculating surface tangents. +Defining alternative initial local tangent directions for contact pair surfaces +If the default local tangent directions are not convenient to prescribe an anisotropic friction model or +to view contact output, you can define the local tangent directions for three-dimensional contact pair +surfaces. You cannot redefine the local tangent directions for the following types of surfaces: +• Surfaces in a general contact domain +• Analytical rigid surfaces +• Two-dimensional surfaces +You define the local tangent directions by associating an orientation definition with a contact pair surface. You can assign an orientation only to one surface of a contact +pair. The surface on which an orientation can be defined is the same surface on which the default +orientation would be calculated . For example, an orientation +can be defined only on the slave surface in deformable versus deformable finite-sliding contact. If a +second orientation is also given, an error message is issued. Therefore, it is not possible to redefine the +local tangent directions for finite-sliding contact between a deformable slave surface and an analytical +rigid surface. +An orientation that is defined on a slave surface of a contact pair that is generated from three- +dimensional truss-type elements or from a list of nodes without rotational degree of freedoms will not +be rotated if the slave surface undergoes finite motion. In this case a warning message is issued during +input processing. +Input File Usage: +*CONTACT PAIR, INTERACTION=interaction_property_name +slave surface name, master surface name, orientation for slave surface +slave surface name, master surface name, , orientation for master surface +Abaqus/CAE Usage: +You cannot define alternative local tangent directions for contact pairs in +Abaqus/CAE. +Evolution of the local tangent directions +For geometrically nonlinear analyses the local tangent directions rotate with the surface on which these +directions were initially calculated or redefined using an orientation definition as described above with +the exception that the local tangent direction rotates with the master surface for the small-sliding, surface- +to-surface formulation. These rotated local tangent directions are further rotated to ensure that the normal +vector, computed using the cross product of the rotated local tangent directions, corresponds to the normal +vector on the master surface when the slave node comes into contact. +37.1.2 +CONTACT CONSTRAINT ENFORCEMENT METHODS IN Abaqus/Standard +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining general contact interactions in Abaqus/Standard,” Section 35.2.1 +• “Defining contact pairs in Abaqus/Standard,” Section 35.3.1 +• “Mechanical contact properties: overview,” Section 36.1.1 +• “Contact pressure-overclosure relationships,” Section 36.1.2 +• *SURFACE BEHAVIOR +• *CONTACT CONTROLS +• “Defining general contact,” Section 15.13.1 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +• “Defining surface-to-surface contact,” Section 15.13.7 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Defining a contact interaction property,” Section 15.14.1 of the Abaqus/CAE User’s Manual, in +the online HTML version of this manual +Overview +Contact constraint enforcement methods in Abaqus/Standard: +• are specified as part of the surface interaction definition; +• determine how contact constraints imposed by a physical pressure-overclosure relationship are resolved numerically in an +analysis; +• can either strictly enforce or approximate the physical pressure-overclosure relationships; +• can be modified to resolve convergence difficulties due to overconstraints; and +• sometimes utilize Lagrange multiplier degrees of freedom. +The available constraint enforcement methods for normal contact in Abaqus/Standard are discussed in +detail in this section. The frictional constraint enforcement methods in Abaqus/Standard are assigned +independently of those for the normal contact constraints and are discussed in “Frictional behavior,” +Section 36.1.5. The use of Lagrange multipliers in contact calculations is also covered in this section. +Available constraint enforcement methods in Abaqus/Standard +There are three contact constraint enforcement methods available in Abaqus/Standard: +• The direct method attempts to strictly enforce a given pressure-overclosure behavior per constraint, +without approximation or use of augmentation iterations. +• The penalty method is a stiff approximation of hard contact. +• The augmented Lagrange method uses the same kind of stiff approximation as the penalty method, +but also uses augmentation iterations to improve the accuracy of the approximation. +The default constraint enforcement method depends on interaction characteristics, as follows: +• The penalty method is used by default for finite-sliding, surface-to-surface contact (including +general contact) if a “hard” pressure-overclosure relationship is in effect. +• The augmented Lagrange method is used by default for three-dimensional self-contact with node- +to-surface discretization if a “hard” pressure-overclosure relationship is in effect. +• The direct method is the default in all other cases. +You should consider the following factors when choosing the contact enforcement method: +• The direct method must be used for contact pairs with a “softened” pressure-overclosure relationship +. +• The direct method strictly enforces the specified pressure-overclosure behavior consistent with the +constraint formulation +• The penalty or augmented Lagrange constraint enforcement methods sometimes provide more +efficient solutions (generally due to reduced calculation costs per iteration and a lower number +of overall iterations per analysis) at some (typically small) sacrifice in solution accuracy. See the +discussions of the penalty and augmented Lagrange methods below. +• Overconstraints due to overlapping contact definitions or the combination of contact and other +constraint types should be avoided for directly +enforced hard contact. +Direct method +The direct method strictly enforces a given pressure-overclosure behavior for each constraint, without +approximation or use of augmentation iterations. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options: +*SURFACE INTERACTION, NAME=interaction_property_name +*SURFACE BEHAVIOR, DIRECT +Interaction module: contact property editor: Mechanical→Normal +Behavior: Constraint enforcement method: Direct (Standard) +Direct method for hard pressure-overclosure behavior +The direct method can be used to strictly enforce a “hard” pressure-overclosure relationship. Lagrange +multipliers are always used in this case. +Direct method for softened pressure-overclosure relationships +The direct method is the only method that can be used to enforce “softened” pressure-overclosure +relationships. The direct method can be used to model softened contact behavior regardless of the +type of contact formulation; however, modeling stiff interface behavior with a contact formulation +that is prone to overconstraints can be difficult. Lagrange multipliers are used if the slope of the +pressure-overclosure curve exceeds 1000 times the underlying element stiffness (as computed by +Abaqus/Standard); otherwise, the constraints are enforced without Lagrange multipliers. The usage of +Lagrange multipliers, thus, depends on the contact pressure. Softened pressure-overclosure relationships +are discussed in more detail in “Contact pressure-overclosure relationships,” Section 36.1.2. +Limitations of the direct method +Because of its strict interpretation of contact constraints, hard contact simulations utilizing the direct +enforcement method are susceptible to overconstraint issues. As a result, directly enforced hard contact +is not available for contact pairs defined using three-dimensional self-contact with node-to-surface +discretization. In this instance you can use an alternate enforcement method or the direct method with a +softened pressure-overclosure relationship. +You may experience similar overconstraint problems with symmetric master-slave contact pairs . Although directly enforced hard contact is the default for these +contact pairs, it is recommended that you use an alternate enforcement method or a softened contact +relationship. +Certain second-order element faces do not perform well +in directly enforced hard contact +relationships. +See “Three-dimensional surfaces with second-order faces and a node-to-surface +formulation” in “Common difficulties associated with contact modeling in Abaqus/Standard,” +Section 38.1.2, for details on this issue. +Penalty method +The penalty method approximates hard pressure-overclosure behavior. With this method the contact +force is proportional to the penetration distance, so some degree of penetration will occur. Advantages +of the penalty method include: +• Numerical softening associated with the penalty method can mitigate overconstraint issues and +reduce the number of iterations required in an analysis. +• The penalty method can be implemented such that no Lagrange multipliers are used, which allows +for improved solver efficiency. +Choosing a penalty method +Abaqus/Standard offers linear and nonlinear variations of the penalty method. With the linear penalty +method the so-called penalty stiffness is constant, so the pressure-overclosure relationship is linear. +With the nonlinear penalty method the penalty stiffness increases linearly between regions of constant +low initial stiffness and constant high final stiffness, resulting in a nonlinear pressure-overclosure +relationship. The default penalty method is linear. +A comparison of the linear and nonlinear pressure-overclosure relationships with the default settings +is shown in Figure 37.1.2–1. +Contact +pressure +K i=0.1K lin +C0=0 +K f=10K lin +Nonlinear +Linear +Klin +Overclosure +Figure 37.1.2–1 Comparison of linear and nonlinear +pressure-overclosure relationships with default settings. +Linear penalty method +When the linear penalty method is used, Abaqus/Standard will, by default, set the penalty stiffness to 10 +times a representative underlying element stiffness. You can scale or reassign the penalty stiffness, as +discussed in “Modifying a linear penalty stiffness” below. Contact penetrations resulting from the default +penalty stiffness will not significantly affect the results in most cases; however, these penetrations can +sometimes contribute to some degree of stress inaccuracy (for example, with displacement-controlled +loading and a coarse mesh). The linear penalty method is used by default for the finite-sliding, surface- +to-surface contact formulation. +Input File Usage: +Abaqus/CAE Usage: +Nonlinear penalty method +Use both of the following options to specify the linear penalty method: +*SURFACE INTERACTION, NAME=interaction_property_name +*SURFACE BEHAVIOR, PENALTY=LINEAR +Interaction module: contact property editor: Mechanical→Normal Behavior: +Constraint enforcement method: Penalty (Standard), Behavior: Linear +With the nonlinear penalty method, the pressure-overclosure curve has four distinct regions shown in +Figure 37.1.2–2. +• Inactive contact regime: The contact pressure remains zero for clearances greater than +default setting of +is zero. +. The +• Constant initial penalty stiffness regime: The contact pressure varies linearly, with a slope equal +to . The default initial penalty stiffness, +is 1% of a +, is equal to the representative underlying element stiffness. The default value of +for penetrations (overclosures) in the range +to +characteristic length computed by Abaqus/Standard to represent a typical facet size. +Contact +pressure +Final stiffness +Kf +Initial +stiffness +Ki +Clearance +C 0 +Overclosure +Penalty +stiffness +Kf +Ki +Overclosure +Clearance +C0 +Figure 37.1.2–2 Nonlinear penalty pressure-overclosure relationship. +• Stiffening regime: The contact pressure varies quadratically for penetrations in the range +while the penalty stiffness increases linearly from +to +to , +. The default final penalty stiffness, +is +, is equal to 100 times the representative underlying element stiffness. The default value of +3% of the same characteristic length used to compute +(discussed above). +• Constant final penalty stiffness regime: The contact pressure varies linearly, with a slope equal to +for penetrations greater than . +The low initial penalty stiffness typically results in better convergence of the Newton iterations and better +robustness, while the higher final stiffness keeps the overclosure at an acceptable level as the contact +pressure builds up. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options to specify the nonlinear penalty method: +*SURFACE INTERACTION, NAME=interaction_property_name +*SURFACE BEHAVIOR, PENALTY=NONLINEAR +Interaction module: contact property editor: Mechanical→Normal +Behavior: Constraint enforcement method: Penalty +(Standard), Behavior: Nonlinear +Modifying the penalty stiffness +If you are interested in investigating the effects of modifying the penalty stiffness, it is generally +recommended that you consider order-of-magnitude changes. Increasing the penalty stiffness above the +threshold value discussed above will, by default, introduce Lagrange multipliers. +Modifying a linear penalty stiffness +As part of the surface behavior definition, you can specify the linear penalty stiffness, shift the pressure- +overclosure relationship by specifying the clearance at which the contact pressure is zero, or scale the +default or specified penalty stiffness by a factor. +Input File Usage: +To modify the linear penalty behavior in the surface behavior definition: +*SURFACE BEHAVIOR, PENALTY=LINEAR +penalty stiffness, clearance at zero pressure, factor +Abaqus/CAE Usage: +To modify the linear penalty behavior in the surface behavior definition: +Interaction module: contact property editor: Mechanical→Normal Behavior: +Constraint enforcement method: Penalty (Standard), Behavior: Linear, +Stiffness value: Specify: penalty stiffness, Stiffness scale factor: factor, +Clearance at which contact pressure is zero: clearance at zero pressure +Modifying a nonlinear penalty stiffness +As part of the surface behavior definition, you can specify the final nonlinear penalty stiffness, shift the +pressure-overclosure relationship by specifying the clearance at which the contact pressure is zero, or +scale the default or specified penalty stiffness by a factor. In addition, you can control directly the ratio +of the initial to the final penalty stiffness, the scale factor, and the ratio that determines +and . +Input File Usage: +To modify the nonlinear penalty behavior in the surface behavior definition: +*SURFACE BEHAVIOR, PENALTY=NONLINEAR +final penalty stiffness, clearance at zero pressure, factor, upper +quadratic limit scale factor, ratio of initial penalty stiffness over final +penalty stiffness, lower quadratic limit ratio +Abaqus/CAE Usage: +To modify the nonlinear penalty behavior in the surface behavior definition: +Interaction module: contact property editor: Mechanical→Normal +Behavior: Constraint enforcement method: Penalty (Standard), +Behavior: Nonlinear, Maximum stiffness value: Specify: final +penalty stiffness, Stiffness scale factor: factor, Initial/Final stiffness +ratio: ratio of initial penalty stiffness over final penalty stiffness, Upper +quadratic limit scale factor: upper quadratic limit scale factor, Lower +quadratic limit ratio: lower quadratic limit ratio, Clearance at which +contact pressure is zero: clearance at zero pressure +Scaling the penalty stiffness on a step-by-step basis +You can also scale the penalty stiffness on a step-by-step basis, which will act as an additional multiplier +on any scale factor specified as part of the surface behavior definition. +Input File Usage: +Abaqus/CAE Usage: +To scale the penalty stiffness on a step-by-step basis: +*CONTACT CONTROLS, STIFFNESS SCALE FACTOR=factor +To scale the penalty stiffness on a step-by-step basis: +Interaction module: Abaqus/Standard contact controls editor: Augmented +Lagrange: Stiffness scale factor: factor +Limitations of the penalty method +The penalty method cannot be used for debonded surfaces. +If the penalty method is specified, Lagrange multipliers are always used during analysis steps with +the following procedures: +• Design sensitivity analysis +• Direct steady-state dynamic analysis +• Quasi-Newton method +If surface elements have been used to define a contact surface on the exterior of a substructure +, Abaqus/Standard interprets the +underlying element stiffness to be zero. This can lead to difficulty in determining the default penalty +stiffness and may cause numerical problems during the analysis. +Augmented Lagrange method +The linear penalty method can be used within an augmentation iteration scheme that drives +down the penetration distance. This so-called augmented Lagrange method applies only to hard +pressure-overclosure relationships. The following describes the sequence that occurs in each increment +with this approach: +1. Abaqus/Standard finds a converged solution with the penalty method. +2. If a slave node penetrates the master surface by more than a specified penetration tolerance, the +contact pressure is “augmented” and another series of iterations is executed until convergence is +once again achieved. +3. Abaqus/Standard continues to augment the contact pressure and find the corresponding converged +solution until the actual penetration is less than the penetration tolerance. +The augmented Lagrange method may require additional iterations in some cases; however, this approach +can make the resolution of contact conditions easier and avoid problems with overconstraints, while +keeping penetrations small. The augmented Lagrange method is used by default for three-dimensional +self-contact using node-to-surface discretization. +The default penetration tolerance is one-tenth of a percent of the characteristic interface length +except in the following cases: +• if you specify a penalty stiffness scaling factor, +, of less than 1.0 (using the interface discussed +below), Abaqus/Standard will automatically scale the default penetration tolerance by a factor of +(which will be greater than or equal to 1.0); +• the default penetration tolerance for finite-sliding, surface-to-surface contact is five percent of the +characteristic interface length, subject to the scaling discussed in the previous bullet point. +The default penalty stiffness for the augmented Lagrange method is 1000 times the representative +underlying element stiffness. Lagrange multipliers are used for the augmented Lagrange method if +the penalty stiffness exceeds 1000 times the representative underlying element stiffness computed by +Abaqus/Standard; otherwise, no Lagrange multipliers are used. Therefore, Lagrange multipliers are not +used for the augmented Lagrange method with the default penalty stiffness. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options: +*SURFACE INTERACTION, NAME=interaction_property_name +*SURFACE BEHAVIOR, AUGMENTED LAGRANGE +Interaction module: contact property editor: Mechanical→Normal Behavior: +Constraint enforcement method: Augmented Lagrange (Standard) +Modifying the penetration tolerance for the augmented Lagrange method +You can modify the penetration tolerance for the augmented Lagrange method on a step-by-step basis by +specifying an absolute or relative penetration tolerance. The relative penetration tolerance is specified +with respect to a characteristic length computed by Abaqus/Standard. The default penetration tolerance +was discussed above. The default penetration tolerance is increased automatically if you set the penalty +stiffness scale factor to a value less than 1.0 (also discussed above); however, Abaqus/Standard will not +adjust any directly specified penetration tolerance. Choosing a very small penetration tolerance may +result in an excessive number of augmentation iterations. +Input File Usage: +Abaqus/CAE Usage: +To specify an absolute penetration tolerance: +*CONTACT CONTROLS, ABSOLUTE PENETRATION +TOLERANCE=tolerance +To specify a relative penetration tolerance: +*CONTACT CONTROLS, RELATIVE PENETRATION +TOLERANCE=tolerance +Interaction module: Abaqus/Standard contact controls editor: +Augmented Lagrange: Penetration tolerance: Absolute: +tolerance or Relative: tolerance +Modifying the penalty stiffness for the augmented Lagrange method +As with the penalty method, you can specify the penalty stiffness, shift the pressure-overclosure +relationship by specifying the clearance at which the contact pressure is zero, or scale the default or +specified penalty stiffness by a factor as part of the surface behavior definition. You can also scale the +penalty stiffness on a step-by-step basis, which will act as an additional multiplier on any scale factor +specified as part of the surface behavior definition. Choosing a very low penalty stiffness may result +in an excessive number of augmentation iterations. +Input File Usage: +To modify the penalty behavior in the surface behavior definition: +*SURFACE BEHAVIOR, AUGMENTED LAGRANGE +penalty stiffness, clearance at zero pressure, factor +To scale the penalty stiffness on a step-by-step basis: +Abaqus/CAE Usage: +*CONTACT CONTROLS, STIFFNESS SCALE FACTOR=factor +To modify the penalty behavior in the surface behavior definition: +Interaction module: contact property editor: Mechanical→Normal Behavior: +Constraint enforcement method: Augmented Lagrange (Standard), +Stiffness value: Specify: penalty stiffness, Stiffness scale factor: factor, +Clearance at which contact pressure is zero: clearance at zero pressure +To scale the penalty stiffness on a step-by-step basis: +Interaction module: Abaqus/Standard contact controls editor: Augmented +Lagrange: Stiffness scale factor: factor +Modifying the number of allowed augmentations for the augmented Lagrange method +You can define the number of allowed augmentations for the augmented Lagrange method. +Input File Usage: +*CONTROLS, PARAMETERS=TIME INCREMENTATION +, , , , , , , , , , , , +Abaqus/CAE Usage: +Defining the number of allowed augmentations for the augmented Lagrange +method is not supported in Abaqus/CAE. +Limitations of the augmented Lagrange method +The augmented Lagrange method cannot be used for debonded surfaces. +If the augmented Lagrange method is specified, Lagrange multipliers are always used during +analysis steps with the following procedures: +• Design sensitivity analysis +• Direct steady-state dynamic analysis +• Quasi-Newton method +If surface elements have been used to define a contact surface on the exterior of a substructure +, Abaqus/Standard interprets the +underlying element stiffness to be zero. This can lead to difficulty in determining the default penalty +stiffness and may cause numerical problems during the analysis. +Use of Lagrange multiplier degrees of freedom by the various methods +Using Lagrange multipliers to enforce contact constraints can add significantly to the solution cost, but +they also protect against numerical errors related to ill-conditioning that can occur if a high contact +stiffness is in effect. Abaqus/Standard automatically chooses whether the constraint method makes use of +Lagrange multipliers, based on a comparison of the contact stiffness to the underlying element stiffness. +Table 37.1.2–1 summarizes the use of Lagrange multipliers. Lagrange multipliers are not used for the +default contact stiffnesses associated with the penalty and augmented Lagrange approximations of hard +contact. Any Lagrange multipliers associated with contact are present only for active contact constraints, +so the number of equations may change as the contact status changes. +Table 37.1.2–1 Use of Lagrange multipliers in constraint enforcement methods. +Constraint Method +Direct, hard contact +Direct, exponential softened +contact +Direct, linear softened contact +Direct, tabular softened contact +Penalty, hard contact +Augmented Lagrange, hard +contact +If +If +If +If +If +Use Lagrange Multipliers +Yes +Always +No1 +Never +If +If +If +If +If += slope of pressure-overclosure relationship += penalty stiffness += underlying element stiffness +1Lagrange multipliers are always used, regardless of the constraint enforcement method or +stiffness, in the following cases: design sensitivity analyses, direct steady-state dynamics +analyses, analyses using the quasi-Newton method. +37.1.3 +SMOOTHING CONTACT SURFACES IN Abaqus/Standard +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining general contact interactions in Abaqus/Standard,” Section 35.2.1 +• “Defining contact pairs in Abaqus/Standard,” Section 35.3.1 +• *CONTACT +• *CONTACT PAIR +• *SURFACE PROPERTY ASSIGNMENT +• *SURFACE SMOOTHING +Overview +With the finite element method, curved geometric surfaces are naturally approximated as a faceted +group of connected element faces. The use of a faceted surface geometry rather than the true surface +geometry can significantly contribute to contact stress inaccuracy in contact interactions, especially +when the magnitude of the differences between the faceted and true surface is not small with respect to +the deformation of the components in contact. Contact stress output is of primary importance in many +Abaqus/Standard applications; for example, the distribution of contact pressures can be used to identify +wear patterns and peak pressure values to determine relative lives of machine parts. Furthermore, +discontinuities in the surface normal direction at surface facet boundaries can contribute to convergence +difficulties. +Abaqus/Standard offers techniques for overcoming the accuracy and convergence difficulties +associated with faceted surfaces in contact interactions. These techniques allow a discretized surface +with discontinuous surface normals to more closely approximate the behavior of a smooth surface with +continuous normals during an analysis. The smoothing technique used in node-to-surface contact is +different from the smoothing technique used in surface-to-surface and general contact: +• Node-to-surface contact smoothing is applied by default and affects the entire master surface. +• Surface-to-surface contact smoothing is not applied by default, but it can be applied to any surface +regions whose geometry is roughly axisymmetric. +Surface-to-surface contact typically gives the most accurate results. +Smoothing master surfaces for node-to-surface contact pairs +Surface smoothing in node-to-surface contact pairs improves numerical stability and sometimes +improves solution accuracy. Slave nodes traveling along a master surface tend to “snag” on sharp +corners, resulting in convergence difficulties. Because of this behavior, Abaqus/Standard automatically +smooths the master surface in node-to-surface contact pairs. This smoothing technique recalculates +the master surface normals along facet edges and, depending on the type of surface, may affect the +surface geometry. The details of smoothing for node-to-surface contact formulations are discussed in +“Smoothing master surfaces for the finite-sliding, node-to-surface formulation” in “Contact formulations +in Abaqus/Standard,” Section 37.1.1, and “Using the small-sliding tracking approach” in “Contact +formulations in Abaqus/Standard,” Section 37.1.1. +Smoothing contact surfaces for surface-to-surface contact +Smooth surfaces are not usually necessary in surface-to-surface contact to ensure analysis convergence; +therefore, no smoothing is applied to these surfaces by default. However, an optional smoothing +technique is available for improving the contact stress and pressure accuracy for axisymmetric (or +nearly axisymmetric) surfaces in surface-to-surface contact interactions. +Surface-to-surface contact smoothing can be applied to specific surface regions. These regions must +be roughly axisymmetric (all points on the surface are nearly equidistant from a single axis) or roughly +spherical (all points on the surface are nearly equidistant from a single point). The pin insertion model +in Figure 37.1.3–1 could benefit from surface-to-surface contact smoothing: the body of the pin and +the hole are axisymmetric surfaces, and the head of the pin is a spherical surface. Surface-to-surface +contact smoothing would also be effective if the surfaces were not perfectly axisymmetric or spherical; +for example, if the pin body were slightly elliptical. +Figure 37.1.3–1 Surface-to-surface contact model with surface smoothing. +Applying contact smoothing to surface-to-surface contact pairs +Surface-to-surface contact smoothing for contact pairs is enabled by creating a surface smoothing +definition. A contact pair definition references this smoothing definition to apply geometric corrections +in the contact formulation (the physical geometry of the model is not altered). +The surface smoothing definition lists all of the faceted regions in the contact pair surfaces that must +be smoothed, as well as the geometry correction method that should be applied to each region. Three +geometry correction methods can be employed: +• The circumferential smoothing method is applicable to surfaces approximating a portion of a circle +in two dimensions or a portion of a surface of revolution in three dimensions. +• The spherical smoothing method is applicable to surfaces approximating a portion of a sphere in +three dimensions. +• The toroidal smoothing method is applicable to surfaces approximating a portion of a torus in three +dimensions (i.e., a circular arc revolved about an axis). +Each surface-to-surface contact pair refers to a single smoothing definition; therefore, a smoothing +definition must list all of the smoothed regions and applicable geometry correction methods for the +contact pair. Geometry corrections can be applied to master surfaces and to slave surfaces; you can +also apply corrections to selected regions of each surface. A surface smoothing definition can include +multiple regions and different geometric correction methods for each region. For each region, you must +specify the appropriate geometry correction method and either the approximate axis of revolution (for +circumferential or toroidal smoothing) or the approximate spherical center (for spherical smoothing). +For toroidal smoothing, you must also specify the distance of the center of the circular arc from the +axis of revolution, and the line joining point (Xa , Ya , Za ) and the center of the circular arc should be +perpendicular to the axis of revolution. +Input File Usage: +Use both of +smoothing: +the following options to apply surface-to-surface contact +*CONTACT PAIR, GEOMETRIC CORRECTION=smoothing_name +*SURFACE SMOOTHING, NAME=smoothing_name +data lines to define smoothing regions +Use the following data line to apply circumferential smoothing to +surface regions with an axis of symmetry passing through points +(Xa , Ya , Za ) and (Xb , Yb, Zb): +slave_region, master_region, CIRCUMFERENTIAL, Xa , Ya, Za , Xb , Yb, Zb +Use the following data line to apply spherical smoothing to +surface regions with a spherical center at point (Xa , Ya , Za ): +slave_region, master_region, SPHERICAL, Xa, Ya , Za +Use the following data line to apply toroidal smoothing to +surface regions with an axis of symmetry passing through points +(Xa , Ya , Za ) and (Xb , Yb, Zb) with the center of the revolved circular arc +at a distance R from the axis of symmetry: +slave_region, master_region, TOROIDAL, Xa , Ya, Za , Xb , Yb, Zb , R +Repeat the data lines as many times as necessary to define the appropriate +geometry corrections for all surfaces in the contact pair. +Abaqus/CAE Usage: +Abaqus/CAE can automatically identify any circumferential or spherical +surfaces in a contact interaction that will benefit from contact smoothing and +apply the necessary geometry correction methods. +Interaction module: contact interaction editor: Surface Smoothing: +Automatically smooth geometry surfaces +Surface-to-surface contact smoothing cannot be applied to surfaces on orphan +mesh models. Toroidal surface smoothing cannot be defined in Abaqus/CAE. +Example +To improve contact pressure accuracy for the model in Figure 37.1.3–1, contact smoothing can be applied +to both the master and slave surfaces. Two different geometric correction methods are required for the +pin (the slave surface), so additional surfaces are defined corresponding to regions of the slave surface. +Spherical smoothing is defined for the tip of the pin. Since the body of the pin and the hole share an axis +of revolution, a single circumferential smoothing technique is applied to both of these surfaces. This +surface smoothing definition applies even if the cross-sectional shapes of the pin and hole deviate from +perfect circles. +*CONTACT PAIR, TYPE=SURFACE TO SURFACE, INTERACTION=FRICTION1, +GEOMETRIC CORRECTION=SMOOTH1 +PIN, HOLE +*SURFACE INTERACTION, NAME=FRICTION1 +*SURFACE SMOOTHING, NAME=SMOOTH1 +PIN_TIP, , SPHERICAL, Xb , Yb , Zb +PIN_BODY, HOLE, CIRCUMFERENTIAL, Xa , Ya , Za , Xb, Yb , Zb +Applying contact smoothing to general contact surfaces +Contact smoothing can be specified for surfaces in a general contact domain using a surface property +assignment. A single surface property assignment specifies all of the surfaces to be smoothed, as well as +the appropriate geometry correction method for each surface. General contact uses the same geometry +correction methods as contact pairs: +• The circumferential smoothing method is applicable to surfaces approximating a portion of a circle +in two dimensions or a portion of a surface of revolution in three dimensions. +• The spherical smoothing method is applicable to surfaces approximating a portion of a sphere in +three dimensions. +• The toroidal smoothing method is applicable to surfaces approximating a portion of a torus in three +dimensions (i.e., a circular arc revolved about an axis). +For each surface, you must specify the appropriate geometry correction method and either the +approximate axis of revolution (for circumferential or toroidal smoothing) or the approximate spherical +center (for spherical smoothing). For toroidal smoothing, you must also specify the distance of the center +of the circular arc from the axis of revolution, and the line joining point (Xa , Ya , Za ) and the center of +the circular arc should be perpendicular to the axis of revolution. +Input File Usage: +*SURFACE PROPERTY ASSIGNMENT, PROPERTY=GEOMETRIC +CORRECTION +data lines to define smoothing regions +Use the following data line to apply circumferential smoothing to a +surface with an axis of symmetry passing through points (Xa , Ya , Za ) +and (Xb , Yb, Zb ): +surface, CIRCUMFERENTIAL, Xa , Ya, Za , Xb , Yb , Zb +Use the following data line to apply spherical smoothing to a +surface with a spherical center at point (Xa , Ya , Za ): +surface, SPHERICAL, Xa, Ya , Za +Use the following data line to apply toroidal smoothing to a +surface with an axis of symmetry passing through points (Xa , Ya , Za ) +and (Xb , Yb, Zb ) with the center of the revolved circular arc +at a distance R from the axis of symmetry: +surface, TOROIDAL, Xa , Ya, Za , Xb , Yb , Zb, R +Repeat the data lines as many times as necessary to define the appropriate +geometry corrections for all surfaces in the contact domain. +Contact surface smoothing can be applied only to native geometry models +in Abaqus/CAE. +By default, Abaqus/CAE automatically detects all +circumferential and spherical surfaces in the general contact domain that +can be smoothed and applies the appropriate smoothing. +Use the following option to prevent automatic surface smoothing of a model: +Interaction module: Create Interaction: General contact (Standard): +Surface Properties: Surface smoothing assignments: Edit: +toggle off Automatically assign smoothing for geometric faces +Use the following option to manually apply smoothing to a surface: +Interaction module: Create Interaction: General contact (Standard): +Surface Properties: Surface smoothing assignments: Edit: +Select surface, click the arrows to transfer surface to list of smoothing +assignments. +In the Smoothing Option column, select REVOLUTION to apply +circumferential smoothing, select SPHERICAL to apply spherical smoothing, +or select NONE to prevent smoothing of the surface. +Toroidal surface smoothing cannot be defined in Abaqus/CAE. +37.1.3–5 +Considerations for using surface-to-surface contact smoothing +The surface-to-surface contact smoothing technique assumes that the initial locations of surface nodes +lie on the true initial surface geometry, with the exception of midside nodes of higher-order elements. +This smoothing technique remains effective even if the midside nodes of higher-order elements do not +lie on the true initial geometry (models meshed using Abaqus/CAE always have midside nodes placed +on the true initial geometry, but this may not be the case with other meshing preprocessors). +The effects of surface-to-surface contact smoothing tend to be most significant for analyses +involving small deformation and coarse mesh discretization with first-order elements in the contact +region; however, significant improvements to contact stress solutions are common even when the +mesh is quite refined or higher-order elements are used. For analyses with large deformation this +smoothing technique typically has an insignificant effect on solutions. However, in some cases the +smoothing can degrade the solution accuracy after large deformation; therefore, it is not recommended +to use surface-to-surface contact smoothing for large-deformation analyses. The effectiveness of +surface-to-surface contact smoothing does not degrade upon relative motion between contact surfaces; +for example, the smoothing technique works well for cases involving large sliding but small deformation. +Effects of contact surface smoothing +The impact of contact surface smoothing can be demonstrated by a simple model of an interference +fit between concentric cylinders modeled with first-order elements of different sizes, as shown in +Figure 37.1.3–2. Discrepancies between the true surface geometry and the faceted surface geometry +result in noise in the contact pressure solution. If the interference distance and resulting deformation +distance is small with respect to the geometry discrepancy, this noise can have a significant effect on +the accuracy of the solution. Although surface-to-surface contact typically handles these discrepancies +better than node-to-surface contact, it is not unusual for the maximum deviation from the analytical +pressure solution to be upward of 100%. The effects of the noise become less apparent for larger +deformations, but they are never completely eliminated. +Figure 37.1.3–2 Initial mesh geometry for interference fit model. +Modeling the interference fit with a surface-to-surface contact pair and using circumferential +contact smoothing consistently yields low-noise pressure results that are within 3% of the analytical +solution, regardless of the size of the interference distance. The effect is drastically noticeable for +small-deformation analyses, but improvements can be observed even for larger deformations. +For a node-to-surface contact pair, increasing the smoothing fraction to the maximum value of +0.5 marginally reduces the noise in the pressure solution in a two-dimensional model. Increasing the +smoothing factor in a three-dimensional model has little effect on accuracy, since physical surfaces +are not smoothed for three-dimensional node-to-surface smoothing; see “Smoothing master surfaces +for the finite-sliding, node-to-surface formulation” in “Contact formulations in Abaqus/Standard,” +Section 37.1.1, for more information. +37.2 +Contact formulations and numerical methods in Abaqus/Explicit +• “Contact formulation for general contact in Abaqus/Explicit,” Section 37.2.1 +• “Contact formulations for contact pairs in Abaqus/Explicit,” Section 37.2.2 +• “Contact constraint enforcement methods in Abaqus/Explicit,” Section 37.2.3 +37.2.1 +CONTACT FORMULATION FOR GENERAL CONTACT IN Abaqus/Explicit +Products: Abaqus/Explicit Abaqus/CAE +References +• “Defining general contact interactions in Abaqus/Explicit,” Section 35.4.1 +• *CONTACT +• *CONTACT FORMULATION +• “Specifying master-slave assignments for general contact,” Section 15.13.6 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +The contact formulation used with the general contact algorithm in Abaqus/Explicit: +• includes the contact surface weighting, surface polarity, and the sliding formulation; and +• can be applied selectively to particular regions within a general contact domain. +The general contact formulation uses a penalty method to enforce contact constraints between surfaces; +the constraint enforcement method is discussed in “Contact constraint enforcement methods in +Abaqus/Explicit,” Section 37.2.3. +Specifying the contact formulation +Currently you can specify only the contact surface weighting and polarity for the general contact +algorithm. The contact formulation propagates through all analysis steps in which the general contact +interaction is active. +The surface names used to specify the regions where a nondefault contact formulation should be +assigned do not have to correspond to the surface names used to specify the general contact domain. +In many cases the contact interaction will be defined for a large domain, while a nondefault contact +formulation will be assigned to a subset of this domain. Any contact formulation assignments for regions +that fall outside the general contact domain will be ignored. The last assignment will take precedence if +the specified regions overlap. +Input File Usage: +*CONTACT FORMULATION +This option must be used in conjunction with the *CONTACT option. It should +appear at most once per step for each value of the TYPE parameter; the data line +can be repeated as often as necessary to assign contact formulations to different +regions. +Abaqus/CAE Usage: +Interaction module: Create Interaction: General contact +(Explicit): Contact Formulation +Contact surface weighting +Generally, contact constraints in a finite element model are applied in a discrete manner, meaning that for +hard contact a node on one surface is constrained to not penetrate the other surface. In pure master-slave +contact the node with the constraint is part of the slave surface and the surface with which it interacts +is called the master surface. For balanced master-slave contact Abaqus/Explicit calculates the contact +constraints twice for each set of surfaces in contact, in the form of penalty forces: once with the first +surface acting as the master surface and once with the second surface acting as the master surface. The +weighted average of the two corrections (or forces) is applied to the contact interaction. +Balanced master-slave contact minimizes the penetration of the contacting bodies and, thus, +provides better enforcement of contact constraints and more accurate results in most cases. +In pure +master-slave contact the nodes on the master surface can, in principle, penetrate the slave surface +unhindered . +slave nodes cannot penetrate +master segments +master surface +(segments) +penetration +slave surface +(nodes) +gap +master node can penetrate +slave segment +Figure 37.2.1–1 Master surface penetrations into the slave surface +in pure master-slave contact due to coarse discretization. +The general contact algorithm in Abaqus/Explicit uses balanced master-slave weighting whenever +possible; pure master-slave weighting is used for contact interactions involving node-based surfaces, +which can act only as pure slave surfaces and for contact interactions involving analytical rigid surfaces, +which can act only as pure master surfaces. Surface-based cohesive behavior also always uses a pure +master-slave algorithm. However, you can choose to specify a pure master-slave weighting for other +interactions as well. +There is no master-slave relationship for edge-to-edge contact; both contacting edges are given +equal weighting. +Specifying pure master-slave weighting for node-to-face contact +You can specify that a general contact interaction should use pure master-slave weighting for node-to- +face contact. This specification has no effect on edge-to-edge contact and cannot be used to make a +node-based surface act as a master surface. When two originally flat surfaces contact one another, a +more uniform penetration distance distribution (and consequently pressure distribution) may result with +pure master-slave weighting where the more refined surface acts as the slave surface as compared to +balanced master-slave weighting. This can be particularly evident if the mesh densities of the contacting +surfaces differ significantly—with balanced weighting the contact penetrations will be smaller near the +nodes of the coarsely meshed surface. +Abaqus/Explicit will automatically generate contact exclusions for the master-slave orientation +opposite to that specified; therefore, node-to-face self-contact will be excluded for any regions of the +two surfaces that overlap. For example, specifying that the general contact interaction between surf_A +and surf_B should use pure master-slave weighting with surf_A considered to be the slave surface +would result in exclusions being generated internally for faces of surf_A contacting nodes of surf_B; +node-to-face self-contact would be excluded for the region of overlap between surf_A and surf_B. A +warning message will be issued if the second surface name is omitted or is the same as the first surface +name since this input would result in the exclusion of node–face self-contact for the surface. +Input File Usage: +Use the following option to indicate that the first surface should be considered +the slave surface (default): +*CONTACT FORMULATION, TYPE=PURE MASTER-SLAVE +surf_1, surf_2, SLAVE +Use the following option to indicate that the first surface should be considered +the master surface: +*CONTACT FORMULATION, TYPE=PURE MASTER-SLAVE +surf_1, surf_2, MASTER +If the first surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. The second surface name must be specified. +Interaction module: Create Interaction: General contact (Explicit): +Contact Formulation: Pure master-slave assignments: Edit: +select the surfaces in the columns on the left, and click the arrows in the middle +to transfer them to the list of master-slave assignments. +In the First Surface Type column, enter SLAVE to indicate that the first +surface should be considered the slave surface, and enter MASTER to indicate +that the first surface should be considered the master surface. +Abaqus/CAE Usage: +Contact surface polarity +By default, general contact considers both sides of all double-sided elements in surfaces specified to be +included for contact purposes (side labels of double-sided elements are ignored). This default can be +overridden for node-to-face and Eulerian-Lagrangian contact and in some cases results in more accurate +enforcement of contact. +Surface polarity is not considered for edge-to-edge contact, including edges activated on faces of +solid elements. +Specifying surface polarity for node-to-face and Eulerian-Lagrangian contact +Changing the polarity of double-sided elements forces the contact algorithm to treat them as if they +were solid elements. More accuracy may be gained by converting double-sided elements to single-sided +if there is a chance that slave nodes may be “caught” behind the surface in node-to-face contact or if +material contained on one side of a double-sided surface leaks to the other side in Eulerian-Lagrangian +contact. Improvements in performance and memory use may also be observed with Eulerian-Lagrangian +contact if double-sided Lagrangian surfaces are converted to single-sided for contact with all Eulerian +material surfaces. +Input File Usage: +Use the following option to indicate that the sides of the (double-sided) +elements specified in the second surface’s definition should be considered for +contact with the first surface: +*CONTACT FORMULATION, TYPE=POLARITY +surf_1, surf_2 +Use the following option to indicate that the SPOS side of the (double-sided) +elements in the second surface should be considered for contact with the first +surface: +*CONTACT FORMULATION, TYPE=POLARITY +surf_1, surf_2, SPOS +Use the following option to indicate that the SNEG side of the (double-sided) +elements in the second surface should be considered for contact with the first +surface: +*CONTACT FORMULATION, TYPE=POLARITY +surf_1, surf_2, SNEG +Use the following option to indicate that both sides of the (double-sided) +elements in the second surface should be considered for contact with the first +surface: +*CONTACT FORMULATION, TYPE=POLARITY +surf_1, surf_2, TWO SIDED +If the first surface name is omitted, a default surface that encompasses the entire +general contact domain is assumed. The second surface name must be specified. +Sliding formulation +Currently only the finite-sliding formulation is available for general contact in Abaqus/Explicit. This +formulation allows for arbitrary separation, sliding, and rotation of the surfaces in contact. For cases in +which small-sliding or infinitesimal-sliding assumptions would be preferred, the contact pair algorithm +should be used . +Abaqus/Explicit is designed to simulate highly nonlinear events or processes. Because it is possible +for a node on one surface to contact any of the facets on the opposite surface, Abaqus/Explicit must +use sophisticated search algorithms for tracking the motions of the surfaces. The finite-sliding contact +search algorithm is designed to be robust, yet computationally efficient. This algorithm assumes that the +incremental relative tangential motion between surfaces does not significantly exceed the dimensions of +the master surface facets, but there is no limit to the overall relative motion between surfaces. It is rare +for the incremental motion to exceed the facet size because of the small time increment used in explicit +dynamic analyses. In cases involving relative surface velocities that exceed material wave speeds it may +be necessary to reduce the time increment. +The contact search algorithm uses a global search when a contact interaction is first introduced, and +a hierarchical global/local search algorithm is used thereafter. No user control of the search algorithm is +needed. +37.2.2 +CONTACT FORMULATIONS FOR CONTACT PAIRS IN Abaqus/Explicit +Products: Abaqus/Explicit Abaqus/CAE +References +• “Surfaces: overview,” Section 2.3.1 +• “Defining contact pairs in Abaqus/Explicit,” Section 35.5.1 +• *CONTACT PAIR +• “Defining surface-to-surface contact,” Section 15.13.7 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +The contact formulation for the contact pair algorithm in Abaqus/Explicit includes: +• the contact surface weighting (balanced or pure master-slave); and +• the sliding formulation (finite, small, or infinitesimal). +You can also specify the method that is used to enforce contact constraints in the contact pair; these +methods are discussed in “Contact constraint enforcement methods in Abaqus/Explicit,” Section 37.2.3. +Contact surface weighting +Both the pure master-slave and the balanced master-slave contact algorithms are available in +Abaqus/Explicit. By default, Abaqus/Explicit will decide which algorithm to use for any given contact +pair based on the nature of the two surfaces forming the contact pair and whether kinematic or penalty +enforcement of contact constraints is used. You can override the defaults in some cases. +Default choices for the contact pair weighting +Abaqus/Explicit uses the pure master-slave, kinematic contact algorithm, by default, in the following +situations (the first surface in each situation listed is designated the master surface): +• when a rigid surface contacts a deformable surface; +• when an element-based surface contacts a node-based surface; or +• when a surface based on continuum elements contacts a surface based on shell or membrane +elements. +By default, Abaqus/Explicit uses the balanced master-slave, kinematic contact algorithm in the following +situations: +• when a single surface contacts itself (referred to as self-contact or single-surface contact); or +• when two deformable surfaces that are meshed with similar elements (i.e., either both surfaces have +shells or membranes or both have continuum elements) contact each other. +If the penalty contact algorithm is specified, Abaqus/Explicit uses pure master-slave weighting, by +default, in the following situations (the first surface in each situation listed is designated the master +surface): +• when an analytical rigid surface contacts a deformable surface; or +• when an analytical rigid surface or an element-based surface contacts a node-based surface. +If the penalty contact algorithm is specified, Abaqus/Explicit chooses balanced master-slave weighting, +by default, in the following situations: +• when a single surface contacts itself (referred to as self-contact or single-surface contact); or +• when two element-based surfaces contact each other. +Balanced master-slave weighting means that the corrections produced by both sets of contact calculations +are weighted equally. +Modifying the default choices for the contact pair weighting +When the kinematic contact method is chosen, you can override the default contact pair weighting only +when two separate deformable element-based surfaces are contacting each other, which corresponds to +the last situation in each list for kinematic contact given in the previous section. +The following aspects should be considered when deciding whether or not to override the default +choice. First, the balanced master-slave contact algorithm requires more computational time, but it is +typically more accurate. Second, when the densities differ by orders of magnitude, the less dense body +should be a pure slave surface. Contact-induced noise can occur if a surface on a much denser body is +at all weighted as a slave surface. Finally, to avoid significant penetration for hard contact, the surface +with the finer mesh should not be the master surface in the pure master-slave contact pair. +When the penalty contact method is chosen, you can choose to specify a pure master-slave weighting +to reduce computational time. When two originally flat surfaces contact one another, a more uniform +penetration distance distribution (and consequently pressure distribution) may result with pure master- +slave weighting as compared to balanced master-slave weighting. This can be particularly evident if +the mesh densities of the contacting surfaces differ significantly—with balanced weighting the contact +penetrations will be smaller near the nodes of the coarsely meshed surface. However, balanced master- +slave weighting provides better enforcement of contact constraints in most cases. +You define a weighting factor, f, to specify the master-slave weighting. Set f=1.0 to designate the +first surface in the contact pair as the master surface and the second surface as the slave surface. Set +f=0.0 to designate the first surface in the contact pair as the slave surface and the second surface as the +master surface. Specifying any value of f between 0 and 1.0 invokes the balanced master-slave contact +algorithm. When f=0.5, which is the default for balanced master-slave contact pairs, Abaqus/Explicit +weights each set of corrections equally. In contrast, Abaqus/Standard uses a pure master-slave contact +algorithm; the slave surface must always be given first, as in the f=0.0 case above. +*CONTACT PAIR, WEIGHT=f +Interaction module: interaction editor: Weighting factor Specify f +Abaqus/CAE Usage: +Input File Usage: +Sliding formulation +In Abaqus/Explicit there are three approaches to account for the relative motion of the two surfaces +forming a contact pair: +• finite sliding, which is the most general and allows any arbitrary motion of the surfaces; +• small sliding, which assumes that although two bodies may undergo large motions, there will be +relatively little sliding of one surface along the other; or +• infinitesimal sliding and rotation, which assumes that both the relative motion of the surfaces and +the absolute motion of the contacting bodies are small. +The small-sliding and infinitesimal-sliding formulations cannot be used for contact pairs using the penalty +contact algorithm or involving self-contact or analytical rigid surfaces. +Using the finite-sliding formulation +The finite-sliding formulation allows for arbitrary separation, sliding, and rotation of the surfaces. +Abaqus/Explicit uses this formulation by default. Only the finite-sliding approach is available for +self-contact or contact involving analytical rigid surfaces. +Input File Usage: +Abaqus/CAE Usage: +*CONTACT PAIR +Interaction module: interaction editor: Sliding formulation: Finite sliding +Example +The following input defines finite-sliding contact between the surfaces ASURF and BSURF, shown in +Figure 37.2.2–1, with ASURF acting as the slave surface: +*SURFACE,NAME=ASURF +ESETA, +*SURFACE,NAME=BSURF +ESETB, +*CONTACT PAIR,INTERACTION=PAIR1, WEIGHT=0.0 +ASURF, BSURF +*SURFACE INTERACTION,NAME=PAIR1 +In the example shown in Figure 37.2.2–1 slave node 101 may come into contact anywhere along +the master surface BSURF. While in contact, it is constrained to slide along BSURF, irrespective of the +orientation and deformation of this surface. This behavior is possible because Abaqus/Explicit tracks +the position of node 101 relative to the master surface BSURF as the bodies deform. Figure 37.2.2–2 +shows the possible evolution of the contact between node 101 and its master surface BSURF. Node 101 +is in contact with the element face with end nodes 201 and 202 at time +. The load transfer at this time +occurs between node 101 and nodes 201 and 202 only. Later on, at time +, node 101 may find itself in +contact with the element face with end nodes 501 and 502. Then the load transfer will occur between +node 101 and nodes 501 and 502. +ESETB +ESETA +502 +BSURF +201 +501 +202 +101 +102 +103 +ASURF +Figure 37.2.2–1 Contacting bodies. +BSURF +201 +t = t 1 +202 +501 +502 +t = t 2 +101 +t = 0 +Figure 37.2.2–2 Trajectory of node 101 in finite-sliding contact. +Finite sliding in a geometrically linear analysis +Finite-sliding simulations usually include nonlinear geometric effects because such simulations +generally involve large deformations and large rotations. However, it is also possible to use the +finite-sliding formulation in a geometrically linear analysis . The load transfer paths between the surfaces and +the contact direction are updated in finite-sliding, geometrically linear analysis. This capability is useful +for analyzing finite sliding between two stiff bodies that do not undergo large rotations. +Using the small-sliding formulation +For a large class of contact problems the general tracking of the finite-sliding formulation is unnecessary, +even though geometric nonlinearity must be considered. Abaqus/Explicit provides a small-sliding +contact formulation for such problems. This formulation assumes that the surfaces may undergo +arbitrarily large rotations but that a slave node will interact with the same local area of the master +surface throughout the analysis. Contact pairs that use the small-sliding formulation must be defined in +the first step of the simulation, although they may remain active after the first step. +A large-displacement formulation (the default) should be used for the step in which the small-sliding +contact formulation should be used. +In a small-sliding analysis every slave node interacts with its own local tangent plane on the master +surface . The slave node is constrained not to penetrate this local tangent plane. +Each local tangent plane, which is a line in two dimensions, is defined by an anchor point, +, on the +master surface and an orientation vector at the anchor point . +104 +N(X0) +N3 +X0 +103 +slave surface +102 +N2 +local tangent plane +master surface +N4 +Figure 37.2.2–3 Definition of the anchor point and local tangent plane for node 103. +Having a local tangent plane for each slave node means that for the small-sliding formulation +Abaqus/Explicit does not have to monitor slave nodes for possible contact along the entire master +surface. Therefore, small-sliding contact is less expensive computationally than finite-sliding contact. +The cost savings are most dramatic in three-dimensional contact problems. +When the balanced master-slave contact algorithm is invoked with the small-sliding formulation, +anchor points and tangent planes will be computed for both surfaces. +Input File Usage: +Use both of the following options: +*STEP, NLGEOM=YES +… +*CONTACT PAIR, SMALL SLIDING +For example, the following options define small-sliding contact between the +two bodies shown in Figure 37.2.2–1: +*STEP, NLGEOM=YES +… +*SURFACE, NAME=ASURF +ESETA, +*SURFACE, NAME=BSURF +ESETB, +*CONTACT PAIR, SMALL SLIDING, WEIGHT=0.0 +ASURF, BSURF +Abaqus/CAE Usage: +Interaction module: interaction editor: Sliding formulation: Small sliding +Step module: step editor: Nlgeom: On +Anchor point and tangent plane definition +The anchor point and the tangent plane orientation are chosen before the analysis starts using the initial +configuration of the model. The anchor point and the tangent plane orientation remain fixed with respect +to the master surface facet for all steps in which the contact pair is active. No contact constraints are +enforced for slave nodes whose nearest point lies on the free perimeter of the master surface in the +original configuration and that do not project onto any master surface facet. +Abaqus/Explicit chooses the anchor point as the nearest point on the master surface. The orientation +of the tangent plane is calculated by default from the normals at the master surface nodes, or you can +specify it directly. +• Master surface normals: The first step in defining the tangent plane orientation is to construct the +unit normal vectors at each node of the master surface. Abaqus/Explicit forms these nodal normals +by averaging the normals of the element faces making up the master surface; only the element faces +in the surface definition will contribute to the nodal normals. The tangent plane orientation is then +calculated from the master surface nodal normals and the element shape functions at the anchor +point. +Figure 37.2.2–3 shows the nodal unit normals for a master surface, the anchor point +, and +the local tangent plane associated with slave node 103. Abaqus/Explicit uses the closest point on the +master surface as the anchor point. +is the contact direction for slave node 103 and defines +the orientation of the local tangent plane. In this example, as in many cases, the local tangent plane +is only an approximation of the actual mesh geometry. +• Master surface normals at symmetry planes: Sometimes the master surface normal and the local +tangent plane that Abaqus/Explicit calculates are not suitable for the desired analysis. The most +common situation where unsuitable surface normals are calculated occurs when a curved master +surface ends at a symmetry plane and the boundary conditions have been specified in direct +format rather than in symmetry “type” format (XSYMM, YSYMM, or ZSYMM—see “Boundary +conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1). +In this case the correct +normals should be in the symmetry plane; however, because the surface facets that abut the +symmetry plane usually form an angle with the plane, the normal will project away from the +symmetry plane. The effect of this behavior can be that a slave node does not project onto any +master surface facet (the slave node is said not to “intersect” the master surface). No contact +constraints will be enforced for such slave nodes. However, if symmetry “type” format boundary +conditions are specified, contact constraints will be enforced as described below. The finite-sliding +formulations use no special treatment for master surfaces ending at a symmetry plane. +Figure 37.2.2–4 shows two concentric cylinders that contact each other; the inner cylinder is +chosen as the master surface CSURF, and a half-symmetry model is used. Since Abaqus/Explicit +calculates the nodal normals from the approximate, finite element model, the nodal normal +does +not point along the symmetry plane, which means that slave node 100 has no anchor point within the +perimeter of the master surface. Whether or not contact is enforced for node 100 depends on how +the symmetry boundary condition is specified. If the individual components are specified rather than +a symmetry “type” boundary condition, slave node 100 will be free to penetrate the master surface. +If the symmetry “type” format is used, the master normal at the node on the symmetry plane will +be corrected to lie along the symmetry plane and contact will be enforced on the tangent plane as +shown in Figure 37.2.2–5. Defining a YSYMM “type” boundary condition at node 1 to specify the +symmetry plane will allow slave node 100 to see the master surface CSURF. +master surface CSURF +slave surface DSURF +N1 +100 +symmetry plane +Figure 37.2.2–4 Master surface normal at node 1 in a small-sliding model of concentric +cylinders. With the default +slave node 100 will never contact CSURF. +• Modifying the local tangent plane orientation: +In some cases the contact direction, +, +defined from the master surface averaged normals will not define the contact surface accurately. +The most common example of this is a circular surface meshed with nonuniform length facets. +Figure 37.2.2–6 shows how the averaged master normals will not be oriented correctly in the +radial direction. +In this case you should specify the contact direction directly for each slave +node by defining spatially varying initial clearances . The location of the anchor point is not affected by reorienting +the tangent plane using an initial clearance definition. +master surface CSURF +slave surface DSURF +100 +N1 +tangent plane +Figure 37.2.2–5 The modified master surface normal at node 1 +of CSURF now allows slave node 100 to contact CSURF. +averaged +master normal +actual +surface +master surface +Figure 37.2.2–6 Poorly oriented averaged master surface +normals for an irregularly meshed circular surface. +Local tangent plane rotation +The local tangent plane is always orthogonal to the contact direction. The contact direction is taken +as the interpolated normal of the master surface at the anchor point, +, or as the direction +specified with a spatially varying clearance definition . Once the contact direction has been defined, the orientation of the +local tangent plane with respect to the master surface facet remains fixed. Because the small-sliding +formulation considers nonlinear geometric effects, Abaqus/Explicit continuously updates the orientation +of the local tangent plane to account for the rotation of the master surface facet. The position of the +anchor point relative to the surrounding nodes on the master surface facet does not change as the master +surface deforms. +Load transfer +In a small-sliding analysis the slave node will transfer load to the nodes of the master surface facet +containing the anchor point, with the magnitude of the load transferred to each node weighted by its +proximity to the anchor point. For example, in Figure 37.2.2–3 node 103 transmits load to both nodes 2 +and 3 on the master surface. Thus, if node 103 impacts the local tangent plane, a larger share of the force +would be transmitted to node 3 because it is closer to the anchor point +. +As a slave node slides along its local tangent plane, Abaqus/Explicit does not update the distribution +of load transferred by a given slave node to its associated master surface nodes; the distribution is +based solely on the position of the anchor point. This is unlike the small-sliding formulation in +Abaqus/Standard, which does update the load distribution to the master surface nodes as sliding occurs, +so that no net moment is associated with the contact forces acting on slave and master nodes per active +contact constraint, regardless of the amount of sliding. Some net moment will be associated with the +contact forces after sliding has occurred with the small-sliding formulation in Abaqus/Explicit. This +net moment will not be significant if the sliding is truly small compared to element dimensions, but +otherwise it can result in non-physical behavior and poor accounting of energy. +, the anchor point +Figure 37.2.2–7 shows the potential problem that arises if small sliding is used but the relative +tangential motion of the surfaces is not “small.” It shows the possible evolution of contact between slave +node 101 in Figure 37.2.2–1 and its master surface BSURF. Using the unit normal vectors +and +was found for slave node 101; for the purposes of this example, assume that +it lies at the midpoint of the 201–202 face. With this location of +the local tangent plane for node 101 +is parallel with the 201–202 face. The load transfer always occurs at the original anchor point between +nodes 201 and 202, no matter how far node 101 has slid along the local tangent plane. Therefore, if +node 101 moves as shown in Figure 37.2.2–7, it will continue to transmit load equally to nodes 201 and +202 when, in fact, it really slid off the mesh forming the master surface BSURF. +What can be considered small sliding +A contact pair in a small-sliding contact simulation should not grossly violate any of the assumptions or +limitations outlined above. Adhere to the following guidelines: +• Slave nodes should slide less than an element length from their corresponding anchor point and +still be contacting their local tangent plane. If the master surface is highly curved, the slave nodes +should slide only a fraction of an element length. +• The local tangent planes formed by Abaqus/Explicit should be a good approximation of the mesh +geometry; if necessary, use an initial clearance definition (“Specifying initial clearance values +precisely” in “Adjusting initial surface positions and specifying initial clearances for contact pairs +in Abaqus/Explicit,” Section 35.5.4) to improve the tangent plane orientation. +201 +X0 +202 +BSURF +N201 +101 +t = 0 +N202 +101 +t > 0 +Figure 37.2.2–7 Excessive sliding in a small-sliding contact analysis. +• The rotation and deformation of the master surface should not cause the local tangent planes to +become a poor representation of the master surface during the course of the analysis. +Master surface refinement in small-sliding problems +The basic guidelines for pure master-slave contact given previously in this section should still be followed +in a small-sliding simulation. However, in a small-sliding simulation more thought must be given to the +degree of refinement for the master surface. +The smoothly varying master surface normal +and the local tangent planes that are formed +with it are crucial to the success of a small-sliding analysis. As has been mentioned previously, there are +several methods that can be used to modify +; however, they only control the initial configuration of +the local tangent planes. The deformation and rotation of the master surface can reorient the local tangent +planes such that they become a poor representation of the master surface. Figure 37.2.2–8 shows an +example where distortion of the master surface results in such a situation. This problem can be minimized +to some extent by using a more refined mesh on the master surface, thus providing more element faces +to control the motion of the tangent planes. Excessive mesh refinement should not be necessary since +only small sliding should occur. +Using the infinitesimal-sliding formulation +The difference between the infinitesimal-sliding and small-sliding formulations is that the infinitesimal- +sliding formulation ignores nonlinear geometric effects. To specify the infinitesimal-sliding formulation, +you choose the small-sliding contact formulation and a small-displacement formulation for the analysis +step. +Infinitesimal sliding assumes that both the relative motions of the surfaces and the absolute +motions of the model remain small. The orientations of the local tangent planes are not updated, and the +load transfer paths and the weightings assigned to each master surface node remain constant during an +infinitesimal-sliding simulation. +initial +configuration +local tangent +plane +master +surface +slave +surface +large +deformation +Figure 37.2.2–8 Master surface deformation in a small-sliding +contact analysis can cause problems with the local tangent planes. +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*STEP, NLGEOM=NO +… +*CONTACT PAIR, SMALL SLIDING +Interaction module: interaction editor: Sliding formulation: Small sliding +Step module: step editor: Nlgeom: Off +Contact tracking algorithms +A large portion of the computational cost associated with Abaqus/Explicit contact pairs derives from the +algorithms used to track the relative motion between two contacting surfaces. There are two tracking +approaches for the contact pair algorithm in Abaqus/Explicit, depending on the sliding formulation that +is used: finite sliding and small/infinitesimal sliding. +Finite-sliding tracking +Abaqus/Explicit is designed to simulate highly nonlinear events or processes. Because it is possible for +a node on one surface to contact any of the facets on the opposite surface, Abaqus/Explicit must use +sophisticated search algorithms for tracking the motions of the surfaces. +The contact search algorithm is designed to be robust, yet computationally efficient. This algorithm +assumes that the incremental relative tangential motion between surfaces does not significantly exceed +the dimensions of the master surface facets, but there is no limit to the overall relative motion between +surfaces. It is rare for the incremental motion to exceed the facet size because of the small time increment +used in explicit dynamic analyses. In cases involving relative surface velocities that exceed material +wave speeds, it may be necessary to reduce the time increment. +The contact search algorithm uses a global search at the beginning of each step, and a hierarchical +global/local search algorithm is used for the other increments. The default contact search algorithm can +handle the majority of typical contact situations. However, there are some situations that require special +attention. We will consider a pure master-slave contact pair for discussion purposes. For a balanced +master-slave contact pair, the contact search computations are performed twice for each contact pair. +Global contact searches +A global search determines the globally nearest master surface facet for each slave node in a given contact +pair. A bucket sorting algorithm is used to minimize the computational expense of these searches. A +two-dimensional example, without consideration of “buckets,” is shown in Figure 37.2.2–9. +master surface +100 +10 +101 +11 +102 +12 +13 +48 +49 +50 +51 +slave surface +52 +53 +location of tracked master node +searched master faces +Figure 37.2.2–9 Global search in two dimensions. +The global search computes the distance from node 50 to all of the master surface facets in the same +bucket as node 50. It determines that the nearest facet on the master surface to node 50 is the facet of +element 10. Node 100 is the node on this facet that is nearest to node 50, and it is designated the tracked +master surface node. This search is conducted for each slave node, comparing each node against all of +the facets on the master surface that are in the same bucket. +By default, Abaqus/Explicit performs a global search every one hundred increments for two-surface +contact pairs. The frequency of the global search can be manually adjusted, as discussed in “Contact +controls for contact pairs in Abaqus/Explicit,” Section 35.5.5. Despite the bucket sorting algorithm, +global searches are computationally expensive: performing a global contact search in every increment +will more than double the run time of many Abaqus/Explicit contact analyses. +Local contact searches +Abaqus/Explicit uses a local contact search to track the motion of the surfaces during most increments of +an analysis. In this approach a given slave node searches only the facets that are attached to the previously +tracked master surface node. Abaqus/Explicit determines which adjacent facet is the nearest to the slave +node. It then determines which node on that facet is the closest master surface node to the slave node +and updates the tracked master surface node. If the closest master surface node is not the same as the +previously tracked master surface node, Abaqus/Explicit performs another iteration of the local search. +In the example shown in Figure 37.2.2–10, node 50 moves as shown during an increment. In the first +iteration of the search Abaqus/Explicit finds that the master surface facet on element 10 is still the closest +facet of those attached to node 100 but that node 101 is now the tracked master surface node. Because +the previously tracked node was node 100, Abaqus/Explicit performs another iteration. In this second +iteration a new element, element 11, is found to be the closest facet and the closest master surface node is +102. Another iteration is performed because the identity of the tracked master surface node changed. In +the third iteration the identity of the tracked node does not change, so Abaqus/Explicit designates node +102 as the tracked master surface node for slave node 50. +A local search is substantially less expensive computationally than a global search. A slightly more +expensive local search algorithm can be employed in situations where contact is not being properly +enforced; this alternate algorithm is discussed in “Contact controls for contact pairs in Abaqus/Explicit,” +Section 35.5.5. +Tracking approach for self-contact pairs +Abaqus/Explicit uses similar contact searching methods for simulations with self-contact as for two- +surface contact; however, more frequent global searches are often necessary for self-contact problems. +By default, contact pairs with self-contact use a global contact search every four increments, compared to +every 100 increments for two-surface contact pairs; the frequency of the global searches can be manually +adjusted . If several facets +that are unconnected to each other are found to be near a slave node during global tracking, global tracking +automatically will be performed more frequently than the specified number of increments. Despite +this precaution, the self-contact algorithm will be less robust if you specify a search frequency that is +significantly lower than the default. +master surface +100 +101 +10 +11 +102 +12 +13 +48 +49 +50 +slave surface +51 +52 +⇒ motion of +slave surface +location of previously tracked master node +location of currently tracked master node +Figure 37.2.2–10 Local search in two dimensions. +Small-sliding (or infinitesimal-sliding) tracking approach +When the small-sliding or infinitesimal-sliding contact approach is invoked , Abaqus/Explicit performs a +single global search at the beginning of the first step to determine the globally nearest master surface facet +for each slave node in the given contact pair. Once the nearest facet has been determined, the nearest point +on that facet defines the anchor point. Contact constraints will not be applied to slave nodes that do not +project onto any master surface facet. No further tracking is performed during the step or for subsequent +steps in which the contact pair remains active. This makes the small-sliding/infinitesimal-sliding contact +approach less expensive computationally than the finite-sliding contact approach. The cost savings are +most significant for three-dimensional contact problems. +37.2.3 +CONTACT CONSTRAINT ENFORCEMENT METHODS IN Abaqus/Explicit +Products: Abaqus/Explicit Abaqus/CAE +References +• “Defining general contact interactions in Abaqus/Explicit,” Section 35.4.1 +• “Defining contact pairs in Abaqus/Explicit,” Section 35.5.1 +• *CONTACT +• *CONTACT PAIR +• “Specifying master-slave assignments for general contact,” Section 15.13.6 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +Abaqus/Explicit uses two different methods to enforce contact constraints: +• The kinematic contact algorithm uses a kinematic predictor/corrector contact algorithm to strictly +enforce contact constraints (for example, no penetrations are allowed). +• The penalty contact algorithm has a weaker enforcement of contact constraints but allows for +treatment of more general types of contact. +Contact pairs in Abaqus/Explicit use kinematic enforcement by default, but penalty enforcement can be +specified for individual contact pairs. General contact always uses penalty enforcement. Both methods +conserve momentum between the contacting bodies. +Kinematic contact algorithm +A summary of the default kinematic algorithm that Abaqus/Explicit uses to enforce contact with the +contact pair algorithm is presented below. It is a predictor/corrector algorithm and, therefore, has no +influence on the stable time increment. It is easier to describe the algorithm by first considering a pure +master-slave contact pair. +Kinematic enforcement of contact conditions in a pure master-slave contact pair +In this case in each increment of the analysis Abaqus/Explicit first advances the kinematic state of the +model into a predicted configuration without considering the contact conditions. Abaqus/Explicit then +determines which slave nodes in the predicted configuration penetrate the master surfaces. The depth of +each slave node’s penetration, the mass associated with it, and the time increment are used to calculate +the resisting force required to oppose penetration. For hard contact, this is the force which, had it been +applied during the increment, would have caused the slave node to exactly contact the master surface. +The next step depends on the type of master surface used. +• When the master surface is formed by element faces, the resisting forces of all the slave nodes +are distributed to the nodes on the master surface. The mass of each contacting slave node is also +distributed to the master surface nodes and added to their mass to determine the total inertial mass +of the contacting interfaces. Abaqus/Explicit uses these distributed forces and masses to calculate +an acceleration correction for the master surface nodes. Acceleration corrections for the slave +nodes are then determined using the predicted penetration for each node, the time increment, and +the acceleration corrections for the master surface nodes. Abaqus/Explicit uses these acceleration +corrections to obtain a corrected configuration in which the contact constraints are enforced. +• In the case of an analytical rigid master surface, the resisting forces of all slave nodes are applied +as generalized forces on the associated rigid body. The mass of each contacting slave node is added +to the rigid body to determine the total inertial mass of the contacting interfaces. The generalized +forces and added masses are used to calculate an acceleration correction for the analytical rigid +master surface. Acceleration corrections for the slave nodes are then determined by the corrected +motion of the master surface. +When using hard kinematic contact, it is still possible with the pure master-slave algorithm for the +master surface to penetrate the slave surface in the corrected configuration . +slave nodes cannot penetrate +master segments +master surface +(segments) +penetration +slave surface +(nodes) +gap +master node can penetrate +slave segment +Figure 37.2.3–1 Master surface penetrations into the slave surface of a pure master-slave +contact pair due to coarse discretization. +Using a sufficiently refined mesh on the slave surface will minimize such penetrations. Softened +kinematic contact will allow penetrations since corrections are made to satisfy the pressure-overclosure +relationship at the slave-nodes, not the condition of zero penetration. +Kinematic enforcement of contact conditions in a balanced master-slave contact pair +The kinematic contact algorithm for a balanced master-slave contact pair applies acceleration corrections +that are linear combinations of pure master-slave corrections calculated in exactly the same manner as +outlined above. One set of corrections is calculated considering one surface as the master surface, and the +other corrections are calculated considering that same surface as the slave surface. Abaqus/Explicit then +applies a weighted average of the two values. The exact weighting for each correction depends on the +weighting factor specified for the contact pair . The default for balanced master-slave contact is +to weight each correction equally. +Hard kinematic contact will minimize the penetration of the surfaces. However, after the initial +weighted correction is applied, it is possible to still have some penetration of the surfaces. Therefore, +Abaqus/Explicit uses a second contact correction to resolve any remaining overclosure in a balanced +master-slave contact pair that uses hard kinematic contact. Both master-slave assignment combinations +are again considered, but weighting factors are not used when combining the contributions to form the +second applied acceleration correction. It is possible that small gaps between the contacting surfaces +will be created during the second correction if there was some residual penetration after the first +correction: the magnitude of the gaps after the second correction will generally be much smaller than the +penetration after the first correction. The effect of the second correction is illustrated in Figure 37.2.3–2 +to Figure 37.2.3–5. +The second contact correction described above is not conducted in the case when a softened +kinematic contact formulation is used. This may lead to penetration values that may not be exactly +synchronized with the pressure-overclosure curve. Moreover, the frictional shear forces (if any) may +not reflect the specified coefficient of friction exactly when non-sticking sliding occurs. Use a pure +master-slave kinematic formulation to avoid these inaccuracies. +Figure 37.2.3–2 Effect of second contact corrections; initial configuration. +balanced slave-master +contact pair +Figure 37.2.3–3 Final configuration when the second contact correction is used. +balanced slave-master +contact pair +Figure 37.2.3–4 Final configuration if the second contact correction were to be omitted. +Energy considerations for hard kinematic contact +The kinematic contact algorithm strictly enforces contact constraints and conserves momentum. To +achieve these qualities with a discretized model, some energy is absorbed upon impact. For example, +consider a linear elastic beam modeled with several elements that impacts a rigid wall as shown in +Figure 37.2.3–6. The kinetic energy of the leading node is absorbed by the contact algorithm upon +impact. A stress wave passes through the truss, and the truss eventually rebounds from the wall. The +kinetic energy after the rebound is smaller than before the impact because of the contact node’s energy +loss upon impact. As the mesh is refined, this energy loss is reduced because the mass and kinetic energy +of the leading node of the truss become less significant. +Contact forces can also exert negative external work upon impact since contact forces act over the +entire increment in which impact occurs, including the fraction of the increment prior to impact. The +opposing contact forces, which are equal in magnitude, act over different distances, thereby exerting a +pure slave-master +contact pair +master node can +penetrate slave surface +Figure 37.2.3–5 Final configuration when a pure master-slave contact pair is used. The +master surface is defined on the bottom elements. +v0 +Figure 37.2.3–6 Beam impacting a fixed rigid wall. +nonzero net work. The net external work of these forces is negative, and the absolute value of the net +external work does not exceed the contact node’s kinetic energy loss upon impact. These energies are +insignificant in most models but can be significant in high-speed impacts, where high mesh refinement +near the contact interface is recommended. +Penalty contact algorithm +The penalty contact algorithm results in less stringent enforcement of contact constraints than the +kinematic contact algorithm, but the penalty algorithm allows for treatment of more general types of +contact (for example, contact between two rigid bodies). The penalty contact method is well suited for +very general contact modeling, including the following situations: +• multiple contacts per node, +• contact between rigid bodies, and +• contact of surfaces also involved in other types of constraints (such as MPCs). +Since the penalty algorithm introduces additional stiffness behavior into a model, this stiffness can +influence the stable time increment. Abaqus/Explicit automatically accounts for the effect of the penalty +stiffnesses in the automatic time incrementation, although this effect is usually small, as discussed +below. +The penalty enforcement method is always used by the general contact algorithm. For contact pairs, +you can specify the penalty method as an alternative to the default kinematic enforcement method. When +the penalty method is chosen for enforcing contact constraints in the normal direction, it is also used to +enforce sticking friction . +Input File Usage: +Use the following option to select the penalty contact algorithm for a contact +pair: +*CONTACT PAIR, MECHANICAL CONSTRAINT=PENALTY +surface_1, surface_2 +Abaqus/CAE Usage: +Interaction module: interaction editor: Mechanical constraint +formulation: Penalty contact method +Penalty enforcement of contact conditions for pure master-slave surface weighting +The penalty contact algorithm searches for slave node penetrations in the current configuration, including +node-into-face, node-into-analytical rigid surface, and edge-into-edge penetrations. For node-to-face +contact, forces that are a function of the penetration distance are applied to the slave nodes to oppose +the penetration, while equal and opposite forces act on the master surface at the penetration point. The +master surface contact forces are distributed to the nodes of the master faces being penetrated. For node- +to-analytical rigid surface contact, forces that are a function of the penetration distance are applied to +the slave nodes to oppose the penetration, while equal and opposite forces act on the analytical rigid +surface at the penetration point. The contact forces acting at the penetration point of the analytical rigid +surface result in equivalent forces and moments at the reference node of the rigid body corresponding to +the analytical rigid surface. For edge-to-edge contact, the opposing contact forces are distributed to the +nodes of the two contacting edges. +As with the pure master-slave kinematic contact algorithm, there is no resistance to master surface +nodes penetrating slave surface faces with the pure master-slave penalty contact algorithm. Using a +sufficiently refined mesh on the slave surface will help correct this problem. +Penalty enforcement of contact conditions for balanced master-slave surface weighting +The penalty contact algorithm for balanced master-slave contact surfaces computes contact forces that +are linear combinations of pure master-slave forces calculated in the manner outlined above. One set +of forces is calculated considering one surface as the master surface, and the other forces are calculated +considering that same surface as the slave surface. Abaqus/Explicit then applies a weighted average of +the two values. The weighting used with each set of forces depends on the weighting factor specified +for the surfaces . The default for balanced +master-slave contact pairs and general contact is to weight each of the two sets of forces equally. +Scaling the penalty stiffness +The “spring” stiffness that relates the contact force to the penetration distance is chosen automatically +by Abaqus/Explicit for hard penalty contact, such that the effect on the time increment is minimal yet +the allowed penetration is not significant in most analyses. The default penalty stiffness is based on +a representative stiffness of the underlying elements. A scale factor is applied to this representative +stiffness to set the default penalty. Consequently, the penetration distance will typically be greater than +the parent elements’ elastic deformation normal to the contact interface. In purely elastic problems this +penetration can affect the stress solution significantly, as demonstrated in “The Hertz contact problem,” +Section 1.1.11 of the Abaqus Benchmarks Manual. +When element or node-based rigid bodies are involved in contact interactions, for numerical stability +reasons Abaqus/Explicit will compute penalties at each contacting node on the rigid body by considering +the overall inertia properties of the body. Consequently, the contact penalties will be different from the +case when these elements were not converted to rigid and thus the penetrations in the two cases may be +different. +You can specify a factor by which to scale the default penalty stiffnesses, as described in “Contact +controls for general contact in Abaqus/Explicit,” Section 35.4.5, and “Contact controls for contact pairs +in Abaqus/Explicit,” Section 35.5.5. This scaling may affect the automatic time incrementation. Use of +a large scale factor is likely to increase the computational time required for an analysis because of the +reduction in the time increment that is necessary to maintain numerical stability. +Choosing between the kinematic and penalty contact algorithms +The penalty contact algorithm can model some types of contact that the kinematic contact algorithm +cannot. Element-based rigid surfaces are not restricted to acting only as master surfaces within the +penalty algorithm as they are within the kinematic algorithm. Thus, the penalty method allows modeling +of contact between rigid surfaces, except when both surfaces are analytical rigid surfaces or when both +surfaces are node-based. +The penalty contact algorithm must be used for all contact pairs involving a rigid body if a linear +constraint equation, multi-point constraint, surface-based tie constraint, or connector element is defined +for a node on the rigid body. For all other cases, Abaqus/Explicit enforces equations, multi-point +constraints, tie constraints, embedded element constraints, and kinematic constraints (defined using +connector elements) independently of contact constraints; therefore, if a degree of freedom participates +in a linear constraint equation, multi-point constraint, tie constraint, embedded element constraint, or +kinematic constraint in addition to a contact constraint, the contact constraint will usually override +these constraints . Hence, the +penalty contact algorithm is recommended if these constraints need to be strictly enforced. +Impact is plastic when the default hard, kinematic contact algorithm is used; and the kinetic energy +of the contacting nodes is lost. This loss in energy is insignificant for a refined mesh but can be significant +with a coarse mesh. Penalty contact and softened kinematic contact introduce numerical softening to the +contact enforcement analogous to adding elastic springs to the contact interface, which means that these +algorithms do not dissipate energy upon impact (the energy stored in the springs is recoverable). This +distinction between the algorithms is particularly apparent if a point mass with no force acting upon +it impacts a fixed rigid wall: with penalty contact and softened kinematic contact the point mass will +bounce away, but with hard kinematic contact the point mass will stick to the wall. +A further difference between kinematic and penalty contact is that the critical time increment +is unaffected by kinematic contact but can be affected by penalty contact. For hard penalty contact, +default penalty stiffnesses are chosen such that the stable time increments of the deformable parent +elements of contact surface facets are effectively reduced by approximately 4% for increments in +which contact forces are being transmitted; default penalty stiffnesses of node-based surface nodes +require a 1% decrease in the element-by-element time increment to ensure numerical stability. Penalty +stiffnesses between rigid bodies are chosen by default to have no effect on the stable time increment. If +the default penalty stiffnesses are overridden by a penalty scale factor or softened contact behavior , the time increment is modified based on +the maximum stiffness active in the contact interface. Increasing the penalty stiffnesses may decrease +the stable time increment significantly . If the overall stable time increment is not +controlled by elements on the contact interface, the penalty contact algorithm usually will not affect the +time increment. +Penalty contact and softened kinematic contact cannot be used with the breakable bond model; hard +kinematic contact must be used for this model. +Table 37.2.3–1 Effect of scale factor on time increment. +Penalty scale factor +Lower bound to ratio of +the time increment with +contact divided by the time +increment without contact +1.0 +10.0 +100.0 +1000.0 +10000.0 +0.96 +0.34 +0.13 +0.04 +0.013 +38. +Contact Difficulties and Diagnostics +Resolving contact difficulties in Abaqus/Standard +Resolving contact difficulties in Abaqus/Explicit +38.1 +38.1 +Resolving contact difficulties in Abaqus/Standard +• “Contact diagnostics in an Abaqus/Standard analysis,” Section 38.1.1 +• “Common difficulties associated with contact modeling in Abaqus/Standard,” Section 38.1.2 +38.1.1 +CONTACT DIAGNOSTICS IN AN Abaqus/Standard ANALYSIS +Products: Abaqus/Standard Abaqus/CAE +References +• “Output to the data and results files,” Section 4.1.2 +• “Defining general contact interactions in Abaqus/Standard,” Section 35.2.1 +• “Defining contact pairs in Abaqus/Standard,” Section 35.3.1 +• “Contact formulations in Abaqus/Standard,” Section 37.1.1 +• *CONTACT PRINT +• *PREPRINT +• *PRINT +• Chapter 41, “Viewing diagnostic output,” of the Abaqus/CAE User’s Manual +Overview +Diagnostics of an Abaqus/Standard analysis can be used to: +• check the initial contact conditions in a model; and +• track contact statuses over the course of the analysis. +Diagnostic information is available in several locations: +• The output database +• The job diagnostics tool in the Visualization module of Abaqus/CAE +• The data (.dat) file +• The message (.msg) file +Reviewing the adjustments of initially overclosed surfaces +strain-free adjustments of nodal positions are performed by Abaqus/Standard under +Initial +various circumstances to remove contact overclosures or to remove overclosures or gaps +between surfaces of surface-based tie constraints . The +initial configuration of the model is determined after these strain-free adjustments are applied. There +are two sources of information on the adjustments of overclosed surfaces: the data (.dat) file and the +output database (.odb) file. +Output of information on strain-free adjustments to the data file +By default, information about a limited number of strain-free nodal adjustments is provided in the data +(.dat) file. Requesting more detailed output concerning contact constraints provides information for +all strain-free adjustments, regardless of the number of nodes adjusted. +Input File Usage: +Abaqus/CAE Usage: +*PREPRINT, CONTACT=YES +Job module: job editor: General: Preprocessor Printout: +Print contact constraint data +Visualizing strain-free adjustments +Output variable STRAINFREE +contains nodal vectors representing initial strain-free adjustments. By default, this output variable is +written to the output database (.odb) file for the original field output frame at zero time if any strain-free +adjustments are made by Abaqus/Standard. A symbol plot of this variable in the Visualization module of +Abaqus/CAE shows vectors that represent how individual nodes have been adjusted, and a contour plot +of this variable shows the distribution of the adjustment magnitude (you must select the original output +frame at zero time in the Visualization module of Abaqus/CAE before choosing the STRAINFREE +output variable). Initial nodal positions written to the output database file by Abaqus/Standard include +the effects of strain-free adjustments, so plots of the initial configuration show the adjusted nodal +positions. +Reviewing initial contact conditions +Before conducting an analysis, perform a data check on the model to review the initial contact +conditions . The +data check creates an output database and calculates the variable COPEN (contact opening) on each +slave surface based on the initial configuration of the model. You can create a contour plot of COPEN +in the Visualization module of Abaqus/CAE to check for overclosed surfaces in the model assembly (an +overclosure corresponds to a negative value of COPEN). +In addition, you can instruct Abaqus to print detailed information about the initial contact conditions +to the data file during the data check (this information is not printed by default). The data file lists the +status (open or closed) and clearance distance for each constraint point on a slave surface, the internally +generated contact element number associated with each slave node or facet, and a summary of contact +interaction properties. Internally generated contact elements are not user-defined and do not appear in the +input file, so they can be difficult to locate if an error or warning message refers to them. The information +in the data file can be used to locate these contact elements in the model. +The data file also lists the key parameters for every contact interaction in the model. These +parameters include: +• slave and master surface names; +• interaction property; +• value of +; +• degree of smoothing on the master surface ; +• characteristic length used in penetration tolerance calculations ; +• extension ratio applied to master surface edges ; and +• contact formulation. +Parameters are listed only for the interactions to which they are applicable. For example, +, surface +smoothing, and the extension ratio are not used for surface-to-surface contact calculations (including +general contact), so Abaqus does not report values for these parameters in surface-to-surface interactions. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to print information about initial contact conditions +to the data file: +*PREPRINT, CONTACT=YES +Job module: job editor: General: Preprocessor Printout: +Print contact constraint data +Output of master surface nodes associated with slave nodes for small-sliding contact +When you print initial contact conditions to the data file for contact pairs using the small-sliding tracking +approach, Abaqus creates an output table showing the master nodes associated with each slave node. +Each row of the table lists a slave node and the master nodes to which the slave node transfers load when +in contact with the master surface. The number of nodes in the table indicates whether or not the anchor +point for a slave node lies on an element face or at a node. For details on the small-sliding tracking +approach and load transfer, see “Using the small-sliding tracking approach” in “Contact formulations in +Abaqus/Standard,” Section 37.1.1. +In the output shown below for a two-dimensional model, slave node 2 has an anchor point at master +surface node 101 because it interacts with three master surface nodes. Slave node 1 has an anchor point +between nodes 100 and 101. This table also provides a list of slave nodes that did not find an intersection +with the master surface. This is important because these nodes have no local tangent plane and, hence, +can penetrate the master surface. +SMALL SLIDING +NON-RIGID +AX ELEMENT(S) +INTERNALLY GENERATED FOR SLAVE BLANK AND MASTER SPHERE +WITH SURFACE INTERACTION INF1 +ELEMENT +NUMBER +SLAVE +NODE(S) NODE(S) +MASTER +46 +101 +100 +47 +50 +102 +101 +100 +NO INTERSECTION +***WARNING: 1 SLAVE NODES FOUND NO INTERSECTION WITH A MASTER +SURFACE +Tracking contact status during a simulation +Abaqus provides two methods for tracking the status of contact interactions over the course of an analysis: +the diagnostics tool available in the Visualization module of Abaqus/CAE and contact output to the +data (.dat) file.You can write contact output to the data (.dat) file for tracking the status of contact +interactions over the course of an analysis. Tracking contact status helps you ensure contact surfaces +are defined appropriately, troubleshoot a terminated contact analysis, and verify that contact interactions +behave realistically. +The diagnostics tool in Abaqus/CAE provides a good overview of how contact conditions evolve +throughout a simulation. It is useful for reviewing terminated analyses because it reports contact change +calculations in every iteration. The data file offers a more detailed summary of the overall contact +conditions and the forces driving these conditions. However, it only provides output for successfully +completed increments. +Contact diagnostics in the Visualization module of Abaqus/CAE +The diagnostics tool in the Visualization module of Abaqus/CAE can be used with the following +procedure types: +• static stress/displacement; +• coupled thermal/stress; and +• coupled pore fluid flow/stress. +The diagnostics tool tracks all changes in contact during an analysis. Each time a constraint point’s +contact status changes from closed to open, it is recorded as an “opening.” Each time the status changes +from open to closed, it is recorded as an “overclosure.” If the contact interaction involves frictional +effects, the diagnostics note when a constraint point begins sliding along the master surface (“slipping”) +and when a constraint point in motion stops on the master surface (“sticking”). The diagnostics tool +lists the constraint point involved in the status change and allows you to highlight the location of +the constraint point in the model. The calculated clearance or overclosure distance is also shown, +and the maximum penetration is reported when the penetration tolerance for augmented Lagrange +contact is exceeded . +For the default contact convergence criteria, the diagnostics tool shows the maximum penetration +error and the maximum estimated contact force error; these determine whether the contact conditions +have converged (for details, see “Severe discontinuities in Abaqus/Standard” in “Defining an analysis,” +Section 6.1.2). If you choose to use the traditional contact convergence criteria, these error measures +are not reported. For analyses involving Lagrange friction, the diagnostics show the maximum slip error +for points that should be sticking . +For detailed instructions on using the diagnostics tool, see Chapter 41, “Viewing diagnostic output,” +of the Abaqus/CAE User’s Manual. The contact diagnostic information available in Abaqus/CAE can +also be printed to the Abaqus message file. For details, see “The Abaqus/Standard message file” in +“Output,” Section 4.1.1. +Contact output in the data file +When you request contact output to the data file , Abaqus lists the contact status for every constraint point at +each increment of the analysis. The values of CPRESS, CSHEAR, COPEN, and CSLIP at each constraint +point are also reported by default. +Example: Forming a channel +Contact diagnostics are often helpful in confirming that the interactions in a model are behaving +realistically and as intended. The diagnostics also provide a means of tracing the evolution of contact +statuses on a node-by-node basis. +In this example the diagnostics are based on a channel forming +model. The channel is formed from a steel plate (or blank) with appreciable thickness. The blank is +modeled with two-dimensional, plane strain elements; the forming tools (die, holder, and punch) are +modeled as analytical rigid surfaces. The initial and final configurations of the model are displayed in +Figure 38.1.1–1. +Undeformed shape +Deformed shape +Figure 38.1.1–1 Model for channel-forming example. +extruded for visualization purposes.) +(The blank has been +If you include a step or prescribed condition in your model intended to establish contact between +two surfaces, the diagnostics tool in Abaqus/CAE can confirm the success of this modeling technique. +In this example contact must be firmly established between the blank, the die, and the holder before the +forming process begins. Small but consistent overclosures in the nodes along the surface of the blank +indicate that the contact conditions are appropriate to begin forming the channel . +You can also use the contact conditions to review changes in contact status throughout the forming +process. Figure 38.1.1–3 depicts the onset of slipping for two nodes on the blank. This information might +be used to confirm frictional or material effects. For example, you can draw the following conclusions +about these diagnostics in the channel forming analysis: +• If the slipping does not occur until well into the forming process, frictional forces were probably +holding the blank in place between the die and holder. +Overclosures +Figure 38.1.1–2 Diagnostics confirming contact conditions between the blank, die, and holder. +• Since all the nodes on the blank do not slip simultaneously, there is most likely some mild stretching +and nonuniform deformation occurring in the blank. +For more insight on the slipping nodes, refer to the data file. The following excerpt lists a portion +of the blank-die interaction in the same increment depicted in Figure 38.1.1–3: +NODE +FOOT- +NOTE +CPRESS +CSHEAR1 +COPEN +CSLIP1 +290 +295 +300 +305 +OP +SL +ST +ST +0.000 +0.000 +4.4632E+06 -4.4632E+05 +9.5643E+06 -9.3177E+05 +2.9421E+06 -2.7867E+05 +4.1155E-07 -2.8783E-07 +-5.1137E-06 +-4.8711E-06 +-4.7359E-06 +0.000 +0.000 +0.000 +The contact status is indicated in the “footnote” column: open (OP), closed and sticking tangentially (ST), +or closed and sliding tangentially (SL). In the absence of frictional properties the two contact statuses +are open (OP) and closed (CL). +In the output above node 290 is open; consequently, the contact pressure variable CPRESS is zero. +The COPEN variable reports that this node is 4.1155 × 10−7 length units away from the master surface. +The SL footnote for node 295 indicates that it is in contact with the master surface (the die) and is +“slipping.” The critical shear stress, +, where p is +the value of contact pressure shown under CPRESS and +is the coefficient of friction for the contact += 0.1; the critical shear stress (4.4632 × 106 × 0.1 = 4.4632 × 105 ) is equal +interaction. In this model +to the frictional shear stress CSHEAR1, so the node is slipping. In the case of node 300 the critical +shear stress (9.5643 × 106 × 0.1 = 9.5643 × 105 ) is greater than the frictional shear stress, so the node is +sticking. Likewise for node 305. +, can be determined by the equation +The CSLIP1 variable is the total accumulated (integrated) slip at the slave node. Accumulated slip +and slip directions are discussed in more detail in “Output of tangential results” in “Defining contact +pairs in Abaqus/Standard,” Section 35.3.1. +Diagnosing a terminated contact analysis +Contact diagnostics provide invaluable information when trying to resolve errors in a terminated analysis. +The diagnostics let you review trends in the model’s contact status, visually identify regions of the model +involved in contact difficulties, and numerically quantify the severity of an error. +For a more general discussion of common errors associated with using contact in Abaqus/Standard +analyses, refer to “Common difficulties associated with contact modeling in Abaqus/Standard,” +Section 38.1.2. +Excessive severe discontinuity iterations +Establishing contact conditions is a common source of difficulty in an implicit static contact analysis. +If an analysis terminates because it exceeds the maximum number of severe discontinuity iterations +, the contact +diagnostics give insight into how to resolve the problem. You can plot the number of contact status +changes over the course of an attempt, as shown in Figure 38.1.1–4. If the changes are tending toward +zero, increasing the allowed number of severe discontinuity iterations or adjusting the SDI conversion +settings may allow Abaqus to resolve the contact conditions. If the changes are not tending toward zero, +you will need to revise your model or investigate other options. +Using the visualization tools, you can see which areas of the model are involved in contact changes. +If a particular contact pair or surface region is causing a majority of the status fluctuations, you may need +to modify the characteristics of the associated interaction. For example, it is typically easier to resolve +contact conditions for contact pairs using the small-sliding tracking approach (if it is applicable) than for +those using the finite-sliding tracking approach. +Chattering +The contact diagnostics tool makes it very easy to detect chattering in a model. In this situation the same +node or constraint appears in the diagnostics summary for every iteration, alternating as an overclosure +or an opening. The classic chattering scenario produces diagnostics plots that tend toward zero but level +off at a low number due to the oscillating contact status . Techniques +Points now slipping +Figure 38.1.1–3 Diagnostics for the onset of slipping. +Iteration +Iteration +Figure 38.1.1–4 Changes in contact status during an attempt. +for resolving contact chattering problems are discussed in “Excessive iterations in contact simulations” +in “Common difficulties associated with contact modeling in Abaqus/Standard,” Section 38.1.2. +Unrealistic and severe overclosures +When reviewing diagnostics, you may notice overclosures during unconverged iterations for nodes +or constraint points that are located outside of the regions that are contacting in a converged state. +The reported overclosure value for these nodes will be significantly greater than the overclosures for +nodes within the contacting regions, as seen in the highlighted constraint point in Figure 38.1.1–5. +This is an indication of physical or numerical instabilities in the model. You should take steps to +more firmly establish contact before proceeding with the simulation or add some form of stabilization +to the model . Using smaller increments can sometimes enable a solution to be +obtained in these cases. +Nonconverging force equations +Contact diagnostics do not always involve severe discontinuity iterations. Poorly defined contact can lead +to nonconvergence of the force equations in an analysis . If the same node appears +repeatedly as the location of maximum residuals and corrections, investigate the contact conditions +around that node. Consider the example in Figure 38.1.1–7. The diagnostics highlight the “problem +node” on the perimeter of the slave surface. A closer look in the vicinity of this node reveals that the +slave surface mesh is too coarse. Slave nodes along the perimeter of the surface are touching the master +surface, but the next row of nodes is “hanging over” the rim of the master surface. If this contact pair +uses node-to-surface contact discretization, the master surface can penetrate the slave surface with little +resistance between the nodes. Such penetrations can cause the nonconverging force equations seen in +the diagnostics. +Any situation in which the master surface is free to penetrate the slave surface can prevent an +analysis from converging. Potential solutions include: +• switching the master and slave assignments; +• using surface-to-surface discretization (however, using surface-to-surface discretization without +refining a coarse slave mesh may lead to inaccurate stress results, even if the analysis does +converge); or +• refining the mesh on the slave surface. +Figure 38.1.1–5 The overclosure at one constraint point is +significantly higher than the overclosures at other constraint points. +Figure 38.1.1–6 The diagnostics tool reports equilibrium difficulties. +Figure 38.1.1–7 Two surfaces in a region of nonconverging force equations. +38.1.2 +COMMON DIFFICULTIES ASSOCIATED WITH CONTACT MODELING IN +Abaqus/Standard +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining general contact interactions in Abaqus/Standard,” Section 35.2.1 +• “Defining contact pairs in Abaqus/Standard,” Section 35.3.1 +• *CONTACT +• *CONTACT PAIR +• *CONTACT INITIALIZATION DATA +• “Defining general contact,” Section 15.13.1 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +• “Defining surface-to-surface contact,” Section 15.13.7 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Using contact and constraint detection,” Section 15.16 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +This section highlights the difficulties that are most commonly encountered when modeling contact +interactions with Abaqus/Standard. Recommendations on how to circumvent these problems are +presented. +Difficulties resolving initial contact conditions +It is important to understand how Abaqus/Standard interprets and resolves contact conditions at the start +If necessary, you can check initial contact conditions in the message file . Unintentional contact openings or +overclosures can lead to poor interpretations of surface geometry, unintentional motion in a model, and +failure of an analysis to converge. +Removing initial contact openings and overclosures +When modeling the contact between two faceted surfaces, it is often possible for small gaps or +penetrations to occur at individual nodes. This problem is particularly common when the two surfaces +have dissimilar meshes. Abaqus/Standard uses two default methods for dealing with initial penetrations: +• In general contact small initial overclosures are automatically adjusted to remove the penetrations. +• In contact pairs initial overclosures are interpreted as interference fits and resolved accordingly . +You can improve the accuracy of a contact simulation by having Abaqus/Standard adjust +the +position of the slave surface to ensure that all slave nodes that should initially be in contact with the +master surface start out in contact without any penetration . When an intended initial clearance or +overclosure is small compared to typical dimensions of the bodies in contact and a small-sliding contact +pair is used, you can specify the clearance or overclosure precisely . +The small-sliding contact tracking approach is more sensitive than the finite-sliding tracking +approach to initial local gaps at the contact interface. In small-sliding contact each slave node interacts +with a contact plane defined from the finite element approximation of the master surface, as discussed in +“Contact formulations in Abaqus/Standard,” Section 37.1.1. Abaqus/Standard can define these planes +only when each slave node can be projected onto the master surface. Having these slave nodes start +the simulation contacting the master surface allows Abaqus/Standard to form the most accurate contact +planes for the slave nodes. +Large unintended initial overclosures +The contact initialization algorithm may occasionally infer large initial overclosures where you do not +intend initial overclosures to exist. For example, specifying incorrect surface normals can cause the +contact initialization algorithm to interpret a physical gap as a penetration, as discussed in “Orientation +considerations for shell-like surfaces” in “Defining contact pairs in Abaqus/Standard,” Section 35.3.1. +Minor changes to the surface or contact definition will typically avoid undesired overclosures, but these +situations typically call for some diagnosis to determine how to avoid the problem. +Identifying the location of unintended overclosures +The first step in resolving a large initial overclosure is to identify the location of the problem: +• If initial overclosures are treated as interference fits to be resolved in the first increment (which is +the default behavior for contact pairs; see “Modeling contact interference fits in Abaqus/Standard,” +Section 35.3.4), a contour plot of the contact opening distance output variable (COPEN) for the +initial output frame will show which regions have initial overclosures (penetrations correspond to +negative values of COPEN). +• If initial overclosures are resolved with strain-free adjustments, a contour plot of the output +variable STRAINFREE for the initial output frame will show where adjustments occurred . However, large strain-free adjustments may cause the mesh to become highly +distorted, making it difficult to fully diagnose the problem; in such cases, perform a datacheck +analysis +with initial overclosures instead treated as interference fits to be resolved in the first increment to +facilitate diagnosis (as discussed above). +Once you identify the location of an unintended initial overclosure, limiting the display in the +Visualization module of Abaqus/CAE to the master and slave surfaces of the interaction involved in the +initial overclosure is helpful for identifying the cause of an unintended initial overclosure . Viewing the surface normals may help determine whether unintended overclosures are due to +incorrect surface normals. +Overclosures on discontinuous surfaces +In this case a +Figure 38.1.2–1 shows an example with a large, unintended initial overclosure. +single contact pair with discontinuous surfaces is meant to enforce contact in two distinct regions +(Table 35.3.1–1 “Orientation considerations for shell-like surfaces” in “Defining contact pairs in +Abaqus/Standard,” Section 35.3.1, shows which contact formulations allow discontinuous surfaces). +The arrows in Figure 38.1.2–1 show the positive normal direction for each surface region. The +surface-to-surface contact formulation searches along the slave-surface normal direction (in the positive +and negative directions) for potential interaction points on the master surface. The search emanating +from point A identifies point B as the only potential interaction point for point A in this example. The +contact pair interprets this as a valid penetration because no better candidate interaction location is +found and surface normals are opposed at points A and B. Methods to avoid this unintended overclosure +include: +• defining separate contact pairs with continuous surfaces for each of the two distinct contact regions; +and +• specifying general contact, which filters out nearly all unintended initial overclosures. +Interpreted as a penetration for a single +contact pair with discontinuous surfaces +B +A +Slave +Master +Slave +Master +Figure 38.1.2–1 Example of an unintended initial overclosure due +to a modeling error involving discontinuous surfaces. +Overclosures on three-dimensional surfaces +The cause of unintended initial overclosures may be less obvious for three-dimensional models with +complex surfaces. The most important step in overcoming this problem is identifying which regions of +respective surfaces are involved in an unintended initial overclosure. For a surface-to-surface contact +pair without strain-free adjustments, a portion of the master surface should be apparent behind the slave +surface (opposite the slave surface normal direction) at a distance consistent with the reported (negative) +COPEN value. For a node-to-surface contact pair, the direction to the interaction point on the master +surface typically corresponds to a local minimum distance between the slave and master surfaces. +Resolving large interference fits +As previously discussed, Abaqus/Standard optionally interprets initial overclosures as interference +fits. You should use one of the methods discussed above to remove any initial overclosures that are +an unintended result of mesh discretization or errors in defining contact surfaces. In some cases the +interference fit may be intended but may be too large to be resolved robustly with the method that +is used by default for contact pairs in Abaqus/Standard (which is to resolve overclosures in a single +increment). In this situation you should modify the contact model to allow resolution of overclosures +over multiple increments . If you choose to have initial overclosures treated as interference fits for general +contact, they are automatically resolved over multiple increments . +Preventing rigid body motion in contact simulations +Rigid body motion is generally not a problem in dynamic analysis. In static problems rigid body motion +occurs when a body is not sufficiently restrained. “Numerical singularity” warning messages and very +large displacements indicate unconstrained motion in a static analysis. Therefore, if contact is used to +constrain rigid body motion in static problems, ensure that the appropriate surface pairs are initially in +contact . +If necessary, define the model geometry to give a small initial overclosure to the contact pair, or use +boundary conditions to move the structures into contact in the first step. The boundary conditions, which +are unnecessary in subsequent steps, can be removed after the body is adequately constrained through +contact with other components. Similarly, if a rigid body is meant to translate only, constrain its rotational +degrees of freedom. +Frictional sticking can constrain rigid body motion. However, contact pressure must develop +before friction can be generated. Therefore, friction is not effective in constraining rigid body motion +when surfaces first come into contact. You must temporarily eliminate rigid body motion by defining a +boundary condition or by grounding the body with soft springs or dashpots. +If you are unable to prevent rigid body motion through modeling techniques, Abaqus/Standard offers +some tools to automatically stabilize rigid bodies in contact simulations. These tools are discussed in +“Automatic stabilization of rigid body motions in contact problems” in “Adjusting contact controls in +Abaqus/Standard,” Section 35.3.6. +Poorly defined surfaces +Over the course of an analysis, you may notice undesirable behavior between contact surfaces (excessive +penetration, unexpected openings, inaccurate application of forces, etc.). This behavior often results in +nonconvergence and termination of an analysis. These problems can arise from a number of causes +related to mesh, element selection, and surface geometry. +Defining duplicate nodes on the master surface +When defining three-dimensional surfaces for use in finite-sliding applications, avoid defining two +surface nodes with the same coordinates. Such a definition can give rise to a seam, or crack, in the +surface as shown in Figure 38.1.2–2. +Both vertices have the same coordinates. +They are separated to show the crack in the surface. +Figure 38.1.2–2 Example of doubly defined surface node. +If viewed with the default plotting options in Abaqus/CAE, +this surface will appear to be a +valid, continuous surface; however, if this surface is used as the master surface for finite-sliding, +node-to-surface contact, a slave node sliding along the surface may fall through this crack and get +“stuck” behind the master surface. Similar problems can occur for finite-sliding, surface-to-surface +contact. Typically, convergence problems will result that may cause Abaqus/Standard to terminate the +analysis. +Use the edge display options in the Visualization module of Abaqus/CAE to identify any unwanted +cracks in the surfaces used in the model. The cracks will appear as extra perimeter lines in the interior +of the surface. Duplicate nodes can be avoided easily by equivalencing nodes when creating the model +in a preprocessor. +Avoiding problems with contact along the perimeters of surfaces +When modeling finite-sliding contact, ensure that the master surface definition extends far enough to +account for all expected motions of the contacting parts. Contact along the perimeter of master surfaces +should be avoided with the node-to-surface contact formulation.. Abaqus/Standard assumes that the +mating slave surface nodes can fall off the free edge of the master surface, which can cause problems +if a slave node wraps around and approaches its mating master surface from behind. Figure 38.1.2–3 +illustrates appropriate and inappropriate master surface definitions. +trimmed +master +surface +slave +surface +untrimmed +master +surface +Inappropriate master surface definition +Appropriate master surface definition +Figure 38.1.2–3 Example of master surface extension. +A slave node that falls off a master surface in one iteration may find itself contacting the surface in the +very next iteration; this phenomenon is known as chattering. If chattering continues, Abaqus/Standard +may not be able to find a solution. This problem is less likely with the surface-to-surface formulation +approach, because each contact constraint is based on a region of the slave surface rather than individual +slave nodes. Request detailed contact printout to the message (.msg) file to monitor the history of a +slave node that might slide off the master surface . The message file output will show the cyclic opening and closing of contact at a slave +node, which will indicate where the master surface needs to be modified. +For node-to-surface contact you can extend the master surface beyond the perimeter of the physical +body that it approximates to avoid chattering problems. Chattering can also occur with some contact +elements, such as slide line and rigid surface contact elements. Slide line contact elements can also be +extended. See “Extending master surfaces and slide lines,” Section 35.3.8, for details. +Falling off small-sliding master surfaces +Falling off the edge of a master surface in small-sliding contact problems is not an issue since slave +nodes do not slide on the actual surface of the model. Instead, each slave node interacts with a flat, +infinite contact plane. This plane is associated with the set of master surface nodes that are closest to +the slave node in the undeformed configuration. For details about small-sliding contact, see “Contact +formulations in Abaqus/Standard,” Section 37.1.1. +Falling off surfaces modeled with interface elements +Falling off the edge of a surface modeled with interface elements is not an issue since the slave nodes +slide on a flat, infinite contact plane. +Using poorly meshed surfaces +Several problems are caused by surfaces created on very coarse meshes. Some of these problems +depend on your choice of contact discretization, as discussed later in “Discrepancies between contact +formulations.” +Penetrations with coarsely meshed slave surfaces +When a coarsely meshed surface is used as a slave surface for node-to-surface contact, the master surface +nodes can grossly penetrate the slave surface without resistance . This situation is +common when nonmatching meshes come into contact. Refining the slave surface tends to alleviate this +problem. +slave nodes cannot penetrate +master segments +master surface +(segments) +penetration +slave surface +(nodes) +gap +master node can penetrate +slave segment +Figure 38.1.2–4 Master surface penetrations into the slave surface +due to a coarse mesh of the slave surface for node-to-surface contact. +Surface-to-surface contact will generally resist penetrations of master nodes into a coarse +slave surface; however, +this formulation can add significant computational expense if the slave +mesh is significantly coarser than the master mesh . +Contact occurring at a single element +If the mesh on a surface is too coarse, it is possible for a contact interaction to occur entirely within the +bounds of a single element. This typically happens when the two contacting surfaces have dissimilar +curvature, as depicted in Figure 38.1.2–5. +Master surface +Slave surface +Figure 38.1.2–5 The master surface contacts the slave surface at a single element face. +The results from such an interaction are unreliable and generally unrealistic. +If the model in +Figure 38.1.2–5 uses node-to-surface contact, the master surface penetrates the slave surface without +resistance until it encounters a slave node, as discussed above. If the master and slave designations are +reversed, the contact constraint is applied at a single slave node; this concentration creates inaccurately +high calculations of the contact pressure. +If the model uses surface-to-surface contact, excessive +penetration is not likely to occur. However, with only a small number of constraint points involved +in the interaction, the averaging algorithm used to enforce surface-to-surface contact performs poorly. +Inaccurate contact stress and pressure calculations result. +If contact is occurring at a single element, refine the mesh to spread the interaction across multiple +element faces. +Coarsely meshed master surfaces and small-sliding contact +Coarsely meshed, curved master surfaces in small-sliding simulations can lead to unacceptable solution +accuracy due to the approximate nature of the “master planes.” Using a more refined mesh to define the +master surface will improve the overall accuracy of the solution in small-sliding problems. However, +unless perfectly matching meshes are used, local oscillations in the contact stress may still be observed, +even in refined models. +Nonmatched surface meshes with second-order heat transfer elements +Inaccurate local results may occur if second-order heat transfer elements are used to model a thermal +interface and the meshes do not match across the surfaces. The worst results will be obtained when the +midside node of an element on one surface is closest to the corner node of an element on the other surface. +If a nonmatching mesh must be used in the model, use first-order elements or use a more refined mesh. +Three-dimensional surfaces with second-order faces and a node-to-surface formulation +Second-order elements not only provide higher accuracy but also capture stress concentrations more +effectively and are better for modeling geometric features than first-order elements. Surfaces based on +second-order element types work well with the surface-to-surface contact formulation but, in some cases, +do not work well with the node-to-surface formulation . +Some second-order element types are not well-suited for underlying the slave surface with +the combination of a node-to-surface contact formulation and strict enforcement of “hard” contact +conditions, because of the distribution of equivalent nodal forces when a pressure acts on the face of the +element. As shown in Figure 38.1.2–6, a constant pressure applied to the face of a second-order element +without a midface node produces forces at the corner nodes acting in the opposite sense of the pressure. +q = pA +r = pA +12 +Figure 38.1.2–6 Equivalent nodal loads produced by a constant +pressure on the second-order element face in “hard” contact simulations. +Abaqus/Standard bases important decisions for the node-to-surface contact formulation on contact forces +acting on individual slave nodes; the ambiguous nature of the nodal forces in second-order elements +can cause Abaqus/Standard to make a wrong decision. To circumvent this problem, Abaqus/Standard +automatically converts most three-dimensional second-order elements with no midface node (serendipity +elements) that form a slave surface into elements with a midface node. For the three-dimensional 18- +node gasket elements, the midface nodes are also generated automatically if they are not given in the +element connectivity. The presence of the midface node results in a distribution of nodal forces that is +not ambiguous for the contact algorithm. +The element families C3D20(RH), C3D15(H), S8R5, and M3D8 are converted to the families +C3D27(RH), C3D15V(H), S9R5, and M3D9, respectively. Since Abaqus/Standard does not convert +second-order coupled temperature-displacement, coupled thermal-electrical-structural, and coupled +pore pressure–displacement elements, you should specify a penalty or augmented Lagrange constraint +enforcement method to approximate hard pressure-overclosure behavior . Abaqus/Standard will interpolate nodal +quantities, such as temperature and field variables, at the automatically generated midface nodes when +values are prescribed at any of the user-defined nodes. +Second-order tetrahedral elements (C3D10 and C3D10I) have zero contact force at their corner +nodes. This combination of second-order triangular slave facets, a node-to-surface contact formulation, +and strict enforcement of “hard” contact conditions is disallowed to avoid a high likelihood of +convergence problems and poor predictions of contact pressures that would occur with this combination. +To avoid this combination, use at least one of the following alternatives: +• Use the surface-to-surface contact formulation (generally recommended) instead of the node-to- +surface contact formulation; +• Use the penalty constraint enforcement method (generally recommended) or augmented Lagrange +constraint enforcement method instead of strict enforcement of “hard” contact conditions; or +• Use modified 10-node tetrahedral elements (C3D10M) instead of second-order tetrahedral elements. +Excessive iterations in contact simulations +Abaqus/Standard offers a number of methods to adjust the solver iteration scheme, sometimes resulting +in a more efficient analysis with a minimal effect on accuracy. +Converting severe discontinuity iterations in weakly determined contact conditions +By default, Abaqus/Standard continues to iterate until the severe discontinuities associated with changes +in contact status are sufficiently small (or no severe discontinuities occur) and the equilibrium (flux) +tolerances are satisfied. Alternatively, you can choose a different approach in which Abaqus/Standard +continues to iterate until no severe discontinuities occur. These two approaches are discussed in +more detail in “Severe discontinuities in Abaqus/Standard” in “Defining an analysis,” Section 6.1.2. +The default treatment of severe discontinuity iterations reduces the likelihood of excessive iterations +associated with chattering between contact states when the contact conditions are weakly determined. +An example of a region with weakly determined contact conditions is near the center of a flat punch that +contacts a thin plate supported at its edges. +Controlling the increment size based on penetration distance in unconverged iterations +For most types of contact, if during an iteration the penetration calculated for any contact pair exceeds +a specific distance ( +), Abaqus/Standard abandons the increment and tries again with a smaller +increment size. There is no critical penetration distance for finite-sliding, surface-to-surface contact +(including general contact) and for small-sliding contact in geometrically linear analyses. +The default value of +is the radius of a sphere that circumscribes a characteristic surface element +face. When calculating the default value, Abaqus/Standard uses only the slave surface of the contact pair. +for each contact pair in the model is printed in the data (.dat) file. While the default +The value of +value of +should prove to be sufficient for the majority of contact simulations, in some cases it may +be necessary to change the default value for a given contact pair. These cases include: +• Models in which the master surface is highly curved. The default value of +may sometimes lead +to situations as shown in Figure 38.1.2–7. During the iterative solution process a slave node initially +at point a may move to point b, penetrating the master surface with overclosure h less than +. +Abaqus/Standard may attempt to move the slave node to point c on the master surface. To avoid +this situation, specify a smaller value for +to force Abaqus/Standard to abandon the increment +and to try a smaller increment size. +crit + S Slave node + M Master surface +a-b-c Trajectory of slave node +Figure 38.1.2–7 Effect of the critical penetration distance on a highly curved master surface. +• Models in which Abaqus/Standard cannot calculate a reasonable +because a node-based surface +is used. +If there are other contact pairs in the model with surfaces, Abaqus/Standard uses the +average dimension of all of the slave surface element faces. If there are no other contact pairs, +Abaqus/Standard uses a characteristic element dimension of the entire model. +• Models in which the contact face dimensions in a slave surface vary greatly. +• Models in which the slave surface mesh is very refined compared with the typical surface dimensions +so that overclosures much larger than the default +can be resolved easily. +• Models in which contact pairs with softened contact allow significant penetration . +Input File Usage: +Abaqus/CAE Usage: +*CONTACT PAIR, HCRIT= +You cannot adjust the default value of +in Abaqus/CAE. +Difficulties interpreting the results of contact simulations +Although an analysis involving contact runs to completion, the results may seem unrealistic. This is +sometimes due to modeling errors and sometimes due to the specialized output format of certain contact +formulations. In addition to degrading contact output, the factors discussed below also tend to degrade +convergence behavior, so avoiding these factors may improve convergence behavior. +Oscillating contact pressures when using second-order elements in “hard” contact simulations +Nonuniform contact pressure distributions are likely to occur when very different mesh densities are used +on the two deformable surfaces making up a contact interaction. The nonuniformity can be particularly +pronounced when “hard” contact is modeled and both surfaces are modeled with second-order elements, +including modified, second-order tetrahedral elements. In such cases oscillations and “spikes” in the +contact pressure may occur. Smoother contact pressures may be obtained for surfaces modeled with +second-order elements by using penalty-type contact constraint enforcement . +Inaccurate contact stresses when using second-order axisymmetric elements at the symmetry +axis +For second-order axisymmetric elements the contact area is zero at a node lying on the symmetry axis +. To avoid numerical singularity problems caused by a zero contact area, Abaqus/Standard +calculates the contact area as if the node were a small distance from the symmetry axis. This may result +in inaccurate local contact stresses calculated for nodes located on the symmetry axis. +Self-contact +Contact of a surface with itself (self-contact) is provided for cases in which the original geometry is very +different from the (deformed) geometry at which contact takes place. It would then be difficult for you +to predict which parts of the surface will come into contact with each other. Where possible, it is always +computationally more economical to declare parts of the surface as master and parts as slave. The same +unpredictability makes it impossible to determine a priori which side will be the master and which side +the slave. Therefore, Abaqus/Standard uses a symmetric contact model: every single node of the surface +can be a slave node and can simultaneously belong to master segments with respect to all other nodes. +Because each surface is acting as both a slave and a master, the results of symmetric contact analyses +can be confusing and inconsistent. These difficulties are discussed more fully in “Using symmetric +master-slave contact pairs to improve contact modeling” in “Defining contact pairs in Abaqus/Standard,” +Section 35.3.1. +Overconstraining the model +The term overconstraint refers to a situation in which multiple kinematic constraints outnumber +the degrees of freedom on which they act. Overconstraints often lead to inaccurate solutions or +failure to obtain a converged solution. Contact conditions strictly enforced with the direct constraint +enforcement method (using Lagrange multipliers) are sometimes involved in overconstraints. See +“Overconstraint checks,” Section 34.6.1, for a detailed discussion and examples of overconstraints and +how Abaqus/Standard will treat overconstraints based on the following classifications: +• Overconstraints detected in the model preprocessor +• Overconstraints detected and resolved during analysis +• Overconstraints detected in the equation solver +Abaqus/Standard will automatically resolve many types of overconstraints; +however, many +overconstraints involving contact cannot be resolved and will be exposed to the equation solver. The +equation solver will often issue “zero pivot” or “numerical singularity” warning messages as a result of +overconstraints; when this occurs, Abaqus/Standard will provide a warning message with information +that is helpful for determining what contributed to the overconstraint so that you can resolve it. +Occasionally overconstraints do not create warning messages; this does not necessarily mean that the +overconstraints have not adversely affected the analysis. +Overconstraints involving softened contact +Contact conditions with a softened behavior or enforced with the penalty or augmented Lagrange +method will not combine with other constraints to cause “strict overconstraints”; however, “softened +overconstraints” can: +• cause zero pivots or ill-conditioning in the equation solver if the stiffness contributions associated +with contact are many orders of magnitude higher than the stiffness contributions from typical +elements; +• prevent a tight penetration tolerance from being achieved with the augmented Lagrange method; +and +• cause oscillations in contact stress solutions, particularly if the contact stiffness is high. +Some types of contact use the penalty or augmented Lagrange method by default to approximate hard +pressure-overclosure behavior due to the prevalence of redundant or “competing” contact conditions. For +a discussion of available constraint enforcement methods and default behavior, see “Contact constraint +enforcement methods in Abaqus/Standard,” Section 37.1.2. +Inaccurate contact forces due to overconstraints +If nodes in a contact pair are overconstrained but the equation solver does find a solution, the contact +forces become indeterminate and may become excessively high, particularly in tied contact pairs. Check +the time average force (or moment, or flux) reported in the message file, or use Abaqus/CAE to view +the diagnostic information interactively (for more information, see Chapter 41, “Viewing diagnostic +output,” of the Abaqus/CAE User’s Manual). If it is many orders of magnitude larger than the residual +forces (or moments, or fluxes), an overconstraint may have occurred, and there is no guarantee that +Abaqus/Standard has found the correct solution. Another sign that the model is overconstrained is that the +analysis begins to converge in a single iteration in every increment when the nonlinearities should require +at least several iterations. Overconstraints should be avoided only by changing the contact definition or +other constraint type involved. +Overconstraints due to multiple surface interaction definitions at a single node +Automatic resolution of contact overconstraints sometimes depends on whether two contact pairs refer +to the same surface interaction definition. For example, consider a case in which two contact pairs +have a common master surface and share some slave nodes (perhaps along a common edge of two +slave surfaces). Overconstraints will occur at the common slave nodes if the two contact pairs refer +to different surface interaction definitions (even if the surface interactions are equivalent); however, +Abaqus/Standard automatically avoids these overconstraints if the two contact pairs refer to the same +surface interaction definition. +Discrepancies between contact formulations +The different contact formulations available in Abaqus/Standard allow for a great deal of flexibility when modeling contact +simulations. However, two nearly identical simulations that differ only in the contact formulation being +used will sometimes generate varying results. This is primarily because of the different ways that +contact formulations interpret contact conditions. Certain formulations are better suited to particular +situations. +Differences in penetrations +The most observable difference between node-to-surface and surface-to-surface discretization is the +amount of penetration that occurs between surfaces. This is because node-to-surface discretization +computes penetrations only at slave nodes, while surface-to-surface discretization computes penetrations +in an average sense over a finite region. For example, when a slave surface slides across a convex +portion of a master surface, the slave surface will tend to ride a bit higher with surface-to-surface +discretization than with node-to-surface discretization, as shown in Figure 38.1.2–8 (the opposite is +true at a concave portion of a master surface). Figure 38.1.2–9 shows another case in which the two +contact discretizations behave fundamentally differently due to the different approaches to computing +penetrations. Both discretizations converge to the same behavior as the mesh is refined. +The differences in computed penetrations can sometimes fundamentally affect the results of an +analysis. Be aware of this possibility when converting models from one contact formulation to another. +Various aspects of preexisting models, such as the friction coefficient or the pressure-overclosure +relationship, may have been inadvertently “tuned” to the behavior that occurs with a particular contact +formulation. +Contact at a single point +Figure 38.1.2–10 shows an example in which a circular rigid body is pushed into a deformable body. In +the initial configuration shown, the two bodies touch at a single point, which corresponds to a slave node +location. The following scenarios are likely for respective analyses of this model with node-to-surface +and surface-to-surface discretization: +Figure 38.1.2–8 Comparison of contact discretizations in an example with convex +curvature in the master surface (forming application). +master surface +Constraints based on +"averaged" penetration +master surface +Constraints based on +slave nodes penetration +slave surface +Figure 38.1.2–9 Comparison of contact discretizations in an example with a relatively +flexible slave surface wrapping around a corner of a master surface. +• With node-to-surface discretization, +the first iteration is performed with one active contact +constraint. A converged solution is obtained with a reasonable number of iterations and +increments. +Figure 38.1.2–10 Example with two bodies initially touching at a single point. +• With surface-to-surface discretization, penetrations are computed in an average sense over +finite regions of the surface, so a positive gap distance is computed for all potential contact +constraints even though the surfaces touch at one of the slave nodes. However, the finite-sliding, +surface-to-surface contact formulation detects that the surfaces are initially touching and by default +automatically activates localized contact damping in the neighborhood where the gap distance is +zero. Without such damping, Abaqus/Standard may not obtain a converged solution due to an +unconstrained rigid body mode. This contact damping typically has an insignificant effect on the +converged solution, and the damping is completely removed by the end of the step. +If you deactivate the automatic localized damping for +surface-to-surface +formulation—or if you are using the small-sliding, surface-to-surface formulation—you should use one +of the techniques discussed above in “Difficulties resolving initial contact conditions” to remove the +perceived initial gap between surfaces and prevent rigid body modes in the analysis. +the finite-sliding, +Input File Usage: +Abaqus/CAE Usage: +Use the following option to deactivate automatic localized contact damping at +artificial surface gaps for contact pair definitions: +*CONTACT PAIR, MINIMUM DISTANCE=NO +Use the following option to deactivate automatic localized contact damping at +artificial surface gaps for general contact definitions: +*CONTACT INITIALIZATION DATA, MINIMUM DISTANCE=NO +You cannot deactivate automatic localized contact damping at artificial surface +gaps in Abaqus/CAE. +Differences in contact normal direction +Node-to-surface discretization uses a contact normal direction based on the master surface normal, +whereas surface-to-surface discretization uses a contact normal direction based on the slave surface +normal (averaged over a region nearby the slave node). For most active contact definitions the slave +and master surfaces are nearly parallel, so the master and slave normals are approximately aligned; in +which case this distinction in how the contact normal is determined is not significant. However, in some +cases the differences in the contact normal can be significant. +• When modeling large interference fits, surface-to-surface discretization can sometimes cause +tangential motion of the slave surface as the overclosures are resolved. This tangential motion may +have undesirable effects on an analysis. See “Controlling initial contact status in Abaqus/Standard,” +Section 35.2.4, and “Modeling contact interference fits in Abaqus/Standard,” Section 35.3.4, for +more details. +• Contact constraints involving geometric edges of surfaces sometimes use a significantly different +contact normal depending on which contact discretization approach is used, because the normals +for the slave and master surfaces may not directly oppose each other. +• The contact opening distance output variable (COPEN) can vary considerably depending on what +type of contact formulation is used if the contact surfaces are not parallel. For node-to-surface +discretization, the opening distance that is reported approximates the closest distance to the master +surface; for surface-to-surface discretization, the opening distance that is reported corresponds to +the distance from the slave surface to the master surface along the slave normal direction. The +opening distance for surface-to-surface discretization is undefined if a line emanating from the slave +surface in the slave normal direction does not intersect the master surface (as discussed in “Using +the small-sliding tracking approach” in “Contact formulations in Abaqus/Standard,” Section 37.1.1, +if a small-sliding constraint cannot be formed in such a case for the small-sliding, surface-to-surface +formulation, Abaqus/Standard automatically reverts to the node-to-surface approach for individual +constraints). +Contact at corners +The finite-sliding, surface-to-surface formulation is often better-suited than other contact formulations +for modeling contact near corners. In the example shown in Figure 38.1.2–11, the slave surface is on +the “outer” body (i.e., the body with a reentrant corner). With node-to-surface discretization a single +constraint acts at the corner slave node in the “average” normal direction of the master surface, which +often leads to poor resolution of contact, non-physical response, and even early termination of an analysis. +However, surface-to-surface discretization generates two constraints near the corner for the respective +faces, as shown in Figure 38.1.2–11, resulting in more stable contact behavior. +Figure 38.1.2–11 Comparison of contact formulations in an example with abutting +surfaces having respective interior and exterior corners. +38.2 +Resolving contact difficulties in Abaqus/Explicit +• “Contact diagnostics in an Abaqus/Explicit analysis,” Section 38.2.1 +• “Common difficulties associated with contact modeling using contact pairs in Abaqus/Explicit,” +Section 38.2.2 +38.2.1 +CONTACT DIAGNOSTICS IN AN Abaqus/Explicit ANALYSIS +Products: Abaqus/Explicit Abaqus/CAE +References +• “Output to the data and results files,” Section 4.1.2 +• “Contact interaction analysis: overview,” Section 35.1.1 +• *DIAGNOSTICS +• Chapter 41, “Viewing diagnostic output,” of the Abaqus/CAE User’s Manual +Overview +Contact diagnostics in Abaqus/Explicit allow you to get detailed information about the surfaces and +progress of contact interactions. Diagnostics are available: +• to review automatic adjustments between two surfaces, +• to reveal potentially problematic initial surface configurations in a model, +• to track excessive penetrations between two contacting surfaces, and +• to review warnings associated with contact between warped surfaces. +Reviewing the adjustments of initially overclosed surfaces +Contacting surfaces that are overclosed in the initial configuration of the model are adjusted +automatically by Abaqus/Explicit to remove the overclosures . There are three +sources of information on the adjustments of overclosed surfaces: the status (.sta) file, the message +(.msg) file, and the output database (.odb) file. +Obtaining the adjustments of overclosed surfaces in the status and message files +By default, Abaqus/Explicit writes all nodal adjustments and—for general contact surfaces—contact +offsets to the message (.msg) file along with a summary listing of the maximum initial overclosure and +the maximum nodal adjustment to the status (.sta) file for the contact pairs defined in the first step of +a simulation. You can choose to suppress the information written to the message file and write only the +summary information to the status file. The information written to the message and status files is also +written to the output database (.odb) for use in Abaqus/CAE. +Input File Usage: +Use the following option to obtain both detailed diagnostic output to the +message file and summary diagnostic output to the status file: +*DIAGNOSTICS, CONTACT INITIAL OVERCLOSURE=DETAIL (default) +Abaqus/CAE Usage: +Use the following option to obtain only summary diagnostic output to the status +file (no contact diagnostics will be written to the message file): +*DIAGNOSTICS, CONTACT INITIAL OVERCLOSURE=SUMMARY +You cannot control the diagnostic information for contact initial overclosures +from within Abaqus/CAE. Use the following option to view the saved +diagnostic information: +Visualization module: Tools→Job Diagnostics +Viewing the adjustments of surfaces +In the first step the adjustments of initially overclosed surfaces can be viewed in Abaqus/CAE. Displaced +shape plots that show the adjustments to the contact pairs defined in the first step can be plotted for the +original field output frame at zero time. In the case of overclosures in steps other than the first, vector plots +of nodal displacements and accelerations can be particularly helpful in visualizing the adjustments. Such +plots can be viewed in Abaqus/CAE after a data check analysis . +Visualizing the precise initial clearances for small-sliding contact pairs +Abaqus/Explicit does not adjust the coordinates of the slave surface when precise initial clearances are +specified for small-sliding contact pairs . Therefore, the specified clearances +cannot be seen in a postprocessor such as the Visualization module of Abaqus/CAE. Thus, depending +on the initial geometry of the surfaces and the magnitude of the clearances or overclosures, the surfaces +may appear open or closed in the postprocessor when they are actually just in contact in the simulation. +Detecting crossed surfaces in a general contact domain +If a slave surface initially penetrates a double-sided master surface by a distance greater than the master +surface’s thickness, the severely overclosed slave nodes will see the back side of the master surface as +the appropriate contact force direction. These slave nodes in these crossed surfaces effectively become +trapped behind the master surface. This issue is discussed in more detail in “Controlling initial contact +status for general contact in Abaqus/Explicit,” Section 35.4.4, and “Adjusting initial surface positions +and specifying initial clearances for contact pairs in Abaqus/Explicit,” Section 35.5.4. +For general contact definitions, diagnostic testing that identifies regions in which surfaces are +crossed in the initial configuration is activated by default. When the diagnostic tests are activated, a +warning message is issued to the message (.msg) file if two adjacent slave nodes (connected by a facet +edge) are detected on opposite sides of a master surface. No such warning is issued for node-based +surface nodes on opposite sides of a master surface, because adjacency cannot be determined among +the node-based surface nodes. In some cases involving corners of master surfaces this warning message +may be issued even though adjacent slave nodes are really on the same side of a master surface. The +CPU cost of performing diagnostic testing on large models is potentially significant. You can choose to +deactivate the diagnostic testing and avoid the extra CPU cost in such cases. +Input File Usage: +Use the following option to deactivate diagnostic testing for initially crossed +surfaces: +Abaqus/CAE Usage: +*DIAGNOSTICS, DETECT CROSSED SURFACES=OFF +You cannot exclude diagnostic testing for initially crossed surfaces from +within Abaqus/CAE. Use the following option to view the saved diagnostic +information: +Visualization module: Tools→Job Diagnostics +Excessive penetrations between general contact surfaces +As described in “Contact constraint enforcement methods in Abaqus/Explicit,” Section 37.2.3, the +penalty constraint enforcement method used by the general contact algorithm in Abaqus/Explicit allows +slight penetrations of one surface into another surface. A “spring” stiffness is applied automatically to +the surfaces to resist these penetrations. If the nodes involved in general contact do not have adequate +mass, the default “spring” stiffness chosen automatically by Abaqus/Explicit may not be sufficient to +prevent large penetrations. Such a situation can arise, for example, when a cloud of massless nodes, +fully constrained by a kinematic coupling definition, contacts a fully constrained rigid face with no mass. +By default, if during node-to-face contact, the penetration of a node into its tracked face exceeds +50% of the typical face dimension in the general contact domain, the penetration is regarded as excessive +and Abaqus/Explicit issues a diagnostic message to the status (.sta) file. A node set containing deeply +penetrated nodes is also written to the output database (.odb) file for use in Abaqus/CAE. You can +control the fraction of the typical face dimension used to trigger the diagnostic message. +Input File Usage: +Use the following option to control the fraction of the typical element face +dimension used to trigger the diagnostic message for deep penetrations: +Abaqus/CAE Usage: +*DIAGNOSTICS, DEEP PENETRATION FACTOR=value +You cannot control the diagnostic information for deep penetrations from +within Abaqus/CAE. Use the following option to view the saved diagnostic +information: +Visualization module: Tools→Job Diagnostics +Warning messages for highly warped surfaces +Calculating the correct contact conditions along a surface that is highly warped is very difficult, and +Abaqus/Explicit employs a specialized algorithm to enforce contact between warped surfaces; this +specialized algorithm is more expensive than the default contact algorithm . By default, Abaqus/Explicit checks for highly +warped surfaces every 20 increments. +Abaqus/Explicit writes a warning message in the status (.sta) file the first time that it detects that +a surface is highly warped. The message is brief; it states only which surface has a highly warped facet. +If additional facets on this surface become highly warped later in the analysis, no additional warning +messages are issued. +You can request more detailed diagnostic warning messages, if desired. In this case the message +file will contain a warning every time a warped facet is found on a particular surface. The warnings will +give the parent element associated with the warped facet (the parent element is the element whose face +forms the facet) and the warping angle of the facet. +The computation time and the size of the message file can increase significantly if detailed warnings +are requested. You can switch back to the summary warnings in subsequent steps or suppress the warped +surface warnings entirely. +If the analysis terminates with a fatal error, +the preselected output variables will be added +automatically to the output database as field data for the last increment. +Input File Usage: +Use the following option to request detailed diagnostic warning output for +warped surfaces: +*DIAGNOSTICS, WARPED SURFACE=DETAIL +Use the following option to request the default summary diagnostic output for +warped surfaces: +*DIAGNOSTICS, WARPED SURFACE=SUMMARY +Use the following option to suppress diagnostic warning output for warped +surfaces entirely: +*DIAGNOSTICS, WARPED SURFACE=OFF +Diagnostic output +Abaqus/CAE. +requests for warped surfaces are not supported in +Abaqus/CAE Usage: +38.2.2 +COMMON DIFFICULTIES ASSOCIATED WITH CONTACT MODELING USING +CONTACT PAIRS IN Abaqus/Explicit +Products: Abaqus/Explicit Abaqus/CAE +References +• “Defining contact pairs in Abaqus/Explicit,” Section 35.5.1 +• *CONSTRAINT CONTROLS +• *CONTACT PAIR +Overview +This section highlights the difficulties that are most commonly encountered when modeling contact +interactions with contact pairs in Abaqus/Explicit. Most of these issues are not relevant when the +general contact algorithm is used; refer to “Defining general contact interactions in Abaqus/Explicit,” +interactions. +Section 35.4.1, +Recommendations on how to circumvent these problems are presented. +for more information on the issues involved with general contact +Defining duplicate nodes on the master surface +When defining three-dimensional surfaces formed by element faces, avoid defining two surface nodes +with the same coordinates. Such a definition can give rise to a seam, or crack, in the surface as shown in +Figure 38.2.2–1. +Both vertices have the same coordinates. +They are separated to show the crack in the surface. +Figure 38.2.2–1 Example of doubly defined surface node. +If viewed with the default plotting options in Abaqus/CAE, this surface will appear to be a valid, +continuous surface; however, a node sliding along this surface can fall through this crack and violate +the contact conditions. If this were to happen, Abaqus/Explicit would enforce the contact conditions by +applying a large acceleration to the node once overclosure is detected. The large resulting acceleration +may create a noisy solution or cause the elements to distort badly. +Use the edge display options in the Visualization module of Abaqus/CAE to identify any unwanted +cracks in the surfaces used in the model. The cracks will appear as extra perimeter lines in the interior +of the surface. Duplicate nodes can be avoided easily by equivalencing nodes when creating the model +in a preprocessor. +Using an inadequate surface definition for the desired contact conditions +Occasionally, surface definitions may not be suitable for modeling the desired contact conditions in a +problem. Figure 38.2.2–2 shows a two-dimensional model of a simple connection between two parts. +surface 1 +surface 2 +surface 3 +contact pair 1 = surface 1, surface 3 +contact pair 2 = surface 2, surface 3 +Analysis will stop after 1st increment with +message that elements are badly distorted +Figure 38.2.2–2 Surface definitions that are inadequate +for the desired contact conditions. +The surfaces shown in the figure are inadequate for the desired contact conditions that are also shown. +At the start of the simulation, Abaqus/Explicit will detect that some of the nodes on surface 3 are behind +surfaces 1 and 2. When the contact conditions are enforced, the motions of the surfaces will likely cause +badly distorted elements. One solution to this problem is shown in Figure 38.2.2–3. +surface 4 +surface 5 +contact pair = surface 4, surface 5 +Figure 38.2.2–3 Surface definitions that are adequate for the desired contact conditions. +The surfaces shown in that figure are suitable for the desired contact definition. Other solutions, such as +using a pure master-slave contact pair, exist for this problem and may be more suitable, depending on +the details of the intended simulation. +Using poorly discretized surfaces +Several problems are caused by surfaces created on very coarse meshes. +Penetrations with coarsely discretized surfaces when using hard surface behavior +When a coarsely discretized surface is used as the slave surface in a pure master-slave contact pair with +hard surface behavior, an inaccurate solution may be produced as a result of the gross penetration of the +master surface into the slave surface. This situation is shown in Figure 38.2.2–4. This problem can be +minimized if the contact pair can be switched to a balanced master-slave contact pair. However, some +contact pairs in Abaqus/Explicit must always use a pure master-slave formulation. In these cases the +only solution to gross penetration is to refine the slave surface. +Problems with coarsely discretized rigid surfaces +For rigid surfaces formed by element faces, inaccurate results may be obtained if too few elements are +used to represent a curved geometry. When a very coarse mesh is used on a curved geometry, it is possible +for slave nodes to get “snagged” on the sharp vertices. +In general, using a reasonable number of element faces to represent a curved surface will not +increase the computational time of the simulations. However, a large number of element faces can +significantly increase the memory that Abaqus/Explicit will need for the simulation. When a specific +slave nodes cannot penetrate +master segments +master surface +(segments) +penetration +slave surface +(nodes) +gap +master node can penetrate +slave segment +Figure 38.2.2–4 Master surface penetrations into the slave surface due to coarse discretization. +curved surface geometry can be modeled, using an analytical rigid surface may provide a more +accurate geometric description while minimizing computational expense; see “Analytical rigid surface +definition,” Section 2.3.4. +Penalty contact behavior sensitivity in rigid-to-rigid interactions +The contact penalties are, in general, determined from stable time increment considerations and masses +of the nodes involved in contact. To compute a reliable contact penalty when rigid bodies are contacting +each other, Abaqus/Explicit accounts in a comprehensive fashion for the inertial properties of the rigid +bodies by distributing the mass of the rigid bodies at all nodes that might be involved in contact. Hence, +the final contact penalty will depend on the size of the actual rigid surfaces that are included in the contact +definitions. Consequently, the contact response (forces, penetrations) will depend somewhat on your +choice in defining the contacting surfaces on the rigid bodies. If large penetrations occur, specifying +realistic inertial properties for the rigid bodies will help in general to resolve the issue. Alternatively, +you can use a scaling factor for the penalties to enforce contact in a more accurate fashion. +Conflicts with boundary conditions +If boundary constraints are applied to contact nodes on both surfaces of a contact pair in the direction +that the contact constraints are active, the boundary constraints may override the contact constraints. +For kinematic contact, contact force related quantities will be output as the force necessary to resolve +the contact constraint in a single increment, causing misleading results for these output quantities if the +boundary constraints violate the contact constraints. Contact force output for penalty contact does not +show this behavior since the contact force is proportional only to the current penetration and does not +depend on the time increment. Boundary constraints are not affected by contact constraints. +Conflicts with multi-point constraints +Using a multi-point constraint (MPC) with a node on a surface that is part of an active kinematic contact +pair can generate conflicting kinematic constraints in the model. Abaqus/Explicit will not prevent you +from using multi-point constraints on the nodes forming a surface. If the contact constraints and the +constraints formed by the MPC are orthogonal, there will be no problems with the simulations. If they are +not orthogonal, the solution may be noisy as Abaqus/Explicit tries to satisfy the conflicting constraints. +Since within each increment kinematic contact constraints are applied after MPCs are applied, the MPCs +on kinematic contact surfaces may be slightly out of compliance. +In the case of an interaction between an MPC and penalty contact, the MPC is strictly enforced and +any noncompliance in the contact pair will be resisted by penalty forces. +Conflicting contact constraints on shell nodes with hard contact +When a shell or membrane is pinched between two master surfaces using two kinematic contact pairs +with hard contact behavior, one of the contact constraints will not be enforced exactly. In a quasi-static +analysis it may be observed that the pinched slave node will oscillate about an “equilibrium” penetration +depth with a decay rate that depends on the time increment and the ratio of the mass of the pinched +node and the mass of the master surfaces. Decreasing the time increment size will increase the decay +rate (quasi-static equilibrium will be reached more quickly). Reducing the mass of the nodes on the +master surfaces (or increasing the mass of the pinched nodes) will also increase the decay rate, although +a high ratio of slave mass to master mass can also lead to numerical difficulties for kinematic contact, as +discussed below in “Large mass mismatch between contact surfaces.” Applying the loads to the model +gradually will reduce the amplitude of the oscillation. In most analyses it is not desirable to alter the +time increment or nodal masses arbitrarily, so the decay rate of the oscillation will be fixed. Either the +loading rate can be modified or a softened contact model with contact damping can be used to control +this oscillatory behavior. +The quasi-static equilibrium penetration magnitude, +, is approximately given by +where f is the normal contact force, +is the increment size, and m is the mass of the pinched node. +The quasi-static equilibrium penetration will be minimal if it is small compared to the shell or membrane +thickness. A change in the time increment size or loading on the pinched surfaces during the analysis +causes the quasi-static equilibrium penetration to change, which can be responsible for large accelerations +of surface nodes and can contribute to solution noise (typically, this behavior manifests as a jump in +contact results such as CPRESS). Similar noisy behavior for pinched surfaces can occur across a step +boundary, even if the time increment size is uniform across the step boundary. +If one kinematic contact pair and one penalty contact pair are used to model the same type of +pinching problem, the kinematic constraint is enforced exactly and the static value of the penetration +in the penalty contact pair is somewhat larger than that which occurs when kinematic contact is used for +both contact pairs (assuming that the penalty stiffness is set such that the analysis is numerically stable +for the time increment being used). +Multiple kinematic contact constraints on solid nodes +If a node that is not attached to shell or membrane elements acts as a slave node in two or more +simultaneous, kinematic contact constraints, +the resulting contact corrections may be erroneous, +possibly causing the analysis to abort with excessive element distortion. By “not attached to shell or +membrane elements” we are referring to nodes attached to solid elements or point masses, for example. +The majority of solid nodes typically are not involved in simultaneous contacts, but there are common +exceptions where three or more bodies meet at corners. This limitation can be avoided by using penalty +contact. For example, if a solid surface acts as a slave in two contact pairs and there is a possibility of +simultaneous contacts for individual slave nodes, penalty enforcement of contact should be specified +for one or both of the contact pairs. +Redundant and degenerate contact constraints +Redundant contact constraints are caused by overlapping or adjoining surfaces. For example, if +contact is specified between a single surface and multiple overlapping surfaces, the contact constraints +associated with the common nodes of the overlapping surfaces are redundant. Degenerate contact +constraints occur if the slave surface and master surface of the same contact pair contain common nodes +(a contact constraint cannot be formed between a node and itself). +If redundant kinematic contact constraints are specified, Abaqus/Explicit will consolidate the +constraints if both contact pairs use pure master-slave contact, the slave surfaces do not share facets, +and the surface interaction and contact pair set names are identical. If the contact pair definitions differ, +the analysis will terminate with an error, and one of the redundant constraints must be removed from +the model definition to continue the analysis. +Redundant penalty contact constraints may cause excessive initial overclosure adjustments, creating +gaps in the place of initial overclosures. To correct this behavior, one of the constraints must be removed +from the model definition. +Redundant contact constraints involving both a penalty contact pair and a kinematic contact pair +cause inefficiencies in the analysis. The kinematic contact constraints will override the penalty contact +constraints, but the penalty contact constraints will still be considered in the automatic time increment +estimate. +If the surfaces in a two-surface contact pair contain common nodes, the contact constraint for each +shared node cannot be generated. This is the equivalent of defining self-contact between the shared nodes +and each surface. However, the two-surface contact logic (unlike the specialized self-contact logic) +would erroneously detect contact between each shared node and itself. When this condition occurs, +Abaqus/Explicit redefines the slave surfaces so that the shared nodes will not act as slave nodes in the +contact pair. However, the shared nodes will still be used in the definition of a master surface in the +contact pair. +Large mass mismatch between contact surfaces +Often very little mass is assigned to rigid bodies in quasi-static simulations because the mass has little +influence on the physical problem. However, specifying a small rigid body mass can adversely affect +the kinematic contact enforcement method. A force applied to a rigid body with very little mass can +cause a large predicted displacement of the rigid body within an increment prior to the enforcement +of contact constraints, so significant penetration may be present in the “predicted” configuration for +kinematic contact, as shown in Figure 38.2.2–5. +dpred +tensile contact forces +stretched +(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0) +(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0) +(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0) +original configuration +predicted configuration +corrected configuration +Figure 38.2.2–5 Undesirable numerical behavior of contact +algorithm resulting from small rigid body mass. +With hard kinematic contact each slave node that is penetrating its master surface in the predicted +configuration will be brought to the position of its tracked point on the master surface in the corrected +configuration, which, in this example, generates tensile contact forces at the outer slave nodes of the +contact region. This undesirable effect can be avoided by increasing the mass of the rigid body, which +will reduce the predicted displacement increment. A small rigid body mass can also adversely affect +penalty enforcement of contact because small penalty stiffnesses will be assigned. +Similar undesirable numerical behavior can occur for deformable-to-deformable contact if the nodal +masses of the master nodes are orders of magnitude less than those of the slave nodes. This problem +can often be avoided in such cases by using the pure master-slave algorithm with the master surface +containing the more massive nodes. +Contact noise associated with limited computer precision for hard contact +is made for an initial overclosure, a penetration of up to +Some contact noise may occur with hard contact models because of limited computer precision. This +noise is rarely significant in an analysis, but it may be noticeable at the beginning of an analysis if initial +displacements are used to make the mesh comply with contact constraints. For example, if an adjustment +of +may still exist in the first increment, +where +is the “machine epsilon” of the computer. The machine epsilon of a given computer is defined +as the smallest positive number that can be added to 1 with the computed result being greater than 1; on +most systems +is approximately 6E−8 for single precision and 1E−16 for double precision. With the +kinematic contact algorithm you can attribute initial accelerations of up to +to limited machine +precision, where +=1E−6 sec, initial +accelerations of up to 6E4 sec−2 +can be attributed to limited machine precision. These accelerations +is the time increment. For a single precision analysis in which +are typically insignificant. They can be reduced by conducting the analysis with double precision or by +specifying the nodal coordinates to be more compliant with contact constraints. +Finite-sliding contact near a symmetry plane +When a pure master-slave contact constraint with finite sliding is defined near a symmetry plane in the +master surface, the corner slave node (node A in Figure 38.2.2–6) can, under some circumstances, slide +freely along the symmetry plane without experiencing contact. If the master surface wraps around the +corner (node 1), the slave node A may “track” on the master segment (1–6) on the symmetry plane, rather +than on master segment (1–2). The result may be an inaccurate representation of the contact constraint +as shown by the shaded area. +symmetry plane +10 +A0 +B0 +master surface +slave surface +Figure 38.2.2–6 Contact near a symmetry plane. The master +surface is wrapped around the corner. +If the master surface does not wrap around the corner (node 1 in Figure 38.2.2–7), the contact logic +may give different results depending on how the symmetry boundary conditions have been defined for +the master node 1 on the symmetry plane. If the symmetry boundary conditions on the master node +are specified using boundary “type” format (i.e., XSYMM, YSYMM, or ZSYMM—see “Boundary +conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1), the master surface is effectively +extended beyond the symmetry plane (Figure 38.2.2–7); thus, the slave node A will be detected as a +“penetrated” node (penetrated by distance a). Therefore, a correcting force would be applied on slave +node A to push it below the master surface. +symmetry plane +XSYMM boundary +condition +A0 +B0 +master surface +(extended) +slave surface +Figure 38.2.2–7 The master surface is extended across the symmetry plane because the symmetry +boundary condition at node 1 is specified using boundary type XSYMM. +If the symmetry boundary conditions on the master node 1 are specified using “direct” format (i.e., +specifying the components of translations and rotations that are fixed), the master surface is not extended +beyond the symmetry plane (Figure 38.2.2–8) and it is possible that contact will not be enforced correctly. +To ensure proper enforcement of finite-sliding contact near symmetry planes, use balanced master- +slave contact or use pure master-slave contact without extending the surface onto the symmetry plane +and use symmetry “type” boundary conditions on the perimeter of the master surface nodes as discussed +above. Special consideration of small-sliding contact near a symmetry plane is discussed in “Contact +formulations for contact pairs in Abaqus/Explicit,” Section 37.2.2. +Specifying initial clearance values precisely +You can define initial clearances and contact directions precisely for the nodes on the slave surface . The initial clearance or +overclosure value calculated at every slave node based on the coordinates of the slave node and the +master surface is overwritten by the value that you specify; the coordinates of the slave nodes are not +altered. This technique permits exact specification of initial clearances (and, possibly, contact directions) +when they would not be computed accurately enough from the nodal coordinates; for example, if the +symmetry plane +Boundary conditions constraining +degrees of freedom 1, 5, and 6 to 0.0 +A0 +master surface +slave surface +Figure 38.2.2–8 The master surface is not extended across +the symmetry plane because the symmetry boundary conditions +at node 1 are specified using direct format. +initial clearance is very small compared to the coordinate values. It can be used only in small-sliding +contact analyses (“Contact formulations for contact pairs in Abaqus/Explicit,” Section 37.2.2). +When the balanced-master slave contact algorithm is invoked for the contact pair, the initial +clearance values can be defined on one or both of the surfaces. Initial clearances defined on contact +surfaces that act only as master surfaces will be ignored. +Visualizing the precise initial clearances for small-sliding contact pairs +Abaqus/Explicit does not adjust the coordinates of the slave surface when precise initial clearances are +specified for small-sliding contact pairs . Therefore, the specified clearances +cannot be seen in a postprocessor such as the Visualization module of Abaqus/CAE. Thus, depending +on the initial geometry of the surfaces and the magnitude of the clearances or overclosures, the surfaces +may appear open or closed in the postprocessor when they are actually just in contact. +39. +Contact Elements in Abaqus/Standard +Contact modeling with elements +Gap contact elements +Tube-to-tube contact elements +Slide line contact elements +Rigid surface contact elements +39.1 +39.2 +39.3 +39.4 +39.1 +Contact modeling with elements +• “Contact modeling with elements,” Section 39.1.1 +39.1.1 +CONTACT MODELING WITH ELEMENTS +Abaqus/Standard offers a variety of contact elements that can be used when contact between two bodies cannot +be simulated with the surface-based contact approach (Chapter 35, “Defining Contact Interactions”). These +elements include the following: +• Gap contact elements: Mechanical and thermal contact between two nodes is modeled with gap +elements (“Gap contact elements,” Section 39.2.1). For example, these elements can be used to model +the contact between a piping system and its supports. They can also be used to model an inextensible +cable that supports only tensile loads. +• Tube-to-tube contact elements: Contact between two pipes or tubes is modeled using tube-to-tube +contact elements (“Tube-to-tube contact elements,” Section 39.3.1) in conjunction with slide lines. These +elements can, for example, be used to simulate the process of running tubular components into an oil well +(drill rod or J-tube analysis). They might also be used to simulate a catheter being inserted into a blood +vessel. +• Slide line contact elements: Finite-sliding contact between two axisymmetric structures that may +undergo asymmetric deformations can be modeled using slide line contact elements (“Slide line contact +elements,” Section 39.4.1) in conjunction with user-defined slide lines. Slide line elements can, for +example, be used to model threaded connectors. +• Rigid surface contact elements: Contact between an analytical rigid surface and an axisymmetric +deformable body that may undergo asymmetric deformations can be modeled with rigid surface contact +elements (“Rigid surface contact elements,” Section 39.5.1). For example, rigid surface contact elements +might be used to model the contact between a rubber seal and a much stiffer structure. +39.2 +Gap contact elements +• “Gap contact elements,” Section 39.2.1 +• “Gap element library,” Section 39.2.2 +39.2.1 +GAP CONTACT ELEMENTS +Product: Abaqus/Standard +References +• “Gap element library,” Section 39.2.2 +• *GAP +Overview +Gap elements: +• allow for contact between two nodes; +• allow for the nodes to be in contact (gap closed) or separated (gap open) with respect to particular +directions and separation conditions; +• are always defined in three dimensions but can also be used in two-dimensional and axisymmetric +models; +• allow contact to be defined on any type of element, including substructures and user-defined +elements; +• can be used to model contact in fixed or rotating directions; +• can be used to model node-to-node contact and thermal interactions in a fixed direction in space in +coupled temperature-displacement simulations; and +• can be used to model node-to-node thermal interactions in heat transfer analyses. +A general discussion of contact modeling in Abaqus/Standard can be found in Chapter 35, “Defining +Contact Interactions.” +Choosing and defining a gap element +GAPUNI elements model contact between two nodes when the contact direction is fixed in space. +GAPCYL elements model contact between two nodes when the contact direction is orthogonal to an +axis. GAPSPHER elements model contact between two nodes when the contact direction is arbitrary +in space. GAPUNIT elements model contact and thermal interactions between two nodes when the +contact direction is fixed in space. DGAP elements model thermal interactions between two nodes in +heat transfer analysis. +Gap elements are defined by specifying the two nodes forming the gap and providing geometric +data defining the initial state and, if necessary, the direction of the gap. +Defining the gap element’s properties +You must associate the gap behavior with a set of gap elements. +Input File Usage: +*GAP, ELSET=element_set_name +GAPUNI and GAPUNIT elements +The contact behavior of the interface being modeled with GAPUNI and GAPUNIT elements is defined +by the initial separation distance (clearance), d, of the gap and the contact direction, +. In addition, +GAPUNIT elements have temperature degrees of freedom that allow modeling of thermal interactions +in coupled temperature-displacement analyses. +Clearance between GAPUNI nodes +Abaqus/Standard defines the current clearance between two nodes of the gap, h, as +and +where +are the total displacements at the first and the second node forming the GAPUNI +element. Figure 39.2.1–1 shows the configuration of the GAPUNI element. When h becomes negative, +the gap contact element is closed and the constraint +is imposed. +h = d + n · (u2 - u1) ≥ 0 +Figure 39.2.1–1 GAPUNI and GAPUNIT contact elements. +You specify a value for d. If you provide a positive value, the gap is open initially. If d=0, the gap is +initially closed. If d is negative, the gap is considered overclosed at the start of the analysis and an initial +interference fit problem is defined. Details about modeling interference fit problems with gap elements +are discussed below. +Input File Usage: +*GAP +Specifying the contact direction +You can specify the contact direction. Otherwise, Abaqus/Standard will calculate the gap direction, +by using the initial positions of the two nodes forming the element, +and +: +, +An error message is issued if +In this situation you must define . The normal +second, unless the gap is overclosed at the start of the analysis. In that case specify +contact direction is used for the gap element. +(if the two gap element nodes have the same initial coordinates). +usually points from the first node of the element to the +so that the correct +If you specify the gap direction +rather than allowing Abaqus/Standard to calculate it, the contact +calculations consider only , the displacements of the gap element’s nodes, and the ordering of the nodes +in the element definition: the initial coordinates of the nodes play no role in the calculations. +The orientation of +Input File Usage: +does not change during the analysis. +*GAP +, X-direction cosine, Y-direction cosine, Z-direction cosine +Local basis system for GAPUNI element output +Abaqus/Standard reports the pressure transmitted across the gap and the shear stresses that are +orthogonal to the contact direction as element output for GAPUNI elements. You must supply the +contact area associated with these elements for Abaqus/Standard to compute the pressure and the shear +stress values. It also reports the current clearance in the gap, h, and the relative motions of the GAPUNI +nodes orthogonal to the contact direction. The relative motions and the shear stresses are reported in +local surface directions that are formed using the standard Abaqus convention for defining directions on +surfaces in space . The contact direction defines a surface in space +on which the local axes are formed. +Input File Usage: +*GAP +, , , , cross-sectional area +GAPCYL elements +GAPCYL elements can be used to model two very different contact situations: contact between two rigid +tubes, where the smaller one is inside the larger tube, and contact between two rigid tubes along their +external surfaces. Both cases are shown in Figure 39.2.1–2. +The behavior of a GAPCYL element is defined by the initial separation distance between the nodes, +d; the current positions of the element’s node; and the axis of the GAPCYL element. The axis of the +GAPCYL element defines the plane in which the contact direction, +, lies. You specify d and the direction +cosines of the GAPCYL element axis. +The value +is not allowed: it would enforce the distance between the nodes to be exactly zero +at all times, which does not correspond to a contact problem. +Input File Usage: +*GAP +d, X-direction cosine, Y-direction cosine, Z-direction cosine +Defining the gap clearance for Case 1 (when d is positive) +If d is positive, the GAPCYL element models contact between two rigid tubes of different diameter, +where the smaller tube is located inside the larger tube . In this case +d is the maximum allowable separation. Each tube is represented by a node on its axis, with the axes +connected by the GAPCYL element; and d corresponds to the difference between the radii of the tubes. +Case 1 +_ + - x +h = d - | x +d = r2 - r1 +_ + | ≥ 0 +Case 2 +_ + - x +h = | x +) +d = - (r1 + r2 +_ +| - | d | ≥ 0 +Figure 39.2.1–2 Gap clearance for GAPCYL/GAPSPHER contact elements. +The gap between the tubes closes when the two nodes become separated by more than d in any direction +in the plane defined by the axis of the GAPCYL element. +Abaqus/Standard defines the current gap opening, h, in GAPCYL elements for Case 1 as +where +GAPCYL element. +is the current position of node N, d is the specified initial separation, and a is the axis of the +If the initial position of the tube axes is such that the distance between them is less than d, the +GAPCYL element is open initially. If the distance is equal to d, the element is closed initially; and if +the distance is greater than d, an initial overclosure (interference) is defined. Details about modeling +interference fit problems with gap elements are discussed below. +Defining the gap clearance for Case 2 (when d is negative) +If d is negative, the GAPCYL element models external contact between two parallel rigid cylinders . In this case +is the minimum allowable separation of the nodes. Each +cylinder is represented by a node on its axis connected by the GAPCYL element, and +corresponds to +the sum of the radii of the cylinders. The gap closes when the two nodes approach each other to within +in any direction in the plane defined by the axis of the GAPCYL element. +Abaqus/Standard defines the current gap opening, h, in GAPCYL elements for Case 2 as +If the initial position of the cylinder axes is such that the distance between them is greater than +, +, the element is closed initially; and +, an initial overclosure (interference) is defined. Details about modeling +the GAPCYL element is open initially. If the distance is equal to +if the distance is less than +interference fit problems with gap elements are discussed below. +Local basis system for GAPCYL element output +Abaqus/Standard reports the pressure transmitted across the gap and the shear stresses that are orthogonal +to the contact direction as element output for GAPCYL elements. You must supply the contact area +associated with these elements for Abaqus/Standard to compute the pressure and the shear stress values. +It also reports the current clearance in the gap, h, and the relative motions of the element’s nodes that +are orthogonal to the contact direction. The relative motions and the shear stresses are reported in +local surface directions that are formed using the standard Abaqus convention for defining directions +on surfaces in space . The contact direction defines a surface in space +on which the local axes are formed, and the slip is calculated from the relative motions in the surface +directions. +Abaqus/Standard updates the contact direction for GAPCYL elements based on the motion of the +nodes forming the elements. However, the orientation of +*GAP +, , , , cross-sectional area +Input File Usage: +is not updated during the analysis. +GAPSPHER elements +GAPSPHER elements can be used to model two very different contact situations: contact between two +rigid spheres where the smaller sphere is inside the larger, hollow sphere, and contact between two rigid +spheres along their external surfaces. Both cases are shown in Figure 39.2.1–2. +The behavior of a GAPSPHER element is defined by the minimum or maximum separation distance +between the nodes, d, and the current positions of the element’s nodes. You specify the minimum or +maximum separation distance, d. The contact direction is defined by the current position of the nodes. +The value +is not allowed: it would enforce the distance between the nodes to be exactly zero +at all times, which does not correspond to a contact problem. +Input File Usage: +*GAP +Defining the gap clearance for Case 1 (when d is positive) +If d is positive, the GAPSPHER element models contact between a rigid sphere inside another (larger) +hollow rigid sphere . In this case d is the maximum allowable separation of +the nodes forming the gap. Each sphere is represented by a node at its center, with the centers connected +by the GAPSPHER element; and d corresponds to the difference between the radii of the spheres. The +gap closes when the two nodes become separated by more than d. +Abaqus/Standard defines the current gap opening, h, for Case 1 as +with +the current position of node N and d the specified separation. +If the initial position of the tube axes is such that the distance between them is less than d, the +GAPSPHER element is open initially. If the distance is equal to d, the element is closed initially; and +if the distance is greater than d, an initial overclosure (interference) is defined. Details about modeling +interference fit problems with gap elements are discussed below. +Defining the gap clearance for Case 2 (when d is negative) +If d is negative, the GAPSPHER element models external contact between two rigid spheres . +is the minimum allowable separation of the nodes forming the +gap. Each sphere is represented by a node at its center connected by the GAPSPHER element; and +corresponds to the sum of the radii of the spheres. The gap closes when the two nodes approach each +In this case +other to within +. +Abaqus/Standard defines the current gap opening, h, for Case 2 as +If the initial position of the cylinder axes is such that the distance between them is greater than +, +, the element is closed initially; +, an initial overclosure (interference) is defined. Details about modeling +the GAPSPHER element is open initially. If the distance is equal to +and if the distance is less than +interference fit problems with gap elements are discussed below. +Local basis system for GAPSPHER element output +Abaqus/Standard reports the pressure transmitted across the gap and the shear stresses that are orthogonal +to the contact direction as element output for GAPSPHER elements. You must supply the contact area +associated with these elements for Abaqus/Standard to compute the pressure and the shear stress values. +It also reports the current clearance in the gap, h, and the relative motions of the element’s node that +are orthogonal to the contact direction. The relative motions and the shear stresses are reported in +local surface directions that are formed using the standard Abaqus convention for defining directions +on surfaces in space; see “Conventions,” Section 1.2.2. The contact direction defines a surface in space +on which the local axes are formed, and the slip is calculated from the relative motions in the surface +directions. +Abaqus/Standard updates the contact direction for GAPSPHER elements based on the motion of +the nodes forming the elements. +*GAP +, , , , cross-sectional area +Input File Usage: +DGAP elements +DGAP elements are used to model thermal interactions between two nodes in heat transfer analyses. The +behavior of the interaction being modeled is defined by the initial separation distance (clearance), d, of +the gap. +Clearance between DGAP nodes +Abaqus/Standard defines the clearance between two nodes of the gap, h, as +Since there are no displacements in a heat transfer analysis, the clearance remains unchanged. The +clearance is used only for clearance-dependent thermal interactions. +You specify a value for d. If you provide a positive value, the gap is open initially. If d=0, the gap is +closed initially. If d is negative, the gap is considered overclosed but no interference fit is performed. The +contact direction does not need to be specified: any contact direction specified is ignored in the analysis. +You must supply the contact area associated with these elements for Abaqus/Standard to compute the +heat flux value per unit area. +Input File Usage: +*GAP +d, , , , cross-sectional area +Defining nondefault mechanical interactions with gap elements +The default mechanical interaction model for problems modeled with gap elements is “hard,” frictionless +contact. You can assign optional mechanical interaction models. The following mechanical interaction +models are available: +• Friction. See “Frictional behavior,” Section 36.1.5, for details. +• Modified “hard” contact, softened contact, and viscous damping. See “Contact pressure-overclosure +relationships,” Section 36.1.2, and “Contact damping,” Section 36.1.3, for details. +Defining thermal surface interactions with GAPUNIT and DGAP elements +You can assign thermal interaction models to these elements. The following thermal interaction models +are available: +• Gap conduction. +• Gap radiation. +• Gap heat generation. +These thermal interaction models are discussed in “Thermal contact properties,” Section 36.2.1. +Modeling large initial interference with gap elements +Specifying a large negative initial overclosure (interference) may lead to convergence problems as +Abaqus/Standard tries to resolve the overclosure in a single increment. You can prescribe an allowable +interference to allow Abaqus/Standard to resolve the overclosure gradually. See “Modeling contact +interference fits in Abaqus/Standard,” Section 35.3.4, for more details on modeling interference fit +problems. +Input File Usage: +*CONTACT INTERFERENCE, TYPE=ELEMENT +39.2.2 +GAP ELEMENT LIBRARY +Product: Abaqus/Standard +References +• “Gap contact elements,” Section 39.2.1 +• *GAP +Overview +This section provides a reference to the gap elements available in Abaqus/Standard. +Element types +Stress/displacement elements +GAPUNI +Unidirectional gap between two nodes +GAPCYL +Cylindrical gap between two nodes +GAPSPHER +Spherical gap between two nodes +Active degrees of freedom +1, 2, 3 +Additional solution variables +Three additional variables relating to the contact and friction forces. +Coupled temperature-displacement element +GAPUNIT +Unidirectional gap and thermal interactions between two nodes +Active degrees of freedom +1, 2, 3, 11 +Additional solution variables +Three additional variables relating to the contact and friction forces. +Heat transfer element +DGAP +Thermal interactions between two nodes +Active degree of freedom +11 +Additional solution variables +None. +Nodal coordinates required +For DGAP elements, and for GAPUNI and GAPUNIT if you specify the contact direction , the nodal +coordinates are not used in the contact calculations; however, it is useful to define the coordinates of the +two nodes for plotting purposes. +GAPCYL and GAPSPHER: X, Y, Z +Element property definition +You can specify the initial clearance, the contact direction (normal to the interface), and the contact area. +For GAPUNI, GAPUNIT, and DGAP elements, a negative clearance indicates an initial overclosure. +For GAPCYL and GAPSPHER elements, specify the maximum separation as a positive number or the +minimum separation as a negative number. +Input File Usage: +*GAP +Element-based loading +None. +Element output +S11 +S12 +S13 +E11 +E12 +E13 +Pressure transmitted between the surfaces. The pressure is defined as the force +divided by the user-specified area. +First frictional shear stress normal to the gap direction. +Second frictional shear stress normal to the gap direction. +Current opening h of the gap element. +Relative displacement (“slip”) in the first direction orthogonal to the contact +direction. +Relative displacement (“slip”) in the second direction orthogonal to the contact +direction. +Available for elements with temperature degrees of freedom. +HFL1 +Heat flux across the interface in the contact direction. +The increments of shear slip are the relative displacement increments projected onto the two local +directions that are orthogonal to the contact direction. +In two-dimensional or axisymmetric models when the contact direction is along the first axis (X or +r), the active slip direction is E13 and the active shear stress is S13. +In any other two-dimensional +or axisymmetric case, the active slip direction is E12 and the active shear stress is S12. +Two nodes: the ends of the gap. +GAP LIBRARY +39.3 +Tube-to-tube contact elements +• “Tube-to-tube contact elements,” Section 39.3.1 +• “Tube-to-tube contact element library,” Section 39.3.2 +39.3.1 +TUBE-TO-TUBE CONTACT ELEMENTS +Product: Abaqus/Standard +References +• “Tube-to-tube contact element library,” Section 39.3.2 +• *INTERFACE +• *SLIDE LINE +Overview +Tube-to-tube elements: +• model the finite-sliding interaction between two pipelines or tubes where one tube lies inside the +other or between two tubes or rods that lie next to each other; +• are slide line contact elements, in the sense that they assume that the relative motion of the two +tubes or pipes is predominantly along the line defined by the axis of one of the tubes (the relative +rotations of the tube or pipe axis are assumed to be small); +• can be used with pipe, beam, or truss elements; and +• do not consider deformations of the tube or pipe cross-section. +Chapter 35, “Defining Contact Interactions,” contains a general discussion of contact modeling. +Typical applications +The tube-to-tube contact elements can be used to model two specific classes of tube-to-tube contact +problems: internal (tube within a tube) contact and external contact, where the two tubes are roughly +parallel and contact each other along their outer surfaces. It is not possible to use the surface-based +contact approach for problems where two three-dimensional tubes contact each other. +Choosing an appropriate element +Use ITT21 elements with two-dimensional beam, pipe, or truss elements. Use ITT31 elements with +three-dimensional beam, pipe, or truss elements. Each of these elements is defined by a single node. +Associating the tube-to-tube contact elements with a slide line +You must indicate which set of tube-to-tube contact elements will interact with a particular slide line. +Details on defining slide lines are discussed below. +Input File Usage: +*SLIDE LINE, ELSET=element_set_name +Defining the element’s section properties +You must associate the geometric section properties with a set of tube-to-tube contact elements. +*INTERFACE, ELSET=element_set_name +Input File Usage: +Defining the radial clearance when modeling contact between a pipe within another pipe +You define the radial clearance between the pipes. Give a positive value to model contact between two +pipes when one pipe (the one with the tube-to-tube contact elements) lies inside of the other pipe. The +value given is the difference between the inner radius of the outer pipe and the outer radius of the inner +pipe. +Input File Usage: +*INTERFACE +radial clearance +Defining the radial clearance when modeling contact between the outer surfaces of two pipes +You can model external tube-to-tube contact by specifying a negative value for the radial clearance. The +magnitude of the value must be the sum of the outer radii of the two pipes or rods. +Local basis for contact output variables +The element output variables for ITT elements are given in a local basis system associated with the slide +line. The first tangent vector, +, is defined by the sequence of the nodes forming the slide line. The +direction of contact, +, is the normal to the slide line that points toward the nodes of the ITT elements. +For ITT31 elements Abaqus/Standard forms a second tangent vector, +and . As the elements move, the local basis system will rotate with the axis of the slide line. +, that is orthogonal to both +Choosing which pipe (beam or truss) will have the slide line +In the case of internal tube-to-tube contact, the slide line can be placed on the inner tube or the outer +tube. Generally the slide line should be associated with the outer tube ; however, +if the inner tube is stiffer than the outer tube, the slide line should be attached to the inner tube. +If contact occurs between the exterior surface of the tubes, the slide line should be associated with +the stiffer tube if the materials or tube radii are different or with the tube with the coarser mesh if they +are the same. +Defining the slide line +You can specify the nodes that make up the slide line, or they can be generated as described below. If +you choose to specify the nodes directly, you must specify them in a sequence that defines a continuous +slide line. The nodal sequence defines a tangent vector +for the slide line. The slide line must be made +up of linear segments. +Input File Usage: +*SLIDE LINE, ELSET=element_set_name, TYPE=LINEAR +first node number, second node number, etc. +M L +Nodes i, j, k, l, m, and n are specified in that order, thereby identifying a slide line progressing +from i to node n. These nodes must lie on the outer tube. ITT-type elements are defined on +nodes I, J, K, ... and interact with the slide line. +Figure 39.3.1–1 Internal tube-to-tube contact example. +Generating the slide line nodes +Alternatively, you can indicate that the slide line nodes should be generated and specify only a first node +number, a last node number, and an increment between node numbers. +Input File Usage: +*SLIDE LINE, GENERATE +first node number, last node number, increment between node numbers +Smoothing the slide line +Convergence is often improved by smoothing the discontinuities in surface tangents between slide line +segments, thereby providing a smoothly varying tangent along the slide line. For details about smoothing +slide lines, see “Contact formulations in Abaqus/Standard,” Section 37.1.1. +Defining nondefault mechanical surface interactions with tube-to-tube contact elements +By default, Abaqus/Standard uses “hard,” frictionless contact with tube-to-tube contact elements. You +can assign optional mechanical surface interaction models. The following mechanical surface interaction +models are available: +• Friction. See “Frictional behavior,” Section 36.1.5, for details. +• Modified “hard” contact, softened contact, and viscous damping. See “Contact pressure-overclosure +relationships,” Section 36.1.2, and “Contact damping,” Section 36.1.3, for details. +39.3.2 +TUBE-TO-TUBE CONTACT ELEMENT LIBRARY +Product: Abaqus/Standard +References +• “Tube-to-tube contact elements,” Section 39.3.1 +• *INTERFACE +• *SLIDE LINE +Overview +This section provides a reference to the tube-to-tube contact elements available in Abaqus/Standard. +Element types +ITT21 +ITT31 +Tube-to-tube element for use with two-dimensional beam and pipe elements +Tube-to-tube element for use with three-dimensional beam and pipe elements +Active degrees of freedom +ITT21: 1, 2 +ITT31: 1, 2, 3 +Additional solution variables +ITT21: Two additional variables relating to the contact forces. +ITT31: Three additional variables relating to the contact forces. +Nodal coordinates required +ITT21: X, Y +ITT31: X, Y, Z +Element property definition +Input File Usage: +Use the following option to identify the second (outer) pipe with which the +specified ITT contact elements on the first (inner) pipe can interact: +*SLIDE LINE +Use the following option to give the radial clearance between the pipes as a +positive number when modeling a tube sliding within another tube: +*INTERFACE +pipes, the sum of the external radii of the pipes is given as a negative number. +ITT ELEMENT LIBRARY +Element-based loading +None. +Element output +Stress components +S11 +S12 +S13 +Normal component of the force between the two pipes. +Shear force between the two pipes, parallel to the axis of the second (outer) pipe. +Shear force between the two pipes, normal to the contact direction and to the axis of +the second (outer) pipe (for ITT31 only). +Strain components +E11 +E12 +E13 +Overclosure of the surfaces in the direction normal to the tangent to the centerline of +the second (outer) pipe. +Accumulated relative tangential motion between the two pipes, parallel to the axis +of the second (outer) pipe. +Accumulated relative tangential motion between the two pipes, normal to the contact +direction and to the axis of the second (outer) pipe (for ITT31 only). +Outer pipeline nodes +(Slide line) +Node ordering and integration point numbering +2-D internal tube contact +Inner pipeline nodes and +integration points +(ITT21 element) +2-D external tube contact +First pipeline nodes and +integration points +(ITT21 element) +Second pipeline nodes +(Slide line) +3-D internal tube contact +Inner pipeline nodes and +integration points +(ITT31 element) +3-D external tube contact +First pipeline nodes and +integration points +(ITT31 element) +39.3.2–4 +Abaqus Version 6.12 ID: +Printed on: +Outer pipeline nodes +39.4 +Slide line contact elements +• “Slide line contact elements,” Section 39.4.1 +• “Axisymmetric slide line element library,” Section 39.4.2 +39.4.1 +SLIDE LINE CONTACT ELEMENTS +Product: Abaqus/Standard +References +• “Axisymmetric slide line element library,” Section 39.4.2 +• *INTERFACE +• *SLIDE LINE +Overview +Slide line elements: +• can model the finite-sliding interaction between two deforming bodies when the sliding occurs along +a line (“slide line”) that lies in a specific plane; +• assume that tangential motions orthogonal to a slide line are zero or small (Abaqus/Standard treats +such motions as being infinitesimal); +• can be used with axisymmetric stress/displacement elements; +• are recommended for specific applications, such as when a contact surface is the surface of a +substructure or when CAXA or SAXA elements are involved in contact; +• are available for first- and second-order elements; and +• use the same “master-slave” concepts for enforcing contact constraints seen in surface-based +contact. +For a general discussion of contact modeling, see Chapter 35, “Defining Contact Interactions.” +Modeling contact between deformable bodies with slide lines +Determining the location of the areas of contact and the surface tractions between contacting structures +are common goals of Abaqus simulations . Slide lines and slide line contact +elements can provide this information for simulations where both structures are deformable and the +finite sliding of the structures occurs along well-defined lines. +Local basis system for contact stresses and relative motions of the bodies +Abaqus/Standard reports the contact stresses between the bodies and the relative motions of the bodies +in a local basis system that is attached to the slide line surface. The local basis system is defined by the +normal to the slide line, +, and two orthogonal slip directions, +. +and +Contact stress +(including friction) +Deformable +structure +Contact area +Figure 39.4.1–1 Interaction between deformable structures. +t2 +T - stress transmitted + between the surfaces +S11 +S12 +S13 +t1 +Figure 39.4.1–2 Local system for interface contact normal and shear traction. +Defining the local basis system +The sequence of the nodes forming the slide line defines the tangent, +normal, +, where +, and is called the contact plane. Abaqus/Standard defines the slide line normal as +is the vector that is orthogonal to the contact plane. +. The plane formed by the slide line +As shown in Figure 39.4.1–3, a slide line is created using nodes i, j, k, …, p, which are specified in +that order, thereby identifying the slide line tangent. Nodes I, J, K, …, N are the nodes of the slide line +elements that are associated with this slide line. The slide line normal +is defined by specifying , the +normal to the contact plane. +contact plane +ISL element +I +slide line +Figure 39.4.1–3 Defining the local basis for a slide line. +The tangent to the slide line coincides with the first slip direction, +, of the local basis system. The +second slip direction, +, is in the opposite direction of +. +The master-slave concept for slide lines and slide line elements +When creating a model that contains slide line elements, it is useful to remember that Abaqus/Standard +uses a strict “master-slave” concept to enforce the contact constraints. The slide line contact elements +form the “slave” surface. The nodes that you specify to define the slide line define the “master” surface. +The nodes of the slide line contact elements are constrained not to penetrate the master surface. +The considerations for choosing the master and slave surfaces are the same regardless of whether +surfaces or elements are used to define contact. The master surface should be chosen as the surface of +the stiffer body if the materials are different or as the surface with the coarser mesh. If the materials and +mesh density are the same on both surfaces, the choice is arbitrary. +Defining the slide line (master surface) +You can specify the nodes that make up the slide line, or they can be generated as described below. If you +choose to specify the nodes directly, you must specify them in a sequence that defines a continuous slide +line. The nodal sequence defines a tangent vector, +, for the slide line. The slide line can be made up of +linear or parabolic segments, depending on whether the model is made up of first-order or second-order +elements. In either case convergence may be improved by smoothing the slide line. +Defining a linear slide line +When the surfaces of the bodies are meshed with first-order elements, define a slide line made up of +linear element segments. As shown in Figure 39.4.1–4), nodes i, j, k, …, p are specified in that order, +thereby identifying a slide line progressing from i through p. Nodes I, J, K, …, N are the nodes of the +ISL-type elements that are associated with this slide line. +Input File Usage: +*SLIDE LINE, ELSET=element_set_name, TYPE=LINEAR +first node number, second node number, etc. +I +Figure 39.4.1–4 First-order (linear) slide line example. +Defining a parabolic slide line +When the surfaces of the bodies are meshed with second-order elements, define a slide line made up of +second-order element segments. In this case the slide line should consist of an odd number of nodes. +As shown in Figure 39.4.1–5, nodes i, j, k, …, u are specified in that order, thereby identifying a slide +line progressing from i through u. Nodes I, J, K, …, O are the nodes of the ISL-type elements that are +associated with this slide line. +Input File Usage: +*SLIDE LINE, ELSET=element_set_name, TYPE=PARABOLIC +first node number, second node number, etc. +I +Figure 39.4.1–5 Second-order (parabolic) slide line example. +Generating the slide line nodes +Alternatively, you can indicate that the slide line nodes should be generated and specify only a first node +number, a last node number, and an increment between node numbers. +Input File Usage: +*SLIDE LINE, ELSET=element_set_name, GENERATE +first node number, last node number, increment between node numbers +Smoothing the slide line +Convergence is often improved by smoothing the discontinuities in surface tangents between slide line +segments, thereby providing a smoothly varying tangent along the slide line. For details about smoothing +slide lines, see “Contact formulations in Abaqus/Standard,” Section 37.1.1. +Defining slide line elements (slave surface) +Many finite-sliding contact simulations can use the surface-based contact approach, described in +Chapter 35, “Defining Contact Interactions,” to define the model. Axisymmetric stress/displacement +and coupled temperature-displacement slide line elements are recommended only for specific +applications, such as when a contact surface is the surface of a substructure or when CAXA or SAXA +elements are involved in contact . +The slide line contact elements define the slave surface. The contact area associated with each node +on the slave surface is calculated using the current length of the slide line contact element and the constant +“width” assigned to the element, which depends on the underlying finite elements. +Associating the slide line elements with a slide line +You must associate the slide line with a set of slide line contact elements. Details on defining slide lines +are discussed below. +Input File Usage: +*SLIDE LINE, ELSET=element_set_name +Defining the slide line element’s section properties +You must associate the section properties with a set of slide line elements. +There are no section data for axisymmetric slide line elements. +*INTERFACE, ELSET=element_set_name +Input File Usage: +Defining nondefault mechanical surface interactions with slide line elements +By default, Abaqus/Standard uses “hard,” frictionless contact with slide line elements. You can assign +optional mechanical surface interaction models. The following mechanical surface interaction models +are available: +• Friction. See “Frictional behavior,” Section 36.1.5, for details. +• Modified “hard” contact, softened contact, and viscous damping. See “Contact pressure-overclosure +relationships,” Section 36.1.2, and “Contact damping,” Section 36.1.3, for details. +Obtaining the “maximum torque” that can be transmitted across axisymmetric slide lines +When modeling contact with slide lines with axisymmetric elements (type CAX and CGAX elements), +Abaqus/Standard can calculate the maximum torque that can be transmitted across the axisymmetric slide +lines. This capability is often of interest when modeling threaded connectors. The maximum torque, T, +is defined as +where p is the pressure transmitted across the interface, r is the radius to a point on the interface, and s is +the current distance along the interface in the r–z plane. This definition of “torque” effectively assumes +a friction coefficient of unity. +You can request that this torque output be written to the data (.dat) file. The data are provided for +every slide line in the model. You can specify the output frequency to limit how often Abaqus/Standard +writes this output to the data file. The default output frequency is 1. +For surface-based contact with axisymmetric elements, output variable CTRQ provides +functionality similar to this torque output request . +Input File Usage: +*TORQUE PRINT, FREQUENCY=n +39.4.2 +AXISYMMETRIC SLIDE LINE ELEMENT LIBRARY +Product: Abaqus/Standard +References +• “Slide line contact elements,” Section 39.4.1 +• *INTERFACE +• *SLIDE LINE +Overview +This section provides a reference to the axisymmetric slide line elements available in Abaqus/Standard. +Element types +ISL21A +ISL22A +2-node element for use with first-order axisymmetric elements +3-node element for use with second-order axisymmetric elements +Active degrees of freedom +1, 2 at the nodes +Additional solution variables +Two additional variables at each node relating to the contact stresses. +Nodal coordinates required +r, z +Element property definition +Input File Usage: +Use the following option to identify the slide line (master surface) with which +the slide line elements interact: +*SLIDE LINE +Use the following option to define the slide line element’s section properties: +*INTERFACE +Element-based loading +None. +Element output +Stress components +S11 +S12 +Pressure between the node on the body and the slide line with which it interacts. +Shear stress between the node on the body and the slide line with which it interacts. +Strain components +E11 +E12 +Separation between the node on the body and the slide line. +Accumulated relative tangential displacement between the node on the body and the +slide line. +Node ordering and integration point numbering +2 - node element +linear element +master surface +(defined as a +slide line) +integration points +quadratic element +3 - node element +integration points +master surface +(defined as a +slide line) +39.5 +Rigid surface contact elements +• “Rigid surface contact elements,” Section 39.5.1 +• “Axisymmetric rigid surface contact element library,” Section 39.5.2 +39.5.1 +RIGID SURFACE CONTACT ELEMENTS +Product: Abaqus/Standard +References +• “Axisymmetric rigid surface contact element library,” Section 39.5.2 +• “Analytical rigid surface definition,” Section 2.3.4 +• *INTERFACE +• *RIGID SURFACE +Overview +Rigid surface contact elements: +• can be used to model contact between a rigid surface and a deformable body; +• are needed only for several special-purpose applications, such as when a substructure contacts a +rigid surface or when CAXA or SAXA element types are involved in contact; +• can be used in both geometrically linear and nonlinear simulations; and +• use the same “master-slave” concepts for enforcing contact constraints that are used in the surface- +based contact capability in Abaqus/Standard. +For most problems the surface-based contact capability described in Chapter 35, “Defining Contact +Interactions,” provides a more direct and general method for modeling contact between a rigid surface +and a deformable body. +Modeling contact between rigid surfaces and rigid surface contact elements +Determining the location of the areas of contact and the surface tractions between contacting structures +are common goals of Abaqus simulations. Rigid surface contact elements can be used to model contact +when one of the structures is assumed to be rigid. These elements need to be used only for specific +applications, outlined below, because the surface-based contact definitions in Abaqus can be used for +most simulations. +Modeling contact with axisymmetric rigid surface contact elements +Axisymmetric rigid surface contact elements should be used only in the following specific applications: +• when the deformable surface is on a substructure , or +• when CAXA or SAXA elements are involved in contact . +Other planar, axisymmetric, or three-dimensional problems should use the surface-based contact +capability. +Local basis system for contact stress and relative motions of the surfaces +Abaqus/Standard reports the contact stresses between the bodies and the relative motions of the bodies +in a local basis system that is attached to the rigid surface. The normal +to the rigid surface, which is +also the contact direction, is defined when the rigid surface is created. For details, see “Analytical rigid +In axisymmetric problems Abaqus/Standard defines the first local +surface definition,” Section 2.3.4. +tangent to lie in the plane of the model and the second orthogonal to this plane. +The master-slave concept for rigid surface contact elements +Rigid surface contact elements use a “master-slave” concept to enforce the contact constraints. The rigid +surface contact elements form the “slave” surface, and the nodes of these elements are constrained not +to penetrate into the rigid (“master”) surface. +Defining the rigid surface +You define the analytical rigid surface using the methods described in “Defining analytical rigid surfaces +when drag chain or rigid surface elements are used” in “Analytical rigid surface definition,” Section 2.3.4. +Assigning a rigid body reference node to the rigid surface +The motion of a rigid surface is controlled by the motion of a single node, referred to as the rigid body +reference node, that is associated with the rigid surface. When rigid surface contact elements are used +in a model, the rigid body reference node is identified when defining the IRS elements . +Defining the rigid surface contact elements +The rigid surface contact elements define the slave surface. They also define the rigid body reference +node for the rigid surface with which they interact. All IRS elements identify the rigid body reference +node by including its node number as the last node in their connectivity. The nodes on the deformable +body that form the IRS elements are always given first. +In a model defined in terms of an assembly of part instances, the rigid surface definition and the +reference node must appear inside the same part definition as the rigid surface contact elements. +Example +For example, the following input would be used to define IRS elements 1 and 2 that consist of two nodes +on the deformable body and assign node 1000 as the rigid body reference node: +*ELEMENT, TYPE=[IRS21A], ELSET=element_set_name +1, 10, 11, 1000 +2, 11, 12, 1000 +*RIGID SURFACE, ELSET=element_set_name +A similar input structure is used for IRS22A elements. +Associating an analytical rigid surface with a set of rigid surface contact elements +You must identify the set of rigid surface contact elements that interact with a particular rigid surface. +*RIGID SURFACE, ELSET=element_set_name +Input File Usage: +Defining the rigid surface element’s section properties +You must associate the section properties with a set of rigid surface contact elements. +There are no section data for axisymmetric rigid surface contact elements. +Input File Usage: +*INTERFACE, ELSET=element_set_name +Defining nondefault mechanical surface interactions with rigid surface contact elements +By default, Abaqus/Standard uses a “hard,” frictionless mechanical surface interaction model with rigid +surface contact elements. You can assign optional mechanical surface interaction models. The following +mechanical surface interaction models are available: +• Friction. See “Frictional behavior,” Section 36.1.5, for details. +• Modified “hard” contact, softened contact, and viscous damping. See “Contact pressure-overclosure +relationships,” Section 36.1.2, and “Contact damping,” Section 36.1.3, for details. +39.5.2 +AXISYMMETRIC RIGID SURFACE CONTACT ELEMENT LIBRARY +Product: Abaqus/Standard +References +• “Analytical rigid surface definition,” Section 2.3.4 +• “Rigid surface contact elements,” Section 39.5.1 +• *RIGID SURFACE +• *INTERFACE +Overview +This section provides a reference to the axisymmetric rigid surface contact elements available in +Abaqus/Standard. +Element types +IRS21A +IRS22A +Axisymmetric rigid surface contact element for use with first-order axisymmetric +elements +Axisymmetric rigid surface contact element for use with second-order axisymmetric +elements +Active degrees of freedom +1, 2 at each node except the last node +1, 2, 6, the motion of the rigid body reference node, at the last node +Additional solution variables +Two additional variables at each node relating to the contact stresses. +Nodal coordinates required +r, z +Element property definition +Input File Usage: +Use the following option to define the surface with which the elements interact: +*RIGID SURFACE +Use the following option to define the rigid surface element’s section properties: +*INTERFACE +Element-based loading +None. +Element output +S11 +S12 +E11 +E12 +Pressure between the element and the rigid surface in the direction of the normal to +the rigid surface. +Shear component of the stress between the element and the rigid surface in the +direction of the tangent to the rigid surface. +Separation of the surfaces in the direction of the normal to the rigid surface at the +closest point of the surface to the integration point on the element. +Accumulated relative tangential displacement of the surfaces. +Node ordering on elements +The first two nodes in IRS21A and the first three nodes in IRS22A are on the deforming mesh. The last +node is the rigid body reference node that defines the motion of the rigid body. +Numbering of integration points for output +The integration points are located at the nodes that lie on the surface of the deforming model and are +numbered correspondingly. +40. +Defining Cavity Radiation in Abaqus/Standard +Defining cavity radiation +40.1 +Defining cavity radiation +• “Cavity radiation,” Section 40.1.1 +40.1.1 +CAVITY RADIATION +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “Heat transfer analysis procedures: overview,” Section 6.5.1 +• *CAVITY DEFINITION +• *COUPLED THERMAL-ELECTRICAL +• *CYCLIC +• *EMISSIVITY +• *HEAT TRANSFER +• *MOTION +• *PERIODIC +• *PHYSICAL CONSTANTS +• *RADIATION FILE +• *RADIATION PRINT +• *RADIATION OUTPUT +• *RADIATION SYMMETRY +• *RADIATION VIEWFACTOR +• *REFLECTION +• *SURFACE +• *SURFACE PROPERTY +• *VIEWFACTOR OUTPUT +• “Cavity radiation,” Section 2.11.4 of the Abaqus Theory Manual +• “Defining a cavity radiation interaction,” Section 15.13.21 of the Abaqus/CAE User’s Manual, in +the online HTML version of this manual +• “Defining a cavity radiation interaction property,” Section 15.14.3 of the Abaqus/CAE User’s +Manual, in the online HTML version of this manual +Overview +Abaqus/Standard provides a cavity radiation capability for modeling heat transfer effects due to radiation +in enclosures. This cavity radiation functionality: +• can be included in heat transfer analysis problems without deformation (“Uncoupled heat transfer +analysis,” Section 6.5.2, and “Coupled thermal-electrical analysis,” Section 6.7.3); +• is provided for two-dimensional, three-dimensional, and axisymmetric cases; +• accounts for symmetries, surface blocking, and surface motion within cavities; and +• can include closed cavities or open cavities (implying that some radiation takes place to an exterior +medium). +Cavity radiation equations are not symmetric; therefore, the nonsymmetric matrix storage and solution +scheme is invoked automatically in models that include cavity radiation . Each cavity +defines a viewfactor matrix involving the geometric relations between the surfaces in the enclosure. +These matrices may be updated a number of times during the analysis (due to moving surfaces in the +cavity). Therefore, large cavity radiation problems may be computationally expensive. Instead, you +should consider using: +• gap radiation for modeling radiation between +closely spaced surfaces; +• average-temperature radiation conditions for modeling enclosures that are approximately +isothermal, with constant emissivity, and do not require blocking or reflection considerations ; or +• parallel cavity decomposition for parallel calculation of viewfactors and solution of the radiative +heat transfer equations . +Defining a cavity radiation problem +Since cavity radiation effects are calculated only in heat transfer and coupled thermal-electrical +procedures, the only kind of thermal-stress analysis that can include these effects is sequentially coupled +thermal-stress analysis . Moreover, +unless you allow cavity parallel decomposition , +there is a software limit of 16,000 nodes and facets in Abaqus/Standard. +Model definition +When you define the model for a cavity radiation problem, you must: +1. define all of the surfaces in the cavity ; +2. define the radiation properties of each surface (i.e., the emissivity) and the physical constants ; and +3. construct cavities from the surfaces . +History definition +In the first step of a cavity radiation analysis you must associate with each cavity a radiation viewfactor +definition, which controls the calculation of viewfactors for the cavity. You then may: +1. define cavity symmetries, if any ; +2. prescribe the motion of surfaces ; +3. define boundary conditions such as temperature and forced convection ; +4. control the cavity radiation and viewfactor calculations in each step (the specifications from the +previous step are used if they are not redefined in a step; see “Controlling viewfactor calculation +during the analysis”); +5. request output of heat transfer variables to the data and results files ; and +6. request output of the radiation viewfactor matrices . +If any of the above are included in your analysis, they must be defined within a heat transfer or coupled +thermal-electrical step definition. +Defining surfaces +Cavities are defined in Abaqus/Standard as collections of surfaces, which are composed of facets. In +axisymmetric and two-dimensional cases a facet is a side of an element; in three-dimensional cases a +facet is a face of a solid element or a surface of a shell element. Rigid surfaces cannot be used in cavity +radiation problems. +Surfaces are defined as described in “Element-based surface definition,” Section 2.3.2. You may +associate each surface with a surface property definition as part of the surface option, or you may associate +surfaces with surface properties as part of the cavity definition option. The surface properties are defined +as described below. +Input File Usage: +Use the following option to define a surface with a surface property for use in +a cavity radiation analysis: +*SURFACE, TYPE=ELEMENT, NAME=surface_name, +PROPERTY=property_name +Use the following option to define a surface for use in a cavity radiation analysis +in which surface properties are defined as part of the cavity definition: +Abaqus/CAE Usage: +*SURFACE, TYPE=ELEMENT, NAME=surface_name +Interaction module: Create Interaction: Cavity radiation: +select the initial surface region +Restrictions +Surfaces that are associated with cavity radiation are subject to the following restrictions in addition to +the general surface definition restrictions outlined in “Element-based surface definition,” Section 2.3.2: +• Surfaces cannot overlap because of the ambiguity that would result in the associated property +definitions and in the blocking specification. +• A surface can be used only in one cavity definition (the same surface cannot appear in two different +cavities). +In addition, the three-dimensional quadrilateral facets should be as close to planar as possible; otherwise, +the quality of the viewfactor calculations will be compromised. +Controlling spurious spatial oscillations +The radiation flux for each facet is calculated based on the average of the nodal temperatures on that +facet . This value of radiation flux +is then distributed to each node in proportion to its area. Consequently, the mesh must be sufficiently +fine that temperature differences across elements are small. Otherwise, computed fluxes at nodes with +temperatures above the facet average will be excessively low, and the fluxes at nodes with below-average +temperatures will be too high. This tends to induce a spatially oscillatory solution. This effect can be +eliminated by reducing the element size in the vicinity of high temperature gradients. +Defining surface radiation properties +Cavity radiation problems are intrinsically nonlinear, due to the dependence of the radiative flux on +the fourth power of the facet temperature. Further, nonlinearity can be introduced by describing the +emissivity, +, as a function of temperature. +Defining the emissivity +Emissivity is a dimensionless quantity with a value that is greater than or equal to zero and less than or +equal to one. A value of +corresponds to all radiation being reflected by the surface. A value of +corresponds to black body radiation, where all radiation is absorbed by the surface. You can define +, of a surface as a function of temperature and other predefined field variables. +the emissivity, +You must assign a name to the surface property that defines the emissivity. +Input File Usage: +Use both of the following options to define the emissivity of a surface: +*SURFACE PROPERTY, NAME=property_name +*EMISSIVITY +The *EMISSIVITY option must appear directly after +PROPERTY option in the model definition section of the input file. +the *SURFACE +If black body radiation is being defined ( +used in the step definition to improve efficiency: +), the following option can be +Abaqus/CAE Usage: +*RADIATION VIEWFACTOR, REFLECTION=NO +Use the following input to define gray body radiation: +Interaction module: Create Interaction Property: Cavity radiation: +enter the emissivity ( ) +You can define the emissivity as a function of temperature and/or field variables. +Use the following input to define black body radiation: +Interaction module: Create Interaction: Cavity radiation: +Use heat reflection: No +Controlling the accuracy of temperature-dependent emissivity changes +Abaqus/Standard evaluates the emissivity, +, based on the temperature at the start of each increment and +uses that emissivity value throughout the increment. When emissivity is a function of temperature or field +variables, you can control the time incrementation for the heat transfer or coupled thermal-electrical step +by specifying the maximum allowable emissivity change during an increment, +. If this tolerance +is exceeded, Abaqus/Standard will cut back the increment size until the maximum change in emissivity +is less than the specified value. If you do not specify a value for +, a default value of 0.1 is used. +Input File Usage: +Use either of the following options: +Abaqus/CAE Usage: +*HEAT TRANSFER, MXDEM= +*COUPLED THERMAL-ELECTRICAL, MXDEM= +Step module: Create Step: Heat transfer or Coupled thermal-electric: +Incrementation: Automatic: Max. allowable emissivity +change per increment: +Defining the Stefan-Boltzmann constant and value of absolute zero +You must define the Stefan-Boltzmann constant, +default values for these constants. +, and the value of absolute zero, +; there are no +Input File Usage: +*PHYSICAL CONSTANTS, STEFAN BOLTZMANN= , +ABSOLUTE ZERO= +This option can appear anywhere in the model definition portion of the input +file. +Abaqus/CAE Usage: +Any module: Model→Edit Attributes→model_name. Enter values for +Absolute zero temperature and Stefan-Boltzmann constant +Constructing a cavity +You construct cavities as collections of the surfaces defined as described above. Each surface can be +used only in one cavity definition. Each cavity must have a unique name; this name is used to specify +viewfactor calculations. The cavity name can also be used to request output. +Setting surface properties +By default, a cavity is assumed to consist of surfaces for which surface properties have already been +defined. Instead, you may define surface properties as part of the cavity definition. +Input File Usage: +Use the following option to construct a cavity: +*CAVITY DEFINITION, NAME=cavity_name, SET PROPERTY +surface name, surface property name +By using the SET PROPERTY parameter, you define the surface properties +used in the cavity, overriding any property defined as part of the surface option. +Abaqus/CAE Usage: +Interaction module: Create Interaction: Cavity radiation: select the +surface region. Use the Properties table to add or edit surfaces and +cavity radiation interaction properties (emissivity). +Creating a closed cavity +By default, a cavity is assumed to be closed. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to construct a closed cavity: +*CAVITY DEFINITION, NAME=cavity_name +Interaction module: Create Interaction: Cavity radiation: +Definition: Closed +Creating an open cavity +You can specify an open cavity by defining the reference temperature of the external medium. This +ambient temperature value is converted to an absolute temperature scale based on the definition of +absolute zero. You can verify the degree of opening in the cavity by specifying a tolerance for the +accuracy of the viewfactor calculations; radiation to the external medium will take place only if the +deviation of the sum of the viewfactors from unity is more than this tolerance. See “Controlling the +accuracy of viewfactor calculations” below for details. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to create an open cavity: +*CAVITY DEFINITION, NAME=cavity_name, AMBIENT TEMP= +Interaction module: Create Interaction: Cavity radiation: Definition: +Open, Ambient temperature: +Creating a cavity with multiple openings or complex ambient conditions +The open cavity definition allows for a cavity with a single opening into an ambient environment with a +single, constant temperature value. If the cavity has multiple openings or the ambient temperature is not +constant, you should model the surroundings differently. +You should close any cavity openings with elements, and prescribe the temperatures of the external +media on these elements. Since the cavity is now closed, you should not specify an ambient temperature +with the cavity definition. The temperature definition that you use for the closing elements provides the +ambient temperature, and it allows you to specify different temperatures, including variable temperatures, +at the cavity openings. The elements modeling the external media should not share nodes with the cavity +elements (so that conduction will not take place between them). The surfaces defined by the external +media elements should have an emissivity of 1. +Decomposing large cavities in parallel +By default, Abaqus/Standard uses a single working thread for the calculation of the viewfactor matrix +and solution of the radiative heat transfer equations . This method is robust and works well for small cavities composed of hundreds of +facets, but it becomes inefficient and computationally expensive for large cavities composed of thousand +of facets. Moreover, the memory requirements for these cavities may be prohibitively large for a single +computational node (the viewfactor matrix is the size of the number of facets squared). In these cases you +should consider allowing Abaqus/Standard to decompose the cavity among all CPUs during viewfactor +calculations and solution of the radiative heat transfer equations. +Input File Usage: +Use the following option to activate cavity parallel decomposition: +*CAVITY DEFINITION, NAME=cavity_name, PARALLEL +DECOMPOSITION=ON +Abaqus/CAE Usage: +Cavity parallel decomposition is not supported in Abaqus/CAE. +Solving radiative heat transfer equations in parallel +Abaqus/Standard uses an iterative solution technique for obtaining the radiative heat fluxes when cavity +parallel decomposition is enabled. This technique is based on Krylov methods, employs a preconditioner, +and uses only MPI-based parallelization . This iterative technique is used only to solve the cavity radiation equations and does not require +user intervention. You may still opt to use the either the iterative or direct sparse solvers for the solution +of the heat transfer finite element equations. +Convergence of models with decomposed cavities +The exact cavity radiation equations are solved whether parallel decomposition is allowed or not; +however, when parallel decomposition is active, Abaqus/Standard may require more iterations to +obtain a solution. This slower rate of convergence comes from an approximation to the Jacobian (the +linearization of the radiation fluxes) that is based on small changes of the irradiation (any part not due to +emission from the surface). Models involving surfaces with low emissivities and steady-state analyses +might be especially affected. If you encounter convergence problems with parallel decomposed cavities, +you may consider +• changing the analysis from steady-state to transient +Section 6.5.2); or +(“Uncoupled heat +transfer analysis,” +• allowing more solver iterations per time increment (“Convergence criteria for nonlinear problems,” +Section 7.2.3). +Kinematic constraints on models with decomposed cavities +Kinematic constraints (for example, coupling constraints, +linear constraint equations, multi-point +constraints, or surface-based tie constraints) can be applied to any node or surface belonging to a cavity +where parallel decomposition is allowed. However, the nodes or surfaces must be the independent +(master) nodes or surfaces in the constraint definition. +Defining cavity symmetries +Taking advantage of geometric symmetry can reduce computational model size and simulation time. +Instead of modeling all of the parts or components in a symmetric assembly, you can model a smaller +repeated component and take symmetry into account in the definition of the cavity radiation interaction. +In Abaqus/Standard cavity definitions with defined symmetries take into account +the radiation +interactions between each cavity facet and between all of the facets in the cavity and all of its symmetric +images. Abaqus/Standard does not check that the model created using cavity symmetries is physically +realistic. You must check the input and results carefully to ensure that a valid model is created. +You must assign a name to each radiation symmetry definition for reference by a radiation viewfactor +definition. The radiation viewfactor definition and corresponding radiation symmetry definition must +appear in the same step. +Cyclic, periodic, and/or reflection symmetries can be defined as described below. +Input File Usage: +Use all of the following options to define symmetry in a cavity radiation +problem: +*RADIATION VIEWFACTOR, SYMMETRY=symmetry_name +*RADIATION SYMMETRY, NAME=symmetry_name +*REFLECTION and/or *PERIODIC and/or *CYCLIC +Interaction module: Create Interaction: Cavity radiation: Symmetry: +Reflection, Periodic, and/or Cyclic +Abaqus/CAE Usage: +Reflection symmetry +You define reflection symmetry to create a cavity that is composed of the user-defined cavity surface plus +its reflected image through a line or plane. You must identify the dimensionality of the cavity when you +define reflection symmetry. +Reflection of two-dimensional cavities +You can define the cavity symmetry by reflecting the cavity surface through a line, as shown in +Figure 40.1.1–1. This type of reflection can be used only with two-dimensional cavities. +Input File Usage: +Abaqus/CAE Usage: +*REFLECTION, TYPE=LINE +Interaction module: Create Interaction: Cavity radiation: Symmetry: +Reflection: select the symmetry line +Reflection of three-dimensional cavities +You can define the cavity symmetry by reflecting the cavity surface through a plane, as shown in +Figure 40.1.1–2. This type of reflection can be used only with three-dimensional cavities. +Input File Usage: +Abaqus/CAE Usage: +*REFLECTION, TYPE=PLANE +Interaction module: Create Interaction: Cavity radiation: Symmetry: +Reflection: select the symmetry plane +Reflection of axisymmetric cavities +You can define the cavity symmetry by reflecting the cavity surface through a line of constant +z-coordinate, as shown in Figure 40.1.1–3. This type of reflection can be used only with axisymmetric +cavities. +Figure 40.1.1–1 Reflection symmetry through a line. +Figure 40.1.1–2 Reflection symmetry through a plane. +Input File Usage: +Abaqus/CAE Usage: +*REFLECTION, TYPE=ZCONST +Interaction module: Create Interaction: Cavity radiation: Symmetry: +Reflection: enter the z-axis symmetry value for the line of symmetry +z = const +symmetry line +Figure 40.1.1–3 Reflection symmetry through a line +of constant z-coordinate. +Periodic symmetry +You can define cavity symmetry by periodic repetition in a given direction. Physically, periodic +symmetry is understood as an infinite number of repetitions of the same image at a periodic interval. +Numerically, periodic symmetry has to be represented by a finite number of repetitions of the periodic +image. You can define the number of repetitions used in the numerical calculation, n. +The periodic symmetry will result in a cavity composed of the user-defined cavity plus twice n +similar images, since the periodic symmetry is assumed to apply in both the positive and negative +directions. By default, n=2. +Although symmetries do not increase the size of the viewfactor matrix, they do make its calculation +more expensive. Therefore, the number of repetitions should be minimized, but the value of n should +be large enough that the viewfactor matrix is calculated accurately. Output variable VFTOT can be used +to check the amount of closure implied by the symmetry. Periodic symmetry for defining the cavity radiation viewfactor matrix does not +impose symmetry conditions automatically in the heat transfer analysis. It may be necessary to impose +appropriate constraints on the temperature and loading conditions at the nodes on the periodic symmetry +planes to obtain a meaningful solution from the underlying heat transfer analysis. +You must identify the dimensionality of the cavity when you define periodic symmetry. +Periodic symmetry of two-dimensional cavities +You can create a cavity that is composed of a series of similar images generated by repetition along a +two-dimensional distance vector, as shown in Figure 40.1.1–4. +-2d +-d +2d +n = 2 +Figure 40.1.1–4 Two-dimensional periodic symmetry. +The repeated images are bounded by lines parallel to line ab. The distance vector must be defined so +that it points away from line ab and into the domain of the model. This type of periodic symmetry can +be used only with two-dimensional cavities. +Input File Usage: +Abaqus/CAE Usage: +*PERIODIC, TYPE=2D, NR=n +Interaction module: Create Interaction: Cavity radiation: Symmetry: +Periodic: Number of periodic symmetries: n +Periodic symmetry of three-dimensional cavities +You can create a cavity that is composed of a series of similar images generated by repetition along a +three-dimensional distance vector, as shown in Figure 40.1.1–5. The repeated images are bounded by +planes that are parallel to plane abc. The distance vector must be defined so that it points away from +plane abc and into the domain of the model. This type of periodic symmetry can be used only with +three-dimensional cavities. +2d +n = 2 +-d +-2d +Figure 40.1.1–5 Three-dimensional periodic symmetry. +Input File Usage: +Abaqus/CAE Usage: +*PERIODIC, TYPE=3D, NR=n +Interaction module: Create Interaction: Cavity radiation: Symmetry: +Periodic: Number of periodic symmetries: n +Periodic symmetry of axisymmetric cavities +You can create a cavity that is composed of a series of similar images generated by repetition in the +z-direction, as shown in Figure 40.1.1–6. The repeated images are bounded by lines of constant z- +coordinate. The z-distance vector must be defined so that it points away from the z-constant periodic +symmetry reference line and into the domain of the model. This type of periodic symmetry can be used +only with axisymmetric cavities. +Input File Usage: +Abaqus/CAE Usage: +*PERIODIC, TYPE=ZDIR, NR=n +Interaction module: Create Interaction: Cavity radiation: Symmetry: +Periodic: Number of periodic symmetries: n +Cyclic symmetry +You can define cavity symmetry by cyclic repetition of the user-defined cavity surface about a point or +an axis. The cavity defined by cyclic repetition must cover 360°. +You must define the number of cyclically similar images that compose the cavity, n. The angle of +rotation about a point or axis used to create cyclically similar images is equal to 360°/n. +You must identify the dimensionality of the cavity when you define cyclic symmetry. +Cyclic symmetry of two-dimensional cavities +You can define the cavity symmetry by rotating the cavity about a point, l, as shown in Figure 40.1.1–7. +The cavity surface defined in the model must be bounded by the line lk and a line passing through l at an +2d +-d +-2d +n = 2 +z = const periodic +symm reference line +Figure 40.1.1–6 Axisymmetric periodic symmetry. +n = 4 +Figure 40.1.1–7 Cyclic symmetry about a point. +angle, measured counterclockwise when looking into the plane of the model, of 360°/n to lk. This type +of cyclic symmetry can be used only for two-dimensional cavities. +Input File Usage: +Abaqus/CAE Usage: +*CYCLIC, TYPE=POINT, NC=n +Interaction module: Create Interaction: Cavity radiation: +Symmetry: Cyclic: toggle on Use cyclic symmetric, +Total number of sectors: n +Cyclic symmetry of three-dimensional cavities +You can define the cavity symmetry by rotating the cavity about an axis, lm, as shown in Figure 40.1.1–8. +The cavity surface defined in the model must be bounded by the plane lmk and a plane passing through +the line lm at an angle, measured clockwise when looking from l to m, of 360°/n to lmk. Line lk must be +normal to line lm. This type of cyclic symmetry can be used only for three-dimensional cavities. +n = 8 +Figure 40.1.1–8 Cyclic symmetry about an axis. +Input File Usage: +Abaqus/CAE Usage: +*CYCLIC, TYPE=AXIS, NC=n +Interaction module: Create Interaction: Cavity radiation: Symmetry: +Cyclic: toggle on Use cyclic symmetric, +Total number of sectors: n +Combining symmetries +Reflection, periodic, and cyclic symmetries can be combined as shown in Table 40.1.1–1. +Figure 40.1.1–9 through Figure 40.1.1–12 illustrate some possible symmetry combinations. +Table 40.1.1–1 Permissible number of symmetry definitions used in combination. +Reflection +Periodic +Cyclic +2-D +3-D +Axi +Restrictions +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +• +, +, +, +, +, +are normals to lines or planes of reflection symmetry. +are distance vectors used to define periodic symmetry. +is the direction of the axis of cyclic symmetry in three-dimensional cases. +a 2 +n1 +b1 +n2 +b2 +a 1 +Figure 40.1.1–9 Combination of two reflection symmetries in two dimensions. +a1 +1d +(n=3) +b2 +a2 +2d (n=2) +b1 +Figure 40.1.1–10 Combination of two periodic symmetries in two dimensions. +d (n=2) +b1 +a1 +a2 +b2 +Figure 40.1.1–11 Combination of one reflection symmetry +and one periodic symmetry in two dimensions. +10 d +-10 d +n = 4 (cyclic) +n = 10 (periodic) +Figure 40.1.1–12 Combination of one cyclic symmetry and +one periodic symmetry in three dimensions. +Prescribing motion during a cavity radiation analysis +In many cavity radiation problems such as simulations of manufacturing sequences, radiation viewfactors +change because surfaces are moved during the analysis. You can specify surface motions during heat +transfer or coupled thermal-electrical analysis. +The prescribed motions affect only the calculation of viewfactors (and, therefore, radiation fluxes) +in heat transfer due to cavity radiation. They do not affect heat conduction, storage, or distributed flux +contributions. +You can define both the translational and rotational components of the motion within a step +independently. For example, you can prescribe the translational motion of a node set according to +a certain amplitude function and then prescribe the rotational motion of the node set according to a +different amplitude function. In each step, each component of motion can be specified only once for +any particular node. +Motions can also be prescribed during steps in which the cavity radiation is turned off, as described +below. +Translational motion +Translations, +, are specified in terms of global x-, y-, and z-components unless a local coordinate system +is defined at the nodes for which motion is specified; then translations are specified in terms of local x-, +y-, and z-components . +Translational displacements are always specified as total values of translational motion. This +treatment of translations is consistent with that used for displacement boundary conditions (“Boundary +conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1) in stress/displacement analyses. +The default is to apply translational motion. +Translational velocities can also be specified. Translational velocities always refer to the current +step; therefore, the rate of translational motion specified as a velocity is in effect only during the step for +which it is defined. This behavior is different from velocity boundary conditions, where velocities stay +in effect in subsequent steps if they are not redefined. +Input File Usage: +Use either of the following options to prescribe translational motion: +*MOTION, TRANSLATION, TYPE=DISPLACEMENT +*MOTION, TRANSLATION, TYPE=VELOCITY +Surface motion is not supported with cavity radiation in Abaqus/CAE. +Abaqus/CAE Usage: +Rotational motion +, can be defined by specifying the magnitude of the rotation +Displacements due to a rigid body rotation, +and the rotation axis. In three dimensions the rotation axis is defined by specifying two points, +and , +on the axis of rotation. In two dimensions the rotation axis is assumed to be normal to the plane of the +model and is defined by specifying one point, +. +The coordinates of the points defining the axis of rotation must be defined in the configuration at +the beginning of the step for which rigid body rotation is being defined. +Motion due to rigid body rotation during a step is specified as the amount of rotation that takes place +during that step only. Therefore, the rigid body rotation specified during a step is local to that step; if no +rigid body rotation is specified in the following step, no further rotation occurs. +The treatment of rigid body rotations is different from that of translations: rigid body rotations are +specified incrementally from step to step while translations are specified as total values. +Input File Usage: +Use either of the following options to prescribe rotational motion: +Abaqus/CAE Usage: +*MOTION, ROTATION, TYPE=DISPLACEMENT +*MOTION, ROTATION, TYPE=VELOCITY +Surface motion is not supported with cavity radiation in Abaqus/CAE. +Prescribing large rotational motions +radians or complex sequences of rotations about +Prescribed rotational motions of more than +different directions in three-dimensional models are most simply defined by specifying rotational +velocities, which allows the definition to be given in terms of the angular velocity instead of the total +rotation. Abaqus/Standard calculates the increment of rotation as the average of the angular velocities +at the beginning and end of each increment multiplied by the time increment. +Section 1.2.2.) +, 18.84955592, 0., 0., 0., 0., 0., 1. +The angular velocity will be constant since the default variation for motions prescribed using a predefined +velocity field in a heat transfer or coupled thermal-electrical step (both steady-state and transient) is a step +function . An amplitude reference could be used to specify +other variations of the angular velocity. +If, in the next step, the same node (or node set) should have an additional rotation of +radians +about the global x-axis, assuming again a step time of 1.0, prescribe a constant angular velocity as follows: +*MOTION, TYPE=VELOCITY, ROTATION +node (node set), 1.570796327, 0., 0., 0., 1., 0., 0. +Prescribing simultaneous rigid body rotations +Motions involving two or more simultaneous rigid body rotations about different axes cannot be specified +directly. An example of simultaneous rigid body rotations is a satellite rotating about its own axis while +orbiting the earth. Such complex motions can be defined with user subroutine UMOTION. This subroutine +allows specification of the time variation of the magnitude of the translational components of the motion +(degrees of freedom 1–3) at each node. +If you specify the magnitude of the translation as part of the prescribed motion definition, it will be +modified by the amplitude curve (if any) and passed into subroutine UMOTION, where it can be redefined. +When user subroutine UMOTION is used to define the motion of a certain node set in a step, only +one prescribed motion can be defined in that step for that node set. The complete motion of all nodes in +the node set during the step must be defined in the user subroutine. +Input File Usage: +Abaqus/CAE Usage: +*MOTION, USER +Surface motion is not supported with cavity radiation in Abaqus/CAE. +Simultaneous translational and rotational motion +Whenever simultaneous translational and rotational motion is specified, the total motion of a node during +step k is defined as +where +of the node, +and +is the current location of the node due to the specified motion history, +is the original location +is the displacement of the node due to the translational motion specified in the step, +is the displacement of the node due to rigid body rotation during step i. +In these cases the translation is applied first and the rotation is then assumed to be about the translated +due to rigid body rotation during step i is computed +(material) axis. In other words, the displacement +as the rotation about an axis defined by points +and +where +In the preceding equations +the prescribed rotational motion (they refer to the configuration at the beginning of step i) and +the displacement due to translational motion during the step ( +is the time at the end of step +are the locations of the points used to define the axis of rotation for +is +, where +and +). +Example +As an example, consider a three-dimensional problem with x–y planar motion as shown in +Figure 40.1.1–13. +53.13 o +Figure 40.1.1–13 Planar motion example. +The centroid of the object of interest is initially located at +. In the first step the +object is translated 4 length units in the x-direction while at the same time it rotates clockwise 180° ( +radians) about the z-axis at constant angular velocity. This motion moves the object from position A to +position C in Figure 40.1.1–13. Halfway through this motion, at position B, the displacements due to +the rigid body rotation are calculated by applying the translation to the z-axis (the axis of rotation) and +then applying a 90° rotation about this translated axis. +In the second step the object is translated −3 length units in the y-direction only. This motion places +the object at position D with no additional rotation. Finally, in the third step the object is simultaneously +translated 5 length units at an angle of 53.13° to the y-direction and rotated clockwise, again at constant +angular velocity, through 180° about the z-axis. This motion returns the object to its original position. +Assuming that each step time is 1.0, the input required for the above motion sequence is as follows: +First step: +*MOTION +node set, 1, 1, 4. +*MOTION, ROTATION, TYPE=VELOCITY +node set, 3.14159265, 0., 3., 0., 0., 3., -1. +Second step: +*MOTION +node set, 2, 2, -3. +Third step: +*MOTION +node set, 1, 2, 0. +*MOTION, ROTATION, TYPE=VELOCITY +node set, 3.14159265, 4., 0., 0., 4., 0., -1. +Controlling the time variation of the motion +For any prescribed motion you can refer to an amplitude curve that gives the time variation of the motion +throughout a step . +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*AMPLITUDE, NAME=amplitude +*MOTION, AMPLITUDE=amplitude +Surface motion is not supported with cavity radiation in Abaqus/CAE. +Controlling the frequency of viewfactor recalculation due to motion +You can control how viewfactors are recalculated during a step as a result of prescribed motion by +specifying a value for the maximum allowable motion, max, for a particular node set. Viewfactor +recalculation is triggered if a displacement component at any node in the specified node set exceeds the +specified value for max. +You must respecify the value of max and the node set in every step where recalculation is required; +the values do not remain in effect for subsequent steps. +Viewfactor recalculation can be expensive; use discretion when choosing a value for max. +Input File Usage: +*RADIATION VIEWFACTOR, MDISP=max, NSET=nset +The max and nset values must always be specified together. +Abaqus/CAE Usage: +Viewfactor recalculation due to motion is not supported with cavity radiation +in Abaqus/CAE. +Controlling viewfactor calculation during the analysis +The cavity radiation capability can be used in applications such as the simulation of manufacturing +sequences where radiation viewfactors change during the simulation. Therefore, radiation viewfactor +definitions provide significant flexibility for the control of viewfactor calculations during a step. +Multiple radiation viewfactor definitions can be specified within a step definition if different types +of radiation and viewfactor calculations are required for different cavities. Different types of viewfactor +calculations can be specified for the same cavity in different steps of the analysis. +By default, viewfactors are calculated at the beginning of the first step that includes a radiation +viewfactor definition. Viewfactors are recalculated at the beginning of a subsequent step only if the +viewfactor definition changes in that step; for example, if different surface blocking checks are specified +for the same cavity. In a restart analysis Abaqus/Standard reads the radiation viewfactors from the user- +specified restart step and increment and recalculates the viewfactors only if the viewfactor definitions +have changed. +You can specify the name of the cavity for which radiation viewfactor control is being specified. If +you do not specify a cavity name, the radiation viewfactor definition applies to all cavities in the model. +Input File Usage: +Abaqus/CAE Usage: +*RADIATION VIEWFACTOR, CAVITY=cavity_name +Radiation viewfactors are defined separately for each cavity radiation +interaction and apply to all steps in which that interaction is active. +Activating and deactivating cavity radiation +There are practical situations in which it may be useful to switch cavity radiation effects on and off during +the analysis. For example, radiation may be taking place in a cavity that is then filled with a fluid so that +radiation is no longer significant; later in the analysis, radiation may resume when the fluid is drained +from the cavity. In such cases you can use a radiation viewfactor definition to switch the radiation on +and off in any particular cavity during one or more steps of the analysis. +When cavity radiation is switched back on after having been switched off, Abaqus/Standard will +use the last viewfactors calculated in the last step in which cavity radiation was active. However, if +motion is prescribed during the time that the cavity radiation is switched off and one of the displacement +components of a node in the specified node set exceeds the value for the maximum allowable motion, +max, specified in the step during which cavity radiation is switched off, the viewfactors will be +recalculated at the beginning of the step in which the cavity radiation is switched back on. +Input File Usage: +Use the following option to turn viewfactor calculation off for a step: +*RADIATION VIEWFACTOR, OFF +Use one of the following options to turn viewfactor calculation back on in a +subsequent step: +*RADIATION VIEWFACTOR +*RADIATION VIEWFACTOR, MDISP=max, NSET=nset +Abaqus/CAE Usage: +Radiation viewfactors cannot be turned off or on for a selected step. You can +use the following options to turn a cavity radiation interaction off or on: +Interaction module: Interaction Manager: select a step and a cavity +radiation interaction, Activate or Deactivate +Controlling the accuracy of viewfactor calculations +Abaqus/Standard uses a progressive integration scheme for viewfactor calculation. When facets are +sufficiently far from each other, a lumped area approximation is used. If the facets are close to each other +but one of the facets is much larger than the other, an infinitesimal-to-finite approximation is used. For +all other cases a contour integral is numerically calculated to compute the viewfactor. See “Viewfactor +calculation,” Section 2.11.5 of the Abaqus Theory Manual, for details. +Two nondimensional parameters are calculated for each facet pair to determine which integration +scheme is used: +and +is the area of the smaller facet, +is the area of the larger facet, and d is the distance +where +between their centroids. The lumped area approximation is used whenever the nondimensional distance +square parameter +, an infinitesimal-to-finite area +has a default value of 5.0. If +approximation is used if the facet area ratio +has a default value of 64.0. Otherwise, +a more precise calculation is performed, involving the numerical integration of a contour integral. +, where +, where +and +You can customize the accuracy and speed of the viewfactor calculation by specifying the +and the number of integration points per edge. For example, Abaqus/Standard +is set to zero. Likewise, the +are +parameters +will used lumped area approximations throughout the whole model if +more precise, albeit more expensive, numerical integration method will always be used if +set to very large numbers. +and +Input File Usage: +*RADIATION VIEWFACTOR, LUMPED AREA=P1, +INFINITESIMAL=P2, INTEGRATION=integration points per edge +Abaqus/CAE Usage: +Interaction module: Create Interaction: Cavity radiation: +Viewfactors: enter new values or accept the defaults for Infinitesimal +facet area ratio, Gauss integration points per edge, and +Lumped area distance-square value +Viewfactor calculation checks for closed cavities +You can provide a tolerance on the accuracy of the viewfactor calculation. In a closed cavity the sum of +the viewfactors for each cavity facet should be one. Abaqus/Standard compares the value of the specified +tolerance to the largest viewfactor matrix row sum deviation from unity; that is, +. If +the tolerance is violated for a closed cavity, the analysis is terminated. The default viewfactor tolerance +is 0.05. Failure to meet this criterion may indicate a need for mesh refinement. +Input File Usage: +*RADIATION VIEWFACTOR, VTOL=tolerance +Abaqus/CAE Usage: +Interaction module: Create interaction: Cavity radiation: +Viewfactors: Accuracy tolerance: tolerance +Viewfactor calculations in cavities with symmetries +The viewfactor calculations account for the closure of a cavity implied by any cavity symmetries. For +cavities without periodic or cyclic symmetries the viewfactors are calculated exactly for two-dimensional +geometries, but approximations are made for axisymmetric and three-dimensional geometries. These +approximations become less accurate as the distance between surfaces decreases. Define heat radiation +to model closely spaced surfaces . +Viewfactor calculations in open cavities +If the sum of the viewfactors for facets in an open cavity (defined by specifying a value for the ambient +temperature) deviates from unity by more than the specified viewfactor tolerance, radiation to the +ambience will take place. In nearly closed cavities this deviation may be small. If the tolerance is not +violated, radiation to the external medium is not included even though the cavity is defined to be open; +a warning message is issued to this effect. You can loosen the viewfactor tolerance to include such +radiation. +Controlling checks for surface blocking +is transferred between surfaces that have unobstructed direct views of each other ; “blocking” may occur in geometrically complex cavities. +Surface blocking checks may be computationally expensive in cavities with many surfaces; +therefore, significant computational time may be saved by specifying which surfaces are potential +blocking surfaces, as described below. +Viewfactor calculations with blocking surfaces are especially sensitive to mesh refinement. If a +mesh is too coarse, the viewfactors may not add up to one (in a closed cavity). To obtain accurate results, +the mesh should be refined until the viewfactors can be summed accurately. +Full blocking checks +Input File Usage: +By default, Abaqus/Standard will check for blocking of every surface with itself and all other surfaces. +*RADIATION VIEWFACTOR, BLOCKING=ALL +Interaction module: Create interaction: Cavity radiation: +Properties: Blocking surface checks: All +Abaqus/CAE Usage: +Partial blocking checks +You can specify a list of the potential blocking surfaces in the cavity. +Input File Usage: +Abaqus/CAE Usage: +*RADIATION VIEWFACTOR, BLOCKING=PARTIAL +Interaction module: Create interaction: Cavity radiation: Properties: +Blocking surface checks: Partial +Cavity with no blocking +Example of partial blocking +Another example of partial blocking +Figure 40.1.1–14 Illustrations of blocking. +No blocking checks +You can indicate that there are no blocking surfaces in the cavity; in this case Abaqus omits all checks +for blocking. +Input File Usage: +Abaqus/CAE Usage: +*RADIATION VIEWFACTOR, BLOCKING=NO +Interaction module: Create interaction: Cavity radiation: Properties: +Blocking surface checks: None +Reducing computations for surfaces that are far apart +In cases where there are many surfaces in the cavity, surfaces separated by more than a certain distance +may not be able to “see” each other for the purposes of radiation because of blocking by other surfaces. +You can specify the distance beyond which viewfactors need not be calculated, which reduces the +computational effort required for the viewfactor calculations. +Input File Usage: +Abaqus/CAE Usage: +*RADIATION VIEWFACTOR, RANGE=distance +Interaction module: Create interaction: Cavity radiation: Viewfactors: +toggle on Specify blocking range: distance +Memory usage in cavity radiation analyses +The cavity radiation heat transfer between facets of a surface in Abaqus is modeled using a full, +unsymmetric matrix defining interactions between each node and all others in the cavity. For surfaces +with large numbers of nodes this matrix may be large, resulting in memory requirements that are +significantly larger than those for the finite element portion of the analysis without the cavity radiation +interaction. +To minimize memory requirements and computational cost for cavity radiation heat transfer +analysis, the cavity can be defined using a coarser mesh of heat transfer shell elements having a single +degree of freedom per node. The overlaid element should have minimal heat capacity and conduction, +and it should be used for the definition of the cavity in place of the physical, multiple-degree-of-freedom +shell. The overlaid element should be used to define the master surface in a tied coupling constraint +(“Mesh tie constraints,” Section 34.3.1); the multiple-degree-of-freedom, physical, heat transfer shell +element forms the slave surface. +Initial conditions +By default, the initial temperature of all nodes is zero. You can specify nonzero initial temperatures in +a cavity radiation analysis; see “Defining initial temperatures” in “Initial conditions in Abaqus/Standard +and Abaqus/Explicit,” Section 33.2.1. +In a heat transfer analysis involving forced convection through the mesh, you can define nonzero +initial mass flow rates at the nodes of the forced convection/diffusion heat transfer elements in the model +. +Boundary conditions +You can specify boundary conditions to prescribe temperatures (degree of freedom 11) at the nodes +. Shell elements +have additional temperature degrees of freedom 12, 13, etc. through the thickness . Boundary conditions can be specified as functions of time by referring to amplitude +curves (“Amplitude curves,” Section 33.1.2). +For purely diffusive elements, a boundary without any prescribed boundary conditions (natural +boundary condition) corresponds to an insulated surface. For forced convection/diffusion elements, only +the flux associated with conduction is zero; energy is free to convect across an unloaded surface. This +natural boundary condition correctly models areas where fluid is crossing a surface (as, for example, at +the upstream and downstream boundaries of the mesh) and prevents spurious reflections of energy back +into the mesh. +Loads +The following types of loading can be prescribed in addition to the cavity radiation, as described in +“Thermal loads,” Section 33.4.4: +• Concentrated heat fluxes +• Body fluxes and distributed surface fluxes +• Convective film conditions and radiation conditions +Predefined fields +You cannot specify temperatures as field variables in heat transfer or coupled thermal-electrical analyses. +Boundary conditions should be used instead, as described above. +You can specify values of other user-defined field variables during the analysis. These values will +affect field-variable-dependent material properties, if any. See “Predefined fields,” Section 33.6.1. +Material options +You must define the radiation properties of the surfaces as described above in “Defining surface radiation +properties.” Other thermal properties such as conductivity, density, specific heat, and latent heat are +defined as in uncoupled heat transfer analysis—see “Uncoupled heat transfer analysis,” Section 6.5.2, +and “Thermal properties: overview,” Section 26.2.1. +You can specify internal heat generation—see “Internal heat generation” in “Uncoupled heat transfer +analysis,” Section 6.5.2. +Thermal expansion coefficients are not meaningful in cavity radiation heat transfer analysis since +deformation of the structure is not considered. +Elements +Any of the heat transfer or coupled thermal-electrical elements in Abaqus/Standard can be used +in a cavity radiation analysis, +transfer elements . +Coupled +temperature-displacement and coupled thermal-electrical-structural elements cannot be used in a cavity +radiation analysis. +including forced convection/diffusion heat +In addition to the elements that you define, Abaqus/Standard uses internal elements that are +generated automatically from your definition of radiation cavities. +Output +The following output variables are available for cavity radiation: +Surface variables +RADFL +RADFLA +RADTL +RADTLA +VFTOT +FTEMP +Radiation flux per unit area. This variable does include heat flux to ambient in an +open cavity. +Radiation flux over a facet. +Time integrated radiation per unit area. +Time integrated radiation over a facet. +Total viewfactor for a facet (sum of the viewfactor values in the row of the +viewfactor matrix corresponding to the facet). +Facet temperature. +All of the output variables are listed in “Abaqus/Standard output variable identifiers,” Section 4.2.1. +Abaqus/CAE supports motion display and can display surface- and element-based results. +Writing the viewfactor matrices to the results file +You can write the viewfactor matrices for cavity radiation interactions in heat transfer or coupled thermal- +electrical analyses to the results (.fil) file if parallel decomposition for the cavity is not enabled.. The +entire radiation viewfactor matrix is written for each cavity radiation element in the specified cavity. +You can control the frequency of viewfactor matrix output by specifying the required output +frequency in increments. The default output frequency is 1. Specify an output frequency of 0 to +suppress output. The output will always be written at the last increment of each step unless you specify +an output frequency of 0. +The record formats for the results file are described in “Results file output format,” Section 5.1.2. +The file can be written in binary or ASCII format . +Input File Usage: +Abaqus/CAE Usage: +*VIEWFACTOR OUTPUT, CAVITY=cavity_name, FREQUENCY=n +Viewfactor output is not supported in Abaqus/CAE. +Requesting surface variable output +For the cavity radiation interaction, you can request cavity-, element-, or surface-based radiation output +such as radiation fluxes, viewfactor totals for a facet, and facet temperatures to the data, results, and/or +output database files. The output requests can be repeated as often as necessary to request output for +different variables, different cavities, different surfaces, different element sets, etc. The surface variables +that can be requested are listed above. +You can specify the particular cavity, element set, or surface for which output is being requested. If +you do not specify a cavity, element set, or surface, output will be provided for all cavities in the model. +The same cavity, element set, or surface can appear in several radiation output requests. +By default, no cavity radiation data output will be provided. If you define a radiation output request +without specifying the desired output variables, all six cavity radiation surface variables will be output. +You can control the frequency of radiation output by specifying the required output frequency in +increments. The default output frequency is 1. Specify an output frequency of 0 to suppress output. The +output will always be written at the last increment of each step unless you specify an output frequency +of 0. +Input File Usage: +Use one of the following options to obtain output in the data file: +*RADIATION PRINT, CAVITY=cavity_name, FREQUENCY=n +*RADIATION PRINT, ELSET=element_set, FREQUENCY=n +*RADIATION PRINT, SURFACE=surface_name, FREQUENCY=n +Use one of the following options to obtain output in the results file: +*RADIATION FILE, CAVITY=cavity_name, FREQUENCY=n +*RADIATION FILE, ELSET=element_set, FREQUENCY=n +*RADIATION FILE, SURFACE=surface_name, FREQUENCY=n +Use the first option and one of the subsequent options to obtain output in the +output database: +*OUTPUT, FREQUENCY=n +*RADIATION OUTPUT, CAVITY=cavity_name +*RADIATION OUTPUT, ELSET=element_set +*RADIATION OUTPUT, SURFACE=surface_name +Cavity radiation output to the data file and the results file are not supported in +Abaqus/CAE. +Use the following options to obtain output in the output database: +Step module: history output request editor: Thermal: select the output variables +Abaqus/CAE Usage: +Printed output +The output tables generated by a radiation output request to the data file are organized on a surface-by- +surface basis. The rows that will appear in a particular table are defined by choosing a cavity, surface, +or element set: each row of a table corresponds to an individual element face that is part of the cavity, +surface, or element set chosen. If all of the variables in a row of a table are zero, the row is not printed. +The first column of each table is the element number, and the second column is the element face +identifier. You choose the variables to appear in the remaining columns. There is no limit to the number +of tables that can be defined. +As an example, consider a heat transfer model containing a cavity named CAV1, which, in turn, is +composed of surfaces SURF1 and SURF2. If you request output of radiation flux (RADFL) and facet +temperature (FTEMP) to the data file for this model, two tables will appear in the data file. One table +will contain RADFL and FTEMP output for all element faces composing surface SURF1, and the other +table will contain the same output variables for all element faces making up surface SURF2. +By default, Abaqus/Standard writes a summary of the maximum and minimum values in each +column of the table. You can choose to suppress this summary. In addition, you can choose to print +the total of each column in the table, which is useful, for example, to sum radiation fluxes over all facets +composing a radiation surface. By default, these totals are not printed. +Input File Usage: +Use the following option to control output of the summary information to the +data file: +*RADIATION PRINT, SUMMARY=YES or NO +Use the following option to control output of the totals to the data file: +Abaqus/CAE Usage: +*RADIATION PRINT, TOTALS=YES or NO +Cavity radiation output to the data file is not supported in Abaqus/CAE. +Input file template +The following template shows the options required for a transient, cavity radiation analysis of a closed +two-dimensional symmetric cavity. All surfaces within the cavity topcav have the same emissivity. +The surface surf2 moves (translation only) during the analysis. In the second step surface surf2 stops +moving, cavity radiation is turned off, all thermal loads except the surface convection are removed, and +a steady-state heat transfer analysis is conducted to determine the final temperature of the system. +*HEADING +… +*PHYSICAL CONSTANTS, ABSOLUTE ZERO= , STEFAN BOLTZMANN= +*SURFACE, NAME=surf1, PROPERTY=surfp +elset1, S1 +elset2, S2 +*SURFACE, NAME=surf2, PROPERTY=surfp +elset3, +*SURFACE PROPERTY, NAME=surfp +*EMISSIVITY +Data lines to define the emissivity of the surfaces in the model +*CAVITY DEFINITION, NAME=topcav +surf1, surf2 +*INITIAL CONDITIONS, TYPE=TEMPERATURE +Data lines to prescribe initial temperatures at the nodes +*AMPLITUDE, NAME=motion +Data lines to define amplitude curve to be used for motion of surface surf2 +*AMPLITUDE, NAME=film +Data lines to define amplitude curve to be used for the convection film coefficient, h +************* +** Step 1 +************* +*STEP +*HEAT TRANSFER, MXDEM= +Data line to define incrementation +*RADIATION VIEWFACTOR, CAVITY=topcav, VTOL=tol, SYMMETRY=outer, +, DELTMX= +NSET=nset, MDISP=max +*RADIATION SYMMETRY, NAME=outer +*REFLECTION, TYPE=LINE +Data line to define line of symmetry +*MOTION, TRANSLATION, TYPE=DISPLACEMENT, AMPLITUDE=motion +Data line to define motion of nodes on surface surf2 +*CFLUX and/or *DFLUX +Data lines to define concentrated and/or distributed fluxes +*BOUNDARY +Data lines to prescribe temperatures at selected nodes +*FILM, FILM AMPLITUDE=film +Data lines to define surface convection +** +*RADIATION PRINT, CAVITY=topcav, SUMMARY=YES, TOTALS=YES +Data lines requesting cavity radiation surface variable output +*RADIATION FILE, CAVITY=topcav, FREQUENCY=4 +Data lines requesting cavity radiation surface variable output +*NODE PRINT +Data lines requesting nodal output such as temperatures +*EL PRINT +Data lines requesting element output such as heat flux +*END STEP +************* +** Step 2 +************* +*STEP +*HEAT TRANSFER, STEADY STATE +Data line to define incrementation +*RADIATION VIEWFACTOR, OFF +*CFLUX, OP=NEW +*DFLUX, OP=NEW +*END STEP +SIMULIA is the Dassault Systèmes brand that delivers a scalable portfolio of +Realistic Simulation solutions including the Abaqus product suite for Unified Finite +Element Analysis; multiphysics solutions for insight into challenging engineering +problems; and lifecycle management solutions for managing simulation data, +processes, and intellectual property. By building on established technology, +respected quality, and superior customer service, SIMULIA makes realistic +simulation an integral business practice that improves product performance, +reduces physical prototypes, and drives innovation. Headquartered in Providence, +RI, USA, with R&D centers in Providence and in Vélizy, France, SIMULIA provides +sales, services, and support through a global network of regional offices and +distributors. For more information, visit www.simulia.com. +About Dassault Systèmes +As a world leader in 3D and Product Lifecycle Management (PLM) solutions, +Dassault Systèmes brings value to more than 100,000 customers in 80 countries. +A pioneer in the 3D software market since 1981, Dassault Systèmes develops and +markets PLM application software and services that support industrial processes +and provide a 3D vision of the entire lifecycle of products from conception to +maintenance to recycling. 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Bhd., Kuala Lumpur, Tel: +603 2039 9000, abaqus.my@worleyparsons.com +Kimeca.NET SA de CV, Mexico, Tel: +52 55 2459 2635 +Matrix Applied Computing Ltd., Auckland, Tel: +64 9 623 1223, abaqus-tech@matrix.co.nz +BudSoft Sp. z o.o., Poznań, Tel: +48 61 8508 466, info@budsoft.com.pl +TESIS Ltd., Moscow, Tel: +7 495 612 44 22, info@tesis.com.ru +WorleyParsons Pte Ltd., Singapore, Tel: +65 6735 8444, abaqus.sg@worleyparsons.com +Finite Element Analysis Services (Pty) Ltd., Parklands, Tel: +27 21 556 6462, feas@feas.co.za +Thailand +Turkey +Simutech Solution Corporation, Taipei, R.O.C., Tel: +886 2 2507 9550, camilla@simutech.com.tw +WorleyParsons Pte Ltd., Singapore, Tel: +65 6735 8444, abaqus.sg@worleyparsons.com +A-Ztech Ltd., Istanbul, Tel: +90 216 361 8850, info@a-ztech.com.tr +Preface +Support +Both technical engineering support (for problems with creating a model or performing an analysis) and +systems support (for installation, licensing, and hardware-related problems) for Abaqus are offered through +a network of local support offices. 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If you contact +us by means outside the system to discuss an existing support problem and you know the incident or support +request number, please mention it so that we can query the database to see what the latest action has been. +Many questions about Abaqus can also be answered by visiting the Products page and the Support +page at www.simulia.com. +Anonymous ftp site +To facilitate data transfer with SIMULIA, an anonymous ftp account is available at ftp.simulia.com. +Login as user anonymous, and type your e-mail address as your password. Contact support before placing +files on the site. +Training +All offices and representatives offer regularly scheduled public training classes. The courses are offered in +a traditional classroom form and via the Web. We also provide training seminars at customer sites. All +training classes and seminars include workshops to provide as much practical experience with Abaqus as +possible. For a schedule and descriptions of available classes, see www.simulia.com or call your local office +or representative. +Feedback +We welcome any suggestions for improvements to Abaqus software, the support program, or documentation. +We will ensure that any enhancement requests you make are considered for future releases. If you wish to +make a suggestion about the service or products, refer to www.simulia.com. Complaints should be made by +contacting your local office or through www.simulia.com by visiting the Quality Assurance section of the +1.1.1 +1.2.1 +1.2.2 +1.3.1 +1.4.1 +2.1.1 +2.1.2 +2.1.3 +2.1.4 +2.1.5 +2.1.6 +2.2.1 +2.2.2 +2.2.3 +2.2.4 +2.2.5 +2.3.1 +2.3.2 +2.3.3 +2.3.4 +Contents +Volume I +PART I +INTRODUCTION, SPATIAL MODELING, AND EXECUTION +1. +Introduction +Introduction: general +Abaqus syntax and conventions +Input syntax rules +Conventions +Abaqus model definition +Defining a model in Abaqus +Parametric modeling +Parametric input +2. Spatial Modeling +Node definition +Node definition +Parametric shape variation +Nodal thicknesses +Normal definitions at nodes +Transformed coordinate systems +Adjusting nodal coordinates +Element definition +Element definition +Element foundations +Defining reinforcement +Defining rebar as an element property +Orientations +Surface definition +Surfaces: overview +Element-based surface definition +Node-based surface definition +Analytical rigid surface definition +Eulerian surface definition +Operating on surfaces +Rigid body definition +Rigid body definition +Integrated output section definition +Integrated output section definition +Mass adjustment +Adjust and/or redistribute mass of an element set +Nonstructural mass definition +Nonstructural mass definition +Distribution definition +Distribution definition +Display body definition +Display body definition +Assembly definition +Defining an assembly +Matrix definition +Defining matrices +3. Job Execution +Execution procedures: overview +Execution procedure for Abaqus: overview +Execution procedures +Obtaining information +Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD execution +SIMULIA Co-Simulation Engine controller execution +Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD co-simulation execution +Abaqus/CAE execution +Abaqus/Viewer execution +Python execution +Parametric studies +Abaqus documentation +Licensing utilities +ASCII translation of results (.fil) files +Joining results (.fil) files +Querying the keyword/problem database +ii +Abaqus ID:usb-toc +Printed on: Fri February 3 -- 18:01:12 2012 +2.3.5 +2.3.6 +2.4.1 +2.5.1 +2.6.1 +2.7.1 +2.8.1 +2.9.1 +2.10.1 +2.11.1 +3.1.1 +3.2.1 +3.2.2 +3.2.3 +3.2.4 +3.2.5 +3.2.6 +3.2.7 +3.2.8 +3.2.9 +3.2.10 +Making user-defined executables and subroutines +Input file and output database upgrade utility +Generating output database reports +Joining output database (.odb) files from restarted analyses +Combining output from substructures +Combining data from multiple output databases +Network output database file connector +Mapping thermal and magnetic loads +Fixed format conversion utility +Translating Nastran bulk data files to Abaqus input files +Translating Abaqus files to Nastran bulk data files +Translating ANSYS input files to Abaqus input files +Translating PAM-CRASH input files to partial Abaqus input files +Translating RADIOSS input files to partial Abaqus input files +Translating Abaqus output database files to Nastran Output2 results files +Translating LS-DYNA data files to Abaqus input files +Exchanging Abaqus data with ZAERO +Encrypting and decrypting Abaqus input data +Job execution control +Environment file settings +Using the Abaqus environment settings +Managing memory and disk resources +Managing memory and disk use in Abaqus +Parallel execution +Parallel execution: overview +Parallel execution in Abaqus/Standard +Parallel execution in Abaqus/Explicit +Parallel execution in Abaqus/CFD +File extension definitions +File extensions used by Abaqus +FORTRAN unit numbers +FORTRAN unit numbers used by Abaqus +CONTENTS +3.2.14 +3.2.15 +3.2.16 +3.2.17 +3.2.18 +3.2.19 +3.2.20 +3.2.21 +3.2.22 +3.2.23 +3.2.24 +3.2.25 +3.2.26 +3.2.27 +3.2.28 +3.2.29 +3.2.30 +3.2.31 +3.2.32 +3.2.33 +3.3.1 +3.4.1 +3.5.1 +3.5.2 +3.5.3 +3.5.4 +3.6.1 +3.7.1 +4.1.2 +4.1.3 +4.1.4 +4.2.1 +4.2.2 +4.2.3 +4.3.1 +5.1.1 +5.1.2 +5.1.3 +5.1.4 +CONTENTS +4. Output +PART II +OUTPUT +Output +Output to the data and results files +Output to the output database +Error indicator output +Output variables +Abaqus/Standard output variable identifiers +Abaqus/Explicit output variable identifiers +Abaqus/CFD output variable identifiers +The postprocessing calculator +The postprocessing calculator +5. File Output Format +Accessing the results file +Accessing the results file: overview +Results file output format +Accessing the results file information +Utility routines for accessing the results file +OI.1 Abaqus/Standard Output Variable Index +OI.2 Abaqus/Explicit Output Variable Index +OI.3 Abaqus/CFD Output Variable Index +6.1.1 +6.1.2 +6.1.3 +6.1.4 +6.1.5 +6.1.6 +6.2.1 +6.2.2 +6.2.3 +6.2.4 +6.2.5 +6.2.6 +6.2.7 +6.3.1 +6.3.2 +6.3.3 +6.3.4 +6.3.5 +6.3.6 +6.3.7 +6.3.8 +6.3.9 +6.3.10 +6.3.11 +6.4.1 +6.5.1 +6.5.2 +Volume II +PART III +ANALYSIS PROCEDURES, SOLUTION, AND CONTROL +6. Analysis Procedures +Introduction +Solving analysis problems: overview +Defining an analysis +General and linear perturbation procedures +Multiple load case analysis +Direct linear equation solver +Iterative linear equation solver +Static stress/displacement analysis +Static stress analysis procedures: overview +Static stress analysis +Eigenvalue buckling prediction +Unstable collapse and postbuckling analysis +Quasi-static analysis +Direct cyclic analysis +Low-cycle fatigue analysis using the direct cyclic approach +Dynamic stress/displacement analysis +Dynamic analysis procedures: overview +Implicit dynamic analysis using direct integration +Explicit dynamic analysis +Direct-solution steady-state dynamic analysis +Natural frequency extraction +Complex eigenvalue extraction +Transient modal dynamic analysis +Mode-based steady-state dynamic analysis +Subspace-based steady-state dynamic analysis +Response spectrum analysis +Random response analysis +Steady-state transport analysis +Steady-state transport analysis +Heat transfer and thermal-stress analysis +Heat transfer analysis procedures: overview +Uncoupled heat transfer analysis +6.5.4 +6.6.1 +6.6.2 +6.7.1 +6.7.2 +6.7.3 +6.7.4 +6.7.5 +6.7.6 +6.8.1 +6.8.2 +6.9.1 +6.10.1 +6.11.1 +6.12.1 +7.1.1 +7.2.1 +7.2.2 +7.2.3 +7.2.4 +CONTENTS +Fully coupled thermal-stress analysis +Adiabatic analysis +Fluid dynamic analysis +Fluid dynamic analysis procedures: overview +Incompressible fluid dynamic analysis +Electromagnetic analysis +Electromagnetic analysis procedures +Piezoelectric analysis +Coupled thermal-electrical analysis +Fully coupled thermal-electrical-structural analysis +Eddy current analysis +Magnetostatic analysis +Coupled pore fluid flow and stress analysis +Coupled pore fluid diffusion and stress analysis +Geostatic stress state +Mass diffusion analysis +Mass diffusion analysis +Acoustic and shock analysis +Acoustic, shock, and coupled acoustic-structural analysis +Abaqus/Aqua analysis +Abaqus/Aqua analysis +Annealing +Annealing procedure +7. Analysis Solution and Control +Solving nonlinear problems +Solving nonlinear problems +Analysis convergence controls +Convergence and time integration criteria: overview +Commonly used control parameters +Convergence criteria for nonlinear problems +Time integration accuracy in transient problems +ANALYSIS TECHNIQUES +8. Analysis Techniques: Introduction +Analysis techniques: overview +9. Analysis Continuation Techniques +Restarting an analysis +Restarting an analysis +Importing and transferring results +Transferring results between Abaqus analyses: overview +Transferring results between Abaqus/Explicit and Abaqus/Standard +Transferring results from one Abaqus/Standard analysis to another +Transferring results from one Abaqus/Explicit analysis to another +10. Modeling Abstractions +Substructuring +Using substructures +Defining substructures +Submodeling +Submodeling: overview +Node-based submodeling +Surface-based submodeling +Generating global matrices +Generating matrices +CONTENTS +8.1.1 +9.1.1 +9.2.1 +9.2.2 +9.2.3 +9.2.4 +10.1.1 +10.1.2 +10.2.1 +10.2.2 +10.2.3 +10.3.1 +Symmetric model generation, results transfer, and analysis of cyclic symmetry models +Symmetric model generation +Transferring results from a symmetric mesh or a partial three-dimensional mesh to +a full three-dimensional mesh +Analysis of models that exhibit cyclic symmetry +Periodic media analysis +Periodic media analysis +Meshed beam cross-sections +Meshed beam cross-sections +vii +10.4.1 +10.4.2 +10.4.3 +10.5.1 +Modeling discontinuities as an enriched feature using the extended finite element method +Modeling discontinuities as an enriched feature using the extended finite element +10.7.1 +11.1.1 +11.2.1 +11.3.1 +11.4.1 +11.4.2 +11.4.3 +11.5.1 +11.5.2 +11.5.3 +11.5.4 +11.6.1 +11.7.1 +11.8.1 +12.1.1 +12.2.1 +12.2.2 +12.2.3 +12.2.4 +method +11. Special-Purpose Techniques +Inertia relief +Inertia relief +Mesh modification or replacement +Element and contact pair removal and reactivation +Geometric imperfections +Introducing a geometric imperfection into a model +Fracture mechanics +Fracture mechanics: overview +Contour integral evaluation +Crack propagation analysis +Surface-based fluid modeling +Surface-based fluid cavities: overview +Fluid cavity definition +Fluid exchange definition +Inflator definition +Mass scaling +Mass scaling +Selective subcycling +Selective subcycling +Steady-state detection +Steady-state detection +12. Adaptivity Techniques +Adaptivity techniques: overview +Adaptivity techniques +ALE adaptive meshing +ALE adaptive meshing: overview +Defining ALE adaptive mesh domains in Abaqus/Explicit +ALE adaptive meshing and remapping in Abaqus/Explicit +Modeling techniques for Eulerian adaptive mesh domains in Abaqus/Explicit +12.2.5 +12.2.6 +12.2.7 +12.3.1 +12.3.2 +12.3.3 +12.4.1 +13.1.1 +13.2.1 +13.2.2 +13.2.3 +14.1.1 +14.1.2 +14.1.3 +14.1.4 +15.1.1 +15.1.2 +16.1.1 +16.1.2 +16.1.3 +17.1.1 +17.2.1 +Output and diagnostics for ALE adaptive meshing in Abaqus/Explicit +Defining ALE adaptive mesh domains in Abaqus/Standard +ALE adaptive meshing and remapping in Abaqus/Standard +Adaptive remeshing +Adaptive remeshing: overview +Selection of error indicators influencing adaptive remeshing +Solution-based mesh sizing +Analysis continuation after mesh replacement +Mesh-to-mesh solution mapping +13. Optimization Techniques +Structural optimization: overview +Structural optimization: overview +Optimization models +Design responses +Objectives and constraints +Creating Abaqus optimization models +14. Eulerian Analysis +Eulerian analysis +Defining Eulerian boundaries +Eulerian mesh motion +Defining adaptive mesh refinement in the Eulerian domain +15. Particle Methods +Smoothed particle hydrodynamic analyses +Smoothed particle hydrodynamic analysis +Finite element conversion to SPH particles +16. Sequentially Coupled Multiphysics Analyses +Predefined fields for sequential coupling +Sequentially coupled thermal-stress analysis +Predefined loads for sequential coupling +17. Co-simulation +Co-simulation: overview +Preparing an Abaqus analysis for co-simulation +Preparing an Abaqus analysis for co-simulation +Co-simulation between Abaqus solvers +Abaqus/Standard to Abaqus/Explicit co-simulation +Abaqus/CFD to Abaqus/Standard or to Abaqus/Explicit co-simulation +18. Extending Abaqus Analysis Functionality +User subroutines and utilities +User subroutines: overview +Available user subroutines +Available utility routines +19. Design Sensitivity Analysis +Design sensitivity analysis +20. Parametric Studies +Scripting parametric studies +Scripting parametric studies +Parametric studies: commands +aStudy.combine(): Combine parameter samples for parametric studies. +aStudy.constrain(): Constrain parameter value combinations in parametric studies. +aStudy.define(): Define parameters for parametric studies. +aStudy.execute(): Execute the analysis of parametric study designs. +aStudy.gather(): Gather the results of a parametric study. +aStudy.generate(): Generate the analysis job data for a parametric study. +aStudy.output(): Specify the source of parametric study results. +aStudy=ParStudy(): Create a parametric study. +aStudy.report(): Report parametric study results. +aStudy.sample(): Sample parameters for parametric studies. +17.3.1 +17.3.2 +18.1.1 +18.1.2 +18.1.3 +19.1.1 +20.1.1 +20.2.1 +20.2.2 +20.2.3 +20.2.4 +20.2.5 +20.2.6 +20.2.7 +20.2.8 +20.2.9 +20.2.10 +21.1.1 +21.1.2 +21.1.3 +21.2.1 +22.1.1 +22.2.1 +22.2.2 +22.2.3 +22.3.1 +22.4.1 +22.5.1 +22.5.2 +22.5.3 +22.6.1 +22.6.2 +22.7.1 +22.7.2 +Volume III +PART V MATERIALS +21. Materials: Introduction +Introduction +Material library: overview +Material data definition +Combining material behaviors +General properties +Density +22. Elastic Mechanical Properties +Overview +Elastic behavior: overview +Linear elasticity +Linear elastic behavior +No compression or no tension +Plane stress orthotropic failure measures +Porous elasticity +Elastic behavior of porous materials +Hypoelasticity +Hypoelastic behavior +Hyperelasticity +Hyperelastic behavior of rubberlike materials +Hyperelastic behavior in elastomeric foams +Anisotropic hyperelastic behavior +Stress softening in elastomers +Mullins effect +Energy dissipation in elastomeric foams +Viscoelasticity +Time domain viscoelasticity +Frequency domain viscoelasticity +Nonlinear viscoelasticity +Hysteresis in elastomers +Parallel network viscoelastic model +Rate sensitive elastomeric foams +Low-density foams +23. +Inelastic Mechanical Properties +Overview +Inelastic behavior +Metal plasticity +Classical metal plasticity +Models for metals subjected to cyclic loading +Rate-dependent yield +Rate-dependent plasticity: creep and swelling +Annealing or melting +Anisotropic yield/creep +Johnson-Cook plasticity +Dynamic failure models +Porous metal plasticity +Cast iron plasticity +Two-layer viscoplasticity +ORNL – Oak Ridge National Laboratory constitutive model +Deformation plasticity +Other plasticity models +Extended Drucker-Prager models +Modified Drucker-Prager/Cap model +Mohr-Coulomb plasticity +Critical state (clay) plasticity model +Crushable foam plasticity models +Fabric materials +Fabric material behavior +Jointed materials +Jointed material model +Concrete +Concrete smeared cracking +Cracking model for concrete +Concrete damaged plasticity +xii +Abaqus ID:usb-toc +Printed on: Fri February 3 -- 18:01:12 2012 +22.8.1 +22.8.2 +22.9.1 +23.1.1 +23.2.1 +23.2.2 +23.2.3 +23.2.4 +23.2.5 +23.2.6 +23.2.7 +23.2.8 +23.2.9 +23.2.10 +23.2.11 +23.2.12 +23.2.13 +23.3.1 +23.3.2 +23.3.3 +23.3.4 +23.3.5 +23.4.1 +23.5.1 +23.7.1 +24.1.1 +24.2.1 +24.2.2 +24.2.3 +24.3.1 +24.3.2 +24.3.3 +24.4.1 +24.4.2 +24.4.3 +25.1.1 +25.2.1 +26.1.1 +26.1.2 +26.1.3 +26.1.4 +26.2.1 +26.2.2 +26.2.3 +26.2.4 +Permanent set in rubberlike materials +Permanent set in rubberlike materials +24. Progressive Damage and Failure +Progressive damage and failure: overview +Progressive damage and failure +Damage and failure for ductile metals +Damage and failure for ductile metals: overview +Damage initiation for ductile metals +Damage evolution and element removal for ductile metals +Damage and failure for fiber-reinforced composites +Damage and failure for fiber-reinforced composites: overview +Damage initiation for fiber-reinforced composites +Damage evolution and element removal for fiber-reinforced composites +Damage and failure for ductile materials in low-cycle fatigue analysis +Damage and failure for ductile materials in low-cycle fatigue analysis: overview +Damage initiation for ductile materials in low-cycle fatigue +Damage evolution for ductile materials in low-cycle fatigue +25. Hydrodynamic Properties +Overview +Hydrodynamic behavior: overview +Equations of state +Equation of state +26. Other Material Properties +Mechanical properties +Material damping +Thermal expansion +Field expansion +Viscosity +Heat transfer properties +Thermal properties: overview +Conductivity +Specific heat +Latent heat +Acoustic properties +Acoustic medium +Mass diffusion properties +Diffusivity +Solubility +Electromagnetic properties +Electrical conductivity +Piezoelectric behavior +Magnetic permeability +Pore fluid flow properties +Pore fluid flow properties +Permeability +Porous bulk moduli +Sorption +Swelling gel +Moisture swelling +User materials +User-defined mechanical material behavior +User-defined thermal material behavior +26.3.1 +26.4.1 +26.4.2 +26.5.1 +26.5.2 +26.5.3 +26.6.1 +26.6.2 +26.6.3 +26.6.4 +26.6.5 +26.6.6 +26.7.1 +26.7.2 +27.1.1 +27.1.2 +27.1.3 +27.1.4 +28.1.1 +28.1.2 +28.1.3 +28.1.4 +28.1.5 +28.1.6 +28.1.7 +28.2.1 +28.2.2 +28.3.1 +28.3.2 +28.4.1 +28.4.2 +28.5.1 +28.5.2 +29.1.1 +29.1.2 +29.1.3 +Volume IV +PART VI +ELEMENTS +27. Elements: Introduction +Element library: overview +Choosing the element’s dimensionality +Choosing the appropriate element for an analysis type +Section controls +28. Continuum Elements +General-purpose continuum elements +Solid (continuum) elements +One-dimensional solid (link) element library +Two-dimensional solid element library +Three-dimensional solid element library +Cylindrical solid element library +Axisymmetric solid element library +Axisymmetric solid elements with nonlinear, asymmetric deformation +Fluid continuum elements +Fluid (continuum) elements +Fluid element library +Infinite elements +Infinite elements +Infinite element library +Warping elements +Warping elements +Warping element library +Particle elements +Particle elements +Particle element library +29. Structural Elements +Membrane elements +Membrane elements +General membrane element library +Cylindrical membrane element library +Axisymmetric membrane element library +Truss elements +Truss elements +Truss element library +Beam elements +Beam modeling: overview +Choosing a beam cross-section +Choosing a beam element +Beam element cross-section orientation +Beam section behavior +Using a beam section integrated during the analysis to define the section behavior +Using a general beam section to define the section behavior +Beam element library +Beam cross-section library +Frame elements +Frame elements +Frame section behavior +Frame element library +Elbow elements +Pipes and pipebends with deforming cross-sections: elbow elements +Elbow element library +Shell elements +Shell elements: overview +Choosing a shell element +Defining the initial geometry of conventional shell elements +Shell section behavior +Using a shell section integrated during the analysis to define the section behavior +Using a general shell section to define the section behavior +Three-dimensional conventional shell element library +Continuum shell element library +Axisymmetric shell element library +Axisymmetric shell elements with nonlinear, asymmetric deformation +29.1.4 +29.2.1 +29.2.2 +29.3.1 +29.3.2 +29.3.3 +29.3.4 +29.3.5 +29.3.6 +29.3.7 +29.3.8 +29.3.9 +29.4.1 +29.4.2 +29.4.3 +29.5.1 +29.5.2 +29.6.1 +29.6.2 +29.6.3 +29.6.4 +29.6.5 +29.6.6 +29.6.7 +29.6.8 +29.6.9 +29.6.10 +30.1.1 +30.1.2 +30.2.1 +30.2.2 +30.3.1 +30.3.2 +30.4.1 +30.4.2 +31.1.1 +31.1.2 +31.1.3 +31.1.4 +31.1.5 +31.2.1 +31.2.2 +31.2.3 +31.2.4 +31.2.5 +31.2.6 +31.2.7 +31.2.8 +31.2.9 +31.2.10 +32.1.1 +32.1.2 +30. +Inertial, Rigid, and Capacitance Elements +Point mass elements +Point masses +Mass element library +Rotary inertia elements +Rotary inertia +Rotary inertia element library +Rigid elements +Rigid elements +Rigid element library +Capacitance elements +Point capacitance +Capacitance element library +31. Connector Elements +Connector elements +Connectors: overview +Connector elements +Connector actuation +Connector element library +Connection-type library +Connector element behavior +Connector behavior +Connector elastic behavior +Connector damping behavior +Connector functions for coupled behavior +Connector friction behavior +Connector plastic behavior +Connector damage behavior +Connector stops and locks +Connector failure behavior +Connector uniaxial behavior +32. Special-Purpose Elements +Spring elements +Springs +Spring element library +Dashpot elements +Dashpots +Dashpot element library +Flexible joint elements +Flexible joint element +Flexible joint element library +Distributing coupling elements +Distributing coupling elements +Distributing coupling element library +Cohesive elements +Cohesive elements: overview +Choosing a cohesive element +Modeling with cohesive elements +Defining the cohesive element’s initial geometry +Defining the constitutive response of cohesive elements using a continuum approach +Defining the constitutive response of cohesive elements using a traction-separation +description +Defining the constitutive response of fluid within the cohesive element gap +Two-dimensional cohesive element library +Three-dimensional cohesive element library +Axisymmetric cohesive element library +Gasket elements +Gasket elements: overview +Choosing a gasket element +Including gasket elements in a model +Defining the gasket element’s initial geometry +Defining the gasket behavior using a material model +Defining the gasket behavior directly using a gasket behavior model +Two-dimensional gasket element library +Three-dimensional gasket element library +Axisymmetric gasket element library +Surface elements +Surface elements +General surface element library +Cylindrical surface element library +Axisymmetric surface element library +32.2.1 +32.2.2 +32.3.1 +32.3.2 +32.4.1 +32.4.2 +32.5.1 +32.5.2 +32.5.3 +32.5.4 +32.5.5 +32.5.6 +32.5.7 +32.5.8 +32.5.9 +32.5.10 +32.6.1 +32.6.2 +32.6.3 +32.6.4 +32.6.5 +32.6.6 +32.6.7 +32.6.8 +32.6.9 +32.7.1 +32.7.2 +32.7.3 +32.7.4 +32.8.1 +32.8.2 +32.9.1 +32.9.2 +32.10.1 +32.10.2 +32.11.1 +32.11.2 +32.12.1 +32.12.2 +32.13.1 +32.13.2 +32.14.1 +32.14.2 +32.15.1 +32.15.2 +Tube support elements +Tube support elements +Tube support element library +Line spring elements +Line spring elements for modeling part-through cracks in shells +Line spring element library +Elastic-plastic joints +Elastic-plastic joints +Elastic-plastic joint element library +Drag chain elements +Drag chains +Drag chain element library +Pipe-soil elements +Pipe-soil interaction elements +Pipe-soil interaction element library +Acoustic interface elements +Acoustic interface elements +Acoustic interface element library +Eulerian elements +Eulerian elements +Eulerian element library +User-defined elements +User-defined elements +User-defined element library +EI.1 Abaqus/Standard Element Index +EI.2 Abaqus/Explicit Element Index +EI.3 Abaqus/CFD Element Index +Volume V +PART VII +PRESCRIBED CONDITIONS +33. Prescribed Conditions +Overview +Prescribed conditions: overview +Amplitude curves +Initial conditions +Initial conditions in Abaqus/Standard and Abaqus/Explicit +Initial conditions in Abaqus/CFD +Boundary conditions +Boundary conditions in Abaqus/Standard and Abaqus/Explicit +Boundary conditions in Abaqus/CFD +Loads +Applying loads: overview +Concentrated loads +Distributed loads +Thermal loads +Electromagnetic loads +Acoustic and shock loads +Pore fluid flow +Prescribed assembly loads +Prescribed assembly loads +Predefined fields +Predefined fields +PART VIII +CONSTRAINTS +34. Constraints +Overview +Kinematic constraints: overview +Multi-point constraints +Linear constraint equations +xx +Abaqus ID:usb-toc +Printed on: Fri February 3 -- 18:01:12 2012 +33.1.1 +33.1.2 +33.2.1 +33.2.2 +33.3.1 +33.3.2 +33.4.1 +33.4.2 +33.4.3 +33.4.4 +33.4.5 +33.4.6 +33.4.7 +33.5.1 +34.2.2 +34.2.3 +34.3.1 +34.3.2 +34.3.3 +34.3.4 +34.4.1 +34.5.1 +34.6.1 +35.1.1 +35.2.1 +35.2.2 +35.2.3 +35.2.4 +35.2.5 +35.2.6 +35.3.1 +35.3.2 +35.3.3 +35.3.4 +35.3.5 +35.3.6 +35.3.7 +35.3.8 +General multi-point constraints +Kinematic coupling constraints +Surface-based constraints +Mesh tie constraints +Coupling constraints +Shell-to-solid coupling +Mesh-independent fasteners +Embedded elements +Embedded elements +Element end release +Element end release +Overconstraint checks +Overconstraint checks +PART IX +INTERACTIONS +35. Defining Contact Interactions +Overview +Contact interaction analysis: overview +Defining general contact in Abaqus/Standard +Defining general contact interactions in Abaqus/Standard +Surface properties for general contact in Abaqus/Standard +Contact properties for general contact in Abaqus/Standard +Controlling initial contact status in Abaqus/Standard +Stabilization for general contact in Abaqus/Standard +Numerical controls for general contact in Abaqus/Standard +Defining contact pairs in Abaqus/Standard +Defining contact pairs in Abaqus/Standard +Assigning surface properties for contact pairs in Abaqus/Standard +Assigning contact properties for contact pairs in Abaqus/Standard +Modeling contact interference fits in Abaqus/Standard +Adjusting initial surface positions and specifying initial clearances in Abaqus/Standard +contact pairs +Adjusting contact controls in Abaqus/Standard +Defining tied contact in Abaqus/Standard +Extending master surfaces and slide lines +Contact modeling if substructures are present +Contact modeling if asymmetric-axisymmetric elements are present +Defining general contact in Abaqus/Explicit +Defining general contact interactions in Abaqus/Explicit +Assigning surface properties for general contact in Abaqus/Explicit +Assigning contact properties for general contact in Abaqus/Explicit +Controlling initial contact status for general contact in Abaqus/Explicit +Contact controls for general contact in Abaqus/Explicit +Defining contact pairs in Abaqus/Explicit +Defining contact pairs in Abaqus/Explicit +Assigning surface properties for contact pairs in Abaqus/Explicit +Assigning contact properties for contact pairs in Abaqus/Explicit +Adjusting initial surface positions and specifying initial clearances for contact pairs +in Abaqus/Explicit +Contact controls for contact pairs in Abaqus/Explicit +36. Contact Property Models +Mechanical contact properties +Mechanical contact properties: overview +Contact pressure-overclosure relationships +Contact damping +Contact blockage +Frictional behavior +User-defined interfacial constitutive behavior +Pressure penetration loading +Interaction of debonded surfaces +Breakable bonds +Surface-based cohesive behavior +Thermal contact properties +Thermal contact properties +Electrical contact properties +Electrical contact properties +Pore fluid contact properties +Pore fluid contact properties +37. Contact Formulations and Numerical Methods +Contact formulations and numerical methods in Abaqus/Standard +Contact formulations in Abaqus/Standard +xxii +Abaqus ID:usb-toc +Printed on: Fri February 3 -- 18:01:12 2012 +35.3.9 +35.3.10 +35.4.1 +35.4.2 +35.4.3 +35.4.4 +35.4.5 +35.5.1 +35.5.2 +35.5.3 +35.5.4 +35.5.5 +36.1.1 +36.1.2 +36.1.3 +36.1.4 +36.1.5 +36.1.6 +36.1.7 +36.1.8 +36.1.9 +36.1.10 +36.2.1 +37.1.2 +37.1.3 +37.2.1 +37.2.2 +37.2.3 +38.1.1 +38.1.2 +38.2.1 +38.2.2 +39.1.1 +39.2.1 +39.2.2 +39.3.1 +39.3.2 +39.4.1 +39.4.2 +39.5.1 +39.5.2 +40.1.1 +Contact constraint enforcement methods in Abaqus/Standard +Smoothing contact surfaces in Abaqus/Standard +Contact formulations and numerical methods in Abaqus/Explicit +Contact formulation for general contact in Abaqus/Explicit +Contact formulations for contact pairs in Abaqus/Explicit +Contact constraint enforcement methods in Abaqus/Explicit +38. Contact Difficulties and Diagnostics +Resolving contact difficulties in Abaqus/Standard +Contact diagnostics in an Abaqus/Standard analysis +Common difficulties associated with contact modeling in Abaqus/Standard +Resolving contact difficulties in Abaqus/Explicit +Contact diagnostics in an Abaqus/Explicit analysis +Common difficulties associated with contact modeling using contact pairs in +Abaqus/Explicit +39. Contact Elements in Abaqus/Standard +Contact modeling with elements +Contact modeling with elements +Gap contact elements +Gap contact elements +Gap element library +Tube-to-tube contact elements +Tube-to-tube contact elements +Tube-to-tube contact element library +Slide line contact elements +Slide line contact elements +Axisymmetric slide line element library +Rigid surface contact elements +Rigid surface contact elements +Axisymmetric rigid surface contact element library +40. Defining Cavity Radiation in Abaqus/Standard +Cavity radiation +Printed on: +• Chapter 21, “Materials: Introduction” +• Chapter 22, “Elastic Mechanical Properties” +• Chapter 23, “Inelastic Mechanical Properties” +• Chapter 24, “Progressive Damage and Failure” +• Chapter 25, “Hydrodynamic Properties” +21. +Materials: Introduction +Introduction +General properties +21.1 +21.1 +Introduction +• “Material library: overview,” Section 21.1.1 +• “Material data definition,” Section 21.1.2 +• “Combining material behaviors,” Section 21.1.3 +21.1.1 +MATERIAL LIBRARY: OVERVIEW +This chapter describes how to define materials in Abaqus and contains brief descriptions of each of the material +behaviors provided. Further details of the more advanced behaviors are provided in the Abaqus Theory +Manual. +Defining materials +Materials are defined by: +• selecting material behaviors and defining them (“Material data definition,” Section 21.1.2); and +• combining complementary material behaviors such as elasticity and plasticity (“Combining material +behaviors,” Section 21.1.3). +A local coordinate system can be used for material calculations (“Orientations,” Section 2.2.5). Any +anisotropic properties must be given in this local system. +Available material behaviors +The material library in Abaqus is intended to provide comprehensive coverage of both linear and +nonlinear, +isotropic and anisotropic material behaviors. The use of numerical integration in the +elements, including numerical integration across the cross-sections of shells and beams, provides the +flexibility to analyze the most complex composite structures. +Material behaviors fall into the following general categories: +• general properties (material damping, density, thermal expansion); +• elastic mechanical properties; +• inelastic mechanical properties; +• thermal properties; +• acoustic properties; +• hydrostatic fluid properties; +• equations of state; +• mass diffusion properties; +• electrical properties; and +• pore fluid flow properties. +Some of the mechanical behaviors offered are mutually exclusive: such behaviors cannot appear together +in a single material definition. Some behaviors require the presence of other behaviors; for example, +plasticity requires linear elasticity. Such requirements are discussed at the end of each material behavior +description, as well as in “Combining material behaviors,” Section 21.1.3. +Using material behaviors with various element types +There are no general restrictions on the use of particular material behaviors with solid, shell, beam, and +pipe elements. Any combination that makes sense is acceptable. The few restrictions that do exist are +mentioned when that particular behavior is described in the pages that follow. A section on the elements +available for use with a material behavior appears at the end of each material behavior description. +Using complete material definitions +A material definition can include behaviors that are not meaningful for the elements or analysis in which +the material is being used. Such behaviors will be ignored. For example, a material definition can include +heat transfer properties (conductivity, specific heat) as well as stress-strain properties (elastic moduli, +yield stress, etc). When this material definition is used with uncoupled stress/displacement elements, the +heat transfer properties are ignored by Abaqus; when it is used with heat transfer elements, the mechanical +strength properties are ignored. This capability allows you to develop complete material definitions and +use them in any analysis. +Defining spatially varying material behavior for homogenous solid continuum elements using +distributions in Abaqus/Standard +In Abaqus/Standard spatially varying mass density (“Density,” Section 21.2.1), linear elastic behavior +(“Linear elastic behavior,” Section 22.2.1), and thermal expansion (“Thermal expansion,” Section 26.1.2) +can be defined for homogeneous solid continuum elements using distributions (“Distribution definition,” +Section 2.8.1). Using distributions in a model with significant variation in material behavior can greatly +simplify pre- and postprocessing and improve performance during the analysis by allowing a single +material definition to define the spatially varying material behavior. Without distributions such a model +may require many material definitions and associated section assignments. +21.1.2 +MATERIAL DATA DEFINITION +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Combining material behaviors,” Section 21.1.3 +• *MATERIAL +• “Creating materials,” Section 12.4.1 of the Abaqus/CAE User’s Manual +Overview +A material definition in Abaqus: +• specifies the behavior of a material and supplies all the relevant property data; +• can contain multiple material behaviors; +• is assigned a name, which is used to refer to those parts of the model that are made of that material; +• can have temperature and/or field variable dependence; +• can have solution variable dependence in Abaqus/Standard; and +• can be specified in a local coordinate system (“Orientations,” Section 2.2.5), which is required if +the material is not isotropic. +Material definitions +Any number of materials can be defined in an analysis. Each material definition can contain any number +of material behaviors, as required, to specify the complete material behavior. For example, in a linear +static stress analysis only elastic material behavior may be needed, while in a more complicated analysis +several material behaviors may be required. +A name must be assigned to each material definition. This name allows the material to be referenced +Input File Usage: +from the section definitions used to assign this material to regions in the model. +*MATERIAL, NAME=name +Each material definition is specified in a data block, which is initiated by a +*MATERIAL option. The material definition continues until an option that +does not define a material behavior (such as another *MATERIAL option) is +introduced, at which point the material definition is assumed to be complete. +The order of the material behavior options is not important. All material +behavior options within the data block are assumed to define the same material. +Abaqus/CAE Usage: +Property module: material editor: Name +Use the menu bar under the Material Options list to add behaviors to +a material. +Large-strain considerations +When giving material properties for finite-strain calculations, “stress” means “true” (Cauchy) stress +(force per current area) and “strain” means logarithmic strain. For example, unless otherwise indicated, +for uniaxial behavior +Specifying material data as functions of temperature and independent field variables +Material data are often specified as functions of independent variables such as temperature. Material +properties are made temperature dependent by specifying them at several different temperatures. +In some cases a material property can be defined as a function of variables calculated by Abaqus; +for example, to define a work-hardening curve, stress must be given as a function of equivalent plastic +strain. +Material properties can also be dependent on “field variables” (user-defined variables that can +represent any independent quantity and are defined at the nodes, as functions of time). For example, +material moduli can be functions of weave density in a composite or of phase fraction in an alloy. See +“Specifying field variable dependence” for details. The initial values of field variables are given as +initial conditions and +can be modified as functions of time during an analysis . This +capability is useful if, for example, material properties change with time because of irradiation or some +other precalculated environmental effect. +Any material behaviors defined using a distribution in Abaqus/Standard (mass density, linear +elastic behavior, and/or thermal expansion) cannot be defined with temperature and/or field dependence. +However, material behaviors defined with distributions can be included in a material definition with +other material behaviors that have temperature and/or field dependence. See “Density,” Section 21.2.1; +“Linear elastic behavior,” Section 22.2.1; and “Thermal expansion,” Section 26.1.2. +Interpolation of material data +In the simplest case of a constant property, only the constant value is entered. When the material data are +functions of only one variable, the data must be given in order of increasing values of the independent +variable. Abaqus then interpolates linearly for values between those given. The property is assumed +to be constant outside the range of independent variables given (except for fabric materials, where it is +extrapolated linearly outside the specified range using the slope at the last specified data point). Thus, +you can give as many or as few input values as are necessary for the material model. If the material data +depend on the independent variable in a strongly nonlinear manner, you must specify enough data points +so that a linear interpolation captures the nonlinear behavior accurately. +When material properties depend on several variables, the variation of the properties with respect +to the first variable must be given at fixed values of the other variables, in ascending values of the second +variable, then of the third variable, and so on. The data must always be ordered so that the independent +variables are given increasing values. This process ensures that the value of the material property is +completely and uniquely defined at any values of the independent variables upon which the property +depends. See “Input syntax rules,” Section 1.2.1, for further explanation and an example. +Example: Temperature-dependent linear isotropic elasticity +Figure 21.1.2–1 shows a simple, isotropic, linear elastic material, giving the Young’s modulus and the +Poisson’s ratio as functions of temperature. +Young s +modulus, E +Poisson s +ratio, ν +Temperature, θ +Figure 21.1.2–1 Example of material definition. +In this case six sets of values are used to specify the material description, as shown in the following table: +Elastic Modulus +Poisson’s Ratio +Temperature +, Abaqus assumes constant values for +For temperatures that are outside the range defined by +E and . The dotted lines on the graph represent the straight-line approximations that will be used for +this model. In this example only one value of the thermal expansion coefficient is given, +, and it is +independent of temperature. +and +Example: Elastic-plastic material +Figure 21.1.2–2 shows an elastic-plastic material for which the yield stress is dependent on the equivalent +plastic strain and temperature. +Elastic data: E1, ν +(ε +11, σ +11 ) +(ε +12 , σ +12 ) +(ε +01 , σ +01 ) +(ε +02 , σ +02 ) +(ε +21, σ +21 ) +(ε +31 , σ +31 ) +(ε +22 , σ +22 ) +(ε +32 , σ +32 ) +θ = θ +θ = θ2 +εpl +Figure 21.1.2–2 Example of material definition with two independent variables. +In this case the second independent variable (temperature) must be held constant, while the yield stress is +described as a function of the first independent variable (equivalent plastic strain). Then, a higher value +of temperature is chosen and the dependence on equivalent plastic strain is given at this temperature. +This process, as shown in the following table, is repeated as often as necessary to describe the property +variations in as much detail as required: +Yield Stress +Equivalent +Plastic Strain +Temperature +Specifying field variable dependence +You can specify the number of user-defined field variable dependencies required for many material +behaviors . If you do not specify a number of field variable +dependencies for a material behavior with which field variable dependence is available, the material data +are assumed not to depend on field variables. +Input File Usage: +*MATERIAL BEHAVIOR OPTION, DEPENDENCIES=n +*MATERIAL BEHAVIOR OPTION refers to any material behavior option for +which field dependence can be specified. Each data line can hold up to eight +data items. If more field variable dependencies are required than fit on a single +data line, more data lines can be added. For example, a linear, isotropic elastic +material can be defined as a function of temperature and seven field variables +( +*ELASTIC, TYPE=ISOTROPIC, DEPENDENCIES=7 +) as follows: +E, , , +, +, +, +, +, +This pair of data lines would be repeated as often as necessary to define the +material as a function of the temperature and field variables. +Abaqus/CAE Usage: +Property module: material editor: material behavior: Number of field +variables: n +material behavior refers to any material behavior for which field dependence +can be specified. +Specifying material data as functions of solution-dependent variables +In Abaqus you can introduce dependence on solution variables with a user subroutine. User subroutines +USDFLD in Abaqus/Standard and VUSDFLD in Abaqus/Explicit allow you to define field variables at +a material point as functions of time, of material directions, and of any of the available material point +quantities: those listed in “Abaqus/Standard output variable identifiers,” Section 4.2.1, for the case of +USDFLD, and those listed in “Available output variable keys” in “Obtaining material point information +in an Abaqus/Explicit analysis,” Section 2.1.7 of the Abaqus User Subroutines Reference Manual, for +the case of VUSDFLD. Material properties defined as functions of these field variables may, thus, be +dependent on the solution. +User subroutines USDFLD and VUSDFLD are called at each material point for which the material +definition includes a reference to the user subroutine. +For general analysis steps the values of variables provided in user subroutines USDFLD and +VUSDFLD are those corresponding to the start of the increment. Hence, the solution dependence +introduced in this way is explicit: the material properties for a given increment are not influenced by the +results obtained during the increment. Consequently, the accuracy of the results will generally depend +on the time increment size. This is usually not a concern in Abaqus/Explicit because the stable time +increment is usually sufficiently small to ensure good accuracy. In Abaqus/Standard you can control +the time increment from inside subroutine USDFLD. For linear perturbation steps the solution variables +in the base state are available. +*USER DEFINED FIELD +User subroutines USDFLD and VUSDFLD are not supported in Abaqus/CAE. +Abaqus/CAE Usage: +Input File Usage: +Regularizing user-defined data in Abaqus/Explicit and Abaqus/CFD +Interpolating material data as functions of independent variables requires table lookups of the material +data values during the analysis. The table lookups occur frequently in Abaqus/Explicit and Abaqus/CFD, +and are most economical if the interpolation is from regular intervals of the independent variables. For +example, the data shown in Figure 21.1.2–1 are not regular because the intervals in temperature (the +independent variable) between adjacent data points vary. You are not required to specify regular material +data. Abaqus/Explicit and Abaqus/CFD will automatically regularize user-defined data. For example, +the temperature values in Figure 21.1.2–1 may be defined at 10°, 20°, 25°, 28°, 30°, and 35° C. In this case +Abaqus/Explicit and Abaqus/CFD can regularize the data by defining the data over 25 increments of 1° +C and your piecewise linear data will be reproduced exactly. This regularization requires the expansion +of your data from values at 6 temperature points to values at 26 temperature points. This example is a +case where a simple regularization can reproduce your data exactly. +If there are multiple independent variables, the concept of regular data also requires that the +minimum and maximum values (the range) be constant for each independent variable while specifying +the other independent variables. The material definition in Figure 21.1.2–2 illustrates a case where +the material data are not regular since +. Abaqus/Explicit will also +regularize data involving multiple independent variables, although the data provided must satisfy the +rules specified in “Input syntax rules,” Section 1.2.1. +, and +, +Error tolerance used in regularizing user-defined data +It is not always desirable to regularize the input data so that they are reproduced exactly in a piecewise +linear manner. Suppose the yield stress is defined as a function of plastic strain in Abaqus/Explicit as +follows: +Yield Stress +Plastic +Strain +50000 +75000 +80000 +85000 +86000 +.0 +.001 +.003 +.010 +1.0 +It is possible to regularize the data exactly but it is not very economical, since it requires the subdivision +of the data into 1000 regular intervals. Regularization is more difficult if the smallest interval you defined +is small compared to the range of the independent variable. +Abaqus/Explicit and Abaqus/CFD use an error tolerance to regularize the input data. The number +of intervals in the range of each independent variable is chosen such that the error between the piecewise +linear regularized data and each of your defined points is less than the tolerance times the range of the +dependent variable. In some cases the number of intervals becomes excessive and Abaqus/Explicit or +Abaqus/CFD cannot regularize the data using a reasonable number of intervals. The number of intervals +considered reasonable depends on the number of intervals you define. If you defined 50 or less intervals, +the maximum number of intervals used by Abaqus/Explicit and Abaqus/CFD for regularization is equal +to 100 times the number of user-defined intervals. If you defined more than 50 intervals, the maximum +number of intervals used for regularization is equal to 5000 plus 10 times the number of user-defined +intervals above 50. If the number of intervals becomes excessive, the program stops during the data +checking phase and issues an error message. You can either redefine the material data or change the +tolerance value. The default tolerance is 0.03. +The yield stress data in the example above are a typical case where such an error message may be +issued. In this case you can simply remove the last data point since it produces only a small difference +in the ultimate yield value. +Input File Usage: +Abaqus/CAE Usage: +*MATERIAL, RTOL=tolerance +Property module: material editor: General→Regularization: Rtol: tolerance +Regularization of strain-rate-dependent data in Abaqus/Explicit +Since strain rate dependence of data is usually measured at logarithmic intervals, Abaqus/Explicit +regularizes strain rate data using logarithmic intervals rather than uniformly spaced intervals by default. +This will generally provide a better match to typical strain-rate-dependent curves. You can specify +linear strain rate regularization to use uniform intervals for regularization of strain rate data. The use of +linear strain rate regularization affects only the regularization of strain rate as an independent variable +and is relevant only if one of the following behaviors is used to define the material data: +• low-density foams (“Low-density foams,” Section 22.9.1) +• rate-dependent metal plasticity (“Classical metal plasticity,” Section 23.2.1) +• rate-dependent viscoplasticity defined by yield stress ratios (“Rate-dependent yield,” Section 23.2.3) +• shear failure defined using direct tabular data (“Dynamic failure models,” Section 23.2.8) +• rate-dependent Drucker-Prager hardening (“Extended Drucker-Prager models,” Section 23.3.1) +• rate-dependent concrete damaged plasticity (“Concrete damaged plasticity,” Section 23.6.3) +• rate-dependent damage initiation criterion (“Damage initiation for ductile metals,” Section 24.2.2) +Input File Usage: +Use the following option to specify logarithmic regularization (default): +*MATERIAL, STRAIN RATE REGULARIZATION=LOGARITHMIC +Use the following option to specify linear regularization: +Abaqus/CAE Usage: +*MATERIAL, STRAIN RATE REGULARIZATION=LINEAR +Property module: material editor: General→Regularization: Strain +rate regularization: Logarithmic or Linear +Evaluation of strain-rate-dependent data in Abaqus/Explicit +Rate-sensitive material constitutive behavior may introduce nonphysical high-frequency oscillations in +an explicit dynamic analysis. To overcome this problem, Abaqus/Explicit computes the equivalent plastic +strain rate used for the evaluation of strain-rate-dependent data as +Here +and +( +is the incremental change in equivalent plastic strain during the time increment +, and +are the strain rates at the beginning and end of the increment, respectively. The factor +) facilitates filtering high-frequency oscillations associated with strain-rate-dependent +, directly. The default value is +material behavior. You can specify the value of the strain rate factor, +0.9. A value of +does not provide the desired filtering effect and should be avoided. +Input File Usage: +Abaqus/CAE Usage: +*MATERIAL, SRATE FACTOR= +You cannot specify the value of the strain rate factor in Abaqus/CAE. +21.1.3 +COMBINING MATERIAL BEHAVIORS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Material data definition,” Section 21.1.2 +• “Creating materials,” Section 12.4.1 of the Abaqus/CAE User’s Manual +Overview +Abaqus provides a broad range of possible material behaviors. A material is defined by choosing +the appropriate behaviors for the purpose of an analysis. This section describes the general rules for +combining material behaviors. Specific information for each material behavior is also summarized at +the end of each material behavior description section in this chapter. +Some of the material behaviors in Abaqus are completely unrestricted: they can be used alone or +together with other behaviors. For example, thermal properties such as conductivity can be used in any +material definition. They will be used in an analysis if the material is associated with elements that can +solve heat transfer problems and if the analysis procedure allows for the thermal equilibrium equation to +be solved. +Some material behaviors in Abaqus require the presence of other material behaviors, and some +exclude the use of other material behaviors. For example, metal plasticity requires the definition of elastic +material behavior or an equation of state and excludes all other rate-independent plasticity behaviors. +Complete material definitions +Abaqus requires that the material be sufficiently defined to provide suitable properties for those elements +with which the material is associated and for all of the analysis procedures through which the model +will be run. Thus, a material associated with displacement or structural elements must include either a +“Complete mechanical” category behavior or an “Elasticity” category behavior, as discussed below. In +Abaqus/Explicit density (“Density,” Section 21.2.1) is required for all materials except hydrostatic fluids. +It is not possible to modify or add to material definitions once an analysis is started. However, +material definitions can be modified in an import analysis. For example, a static analysis can be run in +Abaqus/Standard using a material definition that does not include a density specification. Density can +be added to the material definition when the analysis is imported into Abaqus/Explicit. +All aspects of a material’s behavior need not be fully defined; any behavior that is omitted is assumed +not to exist in that part of the model. For example, if elastic material behavior is defined for a metal but +metal plasticity is not defined, the material is assumed not to have a yield stress. You must ensure that +the material is adequately defined for the purpose of the analysis. The material can include behaviors +that are not relevant for the analysis, as described in “Material library: overview,” Section 21.1.1. Thus, +you can include general material behavior libraries, without having to delete those behaviors that are not +needed for a particular application. This generality offers great flexibility in material modeling. +In Abaqus/Standard any material behaviors defined using a distribution (“Distribution definition,” +Section 2.8.1) can be combined with almost all material behaviors in a manner identical to how they +are combined when no distributions are used. For example, if the linear elastic material behavior is +defined using a distribution, it can be combined with metal plasticity or any other material behavior that +can normally be combined with linear elastic behavior. In addition, more than one material behavior +defined with a distribution (linear elastic behavior and thermal expansion, for example) can be included +in the same material definition. The only exception is that a material defined with concrete damaged +plasticity (“Concrete damaged plasticity,” Section 23.6.3) cannot have any material behaviors defined +with a distribution. +Material behavior combination tables +The material behavior combination tables that follow explain which behaviors must be used together. +The tables also show the material behaviors that cannot be combined. Behaviors designated with +an (S) are available only in Abaqus/Standard; behaviors designated with an (E) are available only in +Abaqus/Explicit. +The behaviors are assigned to categories because exclusions are best described in terms of those +categories. Some of the categories require explanation: +• “Complete mechanical behaviors” are those behaviors in Abaqus that, individually, completely +define a material’s mechanical (stress-strain) behavior. A behavior in this category, therefore, +excludes any other such behavior and also excludes any behavior that defines part of a material’s +mechanical behavior: those behaviors that belong to the elasticity and plasticity categories. +• “Elasticity, fabric, and equation of state behaviors” contains all of the basic elasticity behaviors +in Abaqus. +If a behavior from the “Complete mechanical behaviors” category is not used and +mechanical behavior is required, a behavior must be selected from this category. This selection +then excludes any other elasticity behavior. +• “Enhancements for elasticity behaviors” contains behaviors that extend the modeling provided by +the elasticity behaviors in Abaqus. +• “Rate-independent plasticity behaviors” contains all of the basic plasticity behaviors in Abaqus +except deformation plasticity, which is in the “Complete mechanical behaviors” category because +it completely defines the material’s mechanical behavior. +• “Rate-dependent plasticity behaviors” contains behaviors that extend the modeling provided by the +rate-independent plasticity behaviors and by the linear elastic material behavior. +If elastic-plastic behavior must be modeled, you should select an appropriate plasticity behavior from +one of the plasticity behaviors categories and an elasticity behavior from one of the elasticity behaviors +categories. +General behaviors: +These behaviors are unrestricted. +Behavior +Keyword +Requires +Elasticity, fabric, hyperelasticity, hyperfoam, +low-density foam, or anisotropic hyperelasticity (except +when used with beam or shell general sections or +substructures) +Required in Abaqus/Explicit, except for hydrostatic +fluid elements +Material damping +*DAMPING +Density +*DENSITY +Solution-dependent +state variables +*DEPVAR +Thermal expansion +*EXPANSION +Complete mechanical behaviors: +These behaviors are mutually exclusive and exclude all behaviors listed for elasticity, plasticity, and +hydrostatic fluid behaviors, including all related enhancements. +Behavior +Keyword +Acoustic medium +Deformation plasticity(S) +Mechanical user material +*ACOUSTIC MEDIUM +*DEFORMATION PLASTICITY +*USER MATERIAL (, TYPE=MECHANICAL +in Abaqus/Standard) +Requires +Density +Elasticity, fabric, and equation of state behaviors: +These behaviors are mutually exclusive. +Behavior +Elasticity +Equation of state(E) +Fabric(E) +Hyperelasticity +Hyperfoam +Anisotropic hyperelasticity +Hypoelasticity(S) +Keyword +Requires +*ELASTIC +*EOS +*FABRIC +*HYPERELASTIC +*HYPERFOAM +*ANISOTROPIC HYPERELASTIC +*HYPOELASTIC +Behavior +Keyword +Requires +Porous elasticity (S) +Low-density foam (E) +*POROUS ELASTIC +*LOW DENSITY FOAM +Enhancements for elasticity behaviors: +Behavior +Keyword +Requires +*ELASTIC, TYPE=SHEAR +Equation of state +Elastic shear behavior +for an equation of state(E) +Strain-based failure +measures +Stress-based failure +measures +Hysteresis(S) +*FAIL STRAIN +*FAIL STRESS +*HYSTERESIS +Mullins effect +*MULLINS EFFECT +*NO COMPRESSION +Elasticity +Compressive failure +theory(S) +Tension failure theory(S) +Viscoelasticity +*NO TENSION +*VISCOELASTIC +Elasticity +Elasticity +Hyperelasticity (excludes all plasticity +behaviors and Mullins effect) +Hyperelasticity (excludes hysteresis), +hyperfoam or anisotropic hyperelasticity +Elasticity +Elasticity, hyperelasticity, or hyperfoam +(excludes all plasticity behaviors and all +associated plasticity enhancements); or +anisotropic hyperelasticity +Equation of state +Shear viscosity for an +equation of state(E) +*VISCOSITY +Rate-independent plasticity behaviors: +These behaviors are mutually exclusive. +Behavior +Keyword +Requires +Brittle cracking(E) +Modified Drucker- +Prager/Cap plasticity +Cast iron plasticity +*BRITTLE CRACKING +*CAP PLASTICITY +Isotropic elasticity and brittle shear +Drucker-Prager/Cap plasticity hardening and +isotropic elasticity or porous elasticity +*CAST IRON PLASTICITY Cast iron compression hardening, cast iron +tension hardening, and isotropic elasticity +Keyword +Requires +MATERIAL BEHAVIORS +Cam-clay plasticity +*CLAY PLASTICITY +Concrete(S) +Concrete damaged +plasticity +Crushable foam +plasticity +Drucker-Prager +plasticity +*CONCRETE +*CONCRETE DAMAGED +PLASTICITY +*CRUSHABLE FOAM +*DRUCKER PRAGER +Elasticity or porous elasticity (in +Abaqus/Standard) +Isotropic elasticity (in Abaqus/Explicit) +Isotropic elasticity +Concrete compression hardening, concrete +tension stiffening, and isotropic elasticity +Crushable foam hardening and isotropic +elasticity +Drucker-Prager hardening and isotropic +elasticity or porous elasticity (in +Abaqus/Standard) +Drucker-Prager hardening and isotropic +elasticity or the combination of an equation +of state and isotropic linear elastic shear +behavior for an equation of state (in +Abaqus/Explicit) +Plastic compaction +behavior for an equation +of state(E) +Jointed material(S) +Mohr-Coulomb +plasticity +Metal plasticity +*EOS COMPACTION +Linear +equation of state +*JOINTED MATERIAL +*MOHR COULOMB +*PLASTIC +Isotropic elasticity and a local orientation +Mohr-Coulomb hardening and isotropic +elasticity +Elasticity or hyperelasticity (in +Abaqus/Standard) +Isotropic elasticity, orthotropic elasticity +(requires anisotropic yield), hyperelasticity, +or the combination of an equation of state +and isotropic linear elastic shear behavior for +an equation of state (in Abaqus/Explicit) +Rate-dependent plasticity behaviors: +These behaviors are mutually exclusive, except metal creep and time-dependent volumetric swelling. +Behavior +Cap creep(S) +Keyword +*CAP CREEP +Metal creep(S) +*CREEP +Requires +Elasticity, modified Drucker-Prager/Cap +plasticity, and Drucker-Prager/Cap +plasticity hardening +Elasticity (except when used to define +rate-dependent gasket behavior; excludes +all rate-independent plasticity behaviors +except metal plasticity) +Drucker-Prager creep(S) +*DRUCKER PRAGER +CREEP +Elasticity, Drucker-Prager plasticity, and +Drucker-Prager hardening +Metal plasticity +*PLASTIC, RATE +Nonlinear +viscoelasticity(S) +Rate-dependent +viscoplasticity +*VISCOELASTIC, +NONLINEAR +*RATE DEPENDENT +Time-dependent +volumetric swelling(S) +*SWELLING +Elasticity or hyperelasticity (in +Abaqus/Standard) +Isotropic elasticity, orthotropic +elasticity (requires anisotropic yield), +hyperelasticity, or the combination of +an equation of state and isotropic linear +elastic shear behavior for an equation of +state (in Abaqus/Explicit) +Hyperelasticity +Drucker-Prager plasticity, crushable foam +plasticity, or metal plasticity +Elasticity (excludes all rate-independent +plasticity behaviors except metal +plasticity) +Two-layer +viscoplasticity(S) +*VISCOUS +Elasticity and metal plasticity +Enhancements for plasticity behaviors: +Behavior +Keyword +Annealing temperature +Brittle failure(E) +*ANNEAL TEMPERATURE +*BRITTLE FAILURE +Requires +Metal plasticity +Brittle cracking and brittle shear +Behavior +Keyword +Requires +Cyclic hardening +*CYCLIC HARDENING +Inelastic heat fraction +*INELASTIC HEAT +FRACTION +Oak Ridge National +Laboratory constitutive +model(S) +*ORNL +Porous material failure +criteria(E) +*POROUS FAILURE +CRITERIA +Porous metal plasticity +*POROUS METAL +PLASTICITY +Anisotropic yield/creep +*POTENTIAL +Shear failure(E) +Tension cutoff +*SHEAR FAILURE +*TENSION CUTOFF +Metal plasticity with nonlinear +isotropic/kinematic hardening +Metal plasticity and specific heat +Metal plasticity, cycled yield +stress data, and, usually, metal +creep +Porous metal plasticity +Metal plasticity +Metal plasticity, metal creep, or +two-layer viscoplasticity +Metal plasticity +Mohr-Coulomb plasticity +Enhancement for elasticity or plasticity behaviors: +Behavior +Tensile failure(E) +Keyword +Requires +*TENSILE FAILURE +Damage initiation +*DAMAGE INITIATION +Metal plasticity or equation of +state +For elasticity behaviors: elasticity +based on a traction-separation +description for cohesive +elements or elasticity model +for fiber-reinforced composites +For plasticity behaviors: +elasticity and metal plasticity or +Drucker-Prager plasticity +Damage evolution +Damage stabilization +*DAMAGE EVOLUTION +*DAMAGE STABILIZATION +Damage initiation +Damage evolution +Thermal behaviors: +These behaviors are unrestricted but exclude thermal user materials. +Behavior +Keyword +Requires +Thermal conductivity +Volumetric heat generation(S) +Latent heat +Specific heat +*CONDUCTIVITY +*HEAT GENERATION +*LATENT HEAT +*SPECIFIC HEAT +Density +Density +Complete thermal behavior: +This behavior is unrestricted but excludes the thermal behaviors in the previous table. +Behavior +Keyword +Requires +Thermal user material(S) +*USER MATERIAL, TYPE=THERMAL Density +Pore fluid flow behaviors: +These behaviors are unrestricted. +Behavior +Swelling gel(S) +Keyword +*GEL +Moisture-driven swelling(S) +*MOISTURE SWELLING +Requires +Permeability, porous bulk moduli, +and absorption/exsorption +behavior +Permeability and +absorption/exsorption behavior +Permeability(S) +Porous bulk moduli(S) +*PERMEABILITY +*POROUS BULK MODULI Permeability and either elasticity +Absorption/exsorption +behavior(S) +*SORPTION +or porous elasticity +Permeability +Electrical behaviors: +These behaviors are unrestricted. +Behavior +Dielectricity(S) +Electrical conductivity(S) +Fraction of electric +energy released as +heat(S) +Piezoelectricity(S) +Keyword +Requires +*DIELECTRIC +*ELECTRICAL CONDUCTIVITY +*JOULE HEAT FRACTION +*PIEZOELECTRIC +Mass diffusion behaviors: +These behaviors exclude all other behaviors. +Behavior +Keyword +Mass diffusivity(S) +Solubility(S) +*DIFFUSIVITY +*SOLUBILITY +Requires +Solubility +Mass diffusivity +Hydrostatic fluid behaviors: +Behavior +Keyword +Requires +Fluid bulk modulus(S) +Hydrostatic fluid density +Fluid thermal expansion +coefficient(S) +*FLUID BULK MODULUS Hydraulic fluid +*FLUID DENSITY +*FLUID EXPANSION +Hydraulic fluid +21.2 +General properties +• “Density,” Section 21.2.1 +21.2.1 +DENSITY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• *DENSITY +• “Specifying material mass density,” Section 12.8.1 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +A material’s mass density: +• must be defined in Abaqus/Standard for eigenfrequency and transient dynamic analysis, transient +heat transfer analysis, adiabatic stress analysis, and acoustic analysis; +• must be defined in Abaqus/Standard for gravity, centrifugal, and rotary acceleration loading; +• must be defined in Abaqus/Explicit for all materials except hydrostatic fluids; +• must be defined in Abaqus/CFD for all fluids; +• can be specified as a function of temperature and predefined variables; +• can be distributed from nonstructural features (such as paint on sheet metal panels in a car) to the +underlying elements using a nonstructural mass definition; and +• can be defined with a distribution for solid continuum elements in Abaqus/Standard. +Defining density +Density can be defined as a function of temperature and field variables. However, for all elements in +Abaqus/Standard with the exception of acoustic, heat transfer, coupled temperature-displacement, and +coupled thermal-electrical elements , the density is a function of the initial values of temperature and +field variables and changes in volume only. It will not be updated if temperatures and field variables +change during the analysis. For Abaqus/Explicit the exception includes acoustic elements only. For +Abaqus/CFD the density is considered constant for incompressible flows. +For acoustic, heat transfer, coupled temperature-displacement, and coupled thermal-electrical +elements in Abaqus/Standard and acoustic elements in Abaqus/Explicit, the density will be continually +updated to the value corresponding to the current temperature and field variables. +In an Abaqus/Standard analysis a spatially varying mass density can be defined for homogeneous +solid continuum elements by using a distribution (“Distribution definition,” Section 2.8.1). The +distribution must include a default value for the density. If a distribution is used, no dependencies on +temperature and/or field variables for the density can be defined. +Input File Usage: +Use either of the following options: +Abaqus/CAE Usage: +*DENSITY +*DENSITY, DEPENDENCIES=n +Property module: material editor: General→Density +You can toggle on Use temperature-dependent data to define the density +as a function of temperature and/or select the Number of field variables to +define the density as a function of field variables. +Units +Since Abaqus has no built-in dimensions, you must ensure that the density is given in consistent units. +The use of consistent units, and density in particular, is discussed in “Conventions,” Section 1.2.2. If +American or English units are used, you must be particularly careful that the density used is in units of +ML , where mass is defined in units of FT L . +Elements +The density behavior described in this section is used to specify mass density for all elements, except +rigid elements. Mass density for rigid elements is specified as part of the rigid body definition . +In Abaqus/Explicit a nonzero mass density must be defined for all elements that are not part of a +rigid body. +In Abaqus/Standard density must be defined for heat transfer elements and acoustic elements; mass +density can be defined for stress/displacement elements, coupled temperature-displacement elements, +and elements including pore pressure. For elements that include pore pressure as a degree of freedom, +the density of the dry material should be given for the porous medium in a coupled pore fluid flow/stress +analysis. +If you have a complex density for an acoustic medium, you should enter its real part here and convert +the imaginary part into a volumetric drag, as discussed in “Acoustic medium,” Section 26.3.1. +The mass contribution from features that have negligible structural stiffness can be added to the +model by smearing the mass over an element set that is typically adjacent to the nonstructural feature. +The nonstructural mass can be specified in the form of a total mass value, a mass per unit volume, a +mass per unit area, or a mass per unit length . A +nonstructural mass definition contributes additional mass to the specified element set and does not alter +the underlying material density. +22. +Elastic Mechanical Properties +Overview +Linear elasticity +Porous elasticity +Hypoelasticity +Hyperelasticity +Stress softening in elastomers +Viscoelasticity +Nonlinear Viscoelasticity +Rate sensitive elastomeric foams +22.1 +22.2 +22.3 +22.4 +22.5 +22.6 +22.7 +22.8 +22.1 +Overview +• “Elastic behavior: overview,” Section 22.1.1 +22.1.1 +ELASTIC BEHAVIOR: OVERVIEW +The material library in Abaqus includes several models of elastic behavior: +• Linear elasticity: Linear elasticity (“Linear elastic behavior,” Section 22.2.1) is the simplest form of +elasticity available in Abaqus. The linear elastic model can define isotropic, orthotropic, or anisotropic +material behavior and is valid for small elastic strains. +• Plane stress orthotropic failure: Failure theories are provided (“Plane stress orthotropic failure +measures,” Section 22.2.3) for use with linear elasticity. They can be used to obtain postprocessed output +requests. +• Porous elasticity: The porous elastic model in Abaqus/Standard (“Elastic behavior of porous +materials,” Section 22.3.1) is used for porous materials in which the volumetric part of the elastic strain +varies with the logarithm of the equivalent pressure stress. This form of nonlinear elasticity is valid for +small elastic strains. +• Hypoelasticity: The hypoelastic model in Abaqus/Standard (“Hypoelastic behavior,” Section 22.4.1) +is used for materials in which the rate of change of stress is defined by an elasticity matrix multiplying +the rate of change of elastic strain, where the elasticity matrix is a function of the total elastic strain. This +general, nonlinear elasticity is valid for small elastic strains. +• Rubberlike hyperelasticity: For +rubberlike material at finite strain the hyperelastic model +(“Hyperelastic behavior of rubberlike materials,” Section 22.5.1) provides a general strain energy +potential to describe the material behavior for nearly incompressible elastomers. This nonlinear +elasticity model is valid for large elastic strains. +• Foam hyperelasticity: The hyperfoam model (“Hyperelastic behavior in elastomeric foams,” +Section 22.5.2) provides a general capability for elastomeric compressible foams at finite strains. +This nonlinear elasticity model is valid for large strains (especially large volumetric changes). The +low-density foam model in Abaqus/Explicit (“Low-density foams,” Section 22.9.1) is a nonlinear +viscoelastic model suitable for specifying strain-rate sensitive behavior of low-density elastomeric foams +such as used in crash and impact applications. The foam plasticity model (“Crushable foam plasticity +models,” Section 23.3.5) should be used for foam materials that undergo permanent deformation. +• Anisotropic hyperelasticity: The anisotropic hyperelastic model +(“Anisotropic hyperelastic +behavior,” Section 22.5.3) provides a general capability for modeling materials that exhibit highly +anisotropic and nonlinear elastic behavior (such as biomedical soft tissues, fiber-reinforced elastomers, +etc.). The model is valid for large elastic strains and captures the changes in the preferred material +directions (or fiber directions) with deformation. +• Fabric materials: The fabric model in Abaqus/Explicit (“Fabric material behavior,” Section 23.4.1) +for woven fabrics captures the directional nature of the stiffness along the fill and the warp yarn directions. +It also captures the shear response as the yarn directions rotate relative to each other. The model takes +into account finite strains including large shear rotations. It captures the highly nonlinear elastic response +of fabrics through the use of test data or a user subroutine, VFABRIC for the material characterization. The test data based +fabric behavior can include nonlinear elasticity, permanent deformation, rate-dependent response, and +damage accumulation. +• Viscoelasticity: The viscoelastic model +is used to specify time-dependent material behavior +(“Time domain viscoelasticity,” Section 22.7.1). +In Abaqus/Standard it is also used to specify +frequency-dependent material behavior (“Frequency domain viscoelasticity,” Section 22.7.2). It must +be combined with linear elasticity, rubberlike hyperelasticity, or foam hyperelasticity. +• Parallel network viscoelastic model: The parallel network viscoelastic model in Abaqus/Standard +(“Parallel network viscoelastic model,” Section 22.8.2) is intended for modeling nonlinear viscous +behavior for materials subjected to large strains, such as polymers. The model consists of multiple +parallel elastic and viscoelastic networks. The elastic response is defined using the hyperelastic material +model, and the viscous response is specified using the flow rule derived from a creep potential. +• Hysteresis: The hysteresis model in Abaqus/Standard (“Hysteresis in elastomers,” Section 22.8.1) is +used to specify rate-dependent behavior of elastomers. It is used in conjunction with hyperelasticity. +• Mullins effect: The Mullins effect model (“Mullins effect,” Section 22.6.1) is used to specify stress +softening of filled rubber elastomers due to damage, a phenomenon referred to as Mullins effect. +The model can also be used to include permanent energy dissipation and stress softening effects in +elastomeric foams (“Energy dissipation in elastomeric foams,” Section 22.6.2). It is used in conjunction +with rubberlike hyperelasticity or foam hyperelasticity. +• No compression or no tension elasticity: The no compression or no tension models in +Abaqus/Standard (“No compression or no tension,” Section 22.2.2) can be used when compressive or +tensile principal stresses should not be generated. These options can be used only with linear elasticity. +Thermal strain +Thermal expansion can be introduced for any of the elasticity or fabric models (“Thermal expansion,” +Section 26.1.2). +Elastic strain magnitude +Except in the hyperelasticity and fabric material models, the stresses are always assumed to be small +compared to the tangent modulus of the elasticity relationship; that is, the elastic strain must be small +(less than 5%). The total strain can be arbitrarily large if inelastic response such as metal plasticity is +included in the material definition. +For finite-strain calculations where the large strains are purely elastic, the fabric model (for +woven fabrics), the hyperelastic model (for rubberlike behavior), or the foam hyperelasticity model +(for elastomeric foams) should be used. The hyperelasticity and fabric models are the only models +that give realistic predictions of actual material behavior at large elastic strains. The linear or, in +Abaqus/Standard, porous elasticity models are appropriate in other cases where the large strains are +inelastic. +In Abaqus/Standard the linear elastic, porous elastic, and hypoelastic models will exhibit poor +convergence characteristics if the stresses reach levels of 50% or more of the elastic moduli; this +large strains. +ELASTIC BEHAVIOR +22.2 +Linear elasticity +• “Linear elastic behavior,” Section 22.2.1 +• “No compression or no tension,” Section 22.2.2 +• “Plane stress orthotropic failure measures,” Section 22.2.3 +22.2.1 +LINEAR ELASTIC BEHAVIOR +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Elastic behavior: overview,” Section 22.1.1 +• *ELASTIC +• “Creating a linear elastic material model” in “Defining elasticity,” Section 12.9.1 of the +Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +A linear elastic material model: +• is valid for small elastic strains (normally less than 5%); +• can be isotropic, orthotropic, or fully anisotropic; +• can have properties that depend on temperature and/or other field variables; and +• can be defined with a distribution for solid continuum elements in Abaqus/Standard. +Defining linear elastic material behavior +The total stress is defined from the total elastic strain as +is the total stress (“true,” or Cauchy stress in finite-strain problems), +is the fourth-order +where +elasticity tensor, and +is the total elastic strain (log strain in finite-strain problems). Do not use the +linear elastic material definition when the elastic strains may become large; use a hyperelastic model +instead. Even in finite-strain problems the elastic strains should still be small (less than 5%). +Defining linear elastic response for viscoelastic materials +The elastic response of a viscoelastic material (“Time domain viscoelasticity,” Section 22.7.1) can be +specified by defining either the instantaneous response or the long-term response of the material. To +define the instantaneous response, experiments to determine the elastic constants have to be performed +within time spans much shorter than the characteristic relaxation time of the material. +Input File Usage: +Abaqus/CAE Usage: +*ELASTIC, MODULI=INSTANTANEOUS +Property module: material editor: Mechanical→Elasticity→Elastic: +Moduli time scale (for viscoelasticity): Instantaneous +If, on the other hand, the long-term elastic response is used, data from experiments have to be +collected after time spans much longer than the characteristic relaxation time of the viscoelastic material. +Long-term elastic response is the default elastic material behavior. +Input File Usage: +Abaqus/CAE Usage: +*ELASTIC, MODULI=LONG TERM +Property module: material editor: Mechanical→Elasticity→Elastic: +Moduli time scale (for viscoelasticity): Long-term +Directional dependence of linear elasticity +Depending on the number of symmetry planes for the elastic properties, a material can be classified as +either isotropic (an infinite number of symmetry planes passing through every point) or anisotropic +(no symmetry planes). Some materials have a restricted number of symmetry planes passing through +every point; for example, orthotropic materials have two orthogonal symmetry planes for the elastic +properties. The number of independent components of the elasticity tensor +depends on such +symmetry properties. You define the level of anisotropy and method of defining the elastic properties, +as described below. +If the material is anisotropic, a local orientation (“Orientations,” Section 2.2.5) +must be used to define the direction of anisotropy. +Stability of a linear elastic material +Linear elastic materials must satisfy the conditions of material or Drucker stability . Stability requires +that the tensor +be positive definite, which leads to certain restrictions on the values of the elastic +constants. The stress-strain relations for several different classes of material symmetries are given below. +The appropriate restrictions on the elastic constants stemming from the stability criterion are also given. +Defining isotropic elasticity +The simplest form of linear elasticity is the isotropic case, and the stress-strain relationship is given by +The elastic properties are completely defined by giving the Young’s modulus, E, and the Poisson’s +. These +ratio, +parameters can be given as functions of temperature and of other predefined fields, if necessary. +. The shear modulus, G, can be expressed in terms of E and +as +In Abaqus/Standard spatially varying isotropic elastic behavior can be defined for homogeneous +solid continuum elements by using a distribution (“Distribution definition,” Section 2.8.1). The +distribution must include default values for E and . +If a distribution is used, no dependencies on +temperature and/or field variables for the elastic constants can be defined. +Input File Usage: +Abaqus/CAE Usage: +*ELASTIC, TYPE=ISOTROPIC +Property module: material editor: Mechanical→Elasticity→Elastic: +Type: Isotropic +Stability +The stability criterion requires that +. Values of Poisson’s ratio +approaching 0.5 result in nearly incompressible behavior. With the exception of plane stress cases +(including membranes and shells) or beams and trusses, such values generally require the use of +“hybrid” elements in Abaqus/Standard and generate high frequency noise and result in excessively +small stable time increments in Abaqus/Explicit. +, and +, +Defining orthotropic elasticity by specifying the engineering constants +Linear elasticity in an orthotropic material is most easily defined by giving the “engineering constants”: +the three moduli +, +associated with the material’s principal directions. These moduli define the elastic compliance according +to +; and the shear moduli +; Poisson’s ratios +, and +, +, +, +, +The quantity +strain in the j-direction, when the material is stressed in the i-direction. In general, +has the physical interpretation of the Poisson’s ratio that characterizes the transverse +is not equal to +. The engineering constants can also be given as functions of +: they are related by += +temperature and other predefined fields, if necessary. +In Abaqus/Standard spatially varying orthotropic elastic behavior can be defined for homogeneous +solid continuum elements by using a distribution (“Distribution definition,” Section 2.8.1). The +distribution must include default values for the elastic moduli and Poisson’s ratios. If a distribution is +used, no dependencies on temperature and/or field variables for the elastic constants can be defined. +Input File Usage: +Abaqus/CAE Usage: +*ELASTIC, TYPE=ENGINEERING CONSTANTS +Property module: material editor: Mechanical→Elasticity→Elastic: +Type: Engineering Constants +Stability +Material stability requires +When the left-hand side of the inequality approaches zero, the material exhibits incompressible +, the second, third, and fourth restrictions in the above set += +behavior. Using the relations +can also be expressed as +Defining transversely isotropic elasticity +A special subclass of orthotropy is transverse isotropy, which is characterized by a plane of isotropy at +every point in the material. Assuming the 1–2 plane to be the plane of isotropy at every point, transverse +isotropy requires that +, where p and t stand += +for “in-plane” and “transverse,” respectively. Thus, while +has the physical interpretation of the +Poisson’s ratio that characterizes the strain in the plane of isotropy resulting from stress normal to it, +characterizes the transverse strain in the direction normal to the plane of isotropy resulting from +are not equal and are related by +stress in the plane of isotropy. In general, the quantities +, and +and += += += += += += += +, +, += +. The stress-strain laws reduce to += +where +and the total number of independent constants is only five. +In Abaqus/Standard spatially varying transverse isotropic elastic behavior can be defined for +homogeneous solid continuum elements by using a distribution (“Distribution definition,” Section 2.8.1). +The distribution must include default values for the elastic moduli and Poisson’s ratio. If a distribution +is used, no dependencies on temperature and/or field variables for the elastic constants can be defined. +*ELASTIC, TYPE=ENGINEERING CONSTANTS +Property module: material editor: Mechanical→Elasticity→Elastic: +Type: Engineering Constants +Abaqus/CAE Usage: +Input File Usage: +Stability +In the transversely isotropic case the stability relations for orthotropic elasticity simplify to +Defining orthotropic elasticity in plane stress +Under plane stress conditions, such as in a shell element, only the values of +, +, +, +, +, and +are required to define an orthotropic material. (In all of the plane stress elements in Abaqus the +and +surface is the surface of plane stress, so that the plane stress condition is +.) The shear moduli +are included because they may be required for modeling transverse shear deformation in +. In this case the stress-strain +a shell. The Poisson’s ratio +relations for the in-plane components of the stress and strain are of the form +is implicitly given as +In Abaqus/Standard spatially varying plane stress orthotropic elastic behavior can be defined for +homogeneous solid continuum elements by using a distribution (“Distribution definition,” Section 2.8.1). +The distribution must include default values for the elastic moduli and Poisson’s ratio. If a distribution +is used, no dependencies on temperature and/or field variables for the elastic constants can be defined. +Input File Usage: +Abaqus/CAE Usage: +*ELASTIC, TYPE=LAMINA +Property module: material editor: Mechanical→Elasticity→Elastic: +Type: Lamina +Stability +Material stability for plane stress requires +Defining orthotropic elasticity by specifying the terms in the elastic stiffness matrix +Linear elasticity in an orthotropic material can also be defined by giving the nine independent elastic +stiffness parameters, as functions of temperature and other predefined fields, if necessary. In this case +the stress-strain relations are of the form +For an orthotropic material the engineering constants define the matrix as +where +When the material stiffness parameters (the +) are given directly, Abaqus imposes the constraint +for the plane stress case to reduce the material’s stiffness matrix as required. +In Abaqus/Standard spatially varying orthotropic elastic behavior can be defined for homogeneous +solid continuum elements by using a distribution (“Distribution definition,” Section 2.8.1). The +distribution must include default values for the elastic moduli. If a distribution is used, no dependencies +on temperature and/or field variables for the elastic constants can be defined. +Input File Usage: +Abaqus/CAE Usage: +*ELASTIC, TYPE=ORTHOTROPIC +Property module: material editor: Mechanical→Elasticity→Elastic: +Type: Orthotropic +Stability +The restrictions on the elastic constants due to material stability are +The last relation leads to +These restrictions in terms of the elastic stiffness parameters are equivalent to the restrictions in +terms of the “engineering constants.” Incompressible behavior results when the left-hand side of the +inequality approaches zero. +Defining fully anisotropic elasticity +For fully anisotropic elasticity 21 independent elastic stiffness parameters are needed. The stress-strain +relations are as follows: +When the material stiffness parameters (the +) are given directly, Abaqus imposes the constraint +for the plane stress case to reduce the material’s stiffness matrix as required. +In Abaqus/Standard spatially varying anisotropic elastic behavior can be defined for homogeneous +solid continuum elements by using a distribution (“Distribution definition,” Section 2.8.1). The +distribution must include default values for the elastic moduli. If a distribution is used, no dependencies +on temperature and/or field variables for the elastic constants can be defined. +Input File Usage: +Abaqus/CAE Usage: +*ELASTIC, TYPE=ANISOTROPIC +Property module: material editor: Mechanical→Elasticity→Elastic: +Type: Anisotropic +Stability +The restrictions imposed upon the elastic constants by stability requirements are too complex to express +in terms of simple equations. However, the requirement that +is positive definite requires that all of +the eigenvalues of the elasticity matrix +be positive. +Defining orthotropic elasticity for warping elements +For two-dimensional meshed models of solid cross-section Timoshenko beam elements modeled with +warping elements , Abaqus offers a linear elastic +material definition that can have two different shear moduli in the user-specified material directions. In +the user-specified directions the stress-strain relations are as follows: +A local orientation is used to define the angle +material directions. In the cross-section directions the stress-strain relations are as follows: +between the global directions and the user-specified +where +represents the beam’s axial stress and +and +represent two shear stresses. +Input File Usage: +Abaqus/CAE Usage: +*ELASTIC, TYPE=TRACTION +Property module: material editor: Mechanical→Elasticity→Elastic: +Type: Traction +Stability +The stability criterion requires that +, +, and +. +Defining elasticity in terms of tractions and separations for cohesive elements +For cohesive elements used to model bonded interfaces Abaqus offers an elasticity +definition that can be written directly in terms of the nominal tractions and the nominal strains. Both +uncoupled and coupled behaviors are supported. For uncoupled behavior each traction component +depends only on its conjugate nominal strain, while for coupled behavior the response is more general +(as shown below). In the local element directions the stress-strain relations for uncoupled behavior are +as follows: +, +The quantities +directions, respectively; while the quantities +For coupled traction separation behavior the stress-strain relations are as follows: +represent the nominal tractions in the normal and the two local shear +represent the corresponding nominal strains. +, and +, and +, +Input File Usage: +Abaqus/CAE Usage: +Use the following option to define uncoupled elastic behavior for cohesive +elements: +*ELASTIC, TYPE=TRACTION +Use the following option to define coupled elastic behavior for cohesive +elements: +*ELASTIC, TYPE=COUPLED TRACTION +Use the following option to define uncoupled elastic behavior for cohesive +elements: +Property module: material editor: Mechanical→Elasticity→Elastic: +Type: Traction +Use the following option to define coupled elastic behavior for cohesive +elements: +Property module: material editor: Mechanical→Elasticity→Elastic: +Type: Coupled Traction +Stability +The stability criterion for uncoupled behavior requires that +coupled behavior the stability criterion requires that: +, +, and +. For +Defining isotropic shear elasticity for equations of state in Abaqus/Explicit +Abaqus/Explicit allows you to define isotropic shear elasticity to describe the deviatoric response of +materials whose volumetric response is governed by an equation of state (“Elastic shear behavior” in +“Equation of state,” Section 25.2.1). In this case the deviatoric stress-strain relationship is given by +is the deviatoric stress and +is the deviatoric elastic strain. You must provide the elastic shear +where +modulus, +, when you define the elastic deviatoric behavior. +Input File Usage: +Abaqus/CAE Usage: +*ELASTIC, TYPE=SHEAR +Property module: material editor: Mechanical→Elasticity→Elastic: Type: +Shear +Elements +Linear elasticity can be used with any stress/displacement element or coupled temperature-displacement +element in Abaqus. The exceptions are traction elasticity, which can be used only with warping elements +and cohesive elements; coupled traction elasticity, which can be used only with cohesive elements; shear +elasticity, which can be used only with solid (continuum) elements except plane stress elements; and, in +Abaqus/Explicit, anisotropic elasticity, which is not supported for truss, rebar, pipe, and beam elements. +for isotropic elasticity), hybrid +elements should be used in Abaqus/Standard. Compressible anisotropic elasticity should not be used with +second-order hybrid continuum elements: inaccurate results and/or convergence problems may occur. +If the material is (almost) incompressible (Poisson’s ratio +22.2.2 +NO COMPRESSION OR NO TENSION +Products: Abaqus/Standard Abaqus/CAE +WARNING: Except when used with truss or beam elements, Abaqus/Standard does +not form an exact material stiffness for this option. Therefore, the convergence +can sometimes be slow. +References +• “Material library: overview,” Section 21.1.1 +• “Elastic behavior: overview,” Section 22.1.1 +• “Linear elastic behavior,” Section 22.2.1 +• *NO COMPRESSION +• *NO TENSION +• “Specifying elastic material properties” in “Defining elasticity,” Section 12.9.1 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +The no compression and no tension elasticity models: +• are used to modify the linear elasticity of the material so that compressive stress or tensile stress +cannot be generated; and +• can be used only in conjunction with an elasticity definition. +Defining the modified elastic behavior +The modified elastic behavior is obtained by first solving for the principal stresses assuming linear +elasticity and then setting the appropriate principal stress values to zero. The associated stiffness matrix +components will also be set to zero. These models are not history dependent: the directions in which +the principal stresses are set to zero are recalculated at every iteration. +The no compression effect for a one-dimensional stress case such as a truss or a layer of a beam +in a plane is illustrated in Figure 22.2.2–1. No compression and no tension definitions modify only the +elastic response of the material. +Strain +Stress +A B C +Time +A B C +Time +Stress + Strain +Figure 22.2.2–1 A no compression elastic case with an imposed strain cycle. +Input File Usage: +Use one of the following options: +*NO COMPRESSION +*NO TENSION +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Elasticity→Elastic: +No compression or No tension +Stability +Using no compression or no tension elasticity can make a model unstable: convergence difficulties +may occur. Sometimes these difficulties can be overcome by overlaying each element that uses the +no compression (or no tension) model with another element that uses a small value of Young’s modulus +(small in comparison with the Young’s modulus of the element using modified elasticity). This technique +creates a small “artificial” stiffness, which can stabilize the model. +Use with other material models +No compression and no tension definitions can be used only in conjunction with an elasticity definition. +These definitions cannot be used with any other material option. +Elements +The no compression and no tension elasticity models can be used with any stress/displacement element +in Abaqus/Standard. However, they cannot be used with shell elements or beam elements if section +properties are pre-integrated using a general section definition. +22.2.3 +PLANE STRESS ORTHOTROPIC FAILURE MEASURES +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Elastic behavior: overview,” Section 22.1.1 +• “Linear elastic behavior,” Section 22.2.1 +• *FAIL STRAIN +• *FAIL STRESS +• *ELASTIC +• “Defining stress-based failure measures for an elastic model” in “Defining elasticity,” Section 12.9.1 +of the Abaqus/CAE User’s Manual, in the online HTML version of this manual +• “Defining strain-based failure measures for an elastic model” in “Defining elasticity,” Section 12.9.1 +of the Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +The orthotropic plane stress failure measures: +• are indications of material failure (normally used for fiber-reinforced composite materials; for +alternative damage and failure models for fiber-reinforced composite materials, see “Damage and +failure for fiber-reinforced composites: overview,” Section 24.3.1); +• can be used only in conjunction with a linear elastic material model (with or without local material +orientations); +• can be used for any element that uses a plane stress formulation; that is, for plane stress continuum +elements, shell elements, and membrane elements; +• are postprocessed output requests and do not cause any material degradation; and +• take values that are greater than or equal to 0.0, with values that are greater than or equal to 1.0 +implying failure. +Failure theories +Five different failure theories are provided: four stress-based theories and one strain-based theory. +We denote orthotropic material directions by 1 and 2, with the 1-material direction aligned with the +fibers and the 2-material direction transverse to the fibers. For the failure theories to work correctly, the 1- +and 2-directions of the user-defined elastic material constants must align with the fiber and the transverse- +to-fiber directions, respectively. For applications other than fiber-reinforced composites, the 1- and 2- +material directions should represent the strong and weak orthotropic-material directions, respectively. +In all cases tensile values must be positive and compressive values must be negative. +Stress-based failure theories +The input data for the stress-based failure theories are tensile and compressive stress limits, +in the 1-direction; tensile and compressive stress limits, +(maximum shear stress), S, in the X–Y plane. +, +, in the 2-direction; and shear strength +and +and +All four stress-based theories are defined and available with a single definition in Abaqus; the desired +output is chosen by the output variables described at the end of this section. +Input File Usage: +Abaqus/CAE Usage: +*FAIL STRESS +Property module: material editor: Mechanical→Elasticity→Elastic: +Suboptions→Fail Stress +Maximum stress theory +If +stress failure criterion requires that +; otherwise, +, +. If +, +; otherwise, +. The maximum +max +Tsai-Hill theory +If +, +criterion requires that +; otherwise, +. If +, +; otherwise, +. The Tsai-Hill failure +Tsai-Wu theory +The Tsai-Wu failure criterion requires that +The Tsai-Wu coefficients are defined as follows: +is the equibiaxial stress at failure. If it is known, then +otherwise, +where +. The default value of +is zero. For the Tsai-Wu failure criterion either +or +must be given as input data. The coefficient +is ignored if +is given. +Azzi-Tsai-Hill theory +The Azzi-Tsai-Hill failure theory is the same as the Tsai-Hill theory, except that the absolute value of the +cross product term is taken: +This difference between the two failure criteria shows up only when +and +have opposite signs. +Stress-based failure measures—failure envelopes +) in ( +To illustrate the four stress-based failure measures, Figure 22.2.3–1, Figure 22.2.3–2, and Figure 22.2.3–3 +show each failure envelope (i.e., +) stress space compared to the Tsai-Hill envelope +– +for a given value of in-plane shear stress. In each case the Tsai-Hill surface is the piecewise continuous +elliptical surface with each quadrant of the surface defined by an ellipse centered at the origin. The +parallelogram in Figure 22.2.3–1 defines the maximum stress surface. In Figure 22.2.3–2 the Tsai-Wu +surface appears as the ellipse. In Figure 22.2.3–3 the Azzi-Tsai-Hill surface differs from the Tsai-Hill +surface only in the second and fourth quadrants, where it is the outside bounding surface (i.e., further +from the origin). Since all of the failure theories are calibrated by tensile and compressive failure under +uniaxial stress, they all give the same values on the stress axes. +22 +11 +Figure 22.2.3–1 Tsai-Hill versus maximum stress failure envelope ( +). +22 +11 +Tsai-Hill +Tsai-Wu +Figure 22.2.3–2 Tsai-Hill versus Tsai-Wu failure envelope ( +, +). +22 +11 +Tsai-Hill +Azzi-Tsai-Hill +Figure 22.2.3–3 Tsai-Hill versus Azzi-Tsai-Hill failure envelope ( +). +Strain-based failure theory +The input data for the strain-based theory are tensile and compressive strain limits, +1-direction; tensile and compressive strain limits, +, in the +, in the 2-direction; and shear strain limit, +and +and +, in the X–Y plane. +Input File Usage: +Abaqus/CAE Usage: +Maximum strain theory +*FAIL STRAIN +Property module: material editor: Mechanical→Elasticity→Elastic: +Suboptions→Fail Strain +If +strain failure criterion requires that +; otherwise, +, +. If +, +; otherwise, +. The maximum +max +Elements +The plane stress orthotropic failure measures can be used with any plane stress, shell, or membrane +element in Abaqus. +Output +Abaqus provides output of the failure index, R, if failure measures are defined with the material +description. The definition of the failure index and the different output variables are described below. +Output failure indices +Each of the stress-based failure theories defines a failure surface surrounding the origin in the three- +dimensional space +. Failure occurs any time a state of stress is either on or outside this +surface. The failure index, R, is used to measure the proximity to the failure surface. R is defined as the +scaling factor such that, for the given stress state +, +that is, +simultaneously to lie on the failure surface. Values +failure surface, while values +is the scaling factor with which we need to multiply all of the stress components +indicate that the state of stress is within the +indicate failure. For the maximum stress theory +. +The failure index R is defined similarly for the maximum strain failure theory. R is the scaling +factor such that, for the given strain state +, +For the maximum strain theory +. +Output variables +Output variable CFAILURE will provide output for all of the stress- and strain-based failure theories +. In Abaqus/Standard history output can also be requested for the individual +stress theories with output variables MSTRS, TSAIH, TSAIW, and AZZIT and for the strain theory with +output variable MSTRN. +Output variables for the stress- and strain-based failure theories are always calculated at the material +points of the element. In Abaqus/Standard element output can be requested at a location other than the +material points ; in this case the output variables +are first calculated at the material points, then interpolated to the element centroid or extrapolated to the +nodes. +22.3 +Porous elasticity +• “Elastic behavior of porous materials,” Section 22.3.1 +22.3.1 +ELASTIC BEHAVIOR OF POROUS MATERIALS +Products: Abaqus/Standard Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Elastic behavior: overview,” Section 22.1.1 +• *POROUS ELASTIC +• *INITIAL CONDITIONS +• “Creating a porous elastic material model” in “Defining elasticity,” Section 12.9.1 of the +Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +A porous elastic material model: +• is valid for small elastic strains (normally less than 5%); +• is a nonlinear, isotropic elasticity model in which the pressure stress varies as an exponential +function of volumetric strain; +• allows a zero or nonzero elastic tensile stress limit; and +• can have properties that depend on temperature and other field variables. +Defining the volumetric behavior +Often, the elastic part of the volumetric behavior of porous materials is modeled accurately by assuming +that the elastic part of the change in volume of the material is proportional to the logarithm of the pressure +stress (Figure 22.3.1–1): +is the “logarithmic bulk modulus”; +where +defined by +is the initial void ratio; p is the equivalent pressure stress, +is the initial value of the equivalent pressure stress; +the current and reference configurations; and +sense that +as +). +is the elastic part of the volume ratio between +is the “elastic tensile strength” of the material (in the +Input File Usage: +Use all three of the following options to define a porous elastic material: +*POROUS ELASTIC, SHEAR=G or POISSON to define +and +ol +el +-p +p0 +p0 +el +p +Figure 22.3.1–1 Porous elastic volumetric behavior. +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=STRESS to define +*INITIAL CONDITIONS, TYPE=RATIO to define +Use all three of the following options to define a porous elastic material: +Property module: material editor: Mechanical→Elasticity→Porous Elastic +Load module: Create Predefined Field: Step: Initial: choose Mechanical +for the Category and Stress for the Types for Selected Step +Load module: Create Predefined Field: Step: Initial: choose Other for +the Category and Void ratio for the Types for Selected Step +Defining the shear behavior +The deviatoric elastic behavior of a porous material can be defined in either of two ways. +By defining the shear modulus +Give the shear modulus, G. The deviatoric stress, +elastic strain, +, by +, is then related to the deviatoric part of the total +In this case the shear behavior is not affected by compaction of the material. +Input File Usage: +*POROUS ELASTIC, SHEAR=G +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Elasticity→Porous +Elastic: Shear: G +By defining Poisson’s ratio +Define Poisson’s ratio, +modulus and Poisson’s ratio as +. The instantaneous shear modulus is then defined from the instantaneous bulk +where +is the logarithmic measure of the elastic volume change. In this case +Thus, the elastic shear stiffness increases as the material is compacted. This equation is integrated to +give the total stress–total elastic strain relationship. +Input File Usage: +Abaqus/CAE Usage: +*POROUS ELASTIC, SHEAR=POISSON +Property module: material editor: Mechanical→Elasticity→Porous +Elastic: Shear: Poisson +Use with other material models +The porous elasticity model can be used by itself, or it can be combined with: +• the “Extended Drucker-Prager models,” Section 23.3.1; +• the “Modified Drucker-Prager/Cap model,” Section 23.3.2; +• the “Critical state (clay) plasticity model,” Section 23.3.4; or +• isotropic expansion to introduce thermal volume changes (“Thermal expansion,” Section 26.1.2). +It is not possible to use porous elasticity with rate-dependent plasticity or viscoelasticity. +Porous elasticity cannot be used with the porous metal plasticity model (“Porous metal plasticity,” +Section 23.2.9). +See “Combining material behaviors,” Section 21.1.3, for more details. +Elements +Porous elasticity cannot be used with hybrid elements or plane stress elements (including shells and +membranes), but it can be used with any other pure stress/displacement element in Abaqus/Standard. +If used with reduced-integration elements with total-stiffness hourglass control, Abaqus/Standard +cannot calculate a default value for the hourglass stiffness of the element if the shear behavior is defined +through Poisson’s ratio. Hence, you must specify the hourglass stiffness. See “Section controls,” +Section 27.1.4, for details. +If fluid pore pressure is important (such as in undrained soils), stress/displacement elements that +include pore pressure can be used. +22.4 +Hypoelasticity +• “Hypoelastic behavior,” Section 22.4.1 +22.4.1 +HYPOELASTIC BEHAVIOR +Products: Abaqus/Standard Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Elastic behavior: overview,” Section 22.1.1 +• *HYPOELASTIC +• “Creating a hypoelastic material model” in “Defining elasticity,” Section 12.9.1 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +The hypoelastic material model: +• is valid for small elastic strains—the stresses should not be large compared to the elastic modulus +of the material; +• is used when the load path is monotonic; and +• must be defined by user subroutine UHYPEL if temperature dependence is to be included. +Defining hypoelastic material behavior +In a hypoelastic material the rate of change of stress is defined as a tangent modulus matrix multiplying +the rate of change of the elastic strain: +where +tangent elasticity matrix, and +problems). +is the rate of change of the stress (the “true,” Cauchy, stress in finite-strain problems), +is the +is the rate of change of the elastic strain (the log strain in finite-strain +Determining the hypoelastic material parameters +The entries in +strain invariants. The strain invariants are defined for this purpose as +are provided by giving Young’s modulus, E, and Poisson’s ratio, +, as functions of +You can define the material parameters directly or by using a user subroutine. +Direct specification +You can define the variation of Young’s modulus and Poisson’s ratio directly by specifying E, +and +. +, +, +, +Input File Usage: +Abaqus/CAE Usage: +*HYPOELASTIC +Property module: material editor: Mechanical→Elasticity→Hypoelastic +User subroutine +If specifying E and +you can define the hypoelastic material by user subroutine UHYPEL. +as functions of the strain invariants directly does not allow sufficient flexibility, +Input File Usage: +Abaqus/CAE Usage: +*HYPOELASTIC, USER +Property module: material editor: Mechanical→Elasticity→Hypoelastic: +Use user subroutine UHYPEL +Plane or uniaxial stress +For plane stress and uniaxial stress states Abaqus/Standard does not compute the out-of-plane strain +components. For the purpose of defining the above invariants, it is assumed that +; that is, the +material is assumed to be incompressible. For example, in a uniaxial stress case (such as a truss element) +this assumption implies that +Large-displacement analysis +For large-displacement analysis the strain measure in Abaqus is the integration of the rate of deformation. +This strain measure corresponds to log strain if the principal directions do not rotate relative to the +material. The strain invariant definitions should be interpreted in this way. +Use with other material models +The hypoelastic material model can be used only by itself in the material definition. +It cannot +be combined with viscoelasticity or with any inelastic response model. See “Combining material +behaviors,” Section 21.1.3, for more details. +Elements +The hypoelastic material model can be used with any of the stress/displacement elements in +Abaqus/Standard. +22.5 +Hyperelasticity +• “Hyperelastic behavior of rubberlike materials,” Section 22.5.1 +• “Hyperelastic behavior in elastomeric foams,” Section 22.5.2 +• “Anisotropic hyperelastic behavior,” Section 22.5.3 +22.5.1 +HYPERELASTIC BEHAVIOR OF RUBBERLIKE MATERIALS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Elastic behavior: overview,” Section 22.1.1 +• “Mullins effect,” Section 22.6.1 +• “Permanent set in rubberlike materials,” Section 23.7.1 +• *HYPERELASTIC +• *UNIAXIAL TEST DATA +• *BIAXIAL TEST DATA +• *PLANAR TEST DATA +• *VOLUMETRIC TEST DATA +• *MULLINS EFFECT +• “Creating an isotropic hyperelastic material model” in “Defining elasticity,” Section 12.9.1 of the +Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +The hyperelastic material model: +• is isotropic and nonlinear; +• is valid for materials that exhibit instantaneous elastic response up to large strains (such as rubber, +solid propellant, or other elastomeric materials); and +• requires that geometric nonlinearity be accounted for during the analysis step (“General and linear +perturbation procedures,” Section 6.1.3), since it is intended for finite-strain applications. +Compressibility +Most elastomers (solid, rubberlike materials) have very little compressibility compared to their shear +flexibility. This behavior does not warrant special attention for plane stress, shell, membrane, beam, truss, +or rebar elements, but the numerical solution can be quite sensitive to the degree of compressibility for +three-dimensional solid, plane strain, and axisymmetric analysis elements. In cases where the material is +highly confined (such as an O-ring used as a seal), the compressibility must be modeled correctly to obtain +accurate results. In applications where the material is not highly confined, the degree of compressibility +is typically not crucial; for example, it would be quite satisfactory in Abaqus/Standard to assume that the +material is fully incompressible: the volume of the material cannot change except for thermal expansion. +Another class of rubberlike materials is elastomeric foam, which is elastic but very compressible. +Elastomeric foams are discussed in “Hyperelastic behavior in elastomeric foams,” Section 22.5.2. +We can assess the relative compressibility of a material by the ratio of its initial bulk modulus, +, since +. This ratio can also be expressed in terms of Poisson’s ratio, +to its initial shear modulus, +, +The table below provides some representative values. +10 +20 +50 +100 +1000 +10,000 +Poisson’s ratio +0.452 +0.475 +0.490 +0.495 +0.4995 +0.49995 +Compressibility in Abaqus/Standard +In Abaqus/Standard the use of “hybrid” (mixed formulation) elements is recommended in both +incompressible and almost incompressible cases. +In plane stress, shell, and membrane elements the +material is free to deform in the thickness direction. Similarly, in one-dimensional elements (such as +beams, trusses, and rebars) the material is free to deform in the lateral directions. In these cases special +treatment of the volumetric behavior is not necessary; the use of regular stress/displacement elements is +satisfactory. +Compressibility in Abaqus/Explicit +Except for plane stress and uniaxial cases, it is not possible to assume that the material is fully +incompressible in Abaqus/Explicit because the program has no mechanism for imposing such a +Instead, we must provide some compressibility. The +constraint at each material calculation point. +difficulty is that, in many cases, the actual material behavior provides too little compressibility for +the algorithms to work efficiently. Thus, except for plane stress and uniaxial cases, you must provide +enough compressibility for the code to work, knowing that this makes the bulk behavior of the model +softer than that of the actual material. Some judgment is, therefore, required to decide whether or not +the solution is sufficiently accurate, or whether the problem can be modeled at all with Abaqus/Explicit +because of this numerical limitation. +If no value is given for the material compressibility in the hyperelastic model, by default +Abaqus/Explicit assumes +20, corresponding to Poisson’s ratio of 0.475. Since typical unfilled +elastomers have +0.49995) and filled +elastomers have +0.497), this default provides +much more compressibility than is available in most elastomers. However, if the elastomer is relatively +unconfined, this softer modeling of the material’s bulk behavior usually provides quite accurate results. +ratios in the range of 1,000 to 10,000 ( +ratios in the range of 50 to 200 ( +0.4995 to +0.490 to +Unfortunately, in cases where the material is highly confined—such as when it is in contact with +stiff, metal parts and has a very small amount of free surface, especially when the loading is highly +compressive—it may not be feasible to obtain accurate results with Abaqus/Explicit. +If you are defining the compressibility rather than accepting the default value, an upper limit of +. Larger ratios introduce high frequency noise into the dynamic +100 is suggested for the ratio of +solution and require the use of excessively small time increments. +Isotropy assumption +In Abaqus all hyperelastic models are based on the assumption of isotropic behavior throughout the +deformation history. Hence, the strain energy potential can be formulated as a function of the strain +invariants. +Strain energy potentials +the Marlow form, +Hyperelastic materials are described in terms of a “strain energy potential,” +, which defines the +strain energy stored in the material per unit of reference volume (volume in the initial configuration) as +a function of the strain at that point in the material. There are several forms of strain energy potentials +the Arruda-Boyce +available in Abaqus to model approximately incompressible isotropic elastomers: +form, +the +polynomial form, the reduced polynomial form, the Yeoh form, and the Van der Waals form. As will +be pointed out below, the reduced polynomial and Mooney-Rivlin models can be viewed as particular +cases of the polynomial model; the Yeoh and neo-Hookean potentials, in turn, can be viewed as special +cases of the reduced polynomial model. Thus, we will occasionally refer collectively to these models as +“polynomial models.” +the Mooney-Rivlin form, +the neo-Hookean form, +the Ogden form, +Generally, when data from multiple experimental tests are available (typically, this requires at least +uniaxial and equibiaxial test data), the Ogden and Van der Waals forms are more accurate in fitting +experimental results. If limited test data are available for calibration, the Arruda-Boyce, Van der Waals, +Yeoh, or reduced polynomial forms provide reasonable behavior. When only one set of test data (uniaxial, +equibiaxial, or planar test data) is available, the Marlow form is recommended. In this case a strain energy +potential is constructed that will reproduce the test data exactly and that will have reasonable behavior +in other deformation modes. +Evaluating hyperelastic materials +Abaqus/CAE allows you to evaluate hyperelastic material behavior by automatically creating response +curves using selected strain energy potentials. In addition, you can provide experimental test data for +a material without specifying a particular strain energy potential and have Abaqus/CAE evaluate the +material to determine the optimal strain energy potential. See “Evaluating hyperelastic and viscoelastic +material behavior,” Section 12.4.7 of the Abaqus/CAE User’s Manual, for details. Alternatively, you can +use single-element test cases to evaluate the strain energy potential. +You can use single-element test cases to evaluate the strain energy potential. +Arruda-Boyce form +The form of the Arruda-Boyce strain energy potential is +where U is the strain energy per unit of reference volume; +material parameters; +is the first deviatoric strain invariant defined as +, +, and D are temperature-dependent +where the deviatoric stretches +as defined below in “Thermal expansion”; and +; J is the total volume ratio; +is the elastic volume ratio +are the principal stretches. The initial shear modulus, +, is related to with the expression +A typical value of +, and the parameter +are printed in the data (.dat) file if you request a printout of the model data from the analysis input +. Both the initial shear modulus, +is 7, for which +file processor. The initial bulk modulus is related to D with the expression +Marlow form +The form of the Marlow strain energy potential is +where U is the strain energy per unit of reference volume, with +volumetric part; +is the first deviatoric strain invariant defined as +as its deviatoric part and +as its +where the deviatoric stretches +is the elastic volume ratio +as defined below in “Thermal expansion”; and +are the principal stretches. The deviatoric part of the +potential is defined by providing either uniaxial, equibiaxial, or planar test data; while the volumetric +part is defined by providing the volumetric test data, defining the Poisson’s ratio, or specifying the lateral +strains together with the uniaxial, equibiaxial, or planar test data. +; J is the total volume ratio; +Mooney-Rivlin form +The form of the Mooney-Rivlin strain energy potential is +where U is the strain energy per unit of reference volume; +material parameters; +, +are the first and second deviatoric strain invariants defined as +, and +and +are temperature-dependent +where the deviatoric stretches +defined below in “Thermal expansion”; and +bulk modulus are given by +; J is the total volume ratio; +is the elastic volume ratio as +are the principal stretches. The initial shear modulus and +Neo-Hookean form +The form of the neo-Hookean strain energy potential is +where U is the strain energy per unit of reference volume; +parameters; +is the first deviatoric strain invariant defined as +and +are temperature-dependent material +where the deviatoric stretches +defined below in “Thermal expansion”; and +bulk modulus are given by +; J is the total volume ratio; +is the elastic volume ratio as +are the principal stretches. The initial shear modulus and +Ogden form +The form of the Ogden strain energy potential is +are the deviatoric principal stretches +where +parameter; and +and bulk modulus for the Ogden form are given by +, and +, +are the principal stretches; N is a material +are temperature-dependent material parameters. The initial shear modulus +; +The particular material models described above—the Mooney-Rivlin and neo-Hookean forms—can +also be obtained from the general Ogden strain energy potential for special choices of +and +. +Polynomial form +The form of the polynomial strain energy potential is +where U is the strain energy per unit of reference volume; N is a material parameter; +temperature-dependent material parameters; +defined as +are +are the first and second deviatoric strain invariants +and +and +where the deviatoric stretches +defined below in “Thermal expansion”; and +bulk modulus are given by +; J is the total volume ratio; +is the elastic volume ratio as +are the principal stretches. The initial shear modulus and +For cases where the nominal strains are small or only moderately large (< 100%), the first terms +in the polynomial series usually provide a sufficiently accurate model. Some particular material +models—the Mooney-Rivlin, neo-Hookean, and Yeoh forms—are obtained for special choices of +. +Reduced polynomial form +The form of the reduced polynomial strain energy potential is +where U is the strain energy per unit of reference volume; N is a material parameter; +temperature-dependent material parameters; +and +is the first deviatoric strain invariant defined as +are +where the deviatoric stretches +defined below in “Thermal expansion”; and +bulk modulus are given by +; J is the total volume ratio; +is the elastic volume ratio as +are the principal stretches. The initial shear modulus and +Van der Waals form +The form of the Van der Waals strain energy potential is +where +and +Here, U is the strain energy per unit of reference volume; +stretch; a is the global interaction parameter; +compressibility. These parameters can be temperature-dependent. +deviatoric strain invariants defined as +is the initial shear modulus; +is the locking +is an invariant mixture parameter; and D governs the +are the first and second +and +where the deviatoric stretches +defined below in “Thermal expansion”; and +bulk modulus are given by +; J is the total volume ratio; +is the elastic volume ratio as +are the principal stretches. The initial shear modulus and +Yeoh form +The form of the Yeoh strain energy potential is +where U is the strain energy per unit of reference volume; +parameters; +is the first deviatoric strain invariant defined as +and +are temperature-dependent material +where the deviatoric stretches +defined below in “Thermal expansion”; and +bulk modulus are given by +; J is the total volume ratio; +is the elastic volume ratio as +are the principal stretches. The initial shear modulus and +Thermal expansion +Only isotropic thermal expansion is permitted with the hyperelastic material model. +The elastic volume ratio, +, relates the total volume ratio, J, and the thermal volume ratio, +: +is given by +where +thermal expansion coefficient (“Thermal expansion,” Section 26.1.2). +is the linear thermal expansion strain that is obtained from the temperature and the isotropic +Defining the hyperelastic material response +The mechanical response of a material is defined by choosing a strain energy potential to fit the +particular material. The strain energy potential forms in Abaqus are written as separable functions of a +deviatoric component and a volumetric component; i.e., +. Alternatively, +in Abaqus/Standard you can define the strain energy potential with user subroutine UHYPER, in which +case the strain energy potential need not be separable. +Generally for the hyperelastic material models available in Abaqus, you can either directly specify +material coefficients or provide experimental test data and have Abaqus automatically determine +appropriate values of the coefficients. An exception is the Marlow form: in this case the deviatoric part +of the strain energy potential must be defined with test data. The different methods for defining the +strain energy potential are described in detail below. +The properties of rubberlike materials can vary significantly from one batch to another; therefore, if +data are used from several experiments, all of the experiments should be performed on specimens taken +from the same batch of material, regardless of whether you or Abaqus compute the coefficients. +Viscoelastic and hysteretic materials +The elastic response of viscoelastic materials (“Time domain viscoelasticity,” Section 22.7.1, and +“Parallel network viscoelastic model,” Section 22.8.2) and hysteretic materials (“Hysteresis in +elastomers,” Section 22.8.1) can be specified by defining either the instantaneous response or the +long-term response of such materials. To define the instantaneous response, the experiments outlined in +the “Experimental tests” section that follows have to be performed within time spans much shorter than +the characteristic relaxation times of these materials. +Input File Usage: +Abaqus/CAE Usage: +*HYPERELASTIC, MODULI=INSTANTANEOUS +Property module: material editor: Mechanical→Elasticity→Hyperelastic: +Material type: Isotropic; any Strain energy potential except Unknown: +Moduli time scale (for viscoelasticity): Instantaneous +If, on the other hand, the long-term elastic response is used, data from experiments have to be +collected after time spans much longer than the characteristic relaxation times of these materials. Long- +term elastic response is the default elastic material behavior. +Input File Usage: +Abaqus/CAE Usage: +*HYPERELASTIC, MODULI=LONG TERM +Property module: material editor: Mechanical→Elasticity→Hyperelastic: +Material type: Isotropic; any Strain energy potential except Unknown: +Moduli time scale (for viscoelasticity): Long-term +Accounting for compressibility +Compressibility can be defined by specifying nonzero values for +(except for the Marlow model), +by setting the Poisson’s ratio to a value less than 0.5, or by providing test data that characterize the +compressibility. The test data method is described later in this section. If you specify the Poisson’s ratio +for hyperelasticity other than the Marlow model, Abaqus computes the initial bulk modulus from the +initial shear modulus +For the Marlow model the specified Poisson’s ratio represents a constant value, which determines the +volumetric response throughout the deformation process. If +must be +equal to zero. In such a case the material is assumed to be fully incompressible in Abaqus/Standard, +while Abaqus/Explicit will assume compressible behavior with +(Poisson’s ratio of 0.475). +is equal to zero, all of the +Input File Usage: +Abaqus/CAE Usage: +*HYPERELASTIC, POISSON= +Property module: material editor: Mechanical→Elasticity→Hyperelastic: +Material type: Isotropic; any Strain energy potential except Unknown +or User-defined: Input source: Test data: Poisson's ratio: +Specifying material coefficients directly +The parameters of the hyperelastic strain energy potentials can be given directly as functions of +temperature for all forms of the strain energy potential except the Marlow form. +Input File Usage: +Use one of the following options: +*HYPERELASTIC, ARRUDA-BOYCE +*HYPERELASTIC, MOONEY-RIVLIN +*HYPERELASTIC, NEO HOOKE +Abaqus/CAE Usage: +) +) +*HYPERELASTIC, OGDEN, N=n ( +*HYPERELASTIC, POLYNOMIAL, N=n ( +*HYPERELASTIC, REDUCED POLYNOMIAL, N=n ( +*HYPERELASTIC, VAN DER WAALS +*HYPERELASTIC, YEOH +Property module: material editor: Mechanical→Elasticity→Hyperelastic: +Material type: Isotropic; Input source: Coefficients and Strain +energy potential: Arruda-Boyce, Mooney-Rivlin, Neo Hooke, Ogden, +Polynomial, Reduced Polynomial, Van der Waals, or Yeoh +) +Using test data to calibrate material coefficients +The material coefficients of the hyperelastic models can be calibrated by Abaqus from experimental +stress-strain data. In the case of the Marlow model, the test data directly characterize the strain energy +potential (there are no material coefficients for this model); the Marlow model is described in detail below. +The value of N and experimental stress-strain data can be specified for up to four simple tests: uniaxial, +equibiaxial, planar, and, if the material is compressible, a volumetric compression test. Abaqus will +then compute the material parameters. The material constants are determined through a least-squares-fit +procedure, which minimizes the relative error in stress. For the n nominal-stress–nominal-strain data +pairs, the relative error measure E is minimized, where +is a stress value from the test data, and +comes from one of the nominal stress expressions +derived below . Abaqus minimizes the relative error rather than an absolute +error measure since this provides a better fit at lower strains. This method is available for all strain +energy potentials and any order of N except for the polynomial form, where a maximum of +is allowed. The polynomial models are linear in terms of the constants +; therefore, a linear least- +squares procedure can be used. The Arruda-Boyce, Ogden, and Van der Waals potentials are nonlinear +in some of their coefficients, thus necessitating the use of a nonlinear least-squares procedure. “Fitting of +hyperelastic and hyperfoam constants,” Section 4.6.2 of the Abaqus Theory Manual, contains a detailed +derivation of the related equations. +It is generally best to obtain data from several experiments involving different kinds of deformation +over the range of strains of interest in the actual application and to use all of these data to determine the +parameters. This is particularly true for the phenomenological models; i.e., the Ogden and the polynomial +models. It has been observed that to achieve good accuracy and stability, it is necessary to fit these models +using test data from more than one deformation state. In some cases, especially at large strains, removing +the dependence on the second invariant may alleviate this limitation. The Arruda-Boyce, neo-Hookean, +and Van der Waals models with += 0 offer a physical interpretation and provide a better prediction of +general deformation modes when the parameters are based on only one test. An extensive discussion of +this topic can be found in “Hyperelastic material behavior,” Section 4.6.1 of the Abaqus Theory Manual. +This method does not allow the hyperelastic properties to be temperature dependent. However, if +temperature-dependent test data are available, several curve fits can be conducted by performing a data +check analysis on a simple input file. The temperature-dependent coefficients determined by Abaqus can +then be entered directly in the actual analysis run. +Optionally, the parameter +in the Van der Waals model can be set to a fixed value while the other +parameters are found using a least-squares curve fit. +As many data points as required can be entered from each test. It is recommended that data from +all four tests (on samples taken from the same piece of material) be included and that the data points +cover the range of nominal strains expected to arise in the actual loading. For the (general) polynomial +and Ogden models and for the coefficient +in the Van der Waals model, the planar test data must be +accompanied by the uniaxial test data, the biaxial test data, or both of these types of test data; otherwise, +the solution to the least-squares fit will not be unique. +The strain data should be given as nominal strain values (change in length per unit of original length). +For the uniaxial, equibiaxial, and planar tests stress data are given as nominal stress values (force per +unit of original cross-sectional area). These tests allow for entering both compression and tension data. +Compressive stresses and strains are entered as negative values. +If compressibility is to be specified, the +or D can be computed from volumetric compression test +data. Alternatively, compressibility can be defined by specifying a Poisson’s ratio, in which case Abaqus +computes the bulk modulus from the initial shear modulus. If no such data are given, Abaqus/Standard +assumes that D or all of the +are zero, whereas Abaqus/Explicit assumes compressibility corresponding +to a Poisson’s ratio of 0.475 . For these compression +tests the stress data are given as pressure values. +Input File Usage: +Use one of the following options to select the strain energy potential: +*HYPERELASTIC, TEST DATA INPUT, ARRUDA-BOYCE +*HYPERELASTIC, TEST DATA INPUT, MOONEY-RIVLIN +*HYPERELASTIC, TEST DATA INPUT, NEO HOOKE +*HYPERELASTIC, TEST DATA INPUT, OGDEN, N=n ( +) +*HYPERELASTIC, TEST DATA INPUT, POLYNOMIAL, N=n ( +*HYPERELASTIC, TEST DATA INPUT, REDUCED POLYNOMIAL, +N=n ( +*HYPERELASTIC, TEST DATA INPUT, VAN DER WAALS +*HYPERELASTIC, TEST DATA INPUT, VAN DER WAALS, +BETA= ( +*HYPERELASTIC, TEST DATA INPUT, YEOH +In addition, use at least one and up to four of the following options to give the +test data : +) +) +) +*UNIAXIAL TEST DATA +*BIAXIAL TEST DATA +*PLANAR TEST DATA +*VOLUMETRIC TEST DATA +Property module: material editor: Mechanical→Elasticity→Hyperelastic: +Abaqus/CAE Usage: +Material type: Isotropic; Input source: Test data and Strain +energy potential: Arruda-Boyce, Mooney-Rivlin, Neo Hooke, +Ogden, Polynomial, Reduced Polynomial, Van der Waals +(Beta: Fitted value or Specify), or Yeoh +In addition, use at least one and up to four of the following options to give the +test data : +Test Data→Uniaxial Test Data +Test Data→Biaxial Test Data +Test Data→Planar Test Data +Test Data→Volumetric Test Data +Alternatively, you can select Strain energy potential: Unknown to define +the material temporarily without specifying a particular strain energy potential. +Then select Material→Evaluate to have Abaqus/CAE evaluate the material to +determine the optimal strain energy potential. +Specifying the Marlow model +The Marlow model assumes that the strain energy potential is independent of the second deviatoric +invariant +. This model is defined by providing test data that define the deviatoric behavior, and, +optionally, the volumetric behavior if compressibility must be taken into account. Abaqus will construct +a strain energy potential that reproduces the test data exactly, as shown in Figure 22.5.1–1. +MARLOW +TEST DATA +Figure 22.5.1–1 The results of the Marlow model with test data. +The interpolation and extrapolation of stress-strain data with the Marlow model is approximately linear +for small and large strains. For intermediate strains in the range 0.1 to 1.0 a noticeable degree of +nonlinearity may be observed in the interpolation/extrapolation with the Marlow model; for example, +some nonlinearity is apparent between the 4th and 5th data points in Figure 22.5.1–1. To minimize +undesirable nonlinearity, make sure that enough data points are specified in the intermediate strain range. +The deviatoric behavior is defined by specifying uniaxial, biaxial, or planar test data. Generally, +you can specify either the data from tension tests or the data from compression tests because the tests are +equivalent . However, for beams, trusses, and rebars, the data from +tension and compression tests can be specified together. Volumetric behavior is defined by using one of +the following three methods: +• Specify nominal lateral strains, in addition to nominal stresses and nominal strains, as part of the +uniaxial, biaxial, or planar test data. +• Specify Poisson’s ratio for the hyperelastic material. +• Specify volumetric test data directly. Both hydrostatic tension and hydrostatic compression data +can be specified. If only hydrostatic compression data are available, as is usually the case, Abaqus +will assume that the hydrostatic pressure is an antisymmetric function of the nominal volumetric +strain, +. +If you do not define volumetric behavior, Abaqus/Standard assumes fully incompressible behavior, while +Abaqus/Explicit assumes compressibility corresponding to a Poisson’s ratio of 0.475. +Material test data in which the stress does not vary smoothly with increasing strain may lead to +convergence difficulty during the simulation. It is highly recommended that smooth test data be used to +define the Marlow form. Abaqus provides a smoothing algorithm, which is described in detail later in +this section. +The test data for the Marlow model can also be given as a function of temperature and field variables. +You must specify the number of user-defined field variable dependencies required. +Uniaxial, biaxial, and planar test data must be given in ascending order of the nominal strains; +volumetric test data must be given in descending order of the volume ratio. +Input File Usage: +To define the Marlow test data as a function of temperature and/or field +variables, use the following option: +Abaqus/CAE Usage: +*HYPERELASTIC, MARLOW +with one of the following first three options and, optionally, the fourth option: +*UNIAXIAL TEST DATA, DEPENDENCIES=n +*BIAXIAL TEST DATA, DEPENDENCIES=n +*PLANAR TEST DATA, DEPENDENCIES=n +*VOLUMETRIC TEST DATA, DEPENDENCIES=n +Property module: material editor: Mechanical→Elasticity→Hyperelastic: +Material type: Isotropic; Input source: Test data and +Strain energy potential: Marlow +In addition, select one of the following first three options and, optionally, the +fourth option to give the test data : +Test Data→Uniaxial Test Data +Test Data→Biaxial Test Data +Test Data→Planar Test Data +Test Data→Volumetric Test Data +In each of the Test Data Editor dialog boxes, you can toggle on Use +temperature-dependent data to define the test data as a function of +temperature and/or select the Number of field variables to define the test +data as a function of field variables. +Alternatively, you can select Material→Evaluate to have Abaqus/CAE +evaluate the material. If you included temperature dependencies, field variable +dependencies, or lateral nominal strain in the test data—which can only be +defined in the Marlow hyperelastic definition—Marlow will be the only strain +energy potential available for evaluation. +User subroutine specification in Abaqus/Standard +An alternative method provided in Abaqus/Standard for defining the hyperelastic material parameters +allows the strain energy potential to be defined in user subroutine UHYPER. Either compressible or +incompressible behavior can be specified. Optionally, you can specify the number of property values +needed as data in the user subroutine. The derivatives of the strain energy potential with respect to the +strain invariants must be provided directly through user subroutine UHYPER. If needed, you can specify +the number of solution-dependent variables . +Input File Usage: +Use one of the following two options: +Abaqus/CAE Usage: +*HYPERELASTIC, USER, TYPE=COMPRESSIBLE, PROPERTIES=n +*HYPERELASTIC, USER, TYPE=INCOMPRESSIBLE, PROPERTIES=n +Property module: material editor: Mechanical→Elasticity→Hyperelastic: +Material type: Isotropic; Input source: Coefficients and Strain energy +potential: User-defined: optionally, toggle on Include compressibility +and/or specify the Number of property values +Experimental tests +For a homogeneous material, homogeneous deformation modes suffice to characterize the material +constants. Abaqus accepts test data from the following deformation modes: +• Uniaxial tension and compression +• Equibiaxial tension and compression +• Planar tension and compression (also known as pure shear) +• Volumetric tension and compression +These modes are illustrated schematically in Figure 22.5.1–2 and are described below. The most +commonly performed experiments are uniaxial tension, uniaxial compression, and planar tension. +TENSION +COMPRESSION +UNIAXIAL TEST DATA + TU, +∋ +BIAXIAL TEST DATA + TB, +∋ +PLANAR TEST DATA + TS, +∋ +VOLUMETRIC TEST DATA +p, +1=λ +U= 1 + +U , λ +∋ +2=λ +3= 1/ λ +÷ +1=λ +2=λ +B= 1 + +B , λ +∋ +3= 1/ λ +1=λ +S= 1+ +∋ +S , λ +2= 1, λ +3= 1/ λ +1=λ +2=λ +3= λ +v , += λ +Figure 22.5.1–2 Schematic illustrations of deformation modes. +Combine data from these three test types to get a good characterization of the hyperelastic material +behavior. +For the incompressible version of the material model, the stress-strain relationships for the different +tests are developed using derivatives of the strain energy function with respect to the strain invariants. +We define these relations in terms of the nominal stress (the force divided by the original, undeformed +area) and the nominal, or engineering, strain defined below. +The deformation gradient, expressed in the principal directions of stretch, is +, +, and +where +configuration in the principal directions of a material fiber. The principal stretches, +principal nominal strains, +are the principal stretches: the ratios of current length to length in the original +, are related to the +, by +Because we assume incompressibility and isothermal response, +The deviatoric strain invariants in terms of the principal stretches are then +and, hence, += 1. +and +Uniaxial tests +The uniaxial deformation mode is characterized in terms of the principal stretches, +, as +where +is the stretch in the loading direction. The nominal strain is defined by +To derive the uniaxial nominal stress +, we invoke the principle of virtual work: +so that +The uniaxial tension test is the most common of all the tests and is usually performed by pulling +a “dog-bone” specimen. The uniaxial compression test is performed by loading a compression button +between lubricated surfaces. The loading surfaces are lubricated to minimize any barreling effect in the +button that would cause deviations from a homogeneous uniaxial compression stress-strain state. +Input File Usage: +Abaqus/CAE Usage: +*UNIAXIAL TEST DATA +Property module: material editor: Mechanical→Elasticity→Hyperelastic: +Material type: Isotropic; Input source: Test data and +Test Data→Uniaxial Test Data +Equibiaxial tests +The equibiaxial deformation mode is characterized in terms of the principal stretches, +, as +where +is the stretch in the two perpendicular loading directions. The nominal strain is defined by +To develop the expression for the equibiaxial nominal stress, +, we again use the principle of +virtual work (assuming that the stress perpendicular to the loading direction is zero), +so that +In practice, the equibiaxial compression test is rarely performed because of experimental setup +In addition, this deformation mode is equivalent to a uniaxial tension test, which is +difficulties. +straightforward to conduct. +A more common test is the equibiaxial tension test, in which a stress state with two equal tensile +stresses and zero shear stress is created. This state is usually achieved by stretching a square sheet in a +biaxial testing machine. It can also be obtained by inflating a circular membrane into a spheroidal shape +(like blowing up a balloon). The stress field in the middle of the membrane then closely approximates +equibiaxial tension, provided that the thickness of the membrane is very much smaller than the radius +of curvature at this point. However, the strain distribution will not be quite uniform, and local strain +measurements will be required. Once the strain and radius of curvature are known, the nominal stress +can be derived from the inflation pressure. +Input File Usage: +Abaqus/CAE Usage: +*BIAXIAL TEST DATA +Property module: material editor: Mechanical→Elasticity→Hyperelastic: +Material type: Isotropic; Input source: Test data and +Test Data→Biaxial Test Data +Planar tests +The planar deformation mode is characterized in terms of the principal stretches, +, as +where +is the stretch in the loading direction. Then, the nominal strain in the loading direction is +This test is also called a “pure shear” test since, in terms of logarithmic strains, +which corresponds to a state of pure shear at an angle of 45° to the loading direction. +The principle of virtual work gives +where +is the nominal planar stress, so that +For the (general) polynomial and Ogden models and for the coefficient +in the Van der Waals model +this equation alone will not determine the constants uniquely. The planar test data must be augmented +by uniaxial test data and/or biaxial test data to determine the material parameters. +Planar tests are usually done with a thin, short, and wide rectangular strip of material fixed on its +wide edges to rigid loading clamps that are moved apart. If the separation direction is the 1-direction and +the thickness direction is the 3-direction, the comparatively long size of the specimen in the 2-direction +and the rigid clamps allow us to use the approximation +; that is, there is no deformation in the +wide direction of the specimen. This deformation mode could also be called planar compression if the +3-direction is considered to be the primary direction. All forms of incompressible plane strain behavior +are characterized by this deformation mode. Consequently, if plane strain analysis is performed, planar +test data represent the relevant form of straining of the material. +Input File Usage: +Abaqus/CAE Usage: +*PLANAR TEST DATA +Property module: material editor: Mechanical→Elasticity→Hyperelastic: +Material type: Isotropic; Input source: Test data and +Test Data→Planar Test Data +Volumetric tests +values (or D, for the Arruda-Boyce and +The following discussion describes procedures for obtaining +Van der Waals models) corresponding to the actual material behavior. With these values you can compare +the material’s initial bulk modulus, +for +the polynomial model, +values that will +for Ogden’s model) and then judge whether +, to its initial shear modulus ( +provide results are sufficiently realistic. For Abaqus/Explicit caution should be used; +should be +less than 100. Otherwise, noisy solutions will be obtained and time increments will be excessively small +. The +and D can be calculated from data obtained in +pure volumetric compression of a specimen (volumetric tension tests are much more difficult to perform). +In a pure volumetric test +(the +volume ratio). Using the polynomial form of the strain energy potential, the total pressure stress on the +specimen is obtained as +; therefore, +and +This equation can be used to determine the +have +curve are required to give two equations for the +. If we are using a second-order polynomial series for U, we +are needed. Therefore, a minimum of two points on the pressure-volume ratio +. For the Ogden and reduced polynomial potentials +. A linear least-squares fit is performed when more than N data +can be determined for up to +, and so two +points are provided. +An approximate way of conducting a volumetric test consists of using a cylindrical rubber specimen +that fits snugly inside a rigid container and whose top surface is compressed by a rigid piston. Although +both volumetric and deviatoric deformation are present, the deviatoric stresses will be several orders of +magnitude smaller than the hydrostatic stresses (because the bulk modulus is much higher than the shear +modulus) and can be neglected. The compressive stress imposed by the rigid piston is effectively the +pressure, and the volumetric strain in the rubber cylinder is computed from the piston displacement. +Nonzero values of +affect the uniaxial, equibiaxial, and planar stress results. However, since the +material is assumed to be only slightly compressible, the techniques described for obtaining the deviatoric +coefficients should give sufficiently accurate values even though they assume that the material is fully +incompressible. +Input File Usage: +Abaqus/CAE Usage: +*VOLUMETRIC TEST DATA +Property module: material editor: Mechanical→Elasticity→Hyperelastic: +Material type: Isotropic; Input source: Test data and Test +Data→Volumetric Test Data +Equivalent experimental tests +The superposition of a tensile or compressive hydrostatic stress on a loaded, fully incompressible elastic +body results in different stresses but does not change the deformation. Thus, Figure 22.5.1–3 shows that +some apparently different loading conditions are actually equivalent in their deformations and, therefore, +are equivalent tests: +• Uniaxial tension +• Uniaxial compression +• Planar tension +Equibiaxial compression +Equibiaxial tension +Planar compression +On the other hand, the tensile and compressive cases of the uniaxial and equibiaxial modes are +independent from each other: uniaxial tension and uniaxial compression provide independent data. +p = -σ +B = -σ ++ += +Uniaxial tension +Hydrostatic compression +Equibiaxial compression +p = -σ +B = -σ ++ += +Uniaxial compression +Hydrostatic tension +Equibiaxial tension + The stresses, σi, shown here are true +(Cauchy) stresses and not nominal stresses. +Figure 22.5.1–3 Equivalent deformation modes through superposition of hydrostatic stress. +Smoothing the test data +Experimental test data often contain noise in the sense that the test variable is both slowly varying and also +corrupted by random noise. This noise can affect the quality of the strain energy potential that Abaqus +derives. This noise is particularly a problem with the Marlow form, where a strain energy potential that +exactly describes the test data that are used to calibrate the model is computed. It is less of a concern +with the other forms, since smooth functions are fitted through the test data. +Abaqus provides a smoothing technique to remove the noise from the test data based on the +Savitzky-Golay method. The idea is to replace each data point by a local average of its surrounding +data points, so that the level of noise can be reduced without biasing the dominant trend of the test data. +In the implementation a cubic polynomial is fitted through each data point i and n data points to the +immediate left and right of that point. A least-squares method is used to fit the polynomial through these +points. The value of data point i is then replaced by the value of the polynomial at the same +position. Each polynomial is used to adjust one data point except near the ends of the curve, where a +polynomial is used to adjust multiple points, because the first and last few points cannot be the center of +the fitting set of data points. This process is applied repeatedly to all data points until two consecutive +passes through the data produce nearly the same results. +By default, the test data are not smoothed. +If smoothing is specified, the default value is n=3. +Alternatively, you can specify the number of data points to the left and right of a data point in the moving +window within which a least-squares polynomial is fit. +Input File Usage: +For the Marlow form, use one of the first three options and, optionally, the fourth +option; for the other potential forms, use one and up to four of the following +options: +Abaqus/CAE Usage: +) +*UNIAXIAL TEST DATA, SMOOTH=n ( +*BIAXIAL TEST DATA, SMOOTH=n ( +) +*PLANAR TEST DATA, SMOOTH=n ( +) +*VOLUMETRIC TEST DATA, SMOOTH=n ( +Property module: material editor: Mechanical→Elasticity→Hyperelastic: +Material type: Isotropic; Input source: Test data and Test +Data→Uniaxial Test Data, Biaxial Test Data, Planar Test +Data, or Volumetric Test Data +) +In each of the Test Data Editor dialog boxes, toggle on Apply smoothing, +and select a value for n ( +). +Model prediction of material behavior versus experimental data +Once the strain energy potential is determined, the behavior of the hyperelastic model in Abaqus is +established. However, the quality of this behavior must be assessed: the prediction of material behavior +under different deformation modes must be compared against the experimental data. You must judge +whether the strain energy potentials determined by Abaqus are acceptable, based on the correlation +between the Abaqus predictions and the experimental data. You can evaluate the hyperelastic behavior +automatically in Abaqus/CAE. Alternatively, single-element test cases can be used to derive the nominal +stress–nominal strain response of the material model.Single-element test cases can be used to derive the +nominal stress–nominal strain response of the material model. +See “Fitting of rubber test data,” Section 3.1.4 of the Abaqus Benchmarks Manual, which illustrates +the entire process of fitting hyperelastic constants to a set of test data. +Hyperelastic material stability +An important consideration in judging the quality of the fit to experimental data is the concept of material +or Drucker stability. Abaqus checks the Drucker stability of the material for the first three deformation +modes described above. +The Drucker stability condition for an incompressible material requires that the change in the stress, +, following from any infinitesimal change in the logarithmic strain, +, satisfies the inequality +Using +, where +is the tangent material stiffness, the inequality becomes +thus requiring the tangential material stiffness to be positive-definite. +For an isotropic elastic formulation the inequality can be represented in terms of the principal +stresses and strains, +As before, since the material is assumed to be incompressible, we can choose any value for the hydrostatic +pressure without affecting the strains. A convenient choice for the stability calculation is +, +which allows us to ignore the third term in the above equation. +The relation between the changes in stress and in strain can then be obtained in the form of the +matrix +where +that +. For material stability must be positive-definite; thus, it is necessary +This stability check is performed for the polynomial models, the Ogden potential, the Van der Waals +); +form, and the Marlow form. The Arruda-Boyce form is always stable for positive values of ( , +hence, it suffices to check the material coefficients to ensure stability. +You should be careful when defining the +or +for the polynomial models or the Ogden +form: especially when +or +some of the coefficients are strongly negative, instability at higher strain levels is likely to occur. +, and unstable material behavior may result if these values are not defined correctly. When +, the behavior at higher strains is strongly sensitive to the values of the +Abaqus performs a check on the stability of the material for six different forms of loading—uniaxial +tension and compression, equibiaxial tension and compression, and planar tension and compression—for +. If an instability +is found, Abaqus issues a warning message and prints the lowest absolute value of +for which the +instability is observed. Ideally, no instability occurs. If instabilities are observed at strain levels that are +likely to occur in the analysis, it is strongly recommended that you either change the material model or +(nominal strain range of +) at intervals +carefully examine and revise the material input data. If user subroutine UHYPER is used to define the +hyperelastic material, you are responsible for ensuring stability. +Improving the accuracy and stability of the test data fit +Unfortunately, the initial fit of the models to experimental data may not come out as well as expected. +This is particularly true for the most general models, such as the (general) polynomial model and the +Ogden model. For some of the simpler models, stability is assured by following some simple rules. +• For positive values of the initial shear modulus, +form is always stable. +, and the locking stretch, +, the Arruda-Boyce +• For positive values of the coefficient +• Given positive values of the initial shear modulus, +the neo-Hookean form is always stable. +, and the locking stretch, +, the stability of +the Van der Waals model depends on the global interaction parameter, a. +• For the Yeoh model stability is assured if all +will be negative, +since this helps capture the S-shape feature of the stress-strain curve. Thus, reducing the absolute +value of +will help make the Yeoh model more stable. +or magnifying the absolute value of +. Typically, however, +In all cases the following suggestions may improve the quality of the fit: +• Both tension and compression data are allowed; compressive stresses and strains are entered as +negative values. Use compression or tension data depending on the application: it is difficult to fit +a single material model accurately to both tensile and compressive data. +• Always use many more experimental data points than unknown coefficients. +• If +is used, experimental data should be available to at least 100% tensile strain or 50% +compressive strain. +• Perform different types of tests (e.g., compression and simple shear tests). Proper material behavior +for a deformation mode requires test data to characterize that mode. +• Check for warning messages about material instability or error messages about lack of convergence +in fitting the test data. This check is especially important with new test data; a simple finite element +model with the new test data can be run through the analysis input file processor to check the material +stability. +• Use the material evaluation capability in Abaqus/CAE to compare the response curves for different +strain energy potentials to the experimental data. Alternatively, you can perform one-element +simulations for simple deformation modes and compare the Abaqus results against the experimental +data. The X–Y plotting options in the Visualization module of Abaqus/CAE can be used for this +comparison. +You can perform one-element simulations for simple deformation modes and compare the +Abaqus results against the experimental data. +• Delete some data points at very low strains if large strains are anticipated. A disproportionate +number of low strain points may unnecessarily bias the accuracy of the fit toward the low strain +range and cause greater errors in the large strain range. +• Delete some data points at the highest strains if small to moderate strains are expected. The high +strain points may force the fitting to lose accuracy and/or stability in the low strain range. +• Pick data points at evenly spaced strain intervals over the expected range of strains, which will result +in similar accuracy throughout the entire strain range. +• The higher the order of N, the more oscillations are likely to occur, leading to instabilities in the +stress-strain curves. If the (general) polynomial model is used, lower the order of N from 2 to 1 (3 +to 2 for Ogden), especially if the maximum strain level is low (say, less than 100% strain). +• If multiple types of test data are used and the fit still comes out poorly, some of the test data probably +contain experimental errors. New tests may be needed. One way of determining which test data +are erroneous is to first calibrate the initial shear modulus +of the material. Then fit each type +of test data separately in Abaqus and compute the shear modulus, +, from the material constants +using the relations +Alternatively, the initial Young’s modulus, +, can be calibrated and compared with +The values of +data. +Elements +or +that are most different from +or +indicate the erroneous test +The hyperelastic material model can be used with solid (continuum) elements, finite-strain shells +(except S4), continuum shells, membranes, and one-dimensional elements (trusses and rebars). +In +Abaqus/Standard the hyperelastic material model can be also used with Timoshenko beams (B21, +B22, B31, B31OS, B32, B32OS, PIPE21, PIPE22, PIPE31, PIPE32, and their “hybrid” equivalents). +It cannot be used with Euler-Bernoulli beams (B23, B23H, B33, and B33H) and small-strain shells +(STRI3, STRI65, S4R5, S8R, S8R5, S9R5). +Pure displacement formulation versus hybrid formulation in Abaqus/Standard +For continuum elements in Abaqus/Standard hyperelasticity can be used with the pure displacement +formulation elements or with the “hybrid” (mixed formulation) elements. Because elastomeric +materials are usually almost incompressible, fully integrated pure displacement method elements +are not recommended for use with this material, except for plane stress cases. If fully or selectively +reduced-integration displacement method elements are used with the almost incompressible form of this +material model, a penalty method is used to impose the incompressibility constraint in anything except +plane stress analysis. The penalty method can sometimes lead to numerical difficulties; therefore, the +fully or selectively reduced-integrated “hybrid” formulation elements are recommended for use with +hyperelastic materials. +In general, an analysis using a single hybrid element will be only slightly more computationally +expensive than an analysis using a regular displacement-based element. However, when the wavefront is +optimized, the Lagrange multipliers may not be ordered independently of the regular degrees of freedom +associated with the element. Thus, the wavefront of a very large mesh of second-order hybrid tetrahedra +may be noticeably larger than that of an equivalent mesh using regular second-order tetrahedra. This +may lead to significantly higher CPU costs, disk space, and memory requirements. +Incompatible mode elements in Abaqus/Standard +Incompatible mode elements should be used with caution in applications involving large strains. +Convergence may be slow, and in hyperelastic applications inaccuracies may accumulate. Erroneous +stresses may sometimes appear in incompatible mode hyperelastic elements that are unloaded after +having been subjected to a complex deformation history. +Procedures +Hyperelasticity must always be used with geometrically nonlinear analyses (“General and linear +perturbation procedures,” Section 6.1.3). +22.5.2 +HYPERELASTIC BEHAVIOR IN ELASTOMERIC FOAMS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Elastic behavior: overview,” Section 22.1.1 +• “Energy dissipation in elastomeric foams,” Section 22.6.2 +• *HYPERFOAM +• *UNIAXIAL TEST DATA +• *BIAXIAL TEST DATA +• *PLANAR TEST DATA +• *VOLUMETRIC TEST DATA +• *SIMPLE SHEAR TEST DATA +• *MULLINS EFFECT +• “Creating a hyperfoam material model” in “Defining elasticity,” Section 12.9.1 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +The elastomeric foam material model: +• is isotropic and nonlinear; +• is valid for cellular solids whose porosity permits very large volumetric changes; +• optionally allows the specification of energy dissipation and stress softening effects ; +• can deform elastically to large strains, up to 90% strain in compression; and +• requires that geometric nonlinearity be accounted for during the analysis step , since it +is intended for finite-strain applications. +Abaqus/Explicit also provides a separate foam material model intended to capture the strain-rate +sensitive behavior of low-density elastomeric foams such as used in crash and impact applications . +Mechanical behavior of elastomeric foams +Cellular solids are made up of interconnected networks of solid struts or plates that form the edges and +faces of cells. Foams are made up of polyhedral cells that pack in three dimensions. The foam cells +can be either open (e.g., sponge) or closed (e.g., flotation foam). Common examples of elastomeric +foam materials are cellular polymers such as cushions, padding, and packaging materials that utilize the +excellent energy absorption properties of foams: the energy absorbed by foams is substantially greater +than that absorbed by ordinary stiff elastic materials for a certain stress level. +Another class of foam materials is crushable foams, which undergo permanent (plastic) deformation. +Crushable foams are discussed in “Crushable foam plasticity models,” Section 23.3.5. +Foams are commonly loaded in compression. Figure 22.5.2–1 shows a typical compressive stress- +strain curve. +Densification +Plateau: Elastic buckling + of cell walls +Cell wall bending +STRAIN +Figure 22.5.2–1 Typical compressive stress-strain curve. +Three stages can be distinguished during compression: +5%) the foam deforms in a linear elastic manner due to cell wall bending. +1. At small strains ( +2. The next stage is a plateau of deformation at almost constant stress, caused by the elastic buckling of +the columns or plates that make up the cell edges or walls. In closed cells the enclosed gas pressure +and membrane stretching increase the level and slope of the plateau. +3. Finally, a region of densification occurs, where the cell walls crush together, resulting in a rapid +increase of compressive stress. Ultimate compressive nominal strains of 0.7 to 0.9 are typical. +The tensile deformation mechanisms for small strains are similar to the compression mechanisms, but +they differ for large strains. Figure 22.5.2–2 shows a typical tensile stress-strain curve. There are two +stages during tension: +1. At small strains the foam deforms in a linear, elastic manner as a result of cell wall bending, similar +to that in compression. +2. The cell walls rotate and align, resulting in rising stiffness. The walls are substantially aligned at a +tensile strain of about +. Further stretching results in increased axial strains in the walls. +Cell wall + alignment +Cell wall bending +STRAIN +Figure 22.5.2–2 Typical tensile stress-strain curve. +At small strains for both compression and tension, the average experimentally observed Poisson’s ratio, +, of foams is 1/3. At larger strains it is commonly observed that Poisson’s ratio is effectively zero +during compression: the buckling of the cell walls does not result in any significant lateral deformation. +However, +is nonzero during tension, which is a result of the alignment and stretching of the cell walls. +The manufacture of foams often results in cells with different principal dimensions. This shape +anisotropy results in different loading responses in different directions. However, the hyperfoam model +does not take this kind of initial anisotropy into account. +Strain energy potential +In the elastomeric foam material model the elastic behavior of the foams is based on the strain energy +function +where N is a material parameter; +, +, and +are temperature-dependent material parameters; +and +are the principal stretches. The elastic and thermal volume ratios, +, by +are related to the initial shear modulus, +The coefficients +and +, are defined below. +while the initial bulk modulus, +, follows from +For each term in the energy function, the coefficient +determines the degree of compressibility. +is related to the Poisson’s ratio, +, by the expressions +Thus, if +ratio is valid for finite values of the logarithmic principal strains +is the same for all terms, we have a single effective Poisson’s ratio, +; in uniaxial tension +. This effective Poisson’s +. +Thermal expansion +Only isotropic thermal expansion is permitted with the hyperfoam material model. +The elastic volume ratio, +and the thermal volume ratio, +, relates the total volume ratio (current volume/reference volume), J, +: +is given by +where +thermal expansion coefficient (“Thermal expansion,” Section 26.1.2). +is the linear thermal expansion strain that is obtained from the temperature and the isotropic +Determining the hyperfoam material parameters +The response of the material is defined by the parameters in the strain energy function, U; these +parameters must be determined to use the hyperfoam model. Two methods are provided for defining the +material parameters: you can specify the hyperfoam material parameters directly or specify test data +and allow Abaqus to calculate the material parameters. +The elastic response of a viscoelastic material (“Time domain viscoelasticity,” Section 22.7.1) can +be specified by defining either the instantaneous response or the long-term response of such a material. +To define the instantaneous response, the experiments outlined in the “Experimental tests” section that +follows have to be performed within time spans much shorter than the characteristic relaxation time of +the material. +Input File Usage: +Abaqus/CAE Usage: +*HYPERFOAM, MODULI=INSTANTANEOUS +Property module: material editor: Mechanical→Elasticity→Hyperfoam: +Moduli time scale (for viscoelasticity): Instantaneous +If, on the other hand, the long-term elastic response is used, data from experiments have to be +collected after time spans much longer than the characteristic relaxation time of the viscoelastic material. +Long-term elastic response is the default elastic material behavior. +Input File Usage: +Abaqus/CAE Usage: +*HYPERFOAM, MODULI=LONG TERM +Property module: material editor: Mechanical→Elasticity→Hyperfoam: +Moduli time scale (for viscoelasticity): Long-term +Direct specification +, +The default value of +When the parameters N, +, and +is zero, which corresponds to an effective Poisson’s ratio of zero. The +incompressible limit corresponds to all +. However, this material model should not be used +for approximately incompressible materials: use of the hyperelastic model (“Hyperelastic behavior of +rubberlike materials,” Section 22.5.1) is recommended if the effective Poisson’s ratio +are specified directly, they can be functions of temperature. +. +Input File Usage: +Abaqus/CAE Usage: +Test data specification +*HYPERFOAM, N=n ( +Property module: material editor: Mechanical→Elasticity→Hyperfoam: +Strain energy potential order: n ( +on Use temperature-dependent data +); optionally, toggle +) +The value of N and the experimental stress-strain data can be specified for up to five simple tests: uniaxial, +equibiaxial, simple shear, planar, and volumetric. Abaqus contains a capability for obtaining the +, +and +for the hyperfoam model with up to six terms (N=6) directly from test data. Poisson effects can +be included either by means of a constant Poisson’s ratio or through specification of volumetric test data +and/or lateral strains in the other test data. +, +It is important to recognize that the properties of foam materials can vary significantly from one +batch to another. Therefore, all of the experiments should be performed on specimens taken from the +same batch of material. +This method does not allow the properties to be temperature dependent. +As many data points as required can be entered from each test. Abaqus will then compute +, +. The technique uses a least squares fit to the experimental data so that the relative +, +and, if necessary, +error in the nominal stress is minimized. +It is recommended that data from the uniaxial, biaxial, and simple shear tests (on samples taken +from the same piece of material) be included and that the data points cover the range of nominal strains +expected to arise in the actual loading. The planar and volumetric tests are optional. +For all tests the strain data, including the lateral strain data, should be given as nominal strain values +(change in length per unit of original length). For the uniaxial, equibiaxial, simple shear, and planar +tests, stress data are given as nominal stress values (force per unit of original cross-sectional area). The +tests allow for both compression and tension data; compressive stresses and strains should be entered as +negative values. For the volumetric tests the stress data are given as pressure values. +Input File Usage: +for all i), or +Use the first option to define an effective Poisson’s ratio ( +use the second option to define the lateral strains as part of the test data input: +*HYPERFOAM, N=n, POISSON= , TEST DATA INPUT ( +*HYPERFOAM, N=n, TEST DATA INPUT ( +In addition, use at least one and up to five of these additional options to give +the experimental stress-strain data : +). +) +Abaqus/CAE Usage: +*UNIAXIAL TEST DATA +*BIAXIAL TEST DATA +*PLANAR TEST DATA +*SIMPLE SHEAR TEST DATA +*VOLUMETRIC TEST DATA +Property module: material editor: Mechanical→Elasticity→Hyperfoam: +toggle on Use test data; Strain energy potential order: n ( +); +optionally, toggle on Use constant Poisson's ratio: and enter a value +for the effective Poisson's ratio ( +for all i) +In addition, use at least one and up to five of the suboptions to give the +experimental stress-strain data : +Suboptions→Uniaxial Test Data +Suboptions→Biaxial Test Data +Suboptions→Planar Test Data +Suboptions→Simple Shear Test Data +Suboptions→Volumetric Test Data +Experimental tests +For a homogeneous material, homogeneous deformation modes suffice to characterize the material +parameters. Abaqus accepts test data from the following deformation modes: +• Uniaxial tension and compression +• Equibiaxial tension and compression +• Planar tension and compression (pure shear) +• Simple shear +• Volumetric tension and compression +The stress-strain relations are defined in terms of the nominal stress (the force divided by the original, +undeformed area) and the nominal, or engineering, strains, +, are related to +the principal nominal strains, +. The principal stretches, +, by +Uniaxial, equibiaxial, and planar tests +The deformation gradient, expressed in the principal directions of stretch, is +, +, and +where +are the principal stretches: the ratios of current length to length in the original +configuration in the principal directions of a material fiber. The deformation modes are characterized in +terms of the principal stretches, +. The elastomeric foams are not +incompressible, so that +, are independently +specified in the test data either as individual values from the measured lateral deformations or through +the definition of an effective Poisson’s ratio. +. The transverse stretches, +, and the volume ratio, +and/or +The three deformation modes use a single form of the nominal stress-stretch relation, +is the nominal stress and +is the stretch in the loading direction. Because of the compressible +where +behavior, the planar mode does not result in a state of pure shear. In fact, if the effective Poisson’s ratio +is zero, planar deformation is identical to uniaxial deformation. +Uniaxial mode +In uniaxial mode +Input File Usage: +Abaqus/CAE Usage: +Equibiaxial mode +. +, +, and +*UNIAXIAL TEST DATA +Property module: material editor: Mechanical→Elasticity→Hyperfoam: +toggle on Use test data, Suboptions→Uniaxial Test Data +In equibiaxial mode +Input File Usage: +Abaqus/CAE Usage: +. +and +*BIAXIAL TEST DATA +Property module: material editor: Mechanical→Elasticity→Hyperfoam: +toggle on Use test data, Suboptions→Biaxial Test Data +Planar mode +In planar mode +or biaxial test data. +Input File Usage: +Abaqus/CAE Usage: +Simple shear tests +, +, and +. Planar test data must be augmented by either uniaxial +*PLANAR TEST DATA +Property module: material editor: Mechanical→Elasticity→Hyperfoam: +toggle on Use test data, Suboptions→Planar Test Data +Simple shear is described by the deformation gradient +is the shear strain. For this deformation +where +shear deformation is shown in Figure 22.5.2–3. +. A schematic illustration of simple +shear strain +γ = +Δx +fixed distance h +Δx +22=TT +τ =TS +11 +Figure 22.5.2–3 Simple shear test. +The nominal shear stress, +, is +where +are the principal stretches in the plane of shearing, related to the shear strain +by +The stretch in the direction perpendicular to the shear plane is +The transverse (tensile) stress, +, developed during simple shear deformation due to the Poynting effect, is +Input File Usage: +Abaqus/CAE Usage: +*SIMPLE SHEAR TEST DATA +Property module: material editor: Mechanical→Elasticity→Hyperfoam: +toggle on Use test data, Suboptions→Simple Shear Test Data +Volumetric tests +The deformation gradient, +deformation mode consists of all principal stretches being equal; +, is the same for volumetric tests as for uniaxial tests. The volumetric +The pressure-volumetric ratio relation is +A volumetric compression test is illustrated in Figure 22.5.2–4. The pressure exerted on the foam +specimen is the hydrostatic pressure of the fluid, and the decrease in the specimen volume is equal to the +additional fluid entering the pressure chamber. The specimen is sealed against fluid penetration. +Input File Usage: +Abaqus/CAE Usage: +*VOLUMETRIC TEST DATA +Property module: material editor: Mechanical→Elasticity→Hyperfoam: +toggle on Use test data, Suboptions→Volumetric Test Data +Difference between compression and tension deformation +5%) foams behave similarly for both compression and tension. However, at +For small strains ( +large strains the deformation mechanisms differ for compression (buckling and crushing) and tension +(alignment and stretching). Therefore, accurate hyperfoam modeling requires that the experimental data +used to define the material parameters correspond to the dominant deformation modes of the problem +being analyzed. If compression dominates, the pertinent tests are: +• Uniaxial compression +• Simple shear +• Planar compression (if Poisson’s ratio +) +volumetric gauge +pressure gauge +pump +valve +fluid +foam +rigid pressure chamber +Figure 22.5.2–4 Volumetric compression test. +• Volumetric compression (if Poisson’s ratio +) +If tension dominates, the pertinent tests are: +• Uniaxial tension +• Simple shear +• Biaxial tension (if Poisson’s ratio +• Planar tension (if Poisson’s ratio +) +) +Lateral strain data can also be used to define the compressibility of the foam. Measurement of the lateral +strains may make other tests redundant; for example, providing lateral strains for a uniaxial test eliminates +the need for a volumetric test. However, if volumetric test data are provided in addition to the lateral strain +data for other tests, both the volumetric test data and the lateral strain data will be used in determining +the compressibility of the foam. The hyperfoam model may not accurately fit Poisson’s ratio if it varies +significantly between compression and tension. +Model prediction of material behavior versus experimental data +Once the elastomeric foam constants are determined, the behavior of the hyperfoam model in Abaqus is +established. However, the quality of this behavior must be assessed: the prediction of material behavior +under different deformation modes must be compared against the experimental data. You must judge +whether the elastomeric foam constants determined by Abaqus are acceptable, based on the correlation +between the Abaqus predictions and the experimental data. Single-element test cases can be used to +calculate the nominal stress–nominal strain response of the material model. +See “Fitting of elastomeric foam test data,” Section 3.1.5 of the Abaqus Benchmarks Manual, which +illustrates the entire process of fitting elastomeric foam constants to a set of test data. +Elastomeric foam material stability +As with incompressible hyperelasticity, Abaqus checks the Drucker stability of the material for the +deformation modes described above. The Drucker stability condition for a compressible material requires +that the change in the Kirchhoff stress, +, following from an infinitesimal change in the logarithmic +strain, +, satisfies the inequality +where the Kirchhoff stress +. Using +, the inequality becomes +This restriction requires that the tangential material stiffness +be positive definite. +For an isotropic elastic formulation the inequality can be represented in terms of the principal +stresses and strains +Thus, the relation between changes in the stress and changes in the strain can be obtained in the +form of the matrix equation +where +Since must be positive definite, it is necessary that +, +, and +: especially when +You should be careful about defining the parameters +, +the behavior at higher strains is strongly sensitive to the values of these parameters, and unstable +material behavior may result if these values are not defined correctly. When some of the coefficients +are strongly negative, instability at higher strain levels is likely to occur. Abaqus performs a check +on the stability of the material for nine different forms of loading—uniaxial tension and compression, +equibiaxial tension and compression, simple shear, planar tension and compression, and volumetric +tension and compression—for +), at +intervals +. If an instability is found, Abaqus issues a warning message and prints the lowest +absolute value of +for which the instability is observed. Ideally, no instability occurs. If instabilities +are observed at strain levels that are likely to occur in the analysis, it is strongly recommended that you +carefully examine and revise the material input data. +(nominal strain range of +Improving the accuracy and stability of the test data fit +“Hyperelastic behavior of rubberlike materials,” Section 22.5.1, contains suggestions for improving the +accuracy and stability of elastomeric modeling. “Fitting of elastomeric foam test data,” Section 3.1.5 of +the Abaqus Benchmarks Manual, illustrates the process of fitting elastomeric foam test data. +Elements +The hyperfoam model can be used with solid (continuum) elements, finite-strain shells (except S4), +and membranes. However, it cannot be used with one-dimensional solid elements (trusses and beams), +small-strain shells (STRI3, STRI65, S4R5, S8R, S8R5, S9R5), or the Eulerian elements (EC3D8R and +EC3D8RT). +For continuum elements elastomeric foam hyperelasticity can be used with pure displacement +formulation elements or, in Abaqus/Standard, with the “hybrid” (mixed formulation) elements. Since +elastomeric foams are assumed to be very compressible, the use of hybrid elements will generally not +yield any advantage over the use of purely displacement-based elements. +Procedures +The hyperfoam model must always be used with geometrically nonlinear analyses (“General and linear +perturbation procedures,” Section 6.1.3). +22.5.3 +ANISOTROPIC HYPERELASTIC BEHAVIOR +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Elastic behavior: overview,” Section 22.1.1 +• “Mullins effect,” Section 22.6.1 +• *ANISOTROPIC HYPERELASTIC +• *VISCOELASTIC +• *MULLINS EFFECT +• “Creating an anisotropic hyperelastic material model” in “Defining elasticity,” Section 12.9.1 of the +Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +The anisotropic hyperelastic material model: +• provides a general capability for modeling materials that exhibit highly anisotropic and nonlinear +elastic behavior (such as biomedical soft tissues, fiber-reinforced elastomers, etc.); +• can be used in combination with large-strain time-domain viscoelasticity (“Time domain +viscoelasticity,” Section 22.7.1); however, viscoelasticity is isotropic; +• optionally allows the specification of energy dissipation and stress softening effects ; and +• requires that geometric nonlinearity be accounted for during the analysis step (“General and linear +perturbation procedures,” Section 6.1.3) since it is intended for finite-strain applications. +Anisotropic hyperelasticity formulations +Many materials of industrial and technological interest exhibit anisotropic elastic behavior due to the +presence of preferred directions in their microstructure. Examples of such materials include common +engineering materials (such as fiber-reinforced composites, reinforced rubber, wood, etc.) as well +as soft biological tissues (arterial walls, heart tissue, etc.). When these materials are subjected to +small deformations (less than 2–5%), their mechanical behavior can generally be modeled adequately +using conventional anisotropic linear elasticity ( see “Defining fully anisotropic elasticity” in “Linear +elastic behavior,” Section 22.2.1). Under large deformations, however, these materials exhibit highly +anisotropic and nonlinear elastic behavior due to rearrangements in the microstructure, such as +reorientation of the fiber directions with deformation. The simulation of these nonlinear large-strain +effects calls for more advanced constitutive models formulated within the framework of anisotropic +hyperelasticity. Hyperelastic materials are described in terms of a “strain energy potential,” +, which +defines the strain energy stored in the material per unit of reference volume (volume in the initial +configuration) as a function of the deformation at that point in the material. Two distinct formulations +are used for the representation of the strain energy potential of anisotropic hyperelastic materials: +strain-based and invariant-based. +Strain-based formulation +In this case the strain energy function is expressed directly in terms of the components of a suitable +strain tensor, such as the Green strain tensor : +where +is the +deformation gradient; and is the identity matrix. Without loss of generality, the strain energy function +can be written in the form +is the right Cauchy-Green strain tensor; +is Green’s strain; +where +right Cauchy-Green strain; +as defined below in “Thermal expansion.” +is the modified Green strain tensor; +is the total volume change; and +is the distortional part of the +is the elastic volume ratio +The underlying assumption in models based on the strain-based formulation is that the preferred +material directions are initially aligned with an orthogonal coordinate system in the reference (stress-free) +configuration. These directions may become non-orthogonal only after deformation. Examples of this +form of strain energy function include the generalized Fung-type form described below. +Invariant-based formulation +Using the continuum theory of fiber-reinforced composites (Spencer, 1984) the strain energy function +can be expressed directly in terms of the invariants of the deformation tensor and fiber directions. For +example, consider a composite material that consists of an isotropic hyperelastic matrix reinforced with +families of fibers. The directions of the fibers in the reference configuration are characterized by a set +). Assuming that the strain energy depends not only on deformation, +of unit vectors +but also on the fiber directions, the following form is postulated +, ( +The strain energy of the material must remain unchanged if both matrix and fibers in the reference +configuration undergo a rigid body rotation. Then, following Spencer (1984), the strain energy can be +expressed in terms of an irreducible set of scalar invariants that form the integrity basis of the tensor +and the vectors +: +where +and +third strain invariant); +are the first and second deviatoric strain invariants; +are the pseudo-invariants of +and +is the elastic volume ratio (or +, +; and +, defined as: +The terms +between the directions of any two families of fibers in the reference configuration: +are geometrical constants (independent of deformation) equal to the cosine of the angle +Unlike for the case of the strain-based formulation, in the invariant-based formulation the fiber +directions need not be orthogonal in the initial configuration. An example of an invariant-based energy +function is the form proposed by Holzapfel, Gasser, and Ogden (2000) for arterial walls . +Anisotropic strain energy potentials +There are two forms of strain energy potentials available in Abaqus to model approximately +incompressible anisotropic materials: +the generalized Fung form (including fully anisotropic and +orthotropic cases) and the form proposed by Holzapfel, Gasser, and Ogden for arterial walls. Both +forms are adequate for modeling soft biological tissue. However, whereas Fung’s form is purely +phenomenological, the Holzapfel-Gasser-Ogden form is micromechanically based. +In addition, Abaqus provides a general capability to support user-defined forms of the strain energy +potential via two sets of user subroutines: one for strain-based and one for invariant-based formulations. +Generalized Fung form +The generalized Fung strain energy potential has the following form: +where U is the strain energy per unit of reference volume; +parameters; +is the elastic volume ratio as defined below in “Thermal expansion”; and +and D are temperature-dependent material +is defined as +where +be temperature dependent and +is a dimensionless symmetric fourth-order tensor of anisotropic material constants that can +are the components of the modified Green strain tensor. +The initial deviatoric elasticity tensor, +, and bulk modulus, +, are given by +Abaqus supports two forms of the generalized Fung model: fully anisotropic and orthotropic. The +that must be specified depends on the level of anisotropy of the +number of independent components +material: 21 for the fully anisotropic case and 9 for the orthotropic case. +Input File Usage: +Use one of the following options: +*ANISOTROPIC HYPERELASTIC, FUNG-ANISOTROPIC +*ANISOTROPIC HYPERELASTIC, FUNG-ORTHOTROPIC +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Elasticity→Hyperelastic; +Material type: Anisotropic; Strain energy potential: Fung- +Anisotropic or Fung-Orthotropic +Holzapfel-Gasser-Ogden form +The form of the strain energy potential is based on that proposed by Holzapfel, Gasser, and Ogden (2000) +and Gasser, Ogden, and Holzapfel (2006) for modeling arterial layers with distributed collagen fiber +orientations: +with +where U is the strain energy per unit of reference volume; +dependent material parameters; +strain invariant; +pseudo-invariants of +, D, +is the number of families of fibers ( +and +. +is the elastic volume ratio as defined below in “Thermal expansion” and +, +, and +); +are temperature- +is the first deviatoric +are +The model assumes that the directions of the collagen fibers within each family are dispersed (with +) describes the +is the orientation density function that characterizes +rotational symmetry) about a mean preferred direction. The parameter +level of dispersion in the fiber directions. If +the distribution (it represents the normalized number of fibers with orientations in the range +with respect to the mean direction), the parameter +is defined as +( +It is also assumed that all families of fibers have the same mechanical properties and the same +dispersion. When +the fibers +are randomly distributed and the material becomes isotropic; this corresponds to a spherical orientation +density function. +the fibers are perfectly aligned (no dispersion). When +The strain-like quantity +characterizes the deformation of the family of fibers with mean direction +. For perfectly aligned fibers ( +), +. +), +; and for randomly distributed fibers ( +The first two terms in the expression of the strain energy function represent the distortional and +volumetric contributions of the non-collagenous isotropic ground material, and the third term represents +the contributions from the different families of collagen fibers, taking into account the effects of +dispersion. A basic assumption of the model is that collagen fibers can support tension only, because +they would buckle under compressive loading. Thus, the anisotropic contribution in the strain energy +function appears only when the strain of the fibers is positive or, equivalently, when +. This +condition is enforced by the term +stands for the Macauley bracket and is +defined as +, where the operator +. +See “Anisotropic hyperelastic modeling of arterial layers,” Section 3.1.7 of the Abaqus Benchmarks +Manual, for an example of an application of the Holzapfel-Gasser-Ogden energy potential to model +arterial layers with distributed collagen fiber orientation. +The initial deviatoric elasticity tensor, +, and bulk modulus, +, are given by +where +is the fourth-order unit tensor, and +is the Heaviside unit step function. +Input File Usage: +*ANISOTROPIC HYPERELASTIC, HOLZAPFEL, +LOCAL DIRECTIONS=N +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Elasticity→Hyperelastic; +Material type: Anisotropic; Strain energy potential: Holzapfel, +Number of local directions: N +User-defined form: strain-based +Alternatively, you can define the form of a strain-based strain energy potential directly with +user subroutine UANISOHYPER_STRAIN in Abaqus/Standard or VUANISOHYPER_STRAIN in +Abaqus/Explicit. The derivatives of the strain energy potential with respect to the components of the +modified Green strain and the elastic volume ratio, +, must be provided directly through these user +subroutines. +Either compressible or incompressible behavior can be specified in Abaqus/Standard; only nearly +incompressible behavior is allowed in Abaqus/Explicit. +Optionally, you can specify the number of property values needed as data in the user subroutine as +well as the number of solution-dependent variables . +Input File Usage: +In Abaqus/Standard use the following option to define compressible behavior: +*ANISOTROPIC HYPERELASTIC, USER, FORMULATION=STRAIN, +TYPE=COMPRESSIBLE, PROPERTIES=n +In Abaqus/Standard use the following option to define incompressible behavior: +*ANISOTROPIC HYPERELASTIC, USER, FORMULATION=STRAIN, +TYPE=INCOMPRESSIBLE, PROPERTIES=n +In Abaqus/Explicit use the following option to define nearly incompressible +behavior: +*ANISOTROPIC HYPERELASTIC, USER, FORMULATION=STRAIN, +PROPERTIES=n +Property module: material editor: Mechanical→Elasticity→Hyperelastic; +Material type: Anisotropic, Strain energy potential: User, +Formulation: Strain, Type: Incompressible or Compressible, +Number of property values: n +Abaqus/CAE Usage: +User-defined form: invariant-based +Alternatively, you can define the form of an invariant-based strain energy potential directly with user +subroutine UANISOHYPER_INV in Abaqus/Standard or VUANISOHYPER_INV in Abaqus/Explicit. +Either compressible or incompressible behavior can be specified in Abaqus/Standard; only nearly +incompressible behavior is allowed in Abaqus/Explicit. +Optionally, you can specify the number of property values needed as data in the user subroutine and +the number of solution-dependent variables . +The derivatives of the strain energy potential with respect to the strain invariants must be provided +directly through user subroutine UANISOHYPER_INV in Abaqus/Standard and VUANISOHYPER_INV +in Abaqus/Explicit. +Input File Usage: +In Abaqus/Standard use the following option to define compressible behavior: +*ANISOTROPIC HYPERELASTIC, USER, +FORMULATION=INVARIANT, LOCAL DIRECTIONS=N, +TYPE=COMPRESSIBLE, PROPERTIES=n +In Abaqus/Standard use the following option to define incompressible behavior: +*ANISOTROPIC HYPERELASTIC, USER, +FORMULATION=INVARIANT, LOCAL DIRECTIONS=N, +TYPE=INCOMPRESSIBLE, PROPERTIES=n +In Abaqus/Explicit use the following option to define nearly incompressible +behavior: +*ANISOTROPIC HYPERELASTIC, USER, +FORMULATION=INVARIANT, PROPERTIES=n +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Elasticity→Hyperelastic; +Material type: Anisotropic, Strain energy potential: User, Formulation: +Invariant, Type: Incompressible or Compressible, Number of +local directions: N, Number of property values: n +Definition of preferred material directions +You must define the preferred material directions (or fiber directions) of the anisotropic hyperelastic +material. +For strain-based forms (such as the Fung form and user-defined forms using user subroutines +UANISOHYPER_STRAIN or VUANISOHYPER_STRAIN), you must specify a local orientation system +(“Orientations,” Section 2.2.5) to define the directions of anisotropy. Components of the modified +Green strain tensor are calculated with respect to this system. +For invariant-based forms of the strain energy function (such as the Holzapfel form and user-defined +forms using user subroutines UANISOHYPER_INV or VUANISOHYPER_INV), you must specify the +local direction vectors, +, that characterize each family of fibers. These vectors need not be orthogonal +in the initial configuration. Up to three local directions can be specified as part of the definition of a local +orientation system (“Defining a local coordinate system directly” in “Orientations,” Section 2.2.5); the +local directions are referred to this system. +In Abaqus/CAE, the local direction vectors of the material are orthogonal and align with the axes of +the assigned material orientation. The best practice is to assign the orientation using discrete orientations +in Abaqus/CAE. +Material directions can be output to the output database as described in “Output,” below. +Compressibility +Most soft tissues and fiber-reinforced elastomers have very little compressibility compared to their shear +flexibility. This behavior does not warrant special attention for plane stress, shell, or membrane elements, +but the numerical solution can be quite sensitive to the degree of compressibility for three-dimensional +solid, plane strain, and axisymmetric elements. In cases where the material is highly confined (such +as an O-ring used as a seal), the compressibility must be modeled correctly to obtain accurate results. +In applications where the material is not highly confined, the degree of compressibility is typically not +crucial; for example, it would be quite satisfactory in Abaqus/Standard to assume that the material is +fully incompressible: the volume of the material cannot change except for thermal expansion. +Compressibility in Abaqus/Standard +In Abaqus/Standard the use of “hybrid” (mixed formulation) elements is required for incompressible +materials. In plane stress, shell, and membrane elements the material is free to deform in the thickness +direction. In this case special treatment of the volumetric behavior is not necessary; the use of regular +stress/displacement elements is satisfactory. +Compressibility in Abaqus/Explicit +With the exception of the plane stress case, it is not possible to assume that the material is fully +incompressible in Abaqus/Explicit because the program has no mechanism for imposing such a +constraint at each material calculation point. +Instead, some compressibility must be modeled. The +difficulty is that, in many cases, the actual material behavior provides too little compressibility for +the algorithms to work efficiently. Thus, except for the plane stress case, you must provide enough +compressibility for the code to work, knowing that this makes the bulk behavior of the model softer than +that of the actual material. Failing to provide enough compressibility may introduce high frequency +noise into the dynamic solution and require the use of excessively small time increments. Some +judgment is, therefore, required to decide whether or not the solution is sufficiently accurate or whether +the problem can be modeled at all with Abaqus/Explicit because of this numerical limitation. +If no value is given for the material compressibility of the anisotropic hyperelastic model, by default +Abaqus/Explicit assumes the value +is the largest value of the initial shear +, where +modulus (among the different material directions). The exception is for the case of user-defined forms, +where some compressibility must be defined directly within user subroutine UANISOHYPER_INV or +VUANISOHYPER_INV. +Thermal expansion +Both isotropic and orthotropic thermal expansion is permitted with the anisotropic hyperelastic material +model. +The elastic volume ratio, +, relates the total volume ratio, J, and the thermal volume ratio, +: +is given by +where +thermal expansion coefficients (“Thermal expansion,” Section 26.1.2). +are the principal thermal expansion strains that are obtained from the temperature and the +Viscoelasticity +Anisotropic hyperelastic models can be used in combination with isotropic viscoelasticity to model rate- +dependent material behavior (“Time domain viscoelasticity,” Section 22.7.1). Because of the isotropy +of viscoelasticity, the relaxation function is independent of the loading direction. This assumption may +not be acceptable for modeling materials that exhibit strong anisotropy in their rate-dependent behavior; +therefore, this option should be used with caution. +The anisotropic hyperelastic response of rate-dependent materials (“Time domain viscoelasticity,” +Section 22.7.1) can be specified by defining either the instantaneous response or the long-term response +of such materials. +Input File Usage: +Use either of the following options: +Abaqus/CAE Usage: +*ANISOTROPIC HYPERELASTIC, MODULI=INSTANTANEOUS +*ANISOTROPIC HYPERELASTIC, MODULI=LONG TERM +Property module: material editor: Mechanical→Elasticity→Hyperelastic; +Material type: Anisotropic; Moduli: Long term or Instantaneous +Stress softening +The response of typical anisotropic hyperelastic materials, such as reinforced rubbers and biological +tissues, under cyclic loading and unloading usually displays stress softening effects during the first few +cycles. After a few cycles the response of the material tends to stabilize and the material is said to be pre- +conditioned. Stress softening effects, often referred to in the elastomers literature as Mullins effect, can +be accounted for by using the anisotropic hyperelastic model in combination with the pseudo-elasticity +model for Mullins effect in Abaqus . The stress softening effects +provided by this model are isotropic. +Elements +The anisotropic hyperelastic material model can be used with solid (continuum) elements, finite-strain +shells (except S4), continuum shells, and membranes. When used in combination with elements with +plane stress formulations, Abaqus assumes fully incompressible behavior and ignores any amount of +compressibility specified for the material. +Pure displacement formulation versus hybrid formulation in Abaqus/Standard +For continuum elements in Abaqus/Standard anisotropic hyperelasticity can be used with the +pure displacement formulation elements or with the “hybrid” (mixed formulation) elements. Pure +displacement formulation elements must be used with compressible materials, and “hybrid” (mixed +formulation) elements must be used with incompressible materials. +In general, an analysis using a single hybrid element will be only slightly more computationally +expensive than an analysis using a regular displacement-based element. However, when the wavefront is +optimized, the Lagrange multipliers may not be ordered independently of the regular degrees of freedom +associated with the element. Thus, the wavefront of a very large mesh of second-order hybrid tetrahedra +may be noticeably larger than that of an equivalent mesh using regular second-order tetrahedra. This +may lead to significantly higher CPU costs, disk space, and memory requirements. +Incompatible mode elements in Abaqus/Standard +Incompatible mode elements should be used with caution in applications involving large strains. +Convergence may be slow, and in hyperelastic applications inaccuracies may accumulate. Erroneous +stresses may sometimes appear in incompatible mode anisotropic hyperelastic elements that are +unloaded after having been subjected to a complex deformation history. +Procedures +Anisotropic hyperelasticity must always be used with geometrically nonlinear analyses (“General and +linear perturbation procedures,” Section 6.1.3). +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2), +local +material directions will be output whenever element field output is requested to the output database. The +local directions are output as field variables (LOCALDIR1, LOCALDIR2, LOCALDIR3) representing +the direction cosines; these variables can be visualized as vector plots in the Visualization module of +Abaqus/CAE (Abaqus/Viewer). +Output of local material directions is suppressed if no element field output is requested or if +you specify not to have element material directions written to the output database . +Additional references +• Gasser, T. C., R. W. Ogden, and G. A. Holzapfel, “Hyperelastic Modelling of Arterial Layers with +Distributed Collagen Fibre Orientations,” Journal of the Royal Society Interface, vol. 3, pp. 15–35, +2006. +• Holzapfel, G. A., T. C. Gasser, and R. W. Ogden, “A New Constitutive Framework for Arterial +Wall Mechanics and a Comparative Study of Material Models,” Journal of Elasticity, vol. 61, +pp. 1–48, 2000. +• Spencer, A. J. M., “Constitutive Theory for Strongly Anisotropic Solids,” A. J. M. Spencer (ed.), +Continuum Theory of the Mechanics of Fibre-Reinforced Composites, CISM Courses and Lectures +No. 282, International Centre for Mechanical Sciences, Springer-Verlag, Wien, pp. 1–32, 1984. +22.6 +Stress softening in elastomers +• “Mullins effect,” Section 22.6.1 +• “Energy dissipation in elastomeric foams,” Section 22.6.2 +22.6.1 +MULLINS EFFECT +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Combining material behaviors,” Section 21.1.3 +• “Elastic behavior: overview,” Section 22.1.1 +• “Hyperelastic behavior of rubberlike materials,” Section 22.5.1 +• “Anisotropic hyperelastic behavior,” Section 22.5.3 +• “Permanent set in rubberlike materials,” Section 23.7.1 +• “Energy dissipation in elastomeric foams,” Section 22.6.2 +• *HYPERELASTIC +• *MULLINS EFFECT +• *PLASTIC +• *UNIAXIAL TEST DATA +• *BIAXIAL TEST DATA +• *PLANAR TEST DATA +• “Mullins effect” in “Defining damage,” Section 12.9.3 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +The Mullins effect model: +• is intended for modeling stress softening of filled rubber elastomers under quasi-static cyclic +loading, a phenomenon referred to in the literature as Mullins effect; +• provides an extension to the well-known isotropic hyperelastic models; +• is based on the theory of incompressible isotropic elasticity modified by the addition of a single +variable, referred to as the damage variable; +• assumes that only the deviatoric part of the material response is associated with damage; +• is intended for modeling material response in situations where different parts of the model undergo +different levels of damage resulting in a different material response; +• is applied to the long-term modulus when combined with viscoelasticity; and +• cannot be used with hysteresis. +Abaqus provides a similar capability that can be applied to elastomeric foams . +Material behavior +The real behavior of filled rubber elastomers under cyclic loading conditions is quite complex. Certain +idealizations have been made for modeling purposes. In essence, these idealizations result in two main +components to the material behavior: the first component describes the response of a material point (from +an undeformed state) under monotonic straining, and the second component is associated with damage +and describes the unloading-reloading behavior. The idealized response and the two components are +described in the following sections. +Idealized material behavior +When an elastomeric test specimen is subjected to simple tension from its virgin state, unloaded, and +then reloaded, the stress required on reloading is less than that on the initial loading for stretches up to +the maximum stretch achieved during the initial loading. This stress softening phenomenon is known as +the Mullins effect and reflects damage incurred during previous loading. This type of material response +is depicted qualitatively in Figure 22.6.1–1. +c' +b' +stretch +Figure 22.6.1–1 Idealized response of the Mullins effect model. +This figure and the accompanying description is based on work by Ogden and Roxburgh (1999), which +forms the basis of the model implemented in Abaqus. Consider the primary loading path +of a +previously unstressed material, with loading to an arbitrary point +. On unloading from , the path +. If further +is a continuation of the primary loading path +(which is the path that would be followed if there was no unloading). If loading is now stopped +on reloading. If no further +is followed. When the material is loaded again, the softened path is retraced as +is followed, where +is followed on unloading and then retraced back to +loading is then applied, the path +, the path +at +is applied, the curve +loading beyond +elastic. For loading beyond +represents the subsequent material response, which is then +, the primary path is again followed and the pattern described is repeated. +This is an ideal representation of Mullins effect since in practice there is some permanent set upon +unloading and/or viscoelastic effects such as hysteresis. Points such as +and may not exist in reality +in the sense that unloading from the primary curve followed by reloading to the maximum strain level +attained earlier usually results in a stress that is somewhat lower than the stress corresponding to the +primary curve. In addition, the cyclic response for some filled elastomers shows evidence of progressive +damage during unloading from and subsequent reloading to a certain maximum strain level. Such +progressive damage usually occurs during the first few cycles, and the material behavior soon stabilizes +to a loading/unloading cycle that is followed beyond the first few cycles. More details regarding the +actual behavior and how test data that display such behavior can be used to calibrate the Abaqus model +for Mullins effect are discussed later and in “Analysis of a solid disc with Mullins effect and permanent +set,” Section 3.1.7 of the Abaqus Example Problems Manual. +The loading path +will henceforth be referred to as the “primary hyperelastic behavior.” The +primary hyperelastic behavior is defined by using a hyperelastic material model. +Stress softening is interpreted as being due to damage at the microscopic level. As the material +is loaded, the damage occurs by the severing of bonds between filler particles and the rubber molecular +chains. Different chain links break at different deformation levels, thereby leading to continuous damage +with macroscopic deformation. An equivalent interpretation is that the energy required to cause the +damage is not recoverable. +Primary hyperelastic behavior +Hyperelastic materials are described in terms of a “strain energy potential” function +that defines +the strain energy stored in the material per unit reference volume (volume in the initial configuration). +The quantity +is the deformation gradient tensor. To account for Mullins effect, Ogden and Roxburgh +propose a material description that is based on an energy function of the form +, where the +additional scalar variable, +, represents damage in the material. The damage variable controls the +material properties in the sense that it enables the material response to be governed by an energy +function on unloading and subsequent submaximal reloading different from that on the primary (initial) +loading path from a virgin state. Because of the above interpretation of +, it is no longer appropriate to +think of U as the stored elastic energy potential. Part of the energy is stored as strain energy, while the +rest is dissipated due to damage. The shaded area in Figure 22.6.1–1 represents the energy dissipated by +damage as a result of deformation until the point +, while the unshaded part represents the recoverable +strain energy. +The following paragraphs provide a summary of the Mullins effect model in Abaqus. For further +details, see “Mullins effect,” Section 4.7.1 of the Abaqus Theory Manual. In preparation for writing the +constitutive equations for Mullins effect, it is useful to separate the deviatoric and the volumetric parts +of the total strain energy density as +In the above equation U, +are the total, deviatoric, and volumetric parts of the strain energy +density, respectively. All the hyperelasticity models in Abaqus use strain energy potential functions that +are already separated into deviatoric and volumetric parts. For example, the polynomial models use a +strain energy potential of the form +, and +where the symbols have the usual interpretations. The first term on the right represents the deviatoric +part of the elastic strain energy density function, and the second term represents the volumetric part. +Modified strain energy density function +The Mullins effect is accounted for by using an augmented energy function of the form +is a continuous function of the damage variable +is the deviatoric part of the strain energy density of the primary hyperelastic behavior, +where +defined, for example, by the first term on the right-hand-side of the polynomial strain energy function +given above; +is the volumetric part of the strain energy density, defined, for example, by the +second term on the right-hand-side of the polynomial strain energy function given above; +represent the deviatoric principal stretches; and +represents the elastic volume ratio. The function +and is referred to as the “damage function.” When +the deformation state of the material is on a point on the curve that represents the primary hyperelastic +behavior, +, and the augmented energy function +reduces to the strain energy density function of the primary hyperelastic behavior. The damage variable +varies continuously during the course of the deformation and always satisfies +. The above +form of the energy function is an extension of the form proposed by Ogden and Roxburgh to account for +material compressibility. +, +, +Stress computation +With the above modification to the energy function, the stresses are given by +and +is the deviatoric stress corresponding to the primary hyperelastic behavior at the current +where +deviatoric deformation level +is the hydrostatic pressure of the primary hyperelastic behavior +at the current volumetric deformation level +. Thus, the deviatoric stress as a result of Mullins +effect is obtained by simply scaling the deviatoric stress of the primary hyperelastic behavior with the +damage variable . The pressure stress is the same as that of the primary behavior. The model predicts +loading/unloading along a single curve (that is different, in general, from the primary hyperelastic +behavior) from any given strain level that passes through the origin of the stress-strain plot. It cannot +capture permanent strains upon removal of load. The model also predicts that a purely volumetric +deformation will not have any damage or Mullins effect associated with it. +Damage variable +The damage variable, +, varies with the deformation according to +where +m are material parameters; and +is the maximum value of +at a material point during its deformation history; r, +, and +is the error function defined as +When +its minimum value, +, given by +, corresponding to a point on the primary curve, +. On the other hand, +attains +and +. While the parameters r and +. For all intermediate values of +varies +upon removal of deformation, when +monotonically between +are dimensionless, the parameter m +has the dimensions of energy. The equation for +reduces to that proposed by Ogden and Roxburgh +when +. The material parameters may be specified directly or may be computed by Abaqus +based on curve-fitting of unloading-reloading test data. These parameters are subject to the restrictions +and m cannot both be zero). Alternatively, the damage +can be defined through user subroutine UMULLINS in Abaqus/Standard and VUMULLINS in +(the parameters +, and +, +, +variable +Abaqus/Explicit. +If the parameter +and the parameter m has a value that is small compared to +, the slope of +the stress-strain curve at the initiation of unloading from relatively large strain levels may become very +high. As a result, the response may become discontinuous, as illustrated in Figure 22.6.1–2. This kind of +behavior may lead to convergence problems in Abaqus/Standard. In Abaqus/Explicit the high stiffness +will lead to very small stable time increments, thereby leading to a degradation in performance. This +problem can be avoided by choosing a small value for +can be used to define the +original Ogden-Roxburgh model. In Abaqus/Standard the default value of +is 0. In Abaqus/Explicit, +however, the default value of +, it is assumed to be 0 in +Abaqus/Standard and 0.1 in Abaqus/Explicit. +is 0.1. Thus, if you do not specify a value for +. The choice +The parameters r, +, and m do not have direct physical interpretations in general. The parameter m +controls whether damage occurs at low strain levels. If +, there is a significant amount of damage +at low strain levels. On the other hand, a nonzero m leads to little or no damage at low strain levels. +For further discussion regarding the implications of this model to the energy dissipation, see “Mullins +' +' +stretch +Figure 22.6.1–2 Overly stiff response at the initiation of unloading. +effect,” Section 4.7.1 of the Abaqus Theory Manual. The qualitative effects of varying the parameters r +and +individually, while holding the other parameters fixed, are shown in Figure 22.6.1–3. +σ~ +η (β ) +m 2 + η (β ) +m 1 +σ~ +σ~ +increasing + r +increasing + β +stretch +stretch +Figure 22.6.1–3 Qualitative dependence of damage on material properties. +The left figure shows the unloading-reloading curve from a certain maximum strain level for increasing +values of r. It suggests that the parameter r controls the amount of damage, with decreasing damage +for increasing r. This behavior follows from the fact that the larger the value of r, the less the damage +variable +can deviate from unity. The figure on the right shows the unloading-reloading curve from +a certain maximum strain level for increasing values of +also +leads to lower amounts of damage. It also shows that the unloading-reloading response approaches the +asymptotic response given by +. +. The figure suggests that increasing +, faster for lower values of +is the minimum value of +, where +values of r and m, +. In particular, if +is a function of +, +MULLINS EFFECT +( +and +). For fixed +The above relation is approximately true if +is much greater than m. +Specifying the Mullins effect material model in Abaqus +The primary hyperelastic behavior is defined by using the hyperelastic material model . The Mullins effect model can be defined by specifying +the Mullins effect parameters directly or by using test data to calibrate the parameters. Alternatively, +you can define the Mullins effect model with user subroutine UMULLINS in Abaqus/Standard and +VUMULLINS in Abaqus/Explicit. +Specifying the parameters directly +The parameters r, m, and +field variables. +Input File Usage: +Abaqus/CAE Usage: +of the Mullins effect can be given directly as functions of temperature and/or +*MULLINS EFFECT +Property module: material editor: +Mechanical→Damage for Elastomers→Mullins Effect: +Definition: Constants +Using test data to calibrate the parameters +Experimental unloading-reloading data from different strain levels can be specified for up to three +simple tests: uniaxial, biaxial, and planar. Abaqus will then compute the material parameters using +a nonlinear least-squares curve fitting algorithm. +It is generally best to obtain data from several +experiments involving different kinds of deformation over the range of strains of interest in the actual +application and to use all these data to determine the parameters. It is also important to obtain a good +curve-fit for the primary hyperelastic behavior if the primary behavior is defined using test data. +. In this case the parameters m and +By default, Abaqus attempts to fit all three parameters to the given data. This is possible in general, +except in the situation when the test data correspond to unloading-reloading from only a single value +of +cannot be determined independently; one of them must +be specified. If you specify neither m nor +, Abaqus needs to assume a default value for one of these +parameters. In light of the potential problems discussed earlier with +in the above situation. The curve-fitting may also be carried out by specifying any one or two of the +material parameters to be fixed, predetermined values. +, Abaqus assumes that +As many data points as required can be entered from each test. It is recommended that data from all +three tests (on samples taken from the same piece of material) be included and that the data points cover +unloading/reloading from/to the range of nominal strain expected to arise in the actual loading. +The strain data should be given as nominal strain values (change in length per unit of original length). +The stress data should be given as nominal stress values (force per unit of original cross-sectional area). +These tests allow for entering both compression and tension data. Compressive stresses and strains are +entered as negative values. +For each set of test input, the data point with the maximum nominal strain identifies the point of +unloading. This point is used by the curve-fitting algorithm to compute +for that curve. +Figure 22.6.1–4 shows some typical unloading-reloading data from three different strain levels. +Nominal Strain +Figure 22.6.1–4 Typical available test data for Mullins effect. +The data include multiple loading and unloading cycles from each strain level. As Figure 22.6.1–4 +indicates, the loading/unloading cycles from any given strain level do not occur along a single curve, +and there is some amount of hysteresis. There is also some amount of permanent set upon removal of +the applied load. The data also show evidence of progressive damage with repeated cycling at any given +maximum strain level. The response appears to stabilize after a number of cycles. When such data +are used to calibrate the Mullins effect model, the resulting response will capture the overall stiffness +characteristics, while ignoring effects such as hysteresis, permanent set, or progressive damage. The +above data can be provided to Abaqus in the following manner: +• The primary curve can be made up of the data points indicated by the dashed curve in +Figure 22.6.1–4. Essentially, this consists of an envelope of the first loading curves to the different +strain levels. +• The unloading-reloading curves from the three different strain levels can be specified by providing +the data points as is; i.e., as the repeated unloading-reloading cycles shown in Figure 22.6.1–4. As +discussed earlier, the data from the different strain levels need to be distinguished by providing +them as different tables. For example, assuming that the test data correspond to the uniaxial tension +state, three tables of uniaxial test data would have to be defined for the three different strain levels +shown in Figure 22.6.1–4. In this case Abaqus will provide a best fit using all the data points (from +all strain levels). The resulting fit would result in a response that is an average of all the test data +at any given strain level. While permanent set may be modeled , hysteresis will be lost in the process. +• Alternatively, you may provide any one unloading-reloading cycle from each different strain level. +If the component is expected to undergo repeated cyclic loading, the latter may be, for example, +the stabilized cycle at each strain level. On the other hand, if the component is expected to undergo +predominantly monotonic loading with perhaps small amounts of unloading, the very first unloading +curve at each strain level may be the appropriate input data for calibrating the Mullins coefficients. +Once the Mullins effect constants are determined, the behavior of the Mullins effect model in +the prediction of +Abaqus is established. However, the quality of this behavior must be assessed: +material behavior under different deformation modes must be compared against the experimental data. +You must judge whether the Mullins effect constants determined by Abaqus are acceptable, based on +the correlation between the Abaqus predictions and the experimental data. Single-element test cases +can be used to derive the nominal stress–nominal strain response of the material model. +The steps that can be taken for improving the quality of the fit for the Mullins effect parameters +are similar in essence to the guidelines provided for curve fitting the primary hyperelastic behavior . In addition, the quality of +the fit for the Mullins effect parameters depends on a good fit for the primary hyperelastic behavior, if +the primary behavior is defined using test data. +The quality of the fit can be evaluated by carrying out a numerical experiment with a single element +that is loaded in the same mode for which test data has been provided. Alternatively, the numerical +response for both the primary and the softening behavior can be obtained by requesting model definition +data output and carrying out a data check analysis. The response computed +by Abaqus is printed in the data (.dat) file along with the experimental data. This tabular data can be +plotted in Abaqus/CAE for comparison and evaluation purposes. The primary hyperelastic behavior can +also be evaluated with the automated material evaluation tools in Abaqus/CAE. +Input File Usage: +*MULLINS EFFECT, TEST DATA INPUT, BETA and/or M and/or R +In addition, use at least one and up to three of the following options to give +the unloading-reloading test data : +*UNIAXIAL TEST DATA +*BIAXIAL TEST DATA +*PLANAR TEST DATA +Abaqus/CAE Usage: +Multiple unloading-reloading curves from different strain levels for any given +test type can be entered by repeated specification of the appropriate test data +option. +Property module: material editor: +Mechanical→Damage for Elastomers→Mullins Effect: Definition: +Test Data Input: enter the values for up to two of the values r, m, and +beta. In addition, select and enter data for at least one of the following: +Add Test→Biaxial Test, Planar Test, or Uniaxial Test +User subroutine specification +An alternative method for defining the Mullins effect involves defining the damage variable in user +subroutine UMULLINS in Abaqus/Standard and VUMULLINS in Abaqus/Explicit. Optionally, you +can specify the number of property values needed as data in the user subroutine. You must provide +the damage variable, +. The latter contributes to the Jacobian of the overall +system of equations and is necessary to ensure good convergence characteristics in Abaqus/Standard. +If needed, you can specify the number of solution-dependent variables (“User subroutines: overview,” +Section 18.1.1). These solution-dependent variables can be updated in the user subroutine. The damage +dissipation energy and the recoverable part of the energy may also be defined for output purposes. +, and its derivative, +User +subroutines UMULLINS and VUMULLINS can be used in combination with all +hyperelastic potentials in Abaqus, including user-defined potentials (via user subroutines UHYPER, +UANISOHYPER_INV, and UANISOHYPER_STRAIN Abaqus/Standard, and VUANISOHYPER_INV +and VUANISOHYPER_STRAIN in Abaqus/Explicit). +Input File Usage: +Abaqus/CAE Usage: +*MULLINS EFFECT, USER, PROPERTIES=constants +Property module: material editor: +Mechanical→Damage for Elastomers→Mullins Effect: +Definition: User Defined +Viscoelasticity +When viscoelasticity is used in combination with Mullins effect, stress softening is applied to the long- +term behavior. +In this case specification of the parameter +(which has units of energy) should be done carefully. +If the underlying hyperelastic behavior is defined with an instantaneous modulus, will be interpreted +to be instantaneous. Otherwise, +is considered to be long term. +Elements +The Mullins effect material model can be used with all element types that support the use of the +hyperelastic material model. +Procedures +The Mullins effect material model can be used in all procedure types that support the use of the +hyperelastic material model. +In linear perturbation steps in Abaqus/Standard the current material +tangent stiffness is used to determine the response. Specifically, when a linear perturbation is carried +out about a base state that is on the primary curve, the unloading tangent stiffness will be used. +In Abaqus/Explicit the unloading tangent stiffness is always used to compute the stable time +increment. As a result, the inclusion of Mullins effect leads to more increments in the analysis, even +when no unloading actually takes place. +The Mullins effect material model can also be used in a steady-state transport analysis in +Abaqus/Standard to obtain steady-state rolling solutions. Issues related to the use of the Mullins effect +in a steady-state transport analysis can be found in “Steady-state transport analysis,” Section 6.4.1, and +“Analysis of a solid disc with Mullins effect and permanent set,” Section 3.1.7 of the Abaqus Example +Problems Manual. +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2), +the +following variables have special meaning for the Mullins effect material model: +DMENER +ELDMD +ALLDMD +Energy dissipated per unit volume by damage. +Total energy dissipated in element by damage. +Energy dissipated in whole (or partial) model by damage. The contribution from +ALLDMD is included in the total strain energy ALLIE. +EDMDDEN +Energy dissipated per unit volume in the element by damage. +SENER +ELSE +ALLSE +The recoverable part of the energy per unit volume. +The recoverable part of the energy in the element. +The recoverable part of the energy in the whole (partial) model. +ESEDEN +The recoverable part of the energy per unit volume in the element. +The damage energy dissipation, represented by the shaded area in Figure 22.6.1–1 for deformation +, is computed as follows. When the damaged material is in a fully unloaded state, the augmented +until +energy function has the residual value +. The residual value of the energy function upon +complete unloading represents the energy dissipated due to damage in the material. The recoverable part +of the energy is obtained by subtracting the dissipated energy from the augmented energy as +. +The damage energy accumulates with progressive deformation along the primary curve and remains +constant during unloading. During unloading, the recoverable part of the strain energy is released. The +latter becomes zero when the material point is completely unloaded. Upon further reloading from a +completely unloaded state, the recoverable part of the strain energy increases from zero. When the +maximum strain that was attained earlier is exceeded upon reloading, further accumulation of damage +energy occurs. +Additional reference +• Ogden, R. W., and D. G. Roxburgh, “A Pseudo-Elastic Model for the Mullins Effect in Filled +Rubber,” Proceedings of the Royal Society of London, Series A, vol. 455, p. 2861–2877, 1999. +22.6.2 +ENERGY DISSIPATION IN ELASTOMERIC FOAMS +Products: Abaqus/Standard Abaqus/Explicit +References +• “Material library: overview,” Section 21.1.1 +• “Combining material behaviors,” Section 21.1.3 +• “Elastic behavior: overview,” Section 22.1.1 +• “Hyperelastic behavior in elastomeric foams,” Section 22.5.2 +• “Mullins effect,” Section 22.6.1 +• *HYPERFOAM +• *MULLINS EFFECT +• *UNIAXIAL TEST DATA +• *BIAXIAL TEST DATA +• *PLANAR TEST DATA +Overview +Energy dissipation in elastomeric foams in Abaqus: +• allows the modeling of permanent energy dissipation and stress softening effects in elastomeric +foams; +• uses an approach based on the Mullins effect for elastomeric rubbers (“Mullins effect,” +Section 22.6.1); +• provides an extension to the isotropic elastomeric foam model (“Hyperelastic behavior in +elastomeric foams,” Section 22.5.2); +• is intended for modeling energy absorption in foam components subjected to dynamic loading under +deformation rates that are high compared to the characteristic relaxation time of the foam; and +• cannot be used with viscoelasticity. +Energy dissipation in elastomeric foams +Abaqus provides a mechanism to include permanent energy dissipation and stress softening effects +in elastomeric foams. The approach is similar to that used to model the Mullins effect in elastomeric +rubbers, described in “Mullins effect,” Section 22.6.1. The functionality is primarily intended for +modeling energy absorption in foam components subjected to dynamic loading under deformation rates +that are high compared to the characteristic relaxation time of the foam; in such cases it is acceptable to +assume that the foam material is damaged permanently. +The material response is depicted qualitatively in Figure 22.6.2–1. +c' +b' +stretch +Figure 22.6.2–1 Typical stress-stretch response of an elastomeric +foam material with energy dissipation. +. On unloading from , the path +. If further loading is then applied, the path +of a previously unstressed foam, with loading to an arbitrary +is followed. When the material is loaded again, the +Consider the primary loading path +point +softened path is retraced as +(which is the path that would be followed if there +is a continuation of the primary loading path +were no unloading). If loading is now stopped at +is followed on unloading and then +retraced back to +represents +the subsequent material response, which is then elastic. For loading beyond , the primary path is again +followed and the pattern described is repeated. The shaded area in Figure 22.6.2–1 represents the energy +dissipated by damage in the material for deformation until +, the path +on reloading. If no further loading beyond +is applied, the curve +is followed, where +. +Modified strain energy density function +Energy dissipation effects are accounted for by introducing an augmented strain energy density function +of the form +where +is the strain energy potential +for the primary foam behavior described in “Hyperelastic behavior in elastomeric foams,” Section 22.5.2, +defined by the polynomial strain energy function +represent the principal mechanical stretches and +is a continuous function of the damage variable, +The function +, and is referred to as the “damage +function.” The damage variable varies continuously during the course of the deformation and always +satisfies +satisfies +the condition +; thus, when the deformation state of the material is on a point on the curve that +and the augmented energy function reduces to +represents the primary foam behavior, +the strain energy potential for the primary foam behavior. +on the points of the primary curve. The damage function +, with +The above expression of the augmented strain energy density function is similar to the form +proposed by Ogden and Roxburgh to model the Mullins effect in filled rubber elastomers , with the difference that in the case of elastomeric foams an augmentation of the +total strain energy (including the volumetric part) is considered. This modification is required for the +model to predict energy absorption under pure hydrostatic loading of the foam. +Stress computation +With the above modification to the energy function, the stresses are given by +is the stress corresponding to the primary foam behavior at the current deformation level +where +. +Thus, the stress is obtained by simply scaling the stress of the primary foam behavior by the damage +variable, +. From any given strain level the model predicts unloading/reloading along a single curve (that +is different, in general, from the primary foam behavior) that passes through the origin of the stress-strain +plot. The model also predicts energy dissipation under purely volumetric deformation. +Damage variable +The damage variable, +, varies with the deformation according to +where +are material parameters; and +the primary curve, +variable, +is the maximum value of +at a material point during its deformation history; r, +is the error function. When +. On the other hand, upon removal of deformation, when +, and m +, corresponding to a point on +, the damage +, attains its minimum value, +, given by +For all intermediate values of +and +. While the parameters r +are dimensionless, the parameter m has the dimensions of energy. The material parameters can +varies monotonically between +and +, +be specified directly or can be computed by Abaqus based on curve fitting of unloading-reloading test +data. These parameters are subject to the restrictions +and +, +m cannot both be zero). Alternatively, the damage variable +can be defined through user subroutine +UMULLINS in Abaqus/Standard and VUMULLINS in Abaqus/Explicit. +(the parameters +, and +If the parameter +and the parameter m has a value that is small compared to +, the slope +of the stress-strain curve at the initiation of unloading from relatively large strain levels may become +very high. As a result, the response may become discontinuous. This kind of behavior may lead to +convergence problems in Abaqus/Standard. In Abaqus/Explicit the high stiffness will lead to very small +stable time increments, thereby leading to a degradation in performance. This problem can be avoided +by choosing a small value for +is 0. In Abaqus/Explicit, +however, the default value of +, it is assumed to be 0 in +Abaqus/Standard and 0.1 in Abaqus/Explicit. +. In Abaqus/Standard the default value of +is 0.1. Thus, if you do not specify a value for +The parameters r, +, and m do not have direct physical interpretations in general. The parameter m +controls whether damage occurs at low strain levels. If +, there is a significant amount of damage +at low strain levels. On the other hand, a nonzero m leads to little or no damage at low strain levels. +For further discussion regarding the implications of this model on the energy dissipation, see “Mullins +effect,” Section 4.7.1 of the Abaqus Theory Manual. +Specifying properties for energy dissipation in elastomeric foams +The primary elastomeric foam behavior is defined by using the hyperfoam material model. Energy +dissipation can be defined by specifying the parameters in the expression of the damage variable directly +or by using test data to calibrate the parameters. Alternatively, you can define the Mullins effect model +with user subroutine UMULLINS in Abaqus/Standard and VUMULLINS in Abaqus/Explicit. +Specifying the parameters directly +The parameters r, m, and +of temperature and/or field variables. +in the expression of the damage variable can be given directly as functions +Input File Usage: +Abaqus/CAE Usage: +*MULLINS EFFECT +Property module: material editor: +Mechanical→Damage for Elastomers→Mullins Effect: +Definition: Constants +Using test data to calibrate the parameters +Experimental unloading-reloading data from different strain levels can be specified for up to three simple +tests: uniaxial, biaxial, and planar. Abaqus will then compute the material parameters using a nonlinear +least-squares curve fitting algorithm. See “Mullins effect,” Section 22.6.1, for a detailed discussion of +this approach. +Input File Usage: +*MULLINS EFFECT, TEST DATA INPUT, BETA and/or M and/or R +In addition, use at least one and up to three of the following options to give the +unloading-reloading test data: +*UNIAXIAL TEST DATA +*BIAXIAL TEST DATA +*PLANAR TEST DATA +Multiple unloading-reloading curves from different strain levels for any given +test type can be entered by repeated specification of the appropriate test data +option. +Property module: material editor: +Mechanical→Damage for Elastomers→Mullins Effect: Definition: +Test Data Input: enter the values for up to two of the values r, m, +and beta. In addition, enter data for at least one of the following +Suboptions→Biaxial Test, Planar Test, or Uniaxial Test +Abaqus/CAE Usage: +User subroutine specification +An alternative method for specifying energy dissipation involves defining the damage variable in user +subroutine UMULLINS in Abaqus/Standard and VUMULLINS in Abaqus/Explicit. Optionally, you can +specify the number of property values needed as data in the user subroutine. You must provide the damage +variable, +. The latter contributes to the Jacobian of the overall system of equations +and is necessary to ensure good convergence characteristics in Abaqus/Standard. If needed, you can +specify the number of solution-dependent variables (“User subroutines: overview,” Section 18.1.1). +These solution-dependent variables can be updated in the user subroutine. The damage dissipation energy +and the recoverable part of the energy can also be defined for output purposes. +, and its derivative, +Input File Usage: +Abaqus/CAE Usage: +*MULLINS EFFECT, USER, PROPERTIES=constants +Property module: material editor: +Mechanical→Damage for Elastomers→Mullins Effect: +Definition: User Defined +Elements +The model can be used with all element types that support the use of the elastomeric foam material model. +Procedures +The model can be used in all procedure types that support the use of the elastomeric foam material model. +In linear perturbation steps in Abaqus/Standard the current material tangent stiffness is used to determine +the response. Specifically, when a linear perturbation is carried out about a base state that is on the +primary curve, the unloading tangent stiffness will be used. +In Abaqus/Explicit the unloading tangent stiffness is always used to compute the stable time +increment. As a result, the inclusion of stress-softening effects may lead to more increments in the +analysis, even when no unloading actually takes place. +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2), +the +following variables have special meaning when energy dissipation is present in the model: +DMENER +ELDMD +ALLDMD +Energy dissipated per unit volume by damage. +Total energy dissipated in element by damage. +Energy dissipated in whole (or partial) model by damage. The contribution from +ALLDMD is included in the total strain energy ALLIE. +EDMDDEN +Energy dissipated per unit volume in the element by damage. +SENER +ELSE +ALLSE +The recoverable part of the energy per unit volume. +The recoverable part of the energy in the element. +The recoverable part of the energy in the whole (partial) model. +ESEDEN +The recoverable part of the energy per unit volume in the element. +The damage energy dissipation, represented by the shaded area in Figure 22.6.2–1 for deformation +until +, is computed as follows. When the damaged material is in a fully unloaded state, the augmented +energy function has the residual value +. The residual value of the energy function upon +complete unloading represents the energy dissipated due to damage in the material. The recoverable part +of the energy is obtained by subtracting the dissipated energy from the augmented energy as +. +The damage energy accumulates with progressive deformation along the primary curve and remains +constant during unloading. During unloading, the recoverable part of the strain energy is released. The +latter becomes zero when the material point is unloaded completely. Upon further reloading from a +completely unloaded state, the recoverable part of the strain energy increases from zero. When the +maximum strain that was attained earlier is exceeded upon reloading, further accumulation of damage +energy occurs. +22.7 +Viscoelasticity +• “Time domain viscoelasticity,” Section 22.7.1 +• “Frequency domain viscoelasticity,” Section 22.7.2 +22.7.1 +TIME DOMAIN VISCOELASTICITY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Elastic behavior: overview,” Section 22.1.1 +• “Frequency domain viscoelasticity,” Section 22.7.2 +• *VISCOELASTIC +• *SHEAR TEST DATA +• *VOLUMETRIC TEST DATA +• *COMBINED TEST DATA +• *TRS +• “Defining time domain viscoelasticity” in “Defining elasticity,” Section 12.9.1 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +The time domain viscoelastic material model: +• describes isotropic rate-dependent material behavior for materials in which dissipative losses +primarily caused by “viscous” (internal damping) effects must be modeled in the time domain; +• assumes that the shear (deviatoric) and volumetric behaviors are independent in multiaxial stress +states (except when used for an elastomeric foam); +• can be used only in conjunction with “Linear elastic behavior,” Section 22.2.1; “Hyperelastic +behavior of rubberlike materials,” Section 22.5.1; or “Hyperelastic behavior in elastomeric foams,” +Section 22.5.2, to define the continuum elastic material properties; +• can be used in Abaqus/Explicit with “Linear elastic traction-separation behavior” in “Defining the +constitutive response of cohesive elements using a traction-separation description,” Section 32.5.6; +• is active only during a transient static analysis (“Quasi-static analysis,” Section 6.2.5), a +integration,” +transient +implicit dynamic analysis (“Implicit dynamic analysis using direct +Section 6.3.2), an explicit dynamic analysis (“Explicit dynamic analysis,” Section 6.3.3), a +steady-state transport analysis (“Steady-state transport analysis,” Section 6.4.1), a fully coupled +temperature-displacement analysis (“Fully coupled thermal-stress analysis,” Section 6.5.3), a +fully coupled thermal-electrical-structural analysis (“Fully coupled thermal-electrical-structural +analysis,” Section 6.7.4), or a transient (consolidation) coupled pore fluid diffusion and stress +analysis (“Coupled pore fluid diffusion and stress analysis,” Section 6.8.1); +• can be used in large-strain problems; +• can be calibrated using time-dependent creep test data, time-dependent relaxation test data, or +frequency-dependent cyclic test data; and +• can be used to couple viscous dissipation with the temperature field in a fully coupled +temperature-displacement analysis (“Fully coupled thermal-stress analysis,” Section 6.5.3) or a +fully coupled thermal-electrical-structural analysis (“Fully coupled thermal-electrical-structural +analysis,” Section 6.7.4). +Defining the shear behavior +Time domain viscoelasticity is available in Abaqus for small-strain applications where the +rate-independent elastic response can be defined with a linear elastic material model and for large-strain +applications where the rate-independent elastic response must be defined with a hyperelastic or +hyperfoam material model. +Small strain +Consider a shear test at small strain in which a time varying shear strain, +The response is the shear stress +. The viscoelastic material model defines +as +, is applied to the material. +where +is the time-dependent “shear relaxation modulus” that characterizes the material’s response. +This constitutive behavior can be illustrated by considering a relaxation test in which a strain is suddenly +applied to a specimen and then held constant for a long time. The beginning of the experiment, when the +strain is suddenly applied, is taken as zero time, so that +(since +for +), +where +is the fixed strain. The viscoelastic material model is “long-term elastic” in the sense that, after +having been subjected to a constant strain for a very long time, the response settles down to a constant +stress; i.e., +as +. +The shear relaxation modulus can be written in dimensionless form: +where +form +is the instantaneous shear modulus, so that the expression for the stress takes the +The dimensionless relaxation function has the limiting values +and +. +Anisotropic elasticity in Abaqus/Explicit +The equation for the shear stress can be transformed by using integration by parts: +It is convenient to write this equation in the form +where +is the instantaneous shear stress at time t. This can be generalized to multi-dimensions as +is the deviatoric part of the stress tensor and +where +stress tensor. Here the viscoelasticity is assumed to be isotropic; +independent of the loading direction. +is the deviatoric part of the instantaneous +i.e., the relaxation function is +This form allows a straightforward generalization to anisotropic elastic deformations, where +is the +the deviatoric part of instantaneous stress tensor is computed as +instantaneous deviatoric elasticity tensor, and +is the deviatoric part of the strain tensor. +. Here +Large strain +The above form also allows a straightforward generalization to nonlinear elastic deformations, where +the deviatoric part of the instantaneous stress +is computed using a hyperelastic strain enery +potential. This generalization yields a linear viscoelasticity model, in the sense that the dimensionless +stress relaxation function is independent of the magnitude of the deformation. +In the above equation the instantaneous stress, +, at +time t. Therefore, to create a proper finite-strain formulation, it is necessary to map the stress that existed +in the configuration at time +into the configuration at time t. In Abaqus this is done by means of the +“standard-push-forward” transformation with the relative deformation gradient +influences the stress, +, applied at time +: +which results in the following hereditary integral: +where +is the deviatoric part of the Kirchhoff stress. +The finite-strain theory is described in more detail in “Finite-strain viscoelasticity,” Section 4.8.2 +of the Abaqus Theory Manual. +Defining the volumetric behavior +The volumetric behavior can be written in a form that is similar to the shear behavior: +where p is the hydrostatic pressure, +dimensionless bulk relaxation modulus, and +is the instantaneous elastic bulk modulus, +is the +is the volume strain. +The above expansion applies to small as well as finite strain since the volume strains are generally +small and there is no need to map the pressure from time +to time t. +Defining viscoelastic behavior for traction-separation elasticity in Abaqus/Explicit +Time domain viscoelasticity can be used in Abaqus/Explicit to model rate-dependent behavior of +cohesive elements with traction-separation elasticity (“Defining elasticity in terms of tractions and +separations for cohesive elements” in “Linear elastic behavior,” Section 22.2.1). +In this case the +evolution equation for the normal and two shear nominal tractions take the form: +, +, and +are the instantaneous nominal tractions at time t in the normal and the two +where +local shear directions, respectively. The functions +now represent the dimensionless +shear and normal relaxation moduli, respectively. Note the close similarity between the viscoelastic +formulation for the continuum elastic response discussed in the previous sections and the formulation +for cohesive behavior with traction-separation elasticity after reinterpreting shear and bulk relaxation as +shear and normal relaxation. +and +For the case of uncoupled traction elasticity, the viscoelastic normal and shear behaviors are assumed +to be independent. The normal relaxation modulus is defined as +where +and, therefore, independent of the local shear directions: +is the instantaneous normal moduli. The shear relaxation modulus is assumed to be isotropic +where +and +are the instantaneous shear moduli. +For the case of coupled traction-separation elasticity the normal and shear relaxation moduli must +be the same, +, and you must use the same relaxation data for both behaviors. +Temperature effects +The effect of temperature, +instantaneous stress, +linear-elastic shear stress is rewritten as +, on the material behavior is introduced through the dependence of the +, on temperature and through a reduced time concept. The expression for the +where the instantaneous shear modulus +by +is temperature dependent and +is the reduced time, defined +where +is a shift function at time t. This reduced time concept for temperature dependence +is usually referred to as thermo-rheologically simple (TRS) temperature dependence. Often the shift +function is approximated by the Williams-Landel-Ferry (WLF) form. See “Thermo-rheologically simple +temperature effects” below, for a description of the WLF and other forms of the shift function available +in Abaqus. +The reduced time concept is also used for the volumetric behavior, the large-strain formulation, and +the traction-separation formulation. +Numerical implementation +Abaqus assumes that the viscoelastic material is defined by a Prony series expansion of the dimensionless +relaxation modulus: +where N, +in the small-strain expression for the shear stress yields +, and +, +, are material constants. For linear isotropic elasticity, substitution +where +The +are interpreted as state variables that control the stress relaxation, and +is the “creep” strain: the difference between the total mechanical strain and the instantaneous elastic +strain (the stress divided by the instantaneous elastic modulus). In Abaqus/Standard +is available as +the creep strain output variable CE (“Abaqus/Standard output variable identifiers,” Section 4.2.1). +A similar Prony series expansion is used for the volumetric response, which is valid for both small- +and finite-strain applications: +where +Abaqus assumes that +. +For linear anisotropic elasticity, the Prony series expansion, in combination with the generalized +small-strain expression for the deviatoric stress, yields +where +The +are interpreted as state variables that control the stress relaxation. +For finite strains, the Prony series expansion, in combination with the finite-strain expression for +the shear stress, produces the following expression for the deviatoric stress: +where +The +are interpreted as state variables that control the stress relaxation. +For traction-separation elasticity, the Prony series expansion yields +where +The +are interpreted as state variables that control the relaxation of the traction stresses. +If the instantaneous material behavior is defined by linear elasticity or hyperelasticity, the bulk and +shear behavior can be defined independently. However, if the instantaneous behavior is defined by the +hyperfoam model, the deviatoric and volumetric constitutive behavior are coupled and it is mandatory +to use the same relaxation data for both behaviors. For linear anisotropic elasticity, the same relaxation +data should be used for both behaviors when the elasticity definition is such that the deviatoric and +volumetric response is coupled. Similarly, for coupled traction-separation elasticity you must use the +same relaxation data for the normal and shear behaviors. +In all of the above expressions temperature dependence is readily introduced by replacing +by +and +by +. +Determination of viscoelastic material parameters +The above equations are used to model the time-dependent shear and volumetric behavior of a +viscoelastic material. The relaxation parameters can be defined in one of four ways: direct specification +of the Prony series parameters, inclusion of creep test data, inclusion of relaxation test data, or inclusion +of frequency-dependent data obtained from sinusoidal oscillation experiments. Temperature effects are +included in the same manner regardless of the method used to define the viscoelastic material. +Abaqus/CAE allows you to evaluate the behavior of viscoelastic materials by automatically +creating response curves based on experimental test data or coefficients. A viscoelastic material can be +evaluated only if it is defined in the time domain and includes hyperelastic and/or elastic material data. +See “Evaluating hyperelastic and viscoelastic material behavior,” Section 12.4.7 of the Abaqus/CAE +User’s Manual. +Direct specification +, +, and +The Prony series parameters +can be defined directly for each term in the Prony series. +There is no restriction on the number of terms that can be used. If a relaxation time is associated with only +one of the two moduli, leave the other one blank or enter a zero. The data should be given in ascending +order of the relaxation time. The number of lines of data given defines the number of terms in the Prony +series, N. If this model is used in conjunction with the hyperfoam material model, the two modulus ratios +have to be the same ( +). +Input File Usage: +*VISCOELASTIC, TIME=PRONY +The data line is repeated as often as needed to define the first, second, third, +etc. terms in the Prony series. +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Elasticity→Viscoelastic: +Domain: Time and Time: Prony +Enter as many rows of data in the table as needed to define the first, second, +third, etc. terms in the Prony series. +Creep test data +If creep test data are specified, Abaqus will calculate the terms in the Prony series automatically. The +normalized shear and bulk compliances are defined as +where +shear stress in a shear creep test; +volumetric strain, and +. +is the shear compliance, +is the total shear strain, and +is the volumetric compliance, +is the constant pressure in a volumetric creep test. At time +is the constant +is the total +, +The creep data are converted to relaxation data through the convolution integrals +Abaqus then uses the normalized shear modulus +least-squares fit to determine the Prony series parameters. +and normalized bulk modulus +in a nonlinear +Using the shear and volumetric test data consecutively +The shear test data and volumetric test data can be used consecutively to define the normalized shear +and bulk compliances as functions of time. A separate least-squares fit is performed on each data set; +and the two derived sets of Prony series parameters, +, are merged into one set of +parameters, +and +. +Input File Usage: +Use the following three options. The first option is required. Only one of the +second and third options is required. +Abaqus/CAE Usage: +*VISCOELASTIC, TIME=CREEP TEST DATA +*SHEAR TEST DATA +*VOLUMETRIC TEST DATA +Property module: material editor: Mechanical→Elasticity→Viscoelastic: +Domain: Time and Time: Creep test data +In addition, select one or both of the following: +Test Data→Shear Test Data +Test Data→Volumetric Test Data +Using the combined test data +Alternatively, the combined test data can be used to specify the normalized shear and bulk compliances +simultaneously as functions of time. A single least-squares fit is performed on the combined set of test +data to determine one set of Prony series parameters, +. +Input File Usage: +Use both of the following options: +*VISCOELASTIC, TIME=CREEP TEST DATA +*COMBINED TEST DATA +Property module: material editor: Mechanical→Elasticity→Viscoelastic: +Domain: Time, Time: Creep test data, and +Test Data→Combined Test Data +Abaqus/CAE Usage: +Relaxation test data +As with creep test data, Abaqus will calculate the Prony series parameters automatically from relaxation +test data. +Using the shear and volumetric test data consecutively +Again, the shear test data and volumetric test data can be used consecutively to define the relaxation +moduli as functions of time. A separate nonlinear least-squares fit is performed on each data set; and +the two derived sets of Prony series parameters, +, are merged into one set of +parameters, +. +and +Input File Usage: +Use the following three options. The first option is required. Only one of the +second and third options is required. +Abaqus/CAE Usage: +*VISCOELASTIC, TIME=RELAXATION TEST DATA +*SHEAR TEST DATA +*VOLUMETRIC TEST DATA +Property module: material editor: Mechanical→Elasticity→Viscoelastic: +Domain: Time and Time: Relaxation test data +In addition, select one or both of the following: +Test Data→Shear Test Data +Test Data→Volumetric Test Data +Using the combined test data +Alternatively, the combined test data can be used to specify the relaxation moduli simultaneously as +functions of time. A single least-squares fit is performed on the combined set of test data to determine +one set of Prony series parameters, +. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options: +*VISCOELASTIC, TIME=RELAXATION TEST DATA +*COMBINED TEST DATA +Property module: material editor: Mechanical→Elasticity→Viscoelastic: +Domain: Time, Time: Relaxation test data, and +Test Data→Combined Test Data +Frequency-dependent test data +The Prony series terms can also be calibrated using frequency-dependent test data. In this case Abaqus +uses analytical expressions that relate the Prony series relaxation functions to the storage and loss moduli. +The expressions for the shear moduli, obtained by converting the Prony series terms from the time domain +to the frequency domain by making use of Fourier transforms, can be written as follows: +is the storage modulus, +where +is the angular frequency, and N is +the number of terms in the Prony series. These expressions are used in a nonlinear least-squares fit to +determine the Prony series parameters from the storage and loss moduli cyclic test data obtained at M +frequencies by minimizing the error function +is the loss modulus, +: +where +shear moduli. The expressions for the bulk moduli, +are the test data and +and +and +, respectively, are the instantaneous and long-term +and +, are written analogously. +The frequency domain data are defined in tabular form by giving the real and imaginary parts of +and —where +is the circular frequency—as functions of frequency in cycles per time. +is the Fourier transform of the nondimensional shear relaxation function +frequency-dependent storage and loss moduli +, and +parts of +are then given as +and +, +, +. Given the +, the real and imaginary +where +properties. +and +are the long-term shear and bulk moduli determined from the elastic or hyperelastic +Input File Usage: +Abaqus/CAE Usage: +*VISCOELASTIC, TIME=FREQUENCY DATA +Property module: material editor: Mechanical→Elasticity→Viscoelastic: +Domain: Time and Time: Frequency data +Calibrating the Prony series parameters +the error tolerance and +You can specify two optional parameters related to the calibration of Prony series parameters for +viscoelastic materials: +. The error tolerance is the allowable average +root-mean-square error of data points in the least-squares fit, and its default value is 0.01. +is the +maximum number of terms N in the Prony series, and its default (and maximum) value is 13. Abaqus +will perform the least-squares fit from +until convergence is achieved for the +lowest N with respect to the error tolerance. +to +The following are some guidelines for determining the number of terms in the Prony series from +test data. Based on these guidelines, you can choose +. +• There should be enough data pairs for determining all the parameters in the Prony series terms. +Thus, assuming that N is the number of Prony series terms, there should be a total of at least +data points in shear test data, +test data, and +data points in the frequency domain. +data points in volumetric test data, +data points in combined +• The number of terms in the Prony series should be typically not more than the number of +logarithmic “decades” spanned by the test data. The number of logarithmic “decades” is defined +as +are the maximum and minimum time in the test data, +respectively. +, where +and +Input File Usage: +Abaqus/CAE Usage: +*VISCOELASTIC, ERRTOL=error_tolerance, NMAX= +Property module: material editor: Mechanical→Elasticity→Viscoelastic: +Domain: Time; Time: Creep test data, Relaxation test data, or +Frequency data; Maximum number of terms in the Prony series: +; and Allowable average root-mean-square error: error_tolerance +Thermo-rheologically simple temperature effects +Regardless of the method used to define the viscoelastic behavior, +thermo-rheologically simple +temperature effects can be included by specifying the method used to define the shift function. Abaqus +supports the following forms of the shift function: +the +Arrhenius form, and user-defined forms. +the Williams-Landel-Ferry (WLF) form, +Thermo-rheologically simple temperature effects can also be included in the definition of equation +of state models with viscous shear behavior . +Williams-Landel-Ferry (WLF) form +The shift function can be defined by the Williams-Landel-Ferry (WLF) approximation, which takes the +form: +is the reference temperature at which the relaxation data are given; +where +interest; and +changes will be elastic, based on the instantaneous moduli. +are calibration constants obtained at this temperature. If +, +is the temperature of +, deformation +For additional information on the WLF equation, see “Viscoelasticity,” Section 4.8.1 of the Abaqus +Theory Manual. +Input File Usage: +Abaqus/CAE Usage: +Arrhenius form +*TRS, DEFINITION=WLF +Property module: material editor: Mechanical→Elasticity→Viscoelastic: +Domain: Time, Time: any method, and Suboptions→Trs: +Shift function: WLF +The Arrhenius shift function is commonly used for semi-crystalline polymers. It takes the form +is the activation energy, +where +temperature scale being used, +and +is the temperature of interest. +is the universal gas constant, +is the absolute zero in the +is the reference temperature at which the relaxation data are given, +Input File Usage: +Use the following option to define the Arrhenius shift function: +*TRS, DEFINITION=ARRHENIUS +In addition, use the *PHYSICAL CONSTANTS option to specify the universal +gas constant and absolute zero. +Abaqus/CAE Usage: +The Arrhenius shift function is not supported in Abaqus/CAE. +User-defined form +The shift function can be specified alternatively in user subroutines UTRS in Abaqus/Standard and +VUTRS in Abaqus/Explicit. +Input File Usage: +Abaqus/CAE Usage: +*TRS, DEFINITION=USER +Property module: material editor: Mechanical→Elasticity→Viscoelastic: +Domain: Time, Time: any method, and Suboptions→Trs: +Shift function: User subroutine UTRS +Defining the rate-independent part of the material response +In all cases elastic moduli must be specified to define the rate-independent part of the material behavior. +Small-strain linear elastic behavior is defined by an elastic material model (“Linear elastic behavior,” +Section 22.2.1), and large-deformation behavior is defined by a hyperelastic (“Hyperelastic behavior +of rubberlike materials,” Section 22.5.1) or hyperfoam (“Hyperelastic behavior in elastomeric foams,” +Section 22.5.2) material model. The rate-independent elasticity for any of these models can be defined +in terms of either instantaneous elastic moduli or long-term elastic moduli. The choice of defining the +elasticity in terms of instantaneous or long-term moduli is a matter of convenience only; it does not have +an effect on the solution. +The effective relaxation moduli are obtained by multiplying the instantaneous elastic moduli with +the dimensionless relaxation functions as described below. +Linear elastic isotropic materials +For linear elastic isotropic material behavior +and +where +defined instantaneous elastic moduli +and +: +If long-term elastic moduli are defined, the instantaneous moduli are determined from +and +and +. +are the instantaneous shear and bulk moduli determined from the values of the user- +Linear elastic anisotropic materials +For linear elastic anisotropic material behavior the relaxation coefficients are applied to the elastic moduli +as +and +and +where +values of the user-defined instantaneous elastic moduli +are specified and they are unequal, Abaqus issues an error message if the elastic moduli +the deviatoric and volumetric response is coupled. +are the instantaneous deviatoric elasticity tensor and bulk moduli determined from the +. If both shear and bulk relaxation coefficients +is such that +If long-term elastic moduli are defined, the instantaneous moduli are determined from +Hyperelastic materials +For hyperelastic material behavior the relaxation coefficients are applied either to the constants that define +the energy function or directly to the energy function. For the polynomial function and its particular cases +(reduced polynomial, Mooney-Rivlin, neo-Hookean, and Yeoh) +for the Ogden function +for the Arruda-Boyce and Van der Waals functions +and for the Marlow function +For the coefficients governing the compressible behavior of the polynomial models and the Ogden model +for the Arruda-Boyce and Van der Waals functions +and for the Marlow function +If long-term elastic moduli are defined, the instantaneous moduli are determined from +while the instantaneous bulk compliance moduli are obtained from +for the Marlow functions we have +Mullins effect +If long-term moduli are defined for the underlying hyperelastic behavior, the instantaneous value of the +parameter +in Mullins effect is determined from +Elastomeric foams +For elastomeric foam material behavior the instantaneous shear and bulk relaxation coefficients are +assumed to be equal and are applied to the material constants +in the energy function: +If only the shear relaxation coefficients are specified, the bulk relaxation coefficients are set equal +to the shear relaxation coefficients and vice versa. If both shear and bulk relaxation coefficients are +specified and they are unequal, Abaqus issues an error message. +If long-term elastic moduli are defined, the instantaneous moduli are determined from +Traction-separation elasticity +For cohesive elements with uncoupled traction-separation elastic behavior: +and +where +If long-term elastic moduli are defined, the instantaneous moduli are determined from +is the instantaneous normal modulus and +and +are the instantaneous shear moduli. +For cohesive elements with coupled traction-separation elastic behavior the shear and bulk +relaxation coefficients must be equal: +where +instantaneous moduli are determined from +is the user-defined instantaneous elasticity matrix. If long-term elastic moduli are defined, the +Material response in different analysis procedures +The time-domain viscoelastic material model is active during the following procedures: +• transient static analysis (“Quasi-static analysis,” Section 6.2.5), +• transient +implicit dynamic analysis (“Implicit dynamic analysis using direct +Section 6.3.2), +integration,” +• explicit dynamic analysis (“Explicit dynamic analysis,” Section 6.3.3), +• steady-state transport analysis (“Steady-state transport analysis,” Section 6.4.1), +• fully coupled temperature-displacement analysis (“Fully coupled thermal-stress analysis,” +Section 6.5.3), +• fully coupled thermal-electrical-structural analysis (“Fully coupled thermal-electrical-structural +analysis,” Section 6.7.4), and +• transient (consolidation) coupled pore fluid diffusion and stress analysis (“Coupled pore fluid +diffusion and stress analysis,” Section 6.8.1). +Viscoelastic material response is always ignored in a static analysis. It can also be ignored in a +coupled temperature-displacement analysis, a coupled thermal-electrical-structural analysis, or a soils +consolidation analysis by specifying that no creep or viscoelastic response is occurring during the step +even if creep or viscoelastic material properties are defined . In these cases it +is assumed that the loading is applied instantaneously, so that the resulting response corresponds to an +elastic solution based on instantaneous elastic moduli. +Abaqus/Standard also provides the option to obtain the fully relaxed long-term elastic solution +directly in a static or steady-state transport analysis without having to perform a transient analysis. The +long-term value is used for this purpose. The viscous damping stresses (the internal stresses associated +with each of the Prony-series terms) are increased gradually from their values at the beginning of the +step to their long-term values at the end of the step if the long-term value is specified. +Use with other material models +The viscoelastic material model must be combined with an elastic material model. +It is used with +the isotropic linear elasticity model (“Linear elastic behavior,” Section 22.2.1) to define classical, +linear, small-strain, viscoelastic behavior or with the hyperelastic (“Hyperelastic behavior of rubberlike +materials,” Section 22.5.1) or hyperfoam (“Hyperelastic behavior in elastomeric foams,” Section 22.5.2) +models to define large-deformation, nonlinear, viscoelastic behavior. It can also be used with anisotropic +linear elasticity and with traction-separation elastic behavior in Abaqus/Explicit. The elastic properties +defined for these models can be temperature dependent. +Viscoelasticity cannot be combined with any of the plasticity models. See “Combining material +behaviors,” Section 21.1.3, for more details. +Elements +The time domain viscoelastic material model can be used with any stress/displacement, coupled +temperature-displacement, or thermal-electrical-structural element in Abaqus. +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2), +the +following variables have special meaning in Abaqus/Standard if viscoelasticity is defined: +EE +CE +Elastic strain corresponding to the stress state at time t and the instantaneous elastic +material properties. +Equivalent creep strain defined as the difference between the total strain and the +elastic strain. +Considerations for steady-state transport analysis +When a steady-state transport analysis (“Steady-state transport analysis,” Section 6.4.1) is combined +with large-strain viscoelasticity, the viscous dissipation, CENER, is computed as the energy dissipated +per revolution as a material point is transported around its streamline; that is, +Consequently, all the material points in a given streamline report the same value for CENER, and other +derived quantities such as ELCD and ALLCD also have the meaning of dissipation per revolution. The +recoverable elastic strain energy density, SENER, is approximated as +is the incremental energy input and is the time at the beginning of the current increment. +where +Since two different units are used in the quantities appearing in the above equation, a proper meaning +cannot be assigned to quantities such as SENER, ELSE, ALLSE, and ALLIE. +Considerations for large-strain viscoelasticity in Abaqus/Explicit +For the case of large-strain viscoelasticity, Abaqus/Explicit does not compute the viscous dissipation +for performance reasons. Instead, the contribution of viscous dissipation is included in the strain energy +output, SENER; and CENER is output as zero. Consequently, special care must be exercised when +interpreting strain energy results of large-strain viscoelastic materials in Abaqus/Explicit since they +include viscous dissipation effects. +22.7.2 +FREQUENCY DOMAIN VISCOELASTICITY +Products: Abaqus/Standard Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Elastic behavior: overview,” Section 22.1.1 +• “Time domain viscoelasticity,” Section 22.7.1 +• *VISCOELASTIC +• “Defining frequency domain viscoelasticity” in “Defining elasticity,” Section 12.9.1 of the +Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +The frequency domain viscoelastic material model: +• describes frequency-dependent material behavior in small steady-state harmonic oscillations for +those materials in which dissipative losses caused by “viscous” (internal damping) effects must be +modeled in the frequency domain; +• assumes that the shear (deviatoric) and volumetric behaviors are independent in multiaxial stress +states; +• can be used in large-strain problems; +• can be used only in conjunction with “Linear elastic behavior,” Section 22.2.1; “Hyperelastic +behavior of rubberlike materials,” Section 22.5.1; and “Hyperelastic behavior in elastomeric +foams,” Section 22.5.2, to define the long-term elastic material properties; +• can be used in conjunction with the elastic-damage gasket behavior (“Defining a nonlinear elastic +model with damage” in “Defining the gasket behavior directly using a gasket behavior model,” +Section 32.6.6 ) to define the effective thickness-direction storage and loss moduli for gasket +elements; and +• is active only during the direct-solution steady-state dynamic (“Direct-solution steady-state +dynamic analysis,” Section 6.3.4), the subspace-based steady-state dynamic (“Subspace-based +the natural frequency extraction (“Natural +steady-state dynamic analysis,” Section 6.3.9), +frequency extraction,” Section 6.3.5), and the complex eigenvalue extraction (“Complex +eigenvalue extraction,” Section 6.3.6) procedures. +Defining the shear behavior +Consider a shear test at small strain, in which a harmonically varying shear strain +is applied: +is the amplitude, +where +is the circular frequency, and t is time. We assume that the +specimen has been oscillating for a very long time so that a steady-state solution is obtained. The solution +for the shear stress then has the form +, +where +(complex) Fourier transform +are the shear storage and loss moduli. These moduli can be expressed in terms of the +: +of the nondimensional shear relaxation function +and +is the time-dependent shear relaxation modulus, +where +imaginary parts of +viscoelasticity,” Section 4.8.3 of the Abaqus Theory Manual, for details. +is the long-term shear modulus. +, and +and +are the real and +See “Frequency domain +The above equation states that the material responds to steady-state harmonic strain with a stress of +that lags the excitation +that is in phase with the strain and a stress of magnitude +magnitude +by +. Hence, we can regard the factor +as the complex, frequency-dependent shear modulus of the steadily vibrating material. The absolute +magnitude of the stress response is +and the phase lag of the stress response is +Measurements of +and, thus, +and +as functions of frequency in an experiment can, thus, be used to define +and +as functions of frequency. +Unless stated otherwise explicitly, all modulus measurements are assumed to be “true” quantities. +and +Defining the volumetric behavior +In multiaxial stress states Abaqus/Standard assumes that the frequency dependence of the shear +(deviatoric) and volumetric behaviors are independent. The volumetric behavior is defined by the +bulk storage and loss moduli +. Similar to the shear moduli, these moduli can also be +expressed in terms of the (complex) Fourier transform +of the nondimensional bulk relaxation +function +and +: +where +is the long-term elastic bulk modulus. +Large-strain viscoelasticity +The linearized vibrations can also be associated with an elastomeric material whose long-term (elastic) +response is nonlinear and involves finite strains (a hyperelastic material). We can retain the simplicity +of the steady-state small-amplitude vibration response analysis in this case by assuming that the linear +expression for the shear stress still governs the system, except that now the long-term shear modulus +can vary with the amount of static prestrain : +The essential simplification implied by this assumption is that the frequency-dependent part of the +material’s response, defined by the Fourier transform +of the relaxation function, is not affected by +the magnitude of the prestrain. Thus, strain and frequency effects are separated, which is a reasonable +approximation for many materials. +Another implication of the above assumption is that the anisotropy of the viscoelastic moduli has +the same strain dependence as the anisotropy of the long-term elastic moduli. Hence, the viscoelastic +behavior in all deformed states can be characterized by measuring the (isotropic) viscoelastic moduli in +the undeformed state. +In situations where the above assumptions are not reasonable, the data can be specified based on +measurements at the prestrain level about which the steady-state dynamic response is desired. In this +case you must measure +) at the prestrain level of interest. +Alternatively, the viscoelastic data can be given directly in terms of uniaxial and volumetric storage and +loss moduli that may be specified as functions of frequency and prestrain +(likewise +, and +, and +, +, +The generalization of these concepts to arbitrary three-dimensional deformations is provided in +Abaqus/Standard by assuming that the frequency-dependent material behavior has two independent +components: one associated with shear (deviatoric) straining and the other associated with volumetric +straining. +therefore, defined for +In the general case of a compressible material, +kinematically small perturbations about a predeformed state as +the model is, +; +is the deviatoric stress, +is the equivalent pressure stress, +is the part of the stress increment caused by incremental straining (as distinct from +the part of the stress increment caused by incremental rotation of the preexisting +stress with respect to the coordinate system); +; +22.7.2–3 +and +where +; +; +is the ratio of current to original volume; +is the (small) incremental deviatoric strain, +is the deviatoric strain rate, +is the (small) incremental volumetric strain, +is the rate of volumetric strain, +is the deviatoric tangent elasticity matrix of the material in its predeformed state +(for example, +is the volumetric strain-rate/deviatoric stress-rate tangent elasticity matrix of the +material in its predeformed state; and +is the tangent bulk modulus of the predeformed material. +is the tangent shear modulus of the prestrained material); +; +; +For a fully incompressible material only the deviatoric terms in the first constitutive equation above +remain and the viscoelastic behavior is completely defined by +. +Determination of viscoelastic material parameters +The dissipative part of the material behavior is defined by giving the real and imaginary parts of +and +(for compressible materials) as functions of frequency. The moduli can be defined as functions of the +frequency in one of three ways: by a power law, by tabular input, or by a Prony series expression for the +shear and bulk relaxation moduli. +Power law frequency dependence +The frequency dependence can be defined by the power law formulæ +and +where a and b are real constants, +cycles per time. +and +are complex constants, and +is the frequency in +Input File Usage: +Abaqus/CAE Usage: +*VISCOELASTIC, FREQUENCY=FORMULA +Property module: material editor: Mechanical→Elasticity→Viscoelastic: +Domain: Frequency and Frequency: Formula +Tabular frequency dependence +The frequency domain response can alternatively be defined in tabular form by giving the real and +imaginary parts of +is the circular frequency—as functions of frequency in cycles +per time. Given the frequency-dependent storage and loss moduli +, +the real and imaginary parts of +are then given as +and —where +, and +and +, +, +where +properties. +and +are the long-term shear and bulk moduli determined from the elastic or hyperelastic +Input File Usage: +Abaqus/CAE Usage: +*VISCOELASTIC, FREQUENCY=TABULAR +Property module: material editor: Mechanical→Elasticity→Viscoelastic: +Domain: Frequency and Frequency: Tabular +Abaqus provides an alternative approach for specifying the viscoelastic properties of hyperelastic +and hyperfoam materials. This approach involves the direct (tabular) specification of storage and loss +moduli from uniaxial and volumetric tests, as functions of excitation frequency and a measure of the +level of pre-strain. The level of pre-strain refers to the level of elastic deformation at the base state about +which the steady-state harmonic response is desired. This approach is discussed in “Direct specification +of storage and loss moduli for large-strain viscoelasticity” below. +Prony series parameters +The frequency dependence can also be obtained from a time domain Prony series description of the +dimensionless shear and bulk relaxation moduli: +where N, +expression for the time-dependent shear modulus can be written in the frequency domain as follows: +, are material constants. Using Fourier transforms, the +, and +, +, +is the loss modulus, +is the storage modulus, +is the angular frequency, and N is the +where +number of terms in the Prony series. The expressions for the bulk moduli, +, are written +analogously. Abaqus/Standard will automatically perform the conversion from the time domain to the +frequency domain. The Prony series parameters +can be defined in one of three ways: direct +specification of the Prony series parameters, inclusion of creep test data, or inclusion of relaxation test +data. If creep test data or relaxation test data are specified, Abaqus/Standard will determine the Prony +series parameters in a nonlinear least-squares fit. A detailed description of the calibration of Prony series +terms is provided in “Time domain viscoelasticity,” Section 22.7.1. +and +For the test data you can specify the normalized shear and bulk data separately as functions of time +or specify the normalized shear and bulk data simultaneously. A nonlinear least-squares fit is performed +to determine the Prony series parameters, +. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options to specify Prony data, creep test data, or +relaxation test data: +*VISCOELASTIC, FREQUENCY=PRONY +*VISCOELASTIC, FREQUENCY=CREEP TEST DATA +*VISCOELASTIC, FREQUENCY=RELAXATION TEST DATA +Use one or both of the following options to specify the normalized shear and +bulk data separately as functions of time: +*SHEAR TEST DATA +*VOLUMETRIC TEST DATA +Use the following option to specify the normalized shear and bulk data +simultaneously: +*COMBINED TEST DATA +Property module: material editor: Mechanical→Elasticity→Viscoelastic: +Domain: Frequency and Frequency: Prony, Creep test data, or +Relaxation test data +Use one or both of the following options to specify the normalized shear and +bulk data separately as functions of time: +Test Data→Shear Test Data +Test Data→Volumetric Test Data +Use the following option to specify the normalized shear and bulk data +simultaneously: +Test Data→Combined Test Data +Conversion of frequency-dependent elastic moduli +For some cases of small straining of isotropic viscoelastic materials, the material data are provided as +frequency-dependent uniaxial storage and loss moduli, +and +. In that case the data must be converted to obtain the frequency-dependent shear storage and loss +, and bulk moduli, +and +moduli +and +. +The complex shear modulus is obtained as a function of the complex uniaxial and bulk moduli with +the expression +Replacing the complex moduli by the appropriate storage and loss moduli, this expression transforms +into +After some algebra one obtains +Shear strain only +In many cases the viscous behavior is associated only with deviatoric straining, so that the bulk modulus +is real and constant: +. For this case the expressions for the shear moduli simplify +to +and +Incompressible materials +If the bulk modulus is very large compared to the shear modulus, the material can be considered to be +incompressible and the expressions simplify further to +Direct specification of storage and loss moduli for large-strain viscoelasticity +For large-strain viscoelasticity Abaqus allows direct specification of storage and loss moduli from +uniaxial and volumetric tests. This approach can be used when the assumption of the independence of +viscoelastic properties on the pre-strain level is too restrictive. +You specify the storage and loss moduli directly as tabular functions of frequency, and you specify +the level of pre-strain at the base state about which the steady-state dynamic response is desired. For +uniaxial test data the measure of pre-strain is the uniaxial nominal strain; for volumetric test data the +measure of pre-strain is the volume ratio. Abaqus internally converts the data that you specify to ratios +of shear/bulk storage and loss moduli to the corresponding long-term elastic moduli. Subsequently, the +basic formulation described in “Large-strain viscoelasticity” above is used. +For a general three-dimensional stress state it is assumed that the deviatoric part of the viscoelastic +response depends on the level of pre-strain through the first invariant of the deviatoric left Cauchy-Green +strain tensor , while the volumetric part depends on the pre-strain through the volume +ratio. A consequence of these assumptions is that for the uniaxial case, data can be specified from a +uniaxial-tension preload state or from a uniaxial-compression preload state but not both. +The storage and loss moduli that you specify are assumed to be nominal quantities. +Input File Usage: +Use the following option to specify only the uniaxial storage and loss moduli: +*VISCOELASTIC, PRELOAD=UNIAXIAL +You can also use the following option to specify the volumetric (bulk) storage +and loss moduli: +*VISCOELASTIC, PRELOAD=VOLUMETRIC +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Elasticity→Viscoelastic: +Domain: Frequency and Frequency: Tabular +Use the following option to specify only the uniaxial storage and loss moduli: +Type: Isotropic or Traction: Preload: Uniaxial +Use the following option to specify only the volumetric storage and loss moduli: +Type: Isotropic: Preload: Volumetric +Use the following option to specify both uniaxial and volumetric moduli: +Type: Isotropic: Preload: Uniaxial and Volumetric +Defining the rate-independent part of the material behavior +In all cases elastic moduli must be specified to define the rate-independent part of the material behavior. +The elastic behavior is defined by an elastic, hyperelastic, or hyperfoam material model. Since the +frequency domain viscoelastic material model is developed around the long-term elastic moduli, the +rate-independent elasticity must be defined in terms of long-term elastic moduli. This implies that the +response in any analysis procedure other than a direct-solution steady-state dynamic analysis (such as a +static preloading analysis) corresponds to the fully relaxed long-term elastic solution. +Use with other material models +The viscoelastic material model must be combined with the isotropic linear elasticity model to define +classical, linear, small-strain, viscoelastic behavior. It is combined with the hyperelastic or hyperfoam +model to define large-deformation, nonlinear, viscoelastic behavior. The long-term elastic properties +defined for these models can be temperature dependent. +Viscoelasticity cannot be combined with any of the plasticity models. See “Combining material +behaviors,” Section 21.1.3, for more details. +Elements +The frequency domain viscoelastic material model can be used with any stress/displacement element in +Abaqus/Standard. +22.8 +Nonlinear viscoelasticity +• “Hysteresis in elastomers,” Section 22.8.1 +• “Parallel network viscoelastic model,” Section 22.8.2 +22.8.1 +HYSTERESIS IN ELASTOMERS +Products: Abaqus/Standard Abaqus/CAE +References +• “Elastic behavior: overview,” Section 22.1.1 +• *HYSTERESIS +• “Defining hysteretic behavior for an isotropic hyperelastic material model” in “Defining elasticity,” +Section 12.9.1 of the Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +The hysteresis material model: +• defines strain-rate-dependent, hysteretic behavior of materials that undergo comparable elastic and +inelastic strains; +• provides inelastic response only for shear distortional behavior—the response to volumetric +deformations is purely elastic; +• can be used only in conjunction with “Hyperelastic behavior of +rubberlike materials,” +Section 22.5.1, to define the elastic response of the material—the elasticity can be defined either in +terms of the instantaneous moduli or the long-term moduli; +• is active during a static analysis (“Static stress analysis,” Section 6.2.2), a quasi-static analysis +(“Quasi-static analysis,” Section 6.2.5), or a transient dynamic analysis using direct integration +(“Implicit dynamic analysis using direct integration,” Section 6.3.2)—it cannot be used in fully +coupled temperature-displacement analysis (“Fully coupled thermal-stress analysis,” Section 6.5.3), +fully coupled thermal-electrical-structural analysis (“Fully coupled thermal-electrical-structural +analysis,” Section 6.7.4), or steady-state transport analysis (“Steady-state transport analysis,” +Section 6.4.1); +• cannot be used to model temperature-dependent creep material properties—however, the elastic +material properties can be temperature dependent; and +• uses unsymmetric matrix storage and solution by default. +Strain-rate-dependent material behavior for elastomers +Nonlinear strain-rate dependence of elastomers is modeled by decomposing the mechanical response +into that of an equilibrium network (A) corresponding to the state that is approached in long-time stress +relaxation tests and that of a time-dependent network (B) that captures the nonlinear rate-dependent +deviation from the equilibrium state. The total stress is assumed to be the sum of the stresses in the +two networks. The deformation gradient, +, is assumed to act on both networks and is decomposed into +elastic and inelastic parts in network B according to the multiplicative decomposition +The +nonlinear rate-dependent material model is capable of reproducing the hysteretic behavior of elastomers +subjected to repeated cyclic loading. It does not model “Mullins effect”—the initial softening of an +elastomer when it is first subjected to a load. +The material model is defined completely by: +• a hyperelastic material model that characterizes the elastic response of the model; +• a stress scaling factor, S, that defines the ratio of the stress carried by network B to the stress carried +by network A under instantaneous loading; i.e., identical elastic stretching in both networks; +• a positive exponent, m, generally greater than 1, characterizing the effective stress dependence of +the effective creep strain rate in network B; +• an exponent, C, restricted to lie in +creep strain rate in network B; +, characterizing the creep strain dependence of the effective +• a nonnegative constant, A, in the expression for the effective creep strain rate—this constant also +maintains dimensional consistency in the equation; and +• a constant, E, in the expression for the effective creep strain rate—this constant regularizes the creep +strain rate near the undeformed state. +The effective creep strain rate in network B is given by the expression +where +B, and +is the effective creep strain rate in network B, +is the effective stress in network B. The chain stretch in network B, +is the nominal creep strain in network +, is defined as +where +is the deviatoric Cauchy stress tensor. +. The effective stress in network B is defined as +, where +Defining strain-rate-dependent material behavior for elastomers +The elasticity of the model is defined by a hyperelastic material model. You input the stress scaling factor +and the creep parameters for network B directly when you define the hysteresis material model. Typical +(sec)−1(MPa)−m , +values of the material parameters for a common elastomer are +, +, +, and +(Bergstrom and Boyce, 1998; 2001). +Input File Usage: +Use both of the following options within the same material data block: +Abaqus/CAE Usage: +*HYSTERESIS +*HYPERELASTIC +Property module: material editor: Mechanical→Elasticity→Hyperelastic: +Suboptions→Hysteresis +The input of the parameter +is not supported in Abaqus/CAE. +Elements +The use of the hysteresis material model is restricted to elements that can be used with hyperelastic +materials (“Hyperelastic behavior of rubberlike materials,” Section 22.5.1). +this +model cannot be used with elements based on the plane stress assumption (shell, membrane, and +continuum plane stress elements). Hybrid elements can be used with this model only when the +accompanying hyperelasticity definition is completely incompressible. When this model is used +with reduced-integration elements, the instantaneous elastic moduli are used to calculate the default +hourglass stiffness. +In addition, +Output +In addition to the standard output identifiers available in Abaqus/Standard (“Abaqus/Standard output +variable identifiers,” Section 4.2.1), the following variables have special meaning if hysteretic behavior +is defined: +EE +CE +Elastic strain corresponding to the stress state at time t and the instantaneous elastic +material properties. +Equivalent creep strain defined as the difference between the total strain and the +elastic strain. +These strain measures are used to approximate the strain energy, SENER, and the viscous dissipation, +CENER. These approximations may lead to underestimation of the strain energy and overestimation of +the viscous dissipation since the effects of internal stresses on these energy quantities are neglected. This +inaccuracies may be particularly noticeable in the case of nonmonotonic loading. +Additional references +• Bergstrom, J. S., and M. C. Boyce, “Constitutive Modeling of the Large Strain Time-Dependent +Behavior of Elastomers,” Journal of the Mechanics and Physics of Solids, vol. 46, no. 5, +pp. 931–954, May 1998. +• Bergstrom, J. S., and M. C. Boyce, “Constitutive Modeling of the Time-Dependent and Cyclic +Loading of Elastomers and Application to Soft Biological Tissues,” Mechanics of Materials, +vol. 33, no. 9, pp. 523–530, 2001. +22.8.2 +PARALLEL NETWORK VISCOELASTIC MODEL +Product: Abaqus/Standard +References +• “Material library: overview,” Section 21.1.1 +• “Combining material behaviors,” Section 21.1.3 +• “Inelastic behavior,” Section 23.1.1 +• *HYPERELASTIC +• *VISCOELASTIC +Overview +The parallel network nonlinear viscoelastic model: +• is intended for modeling materials that exhibit nonlinear viscous behavior and undergo large +deformations; +• consists of multiple elastic and viscoelastic networks in parallel; +• uses a hyperelastic material model to specify the elastic response; and +• uses multiplicative split of the deformation gradient and a flow rule derived from a creep potential +to specify the viscous behavior. +Material behavior +The parallel network nonlinear viscoelastic model consists of multiple elastic and viscoelastic networks +connected in parallel, as shown in Figure 22.8.2–1. The number of viscoelastic networks, N, can be +arbitrary; however, at most one purely elastic equilibrium network (network 0 in Figure 22.8.2–1) is +allowed in the model. If the elastic network is not defined, the stress in the material will relax completely +over time. +The model can be used to predict complex behavior of viscous materials subjected to finite strains, +which cannot be modeled accurately using the linear viscoelastic model available in Abaqus . An example of such complex behavior is depicted in +Figure 22.8.2–2, which shows normalized stress relaxation curves for three different strain levels. This +behavior can be modeled accurately using the nonlinear viscoelastic model, but it cannot be captured +with the linear model. In the latter case, the three curves would coincide. +Elastic behavior +The elastic part of the response for all the networks is specified using the hyperelastic material model. +Any of the hyperelastic models available in Abaqus can be used . The same hyperelastic material definition is used for all the networks, scaled +. . . . . . + 0 + . . . . . . +Figure 22.8.2–1 Nonlinear viscoelastic model with multiple parallel networks. +1.00 +0.95 +0.90 +0.85 +sigma1 +sigma2 +sigma3 +0.80 +1.0 +1.5 +2.0 +2.5 +Time +3.0 +3.5 +4.0 +Figure 22.8.2–2 Normalized stress relaxation curves for three different strain levels. +by a stiffness ratio specific to each network. Consequently, only one hyperelastic material definition +is required by the model along with the stiffness ratio for each network. The elastic response can be +specified by defining either the instantaneous response or the long-term response. +Viscous behavior +Viscous behavior must be defined for each viscoelastic network. +multiplicative split of the deformation gradient and the existence of the creep potential, +which the flow rule is derived. In the multiplicative split the deformation gradient is expressed as +It is modeled by assuming the +, from +is the elastic part of the deformation gradient (representing the hyperelastic behavior) and +where +is +the creep part of the deformation gradient (representing the stress-free intermediate configuration). The +creep potential is assumed to have the general form +where +is the Cauchy stress. If the potential is specified, the flow rule can be obtained from +where +is the symmetric part of the velocity gradient, +, expressed in the current configuration and +is the proportionality factor. In this model the creep potential is given by +and the proportionality factor is taken as +, where +is the equivalent deviatoric Cauchy stress and +is the equivalent creep stain rate. In this case the flow rule has the form +or, equivalently +is the Kirchhoff stress, +where +the deviatoric Kirchhoff stress, and +be provided. In this model +hyperborlic-sine model. +is the determinant of +is +must +can be determined from either a power-law strain hardening model or a +. To complete the derivation, the evolution law for +is the deviatoric Cauchy stress, +, +Power-law strain hardening model +The power-law strain hardening model is available in the form +is the equivalent creep strain rate, +is the equivalent creep strain, +is the equivalent deviatoric Kirchhoff stress, and +are material parameters. +A, m, and n +Hyperbolic-sine law model +The hyperbolic-sine law is available in the form +where +and +are defined above, and +A, B, and n +are material parameters. +Thermal expansion +Only the isotropic thermal expansion is permitted with the nonlinear viscoelastic material (“Thermal +expansion,” Section 26.1.2). +Defining viscoelastic response +The nonlinear viscoelastic response is defined by specifying the identifier, stiffness ratio, and creep law +for each viscoelastic network. +Specifying network identifier +Each viscoelastic network in the material model must be assigned a unique network identifier or network +id. The network identifiers must be consecutive integers starting with 1. The order in which they are +specified is not important. +Input File Usage: +Use the following option to specify the network identifier: +*VISCOELASTIC, NONLINEAR, NETWORKID=networkId +Defining the stiffness ratio +The contribution of each network to the overall response of the material is determined by the value of +the stiffness ratio, +, which is used to scale the elastic response of the network material. The sum of the +stiffness ratios of the viscoelastic networks must be smaller than or equal to 1. If the sum of the ratios is +equal to 1, the purely elastic equilibrium network is not created. If the sum of the ratios is smaller than +1, the equilibrium network is created with a stiffness ratio, +, equal to +where +denotes the number of viscoelastic networks and +is the stiffness ratio of network . +Input File Usage: +Use the following option to specify the network’s stiffness ratio: +*VISCOELASTIC, NONLINEAR, SRATIO=ratio +Specifying the creep law +The definition of creep behavior in Abaqus/Standard is completed by specifying the creep law. +Strain hardening power law creep model +The strain hardening law is defined by specifying three material parameters: A, n, and m. For physically +reasonable behavior A and n must be positive and −1 < m ≤ 0. +Input File Usage: +*VISCOELASTIC, NONLINEAR, LAW=STRAIN +Hyperbolic sine creep model +The hyperbolic sine creep law is specified by providing three nonnegative parameters: A, B, and n. +Input File Usage: +*VISCOELASTIC, NONLINEAR, LAW=HYPERB +Material response in different analysis steps +The material is active during all stress/displacement procedure types. However, the creep effects are +taken into account only in a quasi-static analysis . In other +stress/displacement procedures the evolution of the state variables is suppressed and the creep strain +remains unchanged. +Elements +The nonlinear viscoelastic model is available with continuum elements that include mechanical behavior +(elements that have displacement degrees of freedom), except for one-dimensional and plane stress +elements. +Output +In addition to the standard output identifiers available in Abaqus/Standard (“Abaqus/Standard output +variable identifiers,” Section 4.2.1), the following variables have special meaning for the nonlinear +viscoelastic material model: +CEEQ +CE +CENER +SENER +The overall equivalent creep strain, defined as +. +The overall creep strain, defined as +. +The overall viscous dissipated energy per unit volume, defined as +. +The overall elastic strain energy density per unit volume, defined as +. +In the above definitions +networks, the subscript or superscript +to be the purely elastic network. +denotes the stiffness ratio for network , +denotes the number of viscoelastic +is used to denote network quantities, and the network is assumed +22.9 +Rate sensitive elastomeric foams +• “Low-density foams,” Section 22.9.1 +22.9.1 +LOW-DENSITY FOAMS +Products: Abaqus/Explicit Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Elastic behavior: overview,” Section 22.1.1 +• *LOW DENSITY FOAM +• *UNIAXIAL TEST DATA +• “Creating a low-density foam material model” in “Defining elasticity,” Section 12.9.1 of the +Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +The low-density foam material model: +• is intended for low-density, highly compressible elastomeric foams with significant rate sensitive +behavior (such as polyurethane foam); +• requires the direct specification of uniaxial stress-strain curves at different strain rates for both +tension and compression; +• optionally allows the specification of lateral strain data to include Poisson effects; +• allows for the specification of optional unloading stress-strain curves for better representation of the +hysteretic behavior and energy absorption during cyclic loading; and +• requires that geometric nonlinearity be accounted for during the analysis step , since it +is intended for finite-strain applications. +Mechanical response +Low-density, highly compressible elastomeric foams are widely used in the automotive industry as +energy absorbing materials. Foam padding is used in many passive safety systems, such as behind +headliners for head impact protection, in door trims for pelvis and thorax protection, etc. Energy +absorbing foams are also commonly used in packaging of hand-held and other electronic devices. +The low-density foam material model in Abaqus/Explicit is intended to capture the highly strain-rate +sensitive behavior of these materials. The model uses a pseudo visco-hyperelastic formulation whereby +the strain energy potential is constructed numerically as a function of principal stretches and a set of +internal variables associated with strain rate. By default the Poisson’s ratio of the material is assumed +to be zero. With this assumption, the evaluation of the stress-strain response becomes uncoupled along +the principal deformation directions. Optionally, nonzero Poisson effects can be specified to include +coupling along the principal directions. +The model requires as input the stress-strain response of the material for both uniaxial tension and +uniaxial compression tests. Poisson effects can be included by also specifying lateral strain data for each +of these tests. The tests can be performed at different strain rates. For each test the strain data should be +given in nominal strain values (change in length per unit of original length), and the stress data should +be given in nominal stress values (force per unit of original cross-sectional area). Uniaxial tension and +compression curves are specified separately. The uniaxial stress and strain data are given in absolute +values (positive in both tension and compression). On the other hand, when specified, the lateral strain +data must be negative in tension and positive in compression, corresponding to a positive Poisson’s effect. +The model does not support negative Poisson’s effect. Rate-dependent behavior is specified by providing +the uniaxial stress-strain curves for different values of nominal strain rates. +Both loading and unloading rate-dependent curves can be specified to better characterize the +hysteretic behavior and energy absorption properties of the material during cyclic loading. Use +positive values of nominal strain rates for loading curves and negative values for the unloading curves. +Currently this option is available only with linear strain rate regularization . When +the unloading behavior is not specified directly, the model assumes that unloading occurs along the +loading curve associated with the smallest deformation rate. A representative schematic of typical +rate-dependent uniaxial compression data is shown in Figure 22.9.1–1 with both loading and unloading +curves. It is important that the specified rate-dependent stress-strain curves do not intersect. Otherwise, +the material is unstable, and Abaqus issues an error message if an intersection between curves is found. + +Figure 22.9.1–1 Rate-dependent loading/unloading stress-strain curves. +During the analysis, +the stress along each principal deformation direction is evaluated by +interpolating the specified loading/unloading stress-strain curves using the corresponding values of +principal nominal strain and strain rate. The stress is then corrected by a coupling term if non-zero +Poisson effects are included. The representative response of the model for a uniaxial compression cycle +is shown in Figure 22.9.1–1. +Input File Usage: +Use the following options to specify a low-density foam material: +*LOW DENSITY FOAM +*UNIAXIAL TEST DATA, DIRECTION=TENSION +*UNIAXIAL TEST DATA, DIRECTION=COMPRESSION +Use the first option to specify a low-density foam material with zero Poisson’s +ratio (default), or use the second option to include Poisson effects by defining +lateral strains as part of the test data input: +*LOW DENSITY FOAM,LATERAL STRAIN DATA=NO (default) +*LOW DENSITY FOAM, LATERAL STRAIN DATA=YES +In addition, use these two options to give the experimental stress-strain data +*UNIAXIAL TEST DATA, DIRECTION=TENSION +*UNIAXIAL TEST DATA, DIRECTION=COMPRESSION +Property module: material editor: Mechanical→Elasticity→Low Density +Foam: Uniaxial Test Data→Uniaxial Tension Test Data, Uniaxial +Test Data→Uniaxial Compression Test Data +Input File Usage: +Abaqus/CAE Usage: +Relaxation coefficients +, +Unphysical jumps in stress due to sudden changes in the deformation rate are prevented using a technique +based on viscous regularization. This technique also models stress relaxation effects in a very simplistic +manner. In the case of a uniaxial test, for example, the relaxation time is given as +, +where +is a linear viscosity parameter that +, and +controls the relaxation time when +, and typically small values of this parameter should be used. +is a nonlinear viscosity parameter that controls the relaxation time at higher values of deformation. +controls the sensitivity of the relaxation speed +(time +The smaller this value, the shorter the relaxation time. +to the stretch. The default values of these parameters are +units), and +are material parameters and +is the stretch. +(time units), +. +Input File Usage: +Use the following option to specify relaxation coefficients: +*LOW DENSITY FOAM +, +, +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Elasticity→Low Density +Foam: Relaxation coefficients: mu0, mu1, alpha +Strain rate +When Poisson’s ratio is zero, three different strain rate measures can be used for the evaluation of +the stress-strain response along each principal deformation direction for general three-dimensional +the nominal volumetric strain rate, the nominal strain rate along each principal +deformation states: +deformation direction, or the maximum of the nominal strain rates along the principal deformation +directions. By default, the nominal volumetric strain rate is used; this approach does not produce +rate-sensitive behavior under volume-preserving deformation modes (e.g., simple shear). Alternatively, +each principal stress can be evaluated based either on the nominal strain rate along the corresponding +principal direction or the maximum of the nominal strain rates; both these approaches can provide +rate-sensitive behavior for volume-preserving deformation modes. All three strain rate measures +produce identical rate-dependent behavior for uniaxial loading conditions when the Poisson’s ratio is +zero. +When non-zero Poisson effects are defined, the model uses the maximum nominal strain rate along +the principal deformation directions for the evaluation of the stress-strain response. This is the default +and only strain rate measure available for this case. +Input File Usage: +Use the following option to use the volumetric strain rate (default when +Poisson’s ratio is zero): +*LOW DENSITY FOAM, STRAIN RATE=VOLUMETRIC +Use the following option to use the nominal strain rate evaluated along each +principal direction: +*LOW DENSITY FOAM, STRAIN RATE=PRINCIPAL +Use the following option to use the maximum of the nominal strain rates along +the principal directions (default and only option available when Poisson’s ratio +is not zero): +Abaqus/CAE Usage: +*LOW DENSITY FOAM, STRAIN RATE=MAX PRINCIPAL +Use the following option to use the volumetric strain rate (default): +Property module: material editor: Mechanical→Elasticity→Low +Density Foam: Strain rate measure: Volumetric +Use the following option to use the strain rate evaluated along each principal +direction: +Property module: material editor: Mechanical→Elasticity→Low +Density Foam: Strain rate measure: Principal +Extrapolation of stress-strain curves +By default, for this material model and for strain values beyond the range of specified strains, +Abaqus/Explicit extrapolates the stress-strain curves using the slope at the last data point. +When the strain rate value exceeds the maximum specified strain rate, Abaqus/Explicit uses the +stress-strain curve corresponding to the maximum specified strain rate by default. You can override this +default and activate strain rate extrapolation based on the slope (with respect to strain rate). +Input File Usage: +Use the following option to activate strain rate extrapolation of loading curves: +*LOW DENSITY FOAM, RATE EXTRAPOLATION=YES +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Elasticity→Low +Density Foam: toggle on Extrapolate stress-strain curve +beyond maximum strain rate +Tension cutoff and failure +Low-density foams have limited strength in tension and can easily rupture under excessive tensile +loading. The model in Abaqus/Explicit provides the option to specify a cutoff value for the maximum +principal tensile stress that the material can sustain. The maximum principal stresses computed by the +program will stay at or below this value. You can also activate deletion (removal) of the element from +the simulation when the tension cutoff value is reached, which provides a simple method for modeling +rupture. +Input File Usage: +Use the following option to define a tension cutoff value without element +deletion: +*LOW DENSITY FOAM, TENSION CUTOFF=value +Use the following option to allow element deletion when the tension cutoff +value is met: +Abaqus/CAE Usage: +*LOW DENSITY FOAM, TENSION CUTOFF=value, FAIL=YES +Use the following option to define a tension cutoff value: +Property module: material editor: Mechanical→Elasticity→Low Density +Foam: toggle on Maximum allowable principal tensile stress: value +Use the following option to allow element deletion when the tension cutoff +value is met: +Property module: material editor: Mechanical→Elasticity→Low Density +Foam: toggle on Remove elements exceeding maximum +Thermal expansion +Only isotropic thermal expansion is permitted with the low-density foam material model. +The elastic volume ratio, +and the thermal volume ratio, +, relates the total volume ratio (current volume/reference volume), J, +, via the simple relationship: +is given by +where +thermal expansion coefficient (“Thermal expansion,” Section 26.1.2). +is the linear thermal expansion strain that is obtained from the temperature and the isotropic +Material stability +The Drucker stability condition for a compressible material requires that the change in the Kirchhoff +stress, +, following from an infinitesimal change in the logarithmic strain, +, satisfies the inequality +where the Kirchhoff stress +. Using +, the inequality becomes +This restriction requires that the tangential material stiffness +be positive definite. +For an isotropic elastic formulation the inequality can be represented in terms of the principal +stresses and strains +Thus, the relation between changes in the stress and changes in the strain can be obtained in the +form of the matrix equation +where +. Since must be positive definite, it is necessary that +When Poisson’s ratio is zero, the off diagonal terms of +conditions for a positive definite matrix reduce to +stress-strain curves in the space of Kirchhoff stress versus logarithmic strain must be positive. +become zero. In that case the necessary +; that is, the slope of the specified uniaxial +You should be careful defining the input data for the low-density foam model to ensure stable +If an instability is found, Abaqus issues a warning message +material response for all strain rates. +and prints the lowest value of strain for which the instability is observed. +Ideally, no instability +should occur. If instabilities are observed at strain levels that are likely to occur in the analysis, it is +strongly recommended that you carefully examine and revise the material input data. When nonzero +Poisson effects are defined, it is highly recommended that you provide uniaxial test data in tension and +compression for the same range of strain rates. +Elements +The low-density foam model can be used with solid (continuum) elements and generalized plane strain +elements. One-dimensional solid elements (truss and rebar) are also available for the case when no lateral +strains are specified (Poisson’s ratio is zero). The model cannot be used with shells, membranes, or the +Eulerian elements (EC3D8R and EC3D8RT). +Procedures +The low-density foam model must always be used with geometrically nonlinear analyses (“General and +linear perturbation procedures,” Section 6.1.3). +23. +Inelastic Mechanical Properties +Overview +Metal plasticity +Other plasticity models +Fabric materials +Jointed materials +Concrete +Permanent set in rubberlike materials +23.1 +23.2 +23.3 +23.4 +23.5 +23.6 +23.1 +Overview +• “Inelastic behavior,” Section 23.1.1 +23.1.1 +INELASTIC BEHAVIOR +The material library in Abaqus includes several models of inelastic behavior: +• Classical metal plasticity: The yield and inelastic flow of a metal at relatively low temperatures, +where loading is relatively monotonic and creep effects are not important, can typically be described +with the classical metal plasticity models (“Classical metal plasticity,” Section 23.2.1). In Abaqus these +models use standard Mises or Hill yield surfaces with associated plastic flow. Perfect plasticity and +isotropic hardening definitions are both available in the classical metal plasticity models. Common +applications include crash analyses, metal forming, and general collapse studies; the models are simple +and adequate for such cases. +• Models for metals subjected to cyclic loading: A linear kinematic hardening model or a nonlinear +isotropic/kinematic hardening model (“Models for metals subjected to cyclic loading,” Section 23.2.2) +can be used in Abaqus to simulate the behavior of materials that are subjected to cyclic loading. The +evolution law in these models consists of a kinematic hardening component (which describes the +translation of the yield surface in stress space) and, for the nonlinear isotropic/kinematic hardening +model, of an isotropic component (which describes the change of the elastic range). The Bauschinger +effect and plastic shakedown can be modeled with both models, but the nonlinear isotropic/kinematic +hardening model provides more accurate predictions. Ratchetting and relaxation of the mean stress are +accounted for only by the nonlinear isotropic/kinematic model. In addition to these two models, the +ORNL model in Abaqus/Standard can be used when simple life estimation is desired for the design of +stainless steels subjected to low-cycle fatigue and creep fatigue . +• Rate-dependent yield: As strain rates increase, many materials show an increase in their yield +strength. Rate dependence (“Rate-dependent yield,” Section 23.2.3) can be defined in Abaqus for a +number of plasticity models. Rate dependence can be used in both static and dynamic procedures. +Applicable models include classical metal plasticity, extended Drucker-Prager plasticity, and crushable +foam plasticity. +• Creep and swelling: Abaqus/Standard provides a material model for classical metal creep behavior +and time-dependent volumetric swelling behavior (“Rate-dependent plasticity: creep and swelling,” +Section 23.2.4). This model is intended for relatively slow (quasi-static) inelastic deformation of a +model such as the high-temperature creeping flow of a metal or a piece of glass. The creep strain rate +is assumed to be purely deviatoric, meaning that there is no volume change associated with this part +of the inelastic straining. Creep can be used with the classical metal plasticity model, with the ORNL +model, and to define rate-dependent gasket behavior (“Defining the gasket behavior directly using a +gasket behavior model,” Section 32.6.6). Swelling can be used with the classical metal plasticity model. +(Usage with the Drucker-Prager models is explained below.) +• Annealing or melting: Abaqus provides a modeling capability for situations in which a loss of +memory related to hardening occurs above a certain user-defined temperature, known as the annealing +temperature (“Annealing or melting,” Section 23.2.5). +It is intended for use with metals subjected +to high-temperature deformation processes, in which the material may undergo melting and possibly +In Abaqus annealing or melting can be modeled +resolidification or some other form of annealing. +with classical metal plasticity (Mises and Hill); in Abaqus/Explicit annealing or melting can also be +modeled with Johnson-Cook plasticity. The annealing temperature is assumed to be a material property. +See “Annealing procedure,” Section 6.12.1, for information on an alternative method for simulating +annealing in Abaqus/Explicit. +• Anisotropic yield and creep: Abaqus provides an anisotropic yield model +(“Anisotropic +yield/creep,” Section 23.2.6), which is available for use with materials modeled with classical +metal plasticity (“Classical metal plasticity,” Section 23.2.1), kinematic hardening (“Models for +metals subjected to cyclic loading,” Section 23.2.2), and/or creep (“Rate-dependent plasticity: +creep and swelling,” Section 23.2.4) that exhibit different yield stresses in different directions. The +Abaqus/Standard model includes creep; creep behavior is not available in Abaqus/Explicit. The model +allows for the specification of different stress ratios for each stress component to define the initial +anisotropy. The model is not adequate for cases in which the anisotropy changes significantly as the +material deforms as a result of loading. +• Johnson-Cook plasticity: The Johnson-Cook plasticity model in Abaqus/Explicit (“Johnson-Cook +plasticity,” Section 23.2.7) is particularly suited to model high-strain-rate deformation of metals. This +model is a particular type of Mises plasticity that includes analytical forms of the hardening law and rate +dependence. It is generally used in adiabatic transient dynamic analysis. +• Dynamic failure models: Two types of dynamic failure models are offered in Abaqus/Explicit for the +Mises and Johnson-Cook plasticity models (“Dynamic failure models,” Section 23.2.8). One is the shear +failure model, where the failure criterion is based on the accumulated equivalent plastic strain. Another +is the tensile failure model, which uses the hydrostatic pressure stress as a failure measure to model +dynamic spall or a pressure cutoff. Both models offer a number of failure choices including element +removal and are applicable mainly in truly dynamic situations. In contrast, the progressive failure and +damage models (Chapter 24, “Progressive Damage and Failure”) are suitable for both quasi-static and +dynamic situations and have other significant advantages. +• Porous metal plasticity: The porous metal plasticity model +(“Porous metal plasticity,” +Section 23.2.9) is used to model materials that exhibit damage in the form of void initiation and growth, +and it can also be used for some powder metal process simulations at high relative densities (relative +density is defined as the ratio of the volume of solid material to the total volume of the material). The +model is based on Gurson’s porous metal plasticity theory with void nucleation and is intended for use +with materials that have a relative density that is greater than 0.9. The model is adequate for relatively +monotonic loading. +• Cast iron plasticity: The cast iron plasticity model (“Cast iron plasticity,” Section 23.2.10) is used to +model gray cast iron, which exhibits markedly different inelastic behavior in tension and compression. +The microstructure of gray cast iron consists of a distribution of graphite flakes in a steel matrix. In +tension the graphite flakes act as stress concentrators, while in compression the flakes serve to transmit +stresses. The resulting material is brittle in tension, but in compression it is similar in behavior to steel. +The differences in tensile and compressive plastic response include: (i) a yield stress in tension that is +three to five times lower than the yield stress in compression; (ii) permanent volume increase in tension, +but negligible inelastic volume change in compression; (iii) different hardening behavior in tension and +compression. The model is adequate for relatively monotonic loading. +• Two-layer viscoplasticity: The two-layer viscoplasticity model in Abaqus/Standard (“Two-layer +viscoplasticity,” Section 23.2.11) is useful for modeling materials in which significant time-dependent +behavior as well as plasticity is observed. For metals this typically occurs at elevated temperatures. The +model has been shown to provide good results for thermomechanical loading. +• ORNL constitutive model: The ORNL plasticity model in Abaqus/Standard (“ORNL – Oak +Ridge National Laboratory constitutive model,” Section 23.2.12) is intended for cyclic loading and +high-temperature creep of type 304 and 316 stainless steel. Plasticity and creep calculations are +provided according to the specification in Nuclear Standard NEF 9-5T, “Guidelines and Procedures +for Design of Class I Elevated Temperature Nuclear System Components.” This model is an extension +of the linear kinematic hardening model (discussed above), which attempts to provide for simple life +estimation for design purposes when low-cycle fatigue and creep fatigue are critical issues. +• Deformation plasticity: Abaqus/Standard provides a deformation theory Ramberg-Osgood plasticity +model (“Deformation plasticity,” Section 23.2.13) for use in developing fully plastic solutions for fracture +mechanics applications in ductile metals. The model is most commonly applied in static loading with +small-displacement analysis for which the fully plastic solution must be developed in a part of the model. +• Extended Drucker-Prager plasticity and creep: The extended Drucker-Prager family of plasticity +models (“Extended Drucker-Prager models,” Section 23.3.1) describes the behavior of granular +materials or polymers in which the yield behavior depends on the equivalent pressure stress. The +inelastic deformation may sometimes be associated with frictional mechanisms such as sliding of +particles across each other. +This class of models provides a choice of three different yield criteria. The differences in criteria are +based on the shape of the yield surface in the meridional plane, which can be a linear form, a hyperbolic +form, or a general exponent form. Inelastic time-dependent (creep) behavior coupled with the plastic +behavior is also available in Abaqus/Standard for the linear form of the model. Creep behavior is not +available in Abaqus/Explicit. +• Modified Drucker-Prager/Cap plasticity and creep: The modified Drucker-Prager/Cap plasticity +model (“Modified Drucker-Prager/Cap model,” Section 23.3.2) can be used to simulate geological +materials that exhibit pressure-dependent yield. The addition of a cap yield surface helps control volume +dilatancy when the material yields in shear and provides an inelastic hardening mechanism to represent +In Abaqus/Standard inelastic time-dependent (creep) behavior coupled with the +plastic compaction. +plastic behavior is also available for this model; two creep mechanisms are possible: a cohesion, +Drucker-Prager-like mechanism and a consolidation, cap-like mechanism. +• Mohr-Coulomb plasticity: The Mohr-Coulomb plasticity model (“Mohr-Coulomb plasticity,” +Section 23.3.3) can be used for design applications in the geotechnical engineering area. The model +uses the classical Mohr-Coloumb yield criterion: a straight line in the meridional plane and an irregular +hexagonal section in the deviatoric plane. However, the Abaqus Mohr-Coulomb model has a completely +smooth flow potential instead of the classical hexagonal pyramid: the flow potential is a hyperbola in +the meridional plane, and it uses the smooth deviatoric section proposed by Menétrey and Willam. +• Critical state (clay) plasticity: The clay plasticity model (“Critical state (clay) plasticity model,” +Section 23.3.4) describes the inelastic response of cohesionless soils. The model provides a reasonable +match to the experimentally observed behavior of saturated clays. This model defines the inelastic +behavior of a material by a yield function that depends on the three stress invariants, an associated flow +assumption to define the plastic strain rate, and a strain hardening theory that changes the size of the +yield surface according to the inelastic volumetric strain. +• Crushable foam plasticity: The foam plasticity model (“Crushable foam plasticity models,” +Section 23.3.5) is intended for modeling crushable foams that are typically used as energy absorption +structures; however, other crushable materials such as balsa wood can also be simulated with this +model. This model is most appropriate for relatively monotonic loading. The crushable foam model +with isotropic hardening is applicable to polymeric foams as well as metallic foams. +• Jointed material: The jointed material model +in Abaqus/Standard (“Jointed material model,” +Section 23.5.1) is intended to provide a simple, continuum model for a material that contains a high +density of parallel joint surfaces in different orientations, such as sedimentary rock. This model +is intended for applications where stresses are mainly compressive, and it provides a joint opening +capability when the stress normal to the joint tries to become tensile. +• Concrete: Three different constitutive models are offered in Abaqus for the analysis of concrete at +low confining pressures: the smeared crack concrete model in Abaqus/Standard (“Concrete smeared +cracking,” Section 23.6.1); the brittle cracking model in Abaqus/Explicit (“Cracking model for concrete,” +Section 23.6.2); and the concrete damaged plasticity model in both Abaqus/Standard and Abaqus/Explicit +(“Concrete damaged plasticity,” Section 23.6.3). Each model is designed to provide a general capability +for modeling plain and reinforced concrete (as well as other similar quasi-brittle materials) in all types +of structures: beams, trusses, shells, and solids. +The smeared crack concrete model in Abaqus/Standard is intended for applications in which the +concrete is subjected to essentially monotonic straining and a material point exhibits either tensile +cracking or compressive crushing. Plastic straining in compression is controlled by a “compression” +yield surface. Cracking is assumed to be the most important aspect of the behavior, and the +representation of cracking and postcracking anisotropic behavior dominates the modeling. +The brittle cracking model in Abaqus/Explicit is intended for applications in which the concrete +behavior is dominated by tensile cracking and compressive failure is not important. The model includes +consideration of the anisotropy induced by cracking. In compression, the model assumes elastic behavior. +A simple brittle failure criterion is available to allow the removal of elements from a mesh. +The concrete damaged plasticity model in Abaqus/Standard and Abaqus/Explicit is based on +the assumption of scalar (isotropic) damage and is designed for applications in which the concrete is +subjected to arbitrary loading conditions, including cyclic loading. The model takes into consideration +the degradation of the elastic stiffness induced by plastic straining both in tension and compression. It +also accounts for stiffness recovery effects under cyclic loading. +• Progressive damage and failure: Abaqus/Explicit offers a general capability for modeling +progressive damage and failure in ductile metals and fiber-reinforced composites (Chapter 24, +“Progressive Damage and Failure”). +Plasticity theories +Most materials of engineering interest initially respond elastically. Elastic behavior means that the +deformation is fully recoverable: when the load is removed, the specimen returns to its original shape. +If the load exceeds some limit (the “yield load”), the deformation is no longer fully recoverable. Some +part of the deformation will remain when the load is removed, as, for example, when a paperclip is bent +too much or when a billet of metal is rolled or forged in a manufacturing process. Plasticity theories +model the material’s mechanical response as it undergoes such nonrecoverable deformation in a ductile +fashion. The theories have been developed most intensively for metals, but they are also applied to +soils, concrete, rock, ice, crushable foam, and so on. These materials behave in very different ways. +For example, large values of pure hydrostatic pressure cause very little inelastic deformation in metals, +but quite small hydrostatic pressure values may cause a significant, nonrecoverable volume change in +a soil sample. Nonetheless, the fundamental concepts of plasticity theories are sufficiently general that +models based on these concepts have been developed successfully for a wide range of materials. +Most of the plasticity models in Abaqus are “incremental” theories in which the mechanical strain +rate is decomposed into an elastic part and a plastic (inelastic) part. Incremental plasticity models are +usually formulated in terms of +• a yield surface, which generalizes the concept of “yield load” into a test function that can be used to +determine if the material responds purely elastically at a particular state of stress, temperature, etc; +• a flow rule, which defines the inelastic deformation that occurs if the material point is no longer +responding purely elastically; and +• evolution laws that define the hardening—the way in which the yield and/or flow definitions change +as inelastic deformation occurs. +Abaqus/Standard also has a “deformation” plasticity model, in which the stress is defined from the +total mechanical strain. This is a Ramberg-Osgood model (“Deformation plasticity,” Section 23.2.13) +and is intended primarily for ductile fracture mechanics applications, where fully plastic solutions are +often required. +Elastic response +The Abaqus plasticity models also need an elasticity definition to deal with the recoverable part of the +strain. In Abaqus the elasticity is defined by including linear elastic behavior or, if relevant for some +plasticity models, porous elastic behavior in the same material definition . In the case of the Mises and Johnson-Cook plasticity models in Abaqus/Explicit the +elasticity can alternatively be defined using an equation of state with associated deviatoric behavior . +When performing an elastic-plastic analysis at finite strains, Abaqus assumes that the plastic strains +dominate the deformation and that the elastic strains are small. This restriction is imposed by the elasticity +models that Abaqus uses. It is justified because most materials have a well-defined yield point that is a +very small percentage of their Young’s modulus; for example, the yield stress of metals is typically less +than 1% of the Young’s modulus of the material. Therefore, the elastic strains will also be less than this +percentage, and the elastic response of the material can be modeled quite accurately as being linear. +In Abaqus/Explicit the elastic strain energy reported is updated incrementally. The incremental +is the incremental +) is computed as +, where +change in elastic strain energy ( +change in total strain energy and +is much smaller than +and +is the incremental change in plastic energy dissipation. +for increments in which the deformation is almost all plastic. +and +and +result in deviations from the true solutions that are +Approximations in the calculations of +insignificant compared to +. Typically, the elastic +strain energy solution is quite accurate, but in some rare cases the approximations in the calculations of +can lead to a negative value reported for the elastic strain energy. These negative values +are most likely to occur in an analysis that uses rate-dependent plasticity. As long as the absolute value +of the elastic strain energy is very small compared to the total strain energy, a negative value for the +elastic strain energy should not be considered an indication of a serious solution problem. +but can be significant relative to +and +Stress and strain measures +Most materials that exhibit ductile behavior (large inelastic strains) yield at stress levels that are orders of +magnitude less than the elastic modulus of the material, which implies that the relevant stress and strain +measures are “true” stress (Cauchy stress) and logarithmic strain. Material data for all of these models +should, therefore, be given in these measures. +If you have nominal stress-strain data for a uniaxial test and the material is isotropic, a simple +conversion to true stress and logarithmic plastic strain is +where E is the Young’s modulus. +Example of stress-strain data input +The example below illustrates the input of material data for the classical metal plasticity model with +isotropic hardening (“Classical metal plasticity,” Section 23.2.1). Stress-strain data representing the +material hardening behavior are necessary to define the model. An experimental hardening curve might +appear as that shown in Figure 23.1.1–1. First yield occurs at 200 MPa (29000 lb/in2). The material then +hardens to 300 MPa (43511 lb/in2 ) at one percent strain, after which it is perfectly plastic. Assuming that +the Young’s modulus is 200000 MPa (29 × 106 lb/in2 ), the plastic strain at the one percent strain point is +.01 − 300/200000=.0085. When the units are newtons and millimeters, the input is +Yield Stress +Plastic Strain +200. +300. +0. +.0085 +Plastic strain values, not +total strain values, are used in defining the hardening behavior. +Furthermore, the first data pair must correspond with the onset of plasticity (the plastic strain value must +be zero in the first pair). These concepts are applicable when hardening data are defined in a tabular +form for any of the following plasticity models: +True stress, + MPa +300 +200 +True stress, + lb/in2 +40000 +30000 +0.85 1.0 +Log strain, percent +Figure 23.1.1–1 Experimental hardening curve. +• “Classical metal plasticity,” Section 23.2.1 +• “Models for metals subjected to cyclic loading,” Section 23.2.2 +• “Porous metal plasticity,” Section 23.2.9 (isotropic hardening classical metal plasticity must be +defined for use with this model) +• “Cast iron plasticity,” Section 23.2.10 +• “ORNL – Oak Ridge National Laboratory constitutive model,” Section 23.2.12 +• “Extended Drucker-Prager models,” Section 23.3.1 +• “Modified Drucker-Prager/Cap model,” Section 23.3.2 +• “Mohr-Coulomb plasticity,” Section 23.3.3 +• “Critical state (clay) plasticity model,” Section 23.3.4 +• “Crushable foam plasticity models,” Section 23.3.5 +• “Concrete smeared cracking,” Section 23.6.1 +The input required to define hardening is discussed in the referenced sections. +Specifying initial equivalent plastic strains +Initial values of equivalent plastic strain can be specified in Abaqus for elements that use classical +metal plasticity (“Classical metal plasticity,” Section 23.2.1) or Drucker-Prager plasticity (“Extended +Drucker-Prager models,” Section 23.3.1) by defining initial hardening conditions (“Initial conditions in +Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1). The equivalent plastic strain (output variable +PEEQ) then contains the initial value of equivalent plastic strain plus any additional equivalent plastic +strain due to plastic straining during the analysis. However, the plastic strain tensor (output variable +PE) contains only the amount of straining due to deformation during the analysis. +The simple one-dimensional example shown in Figure 23.1.1–2 illustrates the concept. The material +. It is then hardened by loading it along +. A new analysis that employs the same hardening curve +is in an annealed configuration at point A; its yield stress is +the path +; the new yield stress is +εpl +21 +C, E +εpl +ε +Figure 23.1.1–2 Initial equivalent plastic strain example. +. Plastic strain +, starting from point D, by specifying a +as the first analysis takes this material along the path +total strain, +will result and can be output (for instance) using output variable PE11. +To obtain the correct yield stress, +, should be provided as +an initial condition. Likewise, the correct yield stress at point F is obtained from an equivalent plastic +strain PEEQ +, the equivalent plastic strain at point E, +. +23.2 +Metal plasticity +• “Classical metal plasticity,” Section 23.2.1 +• “Models for metals subjected to cyclic loading,” Section 23.2.2 +• “Rate-dependent yield,” Section 23.2.3 +• “Rate-dependent plasticity: creep and swelling,” Section 23.2.4 +• “Annealing or melting,” Section 23.2.5 +• “Anisotropic yield/creep,” Section 23.2.6 +• “Johnson-Cook plasticity,” Section 23.2.7 +• “Dynamic failure models,” Section 23.2.8 +• “Porous metal plasticity,” Section 23.2.9 +• “Cast iron plasticity,” Section 23.2.10 +• “Two-layer viscoplasticity,” Section 23.2.11 +• “ORNL – Oak Ridge National Laboratory constitutive model,” Section 23.2.12 +• “Deformation plasticity,” Section 23.2.13 +23.2.1 +CLASSICAL METAL PLASTICITY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Rate-dependent yield,” Section 23.2.3 +• “Anisotropic yield/creep,” Section 23.2.6 +• “Johnson-Cook plasticity,” Section 23.2.7 +• Chapter 24, “Progressive Damage and Failure” +• “Dynamic failure models,” Section 23.2.8 +• “Material library: overview,” Section 21.1.1 +• “Inelastic behavior,” Section 23.1.1 +• “UHARD,” Section 1.1.35 of the Abaqus User Subroutines Reference Manual +• *PLASTIC +• *RATE DEPENDENT +• *POTENTIAL +• “Defining classical metal plasticity” in “Defining plasticity,” Section 12.9.2 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +The classical metal plasticity models: +• use Mises or Hill yield surfaces with associated plastic flow, which allow for isotropic and +anisotropic yield, respectively; +• use perfect plasticity or isotropic hardening behavior; +• can be used when rate-dependent effects are important; +• are intended for applications such as crash analyses, metal forming, and general collapse studies +(Plasticity models that include kinematic hardening and are, therefore, more suitable for cases +involving cyclic loading are also available in Abaqus: see “Models for metals subjected to cyclic +loading,” Section 23.2.2.); +• can be used in any procedure that uses elements with displacement degrees of freedom; +• can be used in a fully coupled temperature-displacement analysis (“Fully coupled thermal-stress +analysis,” Section 6.5.3), a fully coupled thermal-electrical-structural analysis (“Fully coupled +thermal-electrical-structural analysis,” Section 6.7.4), or an adiabatic thermal-stress analysis +(“Adiabatic analysis,” Section 6.5.4) such that plastic dissipation results in the heating of a material; +• can be used in conjunction with the models of progressive damage and failure in Abaqus (“Damage +and failure for ductile metals: overview,” Section 24.2.1) to specify different damage initiation +criteria and damage evolution laws that allow for the progressive degradation of the material +stiffness and the removal of elements from the mesh; +• can be used in conjunction with the shear failure model in Abaqus/Explicit to provide a simple +ductile dynamic failure criterion that allows for the removal of elements from the mesh, although +the progressive damage and failure methods discussed above are generally recommended instead; +• can be used in conjunction with the tensile failure model in Abaqus/Explicit to provide a tensile +spall criterion offering a number of failure choices and removal of elements from the mesh; and +• must be used in conjunction with either the linear elastic material model (“Linear elastic behavior,” +Section 22.2.1) or the equation of state material model (“Equation of state,” Section 25.2.1). +Yield surfaces +The Mises and Hill yield surfaces assume that yielding of the metal is independent of the equivalent +pressure stress: this observation is confirmed experimentally for most metals (except voided metals) +under positive pressure stress but may be inaccurate for metals under conditions of high triaxial tension +when voids may nucleate and grow in the material. Such conditions can arise in stress fields near crack +tips and in some extreme thermal loading cases such as those that might occur during welding processes. +A porous metal plasticity model is provided in Abaqus for such situations. This model is described in +“Porous metal plasticity,” Section 23.2.9. +Mises yield surface +The Mises yield surface is used to define isotropic yielding. It is defined by giving the value of the +uniaxial yield stress as a function of uniaxial equivalent plastic strain, temperature, and/or field variables. +In Abaqus/Standard the yield stress can alternatively be defined in user subroutine UHARD. +Input File Usage: +Abaqus/CAE Usage: +*PLASTIC +Property module: material editor: Mechanical→Plasticity→Plastic +Hill yield surface +, for the metal plasticity model and define a set of yield ratios, +The Hill yield surface allows anisotropic yielding to be modeled. You must specify a reference yield +stress, +, separately. These data define +the yield stress corresponding to each stress component as +. Hill’s potential function is discussed +in detail in “Anisotropic yield/creep,” Section 23.2.6. Yield ratios can be used to define three common +forms of anisotropy associated with sheet metal forming: transverse anisotropy, planar anisotropy, and +general anisotropy. +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*PLASTIC (to specify the reference yield stress +*POTENTIAL (to specify the yield ratios +) +Property module: material editor: Mechanical→Plasticity→Plastic: +Suboptions→Potential +) +Hardening +In Abaqus a perfectly plastic material (with no hardening) can be defined, or work hardening can be +specified. Isotropic hardening, including Johnson-Cook hardening, is available in both Abaqus/Standard +and Abaqus/Explicit. In addition, Abaqus provides kinematic hardening for materials subjected to cyclic +loading. +Perfect plasticity +Perfect plasticity means that the yield stress does not change with plastic strain. It can be defined in +tabular form for a range of temperatures and/or field variables; a single yield stress value per temperature +and/or field variable specifies the onset of yield. +Input File Usage: +Abaqus/CAE Usage: +*PLASTIC +Property module: material editor: Mechanical→Plasticity→Plastic +Isotropic hardening +Isotropic hardening means that the yield surface changes size uniformly in all directions such that the +yield stress increases (or decreases) in all stress directions as plastic straining occurs. Abaqus provides an +isotropic hardening model, which is useful for cases involving gross plastic straining or in cases where +the straining at each point is essentially in the same direction in strain space throughout the analysis. +Although the model is referred to as a “hardening” model, strain softening or hardening followed by +softening can be defined. Isotropic hardening plasticity is discussed in more detail in “Isotropic elasto- +plasticity,” Section 4.3.2 of the Abaqus Theory Manual. +If isotropic hardening is defined, the yield stress, +, can be given as a tabular function of plastic +strain and, if required, of temperature and/or other predefined field variables. The yield stress at a given +state is simply interpolated from this table of data, and it remains constant for plastic strains exceeding +the last value given as tabular data. +Abaqus/Explicit will regularize the data into tables that are defined in terms of even intervals of +the independent variables. In some cases where the yield stress is defined at uneven intervals of the +independent variable (plastic strain) and the range of the independent variable is large compared to +the smallest interval, Abaqus/Explicit may fail to obtain an accurate regularization of your data in a +reasonable number of intervals. In this case the program will stop after all data are processed with an +error message that you must redefine the material data. See “Material data definition,” Section 21.1.2, +for a more detailed discussion of data regularization. +Input File Usage: +Abaqus/CAE Usage: +*PLASTIC, HARDENING=ISOTROPIC (default if parameter is omitted) +Property module: material editor: Mechanical→Plasticity→Plastic: +Hardening: Isotropic +Johnson-Cook isotropic hardening +Johnson-Cook hardening is a particular type of isotropic hardening where the yield stress is given as an +analytical function of equivalent plastic strain, strain rate, and temperature. This hardening law is suited +for modeling high-rate deformation of many materials including most metals. Hill’s potential function + cannot be used with Johnson-Cook hardening. For more +details, see “Johnson-Cook plasticity,” Section 23.2.7. +Input File Usage: +Abaqus/CAE Usage: +*PLASTIC, HARDENING=JOHNSON COOK +Property module: material editor: Mechanical→Plasticity→Plastic: +Hardening: Johnson-Cook +User subroutine +In Abaqus/Standard the yield stress for isotropic hardening, +user subroutine UHARD. +, can alternatively be described through +Input File Usage: +Abaqus/CAE Usage: +*PLASTIC, HARDENING=USER +Property module: material editor: Mechanical→Plasticity→Plastic: +Hardening: User +Kinematic hardening +Two kinematic hardening models are provided in Abaqus to model the cyclic loading of metals. The +linear kinematic model approximates the hardening behavior with a constant rate of hardening. The +more general nonlinear isotropic/kinematic model will give better predictions but requires more detailed +calibration. For more details, see “Models for metals subjected to cyclic loading,” Section 23.2.2. +Input File Usage: +Use the following option to specify the linear kinematic model: +*PLASTIC, HARDENING=KINEMATIC +Use the following option to specify the nonlinear combined isotropic/kinematic +model: +Abaqus/CAE Usage: +*PLASTIC, HARDENING=COMBINED +Property module: material editor: Mechanical→Plasticity→Plastic: +Hardening: Kinematic or Combined +Flow rule +Abaqus uses associated plastic flow. Therefore, as the material yields, the inelastic deformation rate is +in the direction of the normal to the yield surface (the plastic deformation is volume invariant). This +assumption is generally acceptable for most calculations with metals; the most obvious case where it +is not appropriate is the detailed study of the localization of plastic flow in sheets of metal as the sheet +develops texture and eventually tears apart. So long as the details of such effects are not of interest (or +can be inferred from less detailed criteria, such as reaching a forming limit that is defined in terms of +strain), the associated flow models in Abaqus used with the smooth Mises or Hill yield surfaces generally +predict the behavior accurately. +Rate dependence +As strain rates increase, many materials show an increase in their yield strength. This effect becomes +important in many metals when the strain rates range between 0.1 and 1 per second; and it can be very +important for strain rates ranging between 10 and 100 per second, which are characteristic of high-energy +dynamic events or manufacturing processes. +There are multiple ways to introduce a strain-rate-dependent yield stress. +Direct tabular data +Test data can be provided as tables of yield stress values versus equivalent plastic strain at different +); one table per strain rate. Direct tabular data cannot be used +equivalent plastic strain rates ( +with Johnson-Cook hardening. The guidelines that govern the entry of this data are provided in +“Rate-dependent yield,” Section 23.2.3. +Input File Usage: +Abaqus/CAE Usage: +*PLASTIC, RATE= +Property module: material editor: Mechanical→Plasticity→Plastic: +Use strain-rate-dependent data +Yield stress ratios +Alternatively, you can specify the strain rate dependence by means of a scaling function. In this case you +enter only one hardening curve, the static hardening curve, and then express the rate-dependent hardening +curves in terms of the static relation; that is, we assume that +where +is the static yield stress, +rate, and R is a ratio, defined as +dependent yield,” Section 23.2.3. +is the equivalent plastic strain, +is the equivalent plastic strain +. This method is described further in “Rate- +at +Input File Usage: +Abaqus/CAE Usage: +User subroutine +Use both of the following options: +*PLASTIC (to specify the static yield stress +*RATE DEPENDENT (to specify the ratio +Property module: material editor: Mechanical→Plasticity→Plastic: +Suboptions→Rate Dependent +) +) +In Abaqus/Standard user subroutine UHARD can be used to define a rate-dependent yield stress. You are +provided the current equivalent plastic strain and equivalent plastic strain rate and are responsible for +returning the yield stress and derivatives. +Input File Usage: +Abaqus/CAE Usage: +*PLASTIC, HARDENING=USER +Property module: material editor: Mechanical→Plasticity→Plastic: +Hardening: User +Progressive damage and failure +In Abaqus the metal plasticity material models can be used in conjunction with the progressive damage +and failure models discussed in “Damage and failure for ductile metals: overview,” Section 24.2.1. +The capability allows for the specification of one or more damage initiation criteria, including ductile, +shear, forming limit diagram (FLD), forming limit stress diagram (FLSD), Müschenborn-Sonne forming +limit diagram (MSFLD), and, in Abaqus/Explicit, Marciniak-Kuczynski (M-K) criteria. After damage +initiation, the material stiffness is degraded progressively according to the specified damage evolution +response. The model offers two failure choices, including the removal of elements from the mesh as +a result of tearing or ripping of the structure. The progressive damage models allow for a smooth +degradation of the material stiffness, making them suitable for both quasi-static and dynamic situations. +This is a great advantage over the dynamic failure models discussed next. +Input File Usage: +Use the following options: +Abaqus/CAE Usage: +*PLASTIC +*DAMAGE INITIATION +*DAMAGE EVOLUTION +Property module: material editor: Mechanical→Damage for Ductile +Metals→criterion: Suboptions→Damage Evolution +Shear and tensile dynamic failure in Abaqus/Explicit +In Abaqus/Explicit the metal plasticity material models can be used in conjunction with the shear and +tensile failure models (“Dynamic failure models,” Section 23.2.8) that are applicable in truly dynamic +situations; however, the progressive damage and failure models discussed above are generally preferred. +Shear failure +The shear failure model provides a simple failure criterion that is suitable for high-strain-rate deformation +of many materials including most metals. It offers two failure choices, including the removal of elements +from the mesh as a result of tearing or ripping of the structure. The shear failure criterion is based on the +value of the equivalent plastic strain and is applicable mainly to high-strain-rate, truly dynamic problems. +For more details, see “Dynamic failure models,” Section 23.2.8. +Input File Usage: +Use both of the following options: +*PLASTIC +*SHEAR FAILURE +The shear failure model is not supported in Abaqus/CAE. +Abaqus/CAE Usage: +Tensile failure +The tensile failure model uses the hydrostatic pressure stress as a failure measure to model dynamic spall +or a pressure cutoff. It offers a number of failure choices including element removal. Similarly to the +shear failure model, the tensile failure model is suitable for high-strain-rate deformation of metals and is +applicable to truly dynamic problems. For more details, see “Dynamic failure models,” Section 23.2.8. +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*PLASTIC +*TENSILE FAILURE +The tensile failure model is not supported in Abaqus/CAE. +Heat generation by plastic work +Abaqus optionally allows for plastic dissipation to result +in the heating of a material. Heat +generation is typically used in the simulation of bulk metal forming or high-speed manufacturing +processes involving large amounts of inelastic strain where the heating of the material caused by its +deformation is an important effect because of temperature dependence of the material properties. It is +applicable only to adiabatic thermal-stress analysis (“Adiabatic analysis,” Section 6.5.4), fully coupled +temperature-displacement analysis (“Fully coupled thermal-stress analysis,” Section 6.5.3), or fully +coupled thermal-electrical-structural analysis (“Fully coupled thermal-electrical-structural analysis,” +Section 6.7.4). +This effect is introduced by defining the fraction of the rate of inelastic dissipation that appears as +a heat flux per volume. +Input File Usage: +Use all of the following options in the same material data block: +*PLASTIC +*SPECIFIC HEAT +*DENSITY +*INELASTIC HEAT FRACTION +Use all of the following options for the same material: +Property module: material editor: +Mechanical→Plasticity→Plastic +Thermal→Specific Heat +General→Density +Thermal→Inelastic Heat Fraction +Abaqus/CAE Usage: +Initial conditions +When we need to study the behavior of a material that has already been subjected to some work hardening, +initial equivalent plastic strain values can be provided to specify the yield stress corresponding to the +work hardened state . +*INITIAL CONDITIONS, TYPE=HARDENING +Load module: Create Predefined Field: Step: Initial, choose Mechanical +for the Category and Hardening for the Types for Selected Step +Abaqus/CAE Usage: +Input File Usage: +User subroutine specification in Abaqus/Standard +For more complicated cases, initial conditions can be defined in Abaqus/Standard through user subroutine +HARDINI. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=HARDENING, USER +Load module: Create Predefined Field: Step: Initial, choose +Mechanical for the Category and Hardening for the Types for +Selected Step; Definition: User-defined +Elements +Classical metal plasticity can be used with any elements that include mechanical behavior (elements that +have displacement degrees of freedom). +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Standard output variable +the +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2), +following variable has special meaning for the classical metal plasticity models: +PEEQ +Equivalent plastic strain, +equivalent plastic strain (zero or user-specified; see “Initial conditions”). +where +is the initial +23.2.2 +MODELS FOR METALS SUBJECTED TO CYCLIC LOADING +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Inelastic behavior,” Section 23.1.1 +• “Anisotropic yield/creep,” Section 23.2.6 +• “UHARD,” Section 1.1.35 of the Abaqus User Subroutines Reference Manual +• *CYCLIC HARDENING +• *PLASTIC +• *POTENTIAL +• “Defining classical metal plasticity” in “Defining plasticity,” Section 12.9.2 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +The kinematic hardening models: +• are used to simulate the inelastic behavior of materials that are subjected to cyclic loading; +• include a linear kinematic hardening model and a nonlinear isotropic/kinematic hardening model; +• include a nonlinear isotropic/kinematic hardening model with multiple backstresses; +• can be used in any procedure that uses elements with displacement degrees of freedom; +• in Abaqus/Standard cannot be used in adiabatic analyses, and the nonlinear isotropic/kinematic +hardening model cannot be used in coupled temperature-displacement analyses; +• can be used to model rate-dependent yield; +• can be used with creep and swelling in Abaqus/Standard; and +• require the use of the linear elasticity material model to define the elastic part of the response. +Yield surfaces +The kinematic hardening models used to model the behavior of metals subjected to cyclic loading +are pressure-independent plasticity models; in other words, yielding of the metals is independent of +the equivalent pressure stress. These models are suited for most metals subjected to cyclic loading +conditions, except voided metals. The linear kinematic hardening model can be used with the Mises +or Hill yield surface. The nonlinear isotropic/kinematic model can be used only with the Mises +yield surface in Abaqus/Standard and with the Mises or Hill yield surface in Abaqus/Explicit. The +pressure-independent yield surface is defined by the function +where +to the backstress +is the yield stress and +. For example, the equivalent Mises stress is defined as +is the equivalent Mises stress or Hill’s potential with respect +is the deviatoric stress tensor (defined as +where +equivalent pressure stress, and +tensor. +is the identity tensor) and +, where +is the stress tensor, p is the +is the deviatoric part of the backstress +Flow rule +The kinematic hardening models assume associated plastic flow: +where +equivalent plastic strain is obtained from the following equivalent plastic work expression: +is the equivalent plastic strain rate. The evolution of the +is the rate of plastic flow and +for isotropic Mises plasticity. The assumption of associated plastic flow +which yields +is acceptable for metals subjected to cyclic loading as long as microscopic details, such as localization +of plastic flow occurring as a metal component ruptures due to cyclic fatigue loads, are not of interest. +Hardening +The linear kinematic hardening model has a constant hardening modulus, and the nonlinear +isotropic/kinematic hardening model has both nonlinear kinematic and nonlinear isotropic hardening +components. +Linear kinematic hardening model +The evolution law of this model consists of a linear kinematic hardening component that describes the +translation of the yield surface in stress space through the backstress, +. When temperature dependence +is omitted, this evolution law is the linear Ziegler hardening law +where +the equivalent stress defining the size of the yield surface, +, remains constant, +the equivalent stress defining the size of the yield surface at zero plastic strain. +is the equivalent plastic strain rate and C is the kinematic hardening modulus. In this model +is +, where +Nonlinear isotropic/kinematic hardening model +The evolution law of this model consists of two components: a nonlinear kinematic hardening +component, which describes the translation of the yield surface in stress space through the backstress, +; and an isotropic hardening component, which describes the change of the equivalent stress defining +the size of the yield surface, +, as a function of plastic deformation. +The kinematic hardening component is defined to be an additive combination of a purely kinematic +term (linear Ziegler hardening law) and a relaxation term (the recall term), which introduces the +nonlinearity. In addition, several kinematic hardening components (backstresses) can be superposed, +which may considerably improve results in some cases. When temperature and field variable +dependencies are omitted, the hardening laws for each backstress are +and the overall backstress is computed from the relation +and +is the number of backstresses, and +are material parameters that must be calibrated +where +from cyclic test data. +determine the rate at +are the initial kinematic hardening moduli, and +which the kinematic hardening moduli decrease with increasing plastic deformation. The kinematic +hardening law can be separated into a deviatoric part and a hydrostatic part; only the deviatoric part +has an effect on the material behavior. When +are zero, the model reduces to an isotropic +hardening model. When all +equal zero, the linear Ziegler hardening law is recovered. Calibration +of the material parameters is discussed in “Usage and calibration of the kinematic hardening models,” +below. Figure 23.2.2–1 shows an example of nonlinear kinematic hardening with three backstresses. +Each of the backstresses covers a different range of strains, and the linear hardening law is retained for +large strains. +and +The isotropic hardening behavior of the model defines the evolution of the yield surface size, +. This evolution can be introduced by specifying +, as a +directly +in user subroutine UHARD (in Abaqus/Standard +function of the equivalent plastic strain, +as a function of +only), or by using the simple exponential law +in tabular form, by specifying +where +is the +maximum change in the size of the yield surface, and b defines the rate at which the size of the yield +is the yield stress at zero plastic strain and +and b are material parameters. +[x1.E3] +70. +] +[ +60. +50. +40. +30. +20. +10. += ++ ++ +) +) +4 0 10 1 0( +× +. +. +pl +20 +2 0 10 1 0( +× +. +. +500 +pl +× +4 0 10 +. +pl +0. +0.00 +0.05 +0.10 +0.15 +equivalent plastic strain +0.20 +0.25 +0.30 +Figure 23.2.2–1 Kinematic hardening model with three backstresses. +surface changes as plastic straining develops. When the equivalent stress defining the size of the yield +surface remains constant ( +), the model reduces to a nonlinear kinematic hardening model. +The evolution of the kinematic and the isotropic hardening components is illustrated in +Figure 23.2.2–2 for unidirectional loading and in Figure 23.2.2–3 for multiaxial loading. The evolution +law for the kinematic hardening component implies that the backstress is contained within a cylinder +of radius +at saturation (large plastic +strains). It also implies that any stress point must lie within a cylinder of radius +(using +the notation of Figure 23.2.2–2) since the yield surface remains bounded. At large plastic strain any +stress point is contained within a cylinder of radius +is the equivalent stress +defining the size of the yield surface at large plastic strain. If tabular data are provided for the isotropic +is the last value given to define the size of the yield surface. If user subroutine UHARD +component, +is used, this value will depend on your implementation; otherwise, +is the magnitude of +, where +, where +. +Predicted material behavior +In the kinematic hardening models the center of the yield surface moves in stress space due to the +kinematic hardening component. In addition, when the nonlinear isotropic/kinematic hardening model is +used, the yield surface range may expand or contract due to the isotropic component. These features allow +modeling of inelastic deformation in metals that are subjected to cycles of load or temperature, resulting +in significant inelastic deformation and, possibly, low-cycle fatigue failure. These models account for +the following phenomena: + +max + 0 +0 + 0 + += + 0 + +N C + + +=1 +s +  0 +pl +Figure 23.2.2–2 One-dimensional representation of the hardening +in the nonlinear isotropic/kinematic model. +s3 +limit surface +Ck +∑ +γ= +3 1 +∂F +s1 +s2 +yield surface +Figure 23.2.2–3 Three-dimensional representation of the hardening +in the nonlinear isotropic/kinematic model. +• Bauschinger effect: This effect is characterized by a reduced yield stress upon load reversal +after plastic deformation has occurred during the initial loading. This phenomenon decreases with +continued cycling. The linear kinematic hardening component takes this effect into consideration, +but a nonlinear component improves the shape of the cycles. Further improvement of the shape of +the cycle can be obtained by using a nonlinear model with multiple backstresses. +• Cyclic hardening with plastic shakedown: This phenomenon is characteristic of symmetric +stress- or strain-controlled experiments. Soft or annealed metals tend to harden toward a stable limit, +and initially hardened metals tend to soften. Figure 23.2.2–4 illustrates the behavior of a metal that +hardens under prescribed symmetric strain cycles. +Δε = constant +time +stabilized +plastic shakedown +Δε = constant +Figure 23.2.2–4 Plastic shakedown. +The kinematic hardening component of the models used alone predicts plastic shakedown after one +stress cycle. The combination of the isotropic component together with the nonlinear kinematic +component predicts shakedown after several cycles. +• Ratchetting: Unsymmetric cycles of stress between prescribed limits will cause progressive +“creep” or “ratchetting” in the direction of the mean stress (Figure 23.2.2–5). Typically, transient +ratchetting is followed by stabilization (zero ratchet strain) for low mean stresses, while a constant +increase in the accumulated ratchet strain is observed at high mean stresses. The nonlinear +kinematic hardening component, used without +the isotropic hardening component, predicts +constant ratchet strain. The prediction of ratchetting is improved by adding isotropic hardening, +in which case the ratchet strain may decrease until it becomes constant. However, in general the +nonlinear hardening model with a single backstress predicts a too significant ratchetting effect. +A considerable improvement in modeling ratchetting can be achieved by superposing several +kinematic hardening models (backstresses) and choosing one of the models to be linear or nearly +linear ( +), which results in a less pronounced ratchetting effect. +1 2 +δε +mean +stress +1 2 +δε +ratchet strain +Figure 23.2.2–5 Ratchetting. +• Relaxation of the mean stress: This phenomenon is characteristic of an unsymmetric strain +experiment, as shown in Figure 23.2.2–6. +Figure 23.2.2–6 Relaxation of the mean stress. +As the number of cycles increases, the mean stress tends to zero. The nonlinear kinematic hardening +component of the nonlinear isotropic/kinematic hardening model accounts for this behavior. +Limitations +The linear kinematic model is a simple model that gives only a first approximation of the behavior of +metals subjected to cyclic loading, as explained above. The nonlinear isotropic/kinematic hardening +model can provide more accurate results in many cases involving cyclic loading, but it still has the +following limitations: +• The isotropic hardening is the same at all strain ranges. Physical observations, however, indicate +that the amount of isotropic hardening depends on the magnitude of the strain range. Furthermore, +if the specimen is cycled at two different strain ranges, one followed by the other, the deformation +in the first cycle affects the isotropic hardening in the second cycle. Thus, the model is only a coarse +approximation of actual cyclic behavior. It should be calibrated to the expected size of the strain +cycles of importance in the application. +• The same cyclic hardening behavior is predicted for proportional and nonproportional load +cycles. Physical observations indicate that the cyclic hardening behavior of materials subjected to +nonproportional loading may be very different from uniaxial behavior at a similar strain amplitude. +The example problems “Simple proportional and nonproportional cyclic tests,” Section 3.2.8 of the +Abaqus Benchmarks Manual, “Notched beam under cyclic loading,” Section 1.1.7 of the Abaqus +Example Problems Manual and “Uniaxial ratchetting under tension and compression,” Section 1.1.8 +of the Abaqus Example Problems Manual, illustrate the phenomena of cyclic hardening with plastic +shakedown, ratchetting, and relaxation of the mean stress for the nonlinear isotropic/kinematic +hardening model, as well as its limitations. +Usage and calibration of the kinematic hardening models +The linear kinematic model approximates the hardening behavior with a constant rate of hardening. This +hardening rate should be matched to the average hardening rate measured in stabilized cycles over a +strain range corresponding to that expected in the application. A stabilized cycle is obtained by cycling +over a fixed strain range until a steady-state condition is reached; that is, until the stress-strain curve no +longer changes shape from one cycle to the next. The more general nonlinear model will give better +predictions but requires more detailed calibration. +Linear kinematic hardening model +The test data obtained from a half cycle of a unidirectional tension or compression experiment must be +linearized, since this simple model can predict only linear hardening. The data are usually based on +measurements of the stabilized behavior in strain cycles covering a strain range corresponding to the +strain range that is anticipated to occur in the application. Abaqus expects you to provide only two data +pairs to define this linear behavior: the yield stress, +, at +a finite plastic strain value, +. The linear kinematic hardening modulus, C, is determined from the +relation +, at zero plastic strain and a yield stress, +You can provide several sets of two data pairs as a function of temperature to define the variation of +the linear kinematic hardening modulus with respect to temperature. If the Hill yield surface is desired +for this model, you must specify a set of yield ratios, +, independently . +This model gives physically reasonable results for only relatively small strains (less than 5%). +Input File Usage: +Abaqus/CAE Usage: +*PLASTIC, HARDENING=KINEMATIC +Property module: material editor: Mechanical→Plasticity→Plastic: +Hardening: Kinematic +Nonlinear isotropic/kinematic hardening model +, as a function of the +The evolution of the equivalent stress defining the size of the yield surface, +equivalent plastic strain, +, defines the isotropic hardening component of the model. You can define +this isotropic hardening component through an exponential law or directly in tabular form. It need not +be defined if the yield surface remains fixed throughout the loading. +In Abaqus/Explicit if the Hill +yield surface is desired for this model, you must specify a set of yield ratios, +, independently . The Hill +yield surface cannot be used with this model in Abaqus/Standard. +and +The material parameters +determine the kinematic hardening component of the model. +Abaqus offers three different ways of providing data for the kinematic hardening component of the +model: the parameters +can be specified directly, half-cycle test data can be given, or test +data obtained from a stabilized cycle can be given. The experiments required to calibrate the model are +described below. +and +Defining the isotropic hardening component by the exponential law +Specify the material parameters of the exponential law +, and b directly if they are already +calibrated from test data. These parameters can be specified as functions of temperature and/or field +variables. +, +Input File Usage: +Abaqus/CAE Usage: +*CYCLIC HARDENING, PARAMETERS +Property module: material editor: Mechanical→Plasticity→Plastic: +Suboptions→Cyclic Hardening: toggle on Use parameters. +Defining the isotropic hardening component by tabular data +, as a tabular function of the equivalent plastic strain, +Isotropic hardening can be introduced by specifying the equivalent stress defining the size of the yield +surface, +. The simplest way to obtain these +data is to conduct a symmetric strain-controlled cyclic experiment with strain range +. Since the +material’s elastic modulus is large compared to its hardening modulus, this experiment can be interpreted +approximately as repeated cycles over the same plastic strain range +(using the +notation of Figure 23.2.2–7, where E is the Young’s modulus of the material). The equivalent stress +defining the size of the yield surface is +at zero equivalent plastic strain; for the peak tensile stress +points it is obtained by isolating the kinematic component from the yield stress as +for each cycle i, where +value in each cycle at a particular strain level, +corresponding to +is +. Since the model predicts approximately the same backstress +. The equivalent plastic strain +εpl +εpl +Δεpl + = +εpl +εpl − εpl +Figure 23.2.2–7 Symmetric strain cycle experiment. +, +Data pairs ( +), including the value +at zero equivalent plastic strain, are specified in +tabulated form. The tabulated values defining the size of the yield surface should be provided for the +entire equivalent plastic strain range to which the material may be subjected. The data can be provided +as functions of temperature and/or field variables. +To obtain accurate cyclic hardening data, such as would be needed for low-cycle fatigue +calculations, the calibration experiment should be performed at a strain range, +, that corresponds +to the strain range anticipated in the analysis because the material model does not predict different +isotropic hardening behavior at different strain ranges. This limitation also implies that, even though a +component is made from the same material, it may have to be divided into several regions with different +hardening properties corresponding to different anticipated strain ranges. Field variables and field +variable dependence of these properties can also be used for this purpose. +Abaqus allows the specification of strain rate effects in the isotropic component of the nonlinear +isotropic/kinematic hardening model. The rate-dependent isotropic hardening data can be defined by +, as a tabular function of the +specifying the equivalent stress defining the size of the yield surface, +equivalent plastic strain, +, at different values of the equivalent plastic strain rate, +. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to define isotropic hardening with tabular data: +*CYCLIC HARDENING +Use the following option to define rate-dependent isotropic hardening with +tabular data: +*CYCLIC HARDENING, RATE= +Property module: material editor: Mechanical→Plasticity→Plastic: +Hardening: Combined: Suboptions→Cyclic Hardening +Defining the isotropic hardening component in a user subroutine in Abaqus/Standard +directly in user subroutine UHARD. +Specify +may be dependent on equivalent plastic strain and +temperature. This method cannot be used if the kinematic hardening component is specified by using +half-cycle test data. +Input File Usage: +Abaqus/CAE Usage: +*CYCLIC HARDENING, USER +You cannot define the isotropic hardening component in user subroutine UHARD +in Abaqus/CAE. +Defining the kinematic hardening component by specifying the material parameters directly +and +can be specified directly as a function of temperature and/or field variables +The parameters +if they are already calibrated from test data. When +depend on temperature and/or field variables, +the response of the model under thermomechanical loading will generally depend on the history of +temperature and/or field variables experienced at a material point. This dependency on temperature- +history is small and fades away with increasing plastic deformation. However, if this effect is not desired, +constant values for +should be specified to make the material response completely independent of +the history of temperature and field variables. The algorithm currently used to integrate the nonlinear +isotropic/kinematic hardening model provides accurate solutions if the values of +change moderately +in an increment due to temperature and/or field variable dependence; however, this algorithm may not +yield a solution with sufficient accuracy if the values of +change abruptly in an increment. +Input File Usage: +Abaqus/CAE Usage: +*PLASTIC, HARDENING=COMBINED, DATA TYPE=PARAMETERS, +NUMBER BACKSTRESSES=n +Property module: material editor: Mechanical→Plasticity→Plastic: +Hardening: Combined, Data type: Parameters, Number +of backstresses: n +Defining the kinematic hardening component by specifying half-cycle test data +can be based on the stress-strain data obtained from the first +If limited test data are available, +half cycle of a unidirectional tension or compression experiment. An example of such test data is shown +in Figure 23.2.2–8. This approach is usually adequate when the simulation will involve only a few cycles +of loading. +and +For each data point ( +) a value of +( +is the overall backstress obtained by summing all the +backstresses at this data point) is obtained from the test data as +where +hardening component or the initial yield stress if the isotropic hardening component is not defined. +is the user-defined size of the yield surface at the corresponding plastic strain for the isotropic +Integration of the backstress evolution laws over a half cycle yields the expressions +3, εpl +1, εpl +2, εpl +σ +εpl +Figure 23.2.2–8 Half cycle of stress-strain data. +which are used for calibrating +and +. +, +,..., +When test data are given as functions of temperature and/or field variables, Abaqus determines +several sets of material parameters ( +), each corresponding to a given combination of +, +temperature and/or field variables. Generally, this results in temperature-history (and/or field variable- +history) dependent material behavior because the values of +vary with changes in temperature and/or +field variables. This dependency on temperature-history is small and fades away with increasing plastic +deformation. However, you can make the response of the material completely independent of the history +of temperature and field variables by using constant values for the parameters +. This can be achieved +by running a data check analysis first; an appropriate constant values of +can be determined from the +information provided in the data file during the data check. The values for the parameters +and the +constant parameters +can then be entered directly as described above. +If the model with multiple backstresses is used, Abaqus obtains hardening parameters for different +values of initial guesses and chooses the ones that give the best correlation with the experimental data +provided. However, you should carefully examine the obtained parameters. In some cases it might be +advantageous to obtain hardening parameters for different numbers of backstresses before choosing the +set of parameters. +Input File Usage: +*PLASTIC, HARDENING=COMBINED, DATA TYPE=HALF +CYCLE, NUMBER BACKSTRESSES=n +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Plasticity→Plastic: +Hardening: Combined, Data type: Half Cycle, Number +of backstresses: n +Defining the kinematic hardening component by specifying test data from a stabilized cycle +Stress-strain data can be obtained from the stabilized cycle of a specimen that is subjected to symmetric +strain cycles. A stabilized cycle is obtained by cycling the specimen over a fixed strain range +until a +steady-state condition is reached; that is, until the stress-strain curve no longer changes shape from one +cycle to the next. Such a stabilized cycle is shown in Figure 23.2.2–9. Each data pair ( +) must be +specified with the strain axis shifted to +, so that +and, thus, +. +Δε +pl += ε +i − +σi − +Figure 23.2.2–9 Stress-strain data for a stabilized cycle. +For each pair ( +) values of +backstresses at this data point) are obtained from the test data as +( +is the overall backstress obtained by summing all the +where +is the stabilized size of the yield surface. +Integration of the backstress evolution laws over this uniaxial strain cycle, with an exact match for +the first data pair ( +), provides the expressions +where +above equations enable calibration of the parameters +denotes the +and +. +backstress at the first data point (initial value of the +backstress). The +If the shapes of the stress-strain curves are significantly different for different strain ranges, you may +want to obtain several calibrated values of +. The tabular data of the stress-strain curves obtained +at different strain ranges can be entered directly in Abaqus. Calibrated values corresponding to each +strain range are reported in the data file, together with an averaged set of parameters, if model definition +data are requested (see “Controlling the amount of analysis input file processor information written to the +and +, +,..., +data file” in “Output,” Section 4.1.1). Abaqus will use the averaged set in the analysis. These parameters +may have to be adjusted to improve the match to the test data at the strain range anticipated in the analysis. +When test data are given as functions of temperature and/or field variables, Abaqus determines +several sets of material parameters ( +), each corresponding to a given combination of +, +temperature and/or field variables. Generally, this results in temperature-history (and/or field variable- +history) dependent material behavior because the values of +vary with changes in temperature and/or +field variables. This dependency on temperature-history is small and fades away with increasing plastic +deformation. However, you can make the response of the material completely independent of the history +of temperature and field variables by using constant values for the parameters +. This can be achieved +by running a data check analysis first; an appropriate constant values of +can be determined from the +information provided in the data file during the data check. The values for the parameters +and the +constant parameters +can then be entered directly as described above. +If the model with multiple backstresses is used, Abaqus obtains hardening parameters for different +values of initial guesses and chooses the ones that give the best correlation with the experimental data +provided. However, you should carefully examine the obtained parameters. In some cases it might be +advantageous to obtain hardening parameters for different numbers of backstresses before choosing the +set of parameters. +The isotropic hardening component should be defined by specifying the equivalent stress defining +the size of the yield surface at zero plastic strain, as well as the evolution of the equivalent stress as a +function of equivalent plastic strain. If this component is not defined, Abaqus will assume that no cyclic +hardening occurs so that the equivalent stress defining the size of the yield surface is constant and equal +to +(or the average of these quantities over several strain ranges when more than one strain +range is provided). Since this size corresponds to the size of a saturated cycle, this is unlikely to provide +accurate predictions of actual behavior, particularly in the initial cycles. +Input File Usage: +*PLASTIC, HARDENING=COMBINED, DATA TYPE=STABILIZED, +NUMBER BACKSTRESSES=n +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Plasticity→Plastic: +Hardening: Combined, Data type: Stabilized, Number +of backstresses: n +Initial conditions +When we need to study the behavior of a material that has already been subjected to some hardening, +Abaqus allows you to prescribe initial conditions for the equivalent plastic strain, +, and for the +backstresses, +. When the nonlinear isotropic/kinematic hardening model is used, the initial conditions +for each backstress, +, must satisfy the condition +for the model to produce a kinematic hardening response. Abaqus allows the specification of initial +backstresses that violate these conditions. However, in this case the response corresponding to the +backstress for which the condition is violated produces kinematic softening response: the magnitude +of the backstress decreases with plastic straining from its initial value to the saturation value. If the +condition is violated for any of the backstresses, the overall response of the material is not guaranteed to +produce kinematic hardening response. The initial condition for the backstress has no limitations when +the linear kinematic hardening model is used. +You can specify the initial values of +directly as initial conditions . +Input File Usage: +*INITIAL CONDITIONS, TYPE=HARDENING, NUMBER +BACKSTRESSES=n +Abaqus/CAE Usage: +Load module: Create Predefined Field: Step: Initial, choose +Mechanical for the Category and Hardening for the Types for +Selected Step; Number of backstresses: n +User subroutine specification in Abaqus/Standard +For more complicated cases in Abaqus/Standard initial conditions can be defined through user subroutine +HARDINI. +Input File Usage: +*INITIAL CONDITIONS, TYPE=HARDENING, USER, +NUMBER BACKSTRESSES=n +Abaqus/CAE Usage: +Load module: Create Predefined Field: Step: Initial, choose Mechanical +for the Category and Hardening for the Types for Selected Step; +Definition: User-defined, Number of backstresses: n +Elements +These models can be used with elements in Abaqus/Standard that include mechanical behavior (elements +that have displacement degrees of freedom), except some beam elements in space. Beam elements in +space that include shear stress caused by torsion (i.e., not thin-walled, open sections) and do not include +hoop stress (i.e., not PIPE elements) cannot be used. In Abaqus/Explicit the kinematic hardening models +can be used with any elements that include mechanical behavior, with the exception of one-dimensional +elements (beams, pipes, and trusses) when the models are used with the Hill yield surface. +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2), +the +following variables have special meaning for the kinematic hardening models: +Total kinematic hardening shift tensor components, +kinematic hardening shift tensor components ( +. +). +All tensor components of all the kinematic hardening shift tensors, except the total +shift tensor. +Equivalent plastic strain, +equivalent plastic strain (zero or user-specified; see “Initial conditions”). +is the initial +where +23.2.2–15 +ALPHA +ALPHAk +ALPHAN +PENER +Plastic work, defined as: +. This quantity is not guaranteed +to be monotonically increasing for kinematic hardening models. To get a quantity +that is monotonically increasing, the plastic dissipation needs to be computed as: +. In Abaqus/Standard this quantity can be computed +as a user-defined output variable in user subroutine UVARM. +23.2.3 +RATE-DEPENDENT YIELD +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Classical metal plasticity,” Section 23.2.1 +• “Models for metals subjected to cyclic loading,” Section 23.2.2 +• “Johnson-Cook plasticity,” Section 23.2.7 +• “Extended Drucker-Prager models,” Section 23.3.1 +• “Crushable foam plasticity models,” Section 23.3.5 +• “Material library: overview,” Section 21.1.1 +• “Inelastic behavior,” Section 23.1.1 +• *RATE DEPENDENT +• “Defining rate-dependent yield with yield stress ratios” in “Defining plasticity,” Section 12.9.2 of +the Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +Rate-dependent yield: +• is needed to define a material’s yield behavior accurately when the yield strength depends on the +rate of straining and the anticipated strain rates are significant; +• is available only for the isotropic hardening metal plasticity models (Mises and Johnson-Cook), the +isotropic component of the nonlinear isotropic/kinematic plasticity models, the extended Drucker- +Prager plasticity model, and the crushable foam plasticity model; +• can be conveniently defined on the basis of work hardening parameters and field variables by +providing tabular data for the isotropic hardening metal plasticity models, the isotropic component +of the nonlinear isotropic/kinematic plasticity models, and the extended Drucker-Prager plasticity +model; +• can be defined through specification of user-defined overstress power law parameters, yield stress +ratios, or Johnson-Cook rate dependence parameters (this last option is not available for the +crushable foam plasticity model and is the only option available for the Johnson-Cook plasticity +model); +• cannot be used with any of the Abaqus/Standard creep models (metal creep, time-dependent +volumetric swelling, Drucker-Prager creep, or cap creep) since creep behavior is already a +rate-dependent mechanism; and +• in dynamic analysis should be specified such that the yield stress increases with increasing strain +rate. +Work hardening dependencies +Generally, a material’s yield stress, +for the crushable foam model), is dependent on work +hardening, which for isotropic hardening models is usually represented by a suitable measure of +equivalent plastic strain, +; and predefined field variables, +; the inelastic strain rate, +; temperature, +(or +: +Many materials show an increase in their yield strength as strain rates increase; this effect becomes +important in many metals and polymers when the strain rates range between 0.1 and 1 per second, and it +can be very important for strain rates ranging between 10 and 100 per second, which are characteristic +of high-energy dynamic events or manufacturing processes. +Defining hardening dependencies for various material models +Strain rate dependence can be defined by entering hardening curves at different strain rates directly or +by defining yield stress ratios to specify the rate dependence independently. +Direct entry of test data +Work hardening dependencies can be given quite generally as tabular data for the isotropic hardening +Mises plasticity model, the isotropic component of the nonlinear isotropic/kinematic hardening model, +and the extended Drucker-Prager plasticity model. The test data are entered as tables of yield stress +values versus equivalent plastic strain at different equivalent plastic strain rates. The yield stress must be +given as a function of the equivalent plastic strain and, if required, of temperature and of other predefined +field variables. In defining this dependence at finite strains, “true” (Cauchy) stress and log strain values +should be used. The hardening curve at each temperature must always start at zero plastic strain. For +perfect plasticity only one yield stress, with zero plastic strain, should be defined at each temperature. It +is possible to define the material to be strain softening as well as strain hardening. The work hardening +data are repeated as often as needed to define stress-strain curves at different strain rates. The yield stress +at a given strain and strain rate is interpolated directly from these tables. +Input File Usage: +Use one of the following options: +*PLASTIC, HARDENING=ISOTROPIC, RATE= +*CYCLIC HARDENING, RATE= +*DRUCKER PRAGER HARDENING, RATE= +Use one of the following models: +Abaqus/CAE Usage: +Property module: material editor: +Mechanical→Plasticity→Plastic: Hardening: Isotropic, +Use strain-rate-dependent data +Mechanical→Plasticity→Drucker Prager: Suboptions→Drucker +Prager Hardening: Use strain-rate-dependent data +Cyclic hardening is not supported in Abaqus/CAE. +Using yield stress ratios +Alternatively, and as the only means of defining rate-dependent yield stress for the Johnson-Cook and +the crushable foam plasticity models, the strain rate behavior can be assumed to be separable, so that the +stress-strain dependence is similar at all strain rate levels: +where +(or +in the foam model) is the static stress-strain behavior and +is the ratio of the yield stress at nonzero strain rate to the static yield stress (so that +). +Three methods are offered to define R in Abaqus: specifying an overstress power law, defining R +directly as a tabular function, or specifying an analytical Johnson-Cook form to define R. +Overstress power law +The Cowper-Symonds overstress power law has the form +where +and +of other predefined field variables. +are material parameters that can be functions of temperature and, possibly, +Input File Usage: +Abaqus/CAE Usage: +*RATE DEPENDENT, TYPE=POWER LAW +Property module: material editor: Suboptions→Rate Dependent: +Hardening: Power Law (available for valid plasticity models) +Tabular function +Alternatively, R can be entered directly as a tabular function of the equivalent plastic strain rate (or the +axial plastic strain rate in a uniaxial compression test for the crushable foam model), +; temperature, +; and field variables, +. +Input File Usage: +Abaqus/CAE Usage: +*RATE DEPENDENT, TYPE=YIELD RATIO +Property module: material editor: Suboptions→Rate Dependent: +Hardening: Yield Ratio (available for valid plasticity models) +Johnson-Cook rate dependence +Johnson-Cook rate dependence has the form +where +and C are material constants that do not depend on temperature and are assumed not to +depend on predefined field variables. Johnson-Cook rate dependence can be used in conjunction with +the Johnson-Cook plasticity model, the isotropic hardening metal plasticity models, and the extended +Drucker-Prager plasticity model (it cannot be used in conjunction with the crushable foam plasticity +model). +This is the only form of rate dependence available for the Johnson-Cook plasticity model. For more +details, see “Johnson-Cook plasticity,” Section 23.2.7. +Input File Usage: +Abaqus/CAE Usage: +*RATE DEPENDENT, TYPE=JOHNSON COOK +Property module: material editor: Suboptions→Rate Dependent: +Hardening: Johnson-Cook (available for valid plasticity models) +Elements +Rate-dependent yield can be used with all elements that include mechanical behavior (elements that have +displacement degrees of freedom). +23.2.4 +RATE-DEPENDENT PLASTICITY: CREEP AND SWELLING +Products: Abaqus/Standard Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Inelastic behavior,” Section 23.1.1 +• “Defining the gasket behavior directly using a gasket behavior model,” Section 32.6.6 +• *CREEP +• *CREEP STRAIN RATE CONTROL +• *POTENTIAL +• *SWELLING +• *RATIOS +• “Defining a creep law” in “Defining plasticity,” Section 12.9.2 of the Abaqus/CAE User’s Manual, +in the online HTML version of this manual +• “Defining swelling” in “Defining plasticity,” Section 12.9.2 of the Abaqus/CAE User’s Manual, in +the online HTML version of this manual +Overview +The classical deviatoric metal creep behavior in Abaqus/Standard: +• can be defined using user subroutine CREEP or by providing parameters as input for some simple +creep laws; +• can model either isotropic creep (using Mises stress potential) or anisotropic creep (using Hill’s +anisotropic stress potential); +• is active only during steps using the coupled temperature-displacement procedure, the transient soils +consolidation procedure, and the quasi-static procedure; +• requires that the material’s elasticity be defined as linear elastic behavior; +• can be modified to implement the auxiliary creep hardening rules specified in Nuclear Standard +NEF 9-5T, “Guidelines and Procedures for Design of Class 1 Elevated Temperature Nuclear +System Components”; these rules are exercised by means of a constitutive model developed by +Oak Ridge National Laboratory (“ORNL – Oak Ridge National Laboratory constitutive model,” +Section 23.2.12); +• can be used in combination with creep strain rate control in analyses in which the creep strain rate +must be kept within a certain range; and +• can potentially result in errors in calculated creep strains if anisotropic creep and plasticity occur +simultaneously (discussed below). +Rate-dependent gasket behavior in Abaqus/Standard: +• uses unidirectional creep as part of the model of the gasket’s thickness-direction behavior; +• can be defined using user subroutine CREEP or by providing parameters as input for some simple +creep laws; +• is active only during steps using the quasi-static procedure; and +• requires that an elastic-plastic model be used to define the rate-independent part of the thickness- +direction behavior of the gasket. +Volumetric swelling behavior in Abaqus/Standard: +• can be defined using user subroutine CREEP or by providing tabular input; +• can be either isotropic or anisotropic; +• is active only during steps using the coupled temperature-displacement procedure, the transient soils +consolidation procedure, and the quasi-static procedure; and +• requires that the material’s elasticity be defined as linear elastic behavior. +Creep behavior +Creep behavior is specified by the equivalent uniaxial behavior—the creep “law.” In practical cases creep +laws are typically of very complex form to fit experimental data; therefore, the laws are defined with +user subroutine CREEP, as discussed below. Alternatively, two common creep laws are provided in +Abaqus/Standard: the power law and the hyperbolic-sine law models. These standard creep laws are +used for modeling secondary or steady-state creep. Creep is defined by including creep behavior in the +material model definition (“Material data definition,” Section 21.1.2). Alternatively, creep can be defined +in conjunction with gasket behavior to define the rate-dependent behavior of a gasket. +Input File Usage: +Use the following options to include creep behavior in the material model +definition: +*MATERIAL +*CREEP +Use the following options to define creep in conjunction with gasket behavior: +*GASKET BEHAVIOR +*CREEP +Property module: material editor: Mechanical→Plasticity→Creep +Abaqus/CAE Usage: +Choosing a creep model +The power-law creep model is attractive for its simplicity. However, it is limited in its range of +application. The time-hardening version of the power-law creep model is typically recommended +only in cases when the stress state remains essentially constant. The strain-hardening version of +power-law creep should be used when the stress state varies during an analysis. +In the case where +the stress is constant and there are no temperature and/or field dependencies, the time-hardening and +the stresses should be relatively low. +CREEP AND SWELLING +In regions of high stress, such as around a crack tip, the creep strain rates frequently show an +exponential dependence of stress. The hyperbolic-sine creep law shows exponential dependence on the +stress, +is the yield stress) and reduces to the power-law at +low stress levels (with no explicit time dependence). +, at high stress levels ( +, where +None of the above models is suitable for modeling creep under cyclic loading. The ORNL model +(“ORNL – Oak Ridge National Laboratory constitutive model,” Section 23.2.12) is an empirical model +for stainless steel that gives approximate results for cyclic loading without having to perform the cyclic +loading numerically. Generally, creep models for cyclic loading are complicated and must be added to +a model with user subroutine CREEP or with user subroutine UMAT. +Modeling simultaneous creep and plasticity +If creep and plasticity occur simultaneously and implicit creep integration is in effect, both behaviors +may interact and a coupled system of constitutive equations needs to be solved. If creep and plasticity +are isotropic, Abaqus/Standard properly takes into account such coupled behavior, even if the elasticity +is anisotropic. However, if creep and plasticity are anisotropic, Abaqus/Standard integrates the creep +equations without taking plasticity into account, which may lead to substantial errors in the creep +strains. This situation develops only if plasticity and creep are active at the same time, such as +would occur during a long-term load increase; one would not expect to have a problem if there is a +short-term preloading phase in which plasticity dominates, followed by a creeping phase in which no +further yielding occurs. +Integration of the creep laws and rate-dependent plasticity are discussed in +“Rate-dependent metal plasticity (creep),” Section 4.3.4 of the Abaqus Theory Manual. +Power-law model +The power-law model can be used in its “time hardening” form or in the corresponding “strain hardening” +form. +Time hardening form +The “time hardening” form is the simpler of the two forms of the power-law model: +where +A, n, and m +is the uniaxial equivalent creep strain rate, +is the uniaxial equivalent deviatoric stress, +is the total time, and +are defined by you as functions of temperature. +is Mises equivalent stress or Hill’s anisotropic equivalent deviatoric stress according to whether +isotropic or anisotropic creep behavior is defined (discussed below). For physically reasonable behavior +A and n must be positive and +. Since total time is used in the expression, such reasonable +behavior also typically requires that small step times compared to the creep time be used for any steps +for which creep is not active in an analysis; this is necessary to avoid changes in hardening behavior in +subsequent steps. +Input File Usage: +Abaqus/CAE Usage: +*CREEP, LAW=TIME +Property module: material editor: Mechanical→Plasticity→Creep: +Law: Time-Hardening +Strain hardening form +The “strain hardening” form of the power law is +where +and +are defined above and +is the equivalent creep strain. +Input File Usage: +Abaqus/CAE Usage: +*CREEP, LAW=STRAIN +Property module: material editor: Mechanical→Plasticity→Creep: +Law: Strain-Hardening +Numerical difficulties +Depending on the choice of units for either form of the power law, the value of A may be very small for +typical creep strain rates. If A is less than 10−27 , numerical difficulties can cause errors in the material +calculations; therefore, use another system of units to avoid such difficulties in the calculation of creep +strain increments. +Hyperbolic-sine law model +The hyperbolic-sine law is available in the form +where +and +A, B, and n +are defined above, +is the temperature, +is the user-defined value of absolute zero on the temperature scale used, +is the activation energy, +is the universal gas constant, and +are other material parameters. +This model includes temperature dependence, which is apparent in the above expression; however, the +parameters A, B, n, +, and R cannot be defined as functions of temperature. +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*CREEP, LAW=HYPERB +*PHYSICAL CONSTANTS, ABSOLUTE ZERO= +Define both of the following: +Property module: material editor: Mechanical→Plasticity→Creep: +Law: Hyperbolic-Sine +Any module: Model→Edit Attributes→model_name: +Absolute zero temperature +Numerical difficulties +As with the power law, A may be very small for typical creep strain rates. If A is very small (such as less +than 10−27), use another system of units to avoid numerical difficulties in the calculation of creep strain +increments. +Anisotropic creep +Anisotropic creep can be defined to specify the stress ratios that appear in Hill’s function. You must +define the ratios +in each direction that will be used to scale the stress value when the creep strain rate +is calculated. The ratios can be defined as constant or dependent on temperature and other predefined field +variables. The ratios are defined with respect to the user-defined local material directions or the default +directions . Further details are provided in “Anisotropic yield/creep,” +Section 23.2.6. Anisotropic creep is not available when creep is used to define a rate-dependent gasket +behavior since only the gasket thickness-direction behavior can have rate-dependent behavior. +Input File Usage: +Abaqus/CAE Usage: +*POTENTIAL +Property module: material editor: Mechanical→Plasticity→Creep: +Suboptions→Potential +Volumetric swelling behavior +As with the creep laws, volumetric swelling laws are usually complex and are most conveniently specified +in user subroutine CREEP as discussed below. However, a means of tabular input is also provided for +the form +where +are predefined fields such as +irradiation fluxes in cases involving nuclear radiation effects. Up to six predefined fields can be specified. +is the volumetric strain rate caused by swelling and +, +, +Volumetric swelling cannot be used to define a rate-dependent gasket behavior. +Input File Usage: +Abaqus/CAE Usage: +*SWELLING +Property module: material editor: Mechanical→Plasticity→Swelling +Anisotropic swelling +Anisotropy can easily be included in the swelling behavior. If anisotropic swelling behavior is defined, +the anisotropic swelling strain rate is expressed as +is the volumetric swelling strain rate that you define either directly (discussed above) or in user +where +subroutine CREEP. The ratios +are also user-defined. The directions of the components +of the swelling strain rate are defined by the local material directions, which can be either user-defined +or the default directions . +, and +, +Input File Usage: +Use both of the following options: +*SWELLING +*RATIOS +Property module: material editor: Mechanical→Plasticity→Swelling: +Suboptions→Ratios +Abaqus/CAE Usage: +User subroutine CREEP +User subroutine CREEP provides a very general capability for implementing viscoplastic models +such as creep and swelling models in which the strain rate potential can be written as a function of +equivalent pressure stress, p; the Mises or Hill’s equivalent deviatoric stress, +; and any number of +solution-dependent state variables. Solution-dependent state variables are used in conjunction with +the constitutive definition; their values evolve with the solution and can be defined in this subroutine. +Examples are hardening variables associated with the model. +The user subroutine can also be used to define very general rate- and time-dependent thickness- +direction gasket behavior. When an even more general form is required for the strain rate potential, user +subroutine UMAT (“User-defined mechanical material behavior,” Section 26.7.1) can be used. +Input File Usage: +Use one or both of the following options. Only the first option can be used to +define gasket behavior. +Abaqus/CAE Usage: +*CREEP, LAW=USER +*SWELLING, LAW=USER +Use one or both of the following models. Only the first model can be used to +define gasket behavior. +Property module: material editor: +Mechanical→Plasticity→Creep: Law: User defined +Mechanical→Plasticity→Swelling: Law: User subroutine CREEP +Removing creep effects in an analysis step +You can specify that no creep (or viscoelastic) response can occur during certain analysis steps, even if +creep (or viscoelastic) material properties have been defined. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options: +*COUPLED TEMPERATURE-DISPLACEMENT, CREEP=NONE +*SOILS, CONSOLIDATION, CREEP=NONE +Use one of the following options: +Step module: Create Step: +Coupled temp-displacement: toggle off Include creep/swelling/ +viscoelastic behavior +Soils: Pore fluid response: Transient consolidation: toggle off +Include creep/swelling/viscoelastic behavior +Integration +Explicit integration, implicit integration, or both integration schemes can be used in a creep analysis, +depending on the procedure used, the parameters specified for the procedure, the presence of plasticity, +and whether or not geometric nonlinearity is requested. +Application of explicit and implicit schemes +Nonlinear creep problems are often solved efficiently by forward-difference integration of the inelastic +strains (the “initial strain” method). This explicit method is computationally efficient because, unlike +implicit methods, iteration is not required. Although this method is only conditionally stable, the +numerical stability limit of the explicit operator is usually sufficiently large to allow the solution to be +developed in a small number of time increments. +Abaqus/Standard uses either an explicit or an implicit integration scheme or switches from explicit +to implicit in the same step. These schemes are outlined first, followed by a description of which +procedures use these integration schemes. +1. Integration scheme 1: Starts with explicit integration and switches to implicit integration based on +either stability or if plasticity is active. The stability limit used in explicit integration is discussed +in the next section. +2. Integration scheme 2: Starts with explicit integration and switches to implicit integration when +plasticity is active. The stability criterion does not play a role here. +3. Integration scheme 3: Always uses implicit integration. +The use of the above integration schemes is determined by the procedure type, your choice of +the integration type to be used, as well as whether or not geometric nonlinearity is requested. For +quasi-static and coupled temperature-displacement procedures, if you do not choose an integration type, +integration scheme 1 is used for a geometrically linear analysis and integration scheme 3 is used for a +geometrically nonlinear analysis. You can force Abaqus/Standard to use explicit integration for creep and +swelling effects in coupled temperature-displacement or quasi-static procedures, when plasticity is not +active throughout the step (integration scheme 2). Explicit integration can be used regardless of whether +or not geometric nonlinearity has been requested . +For a transient soils consolidation procedure, the implicit integration scheme (integration scheme 3) +is always used, irrespective of whether a geometrically linear or nonlinear analysis is performed. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options to restrict Abaqus/Standard to using explicit +integration: +*VISCO, CREEP=EXPLICIT +*COUPLED TEMPERATURE-DISPLACEMENT, CREEP=EXPLICIT +Use one of the following options to restrict Abaqus/Standard to using explicit +integration: +Step module: Create Step: +Visco: Incrementation: Creep/swelling/viscoelastic integration: +Explicit +Coupled temp-displacement: toggle on Include creep/swelling/ +viscoelastic behavior: Incrementation: Creep/swelling/viscoelastic +integration: Explicit +Automatic monitoring of stability limit during explicit integration +Abaqus/Standard monitors the stability limit automatically during explicit integration. If, at any point +in the model, the creep strain increment +is larger than the total elastic strain, the problem will +become unstable. Therefore, a stable time step, +, is calculated every increment by +where +equivalent creep strain rate at time t. Furthermore, +is the equivalent total elastic strain at time t, the beginning of the increment, and +is the +where +is the Mises stress at time t, and +where +is the gradient of the deviatoric stress potential, +is the elasticity matrix, and +is an effective elastic modulus—for isotropic elasticity +by Young’s modulus. +can be approximated +, is +compared to the critical time increment, +, which is calculated as follows: +CREEP AND SWELLING +The quantity errtol is an error tolerance that you define as discussed below. If +is +used as the time increment, which would mean that the stability criterion was limiting the size of the time +step further than required by accuracy considerations. Abaqus/Standard will automatically switch to the +backward difference operator (the implicit method, which is unconditionally stable) if +is less than +for nine consecutive increments, you have not restricted Abaqus/Standard to explicit integration as +). The stiffness matrix +discussed above, and there is sufficient time left in the analysis (time left +will be reformed at every iteration if the implicit algorithm is used. +is less than +, +Specifying the tolerance for automatic incrementation +The integration tolerance must be chosen so that increments in stress, +Consider a one-dimensional example. The stress increment, +, is +, are calculated accurately. +where +E is the elastic modulus. For +, and +are the uniaxial elastic, total, and creep strain increments, respectively, and +to be calculated accurately, the error in the creep strain increment, +, +, must be small compared to +; that is, +Measuring the error in +as +leads to +You define errtol for the applicable procedure by choosing an acceptable stress error tolerance and +dividing this by a typical elastic modulus; therefore, it should be a small fraction of the ratio of the typical +stress and the effective elastic modulus in a problem. It is important to recognize that this approach for +selecting a value for errtol is often very conservative, and acceptable solutions can usually be obtained +with higher values. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options: +*VISCO, CETOL=errtol +*COUPLED TEMPERATURE-DISPLACEMENT, CETOL=errtol +*SOILS, CONSOLIDATION, CETOL=errtol +Use one of the following options: +Step module: Create Step: +Visco: Incrementation: toggle on Creep/swelling/viscoelastic strain error +tolerance, and enter a value +Coupled temp-displacement: toggle on Include creep/swelling/ +viscoelastic behavior: Incrementation: toggle on Creep/swelling/ +viscoelastic strain error tolerance, and enter a value +Soils: Pore fluid response: Transient consolidation: toggle on Include +creep/swelling/viscoelastic behavior: Incrementation: toggle on +Creep/swelling/viscoelastic strain error tolerance, and enter a value +Loading control using creep strain rate +In superplastic forming a controllable pressure is applied to deform a body. Superplastic materials can +deform to very large strains, provided that the strain rates of the deformation are maintained within +very tight tolerances. The objective of the superplastic analysis is to predict how the pressure must be +controlled to form the component as fast as possible without exceeding a superplastic strain rate anywhere +in the material. +To achieve this using Abaqus/Standard, the controlling algorithm is as follows. During an increment +Abaqus/Standard calculates +, the maximum value of the ratio of the equivalent creep strain rate to +the target creep strain rate for any integration point in a specified element set. If +is less than 0.2 or +greater than 3.0 in a given increment, the increment is abandoned and restarted with the following load +modifications: +or +where p is the new load magnitude and +, the increment +is accepted; and at the beginning of the following time increment, the load magnitudes are modified as +follows: +is the old load magnitude. If +When you activate the above algorithm, the loading in a creep and/or swelling problem can be +controlled on the basis of the maximum equivalent creep strain rate found in a defined element set. As +or +a minimum requirement, this method is used to define a target equivalent creep strain rate; however, if +required, it can also be used to define the target creep strain rate as a function of equivalent creep strain +(measured as log strain), temperature, and other predefined field variables. The creep strain dependency +curve at each temperature must always start at zero equivalent creep strain. +A solution-dependent amplitude is used to define the minimum and maximum limits of the loading +. Any number or combination of loads can be used. The current value of +is available +for output as discussed below. +Input File Usage: +Use all of the following options: +*AMPLITUDE, NAME=name, DEFINITION=SOLUTION DEPENDENT +*CLOAD, *DLOAD, *DSLOAD, and/or *BOUNDARY with +AMPLITUDE=name +*CREEP STRAIN RATE CONTROL, AMPLITUDE=name, ELSET=elset +The *AMPLITUDE option must appear in the model definition portion of an +input file, while the loading options (*CLOAD, *DLOAD, *DSLOAD, and +*BOUNDARY) and the *CREEP STRAIN RATE CONTROL option should +appear in each relevant step definition. +Abaqus/CAE Usage: +Creep strain rate control is not supported in Abaqus/CAE. +Elements +Rate-dependent plasticity (creep and swelling behavior) can be used with any continuum, shell, +membrane, gasket, and beam element in Abaqus/Standard that has displacement degrees of freedom. +Creep (but not swelling) can also be defined in the thickness direction of any gasket element in +conjunction with the gasket behavior definition. +Output +In addition to the standard output identifiers available in Abaqus/Standard (“Abaqus/Standard output +variable identifiers,” Section 4.2.1), the following variables relate directly to creep and swelling models: +CEEQ +CESW +Equivalent creep strain, +. +Magnitude of swelling strain. +The following output, which is relevant only for an analysis with creep strain rate loading control as +discussed above, is printed at the beginning of an increment and is written automatically to the results +file and output database file when any output to these files is requested: +RATIO +Maximum value of the ratio of the equivalent creep strain rate to the target creep +strain rate, +. +AMPCU +Current value of the solution-dependent amplitude. +23.2.5 +ANNEALING OR MELTING +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• *ANNEAL TEMPERATURE +• “Specifying the annealing temperature of an elastic-plastic material” in “Defining plasticity,” +Section 12.9.2 of the Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +This capability: +• is intended to model +the effects of melting and resolidification in metals subjected to +high-temperature processes or the effects of annealing at a material point when its temperature +rises above a certain level; +• is available for only the Mises, Johnson-Cook, and Hill plasticity models; +• is intended to be used in conjunction with appropriate temperature-dependent material properties +(in particular, the model assumes perfectly plastic behavior at or above the annealing or melting +temperature); and +• can be modeled simply by defining an annealing or melting temperature. +Effects of annealing or melting +When the temperature of a material point exceeds a user-specified value called the annealing temperature, +Abaqus assumes that the material point loses its hardening memory. The effect of prior work hardening +is removed by setting the equivalent plastic strain to zero. For kinematic and combined hardening +models the backstress tensor is also reset to zero. If the temperature of the material point falls below +the annealing temperature at a subsequent point in time, the material point can work harden again. +Depending on the temperature history a material point may lose and accumulate memory several times, +which in the context of modeling melting would correspond to repeated melting and resolidification. +Any accumulated material damage is not healed when the annealing temperature is reached. Damage +will continue to accumulate after annealing according to any damage model in effect . +In Abaqus/Explicit an annealing step can be defined to simulate the annealing process for the entire +model, independent of temperature; see “Annealing procedure,” Section 6.12.1, for details. +Material properties +The annealing temperature is a material property that can optionally be defined as a function of field +variables. This material property must be used in conjunction with an appropriate definition of material +properties as functions of temperature for the Mises plasticity model. +In particular, the hardening +behavior must be defined as a function of temperature and zero hardening must be specified at or above +the annealing temperature. In general, hardening receives contributions from two sources. The first +source of hardening can be classified broadly as static, and its effect is measured by the rate of change +of the yield stress with respect to the plastic strain at a fixed strain rate. The second source of hardening +can be classified broadly as rate dependent, and its effect is measured by the rate of change of the yield +stress with respect to the strain rate at a fixed plastic strain. +For the Mises plasticity model, if the material data that describe hardening (both static and rate- +dependent contributions) are completely specified through tabular input of yield stress versus plastic +strain at different values of the strain rate , the (temperature- +dependent) static part of the hardening at each strain rate is specified by defining several yield stress +versus plastic strain curves (each at a different temperature). For metals the yield stress at a fixed strain +rate typically decreases with increasing temperature. Abaqus expects the hardening at each strain rate to +vanish at or above the annealing temperature and issues an error message if you specify otherwise in the +material definition. Zero (static) hardening can be specified by simply specifying a single data point (at +zero plastic strain) in the yield stress versus plastic strain curve at or above the annealing temperature. In +addition, you must also ensure that at or above the annealing temperature, the yield stress does not vary +with the strain rate. This can be accomplished by specifying the same value of yield stress at all values +of strain rate in the single data point approach discussed above. +Alternatively, +the static part of the hardening can be defined at zero strain rate, and the +rate-dependent part can be defined utilizing the overstress power law . In that case, zero static hardening at or above the annealing temperature can be specified +by specifying a single data point (at zero plastic strain) in the yield stress versus plastic strain curve at +or above the annealing temperature. The overstress power law parameters can also be appropriately +selected to ensure that at or above the annealing temperature the yield stress does not vary with strain +rate. This can be accomplished by selecting a large value for the parameter +(relative to the static yield +stress) and setting the parameter +. +For hardening defined in Abaqus/Standard with user subroutine UHARD, Abaqus/Standard checks +the hardening slope at or above the annealing temperature during the actual computations and issues an +error message if appropriate. +The Johnson-Cook plasticity model in Abaqus/Explicit requires a separate melting temperature +to define the hardening behavior. If the annealing temperature is defined to be less than the melting +temperature specified for the metal plasticity model, the hardening memory is removed at the annealing +temperature and the melting temperature is used strictly to define the hardening function. Otherwise, the +hardening memory is removed automatically at the melting temperature. +Input File Usage: +Abaqus/CAE Usage: +*ANNEAL TEMPERATURE +Property module: material editor: Mechanical→Plasticity→Plastic: +Suboptions→Anneal Temperature +Example: Annealing or melting +The following input is an example of a typical usage of the annealing or melting capability. It is assumed +that you have defined the static stress versus plastic strain behavior for the isotropic +that the plastic behavior is rate independent. +ANNEALING OR MELTING + + + + + + + + + + + + + + +pl +2 +pl +1 +pl + +Figure 23.2.5–1 Stress versus plastic strain behavior. +The plastic response corresponds to linear hardening below the annealing temperature and perfect +plasticity at the annealing temperature. The elastic properties, which may also be temperature +dependent, are not shown. +Plasticity Data, Isotropic Hardening: +Yield Stress +Plastic Strain +Temperature +Anneal Temperature: +Elements +This capability can be used with all elements that include mechanical behavior (elements that have +displacement degrees of freedom). +Output +Only the equivalent plastic strain (output variable PEEQ) and the backstress (output variable ALPHA) +are reset to zero at the melting temperature. The plastic strain tensor (output variable PE) is not reset to +zero and provides a measure of the total plastic deformation during the analysis. In Abaqus/Standard the +plastic strain tensor also provides a measure of the plastic strain magnitude (output variable PEMAG). +23.2.6 +ANISOTROPIC YIELD/CREEP +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Inelastic behavior,” Section 23.1.1 +• “Classical metal plasticity,” Section 23.2.1 +• “Models for metals subjected to cyclic loading,” Section 23.2.2 +• “Rate-dependent plasticity: creep and swelling,” Section 23.2.4 +• *POTENTIAL +• “Defining anisotropic yield and creep” in “Defining plasticity,” Section 12.9.2 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +Anisotropic yield and/or creep: +• can be used for materials that exhibit different yield and/or creep behavior in different directions; +• is introduced through user-defined stress ratios that are applied in Hill’s potential function; +• can be used only in conjunction with the metal plasticity and, in Abaqus/Standard, the metal creep +material models; +• is available for the nonlinear isotropic/kinematic hardening model in Abaqus/Explicit (“Models for +metals subjected to cyclic loading,” Section 23.2.2); and +• can be used in conjunction with the models of progressive damage and failure in Abaqus/Explicit +(“Damage and failure for ductile metals: overview,” Section 24.2.1) to specify different damage +initiation criteria and damage evolution laws that allow for the progressive degradation of the +material stiffness and the removal of elements from the mesh. +Yield and creep stress ratios +Anisotropic yield or creep behavior is modeled through the use of yield or creep stress ratios, +case of anisotropic yield the yield ratios are defined with respect to a reference yield stress, +the metal plasticity definition), such that if +yield stress is +. In the +(given for +is applied as the only nonzero stress, the corresponding +. The plastic flow rule is defined below. +In the case of anisotropic creep the +creep strain rate is calculated. Thus, if +user-defined creep law is +. +are creep ratios used to scale the stress value when the +, used in the +is the only nonzero stress, the equivalent stress, +Yield and creep stress ratios can be defined as constants or as tabular functions of temperature and +predefined field variables. A local orientation must be used to define the direction of anisotropy . +Input File Usage: +Use the following option to define the yield or creep stress ratios: +*POTENTIAL +This option must appear immediately after the *PLASTIC or the *CREEP +material option data to which it applies. Thus, if anisotropic metal plasticity +and anisotropic creep behavior are both required, the *POTENTIAL option +must appear twice in the material definition, once after the metal plasticity data +and again after the creep data. +Abaqus/CAE Usage: +Use one of the following models: +Property module: material editor: +Mechanical→Plasticity→Plastic: Suboptions→Potential +Mechanical→Plasticity→Creep: Suboptions→Potential +Anisotropic yield +Hill’s potential function is a simple extension of the Mises function, which can be expressed in terms of +rectangular Cartesian stress components as +where +are defined as +and N are constants obtained by tests of the material in different orientations. They +where each +component; +, +, +, +is the measured yield stress value when +is applied as the only nonzero stress +is the user-defined reference yield stress specified for the metal plasticity definition; +. The six yield +are anisotropic yield stress ratios; and +, and +, +stress ratios are, therefore, defined as follows (in the order in which you must provide them): +Because of the form of the yield function, all of these ratios must be positive. If the constants F, G, and +H are positive, the yield function is always well-defined. However, if one or more of these constants +is negative, the yield function may be undefined for some stress states because the quantity under the +square root is negative. +The flow rule is +where, from the definition of f above, +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options: +*PLASTIC +*POTENTIAL +Property module: material editor: Mechanical→Plasticity→Plastic: +Suboptions→Potential +Anisotropic creep +For anisotropic creep in Abaqus/Standard Hill’s function can be expressed as +is the equivalent stress and F, G, H, L, M, and N are constants obtained by tests of the +where +material in different orientations. The constants are defined with the same general relations as those +used for anisotropic yield (above); however, the reference yield stress, +, is replaced by the uniaxial +equivalent deviatoric stress, +are referred +(found in the creep law), and +, and +, +, +, +, +to as “anisotropic creep stress ratios.” The six creep stress ratios are, therefore, defined as follows (in the +order in which they must be provided): +You must define the ratios +strain rate is calculated. If all six +in each direction that will be used to scale the stress value when the creep +values are set to unity, isotropic creep is obtained. +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*CREEP +*POTENTIAL +Property module: material editor: Mechanical→Plasticity→Creep: +Suboptions→Potential +Defining anisotropic yield behavior on the basis of strain ratios (Lankford’s r-values) +As discussed above, Hill’s anisotropic plasticity potential is defined in Abaqus from user input consisting +of ratios of yield stress in different directions with respect to a reference stress. However, in some cases, +such as sheet metal forming applications, it is common to find the anisotropic material data given in terms +of ratios of width strain to thickness strain. Mathematical relationships are then necessary to convert the +strain ratios to stress ratios that can be input into Abaqus. +In sheet metal forming applications we are generally concerned with plane stress conditions. +Consider +to be the “rolling” and “cross” directions in the plane of the sheet; z is the thickness +direction. From a design viewpoint, the type of anisotropy usually desired is that in which the sheet +is isotropic in the plane and has an increased strength in the thickness direction, which is normally +referred to as transverse anisotropy. Another type of anisotropy is characterized by different strengths +in different directions in the plane of the sheet, which is called planar anisotropy. +In a simple tension test performed in the x-direction in the plane of the sheet, the flow rule for this +potential (given above) defines the incremental strain ratios (assuming small elastic strains) as +Therefore, the ratio of width to thickness strain, often referred to as Lankford’s r-value, is +Similarly, for a simple tension test performed in the y-direction in the plane of the sheet, the +incremental strain ratios are +and +Transverse anisotropy +A transversely anisotropic material is one where +to be equal to +, +. If we define +in the metal plasticity model +and, using the relationships above, +If +(isotropic material), +and the Mises isotropic plasticity model is recovered. +Planar anisotropy +In the case of planar anisotropy +define +in the metal plasticity model to be equal to +, +and +are different and +will all be different. If we +and, using the relationships above, we obtain +Again, if +, +and the Mises isotropic plasticity model is recovered. +General anisotropy +Thus far, we have only considered loading applied along the axes of anisotropy. To derive a more general +anisotropic model in plane stress, the sheet must be loaded in one other direction in its plane. Suppose +we perform a simple tension test at an angle +to the x-direction; then, from equilibrium considerations +we can write the nonzero stress components as +is the applied tensile stress. Substituting these values in the flow equations and assuming small +where +elastic strains yields +and +Assuming small geometrical changes, the width strain increment (the increment of strain at right +angles to the direction of loading, +) is written as +and Lankford’s r-value for loading at an angle +is +One of the more commonly performed tests is that in which the loading direction is at 45°. In this +case +If +. +transverse or planar anisotropy and, using the relationships above, +in the metal plasticity model, +is equal to +are as defined before for +Progressive damage and failure +In Abaqus/Explicit anisotropic yield can be used in conjunction with the models of progressive damage +and failure discussed in “Damage and failure for ductile metals: overview,” Section 24.2.1. The +capability allows for the specification of one or more damage initiation criteria, including ductile, +shear, forming limit diagram (FLD), forming limit stress diagram (FLSD), and Müschenborn-Sonne +forming limit diagram (MSFLD) criteria. After damage initiation, the material stiffness is degraded +progressively according to the specified damage evolution response. The model offers two failure +choices, including the removal of elements from the mesh as a result of tearing or ripping of the +structure. The progressive damage models allow for a smooth degradation of the material stiffness, +making them suitable for both quasi-static and dynamic situations. +Input File Usage: +Use the following options: +*PLASTIC +*DAMAGE INITIATION +*DAMAGE EVOLUTION +Property module: material editor: Mechanical→Damage for Ductile +Metals→damage initiation type: specify the damage initiation criterion: +Suboptions→Damage Evolution: specify the damage evolution parameters +Abaqus/CAE Usage: +Initial conditions +When we need to study the behavior of a material that has already been subjected to some work hardening, +Abaqus allows you to prescribe initial conditions for the equivalent plastic strain, +, by specifying the +conditions directly (“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1). +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=HARDENING +Load module: Create Predefined Field: Step: Initial, choose Mechanical +for the Category and Hardening for the Types for Selected Step +User subroutine specification in Abaqus/Standard +For more complicated cases, initial conditions can be defined in Abaqus/Standard through user subroutine +HARDINI. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=HARDENING, USER +Load module: Create Predefined Field: Step: Initial, choose +Mechanical for the Category and Hardening for the Types for +Selected Step; Definition: User-defined +Elements +Anisotropic yield can be defined for any element that can be used with the classical metal plasticity +models in Abaqus (“Classical metal plasticity,” Section 23.2.1) except one-dimensional elements in +Abaqus/Explicit (beams and trusses). In Abaqus/Standard it can also be defined for any element that +can be used with the linear kinematic hardening plasticity model (“Models for metals subjected to cyclic +loading,” Section 23.2.2) but not with the nonlinear isotropic/kinematic hardening model. Likewise, +anisotropic creep can be defined for any element that can be used with the classical metal creep model +in Abaqus/Standard (“Rate-dependent plasticity: creep and swelling,” Section 23.2.4). +Output +The standard output identifiers available in Abaqus (“Abaqus/Standard output variable identifiers,” +Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2) and all output variables +associated with the creep model (“Rate-dependent plasticity: creep and swelling,” Section 23.2.4), +classical metal plasticity models (“Classical metal plasticity,” Section 23.2.1), and the linear kinematic +hardening plasticity model (“Models for metals subjected to cyclic loading,” Section 23.2.2) are +available when anisotropic yield and creep are defined. +The following variables have special meaning if anisotropic yield and creep are defined: +PEEQ +CEEQ +is +Equivalent plastic strain, +the initial equivalent plastic strain (zero or user-specified; see “Initial conditions”). +where +Equivalent creep strain, +23.2.7 +JOHNSON-COOK PLASTICITY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Classical metal plasticity,” Section 23.2.1 +• “Rate-dependent yield,” Section 23.2.3 +• “Equation of state,” Section 25.2.1 +• Chapter 24, “Progressive Damage and Failure” +• “Dynamic failure models,” Section 23.2.8 +• “Annealing or melting,” Section 23.2.5 +• “Material library: overview,” Section 21.1.1 +• “Inelastic behavior,” Section 23.1.1 +• *ANNEAL TEMPERATURE +• *PLASTIC +• *RATE DEPENDENT +• *SHEAR FAILURE +• *TENSILE FAILURE +• *DAMAGE INITIATION +• *DAMAGE EVOLUTION +• “Using the Johnson-Cook hardening model to define classical metal plasticity” in “Defining +plasticity,” Section 12.9.2 of the Abaqus/CAE User’s Manual, in the online HTML version of this +manual +Overview +The Johnson-Cook plasticity model: +• is a particular type of Mises plasticity model with analytical forms of the hardening law and rate +dependence; +• is suitable for high-strain-rate deformation of many materials, including most metals; +• is typically used in adiabatic transient dynamic simulations; +• can be used in conjunction with the Johnson-Cook dynamic failure model in Abaqus/Explicit; +• can be used in conjunction with the tensile failure model to model tensile spall or a pressure cutoff +in Abaqus/Explicit; +• can be used in conjunction with the progressive damage and failure models (Chapter 24, +“Progressive Damage and Failure”) to specify different damage initiation criteria and damage +evolution laws that allow for the progressive degradation of the material stiffness and the removal +of elements from the mesh; and +• must be used in conjunction with either the linear elastic material model (“Linear elastic behavior,” +Section 22.2.1) or the equation of state material model (“Equation of state,” Section 25.2.1). +Yield surface and flow rule +A Mises yield surface with associated flow is used in the Johnson-Cook plasticity model. +Johnson-Cook hardening +Johnson-Cook hardening is a particular type of isotropic hardening where the static yield stress, +assumed to be of the form +, is +where +the transition temperature, +is the equivalent plastic strain and A, B, n and m are material parameters measured at or below +. +is the nondimensional temperature defined as +is the current temperature, +where +is the transition +temperature defined as the one at or below which there is no temperature dependence on the expression +of the yield stress. The material parameters must be measured at or below the transition temperature. +is the melting temperature, and +When +resistance since +to zero. If backstresses are specified for the model, these will also be set to zero. +, the material will be melted and will behave like a fluid; there will be no shear +. The hardening memory will be removed by setting the equivalent plastic strain +If you include annealing behavior in the material definition and the annealing temperature is +defined to be less than the melting temperature specified for the metal plasticity model, the hardening +memory will be removed at the annealing temperature and the melting temperature will be used strictly +to define the hardening function. Otherwise, the hardening memory will be removed automatically at the +melting temperature. If the temperature of the material point falls below the annealing temperature at a +subsequent point in time, the material point can work harden again. For more details, see “Annealing +or melting,” Section 23.2.5. +You provide the values of A, B, n, m, +, and +as part of the metal plasticity material +definition. +Input File Usage: +Abaqus/CAE Usage: +*PLASTIC, HARDENING=JOHNSON COOK +Property module: material editor: Mechanical→Plasticity→Plastic: +Hardening: Johnson-Cook +Johnson-Cook strain rate dependence +Johnson-Cook strain rate dependence assumes that +and +where +is the yield stress at nonzero strain rate; +and C +is the equivalent plastic strain rate; +are material parameters measured at or below the transition temperature, +; +is the static yield stress; and +is the ratio of the yield stress at nonzero strain rate to the static yield stress (so +that +). +The yield stress is, therefore, expressed as +You provide the values of C and +The use of Johnson-Cook hardening does not necessarily require the use of Johnson-Cook strain +when you define Johnson-Cook rate dependence. +rate dependence. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options: +*PLASTIC, HARDENING=JOHNSON COOK +*RATE DEPENDENT, TYPE=JOHNSON COOK +Property module: material editor: Mechanical→Plasticity→Plastic: +Hardening: Johnson-Cook: Suboptions→Rate Dependent: +Hardening: Johnson-Cook +Johnson-Cook dynamic failure +Abaqus/Explicit provides a dynamic failure model specifically for the Johnson-Cook plasticity model, +which is suitable only for high-strain-rate deformation of metals. This model is referred to as the +“Johnson-Cook dynamic failure model.” Abaqus/Explicit also offers a more general implementation +of the Johnson-Cook failure model as part of the family of damage initiation criteria, which is the +recommended technique for modeling progressive damage and failure of materials (see “Damage and +failure for ductile metals: overview,” Section 24.2.1). The Johnson-Cook dynamic failure model is +based on the value of the equivalent plastic strain at element integration points; failure is assumed to +occur when the damage parameter exceeds 1. The damage parameter, +, is defined as +is the strain at failure, and the summation +where +is an increment of the equivalent plastic strain, +, is assumed to be dependent on +is performed over all increments in the analysis. The strain at failure, +(where +a nondimensional plastic strain rate, +, defined earlier +p is the pressure stress and q is the Mises stress); and the nondimensional temperature, +in the Johnson-Cook hardening model. The dependencies are assumed to be separable and are of the +form +; a dimensionless pressure-deviatoric stress ratio, +– +are failure parameters measured at or below the transition temperature, +where +the reference strain rate. You provide the values of +failure model. This expression for +(1985) in the sign of the parameter +experience an increase in +expression will usually take positive values. +is +– when you define the Johnson-Cook dynamic +differs from the original formula published by Johnson and Cook +. This difference is motivated by the fact that most materials +in the above +with increasing pressure-deviatoric stress ratio; therefore, +, and +When this failure criterion is met, the deviatoric stress components are set to zero and remain zero +for the rest of the analysis. Depending on your choice, the pressure stress may also be set to zero for the +rest of calculation (if this is the case, you must specify element deletion and the element will be deleted) +or it may be required to remain compressive for the rest of the calculation (if this is the case, you must +choose not to use element deletion). By default, the elements that meet the failure criterion are deleted. +The Johnson-Cook dynamic failure model is suitable for high-strain-rate deformation of metals; +therefore, it is most applicable to truly dynamic situations. For quasi-static problems that require element +removal, the progressive damage and failure models (Chapter 24, “Progressive Damage and Failure”) or +the Gurson metal plasticity model (“Porous metal plasticity,” Section 23.2.9) are recommended. +The use of the Johnson-Cook dynamic failure model requires the use of Johnson-Cook hardening +but does not necessarily require the use of Johnson-Cook strain rate dependence. However, the rate- +dependent term in the Johnson-Cook dynamic failure criterion will be included only if Johnson-Cook +strain rate dependence is defined. The Johnson-Cook damage initiation criterion described in “Damage +initiation for ductile metals,” Section 24.2.2, does not have these limitations. +Input File Usage: +Use both of the following options: +*PLASTIC, HARDENING=JOHNSON COOK +*SHEAR FAILURE, TYPE=JOHNSON COOK, +ELEMENT DELETION=YES or NO +Abaqus/CAE Usage: +Johnson-Cook dynamic failure is not supported in Abaqus/CAE. +Progressive damage and failure +The Johnson-Cook plasticity model can be used in conjunction with the progressive damage and failure +models discussed in “Damage and failure for ductile metals: overview,” Section 24.2.1. The capability +allows for the specification of one or more damage initiation criteria, including ductile, shear, forming +limit diagram (FLD), forming limit stress diagram (FLSD), Müschenborn-Sonne forming limit diagram +(MSFLD), and, in Abaqus/Explicit, Marciniak-Kuczynski (M-K) criteria. After damage initiation, the +material stiffness is degraded progressively according to the specified damage evolution response. The +models offer two failure choices, including the removal of elements from the mesh as a result of tearing or +ripping of the structure. The progressive damage models allow for a smooth degradation of the material +stiffness, making them suitable for both quasi-static and dynamic situations. This is a great advantage +over the dynamic failure models discussed above. +Input File Usage: +Abaqus/CAE Usage: +Use the following options: +*PLASTIC, HARDENING=JOHNSON COOK +*DAMAGE INITIATION +*DAMAGE EVOLUTION +Property module: material editor: Mechanical→Damage for Ductile +Metals→damage initiation type: specify the damage initiation criterion: +Suboptions→Damage Evolution: specify the damage evolution parameters +Tensile failure +In Abaqus/Explicit the tensile failure model can be used in conjunction with the Johnson-Cook +plasticity model to define tensile failure of the material. The tensile failure model uses the hydrostatic +pressure stress as a failure measure to model dynamic spall or a pressure cutoff and offers a number of +failure choices including element removal. Similar to the Johnson-Cook dynamic failure model, the +Abaqus/Explicit tensile failure model is suitable for high-strain-rate deformation of metals and is most +applicable to truly dynamic problems. For more details, see “Dynamic failure models,” Section 23.2.8. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options: +*PLASTIC, HARDENING=JOHNSON COOK +*TENSILE FAILURE +The tensile failure model is not supported in Abaqus/CAE. +Heat generation by plastic work +Abaqus allows for an adiabatic thermal-stress analysis (“Adiabatic analysis,” Section 6.5.4), a fully +coupled temperature-displacement analysis (“Fully coupled thermal-stress analysis,” Section 6.5.3), +or a fully coupled thermal-electrical-structural analysis (“Fully coupled thermal-electrical-structural +analysis,” Section 6.7.4) to be performed in which heat generated by plastic straining of a material +is calculated. This method is typically used in the simulation of bulk metal forming or high-speed +manufacturing processes involving large amounts of inelastic strain, where the heating of the material +caused by its deformation is an important effect because of temperature dependence of the material +properties. Since the Johnson-Cook plasticity model is motivated by high-strain-rate transient dynamic +applications, temperature change in this model is generally computed by assuming adiabatic conditions +(no heat transfer between elements). Heat is generated in an element by plastic work, and the resulting +temperature rise is computed using the specific heat of the material. +This effect is introduced by defining the fraction of the rate of inelastic dissipation that appears as +a heat flux per volume. +Input File Usage: +Use all of the following options in the same material data block: +*PLASTIC, HARDENING=JOHNSON COOK +*SPECIFIC HEAT +*DENSITY +*INELASTIC HEAT FRACTION +Abaqus/CAE Usage: +Use all of the following options in the same material definition: +Property module: material editor: +Mechanical→Plasticity→Plastic: Hardening: Johnson-Cook +Thermal→Specific Heat +General→Density +Thermal→Inelastic Heat Fraction +Initial conditions +When we need to study the behavior of a material that has already been subjected to some work hardening, +initial equivalent plastic strain values can be provided to specify the yield stress corresponding to the +work hardened state . +An initial backstress, +represents a constant kinematic shift +of the yield surface, which can be useful for modeling the effects of residual stresses without considering +them in the equilibrium solution. +, can also be specified. The backstress +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=HARDENING +Load module: Create Predefined Field: Step: Initial, choose Mechanical +for the Category and Hardening for the Types for Selected Step +Elements +The Johnson-Cook plasticity model can be used with any elements in Abaqus that include mechanical +behavior (elements that have displacement degrees of freedom). +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2), +the +following variables have special meaning for the Johnson-Cook plasticity model: +PEEQ +STATUS +Additional reference +Equivalent plastic strain, +equivalent plastic strain (zero or user-specified; see “Initial conditions”). +where +is the initial +Status of element. The status of an element is 1.0 if the element is active and 0.0 +if the element is not. +• Johnson, G. R., and W. H. Cook, “Fracture Characteristics of Three Metals Subjected to Various +Strains, Strain rates, Temperatures and Pressures,” Engineering Fracture Mechanics, vol. 21, no. 1, +pp. 31–48, 1985. +23.2.8 +DYNAMIC FAILURE MODELS +Product: Abaqus/Explicit +References +• “Equation of state,” Section 25.2.1 +• “Classical metal plasticity,” Section 23.2.1 +• “Rate-dependent yield,” Section 23.2.3 +• “Johnson-Cook plasticity,” Section 23.2.7 +• “Material library: overview,” Section 21.1.1 +• “Inelastic behavior,” Section 23.1.1 +• *SHEAR FAILURE +• *TENSILE FAILURE +Overview +The progressive damage and failure models described in “Damage and failure for ductile metals: +overview,” Section 24.2.1, are the recommended method for modeling material damage and failure in +Abaqus; these models are suitable for both quasi-static and dynamic situations. Abaqus/Explicit offers +two additional element failure models suitable only for high-strain-rate dynamic problems. The shear +failure model is driven by plastic yielding. The tensile failure model is driven by tensile loading. These +failure models can be used to limit subsequent load-carrying capacity of an element (up to the point of +removing the element) once a stress limit is reached. Both models can be used for the same material. +The shear failure model: +• is designed for high-strain-rate deformation of many materials, including most metals; +• uses the equivalent plastic strain as a failure measure; +• offers two choices for what occurs upon failure, including the removal of elements from the mesh; +• can be used in conjunction with either the Mises or the Johnson-Cook plasticity models; and +• can be used in conjunction with the tensile failure model. +The tensile failure model: +• is designed for high-strain-rate deformation of many materials, including most metals; +• uses the hydrostatic pressure stress as a failure measure to model dynamic spall or a pressure cutoff; +• offers a number of choices for what occurs upon failure, including the removal of elements from +the mesh; +• can be used in conjunction with either the Mises or the Johnson-Cook plasticity models or the +equation of state material model; and +• can be used in conjunction with the shear failure model. +Shear failure model +The shear failure model can be used in conjunction with the Mises or the Johnson-Cook plasticity models +in Abaqus/Explicit to define shear failure of the material. +Shear failure criterion +The shear failure model is based on the value of the equivalent plastic strain at element integration points; +failure is assumed to occur when the damage parameter exceeds 1. The damage parameter, +, is defined +as +where +strain, +is an increment of the equivalent plastic +is any initial value of the equivalent plastic strain, +is the strain at failure, and the summation is performed over all increments in the analysis. +, is assumed to depend on the plastic strain rate, +The strain at failure, +; a dimensionless +pressure-deviatoric stress ratio, +(where p is the pressure stress and q is the Mises stress); temperature; +and predefined field variables. There are two ways to define the strain at failure, +. One is to use direct +tabular data, where the dependencies are given in a tabular form. Alternatively, the analytical form +proposed by Johnson and Cook can be invoked . +When direct tabular data are used to define the shear failure model, the strain at failure, +, must +be given as a tabular function of the equivalent plastic strain rate, the pressure-deviatoric stress ratio, +temperature, and predefined field variables. This method requires the use of the Mises plasticity model. +. The shear failure +data must be calibrated at or below the transition temperature, +, defined in “Johnson-Cook +plasticity,” Section 23.2.7. This method requires the use of the Johnson-Cook plasticity model. +For the Johnson-Cook shear failure model, you must specify the failure parameters, +– +Input File Usage: +Use both of the following options for the Mises plasticity model: +*PLASTIC, HARDENING=ISOTROPIC +*SHEAR FAILURE, TYPE=TABULAR +Use both of the following options for the Johnson-Cook plasticity model: +*PLASTIC, HARDENING=JOHNSON COOK +*SHEAR FAILURE, TYPE=JOHNSON COOK +Element removal +When the shear failure criterion is met at an integration point, all the stress components will be set to zero +and that material point fails. By default, if all of the material points at any one section of an element fail, +the element is removed from the mesh; it is not necessary for all material points in the element to fail. For +example, in a first-order reduced-integration solid element removal of the element takes place as soon as +its only integration point fails. However, in a shell element all through-the-thickness integration points +must fail before the element is removed from the mesh. In the case of second-order reduced-integration +beam elements, failure of all integration points through the section at either of the two element integration +locations along the beam axis leads, by default, to element removal. Similarly, in the modified triangular +and tetrahedral solid elements failure at any one integration point leads, by default, to element removal. +Element deletion is the default failure choice. +An alternative failure choice, where the element is not deleted, is to specify that when the shear +failure criterion is met at a material point, the deviatoric stress components will be set to zero for that +point and will remain zero for the rest of the calculation. The pressure stress is then required to remain +compressive; that is, if a negative pressure stress is computed in a failed material point in an increment, +it is reset to zero. This failure choice is not allowed when using plane stress, shell, membrane, beam, +pipe, and truss elements because the structural constraints may be violated. +Input File Usage: +Use the following option to allow element deletion when the failure criterion is +met (the default): +*SHEAR FAILURE, ELEMENT DELETION=YES +Use the following option to allow the element to take hydrostatic compressive +stress only when the failure criterion is met: +*SHEAR FAILURE, ELEMENT DELETION=NO +Determining when to use the shear failure model +The shear failure model in Abaqus/Explicit is suitable for high-strain-rate dynamic problems where +inertia is important. Improper use of the shear failure model may result in an incorrect simulation. +For quasi-static problems that may require element removal, the progressive damage and failure +models (Chapter 24, “Progressive Damage and Failure”) or the Gurson porous metal plasticity model +(“Porous metal plasticity,” Section 23.2.9) are recommended. +Tensile failure model +The tensile failure model can be used in conjunction with either the Mises or the Johnson-Cook plasticity +models or the equation of state material model in Abaqus/Explicit to define tensile failure of the material. +Tensile failure criterion +The Abaqus/Explicit tensile failure model uses the hydrostatic pressure stress as a failure measure to +model dynamic spall or a pressure cutoff. The tensile failure criterion assumes that failure occurs when +the pressure stress, p, becomes more tensile than the user-specified hydrostatic cutoff stress, +. The +hydrostatic cutoff stress may be a function of temperature and predefined field variables. There is no +default value for this stress. +The tensile failure model can be used with either the Mises or the Johnson-Cook plasticity models +or the equation of state material model. +Input File Usage: +Use both of the following options for the Mises or Johnson-Cook plasticity +models: +*PLASTIC +*TENSILE FAILURE +Use both of the following options for the equation of state material model: +*EOS +*TENSILE FAILURE +Failure choices +When the tensile failure criterion is met at an element integration point, the material point fails. Five +failure choices are offered for the failed material points: the default choice, which includes element +removal, and four different spall models. These failure choices are described below. +Element removal +When the tensile failure criterion is met at an integration point, all the stress components will be set to +zero and that material point fails. By default, if all of the material points at any one section of an element +fail, the element is removed from the mesh; it is not necessary for all material points in the element +to fail. For example, in a first-order reduced-integration solid element removal of the element takes +place as soon as its only integration point fails. However, in a shell element all through-the-thickness +integration points must fail before the element is removed from the mesh. In the case of second-order +reduced-integration beam elements, failure of all integration points through the section at either of the +two element integration locations along the beam axis leads, by default, to element removal. Similarly, +in the modified triangular and tetrahedral solid elements failure at any one integration point leads, by +default, to element removal. +Input File Usage: +*TENSILE FAILURE, ELEMENT DELETION=YES (default) +Spall models +An alternative failure choice that is based on spall (the crumbling of a material), rather than element +removal, is also available. Four failure combinations are available in this category. When the tensile +failure criterion is met at a material point, the deviatoric stress components may be unaffected or +may be required to be zero, and the pressure stress may be limited by the hydrostatic cutoff stress +or may be required to be compressive. Therefore, there are four possible failure combinations . +These failure combinations are as follows: +• Ductile shear and ductile pressure: this choice corresponds to point 1 in Figure 23.2.8–1 and models +the case in which the deviatoric stress components are unaffected and the pressure stress is limited +by the hydrostatic cutoff stress; i.e., +. +Input File Usage: +*TENSILE FAILURE, ELEMENT DELETION=NO, +SHEAR=DUCTILE, PRESSURE=DUCTILE +• Brittle shear and ductile pressure: +this choice corresponds to point 2 in Figure 23.2.8–1 and +models the case in which the deviatoric stress components are set to zero and remain zero for +−σ +cutoff +Figure 23.2.8–1 Tensile failure choices. +the rest of the calculation, and the pressure stress is limited by the hydrostatic cutoff stress; i.e., +. +Input File Usage: +*TENSILE FAILURE, ELEMENT DELETION=NO, +SHEAR=BRITTLE, PRESSURE=DUCTILE +• Brittle shear and brittle pressure: this choice corresponds to point 3 in Figure 23.2.8–1 and models +the case in which the deviatoric stress components are set to zero and remain zero for the rest of the +calculation, and the pressure stress is required to be compressive; i.e., +. +Input File Usage: +*TENSILE FAILURE, ELEMENT DELETION=NO, +SHEAR=BRITTLE, PRESSURE=BRITTLE +• Ductile shear and brittle pressure: this choice corresponds to point 4 in Figure 23.2.8–1 and models +the case in which the deviatoric stress components are unaffected and the pressure stress is required +to be compressive; i.e., +. +Input File Usage: +*TENSILE FAILURE, ELEMENT DELETION=NO, +SHEAR=DUCTILE, PRESSURE=BRITTLE +There is no default failure combination for the spall models. If you choose not to use the element +deletion model, you must specify the failure combination explicitly. If the material’s deviatoric behavior +is not defined (for example, the equation of state model without deviatoric behavior is used), the +deviatoric part of the combination is meaningless and will be ignored. The spall models are not allowed +when using plane stress, shell, membrane, beam, pipe, and truss elements. +Determining when to use the tensile failure model +The tensile failure model in Abaqus/Explicit is suitable for high-strain-rate dynamic problems in which +inertia effects are important. +Improper use of the tensile failure model may result in an incorrect +simulation. +Using the failure models with rebar +It is possible to use the shear failure and/or the tensile failure models in elements for which rebars are also +defined. When such elements fail according to the failure criterion, the base material contribution to the +element stress-carrying capacity is removed or adjusted depending on the type of failure chosen, but the +rebar contribution to the element stress-carrying capacity is not removed. However, if you also include +failure in the rebar material definition, the rebar contribution to the element stress-carrying capacity will +also be removed or adjusted if the failure criterion specified for the rebar is met. +Elements +The shear and tensile failure models with element deletion can be used with any elements in +Abaqus/Explicit +include mechanical behavior (elements that have displacement degrees of +freedom). The shear and tensile failure models without element deletion can be used only with plane +strain, axisymmetric, and three-dimensional solid (continuum) elements in Abaqus/Explicit. +that +Output +In addition to the standard output identifiers available in Abaqus/Explicit (“Abaqus/Explicit output +variable identifiers,” Section 4.2.2), the following variable has special meaning for the shear and tensile +failure models: +STATUS +Status of element (the status of an element is 1.0 if the element is active, 0.0 if the +element is not). +23.2.9 +POROUS METAL PLASTICITY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Inelastic behavior,” Section 23.1.1 +• *POROUS METAL PLASTICITY +• *POROUS FAILURE CRITERIA +• *VOID NUCLEATION +• “Defining porous metal plasticity” in “Defining plasticity,” Section 12.9.2 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +The porous metal plasticity model: +• is used to model materials with a dilute concentration of voids in which the relative density is greater +than 0.9; +• is based on Gurson’s porous metal plasticity theory (Gurson, 1977) with void nucleation and, in +Abaqus/Explicit, a failure definition; and +• defines the inelastic flow of the porous metal on the basis of a potential function that characterizes +the porosity in terms of a single state variable, the relative density. +Elastic and plastic behavior +You specify the elastic part of the response separately; only linear isotropic elasticity can be specified +. +You specify the hardening behavior of the fully dense matrix material by defining a metal plasticity +model . Only isotropic hardening can be specified. The +hardening curve must describe the yield stress of the matrix material as a function of plastic strain in the +matrix material. In defining this dependence at finite strains, “true” (Cauchy) stress and log strain values +should be given. Rate dependency effects for the matrix material can be modeled . +Yield condition +The relative density of a material, r, is defined as the ratio of the volume of solid material to the total +volume of the material. The relationships defining the model are expressed in terms of the void volume +fraction, f, which is defined as the ratio of the volume of voids to the total volume of the material. It +follows that +For a metal containing a dilute concentration of voids, Gurson (1977) proposed +a yield condition as a function of the void volume fraction. This yield condition was later modified by +Tvergaard (1981) to the form +where +is the deviatoric part of the Cauchy stress tensor +; +is the effective Mises stress; +is the hydrostatic pressure; +is the yield stress of the fully dense matrix material as a function of +equivalent plastic strain in the matrix; and +are material parameters. +, the +, +, +The Cauchy stress is defined as the force per “current unit area,” comprised of voids and the solid +(matrix) material. +f = 0 (r = 1) implies that the material is fully dense, and the Gurson yield condition reduces to the +Mises yield condition. f = 1 (r = 0) implies that the material is completely voided and has no stress +carrying capacity. The model generally gives physically reasonable results only for +0.1 ( +0.9). +The model is described in detail in “Porous metal plasticity,” Section 4.3.6 of the Abaqus Theory +Manual, along with a discussion of its numerical implementation. +If the porous metal plasticity model is used during a pore pressure analysis , the relative density, r, is tracked independently of the void +ratio. +Specifying q1 , q2 , and q3 +, +, and +You specify the parameters +metals the ranges of the parameters reported in the literature are += 1.0 to 2.25 . +The original Gurson model is recovered when += 1.0. You can define these parameters as += +tabular functions of temperature and/or field variables. +directly for the porous metal plasticity model. For typical += 1.0 to 1.5, += 1.0, and += += +Input File Usage: +Abaqus/CAE Usage: +*POROUS METAL PLASTICITY +Property module: material editor: Mechanical→Plasticity→Porous +Metal Plasticity +Failure criteria in Abaqus/Explicit +The porous metal plasticity model in Abaqus/Explicit allows for failure. In this case the yield condition +is written as +coalescence. This function is defined in terms of the void volume fraction: +models the rapid loss of stress carrying capacity that accompanies void +POROUS METAL PLASTICITY +where +is a critical value of the void volume fraction, and +In the above relationship +is the value of void +volume fraction at which there is a complete loss of stress carrying capacity in the material. The user- +specified parameters +, due to mechanisms such +as micro fracture and void coalescence. When +, total failure at the material point occurs. In +Abaqus/Explicit an element is removed once all of its material points have failed. +model the material failure when +and +Input File Usage: +Abaqus/CAE Usage: +Use the following option in conjunction with the *POROUS METAL +PLASTICITY option: +*POROUS FAILURE CRITERIA +Property module: material editor: Mechanical→Plasticity→Porous +Metal Plasticity: Suboptions→Porous Failure Criteria +Specifying the initial relative density +You can specify the initial relative density of the porous material, +you do not specify the initial relative density, Abaqus will assign it a value of 1.0. +, at material points or at nodes. If +At material points +You can specify the initial relative density as part of the porous metal plasticity material definition. +Input File Usage: +Abaqus/CAE Usage: +*POROUS METAL PLASTICITY, RELATIVE DENSITY= +Property module: material editor: Mechanical→Plasticity→Porous +Metal Plasticity: Relative density: +At nodes +Alternatively, you can specify the initial relative density at nodes as initial conditions (“Initial conditions +in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1); these values are interpolated to the material +points. The initial conditions are applied only if the relative density is not specified as part of the porous +metal plasticity material definition. When a discontinuity of the initial relative density field occurs at +the element boundaries, separate nodes must be used to define the elements at these boundaries, with +multi-point constraints applied to make the nodal displacements and rotations equivalent. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=RELATIVE DENSITY +Initial relative density is not supported in Abaqus/CAE. +Flow rule and hardening +The presence of pressure in the yield condition results in nondeviatoric plastic strains. Plastic flow is +assumed to be normal to the yield surface: +The hardening of the fully dense matrix material is described through +. The evolution of +the equivalent plastic strain in the matrix material is obtained from the following equivalent plastic work +expression: +The model is illustrated in Figure 23.2.9–1, where the yield surfaces for different levels of void +volume fraction are shown in the p–q plane. +f = 0 (Mises) +f = 0.01 +f = 0.2 +f = 0.4 +| p | +Figure 23.2.9–1 Schematic of the yield surface in the p–q plane. +Figure 23.2.9–2 compares the behavior of a porous material (whose initial yield stress is +) in +tension and compression against the behavior of the perfectly plastic matrix material. In compression +the porous material “hardens” due to closing of the voids, and in tension it “softens” due to growth and +nucleation of the voids. +Void growth and nucleation +The total change in void volume fraction is given as +f = 0 (Mises) +σ +tension (f )0 +compression (f )0 +−σ +Figure 23.2.9–2 Schematic of uniaxial behavior of a porous metal (perfectly plastic +matrix material with initial volume fraction of voids = +). +is change due to growth of existing voids and +where +is change due to nucleation of new voids. +Growth of the existing voids is based on the law of conservation of mass and is expressed in terms of +the void volume fraction: +The nucleation of voids is given by a strain-controlled relationship: +where +The normal distribution of the nucleation strain has a mean value +the volume fraction of the nucleated voids, and voids are nucleated only in tension. +and standard deviation +. +is +The nucleation function +is assumed to have a normal distribution, as shown in Figure 23.2.9–3 +for different values of the standard deviation +. +fN +√2π +√2π +sN +s < sN +Material 1 +Material 2 +Figure 23.2.9–3 Nucleation function +ε pl +. +Figure 23.2.9–4 shows the extent of softening in a uniaxial tension test of a porous material for different +values of +. +f N +f N +f < f +ε = ε +s = s +f = f +0 2 +Figure 23.2.9–4 Softening (in uniaxial tension) as a function of +. +The following ranges of values are reported in the literature for typical metals: += 0.1 to 0.3, +0.05 to 0.1, and += 0.04 . You specify these parameters, which can be defined as tabular functions of temperature and +predefined field variables. Abaqus will include void nucleation in a tensile field only when you include +it in the material definition. +In Abaqus/Standard the accuracy of the implicit integration of the void nucleation and growth +equation is controlled by prescribing the maximum allowable time increment in the automatic time +incrementation scheme. +Input File Usage: +Abaqus/CAE Usage: +*VOID NUCLEATION +Property module: material editor: Mechanical→Plasticity→Porous +Metal Plasticity: Suboptions→Void Nucleation +Initial conditions +When we need to study the behavior of a material that has already been subjected to some work hardening, +Abaqus allows you to prescribe initial conditions directly for the equivalent plastic strain, +(“Initial +conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1). +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=HARDENING +Load module: Create Predefined Field: Step: Initial, choose Mechanical +for the Category and Hardening for the Types for Selected Step +Defining initial hardening conditions in a user subroutine +For more complicated cases, initial conditions can be defined in Abaqus/Standard through user subroutine +HARDINI. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=HARDENING, USER +Load module: Create Predefined Field: Step: Initial, choose +Mechanical for the Category and Hardening for the Types for +Selected Step; Definition: User-defined +Elements +The porous metal plasticity model can be used with any stress/displacement elements other than one- +dimensional elements (beam, pipe, and truss elements) or elements for which the assumed stress state is +plane stress (plane stress, shell, and membrane elements). +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2), +the +following variables have special meaning in the porous metal plasticity model: +Equivalent plastic strain, +equivalent plastic strain (zero or user-specified; see “Initial conditions”). +where +is the initial +Void volume fraction. +23.2.9–7 +PEEQ +VVFG +VVFN +Void volume fraction due to void growth. +Void volume fraction due to void nucleation. +Additional references +• Gurson, A. L., “Continuum Theory of Ductile Rupture by Void Nucleation and Growth: +Part I—Yield Criteria and Flow Rules for Porous Ductile Materials,” Journal of Engineering +Materials and Technology, vol. 99, pp. 2–15, 1977. +• Tvergaard, V., “Influence of Voids on Shear Band Instabilities under Plane Strain Condition,” +International Journal of Fracture Mechanics, vol. 17, pp. 389–407, 1981. +23.2.10 +CAST IRON PLASTICITY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Combining material behaviors,” Section 21.1.3 +• “Inelastic behavior,” Section 23.1.1 +• *CAST IRON COMPRESSION HARDENING +• *CAST IRON PLASTICITY +• *CAST IRON TENSION HARDENING +• “Defining cast iron plasticity” in “Defining plasticity,” Section 12.9.2 of the Abaqus/CAE User’s +Manual, in the online HTML version of this manual +Overview +The cast iron plasticity model: +• is intended for the constitutive modeling of gray cast iron; +• provides elastic-plastic behavior with different yield strengths, flow, and hardening in tension and +compression; +• is based on a yield function that depends on the maximum principal stress under tensile loading +conditions and pressure-independent (von Mises type) behavior under compressive loading +conditions; +• allows for simultaneous inelastic dilatation and inelastic shearing under tensile loading conditions; +• allows only inelastic shearing under compressive loading conditions; +• is intended for the simulation of material response only under essentially monotonic loading +conditions; and +• cannot be used to model rate dependence. +Elastic and plastic behavior +The cast iron plasticity model describes the mechanical behavior of gray cast iron, a material with a +microstructure consisting of a distribution of graphite flakes in a steel matrix. In tension the graphite +flakes act as stress concentrators, resulting in yielding as a function of the maximum principal stress, +followed by brittle behavior. In compression the graphite flakes do not have an appreciable effect on the +macroscopic response, resulting in a ductile behavior similar to that of many steels. +You specify the elastic part of the response separately; only linear isotropic elasticity can be used +. The elastic stiffness is assumed to be the same under +tension and compression. +The cast iron plasticity model is used to provide the value of the plastic “Poisson’s ratio,” which is +the absolute value of the ratio of the transverse to the longitudinal plastic strain under uniaxial tension. +The plastic Poisson’s ratio can vary with the plastic deformation. However, the model in Abaqus assumes +that it is constant with respect to plastic deformation. It can depend on temperature and field variables. +If no value is specified for the plastic Poisson’s ratio, a default value of 0.04 is assumed. This default +value is based on experimental results for permanent volumetric strain under uniaxial tension . +Independent hardening of the material under tension and compression can +be specified as described below. The tension hardening data provide the uniaxial tension yield stress +as a function of plastic strain, temperature, and field variables under uniaxial tension. The compression +hardening data provide the uniaxial compression yield stress as a function of plastic strain, temperature, +and field variables under uniaxial compression. +compression +tension +Figure 23.2.10–1 Typical stress-strain response of gray cast +iron under uniaxial tension and uniaxial compression. +Input File Usage: +Abaqus/CAE Usage: +*CAST IRON PLASTICITY +Property module: material editor: Mechanical→Plasticity→Cast +Iron Plasticity +Yield condition +Abaqus makes use of a composite yield surface to describe the different behavior in tension and +compression. In tension yielding is assumed to be governed by the maximum principal stress, while in +compression yielding is assumed to be pressure independent and governed by the deviatoric stresses +alone (Mises yield condition). +The model is described in detail in “Cast iron plasticity,” Section 4.3.7 of the Abaqus Theory +Manual. +Flow rule +For the purposes of discussing the flow and hardening behavior, it is useful to divide the meridional plane +into the two regions shown in Figure 23.2.10–2. +Mises stress, q +Gt +tensile +region +UC +Gc +compressive +region +equivalent pressure +stress, p +Figure 23.2.10–2 Schematic of the flow potentials in the p–q plane. +The region to the left of the uniaxial compression line (labeled UC) is referred to as the “tensile region,” +while the region to the right of the uniaxial compression line is referred to as the “compressive region.” +The flow potential consists of the Mises cylinder in the compressive region and an ellipsoidal “cap” +in the tensile region. The transition between the two surfaces is smooth. The projection of the flow +potential on the meridional plane consists of a straight line in the compressive +region and an ellipse in the tensile region. The corresponding projection on the deviatoric plane is a +circle. A consequence of the above choice is that plastic flow results in inelastic volume expansion in +the tensile region and no inelastic volume change in the compressive region . +Nonassociated flow +Since the flow potential is different from the yield surface (“nonassociated” flow), the material Jacobian +matrix is unsymmetric. Hence, to improve convergence, use the unsymmetric matrix storage and solution +scheme . +Hardening +Since the hardening of gray cast iron is different in uniaxial tension and uniaxial compression, you +need to provide two sets of hardening data in tabular form: one based on a uniaxial tension experiment +that defines +. Here, +compression, respectively. +and the other based on a uniaxial compression experiment that defines +are the equivalent plastic strains in uniaxial tension and uniaxial +and +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options in conjunction with the *CAST IRON +PLASTICITY option: +*CAST IRON COMPRESSION HARDENING +*CAST IRON TENSION HARDENING +Property module: material editor: Mechanical→Plasticity→Cast Iron +Plasticity: Compression Hardening and Tension Hardening +Restrictions on material data +The plastic Poisson’s ratio, +, is expected to be less than 0.5 since experimental results suggest that +there is a permanent increase in the volume of gray cast iron when it is loaded in uniaxial tension beyond +yield. For the potential to be well-defined, +must be greater than −1.0. Thus, the plastic Poisson’s +ratio must satisfy −1.0 +0.5. +The cast iron plasticity material model is intended for modeling cast iron and other materials like +cast iron for which the behavior in uniaxial tension and uniaxial compression matches the behavior shown +in Figure 23.2.10–1. In particular, the model expects the initial yield stress in uniaxial tension to be +less than the initial yield stress in uniaxial compression. Even if the overall stress-strain response and +hardening behavior in uniaxial stress states of some material other than cast iron is consistent with that +of cast iron, you must also ensure that the flow potential (which has been constructed specifically for +modeling cast iron) for the model is meaningful for other materials. Abaqus issues a warning message +only if the initial yield stress in uniaxial tension is equal to or greater than that in uniaxial compression. +No other checks are carried out in this regard. +If the yield stress in uniaxial tension is higher than that in uniaxial compression, a material point +in uniaxial tension may actually yield at the initial yield stress specified for uniaxial compression. This +apparent anomalous behavior is due to the fact that (as a result of unrealistic user-specified material +properties) a uniaxial tension stressing path in stress space meets the compressive (Mises) part of the +yield surface first. +Elements +The cast iron plasticity model can be used with any stress/displacement element in Abaqus other +than elements for which the assumed stress state is plane stress (plane stress continuum, shell, and +membrane elements). It can be used with one-dimensional elements (trusses and beams in a plane) and, +in Abaqus/Standard, with beams in space. +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Standard output variable +the +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2), +following variables have special meaning for the cast iron plasticity material model: +PEEQ +PEEQT +Equivalent plastic strain in uniaxial compression, +Equivalent plastic strain in uniaxial tension, +. +. +23.2.11 +TWO-LAYER VISCOPLASTICITY +Products: Abaqus/Standard Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Combining material behaviors,” Section 21.1.3 +• “Inelastic behavior,” Section 23.1.1 +• *ELASTIC +• *PLASTIC +• *VISCOUS +• “Defining the viscous component of a two-layer viscoplasticity model” in “Defining plasticity,” +Section 12.9.2 of the Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +The two-layer viscoplastic model: +• is intended for modeling materials in which significant time-dependent behavior as well as plasticity +is observed, which for metals typically occurs at elevated temperatures; +• consists of an elastic-plastic network that is in parallel with an elastic-viscous network (in contrast +to the coupled creep and plasticity capabilities in which the plastic and the viscous networks are in +series); +• is based on a Mises or Hill yield condition in the elastic-plastic network and any of the available +creep models in Abaqus/Standard (except the hyperbolic creep law) in the elastic-viscous network; +• assumes a deviatoric inelastic response (hence, the pressure-dependent plasticity or creep models +cannot be used to define the behavior of the two networks); +• is intended for modeling material response under fluctuating loads over a wide range of +temperatures; and +• has been shown to provide good results for thermomechanical loading. +Material behavior +The material behavior is broken down into three parts: elastic, plastic, and viscous. Figure 23.2.11–1 +shows a one-dimensional idealization of this material model, with the elastic-plastic and the elastic- +viscous networks in parallel. The following subsections describe the elastic and the inelastic (plastic and +viscous) behavior in detail. +K p +H’ + σ +K +η, m +Figure 23.2.11–1 One-dimensional idealization of the two-layer viscoplasticity model. +Elastic behavior +The elastic part of the response for both networks is specified using a linear isotropic elasticity definition. +Any one of the available elasticity models in Abaqus/Standard can be used to define the elastic behavior +of the networks. Referring to the one-dimensional idealization (Figure 23.2.11–1), the ratio of the elastic +modulus of the elastic-viscous network ( +) is given +by +) to the total (instantaneous) modulus ( +The user-specified ratio f, given as part of the viscous behavior definition as discussed later, apportions the +total moduli specified for the elastic behavior among the elastic-viscous and the elastic-plastic networks. +As a result, if isotropic elastic properties are defined, the Poisson’s ratios are the same in both networks. +On the other hand, if anisotropic elasticity is defined, the same type of anisotropy holds for both networks. +The properties specified for the elastic behavior are assumed to be the instantaneous properties ( +). +Input File Usage: +Abaqus/CAE Usage: +*ELASTIC +Property module: material editor: Mechanical→Elasticity→Elastic +Plastic behavior +A plasticity definition can be used to provide the static hardening data for the material model. +All available metal plasticity models, including Hill’s plasticity model to define anisotropic yield +(“Anisotropic yield/creep,” Section 23.2.6), can be used. +The elastic-plastic network does not +take into account rate-dependent yield. Hence, any +specification of strain rate dependence for the plasticity model is not allowed. +Input File Usage: +Use the following options: +*PLASTIC +*POTENTIAL +Property module: material editor: Mechanical→Plasticity→Plastic: +Suboptions→Potential +Abaqus/CAE Usage: +Viscous behavior +creep and swelling,” Section 23.2.4), except +The viscous behavior of the material can be governed by any of the available creep laws in +the +Abaqus/Standard (“Rate-dependent plasticity: +hyperbolic creep law. When you define the viscous behavior, you specify the viscosity parameters +and choose the specific type of viscous behavior. If you choose to input the creep law through user +subroutine CREEP, only deviatoric creep should be defined—more specifically, volumetric swelling +behavior should not be defined within user subroutine CREEP. In addition, you also specify the +fraction, f, that defines the ratio of the elastic modulus of the elastic-viscous network to the total +(instantaneous) modulus. Viscous stress ratios can be specified under the viscous behavior definition to +define anisotropic viscosity . +All material properties can be specified as functions of temperature and predefined field variables. +Input File Usage: +Use the following options: +*VISCOUS, LAW=TIME or STRAIN or USER +*POTENTIAL +Property module: material editor: Mechanical→Plasticity→Viscous: +Suboptions→Potential +Abaqus/CAE Usage: +Thermal expansion +Thermal expansion can be modeled by providing the thermal expansion coefficient of the material +(“Thermal expansion,” Section 26.1.2). Anisotropic expansion can be defined in the usual manner. In +the one-dimensional idealization the expansion element is assumed to be in series with the rest of the +network. +Calibration of material parameters +The calibration procedure is best explained in the context of the one-dimensional idealization of the +In the following discussion the viscous behavior is assumed to be governed by the +material model. +Norton-Hoff rate law, which is given by +In the expression above the subscript V denotes quantities in the elastic-viscous network alone. This +form of the rate law may be chosen, for example, by choosing a time-hardening power law for the +viscous behavior and setting +. For this basic case there are six material parameters that need to +be calibrated (Figure 23.2.11–1). These are the elastic properties of the two networks, +initial yield stress +; and the Norton-Hoff rate parameters, A and n. +; the hardening +and +; the +; and the hardening, +The experiment that needs to be performed is uniaxial tension under different constant strain rates. +A static (effectively zero strain rate) uniaxial tension test determines the long-term modulus, +; the +initial yield stress, +. The hardening is assumed to be linear for illustration +purposes. The material model is not limited to linear hardening, and any general hardening behavior +can be defined for the plasticity model. The instantaneous elastic modulus, +, can be +measured by measuring the initial elastic response of the material under nonzero, relatively high, strain +rates. Several such measurements at different applied strain rates can be compared until the instantaneous +moduli does not change with a change in the applied strain rate. The difference between K and +determines +. +To calibrate the parameters A and n, it is useful to recognize that the long-term (steady-state) +, is a constant stress of +. Under the assumption that the hardening modulus is negligible compared to +), the steady-state response of the overall material is given by +behavior of the elastic-viscous network under a constant applied strain rate, +magnitude +the elastic modulus ( +where +one can plot the quantity +constant value of +applied strain rate +is the total stress for a given total strain . To determine whether steady state has been reached, +and note when it becomes a constant. The +. By performing several tests at different values of the constant +as a function of +is equal to +, it is possible to determine the constants A and n. +Material response in different analysis steps +The material is active during all stress/displacement procedure types. In a static analysis step where +the long-term response is requested , only the elastic-plastic +network will be active; the elastic-viscous network will not contribute in any manner. In particular, +the stress in the viscous network will be zero during a long-term static response. If the creep effects +are removed in a coupled temperature-displacement procedure or a soils consolidation procedure, the +response of the elastic-viscous network will be assumed to be elastic only. During a linear perturbation +step, only the elastic response of the networks is considered. +Some stress/displacement procedure types (coupled temperature-displacement, soils consolidation, +and quasi-static) allow user control of the time integration accuracy of the viscous constitutive equations +through a user-specified error tolerance. In other procedure types where no such direct control is currently +available (static, dynamic), you must choose appropriate time increments. These time increments must +be small compared to the typical relaxation time of the material. +Elements +The two-layer viscoplastic model is not available for one-dimensional elements (beams and trusses). It +can be used with any other element in Abaqus/Standard that includes mechanical behavior (elements that +have displacement degrees of freedom). +Output +In addition to the standard output identifiers available in Abaqus/Standard (“Abaqus/Standard output +variable identifiers,” Section 4.2.1), the following variables have special meaning for the two-layer +viscoplastic material model: +EE +PE +VE +PS +VS +PEEQ +VEEQ +SENER +PENER +VENER +The elastic strain is defined as: +. +Plastic strain, +, in the elastic-plastic network. +Viscous strain, +, in the elastic-viscous network. +Stress, +Stress, +, in the elastic-plastic network. +, in the elastic-viscous network. +The equivalent plastic strain, defined as +The equivalent viscous strain, defined as +. +. +The elastic strain energy density per unit volume, defined as +. +The plastic dissipated energy per unit volume, defined as +The viscous dissipated energy per unit volume, defined as +. +. +The above definitions of the strain tensors imply that the total strain is related to the elastic, plastic, +and viscous strains through the following relation: +. The above definitions of the +where according to the definitions given above +output variables apply to all procedure types. In particular, when the long-term response is requested for +a static procedure, the elastic-viscous network does not carry any stress and the definition of the elastic +strain reduces to +, which implies that the total stress is related to the elastic strain through +the instantaneous elastic moduli. +and +Additional reference +• Kichenin, J., “Comportement Thermomécanique du Polyéthylène—Application aux Structures +Gazières,” Thèse de Doctorat de l’Ecole Polytechnique, Spécialité: Mécanique et Matériaux, 1992. +23.2.12 +ORNL – OAK RIDGE NATIONAL LABORATORY CONSTITUTIVE MODEL +Products: Abaqus/Standard Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Inelastic behavior,” Section 23.1.1 +• “Classical metal plasticity,” Section 23.2.1 +• “Rate-dependent plasticity: creep and swelling,” Section 23.2.4 +• *ORNL +• *PLASTIC +• *CREEP +• “Using the Oak Ridge National Laboratory (ORNL) constitutive model in plasticity and creep +calculations” in “Defining plasticity,” Section 12.9.2 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Specifying cycled yield stress data for the ORNL model” in “Defining plasticity,” Section 12.9.2 +of the Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +The Oak Ridge National Laboratory (ORNL) constitutive model: +• allows for use of the rules defined in the Nuclear Standard NEF 9–5T, “Guidelines and Procedures +for Design of Class 1 Elevated Temperature Nuclear System Components,” in plasticity and creep +calculations; +• is intended for use in modeling types 304 and 316 stainless steel at relatively high temperatures; +• can be used only with the metal plasticity models (linear kinematic hardening only) and/or the strain +hardening form of the metal creep law; and +• is described in detail in “ORNL constitutive theory,” Section 4.3.8 of the Abaqus Theory Manual. +Usage with plasticity +The ORNL constitutive model in Abaqus/Standard is based on the March 1981 issue of the Nuclear +Standard NEF 9–5T and on the October 1986 issue, which revises the constitutive model extensively. +This model adds isotropic hardening of the plastic yield surface from a virgin material state to a +Initially the material is assumed to harden kinematically according to a bilinear +fully cycled state. +If a strain reversal takes place or if the creep strain +representation of the virgin stress-strain curve. +reaches 0.2%, +the yield surface expands isotropically to the user-defined tenth-cycle stress-strain +curve. Further hardening occurs kinematically according to a bilinear representation of the tenth-cycle +stress-strain curve. +You must specify the virgin yield stress and the hardening through a plasticity model definition and +the elastic part of the response through a linear elasticity model definition. You specify the tenth-cycle +yield stress and hardening values separately. The yield stress at each temperature should be defined by +giving its value at zero plastic strain and at one additional nonzero plastic strain point, thus giving a +constant hardening rate (linear work hardening). +Input File Usage: +Use all of the following options in the same material data block: +Abaqus/CAE Usage: +*PLASTIC +*ORNL +*CYCLED PLASTIC +Property module: material editor: Mechanical→Plasticity→Plastic: +Suboptions→Ornl and Suboptions→Cycled Plastic +Abaqus/Standard also allows you to invoke the optional kinematic shift ( ) reset procedure that is +reset procedure explicitly, +described in Section 4.3.5 of the Nuclear Standard. If you do not specify the +it is not used. +Input File Usage: +Abaqus/CAE Usage: +*ORNL, RESET +Property module: material editor: Suboptions→Ornl: Invoke reset +procedure +Usage with creep +The ORNL constitutive model assumes that creep uses the strain hardening formulation. It introduces +auxiliary hardening rules when strain reversals occur. An algorithm providing details is presented in +“ORNL constitutive theory,” Section 4.3.8 of the Abaqus Theory Manual. It can be used only when the +creep behavior is defined by a strain-hardening power law. +Input File Usage: +Use both of the following options in the same material data block: +Abaqus/CAE Usage: +*CREEP, LAW=STRAIN +*ORNL +Property module: material editor: Mechanical→Plasticity→Creep: +Law: Strain-Hardening: Suboptions→Ornl +Translation of the yield surface during creep +The ORNL formulation can also cause the center of the yield surface to translate during creep for use in +subsequent plastic increments; this behavior is defined through two optional user-defined parameters. +Specifying saturation rates for kinematic shift +You can specify A, the saturation rates for kinematic shift caused by creep strain as defined by +Equation (15) of Section 4.3.3–3 of the Nuclear Standard. The default value is 0.3. Set A=0.0 to use +the 1986 revision of the standard. +Input File Usage: +*ORNL, A=A +Abaqus/CAE Usage: +Property module: material editor: Suboptions→Ornl: Saturation +rates for kinematic shift: A +Specifying the rate of kinematic shift +You can specify H, the rate of kinematic shift with respect to creep strain (Equation (7) of Section 4.3.2–1 +of the Nuclear Standard). Set H=0.0 to use the 1986 revision of the standard. If you do not specify a +value for H, it is determined according to Section 4.3.3–3 of the 1981 revision of the standard. +Input File Usage: +Abaqus/CAE Usage: +*ORNL, H=H +Property module: material editor: Suboptions→Ornl: Rate of +kinematic shift wrt creep strain: H +Initial conditions +When we need to study the behavior of a material that has already been subjected to some work hardening, +initial equivalent plastic strain values can be provided to specify the yield stress corresponding to the work +hardened state. See “Inelastic behavior,” Section 23.1.1, for additional details. Initial values can also +be provided for the backstress tensor, +, to include strain-induced anisotropy. See “Initial conditions +in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1, for more information. For more complicated +cases initial conditions can be defined through user subroutine HARDINI. +Input File Usage: +Use the following option to specify the initial equivalent plastic strain directly: +*INITIAL CONDITIONS, TYPE=HARDENING +Use the following option in Abaqus/Standard to specify the initial equivalent +plastic strain in user subroutine HARDINI: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=HARDENING, USER +Use the following options to specify the initial equivalent plastic strain directly: +Load module: Create Predefined Field: Step: Initial, choose Mechanical +for the Category and Hardening for the Types for Selected Step +Use the following options in Abaqus/Standard to specify the initial equivalent +plastic strain in user subroutine HARDINI: +Load module: Create Predefined Field: Step: Initial, choose +Mechanical for the Category and Hardening for the Types for +Selected Step; Definition: User-defined +Elements +The ORNL constitutive model can be used with any elements in Abaqus/Standard that include +mechanical behavior (elements that have displacement degrees of freedom). +Output +In addition to the standard output identifiers available in Abaqus/Standard (“Abaqus/Standard output +variable identifiers,” Section 4.2.1), variables associated with creep (“Rate-dependent plasticity: creep +and swelling,” Section 23.2.4) and the kinematic hardening plasticity models (“Models for metals +subjected to cyclic loading,” Section 23.2.2) are available for the ORNL constitutive model. +23.2.13 +DEFORMATION PLASTICITY +Products: Abaqus/Standard Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Inelastic behavior,” Section 23.1.1 +• *DEFORMATION PLASTICITY +• “Defining deformation plasticity” in “Defining other mechanical models,” Section 12.9.4 of the +Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +The deformation theory Ramberg-Osgood plasticity model: +• is primarily intended for use in developing fully plastic solutions for fracture mechanics applications +in ductile metals; and +• cannot appear with any other mechanical response material models since it completely describes +the mechanical response of the material. +One-dimensional model +In one dimension the model is +where +is the stress; +is the strain; +is Young’s modulus (defined as the slope of the stress-strain curve at zero stress); +is the “yield” offset; +is the yield stress, in the sense that, when +, +; and +is the hardening exponent for the “plastic” (nonlinear) term: +. +The material behavior described by this model is nonlinear at all stress levels, but for commonly +or more) the nonlinearity becomes significant only at +used values of the hardening exponent ( +stress magnitudes approaching or exceeding +. +Generalization to multiaxial stress states +The one-dimensional model is generalized to multiaxial stress states using Hooke’s law for the linear +term and the Mises stress potential and associated flow law for the nonlinear term: +where +is the strain tensor, +is the stress tensor, +is the equivalent hydrostatic stress, +is the Mises equivalent stress, +is the stress deviator, and +is the Poisson’s ratio. +The linear part of the behavior can be compressible or incompressible, depending on the value of the +Poisson’s ratio, but the nonlinear part of the behavior is incompressible (because the flow is normal to +the Mises stress potential). The model is described in detail in “Deformation plasticity,” Section 4.3.9 +of the Abaqus Theory Manual. +You specify the parameters E, +, +, n, and +directly. They can be defined as a tabular function of +temperature. +Input File Usage: +Abaqus/CAE Usage: +Typical applications +*DEFORMATION PLASTICITY +Property module: material editor: Mechanical→Deformation Plasticity +The deformation plasticity model is most commonly applied in static loading with small-displacement +analysis, where the fully plastic solution must be developed in a part of the model. Generally, the load +is ramped on until all points in the region being monitored satisfy the condition that the “plastic strain” +dominates and, hence, exhibit fully plastic behavior, which is defined as +or +You can specify the name of a particular element set to be monitored in a static analysis step for fully +plastic behavior. The step will end when the solutions at all constitutive calculation points in the element +set are fully plastic, when the maximum number of increments specified for the step is reached, or when +the time period specified for the static step is exceeded, whichever comes first. +Input File Usage: +Abaqus/CAE Usage: +*STATIC, FULLY PLASTIC=ElsetName +Step module: Create Step: General: Static, General: Other: +Stop when region region is fully plastic. +Elements +Deformation plasticity can be used with any stress/displacement element in Abaqus/Standard. Since it +will generally be used for cases when the deformation is dominated by plastic flow, the use of “hybrid” +(mixed formulation) or reduced-integration elements is recommended with this material model. +23.3 +Other plasticity models +• “Extended Drucker-Prager models,” Section 23.3.1 +• “Modified Drucker-Prager/Cap model,” Section 23.3.2 +• “Mohr-Coulomb plasticity,” Section 23.3.3 +• “Critical state (clay) plasticity model,” Section 23.3.4 +• “Crushable foam plasticity models,” Section 23.3.5 +23.3.1 +EXTENDED DRUCKER-PRAGER MODELS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Inelastic behavior,” Section 23.1.1 +• “Rate-dependent yield,” Section 23.2.3 +• “Rate-dependent plasticity: creep and swelling,” Section 23.2.4 +• Chapter 24, “Progressive Damage and Failure” +• *DRUCKER PRAGER +• *DRUCKER PRAGER HARDENING +• *RATE DEPENDENT +• *DRUCKER PRAGER CREEP +• *TRIAXIAL TEST DATA +• “Defining Drucker-Prager plasticity” in “Defining plasticity,” Section 12.9.2 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +The extended Drucker-Prager models: +• are used to model frictional materials, which are typically granular-like soils and rock, and exhibit +pressure-dependent yield (the material becomes stronger as the pressure increases); +• are used to model materials in which the compressive yield strength is greater than the tensile yield +strength, such as those commonly found in composite and polymeric materials; +• allow a material to harden and/or soften isotropically; +• generally allow for volume change with inelastic behavior: +the flow rule, defining the inelastic +straining, allows simultaneous inelastic dilation (volume increase) and inelastic shearing; +• can include creep in Abaqus/Standard if the material exhibits long-term inelastic deformations; +• can be defined to be sensitive to the rate of straining, as is often the case in polymeric materials; +• can be used in conjunction with either the elastic material model (“Linear elastic behavior,” +Section 22.2.1) or, in Abaqus/Standard if creep is not defined, the porous elastic material model +(“Elastic behavior of porous materials,” Section 22.3.1); +• can be used in conjunction with an equation of state model (“Equation of state,” Section 25.2.1) to +describe the hydrodynamic response of the material in Abaqus/Explicit; +• can be used in conjunction with the models of progressive damage and failure (“Damage and failure +for ductile metals: overview,” Section 24.2.1) to specify different damage initiation criteria and +damage evolution laws that allow for the progressive degradation of the material stiffness and the +removal of elements from the mesh; and +• are intended to simulate material response under essentially monotonic loading. +Yield criteria +The yield criteria for this class of models are based on the shape of the yield surface in the meridional +plane. The yield surface can have a linear form, a hyperbolic form, or a general exponent form. These +surfaces are illustrated in Figure 23.3.1–1. The stress invariants and other terms in each of the three +related yield criteria are defined later in this section. +The linear model (Figure 23.3.1–1a) provides for a possibly noncircular yield surface in the +deviatoric plane ( +-plane) to match different yield values in triaxial tension and compression, associated +inelastic flow in the deviatoric plane, and separate dilation and friction angles. Input data parameters +define the shape of the yield and flow surfaces in the meridional and deviatoric planes as well as other +characteristics of inelastic behavior such that a range of simple theories is provided—the original +Drucker-Prager model is available within this model. However, this model cannot provide a close +match to Mohr-Coulomb behavior, as described later in this section. +The hyperbolic and general exponent models use a von Mises (circular) section in the deviatoric +In the meridional plane a hyperbolic flow potential is used for both models, which, in +stress plane. +general, means nonassociated flow. +The choice of model to be used depends largely on the analysis type, the kind of material, the +experimental data available for calibration of the model parameters, and the range of pressure stress +values that the material is likely to experience. It is common to have either triaxial test data at different +levels of confining pressure or test data that are already calibrated in terms of a cohesion and a friction +angle and, sometimes, a triaxial tensile strength value. If triaxial test data are available, the material +parameters must be calibrated first. The accuracy with which the linear model can match these test data +is limited by the fact that it assumes linear dependence of deviatoric stress on pressure stress. Although +the hyperbolic model makes a similar assumption at high confining pressures, it provides a nonlinear +relationship between deviatoric and pressure stress at low confining pressures, which may provide a +better match of the triaxial experimental data. The hyperbolic model is useful for brittle materials for +which both triaxial compression and triaxial tension data are available, which is a common situation for +materials such as rocks. The most general of the three yield criteria is the exponent form. This criterion +provides the most flexibility in matching triaxial test data. Abaqus determines the material parameters +required for this model directly from the triaxial test data. A least-squares fit that minimizes the relative +error in stress is used for this purpose. +For cases where the experimental data are already calibrated in terms of a cohesion and a friction +angle, the linear model can be used. If these parameters are provided for a Mohr-Coulomb model, it is +necessary to convert them to Drucker-Prager parameters. The linear model is intended primarily for +If tensile stresses are significant, +applications where the stresses are for the most part compressive. +hydrostatic tension data should be available (along with the cohesion and friction angle) and the +hyperbolic model should be used. +Calibration of these models is discussed later in this section. +a) Linear Drucker-Prager: F = t − p tan β − d = 0 +−d /tanβ +−p +b) Hyperbolic: F = √(d − p tan β) + q +|0 +|0 + − p tan β − d = 0 +−p +c) Exponent form: F = aq − p − p = 0 +Figure 23.3.1–1 Yield surfaces in the meridional plane. +Hardening and rate dependence +For granular materials these models are often used as a failure surface, in the sense that the material +can exhibit unlimited flow when the stress reaches yield. This behavior is called perfect plasticity. The +models are also provided with isotropic hardening. In this case plastic flow causes the yield surface +to change size uniformly with respect to all stress directions. This hardening model is useful for cases +involving gross plastic straining or in which the straining at each point is essentially in the same direction +in strain space throughout the analysis. Although the model is referred to as an isotropic “hardening” +model, strain softening, or hardening followed by softening, can be defined. +As strain rates increase, many materials show an increase in their yield strength. This effect +becomes important in many polymers when the strain rates range between 0.1 and 1 per second; it can +be very important for strain rates ranging between 10 and 100 per second, which are characteristic of +high-energy dynamic events or manufacturing processes. The effect is generally not as important in +granular materials. The evolution of the yield surface with plastic deformation is described in terms of +the equivalent stress +, which can be chosen as either the uniaxial compression yield stress, the uniaxial +tension yield stress, or the shear (cohesion) yield stress: +where +is the equivalent plastic strain rate, defined for the linear +Drucker-Prager model as +if hardening is defined in uniaxial += +compression; += += +if hardening is defined in uniaxial tension; +if hardening is defined in pure shear, +and defined for the hyperbolic and exponential Drucker-Prager +models as +is the equivalent plastic strain; +is temperature; and +are other predefined field variables. +The functional dependence +includes hardening as well as rate-dependent effects. +The material data can be input either directly in a tabular format or by correlating it to static relations +based on yield stress ratios. +Rate dependence as described here is most suitable for moderate- to high-speed events in +Abaqus/Standard. Time-dependent inelastic deformation at low deformation rates can be better +represented by creep models. Such inelastic deformation, which can coexist with rate-independent +plastic deformation, +the existence of creep in an +is described later in this section. However, +Abaqus/Standard material definition precludes the use of rate dependence as described here. +When using the Drucker-Prager material model, Abaqus allows you to prescribe initial hardening +by defining initial equivalent plastic strain values, as discussed below along with other details regarding +the use of initial conditions. +Direct tabular data +Test data are entered as tables of yield stress values versus equivalent plastic strain at different equivalent +plastic strain rates; one table per strain rate. Compression data are more commonly available for +geological materials, whereas tension data are usually available for polymeric materials. The guidelines +on how to enter these data are provided in “Rate-dependent yield,” Section 23.2.3. +Input File Usage: +Abaqus/CAE Usage: +*DRUCKER PRAGER HARDENING, RATE= +Property module: material editor: Mechanical→Plasticity→Drucker +Prager: Suboptions→Drucker Prager Hardening: toggle on +Use strain-rate-dependent data +Yield stress ratios +Alternatively, the strain rate behavior can be assumed to be separable, so that the stress-strain dependence +is similar at all strain rates: +where +nonzero strain rate to the static yield stress (so that +is the static stress-strain behavior and +). +is the ratio of the yield stress at +Two methods are offered to define R in Abaqus: specifying an overstress power law or defining the +variable R directly as a tabular function of +. +Overstress power law +The Cowper-Symonds overstress power law has the form +and +where +of other predefined field variables. +are material parameters that can be functions of temperature and, possibly, +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*DRUCKER PRAGER HARDENING +*RATE DEPENDENT, TYPE=POWER LAW +Property module: material editor: Mechanical→Plasticity→Drucker +Prager: Suboptions→Drucker Prager Hardening; Suboptions→Rate +Dependent: Hardening: Power Law +Tabular function +When R is entered directly, it is entered as a tabular function of the equivalent plastic strain rate, +temperature, +. +; and predefined field variables, +; +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*DRUCKER PRAGER HARDENING +*RATE DEPENDENT, TYPE=YIELD RATIO +Property module: material editor: Mechanical→Plasticity→Drucker +Prager: Suboptions→Drucker Prager Hardening; Suboptions→Rate +Dependent: Hardening: Yield Ratio +Johnson-Cook rate dependence +Johnson-Cook rate dependence has the form +where +on predefined field variables. +and C are material constants that do not depend on temperature and are assumed not to depend +Input File Usage: +Abaqus/CAE Usage: +*DRUCKER PRAGER HARDENING +*RATE DEPENDENT, TYPE=JOHNSON COOK +Property module: material editor: Mechanical→Plasticity→Drucker +Prager: Suboptions→Drucker Prager Hardening; Suboptions→Rate +Dependent: Hardening: Johnson-Cook +Stress invariants +The yield stress surface makes use of two invariants, defined as the equivalent pressure stress, +and the Mises equivalent stress, +where +is the stress deviator, defined as +In addition, the linear model also uses the third invariant of deviatoric stress, +Linear Drucker-Prager model +The linear model is written in terms of all three stress invariants. It provides for a possibly noncircular +yield surface in the deviatoric plane to match different yield values in triaxial tension and compression, +associated inelastic flow in the deviatoric plane, and separate dilation and friction angles. +Yield criterion +The linear Drucker-Prager criterion is written as +where +is the slope of the linear yield surface in the p–t stress plane and is commonly +referred to as the friction angle of the material; +is the cohesion of the material; and +is the ratio of the yield stress in triaxial tension to the yield stress in triaxial +compression and, thus, controls the dependence of the yield surface on the value +of the intermediate principal stress . +In the case of hardening defined in uniaxial compression, the linear yield criterion precludes friction +angles +When +71.5° ( +, +3), which is unlikely to be a limitation for real materials. +, which implies that the yield surface is the von Mises circle in the deviatoric +-plane), in which case the yield stresses in triaxial tension and compression +principal stress plane (the +are the same. To ensure that the yield surface remains convex requires +The cohesion, d, of the material is related to the input data as +. +Plastic flow +G is the flow potential, chosen in this model as +S3 +t = + q 1+ +1_ +) + - 1- +1_ +K 3 +)r +)) +_ +1_ +Curve +1.0 +0.8 +S2 +S1 +Figure 23.3.1–2 Typical yield/flow surfaces of the linear model in the deviatoric plane. +is the dilation angle in the p–t plane. A geometric interpretation of +is shown in the +where +p–t diagram of Figure 23.3.1–3. In the case of hardening defined in uniaxial compression, this flow rule +definition precludes dilation angles +3). This restriction is not seen as a limitation +since it is unlikely this will be the case for real materials. +71.5° ( +dεpl +hardening +Figure 23.3.1–3 Linear Drucker-Prager model: yield surface +and flow direction in the p–t plane. +For granular materials the linear model is normally used with nonassociated flow in the p–t plane, +in the sense that the flow is assumed to be normal to the yield surface in the +-plane but at an angle +to the t-axis in the p–t plane, where usually +results from setting +and +Nonassociated flow is also generally assumed when the model is used for polymeric materials. If +the inelastic deformation is incompressible; if +dilation angle. +, as illustrated in Figure 23.3.1–3. Associated flow +. +, +is referred to as the +. The original Drucker-Prager model is available by setting +, the material dilates. Hence, +The relationship between the flow potential and the incremental plastic strain for the linear model +is discussed in detail in “Models for granular or polymer behavior,” Section 4.4.2 of the Abaqus Theory +Manual. +Input File Usage: +Abaqus/CAE Usage: +*DRUCKER PRAGER, SHEAR CRITERION=LINEAR +Property module: material editor: Mechanical→Plasticity→Drucker +Prager: Shear criterion: Linear +Nonassociated flow +the material stiffness matrix is not symmetric; +Nonassociated flow implies that +the +unsymmetric matrix storage and solution scheme should be used in Abaqus/Standard . If the difference between +is not large and the region of the model in +which inelastic deformation is occurring is confined, it is possible that a symmetric approximation to +the material stiffness matrix will give an acceptable rate of convergence and the unsymmetric matrix +scheme may not be needed. +therefore, +and +Hyperbolic and general exponent models +The hyperbolic and general exponent models available are written in terms of the first two stress +invariants only. +Hyperbolic yield criterion +The hyperbolic yield criterion is a continuous combination of the maximum tensile stress condition of +Rankine (tensile cutoff) and the linear Drucker-Prager condition at high confining stress. It is written as +where +and +is the initial hydrostatic tension strength of the material; +is the hardening parameter; +is the initial value of +; and +is the friction angle measured at high confining pressure, as shown in +Figure 23.3.1–1(b). +The hardening parameter, +, can be obtained from test data as follows: +The isotropic hardening assumed in this model treats +Figure 23.3.1–4. +as constant with respect to stress as depicted in +hardening +l0/tanβ +l0/tanβ +l0/tanβ +Figure 23.3.1–4 Hyperbolic model: yield surface and hardening in the p–q plane. +Input File Usage: +Abaqus/CAE Usage: +*DRUCKER PRAGER, SHEAR CRITERION=HYPERBOLIC +Property module: material editor: Mechanical→Plasticity→Drucker +Prager: Shear criterion: Hyperbolic +General exponent yield criterion +The general exponent form provides the most general yield criterion available in this class of models. +The yield function is written as +where +and +are material parameters that are independent of plastic +deformation; and +is the hardening parameter that represents the hydrostatic +tension strength of the material as shown in Figure 23.3.1–1(c). +is related to the input test data as +The isotropic hardening assumed in this model treats a and b as constant with respect to stress, as depicted +in Figure 23.3.1–5. +1/b +t( )a +hardening +Figure 23.3.1–5 General exponent model: yield surface and hardening in the p–q plane. +The material parameters a and b can be given directly. Alternatively, if triaxial test data at different levels +of confining pressure are available, Abaqus will determine the material parameters from the triaxial test +data, as discussed below. +Input File Usage: +Abaqus/CAE Usage: +*DRUCKER PRAGER, SHEAR CRITERION=EXPONENT FORM +Property module: material editor: Mechanical→Plasticity→Drucker +Prager: Shear criterion: Exponent Form +Plastic flow +G is the flow potential, chosen in these models as a hyperbolic function: +where +is the dilation angle measured in the p–q plane at high confining +pressure; +is the initial yield stress, taken from the user-specified Drucker- +Prager hardening data; and +is a parameter, referred to as the eccentricity, that defines the +rate at which the function approaches the asymptote (the flow +potential tends to a straight line as the eccentricity tends to +zero). +Suitable default values are provided for +stress used. +, as described below. The value of will depend on the yield +This flow potential, which is continuous and smooth, ensures that the flow direction is always +uniquely defined. The function approaches the linear Drucker-Prager flow potential asymptotically at +high confining pressure stress and intersects the hydrostatic pressure axis at 90°. A family of hyperbolic +potentials in the meridional stress plane is shown in Figure 23.3.1–6. The flow potential is the von Mises +circle in the deviatoric stress plane (the +-plane). +dεpl + σ|0 +∋ +Figure 23.3.1–6 Family of hyperbolic flow potentials in the p–q plane. +, and the material +For the hyperbolic model flow is nonassociated in the p–q plane if the dilation angle, +friction angle, +, are different. The hyperbolic model provides associated flow in the p–q plane only +when +) +is assumed if the flow potential is used with the hyperbolic model, so that associated flow is recovered +when +. A default value of +and +. +For the general exponent model flow is always nonassociated in the p–q plane. The default flow +potential eccentricity is +, which implies that the material has almost the same dilation angle +over a wide range of confining pressure stress values. Increasing the value of provides more curvature +to the flow potential, implying that the dilation angle increases more rapidly as the confining pressure +decreases. Values of +that are significantly less than the default value may lead to convergence problems +if the material is subjected to low confining pressures because of the very tight curvature of the flow +potential locally where it intersects the p-axis. +The relationship between the flow potential and the incremental plastic strain for the hyperbolic +and general exponent models is discussed in detail in “Models for granular or polymer behavior,” +Section 4.4.2 of the Abaqus Theory Manual. +DRUCKER-PRAGER +the material stiffness matrix is not symmetric; +Nonassociated flow implies that +the +unsymmetric matrix storage and solution scheme should be used in Abaqus/Standard . If the difference between +in the hyperbolic model is not large and +if the region of the model in which inelastic deformation is occurring is confined, it is possible that a +symmetric approximation to the material stiffness matrix will give an acceptable rate of convergence. +In such cases the unsymmetric matrix scheme may not be needed. +therefore, +and +Progressive damage and failure +In Abaqus/Explicit the extended Drucker-Prager models can be used in conjunction with the models +of progressive damage and failure discussed in “Damage and failure for ductile metals: overview,” +Section 24.2.1. The capability allows for the specification of one or more damage initiation criteria, +including ductile, shear, forming limit diagram (FLD), forming limit stress diagram (FLSD), and +Müschenborn-Sonne forming limit diagram (MSFLD) criteria. After damage initiation, the material +stiffness is degraded progressively according to the specified damage evolution response. The model +offers two failure choices, including the removal of elements from the mesh as a result of tearing or +ripping of the structure. The progressive damage models allow for a smooth degradation of the material +stiffness, making them suitable for both quasi-static and dynamic situations. +Input File Usage: +Use the following options: +Abaqus/CAE Usage: +*DAMAGE INITIATION +*DAMAGE EVOLUTION +Property module: material editor: Mechanical→Damage for Ductile +Metals→damage initiation type: specify the damage initiation criterion: +Suboptions→Damage Evolution: specify the damage evolution parameters +Matching experimental triaxial test data +In such a test the +Data for geological materials are most commonly available from triaxial testing. +specimen is confined by a pressure stress that is held constant during the test. The loading is an +additional tension or compression stress applied in one direction. Typical results include stress-strain +curves at different levels of confinement, as shown in Figure 23.3.1–7. To calibrate the yield parameters +for this class of models, you need to decide which point on each stress-strain curve will be used for +calibration. For example, if you wish to calibrate the initial yield surface, the point in each stress-strain +curve corresponding to initial deviation from elastic behavior should be used. Alternatively, if you wish +to calibrate the ultimate yield surface, the point in each stress-strain curve corresponding to the peak +stress should be used. +One stress data point from each stress-strain curve at a different level of confinement is plotted in the +meridional stress plane (p–t plane if the linear model is to be used, or p–q plane if the hyperbolic or general +exponent model will be used). This technique calibrates the shape and position of the yield surface, as +shown in Figure 23.3.1–8, and is adequate to define a model if it is to be used as a failure surface (perfect +points chosen to define +shape and position of +yield surface +-σ +-σ +-σ2 +increasing +confinement +Figure 23.3.1–7 Triaxial tests with stress-strain curves for typical +geological materials at different levels of confinement. +Figure 23.3.1–8 Yield surface in meridional plane. +plasticity). The models are also available with isotropic hardening, in which case hardening data are +required to complete the calibration. In an isotropic hardening model plastic flow causes the yield surface +to change size uniformly; in other words, only one of the stress-strain curves depicted in Figure 23.3.1–7 +can be used to represent hardening. The curve that represents hardening most accurately over the range +of loading conditions anticipated should be selected (usually the curve for the average anticipated value +of pressure stress). +As stated earlier, two types of triaxial test data are commonly available for geological materials. +In a triaxial compression test the specimen is confined by pressure and an additional compression stress +is superposed in one direction. Thus, the principal stresses are all negative, with +(Figure 23.3.1–9a). +minimum principal stresses, respectively. +are the maximum, intermediate, and +In the preceding inequality +, and +, +-σ +1= σ +≥ +2 σ +-σ +-σ +-σ +DRUCKER-PRAGER +≥ +1 +2 = σ +-σ +Figure 23.3.1–9 a) Triaxial compression and b) tension. +The values of the stress invariants are +and +so that +The triaxial compression results can, thus, be plotted in the meridional plane shown in Figure 23.3.1–8. +Linear Drucker-Prager model +Fitting the best straight line through the triaxial compression results provides +Drucker-Prager model. +and d for the linear +Triaxial tension data are also needed to define K in the linear Drucker-Prager model. Under triaxial +tension the specimen is again confined by pressure, after which the pressure in one direction is reduced. +In this case the principal stresses are +(Figure 23.3.1–9b). +The stress invariants are now +and +so that +Thus, K can be found by plotting these test results as q versus p and again fitting the best straight +line. The triaxial compression and tension lines must intercept the p-axis at the same point, and the ratio +of values of q for triaxial tension and compression at the same value of p then gives K (Figure 23.3.1–10). +Best fit to triaxial +compression data +Best fit to triaxial +tension data +qc +qt +qt = K +qc +Figure 23.3.1–10 Linear model: fitting triaxial compression and tension data. +Hyperbolic model +and +for the hyperbolic model. This fit is performed in the same manner as that used to obtain +Fitting the best straight line through the triaxial compression results at high confining pressures provides +and +d for the linear Drucker-Prager model. In addition, hydrostatic tension data are required to complete the +calibration of the hyperbolic model so that the initial hydrostatic tension strength, +, can be defined. +DRUCKER-PRAGER +Given triaxial data in the meridional plane, Abaqus provides a capability to determine the material +parameters a, b, and +required for the exponent model. The parameters are determined on the basis +of a “best fit” of the triaxial test data at different levels of confining stress. A least-squares fit which +minimizes the relative error in stress is used to obtain the “best fit” values for a, b, and +. The capability +allows all three parameters to be calibrated or, if some of the parameters are known, only the remaining +parameters to be calibrated. This ability is useful if only a few data points are available, in which case +you may wish to fit the best straight line ( +) through the data points (effectively reducing the model +to a linear Drucker-Prager model). Partial calibration can also be useful in a case when triaxial test data +at low confinement are unreliable or unavailable, as is often the case for cohesionless materials. In this +case a better fit may be obtained if the value of +The data must be provided in terms of the principal stresses +is the +confining stress and +is the stress in the loading direction. The Abaqus sign convention must be +followed such that tensile stresses are positive and compressive stresses are negative. One pair of stresses +must be entered from each triaxial test. As many data points as desired can be entered from triaxial tests +at different levels of confining stress. +and +is specified and only a and b are calibrated. +, where +If the exponent model is used as a failure surface (perfect plasticity), the Drucker-Prager hardening +behavior does not have to be specified. The hydrostatic tension strength, +, obtained from the calibration +will then be used as the failure stress. However, if the Drucker-Prager hardening behavior is specified +together with the triaxial test data, the value of +obtained from the calibration will be ignored. In this +case Abaqus will interpolate +directly from the hardening data. +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*DRUCKER PRAGER, SHEAR CRITERION=EXPONENT FORM, +TEST DATA +*TRIAXIAL TEST DATA +Property module: material editor: Mechanical→Plasticity→Drucker +Prager: Shear criterion: Exponent Form, toggle on Use Suboption +Triaxial Test Data, and select Suboptions→Triaxial Test Data +Matching Mohr-Coulomb parameters to the Drucker-Prager model +Sometimes experimental data are not directly available. Instead, you are provided with the friction angle +and cohesion values for the Mohr-Coulomb model. In that case the simplest way to proceed is to use +the Mohr-Coulomb model . In some situations it may +be necessary to use the Drucker-Prager model instead of the Mohr-Coulomb model (such as when rate +effects need to be considered), in which case we need to calculate values for the parameters of a Drucker- +Prager model to provide a reasonable match to the Mohr-Coulomb parameters. +The Mohr-Coulomb failure model is based on plotting Mohr’s circle for states of stress at failure in +the plane of the maximum and minimum principal stresses. The failure line is the best straight line that +touches these Mohr’s circles (Figure 23.3.1–11). +σ +s = +1 σ +- +m= +1+σ + 2 +σ +(compressive stress) +Figure 23.3.1–11 Mohr-Coulomb failure model. +Therefore, the Mohr-Coulomb model is defined by +where +is negative in compression. From Mohr’s circle, +Substituting for +and , multiplying both sides by +, and reducing, the Mohr-Coulomb model +can be written as +where +is half of the difference between the maximum principal stress, +(and is, therefore, the maximum shear stress), +, and the minimum principal stress, +is the average of the maximum and minimum principal stresses, and +is the friction angle. Thus, the +model assumes a linear relationship between deviatoric and pressure stress and, so, can be matched by +the linear or hyperbolic Drucker-Prager models provided in Abaqus. +The Mohr-Coulomb model assumes that failure is independent of the value of the intermediate +principal stress, but the Drucker-Prager model does not. The failure of typical geotechnical materials +generally includes some small dependence on the intermediate principal stress, but the Mohr-Coulomb +model is generally considered to be sufficiently accurate for most applications. This model has vertices +in the deviatoric plane . +S3 +Mohr-Coulomb +S1 +S2 +Drucker-Prager +Figure 23.3.1–12 Mohr-Coulomb model in the deviatoric plane. +The implication is that, whenever the stress state has two equal principal stress values, the flow +direction can change significantly with little or no change in stress. None of the models currently +available in Abaqus can provide such behavior; even in the Mohr-Coulomb model the flow potential +is smooth. This limitation is generally not a key concern in many design calculations involving +Coulomb-like materials, but it can limit the accuracy of the calculations, especially in cases where flow +localization is important. +Matching plane strain response +Plane strain problems are often encountered in geotechnical analysis; for example, long tunnels, footings, +and embankments. Therefore, the constitutive model parameters are often matched to provide the same +flow and failure response in plane strain. +The matching procedure described below is carried out in terms of the linear Drucker-Prager model +but is also applicable to the hyperbolic model at high levels of confining stress. +The linear Drucker-Prager flow potential defines the plastic strain increment as +where +plane, we can take +is the equivalent plastic strain increment. Since we wish to match the behavior in only one +. Thus, +, which implies that +Writing this expression in terms of principal stresses provides +with similar expressions for +have +, which provides the constraint +and +. Assume plane strain in the 1-direction. At limit load we must +Using this constraint we can rewrite q and p in terms of the principal stresses in the plane of deformation, +and +, as +and +With these expressions the Drucker-Prager yield surface can be written in terms of +and +as +The Mohr-Coulomb yield surface in the +plane is +By comparison, +These relationships provide a match between the Mohr-Coulomb material parameters and linear +Drucker-Prager material parameters in plane strain. Consider the two extreme cases of flow definition: +associated flow, +, and nondilatant flow, when +. For associated flow +and for nondilatant flow +In either case +is immediately available as +and +and +The difference between these two approaches increases with the friction angle; however, the results +are not very different for typical friction angles, as illustrated in Table 23.3.1–1. +Table 23.3.1–1 Plane strain matching of Drucker-Prager and Mohr-Coulomb models. +Mohr-Coulomb +friction angle, +Associated flow +Nondilatant flow +Drucker-Prager +friction angle, +Drucker-Prager +friction angle, +10° +20° +30° +40° +50° +16.7° +30.2° +39.8° +46.2° +50.5° +1.70 +1.60 +1.44 +1.24 +1.02 +16.7° +30.6° +40.9° +48.1° +53.0° +1.70 +1.63 +1.50 +1.33 +1.11 +“Limit load calculations with granular materials,” Section 1.15.4 of the Abaqus Benchmarks +Manual, and “Finite deformation of an elastic-plastic granular material,” Section 1.15.5 of the Abaqus +Benchmarks Manual, show a comparison of the response of a simple loading of a granular material +using the Drucker-Prager and Mohr-Coulomb models, using the plane strain approach to match the +parameters of the two models. +Matching triaxial test response +Another approach to matching Mohr-Coulomb and Drucker-Prager model parameters for materials with +low friction angles is to make the two models provide the same failure definition in triaxial compression +and tension. The following matching procedure is applicable only to the linear Drucker-Prager model +since this is the only model in this class that allows for different yield values in triaxial compression and +tension. +We can rewrite the Mohr-Coulomb model in terms of principal stresses: +Using the results above for the stress invariants p, q, and r in triaxial compression and tension allows the +linear Drucker-Prager model to be written for triaxial compression as +and for triaxial tension as +We wish to make these expressions identical to the Mohr-Coulomb model for all values of +. +This is possible by setting +By comparing the Mohr-Coulomb model with the linear Drucker-Prager model, +and, hence, from the previous result +These results for +and +provide linear Drucker-Prager parameters that match the Mohr- +Coulomb model in triaxial compression and tension. +The value of K in the linear Drucker-Prager model is restricted to +to remain convex. The result for K shows that this implies +Mohr-Coulomb friction angle than this value. One approach in such circumstances is to choose +for the yield surface +. Many real materials have a larger +and then to use the remaining equations to define +. This approach matches the models +for triaxial compression only, while providing the closest approximation that the model can provide to +failure being independent of the intermediate principal stress. If +is significantly larger than 22°, this +approach may provide a poor Drucker-Prager match of the Mohr-Coulomb parameters. Therefore, this +matching procedure is not generally recommended; use the Mohr-Coulomb model instead. +and +While using one-element tests to verify the calibration of the model, it should be noted that +, +the Abaqus output variables SP1, SP2, and SP3 correspond to the principal stresses +respectively. +, and +, +Creep models for the linear Drucker-Prager model +Classical “creep” behavior of materials that exhibit plasticity according to the extended Drucker-Prager +models can be defined in Abaqus/Standard. The creep behavior in such materials is intimately tied to +the plasticity behavior (through the definitions of creep flow potentials and definitions of test data), so +Drucker-Prager plasticity and Drucker-Prager hardening must be included in the material definition. +Creep and plasticity can be active simultaneously, in which case the resulting equations are solved +in a coupled manner. To model creep only (without rate-independent plastic deformation), large values +for the yield stress should be provided in the Drucker-Prager hardening definition: +the result is that +the material follows the Drucker-Prager model while it creeps, without ever yielding. When using this +technique, a value must also be defined for the eccentricity, since, as described below, both the initial +yield stress and eccentricity affect the creep potentials. This capability is limited to the linear model with +a von Mises (circular) section in the deviatoric stress plane ( +; i.e., no third stress invariant effects +are taken into account) and can be combined only with linear elasticity. +Creep behavior defined by the extended Drucker-Prager model +is active only during soils +consolidation, coupled temperature-displacement, and transient quasi-static procedures. +Creep formulation +The creep potential is hyperbolic, similar to the plastic flow potentials used in the hyperbolic and general +exponent plasticity models. If creep properties are defined in Abaqus/Standard, the linear Drucker-Prager +plasticity model also uses a hyperbolic plastic flow potential. As a consequence, if two analyses are +run, one in which creep is not activated and another in which creep properties are specified but produce +virtually no creep flow, the plasticity solutions will not be exactly the same: the solution with creep +not activated uses a linear plastic potential, whereas the solution with creep activated uses a hyperbolic +plastic potential. +Equivalent creep surface and equivalent creep stress +We adopt the notion of the existence of creep isosurfaces of stress points that share the same creep +“intensity,” as measured by an equivalent creep stress. When the material plastifies, it is desirable to have +the equivalent creep surface coincide with the yield surface; therefore, we define the equivalent creep +surfaces by homogeneously scaling down the yield surface. In the p–q plane that translates into parallels +to the yield surface, as depicted in Figure 23.3.1–13. Abaqus/Standard requires that creep properties be +described in terms of the same type of data used to define work hardening properties. The equivalent +creep stress, +, is then determined as follows: +material point +yield surface +equivalent creep +surface +σ−cr +no creep +Figure 23.3.1–13 Equivalent creep stress defined as the shear stress. +Figure 23.3.1–13 shows how the equivalent point is determined when the material properties are in +shear, with stress d. A consequence of these concepts is that there is a cone in p–q space inside which +creep is not active since any point inside this cone would have a negative equivalent creep stress. +Creep flow +The creep strain rate in Abaqus/Standard is assumed to follow from the same hyperbolic potential as the +plastic strain rate : +where +is the dilation angle measured in the p–q plane at high confining +pressure; +is the initial yield stress taken from the user-specified Drucker- +Prager hardening data; and +is a parameter, referred to as the eccentricity, that defines the +rate at which the function approaches the asymptote (the creep +potential tends to a straight line as the eccentricity tends to +zero). +Suitable default values are provided for , as described below. This creep potential, which is continuous +and smooth, ensures that the creep flow direction is always uniquely defined. The function approaches +the linear Drucker-Prager flow potential asymptotically at high confining pressure stress and intersects +the hydrostatic pressure axis at 90°. A family of hyperbolic potentials in the meridional stress plane was +shown in Figure 23.3.1–6. The creep potential is the von Mises circle in the deviatoric stress plane (the +-plane). +The default creep potential eccentricity is +, which implies that the material has almost the +same dilation angle over a wide range of confining pressure stress values. Increasing the value of +provides more curvature to the creep potential, implying that the dilation angle increases as the confining +pressure decreases. Values of +that are significantly less than the default value may lead to convergence +problems if the material is subjected to low confining pressures, because of the very tight curvature of +the creep potential locally where it intersects the p-axis. For details on the behavior of these models refer +to “Verification of creep integration,” Section 3.2.6 of the Abaqus Benchmarks Manual. +If the creep material properties are defined by a compression test, numerical problems may arise for +very low stress values. Abaqus/Standard protects for such a case, as described in “Models for granular +or polymer behavior,” Section 4.4.2 of the Abaqus Theory Manual. +Nonassociated flow +The use of a creep potential different from the equivalent creep surface implies that the material stiffness +matrix is not symmetric; therefore, the unsymmetric matrix storage and solution scheme should be +used . If the difference between +is not large and +the region of the model in which inelastic deformation is occurring is confined, it is possible that a +symmetric approximation to the material stiffness matrix will give an acceptable rate of convergence +and the unsymmetric matrix scheme may not be needed. +and +Specifying a creep law +The definition of creep behavior in Abaqus/Standard is completed by specifying the equivalent “uniaxial +behavior”—the creep “law.” In many practical cases the creep “law” is defined through user subroutine +CREEP because creep laws are usually of very complex form to fit experimental data. Data input methods +are provided for some simple cases, including two forms of a power law model and a variation of the +Singh-Mitchell law. +User subroutine CREEP +User subroutine CREEP provides a very general capability for implementing viscoplastic models in +Abaqus/Standard in which the strain rate potential can be written as a function of the equivalent stress +and any number of “solution-dependent state variables.” When used in conjunction with these material +models, the equivalent creep stress, +, is made available in the routine. Solution-dependent state +variables are any variables that are used in conjunction with the constitutive definition and whose values +evolve with the solution. Examples are hardening variables associated with the model. When a more +general form is required for the stress potential, user subroutine UMAT can be used. +Input File Usage: +*DRUCKER PRAGER CREEP, LAW=USER +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Plasticity→Drucker +Prager: Suboptions→Drucker Prager Creep: Law: User +“Time hardening” form of the power law model +The “time hardening” form of the power law model is +where +A, n, and m +if defined in pure shear, where +is the equivalent creep strain rate, defined so that +creep stress is defined in uniaxial compression, +tension, and +shear creep strain; +is the equivalent creep stress; +is the total time; and +are user-defined creep material parameters specified as functions of temperature +and field variables. +if the equivalent +if defined in uniaxial +is the engineering +Input File Usage: +Abaqus/CAE Usage: +*DRUCKER PRAGER CREEP, LAW=TIME +Property module: material editor: Mechanical→Plasticity→Drucker +Prager: Suboptions→Drucker Prager Creep: Law: Time +“Strain hardening” form of the power law model +As an alternative to the “time hardening” form of the power law, as defined above, the corresponding +“strain hardening” form can be used: +For physically reasonable behavior A and n must be positive and +. +Input File Usage: +Abaqus/CAE Usage: +*DRUCKER PRAGER CREEP, LAW=STRAIN +Property module: material editor: Mechanical→Plasticity→Drucker +Prager: Suboptions→Drucker Prager Creep: Law: Strain +Singh-Mitchell law +A second creep law available as data input is a variation of the Singh-Mitchell law: +, t, and +where +, +specified as functions of temperature and field variables. For physically reasonable behavior A and +must be positive, +, and m are user-defined creep material parameters +should be small compared to the total time. +are defined above and A, +, and +Input File Usage: +Abaqus/CAE Usage: +*DRUCKER PRAGER CREEP, LAW=SINGHM +Property module: material editor: Mechanical→Plasticity→Drucker +Prager: Suboptions→Drucker Prager Creep: Law: SinghM +Numerical difficulties +Depending on the choice of units for the creep laws described above, the value of A may be very small for +typical creep strain rates. If A is less than +, numerical difficulties can cause errors in the material +calculations; therefore, use another system of units to avoid such difficulties in the calculation of creep +strain increments. +Creep integration +Abaqus/Standard provides both explicit and implicit time integration of creep and swelling behavior. +The choice of the time integration scheme depends on the procedure type, the parameters specified for +the procedure, the presence of plasticity, and whether or not a geometric linear or nonlinear analysis is +requested, as discussed in “Rate-dependent plasticity: creep and swelling,” Section 23.2.4. +Initial conditions +When we need to study the behavior of a material that has already been subjected to some work hardening, +Abaqus allows you to prescribe initial conditions for the equivalent plastic strain, +, by specifying the +conditions directly . +For more complicated cases initial conditions can be defined in Abaqus/Standard through user subroutine +HARDINI. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to specify the initial equivalent plastic strain directly: +*INITIAL CONDITIONS, TYPE=HARDENING +Use the following option in Abaqus/Standard to specify the initial equivalent +plastic strain in user subroutine HARDINI: +*INITIAL CONDITIONS, TYPE=HARDENING, USER +Use the following options to specify the initial equivalent plastic strain directly: +Load module: Create Predefined Field: Step: Initial, choose Mechanical +for the Category and Hardening for the Types for Selected Step +Use the following options in Abaqus/Standard to specify the initial equivalent +plastic strain in user subroutine HARDINI: +Load module: Create Predefined Field: Step: Initial, choose +Mechanical for the Category and Hardening for the Types for +Selected Step; Definition: User-defined +Elements +The Drucker-Prager models can be used with the following element types: plane strain, generalized plane +strain, axisymmetric, and three-dimensional solid (continuum) elements. All Drucker-Prager models are +also available in plane stress (plane stress, shell, and membrane elements), except for the linear Drucker- +Prager model with creep. +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2), +the +following variables have special meaning for the Drucker-Prager plasticity/creep model: +PEEQ +Equivalent plastic strain. +For the linear Drucker-Prager plasticity model PEEQ is defined as +; where +is the initial equivalent plastic strain (zero or user-specified; +see “Initial conditions”) and +is the equivalent plastic strain rate. +For the hyperbolic and exponential Drucker-Prager plasticity models PEEQ +is the initial equivalent plastic strain and +, where +is defined as +CEEQ +Equivalent creep strain, +. +is the yield stress. +23.3.2 +MODIFIED DRUCKER-PRAGER/CAP MODEL +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Inelastic behavior,” Section 23.1.1 +• “Material library: overview,” Section 21.1.1 +• “Rate-dependent plasticity: creep and swelling,” Section 23.2.4 +• “CREEP,” Section 1.1.1 of the Abaqus User Subroutines Reference Manual +• *CAP PLASTICITY +• *CAP HARDENING +• *CAP CREEP +• “Defining cap plasticity” in “Defining plasticity,” Section 12.9.2 of the Abaqus/CAE User’s Manual, +in the online HTML version of this manual +Overview +The modified Drucker-Prager/Cap plasticity/creep model: +• is intended to model cohesive geological materials that exhibit pressure-dependent yield, such as +soils and rocks; +• is based on the addition of a cap yield surface to the Drucker-Prager plasticity model (“Extended +Drucker-Prager models,” Section 23.3.1), which provides an inelastic hardening mechanism to +account for plastic compaction and helps to control volume dilatancy when the material yields in +shear; +• can be used in Abaqus/Standard to simulate creep in materials exhibiting long-term inelastic +deformation through a cohesion creep mechanism in the shear failure region and a consolidation +creep mechanism in the cap region; +• can be used in conjunction with either the elastic material model (“Linear elastic behavior,” +Section 22.2.1) or, in Abaqus/Standard if creep is not defined, the porous elastic material model +(“Elastic behavior of porous materials,” Section 22.3.1); and +• provides a reasonable response to large stress reversals in the cap region; however, in the failure +surface region the response is reasonable only for essentially monotonic loading. +Yield surface +The addition of the cap yield surface to the Drucker-Prager model serves two main purposes: it bounds +the yield surface in hydrostatic compression, thus providing an inelastic hardening mechanism to +represent plastic compaction; and it helps to control volume dilatancy when the material yields in shear +by providing softening as a function of the inelastic volume increase created as the material yields on +the Drucker-Prager shear failure surface. +The yield surface has two principal segments: a pressure-dependent Drucker-Prager shear failure +segment and a compression cap segment, as shown in Figure 23.3.2–1. The Drucker-Prager failure +segment is a perfectly plastic yield surface (no hardening). Plastic flow on this segment produces inelastic +volume increase (dilation) that causes the cap to soften. On the cap surface plastic flow causes the +material to compact. The model is described in detail in “Drucker-Prager/Cap model for geological +materials,” Section 4.4.4 of the Abaqus Theory Manual. +Transition +surface, Ft +Shear failure, FS +α(d+patanβ) +Cap, Fc +d+patanβ +pa +R(d+patanβ) +pb +Figure 23.3.2–1 Modified Drucker-Prager/Cap model: yield surfaces in the p–t plane. +Failure surface +The Drucker-Prager failure surface is written as +where +and +and can depend on temperature, +measure t is defined as +represent the angle of friction of the material and its cohesion, respectively, +. The deviatoric stress +, and other predefined fields +and +is the equivalent pressure stress, +is the Mises equivalent stress, +is the third stress invariant, and +is the deviatoric stress. +is a material parameter that controls the dependence of the yield surface on the value of the +intermediate principal stress, as shown in Figure 23.3.2–2. +S3 +t = + q 1+ +1_ +) + - 1- +1_ +K 3 +)r +)) +_ +1_ +Curve +1.0 +0.8 +S2 +S1 +Figure 23.3.2–2 Typical yield/flow surfaces in the deviatoric plane. +The yield surface is defined so that K is the ratio of the yield stress in triaxial tension to the yield stress +in triaxial compression. +implies that the yield surface is the von Mises circle in the deviatoric +principal stress plane (the +-plane), so that the yield stresses in triaxial tension and compression are the +same; this is the default behavior in Abaqus/Standard and the only behavior available in Abaqus/Explicit. +To ensure that the yield surface remains convex requires +. +Cap yield surface +The cap yield surface has an elliptical shape with constant eccentricity in the meridional (p–t) plane +(Figure 23.3.2–1) and also includes dependence on the third stress invariant in the deviatoric plane +(Figure 23.3.2–2). The cap surface hardens or softens as a function of the volumetric inelastic strain: +volumetric plastic and/or creep compaction (when yielding on the cap and/or creeping according to +the consolidation mechanism, as described later in this section) causes hardening, while volumetric +plastic and/or creep dilation (when yielding on the shear failure surface and/or creeping according to +the cohesion mechanism, as described later in this section) causes softening. The cap yield surface is +is a material parameter that controls the shape of the cap, +is a small number +where +that we discuss later, and +is an evolution parameter that represents the volumetric +inelastic strain driven hardening/softening. The hardening/softening law is a user-defined piecewise +linear function relating the hydrostatic compression yield stress, +, and volumetric inelastic strain +(Figure 23.3.2–3): +pb +-(ε in + vol + ε + ε ) + cr + vol + pl + vol +Figure 23.3.2–3 Typical Cap hardening. +The volumetric inelastic strain axis in Figure 23.3.2–3 has an arbitrary origin: +is the position on this axis corresponding to the initial state of the material when the analysis begins, +thus defining the position of the cap ( +) in Figure 23.3.2–1 at the start of the analysis. The evolution +parameter +is given as +The parameter +is a small number (typically 0.01 to 0.05) used to define a transition yield surface, +so that the model provides a smooth intersection between the cap and failure surfaces. +Defining yield surface variables +In +You provide the variables d, +Abaqus/Standard +). If desired, combinations +of these variables can also be defined as a tabular function of temperature and other predefined field +variables. +, and K to define the shape of the yield surface. +, while in Abaqus/Explicit K = 1 ( +, R, +, +Input File Usage: +Abaqus/CAE Usage: +*CAP PLASTICITY +Property module: material editor: Mechanical→Plasticity→Cap Plasticity +Defining hardening parameters +The hardening curve specified for this model interprets yielding in the hydrostatic pressure sense: the +hydrostatic pressure yield stress is defined as a tabular function of the volumetric inelastic strain, and, if +desired, a function of temperature and other predefined field variables. The range of values for which +is defined should be sufficient to include all values of effective pressure stress that the material will be +subjected to during the analysis. +Input File Usage: +Abaqus/CAE Usage: +*CAP HARDENING +Property module: material editor: Mechanical→Plasticity→Cap +Plasticity: Suboptions→Cap Hardening +Plastic flow +Plastic flow is defined by a flow potential that is associated in the deviatoric plane, associated in the +cap region in the meridional plane, and nonassociated in the failure surface and transition regions +in the meridional plane. The flow potential surface that we use in the meridional plane is shown in +Figure 23.3.2–4: it is made up of an elliptical portion in the cap region that is identical to the cap yield +surface, +and another elliptical portion in the failure and transition regions that provides the nonassociated flow +component in the model, +The two elliptical portions form a continuous and smooth potential surface. +Similar +ellipses +Gs (Shear failure) +Gc (cap) +d+patanβ +(1+α-α secβ)(d+patanβ) +pa +R(d+patanβ) +Figure 23.3.2–4 Modified Drucker-Prager/Cap model: flow potential in the p–t plane. +Nonassociated flow +Nonassociated flow implies that the material stiffness matrix is not symmetric and the unsymmetric +matrix storage and solution scheme should be used in Abaqus/Standard . If the region of the model in which nonassociated inelastic deformation is occurring +is confined, it is possible that a symmetric approximation to the material stiffness matrix will give an +acceptable rate of convergence; in such cases the unsymmetric matrix scheme may not be needed. +Calibration +At least three experiments are required to calibrate the simplest version of the Cap model: a hydrostatic +compression test (an oedometer test is also acceptable) and either two triaxial compression tests or one +triaxial compression test and one uniaxial compression test (more than two tests are recommended for a +more accurate calibration). +The hydrostatic compression test is performed by pressurizing the sample equally in all directions. +The applied pressure and the volume change are recorded. +The uniaxial compression test involves compressing the sample between two rigid platens. The +load and displacement in the direction of loading are recorded. The lateral displacements should also be +recorded so that the correct volume changes can be calibrated. +Triaxial compression experiments are performed using a standard triaxial machine where a fixed +confining pressure is maintained while the differential stress is applied. Several tests covering the range +of confining pressures of interest are usually performed. Again, the stress and strain in the direction of +loading are recorded, together with the lateral strain so that the correct volume changes can be calibrated. +The friction angle, +Unloading measurements in these tests are useful to calibrate the elasticity, particularly in cases +where the initial elastic region is not well defined. +The hydrostatic compression test stress-strain curve gives the evolution of the hydrostatic +CAP MODEL +, required for the cap hardening curve definition. +, and cohesion, d, which define the shear failure dependence on hydrostatic +pressure, are calculated by plotting the failure stresses of the two triaxial compression tests (or the triaxial +compression test and the uniaxial compression test) in the pressure stress (p) versus shear stress (q) space: +the slope of the straight line passing through the two points gives the angle +and the intersection with +the q-axis gives d. For more details on the calibration of +and d, see the discussion on calibration in +“Extended Drucker-Prager models,” Section 23.3.1. +R represents the curvature of the cap part of the yield surface and can be calibrated from a number +of triaxial tests at high confining pressures (in the cap region). R must be between 0.0001 and 1000.0. +Abaqus/Standard creep model +Classical “creep” behavior of materials that exhibit plasticity according to the capped Drucker-Prager +plasticity model can be defined in Abaqus/Standard. The creep behavior in such materials is intimately +tied to the plasticity behavior (through the definitions of creep flow potentials and definitions of test data), +so cap plasticity and cap hardening must be included in the material definition. If no rate-independent +plastic behavior is desired in the model, large values for the cohesion, d, as well as large values for the +compression yield stress, +, should be provided in the plasticity definition: as a result the material +follows the capped Drucker-Prager model while it creeps, without ever yielding. This capability is +limited to cases in which there is no third stress invariant dependence of the yield surface ( +) +and cases in which the yield surface has no transition region ( +). The elastic behavior must be +defined using linear isotropic elasticity . +Creep behavior defined for the modified Drucker-Prager/Cap model is active only during soils +consolidation, coupled temperature-displacement, and transient quasi-static procedures. +Creep formulation +This model has two possible creep mechanisms that are active in different loading regions: one is a +cohesion mechanism, which follows the type of plasticity active in the shear-failure plasticity region, and +the other is a consolidation mechanism, which follows the type of plasticity active in the cap plasticity +region. Figure 23.3.2–5 shows the regions of applicability of the creep mechanisms in p–q space. +Equivalent creep surface and equivalent creep stress for the cohesion creep mechanism +Consider the cohesion creep mechanism first. We adopt the notion of the existence of creep isosurfaces +of stress points that share the same creep “intensity,” as measured by an equivalent creep stress. Since it +is desirable to have the equivalent creep surface coincide with the yield surface, we define the equivalent +creep surfaces by homogeneously scaling down the yield surface. In the p–q plane the equivalent creep +surfaces translate into surfaces that are parallel to the yield surface, as depicted in Figure 23.3.2–6. +cohesion and +consolidation +creep +n c r e +si o +(d+patanβ) +no creep +consolidation +creep +pa +R(d+patanβ) +Figure 23.3.2–5 Regions of activity of creep mechanisms. +Abaqus/Standard requires that cohesion creep properties be measured in a uniaxial compression test. +The equivalent creep stress, +, is determined as follows: +Abaqus/Standard also requires that +be positive. Figure 23.3.2–6 shows such an equivalent creep +stress. A consequence of these concepts is that there is a cone in p–q space inside which creep is not +active. Any point inside this cone would have a negative equivalent creep stress. +Equivalent creep surface and equivalent creep stress for the consolidation creep mechanism +Next, consider the consolidation creep mechanism. In this case we wish to make creep dependent on +the hydrostatic pressure above a threshold value of +, with a smooth transition to the areas in which the +mechanism is not active ( +). Therefore, we define equivalent creep surfaces as constant hydrostatic +pressure surfaces (vertical lines in the p–q plane). Abaqus/Standard requires that consolidation creep +properties be measured in a hydrostatic compression test. The effective creep pressure, +, is then the +point on the p-axis with a relative pressure of +. This value is used in the uniaxial creep +law. The equivalent volumetric creep strain rate produced by this type of law is defined as positive for +a positive equivalent pressure. The internal tensor calculations in Abaqus/Standard account for the fact +that a positive pressure will produce negative (that is, compressive) volumetric creep components. +yield surface +material point +equivalent creep +surface +σ−cr +no creep +Figure 23.3.2–6 Equivalent creep stress for cohesion creep. +Creep flow +The creep strain rate produced by the cohesion mechanism is assumed to follow a potential that is similar +to that of the creep strain rate in the Drucker-Prager creep model (“Extended Drucker-Prager models,” +Section 23.3.1); that is, a hyperbolic function: +This creep flow potential, which is continuous and smooth, ensures that the flow direction is always +uniquely defined. The function approaches a parallel to the shear-failure yield surface asymptotically +at high confining pressure stress and intersects the hydrostatic pressure axis at a right angle. A family +of hyperbolic potentials in the meridional stress plane is shown in Figure 23.3.2–7. The cohesion creep +potential is the von Mises circle in the deviatoric stress plane (the +-plane). +Abaqus/Standard protects for numerical problems that may arise for very low stress values. See +“Drucker-Prager/Cap model for geological materials,” Section 4.4.4 of the Abaqus Theory Manual, for +details. +The creep strain rate produced by the consolidation mechanism is assumed to follow a potential that +is similar to that of the plastic strain rate in the cap yield surface (Figure 23.3.2–8): +The consolidation creep potential is the von Mises circle in the deviatoric stress plane (the +-plane). +The volumetric components of creep strain from both mechanisms contribute to the hardening/softening +of the cap, as described previously. For details on the behavior of these models refer to “Verification of +creep integration,” Section 3.2.6 of the Abaqus Benchmarks Manual. +Δε cr +Δε cr +similar +hyperboles +material point +Figure 23.3.2–7 Cohesion creep potentials in the p–q plane. +pa +material point +Δε cr +similar +ellipses +pa +Δε cr +Figure 23.3.2–8 Consolidation creep potentials in the p–q plane. +Nonassociated flow +The use of a creep potential for the cohesion mechanism different from the equivalent creep surface +implies that the material stiffness matrix is not symmetric, and the unsymmetric matrix storage and +If the region of the +solution scheme should be used . +model in which cohesive inelastic deformation is occurring is confined, it is possible that a symmetric +approximation to the material stiffness matrix will give an acceptable rate of convergence; in such cases +the unsymmetric matrix scheme may not be needed. +Specifying creep laws +The definition of the creep behavior is completed by specifying the equivalent “uniaxial behavior”—the +creep “laws.” In many practical cases the creep laws are defined through user subroutine CREEP because +creep laws are usually of complex form to fit experimental data. Data input methods are provided for +some simple cases. +User subroutine CREEP +User subroutine CREEP provides a general capability for implementing viscoplastic models in which the +strain rate potential can be written as a function of the equivalent stress and any number of “solution- +dependent state variables.” When used in conjunction with these materials, the equivalent cohesion creep +stress, +, are made available in the routine. Solution-dependent +state variables are any variables that are used in conjunction with the constitutive definition and whose +values evolve with the solution. Examples are hardening variables associated with the model. When a +more general form is required for the stress potential, user subroutine UMAT can be used. +, and the effective creep pressure, +Input File Usage: +Abaqus/CAE Usage: +Use either or both of the following options: +*CAP CREEP, MECHANISM=COHESION, LAW=USER +*CAP CREEP, MECHANISM=CONSOLIDATION, LAW=USER +Define one or both of the following: +Property module: material editor: Mechanical→Plasticity→Cap Plasticity: +Suboptions→Cap Creep Cohesion: Law: User +Suboptions→Cap Creep Consolidation: Law: User +“Time hardening” form of the power law model +With respect to the cohesion mechanism, the power law is available +where +A, n, and m +is the equivalent creep strain rate; +is the equivalent cohesion creep stress; +is the total time; and +are user-defined creep material parameters specified as functions of temperature +and field variables. +In using this form of the power law model with the consolidation mechanism, +can be replaced +by +, the effective creep pressure, in the above relation. +Input File Usage: +Use either or both of the following options: +*CAP CREEP, MECHANISM=COHESION, LAW=TIME +*CAP CREEP, MECHANISM=CONSOLIDATION, LAW=TIME +Abaqus/CAE Usage: +Define one or both of the following: +Property module: material editor: Mechanical→Plasticity→Cap Plasticity: +Suboptions→Cap Creep Cohesion: Law: Time +Suboptions→Cap Creep Consolidation: Law: Time +“Strain hardening” form of the power law model +As an alternative to the “time hardening” form of the power law, as defined above, the corresponding +“strain hardening” form can be used. For the cohesion mechanism this law has the form +In using this form of the power law model with the consolidation mechanism, +can be replaced +by +, the effective creep pressure, in the above relation. +Input File Usage: +For physically reasonable behavior A and n must be positive and +Use either or both of the following options: +*CAP CREEP, MECHANISM=COHESION, LAW=STRAIN +*CAP CREEP, MECHANISM=CONSOLIDATION, LAW=STRAIN +Define one or both of the following: +. +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Plasticity→Cap Plasticity: +Suboptions→Cap Creep Cohesion: Law: Strain +Suboptions→Cap Creep Consolidation: Law: Strain +Singh-Mitchell law +A second cohesion creep law available as data input is a variation of the Singh-Mitchell law: +, t, and +, +where +specified as functions of temperature and field variables. For physically reasonable behavior A and +must be positive, +, and m are user-defined creep material parameters +should be small compared to the total time. +are defined above and A, +, and +In using this variation of the Singh-Mitchell law with the consolidation mechanism, +can be +replaced by +, the effective creep pressure, in the above relation. +Input File Usage: +Abaqus/CAE Usage: +Use either or both of the following options: +*CAP CREEP, MECHANISM=COHESION, LAW=SINGHM +*CAP CREEP, MECHANISM=CONSOLIDATION, LAW=SINGHM +Define one or both of the following: +Property module: material editor: Mechanical→Plasticity→Cap Plasticity: +Suboptions→Cap Creep Cohesion: Law: SinghM +Suboptions→Cap Creep Consolidation: Law: SinghM +Numerical difficulties +Depending on the choice of units for the creep laws described above, the value of A may be very small +for typical creep strain rates. If A is less than 10−27, numerical difficulties can cause errors in the material +calculations; therefore, use another system of units to avoid such difficulties in the calculation of creep +strain increments. +Creep integration +Abaqus/Standard provides both explicit and implicit time integration of creep and swelling behavior. +The choice of the time integration scheme depends on the procedure type, the parameters specified for +the procedure, the presence of plasticity, and whether or not a geometric linear or nonlinear analysis is +requested, as discussed in “Rate-dependent plasticity: creep and swelling,” Section 23.2.4. +Initial conditions +The initial stress at a point can be defined . If such a stress point lies outside the initially +defined cap or transition yield surfaces and under the projection of the shear failure surface in the p–t +plane (illustrated in Figure 23.3.2–1), Abaqus will try to adjust the initial position of the cap to make +the stress point lie on the yield surface and a warning message will be issued. If the stress point lies +outside the Drucker-Prager failure surface (or above its projection), an error message will be issued and +execution will be terminated. +Elements +The modified Drucker-Prager/Cap material behavior can be used with plane strain, generalized plane +strain, axisymmetric, and three-dimensional solid (continuum) elements. This model cannot be used with +elements for which the assumed stress state is plane stress (plane stress, shell, and membrane elements). +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2), +the +following variables have special meaning in the cap plasticity/creep model: +PEEQ +PEQC +, the cap position. +Equivalent plastic strains for all three possible yield/failure surfaces (Drucker- +Prager failure surface - PEQC1, cap surface - PEQC2, and transition surface - +PEQC3) and the total volumetric inelastic strain (PEQC4). For each yield/failure +is the +surface, the equivalent plastic strain is +corresponding rate of plastic flow. The total volumetric inelastic strain is defined +as +where +CEEQ +CESW +Equivalent creep strain produced by the cohesion creep mechanism, defined as +where +is the equivalent creep stress. +Equivalent creep strain produced by the consolidation creep mechanism, defined +as +is the equivalent creep pressure. +, where +23.3.3 +MOHR-COULOMB PLASTICITY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Inelastic behavior,” Section 23.1.1 +• *MOHR COULOMB +• *MOHR COULOMB HARDENING +• *TENSION CUTOFF +• “Defining Mohr-Coulomb plasticity” in “Defining plasticity,” Section 12.9.2 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +The Mohr-Coulomb plasticity model: +• is used to model materials with the classical Mohr-Coloumb yield criterion; +• allows the material to harden and/or soften isotropically; +• uses a smooth flow potential that has a hyperbolic shape in the meridional stress plane and a +piecewise elliptic shape in the deviatoric stress plane; +• is used with the linear elastic material model (“Linear elastic behavior,” Section 22.2.1); +• can be used with the Rankine surface (tension cutoff) to limit load carrying capacity near the tensile +region; and +• can be used for design applications in the geotechnical engineering area to simulate material +response under essentially monotonic loading. +Elastic behavior +The elastic part of the response is specified as described in “Linear elastic behavior,” Section 22.2.1. +Linear isotropic elasticity is assumed. +Plastic behavior: yield criteria +The yield surface is a composite of two different criteria: a shear criterion, known as the Mohr-Coulomb +surface, and an optional tension cutoff criterion, modeled using the Rankine surface. +Mohr-Coulomb surface +The Mohr-Coulomb criterion assumes that yield occurs when the shear stress on any point in a material +reaches a value that depends linearly on the normal stress in the same plane. The Mohr-Coulomb +model is based on plotting Mohr’s circle for states of stress at yield in the plane of the maximum and +minimum principal stresses. The yield line is the best straight line that touches these Mohr’s circles +(Figure 23.3.3–1). +s = + σ +1 σ +- +m= +1+σ + 2 +σ +(compressive stress) +Figure 23.3.3–1 Mohr-Coulomb yield model. +Therefore, the Mohr-Coulomb model is defined by +where +is negative in compression. From Mohr’s circle, +Substituting for +and , multiplying both sides by +, and reducing, the Mohr-Coulomb model +can be written as +where +is half of the difference between the maximum principal stress, +(and is, therefore, the maximum shear stress), +, and the minimum principal stress, +is the average of the maximum and minimum principal stresses, and +is the friction angle. +For general states of stress the model is more conveniently written in terms of three stress invariants +as +where +and +is the slope of the Mohr-Coulomb yield surface in the p– +stress plane , which is commonly referred +to as the friction angle of the material and can depend on +temperature and predefined field variables; +is the cohesion of the material; and +is the deviatoric polar angle defined as +is the equivalent pressure stress, +is the Mises equivalent stress, +is the third invariant of deviatoric stress, and +is the deviatoric stress. +The friction angle, +, controls the shape of the yield surface in the deviatoric plane as shown in +Figure 23.3.3–2. The tension cutoff surface is shown for a meridional angle of +. The friction +angle range is +the Mohr-Coulomb model reduces to the pressure- +independent Tresca model with a perfectly hexagonal deviatoric section. In the case of +the +Mohr-Coulomb model reduces to the “tension cutoff” Rankine model with a triangular deviatoric section +and +(this limiting case is not permitted within the Mohr-Coulomb model described here). +. In the case of +When using one-element tests to verify the calibration of the model, the output variables SP1, SP2, +, and +and SP3 correspond to the principal stresses +, respectively. +, +Tension cutoff +Mohr-Coulomb +Rmcq +Meridional plane +Θ = 0 +Mohr-Coulomb +(φ = 20°) +Tresca +(φ = 0°) +Rankine +(φ = 90°) +Θ = 4π/3 +Drucker-Prager +(Mises) +Θ = π/3 +Θ = 2π/3 +Deviatoric plane +Figure 23.3.3–2 Mohr-Coulomb and tension cutoff surfaces in meridional and deviatoric planes. +Isotropic cohesion hardening is assumed for the hardening behavior of the Mohr-Coulomb yield +surface. The hardening curve must describe the cohesion yield stress as a function of plastic strain and, +possibly, temperature and predefined field variables. In defining this dependence at finite strains, “true” +(Cauchy) stress and logarithmic strain values should be given. An optional tension cutoff hardening (or +softening) curve can be specified +Rate dependency effects are not accounted for in this plasticity model. +Input File Usage: +Use the following options to specify the Mohr-Coulomb yield surface and +cohesion hardening: +Abaqus/CAE Usage: +*MOHR COULOMB +*MOHR COULOMB HARDENING +Use the following options to specify the Mohr-Coulomb yield surface and +cohesion hardening: +Property module: material editor: Mechanical→Plasticity→Mohr +Coulomb Plasticity +Property module: material editor: Mechanical→Plasticity→Mohr +Coulomb Plasticity: Cohesion +Rankine surface +In Abaqus tension cutoff is modeled using the Rankine surface, which is written as +where +the Rankine surface, as a function of tensile equivalent plastic strain, +, and +is the tension cutoff value representing softening (or hardening) of +. +Input File Usage: +Use the following option to specify hardening or softening for the Rankine +surface: +Abaqus/CAE Usage: +*TENSION CUTOFF +Use the following option to specify hardening or softening for the Rankine +surface: +Property module: material editor: Mechanical→Plasticity→Mohr +Coulomb Plasticity: toggle on Specify tension cutoff; Tension Cutoff +Plastic behavior: flow potentials +The flow potentials used for the Mohr-Coulomb yield surface and the tension cutoff surface are described +below. +Plastic flow on the Mohr-Coulomb yield surface +The flow potential, G, for the Mohr-Coulomb yield surface is chosen as a hyperbolic function in the +meridional stress plane and the smooth elliptic function proposed by Menétrey and Willam (1995) in the +deviatoric stress plane: +where +and +is the dilation angle measured in the p– +depend on temperature and predefined field variables; +plane at high confining pressure and can +is the initial cohesion yield stress, +; +is the deviatoric polar angle defined previously; +is a parameter, referred to as the meridional eccentricity, that defines the rate at which the +hyperbolic function approaches the asymptote (the flow potential tends to a straight line in +the meridional stress plane as the meridional eccentricity tends to zero); and +is a parameter, referred to as the deviatoric eccentricity, +that describes the “out-of- +roundedness” of the deviatoric section in terms of the ratio between the shear stress along +the extension meridian ( +) and the shear stress along the compression meridian +( +). +A default value of +is provided for the meridional eccentricity, +. +By default, the deviatoric eccentricity, e, is calculated as +is the Mohr-Coulomb friction angle; this calculation corresponds to matching the flow potential +where +to the yield surface in both triaxial tension and compression in the deviatoric plane. Alternatively, Abaqus +allows you to consider this deviatoric eccentricity as an independent material parameter; in this case you +provide its value directly. Convexity and smoothness of the elliptic function requires that +. +The upper limit, +0° when you do not specify the value of e), leads to +(or +90° when you do not specify the value of e), leads to +, which describes the Mises circle in the deviatoric plane. The lower limit, +(or +and +would describe the Rankine triangle in the deviatoric plane (this limiting case is not permitted within the +Mohr-Coulomb model described here). +This flow potential, which is continuous and smooth, ensures that the flow direction is always +uniquely defined. A family of hyperbolic potentials in the meridional stress plane is shown in +Figure 23.3.3–3, and the flow potential in the deviatoric stress plane is shown in Figure 23.3.3–4. +dεpl +Rmwq +εc +|0 +Figure 23.3.3–3 Family of hyperbolic flow potentials in the meridional stress plane. +Θ = 0 +Rankine (e = 1/2) +Θ = π/3 +Θ = 2π/3 +Menetrey-Willam (1/2 < e ≤ 1) +Θ = 4π/3 +Mises (e = 1) +Figure 23.3.3–4 Menétrey-Willam flow potential in the deviatoric stress plane. +Flow in the meridional stress plane can be close to associated when the angle of friction, +the angle of dilation, +plane is, in general, nonassociated. Flow in the deviatoric stress plane is always nonassociated. +, are equal and the meridional eccentricity, +, and +, is very small; however, flow in this +Input File Usage: +Use the following option to allow Abaqus to calculate the value of e (default): +*MOHR COULOMB +Use the following option to specify the value of e directly: +*MOHR COULOMB, DEVIATORIC ECCENTRICITY=e +Abaqus/CAE Usage: +Use the following option to allow Abaqus to calculate the value of e (default): +Property module: material editor: Mechanical→Plasticity→Mohr Coulomb +Plasticity: Plasticity: Deviatoric eccentricity: Calculated default +Use the following option to specify the value of e directly: +Property module: material editor: Mechanical→Plasticity→Mohr +Coulomb Plasticity: Plasticity: Deviatoric eccentricity: Specify: e +Plastic flow on the Rankine surface +A flow potential that results in a nearly associative flow is chosen for the Rankine surface and is +constructed by modifying the Menétrey-Willam potential described earlier: +where +is the initial value of tension cutoff; +is the meridional eccentricity, similar to defined earlier; and +is the deviatoric eccentricity, similar to +defined earlier. +Abaqus uses values of +and +, for +and +, respectively. +Nonassociated flow +Since the plastic flow is nonassociated in general, the use of this Mohr-Coulomb model generally requires +the unsymmetric matrix storage and solution scheme in Abaqus/Standard . +Elements +The Mohr-Coulomb plasticity model can be used with any stress/displacement elements other than one- +dimensional elements (beam, pipe, and truss elements) or elements for which the assumed stress state is +plane stress (plane stress, shell, and membrane elements). +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Standard output variable +the +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2), +following variables are available for the Mohr-Coulomb plasticity model: +PEEQ +PEEQT +Equivalent plastic strain, +Tensile equivalent plastic strain, +, where c is the cohesion yield stress. +, on the tension cutoff yield surface. +Additional reference +• Menétrey, Ph., and K. J. Willam, “Triaxial Failure Criterion for Concrete and its Generalization,” +ACI Structural Journal, vol. 92, pp. 311–318, May/June 1995. +23.3.4 +CRITICAL STATE (CLAY) PLASTICITY MODEL +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Inelastic behavior,” Section 23.1.1 +• *CLAY PLASTICITY +• *CLAY HARDENING +• “Defining clay plasticity” in “Defining plasticity,” Section 12.9.2 of the Abaqus/CAE User’s +Manual, in the online HTML version of this manual +• “Critical state models,” Section 4.4.3 of the Abaqus Theory Manual +Overview +The clay plasticity model provided in Abaqus: +• describes the inelastic behavior of the material by a yield function that depends on the three stress +invariants, an associated flow assumption to define the plastic strain rate, and a strain hardening +theory that changes the size of the yield surface according to the inelastic volumetric strain; +• requires that the elastic part of the deformation be defined by using the linear elastic material model +(“Linear elastic behavior,” Section 22.2.1) or, in Abaqus/Standard, the porous elastic material model +(“Elastic behavior of porous materials,” Section 22.3.1) within the same material definition; and +• allows for the hardening law to be defined by a piecewise linear form or, in Abaqus/Standard, by +an exponential form. +Yield surface +The model is based on the yield surface +is the equivalent pressure stress; +is a deviatoric stress measure; +is the Mises equivalent stress; +is the third stress invariant; +is a constant that defines the slope of the critical state line; +23.3.4–1 +where +is a constant that is equal to 1.0 on the “dry” side of the critical +state line ( +) but may be different from 1.0 on the “wet” +side of the critical state line ( +introduces a different +ellipse on the wet side of the critical state line; i.e., a tighter +“cap” is obtained if +as shown in Figure 23.3.4–1); +is the size of the yield surface (Figure 23.3.4–1); and +is the ratio of the flow stress in triaxial tension to the flow +stress in triaxial compression and determines the shape of the +yield surface in the plane of principal deviatoric stresses (the +“ -plane”: see Figure 23.3.4–2); Abaqus requires that +to ensure that the yield surface remains convex. +The user-defined parameters M, +variables, +Theory Manual. +as well as other predefined field +. The model is described in detail in “Critical state models,” Section 4.4.3 of the Abaqus +, and K can depend on temperature +Input File Usage: +Abaqus/CAE Usage: +*CLAY PLASTICITY +Property module: material editor: Mechanical→Plasticity→Clay Plasticity +critical state line +K = 1.0 +β = 0.5 +β = 1.0 +Figure 23.3.4–1 Clay yield surfaces in the p–t plane. +S3 +t = 1_ + q 1+ 1_ + - 1- 1_ +) +K 3 +)r +)) +_ +Curve +1.0 +0.8 +S2 +Figure 23.3.4–2 Clay yield surface sections in the +-plane. +S1 +Hardening law +The hardening law can have an exponential form (Abaqus/Standard only), or a piecewise linear form. +Exponential form in Abaqus/Standard +The exponential form of the hardening law is written in terms of some of the porous elasticity parameters +and, therefore, can be used only in conjunction with the Abaqus/Standard porous elastic material model. +The size of the yield surface at any time is determined by the initial value of the hardening parameter, +, and the amount of inelastic volume change that occurs according to the equation +where +is the inelastic volume change (that part of J, the ratio of current volume to initial volume, +attributable to inelastic deformation); +is the logarithmic bulk modulus of the material defined for the porous elastic material +behavior; +is the logarithmic hardening constant defined for the clay plasticity material behavior; and +is the user-defined initial void ratio (“Defining initial void ratios in a porous medium” in +“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1). +Specifying the initial size of the yield surface directly +The initial size of the yield surface is defined for clay plasticity by specifying the hardening parameter, +, as a tabular function or by defining it analytically. +can be defined along with , M, +, and K, as a tabular function of temperature and other +is a function only of the initial conditions; it will not change if +predefined field variables. However, +temperatures and field variables change during the analysis. +Input File Usage: +Use all of the following options: +*INITIAL CONDITIONS, TYPE=RATIO +*POROUS ELASTIC +*CLAY PLASTICITY, HARDENING=EXPONENTIAL +Use all of the following options: +Abaqus/CAE Usage: +Property module: material editor: +Mechanical→Elasticity→Porous Elastic +Mechanical→Plasticity→Clay Plasticity: Hardening: Exponential +Load module: Create Predefined Field: Step: Initial: choose Other for +the Category and Void ratio for the Types for Selected Step +Specifying the initial size of the yield surface indirectly +, which is the intercept of the +The hardening parameter +virgin consolidation line with the void ratio axis in the plot of void ratio, e, versus the logarithm of the +effective pressure stress, +(Figure 23.3.4–3). If this method is used, +can be defined indirectly by specifying +is defined by +where +is the user-defined initial value of the equivalent hydrostatic pressure stress . You +define +can be dependent on temperature and other +predefined field variables. However, +is a function only of the initial conditions; it will not change if +temperatures and field variables change during the analysis. +, and K; all the parameters except +, M, +, +Input File Usage: +Use all of the following options: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=RATIO +*INITIAL CONDITIONS, TYPE=STRESS +*POROUS ELASTIC +*CLAY PLASTICITY, HARDENING=EXPONENTIAL, INTERCEPT= +Use all of the following options: +Property module: material editor: +Mechanical→Elasticity→Porous Elastic +e1 - locates initial consolidation state, by the + intercept of the plastic line with In p = 0. +, +elastic slope +de +d( In p) += -κ +plastic slope de +d( In p) += -λ +In p +(p = effective pressure + stress) +Figure 23.3.4–3 Pure compression behavior for clay model. +Mechanical→Plasticity→Clay Plasticity: Hardening: +Exponential, Intercept: +Load module: Create Predefined Field: Step: Initial: choose Other for +the Category and Void ratio for the Types for Selected Step +Load module: Create Predefined Field: Step: Initial: choose Other for +the Category and Stress for the Types for Selected Step +Piecewise linear form +If the piecewise linear form of the hardening rule is used, the user-defined relationship relates the +yield stress in hydrostatic compression, +(Figure 23.3.4–4): +to the corresponding volumetric plastic strain, +, +The evolution parameter, a, is then given by +0C +-ε + pl + vol +-(ε pl + vol + + ε ) + pl + vol +Figure 23.3.4–4 Typical piecewise linear clay hardening/softening curve. +The volumetric plastic strain axis has an arbitrary origin: +to the initial state of the material, thus defining the initial hydrostatic pressure, +yield surface size, +values for which +which the material will be subjected during the analysis. +is the position on this axis corresponding +, and, hence, the initial +. This relationship is defined in tabular form as clay hardening data. The range of +is defined should be sufficient to include all values of equivalent pressure stress to +This form of the hardening law can be used in conjunction with either the linear elastic or, in +Abaqus/Standard, the porous elastic material models. This is the only form of the hardening law +supported in Abaqus/Explicit +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options: +*CLAY PLASTICITY, HARDENING=TABULAR +*CLAY HARDENING +Property module: material editor: Mechanical→Plasticity→Clay +Plasticity: Hardening: Tabular, Suboptions→Clay Hardening +Calibration +At least two experiments are required to calibrate the simplest version of the Cam-clay model: a +hydrostatic compression test (an oedometer test is also acceptable) and a triaxial compression test (more +than one triaxial test is useful for a more accurate calibration). +Hydrostatic compression tests +The hydrostatic compression test is performed by pressurizing the sample equally in all directions. The +applied pressure and the volume change are recorded. +The onset of yielding in the hydrostatic compression test immediately provides the initial position +of the yield surface, +and , are determined from the hydrostatic +compression experimental data by plotting the logarithm of pressure versus void ratio. The void ratio, e, +is related to the measured volume change as +. The logarithmic bulk moduli, +The slope of the line obtained for the elastic regime is +a valid model +. +, and the slope in the inelastic range is +. For +Triaxial tests +Triaxial compression experiments are performed using a standard triaxial machine where a fixed +confining pressure is maintained while the differential stress is applied. Several tests covering the range +of confining pressures of interest are usually performed. Again, the stress and strain in the direction of +loading are recorded, together with the lateral strain so that the correct volume changes can be calibrated. +The triaxial compression tests allow the calibration of the yield parameters M and . M is the ratio +of the shear stress, q, to the pressure stress, p, at critical state and can be obtained from the stress values +when the material has become perfectly plastic (critical state). +represents the curvature of the cap part +of the yield surface and can be calibrated from a number of triaxial tests at high confining pressures (on +the “wet” side of critical state). must be between 0.0 and 1.0. +To calibrate the parameter K, which controls the yield dependence on the third stress invariant, +experimental results obtained from a true triaxial (cubical) test are necessary. These results are generally +not available, and you may have to guess (the value of K is generally between 0.8 and 1.0) or ignore this +effect. +Unloading measurements +Unloading measurements in hydrostatic and triaxial compression tests are useful to calibrate the elasticity, +particularly in cases where the initial elastic region is not well defined. From these we can identify +whether a constant shear modulus or a constant Poisson’s ratio should be used and what their values are. +Initial conditions +If an initial stress at a point +is given such that the stress point lies outside the +initially defined yield surface, Abaqus will try to adjust the initial position of the surface to make the +stress point lie on it and issue a warning. However, if the stress point is such that the equivalent pressure +stress, p, is negative, an error message will be issued and execution will be terminated. +Elements +The clay plasticity model can be used with plane strain, generalized plane strain, axisymmetric, and +three-dimensional solid (continuum) elements in Abaqus. This model cannot be used with elements for +which the assumed stress state is plane stress (plane stress, shell, and membrane elements). +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2), +the +following variable has special meaning for material points in the clay plasticity model: +PEEQ +Center of the yield surface, a. +23.3.5 +CRUSHABLE FOAM PLASTICITY MODELS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Inelastic behavior,” Section 23.1.1 +• “Rate-dependent yield,” Section 23.2.3 +• *CRUSHABLE FOAM +• *CRUSHABLE FOAM HARDENING +• *RATE DEPENDENT +• “Defining crushable foam plasticity” in “Defining plasticity,” Section 12.9.2 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +The crushable foam plasticity models: +• are intended for the analysis of crushable foams that are typically used as energy absorption +structures; +• can be used to model crushable materials other than foams (such as balsa wood); +• are used to model the enhanced ability of a foam material to deform in compression due to cell wall +buckling processes (it is assumed that the resulting deformation is not recoverable instantaneously +and can, thus, be idealized as being plastic for short duration events); +• can be used to model the difference between a foam material’s compressive strength and its much +smaller tensile bearing capacity resulting from cell wall breakage in tension; +• must be used in conjunction with the linear elastic material model (“Linear elastic behavior,” +Section 22.2.1); +• can be used when rate-dependent effects are important; and +• are intended to simulate material response under essentially monotonic loading. +Elastic and plastic behavior +The elastic part of the response is specified as described in “Linear elastic behavior,” Section 22.2.1. +Only linear isotropic elasticity can be used. +For the plastic part of the behavior, the yield surface is a Mises circle in the deviatoric stress plane +and an ellipse in the meridional (p–q) stress plane. Two hardening models are available: the volumetric +hardening model, where the point on the yield ellipse in the meridional plane that represents hydrostatic +tension loading is fixed and the evolution of the yield surface is driven by the volumetric compacting +plastic strain, and the isotropic hardening model, where the yield ellipse is centered at the origin in the +p–q stress plane and evolves in a geometrically self-similar manner. This phenomenological isotropic +model was originally developed for metallic foams by Deshpande and Fleck (2000). +The hardening curve must describe the uniaxial compression yield stress as a function of +the corresponding plastic strain. +In defining this dependence at finite strains, “true” (Cauchy) +stress and logarithmic strain values should be given. Both models predict similar behavior for +compression-dominated loading. However, for hydrostatic tension loading the volumetric hardening +model assumes a perfectly plastic behavior, while the isotropic hardening model predicts the same +behavior in both hydrostatic tension and hydrostatic compression. +Crushable foam model with volumetric hardening +The crushable foam model with volumetric hardening uses a yield surface with an elliptical dependence +of deviatoric stress on pressure stress. It assumes that the evolution of the yield surface is controlled by +the volumetric compacting plastic strain experienced by the material. +Yield surface +The yield surface for the volumetric hardening model is defined as +where +is the pressure stress, +is the Mises stress, +is the deviatoric stress, +is the size of the (horizontal) p-axis of the yield ellipse, +is the size of the (vertical) q-axis of the yield ellipse, +is the shape factor of the yield ellipse that defines the relative +magnitude of the axes, +is the center of the yield ellipse on the p-axis, +is the strength of the material in hydrostatic tension, and +is the yield stress in hydrostatic compression ( +positive). +is always +The yield surface represents the Mises circle in the deviatoric stress plane and is an ellipse on the +meridional stress plane, as depicted in Figure 23.3.5–1. +uniaxial compression + σ +flow potential +original surface +yield surface + -pt + σ +0 -pt + pc + pc + pc +Figure 23.3.5–1 Crushable foam model with volumetric hardening: +yield surface and flow potential in the p–q stress plane. +The yield surface evolves in a self-similar fashion (constant +computed using the initial yield stress in uniaxial compression, +compression, +(the initial value of +), and the yield strength in hydrostatic tension, +: +); and the shape factor can be +, the initial yield stress in hydrostatic +with +and +For a valid yield surface the choice of strength ratios must be such that +not the case, Abaqus will issue an error message and terminate execution. +To define the shape of the yield surface, you provide the values of k and +and +. If this is +. If desired, these variables +can be defined as a tabular function of temperature and other predefined field variables. +Input File Usage: +Abaqus/CAE Usage: +*CRUSHABLE FOAM, HARDENING=VOLUMETRIC +Property module: material editor: Mechanical→Plasticity→Crushable +Foam: Hardening: Volumetric +Calibration +; the initial +To use this model, one needs to know the initial yield stress in uniaxial compression, +yield stress in hydrostatic compression, +. Since foam +; and the yield strength in hydrostatic tension, +materials are rarely tested in tension, it is usually necessary to guess the magnitude of the strength of +the foam in hydrostatic tension, +. The choice of tensile strength should not have a strong effect on the +numerical results unless the foam is stressed in hydrostatic tension. A common approximation is to set +equal to 5% to 10% of the initial yield stress in hydrostatic compression +; thus, += 0.05 to 0.10. +Flow potential +The plastic strain rate for the volumetric hardening model is assumed to be +where G is the flow potential, chosen in this model as +and +is the equivalent plastic strain rate defined as +The equivalent plastic strain rate is related to the rate of axial plastic strain, +by +, in uniaxial compression +A geometrical representation of the flow potential in the p–q stress plane is shown in Figure 23.3.5–1. +This potential gives a direction of flow that is identical to the stress direction for radial paths. This is +motivated by simple laboratory experiments that suggest that loading in any principal direction causes +insignificant deformation in the other directions. As a result, the plastic flow is nonassociative for the +volumetric hardening model. For more details regarding plastic flow, see “Plasticity models: general +discussion,” Section 4.2.1 of the Abaqus Theory Manual. +Nonassociated flow +The nonassociated plastic flow rule makes the material stiffness matrix unsymmetric; therefore, the +unsymmetric matrix storage and solution scheme should be used in Abaqus/Standard . Usage of this scheme is especially important when large regions of the model +are expected to flow plastically. +Hardening +remains fixed throughout any +The yield surface intersects the p-axis at +plastic deformation process. By contrast, the compressive strength, +, evolves as a result of compaction +(increase in density) or dilation (reduction in density) of the material. The evolution of the yield surface +can be expressed through the evolution of the yield surface size on the hydrostatic stress axis, +, +as a function of the value of volumetric compacting plastic strain, +constant, this relation +can be obtained from user-provided uniaxial compression test data using +. We assume that +. With +and +along with the fact that +in uniaxial compression for the volumetric hardening model. Thus, +you provide input to the hardening law by specifying, in the usual tabular form, only the value of the yield +stress in uniaxial compression as a function of the absolute value of the axial plastic strain. The table +must start with a zero plastic strain (corresponding to the virgin state of the material), and the tabular +entries must be given in ascending magnitude of +. If desired, the yield stress can also be a function +of temperature and other predefined field variables. +Input File Usage: +Abaqus/CAE Usage: +*CRUSHABLE FOAM HARDENING +Property module: material editor: Mechanical→Plasticity→Crushable +Foam: Suboptions→Foam Hardening +Rate dependence +As strain rates increase, many materials show an increase in the yield stress. For many crushable foam +materials this increase in yield stress becomes important when the strain rates are in the range of 0.1–1 per +second and can be very important if the strain rates are in the range of 10–100 per second, as commonly +occurs in high-energy dynamic events. +Two methods for specifying strain-rate-dependent material behavior are available in Abaqus as +discussed below. Both methods assume that the shapes of the hardening curves at different strain rates +are similar, and either can be used in static or dynamic procedures. When rate dependence is included, +the static stress-strain hardening behavior must be specified for the crushable foam as described above. +Overstress power law +You can specify a Cowper-Symonds overstress power law that defines strain rate dependence. This law +has the form +with +where B is the size of the static yield surface and +rate. The ratio R can be written as +is the size of the yield surface at a nonzero strain +where r is the uniaxial compression yield stress ratio defined by +, specified as part of the crushable foam hardening definition, is the uniaxial compression yield stress +at a given value of +for the experiment with the lowest strain rate and can depend on temperature +and predefined field variables; D and n are material parameters that can be functions of temperature and, +possibly, of other predefined field variables. +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*CRUSHABLE FOAM HARDENING +*RATE DEPENDENT, TYPE=POWER LAW +Property module: material editor: Mechanical→Plasticity→Crushable +Foam: Suboptions→Foam Hardening; Suboptions→Rate +Dependent: Hardening: Power Law +The power-law rate dependency can be rewritten in the following form +The procedure outlined below can be followed to obtain the material parameters D and n based on the +uniaxial compression test data. +1. Compute R using the uniaxial compression yield stress ratio, r. +2. Convert the rate of the axial plastic strain, +, to the corresponding equivalent plastic strain rate, +. +3. Plot +versus +shown in Figure 23.3.5–2, the overstress power law is suitable. The slope of the line is +the intercept of the +. If the curve can be approximated by a straight line such as that +, and +axis is +. +ln +p - p +p + p t +ln (D) +ε pl +( ) +ln +Figure 23.3.5–2 Calibration of overstress power law data. +Tabular input of yield ratio +as a +Rate-dependent behavior can alternatively be specified by giving a table of the ratio +function of the absolute value of the rate of the axial plastic strain and, optionally, temperature and +predefined field variables. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options: +*CRUSHABLE FOAM HARDENING +*RATE DEPENDENT, TYPE=YIELD RATIO +Property module: material editor: Mechanical→Plasticity→Crushable +Foam: Suboptions→Foam Hardening; Suboptions→Rate +Dependent: Hardening: Yield Ratio +Initial conditions +When we need to study the behavior of a material that has already been subjected to some hardening, +Abaqus allows you to prescribe initial conditions for the volumetric compacting plastic strain, +. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=HARDENING +Load module: Create Predefined Field: Step: Initial, choose Mechanical +for the Category and Hardening for the Types for Selected Step +Crushable foam model with isotropic hardening +The isotropic hardening model uses a yield surface that is an ellipse centered at the origin in the p–q +stress plane. The yield surface evolves in a self-similar manner, and the evolution is governed by the +equivalent plastic strain (to be defined later). +Yield surface +The yield surface for the isotropic hardening model is defined as +where +is the pressure stress, +is the Mises stress, +is the deviatoric stress, +is the size of the (vertical) q-axis of the yield ellipse, +is the shape factor of the yield ellipse that defines the relative +magnitude of the axes, +is the yield stress in hydrostatic compression, and +is the absolute value of the yield stress in uniaxial compression. +The yield surface represents the Mises circle in the deviatoric stress plane. The shape of the yield surface +, can be computed using +in the meridional stress plane is depicted in Figure 23.3.5–3. The shape factor, +the initial yield stress in uniaxial compression, +, and the initial yield stress in hydrostatic compression, +), using the relation: +(the initial value of +with +and +. The particular case of +To define the shape of the yield ellipse, you provide the value of k. For a valid yield surface the +strength ratio must be such that +corresponds to the Mises +plasticity. In general, the initial yield strengths in uniaxial compression and in hydrostatic compression, +, can be used to calculate the value of k. However, in many practical cases the stress versus +strain response curves of crushable foam materials do not show clear yielding points, and the initial yield +stress values cannot be determined exactly. Many of these response curves have a horizontal plateau—the +yield stress is nearly a constant for a significantly large range of plastic strain values. If you have data +from both uniaxial compression and hydrostatic compression, the plateau values of the two experimental +curves can be used to calculate the ratio of k. +Input File Usage: +Abaqus/CAE Usage: +*CRUSHABLE FOAM, HARDENING=ISOTROPIC +Property module: material editor: Mechanical→Plasticity→Crushable +Foam: Hardening: Isotropic +Flow potential +The flow potential for the isotropic hardening model is chosen as +flow potential +uniaxial compression +CRUSHABLE FOAM +yield surface +original surface + -pc -p c + σ + pc + pc +Figure 23.3.5–3 Crushable foam model with isotropic hardening: +yield surface and flow potential in the p–q stress plane. +where +plastic Poisson’s ratio, +, via +represents the shape of the flow potential ellipse on the p–q stress plane. It is related to the +The plastic Poisson’s ratio, which is the ratio of the transverse to the longitudinal plastic strain under +uniaxial compression, must be in the range of −1 and 0.5; and the upper limit ( +) corresponds to +the case of incompressible plastic flow ( +). For many low-density foams the plastic Poisson’s ratio +is nearly zero, which corresponds to a value of +. +The plastic flow is associated when the value of +. By default, the plastic +flow is nonassociated to allow for the independent calibrations of the shape of the yield surface and the +plastic Poisson’s ratio. If you have information only about the plastic Poisson’s ratio and choose to use +associated plastic flow, the yield stress ratio k can be calculated from +is the same as that of +Alternatively, if only the shape of the yield surface is known and you choose to use associated plastic +flow, the plastic Poisson’s ratio can be obtained from +You provide the value of +. +Input File Usage: +Abaqus/CAE Usage: +*CRUSHABLE FOAM, HARDENING=ISOTROPIC +Property module: material editor: Mechanical→Plasticity→Crushable +Foam: Hardening: Isotropic +Hardening +A simple uniaxial compression test is sufficient to define the evolution of the yield surface. The hardening +law defines the value of the yield stress in uniaxial compression as a function of the absolute value of +the axial plastic strain. The piecewise linear relationship is entered in tabular form. The table must start +with a zero plastic strain (corresponding to the virgin state of the materials), and the tabular entries must +be given in ascending magnitude of +. For values of plastic strain greater than the last user-specified +value, the stress-strain relationship is extrapolated based on the last slope computed from the data. If +desired, the yield stress can also be a function of temperature and other predefined field variables. +Input File Usage: +Abaqus/CAE Usage: +*CRUSHABLE FOAM HARDENING +Property module: material editor: Mechanical→Plasticity→Crushable +Foam: Suboptions→Foam Hardening +Rate dependence +As strain rates increase, many materials show an increase in the yield stress. For many crushable foam +materials this increase in yield stress becomes important when the strain rates are in the range of 0.1–1 per +second and can be very important if the strain rates are in the range of 10–100 per second, as commonly +occurs in high-energy dynamic events. +Two methods for specifying strain-rate-dependent material behavior are available in Abaqus as +discussed below. Both methods assume that the shapes of the hardening curves at different strain rates +are similar, and either can be used in static or dynamic procedures. When rate dependence is included, +the static stress-strain hardening behavior must be specified for the crushable foam as described above. +Overstress power law +You can specify a Cowper-Symonds overstress power law that defines strain rate dependence. This law +has the form +with +where +yield stress at a given value of +, specified as part of the crushable foam hardening definition, is the static uniaxial compression +is the yield +for the experiment with the lowest strain rate, and +axial plastic strain in uniaxial compression for the isotropic hardening model. +is the equivalent plastic strain rate, which is equal to the rate of the +The power-law rate dependency can be rewritten in the following form +CRUSHABLE FOAM +versus +Plot +in Figure 23.3.5–2, the overstress power law is suitable. The slope of the line is +of the +and, possibly, of other predefined field variables. +. If the curve can be approximated by a straight line such as that shown +, and the intercept +. The material parameters D and n can be functions of temperature +axis is +Input File Usage: +Use both of the following options: +*CRUSHABLE FOAM HARDENING +*RATE DEPENDENT, TYPE=POWER LAW +Property module: material editor: Mechanical→Plasticity→Crushable +Foam: Suboptions→Foam Hardening; Suboptions→Rate +Dependent: Hardening: Power Law +Abaqus/CAE Usage: +Tabular input of yield ratio +Rate-dependent behavior can alternatively be specified by giving a table of the ratio R as a function of +the absolute value of the rate of the axial plastic strain and, optionally, temperature and predefined field +variables. +Input File Usage: +Use both of the following options: +*CRUSHABLE FOAM HARDENING +*RATE DEPENDENT, TYPE=YIELD RATIO +Property module: material editor: Mechanical→Plasticity→Crushable +Foam: Suboptions→Foam Hardening; Suboptions→Rate +Dependent: Hardening: Yield Ratio +Abaqus/CAE Usage: +Elements +The crushable foam plasticity model can be used with plane strain, generalized plane strain, +axisymmetric, and three-dimensional solid (continuum) elements. This model cannot be used with +elements for which the stress state is assumed to be planar (plane stress, shell, and membrane elements) +or with beam, pipe, or truss elements. +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2), +the +following variable has special meaning for the crushable foam plasticity model: +PEEQ +For the volumetric hardening model, PEEQ is the volumetric compacting plastic +strain defined as +. For the isotropic hardening model, PEEQ is the equivalent +is the uniaxial compression yield +plastic strain defined as +stress. +, where +The volumetric plastic strain, +sum of direct plastic strain components. +, is the trace of the plastic strain tensor; you can also calculate it as the +For the volumetric hardening model, the initial values of the volumetric compacting plastic strain +can be specified for elements that use the crushable foam material model, as described above. The +volumetric compacting plastic strain (output variable PEEQ) provided by Abaqus then contains the +initial value of the volumetric compacting plastic strain plus any additional volumetric compacting plastic +strain due to plastic straining during the analysis. However, the plastic strain tensor (output variable PE) +contains only the amount of straining due to deformation during the analysis. +Additional reference +• Deshpande, V. S., and N. A. Fleck, “Isotropic Constitutive Model for Metallic Foams,” Journal of +the Mechanics and Physics of Solids, vol. 48, pp. 1253–1276, 2000. +23.4 +Fabric materials +• “Fabric material behavior,” Section 23.4.1 +23.4.1 +FABRIC MATERIAL BEHAVIOR +Product: Abaqus/Explicit +References +• “Material library: overview,” Section 21.1.1 +• “Elastic behavior: overview,” Section 22.1.1 +• “VFABRIC,” Section 1.2.3 of the Abaqus User Subroutines Reference Manual +• *FABRIC +• *UNIAXIAL +• *LOADING DATA +• *UNLOADING DATA +• *EXPANSION +• *DENSITY +• *INITIAL CONDITIONS +Overview +The fabric material model: +• is anisotropic and nonlinear; +• is a phenomenological model that captures the mechanical response of a woven fabric made of yarns +in the fill and the warp directions; +• is valid for materials that exhibit two “structural” directions that may not be orthogonal to each +other with deformation; +• defines the local fabric stresses as a function of change in angle between the fibers (shear strain) +and the nominal strains along the yarn directions; +• allows for the computation of local fabric stresses based on test data or through user subroutine +VFABRIC, which can be used to define a complex constitutive model; and +• requires that geometric nonlinearity be accounted for during the analysis step (“General and linear +perturbation procedures,” Section 6.1.3), since it is intended for finite-strain applications. +The fabric material model defined based on test data: +• assumes that the responses along the fill and the warp directions are independent of each other and +that the shear response is independent of the direct response along the yarns; +• can include separate loading and unloading responses; +• can exhibit nonlinear elastic behavior, damaged elastic behavior, or elastic-plastic type behavior +with permanent deformation upon complete unloading; +• can deform elastically to large tensile and shear strains; and +• can have properties that depend on temperature and/or other field variables. +Fabric material behavior +Woven fabrics are used in a number of engineering applications across various industries, including +such products as automobile airbags; flexible structures like boat sails and parachutes; reinforcement in +composites; architectural expressions in building roof structures; protective vests for military, police, +and other security circles; and protective layers around the fuselage in planes. +Woven fabrics consist of yarns woven in the fill and the warp directions. The yarn is crimped, or +curved, as it is woven up and down over the cross yarns. The nonlinear mechanical behavior of the +fabric arises from different sources: +the nonlinear response of the individual yarns, the exchange of +crimp between the fill and the warp yarns as they are stretched, and the contact and friction between +the yarns in cross directions and between the yarns in the same direction. In general, the fabric exhibits +a significant stiffness only along the yarn directions under tension. The tensile response in the fill and +warp directions may be coupled due to the crimp exchange mentioned above. Under in-plane shear +deformation, the fill and warp direction yarns rotate with respect to each other. The resistance increases +with shear deformation as lateral contact is formed between the yarns in each direction. The fabrics +typically have negligible stiffness in bending and in-plane compression. +The behavior of woven fabrics is modeled phenomenologically in Abaqus/Explicit to capture the +nonlinear anisotropic behavior of the fabric. The planar kinematic state of a given fabric is described +in terms of the nominal direct strains in the fabric plane along the fill and the warp directions and the +angle between the two yarn directions. The material orthogonal basis and the yarn local directions are +illustrated in Figure 23.4.1–1 showing the reference and the deformed configurations. +E2 +N2 +12 +N1 +E1 +e2 +n2 +12 +12 +12 +n1 +e1 +(a) Reference configuration +(b) Deformed configuration +Figure 23.4.1–1 Fabric kinematics +The engineering nominal shear strain, +, between the two +yarn directions going from the reference to the deformed configuration. The nominal strains along the +yarn directions +in the deformed configuration are computed from the respective yarn stretch +values, +are defined as the +and +work conjugate of the above nominal strains. The fabric nominal stress, +, is converted by Abaqus to the +Cauchy stress, +; and the subsequent internal forces arising from the fabric deformation are computed. +and +. The corresponding nominal stress components +, is defined as the change in angle, +, and +You can obtain output of the fabric nominal strains, the fabric nominal stresses, and the regular Cauchy +stresses. The relationship between the Cauchy stress, +, and the nominal stress, +, is +where +is the volumetric Jacobian. +Either experimental data or a user subroutine, VFABRIC, can be used to characterize the +Abaqus/Explicit fabric material model, providing the nominal fabric stress as a function of the nominal +fabric strains. The user subroutine allows for building a complex material model taking into account +both the fabric structural parameters such as yarn spacing, yarn cross-section shape, etc. and the yarn +material properties. The test data–based fabric model makes some simplifying assumptions but allows +for nonlinear response including energy loss. The two models are presented below in detail. Both +models capture the wrinkling of fabric under compression only in a smeared fashion. +The application of fabric material in a crash simulation is illustrated in “Side curtain airbag impactor +test,” Section 3.3.2 of the Abaqus Example Problems Manual. +Test data–based fabric materials +The fabric material model based on test data assumes that the responses along the fill and the warp +directions are independent of each other and that the shear response is independent of the direct response +along the yarn. Hence, each component-wise fabric stress response depends only on the fabric strain in +that component. Thus, the overall behavior of the fabric consists of three independent component-wise +responses: namely, the direct response along the fill yarn to the nominal strain in the fill yarn, the direct +response along the warp yarn to the nominal strain in the warp yarn, and the shear response to the change +in angle between the two yarns. +Within each component you must provide test data defining the response of the fabric. To fully +define the fabric response, the test data must cover all of the following attributes: +• Within a component, separate test data can be defined for the fabric response in the tensile direction +and in the compressive direction. +• Within a deformation direction (tension or compression), both loading and unloading test data can +be provided. +• The loading and unloading test data can be classified according to three available behavior types: +nonlinear elastic behavior, damaged elastic behavior, or elastic-plastic type behavior with permanent +deformation. The behavior type determines how the fabric transitions from its loading response to +its unloading response. +When elastic, the test data in a particular component can also be rate dependent. When separate +loading and unloading paths are required, the test data for the two deformation directions (tension and +compression) must be given separately. Otherwise, the data for both tension and compression may be +given in a single table. +Input File Usage: +Use the following options to define a fabric material using test data: +*FABRIC +*UNIAXIAL, COMPONENT=component +*LOADING DATA, DIRECTION=deformation direction, +TYPE=behavior type +data lines to define loading data +*UNLOADING DATA +data lines to define unloading data +Repeat all of the options underneath *FABRIC as often as necessary to account +for each component and deformation direction. +Specifying uniaxial behavior in a component direction +Independent loading and unloading test data can be provided in each of the three component directions. +The components correspond to the response along the fill yarn, the response along the warp yarn, and +the shear response. +Input File Usage: +Use the following option to define the response along the fill yarn direction: +*UNIAXIAL, COMPONENT=1 +Use the following option to define the response along the warp yarn direction: +*UNIAXIAL, COMPONENT=2 +Use the following option to define the shear response: +*UNIAXIAL, COMPONENT=SHEAR +Defining the deformation direction +The test data can be defined separately for tension and compression by specifying the deformation +direction. If the deformation direction is defined (tension or compression), the tabular values defining +tensile or compressive behavior should be specified with positive values of the stress and strain in the +specified component and the loading data must start at the origin. If the behavior is not defined in a +loading direction, the stress response will be zero in that direction (the fabric has no resistance in that +direction). +If the deformation direction is not defined, the data apply to both tension and compression. +However, the behavior is then considered to be nonlinear elastic and no unloading response can +be specified. The test data will be considered to be symmetric about the origin if either tensile or +compressive data are omitted. +Input File Usage: +Use the following option to define tensile behavior: +*LOADING DATA, DIRECTION=TENSION +Use the following option to define compressive behavior: +*LOADING DATA, DIRECTION=COMPRESSION +Use the following option to define both tensile and compressive behavior in a +single table: +*LOADING DATA +Compressive behavior +In general, a fabric material does not have significant stiffness under compression. To prevent the collapse +of wrinkled elements under compressive loading, the specified stress-strain curve should reinstate the +compressive stiffness after a range of zero or very small resistance. +Defining loading/unloading component-wise response for a fabric material +To define the loading response, you specify the fabric stress as nonlinear functions of the fabric strain. +This function can also depend on temperature and field variables. See “Input syntax rules,” Section 1.2.1, +for further information about defining data as functions of temperature and field variables. +The unloading response can be defined in the following different ways: +• You can specify several unloading curves that express the fabric stress as nonlinear functions of the +fabric strain; Abaqus interpolates these curves to create an unloading curve that passes through the +point of unloading in an analysis. +• You can specify an energy dissipation factor (and a permanent deformation factor for models with +permanent deformation), from which Abaqus calculates a quadratic unloading function. +• You can specify an energy dissipation factor (and a permanent deformation factor for models with +permanent deformation), from which Abaqus calculates an exponential unloading function. +• You can specify the fabric stress as a nonlinear function of the fabric strain, as well as a transition +slope; the fabric unloads along the specified transition slope until it intersects the specified unloading +function, at which point it unloads according to the function. (This unloading definition is referred +to as combined unloading.) +• You can specify the fabric stress as a nonlinear function of the fabric strain; Abaqus shifts the +specified unloading function along the strain axis so that it passes through the point of unloading in +an analysis. +The behavior type that is specified for the fabric dictates the type of unloading you can define, as +summarized in Table 23.4.1–1. The different behavior types, as well as the associated loading and +unloading curves, are discussed in more detail in the sections that follow. +Defining nonlinear elastic behavior +The elastic behavior can be nonlinear and, optionally, rate dependent. When the loading response is rate +dependent, a separate unloading curve must also be specified. However, the unloading response need +not be rate dependent. +Defining rate-independent elasticity +When the loading response is rate independent, the unloading response is also rate independent and +occurs along the same user-specified loading curve as illustrated in Figure 23.4.1–2. An unloading curve +does not need to be specified. +Input File Usage: +*LOADING DATA, TYPE=ELASTIC +Table 23.4.1–1 Available unloading definitions for the fabric behavior types. +Unloading definition +Interpolated +Quadratic +Exponential +Combined +Shifted +Material behavior +type +Nonlinear elastic +(rate-dependent +only) +Damaged elastic +Permanent +deformation + +loading curve + +Figure 23.4.1–2 Nonlinear elastic rate-independent loading. +Defining rate-dependent elasticity +When the elastic response is rate dependent, both the loading and the unloading curves need to be +specified. If the unloading data are not specified, the unloading occurs along the loading curve specified +with the smallest rate of deformation. +Unphysical jumps in the stress due to sudden changes in the rate of deformation are prevented using +a technique based on viscoplastic regularization. This technique also helps model relaxation effects in a +very simplistic manner, with the relaxation time given as +are +material parameters and +is a linear viscosity parameter that controls the relaxation +time when +is a nonlinear viscosity parameter that controls the relaxation time at higher values of +. Small values of this parameter should be used; a suggested value is 0.0001s. +. The smaller +is the stretch. +, where +, and +, +this value, the shorter the relaxation time. The suggested value for this parameter is 0.005s. +controls +the sensitivity of the relaxation speed to the fabric strain component. Figure 23.4.1–3 illustrates the +loading/unloading behavior as the component is loaded at a rate +and then unloaded at a rate +. + +Figure 23.4.1–3 Rate-dependent loading/unloading. +The unloading path is determined by interpolating the specified unloading curves. The unloading +need not be rate dependent, even though the loading response is rate dependent. When the unloading +is rate dependent, the unloading path at any given component strain and strain rate is determined by +interpolating the specified unloading curves. +Input File Usage: +Use the following options when the unloading is also rate dependent: +*LOADING DATA, TYPE=ELASTIC, RATE DEPENDENT, +DIRECTION +*UNLOADING DATA, DEFINITION=INTERPOLATED CURVE, +RATE DEPENDENT +Use the following options when the unloading is rate independent: +*LOADING DATA, TYPE=ELASTIC, RATE DEPENDENT, +DIRECTION +*UNLOADING DATA, DEFINITION=INTERPOLATED CURVE +Defining models with damage +The damage models dissipate energy upon unloading, and there is no permanent deformation upon +complete unloading. You can specify the onset of damage by defining the strain above which the +material response in unloading does not retrace the loading curve. +The unloading behavior controls the amount of energy dissipated by damage mechanisms and can +be specified in one of the following ways: +• an analytical unloading curve (exponential/quadratic); +• an unloading curve interpolated from multiple user-specified unloading curves; or +• unloading along a transition unloading curve (constant slope specified by user) to the user-specified +unloading curve (combined unloading). +Input File Usage: +Use the following options to define damage with quadratic unloading behavior: +*LOADING DATA, TYPE=DAMAGE, DIRECTION +*UNLOADING DATA, DEFINITION=QUADRATIC +Use the following options to define damage with exponential unloading +behavior: +*LOADING DATA, TYPE=DAMAGE, DIRECTION +*UNLOADING DATA, DEFINITION=EXPONENTIAL +Use the following options to define damage with an interpolated unloading +curve: +*LOADING DATA, TYPE=DAMAGE, DIRECTION +*UNLOADING DATA, DEFINITION=INTERPOLATED CURVE +Use the following options to specify damage with combined unloading +behavior: +*LOADING DATA, TYPE=DAMAGE, DIRECTION +*UNLOADING DATA, DEFINITION=COMBINED +Defining onset of damage +You can specify the onset of damage by defining the strain above which the material response in unloading +does not retrace the loading curve. +Input File Usage: +*LOADING DATA, TYPE=DAMAGE, DAMAGE ONSET=value +Specifying exponential/quadratic unloading +The damage model in Figure 23.4.1–4 is based on an analytical unloading curve that is derived from +an energy dissipation factor, +(fraction of energy that is dissipated at any strain level). As the fabric +component is loaded, the stress follows the path given by the loading curve. If the fabric component +is unloaded (for example, at point B), the stress follows the unloading curve +. Reloading after +unloading follows the unloading curve +until the loading is such that the strain becomes greater +than +, after which the loading path follows the loading curve. The arrows shown in Figure 23.4.1–4 +illustrate the loading/unloading paths of this model. + +primary loading curve +exponential/quadratic +unloading +max + +Figure 23.4.1–4 Exponential/quadratic unloading. +The unloading response follows the loading curve when the calculated unloading curve lies above +the loading curve to prevent energy generation and follows a zero stress response when the unloading +curve yields a negative response. In such cases the dissipated energy will be less than the value specified +by the energy dissipation factor. +Specifying interpolated curve unloading +The damage model in Figure 23.4.1–5 illustrates an interpolated unloading response based on multiple +unloading curves that intersect the primary loading curve at increasing values of stress/strains. You can +specify as many unloading curves as are necessary to define the unloading response. Each unloading +curve always starts at point O, the point of zero stress and zero strains, since the damage models do +not allow any permanent deformation. The unloading curves are stored in normalized form so that they +intersect the loading curve at a unit stress for a unit strain, and the interpolation occurs between these +normalized curves. If unloading occurs from a maximum strain for which an unloading curve is not +specified, the unloading is interpolated from neighboring unloading curves. As the fabric component is +loaded, the stress follows the path given by the loading curve. If the fabric is unloaded (for example, at +point B), the stress follows the unloading curve +. Reloading after unloading follows the unloading +path +, after which the loading +path follows the loading curve. +until the loading is such that the strain becomes greater than +The unloading curve also has the same temperature and field variable dependencies as the loading +curve. +Specifying combined unloading +As illustrated in Figure 23.4.1–6, you can specify an unloading curve +curve +in addition to the loading +as well as a constant transition slope that connects the loading curve to the unloading + +max +primary loading curve +unloading curves + +Figure 23.4.1–5 +Interpolated curve unloading. +curve. As the fabric is loaded, the stress follows the path given by the loading curve. If the fabric is +unloaded (for example at point B) the stress follows the unloading curve +is defined +by the constant transition slope, and +lies on the specified unloading curve. Reloading after unloading +follows the unloading path +, after +which the loading path follows the loading curve. +until the loading is such that the strain becomes greater than +. The path +primary loading curve +transition curve +unloading curve +max +The unloading curve also has the same temperature and field variable dependencies as the loading +Figure 23.4.1–6 Combined unloading. +curve. +Defining models with permanent deformation +These models dissipate energy upon unloading and exhibit permanent deformation upon complete +unloading. You can specify the onset of permanent deformation by defining the strain below which +unloading occurs along the loading curve. +The unloading behavior controls the amount of energy dissipated as well as the amount of +permanent deformation. The unloading behavior can be specified in one of the following ways: +Input File Usage: +• an analytical unloading curve (exponential/quadratic); +• an unloading curve interpolated from multiple user-specified unloading curves; or +• an unloading curve obtained by shifting the user-specified unloading curve to the point of unloading. +Use the following options to define permanent deformation with quadratic +unloading behavior: +*LOADING DATA, TYPE=PERMANENT DEFORMATION, +DIRECTION +*UNLOADING DATA, DEFINITION=QUADRATIC +Use the following options to define permanent damage with exponential +unloading behavior: +*LOADING DATA, TYPE=PERMANENT DEFORMATION, +DIRECTION +*UNLOADING DATA, DEFINITION=EXPONENTIAL +Use the following options to define permanent damage with an interpolated +unloading curve: +*LOADING DATA, TYPE=PERMANENT DEFORMATION, +DIRECTION +*UNLOADING DATA, DEFINITION=INTERPOLATED CURVE +Use the following options to specify permanent damage with a shifted +unloading curve: +*LOADING DATA, TYPE=PERMANENT DEFORMATION, +DIRECTION +*UNLOADING DATA, DEFINITION=SHIFTED CURVE +Defining the onset of permanent deformation +By default, the onset of yield will be obtained as soon as the slope of the loading curve decreases by 10% +from the maximum slope recorded up to that point while traversing along the loading curve. To override +the default method of determining the onset of yield, you can specify either a value for the decrease in +slope of the loading curve other than the default value of 10% (slope drop = 0.1) or by defining the strain +below which unloading occurs along the loading curve. If a slope drop is specified, the onset of yield will +be obtained as soon as the slope of the loading curve decreases by the specified factor from the maximum +slope recorded up to that point. +Input File Usage: +Use the following options to specify the onset of yield by defining the strain +below which unloading occurs along the loading curve: +*LOADING DATA, TYPE=PERMANENT DEFORMATION, +YIELD ONSET=value +Use the following options to specify the onset of yield by defining a slope drop +for the loading curve: +*LOADING DATA, TYPE=PERMANENT DEFORMATION, +SLOPE DROP=value +Specifying exponential/quadratic unloading +The model in Figure 23.4.1–7 illustrates an analytical unloading curve that is derived from an energy +dissipation factor, +(fraction of energy that is dissipated at any strain level), and a permanent +deformation factor, +. As the fabric component is loaded, the fabric stress follows the path given +by the loading curve. If the component is unloaded (for example, at point B), the stress follows the +unloading curve +. Reloading +. The point D corresponds to the permanent deformation, +after unloading follows the unloading curve +until the loading is such that the strain becomes +greater than +, after which the loading path follows the loading curve. The arrows shown in +Figure 23.4.1–7 illustrate the loading/unloading paths of this model. +primary loading curve +max +Dp +max +exponential/quadratic +unloading +Figure 23.4.1–7 Exponential/quadratic unloading. +The unloading response follows the loading curve when the calculated unloading curve lies above +the loading curve to prevent energy generation and follows a zero stress response when the unloading +curve yields a negative response. In such cases the dissipated energy will be less than the value specified +by the energy dissipation factor. +Specifying interpolated curve unloading +The model in Figure 23.4.1–8 illustrates an interpolated unloading response based on multiple unloading +curves that intersect the primary loading curve at increasing values of stresses/strains. + +primary loading curve +unloading curves +max + +Figure 23.4.1–8 Interpolated curve unloading. +You can specify as many unloading curves as are necessary to define the unloading response. The first +point of each unloading curve defines the permanent deformation if the fabric component is completely +unloaded. The unloading curves are stored in normalized form so that they intersect the loading curve at +a unit stress for a unit strain, and the interpolation occurs between these normalized curves. If unloading +occurs from a maximum strain for which an unloading curve is not specified, the unloading is interpolated +from neighboring unloading curves. As the fabric is loaded, the stress follows the path given by the +loading curve. If the fabric is unloaded (for example, at point B), the stress follows the unloading curve +until the loading is such that the +. Reloading after unloading follows the unloading path +strain becomes greater than +, after which the loading path follows the loading curve. +The unloading curve also has the same temperature and field variable dependencies as the loading +curve. +Specifying shifted curve unloading +You can specify an unloading curve passing through the origin in addition to the loading curve. The +actual unloading curve is obtained by horizontally shifting the user-specified unloading curve to pass +through the point of unloading as shown in Figure 23.4.1–9. The permanent deformation upon complete +unloading is the horizontal shift applied to the unloading curve. +The unloading curve also has the same temperature and field variable dependencies as the loading +curve. +unloading curve + +primary loading curve +shifted unloading curve +max + +Figure 23.4.1–9 Shifted curve unloading. +Using different uniaxial models in tension and compression +When appropriate, different uniaxial behavior models can be used in tension and compression. For +example, response under tension can be plastic with exponential unloading, while the response in +compression can be nonlinear elastic . +User-defined fabric materials +The mechanical response of a fabric material depends on a number of micro and meso-scale parameters +covering the fabric construction and that of the individual yarns as a bundle of fibers. Often a multi-scale +model becomes necessary to track the state of the fabric and its response to loading. Abaqus provides a +specialized user subroutine, VFABRIC, to capture the complex fabric response given the deformed yarn +directions and the strains along these directions. +The density (“Density,” Section 21.2.1) is required when using a fabric material. +Input File Usage: +Use the following options to define a fabric material through user subroutine +VFABRIC: +*MATERIAL, NAME=name +*FABRIC, USER +*DENSITY +Properties for a user-defined fabric material +Any material constants that are needed in user subroutine VFABRIC must be specified as part of a +user-defined fabric material definition. Abaqus can be used to compute the isotropic thermal expansion +response under thermal loading, even as the remaining mechanical response is defined by the user +primary loading curve +unloading +nonlinear +elastic +Figure 23.4.1–10 Different uniaxial models in tension and compression. +subroutine. Alternatively, you can include the thermal expansion within the definition of the mechanical +response in user subroutine VFABRIC. +Input File Usage: +Use the following option to define properties for a user-defined fabric material +behavior: +*FABRIC, USER, PROPERTIES=number_of_constants +Material state +Many mechanical constitutive models require the storage of solution-dependent state variables (plastic +strains, “back stress,” saturation values, etc. in rate constitutive forms or historical data for theories +written in integral form). You should allocate storage for these variables in the associated material +definition . There is no +restriction on the number of state variables associated with a user-defined fabric material. +State variables associated with VFABRIC can be output to the output database (.odb) file and +results (.fil) file using output identifiers SDV and SDVn . +User subroutine VFABRIC is called for blocks of material points at each increment. When the +subroutine is called, it is provided with the state at the start of the increment (fabric stress in the local +system, solution-dependent state variables). It is also provided with the nominal fabric strains at the end +of the increment and the incremental nominal fabric strains over the increment, both in the local system. +The VFABRIC user material interface passes a block of material points to the subroutine on each call, +which allows vectorization of the material subroutine. +The temperature is provided to user subroutine VFABRIC at the start and the end of the increment. +The temperature is passed in as information only and cannot be modified, even in a fully coupled thermal- +stress analysis. However, if the inelastic heat fraction is defined in conjunction with the specific heat and +conductivity in a fully coupled thermal-stress analysis, the heat flux due to inelastic energy dissipation +is calculated automatically. If user subroutine VFABRIC is used to define an adiabatic material behavior +(conversion of plastic work to heat) in an explicit dynamic procedure, the temperatures must be stored +and integrated as user-defined state variables. Most often the temperatures are provided by specifying +initial conditions (“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1) and are +constant throughout the analysis. +Deleting elements from an Abaqus/Explicit mesh using state variables +Element deletion in a mesh can be controlled during the course of an Abaqus/Explicit analysis through +user subroutine VFABRIC. Deleted elements have no ability to carry stresses and, therefore, have no +contribution to the stiffness of the model. You specify the state variable number controlling the element +deletion flag. For example, specifying a state variable number of 4 indicates that the fourth state variable +is the deletion flag in VFABRIC. The deletion state variable should be set to a value of one or zero in +VFABRIC. A value of one indicates that the material point is active, while a value of zero indicates that +Abaqus/Explicit should delete the material point from the model by setting the stresses to zero. The +structure of the block of material points passed to user subroutine VFABRIC remains unchanged during +the analysis; deleted material points are not removed from the block. Abaqus/Explicit will pass zero +stresses and strain increments for all deleted material points. Once a material point has been flagged as +deleted, it cannot be reactivated. An element will be deleted from the mesh only after all of the material +points in the element are deleted. The status of an element can be determined by requesting output of +the variable STATUS. This variable is equal to 1 if the element is active and equal to 0 if the element is +deleted. +Input File Usage: +*DEPVAR, DELETE=variable number +Thermal expansion +You can define isotropic thermal expansion to specify the same coefficient of thermal expansion for the +membrane and thickness-direction behaviors. +The membrane thermal strains, +, are obtained as explained in “Thermal expansion,” +Section 26.1.2. +The elastic stretch in a given direction, +, relates the total stretch, +, and the thermal stretch, +: +is given by +where +is the linear thermal expansion strain in that direction. +Fabric thickness +The thickness of a fabric is difficult to measure experimentally. Fortunately, an accurate value for +thickness is not always required due to the fact that a nominal stress measure, defined as force per unit +area in the reference configuration, is used to characterize the in-plane response. An initial thickness can +be specified on the section definition. Accurate tracking of the thickness with deformation is necessary +only if the material is used with shell elements and the bending response needs to be captured accurately. +You can compute the thickness direction strain increment when the fabric is defined through user +subroutine VFABRIC. For test data–based fabric materials the thickness is assumed to remain constant +with deformation. For a test data–based fabric definition, you must use the thickness value specified on +the section definition for converting the experimental load data (which are typically available as force +applied per unit width of the fabric) to stress quantities. +Defining a reference mesh (initial metric) +Abaqus/Explicit allows the specification of a reference mesh (initial metric) for fabrics modeled with +membrane elements. For example, this is useful in airbag simulations to model wrinkles and changes in +yarn orientations that arise from the airbag folding process. A flat mesh may be suitable for the unstressed +reference configuration, but the initial state may require a corresponding folded mesh defining the folded +state. The angular orientation of the yarn in the reference configuration is updated to obtain the new +orientation in the initial configuration. +Input File Usage: +Use the following option to define the reference configuration giving the +element number and its nodal coordinates in the reference configuration: +*INITIAL CONDITIONS, TYPE=REF COORDINATE +Use the following option to define the reference configuration giving the node +number and its coordinates in the reference configuration: +*INITIAL CONDITIONS, TYPE=NODE REF COORDINATE +Yarn behavior under initial compressive strains +Defining a reference configuration that is different from the initial configuration generally results in +nonzero stresses and strains in the initial configuration based on the material definition. By default, +compressive initial strains in the yarn directions generate zero stresses. The stress remains zero as the +strain is continuously recovered from the initial compressive values toward the strain-free state. Once the +initial slack is recovered, any subsequent compressive/tensile strains generate stresses as per the material +definition. +Input File Usage: +initial compressive strains are +Use the following option to specify that +recovered stress free (default): +*FABRIC, STRESS FREE INITIAL SLACK=YES +Use the following option to specify that initial compressive strains generate +nonzero initial stresses: +*FABRIC, STRESS FREE INITIAL SLACK=NO +Defining yarn directions in the reference configuration +In general, the yarn directions may not be orthogonal to each other in the reference configuration. You +can specify these local directions with respect to the in-plane axes of an orthogonal orientation system +at a material point. Both the local directions and the orthogonal system are defined together as a single +orientation definition. See “Orientations,” Section 2.2.5, for more information. +If the local directions are not specified, these directions are assumed to match the in-plane axes of +the orthogonal system defined. The local direction may not remain orthogonal with deformation. Abaqus +updates the local directions with deformation and computes the nominal strains along these directions +and the angle between them (fabric shear strain). The constitutive behavior for the fabric defines the +nominal stresses in the local system in terms of the fabric strain. +Local yarn directions can be output to the output database as described in “Output,” below. +Picture-frame shear fabric test +The shear response of the fabric is typically studied using a picture-frame shear test. The reference and +the deformed configuration for a picture-frame shear test under force +is illustrated in Figure 23.4.1–11, +where +is the initial angle between the yarn directions. The +four sides of the specimen are constrained not to change in their length even as the frame elongates +and the angle between the yarn directions +decreases with deformation.The relationship between the +nominal shear stress, +is the size of the picture-frame, and +, and the applied force, +, is +where +change in the angle between the yarn directions as +is the initial volume of the specimen. The fabric engineering shear strain, +, is related to the +Use with other material models +The fabric material model can be used by itself, or it can be combined with isotropic thermal expansion +to introduce thermal volume changes (“Thermal expansion,” Section 26.1.2). See “Combining material +behaviors,” Section 21.1.3, for more details. Thermal expansion can alternatively be an integral part of +the constitutive model implemented in VFABRIC for user-defined fabric materials. +For a test-data based fabric material, both the mass proportional and the stiffness proportional +damping can be specified . If stiffness proportional damping is +specified, Abaqus calculates the damping stress based on the current elastic stiffness of the material and +the resulting damping stress is included in the reported stress output at the integration points. +For a fabric material defined by user subroutine VFABRIC, mass proportional damping can be +specified, but stiffness proportional damping must be defined within the user subroutine. +L0 +L0 +L0 +L0 +12 +N2 +N1 +12 +n1 +n2 +(a) Reference configuration +(b) Deformed configuration +Figure 23.4.1–11 Picture-frame shear test on a fabric. +Elements +The fabric material model can be used with plane stress elements (plane stress solid elements, finite-strain +shells, and membranes). It is recommended that the fabric material model be used with fully integrated +or triangular membrane elements. When the fabric material model is used with shell elements, Abaqus +does not compute a default transverse shear stiffness and you must specify it directly (see“Defining the +transverse shear stiffness” in “Using a shell section integrated during the analysis to define the section +behavior,” Section 29.6.5). +Procedures +Fabric materials must always be used with geometrically nonlinear analyses (“General and linear +perturbation procedures,” Section 6.1.3). +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Explicit output variable +identifiers,” Section 4.2.2), the following variables have special meaning for the fabric material models: +EFABRIC +SFABRIC +Nominal fabric strain with components similar to that of LE, but with the direct +components measuring the nominal strain along the yarn directions and the +engineering shear component measuring the change in angle between the two +yarn directions. +Nominal fabric stress with components similar to that of the regular Cauchy stress, +S, but with the direct components measuring the nominal stress along the yarn +directions and the shear component measuring response to the change in angle +between the two yarn directions. +By default Abaqus outputs local material directions whenever element field output is requested to +the output database for fabric models. The local directions are output as field variables (LOCALDIR1, +LOCALDIR2, LOCALDIR3) representing the yarn direction cosines; these variables can be visualized +as vector plots in the Visualization module of Abaqus/CAE (Abaqus/Viewer). +Output of local material directions is suppressed if no element field output is requested or if +you specify not to have element material directions written to the output database . +23.5 +Jointed materials +• “Jointed material model,” Section 23.5.1 +23.5.1 +JOINTED MATERIAL MODEL +Product: Abaqus/Standard +References +• “Orientations,” Section 2.2.5 +• “Material library: overview,” Section 21.1.1 +• “Inelastic behavior,” Section 23.1.1 +• *JOINTED MATERIAL +Overview +The jointed material model: +• is intended to provide a simple continuum model for a material containing a high density of parallel +joint surfaces where each system of parallel joints is associated with a particular orientation, such +as sedimentary rock; +• assumes that the spacing of the joints of a particular orientation is sufficiently close compared to +characteristic dimensions in the domain of the model such that the joints can be smeared into a +continuum of slip systems; +• provides for opening or frictional sliding of the joints in each of these systems (a “system” in this +context is a joint orientation in a particular direction at a material calculation point); and +• assumes that the elastic behavior of the material is isotropic and linear when all joints at a point are +closed (isotropic linear elastic behavior must be included in the material definition; see “Defining +isotropic elasticity” in “Linear elastic behavior,” Section 22.2.1). +Joint opening/closing +The jointed material model is intended primarily for applications where the stresses are mainly +compressive. The model provides a joint opening capability when the stress normal to the joint tries +to become tensile. +In this case the stiffness of the material normal to the joint plane becomes zero +instantaneously. Abaqus/Standard uses a stress-based joint opening criterion, whereas joint closing is +monitored based on strain. Joint system a opens when the estimated pressure stress across the joint +(normal to the joint surface) is no longer positive: +In this case the material is assumed to have no elastic stiffness with respect to direct strain across the +joint system. Open joints thus create anisotropic elastic response at a point. The joint system remains +open so long as +where +elastic strain across the joint calculated in plane stress as +is the component of direct elastic strain across the joint and +is the component of direct +where E is the Young’s modulus of the material, +stresses in the plane of the joint. +is the Poisson’s ratio, and +, +are the direct +The shear response of open joints is governed by the shear retention parameter, +, which +represents the fraction of the elastic shear modulus retained when the joints are open ( +=0 means no +shear stiffness associated with open joints, while +=1 corresponds to elastic shear stiffness in open +joints; any value between these two extremes can be used). When a joint opens, the shear behavior +may be brittle, depending on the shear retention factor used for open joints. In addition, the stiffness +of the material normal to the joint plane suddenly goes to zero. For these reasons, in situations where +the confining stresses are low or significant regions experience tensile behavior, the joint systems may +experience a sequence of alternate opening and closing states from iteration to iteration. Typically such +behavior manifests itself as oscillating global residual forces. The convergence rate associated with +such discontinuous behavior may be very slow and, thus, prohibit obtaining a solution. This type of +failure is more probable in cases where more than one joint system is modeled. +Improving convergence when joints open and close repeatedly +When the repeated opening and closing of joints makes convergence difficult, you can improve +convergence by preventing a joint from opening. In this case an elastic stiffness is always associated +with the joint. It is most useful when the opening and closing of joints is limited to small regions of the +model. You can prevent a joint from opening only when the joint direction is specified, as described +below. +Input File Usage: +*JOINTED MATERIAL, NO SEPARATION, JOINT DIRECTION +Specifying nonzero shear retention in open joints +You must specify nonzero shear retention in open joints directly. The parameter +tabular function of temperature and predefined field variables. +can be defined as a +Input File Usage: +*JOINTED MATERIAL, SHEAR RETENTION +Compressive joint sliding +The failure surface for sliding on joint system a is defined by +where +stress acting across the joint, +is the magnitude of the shear stress resolved onto the joint surface, +is the normal pressure +is the cohesion for system a. So +is the friction angle for system a, and +strain on the system is given by +, joint system a does not slip. When +, joint system a slips. The inelastic (“plastic”) +JOINTED MATERIAL +where +on the joint surface ( +are orthogonal +is the rate of inelastic shear strain in direction +directions on the joint surface), +is the magnitude of the inelastic strain rate, +is a component of the shear stress on the joint surface, +is the dilation angle for this joint system (choosing +joint, while +is the inelastic strain normal to the joint surface. +causes dilation of the joint as it slips), and +provides pure shear flow on the +The sliding of the different joint systems at a point is independent, in the sense that sliding on one system +does not change the failure criterion or the dilation angle for any other joint system at the same point. +Up to three joint directions can be included in the material description. The orientations of the +joint directions are given by referring to the names of user-defined local orientations (“Orientations,” +Section 2.2.5) that define the joint orientations in the original configuration. Output of stress and strain +components is in the global directions unless a local orientation is also used in the material’s section +definition. +The parameters +, +, and +can be specified as tabular functions of temperature and/or predefined +field variables for each joint direction. +Input File Usage: +Use both of the following options: +*ORIENTATION, NAME=name +*JOINTED MATERIAL, JOINT DIRECTION=name +Repeat the *JOINTED MATERIAL option for each direction to be specified, +up to three times. +Joint directions and finite rotations +In geometrically nonlinear analysis steps the joint directions always remain fixed in space. +Bulk failure +In addition to the joint systems, the jointed material model includes a bulk material failure mechanism, +which is based on the Drucker-Prager failure criterion: +where +is the Mises equivalent deviatoric stress, +is the deviatoric stress, +is the equivalent pressure stress, +is the friction angle for the bulk material, and +is the cohesion for the bulk material. +If this failure criterion is reached, the bulk inelastic flow is defined by +where +is the magnitude of the inelastic flow rate (chosen so that +is the flow potential. Here +in uniaxial compression in the 1-direction), and +is the dilation angle for the bulk material. This bulk +failure model is a simplified version of the extended Drucker-Prager model (“Extended Drucker-Prager +models,” Section 23.3.1). This bulk failure system is independent of the joint systems in that bulk +inelastic flow does not change the behavior of any joint system. +If bulk material failure is to be modeled, a jointed material behavior must be specified to define the +parameters associated with bulk material failure behavior. Thus, up to five jointed material behaviors +can appear in the same material definition: three joint directions, shear retention in open joints, and bulk +material failure. +The parameters +, +, and +can be specified as a tabular function of temperature and/or predefined +field variables. +Input File Usage: +*JOINTED MATERIAL (the JOINT DIRECTION parameter must be omitted) +Nonassociated flow +in any joint system, whether it be associated with the joint surfaces or the bulk material, the flow +If +in that system is “nonassociated.” The implication is that the material stiffness matrix is not symmetric. +Therefore, the unsymmetric matrix solution scheme should be used for the analysis step (“Defining an +analysis,” Section 6.1.2), especially when large regions of the model are expected to flow plastically and +when the difference between +is not large, a symmetric +approximation to the matrix can provide an acceptable rate of convergence of the equilibrium equations +and, hence, a lower overall solution cost. Therefore, the unsymmetric matrix solution scheme is not +invoked automatically when jointed material behavior is defined. +is large. If the difference between +and +and +Elements +The jointed material model can be used with plane strain, generalized plane strain, axisymmetric, and +three-dimensional solid (continuum) elements in Abaqus/Standard. This model cannot be used with +elements for which the assumed stress state is plane stress (plane stress, shell, and membrane elements). +23.6 +Concrete +• “Concrete smeared cracking,” Section 23.6.1 +• “Cracking model for concrete,” Section 23.6.2 +• “Concrete damaged plasticity,” Section 23.6.3 +23.6.1 +CONCRETE SMEARED CRACKING +Products: Abaqus/Standard Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Inelastic behavior,” Section 23.1.1 +• *CONCRETE +• *TENSION STIFFENING +• *SHEAR RETENTION +• *FAILURE RATIOS +• “Defining concrete smeared cracking” in “Defining plasticity,” Section 12.9.2 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +The smeared crack concrete model in Abaqus/Standard: +• provides a general capability for modeling concrete in all types of structures, including beams, +trusses, shells, and solids; +• can be used for plain concrete, even though it is intended primarily for the analysis of reinforced +concrete structures; +• can be used with rebar to model concrete reinforcement; +• is designed for applications in which the concrete is subjected to essentially monotonic straining at +low confining pressures; +• consists of an isotropically hardening yield surface that is active when the stress is dominantly +compressive and an independent “crack detection surface” that determines if a point fails by +cracking; +• uses oriented damaged elasticity concepts (smeared cracking) to describe the reversible part of the +material’s response after cracking failure; +• requires that the linear elastic material model be used +to define elastic properties; and +• cannot be used with local orientations . +See “Inelastic behavior,” Section 23.1.1, for a discussion of the concrete models available in Abaqus. +Reinforcement +Reinforcement in concrete structures is typically provided by means of rebars, which are one-dimensional +strain theory elements (rods) that can be defined singly or embedded in oriented surfaces. Rebars +are typically used with metal plasticity models to describe the behavior of the rebar material and are +superposed on a mesh of standard element types used to model the concrete. +With this modeling approach, the concrete behavior is considered independently of the rebar. +Effects associated with the rebar/concrete interface, such as bond slip and dowel action, are modeled +approximately by introducing some “tension stiffening” into the concrete modeling to simulate load +transfer across cracks through the rebar. Details regarding tension stiffening are provided below. +Defining the rebar can be tedious in complex problems, but it is important that this be done +accurately since it may cause an analysis to fail due to lack of reinforcement in key regions of a model. +See “Defining reinforcement,” Section 2.2.3, for more information regarding rebars. +Cracking +The model is intended as a model of concrete behavior for relatively monotonic loadings under fairly +low confining pressures (less than four to five times the magnitude of the largest stress that can be carried +by the concrete in uniaxial compression). +Crack detection +Cracking is assumed to be the most important aspect of the behavior, and representation of cracking and +of postcracking behavior dominates the modeling. Cracking is assumed to occur when the stress reaches +a failure surface that is called the “crack detection surface.” This failure surface is a linear relationship +between the equivalent pressure stress, p, and the Mises equivalent deviatoric stress, q, and is illustrated +in Figure 23.6.1–5. When a crack has been detected, its orientation is stored for subsequent calculations. +Subsequent cracking at the same point is restricted to being orthogonal to this direction since stress +components associated with an open crack are not included in the definition of the failure surface used +for detecting the additional cracks. +Cracks are irrecoverable: they remain for the rest of the calculation (but may open and close). No +more than three cracks can occur at any point (two in a plane stress case, one in a uniaxial stress case). +Following crack detection, the crack affects the calculations because a damaged elasticity model is used. +Oriented, damaged elasticity is discussed in more detail in “An inelastic constitutive model for concrete,” +Section 4.5.1 of the Abaqus Theory Manual. +Smeared cracking +The concrete model is a smeared crack model in the sense that it does not track individual “macro” +cracks. Constitutive calculations are performed independently at each integration point of the finite +element model. The presence of cracks enters into these calculations by the way in which the cracks +affect the stress and material stiffness associated with the integration point. +Tension stiffening +The postfailure behavior for direct straining across cracks is modeled with tension stiffening, which +allows you to define the strain-softening behavior for cracked concrete. This behavior also allows for +the effects of the reinforcement interaction with concrete to be simulated in a simple manner. Tension +stiffening is required in the concrete smeared cracking model. You can specify tension stiffening by +means of a postfailure stress-strain relation or by applying a fracture energy cracking criterion. +Postfailure stress-strain relation +Specification of strain softening behavior in reinforced concrete generally means specifying the +postfailure stress as a function of strain across the crack. In cases with little or no reinforcement this +specification often introduces mesh sensitivity in the analysis results in the sense that the finite element +predictions do not converge to a unique solution as the mesh is refined because mesh refinement leads to +narrower crack bands. This problem typically occurs if only a few discrete cracks form in the structure, +and mesh refinement does not result in formation of additional cracks. If cracks are evenly distributed +(either due to the effect of rebar or due to the presence of stabilizing elastic material, as in the case of +plate bending), mesh sensitivity is less of a concern. +In practical calculations for reinforced concrete, the mesh is usually such that each element +contains rebars. The interaction between the rebars and the concrete tends to reduce the mesh sensitivity, +provided that a reasonable amount of tension stiffening is introduced in the concrete model to simulate +this interaction (Figure 23.6.1–1). +Stress, σ +σ u +Abaqus Version 6.6 ID: +Printed on: +Failure point +"tension stiffening" + curve +t = +σ u +Strain, +it depends on such factors as the density of +The tension stiffening effect must be estimated; +reinforcement, the quality of the bond between the rebar and the concrete, the relative size of the +concrete aggregate compared to the rebar diameter, and the mesh. A reasonable starting point for +relatively heavily reinforced concrete modeled with a fairly detailed mesh is to assume that the strain +softening after failure reduces the stress linearly to zero at a total strain of about 10 times the strain +at failure. The strain at failure in standard concretes is typically 10−4, which suggests that tension +stiffening that reduces the stress to zero at a total strain of about 10−3 is reasonable. This parameter +should be calibrated to a particular case. +The choice of tension stiffening parameters is important in Abaqus/Standard since, generally, more +tension stiffening makes it easier to obtain numerical solutions. Too little tension stiffening will cause the +local cracking failure in the concrete to introduce temporarily unstable behavior in the overall response +of the model. Few practical designs exhibit such behavior, so that the presence of this type of response +in the analysis model usually indicates that the tension stiffening is unreasonably low. +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*CONCRETE +*TENSION STIFFENING, TYPE=STRAIN (default) +Property module: material editor: Mechanical→Plasticity→Concrete +Smeared Cracking: Suboptions→Tension Stiffening: Type: Strain +Fracture energy cracking criterion +As discussed earlier, when there is no reinforcement in significant regions of a concrete model, the strain +softening approach for defining tension stiffening may introduce unreasonable mesh sensitivity into the +results. Crisfield (1986) discusses this issue and concludes that Hillerborg’s (1976) proposal is adequate +to allay the concern for many practical purposes. Hillerborg defines the energy required to open a unit area +of crack as a material parameter, using brittle fracture concepts. With this approach the concrete’s brittle +behavior is characterized by a stress-displacement response rather than a stress-strain response. Under +tension a concrete specimen will crack across some section. After it has been pulled apart sufficiently for +most of the stress to be removed (so that the elastic strain is small), its length will be determined primarily +by the opening at the crack. The opening does not depend on the specimen’s length (Figure 23.6.1–2). +Implementation +The implementation of this stress-displacement concept in a finite element model requires the definition +of a characteristic length associated with an integration point. The characteristic crack length is based on +the element geometry and formulation: it is a typical length of a line across an element for a first-order +element; it is half of the same typical length for a second-order element. For beams and trusses it is a +characteristic length along the element axis. For membranes and shells it is a characteristic length in +the reference surface. For axisymmetric elements it is a characteristic length in the r–z plane only. For +cohesive elements it is equal to the constitutive thickness. This definition of the characteristic crack +length is used because the direction in which cracks will occur is not known in advance. Therefore, +elements with large aspect ratios will have rather different behavior depending on the direction in which +Stress, σ +σ u +Figure 23.6.1–2 Fracture energy cracking model. +u 0 +u, displacement +they crack: some mesh sensitivity remains because of this effect, and elements that are as close to square +as possible are recommended. +This approach to modeling the concrete’s brittle response requires the specification of the +at which a linear approximation to the postfailure strain softening gives zero stress +, occurs at a failure strain (defined by the failure stress divided by the Young’s +modulus); however, the stress goes to zero at an ultimate displacement, +, that is independent of the +specimen length. The implication is that a displacement-loaded specimen can remain in static equilibrium +after failure only if the specimen is short enough so that the strain at failure, +, is less than the strain at +this value of the displacement: +displacement +. +The failure stress, +where L is the length of the specimen. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options: +*CONCRETE +*TENSION STIFFENING, TYPE=DISPLACEMENT +Property module: material editor: Mechanical→Plasticity→Concrete +Smeared Cracking: Suboptions→Tension Stiffening: Type: +Displacement +Obtaining the ultimate displacement +, where +The ultimate displacement, +, as +is the maximum tensile stress that the concrete can carry. Typical values for +, can be estimated from the fracture energy per unit area, +are +0.05 mm (2 × 10−3 in) for a normal concrete to 0.08 mm (3 × 10−3 in) for a high strength concrete. A +typical value for +is about 10−4, so that the requirement is that +mm (20 in). +Critical length +If the specimen is longer than the critical length, L, more strain energy is stored in the specimen than +can be dissipated by the cracking process when it cracks under fixed displacement. Some of the strain +energy must, therefore, be converted into kinetic energy, and the failure event must be dynamic even +under prescribed displacement loading. This implies that, when this approach is used in finite elements, +characteristic element dimensions must be less than this critical length, or additional (dynamic) +considerations must be included. The analysis input file processor checks the characteristic length of +each element using this concrete model and will not allow any element to have a characteristic length +that exceeds +. You must remesh with smaller elements where necessary or use the stress-strain +definition of tension stiffening. Since the fracture energy approach is generally used only for plain +concrete, this rarely places any limit on the meshing. +Cracked shear retention +As the concrete cracks, its shear stiffness is diminished. This effect is defined by specifying the reduction +in the shear modulus as a function of the opening strain across the crack. You can also specify a reduced +shear modulus for closed cracks. This reduced shear modulus will also have an effect when the normal +stress across a crack becomes compressive. The new shear stiffness will have been degraded by the +presence of the crack. +The modulus for shearing of cracks is defined as +, where G is the elastic shear modulus of the +is a multiplying factor. The shear retention model assumes that the shear +uncracked concrete and +stiffness of open cracks reduces linearly to zero as the crack opening increases: +for +for +is the direct strain across the crack and +where +that cracks that subsequently close have a reduced shear modulus: +is a user-specified value. The model also assumes +for +where you specify +. +and +can be defined with an optional dependency on temperature and/or predefined field +variables. If shear retention is not included in the material definition for the concrete smeared cracking +model, Abaqus/Standard will automatically invoke the default behavior for shear retention such that the +shear response is unaffected by cracking (full shear retention). This assumption is often reasonable: in +many cases, the overall response is not strongly dependent on the amount of shear retention. +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*CONCRETE +*SHEAR RETENTION +Property module: material editor: Mechanical→Plasticity→Concrete +Smeared Cracking: Suboptions→Shear Retention +Compressive behavior +When the principal stress components are dominantly compressive, the response of the concrete is +modeled by an elastic-plastic theory using a simple form of yield surface written in terms of the +equivalent pressure stress, p, and the Mises equivalent deviatoric stress, q; this surface is illustrated in +Figure 23.6.1–5. Associated flow and isotropic hardening are used. This model significantly simplifies +the actual behavior. The associated flow assumption generally over-predicts the inelastic volume strain. +The yield surface cannot be matched accurately to data in triaxial tension and triaxial compression tests +because of the omission of third stress invariant dependence. When the concrete is strained beyond the +ultimate stress point, the assumption that the elastic response is not affected by the inelastic deformation +is not realistic. In addition, when concrete is subjected to very high pressure stress, it exhibits inelastic +response: no attempt has been made to build this behavior into the model. +The simplifications associated with compressive behavior are introduced for the sake of +In particular, while the assumption of associated flow is not justified by +computational efficiency. +experimental data, it can provide results that are acceptably close to measurements, provided that the +range of pressure stress in the problem is not large. From a computational viewpoint, the associated +flow assumption leads to enough symmetry in the Jacobian matrix of the integrated constitutive model +(the “material stiffness matrix”) such that the overall equilibrium equation solution usually does not +require unsymmetric equation solution. All of these limitations could be removed at some sacrifice in +computational cost. +You can define the stress-strain behavior of plain concrete in uniaxial compression outside the +elastic range. Compressive stress data are provided as a tabular function of plastic strain and, if desired, +temperature and field variables. Positive (absolute) values should be given for the compressive stress +and strain. The stress-strain curve can be defined beyond the ultimate stress, into the strain-softening +regime. +Input File Usage: +Abaqus/CAE Usage: +*CONCRETE +Property module: material editor: Mechanical→Plasticity→Concrete +Smeared Cracking +Uniaxial and multiaxial behavior +The cracking and compressive responses of concrete that are incorporated in the concrete model are +illustrated by the uniaxial response of a specimen shown in Figure 23.6.1–3. +When concrete is loaded in compression, it initially exhibits elastic response. As the stress is +increased, some nonrecoverable (inelastic) straining occurs and the response of the material softens. An +ultimate stress is reached, after which the material loses strength until it can no longer carry any stress. If +the load is removed at some point after inelastic straining has occurred, the unloading response is softer +than the initial elastic response: the elasticity has been damaged. This effect is ignored in the model, +since we assume that the applications involve primarily monotonic straining, with only occasional, minor +unloadings. When a uniaxial concrete specimen is loaded in tension, it responds elastically until, at a +stress that is typically 7%–10% of the ultimate compressive stress, cracks form. Cracks form so quickly +that, even in the stiffest testing machines available, it is very difficult to observe the actual behavior. The +Stress +Failure point in +compression +(peak stress) +Start of inelastic +behavior +Unload/reload response +Idealized (elastic) unload/reload response +Strain +Softening +Cracking failure +Figure 23.6.1–3 Uniaxial behavior of plain concrete. +model assumes that cracking causes damage, in the sense that open cracks can be represented by a loss +of elastic stiffness. It is also assumed that there is no permanent strain associated with cracking. This +will allow cracks to close completely if the stress across them becomes compressive. +In multiaxial stress states these observations are generalized through the concept of surfaces of +failure and flow in stress space. These surfaces are fitted to experimental data. The surfaces used are +shown in Figure 23.6.1–4 and Figure 23.6.1–5. +Failure surface +You can specify failure ratios to define the shape of the failure surface (possibly as a function of +temperature and predefined field variables). Four failure ratios can be specified: +• The ratio of the ultimate biaxial compressive stress to the ultimate uniaxial compressive stress. +• The absolute value of the ratio of the uniaxial tensile stress at failure to the ultimate uniaxial +compressive stress. +• The ratio of the magnitude of a principal component of plastic strain at ultimate stress in biaxial +compression to the plastic strain at ultimate stress in uniaxial compression. +"crack detection" surface +uniaxial tension +biaxial +tension +uniaxial compression +"compression" +surface +biaxial compression +Figure 23.6.1–4 Yield and failure surfaces in plane stress. +• The ratio of the tensile principal stress at cracking, in plane stress, when the other principal stress +is at the ultimate compressive value, to the tensile cracking stress under uniaxial tension. +Input File Usage: +Default values of the above ratios are used if you do not specify them. +*FAILURE RATIOS +Property module: material editor: Mechanical→Plasticity→Concrete +Smeared Cracking: Suboptions→Failure Ratios +Abaqus/CAE Usage: +Response to strain reversals +Because the model is intended for application to problems involving relatively monotonic straining, no +attempt is made to include prediction of cyclic response or of the reduction in the elastic stiffness caused +σ u +"crack detection" surface +"compression" surface +σ u +Figure 23.6.1–5 Yield and failure surfaces in the (p–q) plane. +by inelastic straining under predominantly compressive stress. Nevertheless, it is likely that, even in +those applications for which the model is designed, the strain trajectories will not be entirely radial, so +that the model should predict the response to occasional strain reversals and strain trajectory direction +changes in a reasonable way. Isotropic hardening of the “compressive” yield surface forms the basis +of this aspect of the model’s inelastic response prediction when the principal stresses are dominantly +compressive. +Calibration +A minimum of two experiments, uniaxial compression and uniaxial tension, is required to calibrate the +simplest version of the concrete model (using all possible defaults and assuming temperature and field +variable independence). Other experiments may be required to gain accuracy in postfailure behavior. +Uniaxial compression and tension tests +The uniaxial compression test involves compressing the sample between two rigid platens. The load and +displacement in the direction of loading are recorded. From this, you can extract the stress-strain curve +required for the concrete model directly. The uniaxial tension test is much more difficult to perform in +the sense that it is necessary to have a stiff testing machine to be able to record the postfailure response. +Quite often this test is not available, and you make an assumption about the tensile failure strength of +the concrete (usually about 7%–10% of the compressive strength). The choice of tensile cracking stress +is important; numerical problems may arise if very low cracking stresses are used (less than 1/100 or +1/1000 of the compressive strength). +Postcracking tensile behavior +The calibration of the postfailure response depends on the reinforcement present in the concrete. For +plain concrete simulations the stress-displacement tension stiffening model should be used. Typical +are 0.05 mm (2 × 10−3 in) for a normal concrete to 0.08 mm (3 × 10−3 in) for a high-strength +values for +concrete. For reinforced concrete simulations the stress-strain tension stiffening model should be used. +A reasonable starting point for relatively heavily reinforced concrete modeled with a fairly detailed mesh +is to assume that the strain softening after failure reduces the stress linearly to zero at a total strain of +about 10 times the strain at failure. Since the strain at failure in standard concretes is typically 10−4 , this +suggests that tension stiffening that reduces the stress to zero at a total strain of about 10−3 is reasonable. +This parameter should be calibrated to a particular case. +Postcracking shear behavior +Combined tension and shear experiments are used to calibrate the postcracking shear behavior in +Abaqus/Standard. These experiments are quite difficult to perform. If the test data are not available, a +reasonable starting point is to assume that the shear retention factor, +, goes linearly to zero at the same +crack opening strain used for the tension stiffening model. +Biaxial yield and flow parameters +Biaxial experiments are required to calibrate the biaxial yield and flow parameters used to specify the +failure ratios. If these are not available, the defaults can be used. +Temperature dependence +The calibration of temperature dependence requires the repetition of all the above experiments over the +range of interest. +Comparison with experimental results +With proper calibration, the concrete model should produce reasonable results for mostly monotonic +loadings. Comparison of the predictions of the model with the experimental results of Kupfer and Gerstle +(1973) are shown in Figure 23.6.1–6 and Figure 23.6.1–7. +Elements +Abaqus/Standard offers a variety of elements for use with the smeared crack concrete model: beam, +shell, plane stress, plane strain, generalized plane strain, axisymmetric, and three-dimensional elements. +For general shell analysis more than the default number of five integration points through the +thickness of the shell should be used; nine thickness integration points are commonly used to model +progressive failure of the concrete through the thickness with acceptable accuracy. +30.0 +25.0 +20.0 +15.0 +10.0 +5.0 +0.0000 +0.0005 +30.0 +25.0 +20.0 +15.0 +10.0 +5.0 +5.0 +4.0 +3.0 +2.0 +1.0 +/ +, +Model +Kupfer and Gerstle, 1973 +0.0010 +0.0015 +Compressive strain in loaded direction +0.0020 +0.0025 +0.0030 +5.0 +4.0 +3.0 +2.0 +1.0 +/ +, +Model +Kupfer and Gerstle, 1973 +/ +, +/ +/ +, +, +0.0000 +0.0005 +0.0010 +0.0015 +0.0020 +0.0025 +0.0030 +Tensile strain normal to loaded direction +Figure 23.6.1–6 Comparison of model prediction and Kupfer +and Gerstle’s data for a uniaxial compression test. +5.0 +4.0 +3.0 +2.0 +1.0 +/ +, +Model +Kupfer and Gerstle, 1973 +30.0 +25.0 +20.0 +15.0 +10.0 +5.0 +/ +, +0.0000 +0.0005 +0.0010 +0.0015 +0.0020 +0.0025 +0.0030 +Compressive strain in loaded plane +30.0 +/ +25.0 +, +20.0 +15.0 +10.0 +5.0 +5.0 +4.0 +3.0 +2.0 +1.0 +/ +, +Model +Kupfer and Gerstle, 1973 +0.0000 +0.0005 +0.0010 +0.0015 +0.0020 +0.0025 +0.0030 +Compressive strain normal to loaded plane +Figure 23.6.1–7 Comparison of model prediction and Kupfer +and Gerstle’s data for a biaxial compression test. +Output +In addition to the standard output identifiers available in Abaqus/Standard (“Abaqus/Standard output +variable identifiers,” Section 4.2.1), the following variables relate specifically to material points in the +smeared crack concrete model: +CRACK +CONF +Unit normal to cracks in concrete. +Number of cracks at a concrete material point. +Additional references +• Crisfield, M. A., “Snap-Through and Snap-Back Response in Concrete Structures and the Dangers +of Under-Integration,” International Journal for Numerical Methods in Engineering, vol. 22, +pp. 751–767, 1986. +• Hillerborg, A., M. Modeer, and P. E. Petersson, “Analysis of Crack Formation and Crack Growth +in Concrete by Means of Fracture Mechanics and Finite Elements,” Cement and Concrete Research, +vol. 6, pp. 773–782, 1976. +• Kupfer, H. B., and K. H. Gerstle, “Behavior of Concrete under Biaxial Stresses,” Journal of +Engineering Mechanics Division, ASCE, vol. 99, p. 853, 1973. +23.6.2 +CRACKING MODEL FOR CONCRETE +Products: Abaqus/Explicit Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Inelastic behavior,” Section 23.1.1 +• *BRITTLE CRACKING +• *BRITTLE FAILURE +• *BRITTLE SHEAR +• “Defining brittle cracking” in “Defining other mechanical models,” Section 12.9.4 of the +Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +The brittle cracking model in Abaqus/Explicit: +• provides a capability for modeling concrete in all types of structures: beams, trusses, shells and +solids; +• can also be useful for modeling other materials such as ceramics or brittle rocks; +• is designed for applications in which the behavior is dominated by tensile cracking; +• assumes that the compressive behavior is always linear elastic; +• must be used with the linear elastic material model (“Linear elastic behavior,” Section 22.2.1), which +also defines the material behavior completely prior to cracking; +• is most accurate in applications where the brittle behavior dominates such that the assumption that +the material is linear elastic in compression is adequate; +• can be used for plain concrete, even though it is intended primarily for the analysis of reinforced +concrete structures; +• allows removal of elements based on a brittle failure criterion; and +• is defined in detail in “A cracking model for concrete and other brittle materials,” Section 4.5.3 of +the Abaqus Theory Manual. +See “Inelastic behavior,” Section 23.1.1, for a discussion of the concrete models available in Abaqus. +Reinforcement +Rebars are +in concrete structures is typically provided by means of rebars. +Reinforcement +one-dimensional strain theory elements (rods) that can be defined singly or embedded in oriented +surfaces. Rebars are discussed in “Defining rebar as an element property,” Section 2.2.4. They are +typically used with elastic-plastic material behavior and are superposed on a mesh of standard element +types used to model the plain concrete. With this modeling approach, the concrete cracking behavior +is considered independently of the rebar. Effects associated with the rebar/concrete interface, such as +bond slip and dowel action, are modeled approximately by introducing some “tension stiffening” into +the concrete cracking model to simulate load transfer across cracks through the rebar. +Cracking +Abaqus/Explicit uses a smeared crack model to represent the discontinuous brittle behavior in concrete. It +does not track individual “macro” cracks: instead, constitutive calculations are performed independently +at each material point of the finite element model. The presence of cracks enters into these calculations +by the way in which the cracks affect the stress and material stiffness associated with the material point. +For simplicity of discussion in this section, the term “crack” is used to mean a direction in which +cracking has been detected at the single material calculation point in question: +the closest physical +concept is that there exists a continuum of micro-cracks in the neighborhood of the point, oriented as +determined by the model. The anisotropy introduced by cracking is assumed to be important in the +simulations for which the model is intended. +Crack directions +The Abaqus/Explicit cracking model assumes fixed, orthogonal cracks, with the maximum number of +cracks at a material point limited by the number of direct stress components present at that material +point of the finite element model (a maximum of three cracks in three-dimensional, plane strain, and +axisymmetric problems; two cracks in plane stress and shell problems; and one crack in beam or truss +problems). Internally, once cracks exist at a point, the component forms of all vector- and tensor-valued +quantities are rotated so that they lie in the local system defined by the crack orientation vectors (the +normals to the crack faces). The model ensures that these crack face normal vectors will be orthogonal, +so that this local crack system is rectangular Cartesian. For output purposes you are offered results of +stresses and strains in the global and/or local crack systems. +Crack detection +A simple Rankine criterion is used to detect crack initiation. This criterion states that a crack forms +when the maximum principal tensile stress exceeds the tensile strength of the brittle material. Although +crack detection is based purely on Mode I fracture considerations, ensuing cracked behavior includes +both Mode I (tension softening/stiffening) and Mode II (shear softening/retention) behavior, as described +later. +As soon as the Rankine criterion for crack formation has been met, we assume that a first crack has +formed. The crack surface is taken to be normal to the direction of the maximum tensile principal stress. +Subsequent cracks may form with crack surface normals in the direction of maximum principal tensile +stress that is orthogonal to the directions of any existing crack surface normals at the same point. +Cracking is irrecoverable in the sense that, once a crack has occurred at a point, it remains throughout +the rest of the calculation. However, crack closing and reopening may take place along the directions of +the crack surface normals. The model neglects any permanent strain associated with cracking; that is, it +is assumed that the cracks can close completely when the stress across them becomes compressive. +Tension stiffening +You can specify the postfailure behavior for direct straining across cracks by means of a postfailure +stress-strain relation or by applying a fracture energy cracking criterion. +Postfailure stress-strain relation +In reinforced concrete the specification of postfailure behavior generally means giving the postfailure +stress as a function of strain across the crack (Figure 23.6.2–1). In cases with little or no reinforcement, +this introduces mesh sensitivity in the results, in the sense that the finite element predictions do not +converge to a unique solution as the mesh is refined because mesh refinement leads to narrower crack +bands. +σ Ι +Figure 23.6.2–1 Postfailure stress-strain curve. +e ck +nn +In practical calculations for reinforced concrete, the mesh is usually such that each element contains +rebars. In this case the interaction between the rebars and the concrete tends to mitigate this effect, +provided that a reasonable amount of “tension stiffening” is introduced in the cracking model to simulate +this interaction. This requires an estimate of the tension stiffening effect, which depends on factors such +as the density of reinforcement, the quality of the bond between the rebar and the concrete, the relative +size of the concrete aggregate compared to the rebar diameter, and the mesh. A reasonable starting point +for relatively heavily reinforced concrete modeled with a fairly detailed mesh is to assume that the strain +softening after failure reduces the stress linearly to zero at a total strain about ten times the strain at failure. +Since the strain at failure in standard concretes is typically 10−4 , this suggests that tension stiffening that +reduces the stress to zero at a total strain of about 10−3 is reasonable. This parameter should be calibrated +to each particular case. In static applications too little tension stiffening will cause the local cracking +failure in the concrete to introduce temporarily unstable behavior in the overall response of the model. +Few practical designs exhibit such behavior, so that the presence of this type of response in the analysis +model usually indicates that the tension stiffening is unreasonably low. +Input File Usage: +*BRITTLE CRACKING, TYPE=STRAIN +Abaqus/CAE Usage: +Property module: material editor: +Mechanical→Brittle Cracking: Type: Strain +Fracture energy cracking criterion +When there is no reinforcement in significant regions of the model, the tension stiffening approach +described above will introduce unreasonable mesh sensitivity into the results. However, it is generally +accepted that Hillerborg’s (1976) fracture energy proposal is adequate to allay the concern for many +practical purposes. Hillerborg defines the energy required to open a unit area of crack in Mode I ( +) as +a material parameter, using brittle fracture concepts. With this approach the concrete’s brittle behavior +is characterized by a stress-displacement response rather than a stress-strain response. Under tension a +concrete specimen will crack across some section; and its length, after it has been pulled apart sufficiently +for most of the stress to be removed (so that the elastic strain is small), will be determined primarily by +the opening at the crack, which does not depend on the specimen’s length. +Implementation +In Abaqus/Explicit this fracture energy cracking model can be invoked by specifying the postfailure +stress as a tabular function of displacement across the crack, as illustrated in Figure 23.6.2–2. +σ Ι +Figure 23.6.2–2 Postfailure stress-displacement curve. +u ck +, can be specified directly as a material property; in this +Alternatively, the Mode I fracture energy, +case, define the failure stress, +, as a tabular function of the associated Mode I fracture energy. +This model assumes a linear loss of strength after cracking (Figure 23.6.2–3). The crack normal +displacement at which complete loss of strength takes place is, therefore, +. Typical +values of +range from 40 N/m (0.22 lb/in) for a typical construction concrete (with a compressive +strength of approximately 20 MPa, 2850 lb/in2 ) to 120 N/m (0.67 lb/in) for a high-strength concrete +(with a compressive strength of approximately 40 MPa, 5700 lb/in2). +Input File Usage: +Use the following option to specify the postfailure stress as a tabular function +of displacement: +*BRITTLE CRACKING, TYPE=DISPLACEMENT +σ Ι +tu +CRACKING MODEL +tu +u n +u = 2G /σ +no +Figure 23.6.2–3 Postfailure stress-fracture energy curve. +Use the following option to specify the postfailure stress as a tabular function +of the fracture energy: +*BRITTLE CRACKING, TYPE=GFI +Property module: material editor: +Mechanical→Brittle Cracking: Type: Displacement or GFI +Abaqus/CAE Usage: +Characteristic crack length +The implementation of the stress-displacement concept in a finite element model requires the definition +of a characteristic length associated with a material point. The characteristic crack length is based on +the element geometry and formulation: it is a typical length of a line across an element for a first-order +element; it is half of the same typical length for a second-order element. For beams and trusses it is a +characteristic length along the element axis. For membranes and shells it is a characteristic length in +the reference surface. For axisymmetric elements it is a characteristic length in the r–z plane only. For +cohesive elements it is equal to the constitutive thickness. We use this definition of the characteristic crack +length because the direction in which cracks will occur is not known in advance. Therefore, elements +with large aspect ratios will have rather different behavior depending on the direction in which they crack: +some mesh sensitivity remains because of this effect. Elements that are as close to square as possible +are, therefore, recommended unless you can predict the direction in which cracks will form. +Shear retention model +An important feature of the cracking model is that, whereas crack initiation is based on Mode I fracture +only, postcracked behavior includes Mode II as well as Mode I. The Mode II shear behavior is based +on the common observation that the shear behavior depends on the amount of crack opening. More +specifically, the cracked shear modulus is reduced as the crack opens. Therefore, Abaqus/Explicit offers +a shear retention model in which the postcracked shear stiffness is defined as a function of the opening +strain across the crack; the shear retention model must be defined in the cracking model, and zero shear +retention should not be used. +In these models the dependence is defined by expressing the postcracking shear modulus, +, as a +fraction of the uncracked shear modulus: +where G is the shear modulus of the uncracked material and the shear retention factor, +on the crack opening strain, +Figure 23.6.2–4. +, depends +. You can specify this dependence in piecewise linear form, as shown in +Figure 23.6.2–4 Piecewise linear form of the shear retention model. +Alternatively, shear retention can be defined in the power law form: +e ck +nn +are material parameters. This form, shown in Figure 23.6.2–5, satisfies the +where p and +requirements that +as +(corresponding to complete loss of aggregate interlock). See “A cracking model for +concrete and other brittle materials,” Section 4.5.3 of the Abaqus Theory Manual, for a discussion of +how shear retention is calculated in the case of two or more cracks. +(corresponding to the state before crack initiation) and +as +Input File Usage: +Use the following option to specify the piecewise linear form of the shear +retention model: +*BRITTLE SHEAR, TYPE=RETENTION FACTOR +Use the following option to specify the power law form of the shear retention +model: +*BRITTLE SHEAR, TYPE=POWER LAW +p = 1 +e ck +max +e ck +nn +Figure 23.6.2–5 Power law form of the shear retention model. +Abaqus/CAE Usage: +Property module: material editor: +Mechanical→Brittle Cracking: Suboptions→Brittle Shear +Type: Retention Factor or Power Law +Calibration +One experiment, a uniaxial tension test, is required to calibrate the simplest version of the brittle cracking +model. Other experiments may be required to gain accuracy in postfailure behavior. +Uniaxial tension test +This test is difficult to perform because it is necessary to have a very stiff testing machine to record the +postcracking response. Quite often such equipment is not available; in this situation you must make an +assumption about the tensile failure strength of the material and the postcracking response. For concrete +the assumption usually made is that the tensile strength is 7–10% of the compressive strength. Uniaxial +compression tests can be performed much more easily, so the compressive strength of concrete is usually +known. +Postcracking tensile behavior +The values given for tension stiffening are a very important aspect of simulations using the +Abaqus/Explicit brittle cracking model. The postcracking tensile response is highly dependent on the +reinforcement present in the concrete. In simulations of unreinforced concrete, the tension stiffening +models that are based on fracture energy concepts should be utilized. If reliable experimental data are +not available, typical values that can be used were discussed before: common values of +range from +40 N/m (0.22 lb/in) for a typical construction concrete (with a compressive strength of approximately +20 MPa, 2850 lb/in2 ) to 120 N/m (0.67 lb/in) for a high-strength concrete (with a compressive strength +of approximately 40 MPa, 5700 lb/in2 ). In simulations of reinforced concrete the stress-strain tension +stiffening model should be used; the amount of tension stiffening depends on the reinforcement present, +as discussed before. A reasonable starting point for relatively heavily reinforced concrete modeled with +a fairly detailed mesh is to assume that the strain softening after failure reduces the stress linearly to +zero at a total strain about ten times the strain at failure. Since the strain at failure in standard concretes +is typically 10−4 , this suggests that tension stiffening that reduces the stress to zero at a total strain of +about 10−3 is reasonable. This parameter should be calibrated to each particular case. +Postcracking shear behavior +Calibration of the postcracking shear behavior requires combined tension and shear experiments, which +are difficult to perform. If such test data are not available, a reasonable starting point is to assume that +the shear retention factor, +, goes linearly to zero at the same crack opening strain used for the tension +stiffening model. +Brittle failure criterion +You can define brittle failure of the material. When one, two, or all three local direct cracking strain +(displacement) components at a material point reach the value defined as the failure strain (displacement), +the material point fails and all the stress components are set to zero. If all of the material points in an +element fail, the element is removed from the mesh. For example, removal of a first-order reduced- +integration solid element takes place as soon as its only integration point fails. However, all through- +the-thickness integration points must fail before a shell element is removed from the mesh. +If the postfailure relation is defined in terms of stress versus strain, the failure strain must be given +as the failure criterion. If the postfailure relation is defined in terms of stress versus displacement or +stress versus fracture energy, the failure displacement must be given as the failure criterion. The failure +strain (displacement) can be specified as a function of temperature and/or predefined field variables. +You can control how many cracks at a material point must fail before the material point is considered +to have failed; the default is one crack. The number of cracks that must fail can only be one for beam and +truss elements; it cannot be greater than two for plane stress and shell elements; and it cannot be greater +than three otherwise. +Input File Usage: +Abaqus/CAE Usage: +*BRITTLE FAILURE, CRACKS=n +Property module: material editor: +Mechanical→Brittle Cracking: Suboptions→Brittle Failure and select +Failure Criteria: Unidirectional, Bidirectional, or Tridirectional to +indicate the number of cracks that must fail for the material point to fail. +Determining when to use the brittle failure criterion +The brittle failure criterion is a crude way of modeling failure in Abaqus/Explicit and should be used with +care. The main motivation for including this capability is to help in computations where not removing an +element that can no longer carry stress may lead to excessive distortion of that element and subsequent +premature termination of the simulation. For example, in a monotonically loaded structure whose failure +mechanism is expected to be dominated by a single tensile macrofracture (Mode I cracking), it may be +reasonable to use the brittle failure criterion to remove elements. On the other hand, the fact that the brittle +material loses its ability to carry tensile stress does not preclude it from withstanding compressive stress; +therefore, it may not be appropriate to remove elements if the material is expected to carry compressive +loads after it has failed in tension. An example may be a shear wall subjected to cyclic loading as a result +of some earthquake excitation; in this case cracks that develop completely under tensile stress will be +able to carry compressive stress when load reversal takes place. +Thus, the effective use of the brittle failure criterion relies on you having some knowledge of the +structural behavior and potential failure mechanism. The use of the brittle failure criterion based on an +incorrect user assumption of the failure mechanism will generally result in an incorrect simulation. +Selecting the number of cracks that must fail before the material point is considered to have +failed +When you define brittle failure, you can control how many cracks must open to beyond the failure value +before a material point is considered to have failed. The default number of cracks (one) should be used +for most structural applications where failure is dominated by Mode I type cracking. However, there +are cases in which you should specify a higher number because multiple cracks need to form to develop +the eventual failure mechanism. One example may be an unreinforced, deep concrete beam where the +failure mechanism is dominated by shear; in this case it is possible that two cracks need to form at each +material point for the shear failure mechanism to develop. +Again, the appropriate choice of the number of cracks that must fail relies on your knowledge of +the structural and failure behaviors. +Using brittle failure with rebar +It is possible to use the brittle failure criterion in brittle cracking elements for which rebar are also defined; +the obvious application is the modeling of reinforced concrete. When such elements fail according to the +brittle failure criterion, the brittle cracking contribution to the element stress carrying capacity is removed +but the rebar contribution to the element stress carrying capacity is not removed. However, if you also +include shear failure in the rebar material definition, the rebar contribution to the element stress carrying +capacity will also be removed if the shear failure criterion specified for the rebar is satisfied. This allows +the modeling of progressive failure of an under-reinforced concrete structure where the concrete fails +first followed by ductile failure of the reinforcement. +Elements +Abaqus/Explicit offers a variety of elements for use with the cracking model: +shell; +two-dimensional beam; and plane stress, plane strain, axisymmetric, and three-dimensional continuum +elements. The model cannot be used with pipe and three-dimensional beam elements. Plane triangular, +triangular prism, and tetrahedral elements are not recommended for use in reinforced concrete analysis +since these elements do not support the use of rebar. +truss; +Output +In addition to the standard output identifiers available in Abaqus/Explicit , the following output variables relate directly to material points that +use the brittle cracking model: +CKE +CKLE +All cracking strain components. +All cracking strain components in local crack axes. +CKEMAG +Cracking strain magnitude. +CKLS +CRACK +CKSTAT +STATUS +Additional reference +All stress components in local crack axes. +Crack orientations. +Crack status of each crack. +Status of element (brittle failure model). The status of an element is 1.0 if the +element is active and 0.0 if the element is not. +• Hillerborg, A., M. Modeer, and P. E. Petersson, “Analysis of Crack Formation and Crack Growth +in Concrete by Means of Fracture Mechanics and Finite Elements,” Cement and Concrete Research, +vol. 6, pp. 773–782, 1976. +23.6.3 +CONCRETE DAMAGED PLASTICITY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Inelastic behavior,” Section 23.1.1 +• *CONCRETE DAMAGED PLASTICITY +• *CONCRETE TENSION STIFFENING +• *CONCRETE COMPRESSION HARDENING +• *CONCRETE TENSION DAMAGE +• *CONCRETE COMPRESSION DAMAGE +• “Defining concrete damaged plasticity” in “Defining plasticity,” Section 12.9.2 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +The concrete damaged plasticity model in Abaqus: +• provides a general capability for modeling concrete and other quasi-brittle materials in all types of +structures (beams, trusses, shells, and solids); +• uses concepts of isotropic damaged elasticity in combination with isotropic tensile and compressive +plasticity to represent the inelastic behavior of concrete; +• can be used for plain concrete, even though it is intended primarily for the analysis of reinforced +concrete structures; +• can be used with rebar to model concrete reinforcement; +• is designed for applications in which concrete is subjected to monotonic, cyclic, and/or dynamic +loading under low confining pressures; +• consists of the combination of nonassociated multi-hardening plasticity and scalar (isotropic) +damaged elasticity to describe the irreversible damage that occurs during the fracturing process; +• allows user control of stiffness recovery effects during cyclic load reversals; +• can be defined to be sensitive to the rate of straining; +• can be used in conjunction with a viscoplastic regularization of the constitutive equations in +Abaqus/Standard to improve the convergence rate in the softening regime; +• requires that the elastic behavior of the material be isotropic and linear ; and +• is defined in detail in “Damaged plasticity model for concrete and other quasi-brittle materials,” +Section 4.5.2 of the Abaqus Theory Manual. +See “Inelastic behavior,” Section 23.1.1, for a discussion of the concrete models available in Abaqus. +Mechanical behavior +The model is a continuum, plasticity-based, damage model for concrete. +It assumes that the main +two failure mechanisms are tensile cracking and compressive crushing of the concrete material. The +evolution of the yield (or failure) surface is controlled by two hardening variables, +, linked +to failure mechanisms under tension and compression loading, respectively. We refer to +as +tensile and compressive equivalent plastic strains, respectively. The following sections discuss the main +assumptions about the mechanical behavior of concrete. +and +and +Uniaxial tension and compression stress behavior +The model assumes that the uniaxial tensile and compressive response of concrete is characterized +by damaged plasticity, as shown in Figure 23.6.3–1. Under uniaxial tension the stress-strain response +follows a linear elastic relationship until the value of the failure stress, +, is reached. The failure +stress corresponds to the onset of micro-cracking in the concrete material. Beyond the failure stress the +formation of micro-cracks is represented macroscopically with a softening stress-strain response, which +induces strain localization in the concrete structure. Under uniaxial compression the response is linear +until the value of initial yield, +. In the plastic regime the response is typically characterized by stress +hardening followed by strain softening beyond the ultimate stress, +. This representation, although +somewhat simplified, captures the main features of the response of concrete. +It is assumed that the uniaxial stress-strain curves can be converted into stress versus plastic-strain +curves. (This conversion is performed automatically by Abaqus from the user-provided stress versus +“inelastic” strain data, as explained below.) Thus, +where the subscripts t and c refer to tension and compression, respectively; +plastic strains, +are other predefined field variables. +are the equivalent plastic strain rates, +and +is the temperature, and +and +are the equivalent +As shown in Figure 23.6.3–1, when the concrete specimen is unloaded from any point on the strain +softening branch of the stress-strain curves, the unloading response is weakened: the elastic stiffness of +the material appears to be damaged (or degraded). The degradation of the elastic stiffness is characterized +by two damage variables, +, which are assumed to be functions of the plastic strains, temperature, +and field variables: +and +The damage variables can take values from zero, representing the undamaged material, to one, which +represents total loss of strength. +(a) +(b) +ε +t +σ +t +σ +σ +t0 +E +_ +(1 d )Et 0 +pl~ +ε +t +ε +el +t +σ +c +σ +c u +σ +c 0 +E0 +_ +(1 d )Ec 0 +pl~ +ε +ε +el +ε c +Figure 23.6.3–1 Response of concrete to uniaxial loading in tension (a) and compression (b). +If +is the initial (undamaged) elastic stiffness of the material, the stress-strain relations under +uniaxial tension and compression loading are, respectively: +We define the “effective” tensile and compressive cohesion stresses as +The effective cohesion stresses determine the size of the yield (or failure) surface. +Uniaxial cyclic behavior +Under uniaxial cyclic loading conditions the degradation mechanisms are quite complex, involving the +opening and closing of previously formed micro-cracks, as well as their interaction. Experimentally, +it is observed that there is some recovery of the elastic stiffness as the load changes sign during a +uniaxial cyclic test. The stiffness recovery effect, also known as the “unilateral effect,” is an important +aspect of the concrete behavior under cyclic loading. The effect is usually more pronounced as the load +changes from tension to compression, causing tensile cracks to close, which results in the recovery of +the compressive stiffness. +The concrete damaged plasticity model assumes that the reduction of the elastic modulus is given +in terms of a scalar degradation variable d as +where +is the initial (undamaged) modulus of the material. +This expression holds both in the tensile ( +) sides of the cycle. +The stiffness degradation variable, d, is a function of the stress state and the uniaxial damage variables, +) and the compressive ( +and +. For the uniaxial cyclic conditions Abaqus assumes that +where +associated with stress reversals. They are defined according to +and +are functions of the stress state that are introduced to model stiffness recovery effects +where +and +, which are assumed to be material properties, control the recovery of +The weight factors +the tensile and compressive stiffness upon load reversal. To illustrate this, consider the example in +Figure 23.6.3–2, where the load changes from tension to compression. Assume that there was no previous +compressive damage (crushing) in the material; that is, +. Then +and +ε +t +σ +t +σ +σ +t0 +E +_ +(1 d )Et 0 +w = 1c +w = 0c +Figure 23.6.3–2 Illustration of the effect of the compression stiffness recovery parameter +. +• In tension ( +• In compression ( +), +; therefore, +as expected. +), +; therefore, +the material fully recovers the compressive stiffness (which in this case is the initial undamaged +stiffness, +and there is no stiffness recovery. +Intermediate values of +result in partial recovery of the stiffness. +). If, on the other hand, +, then +, then +, and +. If +Multiaxial behavior +The stress-strain relations for the general three-dimensional multiaxial condition are given by the scalar +damage elasticity equation: +where +is the initial (undamaged) elasticity matrix. +The previous expression for the scalar stiffness degradation variable, d, is generalized to the +with a multiaxial stress weight factor, +multiaxial stress case by replacing the unit step function +, defined as +where +are the principal stress components. The Macauley bracket +is defined by +. +See “Damaged plasticity model for concrete and other quasi-brittle materials,” Section 4.5.2 of the +Abaqus Theory Manual, for further details of the constitutive model. +Reinforcement +In Abaqus reinforcement in concrete structures is typically provided by means of rebars, which are +one-dimensional rods that can be defined singly or embedded in oriented surfaces. Rebars are typically +used with metal plasticity models to describe the behavior of the rebar material and are superposed on a +mesh of standard element types used to model the concrete. +With this modeling approach, the concrete behavior is considered independently of the rebar. +Effects associated with the rebar/concrete interface, such as bond slip and dowel action, are modeled +approximately by introducing some “tension stiffening” into the concrete modeling to simulate load +transfer across cracks through the rebar. Details regarding tension stiffening are provided below. +Defining the rebar can be tedious in complex problems, but it is important that this be done +accurately since it may cause an analysis to fail due to lack of reinforcement in key regions of a model. +See “Defining rebar as an element property,” Section 2.2.4, for more information regarding rebars. +Defining tension stiffening +The postfailure behavior for direct straining is modeled with tension stiffening, which allows you to +define the strain-softening behavior for cracked concrete. This behavior also allows for the effects of +the reinforcement interaction with concrete to be simulated in a simple manner. Tension stiffening is +required in the concrete damaged plasticity model. You can specify tension stiffening by means of a +postfailure stress-strain relation or by applying a fracture energy cracking criterion. +Postfailure stress-strain relation +In reinforced concrete the specification of postfailure behavior generally means giving the postfailure +stress as a function of cracking strain, +. The cracking strain is defined as the total strain minus the +elastic strain corresponding to the undamaged material; that is, +, as +illustrated in Figure 23.6.3–3. To avoid potential numerical problems, Abaqus enforces a lower limit on +the postfailure stress equal to one-hundreth of the initial failure stress: +Tension stiffening data are given in terms of the cracking strain, +available, the data are provided to Abaqus in terms of tensile damage curves, +Abaqus automatically converts the cracking strain values to plastic strain values using the relationship +. When unloading data are +, as discussed below. +, where +. +t +σ +σ +t0 +E +E +_ +(1 d )Et 0 +ck~ +ε +el +ε 0t +~ +ε +pl +ε +el +CONCRETE DAMAGED PLASTICITY +ε +t +Figure 23.6.3–3 Illustration of the definition of the cracking strain +used for the definition of tension stiffening data. +Abaqus will issue an error message if the calculated plastic strain values are negative and/or decreasing +with increasing cracking strain, which typically indicates that the tensile damage curves are incorrect. In +the absence of tensile damage +. +In cases with little or no reinforcement, the specification of a postfailure stress-strain relation +introduces mesh sensitivity in the results, in the sense that the finite element predictions do not converge +to a unique solution as the mesh is refined because mesh refinement leads to narrower crack bands. This +problem typically occurs if cracking failure occurs only at localized regions in the structure and mesh +refinement does not result in the formation of additional cracks. If cracking failure is distributed evenly +(either due to the effect of rebar or due to the presence of stabilizing elastic material, as in the case of +plate bending), mesh sensitivity is less of a concern. +In practical calculations for reinforced concrete, the mesh is usually such that each element +contains rebars. The interaction between the rebars and the concrete tends to reduce the mesh sensitivity, +provided that a reasonable amount of tension stiffening is introduced in the concrete model to simulate +this interaction. This requires an estimate of the tension stiffening effect, which depends on such factors +as the density of reinforcement, the quality of the bond between the rebar and the concrete, the relative +size of the concrete aggregate compared to the rebar diameter, and the mesh. A reasonable starting +point for relatively heavily reinforced concrete modeled with a fairly detailed mesh is to assume that +the strain softening after failure reduces the stress linearly to zero at a total strain of about 10 times the +strain at failure. The strain at failure in standard concretes is typically 10−4 , which suggests that tension +stiffening that reduces the stress to zero at a total strain of about 10−3 is reasonable. This parameter +should be calibrated to a particular case. +The choice of tension stiffening parameters is important since, generally, more tension stiffening +makes it easier to obtain numerical solutions. Too little tension stiffening will cause the local cracking +failure in the concrete to introduce temporarily unstable behavior in the overall response of the model. +Few practical designs exhibit such behavior, so that the presence of this type of response in the analysis +model usually indicates that the tension stiffening is unreasonably low. +Input File Usage: +Abaqus/CAE Usage: +*CONCRETE TENSION STIFFENING, TYPE=STRAIN (default) +Property module: material editor: Mechanical→Plasticity→Concrete +Damaged Plasticity: Tensile Behavior: Type: Strain +Fracture energy cracking criterion +When there is no reinforcement in significant regions of the model, the tension stiffening approach +described above will introduce unreasonable mesh sensitivity into the results. However, it is generally +accepted that Hillerborg’s (1976) fracture energy proposal is adequate to allay the concern for many +practical purposes. Hillerborg defines the energy required to open a unit area of crack, +, as a +material parameter, using brittle fracture concepts. With this approach the concrete’s brittle behavior is +characterized by a stress-displacement response rather than a stress-strain response. Under tension a +concrete specimen will crack across some section. After it has been pulled apart sufficiently for most +of the stress to be removed (so that the undamaged elastic strain is small), its length will be determined +primarily by the opening at the crack. The opening does not depend on the specimen’s length. +This fracture energy cracking model can be invoked by specifying the postfailure stress as a tabular +function of cracking displacement, as shown in Figure 23.6.3–4. +u ck +Figure 23.6.3–4 Postfailure stress-displacement curve. +Alternatively, the fracture energy, +, can be specified directly as a material property; in this case, +, as a tabular function of the associated fracture energy. This model assumes +define the failure stress, +a linear loss of strength after cracking, as shown in Figure 23.6.3–5. +to +G f +u = 2G /σ +to +to +u t +Figure 23.6.3–5 Postfailure stress-fracture energy curve. +. +The cracking displacement at which complete loss of strength takes place is, therefore, +Typical values of +range from 40 N/m (0.22 lb/in) for a typical construction concrete (with a +compressive strength of approximately 20 MPa, 2850 lb/in2 ) to 120 N/m (0.67 lb/in) for a high-strength +concrete (with a compressive strength of approximately 40 MPa, 5700 lb/in2 ). +If tensile damage, +, is specified, Abaqus automatically converts the cracking displacement values +to “plastic” displacement values using the relationship +where the specimen length, +, is assumed to be one unit length, +. +Implementation +The implementation of this stress-displacement concept in a finite element model requires the definition +of a characteristic length associated with an integration point. The characteristic crack length is based on +the element geometry and formulation: it is a typical length of a line across an element for a first-order +element; it is half of the same typical length for a second-order element. For beams and trusses it is a +characteristic length along the element axis. For membranes and shells it is a characteristic length in +the reference surface. For axisymmetric elements it is a characteristic length in the r–z plane only. For +cohesive elements it is equal to the constitutive thickness. This definition of the characteristic crack +length is used because the direction in which cracking occurs is not known in advance. Therefore, +elements with large aspect ratios will have rather different behavior depending on the direction in which +they crack: some mesh sensitivity remains because of this effect, and elements that have aspect ratios +close to one are recommended. +Input File Usage: +Use the following option to specify the postfailure stress as a tabular function +of displacement: +*CONCRETE TENSION STIFFENING, TYPE=DISPLACEMENT +Use the following option to specify the postfailure stress as a tabular function +of the fracture energy: +Abaqus/CAE Usage: +*CONCRETE TENSION STIFFENING, TYPE=GFI +Property module: material editor: Mechanical→Plasticity→Concrete +Damaged Plasticity: Tensile Behavior: Type: Displacement or GFI +Defining compressive behavior +You can define the stress-strain behavior of plain concrete in uniaxial compression outside the elastic +range. Compressive stress data are provided as a tabular function of inelastic (or crushing) strain, +, +and, if desired, strain rate, temperature, and field variables. Positive (absolute) values should be given +for the compressive stress and strain. The stress-strain curve can be defined beyond the ultimate stress, +into the strain-softening regime. +Hardening data are given in terms of an inelastic strain, +. The +compressive inelastic strain is defined as the total strain minus the elastic strain corresponding to the +undamaged material, +, as illustrated in Figure 23.6.3–6. Unloading +data are provided to Abaqus in terms of compressive damage curves, +, as discussed below. +Abaqus automatically converts the inelastic strain values to plastic strain values using the relationship +, instead of plastic strain, +, where +Abaqus will issue an error message if the calculated plastic strain values are negative and/or decreasing +with increasing inelastic strain, which typically indicates that the compressive damage curves are +incorrect. In the absence of compressive damage +. +Input File Usage: +Abaqus/CAE Usage: +*CONCRETE COMPRESSION HARDENING +Property module: material editor: Mechanical→Plasticity→Concrete +Damaged Plasticity: Compressive Behavior +Defining damage and stiffness recovery +Damage, +as a plasticity model; consequently, +, can be specified in tabular form. (If damage is not specified, the model behaves +.) +and/or +and +In Abaqus the damage variables are treated as non-decreasing material point quantities. At any +increment during the analysis, the new value of each damage variable is obtained as the maximum +between the value at the end of the previous increment and the value corresponding to the current state +(interpolated from the user-specified tabular data); that is, +σ +c +σ +c u +σ +c 0 +E0 +E0 +_ +(1 d )Ec 0 +in~ +ε +el +ε 0c +pl~ +ε +el +ε c +ε c +Figure 23.6.3–6 Definition of the compressive inelastic (or crushing) strain +used +for the definition of compression hardening data. +The choice of the damage properties is important since, generally, excessive damage may have +a critical effect on the rate of convergence. It is recommended to avoid using values of the damage +variables above 0.99, which corresponds to a 99% reduction of the stiffness. +Tensile damage +You can define the uniaxial tension damage variable, +cracking displacement. +, as a tabular function of either cracking strain or +Input File Usage: +Use the following option to specify tensile damage as a function of cracking +strain: +*CONCRETE TENSION DAMAGE, TYPE=STRAIN (default) +Use the following option to specify tensile damage as a function of cracking +displacement: +*CONCRETE TENSION DAMAGE, TYPE=DISPLACEMENT +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Plasticity→Concrete +Damaged Plasticity: Tensile Behavior: Suboptions→Tension Damage: +Type: Strain or Displacement +Compressive damage +You can define the uniaxial compression damage variable, +strain. +, as a tabular function of inelastic (crushing) +Input File Usage: +Abaqus/CAE Usage: +*CONCRETE COMPRESSION DAMAGE +Property module: material editor: Mechanical→Plasticity→Concrete +Damaged Plasticity: Compressive Behavior: +Suboptions→Compression Damage +Stiffness recovery +The experimental observation in most quasi-brittle materials, +As discussed above, stiffness recovery is an important aspect of the mechanical response of concrete +under cyclic loading. Abaqus allows direct user specification of the stiffness recovery factors +. +and +is that the +including concrete, +compressive stiffness is recovered upon crack closure as the load changes from tension to compression. +On the other hand, the tensile stiffness is not recovered as the load changes from compression to tension +once crushing micro-cracks have developed. This behavior, which corresponds to +, +is the default used by Abaqus. Figure 23.6.3–7 illustrates a uniaxial load cycle assuming the default +behavior. +and +Input File Usage: +Use the following option to specify the compression stiffness recovery factor, +: +*CONCRETE TENSION DAMAGE, COMPRESSION RECOVERY= +Use the following option to specify the tension stiffness recovery factor, +: +*CONCRETE COMPRESSION DAMAGE, TENSION RECOVERY= +Property module: material editor: Mechanical→Plasticity→Concrete +Damaged Plasticity: +Tensile Behavior: Suboptions→Tension Damage: Compression +recovery: +Compressive Behavior: Suboptions→Compression Damage: +Tension recovery: +Abaqus/CAE Usage: +Rate dependence +The rate-sensitive behavior of quasi-brittle materials is mainly connected to the retardation effects that +high strain rates have on the growth of micro-cracks. The effect is usually more pronounced under tensile +loading. As the strain rate increases, the stress-strain curves exhibit decreasing nonlinearity as well as an +increase in the peak strength. You can specify tension stiffening as a tabular function of cracking strain +σ +t +σ +t 0 +E +w = 1 +t +w = 0 +t +(1-d )Et 0 +(1-d )Ec 0 +(1-d )t +(1-d )Ec 0 +w = 0c +w = 1c +ε +E +Figure 23.6.3–7 Uniaxial load cycle (tension-compression-tension) assuming default values +for the stiffness recovery factors: +and +. +(or displacement) rate, and you can specify compression hardening data as a tabular function of inelastic +strain rate. +Input File Usage: +Use the following options: +Abaqus/CAE Usage: +*CONCRETE TENSION STIFFENING +*CONCRETE COMPRESSION HARDENING +Property module: material editor: Mechanical→Plasticity→Concrete +Damaged Plasticity: +Tensile Behavior: Use strain-rate-dependent data +Compressive Behavior: Use strain-rate-dependent data +Concrete plasticity +You can define flow potential, yield surface, and in Abaqus/Standard viscosity parameters for the concrete +damaged plasticity material model. +Input File Usage: +Abaqus/CAE Usage: +*CONCRETE DAMAGED PLASTICITY +Property module: material editor: Mechanical→Plasticity→Concrete +Damaged Plasticity: Plasticity +Effective stress invariants +The effective stress is defined as +The plastic flow potential function and the yield surface make use of two stress invariants of the effective +stress tensor, namely the hydrostatic pressure stress, +and the Mises equivalent effective stress, +where +is the effective stress deviator, defined as +Plastic flow +The concrete damaged plasticity model assumes nonassociated potential plastic flow. The flow potential +G used for this model is the Drucker-Prager hyperbolic function: +where +is the dilation angle measured in the p–q plane at high confining +pressure; +is the uniaxial tensile stress at failure, taken from the user- +specified tension stiffening data; and +is a parameter, referred to as the eccentricity, that defines the +rate at which the function approaches the asymptote (the flow +potential tends to a straight line as the eccentricity tends to +zero). +This flow potential, which is continuous and smooth, ensures that the flow direction is always uniquely +defined. The function approaches the linear Drucker-Prager flow potential asymptotically at high +confining pressure stress and intersects the hydrostatic pressure axis at 90°. See “Models for granular or +polymer behavior,” Section 4.4.2 of the Abaqus Theory Manual, for further discussion of this potential. +, which implies that the material has almost the +The default flow potential eccentricity is +same dilation angle over a wide range of confining pressure stress values. Increasing the value of +provides more curvature to the flow potential, implying that the dilation angle increases more rapidly as +the confining pressure decreases. Values of +that are significantly less than the default value may lead +to convergence problems if the material is subjected to low confining pressures because of the very tight +curvature of the flow potential locally where it intersects the p-axis. +Yield function +The model makes use of the yield function of Lubliner et. al. (1989), with the modifications proposed by +Lee and Fenves (1998) to account for different evolution of strength under tension and compression. The +evolution of the yield surface is controlled by the hardening variables, +. In terms of effective +stresses, the yield function takes the form +and +with +Here, +is the maximum principal effective stress; +is the ratio of initial equibiaxial compressive yield stress to +initial uniaxial compressive yield stress (the default value is +); +, to that on the compressive meridian, +is the ratio of the second stress invariant on the tensile meridian, +, at initial +yield for any given value of the pressure invariant p such +that the maximum principal stress is negative, +; it must satisfy the condition +(the default value is +is the effective tensile cohesion stress; and +is the effective compressive cohesion stress. +); +_ +S2 +K = 2/3 +_ +S1 +K = 1 +(T.M.) +(C.M.) +_ +S3 +Figure 23.6.3–8 Yield surfaces in the deviatoric plane, corresponding to different values of +. +Typical yield surfaces are shown in Figure 23.6.3–8 on the deviatoric plane and in Figure 23.6.3–9 +for plane stress conditions. +Nonassociated flow +Because plastic flow is nonassociated, the use of concrete damaged plasticity results in a nonsymmetric +material stiffness matrix. Therefore, to obtain an acceptable rate of convergence in Abaqus/Standard, the +unsymmetric matrix storage and solution scheme should be used. Abaqus/Standard will automatically +activate the unsymmetric solution scheme if concrete damaged plasticity is used in the analysis. +If +desired, you can turn off the unsymmetric solution scheme for a particular step . +Viscoplastic regularization +Material models exhibiting softening behavior and stiffness degradation often lead to severe convergence +difficulties in implicit analysis programs, such as Abaqus/Standard. A common technique to overcome +some of these convergence difficulties is the use of a viscoplastic regularization of the constitutive +equations, which causes the consistent tangent stiffness of the softening material to become positive for +sufficiently small time increments. +The concrete damaged plasticity model can be regularized in Abaqus/Standard using viscoplasticity +by permitting stresses to be outside of the yield surface. We use a generalization of the Duvaut-Lions +regularization, according to which the viscoplastic strain rate tensor, +, is defined as +1-α +CONCRETE DAMAGED PLASTICITY +uniaxial tension +∧ +(q - 3α p + βσ ) = σ c0 +∧ +uniaxial compression +σ +t0 +∧ +biaxial +tension +1-α +(q - 3α p + βσ ) = σ c0 +∧ +(σ ,σ ) +b0 b0 +σ +c0 +biaxial compression +1-α +(q - 3α p ) = σ c0 +Figure 23.6.3–9 Yield surface in plane stress. +is the viscosity parameter representing the relaxation time of the viscoplastic system, and +is +Here +the plastic strain evaluated in the inviscid backbone model. +Similarly, a viscous stiffness degradation variable, +, for the viscoplastic system is defined as +where d is the degradation variable evaluated in the inviscid backbone model. The stress-strain relation +of the viscoplastic model is given as +Using the viscoplastic regularization with a small value for the viscosity parameter (small +compared to the characteristic time increment) usually helps improve the rate of convergence of the +model in the softening regime, without compromising results. The basic idea is that the solution of the +viscoplastic system relaxes to that of the inviscid case as +, where t represents time. You can +specify the value of the viscosity parameter as part of the concrete damaged plasticity material behavior +If the viscosity parameter is different from zero, output results of the plastic strain and +definition. +stiffness degradation refer to the viscoplastic values, +. In Abaqus/Standard the default value +of the viscosity parameter is zero, so that no viscoplastic regularization is performed. +and +Material damping +The concrete damaged plasticity model can be used in combination with material damping . If stiffness proportional damping is specified, Abaqus calculates the damping +stress based on the undamaged elastic stiffness. This may introduce large artificial damping forces on +elements undergoing severe damage at high strain rates. +Visualization of “crack directions” +Unlike concrete models based on the smeared crack approach, the concrete damaged plasticity model +does not have the notion of cracks developing at the material integration point. However, it is possible +to introduce the concept of an effective crack direction with the purpose of obtaining a graphical +visualization of the cracking patterns in the concrete structure. Different criteria can be adopted within +the framework of scalar-damage plasticity for the definition of the direction of cracking. Following +(1989), we can assume that cracking initiates at points where the tensile equivalent +Lubliner et. al. +plastic strain is greater than zero, +, and the maximum principal plastic strain is positive. +The direction of the vector normal to the crack plane is assumed to be parallel to the direction of +the maximum principal plastic strain. This direction can be viewed in the Visualization module of +Abaqus/CAE. +Abaqus/CAE Usage: +Visualization module: +Result→Field Output: PE, Max. Principal +Plot→Symbols +Elements +Abaqus offers a variety of elements for use with the concrete damaged plasticity model: truss, shell, plane +stress, plane strain, generalized plane strain, axisymmetric, and three-dimensional elements. Most beam +elements can be used; however, beam elements in space that include shear stress caused by torsion and do +not include hoop stress (such as B31, B31H, B32, B32H, B33, and B33H) cannot be used. Thin-walled, +open-section beam elements and PIPE elements can be used with the concrete damaged plasticity model +in Abaqus/Standard. +For general shell analysis more than the default number of five integration points through the +thickness of the shell should be used; nine thickness integration points are commonly used to model +progressive failure of the concrete through the thickness with acceptable accuracy. +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2), +the +following variables relate specifically to material points in the concrete damaged plasticity model: +DAMAGEC +DAMAGET +PEEQ +PEEQT +SDEG +DMENER +ELDMD +ALLDMD +Compressive damage variable, +. +Tensile damage variable, +. +Compressive equivalent plastic strain, +. +Tensile equivalent plastic strain, +Stiffness degradation variable, d. +Energy dissipated per unit volume by damage. +. +Total energy dissipated in the element by damage. +Energy dissipated in the whole (or partial) model by damage. The contribution +from ALLDMD is included in the total strain energy ALLIE. +EDMDDEN +Energy dissipated per unit volume in the element by damage. +SENER +ELSE +ALLSE +The recoverable part of the energy per unit volume. +The recoverable part of the energy in the element. +The recoverable part of the energy in the whole (partial) model. +ESEDEN +The recoverable part of the energy per unit volume in the element. +Additional references +• Hillerborg, A., M. Modeer, and P. E. Petersson, “Analysis of Crack Formation and Crack Growth +in Concrete by Means of Fracture Mechanics and Finite Elements,” Cement and Concrete Research, +vol. 6, pp. 773–782, 1976. +• Lee, J., and G. L. Fenves, “Plastic-Damage Model for Cyclic Loading of Concrete Structures,” +Journal of Engineering Mechanics, vol. 124, no. 8, pp. 892–900, 1998. +• Lubliner, J., J. Oliver, S. Oller, and E. Oñate, “A Plastic-Damage Model for Concrete,” +International Journal of Solids and Structures, vol. 25, pp. 299–329, 1989. +23.7 +Permanent set in rubberlike materials +• “Permanent set in rubberlike materials,” Section 23.7.1 +23.7.1 +PERMANENT SET IN RUBBERLIKE MATERIALS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Combining material behaviors,” Section 21.1.3 +• “Hyperelastic behavior of rubberlike materials,” Section 22.5.1 +• “Classical metal plasticity,” Section 23.2.1 +• *HYPERELASTIC +• *MULLINS EFFECT +• *PLASTIC +Overview +This feature: +• is intended for modeling permanent set observed in filled elastomers and thermoplastics; +• is based on multiplicative split of the deformation gradient; +• is based on the theory of incompressible isotropic hardening plasticity; +• can be used with any isotropic hyperelasticity model; +• can be combined with Mullins effects; and +• cannot be used to model viscoelastic or hysteresis effects or with the steady-state transport +procedure. +Material behavior +The real behavior of filled rubber elastomers under cyclic loading conditions is quite complex as shown +in Figure 23.7.1–1. The observed mechanical behaviors are progressive damage resulting in a reduction +of load carrying capacity with each cycle, stress softening (also known as Mullins effect) upon reloading +after the first unloading from a previously attained maximum strain level, hysteretic dissipation of energy, +and permanent set. This section is concerned with modeling permanent set; therefore, the idealized +representation of permanent set is described below. +Idealized material behavior +From Figure 23.7.1–1 it is clear that the observed permanent set is different for each cycle, but the +material has a tendency to stabilize after a number of cycles of loading between zero stress and a given +level of strain. For a given load level along the primary loading path shown with the dashed line in +Figure 23.7.1–1, the idealized representation of permanent set will be a single strain value after unloading +has taken place. Since rate and time effects are ignored in this model, idealized loading and unloading +take place along the same path, whether Mullins effect is included or not. +Nominal Strain +Figure 23.7.1–1 Typical behavior of a filled elastomer. +The permanent set behavior is captured by isotropic hardening Mises plasticity with an associated +flow rule. +In the context of finite elastic strains associated with the underlying rubberlike material, +plasticity is modeled using a multiplicative split of the deformation gradient into elastic and plastic +components: +where +is the plastic part of the deformation gradient (representing the stress-free intermediate configuration). +is the elastic part of the deformation gradient (representing the hyperelastic behavior) and +An example of modeling permanent set along with Mullins effect for a rubberlike material can be +found in “Analysis of a solid disc with Mullins effect and permanent set,” Section 3.1.7 of the Abaqus +Example Problems Manual. +Specifying permanent set +The primary hyperelastic behavior can be defined by using any of the hyperelastic material models . +the hyperelastic response of the material, the data must be specified with respect to the stress-free +intermediate configuration after unloading has taken place. +Permanent set can be defined through an isotropic hardening function in terms of the yield stress and +the equivalent plastic strain. In this case the yield stress is the (effective) Kirchoff stress on the primary +loading path from which unloading takes place, and the equivalent plastic strain is the corresponding +logarithmic permanent set observed in the material. If +is the true (Cauchy) stress, Kirchoff stress is +defined as +is the determinant of +, where +. +Depending on what is being modeled, permanent set may be defined as the true permanent set seen +in the material after recovery of viscoelastic strains or it may include viscoelastic strains. In either case, +an initial yield stress is required, below which there will be no permanent set and the behavior of the +material will be fully elastic. In the case of filled rubbers this initial yield stress may correspond to a +small nonzero stress; whereas for the family of thermoplastic materials, there may be a more marked +value of initial yield stress. +Input File Usage: +Abaqus/CAE Usage: +*PLASTIC, HARDENING=ISOTROPIC +Property module: material editor: Mechanical→Plasticity→Plastic +Processing test data +If you have uniaxial and/or biaxial test data, as shown in Figure 23.7.1–1, you can use an interactive +Abaqus/CAE plug-in to obtain the hyperelasticity, plasticity, and Mullins effect data. For information +about the plug-in and instructions about its usage, see “Abaqus/CAE plug-in application for processing +cyclic test data of filled elastomers and thermoplastics” in the Dassault Systèmes Knowledge Base at +www.3ds.com/support/knowledge-base or the SIMULIA Online Support System, which is accessible +through the My Support page at www.simulia.com. +Limitations +The model is intended to capture permanent set under multiaxial stress states and mild reverse loading +conditions, as illustrated by Govindarajan, Hurtado, and Mars (2007). This model is not intended to +capture deformation under complete reverse loading. Any rate effects apply only to the plastic part of +the material definition. +Elements +Permanent set can be modeled with all element types that support the use of the hyperelastic material +model. +Procedures +Permanent set modeling can be carried out in all procedures that support the use of the hyperelastic +material model with the exception of the steady-state transport procedure. In linear perturbation steps +in Abaqus/Standard, the current material tangent stiffness corresponding to the elastic part is used to +determine the response, while ignoring any plasticity effects. +Output +The standard output identifiers available in Abaqus (“Abaqus/Standard output variable identifiers,” +Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2) corresponding to other +isotropic hardening plasticity models can be obtained for permanent set models. +Additional references +• Govindarajan, S. M., J. A. Hurtado, and W. V. Mars, “Simulation of Mullins Effect in Filled +Elastomers Using Multiplicative Decomposition,” European Conference for Constitutive Models +for Rubber, September 2007, Paris, France. +• Simo, J. C., “Algorithms for Static and Dynamic Multiplicative Plasticity that Preserve the Classical +Return Mapping Schemes of the Infinitesimal Theory,” Computer Methods in Applied Mechanics +and Engineering, vol. 99, p. 61–112, 1992. +• Weber, G., and L. Anand, “Finite Deformation Constitutive Equations and Time Integration +Isotropic Hyperelastic-Viscoplastic Solids,” Computer Methods in Applied +Procedure for +Mechanics and Engineering, vol. 79, p. 173–202, 1990. +24. +Progressive Damage and Failure +Progressive damage and failure: overview +Damage and failure for ductile metals +Damage and failure for fiber-reinforced composites +Damage and failure for ductile materials in low-cycle fatigue analysis +24.1 +24.2 +24.3 +24.1 +Progressive damage and failure: overview +• “Progressive damage and failure,” Section 24.1.1 +PROGRESSIVE DAMAGE AND FAILURE +PROGRESSIVE DAMAGE AND FAILURE +Abaqus provides the following models to predict progressive damage and failure: +• Progressive damage and failure for ductile metals: Abaqus offers a general capability for +modeling progressive damage and failure in ductile metals. The functionality can be used in conjunction +with the Mises, Johnson-Cook, Hill, and Drucker-Prager plasticity models (“Damage and failure for +ductile metals: overview,” Section 24.2.1). The capability supports the specification of one or more +damage initiation criteria, including ductile, shear, forming limit diagram (FLD), forming limit stress +diagram (FLSD), Müschenborn-Sonne forming limit diagram (MSFLD), and Marciniak-Kuczynski +(M-K) criteria. After damage initiation, the material stiffness is degraded progressively according to the +specified damage evolution response. The progressive damage models allow for a smooth degradation +of the material stiffness, which makes them suitable for both quasi-static and dynamic situations, a great +advantage over the dynamic failure models (“Dynamic failure models,” Section 23.2.8). +The Johnson-Cook and Marciniak-Kuczynski (M-K) damage initiation criteria are not available in +Abaqus/Standard. +• Progressive damage and failure for fiber-reinforced materials: Abaqus offers a capability +to model anisotropic damage in fiber-reinforced materials (“Damage and failure for fiber-reinforced +composites: overview,” Section 24.3.1). The response of the undamaged material is assumed to be +linearly elastic, and the model is intended to predict behavior of fiber-reinforced materials for which +damage can be initiated without a large amount of plastic deformation. The Hashin’s initiation criteria +are used to predict the onset of damage, and the damage evolution law is based on the energy dissipated +during the damage process and linear material softening. +• Progressive +for +and +failure +damage +ductile materials +fatigue +analysis: Abaqus/Standard offers a capability to model progressive damage and failure for ductile +materials due to stress reversals and the accumulation of inelastic strain in a low-cycle fatigue analysis +using the direct cyclic approach . The damage initiation criterion and damage evolution are characterized by the +accumulated inelastic hysteresis energy per stabilized cycle . After damage initiation, the elastic +material stiffness is degraded progressively according to the specified damage evolution response. +low-cycle +in +In addition, Abaqus offers a concrete damaged model (“Concrete damaged plasticity,” Section 23.6.3), +dynamic failure models (“Dynamic failure models,” Section 23.2.8), and specialized capabilities for +modeling damage and failure in cohesive elements (“Defining the constitutive response of cohesive elements +using a traction-separation description,” Section 32.5.6) and in connectors (“Connector damage behavior,” +Section 31.2.7). +This section provides an overview of the progressive damage and failure capability and a brief description +of the concepts of damage initiation and evolution. The discussion in this section is limited to damage models +for ductile metals and fiber-reinforced materials. +General framework for modeling damage and failure +Abaqus offers a general framework for material failure modeling that allows the combination of multiple +failure mechanisms acting simultaneously on the same material. Material failure refers to the complete +loss of load-carrying capacity that results from progressive degradation of the material stiffness. The +stiffness degradation process is modeled using damage mechanics. +To help understand the failure modeling capabilities in Abaqus, consider the response of a typical +metal specimen during a simple tensile test. The stress-strain response, such as that illustrated in +Figure 24.1.1–1, will show distinct phases. The material response is initially linear elastic, +, +followed by plastic yielding with strain hardening, +. Beyond point c there is a marked reduction of +load-carrying capacity until rupture, +. The deformation during this last phase is localized in a neck +region of the specimen. Point c identifies the material state at the onset of damage, which is referred to +as the damage initiation criterion. Beyond this point, the stress-strain response +is governed by +the evolution of the degradation of the stiffness in the region of strain localization. In the context of +damage mechanics +that the material +can be viewed as the degraded response of the curve +would have followed in the absence of damage. +d’ + d +Figure 24.1.1–1 Typical uniaxial stress-strain response of a metal specimen. +Thus, in Abaqus the specification of a failure mechanism consists of four distinct parts: +• the definition of the effective (or undamaged) material response (e.g., +Figure 24.1.1–1), +in +• a damage initiation criterion (e.g., c in Figure 24.1.1–1), +• a damage evolution law (e.g., +in Figure 24.1.1–1), and +• a choice of element deletion whereby elements can be removed from the calculations once the +material stiffness is fully degraded (e.g., d in Figure 24.1.1–1). +These parts will be discussed separately for ductile metals (“Damage and failure for ductile metals: +overview,” Section 24.2.1) and fiber-reinforced materials (“Damage and failure for fiber-reinforced +composites: overview,” Section 24.3.1). +Mesh dependency +In continuum mechanics the constitutive model is normally expressed in terms of stress-strain relations. +When the material exhibits strain-softening behavior, leading to strain localization, this formulation +results in a strong mesh dependency of the finite element results in that the energy dissipated decreases +upon mesh refinement. +In Abaqus all of the available damage evolution models use a formulation +intended to alleviate the mesh dependency. This is accomplished by introducing a characteristic length +into the formulation, which in Abaqus is related to the element size, and expressing the softening part +of the constitutive law as a stress-displacement relation. In this case the energy dissipated during the +damage process is specified per unit area, not per unit volume. This energy is treated as an additional +material parameter, and it is used to compute the displacement at which full material damage occurs. +This is consistent with the concept of critical energy release rate as a material parameter for fracture +mechanics. This formulation ensures that the correct amount of energy is dissipated and greatly +alleviates the mesh dependency. +24.2 +Damage and failure for ductile metals +• “Damage and failure for ductile metals: overview,” Section 24.2.1 +• “Damage initiation for ductile metals,” Section 24.2.2 +• “Damage evolution and element removal for ductile metals,” Section 24.2.3 +24.2.1 +DAMAGE AND FAILURE FOR DUCTILE METALS: OVERVIEW +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Progressive damage and failure,” Section 24.1.1 +• “Damage initiation for ductile metals,” Section 24.2.2 +• “Damage evolution and element removal for ductile metals,” Section 24.2.3 +• *DAMAGE INITIATION +• *DAMAGE EVOLUTION +• “Defining damage,” Section 12.9.3 of the Abaqus/CAE User’s Manual, in the online HTML version +of this manual +Overview +Abaqus/Standard and Abaqus/Explicit offer a general capability for predicting the onset of failure and a +capability for modeling progressive damage and failure of ductile metals. In the most general case this +requires the specification of the following: +• the undamaged elastic-plastic response of the material (“Classical metal plasticity,” Section 23.2.1); +• a damage initiation criterion (“Damage initiation for ductile metals,” Section 24.2.2); and +• a damage evolution response, including a choice of element removal (“Damage evolution and +element removal for ductile metals,” Section 24.2.3). +A summary of the general framework for progressive damage and failure in Abaqus is given in +“Progressive damage and failure,” Section 24.1.1. This section provides an overview of the damage +initiation criteria and damage evolution law for ductile metals. +In addition, Abaqus/Explicit offers +dynamic failure models that are suitable for high-strain-rate dynamic problems (“Dynamic failure +models,” Section 23.2.8). +Damage initiation criterion +Abaqus offers a variety of choices of damage initiation criteria for ductile metals, each associated with +distinct types of material failure. They can be classified in the following categories: +• Damage initiation criteria for the fracture of metals, including ductile and shear criteria. +• Damage initiation criteria for the necking instability of sheet metal. These include forming limit +diagrams (FLD, FLSD, and MSFLD) intended to assess the formability of sheet metal and the +Marciniak-Kuczynski (M-K) criterion (available only in Abaqus/Explicit) to numerically predict +necking instability in sheet metal taking into account the deformation history. +These criteria are discussed in “Damage initiation for ductile metals,” Section 24.2.2. Each damage +initiation criterion has an associated output variable to indicate whether the criterion has been met during +the analysis. A value of 1.0 or higher indicates that the initiation criterion has been met. +More than one damage initiation criterion can be specified for a given material. If multiple damage +initiation criteria are specified for the same material, they are treated independently. Once a particular +initiation criterion is satisfied, the material stiffness is degraded according to the specified damage +evolution law for that criterion; in the absence of a damage evolution law, however, the material +stiffness is not degraded. A failure mechanism for which no damage evolution response is specified is +said to be inactive. Abaqus will evaluate the initiation criterion for an inactive mechanism for output +purposes only, but the mechanism will have no effect on the material response. +Input File Usage: +Use the following option to define each damage initiation criterion (repeat as +needed to define multiple criteria): +Abaqus/CAE Usage: +*DAMAGE INITIATION, CRITERION=criterion 1 +Property module: material editor: Mechanical→Damage for Ductile +Metals→criterion +Damage evolution +The damage evolution law describes the rate of degradation of the material stiffness once the +corresponding initiation criterion has been reached. For damage in ductile metals Abaqus assumes that +the degradation of the stiffness associated with each active failure mechanism can be modeled using +a scalar damage variable, +represents the set of active mechanisms. At any +given time during the analysis the stress tensor in the material is given by the scalar damage equation +), where +( +where D is the overall damage variable and +the current increment. +material has lost its load-carrying capacity when +mesh if all of the section points at any one integration location have lost their load-carrying capacity. +is the effective (or undamaged) stress tensor computed in +are the stresses that would exist in the material in the absence of damage. The +. By default, an element is removed from the +The overall damage variable, D, captures the combined effect of all active mechanisms and is +computed in terms of the individual damage variables, +, according to a user-specified rule. +Abaqus supports different models of damage evolution in ductile metals and provides controls +associated with element deletion due to material failure, as described in “Damage evolution and element +removal for ductile metals,” Section 24.2.3. All of the available models use a formulation intended to +alleviate the strong mesh dependency of the results that can arise from strain localization effects during +progressive damage. +Input File Usage: +Use the following option immediately after the corresponding *DAMAGE +INITIATION option to specify the damage evolution behavior: +*DAMAGE EVOLUTION +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Damage for Ductile +Metals→criterion: Suboptions→Damage Evolution +Elements +The failure modeling capability for ductile metals can be used with any elements in Abaqus that include +mechanical behavior (elements that have displacement degrees of freedom). +For coupled temperature-displacement elements the thermal properties of the material are not +affected by the progressive damage of the material stiffness until the condition for element deletion is +reached; at this point the thermal contribution of the element is also removed. +The damage initiation criteria for sheet metal necking instability (FLD, FLSD, MSFLD, and M-K) +are available only for elements that include mechanical behavior and use a plane stress formulation (i.e., +plane stress, shell, continuum shell, and membrane elements). +24.2.2 +DAMAGE INITIATION FOR DUCTILE METALS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Progressive damage and failure,” Section 24.1.1 +• *DAMAGE INITIATION +• “Defining damage,” Section 12.9.3 of the Abaqus/CAE User’s Manual, in the online HTML version +of this manual +Overview +The material damage initiation capability for ductile metals: +• is intended as a general capability for predicting initiation of damage in metals, including sheet, +extrusion, and cast metals as well as other materials; +• can be used in combination with the damage evolution models for ductile metals described in +“Damage evolution and element removal for ductile metals,” Section 24.2.3; +• allows the specification of more than one damage initiation criterion; +• includes ductile, shear, forming limit diagram (FLD), forming limit stress diagram (FLSD) and +Müschenborn-Sonne forming limit diagram (MSFLD) criteria for damage initiation; +• includes in Abaqus/Explicit the Marciniak-Kuczynski (M-K) and Johnson-Cook criteria for damage +initiation; +• can be used in Abaqus/Standard in conjunction with Mises, Johnson-Cook, Hill, and Drucker-Prager +plasticity (ductile, shear, FLD, FLSD, and MSFLD criteria); and +• can be used in Abaqus/Explicit in conjunction with Mises and Johnson-Cook plasticity (ductile, +shear, FLD, FLSD, MSFLD, Johnson-Cook, and MK criteria) and in conjunction with Hill and +Drucker-Prager plasticity (ductile, shear, FLD, FLSD, MSFLD, and Johnson-Cook criteria). +Damage initiation criteria for fracture of metals +Two main mechanisms can cause the fracture of a ductile metal: ductile fracture due to the nucleation, +growth, and coalescence of voids; and shear fracture due to shear band localization. Based on +phenomenological observations, these two mechanisms call for different forms of the criteria for the +onset of damage (Hooputra et al., 2004). The functional forms provided by Abaqus for these criteria +are discussed below. These criteria can be used in combination with the damage evolution models for +ductile metals discussed in “Damage evolution and element removal for ductile metals,” Section 24.2.3, +to model fracture of a ductile metal. +Ductile criterion +The ductile criterion is a phenomenological model for predicting the onset of damage due to nucleation, +growth, and coalescence of voids. The model assumes that the equivalent plastic strain at the onset of +damage, +, is a function of stress triaxiality and strain rate: +where +is the stress triaxiality, p is the pressure stress, q is the Mises equivalent stress, and +is the equivalent plastic strain rate. The criterion for damage initiation is met when the following +condition is satisfied: +where +during the analysis the incremental increase in +is computed as +is a state variable that increases monotonically with plastic deformation. At each increment +In Abaqus/Standard the ductile criterion can be used in conjunction with the Mises, Johnson-Cook, +Hill, and Drucker-Prager plasticity models and in Abaqus/Explicit in conjunction with the Mises, +Johnson-Cook, Hill, and Drucker-Prager plasticity models, including equation of state. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to specify the equivalent plastic strain at the onset +of damage as a tabular function of stress triaxality, strain rate, and, optionally, +temperature and predefined field variables: +*DAMAGE INITIATION, CRITERION=DUCTILE, DEPENDENCIES=n +Property module: material editor: Mechanical→Damage for Ductile +Metals→Ductile Damage +Defining dependency of ductile criterion on Lode angle in Abaqus/Explicit +Recent experimental results for aluminum alloys and other metals (Bai and Wierzbicki, 2008) reveal that, +in addition to stress triaxility and strain rate, ductile fracture can also depend on the third invariant of +deviatoric stress, which is related to the Lode angle (or deviatoric polar angle). Abaqus/Explicit allows +the definition of the equivalent plastic strain at the onset of ductile damage, +, as a function of the Lode +angle, +, by way of the functional form +where +q is the Mises equivalent stress, and r is the third invariant of deviatoric stress, +can take values from +function +stress states on the tensile meridian. +, for stress states on the compressive meridian, to +. The +, for +Input File Usage: +Use the following option to indicate that the equivalent plastic strain at the onset +of ductile damage is a function of the Lode angle: +Abaqus/CAE Usage: +*DAMAGE INITIATION, CRITERION=DUCTILE, LODE DEPENDENT +Defining dependency of ductile criterion on Lode angle is not supported in +Abaqus/CAE. +Johnson-Cook criterion +The Johnson-Cook criterion (available only in Abaqus/Explicit) is a special case of the ductile criterion +in which the equivalent plastic strain at the onset of damage, +, is assumed to be of the form +– +are failure parameters and +where +the original formula published by Johnson and Cook (1985) in the sign of the parameter +difference is motivated by the fact that most materials experience a decrease in +stress triaxiality; therefore, +nondimensional temperature defined as +is the reference strain rate. This expression differs from +. This +with increasing +is the +in the above expression will usually take positive values. +is the current temperature, +is the melting temperature, and +where +is the transition +temperature defined as the one at or below which there is no temperature dependence on the expression of +the damage strain +. The material parameters must be measured at or below the transition temperature. +The Johnson-Cook criterion can be used in conjunction with the Mises, Johnson-Cook, Hill, and +Drucker-Prager plasticity models, including equation of state. When used in conjunction with the +Johnson-Cook plasticity model, the specified values of the melting and transition temperatures should +be consistent with the values specified in the plasticity definition. The Johnson-Cook damage initiation +criterion can also be specified together with any other initiation criteria, including the ductile criteria; +each initiation criterion is treated independently. +Input File Usage: +Use the following option to specify the parameters for the Johnson-Cook +initiation criterion: +Abaqus/CAE Usage: +*DAMAGE INITIATION, CRITERION=JOHNSON COOK +Property module: material editor: Mechanical→Damage for Ductile +Metals→Johnson-Cook Damage +Shear criterion +The shear criterion is a phenomenological model for predicting the onset of damage due to shear band +localization. The model assumes that the equivalent plastic strain at the onset of damage, +, is a function +of the shear stress ratio and strain rate: +Here +material parameter. A typical value of +for damage initiation is met when the following condition is satisfied: +is the shear stress ratio, +for aluminum is +is the maximum shear stress, and +is a += 0.3 (Hooputra et al., 2004). The criterion +where +is a state variable that increases monotonically with plastic deformation proportional to the +incremental change in equivalent plastic strain. At each increment during the analysis the incremental +increase in +is computed as +In Abaqus/Explicit the shear criterion can be used in conjunction with the Mises, Johnson-Cook, +Hill, and Drucker-Prager plasticity models, including equation of state. In Abaqus/Standard it can be +used with the Mises, Johnson-Cook, Hill, and Drucker-Prager models. +Input File Usage: +and to specify the equivalent plastic +Use the following option to specify +strain at the onset of damage as a tabular function of the shear stress ratio, strain +rate, and, optionally, temperature and predefined field variables: +*DAMAGE INITIATION, CRITERION=SHEAR, KS= , +DEPENDENCIES=n +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Damage for Ductile +Metals→Shear Damage +Initial conditions +Optionally, you can specify the initial work hardened state of the material by providing the initial +equivalent plastic strain values and, +if residual +stresses are also present, the initial stress values . Abaqus uses this information to initialize the +values of the ductile and shear damage initiation criteria, +, assuming constant values of stress +triaxiality and shear shear ratio (linear stress path). +and +Input File Usage: +Abaqus/CAE Usage: +Use the following options to specify that material hardening and residual +stresses have occurred prior to the current analysis: +*INITIAL CONDITIONS, TYPE=HARDENING +*INITIAL CONDITIONS, TYPE=STRESS +Use the following options to specify that material hardening and residual +stresses have occurred prior to the current analysis: +Load module: Create Predefined Field: Step: Initial, choose +Mechanical for the Category and Hardening and Stress for +the Types for Selected Step +Damage initiation criteria for sheet metal instability +Necking instability plays a determining factor in sheet metal forming processes: the size of the local +neck region is typically of the order of the thickness of the sheet, and local necks can rapidly lead +to fracture. Localized necking cannot be modeled with traditional shell elements used in sheet metal +forming simulations because the size of the neck is of the order of the thickness of the element. Abaqus +supports four criteria for predicting the onset of necking instability in sheet metals: forming limit diagram +(FLD); forming limit stress diagram (FLSD); Müschenborn-Sonne forming limit diagram (MSFLD); and +Marciniak-Kuczynski (M-K) criteria, which is available only in Abaqus/Explicit. These criteria apply +only to elements with a plane stress formulation (plane stress, shell, continuum shell, and membrane +elements); Abaqus ignores these criteria for other elements. The initiation criteria for necking instability +can be used in combination with the damage evolution models discussed in “Damage evolution and +element removal for ductile metals,” Section 24.2.3, to account for the damage induced by necking. +Classical strain-based forming limit diagrams (FLDs) are known to be dependent on the strain +path. Changes in the deformation mode (e.g., equibiaxial loading followed by uniaxial tensile strain) +may result in major modifications in the level of the limit strains. Therefore, the FLD damage initiation +criterion should be used with care if the strain paths in the analysis are nonlinear. In practical industrial +applications, significant changes in the strain path may be induced by multistep forming operations, +complex geometry of the tooling, and interface friction, among other factors. For problems with highly +nonlinear strain paths Abaqus offers three additional damage initiation criteria: the forming limit stress +diagram (FLSD) criterion, the Müschenborn-Sonne forming limit diagram (MSFLD) criterion, and +in Abaqus/Explicit the Marciniak-Kuczynski (M-K) criterion; these alternatives to the FLD damage +initiation criterion are intended to minimize load path dependence. +The characteristics of each criterion available in Abaqus for predicting damage initiation in sheet +metals are discussed below. +Forming limit diagram (FLD) criterion +The forming limit diagram (FLD) is a useful concept introduced by Keeler and Backofen (1964) to +determine the amount of deformation that a material can withstand prior to the onset of necking instability. +The maximum strains that a sheet material can sustain prior to the onset of necking are referred to +as the forming limit strains. A FLD is a plot of the forming limit strains in the space of principal +(in-plane) logarithmic strains. In the discussion that follows major and minor limit strains refer to the +maximum and minimum values of the in-plane principal limit strains, respectively. The major limit +strain is usually represented on the vertical axis and the minor strain on the horizontal axis, as illustrated +in Figure 24.2.2–1. The line connecting the states at which deformation becomes unstable is referred to +as the forming limit curve (FLC). The FLC gives a sense of the formability of a sheet of material. Strains +computed numerically by Abaqus can be compared to a FLC to determine the feasibility of the forming +process under analysis. +major +FLC +ω = +FLD +ε A +ε B +major +major +Figure 24.2.2–1 Forming limit diagram (FLD). +minor +The FLD damage initiation criterion requires the specification of the FLC in tabular form by +giving the major principal strain at damage initiation as a tabular function of the minor principal strain +and, optionally, temperature and predefined field variables, +. The damage initiation +criterion for the FLD is given by the condition +is a function of +the current deformation state and is defined as the ratio of the current major principal strain, +, to +the major limit strain on the FLC evaluated at the current values of the minor principal strain, +; +temperature, +; and predefined field variables, +, where the variable +: +For example, for the deformation state given by point A in Figure 24.2.2–1 the damage initiation criterion +is evaluated as +If the value of the minor strain lies outside the range of the specified tabular values, Abaqus will +extrapolate the value of the major limit strain on the FLC by assuming that the slope at the endpoint +of the curve remains constant. Extrapolation with respect to temperature and field variables follows the +standard conventions: the property is assumed to be constant outside the specified range of temperature +and field variables . +Experimentally, FLDs are measured under conditions of biaxial stretching of a sheet, without +bending effects. Under bending loading, however, most materials can achieve limit strains that are +much greater than those on the FLC. To avoid the prediction of early failure under bending deformation, +Abaqus evaluates the FLD criterion using the strains at the midplane through the thickness of the +element. For composite shells with several layers the criterion is evaluated at the midplane of each layer +for which a FLD curve has been specified, which ensures that only biaxial stretching effects are taken +into account. Therefore, the FLD criterion is not suitable for modeling failure under bending loading; +other failure models (such as ductile and shear failure) are more appropriate for such loading. Once +the FLD damage initiation criterion is met, the evolution of damage is driven independently at each +material point through the thickness of the element based on the local deformation at that point. Thus, +although bending effects do not affect the evaluation of the FLD criterion, they may affect the rate of +evolution of damage. +Input File Usage: +Use the following option to specify the limit major strain as a tabular function +of minor strain: +Abaqus/CAE Usage: +*DAMAGE INITIATION, CRITERION=FLD +Property module: material editor: Mechanical→Damage for Ductile +Metals→FLD Damage +Forming limit stress diagram (FLSD) criterion +When strain-based FLCs are converted into stress-based FLCs, the resulting stress-based curves have +been shown to be minimally affected by changes to the strain path (Stoughton, 2000); that is, different +strain-based FLCs, corresponding to different strain paths, are mapped onto a single stress-based FLC. +This property makes forming limit stress diagrams (FLSDs) an attractive alternative to FLDs for the +prediction of necking instability under arbitrary loading. However, the apparent independence of the +stress-based limit curves on the strain path may simply reflect the small sensitivity of the yield stress to +changes in plastic deformation. This topic is still under discussion in the research community. +A FLSD is the stress counterpart of the FLD, with the major and minor principal in-plane +stresses corresponding to the onset of necking localization plotted on the vertical and horizontal axes, +respectively. In Abaqus the FLSD damage initiation criterion requires the specification of the major +principal in-plane stress at damage initiation as a tabular function of the minor principal in-plane stress +and, optionally, temperature and predefined field variables, +. The damage initiation +criterion for the FLSD is met when the condition +is a +function of the current stress state and is defined as the ratio of the current major principal stress, +, +to the major stress on the FLSD evaluated at the current values of minor stress, +; +and predefined field variables, +is satisfied, where the variable +; temperature, +: +If the value of the minor stress lies outside the range of specified tabular values, Abaqus will extrapolate +the value of the major limit stress assuming that the slope at the endpoints of the curve remains constant. +Extrapolation with respect to temperature and field variables follows the standard conventions: +the +property is assumed to be constant outside the specified range of temperature and field variables . +For reasons similar to those discussed earlier for the FLD criterion, Abaqus evaluates the FLSD +criterion using the stresses averaged through the thickness of the element (or the layer, in the case of +composite shells with several layers), ignoring bending effects. Therefore, the FLSD criterion cannot +be used to model failure under bending loading; other failure models (such as ductile and shear failure) +are more suitable for such loading. Once the FLSD damage initiation criterion is met, the evolution of +damage is driven independently at each material point through the thickness of the element based on the +local deformation at that point. Thus, although bending effects do not affect the evaluation of the FLSD +criterion, they may affect the rate of evolution of damage. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to specify the limit major stress as a tabular function +of minor stress: +*DAMAGE INITIATION, CRITERION=FLSD +Property module: material editor: Mechanical→Damage for Ductile +Metals→FLSD Damage +Marciniak-Kuczynski (M-K) criterion +Another approach available in Abaqus/Explicit for accurately predicting the forming limits for arbitrary +loading paths is based on the localization analysis proposed by Marciniak and Kuczynski (1967). +The approach can be used with the Mises and Johnson-Cook plasticity models, including kinematic +hardening. +In M-K analysis, virtual thickness imperfections are introduced as grooves simulating +preexisting defects in an otherwise uniform sheet material. The deformation field is computed inside +each groove as a result of the applied loading outside the groove. Necking is considered to occur when +the ratio of the deformation in the groove relative to the nominal deformation (outside the groove) is +greater than a critical value. +Figure 24.2.2–2 shows schematically the geometry of the groove considered for M-K analysis. In +the figure a denotes the nominal region in the shell element outside the imperfection, and b denotes the +weak groove region. The initial thickness of the imperfection relative to the nominal thickness is given +by the ratio +, with the subscript 0 denoting quantities in the initial, strain-free state. The +groove is oriented at a zero angle with respect to the 1-direction of the local material orientation. +Abaqus/Explicit allows the specification of an anisotropic distribution of thickness imperfections +as a function of angle with respect to the local material orientation, +. Abaqus/Explicit first solves +for the stress-strain field in the nominal area ignoring the presence of imperfections; then it considers +the effect of each groove alone. The deformation field inside each groove is computed by enforcing the +strain compatibility condition +and the force equilibrium equations +The subscripts n and t refer to the directions normal and tangential to the groove. In the above equilibrium +equations +are forces per unit width in the t-direction. +and +The onset of necking instability is assumed to occur when the ratio of the rate of deformation inside +a groove relative to the rate of deformation if no groove were present is greater than a critical value. In +t =f t +00 +t a +Figure 24.2.2–2 Imperfection model for the M-K analysis. +addition, it may not be possible to find a solution that satisfies equilibrium and compatibility conditions +once localization initiates at a particular groove; consequently, failure to find a converged solution is +also an indicator of the onset of localized necking. For the evaluation of the damage initiation criterion +Abaqus/Explicit uses the following measures of deformation severity: +These deformation severity factors are evaluated on each of the specified groove directions and compared +with the critical values. (The evaluation is performed only if the incremental deformation is primarily +plastic; the M-K criterion will not predict damage initiation if the deformation increment is elastic.) The +most unfavorable groove direction is used for the evaluation of the damage initiation criterion, which is +given as +, and +are the critical values of the deformation severity indices. Damage initiation +where +, +occurs when +or when a converged solution to the equilibrium and compatibility equations +cannot be found. By default, Abaqus/Explicit assumes +; you can specify +different values. If one of these parameters is set equal to zero, its corresponding deformation severity +factor is not included in the evaluation of the damage initiation criterion. If all of these parameters are set +equal to zero, the M-K criterion is based solely on nonconvergence of the equilibrium and compatibility +equations. +You must specify the fraction, +, equal to the initial thickness at the virtual imperfection divided +by the nominal thickness , as well as the number of imperfections to be used for the +evaluation of the M-K damage initiation criterion. It is assumed that these directions are equally spaced +angularly. By default, Abaqus/Explicit uses four imperfections located at 0°, 45°, 90°, and 135° with +respect to the local 1-direction of the material. The initial imperfection size can be defined as a tabular +function of angular direction, +; this allows the modeling of an anisotropic distribution of flaws in +the material. Abaqus/Explicit will use this table to evaluate the thickness of each of the imperfections +that will be used for the evaluation of the M-K analysis method. In addition, the initial imperfection +size can also be a function of initial temperature and field variables; this allows defining a nonuniform +spatial distribution of imperfections. Abaqus/Explicit will compute the initial imperfection size based +on the values of temperature and field variables at the beginning of the analysis. The initial size of the +imperfection remains a constant property during the rest of the analysis. +A general recommendation is to choose the value of +such that the forming limit predicted +numerically for uniaxial strain loading conditions ( +) matches the experimental result. +The virtual grooves are introduced to evaluate the onset of necking instability; they do not influence +the results in the underlying element. Once the criterion for necking instability is met, the material +properties in the element are degraded according to the specified damage evolution law. +Input File Usage: +Use the following option to specify the initial imperfection thickness relative +to the nominal thickness as a tabular function of the angle with respect to the +1-direction of the local material orientation and, optionally, initial temperature +and field variables: +*DAMAGE INITIATION, CRITERION=MK, DEPENDENCIES=n +Use the following option to specify critical deformation severity factors: +*DAMAGE INITIATION, CRITERION=MK, FEQ= +FNT= +, FNN= +, +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Damage for Ductile +Metals→M-K Damage +Performance considerations for the M-K criterion +There can be a substantial increase in the overall computational cost when the M-K criterion is used. +For example, the cost of processing a shell element with three section points through the thickness and +four imperfections, which is the default for the M-K criterion, increases by approximately a factor of +two compared to the cost without the M-K criterion. You can mitigate the cost of evaluating this damage +initiation criterion by reducing the number of flaw directions considered or by increasing the number of +increments between M-K computations, as explained below. Of course, the effect on the overall analysis +cost depends on the fraction of the elements in the model that use this damage initiation criterion. The +computational cost per element with the M-K criterion increases by approximately a factor of +is the number of imperfections specified for the evaluation of the M-K criterion and +where +is +the frequency, in number of increments, at which the M-K computations are performed. The coefficient +of +in the above formula gives a reasonable estimate of the cost increase in most cases, but the actual +cost increase may vary from this estimate. By default, Abaqus/Explicit performs the M-K computations +on each imperfection at each time increment, +. Care must be taken to ensure that the M-K +computations are performed frequently enough to ensure the accurate integration of the deformation +field on each imperfection. +Input File Usage: +Use the following option to specify the number of imperfections and frequency +of the M-K analysis: +*DAMAGE INITIATION, CRITERION=MK, +NUMBER IMPERFECTIONS= +, FREQUENCY= +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Damage for Ductile +Metals→M-K Damage: Number of imperfections and Frequency +Müschenborn-Sonne forming limit diagram (MSFLD) criterion +Müschenborn and Sonne (1975) proposed a method to predict the influence of the deformation path +on the forming limits of sheet metals on the basis of the equivalent plastic strain, by assuming that +the forming limit curve represents the sum of the highest attainable equivalent plastic strains. Abaqus +makes use of a generalization of this idea to establish a criterion of necking instability of sheet metals +for arbitrary deformation paths. The approach requires transforming the original forming limit curve +(without predeformation effects) from the space of major versus minor strains to the space of equivalent +plastic strain, +, versus ratio of principal strain rates, +. +For linear strain paths, assuming plastic incompressibility and neglecting elastic strains: +As illustrated in Figure 24.2.2–3 , linear deformation paths in the FLD transform onto vertical paths in +the +– diagram (constant value of +). +According to the MSFLD criterion, the onset of localized necking occurs when the sequence of +deformation states in the +diagram intersects the forming limit curve, as discussed below. It is +emphasized that for linear deformation paths both FLD and MSFLD representations are identical and +give rise to the same predictions. For arbitrary loading, however, the MSFLD representation takes into +account the effects of the history of deformation through the use of the accumulated equivalent plastic +strain. +– +For the specification of the MSFLD damage initiation criterion in Abaqus, you can directly provide +and, optionally, equivalent +. Alternatively, you +the equivalent plastic strain at damage initiation as a tabular function of +plastic strain rate, temperature, and predefined field variables, +(a) FLD +major + (b) MSFLD +plε +minor +Figure 24.2.2–3 Transformation of the forming limit curve from traditional FLD representation (a) +to MSFLD representation (b). Linear deformation paths transform onto vertical paths. +can specify the curve in the traditional FLD format (in the space of major and minor strains) by providing +a tabular function of the form +. In this case Abaqus will automatically transform +the data into the +Let +– format. +represent the ratio of the current equivalent plastic strain, +; strain rate, +plastic strain on the limit curve evaluated at the current values of +predefined field variables, +: +, to the equivalent +; and +; temperature, +The MSFLD criterion for necking instability is met when the condition +instability also occurs if the sequence of deformation states in the +due to a sudden change in the straining direction. This situation is illustrated in Figure 24.2.2–4. As +changes from to +– diagram intersects +, the line connecting the corresponding points in the +with the forming limit curve. When this situation occurs, the MSFLD criterion is reached despite the +fact that +equal to one +to indicate that the criterion has been met. +is satisfied. Necking +– diagram intersects the limit curve +. For output purposes Abaqus sets the value of +The equivalent plastic strain +used for the evaluation of the MSFLD criterion in Abaqus is +accumulated only over increments that result in an increase of the element area. Strain increments +associated with a reduction of the element area cannot cause necking and do not contribute toward the +evaluation of the MSFLD criterion. +If the value of +lies outside the range of specified tabular values, Abaqus extrapolates the value of +equivalent plastic strain for initiation of necking assuming that the slope at the endpoints of the curve +remains constant. Extrapolation with respect to strain rate, temperature, and field variables follows the +plε +Onset of necking +MSFLD +t +Δ t +Figure 24.2.2–4 Illustration of how a sudden change in the straining direction, from +to +can produce a horizontal intersection with the limit curve and lead to onset of necking. +, +standard conventions: the property is assumed to be constant outside the specified range of strain rate, +temperature, and field variables . +As discussed in “Progressive damage and failure of ductile metals,” Section 2.2.21 of the +Abaqus Verification Manual, predictions of necking instability based on the MSFLD criterion agree +remarkably well with predictions based on the Marciniak and Kuczynski criterion, at significantly less +computational cost than the Marciniak and Kuczynski criterion. There are some situations, however, +in which the MSFLD criterion may overpredict the amount of formability left in the material. This +occurs in situations when, sometime during the loading history, the material reaches a state that is very +close to the point of necking instability and is subsequently strained in a direction along which it can +sustain further deformation. In this case the MSFLD criterion may predict that the amount of additional +formability in the new direction is greater than that predicted with the Marciniak and Kuczynski +criterion. However, this situation is often not a concern in practical forming applications where safety +factors in the forming limit diagrams are commonly used to ensure that the material state is sufficiently +far away from the point of necking. Refer to “Progressive damage and failure of ductile metals,” +Section 2.2.21 of the Abaqus Verification Manual, for a comparative analysis of these two criteria. +For reasons similar to those discussed earlier for the FLD criterion, Abaqus evaluates the MSFLD +criterion using the strains at the midplane through the thickness of the element (or the layer, in the case of +composite shells with several layers), ignoring bending effects. Therefore, the MSFLD criterion cannot +be used to model failure under bending loading; other failure models (such as ductile and shear failure) +are more suitable for such loading. Once the MSFLD damage initiation criterion is met, the evolution +of damage is driven independently at each material point through the thickness of the element based on +the local deformation at that point. Thus, although bending effects do not affect the evaluation of the +MSFLD criterion, they may affect the rate of evolution of damage. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to specify the MSFLD damage initiation criterion by +providing the limit equivalent plastic strain as a tabular function of +(default): +*DAMAGE INITIATION, CRITERION=MSFLD, DEFINITION=MSFLD +Use the following option to specify the MSFLD damage initiation criterion by +providing the limit major strain as a tabular function of minor strain: +*DAMAGE INITIATION, CRITERION=MSFLD, DEFINITION=FLD +Property module: material editor: Mechanical→Damage for Ductile +Metals→MSFLD Damage +Numerical evaluation of the principal strain rates ratio +The ratio of principal strain rates, +, can jump in value due to sudden changes in the +deformation path. Special care is required during explicit dynamic simulations to avoid nonphysical +jumps in +triggered by numerical noise, which may cause a horizontal intersection of the deformation +state with the forming limit curve and lead to the premature prediction of necking instability. +To overcome this problem, rather than computing +as a ratio of instantaneous strain rates, +Abaqus/Explicit periodically updates +based on accumulated strain increments after small but +significant changes in the equivalent plastic strain. The threshold value for the change in equivalent +plastic strain triggering an update of +is approximated as +is denoted as +, and +where +update of +and +are principal values of the accumulated plastic strain since the previous +. The default value of +is 0.002 (0.2%). +In addition, Abaqus/Explicit supports the following filtering method for the computation of +: +represents the accumulated time over the analysis increments required to have an increase in +) facilitates filtering high-frequency +where +equivalent plastic strain of at least +. The factor +oscillations. This filtering method is usually not necessary provided that an appropriate value of +is used. You can specify the value of +directly. The default value is +(no filtering). +( +In Abaqus/Standard +is computed at every analysis increment as +, +without using either of the above filtering methods. However, you can still specify values for +and ; and these values can be imported into any subsequent analysis in Abaqus/Explicit. +Input File Usage: +Abaqus/CAE Usage: +*DAMAGE INITIATION, CRITERION=MSFLD, PEINC= +OMEGA= +Property module: material editor: Mechanical→Damage for Ductile +Metals→MSFLD Damage: Omega: +, +The value for +cannot be specified directly in Abaqus/CAE. +Initial conditions +When we need to study the behavior of a material that has been previously subjected to deformations, +such as those originated during the manufacturing process, initial equivalent plastic strain values can +be provided to specify the initial work hardened state of the material . +In addition, when the initial equivalent plastic strain is greater than the minimum value on the +forming limit curve, the initial value of +plays an important role in determining whether the MSFLD +It is, therefore, important to +damage initiation criterion will be met during subsequent deformation. +specify the initial value of +in these situations. To this end, you can specify initial values of the plastic +strain tensor . Abaqus will use this information to compute the initial value of +as the ratio of the minor and major principal plastic strains; that is, neglecting the elastic component of +deformation and assuming a linear deformation path. +Input File Usage: +Use both of the following options to specify that material hardening and plastic +strain have occurred prior to the current analysis: +*INITIAL CONDITIONS, TYPE=HARDENING +*INITIAL CONDITIONS, TYPE=PLASTIC STRAIN +Load module: Create Predefined Field: Step: Initial, choose Mechanical +for the Category and Hardening for the Types for Selected Step +Initial plastic strain conditions are not supported in Abaqus/CAE. +Abaqus/CAE Usage: +Elements +The damage initiation criteria for ductile metals can be used with any elements in Abaqus that include +mechanical behavior (elements that have displacement degrees of freedom) except for the pipe elements +in Abaqus/Explicit. +The models for sheet metal necking instability (FLD, FLSD, MSFLD, and M-K) are available only +with elements that include mechanical behavior and use a plane stress formulation (i.e., plane stress, +shell, continuum shell, and membrane elements). +Output +In addition to the standard output identifiers available in Abaqus (“Output variables,” Section 4.2), the +following variables have special meaning when a damage initiation criterion is specified: +ERPRATIO +SHRRATIO +TRIAX +Ratio of principal strain rates, +Shear stress ratio, +initiation criterion. +Stress triaxiality, +with damage initiation). +, used for the MSFLD damage initiation criterion. +, used for the evaluation of the shear damage +(available in Abaqus/Standard only in conjunction +DMICRT +DUCTCRT +JCCRT +SHRCRT +FLDCRT +FLSDCRT +MSFLDCRT +MKCRT +All damage initiation criteria components listed below. +Ductile damage initiation criterion, +. +Johnson-Cook damage initiation criterion (available only in Abaqus/Explicit). +Shear damage initiation criterion, +. +Maximum value of the FLD damage initiation criterion, +, during the analysis. +Maximum value of the FLSD damage initiation criterion, +analysis. +Maximum value of the MSFLD damage initiation criterion, +analysis. +, during the +, during the +Marciniak-Kuczynski +Abaqus/Explicit), +. +damage +initiation +criterion +(available +only +in +A value of 1 or greater for output variables associated with a damage initiation criterion indicates that +the criterion has been met. Abaqus will limit the maximum value of the output variable to 1 if a damage +evolution law has been prescribed for that criterion . However, if no damage evolution is specified, the criterion for damage +initiation will continue to be computed beyond the point of damage initiation; in this case the output +variable can take values greater than 1, indicating by how much the initiation criterion has been exceeded. +Additional references +• Hooputra, H., H. Gese, H. Dell, and H. Werner, “A Comprehensive Failure Model +for +Crashworthiness Simulation of Aluminium Extrusions,” International Journal of Crashworthiness, +vol. 9, no. 5, pp. 449–464, 2004. +• Bai, Y., and T. Wierzbicki, “A New Model of Metal Plasticity and Fracture with Pressure and Lode +Dependence,” International Journal of Plasticity, vol. 24, no. 6, pp. 1071–1096, 2008. +• Johnson, G. R., and W. H. Cook, “Fracture Characteristics of Three Metals Subjected to Various +Strains, Strain rates, Temperatures and Pressures,” Engineering Fracture Mechanics, vol. 21, no. 1, +pp. 31–48, 1985. +• Keeler, S. P., and W. A. Backofen, “Plastic Instability and Fracture in Sheets Stretched over Rigid +Punches,” ASM Transactions Quarterly, vol. 56, pp. 25–48, 1964. +• Marciniak, Z., and K. Kuczynski, “Limit Strains in the Processes of Stretch Forming Sheet Metal,” +International Journal of Mechanical Sciences, vol. 9, pp. 609–620, 1967. +• Müschenborn, W., and H. Sonne, “Influence of the Strain Path on the Forming Limits of Sheet +Metal,” Archiv fur das Eisenhüttenwesen, vol. 46, no. 9, pp. 597–602, 1975. +• Stoughton, T. B., “A General Forming Limit Criterion for Sheet Metal Forming,” International +Journal of Mechanical Sciences, vol. 42, pp. 1–27, 2000. +24.2.3 +DAMAGE EVOLUTION AND ELEMENT REMOVAL FOR DUCTILE METALS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Progressive damage and failure,” Section 24.1.1 +• *DAMAGE EVOLUTION +• “Damage evolution” in “Defining damage,” Section 12.9.3 of the Abaqus/CAE User’s Manual, in +the online HTML version of this manual +Overview +The damage evolution capability for ductile metals: +• assumes that damage is characterized by the progressive degradation of the material stiffness, +leading to material failure; +• must be used in combination with a damage initiation criterion for ductile metals (“Damage +initiation for ductile metals,” Section 24.2.2); +• uses mesh-independent measures (either plastic displacement or physical energy dissipation) to +drive the evolution of damage after damage initiation; +• takes into account the combined effect of different damage mechanisms acting simultaneously on +the same material and includes options to specify how each mechanism contributes to the overall +material degradation; and +• offers options for what occurs upon failure, including the removal of elements from the mesh. +Damage evolution +Figure 24.2.3–1 illustrates the characteristic stress-strain behavior of a material undergoing damage. In +the context of an elastic-plastic material with isotropic hardening, the damage manifests itself in two +forms: softening of the yield stress and degradation of the elasticity. The solid curve in the figure +represents the damaged stress-strain response, while the dashed curve is the response in the absence of +damage. As discussed later, the damaged response depends on the element dimensions such that mesh +dependency of the results is minimized. +and +In the figure +are the yield stress and equivalent plastic strain at the onset of damage, and +is the equivalent plastic strain at failure; that is, when the overall damage variable reaches the value +. The overall damage variable, D, captures the combined effect of all active damage mechanisms +, as discussed later in this section . +The value of the equivalent plastic strain at failure, +, depends on the characteristic length of the +element and cannot be used as a material parameter for the specification of the damage evolution law. +(D=0) + D σ +y0 +(1-D)E +ε pl +ε pl +Figure 24.2.3–1 Stress-strain curve with progressive damage degradation. +Instead, the damage evolution law is specified in terms of equivalent plastic displacement, +terms of fracture energy dissipation, +; these concepts are defined next. +, or in +Mesh dependency and characteristic length +When material damage occurs, the stress-strain relationship no longer accurately represents the material’s +behavior. Continuing to use the stress-strain relation introduces a strong mesh dependency based on +strain localization, such that the energy dissipated decreases as the mesh is refined. A different approach +is required to follow the strain-softening branch of the stress-strain response curve. Hillerborg’s (1976) +fracture energy proposal is used to reduce mesh dependency by creating a stress-displacement response +after damage is initiated. Using brittle fracture concepts, Hillerborg defines the energy required to open a +unit area of crack, +, as a material parameter. With this approach, the softening response after damage +initiation is characterized by a stress-displacement response rather than a stress-strain response. +The implementation of this stress-displacement concept in a finite element model requires the +definition of a characteristic length, L, associated with an integration point. The fracture energy is then +given as +This expression introduces the definition of the equivalent plastic displacement, +, as the fracture work +conjugate of the yield stress after the onset of damage (work per unit area of the crack). Before damage +initiation +. +The definition of the characteristic length depends on the element geometry and formulation: it is a +typical length of a line across an element for a first-order element; it is half of the same typical length for +; after damage initiation +a second-order element. For beams and trusses it is a characteristic length along the element axis. For +membranes and shells it is a characteristic length in the reference surface. For axisymmetric elements +it is a characteristic length in the r–z plane only. For cohesive elements it is equal to the constitutive +thickness. This definition of the characteristic length is used because the direction in which fracture +occurs is not known in advance. Therefore, elements with large aspect ratios will have rather different +behavior depending on the direction in which they crack: some mesh sensitivity remains because of this +effect, and elements that have aspect ratios close to unity are recommended. +Each damage initiation criterion described in “Damage initiation for ductile metals,” Section 24.2.2, +may have an associated damage evolution law. The damage evolution law can be specified in terms of +equivalent plastic displacement, +. Both of these options +take into account the characteristic length of the element to alleviate mesh dependency of the results. +, or in terms of fracture energy dissipation, +Evaluating overall damage when multiple criteria are active +The overall damage variable, D, captures the combined effect of all active mechanisms and is computed +in terms of individual damage variables, +, for each mechanism. You can choose to combine some of +the damage variables in a multiplicative sense to form an intermediate variable, +, as follows: +Then, the overall damage variable is computed as the maximum of +variables: +and the remaining damage +In the above expressions +overall damage in a multiplicative and a maximum sense, respectively, with +and +represent the sets of active mechanisms that contribute to the +. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to specify that +the damage associated with a +particular criterion contributes to the overall damage variable in a maximum +sense (default): +*DAMAGE EVOLUTION, DEGRADATION=MAXIMUM +Use the following option to specify that the damage associated with a particular +criterion contributes to the overall damage variable in a multiplicative sense: +*DAMAGE EVOLUTION, DEGRADATION=MULTIPLICATIVE +Use the following options to specify that the damage associated with a +particular criterion contributes to the overall damage variable in a maximum +sense (default) or in a multiplicative sense, respectively: +Property module: material editor: Mechanical→Damage for Ductile +Metals→criterion: Suboptions→Damage Evolution: Degradation: +Maximum or Multiplicative +Defining damage evolution based on effective plastic displacement +As discussed previously, once the damage initiation criterion has been reached, the effective plastic +displacement, +, is defined with the evolution equation +where L is the characteristic length of the element. +The evolution of the damage variable with the relative plastic displacement can be specified in +tabular, linear, or exponential form. Instantaneous failure will occur if the plastic displacement at failure, +, is specified as 0; however, this choice is not recommended and should be used with care because it +causes a sudden drop of the stress at the material point that can lead to dynamic instabilities. +Tabular form +You can specify the damage variable directly as a tabular function of equivalent plastic displacement, +, as shown in Figure 24.2.3–2(a). +Input File Usage: +*DAMAGE EVOLUTION, TYPE=DISPLACEMENT, +SOFTENING=TABULAR +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Damage for Ductile +Metals→criterion: +Suboptions→Damage +Type: +Displacement: Softening: Tabular +Evolution: +Linear form +Assume a linear evolution of the damage variable with effective plastic displacement, as shown in +Figure 24.2.3–2(b). You can specify the effective plastic displacement, +, at the point of failure (full +degradation). Then, the damage variable increases according to +, the +This definition ensures that when the effective plastic displacement reaches the value +material stiffness will be fully degraded ( +). The linear damage evolution law defines a truly linear +stress-strain softening response only if the effective response of the material is perfectly plastic (constant +yield stress) after damage initiation. +Input File Usage: +*DAMAGE EVOLUTION, TYPE=DISPLACEMENT, +SOFTENING=LINEAR +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Damage for Ductile +Metals→criterion: +Suboptions→Damage +Type: +Displacement: Softening: Linear +Evolution: +u pl +u pl +u pl + (a) tabular +u pl +(b) linear +α=10 +α=3 +α=1 +α=0 +u pl + (c) exponential +Figure 24.2.3–2 Different definitions of damage evolution based on +plastic displacement: (a) tabular, (b) linear, and (c) exponential. +Exponential form +Assume an exponential evolution of the damage variable with plastic displacement, as shown in +Figure 24.2.3–2(c). You can specify the relative plastic displacement at failure, +, and the exponent +. The damage variable is given as +Input File Usage: +*DAMAGE EVOLUTION, TYPE=DISPLACEMENT, +SOFTENING=EXPONENTIAL +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Damage for Ductile +Metals→criterion: +Suboptions→Damage +Type: +Displacement: Softening: Exponential +Evolution: +Defining damage evolution based on energy dissipated during the damage process +, to be dissipated during the damage process directly. +You can specify the fracture energy per unit area, +Instantaneous failure will occur if +is specified as 0. However, this choice is not recommended and +should be used with care because it causes a sudden drop in the stress at the material point that can lead +to dynamic instabilities. +The evolution in the damage can be specified in linear or exponential form. +Linear form +Assume a linear evolution of the damage variable with plastic displacement. You can specify the fracture +energy per unit area, +. Then, once the damage initiation criterion is met, the damage variable increases +according to +where the equivalent plastic displacement at failure is computed as +and +is the value of the yield stress at the time when the failure criterion is reached. Therefore, the +model becomes equivalent to that shown in Figure 24.2.3–2(b). The model ensures that the energy +dissipated during the damage evolution process is equal to +only if the effective response of the +material is perfectly plastic (constant yield stress) beyond the onset of damage. +Input File Usage: +*DAMAGE EVOLUTION, TYPE=ENERGY, SOFTENING=LINEAR +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Damage for Ductile +Metals→criterion: Suboptions→Damage Evolution: Type: Energy: +Softening: Linear +Exponential form +Assume an exponential evolution of the damage variable given as +The formulation of the model ensures that the energy dissipated during the damage evolution process +is equal to +In theory, the damage variable reaches a value of +1 only asymptotically at infinite equivalent plastic displacement (Figure 24.2.3–3(b)). +In practice, +Abaqus/Explicit will set d equal to one when the dissipated energy reaches a value of +, as shown in Figure 24.2.3–3(a). +. +Input File Usage: +*DAMAGE EVOLUTION, TYPE=ENERGY, +SOFTENING=EXPONENTIAL +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Damage for Ductile +Metals→criterion: Suboptions→Damage Evolution: Type: Energy: +Softening: Exponential +yo +u pl +u pl +(a) +(b) +Figure 24.2.3–3 Energy-based damage evolution with exponential +law: evolution of (a) yield stress and (b) damage variable. +Maximum degradation and choice of element removal +You have control over how Abaqus treats elements with severe damage. You can specify an upper +bound, +, to the overall damage variable, D; and you can choose whether to delete an element once +maximum degradation is reached. The latter choice also affects which stiffness components are damaged. +Specifying the value of maximum degradation +The default setting of +depends on whether elements are to be deleted upon reaching maximum +degradation (discussed next). For the default case of element deletion and in all cases for cohesive +elements, +. The output variable SDEG contains the value of D. +No further damage is accumulated at an integration point once D reaches +(except, of course, any +remaining stiffness is lost upon element deletion). +; otherwise, +Input File Usage: +Use the following option to specify +: +*SECTION CONTROLS, MAX DEGRADATION= +Removing the element from the mesh +Elements are deleted by default upon reaching maximum degradation. Except for cohesive elements +with traction-separation response , Abaqus applies damage to all stiffness components +equally for elements that may eventually be removed: +In Abaqus/Standard an element is removed from the mesh if D reaches +at all of the section +points at all the integration locations of an element except for cohesive elements (for cohesive elements +the conditions for element deletion are that D reaches +at all integration points and, for traction- +separation response, none of the integration points are in compression). +In Abaqus/Explicit an element is removed from the mesh if D reaches +at all of the section +points at any one integration location of an element except for cohesive elements (for cohesive elements +the conditions for element deletion are that D reaches +at all integration points and, for traction- +separation response, none of the integration points are in compression). For example, removal of a solid +element takes place, by default, when maximum degradation is reached at any one integration point. +However, in a shell element all through-the-thickness section points at any one integration location of +an element must fail before the element is removed from the mesh. In the case of second-order reduced- +integration beam elements, reaching maximum degradation at all section points through the thickness at +either of the two element integration locations along the beam axis leads, by default, to element removal. +Similarly, in modified triangular and tetrahedral solid elements and fully integrated membrane elements +D reaching +at any one integration point leads, by default, to element removal. +In a heat transfer analysis the thermal properties of the material are not affected by the progressive +damage of the material stiffness until the condition for element deletion is reached; at this point the +thermal contribution of the element is also removed. +Input File Usage: +Use the following option to delete the element from the mesh (default): +*SECTION CONTROLS, ELEMENT DELETION=YES +Keeping the element in the computations +Optionally, you may choose not to remove the element from the mesh, except in the case of three- +dimensional beam elements. With element deletion turned off, the overall damage variable is enforced +to be +if element deletion is turned off, which ensures +that elements will remain active in the simulation with a residual stiffness of at least 1% of the original +stiffness. The dimensionality of the stress state of the element affects which stiffness components can +become damaged, as discussed below. +. The default value is +In a heat transfer analysis the thermal properties of the material are not affected by damage of the +material stiffness. +Input File Usage: +Use the following option to keep the element in the computation: +*SECTION CONTROLS, ELEMENT DELETION=NO +Elements with three-dimensional stress states in Abaqus/Explicit +For elements with three-dimensional stress states (including generalized plane strain elements) the shear +stiffness will be degraded up to a maximum value, +, leading to softening of the deviatoric stress +components. The bulk stiffness, however, will be degraded only while the material is subjected to +negative pressures (i.e., hydrostatic tension); there is no bulk degradation under positive pressures. This +corresponds to a fluid-like behavior. Therefore, the degraded deviatoric, +, and pressure, p, stresses are +computed as +where the deviatoric and volumetric damage variables are given as +In this case the output variable SDEG contains the value of +. +Elements with three-dimensional stress states in Abaqus/Standard +For elements with three-dimensional stress states (including generalized plane strain elements) the +stiffness will be degraded uniformly until the maximum degradation, +, is reached. Output variable +SDEG contains the value of D. +Elements with plane stress states +For elements with a plane stress formulation (plane stress, shell, continuum shell, and membrane +elements) the stiffness will be degraded uniformly until the maximum degradation, +, is reached. +Output variable SDEG contains the value of D. +Elements with one-dimensional stress states +For elements with a one-dimensional stress state (i.e., truss elements, rebar, and cohesive elements with +gasket behavior) their only stress component will be degraded if it is positive (tension). The material +stiffness will remain unaffected under compression loading. The stress is, therefore, given by +, where the uniaxial damage variable is computed as +In this case +variable SDEG contains the value of +. +determines the maximum allowed degradation in uniaxial tension ( +). Output +Convergence difficulties in Abaqus/Standard +Material models exhibiting softening behavior and stiffness degradation often lead to severe convergence +difficulties in implicit analysis programs, such as Abaqus/Standard. Some techniques are available in +Abaqus/Standard to improve convergence for analyses involving these materials. +Viscous regularization in Abaqus/Standard +You can overcome some of the convergence difficulties associated with softening and stiffness +degradation by using the viscous regularization scheme, which causes the tangent stiffness matrix of the +softening material to be positive for sufficiently small time increments. +In this regularization scheme a viscous damage variable is defined by the evolution equation: +where +is the viscosity coefficient representing the relaxation time of the viscous system and d is the +damage variable evaluated in the inviscid base model. The damaged response of the viscous material +is computed using the viscous value of the damage variable. Using viscous regularization with a small +value of the viscosity parameter (small compared to the characteristic time increment) usually helps +improve the rate of convergence of the model in the softening regime, without compromising results. +The basic idea is that the solution of the viscous system relaxes to that of the inviscid case as +, +where t represents time. +In Abaqus/Standard you can specify the viscous coefficients as part of a section controls definition. +For more information, see “Using viscous regularization with cohesive elements, connector elements, +and elements that can be used with the damage evolution models for ductile metals and fiber-reinforced +composites in Abaqus/Standard” in “Section controls,” Section 27.1.4. +Unsymmetric equation solver +if any of the ductile evolution models is used, +In general, +the material Jacobian matrix will be +nonsymmetric. To improve convergence, it is recommended that the unsymmetric equation solver is +used in this case. +Using the damage models with rebar +It is possible to use material damage models in elements for which rebar are also defined. The base +material contribution to the element stress-carrying capacity diminishes according to the behavior +described previously in this section. The rebar contribution to the element stress-carrying capacity will +not be affected unless damage is also included in the rebar material definition; in that case the rebar +contribution to the element stress-carrying capacity will also be degraded after the damage initiation +criterion specified for the rebar is met. For the default choice of element deletion, the element is +removed from the mesh when at any one integration location all section points in the base material and +rebar are fully degraded. +Elements +Damage evolution for ductile metals can be defined for any element that can be used with the damage +initiation criteria for ductile metals in Abaqus (“Damage initiation for ductile metals,” Section 24.2.2). +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2), +the +following variables have special meaning when damage evolution is specified: +STATUS +SDEG +Status of element (the status of an element is 1.0 if the element is active, 0.0 if the +element is not). +Overall scalar stiffness degradation, D. +Additional reference +• Hillerborg, A., M. Modeer, and P. E. Petersson, “Analysis of Crack Formation and Crack Growth +in Concrete by Means of Fracture Mechanics and Finite Elements,” Cement and Concrete Research, +vol. 6, pp. 773–782, 1976. +24.3 +Damage and failure for fiber-reinforced composites +• “Damage and failure for fiber-reinforced composites: overview,” Section 24.3.1 +• “Damage initiation for fiber-reinforced composites,” Section 24.3.2 +• “Damage evolution and element removal for fiber-reinforced composites,” Section 24.3.3 +24.3.1 +DAMAGE AND FAILURE FOR FIBER-REINFORCED COMPOSITES: OVERVIEW +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Progressive damage and failure,” Section 24.1.1 +• “Damage initiation for fiber-reinforced composites,” Section 24.3.2 +• “Damage evolution and element removal for fiber-reinforced composites,” Section 24.3.3 +• *DAMAGE INITIATION +• *DAMAGE EVOLUTION +• *DAMAGE STABILIZATION +• “Hashin damage” in “Defining damage,” Section 12.9.3 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +Abaqus offers a damage model enabling you to predict the onset of damage and to model damage +evolution for elastic-brittle materials with anisotropic behavior. The model is primarily intended to be +used with fiber-reinforced materials since they typically exhibit such behavior. +This damage model requires specification of the following: +• the undamaged response of the material, which must be linearly elastic ; +• a damage initiation criterion ; and +• a damage evolution response, including a choice of element removal . +General concepts of damage in unidirectional lamina +Damage is characterized by the degradation of material stiffness. It plays an important role in the analysis +of fiber-reinforced composite materials. Many such materials exhibit elastic-brittle behavior; that is, +damage in these materials is initiated without significant plastic deformation. Consequently, plasticity +can be neglected when modeling behavior of such materials. +The fibers in the fiber-reinforced material are assumed to be parallel, as depicted in Figure 24.3.1–1. +You must specify material properties in a local coordinate system defined by the user. The lamina is in the +1–2 plane, and the local 1 direction corresponds to the fiber direction. You must specify the undamaged +material response using one of the methods for defining an orthotropic linear elastic material (“Linear +elastic behavior,” Section 22.2.1); the most convenient of which is the method for defining an orthotropic +material in plane stress (“Defining orthotropic elasticity in plane stress” in “Linear elastic behavior,” +Figure 24.3.1–1 Unidirectional lamina. +Section 22.2.1). However, the material response can also be defined in terms of the engineering constants +or by specifying the elastic stiffness matrix directly. +The Abaqus anisotropic damage model is based on the work of Matzenmiller et. al (1995), Hashin +and Rotem (1973), Hashin (1980), and Camanho and Davila (2002). +Four different modes of failure are considered: +• fiber rupture in tension; +• fiber buckling and kinking in compression; +• matrix cracking under transverse tension and shearing; and +• matrix crushing under transverse compression and shearing. +In Abaqus the onset of damage is determined by the initiation criteria proposed by Hashin and +Rotem (1973) and Hashin (1980), in which the failure surface is expressed in the effective stress space +(the stress acting over the area that effectively resists the force). These criteria are discussed in detail in +“Damage initiation for fiber-reinforced composites,” Section 24.3.2. +The response of the material is computed from +where +is the strain and +is the elasticity matrix, which reflects any damage and has the form +where +current state of matrix damage, +in the fiber direction, +shear modulus, and +and +, +reflects the current state of fiber damage, +reflects the current state of shear damage, +reflects the +is the Young’s modulus +is the +is the Young’s modulus in the direction perpendicular to the fibers, +are Poisson’s ratios. +The evolution of the elasticity matrix due to damage is discussed in more detail in “Damage +that section also +evolution and element removal for fiber-reinforced composites,” Section 24.3.3; +discusses: +• options for treating severe damage (“Maximum degradation and choice of element removal” in +“Damage evolution and element removal for fiber-reinforced composites,” Section 24.3.3); and +• viscous regularization (“Viscous regularization” in “Damage evolution and element removal for +fiber-reinforced composites,” Section 24.3.3). +Elements +The fiber-reinforced composite damage model must be used with elements with a plane stress +formulation, which include plane stress, shell, continuum shell, and membrane elements. +Additional references +• Camanho, P. P., and C. G. Davila, “Mixed-Mode Decohesion Finite Elements for the Simulation +of Delamination in Composite Materials,” NASA/TM-2002–211737, pp. 1–37, 2002. +• Hashin, Z., “Failure Criteria for Unidirectional Fiber Composites,” Journal of Applied Mechanics, +vol. 47, pp. 329–334, 1980. +• Hashin, Z., and A. Rotem, “A Fatigue Criterion for Fiber-Reinforced Materials,” Journal of +Composite Materials, vol. 7, pp. 448–464, 1973. +• Matzenmiller, A., J. Lubliner, and R. L. Taylor, “A Constitutive Model for Anisotropic Damage in +Fiber-Composites,” Mechanics of Materials, vol. 20, pp. 125–152, 1995. +24.3.2 +DAMAGE INITIATION FOR FIBER-REINFORCED COMPOSITES +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Progressive damage and failure,” Section 24.1.1 +• “Damage evolution and element removal for fiber-reinforced composites,” Section 24.3.3 +• *DAMAGE INITIATION +• “Hashin damage” in “Defining damage,” Section 12.9.3 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +The material damage initiation capability for fiber-reinforced materials: +• requires that the behavior of the undamaged material is linearly elastic ; +• is based on Hashin’s theory (Hashin and Rotem, 1973, and Hashin, 1980); +• takes into account four different failure modes: fiber tension, fiber compression, matrix tension, and +matrix compression; and +• can be used in combination with the damage evolution model described in “Damage evolution and +element removal for fiber-reinforced composites,” Section 24.3.3 . +Damage Initiation +Damage initiation refers to the onset of degradation at a material point. In Abaqus the damage initiation +criteria for fiber-reinforced composites are based on Hashin’s theory . These criteria consider four different damage initiation mechanisms: fiber tension, fiber +compression, matrix tension, and matrix compression. +The initiation criteria have the following general forms: +Fiber tension +: +Fiber compression +: +Matrix tension +: +Matrix compression +: +In the above equations +denotes the longitudinal tensile strength; +denotes the longitudinal compressive strength; +denotes the transverse tensile strength; +denotes the transverse compressive strength; +denotes the longitudinal shear strength; +denotes the transverse shear strength; +is a coefficient that determines the contribution of the shear stress to the fiber +tensile initiation criterion; and +are components of the effective stress tensor, +initiation criteria and which is computed from: +, that is used to evaluate the +where +is the true stress and +is the damage operator: +, +, and +are internal (damage) variables that characterize fiber, matrix, and +, +shear damage, which are derived from damage variables +, +corresponding to the four modes previously discussed, as follows: +, and +, +Prior to any damage initiation and evolution the damage operator, +, is equal to the identity matrix, +so +. Once damage initiation and evolution has occurred for at least one mode, the damage operator +becomes significant in the criteria for damage initiation of other modes (see “Damage evolution and +element removal for fiber-reinforced composites,” Section 24.3.3, for discussion of damage evolution). +The effective stress, +, is intended to represent the stress acting over the damaged area that effectively +resists the internal forces. +The initiation criteria presented above can be specialized to obtain the model proposed in Hashin +or the model proposed in Hashin (1980) by +and +and Rotem (1973) by setting +setting +. +An output variable is associated with each initiation criterion (fiber tension, fiber compression, +matrix tension, matrix compression) to indicate whether the criterion has been met. A value of 1.0 +or higher indicates that the initiation criterion has been met . If you +define a damage initiation model without defining an associated evolution law, the initiation criteria will +affect only output. Thus, you can use these criteria to evaluate the propensity of the material to undergo +damage without modeling the damage process. +Input File Usage: +Use the following option to define the Hashin damage initiation criterion: +*DAMAGE INITIATION, CRITERION=HASHIN, ALPHA= +, +, +, +, +, +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Damage for Fiber- +Reinforced Composites→Hashin Damage +Elements +The damage initiation criteria must be used with elements with a plane stress formulation, which include +plane stress, shell, continuum shell, and membrane elements. +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Standard output variable +the +identifiers,” Section 4.2.1, and, “Abaqus/Explicit output variable identifiers,” Section 4.2.2), +following variables relate specifically to damage initiation at a material point in the fiber-reinforced +composite damage model: +DMICRT +HSNFTCRT +HSNFCCRT +HSNMTCRT +HSNMCCRT +All damage initiation criteria components. +Maximum value of the fiber tensile initiation criterion experienced during the +analysis. +Maximum value of the fiber compressive initiation criterion experienced during +the analysis. +Maximum value of the matrix tensile initiation criterion experienced during the +analysis. +Maximum value of the matrix compressive initiation criterion experienced during +the analysis. +For the variables above that indicate whether an initiation criterion in a damage mode has been satisfied +or not, a value that is less than 1.0 indicates that the criterion has not been satisfied, while a value of +1.0 or higher indicates that the criterion has been satisfied. If you define a damage evolution model, the +maximum value of this variable does not exceed 1.0. However, if you do not define a damage evolution +model, this variable can have values higher than 1.0, which indicates by how much the criterion has been +exceeded. +Additional references +• Hashin, Z., “Failure Criteria for Unidirectional Fiber Composites,” Journal of Applied Mechanics, +vol. 47, pp. 329–334, 1980. +• Hashin, Z., and A. Rotem, “A Fatigue Criterion for Fiber-Reinforced Materials,” Journal of +Composite Materials, vol. 7, pp. 448–464, 1973. +24.3.3 +DAMAGE EVOLUTION AND ELEMENT REMOVAL FOR FIBER-REINFORCED +COMPOSITES +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Progressive damage and failure,” Section 24.1.1 +• “Damage initiation for fiber-reinforced composites,” Section 24.3.2 +• *DAMAGE EVOLUTION +• “Damage evolution” in “Defining damage,” Section 12.9.3 of the Abaqus/CAE User’s Manual, in +the online HTML version of this manual +Overview +The damage evolution capability for fiber-reinforced materials in Abaqus: +• assumes that damage is characterized by progressive degradation of material stiffness, leading to +material failure; +• requires linearly elastic behavior of the undamaged material ; +• takes into account four different failure modes: fiber tension, fiber compression, matrix tension, and +matrix compression; +• uses four damage variables to describe damage for each failure mode; +• must be used in combination with Hashin’s damage initiation criteria (“Damage initiation for fiber- +reinforced composites,” Section 24.3.2); +• is based on energy dissipation during the damage process; +• offers options for what occurs upon failure, including the removal of elements from the mesh; and +• can be used in conjunction with a viscous regularization of the constitutive equations to improve +the convergence rate in the softening regime. +Damage evolution +The previous section (“Damage initiation for fiber-reinforced composites,” Section 24.3.2) discussed the +damage initiation in plane stress fiber-reinforced composites. This section will discuss the post-damage +initiation behavior for cases in which a damage evolution model has been specified. Prior to damage +initiation the material is linearly elastic, with the stiffness matrix of a plane stress orthotropic material. +Thereafter, the response of the material is computed from +where +is the strain and +is the damaged elasticity matrix, which has the form +where +current state of matrix damage, +in the fiber direction, +and +are Poisson’s ratios. +The damage variables +, +reflects the current state of fiber damage, +reflects the current state of shear damage, +reflects the +is the Young’s modulus +is the Young’s modulus in the matrix direction, +is the shear modulus, and +, +, and +are derived from damage variables +, +, +, and +, +corresponding to the four failure modes previously discussed, as follows: +and +are components of the effective stress tensor. The effective stress tensor is primarily +used to evaluate damage initiation criteria; see “Damage initiation for fiber-reinforced composites,” +Section 24.3.2, for a description of how the effective stress tensor is computed. +Evolution of damage variables for each mode +To alleviate mesh dependency during material softening, Abaqus introduces a characteristic length into +the formulation, so that the constitutive law is expressed as a stress-displacement relation. The damage +variable will evolve such that the stress-displacement behaves as shown in Figure 24.3.3–1 in each of +the four failure modes. The positive slope of the stress-displacement curve prior to damage initiation +corresponds to linear elastic material behavior; the negative slope after damage initiation is achieved by +evolution of the respective damage variables according to the equations shown below. +Equivalent displacement and stress for each of the four damage modes are defined as follows: +Fiber tension +: +Fiber compression +: +equivalent +stress +σ eq +δ eq +δ eq +equivalent displacement +Figure 24.3.3–1 Equivalent stress versus equivalent displacement. +Matrix tension +: +Matrix compression +: +The characteristic length, +, is based on the element geometry and formulation: it is a typical length of +a line across an element for a first-order element; it is half of the same typical length for a second-order +element. For membranes and shells it is a characteristic length in the reference surface, computed as the +square root of the area. The symbol +in the equations above represents the Macaulay bracket operator, +which is defined for every +as +. +After damage initiation (i.e., +) for the behavior shown in Figure 24.3.3–1, the damage +variable for a particular mode is given by the following expression +is the initial equivalent displacement at which the initiation criterion for that mode was met +is the displacement at which the material is completely damaged in this failure mode. The above +where +and +relation is presented graphically in Figure 24.3.3–2. +damage +variable +1.0 +δ eq +δ eq +equivalent displacement +Figure 24.3.3–2 Damage variable as a function of equivalent displacement. +for the various modes depend on the elastic stiffness and the strength parameters +The values of +specified as part of the damage initiation definition . For each failure mode you must specify the energy dissipated due to +failure, +for +the various modes depend on the respective +, which corresponds to the area of the triangle OAC in Figure 24.3.3–3. The values of +values. +Unloading from a partially damaged state, such as point B in Figure 24.3.3–3, occurs along a linear +path toward the origin in the plot of equivalent stress vs. equivalent displacement; this same path is +followed back to point B upon reloading as shown in the figure. +equivalent +stress +δ eq +δ eq +equivalent displacement +Figure 24.3.3–3 Linear damage evolution. +Input File Usage: +Use the following option to define the damage evolution law: +*DAMAGE EVOLUTION, TYPE=ENERGY, SOFTENING=LINEAR +, +, +, +, +, +where +are energies dissipated during damage for +fiber tension, fiber compression, matrix tension, and matrix compression failure +modes, respectively. +, and +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Damage for Fiber- +Reinforced Composites→Hashin Damage: +Suboptions→Damage +Evolution: Type: Energy: Softening: Linear +Maximum degradation and choice of element removal +You have control over how Abaqus treats elements with severe damage. By default, the upper bound to +all damage variables at a material point is +. You can reduce this upper bound as discussed +in “Controlling element deletion and maximum degradation for materials with damage evolution” in +“Section controls,” Section 27.1.4. +By default, +in Abaqus/Standard an element +is removed (deleted) once damage variables +for all failure modes at all material points reach +. In +Abaqus/Explicit a material point is assumed to fail when either of the damage variables associated with +fiber failure modes (tensile or compressive) reaches +and the element is removed from the mesh +when this condition is satisfied at all of the section points at any one integration location of an element; +for example, in the case of shell elements all through-the-thickness section points at any one integration +location of the element must fail before the element is removed from the mesh. If an element is removed, +the output variable STATUS is set to zero for the element, and it offers no resistance to subsequent +deformation. Elements that have been removed are not displayed when you view the deformed model +in the Visualization module of Abaqus/CAE (Abaqus/Viewer). However, the elements still remain in +the Abaqus model. You can choose to display removed elements by suppressing use of the STATUS +variable . +Alternatively, you can specify that an element should remain in the model even after all of the +. In this case, once all the damage variables reach the maximum value, the +damage variables reach +stiffness, +, remains constant . +Difficulties associated with element removal in Abaqus/Standard +When elements are removed from the model, their nodes will still remain in the model even if they are not +attached to any active elements. When the solution progresses, these nodes might undergo non-physical +displacements due to the extrapolation scheme used in Abaqus/Standard to speed up the solution . These non-physical displacements can +be prevented by turning off the extrapolation. In addition, applying a point load to a node that is not +attached to an active element will cause convergence difficulties since there is no stiffness to resist the +load. It is the responsibility of the user to prevent such situations. +Viscous regularization +Material models exhibiting softening behavior and stiffness degradation often lead to severe convergence +difficulties in implicit analysis programs, such as Abaqus/Standard. You can overcome some of these +convergence difficulties by using the viscous regularization scheme, which causes the tangent stiffness +matrix of the softening material to be positive for sufficiently small time increments. +In this regularization scheme a viscous damage variable is defined by the evolution equation: +where +is the viscosity coefficient representing the relaxation time of the viscous system and d is the +damage variable evaluated in the inviscid backbone model. The damaged response of the viscous +material is given as +where the damaged elasticity matrix, +, is computed using viscous values of damage variables for each +failure mode. Using viscous regularization with a small value of the viscosity parameter (small compared +to the characteristic time increment) usually helps improve the rate of convergence of the model in the +softening regime, without compromising results. The basic idea is that the solution of the viscous system +relaxes to that of the inviscid case as +, where t represents time. +Viscous regularization is also available in Abaqus/Explicit. Viscous regularization slows down the +rate of increase of damage and leads to increased fracture energy with increasing deformation rates, +which can be exploited as an effective method of modeling rate-dependent material behavior. +In Abaqus/Standard the approximate amount of energy associated with viscous regularization over +the whole model or over an element set is available using output variable ALLCD. +Defining viscous regularization coefficients +You can specify different values of viscous coefficients for different failure modes. +Input File Usage: +Use the following option to define viscous coefficients: +*DAMAGE STABILIZATION +, +, +, +, +, +where +are viscosity coefficients for fiber tension, +fiber compression, matrix tension, and matrix compression failure modes, +respectively. +, +Abaqus/CAE Usage: +Use the following input to define the viscous coefficients for fiber-reinforced +materials: +Property module: material editor: Mechanical→Damage +for Fiber-Reinforced Composites→Hashin Damage: +Suboptions→Damage Stabilization +Applying a single viscous coefficient in Abaqus/Standard +Alternatively, in Abaqus/Standard you can specify the viscous coefficients as part of a section controls +definition. +In this case the same viscous coefficient will be applied to all failure modes. For more +information, see “Using viscous regularization with cohesive elements, connector elements, and elements +that can be used with the damage evolution models for ductile metals and fiber-reinforced composites in +Abaqus/Standard” in “Section controls,” Section 27.1.4. +Material damping +If stiffness proportional damping is specified in combination with the damage evolution law for fiber- +reinforced materials, Abaqus calculates the damping stresses using the damaged elastic stiffness. +Elements +The damage evolution law for fiber-reinforced materials must be used with elements with a plane stress +formulation, which include plane stress, shell, continuum shell, and membrane elements. +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Standard output variable +identifiers,” Section 4.2.1), the following variables relate specifically to damage evolution in the fiber- +reinforced composite damage model: +STATUS +Status of the element (the status of an element is 1.0 if the element is active, 0.0 +if the element is not). The value of this variable is set to 0.0 only if damage has +occurred in all the damage modes. +DAMAGEFT +Fiber tensile damage variable. +DAMAGEFC +Fiber compressive damage variable. +DAMAGEMT +Matrix tensile damage variable. +DAMAGEMC +Matrix compressive damage variable. +DAMAGESHR +Shear damage variable. +EDMDDEN +Energy dissipated per unit volume in the element by damage. +ELDMD +DMENER +ALLDMD +ECDDEN +ELCD +CENER +ALLCD +Total energy dissipated in the element by damage. +Energy dissipated per unit volume by damage. +Energy dissipated in the whole (or partial) model by damage. +Energy per unit volume in the element +regularization. +that +is associated with viscous +Total energy in the element that is associated with viscous regularization. +Energy per unit volume that is associated with viscous regularization. +The approximate amount of energy over the whole model or over an element set +that is associated with viscous regularization. +24.4 +Damage and failure for ductile materials in low-cycle fatigue +analysis +• “Damage and failure for ductile materials in low-cycle fatigue analysis: overview,” Section 24.4.1 +• “Damage initiation for ductile materials in low-cycle fatigue,” Section 24.4.2 +• “Damage evolution for ductile materials in low-cycle fatigue,” Section 24.4.3 +24.4.1 +DAMAGE AND FAILURE FOR DUCTILE MATERIALS IN LOW-CYCLE FATIGUE +ANALYSIS: OVERVIEW +Product: Abaqus/Standard +References +• “Progressive damage and failure,” Section 24.1.1 +• “Damage initiation for ductile materials in low-cycle fatigue,” Section 24.4.2 +• “Damage evolution for ductile materials in low-cycle fatigue,” Section 24.4.3 +• “Low-cycle fatigue analysis using the direct cyclic approach,” Section 6.2.7 +• *DAMAGE INITIATION +• *DAMAGE EVOLUTION +Overview +Abaqus/Standard offers a general capability for modeling progressive damage and failure of ductile +materials due to stress reversals and the accumulation of inelastic strain energy in a low-cycle fatigue +analysis using the direct cyclic approach. In the most general case this requires the specification of the +following: +• the undamaged ductile materials in any elements (including cohesive elements based on a continuum +approach) whose response is defined in terms of a continuum-based constitutive model (“Material +library: overview,” Section 21.1.1); +• a damage initiation criterion (“Damage initiation for ductile materials in low-cycle fatigue,” +Section 24.4.2); and +• a damage evolution response (“Damage evolution for ductile materials in low-cycle fatigue,” +Section 24.4.3). +A summary of the general framework for progressive damage and failure in Abaqus is given in +“Progressive damage and failure,” Section 24.1.1. This section provides an overview of the damage +initiation criteria and damage evolution law for ductile materials in a low-cycle fatigue analysis using +the direct cyclic approach. +General concepts of damage of ductile materials in low-cycle fatigue +Accurately and effectively predicting the fatigue life for an inelastic structure, such as a solder joint in +an electronic chip packaging, subjected to sub-critical cyclic loading is a challenging problem. Cyclic +thermal or mechanical loading often leads to stress reversals and the accumulation of inelastic strain, +which may in turn lead to the initiation and propagation of a crack. The low-cycle fatigue analysis +capability in Abaqus/Standard uses a direct cyclic approach (“Low-cycle fatigue analysis using the +direct cyclic approach,” Section 6.2.7) to model progressive damage and failure based on a continuum +damage approach. The damage initiation (“Damage initiation for ductile materials in low-cycle +fatigue,” Section 24.4.2) and evolution (“Damage evolution for ductile materials in low-cycle fatigue,” +Section 24.4.3) are characterized by the stabilized accumulated inelastic hysteresis strain energy per +cycle proposed by Darveaux (2002) and Lau (2002). +The damage evolution law describes the rate of degradation of the material stiffness per cycle once +the corresponding initiation criterion has been reached. For damage in ductile materials Abaqus/Standard +assumes that the degradation of the stiffness can be modeled using a scalar damage variable, +. At any +given cycle during the analysis the stress tensor in the material is given by the scalar damage equation +where +damage computed in the current increment. The material has lost its load carrying capacity when +is the effective (or undamaged) stress tensor that would exist in the material in the absence of +. +Elements +The failure modeling capability for ductile materials can be used with any elements (including cohesive +elements based on a continuum approach) in Abaqus/Standard that include mechanical behavior +(elements that have displacement degrees of freedom). +Additional references +• Darveaux, R., “Effect of Simulation Methodology on Solder Joint Crack Growth Correlation and +Fatigue Life Prediction,” Journal of Electronic Packaging, vol. 124, pp. 147–154, 2002. +• Lau, J., S. Pan, and C. Chang, “A New Thermal-Fatigue Life Prediction Model for Wafer +Level Chip Scale Package (WLCSP) Solder Joints,” Journal of Electronic Packaging, vol. 124, +pp. 212–220, 2002. +24.4.2 +DAMAGE INITIATION FOR DUCTILE MATERIALS IN LOW-CYCLE FATIGUE +Product: Abaqus/Standard +References +• “Progressive damage and failure,” Section 24.1.1 +• *DAMAGE INITIATION +Overview +The material damage initiation capability for ductile materials based on inelastic hysteresis energy: +• is intended as a general capability for predicting initiation of damage in ductile materials in a low- +cycle fatigue analysis; +• can be used in combination with the damage evolution law for ductile materials described in +“Damage evolution for ductile materials in low-cycle fatigue,” Section 24.4.3; and +• can be used only in a low-cycle fatigue analysis using the direct cyclic approach (“Low-cycle fatigue +analysis using the direct cyclic approach,” Section 6.2.7). +Damage initiation criteria for ductile materials +The damage initiation criterion is a phenomenological model for predicting the onset of damage due to +stress reversals and the accumulation of inelastic strain in a low-cycle fatigue analysis. It is characterized +by the accumulated inelastic hysteresis energy per cycle, +, in a material point when the structure +response is stabilized in the cycle. The cycle number in which damage is initiated is given by +where +are working; some care is required to modify when converting to a different system of units. +are material constants. The value of +is dependent on the system of units in which you +and +The initiation criterion can be used in conjunction with any ductile material. +Input File Usage: +*DAMAGE INITIATION, CRITERION=HYSTERESIS ENERGY +Elements +The damage initiation criteria for ductile materials can be used with any elements in Abaqus/Standard +that include mechanical behavior (elements that have displacement degrees of freedom). This includes +cohesive elements based on a continuum approach (“Modeling of an adhesive layer of finite thickness” in +“Defining the constitutive response of cohesive elements using a continuum approach,” Section 32.5.5). +Output +In addition to the standard output identifiers available in Abaqus/Standard (“Abaqus/Standard output +variable identifiers,” Section 4.2.1), the following variable has special meaning when a damage initiation +criterion is specified: +CYCLEINI +Number of cycles to initialize the damage at the material point. +24.4.3 +DAMAGE EVOLUTION FOR DUCTILE MATERIALS IN LOW-CYCLE FATIGUE +Product: Abaqus/Standard +References +• “Progressive damage and failure,” Section 24.1.1 +• *DAMAGE EVOLUTION +Overview +The damage evolution capability for ductile materials based on inelastic hysteresis energy: +• assumes that damage is characterized by the progressive degradation of the material stiffness, +leading to material failure; +• must be used in combination with a damage initiation criterion for ductile materials in low-cycle +fatigue analysis (“Damage initiation for ductile materials in low-cycle fatigue,” Section 24.4.2); +• uses the inelastic hysteresis energy per stabilized cycle to drive the evolution of damage after damage +initiation; and +• must be used in conjunction with the linear elastic material model (“Linear elastic behavior,” +the porous elastic material model (“Elastic behavior of porous materials,” +Section 22.2.1), +Section 22.3.1), or the hypoelastic material model (“Hypoelastic behavior,” Section 22.4.1). +Damage evolution based on accumulated inelastic hysteresis energy +Once the damage initiation criterion (“Damage initiation for ductile materials in low-cycle fatigue,” +Section 24.4.2) is satisfied at a material point, the damage state is calculated and updated based on the +inelastic hysteresis energy for the stabilized cycle. The rate of the damage in a material point per cycle +is given by +are material constants, and +and +where +point. The value of +required to modify when converting to a different system of units. +is the characteristic length associated with an integration +is dependent on the system of units in which you are working; some care is +For damage in ductile materials Abaqus/Standard assumes that the degradation of the elastic +. At any given loading cycle during the +stiffness can be modeled using the scalar damage variable, +analysis the stress tensor in the material is given by the scalar damage equation +where +is the effective (or undamaged) stress tensor that would exist in the material in the absence of +damage computed in the current increment. The material has completely lost its load carrying capacity +when +. You can remove the element from the mesh if all of the section points at all integration +locations have lost their loading carrying capability. +Input File Usage: +*DAMAGE EVOLUTION, TYPE=HYSTERESIS ENERGY +Mesh dependency and characteristic length +The implementation of the damage evolution model requires the definition of a characteristic length +associated with an integration point. The characteristic length is based on the element geometry and +formulation: it is a typical length of a line across an element for a first-order element; it is half of the +same typical length for a second-order element. For beams and trusses it is a characteristic length along +the element axis. For membranes and shells it is a characteristic length in the reference surface. For +axisymmetric elements it is a characteristic length in the r–z plane only. For cohesive elements it is equal +to the constitutive thickness. This definition of the characteristic length is used because the direction in +which fracture occurs is not known in advance. Therefore, elements with large aspect ratios will have +rather different behavior depending on the direction in which the damage occurs: some mesh sensitivity +remains because of this effect, and elements that are as close to square as possible are recommended. +However, since the damage evolution law is energy based, mesh dependency of the results may be +alleviated. +Maximum degradation and element removal +You can control how Abaqus/Standard treats elements with severe damage. +Defining the upper bound to the damage variable +. You can reduce +By default, the upper bound to all damage variables at a material point is +this upper bound as discussed in “Controlling element deletion and maximum degradation for materials +with damage evolution” in “Section controls,” Section 27.1.4. +Input File Usage: +*SECTION CONTROLS, MAX DEGRADATION= +Controlling element removal for damaged elements +By default, in Abaqus/Standard an element is removed (deleted) once D reaches +at all of the +section points at all integration locations in the element. If an element is removed, the output variable +STATUS is set to zero for the element, and it offers no resistance to subsequent deformation. However, +the element still remains in the Abaqus/Standard model and may be visible during postprocessing. In +the Visualization module of Abaqus/CAE, you can suppress the display of elements based on their status +. +Alternatively, you can specify that an element should remain in the model even after all of the +. In this case, once all the damage variables reach the maximum value, the +damage variables reach +stiffness remains constant. +Input File Usage: +Use the following option to delete failed elements from the mesh (default): +*SECTION CONTROLS, ELEMENT DELETION=YES +Use the following option to keep failed elements in the mesh computations: +*SECTION CONTROLS, ELEMENT DELETION=NO +Difficulties associated with element removal in Abaqus/Standard +When elements are removed from the model, their nodes remain in the model even if they are not +attached to any active elements. When the solution progresses, these nodes might undergo non-physical +displacements in Abaqus/Standard. In addition, applying a point load to a node that is not attached to an +active element will cause convergence difficulties since there is no stiffness to resist the load. It is the +responsibility of the user to prevent such situations. +Elements +Damage evolution for ductile materials can be defined for any element that can be used with the damage +initiation criteria for a low-cycle fatigue analysis in Abaqus/Standard (“Damage initiation for ductile +materials in low-cycle fatigue,” Section 24.4.2). +Output +In addition to the standard output identifiers available in Abaqus/Standard (“Abaqus/Standard output +the following variables have special meaning when damage +variable identifiers,” Section 4.2.1), +evolution is specified: +STATUS +SDEG +Status of element (the status of an element is 1.0 if the element is active, 0.0 if the +element is not). +Overall scalar stiffness degradation, D. +25. +Hydrodynamic Properties +Overview +Equations of state +25.1 +25.1 +Overview +• “Hydrodynamic behavior: overview,” Section 25.1.1 +25.1.1 +HYDRODYNAMIC BEHAVIOR: OVERVIEW +library in Abaqus/Explicit +The material +includes several equation of state models to describe the +hydrodynamic behavior of materials. An equation of state is a constitutive equation that defines the pressure +as a function of the density and the internal energy (“Equation of state,” Section 25.2.1). The following +equations of state are supported in Abaqus/Explicit: +• Mie-Grüneisen equation of state: The Mie-Grüneisen equation of state (“Mie-Grüneisen equations +of state” in “Equation of state,” Section 25.2.1) is used to model materials at high pressure. It is linear +in energy and assumes a linear relationship between the shock velocity and the particle velocity. +• Tabulated equation of state: The tabulated equation of state (“Tabulated equation of state” in +“Equation of state,” Section 25.2.1) is used to model the hydrodynamic response of materials that exhibit +sharp transitions in the pressure-density relationship, such as those induced by phase transformations. +It is linear in energy. +• P – α equation of state: The +equation of state (“P – α equation of state” in “Equation of +state,” Section 25.2.1) is designed for modeling the compaction of ductile porous materials. The +constitutive model captures the irreversible compaction behavior at low stresses and predicts the +correct thermodynamic behavior at high pressures for the fully compacted solid material. +It is used +in combination with either the Mie-Grüneisen equation of state or the tabulated equation of state to +describe the solid phase. +• JWL high explosive equation of state: The Jones-Wilkens-Lee (or JWL) equation of state (“JWL +high explosive equation of state” in “Equation of state,” Section 25.2.1) models the pressure generated +by the release of chemical energy in an explosive. This model is implemented in a form referred to as +a programmed burn, which means that the reaction and initiation of the explosive is not determined by +shock in the material. Instead, the initiation time is determined by a geometric construction using the +detonation wave speed and the distance of the material point from the detonation points. +• Ideal gas equation of state: The ideal gas equation of state (“Ideal gas equation of state” in “Equation +of state,” Section 25.2.1) is an idealization to real gas behavior and can be used to model any gases +approximately under appropriate conditions (e.g., low pressure and high temperature). +Deviatoric behavior +The material modeled by an equation of state may have no deviatoric strength or may have either isotropic +elastic or viscous (both Newtonian and non-Newtonian) deviatoric behavior (“Deviatoric behavior” in +“Equation of state,” Section 25.2.1). The elastic model can be used by itself or in conjunction with +the Mises, the Johnson-Cook, or the extended Drucker-Prager plasticity models to model hydrodynamic +materials with elastic-plastic deviatoric behavior. +Thermal strain +Thermal expansion cannot be introduced for any of the equation of state models. +25.2 +Equations of state +• “Equation of state,” Section 25.2.1 +25.2.1 +EQUATION OF STATE +Products: Abaqus/Explicit Abaqus/CAE +References +• “Hydrodynamic behavior: overview,” Section 25.1.1 +• “Material library: overview,” Section 21.1.1 +• *EOS +• *EOS COMPACTION +• *ELASTIC +• *VISCOSITY +• *DETONATION POINT +• *GAS SPECIFIC HEAT +• *REACTION RATE +• *TENSILE FAILURE +• “Defining equations of state” in “Defining other mechanical models,” Section 12.9.4 of the +Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +Equations of state: +• provide a hydrodynamic material model in which the material’s volumetric strength is determined +by an equation of state; +• determine the pressure (positive in compression) as a function of the density, +energy (the internal energy per unit mass), +: +; +• are available as Mie-Grüneisen equations of state (thus providing the linear +• are available as tabulated equations of state linear in energy; +• are available as +equations of state for the compaction of ductile porous materials and must +be used in conjunction with either the Mie-Grüneisen or the tabulated equation of state for the solid +phase; +, and the specific +Hugoniot form); +• are available as JWL high explosive equations of state; +• are available as ignition and growth equations of state; +• are available in the form of an ideal gas; +• assume an adiabatic condition unless a dynamic fully coupled temperature-displacement analysis is +used; +• can be used to model a material that has only volumetric strength (the material is assumed to have +no shear strength) or a material that also has isotropic elastic or viscous deviatoric behavior; +• can be used with the Mises (“Classical metal plasticity,” Section 23.2.1) or the Johnson-Cook +(“Johnson-Cook plasticity,” Section 23.2.7) plasticity models; +• can be used with the extended Drucker-Prager (“Extended Drucker-Prager models,” Section 23.3.1) +plasticity models (without plastic dilation); and +• can be used with the tensile failure model (“Dynamic failure models,” Section 23.2.8) to model +dynamic spall or a pressure cutoff. +Energy equation and Hugoniot curve +, to the +The equation for conservation of energy equates the increase in internal energy per unit mass, +rate at which work is being done by the stresses and the rate at which heat is being added. In the absence +of heat conduction the energy equation can be written as +where p is the pressure stress defined as positive in compression, +viscosity, +unit mass. +is the deviatoric stress tensor, +is the deviatoric part of strain rate, and +is the pressure stress due to the bulk +is the heat rate per +The equation of state is assumed for the pressure as a function of the current density, +, and the +internal energy per unit mass, +: +which defines all the equilibrium states that can exist in a material. The internal energy can be +eliminated from the above equation to obtain a p versus V relationship (where V is the current volume) +or, equivalently, a p versus +relationship that is unique to the material described by the equation +of state model. This unique relationship is called the Hugoniot curve and is the locus of p–V states +achievable behind a shock . +pH +pH|1 +pH|0 +Figure 25.2.1–1 A schematic representation of a Hugoniot curve. +The Hugoniot pressure, +experimental data. +, is a function of density only and can be defined, in general, from fitting +An equation of state is said to be linear in energy when it can be written in the form +where +and +are functions of density only and depend on the particular equation of state model. +Mie-Grüneisen equations of state +A Mie-Grüneisen equation of state is linear in energy. The most common form is +where +density only, and +and +are the Hugoniot pressure and specific energy (per unit mass) and are functions of +is the Grüneisen ratio defined as +where +is a material constant and +The Hugoniot energy, +is the reference density. +, is related to the Hugoniot pressure by +where +above equations yields +is the nominal volumetric compressive strain. Elimination of +and +from the +The equation of state and the energy equation represent coupled equations for pressure and internal +energy. Abaqus/Explicit solves these equations simultaneously at each material point. +Linear Us − Up Hugoniot form +A common fit to the Hugoniot data is given by +where +velocity, +and s define the linear relationship between the linear shock velocity, +, and the particle +, as follows: +With the above assumptions the linear +Hugoniot form is written as +where +is equivalent to the elastic bulk modulus at small nominal strains. +There is a limiting compression given by the denominator of this form of the equation of state +or +At this limit there is a tensile minimum; thereafter, negative sound speeds are calculated for the material. +Input File Usage: +Abaqus/CAE Usage: +Initial state +Use both of the following options: +*DENSITY (to specify the reference density +*EOS, TYPE=USUP (to specify the variables +Property module: material editor: +General→Density (to specify the reference density +Mechanical→Eos: Type: Us - Up (to specify the variables +, s, and +) +) +) +, s, and +) +, and pressure +The initial state of the material is determined by the initial values of specific energy, +stress, p. Abaqus/Explicit will automatically compute the initial density, +, that satisfies the equation +of state, +. You can define the initial specific energy and initial stress state . The initial pressure used by +the equation of state is inferred from the specified stress states. If no initial conditions are specified, +Abaqus/Explicit will assume that the material is at its reference state: +Input File Usage: +Abaqus/CAE Usage: +Use either or both of the following options, as required: +*INITIAL CONDITIONS, TYPE=SPECIFIC ENERGY +*INITIAL CONDITIONS, TYPE=STRESS +Load module: Create Predefined Field: Step: Initial: choose Mechanical +for the Category and Stress for the Types for Selected Step +Initial specific energy is not supported in Abaqus/CAE. +Tabulated equation of state +The tabulated equation of state provides flexibility in modeling the hydrodynamic response of materials +that exhibit sharp transitions in the pressure-density relationship, such as those induced by phase +transformations. The tabulated equation of state is linear in energy and assumes the form +where +and +are functions of the logarithmic volumetric strain +only, with +, and +is the reference density. +You can specify the functions +directly in tabular form. The tabular entries +must be given in descending values of the volumetric strain (that is, from the most tensile to the most +compressive states). Abaqus/Explicit will use a piecewise linear relationship between data points. +Outside the range of specified values of volumetric strains, the functions are extrapolated based on the +last slope computed from the data. +and +Input File Usage: +Use both of the following options: +*DENSITY (to specify the reference density +*EOS, TYPE=TABULAR (to specify +and +The tabulated equation of state is not supported in Abaqus/CAE. +as functions of +) +) +Abaqus/CAE Usage: +Initial state +, and pressure +The initial state of the material is determined by the initial values of specific energy, +stress, p. Abaqus/Explicit automatically computes the initial density, +, that satisfies the equation +of state. You can define the initial specific energy and initial stress state . The initial pressure used by the equation of +state is inferred from the specified stress states. If no initial conditions are specified, Abaqus/Explicit +assumes that the material is at its reference state: +Input File Usage: +Use either or both of the following options, as required: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=SPECIFIC ENERGY +*INITIAL CONDITIONS, TYPE=STRESS +Load module: Create Predefined Field: Step: Initial: choose Mechanical +for the Category and Stress for the Types for Selected Step +Initial specific energy is not supported in Abaqus/CAE. +P – α equation of state +The +equation of state is designed for modeling the compaction of ductile porous materials. The +implementation in Abaqus/Explicit is based on the model proposed by Hermann (1968) and Carroll +and Holt (1972). The constitutive model provides a detailed description of the irreversible compaction +behavior at low stresses and predicts the correct thermodynamic behavior at high pressures for the fully +compacted solid material. In Abaqus/Explicit the solid phase is assumed to be governed by either the +Mie-Grüneisen equation of state or the tabulated equation of state. The relevant properties of the porous +material in the virgin state, to be discussed later, and the material properties of the solid phase are specified +separately. +The porosity of the material, n, is defined as the ratio of pore volume, +, to total volume, +, where +is the solid volume. The porosity remains in the range +, with 0 indicating +full compaction. It is convenient to introduce a scalar variable , sometimes referred to as “distension,” +defined as the ratio of the density of the solid material, +, both +evaluated at the same temperature and pressure: +, to the density of the porous material, +For a fully compacted material +pores is negligible compared to that of the solid phase, +; otherwise, +is greater than 1. Assuming that the density of the +can be expressed in terms of the porosity n as +An equation of state is assumed for the pressure of the porous material as a function of +; current +density, +; and internal energy per unit mass, +, in the form +Assuming that the pores carry no pressure, it follows from equilibrium considerations that when a +pressure p is applied to the porous material, it gives rise to a volume-average pressure in the solid phase +equal to +. Assuming that the specific internal energies of the porous material and the solid +matrix are the same (i.e., neglecting the surface energy of the pores), the equation of state of the porous +material can be expressed as +where +is, when +correct thermodynamic behavior at high pressures. +is the equation of state of the solid material. For the fully compacted material (that +equation of state reduces to that of the solid phase, therefore predicting the +), the +The +equation of state must be supplemented by an equation that describes the behavior of +as a function of the thermodynamic state. This equation takes the form +is a state variable corresponding to the minimum value attained by +where +(irreversible) compaction of the material. The state variable is initialized to the elastic limit +material that is at its virgin state. The specific form of the function +is illustrated in Figure 25.2.1–2 and is discussed next. +during plastic +for a +used by Abaqus/Explicit +α 0 +α e +α min +α min +A el (p, α )e +A el (p, α )min +A el (p, α )min +A pl (p) +pe +p S +Figure 25.2.1–2 +elastic and plastic curves for the +description of compaction of ductile porous materials. +The function +captures the general behavior to be expected in a ductile porous material. +The unloaded virgin state corresponds to the value +is the reference porosity +of the material. Initial compression of the porous material is assumed to be elastic. Recall that decreasing +porosity corresponds to a reduction in . As the pressure increases beyond the elastic limit, +, the pores +in the material start to crush, leading to irreversible compaction and permanent (plastic) volume change. +Unloading from a partially compacted state follows a new elastic curve that depends on the maximum +compaction (or, alternatively, the minimum value of +) ever attained during the deformation history of +the material. The absolute value of the slope of the elastic curve decreases as +decreases, as will +be quantified later. The material becomes fully compacted when the pressure reaches the compaction +pressure +, a value that is retained forever. The function +; at that point +, where +therefore has multiple branches: a plastic branch, +, +corresponding to elastic unloading from partially compacted states. The appropriate branch of A is +selected according to the following rule: +, and multiple elastic branches, +These expressions can be inverted to solve for p: +The equation for the plastic curve takes the form +or, alternatively, +The elastic curve originally proposed by Hermann (1968) is given by the differential equation +where +the reference density of the solid; and +(porous) materials, respectively. +is the elastic bulk modulus of the solid material at small nominal strains; +is +are the reference sound speeds in the solid and virgin +and +the reference sound speed, +equation of state, +If the solid phase is modeled using the Mie-Grüneisen equation of state, +is given directly by +. On the other hand, if the solid phase is modeled using the tabulated +is computed from the initial bulk modulus and reference density of the solid material, +. In this case the reference density is required to be constant; it cannot be a function of +temperature or field variables. +Following Wardlaw et al. (1996), the above equation for the elastic curve in Abaqus/Explicit is +simplified and replaced by the linear relations +and +Input File Usage: +Use the following option to specify the reference density of the solid phase, +: +*DENSITY +Use one of the following two options to specify additional material properties +for the solid phase: +*EOS, TYPE=USUP (if the solid phase is modeled using the +Mie-Grüneisen equation of state) +*EOS, TYPE=TABULAR (if the solid phase is modeled using +the tabulated equation of state) +Use the following option to specify the properties of the porous material (the +reference sound speed, +; and +the compaction pressure, +; the reference porosity, +; the elastic limit, +): +Abaqus/CAE Usage: +*EOS COMPACTION +Only the Mie-Grüneisen equation of state is supported for the solid phase in +Abaqus/CAE. +Property module: material editor: +General→Density (to specify the reference density +Mechanical→Eos: Type: Us - Up (to specify the variables +Mechanical→Eos: Suboptions→ Eos Compaction (to specify +the reference sound speed, +; the porosity of the unloaded material, +) +, s, and +) +; the pressure required to initialize plastic behavior, +; and the +pressure at which all pores are crushed, +) +Initial state +, that satisfies the equation of state, +The initial state of the porous material is determined from the initial values of porosity, +specific energy, +; +; and pressure stress, p. Abaqus/Explicit automatically computes the initial density, +. You can define the initial porosity, initial +specific energy, and initial stress state . If no initial conditions are given, Abaqus/Explicit assumes that the material is at its +virgin state: +Abaqus/Explicit will issue an error message if the initial +states . When initial conditions are specified only for p (or for +will compute +(or p) assuming that the +state lies on the primary (monotonic loading) curve. +state lies outside the region of allowed +), Abaqus/Explicit +Input File Usage: +Use some or all of the following options, as required: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=SPECIFIC ENERGY +*INITIAL CONDITIONS, TYPE=STRESS +*INITIAL CONDITIONS, TYPE=POROSITY +Load module: Create Predefined Field: Step: Initial: choose Mechanical +for the Category and Stress for the Types for Selected Step +Initial specific energy and initial porosity are not supported in Abaqus/CAE. +JWL high explosive equation of state +The Jones-Wilkens-Lee (or JWL) equation of state models the pressure generated by the release of +chemical energy in an explosive. This model is implemented in a form referred to as a programmed +burn, which means that the reaction and initiation of the explosive is not determined by shock in the +material. Instead, the initiation time is determined by a geometric construction using the detonation +wave speed and the distance of the material point from the detonation points. +The JWL equation of state can be written in terms of the internal energy per unit mass, +, as +where +explosive; and +and +are user-defined material constants; +is the user-defined density of the +is the density of the detonation products. +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*DENSITY (to specify the density of the explosive +*EOS, TYPE=JWL (to specify the material constants +Property module: material editor: +General→Density (to specify the density of the explosive +Mechanical→Eos: Type: JWL (to specify the material constants +) +) +and ) +and +) +Arrival time of detonation wave +Abaqus/Explicit calculates the arrival time of the detonation wave at a material point +from the material point to the nearest detonation point divided by the detonation wave speed: +as the distance +is the position of the material point, +is the +where +detonation delay time of the Nth detonation point, and +is the detonation wave speed of the explosive +material. The minimum in the above formula is over the N detonation points that apply to the material +point. +is the position of the Nth detonation point, +To spread the burn wave over several elements, a burn fraction, +, is computed as +EOS +is a constant that controls the width of the burn wave (set to a value of 2.5) and +where +characteristic length of the element. If the time is less than +otherwise, the pressure is given by the product of +above. +is the +, the pressure is zero in the explosive; +and the pressure determined from the JWL equation +Defining detonation points +You can define any number of detonation points for the explosive material. Coordinates of the points must +be defined along with a detonation delay time. Each material point responds to the first detonation point +that it sees. The detonation arrival time at a material point is based upon the time that it takes a detonation +wave (traveling at the detonation wave speed +) to reach the material point plus the detonation delay +time for the detonation point. If there are multiple detonation points, the arrival time is based on the +minimum arrival time for all the detonation points. In a body with curved surfaces care should be taken +that the detonation arrival times are meaningful. The detonation arrival times are based on the straight +line of sight from the material point to the detonation point. In a curved body the line of sight may pass +outside of the body. +Input File Usage: +Use both of the following options to define the detonation points: +*EOS, TYPE=JWL +*DETONATION POINT +Property module: material editor: Mechanical→Eos: Type: JWL: +Suboptions→Detonation Point +Abaqus/CAE Usage: +Initial state +Explosive materials generally have some nominal volumetric stiffness before detonation. +It may be +useful to incorporate this stiffness when elements modeled with a JWL equation of state are subjected to +stress before initiation of detonation by the arriving detonation wave. You can define the pre-detonation +bulk modulus, +until detonation, +at which time the pressure will be determined by the procedure outlined above. The initial relative density +( +is assumed to +be equal to the user-defined detonation energy +) used in the JWL equation is assumed to be unity. The initial specific energy +. The pressure will be computed from the volumetric strain and +. +If you specify a nonzero value of +, you can also define an initial stress state for the explosive +materials. +Input File Usage: +Use the following option to define the initial stress: +*INITIAL CONDITIONS, TYPE=STRESS +Abaqus/CAE Usage: +Optionally, you can also define the initial specific energy directly: +*INITIAL CONDITIONS, TYPE=SPECIFIC ENERGY +Load module: Create Predefined Field: Step: Initial: choose Mechanical +for the Category and Stress for the Types for Selected Step +Initial specific energy is not supported in Abaqus/CAE. +Ignition and growth equation of state +The ignition and growth equation of state models shock initiation and detonation wave propagation +of solid high explosives. The heterogeneous explosive is modeled as a homogeneous mixture of two +phases: the unreacted solid explosive and the reacted gas products. Separate JWL equations of state are +prescribed for each phase: +where +and +The subscript s refers to the unreacted solid explosive, and g refers to the reacted gas products. +is the +is the density of the +are user-defined material constants used in the JWL equations; +is the user-defined reference density of the explosive, and +and +detonation energy; +unreacted explosive or the reacted products. +Use both of the following options: +*DENSITY(to specify the density of the explosive +*EOS, TYPE=IGNITION AND GROWTH, DETONATION ENERGY= +(to specify the material constants +of the unreacted solid explosive and the reacted gas product) +and +) +Property module: material editor: +General→Density (to specify the density of the explosive +Mechanical→Eos: Type: Ignition and growth: Detonation energy: +Solid Phase tabbed page and Gas Phase tabbed page +(to specify the material constants +of the unreacted solid explosive and the reacted gas product) +and +) +; +25.2.1–12 +Input File Usage: +The mass fraction +The mixture of unreacted solid explosive and reacted gas products is defined by the mass fraction +where +is the mass of the unreacted explosive, and +assumed that the two phases are in thermo-mechanical equilibrium: +is the mass of the reacted products. It is +It is also assumed that the volumes are additive: +Similarly, the internal energy is assumed to be additive: +where +Hence, the specific heat of the mixture is given by +Input File Usage: +Abaqus/CAE Usage: +Use the following options to define the specific heat of the unreacted solid +explosive: +*EOS, TYPE=IGNITION AND GROWTH +*SPECIFIC HEAT, DEPENDENCIES=n +Use the following options to define the specific heat of the reacted gas product: +*EOS, TYPE=IGNITION AND GROWTH +*GAS SPECIFIC HEAT, DEPENDENCIES=n +Use the following options to define the specific heat of the unreacted solid +explosive: +Property module: material editor: +Mechanical→Eos: Type: Ignition and GrowthThermal→Specific Heat +Use the following options to define the specific heat of the reacted gas product: +Property module: material editor: +Mechanical→Eos: Type: Ignition and growth: +Gas Specific tabbed page: Specific Heat +You can toggle on Use temperature-dependent data to define the specific +heat as a function of temperature and/or select the Number of field variables +to define the specific heat as a function of field variables. +The reaction rate +The conversion of unreacted solid explosive to reacted gas products is governed by the reaction rate. The +reaction rate equation in the ignition and growth model is a pressure-driven rule, which includes three +terms: +These three terms are defined as follows: +where +, and z are reaction rate constants. +The first term, +, describes hot spot ignition by igniting some of the material relatively quickly +, represents the growth +but limiting it to a small proportion of the total solid +of reaction from the hot spot sites into the material and describes the inward and outward grain burning +phenomena; this term is limited to a proportion of the total solid +, is used to +describe the rapid transition to detonation observed in some energetic materials. +. The second term, +. The third term, +Input File Usage: +Use both of the following options to define the reaction rate: +Abaqus/CAE Usage: +*EOS, TYPE=IGNITION AND GROWTH +*REACTION RATE +Property module: material editor: +Mechanical→Eos: Type: Ignition and growth: +Reaction Rate tabbed page +Initial state +The initial mass fraction of the unreacted solid explosive is assumed to be one. The initial relative density +( +) used in the ignition and growth equation is assumed to be unity. The initial specific energy and +initial stress can be defined for the unreacted explosive. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to define the initial stress: +*INITIAL CONDITIONS, TYPE=STRESS +Optionally, you can also define the initial specific energy directly: +*INITIAL CONDITIONS, TYPE=SPECIFIC ENERGY +Load module: Create Predefined Field: Step: Initial: choose Mechanical +for the Category and Stress for the Types for Selected Step +Initial specific energy is not supported in Abaqus/CAE. +Ideal gas equation of state +An ideal gas equation of state can be written in the form of +is the ambient pressure, R is the gas constant, +where +is the +absolute zero on the temperature scale being used. It is an idealization to real gas behavior and can +be used to model any gases approximately under appropriate conditions (e.g., low pressure and high +temperature). +is the current temperature, and +One of the important features of an ideal gas is that its specific energy depends only upon its +temperature; therefore, the specific energy can be integrated numerically as +is the initial specific energy at the initial temperature +is the specific heat at constant +where +volume (or the constant volume heat capacity), which depends only upon temperature for an ideal gas. +Modeling with an ideal gas equation of state is typically performed adiabatically; the temperature +increase is calculated directly at the material integration points according to the adiabatic thermal energy +increase caused by the work +). +Therefore, unless a fully coupled temperature-displacement analysis is performed, an adiabatic condition +is always assumed in Abaqus/Explicit. +, where v is the specific volume (the volume per unit mass, +and +When performing a fully coupled temperature-displacement analysis, the pressure stress and +specific energy are updated based on the evolving temperature field. The energy increase due to the +change in state will be accounted for in the heat equation and will be subject to heat conduction. +For the ideal gas model in Abaqus/Explicit you define the gas constant, R, and the ambient pressure, +, and the molecular weight, +. For an ideal gas R can be determined from the universal gas constant, +, as follows: +In general, the value R for any gas can be estimated by plotting +as a function of state (e.g., +pressure or temperature). The ideal gas approximation is adequate in any region where this value is +constant. You must specify the specific heat at constant volume, +is related to the +specific heat at constant pressure, +. For an ideal gas +, by +Input File Usage: +Use both of the following options: +*EOS, TYPE=IDEAL GAS +*SPECIFIC HEAT, DEPENDENCIES=n +Property module: material editor: +Mechanical→Eos: Type: Ideal Gas +Thermal→Specific Heat +Abaqus/CAE Usage: +Initial state +, +There are different methods to define the initial state of the gas. You can specify the initial density, +and either the initial pressure stress, +. The initial value of the unspecified +, or the initial temperature, +field (temperature or pressure) is determined from the equation of state. Alternatively, you can specify +both the initial pressure stress and the initial temperature. In this case the user-specified initial density is +replaced by that derived from the equation of state in terms of initial pressure and temperature. +By default, Abaqus/Explicit automatically computes the initial specific energy, +, from the initial +temperature by numerically integrating the equation +Optionally, you can override this default behavior by defining the initial specific energy for the ideal gas +directly. +Input File Usage: +Use some or all of the following options, as required: +*DENSITY, DEPENDENCIES=n +*INITIAL CONDITIONS, TYPE=STRESS +*INITIAL CONDITIONS, TYPE=TEMPERATURE +Use the following option to specify the initial specific energy directly: +*INITIAL CONDITIONS, TYPE=SPECIFIC ENERGY +Abaqus/CAE Usage: +Property module: material editor: General→Density +Load module: Create Predefined Field: Step: Initial: choose Other for the +Category and Temperature for the Types for Selected Step +Load module: Create Predefined Field: Step: Initial: choose Mechanical +for the Category and Stress for the Types for Selected Step +Initial specific energy is not supported in Abaqus/CAE. +The value of absolute zero +Input File Usage: +When a non-absolute temperature scale is used, you must specify the value of absolute zero temperature. +*PHYSICAL CONSTANTS, ABSOLUTE ZERO= +Any module: Model→Edit Attributes→model_name: +Absolute zero temperature +Abaqus/CAE Usage: +A special case +In the case of an adiabatic analysis with constant specific heat (both +energy is linear in temperature +and +are constant), the specific +The pressure stress can, therefore, be recast in the common form of +where +is the ratio of specific heats and can be defined as +where +for a monatomic; +for a diatomic; and +for a polyatomic gas. +Comparison with the hydrostatic fluid model +The ideal gas equation of state can be used to model wave propagation effects and the dynamics of a +spatially varying state of a gaseous region. For cases in which the inertial effects of the gas are not +important and the state of the gas can be assumed to be uniform throughout a region, the hydrostatic +fluid model (“Surface-based fluid cavities: overview,” Section 11.5.1) is a simpler, more computationally +efficient alternative. +Deviatoric behavior +The equation of state defines only the material’s hydrostatic behavior. It can be used by itself, in which +case the material has only volumetric strength (the material is assumed to have no shear strength). +Alternatively, Abaqus/Explicit allows you to define deviatoric behavior, assuming that the deviatoric +and volumetric responses are uncoupled. Two models are available for the deviatoric response: a linear +isotropic elastic model and a viscous model. The material’s volumetric response is governed then by the +equation of state model, while its deviatoric response is governed by either the linear isotropic elastic +model or the viscous fluid model. +Elastic shear behavior +For the elastic shear behavior the deviatoric stress is related to the deviatoric strain as +is the deviatoric stress and +is the deviatoric elastic strain. See “Defining isotropic shear +where +elasticity for equations of state in Abaqus/Explicit” in “Linear elastic behavior,” Section 22.2.1, for more +details. +Input File Usage: +Use both of the following options to define elastic shear behavior: +*EOS +*ELASTIC, TYPE=SHEAR +Property module: material editor: Mechanical→Elasticity→Elastic; Type: +Shear; Shear Modulus +Abaqus/CAE Usage: +Viscous shear behavior +For the viscous shear behavior the deviatoric stress is related to the deviatoric strain rate as +where +is the engineering shear strain rate. +is the deviatoric stress, +is the deviatoric part of the strain rate, +is the viscosity, and +Abaqus/Explicit provides a wide range of viscosity models to describe both Newtonian and non- +Newtonian fluids. These are described in “Viscosity,” Section 26.1.4. +Input File Usage: +Use both of the following options to define viscous shear behavior: +Abaqus/CAE Usage: +*EOS +*VISCOSITY +Property module: material editor: Mechanical→Viscosity +Use with the Mises or the Johnson-Cook plasticity models +An equation of state model can be used with the Mises (“Classical metal plasticity,” Section 23.2.1) or +the Johnson-Cook (“Johnson-Cook plasticity,” Section 23.2.7) plasticity models to model elastic-plastic +behavior. In this case you must define the elastic part of the shear behavior. The material’s volumetric +response is governed by the equation of state model, while the deviatoric response is governed by the +linear elastic shear and the plasticity model. +Input File Usage: +Use the following options: +*EOS +*ELASTIC, TYPE=SHEAR +*PLASTIC +Property module: material editor: +Mechanical→Elasticity→Elastic; Type: Shear +Mechanical→Plasticity→Plastic +Abaqus/CAE Usage: +Initial conditions +You can specify initial conditions for the equivalent plastic strain, +Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1). +(“Initial conditions in +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=HARDENING +Load module: Create Predefined Field: Step: Initial, choose Mechanical +for the Category and Hardening for the Types for Selected Step +Use with the extended Drucker-Prager plasticity models +An equation of state model can be used in conjunction with the extended Drucker-Prager (“Extended +Drucker-Prager models,” Section 23.3.1) plasticity models to model pressure-dependent plasticity +behavior. This approach can be appropriate for modeling the response of ceramics and other brittle +materials under high velocity impact conditions. In this case you must define the elastic part of the +shear behavior. The material’s deviatoric response is governed by the linear elastic shear and the +pressure-dependent plasticity model, while the volumetric response is governed by the equation of state +model. In particular, no plastic dilation effects are taken into account (if you specify a dilation angle +other than zero, the value is ignored and Abaqus/Explicit issues a warning message). +“High-velocity impact of a ceramic target,” Section 2.1.18 of the Abaqus Example Problems Manual +illustrates the use of an equation of state model with the extended Drucker-Prager plasticity models. +Input File Usage: +Use the following options: +*EOS +*ELASTIC, TYPE=SHEAR +*DRUCKER PRAGER +*DRUCKER PRAGER HARDENING +Property module: material editor: +Abaqus/CAE Usage: +Initial conditions +Mechanical→Elasticity→Elastic; Type: Shear +Mechanical→Plasticity→Drucker Prager: Suboptions→Drucker +Prager Hardening +You can specify initial conditions for the equivalent plastic strain, +Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1). +(“Initial conditions in +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=HARDENING +Load module: Create Predefined Field: Step: Initial, choose Mechanical +for the Category and Hardening for the Types for Selected Step +Use with the tensile failure model +An equation of state model (except the ideal gas equation of state) can also be used with the tensile +failure model (“Dynamic failure models,” Section 23.2.8) to model dynamic spall or a pressure cutoff. +The tensile failure model uses the hydrostatic pressure stress as a failure measure and offers a number of +failure choices. You must provide the hydrostatic cutoff stress. +You can specify that the deviatoric stresses should fail when the tensile failure criterion is met. In +the case where the material’s deviatoric behavior is not defined, this specification is meaningless and is, +therefore, ignored. +The tensile failure model in Abaqus/Explicit is designed for high-strain-rate dynamic problems in +which inertia effects are important. Therefore, it should be used only for such situations. Improper use +of the tensile failure model may result in an incorrect simulation. +Input File Usage: +Abaqus/CAE Usage: +Adiabatic assumption +Use the following options: +*EOS +*TENSILE FAILURE +The tensile failure model is not supported in Abaqus/CAE. +An adiabatic condition is always assumed for materials modeled with an equation of state unless a +dynamic coupled temperature-displacement procedure is used. The adiabatic condition is assumed +irrespective of whether an adiabatic dynamic stress analysis step has been specified. The temperature +increase is calculated directly at the material integration points according to the adiabatic thermal energy +increase caused by the mechanical work +where +effect on the behavior of this model. +is the specific heat at constant volume. Specifying temperature as a predefined field has no +When performing a fully coupled temperature-displacement analysis, the specific energy is updated +based on the evolving temperature field using +Modeling fluids +equation of state model can be used to model incompressible viscous and inviscid +A linear +laminar flow governed by the Navier-Stokes equation of motion. The volumetric response is governed +by the equations of state, where the bulk modulus acts as a penalty parameter for the incompressible +constraint. +To model a viscous laminar flow that follows the Navier-Poisson law of a Newtonian fluid, use +the Newtonian viscous deviatoric model and define the viscosity as the real linear viscosity of the +fluid. To model non-Newtonian viscous flow, use one of the nonlinear viscosity models available in +Abaqus/Explicit. Appropriate initial conditions for velocity and stress are essential to get an accurate +solution for this class of problems. +To model an incompressible inviscid fluid such as water in Abaqus/Explicit, it is useful to define a +small amount of shear resistance to suppress shear modes that can otherwise tangle the mesh. Here the +shear stiffness or shear viscosity acts as a penalty parameter. The shear modulus or viscosity should be +small because flow is inviscid; a high shear modulus or viscosity will result in an overly stiff response. +To avoid an overly stiff response, the internal forces arising due to the deviatoric response of the material +should be kept several orders of magnitude below the forces arising due to the volumetric response. This +can be done by choosing an elastic shear modulus that is several orders of magnitude lower than the bulk +modulus. If the viscous model is used, the shear viscosity specified should be on the order of the shear +modulus, calculated as above, scaled by the stable time increment. The expected stable time increment +can be obtained from a data check analysis of the model. This method is a convenient way to approximate +a shear resistance that will not introduce excessive viscosity in the material. +If a shear model is defined, the hourglass control forces are calculated based on the shear resistance +of the material. Thus, in materials with extremely low or zero shear strengths such as inviscid fluids, the +hourglass forces calculated based on the default parameters are insufficient to prevent spurious hourglass +modes. Therefore, a sufficiently high hourglass scaling factor is recommended to increase the resistance +to such modes. +Elements +Equations of state can be used with any solid (continuum) elements in Abaqus/Explicit except +plane stress elements. For three-dimensional applications exhibiting high confinement, the default +kinematic formulation is recommended with reduced-integration solid elements . +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Explicit output variable +identifiers,” Section 4.2.2), the following variables have special meaning for the equation of state +models: +PALPH +, of the +Distension, +minus the inverse of +: +porous material. The current porosity is equal to one +PALPHMIN +Minimum value, +, of the distension attained during plastic compaction of the +porous material. +PEEQ +Equivalent plastic strain, +is the initial +equivalent plastic strain (zero or user-specified; see “Initial conditions”). This is +relevant only if the equation of state model is used in combination with the Mises, +Johnson-Cook, or extended Drucker-Prage plasticity models. +where +Additional references +• Carroll, M., and A. C. Holt, “Suggested Modification of the +Journal of Applied Physics, vol. 43, no. 2, pp. 759–761, 1972. +Model for Porous Materials,” +• Dobratz, B. M., “LLNL Explosives Handbook, Properties of Chemical Explosives and Explosive +Simulants,” UCRL-52997, Lawrence Livermore National Laboratory, Livermore, California, +January 1981. +• Herrmann, W., “Constitutive Equation for the Dynamic Compaction of Ductile Porous Materials,” +Journal of Applied Physics, vol. 40, no. 6, pp. 2490–2499, 1968. +• Lee, E., M. Finger, and W. Collins, “JWL Equation of State Coefficients for High Explosives,” +UCID-16189, Lawrence Livermore National Laboratory, Livermore, California, January 1973. +• Wardlaw, A. B., R. McKeown, and H. Chen, “Implementation and Application of the +Equation of State in the DYSMAS Code,” Naval Surface Warfare Center, Dahlgren Division, +Report Number: NSWCDD/TR-95/107, May 1996. +Other Material Properties +Mechanical properties +Heat transfer properties +Acoustic properties +Mass diffusion properties +Electromagnetic properties +Pore fluid flow properties +User materials +OTHER MATERIAL PROPERTIES +26.1 +26.2 +26.3 +26.4 +26.5 +26.6 +26.1 +Mechanical properties +• “Material damping,” Section 26.1.1 +• “Thermal expansion,” Section 26.1.2 +• “Field expansion,” Section 26.1.3 +• “Viscosity,” Section 26.1.4 +26.1.1 +MATERIAL DAMPING +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Dynamic analysis procedures: overview,” Section 6.3.1 +• “Material library: overview,” Section 21.1.1 +• *DAMPING +• “Defining damping” in “Defining other mechanical models,” Section 12.9.4 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +Material damping can be defined: +• for direct-integration (nonlinear, +implicit or explicit), +subspace-based direct-integration, +direct-solution steady-state, and subspace-based steady-state dynamic analysis; or +• for mode-based (linear) dynamic analysis in Abaqus/Standard. +Rayleigh damping +In direct-integration dynamic analysis you very often define energy dissipation mechanisms—dashpots, +inelastic material behavior, etc.—as part of the basic model. +In such cases there is usually no need +to introduce additional damping: +it is often unimportant compared to these other dissipative effects. +However, some models do not have such dissipation sources (an example is a linear system with +chattering contact, such as a pipeline in a seismic event). In such cases it is often desirable to introduce +some general damping. Abaqus provides “Rayleigh” damping for this purpose. It provides a convenient +abstraction to damp lower (mass-dependent) and higher (stiffness-dependent) frequency range behavior. +Rayleigh damping can also be used in direct-solution steady-state dynamic analyses and +subspace-based steady-state dynamic analyses to get quantitatively accurate results, especially near +natural frequencies. +for stiffness proportional damping. +To define material Rayleigh damping, you specify two Rayleigh damping factors: +for mass +proportional damping and +In general, damping is a material +property specified as part of the material definition. For the cases of rotary inertia, point mass elements, +and substructures, where there is no reference to a material definition, the damping can be defined in +conjunction with the property references. Any mass proportional damping also applies to nonstructural +features . +For a given mode i the fraction of critical damping, +, can be expressed in terms of the damping +factors +and +as: +where +proportional Rayleigh damping, +damping, +, damps the higher frequencies. +is the natural frequency at this mode. This equation implies that, generally speaking, the mass +, damps the lower frequencies and the stiffness proportional Rayleigh +Mass proportional damping +factor introduces damping forces caused by the absolute velocities of the model and so simulates +The +the idea of the model moving through a viscous “ether” (a permeating, still fluid, so that any motion of +any point in the model causes damping). This damping factor defines mass proportional damping, in +the sense that it gives a damping contribution proportional to the mass matrix for an element. If the +element contains more than one material in Abaqus/Standard, the volume average value of +is used +to multiply the element’s mass matrix to define the damping contribution from this term. If the element +contains more than one material in Abaqus/Explicit, the mass average value of +is used to multiply +the element’s lumped mass matrix to define the damping contribution from this term. +has units of +(1/time). +Input File Usage: +Abaqus/CAE Usage: +*DAMPING, ALPHA= +Property module: material editor: Mechanical→Damping: Alpha: +Defining variable mass proportional damping in Abaqus/Explicit +In Abaqus/Explicit you can define +Therefore, mass proportional damping can vary during an Abaqus/Explicit analysis. +*DAMPING, ALPHA=TABULAR +Input File Usage: +as a tabular function of temperature and/or field variables. +Stiffness proportional damping +factor introduces damping proportional to the strain rate, which can be thought of as damping +The +associated with the material itself. +defines damping proportional to the elastic material stiffness. +Since the model may have quite general nonlinear response, the concept of “stiffness proportional +damping” must be generalized, since it is possible for the tangent stiffness matrix to have negative +eigenvalues (which would imply negative damping). To overcome this problem, +is interpreted +as defining viscous material damping in Abaqus, which creates an additional “damping stress,” +, +proportional to the total strain rate: +is the strain rate. +For hyperelastic (“Hyperelastic behavior of rubberlike materials,” +where +Section 22.5.1) and hyperfoam (“Hyperelastic behavior in elastomeric foams,” Section 22.5.2) materials +is defined as the elastic stiffness in the strain-free state. For all other linear elastic materials +is the material’s current elastic +in Abaqus/Standard and all other materials in Abaqus/Explicit, +stiffness. +will be calculated based on the current temperature during the analysis. +This damping stress is added to the stress caused by the constitutive response at the integration point +when the dynamic equilibrium equations are formed, but it is not included in the stress output. As a result, +damping can be introduced for any nonlinear case and provides standard Rayleigh damping for linear +cases; for a linear case stiffness proportional damping is exactly the same as defining a damping matrix +equal to +times the (elastic) material stiffness matrix. Other contributions to the stiffness matrix (e.g., +hourglass, transverse shear, and drill stiffnesses) are not included when computing stiffness proportional +damping. +has units of (time). +Input File Usage: +Abaqus/CAE Usage: +*DAMPING, BETA= +Property module: material editor: Mechanical→Damping: Beta: +Defining variable stiffness proportional damping in Abaqus/Explicit +In Abaqus/Explicit you can define +Therefore, stiffness proportional damping can vary during an Abaqus/Explicit analysis. +*DAMPING, BETA=TABULAR +Input File Usage: +as a tabular function of temperature and/or field variables. +Structural damping +Structural damping assumes that the damping forces are proportional to the forces caused by stressing of +the structure and are opposed to the velocity. Therefore, this form of damping can be used only when the +displacement and velocity are exactly 90° out of phase. Structural damping is best suited for frequency +domain dynamic procedures . The damping +forces are then +are the damping forces, +where +are the forces caused by stressing of the structure. The damping forces due to structural damping are +intended to represent frictional effects (as distinct from viscous effects). Thus, structural damping is +suggested for models involving materials that exhibit frictional behavior or where local frictional effects +are present throughout the model, such as dry rubbing of joints in a multi-link structure. +, s is the user-defined structural damping factor, and +Structural damping can be added to the model as mechanical dampers such as connector damping +or as a complex stiffness on spring elements. +Structural damping can be used in steady-state dynamic procedures that allow for nondiagonal +damping. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to define structural damping: +*DAMPING, STRUCTURAL= +Property module: material editor: Mechanical→Damping: Structural: +Artificial damping in direct-integration dynamic analysis +In Abaqus/Standard the operators used for implicit direct time integration introduce some artificial +damping in addition to Rayleigh damping. Damping associated with the Hilber-Hughes-Taylor and +hybrid operators is usually controlled by the Hilber-Hughes-Taylor parameter +, which is not the +same as the +and +parameters of the Hilber-Hughes-Taylor and hybrid operators also affect numerical damping. The +parameter controlling the mass proportional part of Rayleigh damping. The +, +, and +parameters are not available for the backward Euler operator. See “Implicit dynamic analysis +using direct integration,” Section 6.3.2, for more information about this other form of damping. +Artificial damping in explicit dynamic analysis +In Abaqus/Explicit a +Rayleigh damping is meant to reflect physical damping in the actual material. +small amount of numerical damping is introduced by default in the form of bulk viscosity to control high +frequency oscillations; see “Explicit dynamic analysis,” Section 6.3.3, for more information about this +other form of damping. +Effects of damping on the stable time increment in Abaqus/Explicit +As the fraction of critical damping for the highest mode ( +Abaqus/Explicit decreases according to the equation +) increases, the stable time increment for +where (by substituting +, the frequency of the highest mode, into the equation for +given previously) +These equations indicate a tendency for stiffness proportional damping to have a greater effect on the +stable time increment than mass proportional damping. +To illustrate the effect that damping has on the stable time increment, consider a cantilever in +bending modeled with continuum elements. The lowest frequency is +1 rad/sec, while for the +particular mesh chosen, the highest frequency is +1000 rad/sec. The lowest mode in this problem +corresponds to the cantilever in bending, and the highest frequency is related to the dilation of a single +element. +With no damping the stable time increment is +If we use stiffness proportional damping to create 1% of critical damping in the lowest mode, the damping +factor is given by +This corresponds to a critical damping factor in the highest mode of +The stable time increment with damping is, thus, reduced by a factor of +and becomes +Thus, introducing 1% critical damping in the lowest mode reduces the stable time increment by a factor +of twenty. +However, if we use mass proportional damping to damp out the lowest mode with 1% of critical +damping, the damping factor is given by +which corresponds to a critical damping factor in the highest mode of +The stable time increment with damping is reduced by a factor of +which is almost negligible. +This example demonstrates that it is generally preferable to damp out low frequency response with +mass proportional damping rather than stiffness proportional damping. However, mass proportional +damping can significantly affect rigid body motion, so large +is often undesirable. To avoid a dramatic +drop in the stable time increment, the stiffness proportional damping factor, +, should be less than or of +the same order of magnitude as the initial stable time increment without damping. With +, +the stable time increment is reduced by about 52%. +Damping in modal superposition procedures +Damping can be specified as part of the step definition for modal superposition procedures. “Damping +in a linear dynamic analysis” in “Dynamic analysis procedures: overview,” Section 6.3.1, describes the +availability of damping types, which depends on the procedure type and the architecture used to perform +the analysis, and provides details on the following types of damping: +• Viscous modal damping (Rayleigh damping and fraction of critical damping) +• Structural modal damping +• Composite modal damping +Use with other material models +The +factor applies to all elements that use a linear elastic material definition (“Linear elastic behavior,” +Section 22.2.1) and to Abaqus/Standard beam and shell elements that use general sections. In the latter +case, if a nonlinear beam section definition is provided, the +factor is multiplied by the slope of the +force-strain (or moment-curvature) relationship at zero strain or curvature. In addition, the +factor +applies to all Abaqus/Explicit elements that use a hyperelastic material definition (“Hyperelastic behavior +of rubberlike materials,” Section 22.5.1), a hyperfoam material definition (“Hyperelastic behavior in +elastomeric foams,” Section 22.5.2), or general shell sections (“Using a general shell section to define +the section behavior,” Section 29.6.6). +In the case of a no tension elastic material the +factor is not used in tension, while for a no +compression elastic material the +factor is not used in compression . In other words, these modified elasticity models exhibit damping only when +they have stiffness. +Elements +factor is applied to all elements that have mass including point mass elements (discrete +The +DASHPOTA elements in each global direction, each with one node fixed, can also be used to introduce +this type of damping). For point mass and rotary inertia elements mass proportional or composite +modal damping are defined as part of the point mass or rotary inertia definitions (“Point masses,” +Section 30.1.1, and “Rotary inertia,” Section 30.2.1). +The +factor is not available for spring elements: discrete dashpot elements should be used in +parallel with spring elements instead. +The +factor is also not applied to the transverse shear terms in Abaqus/Standard beams and shells. +In Abaqus/Standard composite modal damping cannot be used with or within substructures. +Rayleigh damping can be introduced for substructures. When Rayleigh damping is used within a +substructure, +for +the substructure. These are weighted averages, using the mass as the weighting factor for +and the +volume as the weighting factor for +. These averaged damping values can be superseded by providing +them directly in a second damping definition. See “Using substructures,” Section 10.1.1. +are averaged over the substructure to define single values of +and +and +26.1.2 +THERMAL EXPANSION +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “UEXPAN,” Section 1.1.29 of the Abaqus User Subroutines Reference Manual +• *EXPANSION +• “Defining other mechanical models,” Section 12.9.4 of the Abaqus/CAE User’s Manual +• “Defining a fluid-filled porous material,” Section 12.12.3 of the Abaqus/CAE User’s Manual +Overview +Thermal expansion effects: +• can be defined by specifying thermal expansion coefficients so that Abaqus can compute thermal +strains and, in Abaqus/CFD, buoyancy forces; +• can be isotropic, orthotropic, or fully anisotropic; +• are defined as total expansion from a reference temperature; +• can be specified as a function of temperature and/or field variables; +• can be defined with a distribution for solid continuum elements in Abaqus/Standard; and +• in Abaqus/Standard can be specified directly in user subroutine UEXPAN (if the thermal strains are +complicated functions of field variables and state variables). +Defining thermal expansion coefficients +Thermal expansion is a material property included in a material definition except when it refers to the expansion of a gasket whose material properties are not +defined as part of a material definition. In that case expansion must be used in conjunction with the +gasket behavior definition . +In an Abaqus/Standard analysis a spatially varying thermal expansion can be defined for +homogeneous solid continuum elements by using a distribution (“Distribution definition,” Section 2.8.1). +The distribution must include default values for the thermal expansion. +If a distribution is used, no +dependencies on temperature and/or field variables for the thermal expansion can be defined. +Input File Usage: +Use the following options to define thermal expansion for most materials: +*MATERIAL +*EXPANSION +Abaqus/CAE Usage: +Use the following options to define thermal expansion for gaskets whose +constitutive response is defined directly as gasket behavior: +*GASKET BEHAVIOR +*EXPANSION +Use the following option in conjunction with other material behaviors, +including gasket behavior, to include thermal expansion effects: +Property module: material editor: Mechanical→Expansion +Computation of thermal strains +Abaqus requires thermal expansion coefficients, +reference temperature, +, as shown in Figure 26.1.2–1. +, that define the total thermal expansion from a +εth +εth +εth +θ0 +θ1 +θ2 +Figure 26.1.2–1 Definition of the thermal expansion coefficient. +They generate thermal strains according to the formula +where +is the thermal expansion coefficient; +is the current temperature; +is the initial temperature; +are the current values of the predefined field variables; +are the initial values of the field variables; and +is the reference temperature for the thermal expansion coefficient. +The second term in the above equation represents the strain due to the difference between the initial +. This term is necessary to enforce the assumption that +, and the reference temperature, +temperature, +there is no initial thermal strain for cases in which the reference temperature does not equal the initial +temperature. +Defining the reference temperature +If the coefficient of thermal expansion, +the reference temperature, +define +. +, is not needed. If +, is not a function of temperature or field variables, the value of +is a function of temperature or field variables, you can +Input File Usage: +Abaqus/CAE Usage: +*EXPANSION, ZERO= +Property module: material editor: Mechanical→Expansion: +Reference temperature: +Converting thermal expansion coefficients from differential form to total form +Total thermal expansion coefficients are commonly available in tables of material properties. However, +sometimes you are given thermal expansion data in differential form: +that is, the tangent to the strain-temperature curve is provided . To convert to the +total thermal expansion form required by Abaqus, this relationship must be integrated from a suitably +chosen reference temperature, +: +For example, suppose +between +and +; etc. Then, +is a series of constant values: +between +and +; +between +and +; +The corresponding total expansion coefficients required by Abaqus are then obtained as +Defining increments of thermal strain in user subroutine UEXPAN +Increments of thermal strain can be specified in Abaqus/Standard user subroutine UEXPAN as functions +of temperature and/or predefined field variables. User subroutine UEXPAN must be used if the thermal +strain increments depend on state variables. +Input File Usage: +Abaqus/CAE Usage: +*EXPANSION, USER +Property module: material editor: Mechanical→Expansion: +Use user subroutine UEXPAN +Defining the initial temperature and field variable values +If the coefficient of thermal expansion, +temperature and initial field variable values, +in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1. +, is a function of temperature or field variables, the initial +, are given as described in “Initial conditions +and +Element removal and reactivation +If an element has been removed and subsequently reactivated in Abaqus/Standard (“Element and contact +pair removal and reactivation,” Section 11.2.1), +in the equation for the thermal strains represent +and +temperature and field variable values as they were at the moment of reactivation. +Defining directionally dependent thermal expansion +Isotropic or orthotropic thermal expansion can be defined in Abaqus. +thermal expansion can be defined in Abaqus/Standard. +In addition, fully anisotropic +Orthotropic and anisotropic thermal expansion can be used only with materials where the material +directions are defined with local orientations . +Orthotropic thermal expansion in Abaqus/Explicit is allowed only with anisotropic elasticity +(including orthotropic elasticity) and anisotropic yield . +Only isotropic thermal expansion is allowed in Abaqus/CFD, for adiabatic stress analysis, and with +the hyperelastic and hyperfoam material models. +Isotropic expansion +If the thermal expansion coefficient is defined directly, only one value of +If user subroutine UEXPAN is used, only one isotropic thermal strain increment ( +is needed at each temperature. +) must be defined. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to define the thermal expansion coefficient directly: +*EXPANSION, TYPE=ISO +Use the following option to define the thermal expansion with user subroutine +UEXPAN: +*EXPANSION, TYPE=ISO, USER +Use the following input to define the thermal expansion coefficient directly: +Property module: material editor: Mechanical→Expansion: Type: Isotropic +Use the following input to define the thermal expansion with user subroutine +UEXPAN: +Property module: material editor: Mechanical→Expansion: Type: +Isotropic, Use user subroutine UEXPAN +THERMAL EXPANSION +If the thermal expansion coefficients are defined directly, the three expansion coefficients in the principal +material directions ( +) should be given as functions of temperature. If user subroutine +UEXPAN is used, the three components of thermal strain increment in the principal material directions +( +) must be defined. +, and +, and +, +, +Input File Usage: +Use the following option to define the thermal expansion coefficient directly: +*EXPANSION, TYPE=ORTHO +Use the following option to define the thermal expansion with user subroutine +UEXPAN: +Abaqus/CAE Usage: +*EXPANSION, TYPE=ORTHO, USER +Use the following input to define the thermal expansion coefficient directly: +Property module: material editor: Mechanical→Expansion: +Type: Orthotropic +Use the following input to define the thermal expansion with user subroutine +UEXPAN: +Property module: material editor: Mechanical→Expansion: Type: +Orthotropic, Use user subroutine UEXPAN +Anisotropic expansion +If the thermal expansion coefficients are defined directly, all six components of +, +) must be given as functions of temperature. If user subroutine UEXPAN is used, all six +, +, +( +, +, +components of the thermal strain increment ( +, +, +, +, +, +) must be defined. +In an Abaqus/Standard analysis if a distribution is used to define the thermal expansion, the number +of expansion coefficients given for each element in the distribution, which is determined by the associated +distribution table (“Distribution definition,” Section 2.8.1), must be consistent with the level of anisotropy +specified for the expansion behavior. For example, if orthotropic behavior is specified, three expansion +coefficients must be defined for each element in the distribution. +Input File Usage: +Use the following option to define the thermal expansion coefficient directly: +*EXPANSION, TYPE=ANISO +Use the following option to define the thermal expansion with user subroutine +UEXPAN: +Abaqus/CAE Usage: +*EXPANSION, TYPE=ANISO, USER +Use the following input to define the thermal expansion coefficient directly: +Property module: material editor: Mechanical→Expansion: +Type: Anisotropic +Thermal stress +Use the following input to define the thermal expansion with user subroutine +UEXPAN: +Property module: material editor: Mechanical→Expansion: Type: +Anisotropic, Use user subroutine UEXPAN +When a structure is not free to expand, a change in temperature will cause stress. For example, consider +a single two-node truss of length L that is completely restrained at both ends. The cross-sectional area; +the Young’s modulus, E; and the thermal expansion coefficient, +, are all constant. The stress in this +one-dimensional problem can then be calculated from Hooke’s Law as +is the total strain and +element is fully restrained, +is the thermal strain, where +is the temperature change. Since the +. If the temperature at both nodes is the same, we obtain the stress +, where +. +Constrained thermal expansion can cause significant stress. +For typical structural metals, +temperature changes of about 150°C (300°F) can cause yield. Therefore, it is often important to +define boundary conditions with particular care for problems involving thermal loading to avoid +overconstraining the thermal expansion. +Energy balance considerations +Abaqus does not account for thermal expansion effects in the total energy balance equation, which can +lead to an apparent imbalance of the total energy of the model. For example, in the example above of +a two-node truss restrained at both ends, constraint thermal expansion introduces strain energy that will +result in an equivalent increase in the total energy of the model. +Use with other material models +Thermal expansion can be combined with any other (mechanical) material behavior in Abaqus. +Using thermal expansion with other material models +For most materials thermal expansion is defined by a single coefficient or set of orthotropic or anisotropic +coefficients or, in Abaqus/Standard, by defining the incremental thermal strains in user subroutine +UEXPAN. For porous media in Abaqus/Standard, such as soils or rock, thermal expansion can be defined +for the solid grains and for the permeating fluid (when using the coupled pore fluid diffusion/stress +procedure—see “Coupled pore fluid diffusion and stress analysis,” Section 6.8.1). In such a case the +thermal expansion definition should be repeated to define the different thermal expansion effects. +Using thermal expansion with gasket behaviors +Thermal expansion can be used in conjunction with any gasket behavior definition. Thermal expansion +will affect the expansion of the gasket in the membrane direction and/or the expansion in the gasket’s +thickness direction. +Elements +Thermal expansion can be used with any stress/displacement or fluid element in Abaqus. +26.1.3 +FIELD EXPANSION +Product: Abaqus/Standard +References +• “Material library: overview,” Section 21.1.1 +• “UEXPAN,” Section 1.1.29 of the Abaqus User Subroutines Reference Manual +• *EXPANSION +Overview +Field expansion effects: +• can be defined by specifying field expansion coefficients so that Abaqus/Standard can compute field +expansion strains that are driven by changes in predefined field variables; +• can be isotropic, orthotropic, or fully anisotropic; +• are defined as total expansion from a reference value of the predefined field variable; +• can be specified as a function of temperature and/or predefined field variables; +• can be specified directly in user subroutine UEXPAN (if the field expansion strains are complicated +functions of field variables and state variables); and +• can be defined for more than one predefined field variable. +Defining field expansion coefficients +Field expansion is a material property included in a material definition except when it refers to the expansion of a gasket whose material properties are not +defined as part of a material definition. In that case field expansion must be used in conjunction with the +gasket behavior definition . +Input File Usage: +Use the following options to define field expansion associated with predefined +field variable number n for most materials: +*MATERIAL +*EXPANSION, FIELD=n +The *EXPANSION option can be repeated with different values of the +predefined field variable number n to define field expansion associated with +more than one field. +Use the following options to define field expansion associated with predefined +field variable number n for gaskets whose constitutive response is defined +directly as gasket behavior: +*GASKET BEHAVIOR +*EXPANSION, FIELD=n +The *EXPANSION option can be repeated with different values of the +prede��ned field variable number n to define field expansion associated with +more than one field. +Computation of field expansion strains +Abaqus/Standard requires field expansion coefficients, +reference value of the predefined field variable n, +, as shown in Figure 26.1.3–1. +, that define the total field expansion from a +εf +εf +εf +(α +′ +f)2 +(α +′ +f)1 +(α +f)2 +(α +f)1 + 0 +fn + 1 +fn + 2 +fn +fn +Figure 26.1.3–1 Definition of the field expansion coefficient. +The field expansion for each specified field generates field expansion strains according to the formula +where +is the field expansion coefficient; +is the current value of the predefined field variable n; +is the initial value of the predefined field variable n; +are the current values of the predefined field variables; +are the initial values of the predefined field variables; and +is the reference value of the predefined field variable n for the field expansion +coefficient. +The second term in the above equation represents the strain due to the difference between the initial +. This term is +value of the predefined field variablen, +necessary to enforce the assumption that there is no initial field expansion strain for cases in which the +reference value of the predefined field variable n does not equal the corresponding initial value. +, and the corresponding reference value, +Defining the reference value of the predefined field variable +If the coefficient of field expansion, +value of the predefined field variable, +variables, you can define +. +, is not a function of temperature or field variables, the reference +is a function of temperature or field +, is not needed. +If +Input File Usage: +*EXPANSION, FIELD=n, ZERO= +Converting field expansion coefficients from differential form to total form +Total field expansion coefficients can be provided directly as outlined in the previous section. However, +you may have field expansion data available in differential form: +that is, the tangent to the strain-field variable curve is provided . To convert to +the total field expansion form required by Abaqus, this relationship must be integrated from a suitably +chosen reference value of the field variable, +: +For example, suppose +between +and +; +is a series of constant values: +and +; etc. Then, +between +and +; +between +The corresponding total expansion coefficients required by Abaqus are then obtained as +Defining increments of field expansion strain in user subroutine UEXPAN +Increments of field expansion strain can be specified in user subroutine UEXPAN as functions of +temperature and/or predefined field variables. User subroutine UEXPAN must be used if the field +expansion strain increments depend on state variables. +You can use user subroutine UEXPAN only once within a single material definition. In particular, +you cannot define both thermal and field expansions or multiple field expansions within the same material +definition using user subroutine UEXPAN. +Input File Usage: +*EXPANSION, FIELD=n, USER +Defining the initial temperature and field variable values +If the coefficient of field expansion, +the initial temperature and initial predefined field variable values, +“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1. +, is a function of temperature and/or predefined field variables, +, are given as described in +and +Element removal and reactivation +If an element has been removed and subsequently reactivated (“Element and contact pair removal +and reactivation,” Section 11.2.1), +in the equation for the field expansion strains represent +temperature and predefined field variable values as they were at the moment of reactivation. +and +Defining directionally dependent field expansion +Isotropic, orthotropic, or fully anisotropic field expansion can be defined. +Orthotropic and anisotropic field expansion can be used only with materials where the material +directions are defined with local orientations . +Only isotropic field expansion is allowed with the hyperelastic and hyperfoam material models. +Isotropic expansion +If the field expansion coefficient is defined directly, only one value of +is needed at each temperature +and/or predefined field variable. If user subroutine UEXPAN is used, only one isotropic field expansion +strain increment ( +) must be defined. +Input File Usage: +Use the following option to define the field expansion coefficient directly: +*EXPANSION, FIELD=n, TYPE=ISO +Use the following option to define the field expansion with user subroutine +UEXPAN: +*EXPANSION, FIELD=n, TYPE=ISO, USER +Orthotropic expansion +If the field expansion coefficients are defined directly, the three expansion coefficients in the principal +material directions ( +) should be given as functions of temperature and/or predefined +, and +, +field variables. +increment in the principal material directions ( +If user subroutine UEXPAN is used, the three components of field expansion strain +, and +) must be defined. +, +Input File Usage: +Use the following option to define the field expansion coefficients directly: +*EXPANSION, FIELD=n, TYPE=ORTHO +Use the following option to define the field expansion with user subroutine +UEXPAN: +*EXPANSION, FIELD=n, TYPE=ORTHO, USER +Anisotropic expansion +If the field expansion coefficients are defined directly, all six components of +, +) must be given as functions of temperature and/or predefined field variables. If user +, +subroutine UEXPAN is used, all six components of the field expansion strain increment ( +, +, +( +, +, +, +, +, +, +) must be defined. +Input File Usage: +Use the following option to define the field expansion coefficients directly: +*EXPANSION, FIELD=n, TYPE=ANISO +Use the following option to define the field expansion with user subroutine +UEXPAN: +*EXPANSION, FIELD=n, TYPE=ANISO, USER +Field expansion stress +When a structure is not free to expand, a change in a predefined field variable will cause stress if there is +field expansion associated with that predefined field variable. For example, consider a single 2-node truss +of length L that is completely restrained at both ends. The cross-sectional area; the Young’s modulus, E; +and the field expansion coefficient, +, are all constants. The stress in this one-dimensional problem can +then be calculated from Hooke’s Law as +is the field expansion strain, where +n. Since the element is fully restrained, +same, we obtain the stress +is the change in the value of the predefined field variable number +. If the values of the field variable at both nodes are the +is the total strain and +, where +. +Depending on the value of the field expansion coefficient and the change in the value of the +corresponding predefined field variable, a constrained field expansion can cause significant stress +and introduce strain energy that will result in an equivalent increase in the total energy of the model. +Therefore, it is often important to define boundary conditions with particular care for problems involving +this property to avoid overconstraining the field expansion. +Use with other material models +Field expansion can be combined with any other (mechanical) material behavior in Abaqus/Standard. +Using field expansion with other material models +For most materials field expansion is defined by a single coefficient or a set of orthotropic or anisotropic +coefficients or by defining the incremental field expansion strains in user subroutine UEXPAN. +Using field expansion with gasket behavior +Field expansion can be used in conjunction with any gasket behavior definition. Field expansion will +affect the expansion of the gasket in the membrane direction and/or the expansion in the gasket’s +thickness direction. +Elements +Field expansion can be used with any stress/displacement element in Abaqus/Standard, except for beam +and shell elements using a general section behavior. +26.1.4 +VISCOSITY +Products: Abaqus/Explicit Abaqus/CFD Abaqus/CAE +References +• “Viscous shear behavior” in “Equation of state,” Section 25.2.1 +• *VISCOSITY +• *EOS +• *TRS +• “Defining viscosity” in “Defining other mechanical models,” Section 12.9.4 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +Material shear viscosity is an internal property of a fluid that offers resistance to flow. It can be specified +in Abaqus/Explicit and Abaqus/CFD. +Material shear viscosity in Abaqus/Explicit: +• can be a function of temperature and shear strain rate; and +• must be used in combination with an equation of state (“Equation of state,” Section 25.2.1). +Material shear viscosity in Abaqus/CFD: +• can be a function of temperature only for the Newtonian model; +• can be a function of shear strain rate; and +• is not supported for field-dependent variants. +Viscous shear behavior +The resistance to flow of a viscous fluid is described by the following relationship between deviatoric +stress and strain rate +where +is the engineering shear strain rate. +is the deviatoric stress, +is the deviatoric part of the strain rate, +is the viscosity, and +Newtonian fluids are characterized by a viscosity that only depends on temperature, +. In the +more general case of non-Newtonian fluids the viscosity is a function of the temperature and shear strain +rate: +where +is the equivalent shear strain rate. In terms of the equivalent shear stress, +, we have: +Non-Newtonian fluids can be classified as shear-thinning (or pseudoplastic), when the apparent viscosity +decreases with increasing shear rate, and shear-thickening (or dilatant), when the viscosity increases with +strain rate. +In addition to the Newtonian viscous fluid model, Abaqus/CFD and Abaqus/Explicit support several +models of nonlinear viscosity to describe non-Newtonian fluids: power law, Carreau-Yasuda, Cross, +Herschel-Bulkley, Powell-Eyring, and Ellis-Meter. Other functional forms of the viscosity can also be +specified in tabular format. In addition, in Abaqus/Explicit user subroutine VUVISCOSITY can be used. +Newtonian +The Newtonian model is useful to model viscous laminar flow governed by the Navier-Poisson law of +a Newtonian fluid, +. Newtonian fluids are characterized by a viscosity that depends only on +temperature, +. You need to specify the viscosity as a tabular function of temperature when you +define the Newtonian viscous deviatoric behavior. +Input File Usage: +Abaqus/CAE Usage: +*VISCOSITY, DEFINITION=NEWTONIAN (default) +Property module: material editor: Mechanical→Viscosity +Power law +The power law model is commonly used to describe the viscosity of non-Newtonian fluids. The viscosity +is expressed as +is the flow consistency index and +, the fluid is +where +shear-thinning (or pseudoplastic): the apparent viscosity decreases with increasing shear rate. When +, the fluid is Newtonian. Optionally, +, on the value of the viscosity computed +, the fluid is shear-thickening (or dilatant); and when +is the flow behavior index. When +, and/or an upper limit, +you can place a lower limit, +from the power law. +Input File Usage: +Abaqus/CAE Usage: +*VISCOSITY, DEFINITION=POWER LAW +The power law model is not supported in Abaqus/CAE. +Carreau-Yasuda +The Carreau-Yasuda model describes the shear thinning behavior of polymers. This model often provides +a better fit than the power law model for both high and low shear strain rates. The viscosity is expressed +as +is the low shear rate Newtonian viscosity, +is the natural time constant of the fluid ( +where +rates), +from Newtonian to power law behavior), and +regime. The coefficient +is the infinite shear viscosity (at high shear strain +is the critical shear rate at which the fluid changes +represents the flow behavior index in the power law +is a material parameter. The original Carreau model is recovered when =2. +*VISCOSITY, DEFINITION=CARREAU-YASUDA +The Carreau-Yasuda model is not supported in Abaqus/CAE. +Input File Usage: +Abaqus/CAE Usage: +Cross +The Cross model is commonly used when it is necessary to describe the low-shear-rate behavior of the +viscosity. The viscosity is expressed as +is the Newtonian viscosity, +where +the Cross model), +fluid changes from Newtonian to power-law behavior), and +law regime. +is the natural time constant of the fluid ( +is the infinite shear viscosity (usually assumed to be zero for +is the critical shear rate at which the +is the flow behavior index in the power +Input File Usage: +Abaqus/CAE Usage: +*VISCOSITY, DEFINITION=CROSS +The Cross model is not supported in Abaqus/CAE. +Herschel-Bulkley +The Herschel-Bulkley model can be used to describe the behavior of viscoplastic fluids, such as Bingham +plastics, that exhibit a yield response. The viscosity is expressed as +is the “yield” stress and +Here +low strain rate regime ( +strain rates, the viscosity transitions into a power law model once the yield threshold is reached, +The parameters +respectively. Bingham plastics correspond to the case =1. +is a penalty viscosity to model the “rigid-like” behavior in the very +. With increasing +. +are the flow consistency and the flow behavior indexes in the power law regime, +), when the stress is below the yield stress, +and +Input File Usage: +Abaqus/CAE Usage: +*VISCOSITY, DEFINITION=HERSCHEL-BULKLEY +The Herschel-Bulkley model is not supported in Abaqus/CAE. +Powell-Eyring +This model, which is derived from the theory of rate processes, is relevant primarily to molecular fluids +but can be used in some cases to describe the viscous behavior of polymer solutions and viscoelastic +suspensions over a wide range of shear rates. The viscosity is expressed as +where +time of the measured system. +is the Newtonian viscosity, +is the infinite shear viscosity, and +represents a characteristic +Input File Usage: +Abaqus/CAE Usage: +*VISCOSITY, DEFINITION=POWELL-EYRING +The Powell-Eyring model is not supported in Abaqus/CAE. +Ellis-Meter +The Ellis-Meter model expresses the viscosity in terms of the effective shear stress, +, as: +where +and the infinite shear viscosity, +is the effective shear stress at which the viscosity is 50% between the Newtonian limit, +, +, and +represents the flow index in the power law regime. +Input File Usage: +Abaqus/CAE Usage: +*VISCOSITY, DEFINITION=ELLIS-METER +The Ellis-Meter model is not supported in Abaqus/CAE. +Tabular +In Abaqus/Explicit the viscosity can be specified directly as a tabular function of shear strain rate and +temperature. In Abaqus/CFD only shear strain rate dependence is supported. +Input File Usage: +Abaqus/CAE Usage: +*VISCOSITY, DEFINITION=TABULAR +Specifying the viscosity directly as a tabular function is not supported in +Abaqus/CAE. +User-defined (Abaqus/Explicit only) +In Abaqus/Explicit you can specify a user-defined viscosity in user subroutine VUVISCOSITY . +*VISCOSITY, DEFINITION=USER +User-defined viscosity is not supported in Abaqus/CAE. +Abaqus/CAE Usage: +Input File Usage: +Temperature dependence of viscosity (Abaqus/Explicit only) +The temperature-dependence of the viscosity of many polymer materials of industrial interest obeys a +time-temperature shift relationship in the form: +is the shift function and +where +is the reference temperature at which the viscosity versus shear +strain rate relationship is known. This concept for temperature dependence is usually referred to as +thermo-rheologically simple (TRS) temperature dependence. In the Newtonian limit for low shear rates, +when +, we have +Thus, the shift function is defined as the ratio of the Newtonian viscosity at the temperature of interest +to that of the chosen reference state: +. +See “Thermo-rheologically simple temperature effects” in “Time domain viscoelasticity,” +Section 22.7.1, for a description of the different forms of the shift function available in Abaqus. +Input File Usage: +Use the following options to define a thermo-rheologically simple (TRS) +temperature-dependent viscosity: +Abaqus/CAE Usage: +*VISCOSITY +*TRS +Defining a thermo-rheologically simple temperature-dependent viscosity is not +supported in Abaqus/CAE. +Use with other material models +Material shear viscosity in Abaqus/Explicit must be used in combination with an equation of state to +define the material’s volumetric mechanical behavior . +Elements +Material shear viscosity can be used with any solid (continuum) elements in Abaqus/Explicit except +plane stress elements and with any fluid (continuum) elements in Abaqus/CFD. +26.2 +Heat transfer properties +• “Thermal properties: overview,” Section 26.2.1 +• “Conductivity,” Section 26.2.2 +• “Specific heat,” Section 26.2.3 +• “Latent heat,” Section 26.2.4 +26.2.1 +THERMAL PROPERTIES: OVERVIEW +The following properties describe the thermal behavior of a material and can be used in heat transfer and +thermal stress analyses : +• Thermal conductivity: When heat flows by conduction, the thermal conductivity must be defined +(“Conductivity,” Section 26.2.2). +• Specific heat: +In transient heat transfer analyses as well as adiabatic stress analyses the specific heat +of a material must be defined (“Specific heat,” Section 26.2.3). +• Latent heat: When a material changes phase, the change in internal energy can be significant. The +amount of energy liberated or absorbed can be defined by specifying a latent heat for each phase change +a material undergoes (“Latent heat,” Section 26.2.4). +26.2.2 +CONDUCTIVITY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Thermal properties: overview,” Section 26.2.1 +• *CONDUCTIVITY +• “Specifying thermal conductivity,” Section 12.10.1 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +A material’s thermal conductivity: +• must be defined for “Uncoupled heat transfer analysis,” Section 6.5.2; “Fully coupled thermal-stress +analysis,” Section 6.5.3; and “Coupled thermal-electrical analysis,” Section 6.7.3; +• must be defined for an Abaqus/CFD analysis when the energy equation is active (“Energy equation” +in “Incompressible fluid dynamic analysis,” Section 6.6.2); +• can be linear or nonlinear (by defining it as a function of temperature); +• can be isotropic, orthotropic, or fully anisotropic; and +• can be specified as a function of temperature and/or field variables. +Directional dependence of thermal conductivity +Isotropic, orthotropic, or fully anisotropic thermal conductivity can be defined. Only isotropic thermal +conductivity can be defined for an incompressible fluid dynamic analysis that includes an energy +equation. For orthotropic or anisotropic thermal conductivity, a local orientation (“Orientations,” +Section 2.2.5) must be used to specify the material directions used to define the conductivity. +Isotropic conductivity +For isotropic conductivity only one value of conductivity is needed at each temperature and field variable +value. Isotropic conductivity is the default. +Input File Usage: +Abaqus/CAE Usage: +*CONDUCTIVITY, TYPE=ISO +Property module: material editor: Thermal→Conductivity: Type: Isotropic +Orthotropic conductivity +For orthotropic conductivity three values of conductivity ( +and field variable value. +, +, +) are needed at each temperature +Input File Usage: +*CONDUCTIVITY, TYPE=ORTHO +Abaqus/CAE Usage: +Property module: material editor: Thermal→Conductivity: +Type: Orthotropic +Anisotropic conductivity +For fully anisotropic conductivity six values of conductivity ( +each temperature and field variable value. +, +, +, +, +, +) are needed at +Input File Usage: +Abaqus/CAE Usage: +*CONDUCTIVITY, TYPE=ANISO +Property module: material editor: Thermal→Conductivity: +Type: Anisotropic +Elements +Thermal conductivity is active in all heat transfer, coupled temperature-displacement, coupled thermal- +electrical-structural, and coupled thermal-electrical elements in Abaqus. Isotropic thermal conductivity +is active in fluid (continuum) elements in Abaqus/CFD for incompressible fluid dynamic analyses that +include an energy equation. +26.2.3 +SPECIFIC HEAT +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Thermal properties: overview,” Section 26.2.1 +• *SPECIFIC HEAT +• “Defining specific heat,” Section 12.10.6 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +A material’s specific heat: +• is required for transient “Uncoupled heat transfer analysis,” Section 6.5.2; +transient “Fully +coupled thermal-stress analysis,” Section 6.5.3; transient “Coupled thermal-electrical analysis,” +Section 6.7.3; and “Adiabatic analysis,” Section 6.5.4; +• must be defined for an Abaqus/CFD analysis when the energy equation is active (“Energy equation” +in “Incompressible fluid dynamic analysis,” Section 6.6.2); +• must appear in conjunction with a density definition ; +• can be linear or nonlinear (by defining it as a function of temperature); and +• can be specified as a function of temperature and/or field variables. +Defining specific heat +The specific heat of a substance is defined as the amount of heat required to increase the temperature of +a unit mass by one degree. Mathematically, this physical statement can be expressed as: +is the infinitessimal heat added per unit mass and +where +is the entropy per unit mass. Since heat +transfer depends on the conditions encountered during the whole process (a path function), it is necessary +to specify the conditions used in the process to unambiguously characterize the specific heat. Thus, a +process where the heat is supplied keeping the volume constant defines the specific heat as: +where +is the internal energy per unit mass. +Whereas, a process where the heat is supplied keeping the pressure constant defines the specific +heat as: +is the enthalpy per unit mass. In general, the specific heats are functions of temperature. +where +For solids and liquids, +are equivalent; thus, there is no need to distinguish between them. When +possible, large changes in internal energy or enthalpy during a phase change should be modeled using +“Latent heat,” Section 26.2.4, instead of specific heat. +and +Defining constant-volume specific heat +The specific heat per unit mass is given as a function of temperature and field variables. By default, +specific heat at constant volume is assumed. +*SPECIFIC HEAT +The following option can also be used in Abaqus/CFD: +Input File Usage: +Abaqus/CAE Usage: +*SPECIFIC HEAT, TYPE=CONSTANT VOLUME +Property module: material editor: Thermal→Specific Heat; +Type: Constant Volume +Defining constant-pressure specific heat +In Abaqus/CFD the constant-pressure specific heat is required when the energy equation is used for +thermal-flow problems. +Input File Usage: +Abaqus/CAE Usage: +*SPECIFIC HEAT, TYPE=CONSTANT PRESSURE +Property module: material editor: Thermal→Specific Heat; +Type: Constant Pressure +Elements +Specific heat effects can be defined for all heat transfer, coupled thermal-electrical-structural, coupled +temperature-displacement, coupled thermal-electrical, and fluid elements in Abaqus. Specific heat can +also be defined for stress/displacement elements for use in adiabatic stress analysis. +Specific heat must be defined for all transient thermal analyses even if the only elements in the +model are user-defined elements (“User-defined elements,” Section 32.15.1), in which case a dummy +specific heat must be specified. +26.2.4 +LATENT HEAT +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• “Thermal properties: overview,” Section 26.2.1 +• *LATENT HEAT +• “Specifying latent heat data,” Section 12.10.5 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +A material’s latent heat: +• models large changes in internal energy during phase change of a material; +• is active only during transient heat transfer, coupled thermal-stress, coupled thermal-electrical- +structural and coupled thermal-electrical analysis in Abaqus ; +• must appear in conjunction with a density definition ; and +• always makes an analysis nonlinear. +Defining latent heat +Latent heat effects can be significant and must be included in many heat transfer problems involving +phase change. When latent heat is given, it is assumed to be in addition to the specific heat effect . +The latent heat is assumed to be released over a range of temperatures from a lower (solidus) +temperature to an upper (liquidus) temperature. To model a pure material with a single phase change +temperature, these limits can be made very close. +As many latent heats as are necessary can be defined to model several phase changes in the material. +Latent heat can be combined with any other material behavior in Abaqus, but it should not be included +in the material definition unless necessary; it always makes the analysis nonlinear. +Direct data specification +If the phase change occurs within a known temperature range, the solidus and liquidus temperatures can +be given directly. The latent heat should be given per unit mass. +Input File Usage: +Abaqus/CAE Usage: +*LATENT HEAT +Property module: material editor: Thermal→Latent Heat +User subroutine +In some cases it may be necessary to include a kinetic theory for the phase change to model the effect +accurately in Abaqus/Standard; for example, the prediction of crystallization in a polymer casting +process. In such cases you can model the process in considerable detail using solution-dependent state +variables (“User subroutines: overview,” Section 18.1.1) and user subroutine HETVAL. +Input File Usage: +Use the following options: +*HEAT GENERATION +*DEPVAR +Property module: material editor: +Thermal→Heat Generation +General→Depvar +Abaqus/CAE Usage: +Elements +Latent heat effects can be used in all diffusive heat transfer, coupled temperature-displacement, coupled +thermal-electrical-structural and coupled thermal-electrical elements in Abaqus but cannot be used with +convective heat transfer elements. Strong latent heat effects are best modeled with first-order or modified +second-order elements, which use integration methods designed to provide accurate results for such +cases. +See “Freezing of a square solid: the two-dimensional Stefan problem,” Section 1.6.2 of the Abaqus +Benchmarks Manual, for an example of a heat conduction problem involving latent heat. +26.3 +Acoustic properties +• “Acoustic medium,” Section 26.3.1 +26.3.1 +ACOUSTIC MEDIUM +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Acoustic, shock, and coupled acoustic-structural analysis,” Section 6.10.1 +• “Acoustic and shock loads,” Section 33.4.6 +• “Material library: overview,” Section 21.1.1 +• “Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1 +• *ACOUSTIC MEDIUM +• *DENSITY +• *INITIAL CONDITIONS +• “Defining an acoustic medium,” Section 12.12.1 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +An acoustic medium: +• is used to model sound propagation problems; +• can be used in a purely acoustic analysis or in a coupled acoustic-structural analysis such as the +calculation of shock waves in a fluid or noise levels in a vibration problem; +• is an elastic medium (usually a fluid) in which stress is purely hydrostatic (no shear stress) and +pressure is proportional to volumetric strain; +• is specified as part of a material definition; +• must appear in conjunction with a density definition ; +• can include fluid cavitation in Abaqus/Explicit when the absolute pressure drops to a limit value; +• can be defined as a function of temperature and/or field variables; +• can include dissipative effects; +• can model small pressure changes (small amplitude excitation); +• can model waves in the presence of steady underlying flow of the medium; and +• is active only during dynamic analysis procedures (“Dynamic analysis procedures: overview,” +Section 6.3.1). +Defining an acoustic medium +The equilibrium equation for small motions of a compressible, inviscid fluid flowing through a resisting +matrix material is taken to be +where p is the dynamic pressure in the fluid (the pressure in excess of any initial static pressure), +spatial position of the fluid particle, +is the +is the fluid particle acceleration, +is the fluid particle velocity, +is the density of the fluid, and is the “volumetric drag” (force per unit volume per velocity) caused by +the fluid flowing through the matrix material. The d’Alembert term has been written without convection +on the assumption that there is no steady flow of the fluid, which is usually considered to be sufficiently +accurate for steady fluid velocities up to Mach 0.1. +The constitutive behavior of the fluid is assumed to be inviscid and compressible, so that the bulk +modulus of an acoustic medium relates the dynamic pressure in the medium to the volumetric strain by +where +an acoustic medium must be defined. +is the volumetric strain. Both the bulk modulus +and the density +of +The bulk modulus +can be defined as a function of temperature and field variables but does +not vary in value during an implicit dynamic analysis using the subspace projection method (“Implicit +dynamic analysis using direct integration,” Section 6.3.2) or a direct-solution steady-state dynamic +analysis (“Direct-solution steady-state dynamic analysis,” Section 6.3.4); for these procedures the value +of the bulk modulus at the beginning of the step is used. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options to define an acoustic medium: +*ACOUSTIC MEDIUM, BULK MODULUS +*DENSITY +Property module: material editor: +Other→Acoustic Medium: Bulk Modulus +General→Density +Volumetric drag +Dissipation of energy (and attenuation of acoustic waves) may occur in an acoustic medium due to +a variety of factors. Such dissipation effects are phenomenologically characterized in the frequency +domain by the imaginary part of the propagation constant, which gives an exponential decay in amplitude +as a function of distance. In Abaqus the simplest way to model this effect is through a “volumetric drag +coefficient,” +(force per unit volume per velocity). +In frequency-domain procedures, may be frequency dependent. +can be entered as a function of +frequency— , where f is the frequency in cycles per time (usually Hz)—in addition to temperature +and/or field variables only when the acoustic medium is used in a steady-state dynamics procedure. If +the acoustic medium is used in a direct-integration dynamic procedure (including Abaqus/Explicit), the +volumetric drag coefficient is assumed to be independent of frequency and the first value entered for the +current temperature and/or field variable is used. +In all procedures except direct steady-state dynamics the gradient of +is assumed to be small. +Input File Usage: +Abaqus/CAE Usage: +*ACOUSTIC MEDIUM, VOLUMETRIC DRAG +Property module: material editor: Other→Acoustic Medium: +Volumetric Drag: Include volumetric drag +Porous acoustic material models +Porous materials are commonly used to suppress acoustic waves; this attenuating effect arises from a +number of effects as the acoustic fluid interacts with the solid matrix. For many categories of materials, +the solid matrix can be approximated as either fully rigid compared to the acoustic fluid or fully limp. In +these cases a mechanical model that resolves only acoustic waves will suffice. The acoustic behavior of +porous materials can be modeled in a variety of ways in Abaqus/Standard. +Craggs model +The model discussed in Craggs (1978) is readily accommodated in Abaqus. Applying this model results +in the dynamic equilibrium equation for the fluid expressed in this form: +where +“structure factor,” and +is the real-valued resistivity, +is the real-valued dimensionless porosity, +is the dimensionless +is the dimensionless wave number. This equation can be rewritten as +This model, therefore, can be applied straightforwardly in Abaqus by setting the material density equal +to +. The Craggs model is +, the volumetric drag equal to +supported for all acoustic procedures in Abaqus. +, and the bulk modulus equal to +Delany-Bazley and Delany-Bazley-Miki models +Abaqus/Standard supports the well-known empirical model proposed in Delany & Bazley (1970), which +determines the material properties as a function of frequency and user-defined flow resistivity, +; density, +. A variation on this model, proposed by Miki (1990) is also available. These +; and bulk modulus, +models are supported only for steady-state dynamic procedures. +Both models compute frequency-dependent material characteristic impedance, +, according to the following formula: +or propagation constant, +, and wavenumber +where +and +The constants are as given in the table below: +Delany- +Bazley +Miki +0.0978 +–0.7 +0.189 +–0.595 +0.0571 +–0.754 +0.087 +–0.732 +0.1227 +–0.618 +0.1792 +–0.618 +0.0786 +–0.632 +0.1205 +–0.632 +The material characteristic impedance and the wavenumber are converted internally to complex density +and complex bulk modulus for use in Abaqus. The signs of the imaginary parts in these formulae are +consistent with the Abaqus sign convention for time-harmonic dynamics. +Input File Usage: +Abaqus/CAE Usage: +Use the following options to use the Delany-Bazley model: +*DENSITY +*ACOUSTIC MEDIUM, BULK MODULUS +*ACOUSTIC MEDIUM, POROUS MODEL=DELANY BAZLEY +Use the following options to use the Miki model: +*DENSITY +*ACOUSTIC MEDIUM, BULK MODULUS +*ACOUSTIC MEDIUM, POROUS MODEL=MIKI +Porous acoustic material models are not supported in Abaqus/CAE. +General frequency-dependent models +For steady-state dynamic procedures, Abaqus/Standard supports general frequency-dependent complex +bulk modulus and complex density. Using these parameters, data from a wide range of models can be +accommodated in an analysis; for example, see Allard, et. al (1998), Attenborough (1982), Song & +Bolton (1999), and Wilson (1993). These models are used in a variety of applications, such as ocean +acoustics, aerospace, automotive, and architectural acoustic engineering. +The signs of these parameters must be consistent with the sign conventions used in Abaqus, and +with conservation of energy. Abaqus uses a Fourier transform pair formally equivalent to assuming +time dependence. Consequently, the real parts of the density and bulk modulus are positive for all values +of frequency, the imaginary part of the bulk modulus must be positive, and the imaginary part of the +density must be negative. +A linear isotropic acoustic material can be fully described with the two frequency-dependent +. It is common, however, to encounter materials defined +, wave number or propagation +parameters: bulk modulus, +in terms of other parameter pairs, such as characteristic impedance, +, and density, +. Data defined with the pair +complex density and bulk modulus form, beginning from the following standard formulae: +, or speed of sound, +or +can be converted into the +ACOUSTIC MEDIUM +Consistent with the Abaqus sign conventions, the real parts of +and must be positive; the imaginary +part of must be negative, and the imaginary part of must be positive. In commonly observed materials, +the ratio of the magnitude of the imaginary part to the real part for each of these constants is usually much +less than one. +Input File Usage: +Use the following option to use the general frequency-dependent model: +*ACOUSTIC MEDIUM, COMPLEX BULK MODULUS +*ACOUSTIC MEDIUM, COMPLEX DENSITY +If desired, either complex material option can be used instead in conjunction +with a real-valued, frequency-independent material option: +*ACOUSTIC MEDIUM, COMPLEX BULK MODULUS +*DENSITY +or, alternatively, +*ACOUSTIC MEDIUM, BULK MODULUS +*ACOUSTIC MEDIUM, COMPLEX DENSITY +Abaqus/CAE Usage: +General frequency-dependent acoustic material models are not supported in +Abaqus/CAE. +Conversion from complex material impedance and wavenumber +Since +and +the real and imaginary parts of +are, respectively: +and the real and imaginary parts of +are, respectively: +. +Conversion from complex impedance and speed of sound +Since +and +the real and imaginary parts of +are, respectively: +and the real and imaginary parts of +are, respectively: +. +Fluid cavitation +In general, fluids cannot withstand any significant tensile stress and are likely to undergo large volume +expansion when the absolute pressure is close to or less than zero. Abaqus/Explicit allows modeling of +this phenomenon through a cavitation pressure limit for the acoustic medium. When the fluid absolute +pressure (sum of the dynamic and initial static pressures) reduces to this limit, the fluid undergoes free +volume expansion (i.e., cavitation), without a further drop in the pressure. If this limit is not defined, the +fluid is assumed not to undergo cavitation even under a tensile, negative absolute pressure, condition. +The constitutive behavior for an acoustic medium capable of undergoing cavitation can be stated as +where a pseudo-pressure +, a measure of the volumetric strain, is defined as +is the fluid cavitation limit and +where +is the initial acoustic static pressure. A total wave +formulation is used for a nonlinear acoustic medium undergoing cavitation. This formulation is very +similar to the scattered wave formulation except that the pseudo-pressure, defined as the product of +the bulk modulus and the compressive volumetric strain, plays the role of the material state variable +instead of the acoustic dynamic pressure and the acoustic dynamic pressure is readily available from +this pseudo-pressure subject to the cavitation condition. +Input File Usage: +Abaqus/CAE Usage: +*ACOUSTIC MEDIUM, CAVITATION LIMIT +Fluid cavitation is not supported in Abaqus/CAE. +Defining the wave formulation +In the presence of cavitation in Abaqus/Explicit the fluid mechanical behavior is nonlinear. Hence, for +an acoustic problem with incident wave loading and possible cavitation in the fluid, the scattered wave +formulation, which provides a solution for only a scattered wave dynamic acoustic pressure, may not +be appropriate. For these cases the total wave formulation, which solves for the total dynamic acoustic +pressure, should be selected. See “Acoustic and shock loads,” Section 33.4.6, for details. +*ACOUSTIC WAVE FORMULATION, TYPE=TOTAL WAVE +Any module: Model→Edit Attributes→model_name. Toggle on +Specify acoustic wave formulation: Total wave +Abaqus/CAE Usage: +Input File Usage: +Defining the initial acoustic static pressure +Cavitation occurs when the absolute pressure reaches the cavitation limit value. Abaqus/Explicit allows +for an initial linearly varying hydrostatic pressure in the fluid medium . You can +specify pressure values at two locations and a node set of the acoustic medium nodes. Abaqus/Explicit +interpolates from these data to initialize the static pressure at all the nodes in the specified node set. If the +pressure at only one location is specified, the hydrostatic pressure in the fluid is assumed to be uniform. +The acoustic static pressure is used only for determining the cavitation status of the acoustic element +nodes and does not apply any static loads to the acoustic or structural mesh at their common wetted +interface. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=ACOUSTIC STATIC PRESSURE +Initial acoustic pressures are not supported in Abaqus/CAE. +Defining a steady flow field +Acoustic finite elements can be used to simulate time-harmonic wave propagation and natural frequency +analysis in the presence of a steady mean flow of the medium. For example, air may move at a speed +large enough to affect the propagation speed of waves in the direction of flow and against it. These effects +are modeled in Abaqus/Standard by specifying an acoustic flow velocity during the linear perturbation +analysis step definition; you do not need to alter the acoustic material properties. See “Acoustic, shock, +and coupled acoustic-structural analysis,�� Section 6.10.1, for details. +Elements +An acoustic material definition can be used only with the acoustic elements in Abaqus . +In Abaqus/Standard second-order acoustic elements are more accurate than first-order elements. +Use at least six nodes per wavelength +in the acoustic medium to obtain accurate results. +Output +Nodal output variable POR (pressure magnitude) is available for an acoustic medium in Abaqus (in +Abaqus/CAE this output variable is called PAC). When the scattered wave formulation is used with +incident wave loading in Abaqus/Explicit, output variable POR represents only the scattered pressure +response of the model and does not include the incident wave loading itself. When the total wave +formulation is used, output variable POR represents the total dynamic acoustic pressure, which includes +contributions from both incident and scattered waves as well as the dynamic effects of fluid cavitation. +For either formulation output variable POR does not include the acoustic static pressure, which is used +only to evaluate the cavitation status in the acoustic medium. +In addition, in Abaqus/Standard nodal output variable PPOR (the pressure phase) is available for +an acoustic medium. In Abaqus/Explicit nodal output variable PABS (the absolute pressure, equal to the +sum of POR and the acoustic static pressure) is available for an acoustic medium. +Additional references +• Allard, +J. F., M. Henry, +J. Tizianel, L. Kelders, and W. Lauriks, “Sound Propagation in +Air-Saturated Random Packings of Beads,” Journal of the Acoustical Society of America, +vol. 104, no. 4, p. 2004, 1998. +• Attenborough, K. F., “Acoustical Characterisitics of Rigid Fibrous Absorbents and Granular +Materials,” Journal of the Acoustical Society of America, vol. 73, no. 3, p. 785, 1982. +• Craggs, A., “A Finite Element Model for Rigid Porous Absorbing Materials,” Journal of Sound and +Vibration, vol. 61, no. 1, p. 101, 1978. +• Craggs, A., “Coupling of Finite Element Acoustic Absorption Models,” Journal of Sound and +Vibration, vol. 66, no. 4, p. 605, 1979. +• Delany, M. E., and E. N. Bazley, “Acoustic Properties of Fibrous Absorbent Materials,” Applied +Acoustics, vol. 3, p. 105, 1970. +• Miki, Y., “Acoustical Properties of Porous Materials - Modifications of Delany-Bazley Models,” +Journal of the Acoustical Society of Japan (E), vol. 11, no. 1, p. 19, 1990. +• Song, B. H., and J. S. Bolton, “A Transfer-Matrix Approach for Estimating the Characteristic +Impedance and Wavenumbers of Limp and Rigid Porous Materials,” Journal of the Acoustical +Society of America, vol. 107, no. 3, p. 1131, 1999. +• Wilson, D. K., “Relaxation-Matched Modeling of Propagation through Porous Media, Including +Fractal Pore Structure,” Journal of the Acoustical Society of America, vol. 94, no. 2, p. 1136, 1993. +26.4 +Mass diffusion properties +• “Diffusivity,” Section 26.4.1 +• “Solubility,” Section 26.4.2 +26.4.1 +DIFFUSIVITY +Products: Abaqus/Standard Abaqus/CAE +References +• “Mass diffusion analysis,” Section 6.9.1 +• “Material library: overview,” Section 21.1.1 +• *DIFFUSIVITY +• *KAPPA +• “Defining mass diffusion,” Section 12.12.2 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +Diffusivity: +• defines the diffusion or movement of one material through another, such as the diffusion of hydrogen +through a metal; +• must always be defined for mass diffusion analysis; +• must be defined in conjunction with “Solubility,” Section 26.4.2; +• can be defined as a function of concentration, temperature, and/or predefined field variables; +• can be used in conjunction with a “Soret effect” factor to introduce mass diffusion caused by +temperature gradients; +• can be used in conjunction with a pressure stress factor to introduce mass diffusion caused by +gradients of equivalent pressure stress (hydrostatic pressure); and +• can produce a nonlinear mass diffusion analysis when dependence on concentration is included (the +same can be said for the Soret effect factor and the pressure stress factor). +Defining diffusivity +Diffusivity is the relationship between the concentration flux, +, of the diffusing material and the +gradient of the chemical potential that is assumed to drive the mass diffusion process. Either general +mass diffusion behavior or Fick’s diffusion law can be used to define diffusivity, as discussed below. +General chemical potential +Diffusive behavior provides the following general chemical potential: +where +is the diffusivity; +is the solubility ; +is the Soret effect factor, providing diffusion because of temperature gradient ; +is the pressure stress factor, providing diffusion because of the gradient of the +equivalent pressure stress ; +is the normalized concentration; +is the concentration of the diffusing material; +is the temperature; +is the temperature at absolute zero ; +is the equivalent pressure stress; and +are any predefined field variables. +Input File Usage: +Abaqus/CAE Usage: +*DIFFUSIVITY, LAW=GENERAL (default) +Property module: material editor: Other→Mass Diffusion→Diffusivity: +Law: General +Fick’s law +An extended form of Fick’s law can be used as an alternative to the general chemical potential: +Input File Usage: +Abaqus/CAE Usage: +*DIFFUSIVITY, LAW=FICK +Property module: material editor: Other→Mass Diffusion→Diffusivity: +Law: Fick +Directional dependence of diffusivity +Isotropic, orthotropic, or fully anisotropic diffusivity can be defined. For non-isotropic diffusivity a local +orientation of the material directions must be specified . +Isotropic diffusivity +For isotropic diffusivity only one value of diffusivity is needed at each concentration, temperature, and +field variable value. +Input File Usage: +Abaqus/CAE Usage: +*DIFFUSIVITY, TYPE=ISO +Property module: material editor: Other→Mass Diffusion→Diffusivity: +Type: Isotropic +Orthotropic diffusivity +For orthotropic diffusivity three values of diffusivity ( +temperature, and field variable value. +, +, +) are needed at each concentration, +Input File Usage: +Abaqus/CAE Usage: +*DIFFUSIVITY, TYPE=ORTHO +Property module: material editor: Other→Mass Diffusion→Diffusivity: +Type: Orthotropic +Anisotropic diffusivity +For fully anisotropic diffusivity six values of diffusivity ( +each concentration, temperature, and field variable value. +*DIFFUSIVITY, TYPE=ANISO +Property module: material editor: Other→Mass Diffusion→Diffusivity: +Type: Anisotropic +Abaqus/CAE Usage: +Input File Usage: +, +, +, +, +, +) are needed at +Temperature-driven mass diffusion +, governs temperature-driven mass diffusion. It can be defined as a function +The Soret effect factor, +of concentration, temperature, and/or field variables in the context of the constitutive equation presented +above. The Soret effect factor cannot be specified in conjunction with Fick’s law since it is calculated +automatically in this case . +Input File Usage: +Use both of the following options to specify general temperature-driven mass +diffusion: +*DIFFUSIVITY, LAW=GENERAL +*KAPPA, TYPE=TEMP +Use the following option to specify temperature-driven diffusion governed by +Fick’s law: +Abaqus/CAE Usage: +*DIFFUSIVITY, LAW=FICK +Use the following options to specify general temperature-driven mass diffusion: +Property module: material editor: Other→Mass Diffusion→Diffusivity: +Law: General: Suboptions→Soret Effect +Use the following option to specify temperature-driven diffusion governed by +Fick’s law: +Property module: material editor: Other→Mass Diffusion→Diffusivity: +Law: Fick +Pressure stress-driven mass diffusion +The pressure stress factor, +, governs mass diffusion driven by the gradient of the equivalent pressure +stress. It can be defined as a function of concentration, temperature, and/or field variables in the context +of the constitutive equation presented above. +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*DIFFUSIVITY, LAW=GENERAL +*KAPPA, TYPE=PRESS +Property module: material editor: Other→Mass Diffusion→Diffusivity: +Law: General: Suboptions→Pressure Effect +Mass diffusion driven by both temperature and pressure stress +and +causes gradients of temperature and equivalent pressure stress to drive mass +Specifying both +diffusion. +Input File Usage: +Abaqus/CAE Usage: +Use all of the following options to specify general diffusion driven by gradients +of temperature and pressure stress: +*DIFFUSIVITY, LAW=GENERAL +*KAPPA, TYPE=TEMP +*KAPPA, TYPE=PRESS +Use both of the following options to specify diffusion driven by the extended +form of Fick’s law: +*DIFFUSIVITY, LAW=FICK +*KAPPA, TYPE=PRESS +Use the following options to specify general diffusion driven by gradients of +temperature and pressure stress: +Property module: material editor: Other→Mass Diffusion→Diffusivity: +Law: General: Suboptions→Soret Effect and +Suboptions→Pressure Effect +Use the following options to specify diffusion driven by the extended form of +Fick’s law: +Property module: material editor: Other→Mass Diffusion→Diffusivity: +Law: Fick: Suboptions→Pressure Effect +Specifying the value of absolute zero +You can specify the value of absolute zero as a physical constant. +Input File Usage: +*PHYSICAL CONSTANTS, ABSOLUTE ZERO= +Abaqus/CAE Usage: +Any module: Model→Edit Attributes→model_name: +Absolute zero temperature +Elements +The mass diffusion law can be used only with the two-dimensional, three-dimensional, and axisymmetric +solid elements that are included in the heat transfer/mass diffusion element library. +26.4.2 +SOLUBILITY +Products: Abaqus/Standard Abaqus/CAE +References +• “Mass diffusion analysis,” Section 6.9.1 +• “Material library: overview,” Section 21.1.1 +• *SOLUBILITY +• “Defining solubility” in “Defining mass diffusion,” Section 12.12.2 of the Abaqus/CAE User’s +Manual, in the online HTML version of this manual +Overview +Solubility: +• is needed only for mass diffusion analysis; +• is also known as Sievert’s parameter (in Sievert’s law); +• must always accompany a diffusivity definition ; and +• can be defined as a function of temperature and/or predefined field variables. +Defining solubility +Solubility, s, is used to define the “normalized concentration,” , of the diffusing phase in a mass diffusion +process: +where c is the concentration. The normalized concentration is often also referred to as the “activity” +of the diffusing material, and the gradients of the normalized concentration, along with gradients of +temperature and pressure stress, drive the diffusion process . +Input File Usage: +Abaqus/CAE Usage: +*SOLUBILITY +Property module: material editor: Other→Mass Diffusion→Solubility +Elements +The mass diffusion law can be used only with the two-dimensional, three-dimensional, and axisymmetric +solid elements that are included in the heat transfer/mass diffusion element library. +26.5 +Electromagnetic properties +• “Electrical conductivity,” Section 26.5.1 +• “Piezoelectric behavior,” Section 26.5.2 +• “Magnetic permeability,” Section 26.5.3 +26.5.1 +ELECTRICAL CONDUCTIVITY +Products: Abaqus/Standard Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• *ELECTRICAL CONDUCTIVITY +• “Defining electrical conductivity,” Section 12.11.1 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +A material’s electrical conductivity: +• must be defined for “Coupled thermal-electrical analysis,” Section 6.7.3; +• must be defined for “Fully coupled thermal-electrical-structural analysis,” Section 6.7.4; +• must be used to define the electromagnetic response of a conductor for “Eddy current analysis,” +Section 6.7.5; +• can be linear or nonlinear (by defining it as a function of temperature); +• can be isotropic, orthotropic, or fully anisotropic; +• can be specified as a function of temperature and/or field variables; and +• can be specified as a function of frequency for “Eddy current analysis,” Section 6.7.5. +Directional dependence of electrical conductivity +Isotropic, orthotropic, or fully anisotropic electrical conductivity can be defined. For non-isotropic +conductivity a local orientation for the material directions must be specified (“Orientations,” +Section 2.2.5). +Isotropic electrical conductivity +For isotropic electrical conductivity only one value of electrical conductivity is needed at each +temperature and field variable value. Isotropic electrical conductivity is the default. +*ELECTRICAL CONDUCTIVITY, TYPE=ISOTROPIC +Property module: material editor: Electrical/Magnetic→Electrical +Conductivity: Type: Isotropic +Abaqus/CAE Usage: +Input File Usage: +Orthotropic electrical conductivity +For orthotropic electrical conductivity three values of electrical conductivity ( +at each temperature and field variable value. +, +, +) are needed +Input File Usage: +*ELECTRICAL CONDUCTIVITY, TYPE=ORTHOTROPIC +Abaqus/CAE Usage: +Property module: material editor: Electrical/Magnetic→Electrical +Conductivity: Type: Orthotropic +Anisotropic electrical conductivity +For fully anisotropic electrical conductivity six values ( +temperature and field variable value. +, +, +, +, +, +) are needed at each +Input File Usage: +Abaqus/CAE Usage: +*ELECTRICAL CONDUCTIVITY, TYPE=ANISOTROPIC +Property module: material editor: Electrical/Magnetic→Electrical +Conductivity: Type: Anisotropic +Frequency-dependent electrical conductivity +Electrical conductivity can be defined as a function of frequency in an eddy current analysis. +Input File Usage: +Abaqus/CAE Usage: +*ELECTRICAL CONDUCTIVITY, FREQUENCY +Property module: material editor: Electrical/Magnetic→Electrical +Conductivity: Toggle on Use frequency-dependent data +Elements +Electrical conductivity is active only in coupled thermal-electrical elements, coupled thermal-electrical- +structural elements, and electromagnetic elements . +26.5.2 +PIEZOELECTRIC BEHAVIOR +Products: Abaqus/Standard Abaqus/CAE +References +• “Piezoelectric analysis,” Section 6.7.2 +• “Material library: overview,” Section 21.1.1 +• *DIELECTRIC +• *PIEZOELECTRIC +• “Defining dielectric material properties,” Section 12.11.2 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Defining piezoelectric properties,” Section 12.11.3 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +A piezoelectric material: +• is one in which an electrical field causes the material to strain, while stress causes an electric +potential gradient; +• provides linear relations between mechanical and electrical fields; and +• is used in piezoelectric elements, which have both displacement and electrical potential as nodal +variables. +Defining a piezoelectric material +A piezoelectric material responds to an electric potential gradient by straining, while stress causes an +electric potential gradient in the material. This coupling between electric potential gradient and strain is +the material’s piezoelectric property. The material will also have a dielectric property so that an electrical +charge exists when the material has a potential gradient. Piezoelectric material behavior is discussed in +“Piezoelectric analysis,” Section 2.10.1 of the Abaqus Theory Manual. +The mechanical properties of the material must be modeled by linear elasticity (“Linear elastic +behavior,” Section 22.2.1). The mechanical behavior can be defined by +in terms of the piezoelectric stress coefficient matrix, +, or by +in terms of the piezoelectric strain coefficient matrix, +. The electrical behavior is defined by +where +is the mechanical stress tensor; +is the strain tensor; +is the electric “displacement” vector; +is the material’s elastic stiffness matrix defined at zero electrical potential gradient (short +circuit condition); +is the material’s piezoelectric stress coefficient matrix, defining the stress +electrical potential gradient +the electrical displacement +gradient); +is the material’s piezoelectric strain coefficient matrix, defining the strain +electrical potential gradient +is given later in this section); +is the electrical potential; +caused by the +in a fully constrained material (it can also be interpreted as +at a zero electrical potential +caused by the +in an unconstrained material (an alternative interpretation +caused by the applied strain +is the material’s dielectric property, defining the relation between the electric displacement +and the electric potential gradient +is the electrical potential gradient vector, +. +for a fully constrained material; and +The material’s electrical and electro-mechanical coupling behaviors are, +thus, defined by its +, or its piezoelectric strain +. These properties are defined as part of the material definition (“Material data +, and its piezoelectric stress coefficient matrix, +dielectric property, +coefficient matrix, +definition,” Section 21.1.2). +Alternative forms of the constitutive equations +Alternative forms of the piezoelectric constitutive equations are presented in this section. These forms +of the equations involve material properties that cannot be used directly as input for Abaqus/Standard. +However, they are related to the Abaqus/Standard input through simple relations that are presented in +“Piezoelectric analysis,” Section 2.10.1 of the Abaqus Theory Manual. The intent of this section is to +draw connections between the Abaqus/Standard terminology and input to that used commonly in the +piezoelectricity community. The mechanical behavior can also be defined by +in terms of the piezoelectric coefficient matrix +, which defines the +mechanical properties at zero electrical displacement (open circuit condition). Likewise, the electrical +behavior can also be defined by +, and the stiffness matrix +in terms of the dielectric matrix +for an unconstrained material or by +where +is the material’s elastic stiffness matrix defined at zero electrical displacement; +at zero electrical potential gradient; +is the material’s piezoelectric strain coefficient matrix used earlier, and based on the +equations, may alternatively be interpreted as the electrical displacement +caused by the +stress +is the material’s piezoelectric coefficient matrix, which can be interpreted as defining either +the strain +in an unconstrained material or the +electrical potential gradient +at zero electrical displacement; and +caused by the electrical displacement +caused by the stress +is the material’s dielectric property, defining the relation between the electric displacement +and the electric potential gradient +for an unconstrained material. +These are useful relationships that are often seen in the piezoelectric literature. +analysis,” Section 2.10.1 of the Abaqus Theory Manual, the properties +expressed in terms of the properties +In “Piezoelectric +are +, that are used as input for Abaqus/Standard. +, and +, and +, +, +Specifying dielectric material properties +The dielectric matrix can be isotropic, orthotropic, or fully anisotropic. For non-isotropic dielectric +materials a local orientation for the material directions must be specified (“Orientations,” Section 2.2.5). +The entries of the dielectric matrix (what are referred to as “dielectric constants” in Abaqus) refer to what +is more commonly known in the literature as the permittivity of the material. +Isotropic dielectric properties +The dielectric matrix +can be fully isotropic, so that +You specify the single value +material. Isotropic behavior is the default. +for the dielectric constant. +must be determined for a constrained +Input File Usage: +Abaqus/CAE Usage: +*DIELECTRIC, TYPE=ISO +Property module: material editor: Electrical/Magnetic→Dielectric +(Electrical Permittivity): Type: Isotropic +Orthotropic dielectric properties +For orthotropic behavior you must specify three values in the dielectric matrix ( +, +, and +). +Input File Usage: +*DIELECTRIC, TYPE=ORTHO +Abaqus/CAE Usage: +Property module: material editor: Electrical/Magnetic→Dielectric +(Electrical Permittivity): Type: Orthotropic +Anisotropic dielectric properties +For fully anisotropic behavior you must specify six values in the dielectric matrix ( +, +, +, +, +, and +Input File Usage: +Abaqus/CAE Usage: +). +*DIELECTRIC, TYPE=ANISO +Property module: material editor: Electrical/Magnetic→Dielectric +(Electrical Permittivity): Type: Anisotropic +Specifying piezoelectric material properties +The piezoelectric material properties can be defined by giving the stress coefficients, +default), or by giving the strain coefficients, +following order (substitute d for e for strain coefficients): +(this is the +. In either case, 18 components must be given in the +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +. +The first index on these coefficients refers to the component of electric displacement (sometimes called +the electric flux), while the last pair of indices refers to the component of mechanical stress or strain. +Thus, the piezoelectric components causing electrical displacement in the 1-direction are all given +first, then those causing electrical displacement in the 2-direction, and then those causing electrical +displacement in the 3-direction. (Some references list these coupling terms in a different order.) +Input File Usage: +Use the following option to give the stress coefficients: +*PIEZOELECTRIC, TYPE=S +Use the following option to give the strain coefficients: +Abaqus/CAE Usage: +*PIEZOELECTRIC, TYPE=E +Property module: material editor: Electrical/Magnetic→Piezoelectric: +Type: Stress or Strain +Converting double index notation to triple index notation +Industry-supplied piezoelectric data often use a double index notation. A double index notation can +be converted easily to the required triple index notation in Abaqus/Standard by noting the convention +followed in Abaqus for the correspondence between (second-order) tensor and vector notations: the 11, +22, 33, 12, 13, and 23 components of the tensor correspond to the 1, 2, 3, 4, 5, and 6 components, +respectively, of the corresponding vector. +Elements +Piezoelectric coupling is active only in piezoelectric elements (those with displacement degrees of +freedom and electrical potential degree of freedom 9). See “Choosing the appropriate element for an +analysis type,” Section 27.1.3. +26.5.3 +MAGNETIC PERMEABILITY +Products: Abaqus/Standard Abaqus/CAE +References +• “Material library: overview,” Section 21.1.1 +• *MAGNETIC PERMEABILITY +• *NONLINEAR BH +• “Defining magnetic permeability,” Section 12.11.4 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +A material’s magnetic permeability: +• must be defined for “Eddy current analysis,” Section 6.7.5, and “Magnetostatic analysis,” +Section 6.7.6; +• can be specified directly for linear magnetic behavior or through one or more B–H curves for +nonlinear magnetic behavior; +• can be isotropic, orthotropic, or (in the case of linear behavior) fully anisotropic; +• can be specified as a function of temperature and/or field variables; and +• can be specified as a function of frequency in a time-harmonic eddy current procedure. +Linear magnetic behavior +Linear magnetic behavior is defined by direct specification of magnetic permeability. +Directional dependence of magnetic permeability +Isotropic, orthotropic, or fully anisotropic magnetic permeability can be defined. For non-isotropic +magnetic permeability a local orientation for the material directions must be specified (“Orientations,” +Section 2.2.5). +Isotropic magnetic permeability +For isotropic magnetic permeability only one value of magnetic permeability is needed at each +temperature and field variable value. Isotropic magnetic permeability is the default. +Input File Usage: +Abaqus/CAE Usage: +*MAGNETIC PERMEABILITY, TYPE=ISOTROPIC +Property module: material editor: Electrical/Magnetic→Magnetic +Permeability: Type: Isotropic +Orthotropic magnetic permeability +For orthotropic magnetic permeability three values of magnetic permeability ( +at each temperature and field variable value. +, +, +) are needed +Input File Usage: +Abaqus/CAE Usage: +*MAGNETIC PERMEABILITY, TYPE=ORTHOTROPIC +Property module: material editor: Electrical/Magnetic→Magnetic +Permeability: Type: Orthotropic +Anisotropic magnetic permeability +For fully anisotropic magnetic permeability six values ( +temperature and field variable value. +, +, +, +, +, +) are needed at each +Input File Usage: +Abaqus/CAE Usage: +*MAGNETIC PERMEABILITY, TYPE=ANISOTROPIC +Property module: material editor: Electrical/Magnetic→Magnetic +Permeability: Type: Anisotropic +Frequency-dependent magnetic permeability +Magnetic permeability can be defined as a function of frequency in a time-harmonic eddy current +analysis. +Input File Usage: +Abaqus/CAE Usage: +*MAGNETIC PERMEABILITY, FREQUENCY +Property module: material editor: Electrical/Magnetic→Magnetic +Permeability: Toggle on Use frequency-dependent data +Nonlinear magnetic behavior +Nonlinear magnetic behavior is characterized by magnetic permeability that depends on the strength +of the magnetic field. The nonlinear magnetic material model in Abaqus is suitable for ideally soft +magnetic materials (without any hysteresis effects) characterized by a monotonically increasing response +in B–H space, where B and H refer to the strengths of the magnetic flux density vector and the magnetic +field vector, respectively. Nonlinear magnetic behavior is defined through direct specification of one +or more B–H curves that provide B as a function of H and, optionally, temperature and/or predefined +field variables, in one or more directions. Nonlinear magnetic behavior can be isotropic, orthotropic, or +transversely isotropic (which is a special case of the more general orthotropic behavior). More than one +B–H curve is needed to define the nonlinear magnetic behavior if it is not isotropic. +Directional dependence of nonlinear magnetic behavior +Isotropic, orthotropic, or transversely isotropic nonlinear magnetic behavior can be defined. For non- +isotropic nonlinear magnetic behavior a local orientation for the material directions must be specified +(“Orientations,” Section 2.2.5). +Isotropic nonlinear magnetic behavior +For isotropic nonlinear magnetic response only one B–H curve is needed at each temperature and field +variable value. +Isotropic magnetic permeability is the default. Abaqus assumes that the nonlinear +magnetic behavior is governed by +Input File Usage: +You define +through a B–H curve: +*MAGNETIC PERMEABILITY, NONLINEAR, TYPE=ISOTROPIC +*NONLINEAR BH, DIR=direction +The B–H curve in any direction (i.e., the nonlinear behavior in global direction +1, 2, or 3) will suffice as the nonlinear magnetic behavior is assumed to be the +same in all directions. +Abaqus/CAE Usage: +Nonlinear magnetic behavior is not supported in Abaqus/CAE. +Orthotropic nonlinear magnetic behavior +For orthotropic nonlinear magnetic response three B–H curves (one curve to define the behavior in each +of the local directions 1, 2, and 3) are needed at each temperature and field variable value. Abaqus +assumes that the nonlinear magnetic behavior in the local material directions is governed by +where +refers to a diagonal matrix. +Transversely isotropic nonlinear magnetic behavior is a special case of orthotropic behavior, in +which the behavior in any two directions is the same and is different from that in the third direction. +Input File Usage: +You define +independent B–H curves, one in each of the directions 1, 2, and 3: +, and +, respectively, through three +, +*MAGNETIC PERMEABILITY, NONLINEAR, TYPE=ORTHOTROPIC +*NONLINEAR BH, DIR=1 +… +*NONLINEAR BH, DIR=2 +… +*NONLINEAR BH, DIR=3 +… +Abaqus/CAE Usage: +Nonlinear magnetic behavior is not supported in Abaqus/CAE. +Elements +Magnetic material behavior is active only in electromagnetic elements . +26.6 +Pore fluid flow properties +• “Pore fluid flow properties,” Section 26.6.1 +• “Permeability,” Section 26.6.2 +• “Porous bulk moduli,” Section 26.6.3 +• “Sorption,” Section 26.6.4 +• “Swelling gel,” Section 26.6.5 +• “Moisture swelling,” Section 26.6.6 +26.6.1 +PORE FLUID FLOW PROPERTIES +Abaqus/Standard allows specific properties to be defined for a fluid-filled porous material. This type of porous +medium is considered in a coupled pore fluid diffusion/stress analysis (“Coupled pore fluid diffusion and stress +analysis,” Section 6.8.1). The following properties are available: +• Permeability: Permeability defines the relationship between the flow rate of a liquid through a porous +medium and the gradient of the piezometric head of that fluid . +• Porous bulk moduli: The bulk moduli of the solid grains and of the fluid in a porous medium +are defined such that their compressibility is considered in an analysis . +• Sorption: Sorption defines the absorption/exsorption behavior of a porous material under partially +saturated flow conditions . +• Swelling gel: The swelling gel model is used to simulate the growth of gel particles that swell and +trap wetting liquid in a partially saturated porous medium . +• Moisture swelling: Moisture swelling defines the saturation-driven volumetric swelling of a +porous medium’s solid skeleton under partially saturated flow conditions . +Thermal expansion +For porous media such as soils or rock, the thermal expansion of both the solid grains and the permeating +fluid can be defined. See “Thermal expansion” in “Coupled pore fluid diffusion and stress analysis,” +Section 6.8.1, for more details. +26.6.2 +PERMEABILITY +Products: Abaqus/Standard Abaqus/CFD Abaqus/CAE +References +• “Pore fluid flow properties,” Section 26.6.1 +• “Material library: overview,” Section 21.1.1 +• *PERMEABILITY +• “Defining permeability” in “Defining a fluid-filled porous material,” Section 12.12.3 of the +Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +Permeability is the relationship between the volumetric flow rate per unit area of a particular wetting +liquid through a porous medium and the gradient of the effective fluid pressure. It can be specified in +Abaqus/Standard and Abaqus/CFD. +Permeability in Abaqus/Standard: +• must be specified for a wetting liquid for an effective stress/wetting liquid diffusion analysis ; +• is defined, in general, by Forchheimer’s law, which accounts for changes in permeability as a +function of fluid flow velocity; and +• can be isotropic, orthotropic, or fully anisotropic and can be given as a function of void ratio, +saturation, temperature, and field variables. +Permeability in Abaqus/CFD: +• must be specified for porous media flows ; and +• can be isotropic and specified as a function of porosity only or can be specified through the Carman- +Kozeny permeability-porosity relation. +Permeability in Abaqus/Standard +Permeability is defined for pore fluid flow. +Forchheimer’s law +According to Forchheimer’s law, high flow velocities have the effect of reducing the effective +As the fluid flow velocity reduces, +permeability and, +Forchheimer’s law approximates the well-known Darcy’s law. Darcy’s law can, therefore, be used +directly in Abaqus/Standard by omitting the velocity-dependent term in Forchheimer’s law. +therefore, “choking” pore fluid flow. +Forchheimer’s law is written as +where +for a completely +for a fully saturated medium, +is the volumetric flow rate of wetting liquid per unit area of the porous medium +(the effective velocity of the wetting liquid); +is the fluid saturation ( +dry medium); +is the porosity of the porous medium; +is the void ratio; +is the wetting fluid volume in the medium; +is the void volume in the medium; +is the volume of grains of solid material in the medium; +is the volume of trapped wetting liquid in the medium; +is the total volume of the medium; +is the fluid velocity; +is a “velocity coefficient,” which may be dependent on the void ratio of the +material; +is the dependence of permeability on saturation of the wetting liquid such that +at +; +is the density of the fluid; +is the specific weight of the wetting liquid; +is the magnitude of the gravitational acceleration; +is the permeability of the fully saturated medium, which can be a function of +void ratio (e, common in soil consolidation problems), temperature ( ), and/or +field variables ( +is the wetting liquid pore pressure; +is position; and +is the gravitational acceleration. +); +Permeability definitions +Permeability can be defined in different ways by different authors; caution should, therefore, be used to +ensure that the specified input data are consistent with the definitions used in Abaqus/Standard. +Permeability in Abaqus/Standard is defined as +so that Forchheimer’s law can also be written as +The fully saturated permeability, +conditions. +and/or temperature, +, is typically obtained from experiments under low fluid velocity +can be defined as a function of void ratio, e, (common in soil consolidation problems) +. The void ratio can be derived from the porosity, n, using the relationship +. Up to six variables may be needed to define the fully saturated permeability, depending on +whether isotropic, orthotropic, or fully anisotropic permeability is to be modeled (discussed below). +Alternative definition of permeability +Some authors refer to the definition of permeability used in Abaqus/Standard, +“hydraulic conductivity” of the porous medium and define the permeability as +(units of LT ), as the +is the kinematic viscosity of the wetting liquid (the ratio of the liquid’s dynamic viscosity to its +(or Darcy). +where +mass density), g is the magnitude of the gravitational acceleration, and +If the permeability is available in this form, it must be converted such that the appropriate values of +are used in Abaqus/Standard. +has dimensions +Specifying the permeability +Permeability in Abaqus/Standard can be isotropic, orthotropic, or fully anisotropic. For non-isotropic +permeability a local orientation must be used to specify the material +directions. +Isotropic permeability +For isotropic permeability in Abaqus/Standard define one value of the fully saturated permeability at +each value of the void ratio. +Input File Usage: +Abaqus/CAE Usage: +*PERMEABILITY, TYPE=ISOTROPIC +Property module: material editor: Other→Pore Fluid→Permeability: +Type: Isotropic +Orthotropic permeability +For orthotropic permeability in Abaqus/Standard define three values of the fully saturated permeability +( +) at each value of the void ratio. +, and +, +Input File Usage: +Abaqus/CAE Usage: +*PERMEABILITY, TYPE=ORTHOTROPIC +Property module: material editor: Other→Pore Fluid→Permeability: +Type: Orthotropic +Anisotropic permeability +For fully anisotropic permeability in Abaqus/Standard define six values of the fully saturated +permeability ( +) at each value of the void ratio. +, and +, +, +, +, +Input File Usage: +Abaqus/CAE Usage: +*PERMEABILITY, TYPE=ANISOTROPIC +Property module: material editor: Other→Pore Fluid→Permeability: +Type: Anisotropic +Velocity coefficient +Abaqus/Standard assumes that +law is required ( +Input File Usage: +must be defined in tabular form. +), +*PERMEABILITY, TYPE=VELOCITY +by default, meaning that Darcy’s law is used. If Forchheimer’s +This must be a repeated use of the *PERMEABILITY option for the same +material, since +must also be defined. +Abaqus/CAE Usage: +Property module: material editor: Other→Pore Fluid→Permeability: +Suboptions→Velocity Dependence +Saturation dependence +In Abaqus/Standard you can define the dependence of permeability, +; +. Abaqus/Standard assumes by default that +for +must specify +definition of +for +. +, on saturation, s, by specifying +. The tabular +for +Input File Usage: +*PERMEABILITY, TYPE=SATURATION +This must be a repeated use of the *PERMEABILITY option for the same +material, since +must also be defined. +Abaqus/CAE Usage: +Property module: material editor: Other→Pore Fluid→Permeability: +Suboptions→Saturation Dependence +Specific weight of the wetting liquid +In Abaqus/Standard the specific weight of the fluid, +does not consider the weight of the wetting liquid (i.e., if excess pore fluid pressure is calculated). +*PERMEABILITY, TYPE=type, SPECIFIC= +, must be specified correctly even if the analysis +Input File Usage: +Abaqus/CAE Usage: +The SPECIFIC parameter must be defined in conjunction with the fully +saturated *PERMEABILITY option for a given medium. +Property module: material editor: Other→Pore Fluid→Permeability: +Specific weight of wetting liquid: +Permeability in Abaqus/CFD +For flows in fluid-saturated porous medium, the momentum equation in its simplest form can be written +as +where the first term on the right-hand side is the Darcy drag and the second term is the inertial drag (also +called form drag or Forchheimer drag). In the above equation +is the intrinsic average of the pressure (average taken over the fluid-phase only); +is the extrinsic or superficial velocity vector, where the average is taken over a +representative volume incorporating both the solid (matrix) and the fluid phases; +is the density of the fluid; +is the viscosity of the fluid; +is the permeability of the porous medium (units of L2 ); and +is the dimensionless inertial or form drag coefficient and, in general, is a function +of the porosity . +The inertial drag coefficient, +relation is used, which is given by +, is usually a function of the porosity . In Abaqus/CFD the Ergun’s +where the constant +is set by default as +. +A widely used model to specify the permeability +as a function of porosity is the Carman-Kozeny +relation, which is given by +where +represents the average radius of the porous particles/fibers. +represents the Carman-Kozeny constant (parameter that is geometry dependent) and +Specifying the permeability +Permeability in Abaqus/CFD can be isotropic (with dependence only on porosity) or specified using a +Carman-Kozeny relation. +Isotropic permeability +For isotropic permeability define one value of the fully saturated permeability at each value of the +porosity. +Input File Usage: +*PERMEABILITY, TYPE=ISOTROPIC +Abaqus/CAE Usage: +Property module: material editor: Other→Pore Fluid→Permeability: +Type: Isotropic (CFD) +Carman-Kozeny model +For the Carman-Kozeny relation, you can define the permeability +Kozeny constant, and +by specifying +, the Carman- +, the average pore-particle/fiber radius. +*PERMEABILITY, TYPE=CARMAN KOZENY +Property module: material editor: Other→Pore Fluid→Permeability: +Type: Carman-Kozeny +Input File Usage: +Abaqus/CAE Usage: +Inertial drag coefficient +The value of the constant +user-specified value. By default, the value of +in the expression for the inertial drag coefficient, +is 0.142887. +, can be set to any +Input File Usage: +Abaqus/CAE Usage: +*PERMEABILITY, TYPE=type, INERTIAL DRAG COEFFICIENT= +Property module: material editor: Other→Pore Fluid→Permeability: +Inertial drag coefficient: +Elements +In Abaqus/Standard permeability can be used only in elements that allow for pore pressure . Permeability can be used +with any fluid element in Abaqus/CFD. +26.6.3 +POROUS BULK MODULI +Products: Abaqus/Standard Abaqus/CAE +References +• “Pore fluid flow properties,” Section 26.6.1 +• “Material library: overview,” Section 21.1.1 +• *POROUS BULK MODULI +• “Defining porous bulk moduli” in “Defining a fluid-filled porous material,” Section 12.12.3 of the +Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +The porous bulk moduli: +• must be defined whenever the compressibility of the solid grains or the compressibility of the +permeating fluid is to be considered in the analysis of a porous medium; and +• must be defined when a swelling gel is modeled (“Moisture swelling,” Section 26.6.6). +Defining porous bulk moduli +You can specify the bulk modulus of the solid grains and the bulk modulus of the fluid as functions of +temperature. If either modulus is omitted or set to zero, that phase of the material is assumed to be fully +incompressible. +Input File Usage: +Abaqus/CAE Usage: +*POROUS BULK MODULI +Property module: material editor: Other→Pore Fluid→Porous Bulk Moduli +Elements +The porous bulk moduli can be defined only for elements that allow for pore pressure . +26.6.4 +SORPTION +Products: Abaqus/Standard Abaqus/CAE +References +• “Pore fluid flow properties,” Section 26.6.1 +• “Material library: overview,” Section 21.1.1 +• *SORPTION +• “Defining sorption” in “Defining a fluid-filled porous material,” Section 12.12.3 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +Sorption: +• defines a porous material’s absorption/exsorption behavior under partially saturated flow conditions; +and +• is used in the analysis of coupled wetting liquid flow and porous medium stress (“Coupled pore +fluid diffusion and stress analysis,” Section 6.8.1). +Sorption +represent capillary effects in the medium. For +A porous medium becomes partially saturated when the total pore liquid pressure, +, becomes negative +. Negative +values of +it is known that the saturation lies +within certain limits that depend on the value of the capillary pressure, +. Typical +forms of these limits are shown in Figure 26.6.4–1. We write these limits as +is the limit at which exsorption +is the limit at which absorption will occur (so that +will occur (so that +). The transition between absorption and exsorption and vice versa takes place +along “scanning” curves (discussed below). These curves are approximated by the single straight line +shown in Figure 26.6.4–1. +, where +), and +When partial saturation is included in the analysis of flow through a porous medium, the absorption +behavior, the exsorption behavior, and the scanning behavior (between absorption and exsorption) +should each be defined. Each of these behaviors is discussed below. If sorption is not defined at all, +Abaqus/Standard assumes fully saturated flow ( +) for all values of +. +Strongly unsymmetric partially saturated flow coupled equations result from the definition of +sorption. Therefore, Abaqus/Standard automatically uses its unsymmetric matrix storage and solution +scheme if you request partially saturated analysis (i.e., if +sorption is defined). +pore +pressure +-uw +exsorption +absorption +scanning +0.0 +1.0 +saturation +Figure 26.6.4–1 Typical absorption and exsorption behaviors. +Defining absorption and exsorption +Absorption and exsorption behaviors are defined by specifying the pore liquid pressure, +(negative +“capillary tension”), as a function of saturation. In most physical cases the wetting liquid cannot be +driven to zero saturation; to achieve zero saturation, the data would have to define +. +Absorption and exsorption data can be defined in either a tabular form or an analytical form. +as +Tabular form +By default, you define the absorption and exsorption behaviors by specifying +s, where +. +as a tabular function of +Input File Usage: +Use the following options: +*SORPTION, TYPE=ABSORPTION, LAW=TABULAR +*SORPTION, TYPE=EXSORPTION, LAW=TABULAR +If the *SORPTION option is used only once, the behavior defined is taken as +the behavior for absorption and exsorption. +Abaqus/CAE Usage: +Property module: material editor: Other→Pore Fluid→Sorption +Absorption: Law: Tabular +Exsorption: toggle on Include exsorption: Law: Tabular +Analytical form +The absorption and exsorption behaviors can be defined by the following analytical form: +where +the saturation values of interest . +are positive material constants and +are parameters used to define the lower bound of +-uw +-uw s0 +-uw s1 +duw + ds +s1 +0.0 +s0 +s1 +1.0 +Figure 26.6.4–2 Logarithmic form of absorption and exsorption behaviors. +Input File Usage: +Use the following options: +*SORPTION, TYPE=ABSORPTION, LAW=LOG +*SORPTION, TYPE=EXSORPTION, LAW=LOG +If the *SORPTION option is used only once, the behavior defined is taken as +the behavior for absorption and exsorption. +Abaqus/CAE Usage: +Property module: material editor: Other→Pore Fluid→Sorption +Absorption: Law: Log +Exsorption: toggle on Include exsorption: Law: Log +Defining the behavior between absorption and exsorption +The behavior between absorption and exsorption is defined by a scanning line of user-specified constant +slope, +. This slope should be larger than the slope of any segment of the absorption or +exsorption behaviors. +If absorption and exsorption behaviors are defined with no scanning line, the slope of the scanning +given in the absorption and exsorption behavior +line is taken as 1.05 times the largest value of +definitions. +Input File Usage: +Abaqus/CAE Usage: +*SORPTION, TYPE=SCANNING +This must be a repeated use of the *SORPTION option for the same material. +Property module: material editor: Other→Pore Fluid→Sorption: +Exsorption: toggle on Include exsorption and Include +scanning: Slope +Elements +Sorption can be used only in elements that allow for pore pressure . +26.6.5 +SWELLING GEL +Products: Abaqus/Standard Abaqus/CAE +References +• “Pore fluid flow properties,” Section 26.6.1 +• “Material library: overview,” Section 21.1.1 +• *GEL +• “Defining a swelling gel” in “Defining a fluid-filled porous material,” Section 12.12.3 of the +Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +The swelling gel model: +• allows for modeling of the growth of gel particles that swell and trap wetting liquid in a partially +saturated porous medium; +• is intended for use in moisture absorption problems, which typically involve polymeric materials, +such as in the analysis of diapers; and +• can be used in the analysis of coupled pore liquid flow and porous medium stress . +Swelling gel model +The simple swelling gel model is based on the idealization of a gel as a volume of individual spherical +particles of equal radius, +. The swelling evolution (discussed in detail in “Constitutive behavior in a +porous medium,” Section 2.8.3 of the Abaqus Theory Manual) is assumed to be given by +where the value of any grouping of terms in angled brackets +result is not positive, and +is set equal to zero if its mathematical +is the fully swollen radius; +is the relaxation time of the gel particles; +is the saturation of the surrounding medium; +is the radius of the gel particles when they are completely dry; +is the maximum radius that the gel particles can achieve before they must touch; +is the effective gel radius when the volume is entirely occupied with gel; +is the initial porosity of the material; +is the volume change in the material; and +is the number of gel particles per unit volume. +The second term in the definition of gel growth incorporates the assumption that the gel will swell only +when the saturation of the surrounding medium, s, exceeds the effective saturation of the gel. The third +term in the growth equation reduces the swelling rate when the surface of gel particles exposed to free +fluid is limited by the combination of packing density and gel particle radius. +The swelling gel model is defined by specifying the variables +, +, +, and +. +Input File Usage: +Abaqus/CAE Usage: +*GEL +Property module: material editor: Other→Pore Fluid→Gel +Elements +The swelling gel model can be used only in elements that allow for pore pressure . +26.6.6 +MOISTURE SWELLING +Products: Abaqus/Standard Abaqus/CAE +References +• “Pore fluid flow properties,” Section 26.6.1 +• “Material library: overview,” Section 21.1.1 +• *MOISTURE SWELLING +• “Defining moisture swelling” in “Defining a fluid-filled porous material,” Section 12.12.3 of the +Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +Moisture swelling: +• defines the saturation-driven volumetric swelling of the solid skeleton of a porous medium in +partially saturated flow conditions; +• can be used in the analysis of coupled wetting liquid flow and porous medium stress ; and +• can be either isotropic or anisotropic. +Moisture swelling model +The moisture swelling model assumes that the volumetric swelling of the porous medium’s solid +skeleton is a function of the saturation of the wetting liquid in partially saturated flow conditions. The +porous medium is partially saturated when the pore liquid pressure, +, is negative . +The swelling behavior is assumed to be reversible. The logarithmic measure of swelling strain is +calculated with reference to the initial saturation so that +(no sum on ) +and +where +typical curve is shown in Figure 26.6.6–1. The ratios +discussed below. +are the volumetric swelling strains at the current and initial saturations. A +allow for anisotropic swelling as +, and +, +Defining volumetric swelling strain +Define the volumetric swelling strain, +swelling strain must be defined for the range +. +, as a tabular function of the wetting liquid saturation, s. The +Input File Usage: +*MOISTURE SWELLING +εms +εms(s) +εms( sΙ) +0.0 +sI +1.0 +saturation +Figure 26.6.6–1 Typical volumetric moisture swelling versus saturation curve. +Abaqus/CAE Usage: +Property module: material editor: Other→Pore Fluid→Moisture Swelling +Defining initial saturation values +You can define the initial saturation values as initial conditions. If no initial saturation values are given, +the default is fully saturated conditions (saturation of 1.0). For partial saturation the initial saturation +and pore fluid pressure must be consistent, in the sense that the pore fluid pressure must lie within the +absorption and exsorption values for the initial saturation value . If +this is not the case, Abaqus/Standard will adjust the saturation value as needed to satisfy this requirement. +*INITIAL CONDITIONS, TYPE=SATURATION +Load module: Create Predefined Field: Step: Initial: choose Other for +the Category and Saturation for the Types for Selected Step +Abaqus/CAE Usage: +Input File Usage: +Defining anisotropic swelling +Anisotropy can be included in moisture swelling behavior by defining the ratios +that two or more of the three ratios differ. If the ratios +that the swelling is isotropic and that +strain directions depends on the user-specified local orientation . +, such +are not specified, Abaqus/Standard assumes +. The orientation of the moisture swelling +, and +, +Input File Usage: +Use both of the following options: +*MOISTURE SWELLING +*RATIOS +The *RATIOS option should immediately follow the *MOISTURE +SWELLING option. +Abaqus/CAE Usage: +Property module: material editor: Other→Pore Fluid→Moisture +Swelling: Suboptions→Ratios +Elements +The moisture swelling model can be used only in elements that allow for pore pressure . +26.7 +User materials +• “User-defined mechanical material behavior,” Section 26.7.1 +• “User-defined thermal material behavior,” Section 26.7.2 +26.7.1 +USER-DEFINED MECHANICAL MATERIAL BEHAVIOR +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “UMAT,” Section 1.1.40 of the Abaqus User Subroutines Reference Manual +• “VUMAT,” Section 1.2.17 of the Abaqus User Subroutines Reference Manual +• *USER MATERIAL +• *DEPVAR +• “Specifying solution-dependent state variables,” Section 12.8.2 of the Abaqus/CAE User’s Manual, +in the online HTML version of this manual +• “Defining constants for a user material,” Section 12.8.4 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +User-defined mechanical material behavior in Abaqus: +• is provided by means of an interface whereby any mechanical constitutive model can be added to +the library; +• requires that a constitutive model (or a library of models) is programmed in user subroutine UMAT +(Abaqus/Standard) or VUMAT (Abaqus/Explicit); and +• requires considerable effort and expertise: the feature is very general and powerful, but its use is +not a routine exercise. +Stress components and strain increments +The subroutine interface has been implemented using Cauchy stress components (“true” stress). For +soils problems “stress” should be interpreted as effective stress. The strain increments are defined by the +symmetric part of the displacement increment gradient (equivalent to the time integral of the symmetric +part of the velocity gradient). +The orientation of the stress and strain components in user subroutine UMAT depends on the use of +local orientations (“Orientations,” Section 2.2.5). +In user subroutine VUMAT all strain measures are calculated with respect to the midincrement +configuration. All tensor quantities are defined in the corotational coordinate system that rotates +with the material point. To illustrate what this means in terms of stresses, consider the bar shown +in Figure 26.7.1–1, which is stretched and rotated from its original configuration, +, to its new +position, +. This deformation can be obtained in two stages; the bar is first stretched, as shown in +Figure 26.7.1–2, and is then rotated by applying a rigid body rotation to it, as shown in Figure 26.7.1–3. +The stress in the bar after it has been stretched is +, and this stress does not change during the rigid +body rotation. The +coordinate system that rotates as a result of the rigid body rotation is the +A +Figure 26.7.1–1 Stretched and rotated bar. +11 +11 +Figure 26.7.1–2 Stretching of bar. +11 +11 +Figure 26.7.1–3 Rigid body rotation of bar. +corotational coordinate system. The stress tensor and state variables are, therefore, computed directly +and updated in user subroutine VUMAT using the strain tensor since all of these quantities are in the +corotational system; these quantities do not have to be rotated by the user subroutine as is sometimes +required in user subroutine UMAT. +The elastic response predicted by a rate-form constitutive law depends on the objective stress rate +employed. For example, the Green-Naghdi stress rate is used in VUMAT. However, the stress rate used +for built-in material models may differ. For example, most material models used with solid (continuum) +elements in Abaqus/Explicit employ the Jaumann stress rate. This difference in the formulation will +cause significant differences in the results only if finite rotation of a material point is accompanied by +finite shear. For a discussion of the objective stress rates used in Abaqus, see “Stress rates,” Section 1.5.3 +of the Abaqus Theory Manual. +Material constants +Any material constants that are needed in user subroutine UMAT or VUMAT must be specified as part of a +user-defined material behavior definition. Any other mechanical material behaviors included in the same +material definition (except thermal expansion and, in Abaqus/Explicit, density) will be ignored; the user- +defined material behavior requires that all mechanical material behavior calculations be programmed in +subroutine UMAT or VUMAT. In Abaqus/Explicit the density (“Density,” Section 21.2.1) is required when +using a user-defined material behavior. +Input File Usage: +In Abaqus/Standard use the following option to specify a user-defined material +behavior: +*USER MATERIAL, TYPE=MECHANICAL, +CONSTANTS=number_of_constants +In Abaqus/Explicit use both of the following options to specify a user-defined +material behavior: +*USER MATERIAL, CONSTANTS=number_of_constants +*DENSITY +In either case you must specify the number of material constants being entered. +Abaqus/CAE Usage: +In Abaqus/Standard use the following option to specify a user-defined material +behavior: +Property module: material editor: General→User Material: +User material type: Mechanical +In Abaqus/Explicit use both of the following options to specify a user-defined +material behavior: +Property module: material editor: +General→User Material: User material type: Mechanical +General→Density +Unsymmetric equation solver in Abaqus/Standard +If the user material’s Jacobian matrix, +capability in Abaqus/Standard should be invoked . +, is not symmetric, the unsymmetric equation solution +Input File Usage: +*USER MATERIAL, TYPE=MECHANICAL, +CONSTANTS=number_of_constants, UNSYMM +Abaqus/CAE Usage: +Property module: material editor: General→User Material: User material +type: Mechanical, toggle on Use unsymmetric material stiffness matrix +Material state +Many mechanical constitutive models require the storage of solution-dependent state variables (plastic +strains, “back stress,” saturation values, etc. in rate constitutive forms or historical data for theories +written in integral form). You should allocate storage for these variables in the associated material +definition . There is no +restriction on the number of state variables associated with a user-defined material. +The user material subroutines are provided with the material state at the start of each increment, +as described below. They must return values for the new stresses and the new internal state variables. +State variables associated with UMAT and VUMAT can be output to the output database file (.odb) and +results file (.fil) using the output identifiers SDV and SDVn . +Material state in Abaqus/Standard +User subroutine UMAT is called for each material point at each iteration of every increment. +It is +provided with the material state at the start of the increment (stress, solution-dependent state variables, +temperature, and any predefined field variables) and with the increments in temperature, predefined +state variables, strain, and time. +In addition to updating the stresses and the solution-dependent state variables to their values at the +end of the increment, subroutine UMAT must also provide the material Jacobian matrix, +, for +the mechanical constitutive model. This matrix will also depend on the integration scheme used if the +constitutive model is in rate form and is integrated numerically in the subroutine. For any nontrivial +constitutive model these will be challenging tasks. For example, the accuracy with which the Jacobian +matrix is defined will usually be a major determinant of the convergence rate of the solution and, +therefore, will have a strong influence on computational efficiency. +Material state in Abaqus/Explicit +User subroutine VUMAT is called for blocks of material points at each increment. When the subroutine is +called, it is provided with the state at the start of the increment (stress, solution-dependent state variables). +It is also provided with the stretches and rotations at the beginning and the end of the increment. The +VUMAT user material interface passes a block of material points to the subroutine on each call, which +allows vectorization of the material subroutine. +The temperature is provided to user subroutine VUMAT at the start and the end of the increment. The +temperature is passed in as information only and cannot be modified, even in a fully coupled thermal- +stress analysis. However, if the inelastic heat fraction is defined in conjunction with the specific heat and +conductivity in a fully coupled thermal-stress analysis in Abaqus/Explicit, the heat flux due to inelastic +energy dissipation will be calculated automatically. If the VUMAT user subroutine is used to define an +adiabatic material behavior (conversion of plastic work to heat) in an explicit dynamics procedure, you +must specify both the inelastic heat fraction and the specific heat for the material, and you must store +the temperatures and integrate them as user-defined state variables. Most often the temperatures are +provided by specifying initial conditions (“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” +Section 33.2.1) and are constant throughout the analysis. +Deleting elements from an Abaqus/Explicit mesh using state variables +Element deletion in a mesh can be controlled during the course of an Abaqus/Explicit analysis through +user subroutine VUMAT. Deleted elements have no ability to carry stresses and, therefore, have no +contribution to the stiffness of the model. You specify the state variable number controlling the element +deletion flag. For example, specifying a state variable number of 4 indicates that the fourth state +variable is the deletion flag in VUMAT. The deletion state variable should be set to a value of one or zero +in VUMAT. A value of one indicates that the material point is active, while a value of zero indicates that +Abaqus/Explicit should delete the material point from the model by setting the stresses to zero. The +structure of the block of material points passed to user subroutine VUMAT remains unchanged during +the analysis; deleted material points are not removed from the block. Abaqus/Explicit will pass zero +stresses and strain increments for all deleted material points. Once a material point has been flagged as +deleted, it cannot be reactivated. An element will be deleted from the mesh only after all of the material +points in the element are deleted. The status of an element can be determined by requesting output +of the variable STATUS. This variable is equal to one if the element is active and equal to zero if the +element is deleted. +Input File Usage: +Abaqus/CAE Usage: +*DEPVAR, DELETE=variable number +Property module: material editor: General→Depvar: Variable number +controlling element deletion: variable number +Hourglass control and transverse shear stiffness +Normally the default hourglass control stiffness for reduced-integration elements in Abaqus/Standard +and the transverse shear stiffness for shell, pipe, and beam elements are defined based on the +elasticity associated with the material (“Section controls,” Section 27.1.4; “Shell section behavior,” +Section 29.6.4; and “Choosing a beam element,” Section 29.3.3). These stiffnesses are based on a +typical value of the initial shear modulus of the material, which may, for example, be given as part of an +elastic material behavior (“Linear elastic behavior,” Section 22.2.1) included in the material definition. +However, the shear modulus is not available during the preprocessing stage of input for materials +defined with user subroutine UMAT or VUMAT. Therefore, you must provide the hourglass stiffness +parameters +when using UMAT to define the material behavior of elements with hourglassing modes; and you must +specify the transverse shear stiffness when using UMAT or VUMAT to define the material behavior of beams and +shells with transverse shear flexibility. +Use of UMAT with other subroutines +Various utility subroutines are also available in Abaqus/Standard for use with subroutine UMAT. These +utility subroutines are discussed in “Obtaining stress invariants, principal stress/strain values and +directions, and rotating tensors in an Abaqus/Standard analysis,” Section 2.1.11 of the Abaqus User +Subroutines Reference Manual. +User subroutine UMATHT can be used in conjunction with UMAT to define the constitutive thermal +behavior of the material. The solution-dependent variables allocated in the material definition are +accessible in both UMAT and UMATHT. In addition, user subroutines FRIC, GAPCON, and GAPELECTR +are available for defining mechanical, thermal, and electrical interactions between surfaces. +Use with other material models +A number of material behaviors can be used in the definition of a material when its mechanical behavior +is defined by user subroutine UMAT or VUMAT. These behaviors include density, thermal expansion, +permeability, and heat transfer properties. Thermal expansion can alternatively be an integral part of the +constitutive model implemented in UMAT or VUMAT. +The temperature available in UMAT is always the interpolated temperature field at the element +integration points. Naturally, if the thermal expansion behavior is implemented in UMAT, it is defined in +terms of the integration point temperature. When the temperature field is interpolated differently within +an element compared to the displacement field in Abaqus/Standard, implementing the thermal expansion +behavior in UMAT may lead to differences compared to the built-in thermal expansion behavior. This +situation commonly arises for coupled temperature-displacement elements. For example, for first-order +coupled temperature-displacement elements, the built-in thermal expansion behavior uses a constant +temperature field over the whole element , +while the behavior in UMAT will be defined in terms of a linear temperature field. +For a material defined by user subroutine UMAT or VUMAT, mass proportional damping can be +included separately , but stiffness proportional damping must +be defined in the user subroutine by the Jacobian (Abaqus/Standard only) and stress definitions. Stiffness +proportional damping cannot be specified if the user material is used in the direct steady-state dynamics +procedure. +Elements +User subroutines UMAT and VUMAT can be used with all elements in Abaqus that include mechanical +behavior (elements that have displacement degrees of freedom). +26.7.2 +USER-DEFINED THERMAL MATERIAL BEHAVIOR +Products: Abaqus/Standard Abaqus/CAE +References +• “UMATHT,” Section 1.1.41 of the Abaqus User Subroutines Reference Manual +• *USER MATERIAL +• *DEPVAR +• “Defining constants for a user material,” Section 12.8.4 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +User-defined thermal material behavior in Abaqus/Standard: +• is provided by means of an interface whereby any thermal constitutive model can be added to the +library; +• requires that a constitutive model (or a library of models) is programmed in user subroutine +UMATHT; and +• requires considerable effort and expertise: the feature is very general and powerful, but its use is +not a routine exercise. +Material constants +Any material constants that are needed in user subroutine UMATHT must be specified as part of a user- +defined thermal material behavior definition. Any other thermal material behaviors included in the same +material definition will be ignored: the user-defined thermal material behavior requires that all thermal +behavior calculations are programmed in user subroutine UMATHT. +Input File Usage: +*USER MATERIAL, TYPE=THERMAL, +CONSTANTS=number_of_constants +You must specify the number of constants being entered. +Abaqus/CAE Usage: +Property module: material editor: General→User Material: +User material type: Thermal +Unsymmetric equation solver +When the conductivity is defined in user subroutine UMATHT as a strong function of temperature, the heat +transfer equilibrium equations become nonsymmetric and you may choose to invoke the unsymmetric +equation solution capability; otherwise, convergence may be poor. +Input File Usage: +*USER MATERIAL, TYPE=THERMAL, +CONSTANTS=number_of_constants, UNSYMM +Abaqus/CAE Usage: +Property module: material editor: General→User Material: User material +type: Thermal, toggle on Use unsymmetric material stiffness matrix +Material state +Many thermal constitutive models require the storage of solution-dependent state variables. These +state variables might include microstructure or phase content information when the material undergoes +phase changes. You should allocate storage for these variables in the associated material definition . There is no restriction on the +number of state variables associated with a user-defined material. +User subroutine UMATHT is called for each material point at each iteration of every increment. +It is provided with the thermal state of the material at the start of the increment (solution-dependent +state variables, temperature, and any predefined field variables) and with the increments in temperature, +predefined state variables, and time. +Required calculations +Subroutine UMATHT must perform the following functions: it must define the internal energy per unit +mass and its variation with temperature and spatial gradients of temperature; it must define the heat +flux vector and its variation with respect to temperature and spatial gradients of temperature; and it must +update the solution-dependent state variables to their values at the end of the increment. The components +of the heat flux and spatial gradients in user subroutine UMATHT are in directions that depend on the use +of local orientations . +Use with other user subroutines +User subroutine UMAT can be used in conjunction with UMATHT to define the constitutive mechanical +behavior of the material. The solution-dependent variables allocated in the material definition are +accessible in both UMATHT and UMAT. In addition, user subroutines FRIC, GAPCON, and GAPELECTR +are available for defining mechanical, thermal, and electrical interactions between surfaces. +Use with other material models +Density, mechanical properties, and electrical properties can be included in the definition of a material +whose constitutive thermal behavior is defined by user subroutine UMATHT. +Elements +User subroutine UMATHT can be used with all elements in Abaqus/Standard that include thermal behavior +(elements with temperature degrees of freedom such as pure heat transfer, coupled thermal-stress, and +coupled thermal-electrical elements). +SIMULIA is the Dassault Systèmes brand that delivers a scalable portfolio of +Realistic Simulation solutions including the Abaqus product suite for Unified Finite +Element Analysis; multiphysics solutions for insight into challenging engineering +problems; and lifecycle management solutions for managing simulation data, +processes, and intellectual property. 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The Dassault Systèmes portfolio consists of CATIA for +designing the virtual product, SolidWorks for 3D mechanical design, DELMIA for +virtual production, SIMULIA for virtual testing, ENOVIA for global collaborative +lifecycle management, and 3DVIA for online 3D lifelike experiences. Dassault +Systèmes’ shares are listed on Euronext Paris (#13065, DSY.PA), and Dassault +Systèmes’ ADRs may be traded on the US Over-The-Counter (OTC) market (DASTY). +For more information, visit www.3ds.com. +fi +, +, +, +, +, +, +, +, +. +. +, +© +. +, +, +. +/ + +User’s Manual +CAUTION: This documentation is intended for qualified users who will exercise sound engineering judgment and expertise in the use of the Abaqus +Software. The Abaqus Software is inherently complex, and the examples and procedures in this documentation are not intended to be exhaustive or to apply +to any particular situation. Users are cautioned to satisfy themselves as to the accuracy and results of their analyses. +Dassault Systèmes and its subsidiaries, including Dassault Systèmes Simulia Corp., shall not be responsible for the accuracy or usefulness of any analysis +performed using the Abaqus Software or the procedures, examples, or explanations in this documentation. Dassault Systèmes and its subsidiaries shall not +be responsible for the consequences of any errors or omissions that may appear in this documentation. +The Abaqus Software is available only under license from Dassault Systèmes or its subsidiary and may be used or reproduced only in accordance with the +terms of such license. 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Bhd., Kuala Lumpur, Tel: +603 2039 9000, abaqus.my@worleyparsons.com +Kimeca.NET SA de CV, Mexico, Tel: +52 55 2459 2635 +Matrix Applied Computing Ltd., Auckland, Tel: +64 9 623 1223, abaqus-tech@matrix.co.nz +BudSoft Sp. z o.o., Poznań, Tel: +48 61 8508 466, info@budsoft.com.pl +TESIS Ltd., Moscow, Tel: +7 495 612 44 22, info@tesis.com.ru +WorleyParsons Pte Ltd., Singapore, Tel: +65 6735 8444, abaqus.sg@worleyparsons.com +Finite Element Analysis Services (Pty) Ltd., Parklands, Tel: +27 21 556 6462, feas@feas.co.za +Thailand +Turkey +Simutech Solution Corporation, Taipei, R.O.C., Tel: +886 2 2507 9550, camilla@simutech.com.tw +WorleyParsons Pte Ltd., Singapore, Tel: +65 6735 8444, abaqus.sg@worleyparsons.com +A-Ztech Ltd., Istanbul, Tel: +90 216 361 8850, info@a-ztech.com.tr +Preface +Support +Both technical engineering support (for problems with creating a model or performing an analysis) and +systems support (for installation, licensing, and hardware-related problems) for Abaqus are offered through +a network of local support offices. Regional contact information is listed in the front of each Abaqus manual +and is accessible from the Locations page at www.simulia.com. +Support for SIMULIA products +SIMULIA provides a knowledge database of answers and solutions to questions that we have answered, +as well as guidelines on how to use Abaqus, SIMULIA Scenario Definition, Isight, and other SIMULIA +products. You can also submit new requests for support. All support incidents are tracked. If you contact +us by means outside the system to discuss an existing support problem and you know the incident or support +request number, please mention it so that we can query the database to see what the latest action has been. +Many questions about Abaqus can also be answered by visiting the Products page and the Support +page at www.simulia.com. +Anonymous ftp site +To facilitate data transfer with SIMULIA, an anonymous ftp account is available at ftp.simulia.com. +Login as user anonymous, and type your e-mail address as your password. Contact support before placing +files on the site. +Training +All offices and representatives offer regularly scheduled public training classes. The courses are offered in +a traditional classroom form and via the Web. We also provide training seminars at customer sites. All +training classes and seminars include workshops to provide as much practical experience with Abaqus as +possible. For a schedule and descriptions of available classes, see www.simulia.com or call your local office +or representative. +Feedback +We welcome any suggestions for improvements to Abaqus software, the support program, or documentation. +We will ensure that any enhancement requests you make are considered for future releases. If you wish to +make a suggestion about the service or products, refer to www.simulia.com. Complaints should be made by +contacting your local office or through www.simulia.com by visiting the Quality Assurance section of the +1.1.1 +1.2.1 +1.2.2 +1.3.1 +1.4.1 +2.1.1 +2.1.2 +2.1.3 +2.1.4 +2.1.5 +2.1.6 +2.2.1 +2.2.2 +2.2.3 +2.2.4 +2.2.5 +2.3.1 +2.3.2 +2.3.3 +2.3.4 +Contents +Volume I +PART I +INTRODUCTION, SPATIAL MODELING, AND EXECUTION +1. +Introduction +Introduction: general +Abaqus syntax and conventions +Input syntax rules +Conventions +Abaqus model definition +Defining a model in Abaqus +Parametric modeling +Parametric input +2. Spatial Modeling +Node definition +Node definition +Parametric shape variation +Nodal thicknesses +Normal definitions at nodes +Transformed coordinate systems +Adjusting nodal coordinates +Element definition +Element definition +Element foundations +Defining reinforcement +Defining rebar as an element property +Orientations +Surface definition +Surfaces: overview +Element-based surface definition +Node-based surface definition +Analytical rigid surface definition +Eulerian surface definition +Operating on surfaces +Rigid body definition +Rigid body definition +Integrated output section definition +Integrated output section definition +Mass adjustment +Adjust and/or redistribute mass of an element set +Nonstructural mass definition +Nonstructural mass definition +Distribution definition +Distribution definition +Display body definition +Display body definition +Assembly definition +Defining an assembly +Matrix definition +Defining matrices +3. Job Execution +Execution procedures: overview +Execution procedure for Abaqus: overview +Execution procedures +Obtaining information +Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD execution +SIMULIA Co-Simulation Engine controller execution +Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD co-simulation execution +Abaqus/CAE execution +Abaqus/Viewer execution +Python execution +Parametric studies +Abaqus documentation +Licensing utilities +ASCII translation of results (.fil) files +Joining results (.fil) files +Querying the keyword/problem database +ii +Abaqus ID:usb-toc +Printed on: Fri February 3 -- 18:01:12 2012 +2.3.5 +2.3.6 +2.4.1 +2.5.1 +2.6.1 +2.7.1 +2.8.1 +2.9.1 +2.10.1 +2.11.1 +3.1.1 +3.2.1 +3.2.2 +3.2.3 +3.2.4 +3.2.5 +3.2.6 +3.2.7 +3.2.8 +3.2.9 +3.2.10 +Making user-defined executables and subroutines +Input file and output database upgrade utility +Generating output database reports +Joining output database (.odb) files from restarted analyses +Combining output from substructures +Combining data from multiple output databases +Network output database file connector +Mapping thermal and magnetic loads +Fixed format conversion utility +Translating Nastran bulk data files to Abaqus input files +Translating Abaqus files to Nastran bulk data files +Translating ANSYS input files to Abaqus input files +Translating PAM-CRASH input files to partial Abaqus input files +Translating RADIOSS input files to partial Abaqus input files +Translating Abaqus output database files to Nastran Output2 results files +Translating LS-DYNA data files to Abaqus input files +Exchanging Abaqus data with ZAERO +Encrypting and decrypting Abaqus input data +Job execution control +Environment file settings +Using the Abaqus environment settings +Managing memory and disk resources +Managing memory and disk use in Abaqus +Parallel execution +Parallel execution: overview +Parallel execution in Abaqus/Standard +Parallel execution in Abaqus/Explicit +Parallel execution in Abaqus/CFD +File extension definitions +File extensions used by Abaqus +FORTRAN unit numbers +FORTRAN unit numbers used by Abaqus +CONTENTS +3.2.14 +3.2.15 +3.2.16 +3.2.17 +3.2.18 +3.2.19 +3.2.20 +3.2.21 +3.2.22 +3.2.23 +3.2.24 +3.2.25 +3.2.26 +3.2.27 +3.2.28 +3.2.29 +3.2.30 +3.2.31 +3.2.32 +3.2.33 +3.3.1 +3.4.1 +3.5.1 +3.5.2 +3.5.3 +3.5.4 +3.6.1 +3.7.1 +4.1.2 +4.1.3 +4.1.4 +4.2.1 +4.2.2 +4.2.3 +4.3.1 +5.1.1 +5.1.2 +5.1.3 +5.1.4 +CONTENTS +4. Output +PART II +OUTPUT +Output +Output to the data and results files +Output to the output database +Error indicator output +Output variables +Abaqus/Standard output variable identifiers +Abaqus/Explicit output variable identifiers +Abaqus/CFD output variable identifiers +The postprocessing calculator +The postprocessing calculator +5. File Output Format +Accessing the results file +Accessing the results file: overview +Results file output format +Accessing the results file information +Utility routines for accessing the results file +OI.1 Abaqus/Standard Output Variable Index +OI.2 Abaqus/Explicit Output Variable Index +OI.3 Abaqus/CFD Output Variable Index +6.1.1 +6.1.2 +6.1.3 +6.1.4 +6.1.5 +6.1.6 +6.2.1 +6.2.2 +6.2.3 +6.2.4 +6.2.5 +6.2.6 +6.2.7 +6.3.1 +6.3.2 +6.3.3 +6.3.4 +6.3.5 +6.3.6 +6.3.7 +6.3.8 +6.3.9 +6.3.10 +6.3.11 +6.4.1 +6.5.1 +6.5.2 +Volume II +PART III +ANALYSIS PROCEDURES, SOLUTION, AND CONTROL +6. Analysis Procedures +Introduction +Solving analysis problems: overview +Defining an analysis +General and linear perturbation procedures +Multiple load case analysis +Direct linear equation solver +Iterative linear equation solver +Static stress/displacement analysis +Static stress analysis procedures: overview +Static stress analysis +Eigenvalue buckling prediction +Unstable collapse and postbuckling analysis +Quasi-static analysis +Direct cyclic analysis +Low-cycle fatigue analysis using the direct cyclic approach +Dynamic stress/displacement analysis +Dynamic analysis procedures: overview +Implicit dynamic analysis using direct integration +Explicit dynamic analysis +Direct-solution steady-state dynamic analysis +Natural frequency extraction +Complex eigenvalue extraction +Transient modal dynamic analysis +Mode-based steady-state dynamic analysis +Subspace-based steady-state dynamic analysis +Response spectrum analysis +Random response analysis +Steady-state transport analysis +Steady-state transport analysis +Heat transfer and thermal-stress analysis +Heat transfer analysis procedures: overview +Uncoupled heat transfer analysis +6.5.4 +6.6.1 +6.6.2 +6.7.1 +6.7.2 +6.7.3 +6.7.4 +6.7.5 +6.7.6 +6.8.1 +6.8.2 +6.9.1 +6.10.1 +6.11.1 +6.12.1 +7.1.1 +7.2.1 +7.2.2 +7.2.3 +7.2.4 +CONTENTS +Fully coupled thermal-stress analysis +Adiabatic analysis +Fluid dynamic analysis +Fluid dynamic analysis procedures: overview +Incompressible fluid dynamic analysis +Electromagnetic analysis +Electromagnetic analysis procedures +Piezoelectric analysis +Coupled thermal-electrical analysis +Fully coupled thermal-electrical-structural analysis +Eddy current analysis +Magnetostatic analysis +Coupled pore fluid flow and stress analysis +Coupled pore fluid diffusion and stress analysis +Geostatic stress state +Mass diffusion analysis +Mass diffusion analysis +Acoustic and shock analysis +Acoustic, shock, and coupled acoustic-structural analysis +Abaqus/Aqua analysis +Abaqus/Aqua analysis +Annealing +Annealing procedure +7. Analysis Solution and Control +Solving nonlinear problems +Solving nonlinear problems +Analysis convergence controls +Convergence and time integration criteria: overview +Commonly used control parameters +Convergence criteria for nonlinear problems +Time integration accuracy in transient problems +ANALYSIS TECHNIQUES +8. Analysis Techniques: Introduction +Analysis techniques: overview +9. Analysis Continuation Techniques +Restarting an analysis +Restarting an analysis +Importing and transferring results +Transferring results between Abaqus analyses: overview +Transferring results between Abaqus/Explicit and Abaqus/Standard +Transferring results from one Abaqus/Standard analysis to another +Transferring results from one Abaqus/Explicit analysis to another +10. Modeling Abstractions +Substructuring +Using substructures +Defining substructures +Submodeling +Submodeling: overview +Node-based submodeling +Surface-based submodeling +Generating global matrices +Generating matrices +CONTENTS +8.1.1 +9.1.1 +9.2.1 +9.2.2 +9.2.3 +9.2.4 +10.1.1 +10.1.2 +10.2.1 +10.2.2 +10.2.3 +10.3.1 +Symmetric model generation, results transfer, and analysis of cyclic symmetry models +Symmetric model generation +Transferring results from a symmetric mesh or a partial three-dimensional mesh to +a full three-dimensional mesh +Analysis of models that exhibit cyclic symmetry +Periodic media analysis +Periodic media analysis +Meshed beam cross-sections +Meshed beam cross-sections +vii +10.4.1 +10.4.2 +10.4.3 +10.5.1 +Modeling discontinuities as an enriched feature using the extended finite element method +Modeling discontinuities as an enriched feature using the extended finite element +10.7.1 +11.1.1 +11.2.1 +11.3.1 +11.4.1 +11.4.2 +11.4.3 +11.5.1 +11.5.2 +11.5.3 +11.5.4 +11.6.1 +11.7.1 +11.8.1 +12.1.1 +12.2.1 +12.2.2 +12.2.3 +12.2.4 +method +11. Special-Purpose Techniques +Inertia relief +Inertia relief +Mesh modification or replacement +Element and contact pair removal and reactivation +Geometric imperfections +Introducing a geometric imperfection into a model +Fracture mechanics +Fracture mechanics: overview +Contour integral evaluation +Crack propagation analysis +Surface-based fluid modeling +Surface-based fluid cavities: overview +Fluid cavity definition +Fluid exchange definition +Inflator definition +Mass scaling +Mass scaling +Selective subcycling +Selective subcycling +Steady-state detection +Steady-state detection +12. Adaptivity Techniques +Adaptivity techniques: overview +Adaptivity techniques +ALE adaptive meshing +ALE adaptive meshing: overview +Defining ALE adaptive mesh domains in Abaqus/Explicit +ALE adaptive meshing and remapping in Abaqus/Explicit +Modeling techniques for Eulerian adaptive mesh domains in Abaqus/Explicit +12.2.5 +12.2.6 +12.2.7 +12.3.1 +12.3.2 +12.3.3 +12.4.1 +13.1.1 +13.2.1 +13.2.2 +13.2.3 +14.1.1 +14.1.2 +14.1.3 +14.1.4 +15.1.1 +15.1.2 +16.1.1 +16.1.2 +16.1.3 +17.1.1 +17.2.1 +Output and diagnostics for ALE adaptive meshing in Abaqus/Explicit +Defining ALE adaptive mesh domains in Abaqus/Standard +ALE adaptive meshing and remapping in Abaqus/Standard +Adaptive remeshing +Adaptive remeshing: overview +Selection of error indicators influencing adaptive remeshing +Solution-based mesh sizing +Analysis continuation after mesh replacement +Mesh-to-mesh solution mapping +13. Optimization Techniques +Structural optimization: overview +Structural optimization: overview +Optimization models +Design responses +Objectives and constraints +Creating Abaqus optimization models +14. Eulerian Analysis +Eulerian analysis +Defining Eulerian boundaries +Eulerian mesh motion +Defining adaptive mesh refinement in the Eulerian domain +15. Particle Methods +Smoothed particle hydrodynamic analyses +Smoothed particle hydrodynamic analysis +Finite element conversion to SPH particles +16. Sequentially Coupled Multiphysics Analyses +Predefined fields for sequential coupling +Sequentially coupled thermal-stress analysis +Predefined loads for sequential coupling +17. Co-simulation +Co-simulation: overview +Preparing an Abaqus analysis for co-simulation +Preparing an Abaqus analysis for co-simulation +Co-simulation between Abaqus solvers +Abaqus/Standard to Abaqus/Explicit co-simulation +Abaqus/CFD to Abaqus/Standard or to Abaqus/Explicit co-simulation +18. Extending Abaqus Analysis Functionality +User subroutines and utilities +User subroutines: overview +Available user subroutines +Available utility routines +19. Design Sensitivity Analysis +Design sensitivity analysis +20. Parametric Studies +Scripting parametric studies +Scripting parametric studies +Parametric studies: commands +aStudy.combine(): Combine parameter samples for parametric studies. +aStudy.constrain(): Constrain parameter value combinations in parametric studies. +aStudy.define(): Define parameters for parametric studies. +aStudy.execute(): Execute the analysis of parametric study designs. +aStudy.gather(): Gather the results of a parametric study. +aStudy.generate(): Generate the analysis job data for a parametric study. +aStudy.output(): Specify the source of parametric study results. +aStudy=ParStudy(): Create a parametric study. +aStudy.report(): Report parametric study results. +aStudy.sample(): Sample parameters for parametric studies. +17.3.1 +17.3.2 +18.1.1 +18.1.2 +18.1.3 +19.1.1 +20.1.1 +20.2.1 +20.2.2 +20.2.3 +20.2.4 +20.2.5 +20.2.6 +20.2.7 +20.2.8 +20.2.9 +20.2.10 +21.1.1 +21.1.2 +21.1.3 +21.2.1 +22.1.1 +22.2.1 +22.2.2 +22.2.3 +22.3.1 +22.4.1 +22.5.1 +22.5.2 +22.5.3 +22.6.1 +22.6.2 +22.7.1 +22.7.2 +Volume III +PART V MATERIALS +21. Materials: Introduction +Introduction +Material library: overview +Material data definition +Combining material behaviors +General properties +Density +22. Elastic Mechanical Properties +Overview +Elastic behavior: overview +Linear elasticity +Linear elastic behavior +No compression or no tension +Plane stress orthotropic failure measures +Porous elasticity +Elastic behavior of porous materials +Hypoelasticity +Hypoelastic behavior +Hyperelasticity +Hyperelastic behavior of rubberlike materials +Hyperelastic behavior in elastomeric foams +Anisotropic hyperelastic behavior +Stress softening in elastomers +Mullins effect +Energy dissipation in elastomeric foams +Viscoelasticity +Time domain viscoelasticity +Frequency domain viscoelasticity +Nonlinear viscoelasticity +Hysteresis in elastomers +Parallel network viscoelastic model +Rate sensitive elastomeric foams +Low-density foams +23. +Inelastic Mechanical Properties +Overview +Inelastic behavior +Metal plasticity +Classical metal plasticity +Models for metals subjected to cyclic loading +Rate-dependent yield +Rate-dependent plasticity: creep and swelling +Annealing or melting +Anisotropic yield/creep +Johnson-Cook plasticity +Dynamic failure models +Porous metal plasticity +Cast iron plasticity +Two-layer viscoplasticity +ORNL – Oak Ridge National Laboratory constitutive model +Deformation plasticity +Other plasticity models +Extended Drucker-Prager models +Modified Drucker-Prager/Cap model +Mohr-Coulomb plasticity +Critical state (clay) plasticity model +Crushable foam plasticity models +Fabric materials +Fabric material behavior +Jointed materials +Jointed material model +Concrete +Concrete smeared cracking +Cracking model for concrete +Concrete damaged plasticity +xii +Abaqus ID:usb-toc +Printed on: Fri February 3 -- 18:01:12 2012 +22.8.1 +22.8.2 +22.9.1 +23.1.1 +23.2.1 +23.2.2 +23.2.3 +23.2.4 +23.2.5 +23.2.6 +23.2.7 +23.2.8 +23.2.9 +23.2.10 +23.2.11 +23.2.12 +23.2.13 +23.3.1 +23.3.2 +23.3.3 +23.3.4 +23.3.5 +23.4.1 +23.5.1 +23.7.1 +24.1.1 +24.2.1 +24.2.2 +24.2.3 +24.3.1 +24.3.2 +24.3.3 +24.4.1 +24.4.2 +24.4.3 +25.1.1 +25.2.1 +26.1.1 +26.1.2 +26.1.3 +26.1.4 +26.2.1 +26.2.2 +26.2.3 +26.2.4 +Permanent set in rubberlike materials +Permanent set in rubberlike materials +24. Progressive Damage and Failure +Progressive damage and failure: overview +Progressive damage and failure +Damage and failure for ductile metals +Damage and failure for ductile metals: overview +Damage initiation for ductile metals +Damage evolution and element removal for ductile metals +Damage and failure for fiber-reinforced composites +Damage and failure for fiber-reinforced composites: overview +Damage initiation for fiber-reinforced composites +Damage evolution and element removal for fiber-reinforced composites +Damage and failure for ductile materials in low-cycle fatigue analysis +Damage and failure for ductile materials in low-cycle fatigue analysis: overview +Damage initiation for ductile materials in low-cycle fatigue +Damage evolution for ductile materials in low-cycle fatigue +25. Hydrodynamic Properties +Overview +Hydrodynamic behavior: overview +Equations of state +Equation of state +26. Other Material Properties +Mechanical properties +Material damping +Thermal expansion +Field expansion +Viscosity +Heat transfer properties +Thermal properties: overview +Conductivity +Specific heat +Latent heat +Acoustic properties +Acoustic medium +Mass diffusion properties +Diffusivity +Solubility +Electromagnetic properties +Electrical conductivity +Piezoelectric behavior +Magnetic permeability +Pore fluid flow properties +Pore fluid flow properties +Permeability +Porous bulk moduli +Sorption +Swelling gel +Moisture swelling +User materials +User-defined mechanical material behavior +User-defined thermal material behavior +26.3.1 +26.4.1 +26.4.2 +26.5.1 +26.5.2 +26.5.3 +26.6.1 +26.6.2 +26.6.3 +26.6.4 +26.6.5 +26.6.6 +26.7.1 +26.7.2 +27.1.1 +27.1.2 +27.1.3 +27.1.4 +28.1.1 +28.1.2 +28.1.3 +28.1.4 +28.1.5 +28.1.6 +28.1.7 +28.2.1 +28.2.2 +28.3.1 +28.3.2 +28.4.1 +28.4.2 +28.5.1 +28.5.2 +29.1.1 +29.1.2 +29.1.3 +Volume IV +PART VI +ELEMENTS +27. Elements: Introduction +Element library: overview +Choosing the element’s dimensionality +Choosing the appropriate element for an analysis type +Section controls +28. Continuum Elements +General-purpose continuum elements +Solid (continuum) elements +One-dimensional solid (link) element library +Two-dimensional solid element library +Three-dimensional solid element library +Cylindrical solid element library +Axisymmetric solid element library +Axisymmetric solid elements with nonlinear, asymmetric deformation +Fluid continuum elements +Fluid (continuum) elements +Fluid element library +Infinite elements +Infinite elements +Infinite element library +Warping elements +Warping elements +Warping element library +Particle elements +Particle elements +Particle element library +29. Structural Elements +Membrane elements +Membrane elements +General membrane element library +Cylindrical membrane element library +Axisymmetric membrane element library +Truss elements +Truss elements +Truss element library +Beam elements +Beam modeling: overview +Choosing a beam cross-section +Choosing a beam element +Beam element cross-section orientation +Beam section behavior +Using a beam section integrated during the analysis to define the section behavior +Using a general beam section to define the section behavior +Beam element library +Beam cross-section library +Frame elements +Frame elements +Frame section behavior +Frame element library +Elbow elements +Pipes and pipebends with deforming cross-sections: elbow elements +Elbow element library +Shell elements +Shell elements: overview +Choosing a shell element +Defining the initial geometry of conventional shell elements +Shell section behavior +Using a shell section integrated during the analysis to define the section behavior +Using a general shell section to define the section behavior +Three-dimensional conventional shell element library +Continuum shell element library +Axisymmetric shell element library +Axisymmetric shell elements with nonlinear, asymmetric deformation +29.1.4 +29.2.1 +29.2.2 +29.3.1 +29.3.2 +29.3.3 +29.3.4 +29.3.5 +29.3.6 +29.3.7 +29.3.8 +29.3.9 +29.4.1 +29.4.2 +29.4.3 +29.5.1 +29.5.2 +29.6.1 +29.6.2 +29.6.3 +29.6.4 +29.6.5 +29.6.6 +29.6.7 +29.6.8 +29.6.9 +29.6.10 +30.1.1 +30.1.2 +30.2.1 +30.2.2 +30.3.1 +30.3.2 +30.4.1 +30.4.2 +31.1.1 +31.1.2 +31.1.3 +31.1.4 +31.1.5 +31.2.1 +31.2.2 +31.2.3 +31.2.4 +31.2.5 +31.2.6 +31.2.7 +31.2.8 +31.2.9 +31.2.10 +32.1.1 +32.1.2 +30. +Inertial, Rigid, and Capacitance Elements +Point mass elements +Point masses +Mass element library +Rotary inertia elements +Rotary inertia +Rotary inertia element library +Rigid elements +Rigid elements +Rigid element library +Capacitance elements +Point capacitance +Capacitance element library +31. Connector Elements +Connector elements +Connectors: overview +Connector elements +Connector actuation +Connector element library +Connection-type library +Connector element behavior +Connector behavior +Connector elastic behavior +Connector damping behavior +Connector functions for coupled behavior +Connector friction behavior +Connector plastic behavior +Connector damage behavior +Connector stops and locks +Connector failure behavior +Connector uniaxial behavior +32. Special-Purpose Elements +Spring elements +Springs +Spring element library +Dashpot elements +Dashpots +Dashpot element library +Flexible joint elements +Flexible joint element +Flexible joint element library +Distributing coupling elements +Distributing coupling elements +Distributing coupling element library +Cohesive elements +Cohesive elements: overview +Choosing a cohesive element +Modeling with cohesive elements +Defining the cohesive element’s initial geometry +Defining the constitutive response of cohesive elements using a continuum approach +Defining the constitutive response of cohesive elements using a traction-separation +description +Defining the constitutive response of fluid within the cohesive element gap +Two-dimensional cohesive element library +Three-dimensional cohesive element library +Axisymmetric cohesive element library +Gasket elements +Gasket elements: overview +Choosing a gasket element +Including gasket elements in a model +Defining the gasket element’s initial geometry +Defining the gasket behavior using a material model +Defining the gasket behavior directly using a gasket behavior model +Two-dimensional gasket element library +Three-dimensional gasket element library +Axisymmetric gasket element library +Surface elements +Surface elements +General surface element library +Cylindrical surface element library +Axisymmetric surface element library +32.2.1 +32.2.2 +32.3.1 +32.3.2 +32.4.1 +32.4.2 +32.5.1 +32.5.2 +32.5.3 +32.5.4 +32.5.5 +32.5.6 +32.5.7 +32.5.8 +32.5.9 +32.5.10 +32.6.1 +32.6.2 +32.6.3 +32.6.4 +32.6.5 +32.6.6 +32.6.7 +32.6.8 +32.6.9 +32.7.1 +32.7.2 +32.7.3 +32.7.4 +32.8.1 +32.8.2 +32.9.1 +32.9.2 +32.10.1 +32.10.2 +32.11.1 +32.11.2 +32.12.1 +32.12.2 +32.13.1 +32.13.2 +32.14.1 +32.14.2 +32.15.1 +32.15.2 +Tube support elements +Tube support elements +Tube support element library +Line spring elements +Line spring elements for modeling part-through cracks in shells +Line spring element library +Elastic-plastic joints +Elastic-plastic joints +Elastic-plastic joint element library +Drag chain elements +Drag chains +Drag chain element library +Pipe-soil elements +Pipe-soil interaction elements +Pipe-soil interaction element library +Acoustic interface elements +Acoustic interface elements +Acoustic interface element library +Eulerian elements +Eulerian elements +Eulerian element library +User-defined elements +User-defined elements +User-defined element library +EI.1 Abaqus/Standard Element Index +EI.2 Abaqus/Explicit Element Index +EI.3 Abaqus/CFD Element Index +Volume V +PART VII +PRESCRIBED CONDITIONS +33. Prescribed Conditions +Overview +Prescribed conditions: overview +Amplitude curves +Initial conditions +Initial conditions in Abaqus/Standard and Abaqus/Explicit +Initial conditions in Abaqus/CFD +Boundary conditions +Boundary conditions in Abaqus/Standard and Abaqus/Explicit +Boundary conditions in Abaqus/CFD +Loads +Applying loads: overview +Concentrated loads +Distributed loads +Thermal loads +Electromagnetic loads +Acoustic and shock loads +Pore fluid flow +Prescribed assembly loads +Prescribed assembly loads +Predefined fields +Predefined fields +PART VIII +CONSTRAINTS +34. Constraints +Overview +Kinematic constraints: overview +Multi-point constraints +Linear constraint equations +xx +Abaqus ID:usb-toc +Printed on: Fri February 3 -- 18:01:12 2012 +33.1.1 +33.1.2 +33.2.1 +33.2.2 +33.3.1 +33.3.2 +33.4.1 +33.4.2 +33.4.3 +33.4.4 +33.4.5 +33.4.6 +33.4.7 +33.5.1 +34.2.2 +34.2.3 +34.3.1 +34.3.2 +34.3.3 +34.3.4 +34.4.1 +34.5.1 +34.6.1 +35.1.1 +35.2.1 +35.2.2 +35.2.3 +35.2.4 +35.2.5 +35.2.6 +35.3.1 +35.3.2 +35.3.3 +35.3.4 +35.3.5 +35.3.6 +35.3.7 +35.3.8 +General multi-point constraints +Kinematic coupling constraints +Surface-based constraints +Mesh tie constraints +Coupling constraints +Shell-to-solid coupling +Mesh-independent fasteners +Embedded elements +Embedded elements +Element end release +Element end release +Overconstraint checks +Overconstraint checks +PART IX +INTERACTIONS +35. Defining Contact Interactions +Overview +Contact interaction analysis: overview +Defining general contact in Abaqus/Standard +Defining general contact interactions in Abaqus/Standard +Surface properties for general contact in Abaqus/Standard +Contact properties for general contact in Abaqus/Standard +Controlling initial contact status in Abaqus/Standard +Stabilization for general contact in Abaqus/Standard +Numerical controls for general contact in Abaqus/Standard +Defining contact pairs in Abaqus/Standard +Defining contact pairs in Abaqus/Standard +Assigning surface properties for contact pairs in Abaqus/Standard +Assigning contact properties for contact pairs in Abaqus/Standard +Modeling contact interference fits in Abaqus/Standard +Adjusting initial surface positions and specifying initial clearances in Abaqus/Standard +contact pairs +Adjusting contact controls in Abaqus/Standard +Defining tied contact in Abaqus/Standard +Extending master surfaces and slide lines +Contact modeling if substructures are present +Contact modeling if asymmetric-axisymmetric elements are present +Defining general contact in Abaqus/Explicit +Defining general contact interactions in Abaqus/Explicit +Assigning surface properties for general contact in Abaqus/Explicit +Assigning contact properties for general contact in Abaqus/Explicit +Controlling initial contact status for general contact in Abaqus/Explicit +Contact controls for general contact in Abaqus/Explicit +Defining contact pairs in Abaqus/Explicit +Defining contact pairs in Abaqus/Explicit +Assigning surface properties for contact pairs in Abaqus/Explicit +Assigning contact properties for contact pairs in Abaqus/Explicit +Adjusting initial surface positions and specifying initial clearances for contact pairs +in Abaqus/Explicit +Contact controls for contact pairs in Abaqus/Explicit +36. Contact Property Models +Mechanical contact properties +Mechanical contact properties: overview +Contact pressure-overclosure relationships +Contact damping +Contact blockage +Frictional behavior +User-defined interfacial constitutive behavior +Pressure penetration loading +Interaction of debonded surfaces +Breakable bonds +Surface-based cohesive behavior +Thermal contact properties +Thermal contact properties +Electrical contact properties +Electrical contact properties +Pore fluid contact properties +Pore fluid contact properties +37. Contact Formulations and Numerical Methods +Contact formulations and numerical methods in Abaqus/Standard +Contact formulations in Abaqus/Standard +xxii +Abaqus ID:usb-toc +Printed on: Fri February 3 -- 18:01:12 2012 +35.3.9 +35.3.10 +35.4.1 +35.4.2 +35.4.3 +35.4.4 +35.4.5 +35.5.1 +35.5.2 +35.5.3 +35.5.4 +35.5.5 +36.1.1 +36.1.2 +36.1.3 +36.1.4 +36.1.5 +36.1.6 +36.1.7 +36.1.8 +36.1.9 +36.1.10 +36.2.1 +37.1.2 +37.1.3 +37.2.1 +37.2.2 +37.2.3 +38.1.1 +38.1.2 +38.2.1 +38.2.2 +39.1.1 +39.2.1 +39.2.2 +39.3.1 +39.3.2 +39.4.1 +39.4.2 +39.5.1 +39.5.2 +40.1.1 +Contact constraint enforcement methods in Abaqus/Standard +Smoothing contact surfaces in Abaqus/Standard +Contact formulations and numerical methods in Abaqus/Explicit +Contact formulation for general contact in Abaqus/Explicit +Contact formulations for contact pairs in Abaqus/Explicit +Contact constraint enforcement methods in Abaqus/Explicit +38. Contact Difficulties and Diagnostics +Resolving contact difficulties in Abaqus/Standard +Contact diagnostics in an Abaqus/Standard analysis +Common difficulties associated with contact modeling in Abaqus/Standard +Resolving contact difficulties in Abaqus/Explicit +Contact diagnostics in an Abaqus/Explicit analysis +Common difficulties associated with contact modeling using contact pairs in +Abaqus/Explicit +39. Contact Elements in Abaqus/Standard +Contact modeling with elements +Contact modeling with elements +Gap contact elements +Gap contact elements +Gap element library +Tube-to-tube contact elements +Tube-to-tube contact elements +Tube-to-tube contact element library +Slide line contact elements +Slide line contact elements +Axisymmetric slide line element library +Rigid surface contact elements +Rigid surface contact elements +Axisymmetric rigid surface contact element library +40. Defining Cavity Radiation in Abaqus/Standard +Cavity radiation +Printed on: +• Chapter 6, “Analysis Procedures” +Analysis Procedures +Introduction +Static stress/displacement analysis +Dynamic stress/displacement analysis +Steady-state transport analysis +Heat transfer and thermal-stress analysis +Fluid dynamic analysis +Electromagnetic analysis +Coupled pore fluid flow and stress analysis +Mass diffusion analysis +Acoustic and shock analysis +Abaqus/Aqua analysis +Annealing +ANALYSIS PROCEDURES +6.1 +6.2 +6.3 +6.4 +6.5 +6.6 +6.7 +6.8 +6.9 +6.10 +6.11 +6.1 +Introduction +• “Solving analysis problems: overview,” Section 6.1.1 +• “Defining an analysis,” Section 6.1.2 +• “General and linear perturbation procedures,” Section 6.1.3 +• “Multiple load case analysis,” Section 6.1.4 +• “Direct linear equation solver,” Section 6.1.5 +• “Iterative linear equation solver,” Section 6.1.6 +6.1.1 +SOLVING ANALYSIS PROBLEMS: OVERVIEW +Overview +A large class of stress analysis problems can be solved with Abaqus/Standard and Abaqus/Explicit. A +fundamental division of such problems is into static or dynamic response; dynamic problems are those in +which inertia effects are significant. Abaqus/CFD solves a broad range of incompressible flow problems. +An analysis problem history is defined using steps in Abaqus (“Defining an analysis,” Section 6.1.2). +For each step you choose an analysis procedure, which defines the type of analysis to be performed during +the step. The available analysis procedures are listed below and described in more detail in the referenced +sections. +Abaqus provides multiphysics capabilities using built-in fully coupled procedures, sequential +coupling, and co-simulation as solution techniques for multiphysics simulation. An extensive selection +of additional analysis techniques that provide powerful tools for performing your Abaqus analyses more +efficiently and effectively is available; see Part IV, “Analysis Techniques.” +Abaqus/Standard analysis +Abaqus/Standard offers complete flexibility in making the distinction between static and dynamic +response; the same analysis can contain several static and dynamic phases. Thus, a static preload might +be applied, and then the linear or nonlinear dynamic response computed (as in the case of vibrations of +a component of a rotating machine or the response of a flexible offshore system that is initially moved +to an equilibrium position subject to buoyancy and steady current loads and then is excited by wave +loading). Similarly, the static solution can be sought after a dynamic event (by following a dynamic +analysis step with a step of static loading). See “Static stress/displacement analysis,” Section 6.2, and +“Dynamic stress/displacement analysis,” Section 6.3, for information on these types of procedures. In +addition to static and dynamic stress analysis, Abaqus/Standard offers the following analysis types: +• “Steady-state transport analysis,” Section 6.4 +• “Heat transfer and thermal-stress analysis,” Section 6.5 +• “Electromagnetic analysis,” Section 6.7 +• “Coupled pore fluid flow and stress analysis,” Section 6.8 +• “Mass diffusion analysis,” Section 6.9 +• “Acoustic and shock analysis,” Section 6.10 +• “Abaqus/Aqua analysis,” Section 6.11 +Abaqus/Explicit analysis +Abaqus/Explicit solves dynamic response problems using an explicit direct-integration procedure. See +“Dynamic stress/displacement analysis,” Section 6.3, for more information on the explicit dynamic +procedures available in Abaqus. Abaqus/Explicit also provides heat transfer, acoustic, and annealing +analysis capabilities: see “Heat transfer and thermal-stress analysis,” Section 6.5; “Acoustic and shock +analysis,” Section 6.10; and “Annealing,” Section 6.12, for details. +Abaqus/CFD analysis +Abaqus/CFD solves a broad range of incompressible flow problems using a second-order projection +method. See “Fluid dynamic analysis,” Section 6.6, for details on the incompressible flow procedures +available in Abaqus. +Multiphysics analyses +Multiphysics is a coupled approach in the numerical solution of multiple interacting physical domains. +Abaqus provides built-in fully coupled procedures, sequential coupling, and co-simulation as solution +techniques for multiphysics simulation. +Built-in fully coupled procedures +Native Abaqus multiphysics capabilities solve the physics by adding degrees of freedom representing +each of the physical fields and using a single solver. Abaqus provides the following built-in fully coupled +procedures to solve multidisciplinary simulations, where all physics fields are computed by Abaqus: +• “Fully coupled thermal-stress analysis,” Section 6.5.3 +• “Coupled thermal-electrical analysis,” Section 6.7.3 +• “Fully coupled thermal-electrical-structural analysis,” Section 6.7.4 +• “Piezoelectric analysis,” Section 6.7.2 (electrical and mechanical coupling) +• “Eddy current analysis,” Section 6.7.5 (electromagnetic) +• “Coupled pore fluid diffusion and stress analysis,” Section 6.8.1 +• “Acoustic, shock, and coupled acoustic-structural analysis,” Section 6.10.1 +• “Eulerian analysis,” Section 14.1.1 +Sequential coupling +A sequentially coupled multiphysics analysis can be used when the coupling between one or more of +the physical fields in a model is only important in one direction. A common example is a thermal-stress +analysis in which the temperature field does not depend strongly on the stress field. A typical sequentially +coupled thermal-stress analysis consists of two Abaqus/Standard runs: a heat transfer analysis and a +subsequent stress analysis. +You can perform sequentially coupled multiphysics analyses in Abaqus/Standard as described in +the following sections: +• “Predefined fields for sequential coupling,” Section 16.1.1 +• “Sequentially coupled thermal-stress analysis,” Section 16.1.2 +• “Predefined loads for sequential coupling,” Section 16.1.3 +Co-simulation +The co-simulation technique is a multiphysics capability for run-time coupling of Abaqus and another +analysis program. An Abaqus analysis can be coupled to another Abaqus analysis or to a third-party +analysis program to perform multidisciplinary simulations and multidomain (multimodel) coupling. +The co-simulation technique is described in the following sections: +• “Co-simulation: overview,” Section 17.1.1 +• “Preparing an Abaqus analysis for co-simulation,” Section 17.2.1 +• “Abaqus/Standard to Abaqus/Explicit co-simulation,” Section 17.3.1 +• “Abaqus/CFD to Abaqus/Standard or to Abaqus/Explicit co-simulation,” Section 17.3.2 +6.1.2 +DEFINING AN ANALYSIS +Overview +An analysis is defined in Abaqus by: +• dividing the problem history into steps; +• specifying an analysis procedure for each step; and +• prescribing loads, boundary conditions, and output requests for each step. +Abaqus distinguishes between general analysis steps and linear perturbation steps, and you can include +multiple steps in your analysis. You can control how prescribed conditions are applied throughout each +step. In addition, you can specify +• the incrementation scheme used for controlling the solution, +• the matrix storage and solution scheme in Abaqus/Standard, and +• the precision level of the Abaqus/Explicit executable. +Defining an analysis +An analysis in Abaqus is defined using steps, analysis procedures, and optional history data. +Defining steps +A basic concept in Abaqus is the division of the problem history into steps. A step is any convenient +phase of the history—a thermal transient, a creep hold, a dynamic transient, etc. In its simplest form a +step can be just a static analysis in Abaqus/Standard of a load change from one magnitude to another. +You can provide a description of each step that will appear in the data (.dat) file; this description is for +convenience only. +The step definition includes the type of analysis to be performed and optional history data, such as +loads, boundary conditions, and output requests. +Input File Usage: +Abaqus/CAE Usage: +Use the first option to begin a step and the second option to end a step: +*STEP +*END STEP +The optional data lines on the *STEP option can be used to specify the step +description. The first data line given appears in the data (.dat) file. +Step module: Create Step: Description +Specifying the analysis procedure +For each step you choose an analysis procedure. This choice defines the type of analysis to be performed +during the step: static stress analysis, dynamic stress analysis, eigenvalue buckling, transient heat transfer +analysis, etc. The available analysis procedures are described in “Solving analysis problems: overview,” +Section 6.1.1. Only one procedure is allowed per step. +Input File Usage: +The procedure definition option must immediately follow the *STEP option. +Abaqus/CAE Usage: +Step module: Create Step: choose the procedure type +Prescribing loads, boundary conditions, and output requests +The step definition includes optional history data, such as loads, boundary conditions, and output +requests, as defined in “History data” in “Defining a model in Abaqus,” Section 1.3.1. For more +information, see “Boundary conditions,” Section 33.3; “Loads,” Section 33.4; and “Output,” Section 4.1. +Details for prescribing these conditions are discussed in the individual procedure sections. +Input File Usage: +Abaqus/CAE Usage: +The optional history data are defined following the procedure definition within +a *STEP block. +You define history data (step-dependent objects) in the Interaction module, +Load module, and Step module. +General analysis steps versus linear perturbation steps +There are two kinds of steps in Abaqus: general analysis steps, which can be used to analyze linear or +nonlinear response, and linear perturbation steps, which can be used only to analyze linear problems. +General analysis steps can be included in an Abaqus/Standard or Abaqus/Explicit analysis; linear +perturbation analysis steps are available only in Abaqus/Standard. In Abaqus/Standard linear analysis is +always considered to be linear perturbation analysis about the state at the time when the linear analysis +procedure is introduced. This linear perturbation approach allows general application of linear analysis +techniques in cases where the linear response depends on preloading or on the nonlinear response +history of the model. See “General and linear perturbation procedures,” Section 6.1.3, for more details. +Multiple load case analysis +In general analysis steps Abaqus/Standard calculates the solution for a single set of applied loads. This +is also the default for linear perturbation steps. However, for static, direct steady-state dynamic, and +SIM-based steady-state dynamic linear perturbation steps it is possible to find solutions for multiple load +cases. See “Multiple load case analysis,” Section 6.1.4, for a description of this capability. +Multiple steps +The analysis procedure can be changed from step to step in any meaningful way, so you have great +flexibility in performing analyses. Since the state of the model (stresses, strains, temperatures, etc.) is +updated throughout all general analysis steps, the effects of previous history are always included in the +response in each new analysis step. Thus, for example, if natural frequency extraction is performed after +a geometrically nonlinear static analysis step, the preload stiffness will be included. Linear perturbation +steps have no effect on subsequent general analysis steps. +The most obvious reason for using several steps in an analysis is to change analysis procedure +type. However, several steps can also be used as a matter of convenience—for example, to change +output requests, contact pairs in Abaqus/Explicit, boundary conditions, or loading (any information +specified as history, or step-dependent, data). Sometimes an analysis may have progressed to a point +where the present step definition needs to be modified. Abaqus provides for this contingency with the +restart capability, whereby a step can be terminated prematurely and a new step can be defined for the +problem continuation . +Optional history data prescribing the loading, +boundary conditions, output controls, and auxiliary controls will remain in effect for all subsequent +general analysis steps, including those that are defined in a restart analysis, until they are modified or reset. +Abaqus will compare all loads and boundary conditions specified in a step with the loads and boundary +conditions in effect during the previous step to ensure consistency and continuity. This comparison is +expensive if the number of individually specified loads and boundary conditions is very large. Hence, +the number of individually specified loads and boundary conditions should be minimized, which can +usually be done by using element and node sets instead of individual elements and nodes. For linear +perturbation steps only the output controls are continued from one linear perturbation step to the next if +there are no intermediate general analysis steps and the output controls are not redefined . +Within Abaqus/Standard or Abaqus/Explicit, any combination of available procedures can be used +from step to step. However, Abaqus/Standard and Abaqus/Explicit procedures cannot be used in the same +analysis. See “Transferring results between Abaqus analyses: overview,” Section 9.2.1, for information +on importing results from one type of analysis to another. +Defining time varying prescribed conditions +By default, Abaqus assumes that external parameters, such as load magnitudes and boundary conditions, +are constant (step function) or vary linearly (ramped) over a step, depending on the analysis procedure, +as shown in Table 6.1.2–1. Some exceptions in Abaqus/Standard are discussed below. +Table 6.1.2–1 Default amplitude variations for time domain procedures. +Procedure +Default amplitude variation +Coupled pore fluid diffusion/stress (steady-state) +Coupled pore fluid diffusion/stress (transient) +Coupled thermal-electrical (steady-state) +Coupled thermal-electrical (transient) +Direct-integration dynamic +Fully coupled thermal-electrical-structural in +Abaqus/Standard (steady-state) +Fully coupled thermal-electrical-structural in +Abaqus/Standard (transient) +Ramp +Step +Ramp +Step +Step (exception: Ramp if +quasi-static application type +is specified) +Ramp +Step +Procedure +Default amplitude variation +Fully coupled thermal-stress in Abaqus/Standard +(steady-state) +Fully coupled thermal-stress in Abaqus/Standard +(transient) +Fully coupled thermal-stress in Abaqus/Explicit +Incompressible flow +Magnetostatic +Mass diffusion (steady-state) +Mass diffusion (transient) +Quasi-static +Static +Steady-state transport +Transient eddy current +Transient modal dynamic +Uncoupled heat transfer +Uncoupled heat transfer (transient) +Ramp +Step +Step +Step +Ramp +Ramp +Step +Step +Ramp +Ramp +Step +Step +Ramp +Step +No default amplitude variation is defined for a direct cyclic analysis step; for each applied load or +boundary condition, the amplitude must be defined explicitly. +Additional default amplitude variations in Abaqus/Standard +For displacement or rotation degrees of freedom prescribed in Abaqus/Standard using displacement-type +boundary conditions or displacement-type connector motions, the default amplitude variation is a ramp +function for all procedure types; the default amplitude is a step function for all procedure types when +using velocity-type boundary conditions or velocity-type connector motions. +For motions prescribed using a predefined displacement field, the default amplitude variation is a +ramp function for all procedure types; the default amplitude is a step function when using a predefined +velocity field for all procedures except steady-state transport. +The default amplitude variation is a step function for fluid flux loading in all procedure types. +When a displacement or rotation boundary condition is removed, the corresponding reaction force +or moment is reduced to zero according to the amplitude defined for the step. When film or radiation +loads are removed, the variation is always a step function. +Prescribing nondefault amplitude variations +You can define complicated time variations of loadings, boundary conditions, and predefined fields +by referring to an amplitude curve in the prescribed condition definition . User subroutines are also provided in Abaqus/Standard and Abaqus/Explicit for coding +general loadings . +In Abaqus/Standard you can change the default amplitude variation for a step (except the removal +of film or radiation loads, as noted above). +Input File Usage: +In Abaqus/Standard use the following option to change the default amplitude +variation for a step: +Abaqus/CAE Usage: +*STEP, AMPLITUDE=STEP or RAMP +In Abaqus/Standard use the following input to change the default amplitude +variation for a step: +Step module: step editor: Other: Default load variation with time: +Instantaneous or Ramp linearly over step +Boundary conditions in Abaqus/Explicit +Boundary conditions applied during an explicit dynamic response step should use appropriate amplitude +references to define the time variation. If boundary conditions are specified for the step without amplitude +references, they are applied instantaneously at the beginning of the step. Since Abaqus/Explicit does not +admit jumps in displacement, the value of a nonzero displacement boundary condition that is specified +without an amplitude reference will be ignored, and a zero velocity boundary condition will be enforced. +Prescribing nondefault amplitude variations in transient procedures in Abaqus/Standard +The default amplitude is a step function for transient analysis procedures (fully coupled thermal-stress, +fully coupled thermal-electrical-structural, coupled thermal-electrical, direct-integration dynamic, +uncoupled heat transfer, and mass diffusion). Care should be exercised when the nondefault ramp +amplitude variation is specified for transient analysis procedures since unexpected results may occur. +For example, if a step of a transient heat transfer analysis uses the ramp amplitude variation and +temperature boundary conditions are removed in a subsequent step, the reaction fluxes generated in the +previous step will be ramped to zero from their initial values over the duration of the step. Therefore, +heat flux will continue to flow through the affected boundary nodes over the entire subsequent step even +though the temperature boundary conditions were removed. +Incrementation +Each step in an Abaqus analysis is divided into multiple increments. In most cases you have two choices +for controlling the solution: automatic time incrementation or user-specified fixed time incrementation. +Automatic incrementation is recommended for most cases. The methods for selecting automatic or direct +incrementation are discussed in the individual procedure sections. +The issues associated with time incrementation in Abaqus/Standard, Abaqus/Explicit, and +The time increments are generally much smaller in +Abaqus/CFD analyses are quite different. +Abaqus/Explicit than in Abaqus/Standard, while the time increments for Abaqus/CFD may be similar +to those in Abaqus/Standard in many situations. +Incrementation in Abaqus/Standard +In nonlinear problems Abaqus/Standard will increment and iterate as necessary to analyze a step, +depending on the severity of the nonlinearity. In transient cases with a physical time scale, you can +provide parameters to indicate a level of accuracy in the time integration, and Abaqus/Standard will +choose the time increments to achieve this accuracy. Direct user control is provided because it can +sometimes save computational cost in cases where you are familiar with the problem and know a +suitable incrementation scheme. Direct control can also occasionally be useful when automatic control +has trouble with convergence in nonlinear problems. +Specifying the maximum number of increments +You can define the upper limit to the number of increments in an Abaqus/Standard analysis. In a direct +cyclic analysis procedure, this upper limit should be set to the maximum number of increments in a +single loading cycle. The default is 100. The analysis will stop if this maximum is exceeded before the +complete solution for the step has been obtained. To arrive at a solution, it is often necessary to increase +the number of increments allowed by defining a new upper limit. +*STEP, INC=n +Step module: step editor: Incrementation: Maximum number +of increments +Abaqus/CAE Usage: +Input File Usage: +Extrapolation of the solution +In nonlinear analyses Abaqus/Standard uses extrapolation to speed up the solution. Extrapolation refers +to the method used to determine the first guess to the incremental solution. The guess is determined +by the size of the current time increment and by whether linear, displacement-based parabolic, +velocity-based parabolic, or no extrapolation of the previously attained history of each solution +variable is chosen. Displacement-based parabolic extrapolation is not relevant for Riks analyses, and +velocity-based parabolic extrapolation is available only for direct-integration dynamic procedures. +Linear extrapolation (the default for all procedures other than a direct-integration dynamic procedure +using the transient fidelity application setting) uses 100% extrapolation (1% for the Riks method) of the +previous incremental solution at the start of each increment to begin the nonlinear equation solution for +the next increment. No extrapolation is used in the first increment of a step. +In some cases extrapolation can cause Abaqus/Standard to iterate excessively; some common +examples are abrupt changes in the load magnitudes or boundary conditions and if unloading occurs as +a result of cracking (in concrete models) or buckling. In such cases you should suppress extrapolation. +Displacement-based parabolic extrapolation uses two previous incremental solutions to obtain the +first guess to the current incremental solution. This type of extrapolation is useful in situations when the +local variation of the solution with respect to the time scale of the problem is expected to be quadratic, +such as the large rotation of structures. If parabolic extrapolation is used in a step, it begins after the +second increment of the step: the first increment employs no extrapolation, and the second increment +employs linear extrapolation. Consequently, slower convergence rates may occur during the first two +increments of the succeeding steps in a multistep analysis. +Velocity-based parabolic extrapolation uses the previous displacement incremental solution to +It is available only for direct-integration +obtain the first guess to the current incremental solution. +dynamic procedures, and it is the default if the transient fidelity application setting is specified as part +of this procedure . This type of +extrapolation is useful in situations with smooth solutions—i.e., when velocities do not display so called +“saw tooth” patterns—and in such cases it may provide a better first guess than other extrapolations. If +velocity-based parabolic extrapolation is used in a step, it begins after the first increment of the step; the +first increment employs initial velocities. +Input File Usage: +Use the following option to choose linear extrapolation: +*STEP, EXTRAPOLATION=LINEAR (default for all procedures +other than a direct-integration dynamic procedure using the +transient fidelity application setting) +Use the following option to choose displacement-based parabolic extrapolation: +*STEP, EXTRAPOLATION=PARABOLIC +Use the following option to choose velocity-based parabolic extrapolation: +*STEP, EXTRAPOLATION=VELOCITY PARABOLIC (default for a direct- +integration dynamic procedure using the transient fidelity application setting) +Use the following option to choose no extrapolation: +*STEP, EXTRAPOLATION= NO +Step module: step editor: Other: Extrapolation of previous state at +start of each increment: Linear, Parabolic, Velocity parabolic, +None, or Analysis product default +Abaqus/CAE Usage: +Incrementation in Abaqus/Explicit +The time increment used in an Abaqus/Explicit analysis must be smaller than the stability limit of +the central-difference operator ; failure to use a small +enough time increment will result in an unstable solution. Although the time increments chosen by +Abaqus/Explicit generally satisfy the stability criterion, user control over the size of the time increment +is provided to reduce the chance of a solution going unstable. The small increments characteristic of an +explicit dynamic analysis product make Abaqus/Explicit well suited for nonlinear analysis. +Severe discontinuities in Abaqus/Standard +Abaqus/Standard distinguishes between regular, equilibrium iterations (in which the solution varies +smoothly) and severe discontinuity iterations (SDIs) in which abrupt changes in stiffness occur. The +most common of such severe discontinuities involve open-close changes in contact and stick-slip +changes in friction. By default, Abaqus/Standard will continue to iterate until the severe discontinuities +are sufficiently small (or no severe discontinuities occur) and the equilibrium (flux) tolerances are +satisfied. Alternatively, you can choose a different approach in which Abaqus/Standard will continue to +iterate until no severe discontinuities occur. +For contact openings with the default approach, a force discontinuity is generated when the contact +force is set to zero, and this force discontinuity leads to force residuals that are checked against the +time average force in the usual way, as described in “Convergence criteria for nonlinear problems,” +Section 7.2.3. Similarly, in stick-to-slip transitions the frictional force is set to a lower value, which also +leads to force residuals. +For contact closures a severe discontinuity is considered sufficiently small if the penetration error is +smaller than the contact compatibility tolerance times the incremental displacement. The penetration +error is defined as the difference between the actual penetration and the penetration following from +the contact pressure and pressure-overclosure relation. In cases where the displacement increment is +essentially zero, a “zero penetration” check is used, similar to the check used for zero displacement +increments . The same checks are +used for slip-to-stick transitions in Lagrange friction. +To make sure that sufficient accuracy is obtained for contact between hard bodies, it is also required +that the estimated contact force error is smaller than the time average force times the contact force error +tolerance. The estimated contact force error is obtained by multiplying the penetration by an effective +stiffness. For hard contact this effective stiffness is equal to the stiffness of the underlying element, +whereas for softened/penalty contact the effective stiffness is obtained by adding the compliance of the +contact constraint and the underlying element. +Forcing the iteration process to continue until no severe discontinuities occur is the more +traditional, conservative method. However, this method can sometimes lead to convergence problems, +particularly in large problems with many contact points or situations where contact conditions are only +weakly determined. In such cases excessive iteration may occur and convergence may not be obtained +Input File Usage: +Abaqus/CAE Usage: +*STEP, CONVERT SDI=NO +Step module: step editor: Other: Convert severe discontinuity +iterations: Off +Matrix storage and solution scheme in Abaqus/Standard +Abaqus/Standard generally uses Newton’s method to solve nonlinear problems and the stiffness method +to solve linear problems. In both cases the stiffness matrix is needed. In some problems—for example, +with Coulomb friction—this matrix is not symmetric. Abaqus/Standard will automatically choose +whether a symmetric or unsymmetric matrix storage and solution scheme should be used based on the +model and step definition used. In some cases you can override this choice; the rules are explained +below. +Usually it is not necessary to specify the matrix storage and solution scheme. The choice is +available to improve computational efficiency in those cases where you judge that the default value is +not the best choice. In certain cases where the exact tangent stiffness matrix is not symmetric, the extra +iterations required by a symmetric approximation to the tangent matrix use less computer time than +solving the nonsymmetric tangent matrix at each iteration. Therefore, for example, Abaqus/Standard +invokes the symmetric matrix storage and solution scheme automatically in problems with Coulomb +friction where every friction coefficient is less than or equal to 0.2, even though the resulting tangent +matrix will have some nonsymmetric terms. However, if any friction coefficient is greater than 0.2, +Abaqus/Standard will use the unsymmetric matrix storage and solution scheme automatically since it +may significantly improve the convergence history. This choice of the unsymmetric matrix storage and +solution scheme will consider changes to the friction model. Thus, if you modify the friction definition +during the analysis to introduce a friction coefficient greater than 0.2, Abaqus/Standard will activate +the unsymmetric matrix storage and solution scheme automatically. In cases in which the unsymmetric +matrix storage and solution scheme is selected automatically, you must explicitly turn it off if so desired; +it is recommended to do so if friction prevents any sliding motions. +Input File Usage: +Abaqus/CAE Usage: +*STEP, UNSYMM=YES or NO +Step module: step editor: Other: Storage: Use solver default +or Unsymmetric or Symmetric +Rules for using the unsymmetric matrix storage and solution scheme +The following rules apply to matrix storage and solution schemes in Abaqus/Standard: +1. Since Abaqus/Standard provides eigenvalue extraction only for symmetric matrices, steps with +eigenfrequency extraction or eigenvalue buckling prediction procedures always use the symmetric +matrix storage and solution scheme. You cannot change this setting. In such steps Abaqus/Standard +will symmetrize all contributions to the stiffness matrix. +2. In all steps except those with eigenfrequency extraction or eigenvalue buckling procedures, +Abaqus/Standard uses the unsymmetric matrix storage and solution scheme when any of the +following features are included in the model. You cannot change this setting. +a. Heat transfer convection/diffusion elements (element types DCCxxx) +b. General shell sections with unsymmetric section stiffness matrices (“Three-dimensional +conventional shell element library,” Section 29.6.7) +c. User-defined elements with unsymmetric element matrices (“User-defined elements,” +Section 32.15.1) +d. User-defined material models with unsymmetric material stiffness matrices (“User-defined +mechanical material behavior,” Section 26.7.1, or “User-defined thermal material behavior,” +Section 26.7.2) +e. User-defined surface interaction models with unsymmetric interface stiffness matrices (“User- +defined interfacial constitutive behavior,” Section 36.1.6) +3. The following features all trigger the unsymmetric matrix storage and solution scheme for the step. +You cannot change this setting. +a. Fully coupled thermal-stress analysis, except when a separated solution scheme is specified +for the step (“Fully coupled thermal-stress analysis,” Section 6.5.3) +b. Coupled thermal-electrical analysis, except when a separated solution scheme is specified for +the step (“Coupled thermal-electrical analysis,” Section 6.7.3) +c. Fully coupled thermal-electrical-structural analysis (“Fully coupled thermal-electrical- +structural analysis,” Section 6.7.4) +d. Coupled pore fluid diffusion/stress analysis with absorption or exsorption behavior (“Coupled +pore fluid diffusion and stress analysis,” Section 6.8.1) +e. Coupled pore fluid diffusion/stress analysis (steady-state) +f. Coupled pore fluid diffusion/stress analysis (transient with gravity loading) +g. Mass diffusion analysis (“Mass diffusion analysis,” Section 6.9.1) +h. Radiation viewfactor calculation controls (“Cavity radiation,” Section 40.1.1) +4. By default, the unsymmetric matrix storage and solution scheme is used for the complex eigenvalue +extraction procedure. You can change this setting. +5. In all other cases you can control whether a symmetric or a full matrix storage and arithmetic solution +is chosen. If you do not specify the matrix storage and solution scheme, Abaqus/Standard utilizes +the value used in the previous general analysis step. +6. If you do not specify the matrix storage and solution scheme in the first step of an analysis, +Abaqus/Standard will choose the unsymmetric scheme when any of the following are used: +a. Any Abaqus/Aqua load type +b. The concrete damaged plasticity material model +c. Friction with a friction coefficient greater than 0.2 +The default value in the first step is the symmetric scheme for all other cases, except those +covered by rules 2 and 3 above and for cases in which a friction coefficient is increased above 0.2 +after the first step. +7. For radiative heat transfer surface interactions (“Thermal contact properties,” Section 36.2.1), +certain follower forces (such as concentrated follower forces or moments), three-dimensional +finite-sliding analyses, any finite sliding in coupled pore fluid diffusion/stress analyses, and +certain material models (particularly nonassociated flow plasticity models and concrete) introduce +unsymmetric terms in the model’s stiffness matrix. However, Abaqus/Standard does not +automatically use the unsymmetric matrix storage and solution scheme when radiative heat +transfer surface interactions are used. Specifying that the unsymmetric scheme should be used can +sometimes improve convergence in such cases. +8. Coupled structural-acoustic and uncoupled acoustic analysis procedures in Abaqus/Standard +generally use symmetric matrix storage and solution. +Exceptions are the subspace-based +steady-state dynamics or complex frequency procedures used for coupled structural-acoustic +problems, where unsymmetric matrices are a consequence of the coupling procedure used in +these cases. Using acoustic infinite elements or the acoustic flow velocity option triggers the +unsymmetric matrix storage and solution scheme in Abaqus/Standard, except for natural frequency +extraction using the Lanczos eigensolver, which uses symmetric matrix operations. +Precision level of the Abaqus/Explicit executable +You can choose a double-precision executable (with 64-bit word lengths) for Abaqus/Explicit on +machines with a default, single-precision word length of 32 bits . Most new computers have 32-bit default word lengths +even though they may have 64-bit memory addressing. The single-precision executable typically +results in a CPU savings of 20% to 30% compared to the double-precision executable, and single +precision provides accurate results in most cases. Exceptions in which single precision tends to be +inadequate include analyses that require greater than approximately 300,000 increments, have typical +nodal displacement increments less than 10−6 times the corresponding nodal coordinate values, include +hyperelastic materials, or involve multiple revolutions of deformable parts; +the double-precision +executable is recommended in these cases (for example, see “Simulation of propeller rotation,” +Section 2.3.15 of the Abaqus Benchmarks Manual). +You can also run only a part of Abaqus/Explicit using double precision, while using single precision +for the rest . These +options are described below. +• If double=explicit is used or the double option is specified without a value, the Abaqus/Explicit +analysis will run in double precision, while the packager will run in single precision. While this +choice would satisfy higher precision needs in most analyses, the data are written to the state (.abq) +file in single precision. Moreover, analysis-related computations performed in the packager will still +be executed in single precision. Thus, new steps, restart, and import analyses will commence from +data that are stored/computed in single precision despite the fact that calculations during the step +are performed in double precision. Thus, in general, one can expect somewhat noisy solutions at +the beginning of the first step, at step transitions, upon restart, and after import. +• If double=both is used, both the Abaqus/Explicit packager and analysis will run in double +precision. This is the most expensive option but will ensure the highest overall execution precision. +Analysis database floating point data will be written to the state (.abq) file at the end of packager +or of a given step in double precision, thus ensuring in most cases the smoothest transition at step +boundaries, upon restart, and after an import. +• There may be cases where the default single precision analysis is inadequate, while the +double=both option is too expensive. These are typically models that have complex links of +constraints (such as a complex mechanism with connector elements, complex combinations of +distributed/kinematic couplings, tie constraints and multi-point constraints, or interactions of such +constraints with boundary conditions). For such models it is desirable to solve only the constraints +in the model in double precision while the rest of the model is solved in single precision. This +combination gives the desired accuracy of the solution while increasing performance compared to +a full double precision analysis. +• If double=constraint is used, the constraint packager and constraint solver are executed in +double precision, while the remainder of the Abaqus/Explicit packager and analysis are executed in +single precision. +• If double=off is used or the double option is omitted (default), both the Abaqus/Explicit packager +and the analysis will run in single precision. The double=off option is useful when you want to +override the setting in the environment file. +The significance of the precision level is indicated by comparing the solutions obtained with single +and double precision. If no significant difference is found between single- and double-precision solutions +for a particular model, the single-precision executable can be deemed adequate. +6.1.3 +GENERAL AND LINEAR PERTURBATION PROCEDURES +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “Linear and nonlinear procedures,” Section 14.3.2 of the Abaqus/CAE User’s Manual +Overview +An analysis step during which the response can be either linear or nonlinear is called a general analysis +step. An analysis step during which the response can be linear only is called a linear perturbation analysis +step. General analysis steps can be included in an Abaqus/Standard or Abaqus/Explicit analysis; linear +perturbation analysis steps are available only in Abaqus/Standard. +A clear distinction is made in Abaqus/Standard between general analysis and linear perturbation +analysis procedures. Loading conditions are defined differently for the two cases, time measures are +different, and the results should be interpreted differently. These distinctions are defined in this section. +Abaqus/Standard treats a linear perturbation analysis as a linear perturbation about a preloaded, +predeformed state. Abaqus/Foundation, a subset of Abaqus/Standard, is limited entirely to linear +perturbation analysis but does not allow preloading or predeformed states. +General analysis steps +A general analysis step is one in which the effects of any nonlinearities present in the model can be +included. The starting condition for each general step is the ending condition from the last general step, +with the state of the model evolving throughout the history of general analysis steps as it responds to the +history of loading. If the first step of the analysis is a general step, the initial conditions for the step can +be specified directly (“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1). +Abaqus always considers total time to increase throughout a general analysis. Each step also has +its own step time, which begins at zero in each step. If the analysis procedure for the step has a physical +time scale, as in a dynamic analysis, step time must correspond to that physical time. Otherwise, step +time is any convenient time scale—for example, 0.0 to 1.0—for the step. The step times of all general +analysis steps accumulate into total time. Therefore, if an option such as creep (available only in +Abaqus/Standard) whose formulation depends on total time is used in a multistep analysis, any steps +that do not have a physical time scale should have a negligibly small step time compared to the steps +in which a physical time scale does exist. +Sources of nonlinearity +Nonlinear stress analysis problems can contain up to three sources of nonlinearity: material nonlinearity, +geometric nonlinearity, and boundary nonlinearity. +Material nonlinearity +Abaqus offers models for a wide range of nonlinear material behaviors . Many of the materials are history dependent: the material’s response at +any time depends on what has happened to it at previous times. Thus, the solution must be obtained by +following the actual loading sequence. The general analysis procedures are designed with this in view. +Geometric nonlinearity +It is possible in Abaqus to define a problem as a “small-displacement” analysis, which means +that geometric nonlinearity is ignored in the element calculations—the kinematic relationships are +linearized. By default, large displacements and rotations are accounted for in contact constraints +even if the small-displacement element formulations are used for the analysis; i.e., a large-sliding +contact tracking algorithm is used . The elements in a +small-displacement analysis are formulated in the reference (original) configuration, using original +nodal coordinates. The errors in such an approximation are of the order of the strains and rotations +compared to unity. The approximation also eliminates any possibility of capturing bifurcation buckling, +which is sometimes a critical aspect of a structure’s response . You must consider these issues when interpreting the results of such an +analysis. +The alternative to a “small-displacement” analysis in Abaqus is to include large-displacement +In this case most elements are formulated in the current configuration using current nodal +effects. +positions. Elements therefore distort from their original shapes as the deformation increases. With +sufficiently large deformations, the elements may become so distorted that they are no longer suitable +for use; for example, the volume of the element at an integration point may become negative. In this +situation Abaqus will issue a warning message indicating the problem. In addition, Abaqus/Standard will +cut back the time increment before making further attempts to continue the solution. Abaqus/Explicit +also offers element failure models to allow elements that reach high strains to be removed from a model; +see “Dynamic failure models,” Section 23.2.8, for details. +For each step of an analysis you specify whether a small- or large-displacement formulation +should be used (i.e., whether geometric nonlinearity should be ignored or included). By default, +Abaqus/Standard uses a small-displacement formulation and Abaqus/Explicit uses a large-displacement +formulation. The default value for the formulation in an import analysis is the same as the value at the +time of import. If a large-displacement formulation is used during any step of an analysis, it will be +used in all following steps in the analysis; there is no way to turn it off. +Almost all of the elements in Abaqus use a fully nonlinear formulation. The exceptions are the +cubic beam elements in Abaqus/Standard and the small-strain shell elements (those shell elements other +than S3/S3R, S4, S4R, and the axisymmetric shells) in which the cross-sectional thickness change is +ignored so that these elements are appropriate only for large rotations and small strains. Except for these +elements, the strains and rotations can be arbitrarily large. +The calculated stress is the “true” (Cauchy) stress. For beam, pipe, and shell elements the stress +components are given in local directions that rotate with the material. For all other elements the stress +components are given in the global directions unless a local orientation (“Orientations,” Section 2.2.5) is +used at a point. For small-displacement analysis the infinitesimal strain measure is used, which is output +with the strain output variable E; strain output specified with output variables LE and NE is the same as +with E. +Input File Usage: +Use the following option to specify that a large-displacement formulation +should be used for the step: +*STEP, NLGEOM=YES (default in Abaqus/Explicit) +Use the following option to specify that a small-displacement formulation +should be used for the step: +*STEP, NLGEOM=NO (default in Abaqus/Standard) +Omitting the NLGEOM parameter is equivalent to using the default value. +Abaqus/CAE Usage: +Step module: Create Step: select any step type: Basic: Nlgeom: Off (for a +small-displacement formulation) or On (for a large-displacement formulation) +Boundary nonlinearity +Contact problems are a common source of nonlinearity in stress analysis—see “Contact interaction +analysis: overview,” Section 35.1.1. Other sources of boundary nonlinearity are nonlinear elastic +springs, films, radiation, multi-point constraints, etc. +Loading +In a general analysis step the loads must be defined as total values. The rules for applying loads in a +general, multistep analysis are defined in “Applying loads: overview,” Section 33.4.1. +Incrementation +The general analysis procedures in Abaqus offer two approaches for controlling incrementation. +Automatic control is one choice: you define the step and, in some procedures, specify certain tolerances +or error measures. Abaqus then automatically selects the increment size as it develops the response +in the step. Direct user control of increment size is the alternative approach, whereby you specify +the incrementation scheme. The direct approach is sometimes useful in repetitive analyses with +Abaqus/Standard, where you have a good “feel” for the convergence behavior of the problem. The +methods for selecting automatic or direct incrementation are discussed in the individual procedure +sections. +In nonlinear problems in Abaqus/Standard the challenge is always to obtain a convergent solution +in the least possible computational time. +In these cases automatic control of the time increment is +usually more efficient because Abaqus/Standard can react to nonlinear response that you cannot predict +ahead of time. Automatic control is particularly valuable in cases where the response or load varies +widely through the step, as is often the case in diffusion-type problems such as creep, heat transfer, and +consolidation. Ultimately, automatic control allows nonlinear problems to be run with confidence in +Abaqus/Standard without extensive experience with the problem. +Strong nonlinearities typically do not present difficulties in Abaqus/Explicit because of the small +time increments that are characteristic of an explicit dynamic analysis product. +Stabilization of unstable problems in Abaqus/Standard +Some static problems can be naturally unstable, for a variety of reasons. +Unconstrained rigid body motions +Instability may occur because unconstrained rigid body motions exist. Abaqus/Standard may be able +to handle this type of problem with automatic viscous damping when rigid body motions exist during the approach of two bodies +that will eventually come into contact. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options: +*CONTACT STABILIZATION +*CONTACT CONTROLS, STABILIZE +Automatic viscous damping is not supported in Abaqus/CAE. +Localized buckling behavior or material instability +Instability may also be caused by localized buckling behavior or by material instability; such instabilities +are especially significant when no time-dependent behavior exists in the material modeling. The +static, general analysis procedures in Abaqus/Standard can stabilize this type of problem if you request +it . +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options: +*STATIC, STABILIZE +*VISCO, STABILIZE +*STEADY STATE TRANSPORT, STABILIZE +*COUPLED TEMPERATURE-DISPLACEMENT, STABILIZE +*COUPLED TEMPERATURE-DISPLACEMENT, ELECTRICAL, STABILIZE +*SOILS, CONSOLIDATION, STABILIZE +Step module: Create Step: General: any valid step type: Basic: Use +stabilization with dissipated energy fraction +Linear perturbation analysis steps +Linear perturbation analysis steps are available only in Abaqus/Standard (Abaqus/Foundation is +essentially the linear perturbation functionality in Abaqus/Standard). The response in a linear analysis +step is the linear perturbation response about the base state. The base state is the current state of the +model at the end of the last general analysis step prior to the linear perturbation step. If the first step +of an analysis is a perturbation step, the base state is determined from the initial conditions (“Initial +conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1). In Abaqus/Foundation the base +state is always determined from the initial state of the model. +Linear perturbation analyses can be performed from time to time during a fully nonlinear analysis +by including the linear perturbation steps between the general response steps. The linear perturbation +response has no effect as the general analysis is continued. The step time of linear perturbation steps, +which is taken arbitrarily to be a very small number, is never accumulated into the total time. A simple +example of this method is the determination of the natural frequencies of a violin string under increasing +tension . The +tension of the string is increased in several geometrically nonlinear analysis steps. After each of these +steps, the frequencies can be extracted in a linear perturbation analysis step. +If geometric nonlinearity is included in the general analysis upon which a linear perturbation study +is based, stress stiffening or softening effects and load stiffness effects (from pressure and other follower +forces) are included in the linear perturbation analysis. +Load stiffness contributions are also generated for centrifugal and Coriolis loading. In direct steady- +state dynamic analysis Coriolis loading generates an imaginary antisymmetric matrix. This contribution +is accounted for currently in solid and truss elements only and is activated by using the unsymmetric +matrix storage and solution scheme in the step. +Linear perturbation procedures +The following purely linear perturbation procedures are available in Abaqus/Standard: +• “Eigenvalue buckling prediction,” Section 6.2.3 +• “Direct-solution steady-state dynamic analysis,” Section 6.3.4 +• “Natural frequency extraction,” Section 6.3.5 +• “Complex eigenvalue extraction,” Section 6.3.6 +• “Transient modal dynamic analysis,” Section 6.3.7 +• “Mode-based steady-state dynamic analysis,” Section 6.3.8 +• “Subspace-based steady-state dynamic analysis,” Section 6.3.9 +• “Response spectrum analysis,” Section 6.3.10 +• “Random response analysis,” Section 6.3.11 +• “Time-harmonic analysis” in “Eddy current analysis,” Section 6.7.5 +In addition, the following analysis techniques are treated as linear perturbation steps in an analysis: +• “Defining substructures,” Section 10.1.2 +• “Generating matrices,” Section 10.3.1 +Except for these procedures and the static procedure (explained below), all other procedures can be +used only in general analysis steps (in other words, they are not available with Abaqus/Foundation). All +linear perturbation procedures except for the complex eigenvalue extraction procedure are available with +Abaqus/Foundation. +Linear static perturbation analysis +A linear static stress analysis (“Static stress analysis,” Section 6.2.2) can be conducted in +Abaqus/Standard. +Input File Usage: +Use both of the following options to conduct a linear static perturbation +analysis: +*STEP, PERTURBATION +*STATIC +Omitting the PERTURBATION parameter on the *STEP option implies that a +general static analysis is required. +Abaqus/CAE Usage: +Step module: Create Step: Linear perturbation: Static, +Linear perturbation +Loading +Load magnitudes (including the magnitudes of prescribed boundary conditions) during a linear +perturbation analysis step are defined as the magnitudes of the load perturbations only. Likewise, the +value of any solution variable is output as the perturbation value only—the value of the variable in the +base state is not included. +Multiple load case analysis +Multiple load cases can be analyzed simultaneously for static, direct-solution steady-state dynamic and +SIM-based steady-state dynamic (including subspace projection) linear perturbation steps. See “Multiple +load case analysis,” Section 6.1.4, for a description of this capability. +Restrictions +A linear perturbation analysis is subject to the following restrictions: +• Since a linear perturbation analysis has no time period, amplitude references (“Amplitude curves,” +Section 33.1.2) can be used meaningfully only to specify loads or boundary conditions as functions +of frequency (in a steady-state dynamics analysis) or to define base motion (in mode-based dynamics +procedures). If loads or boundary conditions are specified as functions of time, the amplitude value +corresponding to time=0 will be used. +• A general +implicit dynamic analysis (“Implicit dynamic analysis using direct +integration,” +Section 6.3.2) cannot be interrupted to perform perturbation analyses: +before performing +the perturbation analysis, Abaqus/Standard requires that the structure be brought into static +equilibrium. +• During a linear perturbation analysis step, the model’s response is defined by its linear elastic +(or viscoelastic) stiffness at the base state. Plasticity and other inelastic effects are ignored. For +hyperelasticity (“Hyperelastic behavior of rubberlike materials,” Section 22.5.1) or hypoelasticity +(“Hypoelastic behavior,” Section 22.4.1), the tangent elastic moduli in the base state are used. +If cracking has occurred—for example, in the concrete model (“Concrete smeared cracking,” +Section 23.6.1)—the damaged elastic (secant) moduli are used. +• Contact conditions cannot change during a linear perturbation analysis. The open/closed status of +each contact constraint remains as it is in the base state. All points in contact (i.e., with a “closed” +status) are assumed to be sticking if friction is present, except the contact nodes for which a velocity +differential is imposed by the motion of the reference frame or the transport velocity. At those nodes, +slipping conditions are assumed regardless of the friction coefficient. +• The effects of temperature and field variable perturbations are ignored for materials that are +dependent on temperature and field variables. However, temperature perturbations will produce +perturbations of thermal strain. +6.1.4 +MULTIPLE LOAD CASE ANALYSIS +Products: Abaqus/Standard Abaqus/CAE +References +• *LOAD CASE +• *END LOAD CASE +• Chapter 34, “Load cases,” of the Abaqus/CAE User’s Manual +Overview +A multiple load case analysis: +• is used to study the linear responses of a structure subjected to distinct sets of loads and boundary +conditions defined within a step (each set is referred to as a load case); +• can be much more efficient than an equivalent multiple perturbation step analysis; +• allows for the changing of mechanical loads and boundary conditions from load case to load case; +• includes the effects of the base state; and +• can be performed with static perturbation, direct-solution steady-state dynamic and SIM-based +steady-state dynamic analyses. +Load cases +A load case refers to a set of loads, boundary conditions, and base motions comprising a particular +loading condition. For example, in a simplified model the operational environment of an airplane might +be broken into five load cases: (1) take-off, (2) climb, (3) cruise, (4) descent, and (5) landing. Often a +load case is defined in terms of unit loads or prescribed boundary conditions, and a multiple load case +analysis refers to the simultaneous solution for the responses of each load case in a set of such load +cases. These responses can then be scaled and linearly combined during postprocessing to represent the +actual loading environment. Other postprocessing manipulations on load cases are also common, such +as finding the maximum Mises stress among all load cases. These types of load case manipulations can +be requested in the Visualization module of Abaqus/CAE . +Using multiple load cases +A multiple load case analysis is conceptually equivalent to a multiple step analysis in which the load +case definitions are mapped to consecutive perturbation steps. However, a multiple load case analysis is +generally much more efficient than the equivalent multiple step analysis. The exception occurs when a +large number of boundary conditions exist that are not common to all load cases (i.e., degrees of freedom +are constrained in one load case but not others). It is difficult to define what “large” is since it is model +dependent. The relative performance of the two analysis methods can be assessed by performing a data +check analysis for both the multiple load case analysis and the equivalent multiple step analysis. The +data check analysis writes resource information for each step to the data file, including the maximum +wavefront, number of floating point operations, and minimum memory required. If these numbers are +noticeably larger for the multiple load case step compared to those across all steps of the equivalent +multiple step analysis (the number of floating point operations should be summed over all steps before +comparing), the multiple step analysis will be more efficient. +Although generally more efficient, the multiple load case analysis may consume more memory and +disk space than an equivalent multiple step analysis. Thus, for large problems or problems with many +load cases it is again advisable, as described above, to compare resource usage between the multiple load +case analysis and the equivalent multiple step analysis. If resource requirements for the multiple load +case analysis are deemed too large, consider dividing the load cases among a few steps. The resulting +analysis (a hybrid of multiple load cases and multiple steps) will require fewer resources while retaining +an efficiency advantage over an equivalent pure multiple step analysis. +Defining load cases +You define a load case within a static perturbation, direct-solution steady-state dynamic, and SIM-based +steady-state dynamic analyses. Load case definitions do not propagate to subsequent steps. Only the +following types of prescribed conditions can be specified within a load case definition: +• Boundary conditions +• Concentrated loads +• Distributed loads +• Distributed surface loads +• Inertia-based loads +• Base motions +Additional rules governing these prescribed conditions are described in the sections that follow. No other +types of prescribed conditions can appear in a step that contains load case definitions. All other valid +analysis components, such as output requests, must be specified outside load case definitions. +Each load case definition is assigned a name for postprocessing purposes. +Input File Usage: +Use the first option to begin a load case and the second option to end a load +case: +*LOAD CASE, NAME=name +*END LOAD CASE +Prescribed conditions specified within a load case definition apply only +to that load case. +In static perturbation and direct-solution steady-state +dynamic analyses, prescribed conditions can be specified outside the load case +definitions (in this case they apply to all load cases in the step). +Abaqus/CAE Usage: +Load module: Create Load Case: Name: name +In Abaqus/CAE if a step contains load cases, all prescribed conditions in the +step must be included in one or more load cases. +Procedures +Load cases can be defined only in perturbation steps with the following procedures: +• Static +• Direct-solution, steady-state dynamic +• SIM-based, steady-state dynamic +As with other perturbation steps, a multiple load case analysis will include the nonlinear effects of the +previous general step (base state). The following analysis techniques are not supported in the context of +a load case step: +• Restart from a particular load case +• Submodeling using results from other than the first load case in the global analysis +• Importing and transferring results +• Cyclic symmetry analysis +• Contour integrals +• Design sensitivity analysis +Boundary conditions +Boundary conditions can be specified both outside and inside load case definitions in the same step. +Specifying a boundary condition outside the load case definitions in a step is equivalent to including it +in all load case definitions in the step (i.e., the boundary condition will be applied to all load cases). +Unless any boundary conditions are removed in the perturbation step, the boundary conditions that +are active in the base state will propagate to all load cases in the perturbation step. If any boundary +condition is removed in a step with load cases (either outside or inside load case definitions), the base +state boundary conditions will not be propagated to any load case in the step. See “Boundary conditions +in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1, for more information. +Note: In Abaqus/CAE if a step contains load cases, all boundary conditions in the step must be included +in one or more load cases. Boundary conditions can only be used with load cases in static perturbation +and direct-solution steady-state dynamic analyses. +Loads +In static perturbation and direct-solution steady-state dynamic analyses concentrated, distributed, and +distributed surface loads can be specified both outside and inside load case definitions in the same step. +Inertia relief loads can be specified either outside load case definitions or inside load case definitions +in the same step but not both simultaneously. Specifying one of these load types outside the load case +definitions in a step is equivalent to including it in all load case definitions in the step (i.e., the loading +will be applied to all load cases). +In SIM-based steady-state dynamic analyses concentrated, distributed, distributed surface loads, +and base motion can be specified only inside load case definitions in the same step. Inertia relief loads +are not supported. +Load cases cannot be used in models that include aqua loads . +As with any perturbation step, perturbation loads must be defined completely within the perturbation +step . +Note: In Abaqus/CAE if a step contains load cases, all loads in the step must be included in one or more +load cases. +Predefined fields +Field variables cannot be specified in a step with load cases. +Elements +Load cases cannot be used in models that include piezoelectric elements . +Output +In a step containing one or more load cases, field and history output requests to the output database and +output requests to the data file are supported. Output requests to the results file are not supported. Output +requests can be specified only outside load case definitions, and they apply to all load cases in a step. +The step propagation rules for output requests are the same as for other perturbation steps . +Most of the field and history output variables normally available within a particular procedure are +also available during a multiple load case analysis . Additional restrictions apply for a SIM-based steady-state dynamic analysis; see “Using +the SIM architecture for modal superposition dynamic analyses” in “Dynamic analysis procedures: +overview,” Section 6.3.1, for more information. +The field output corresponding to each load case is stored in a separate frame on the output database +with the load case name included as a frame attribute. To distinguish between load cases for history +output variables, the name of the load case is appended to the history variable name. The Visualization +module of Abaqus/CAE and the Abaqus Scripting Interface can be used to access +and manipulate load case output. Abaqus/Standard does not perform consistency checks on the physical +validity of the load case manipulations. For example, the linear superposition of two load cases, each +with different boundary conditions, is allowed even though the combined results may not be physically +meaningful. +Input file template +*HEADING +… +*STEP, PERTURBATION +*STATIC or *STEADY STATE DYNAMICS, DIRECT +… +*OUTPUT, FIELD +… +*BOUNDARY +Data lines to specify boundary conditions for all load cases. +*DLOAD +Data lines to specify distributed loads for all load cases. +*CLOAD +Data lines to specify point loads for all load cases. +*DSLOAD +Data lines to specify distributed surface loads for all load cases. +*INERTIA RELIEF +Data lines to specify inertia relief loading directions. +(This option cannot be used inside load cases if it is used here.) +… +*LOAD CASE, NAME=name1 +*BOUNDARY +Data lines to specify boundary conditions for first load case. +*DLOAD +Data lines to specify distributed loads for first load case. +*CLOAD +Data lines to specify point loads for first load case. +*DSLOAD +Data lines to specify distributed surface loads for first load case. +*INERTIA RELIEF +Data lines to specify inertia relief loading directions. +(This option cannot be used outside load cases if it is used here.) +*END LOAD CASE +*LOAD CASE, NAME=name2 +Load and boundary condition options for second load case +*END LOAD CASE +… +Subsequent load case definitions +… +*END STEP +*STEP, PERTURBATION +*FREQUENCY, SIM or *FREQUENCY, EIGENSOLVER=AMS +*END STEP +… +*STEP, PERTURBATION +*STEADY STATE DYNAMICS +*LOAD CASE, NAME=name3 +*BASE MOTION +Data lines to specify base motion for first load case. +*DLOAD +Data lines to specify distributed loads for first load case. +*CLOAD +Data lines to specify point loads for first load case. +*DSLOAD +Data lines to specify distributed surface loads for first load case. +*END LOAD CASE +*LOAD CASE, NAME=name4 +Load and base motion options for second load case. +*END LOAD CASE +… +Subsequent load case definitions +… +*OUTPUT, HISTORY +… +*END STEP +6.1.5 +DIRECT LINEAR EQUATION SOLVER +Products: Abaqus/Standard Abaqus/CAE +References +• “Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD execution,” Section 3.2.2 +• “Using the Abaqus environment settings,” Section 3.3.1 +• “Iterative linear equation solver,” Section 6.1.6 +• “Parallel execution in Abaqus/Standard,” Section 3.5.2 +• “Configuring analysis procedure settings,” Section 14.11 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +Linear equation solution is used in linear and nonlinear analysis. In nonlinear analysis Abaqus/Standard +uses the Newton method or a variant of it, such as the Riks method, within which it is necessary +to solve a set of linear equations at each iteration. The direct linear equation solver finds the exact +solution to this system of linear equations (up to machine precision). The direct linear equation solver +in Abaqus/Standard: +• uses a sparse, direct, Gauss elimination method; and +• often represents the most time consuming part of the analysis (especially for large models)—the +storage of the equations occupies the largest part of the disk space during the calculations. +The sparse solver +The direct sparse solver uses a “multifront” technique that can reduce the computational time to solve the +equations dramatically if the equation system has a sparse structure. Such a matrix structure typically +arises when the physical model is made from several parts or branches that are connected together; a +spoked wheel is a good example of a structure that has a sparse stiffness matrix. Space frames and other +structures modeled with beams, trusses, and shells often have sparse stiffness matrices. +In contrast, +a blocky structure—such as a single, solid, three-dimensional block —provides little opportunity for the sparse solver to reduce the computer time. For +large blocky structures, the iterative linear equation solver may be more efficient . +Input File Usage: +Use the following option to use the default direct sparse solver: +Abaqus/CAE Usage: +*STEP +Step module: step editor: Other: Method: Direct +Setting controls for the direct linear solver +The linear equation solver can optimize elimination of constraint equations associated with hard contact +and hybrid elements. There are two potential undesirable side-effects associated with this option: +• Possible small degradation of solution accuracy may adversely impact the nonlinear convergence +behavior. +• Possible minor performance degradation for models without hard contact constraints and/or hybrid +elements. +Input File Usage: +Use the following option to turn on constraint optimization: +Abaqus/CAE Usage: +*SOLVER CONTROLS, CONSTRAINT OPTIMIZATION +You cannot specify constraint optimization in Abaqus/CAE. +6.1.6 +ITERATIVE LINEAR EQUATION SOLVER +Products: Abaqus/Standard Abaqus/CAE +References +• *STEP +• *SOLVER CONTROLS +• “Parallel execution in Abaqus/Standard,” Section 3.5.2 +• “Customizing solver controls,” Section 14.15.2 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +The iterative linear equation solver in Abaqus/Standard: +• can be used for linear and nonlinear static, quasi-static, heat transfer, geostatic, and coupled pore +fluid diffusion and stress analysis solution procedures; +• should be used only for large, well-conditioned models for which the direct sparse solver requires a prohibitively large number of floating point +operations; +• is likely to be dramatically faster than the direct equation solver for large, well-conditioned, blocky +structures; +• runs totally in-core and uses less storage than the direct sparse solver (memory and disk combined); +• can be used only with three-dimensional models; +• must be the only solver invoked in the analysis (i.e., you cannot use the iterative solver in one step +and the direct solver in another); +• cannot be used with automatic stabilization with an adaptive damping factor ; +• can be used with a constant damping factor if stabilization is necessary ; +• cannot be used if the system of equations includes Lagrange multiplier degrees of freedom (i.e., +associated with distributing couplings, hybrid elements, connector elements, contact with direct +enforcement); and +• will degrade performance if used with models containing dense linear constraints (e.g., equations, +kinematic couplings, MPCs) that eliminate a large number of slave degrees of freedom per master +degree of freedom and/or eliminate some slave degrees of freedom in favor of a large number of +master degrees of freedom. +Iterative solver basics +The iterative solver in Abaqus/Standard can be used to find the solution to a linear system of equations and +can be invoked in a linear or nonlinear static, quasi-static, geostatic, pore fluid diffusion, or heat transfer +analysis step. Since the technique is iterative, a converged solution to a given system of linear equations +cannot be guaranteed. In cases where the iterative solver fails to converge to a solution, modifications +to the model may be necessary to improve the convergence behavior. In some cases the only choice +may be to use the direct solver to obtain a solution. When the iterative solver converges, the accuracy of +this solution depends on the relative tolerance that is used; the default tolerance is sufficiently accurate +for most purposes. However, tolerance adjustments for particular analyses may improve the overall +performance of the simulation. In addition, the performance of the iterative solver relative to the direct +sparse solver is highly sensitive to the model geometry, favoring blocky type structures (i.e., models that +look more like a cube than a plate) with a high degree of mesh connectivity and a relatively low degree +of sparsity. These types of models often demand the most computational and storage resources for the +direct sparse solver. Models with a lesser degree of connectivity (often said to have a higher degree of +sparsity), such as thin, shell-like structures, are much more suited to the direct sparse solver . +Input File Usage: +Abaqus/CAE Usage: +Use the following option to invoke the iterative solver: +*STEP, SOLVER=ITERATIVE +Step module: step editor: Other: Method: Iterative +The iterative solution technique +The iterative solution technique in Abaqus/Standard is based on Krylov methods employing a +preconditioner. This solver uses the following general strategy: +1. The Krylov method solver iterates on the system of equations generated by the finite element method +while a preconditioner is applied at each iteration. +2. The preconditioner is calculated only once at the beginning of each linear system solve and is used +to accelerate the convergence of the Krylov method. +3. In parallel, all components of the iterative solution process (including matrix assembly, +preconditioner setup, and the actual solve using the Krylov method) are handled locally on each +core with all necessary communication handled through an MPI-based implementation. +The process outlined above is performed entirely internal to Abaqus/Standard, with no user intervention +required. +Convergence of the linear system of equations +To generate the solution to the system of linear algebraic equations (denoted by the matrix equation +, where K is the global stiffness matrix, f is the load vector, and u is the desired displacement +solution), a sequence of Krylov solver iterations is performed, whereby an approximate solution gets +closer to the exact solution at each iteration. The error in the approximate solution is measured by +the relative residual of the linear system, defined by +norm. +, where +is the +The term “convergence” is used to describe this process, and the approximate solution is said to be +converged when the relative residual is below a specified tolerance. By default, this tolerance is 10−3 +for general nonlinear procedures. Linear perturbation procedures have the default tolerance of 10−6 . +While the default tolerance may seem loose for general nonlinear procedures, it is important to note +that the linear solver convergence tolerance is independent from the nonlinear convergence process (i.e., +Newton-Raphson method) tolerances that are used to determine if analysis increments converge. The +latter are the same regardless of the choice of linear equation solver, iterative or direct. +The rate at which the approximate solution converges is directly related to the conditioning of +the original system of equations. A linear system that is well conditioned will converge faster than +an ill-conditioned system. If the residual does not converge to tolerance within the maximum number of +iterations, the iterative solver is said to have encountered a non-convergence and Abaqus/Standard issues +a warning message. However, the analysis will continue running and in some cases the Newton-Raphson +iterations within increments may continue to converge. +Setting controls for the iterative linear solver +The default controls provided in Abaqus/Standard are usually sufficient. However, a method for +overriding the default relative convergence tolerance and maximum number of solver iterations is +provided. +Resetting the solver controls +You can specify that the solver controls be reset to their default values. +Input File Usage: +Abaqus/CAE Usage: +*SOLVER CONTROLS, RESET +Step module: Other→Solver Controls→Edit: Reset all parameters +to their system-defined defaults +Specifying the relative convergence tolerance +By default, this tolerance is 10−3 for procedures other than linear perturbation. Linear perturbation +procedures have the default tolerance of 10−6 . For nonlinear problems the accuracy of the linear solution +can impact the convergence of the Newton method. In some cases it may be necessary to manually +specify the iterative solver relative tolerance to improve the convergence of the Newton-Raphson method +or to improve performance. +Input File Usage: +*SOLVER CONTROLS +relative tolerance for convergence +Abaqus/CAE Usage: +Step module: Other→Solver Controls→Edit: Specify: Relative +tolerance: Specify: relative tolerance for convergence +Specifying the maximum number of solver iterations +In rare instances the linear solver may require more than the default number of iterations to converge to +the desired level of accuracy. In this case you can increase the maximum number of iterations allowed +by the iterative solver (the default value is 300). +Input File Usage: +*SOLVER CONTROLS +, max number of solver iterations +Abaqus/CAE Usage: +Step module: Other→Solver Controls→Edit: Specify: Max. number +of iterations: Specify: max number of solver iterations +Specifying the incomplete factorization fill-in levels for soils and geostatic analyses +The preconditioner used for soils and geostatic analyses employs a factorization-based method, also +In rare instances the linear solver may require more than the default number +known as ILU(k). +Incomplete +of incomplete factorization fill-in levels to converge to the desired accuracy level. +LU factorization of a matrix is a sparse approximation of the LU factorization. LU factorization +typically changes the nonzero structure of the stiffness matrices by adding many nonzero entries; ILU +factorization approximates the fully factorized matrices by limiting the number of nonzero entries +introduced during the factorization. By default, the ILU factorization fill-in level used by the iterative +solver is 0 and no nonzero entries are added. You can increase the fill-in level (maximum value is 3) to +allow nonzero entries to be added based on the connectivity of the stiffness matrices and obtain a better +approximation of the full factorization but with increased computational cost. +*SOLVER CONTROLS +, , ILU factorization fill-in level +Input File Usage: +Abaqus/CAE Usage: +Step module: Other→Solver Controls→Edit: Specify: ILU factorization +fill-in level: Specify: ILU factorization fill-in level +Deciding to use the iterative solver +Many factors must be carefully weighed before deciding to use the iterative solver in Abaqus/Standard, +such as element type, contact and constraint equations, material and geometric nonlinearities, and +material properties, all of which can impact robustness and performance. In cases where the model is +ill-conditioned the iterative solver may converge very slowly or fail to converge. This may occur, for +example, if many elements have poor aspect ratios. +In addition to the robustness issues (relating mainly to the rate of convergence or stagnation), the +iterative solver is expected to outperform the direct sparse solver only for blocky models (even when the +model is well conditioned) that require a very large number of floating point operations for factorization. +Typically, for a well-conditioned solid model, the number of degrees of freedom in the global model +must be greater than one million before the iterative solver will be comparable to the direct solver in +terms of run time. +Element type and model geometry +The most basic modeling issue that will affect the performance of the iterative solver is the model +geometry, which must be carefully considered when deciding if the iterative solver is suited for a +particular model. In general, models that are blocky in nature (i.e., look more like a cube than a plate) +and are dominated by solid elements will behave well with the iterative solver. Although structural +elements such as beams and shells are supported, models with structural elements will not perform +optimally; +the direct sparse solver should be used instead for such models. Common modeling +techniques such as coating solid elements with a thin layer of membrane elements to recover accurate +stresses on the boundary or fixing rigid body motion with weak springs may not work with the iterative +solver. Applying loads or boundary conditions to large node sets using locally transformed coordinate +systems can also cause convergence difficulties. All of these techniques are likely to lead to extremely +slow convergence or stagnation. +Another factor that can influence the convergence of the iterative solver is the quality of the +elements. Blocky models, such as an engine block, that contain many poorly shaped elements with high +aspect ratios can also lead to poor iterative solver convergence. It is a good idea to look for warning +messages about poorly shaped elements when evaluating the performance of the iterative solver. +Currently, hybrid elements and connectors are not supported with the iterative solver. +Using cohesive elements with the iterative solver will likely lead to nonconvergence. +Constraint equations +Although the iterative solver can be used for models that include constraint equations (such as multi-point +constraints, surface-based tie constraints, kinematic couplings, etc.), certain limitations may exist in the +following situations: +• linear or nonlinear multi-point constraints containing more than a few thousand degrees of freedom; +• more than a few thousand linear or nonlinear multi-point constraints containing shared master +degrees of freedom; +• rigid body definition of elements containing more than a few thousand degrees of freedom; or +• kinematic coupling constraints containing more than a few thousand slave degrees of freedom. +If any of these conditions apply to a model, the solution cost of the linear system of equations will +grow linearly with the number of such constraints. Furthermore, it is usually recommended to tighten +the iterative solver tolerance and increase the number of maximum iterations in the linear iterative solver +for nonlinear analysis to achieve convergence. Therefore, it is recommended to keep such constraints to +a minimum if possible; otherwise, the increased cost may offset the performance gains that come from +using the iterative solver. +Distributing couplings are not supported with the iterative solver. +Contact +Since contact is a form of nonlinear analysis, special care must be taken in selecting the convergence +tolerance for the iterative solver . Therefore, it is recommended to run +the model through a static perturbation analysis before proceeding to the nonlinear problem. This will +demonstrate how the iterative solver will perform for the specific model geometry without the added +difficulty of nonlinear convergence. +The iterative solver will work only with the penalty-based contact formulation with reasonable +penalty stiffness. If contact with direct enforcement (i.e., the Lagrange multiplier method) or penalty +contact with an extremely high penalty stiffness is used, Abaqus/Standard may fail to converge. The +iterative solver does not support pore fluid contact, regardless of the contact formulation used. +Material properties +When deciding to use the iterative solver, the variation of material properties in the model should be +considered. Models that have very large discontinuities in material behavior (many orders of magnitude) +will most likely converge slowly and possibly stagnate. +Nonlinear analysis +The iterative solver can be used to solve the linear system of algebraic equations that arises at each +iteration of the Newton procedure. However, the convergence of the nonlinear problem will be affected +by the convergence of the iterative linear solver. The actual impact depends on the particular model and +type of nonlinearities present. In some cases the default iterative solver tolerance of 10−3 is sufficient +to maintain the convergence of the Newton method; in other cases a smaller linear solver tolerance (for +example, 10−6) must be used. +If a nonlinear analysis that uses the iterative solver fails to converge, it is often difficult to +determine if this is due to the approximate linear equation solution of the iterative solver or if the +Newton process itself is failing to converge. If nonlinear convergence problems occur, the direct solver +can be used—given the problem is solvable using the direct solver due to solution cost—to eliminate +the approximate linear solution as a possible source of the problem. +6.2 +Static stress/displacement analysis +• “Static stress analysis procedures: overview,” Section 6.2.1 +• “Static stress analysis,” Section 6.2.2 +• “Eigenvalue buckling prediction,” Section 6.2.3 +• “Unstable collapse and postbuckling analysis,” Section 6.2.4 +• “Quasi-static analysis,” Section 6.2.5 +• “Direct cyclic analysis,” Section 6.2.6 +• “Low-cycle fatigue analysis using the direct cyclic approach,” Section 6.2.7 +6.2.1 +STATIC STRESS ANALYSIS PROCEDURES: OVERVIEW +A static stress procedure is one in which inertia effects are neglected. Several static stress analysis procedures +are available in Abaqus/Standard: +• Static analysis: +“Static stress analysis,” Section 6.2.2, is used for stable problems and can include +linear or nonlinear response. +• Eigenvalue buckling analysis: +“Eigenvalue buckling prediction,” Section 6.2.3, is used to estimate +the critical (bifurcation) load of “stiff” structures. It is a linear perturbation procedure. +• Unstable collapse and postbuckling analysis: +“Unstable collapse and postbuckling analysis,” +Section 6.2.4, is used to estimate the unstable, geometrically nonlinear collapse of a structure. The +method can also be helpful in obtaining a solution in other types of unstable problems, and it is often +suitable for limit load analyses. +• Quasi-static analysis: +“Quasi-static analysis,” Section 6.2.5, is used to analyze the transient response +of structures considering time-dependent material behavior (creep and swelling, viscoelasticity, and +viscoplasticity). A quasi-static analysis can be linear or nonlinear. +• Direct cyclic analysis: +“Direct cyclic analysis,” Section 6.2.6, is used to calculate the stabilized cyclic +response of the structure directly. It uses a combination of Fourier series and time integration of the +nonlinear material behavior to obtain the stabilized cyclic solution iteratively. +• Low-cycle fatigue analysis: +“Low-cycle fatigue analysis using the direct cyclic approach,” +Section 6.2.7, is used to predict progressive damage and failure for ductile bulk materials and/or to +predict delamination/debonding growth at the interfaces in laminated composites based on the direct +cyclic approach in conjunction with the damage extrapolation technique. +6.2.2 +STATIC STRESS ANALYSIS +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “Static stress analysis procedures: overview,” Section 6.2.1 +• *STATIC +• “Configuring a static, general procedure” in “Configuring general analysis procedures,” +Section 14.11.1 of the Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +A static stress analysis: +• is used when inertia effects can be neglected; +• can be linear or nonlinear; and +• ignores time-dependent material effects (creep, swelling, viscoelasticity) but takes rate-dependent +plasticity and hysteretic behavior for hyperelastic materials into account. +Time period +During a static step you assign a time period to the analysis. This is necessary for cross-references to the +amplitude options, which can be used to determine the variation of loads and other externally prescribed +parameters during a step . In some cases this time scale is quite +real—for example, the response may be caused by temperatures varying with time based on a previous +transient heat transfer run; or the material response may be rate dependent (rate-dependent plasticity), +so that a natural time scale exists. Other cases do not have such a natural time scale; for example, when +a vessel is pressurized up to limit load with rate-independent material response. If you do not specify a +time period, Abaqus/Standard defaults to a time period in which “time” varies from 0.0 to 1.0 over the +step. The “time” increments are then simply fractions of the total period of the step. +Linear static analysis +Linear static analysis involves the specification of load cases and appropriate boundary conditions. If +all or part of a problem has linear response, substructuring is a powerful capability for reducing the +computational cost of large analyses . +Nonlinear static analysis +Nonlinearities can arise from large-displacement effects, material nonlinearity, and/or boundary +nonlinearities such as contact and friction (see “General and linear perturbation procedures,” +Section 6.1.3) and must be accounted for. If geometrically nonlinear behavior is expected in a step, the +large-displacement formulation should be used. In most nonlinear analyses the loading variations over +the step follow a prescribed history such as a temperature transient or a prescribed displacement. +Input File Usage: +Use the following option to specify that a large-displacement formulation +should be used for a static step: +Abaqus/CAE Usage: +*STEP, NLGEOM +Step module: Create Step: General: Static, General: Basic: Nlgeom: +On (to activate the large-displacement formulation) +Unstable problems +Some static problems can be naturally unstable, for a variety of reasons. +Buckling or collapse +In some geometrically nonlinear analyses, buckling or collapse may occur. +In these cases a quasi- +static solution can be obtained only if the magnitude of the load does not follow a prescribed history; +it must be part of the solution. When the loading can be considered proportional (the loading over the +complete structure can be scaled with a single parameter), a special approach—called the “modified Riks +method”—can be used, as described in “Unstable collapse and postbuckling analysis,” Section 6.2.4. +Input File Usage: +Abaqus/CAE Usage: +*STATIC, RIKS +Step module: Create Step: General: Static, Riks +Local instabilities +In other unstable analyses the instabilities are local (e.g., surface wrinkling, material instability, or local +buckling), in which case global load control methods such as the Riks method are not appropriate. +Abaqus/Standard offers the option to stabilize this class of problems by applying damping throughout +the model in such a way that the viscous forces introduced are sufficiently large to prevent instantaneous +buckling or collapse but small enough not to affect the behavior significantly while the problem is +stable. The available automatic stabilization schemes are described in detail in “Automatic stabilization +of unstable problems” in “Solving nonlinear problems,” Section 7.1.1. +Incrementation +Abaqus/Standard uses Newton’s method to solve the nonlinear equilibrium equations. Many problems +involve history-dependent response; therefore, the solution usually is obtained as a series of increments, +with iterations to obtain equilibrium within each increment. Increments must sometimes be kept small +(in the sense that rotation and strain increments must be small) to ensure correct modeling of history- +dependent effects. Most commonly the choice of increment size is a matter of computational efficiency: +if the increments are too large, more iterations will be required. Furthermore, Newton’s method has a +finite radius of convergence; too large an increment can prevent any solution from being obtained because +the initial state is too far away from the equilibrium state that is being sought—it is outside the radius of +convergence. Thus, there is an algorithmic restriction on the increment size. +Automatic incrementation +In most cases the default automatic incrementation scheme is preferred because it will select increment +sizes based on computational efficiency. +Input File Usage: +Abaqus/CAE Usage: +*STATIC +Step module: Create Step: General: Static, General: Incrementation: +Type: Automatic (default) +Direct incrementation +Direct user control of the increment size is also provided because if you have considerable experience +with a particular problem, you may be able to select a more economical approach. +Input File Usage: +Abaqus/CAE Usage: +*STATIC, DIRECT +Step module: Create Step: General: Static, General: +Incrementation: Type: Fixed +With direct user control, +the solution to an increment can be accepted after the maximum +number of iterations allowed has been completed (as defined in “Commonly used control parameters,” +Section 7.2.2), even if the equilibrium tolerances are not satisfied. This approach is not recommended; it +should be used only in special cases when you have a thorough understanding of how to interpret results +obtained in this way. Very small increments and a minimum of two iterations are usually necessary if +this option is used. +Input File Usage: +Abaqus/CAE Usage: +*STATIC, DIRECT=NO STOP +Step module: Create Step: General: Static, General: Other: Accept +solution after reaching maximum number of iterations +Steady-state frictional sliding +In a static analysis procedure you can model steady-state frictional sliding between two deformable +bodies or between a deformable and a rigid body that are moving with different velocities by specifying +the motions of the bodies as predefined fields. In this case it is assumed that the slip velocity follows +from the difference in the user-specified velocities and is independent of the nodal displacements, as +described in “Coulomb friction,” Section 5.2.3 of the Abaqus Theory Manual. +Since this frictional behavior is different from the frictional behavior used without steady-state +frictional sliding, discontinuities may arise in the solutions between an analysis step in which relative +velocity is determined from predefined motions and prior steps. An example is the discontinuity that +occurs between the initial preloading of the disc pads in a disc brake system and the subsequent braking +analysis where the disc spins with a prescribed rotation. To ensure a smooth transition in the solution, it is +recommended that all analysis steps prior to the analysis step in which predefined motion is specified use +a zero coefficient of friction. You can then modify the friction properties in the steady-state analysis to use +the desired friction coefficient . +Input File Usage: +Abaqus/CAE Usage: +*MOTION +Predefined motion fields are not supported in Abaqus/CAE. +Initial conditions +Initial values of stresses, temperatures, field variables, solution-dependent state variables, etc. can be +specified. “Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1, describes all of +the available initial conditions. +Boundary conditions +Boundary conditions can be applied to any of the displacement or rotation degrees of freedom (1–6); to +warping degree of freedom 7 in open-section beam elements; or, if hydrostatic fluid elements are included +in the model, to fluid pressure degree of freedom 8. If boundary conditions are applied to rotation degrees +of freedom, you must understand how finite rotations are handled by Abaqus . During the analysis prescribed boundary +conditions can be varied using an amplitude definition . +Loads +The following loads can be prescribed in a static stress analysis: +• Concentrated nodal forces can be applied to the displacement degrees of freedom (1–6); see +“Concentrated loads,” Section 33.4.2. +• Distributed pressure forces or body forces can be applied; see “Distributed loads,” Section 33.4.3. +The distributed load types available with particular elements are described in Part VI, “Elements.” +Predefined fields +The following predefined fields can be specified in a static stress analysis, as described in “Predefined +fields,” Section 33.6.1: +• Although temperature is not a degree of freedom in a static stress analysis, nodal temperatures +can be specified as a predefined field. Any difference between the applied and initial temperatures +will cause thermal strain if a thermal expansion coefficient is given for the material (“Thermal +expansion,” Section 26.1.2). The specified temperature also affects temperature-dependent material +properties, if any. +• The values of user-defined field variables can be specified. These values only affect field-variable- +dependent material properties, if any. +Material options +Most material models that describe mechanical behavior are available for use in a static stress analysis. +The following material properties are not active during a static stress analysis: acoustic properties, +properties, and pore fluid flow properties. +STATIC STRESS ANALYSIS +Rate-dependent yield (“Rate-dependent yield,” Section 23.2.3), +(“Hysteresis +in elastomers,” Section 22.8.1), +and two-layer viscoplasticity (“Two-layer viscoplasticity,” +Section 23.2.11) are the only time-dependent material responses that are active during a static +analysis. The rate-dependent yield response is often important in rapid processes such as metal-working +problems. The hysteresis model is useful in modeling the large-strain, rate-dependent response of +elastomers that exhibit a pronounced hysteresis under cyclic loading. The two-layer viscoplasticity +model is useful in situations where a significant time-dependent behavior as well as plasticity is +observed, which for metals typically occurs at elevated temperatures. An appropriate time scale must +be specified so that Abaqus/Standard can treat the rate dependence of the material responses correctly. +hysteresis +Static creep and swelling problems and time-domain viscoelastic models are analyzed by the quasi- +static procedure (“Quasi-static analysis,” Section 6.2.5). When any of these time-dependent material +models are used in a static analysis, a rate-independent elastic solution is obtained and the chosen time +scale does not have an effect on the material response. For creep and swelling behavior this implies that +the loading is applied instantaneously compared with the natural time scale over which creep effects take +place. +The same concept of instantaneous load application applies to time-domain viscoelastic behavior. +You can also obtain the fully relaxed long-term viscoelastic solution directly in a static procedure without +having to perform a transient analysis; this choice is meaningful only when time-domain viscoelastic +material properties are defined. If the long-term viscoelastic solution is requested, the internal stresses +associated with each of the Prony series terms are increased gradually from their values at the beginning +of the step to their long-term values at the end of the step. +For the two-layer viscoplastic material model, you can obtain the long-term response of the elastic- +plastic network alone. +When frequency-domain viscoelastic material properties are defined , the corresponding elastic moduli must be specified as long-term elastic +moduli. This implies that the response corresponds to the long-term elastic solution, regardless of the +time period specified for the step. +Input File Usage: +Abaqus/CAE Usage: +Elements +Use the following option to obtain the fully relaxed long-term elastic solution +with time-domain viscoelasticity or the long-term elastic-plastic solution for +two-layer viscoplasticity: +*STATIC, LONG TERM +Step module: Create Step: General: Static, General or Static, Riks: +Other: Obtain long-term solution with time-domain material properties +Any of the stress/displacement elements in Abaqus/Standard can be used in a static stress analysis . Although velocities are not +available in a static stress analysis, dashpots can still be used (they can be useful in stabilizing an unstable +problem). The relative velocity will be calculated as described in “Dashpots,” Section 32.2.1. +Acoustic elements are not active in a static step. Consequently, if an acoustic-solid analysis includes +a static step, only the solid elements will deform. If the deformations are large, the acoustic and solid +meshes may not conform, and subsequent acoustic-structural analysis steps may produce misleading +results. See “ALE adaptive meshing: overview,” Section 12.2.1, for information on using the adaptive +meshing technique to deform the acoustic mesh. +Output +The element output available for a static stress analysis includes stress; strain; energies; the values of +state, field, and user-defined variables; and composite failure measures. The nodal output available +includes displacements, reaction forces, and coordinates. All of the output variable identifiers are +outlined in “Abaqus/Standard output variable identifiers,” Section 4.2.1. +Input file template +*HEADING +… +*BOUNDARY +Data lines to specify zero-valued boundary conditions +*INITIAL CONDITIONS +Data lines to specify initial conditions +*AMPLITUDE +Data lines to define amplitude variations +** +*STEP (,NLGEOM) +Once NLGEOM is specified, it will be active in all subsequent steps +*STATIC, DIRECT +Data line to define direct time incrementation +*BOUNDARY +Data lines to prescribe zero-valued or nonzero boundary conditions +*CLOAD and/or *DLOAD +Data lines to specify loads +*TEMPERATURE and/or *FIELD +Data lines to specify values of predefined fields +*END STEP +** +*STEP +*STATIC +Data line to control automatic time incrementation +*BOUNDARY, OP=MOD +Data lines to modify or add zero-valued or nonzero boundary conditions +*CLOAD, OP=NEW +Data lines to specify new concentrated loads; all previous concentrated +loads will be removed +*DLOAD, OP=MOD +Data lines to specify additional or modified distributed loads +*TEMPERATURE and/or *FIELD +Data lines to specify additional or modified values of predefined fields +*END STEP +6.2.3 +EIGENVALUE BUCKLING PREDICTION +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “General and linear perturbation procedures,” Section 6.1.3 +• “Static stress analysis procedures: overview,” Section 6.2.1 +• *BUCKLE +• “Configuring a buckling procedure” in “Configuring linear perturbation analysis procedures,” +Section 14.11.2 of the Abaqus/CAE User’s Manual, in the online HTML version of this manual +• “Creating and modifying prescribed conditions,” Section 16.4 of the Abaqus/CAE User’s Manual +Overview +Eigenvalue buckling analysis: +• is generally used to estimate the critical (bifurcation) load of “stiff” structures; +• is a linear perturbation procedure; +• can be the first step in an analysis of an unloaded structure, or it can be performed after the structure +has been preloaded—if the structure has been preloaded, the buckling load from the preloaded state +is calculated; +• can be used in the investigation of the imperfection sensitivity of a structure; +• works only with symmetric matrices (hence, unsymmetric stiffness contributions such as the load +stiffness associated with follower loads are symmetrized); and +• cannot be used in a model containing substructures. +General eigenvalue buckling +In an eigenvalue buckling problem we look for the loads for which the model stiffness matrix becomes +singular, so that the problem +has nontrivial solutions. +are nontrivial displacement solutions. The applied loads can consist of pressures, concentrated forces, +nonzero prescribed displacements, and/or thermal loading. +is the tangent stiffness matrix when the loads are applied, and the +Eigenvalue buckling is generally used to estimate the critical buckling loads of stiff structures +(classical eigenvalue buckling). Stiff structures carry their design loads primarily by axial or membrane +action, rather than by bending action. Their response usually involves very little deformation prior to +buckling. A simple example of a stiff structure is the Euler column, which responds very stiffly to a +compressive axial load until a critical load is reached, when it bends suddenly and exhibits a much +lower stiffness. However, even when the response of a structure is nonlinear before collapse, a general +eigenvalue buckling analysis can provide useful estimates of collapse mode shapes. +The base state +The buckling loads are calculated relative to the base state of the structure. If the eigenvalue buckling +procedure is the first step in an analysis, the initial conditions form the base state; otherwise, the base +state is the current state of the model at the end of the last general analysis step . Thus, the base state can include preloads (“dead” loads), +. +The preloads are often zero in classical eigenvalue buckling problems. +If geometric nonlinearity was included in the general analysis steps prior to the eigenvalue buckling +analysis , the base state geometry is the +deformed geometry at the end of the last general analysis step. If geometric nonlinearity was omitted, +the base state geometry is the original configuration of the body. +The eigenvalue problem +An incremental loading pattern, +magnitude of this loading is not important; it will be scaled by the load multipliers, +eigenvalue problem: +, is defined in the eigenvalue buckling prediction step. The +, found in the +where +is the stiffness matrix corresponding to the base state, which includes the effects +of the preloads, +(if any); +is the differential initial stress and load stiffness matrix due to the incremental +loading pattern, +; +are the eigenvalues; +are the buckling mode shapes (eigenvectors); +M and N +refer to degrees of freedom M and N of the whole model; and +refers to the ith buckling mode. +The critical buckling loads are then +preload pattern, +thermal loading caused by temperature changes, while +, and perturbation load pattern, +. Normally, the lowest value of +, may be different. For example, +is caused by application of pressure. +is of interest. The +might be +The buckling mode shapes, +, are normalized vectors and do not represent actual magnitudes of +deformation at critical load. They are normalized so that the maximum displacement component is 1.0. +If all displacement components are zero, the maximum rotation component is normalized to 1.0. These +buckling mode shapes are often the most useful outcome of the eigenvalue analysis, since they predict +the likely failure mode of the structure. +Abaqus/Standard can extract eigenvalues and eigenvectors for symmetric matrices only; therefore, +are symmetrized. If the matrices have significant unsymmetric parts, the eigenproblem +and +may not be exactly what you expected to solve. +Selecting the eigenvalue extraction method +Abaqus/Standard offers the Lanczos and the subspace iteration eigenvalue extraction methods. The +Lanczos method is generally faster when a large number of eigenmodes is required for a system with +many degrees of freedom. The subspace iteration method may be faster when only a few (less than 20) +eigenmodes are needed. +By default, the subspace iteration eigensolver is employed. Subspace iteration and the Lanczos +solver can be used for different steps in the same analysis; there is no requirement that the same +eigensolver be used for all appropriate steps. +For both eigensolvers you specify the desired number of eigenvalues; Abaqus/Standard will choose +a suitable number of vectors for the subspace iteration procedure or a suitable block size for the Lanczos +method (although you can override this choice, if needed). Significant overestimation of the actual +number of eigenvalues can create very large files. If the actual number of eigenvalues is underestimated, +Abaqus/Standard will issue a corresponding warning message. +In general, the block size for the Lanczos method should be as large as the largest expected +multiplicity of eigenvalues (that is, the largest number of modes with the same eigenvalue). A block +size larger than 10 is not recommended. +If the number of eigenvalues requested is n, the default +block size is the minimum of (7, n). The number of block Lanczos steps is usually determined by +Abaqus/Standard, but you can change it when you define the eigenvalue buckling prediction step. In +general, if a particular type of eigenproblem converges slowly, providing more block Lanczos steps will +reduce the analysis cost. On the other hand, if you know that a particular type of problem converges +quickly, providing fewer block Lanczos steps will reduce the amount of in-core memory used. If the +number of eigenvalues requested is n, the default is +Block size +n ≤ 10 +n > 10 +≥ 4 +40 +40 +30 +30 +70 +60 +60 +30 +If the subspace iteration technique is requested, you can also specify the maximum eigenvalue of +interest; Abaqus/Standard will extract eigenvalues until either the requested number of eigenvalues has +been extracted or the last eigenvalue extracted exceeds the maximum eigenvalue of interest. +If the Lanczos eigensolver is requested, you can also specify the minimum and/or maximum +eigenvalues of interest; Abaqus/Standard will extract eigenvalues until either the requested number of +eigenvalues has been extracted in the given range or all the eigenvalues in the given range have been +extracted. +Input File Usage: +Use the following option to perform an eigenvalue buckling analysis using the +subspace iteration method: +*BUCKLE, EIGENSOLVER=SUBSPACE (default) +Use the following option to perform an eigenvalue buckling analysis using the +Lanczos method: +Abaqus/CAE Usage: +*BUCKLE, EIGENSOLVER=LANCZOS +Step module: Create Step: Linear perturbation: Buckle: +Eigensolver: Lanczos or Subspace +Limitations associated with applying the Lanczos eigensolver to a buckling analysis +The Lanczos eigensolver cannot be used for buckling analyses in which the stiffness matrix is indefinite, +as in the following cases: +• A model containing hybrid elements or connector elements. +• A model containing distributing coupling constraints, defined either directly (“Coupling +constraints,” Section 34.3.2; “Shell-to-solid coupling,” Section 34.3.3; or “Mesh-independent +fasteners,” Section 34.3.4) or by the distributing coupling elements (DCOUP2D and DCOUP3D). +• A model containing contact pairs or contact elements. +• A model that has been preloaded above the bifurcation (buckling) load. +• A model that has rigid body modes. +In such cases Abaqus/Standard will issue an error message and terminate the analysis. +Order of calculation and formation of the stiffness matrices +. +, due to +In an eigenvalue buckling prediction step Abaqus/Standard first does a static perturbation analysis +to determine the incremental stresses, +If the base state did not include geometric +nonlinearity, the stiffness matrix used in this static perturbation analysis is the tangent elastic stiffness. +If the base state did include geometric nonlinearity, initial stress and load stiffness terms (due to the +preload, +and +In the eigenvalue extraction portion of the buckling step, the stiffness matrix +corresponding +to the base state geometry is formed. Initial stress and the load stiffness terms due to the preload, +, +are always included regardless of whether or not geometric nonlinearity is included and are calculated +based on the geometry of the base state. +When forming the stiffness matrices +, all contact conditions are fixed in the base +) are included. The stiffness matrix +corresponding to +is then formed. +and +state. +Buckling modes with closely spaced eigenvalues +Some structures have many buckling modes with closely spaced eigenvalues, which can cause numerical +problems. In these cases it often helps to apply enough preload, +, to load the structure to just below +the buckling load before performing the eigenvalue extraction. +If +is a scalar constant and the structure is “stiff” and elastic—and if the +—where +problem is linear, the structural stiffness changes to +and the buckling loads are given +by +. The +structure should not be preloaded above the buckling load. In that case the subspace iteration process +may fail to converge or produce incorrect results; the Lanczos eigensolver cannot be used (as discussed +earlier). +. The process is equivalent to a dynamic eigenfrequency extraction with shift +In many cases a series of closely spaced eigenvalues indicates that the structure is imperfection +sensitive. An eigenvalue buckling analysis will not give accurate predictions of the buckling load +for imperfection-sensitive structures; the static Riks procedure should be used instead . +Understanding negative eigenvalues +Sometimes, negative eigenvalues are reported in an eigenvalue buckling analysis. In most cases such +negative eigenvalues indicate that the structure would buckle if the load were applied in the opposite +direction. A classical example is a plate under shear loading; the plate will buckle at the same value for +positive and negative applied shear load. Buckling under reverse loading can also occur in situations +where it may not be expected. For example, a pressure vessel under external pressure may exhibit +a negative eigenvalue (buckling under internal pressure) due to local buckling of a stiffener. Such +“physical” negative buckling modes are usually readily understood once they are displayed and can +usually be avoided by applying a preload before the buckling analysis. +Negative eigenvalues sometimes correspond to buckling modes that cannot be understood readily +in terms of physical behavior, particularly if a preload is applied that causes significant geometric +nonlinearity. +In this case a geometrically nonlinear load-displacement analysis should be performed +(“Unstable collapse and postbuckling analysis,” Section 6.2.4). +Including large geometry changes in a buckling analysis +Because buckling analysis is usually done for “stiff” structures, it is not usually necessary to include +the effects of geometry change in establishing equilibrium for the base state. However, if significant +geometry change is involved in the base state and this effect is considered to be important, it can be +included by specifying that geometric nonlinearity should be considered for the base state step . In such cases it is probably more realistic to +perform a geometrically nonlinear load-displacement analysis (Riks analysis) to determine the collapse +loads, especially for imperfection-sensitive structures. +While large deformation can be included in the preload, the eigenvalue buckling theory relies on +there being little geometric change due to the “live” buckling load, +. If the live load produces +significant geometric change, a nonlinear collapse (Riks) analysis must be used. The total buckling +load predicted by the eigenvalue analysis, +, may be a good estimate for the limit load in +the nonlinear buckling analysis. The Riks method is described in “Unstable collapse and postbuckling +analysis,” Section 6.2.4. +Initial conditions +The initial values of quantities such as stress, temperature, field variables, and solution-dependent +If the buckling step is the first step +variables can be specified for an eigenvalue buckling analysis. +“Initial conditions in +in the analysis, these initial conditions form the base state of the structure. +Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1, describes all of the available initial conditions. +Boundary conditions +Boundary conditions can be applied to any of the displacement or rotation degrees of freedom (1–6) or to +warping degree of freedom 7 in open-section beam elements (“Boundary conditions in Abaqus/Standard +and Abaqus/Explicit,” Section 33.3.1). A nonzero prescribed boundary condition in a general analysis +step preceding the eigenvalue buckling analysis can be used to preload the structure. Nonzero boundary +conditions prescribed in an eigenvalue buckling step will contribute to the incremental stress +and, +thus, will contribute to the differential initial stress stiffness. When prescribing nonzero boundary +conditions, you must interpret the resulting eigenproblem carefully. Nonzero prescribed boundary +conditions will be treated as constraints (i.e., as if they were fixed) during the eigenvalue extraction. +Therefore, unless the prescribed boundary conditions are removed for the eigenvalue extraction by +specifying buckling mode boundary conditions , the mode shapes may be +altered by these boundary conditions. +Amplitude definitions (“Amplitude curves,” Section 33.1.2) cannot be used to vary the magnitudes +of prescribed boundary conditions during an eigenvalue buckling analysis. +You can define perturbation load and buckling mode boundary conditions in an eigenvalue buckling +prediction step. +Input File Usage: +Abaqus/CAE Usage: +Use either of the following two options to define perturbation load boundary +conditions: +*BOUNDARY +*BOUNDARY, LOAD CASE=1 +Use the following option to define buckling mode boundary conditions: +*BOUNDARY, LOAD CASE=2, OP=NEW +The OP=NEW parameter is required when you define buckling mode boundary +conditions in an eigenvalue buckling prediction step; however, the perturbation +load boundary conditions in the step can use either OP=NEW or OP=MOD. +Load module: Create Boundary Condition: choose Mechanical for the +Category and Symmetry/Antisymmetry/Encastre for the Types for +Selected Step: +toggle on Stress perturbation only to +define a perturbation load boundary condition; toggle on Buckling mode +calculation only to define a buckling mode boundary condition; toggle on +Stress perturbation and buckling mode calculation to define both types +of boundary conditions +select region: +Combining boundary conditions +The buckling mode shapes depend on the stresses in the base state as well as the incremental stresses due +to the perturbation loading in the buckling step. These stresses are influenced by the boundary conditions +used in each step. In a general eigenvalue buckling analysis the following types of boundary conditions +can influence the stresses: +1. The boundary conditions in the base state. +2. The boundary conditions used to calculate the linear perturbation stresses, +. These boundary +conditions will be: +a. the perturbation load boundary conditions specified in the eigenvalue buckling step; or +b. the base-state boundary conditions if no perturbation load boundary conditions are specified +in the eigenvalue buckling step; or +c. the buckling mode boundary conditions if neither perturbation load boundary conditions nor +base-state boundary conditions exist. +3. The boundary conditions used for the eigenvalue extraction. These boundary conditions will be: +a. the buckling mode boundary conditions; or +b. the perturbation load boundary conditions if buckling mode boundary conditions are not +specified in the eigenvalue buckling step; or +c. the base-state boundary conditions if no boundary condition definition is used in the eigenvalue +buckling step. +Table 6.2.3–1 summarizes the use of boundary conditions during an eigenvalue buckling step. When +buckling mode boundary conditions are specified, all boundary conditions to be imposed during +eigenvalue extraction must be specified. +Buckling of symmetric structures +The buckling mode shapes of symmetric structures subjected to symmetric loadings are either symmetric +or antisymmetric. In such cases it is often more efficient to model only part of the structure and then +perform the buckling analysis twice for each symmetry plane: once with symmetric boundary conditions +and once with antisymmetric boundary conditions. +The live load pattern is usually symmetric, so symmetric boundary conditions are required for +the calculation of the perturbation stresses used in the formation of the initial stress stiffness matrix. +The boundary conditions must be switched to antisymmetric for the eigenvalue extraction to obtain the +antisymmetric modes. “Buckling of a cylindrical shell under uniform axial pressure,” Section 1.2.3 of +the Abaqus Benchmarks Manual, illustrates such a case. +If the model includes more than one symmetry plane, it may be necessary to study all permutations +of symmetric and antisymmetric boundary conditions for each symmetry plane. +Table 6.2.3–1 Boundary conditions in effect during the different +portions of an eigenvalue buckling analysis. +User-defined boundary conditions +Boundary conditions used by Abaqus +Base state +Eigenvalue +buckling +prediction step +Linear +perturbation +Eigenvalue +extraction +1, 2 +1, 2 +B = base-state boundary conditions; 0 = no boundary conditions specified +1 = perturbation load boundary conditions +2 = buckling mode boundary conditions +Asymmetric buckling of axisymmetric structures +Axisymmetric structures subjected to compressive loading often collapse in nonaxisymmetric modes. +These modes cannot be found with purely axisymmetric modeling such as that provided by shell elements +SAX1 and SAX2 (“Axisymmetric shell element library,” Section 29.6.9) or continuum elements CAX4 +or CAX8 (“Axisymmetric solid element library,” Section 28.1.6). Such analyses must be done with +three-dimensional shell or continuum elements. +Loads +The following types of loading can be prescribed in an eigenvalue buckling analysis: +• Concentrated nodal forces can be applied to the displacement degrees of freedom (1–6); see +“Concentrated loads,” Section 33.4.2. +• Distributed pressure forces or body forces can be applied; see “Distributed loads,” Section 33.4.3. +The distributed load types available with particular elements are described in Part VI, “Elements.” +The load stiffness can have a significant effect on the critical buckling load; +therefore, +Abaqus/Standard will take the load stiffness due to preloads into account when solving the eigenvalue +buckling problem. It is important that the structure not be preloaded above the critical buckling load. +Any load applied during the eigenvalue buckling analysis is called a “live” load. This incremental +, describes the load pattern for which buckling sensitivity is being investigated; its magnitude +load, +is not important. This incremental loading definition represents linear perturbation loads, as described +in “Applying loads: overview,” Section 33.4.1. +Follower forces (such as concentrated loads assumed to rotate with the nodal rotation or pressure +loads) lead to an unsymmetric load stiffness. Since eigenvalue extraction in Abaqus/Standard can be +performed only on symmetric matrices, eigenvalue analysis with follower loads may not yield correct +results. +Amplitude definitions cannot be used during an eigenvalue buckling analysis. “Applying loads: +overview,” Section 33.4.1, describes all of the available loads. +Prescribed boundary conditions can also be used to load the structure in an eigenvalue buckling +analysis, as discussed earlier. +Predefined fields +In an eigenvalue buckling prediction step, nodal temperatures can be specified . The specified temperatures will cause thermal strain during the static +perturbation analysis if a thermal expansion coefficient is given for the material (“Thermal expansion,” +Section 26.1.2), and incremental stresses +will be generated. Hence, Abaqus/Standard can analyze +buckling due to thermal stress. The specified temperature will not affect temperature-dependent +material properties during the eigenvalue buckling prediction step; the material properties are based +on the temperature in the base state. Amplitude definitions cannot be used to vary the magnitudes of +prescribed temperatures during an eigenvalue buckling analysis. +Material options +During an eigenvalue buckling analysis, the model’s response is defined by its linear elastic stiffness in +the base state. All nonlinear and/or inelastic material properties, as well as effects involving time or strain +rate, are ignored during an eigenvalue buckling analysis. In classical eigenvalue buckling the response +in the base state is also linear. +If temperature-dependent elastic properties are used, the eigenvalue buckling analysis will not +account for changes in the stiffness matrix due to temperature changes. The material properties of the +base state will be used. +Acoustic properties, thermal properties (except for thermal expansion), mass diffusion properties, +electrical properties, and pore fluid flow properties are not active during an eigenvalue buckling analysis. +Elements +Any of the stress/displacement elements in Abaqus/Standard (including those with temperature or +pressure degrees of freedom) can be used in an eigenvalue buckling analysis, with the exception that +hybrid and contact elements cannot be used with the Lanczos eigensolver (as discussed earlier). See +“Choosing the appropriate element for an analysis type,” Section 27.1.3. +Output +The values of the eigenvalues, +, will be listed in the printed output file. If output of stresses, strains, +reaction forces, etc. is requested, this information will be printed for each eigenvalue; these quantities are +perturbation values and represent mode shapes, not absolute values. All of the output variable identifiers +are outlined in “Abaqus/Standard output variable identifiers,” Section 4.2.1. +Buckling mode shapes can be plotted in the Visualization module of Abaqus/CAE. +Input file template +The following template describes a very general eigenvalue buckling problem, where as many eigenvalue +buckling prediction steps as needed can be specified. +Symmetric boundary conditions are specified in the model definition part of the Abaqus/Standard +therefore, belong to the base state . In the first buckling step Abaqus/Standard uses the base-state boundary conditions to +solve for the perturbation stresses as well as for the eigenvalue extraction. +In the second buckling step the boundary conditions for the base state, the initial stress calculation, +and the eigenvalue extraction are all different. Abaqus/Standard uses the specified symmetry boundary +conditions to solve for the perturbation stresses but uses the specified antisymmetry boundary conditions +for the eigenvalue extraction. +*HEADING +… +*BOUNDARY +Data lines to specify zero-valued boundary conditions contributing to the base state +** +*STEP, NLGEOM +The load stiffness terms will be included in the eigenvalue buckling steps +since the NLGEOM parameter is used in this (optional) preload step +*STATIC +Data line to control incrementation +*BOUNDARY +Data lines to specify nonzero boundary conditions (dead loads) +*CLOAD and/or *DLOAD and/or *TEMPERATURE +Data lines to specify dead loads, +*END STEP +** +*STEP +*BUCKLE +Data line to request the desired number of symmetric modes +*CLOAD and/or *DLOAD and/or *TEMPERATURE +Data lines to specify perturbation loading, +*END STEP +** +*STEP +*BUCKLE +Data line to request the desired number of antisymmetric modes +*CLOAD and/or *DLOAD and/or *TEMPERATURE +Data lines to specify perturbation loading, +*BOUNDARY, LOAD CASE=1 +Data lines to specify all boundary conditions for perturbation loading +*BOUNDARY, LOAD CASE=2, OP=NEW +Data lines to specify all antisymmetric boundary conditions for eigenvalue extraction +*END STEP +6.2.4 +UNSTABLE COLLAPSE AND POSTBUCKLING ANALYSIS +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “Static stress analysis procedures: overview,” Section 6.2.1 +• “Introducing a geometric imperfection into a model,” Section 11.3.1 +• *STATIC +• *IMPERFECTION +• “Configuring a static, Riks procedure” in “Configuring general analysis procedures,” +in the online HTML version of this +Section 14.11.1 of the Abaqus/CAE User’s Manual, +manual +Overview +The Riks method: +• is generally used to predict unstable, geometrically nonlinear collapse of a structure; +• can include nonlinear materials and boundary conditions; +• often follows an eigenvalue buckling analysis to provide complete information about a structure’s +collapse; and +• can be used to speed convergence of ill-conditioned or snap-through problems that do not exhibit +instability. +Unstable response +Geometrically nonlinear static problems sometimes involve buckling or collapse behavior, where the +load-displacement response shows a negative stiffness and the structure must release strain energy to +remain in equilibrium. Several approaches are possible for modeling such behavior. One is to treat the +buckling response dynamically, thus actually modeling the response with inertia effects included as +the structure snaps. This approach is easily accomplished by restarting the terminated static procedure +(“Restarting an analysis,” Section 9.1.1) and switching to a dynamic procedure (“Implicit dynamic +analysis using direct integration,” Section 6.3.2) when the static solution becomes unstable. In some +simple cases displacement control can provide a solution, even when the conjugate load (the reaction +force) is decreasing as the displacement increases. Another approach would be to use dashpots to +stabilize the structure during a static analysis. Abaqus/Standard offers an automated version of this +stabilization approach for the static analysis procedures . +Alternatively, static equilibrium states during the unstable phase of the response can be found by +using the “modified Riks method.” This method is used for cases where the loading is proportional; +that is, where the load magnitudes are governed by a single scalar parameter. The method can provide +solutions even in cases of complex, unstable response such as that shown in Figure 6.2.4–1. +1.0 +Load, P +Figure 6.2.4–1 Proportional loading with unstable response. +Displacement +The Riks method is also useful for solving ill-conditioned problems such as limit load problems or +almost unstable problems that exhibit softening. +The Riks method +In simple cases linear eigenvalue analysis (“Eigenvalue buckling prediction,” Section 6.2.3) may be +sufficient for design evaluation; but if there is concern about material nonlinearity, geometric nonlinearity +prior to buckling, or unstable postbuckling response, a load-deflection (Riks) analysis must be performed +to investigate the problem further. +The Riks method uses the load magnitude as an additional unknown; it solves simultaneously +for loads and displacements. Therefore, another quantity must be used to measure the progress of the +solution; Abaqus/Standard uses the “arc length,” l, along the static equilibrium path in load-displacement +space. This approach provides solutions regardless of whether the response is stable or unstable. See +the “Modified Riks algorithm,” Section 2.3.2 of the Abaqus Theory Manual, for a detailed description +of the method. +Proportional loading +If the Riks step is a continuation of a previous history, any loads that exist at the beginning of the step +and are not redefined are treated as “dead” loads with constant magnitude. A load whose magnitude is +defined in the Riks step is referred to as a “reference” load. All prescribed loads are ramped from the +initial (dead load) value to the reference values specified. +The loading during a Riks step is always proportional. The current load magnitude, +, is defined +by +is the “dead load,” +is the “load proportionality factor.” +where +The load proportionality factor is found as part of the solution. Abaqus/Standard prints out the current +value of the load proportionality factor at each increment. +is the reference load vector, and +Incrementation +Abaqus/Standard uses Newton’s method (as described in “Static stress analysis,” Section 6.2.2) to solve +the nonlinear equilibrium equations. The Riks procedure uses only a 1% extrapolation of the strain +increment. +You provide an initial increment in arc length along the static equilibrium path, +, when you +define the step. The initial load proportionality factor, +, is computed as +where +is a user-specified total arc length scale factor (typically set equal to 1). This value of +is used during the first iteration of a Riks step. For subsequent iterations and increments the value +is part of +, can be used to control +is computed automatically, so you have no control over the load magnitude. The value of +of +the solution. Minimum and maximum arc length increments, +the automatic incrementation. +and +Input File Usage: +Abaqus/CAE Usage: +*STATIC, RIKS +Step module: Create Step: General: Static, Riks +Direct user control of the increment size is also provided; in this case the incremental arc length, +, +is kept constant. This method is not recommended for a Riks analysis since it prevents Abaqus/Standard +from reducing the arc length when a severe nonlinearity is encountered. +Input File Usage: +Abaqus/CAE Usage: +*STATIC, RIKS, DIRECT +Step module: Create Step: General: Static, Riks: +Incrementation: Type: Fixed +Ending a Riks analysis step +Since the loading magnitude is part of the solution, you need a method to specify when the step is +completed. You can specify a maximum value of the load proportionality factor, +, or a maximum +displacement value at a specified degree of freedom. The step will terminate when either value is crossed. +If neither of these finishing conditions is specified, the analysis will continue for the number of increments +specified in the step definition . +Bifurcation +The Riks method works well in snap-through problems—those in which the equilibrium path in +load-displacement space is smooth and does not branch. Generally you do not need take any special +precautions in problems that do not exhibit branching (bifurcation). “Snap-through buckling analysis +of circular arches,” Section 1.2.1 of the Abaqus Example Problems Manual, is an example of a smooth +snap-through problem. +The Riks method can also be used to solve postbuckling problems, both with stable and unstable +postbuckling behavior. However, the exact postbuckling problem cannot be analyzed directly due to +the discontinuous response at the point of buckling. To analyze a postbuckling problem, it must be +turned into a problem with continuous response instead of bifurcation. This effect can be accomplished +by introducing an initial imperfection into a “perfect” geometry so that there is some response in the +buckling mode before the critical load is reached. +Introducing geometric imperfections +Imperfections are usually introduced by perturbations in the geometry. Unless the precise shape +of an imperfection is known, an imperfection consisting of multiple superimposed buckling modes +must be introduced (“Eigenvalue buckling prediction,” Section 6.2.3). Abaqus allows you to define +imperfections; see “Introducing a geometric imperfection into a model,” Section 11.3.1. +In this way the Riks method can be used to perform postbuckling analyses of structures that show +linear behavior prior to (bifurcation) buckling. An example of this method of introducing geometric +imperfections is presented in “Buckling of a cylindrical shell under uniform axial pressure,” Section 1.2.3 +of the Abaqus Benchmarks Manual. +By performing a load-displacement analysis, other important nonlinear effects, such as material +inelasticity or contact, can be included. In contrast, all inelastic effects are ignored in a linear eigenvalue +buckling analysis and all contact conditions are fixed in the base state. Imperfections based on linear +buckling modes can also be useful for the analysis of structures that behave inelastically prior to reaching +peak load. +Introducing loading imperfections +Perturbations in loads or boundary conditions can also be used to introduce initial imperfections. In +this case fictitious “trigger” loads can be used to initiate the instability. The trigger loads should perturb +the structure in the expected buckling modes. Typically, these loads are applied as dead loads prior to +the Riks step so that they have fixed magnitudes. The magnitudes of trigger loads must be sufficiently +small so that they do not affect the overall postbuckling solution. It is your responsibility to choose +appropriate magnitudes and locations for such fictitious loads; Abaqus/Standard does not check that they +are reasonable. +Obtaining a solution at a particular load or displacement value +The Riks algorithm cannot obtain a solution at a given load or displacement value since these are treated +as unknowns—termination occurs at the first solution that satisfies the step termination criterion. To +obtain solutions at exact values of load or displacement, the solution must be restarted at the desired +point in the step (“Restarting an analysis,” Section 9.1.1) and a new, non-Riks step must be defined. +Since the subsequent step is a continuation of the Riks analysis, the load magnitude in that step must be +given appropriately so that the step begins with the loading continuing to increase or decrease according +to its behavior at the point of restart. For example, if the load was increasing at the restart point and +was positive, a larger load magnitude than the current magnitude should be given in the restart step to +continue this behavior. If the load was decreasing but positive, a smaller magnitude than the current +magnitude should be specified. +Restrictions +A Riks analysis is subject to the following restrictions: +• A Riks step cannot be followed by another step in the same analysis. Subsequent steps must be +analyzed by using the restart capability. +• If a Riks analysis includes irreversible deformation such as plasticity and a restart using another Riks +step is attempted while the magnitude of the load on the structure is decreasing, Abaqus/Standard +will find the elastic unloading solution. Therefore, restart should occur at a point in the analysis +where the load magnitude is increasing if plasticity is present. +• For postbuckling problems involving loss of contact, the Riks method will usually not work; inertia +or viscous damping forces (such as those provided by dashpots) must be introduced in a dynamic +or static analysis to stabilize the solution. +Initial conditions +Initial values of stresses, temperatures, field variables, solution-dependent state variables, etc. can be +specified; “Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1, describes all of +the available initial conditions. +Boundary conditions +Boundary conditions can be applied to any of the displacement or rotation degrees of freedom (1–6) or to +warping degree of freedom 7 in open-section beam elements (“Boundary conditions in Abaqus/Standard +and Abaqus/Explicit,” Section 33.3.1). Amplitude definitions (“Amplitude curves,” Section 33.1.2) +cannot be used to vary the magnitudes of prescribed boundary conditions during a Riks analysis. +Loads +The following loads can be prescribed in a Riks analysis: +• Concentrated nodal forces can be applied to the displacement degrees of freedom (1–6); see +“Concentrated loads,” Section 33.4.2. +• Distributed pressure forces or body forces can be applied; see “Distributed loads,” Section 33.4.3. +The distributed load types available with particular elements are described in Part VI, “Elements.” +Since Abaqus/Standard scales loading magnitudes proportionally based on the user-specified +magnitudes, amplitude references are ignored when the Riks method is chosen. +If follower loads are prescribed, their contribution to the stiffness matrix may be unsymmetric; the +unsymmetric matrix storage and solution scheme can be used to improve computational efficiency in +such cases . +Predefined fields +Nodal temperatures can be specified . Any difference between +the applied and initial temperatures will cause thermal strain if a thermal expansion coefficient is given for +the material (“Thermal expansion,” Section 26.1.2). The loads generated by the thermal strain contribute +to the “reference” load specified for the Riks analysis and are ramped up with the load proportionality +factor. Hence, the Riks procedure can analyze postbuckling and collapse due to thermal straining. +The values of other user-defined field variables can be specified. These values affect only field- +variable-dependent material properties, if any. Since the concept of time is replaced by arc length in a +Riks analysis, the use of properties that change due to changes in temperatures and/or field variables is +not recommended. +Material options +Most material models that describe mechanical behavior are available for use in a Riks analysis. +The following material properties are not active during a Riks analysis: acoustic properties, thermal +properties (except for thermal expansion), mass diffusion properties, electrical properties, and pore fluid +flow properties. Materials with history dependence can be used; however, it should be realized that the +results will depend on the loading history, which is not known in advance. +The concept of time is replaced by arc length in a Riks analysis. Therefore, any effects involving +time or strain rate (such as viscous damping or rate-dependent plasticity) are no longer treated correctly +and should not be used. +See Part V, “Materials,” for details on the material models available in Abaqus/Standard. +Elements +Any of the stress/displacement elements in Abaqus/Standard (including those with temperature or +pressure degrees of freedom) can be used in a Riks analysis . Dashpots should not be used since velocities will be calculated as +displacement increments divided by arc length, which is meaningless. +Output +Output options are provided to allow the magnitudes of individual load components (pressure, point +loads, etc.) to be printed or to be written to the results file. The current value of the load proportionality +factor, LPF, will be given automatically with any results or output database file output request. These +output options are recommended when the Riks method is used so that load magnitudes can be +seen directly. All of the output variable identifiers are outlined in “Abaqus/Standard output variable +identifiers,” Section 4.2.1. +Input file template +*HEADING +… +*INITIAL CONDITIONS +Data lines to define initial conditions +*BOUNDARY +Data lines to specify zero-valued boundary conditions +** +*STEP, NLGEOM +*STATIC +*CLOAD and/or *DLOAD and/or *TEMPERATURE +Data lines to specify preload (dead load), +*END STEP +** +*STEP, NLGEOM +*STATIC, RIKS +Data line to define incrementation and stopping criteria +*CLOAD and/or *DLOAD and/or *TEMPERATURE +Data lines to specify reference loading, +*END STEP +6.2.5 +QUASI-STATIC ANALYSIS +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “Static stress analysis procedures: overview,” Section 6.2.1 +• *VISCO +• “Configuring a transient, static, stress/displacement analysis with time-dependent material +response” in “Configuring general analysis procedures,” Section 14.11.1 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +A quasi-static stress analysis in Abaqus/Standard: +• is used to analyze problems with time-dependent material response (creep, swelling, viscoelasticity, +and two-layer viscoplasticity); +• is used when inertia effects can be neglected; and +• can be linear or nonlinear. +See “Mass scaling,” Section 11.6.1, and “Explicit dynamic analysis,” Section 6.3.3, for information +on conducting quasi-static analysis in Abaqus/Explicit. See “Implicit dynamic analysis using direct +integration,” Section 6.3.2, for information on conducting quasi-static analysis using a dynamic +procedure in Abaqus/Standard. +Incrementation +You can control the time incrementation in a quasi-static analysis directly, or it can be controlled +automatically by Abaqus/Standard. Automatic incrementation is preferred in almost all cases. +Fixed incrementation +If you specify the time increments in a quasi-static analysis directly, fixed time increments equal to the +specified initial time increment will be used throughout the analysis. +Input File Usage: +Abaqus/CAE Usage: +*VISCO +Step module: Create Step: General: Visco +Automatic incrementation +If you select automatic incrementation, the size of the time increment is limited by the accuracy of the +integration. The user-specified accuracy tolerance parameter limits the maximum inelastic strain rate +change allowed over an increment: +where t is the time at the beginning of the increment, +at the end of the increment), and +chosen for the accuracy tolerance parameter should be on the order of +is the time +is the time increment (so that +is the equivalent creep strain rate. To achieve accuracy, the value +for creep problems, where +is an acceptable level of error in the stress and E is a typical elastic modulus, or on the order of the +elastic strains for viscoelasticity problems. +Input File Usage: +Abaqus/CAE Usage: +*VISCO, CETOL=tolerance +Step module: Create Step: General: Visco: Incrementation: +Creep/swelling/viscoelastic strain error tolerance: tolerance +Selecting explicit creep integration +Nonlinear creep problems (“Rate-dependent plasticity: creep and swelling,” Section 23.2.4) that exhibit +no other nonlinearities can be solved efficiently by forward-difference integration of the inelastic strains +if the inelastic strain increments are smaller than the elastic strains. This explicit method is efficient +computationally because, unlike implicit methods, iteration is not required. Although this method is +only conditionally stable, the numerical stability limit of the explicit operator is in many cases sufficiently +large to allow the solution to be developed in a reasonable number of time increments. +For creep at very low stress levels, however, the unconditional stability of the backward difference +In such cases Abaqus/Standard will invoke the implicit +operator (implicit method) is desirable. +integration scheme automatically. +Explicit integration can be less expensive computationally and simplifies implementation of user- +defined creep laws in user subroutine CREEP; you can restrict Abaqus/Standard to using this method +for creep problems (with or without geometric nonlinearity included). See “Rate-dependent plasticity: +creep and swelling,” Section 23.2.4, for further details. +Input File Usage: +Abaqus/CAE Usage: +*VISCO, CETOL=tolerance, CREEP=EXPLICIT +Step module: Create Step: General: Visco: Incrementation: +Creep/swelling/viscoelastic strain error tolerance: tolerance and +Creep/swelling/viscoelastic integration: Explicit +Integration scheme for viscoelasticity and rate-dependent yield +Problems including “Time domain viscoelasticity,” Section 22.7.1, are always integrated with an +unconditionally stable operator. The time step in these problems is limited only by the accuracy +tolerance parameter defined above. +Problems including “Rate-dependent yield,” Section 23.2.3, and “Parallel network viscoelastic +model,” Section 22.8.2, are always integrated using an implicit, unconditionally stable method. The +accuracy tolerance parameter does not limit the inelastic strain rate change and can be set equal to any +nonzero value to activate automatic time incrementation. +Unstable problems +Some types of analyses may develop local instabilities, such as surface wrinkling, material instability, +or local buckling. In such cases it may not be possible to obtain a quasi-static solution, even with the aid +of automatic incrementation. Abaqus/Standard offers the ability to stabilize this class of problems by +applying damping throughout the model in such a way that the viscous forces introduced are sufficiently +large to prevent instantaneous buckling or collapse but small enough not to affect the behavior +significantly while the problem is stable. The available automatic stabilization schemes are described in +detail in “Automatic stabilization of unstable problems” in “Solving nonlinear problems,” Section 7.1.1. +Initial conditions +Initial values of stresses, temperatures, field variables, solution-dependent state variables, etc. can be +specified, as described in “Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1. +Boundary conditions +Boundary conditions can be applied to any of the displacement or rotation degrees of freedom (1–6); +to warping degree of freedom 7 in open-section beam elements; or, if hydrostatic fluid elements are +included in the model, to fluid pressure degree of freedom 8. +If boundary conditions are applied to +rotation degrees of freedom, you must understand how Abaqus handles finite rotations. See “Boundary +conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1. +Loads +The following types of loading can be prescribed in a quasi-static analysis: +• Concentrated nodal forces can be applied to the displacement degrees of freedom (1–6); see +“Concentrated loads,” Section 33.4.2. +• Distributed pressure forces or body forces can be applied; see “Distributed loads,” Section 33.4.3. +The distributed load types available with particular elements are described in Part VI, “Elements.” +Predefined fields +The following predefined fields can be specified in a quasi-static analysis, as described in “Predefined +fields,” Section 33.6.1: +• Although temperature is not a degree of freedom in quasi-static analysis, nodal temperatures can be +specified. Any difference between the applied and initial temperatures will cause thermal strain if a +thermal expansion coefficient is given for the material (“Thermal expansion,” Section 26.1.2). The +specified temperature also affects temperature-dependent material properties, if any. +• The values of user-defined field variables can be specified. These values affect only field-variable- +dependent material properties, if any. +Material options +The quasi-static procedure in Abaqus/Standard is generally used to analyze quasi-static creep and +swelling problems, which occur over fairly long time periods (“Rate-dependent plasticity: creep and +swelling,” Section 23.2.4). This procedure can also be used to analyze viscoelastic materials (“Time +domain viscoelasticity,” Section 22.7.1, and “Parallel network viscoelastic model,” Section 22.8.2) and +two-layer viscoplastic materials (“Two-layer viscoplasticity,” Section 23.2.11). In addition, all material +models that are valid in a static analysis procedure can be used. +Elements +Any of the stress/displacement elements in Abaqus/Standard (including those with temperature or +pressure degrees of freedom) can be used in a quasi-static stress analysis—see “Choosing the appropriate +element for an analysis type,” Section 27.1.3. +Output +In addition to the usual output variables available in Abaqus/Standard , the following variables are provided specifically for creep problems: +Element integration point variables: +CEEQ +CESW +Equivalent creep strain, +. +Magnitude of the swelling strain. +CEMAG +Magnitude of the creep strain, +. +CEP +CE +Principal creep strains. +Output of all of the creep strain components and CEEQ, CESW, and CEMAG. +Input file template +*HEADING +… +*BOUNDARY +Data lines to specify zero-valued boundary conditions +*INITIAL CONDITIONS +Data lines to specify initial conditions +*AMPLITUDE +Data lines to define amplitude variations +** +*STEP (,NLGEOM) +*VISCO, CETOL=tolerance +Data line to define time incrementation and a “real” time scale +*BOUNDARY +Data lines to describe nonzero boundary conditions +*CLOAD and/or *DLOAD and/or *TEMPERATURE and/or *FIELD +Data lines to specify loading +*END STEP +6.2.6 +DIRECT CYCLIC ANALYSIS +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• *DIRECT CYCLIC +• *TIME POINTS +• *CONTROLS +• “Configuring a direct cyclic procedure” in “Configuring general analysis procedures,” +Section 14.11.1 of the Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +A direct cyclic analysis: +• is a quasi-static analysis; +• uses a combination of Fourier series and time integration of the nonlinear material behavior to obtain +the stabilized cyclic response of the structure iteratively; +• avoids the considerable numerical expense associated with a transient analysis; +• is ideally suited for very large problems in which many load cycles must be applied to obtain the +stabilized response if transient analysis is performed; +• can be performed with linear or nonlinear material with localized plastic deformation; +• can be used to predict the likelihood of plastic ratchetting; +• assumes geometrically linear behavior and fixed contact conditions; +• uses the elastic stiffness, so the equation system is inverted only once; and +• can also be used to predict progressive damage and failure for ductile bulk materials and/or to predict +delamination/debonding growth at the interfaces in laminated composites in a low-cycle fatigue +analysis. +Introduction +It is well known that after a number of repetitive loading cycles, the response of an elastic-plastic +structure, such as an automobile exhaust manifold subjected to large temperature fluctuations and +clamping loads, may lead to a stabilized state in which the stress-strain relationship in each successive +cycle is the same as in the previous one. The classical approach to obtain the response of such a structure +is to apply the periodic loading repetitively to the structure until a stabilized state is obtained. This +approach can be quite expensive, since it may require the application of many loading cycles before the +stabilized response is obtained. To avoid the considerable numerical expense associated with a transient +analysis, a direct cyclic analysis can be used to calculate the cyclic response of the structure directly. +The basis of this method is to construct a displacement function +structure at all times t during a load cycle with period T as shown in Figure 6.2.6–1. +that describes the response of the +stabilized solution +solution at iteration n+1 +solution at iteration n +t 1∇ +t n∇ +t n-1 +t n +t n+1 +Figure 6.2.6–1 A displacement function at all times t during +a load cycle with period T at different iterations. +A truncated Fourier series is used for this purpose, +, and +is the angular frequency, +where n stands for the number of terms in the Fourier series, +and +are unknown displacement coefficients associated with each degree of freedom in +the problem. Abaqus/Standard solves for the unknown displacement coefficients by using a modified +Newton method, with the elastic stiffness matrix at the beginning of the analysis step serving as the +Jacobian in the scheme. We expand the residual vector in the modified Newton method using a Fourier +series of the same form as the displacement solution: +where each residual vector coefficient +coefficient +entire load cycle. At each instant in time in the cycle Abaqus/Standard obtains the residual vector +in the Fourier series corresponds to a displacement +, respectively. The residual coefficients are obtained by tracking through the +by +, and +, and +, +the Fourier coef���cients +DIRECT CYCLIC ANALYSIS +The displacement solution is obtained by solving for corrections to the displacement Fourier +coefficients corresponding to each residual coefficient. The updated displacement solution is used in +the next iteration to obtain the displacements at each instant in time. This process is repeated until +convergence is obtained. Each pass through the complete load cycle can, therefore, be thought of as a +single iteration of the solution to the nonlinear problem. Convergence is measured by ensuring that all +entries of the residual coefficients are small. +The algorithm to obtain a stabilized cycle is described in detail in “Direct cyclic algorithm,” +Section 2.2.3 of the Abaqus Theory Manual. +Direct cyclic analysis +A direct cyclic step can be the only step in an analysis, can follow a general or linear perturbation step, +or can be followed by a general or linear perturbation step. If a direct cyclic step is followed by a general +step, the solution at the end of the direct cyclic step will be the initial state of the general step. If a +direct cyclic step follows a general or linear perturbation step, the elastic stiffness matrix at the end of +the last general analysis step prior to the direct cyclic step will serve as the Jacobian in the direct cyclic +procedure. Any prior (non-cyclic) loads are simply included in the constant part of the Fourier expansion +of the residual vectors, and the plastic strains at the end of the preloading step are used as initial conditions +for the direct cyclic step. +Multiple direct cyclic analysis steps can be included in a single analysis. In such a case the Fourier +series coefficients obtained in the previous step can be used as starting values in the current step. By +default, the Fourier coefficients are reset to zero, thus allowing application of cyclic loading conditions +that are very different from those defined in the previous direct cyclic step. +You can specify that a direct cyclic step in a restart analysis should use the Fourier coefficients from +the previous step, thus allowing continuation of an analysis that has not reached a stabilized cycle. In a +direct cyclic analysis a restart file is written at the end of the cycle or time period. Consequently, a restart +analysis that is a continuation of a previous direct cyclic analysis will start with a new iteration at +. +Input File Usage: +Use the following option to reset the Fourier series coefficients to zero: +*DIRECT CYCLIC, CONTINUE=NO (default) +Use the following option to specify that the current step is a continuation of the +previous direct cyclic step: +*DIRECT CYCLIC, CONTINUE=YES +Abaqus/CAE Usage: +Use the following option to reset the Fourier series coefficients to zero (default): +Step module: Create Step: General: Direct cyclic +Use the following option to specify that the current step is a continuation of the +previous direct cyclic step: +Step module: Create Step: General: Direct cyclic; Basic: Use +displacement Fourier coefficients from previous direct cyclic step +Using the direct cyclic approach to perform low-cycle fatigue analysis +The direct cyclic procedure can also be used in conjunction with the damage extrapolation +technique to predict progressive damage and failure for ductile bulk materials and/or to predict +delamination/debonding at the interfaces in laminated composites in a low-cycle fatigue analysis. In +this case multiple cycles can be included in a single direct cyclic analysis, as described in “Low-cycle +fatigue analysis using the direct cyclic approach,” Section 6.2.7. +Input File Usage: +Abaqus/CAE Usage: +*DIRECT CYCLIC, FATIGUE +Step module: Create Step: General: Direct cyclic; Fatigue: +Include low-cycle fatigue analysis +Controlling the solution accuracy +Direct cyclic analysis combines a Fourier series approximation with time integration of the nonlinear +material behavior to obtain the stabilized cyclic solution iteratively using a modified Newton method. +The accuracy of the algorithm depends on the number of Fourier terms used, the number of iterations +taken to obtain the stabilized solution, and the number of time points within the load period at which the +material response and residual vector are evaluated. Abaqus/Standard allows you to control the solution +in several ways, as described below. +Controlling the iterations in the modified Newton method +In the direct cyclic method global Newton iterations are performed to determine corrections to the +displacement Fourier coefficients. During each global iteration Abaqus/Standard tracks through the +entire time cycle to compute the residual vector at a suitable number of time points. This involves +standard element-by-element finite element calculations in which history-dependent material variables +are integrated. The residual vector is integrated over the period to obtain the Fourier residual +coefficients, which in turn yield corrections in displacement coefficients when the system of equations is +solved. Abaqus/Standard will continue with the iterative process until convergence is obtained or until +the maximum number of iterations allowed has been reached. You can specify the maximum number of +iterations when you define the direct cyclic step; the default is 200 iterations. +Input File Usage: +*DIRECT CYCLIC +, , , , , , , max number of iterations +Abaqus/CAE Usage: +Step module: Create Step: General: Direct cyclic; Incrementation: +Maximum number of iterations: max number of iterations +Specifying convergence criteria +Convergence is best measured by ensuring that all the residual coefficients are sufficiently small +compared to the time averaged force and that all the corrections to displacement Fourier coefficients +are sufficiently small compared to the displacement Fourier coefficients. The time averaged force is +defined in “Convergence criteria for nonlinear problems,” Section 7.2.3. Abaqus/Standard requires +that the ratio of the maximum residual coefficient to the time averaged force, +, and the ratio of +the maximum correction to the displacement coefficients to the largest displacement coefficient, +, +are less than the tolerances. The default values are += 0.005. To change these +values, you must define direct cyclic controls. += 0.005 and +plastic ratchetting occurs, the displacement and residual coefficients of all the periodic terms ( +When a stabilized cyclic response does not exist, the method will not converge. In the case where +, and +) in the Fourier series converge. However, the displacement and the residual coefficients of the +) in the Fourier series continue to grow from one iteration to another iteration. +are used to detect the plastic ratchetting. The default values += 0.005. For more information, see “Controlling the solution accuracy in +constant term ( +The user-specified tolerances +are +direct cyclic analysis” in “Commonly used control parameters,” Section 7.2.2. += 0.005 and +and +and +Input File Usage: +Abaqus/CAE Usage: +*CONTROLS, TYPE=DIRECT CYCLIC +Step module: Other→General Solution Controls→Edit; +Specify: Direct Cyclic +Controlling the Fourier representations +The number of Fourier terms required to obtain an accurate solution depends on the variation of the load +as well as the variation of the structural response over the period. In determining the number of terms, +keep in mind that the objective of this kind of analysis is to make low-cycle fatigue predictions. Hence, +the goal is to obtain good approximation of the plastic strain cycle at each point; local inaccuracies in +the stresses are less important. More Fourier terms usually provide a more accurate solution but at the +expense of additional data storage and computational time. In addition, an accurate integration of the +Fourier residual coefficients requires that the residual vector be evaluated at an adequate number of time +points during the cycle. Abaqus/Standard uses a trapezoidal rule, which assumes a linear variation of the +residual over a time increment, to integrate the residual coefficients. For accurate integration the number +of time points must be larger than the number of Fourier coefficients (which is equal to +, where +n represents the number of Fourier terms). Abaqus/Standard will automatically reduce the number of +Fourier coefficients used for the next iteration if it is found to be greater than the number of increments +taken to complete an iteration. +Abaqus/Standard uses an adaptive algorithm to determine the number of Fourier terms. By default, +Abaqus/Standard starts with 11 terms and determines the response of the structure by using the iterative +method described before. Once convergence is obtained (which is measured by ensuring that all the +residual vector coefficients and all the corrections to displacement coefficients in the Fourier series +are sufficiently small), Abaqus/Standard evaluates if a sufficient number of Fourier terms are used by +determining if equilibrium was satisfied at all the time points during the cycle. If equilibrium is satisfied +at all time points, the solution is accepted. Otherwise, Abaqus/Standard increases the number of Fourier +terms (by default, 5 terms are added) and continues with the iterative scheme until convergence with the +new number of Fourier terms is obtained. This process is repeated until equilibrium is reached or until +the maximum number of Fourier terms has been used. This scheme is best illustrated in Figure 6.2.6–2, +where both local equilibrium and overall convergence are obtained when the number of Fourier terms +is equal to 21. A maximum number of 25 Fourier terms is used by default. You can specify the initial +and maximum number of Fourier terms and the increment in the number of terms when you define the +direct cyclic step. +ratio of maximum residual to time average force +equilibrium +tolerance +stabilized iteration with 11 terms +stabilized iteration with 16 terms +stabilized iteration with 21 terms +equilibrium +tolerance +Figure 6.2.6–2 Stabilized iterations with different Fourier terms. +You can also define the convergence criteria for determining convergence and for determining +whether equilibrium is achieved at all time points through the period , with suitable defaults set by Abaqus/Standard. +In a direct cyclic analysis that has not reached a stabilized cycle, you can increase the number of +iterations or Fourier terms upon restart, thus allowing continuation of an analysis. +Abaqus/Standard provides detailed output of the maximum residual at each time point, +the +maximum residual coefficient, the maximum displacement coefficient, the maximum correction to +displacement coefficients, and the number of Fourier terms at the end of each iteration in the message +(.msg) file. This output is described in more detail below. +Input File Usage: +*DIRECT CYCLIC +, , , , initial number of terms, max number of terms, increment in number of terms +Abaqus/CAE Usage: +Step module: Create Step: General: Direct cyclic; Incrementation: +Number of Fourier terms: Initial: initial number of terms, Maximum: +max number of terms, Increment: increment in number of terms +Controlling the incrementation during the cyclic time period +To ensure an accurate solution, the material history as well as the residual vector must be evaluated at a +sufficient number of time points during the cycle. The number of time points, +, at which the response +is computed must be larger than the number of Fourier coefficients; i.e., +. Abaqus/Standard +will automatically adjust the number of Fourier coefficients if such a condition is not satisfied. You +can specify the time incrementation over the cycle directly, or it can be determined automatically by +Abaqus/Standard. +You should specify the maximum number of increments allowed in the time period as part of the +step definition. The default is 100. +Automatic incrementation +There are several ways to choose the automatic incrementation scheme. If you specify only the maximum +allowable nodal temperature change in an increment, the time increments are selected automatically +based on this value. Abaqus/Standard will restrict the time increments to ensure that the maximum +temperature change is not exceeded at any node during any increment of the analysis. +For rate-dependent constitutive equations you can limit the size of the time increment by the +accuracy of the integration. The user-specified accuracy tolerance parameter limits the maximum +inelastic strain rate change allowed over an increment: +where t is the time at the beginning of the increment, +at the end of the increment), and +value chosen for the accuracy tolerance parameter should be on the order of +where +of the elastic strains for viscoelasticity problems. +is the time +is the equivalent creep strain rate. To achieve sufficient accuracy, the +for creep problems, +is an acceptable level of error in the stress and E is a typical elastic modulus, or on the order +is the time increment (so that +If rate-dependent constitutive equations are used in combination with a varying temperature, both +controls can be used simultaneously. Abaqus/Standard will then choose the increments that satisfy both +criteria. +If the time integration accuracy measure specified by either or both of the above controls is satisfied +consecutive increments without cutbacks, the next time increment will be increased by a factor +are user-defined parameters . The defaults are += 3 and += 1.5. +. Both +and +Input File Usage: +Abaqus/CAE Usage: +Use the following option to specify the maximum allowable nodal temperature +change: +*DIRECT CYCLIC, DELTMX= +Use the following option to specify the accuracy tolerance parameter: +*DIRECT CYCLIC, CETOL=tolerance +Use the following option to specify the maximum allowable nodal temperature +change: +Step module: Create Step: General: Direct cyclic; Incrementation: +Max. allowable temperature change per increment: +Use the following option to specify the accuracy tolerance parameter: +Step module: Create Step: General: Direct cyclic; Incrementation: +Creep/swelling/viscoelastic strain error tolerance: tolerance +Fixed time incrementation +If neither the accuracy tolerance parameter nor the maximum allowable nodal temperature change is +specified, the size of the time increment is fixed. You must specify the time increment +and the time +period T. +Input File Usage: +*DIRECT CYCLIC +, T +Abaqus/CAE Usage: +Step module: Create Step: General: Direct cyclic; Basic: Cycle time +period: T; Incrementation: Type: Fixed, Increment size: +Defining the time points at which the response must be evaluated +The user-defined time incrementation for a direct cyclic step can be augmented or superseded by +specifying particular time points in the loading history at which the response of the structure should +be evaluated. This feature is particularly useful if you know prior to the analysis at which time points +in the analysis the load reaches a maximum and/or minimum value or when the response will change +rapidly. An example is the analysis of the heating/cooling thermal cycle of an engine component where +you typically know when the temperature reaches a maximum value. +When time points are used with fixed time incrementation, the time incrementation specified for +the direct cyclic step is ignored and instead the time incrementation precisely follows the specified time +points. If time points are used with automatic incrementation, the time incrementation is variable; but +the response of the structure will be evaluated at the specified time points. +The time points can be listed individually, or they can be generated automatically by specifying the +starting time point, ending time point, and increment in time between the two specified time points. +Input File Usage: +Abaqus/CAE Usage: +Use the following options to list time points individually: +*TIME POINTS, NAME=time points name +*DIRECT CYCLIC, TIME POINTS=time points name +Use the following options to generate time points automatically: +*TIME POINTS, NAME=time points name, GENERATE +*DIRECT CYCLIC, TIME POINTS=time points name +Use the following options to list time points individually: +Step module: Create Step: General: Direct cyclic; Incrementation: +Evaluate structure response at time points: time points name +Use the following options to generate time points automatically: +Step module: Create Step: General: Direct cyclic; Incrementation: +Evaluate structure response at time points: Create; Edit Time +Points: Specify using delimiters: Start, End, Increment +Controlling the application of periodicity conditions +By default, Abaqus/Standard imposes periodic conditions during the iterative solution process by using +the state obtained at the end of the previous iteration as the starting state for the current iteration; i.e., +, where s is a solution variable such as plastic strain. +In cases where the periodic solution is not easily found (for example, when the loading is close +to causing ratchetting), the state around which the periodic solution is obtained may show considerably +more “drift” than would be obtained in a transient analysis. In such cases you may wish to delay the +application of periodic conditions as an artificial method to reduce this drift. Figure 6.2.6–3 compares +the response of two identical structures subjected to the same set of cyclic loads and boundary conditions, +where each structure experienced a different loading history prior to the application of the cyclic loads. +Figure 6.2.6–3 shows that the prior loading history only affects the mean value of stress and strain; it +does not affect the shape of the stress-strain curves or the amount of energy dissipated during the cycle. +periodicity condition imposed +from iteration 5 +periodicity condition imposed +from iteration 1 +Figure 6.2.6–3 Influence of periodicity condition on mean value of the strains over a stabilized cycle. +By delaying the application of periodicity conditions, you can influence the mean stress and strain level. +However, this is rarely necessary since the average stress and strain levels are usually not needed for +low-cycle fatigue life predictions. +You can control when the periodicity conditions are applied by defining direct cyclic controls to +. This variable defines from which iteration onward the application of periodic +means that the periodicity conditions are +specify the variable +conditions will be activated. For example, setting +applied from iteration 6 onwards. The default is +, which is appropriate for most analyses. +Input File Usage: +*CONTROLS, TYPE=DIRECT CYCLIC +Abaqus/CAE Usage: +Step module: Other→General Solution Controls→Edit; +Direct Cyclic: +Initial conditions +Initial values of stresses, temperatures, field variables, solution-dependent state variables, etc. can be +specified . +Boundary conditions +Boundary conditions can be applied to any of the displacement or rotation degrees of freedom. During +the analysis, prescribed boundary conditions must have an amplitude definition that is cyclic over the +step: the start value must be equal to the end value . If the +analysis consists of several steps, the usual rules apply . At each new step the boundary condition can either be modified +or completely defined. All boundary conditions defined in previous steps remain unchanged unless they +are redefined. +Loads +The following loads can be prescribed in a direct cyclic analysis: +• Concentrated nodal forces can be applied to the displacement degrees of freedom (1–6); see +“Concentrated loads,” Section 33.4.2. +• Distributed pressure forces or body forces can be applied; see “Distributed loads,” Section 33.4.3. +The distributed load types available with particular elements are described in Part VI, “Elements.” +During the analysis each load must have an amplitude definition that is cyclic over the step where the start +value must be equal to the end value . If the analysis consists +of several steps, the usual rules apply . At each new +step the loading can either be modified or completely defined. All loads defined in previous steps remain +unchanged unless they are redefined. +Predefined fields +The following predefined fields can be specified in a direct cyclic analysis, as described in “Predefined +fields,” Section 33.6.1: +• Temperature is not a degree of freedom in a direct cyclic analysis, but nodal temperatures can be +specified as a predefined field. The temperature values specified must be cyclic over the step: +the start value must be equal to the end value . If the +temperatures are read from the results file, you should specify initial temperature conditions equal +to the temperature values at the end of the step . Alternatively, you can ramp the temperatures back to their initial +condition values, as described in “Predefined fields,” Section 33.6.1. Any difference between the +applied and initial temperatures will cause thermal strain if a thermal expansion coefficient is given +for the material (“Thermal expansion,” Section 26.1.2). The specified temperature also affects +temperature-dependent material properties, if any. +• The values of user-defined field variables can be specified. These values affect only field-variable- +dependent material properties, if any. The field variable values specified must be cyclic over the +step. +Material options +Most material models, including user-defined materials (defined using user subroutine UMAT), that +describe mechanical behavior are available for use in a direct cyclic analysis. +The following material properties are not active during a direct cyclic analysis: acoustic properties, +thermal properties (except for thermal expansion), mass diffusion properties, electrical conductivity +properties, piezoelectric properties, and pore fluid flow properties. +yield,” Section +yield +(“Rate-dependent plasticity: +(“Two-layer viscoplasticity,” Section 23.2.11) can also be used during a direct cyclic analysis. +(“Rate-dependent +creep +creep and swelling,” Section 23.2.4), and two-layer viscoplasticity +Rate-dependent +rate-dependent +23.2.3), +Elements +Any of the stress/displacement elements in Abaqus/Standard can be used in a direct cyclic analysis . +Output +Different types of output are available for postprocessing and for monitoring a direct cyclic analysis. +Message file information +Abaqus/Standard prints the residual force, time average force, and a flag to indicate if equilibrium was +satisfied in the message (.msg) file at different time increments for each iteration. You can control the +frequency in increments at which information is printed to the message file, and you can suppress the +output; the default is to print output every 10 increments . +Abaqus/Standard also prints the number of Fourier terms used, the maximum residual coefficient, +the maximum correction to displacement coefficients, and the maximum displacement coefficient in the +Fourier series in the message file at the end of each iteration. An example of the output is shown below: +INC +10 +TIME +INC +0.250 +ITERATION +STEP +TIME +2.50 +26 STARTS +LARG. RESI. +FORCE +1.008E+01 +TIME AVG. +FORCE +50.9 +FORCE +EQUV. +20 +30 +0.250 +0.250 +5.00 +7.50 +1.622E+01 +4.622E-02 +76.8 +99.8 +ITERATION +26 SUMMARY +NUMBER OF FOURIER TERMS USED 40, TOTAL NUMBER OF INCREMENTS +CYCLE/STEP TIME +AVERAGE FORCE +TOTAL TIME COMPLETED +TIME AVG. FORCE +30.0, +21.2 +31.0 +25.7 +120 +AT NODE 24 DOF 2 +MAX. COEFFICIENT OF DISP. +AT NODE 44 DOF 1 +MAX. COEFF. OF RESI. FORCE ON CONST. TERM +MAX. COEFF. OF RESI. FORCE ON PERI. TERMS +6 DOF 3 +AT NODE +MAX. CORR. TO COEFF. OF DISP. ON CONST. TERM 0.002 AT NODE 50 DOF 3 +MAX. CORR. TO COEFF. OF DISP. ON PERI. TERMS 0.015 AT NODE 50 DOF 3 +0.142 +31.7 +0.82 +Results output +Element and nodal output are written only when the stabilized cycle is reached. If a stabilized cycle +has not been reached at the end of an analysis, output is written for the last iteration of the step. The +element output available for a direct cyclic analysis includes stress; strain; energies; and the values of +state, field, and user-defined variables. All the energies are set equal to zero at the beginning of each +iteration since energies dissipated over an entire stabilized cycle are of interest in making fatigue life +predictions in direct cyclic analysis. The nodal output available includes displacements, reaction forces, +and coordinates. All of the output variable identifiers are outlined in “Abaqus/Standard output variable +identifiers,” Section 4.2.1. +Recovering additional results for an iteration +You may want to recover additional results for an iteration rather than for the stabilized cycle. You can +extract these results from the restart data . This feature is particularly useful if you want to evaluate +the shift of the strain from one iteration to another iteration when plastic ratchetting occurs. +Input File Usage: +Abaqus/CAE Usage: +*POST OUTPUT, ITERATION=n +Recovering additional results for an iteration is not supported in Abaqus/CAE. +Specifying output at exact times +Output at exact times is not supported for direct cyclic analysis. If output at exact times is requested, +Abaqus will issue a warning message and change the output to an output at approximate times. +Limitations +A direct cyclic analysis is subject to the following limitations: +• Contact conditions cannot change during a direct cyclic analysis; they remain as they were defined +at the beginning of the analysis or at the end of any general step prior to the direct cyclic step. +Frictional slipping is not allowed during direct cyclic analyses; all points in contact are assumed to +be sticking if friction is present. +• Geometric nonlinearity can be included only in any general step prior to a direct cyclic step; +however, only small displacements and strains will be considered during the cyclic step. +Input file template +*HEADING +… +*BOUNDARY +Data lines to specify zero-valued boundary conditions +*INITIAL CONDITIONS +Data lines to specify initial conditions +*AMPLITUDE +Data lines to define amplitude variations +** +*STEP (,INC=) +Set INC equal to the maximum number of increments in a single loading cycle +*DIRECT CYCLIC +Data line to define time increment, cycle time, initial number of Fourier terms, +maximum number of Fourier terms, increment in number of Fourier terms, +and maximum number of iterations +*TIME POINTS +Data lines to list time points +*BOUNDARY, AMPLITUDE= +Data lines to prescribe zero-valued or nonzero boundary conditions +*CLOAD and/or *DLOAD, AMPLITUDE= +Data lines to specify loads +*TEMPERATURE and/or *FIELD, AMPLITUDE= +Data lines to specify values of predefined fields +*END STEP +** +*STEP(,INC=) +*DIRECT CYCLIC, DELTMX +Data line to control automatic time incrementation and Fourier representations +*BOUNDARY, OP=MOD,AMPLITUDE= +Data lines to modify or add zero-valued or nonzero boundary conditions +*CLOAD, OP=NEW, AMPLITUDE= +Data lines to specify new concentrated loads; all previous concentrated +loads will be removed +*DLOAD, OP=MOD, AMPLITUDE= +Data lines to specify additional or modified distributed loads +*TEMPERATURE and/or *FIELD, AMPLITUDE= +Data lines to specify additional or modified values of predefined fields +*END STEP +LOW-CYCLE FATIGUE ANALYSIS USING THE DIRECT CYCLIC APPROACH +LOW-CYCLE FATIGUE ANALYSIS +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “Static stress analysis procedures: overview,” Section 6.2.1 +• “Direct cyclic analysis,” Section 6.2.6 +• “Crack propagation analysis,” Section 11.4.3 +• “Damage and failure for ductile materials in low-cycle fatigue analysis,” Section 24.4 +• “Modeling discontinuities as an enriched feature using the extended finite element method,” +Section 10.7.1 +• *DAMAGE EVOLUTION +• *DAMAGE INITIATION +• *DEBOND +• *DIRECT CYCLIC +• *FRACTURE CRITERION +• *CONTROLS +• “Configuring a direct cyclic procedure” in “Configuring general analysis procedures,” +Section 14.11.1 of the Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +A low-cycle fatigue analysis: +• is characterized by states of stress high enough for inelastic deformation to occur in most cases; +• is a quasi-static analysis on a structure subjected to sub-critical cyclic loading; +• can be associated with thermal as well as mechanical loading; +• uses the direct cyclic approach to obtain the stabilized cyclic response of the structure directly; +• models progressive damage and failure in bulk ductile material based on a continuum damage +mechanics approach, in which case damage initiation and evolution are characterized by the +accumulated inelastic hysteresis strain energy per stabilized cycle; +• models propagation of a discrete crack along an arbitrary, solution-dependent path without +remeshing in the bulk material based on the principles of linear elastic fracture mechanics (LEFM) +with the extended finite element method, in which case the onset and growth of fatigue crack are +characterized by the relative fracture energy release rate; +• models progressive delamination growth along a predefined path at the interfaces in laminated +composites, in which case the onset and growth of fatigue delamination at the interfaces are +characterized by the relative fracture energy release rate; +• uses the damage extrapolation technique to accelerate the low-cycle fatigue analysis; and +• assumes geometrically linear behavior and fixed contact conditions within each loading cycle. +Approaches to low-cycle fatigue analysis +The traditional approach for determining the fatigue limit for a structure is to establish the +curves +(load versus number of cycles to failure) for the materials in the structure. Such an approach is still +used as a design tool in many cases to predict fatigue resistance of engineering structures. However, this +technique is generally conservative, and it does not define a relationship between the cycle number and +the degree of damage or crack length. +One alternative approach is to predict the fatigue life by using a crack/damage evolution law +based on the inelastic strain/energy when the structure’s response is stabilized after many cycles. +Because the computational cost to simulate the slow progressive damage in a material over many +load cycles is prohibitively expensive for all but the simplest models, numerical fatigue life studies +usually involve modeling the response of the structure subjected to a small fraction of the actual loading +history. This response is then extrapolated over many load cycles using empirical formulae such as the +Coffin-Manson relationship to predict the likelihood of crack +initiation and propagation. Since this approach is based on a constant crack/damage growth rate, it may +not realistically predict the evolution of the crack or damage. +Low-cycle fatigue analysis in Abaqus/Standard +The direct cyclic analysis capability in Abaqus/Standard provides a computationally effective modeling +technique to obtain the stabilized response of a structure subjected to periodic loading and is ideally +suited to perform low-cycle fatigue calculations on a large structure. The capability uses a combination +of Fourier series and time integration of the nonlinear material behavior to obtain the stabilized response +of the structure directly. The theory and algorithm to obtain a stabilized response using the direct cyclic +approach are described in detail in “Direct cyclic algorithm,” Section 2.2.3 of the Abaqus Theory Manual. +The direct cyclic low-cycle fatigue procedure models the progressive damage and failure both in +bulk materials (such as in solder joints in an electronic chip packaging or intra-laminar crack growth in +laminated composites) and at material interfaces (such as delamination in laminated composites). The +former can be based on either a continuum damage mechanics approach or the principles of linear elastic +fracture mechanics with the extended finite element method. The response is obtained by evaluating the +behavior of the structure at discrete points along the loading history . The solution +at each of these points is used to predict the degradation and evolution of material properties that will +take place during the next increment, which spans a number of load cycles, +. The degraded material +properties are then used to compute the solution at the next increment in the load history. Therefore, the +crack/damage growth rate is updated continually throughout the analysis. +The elastic material stiffness at a material point remains constant and contact conditions remain +unchanged when the stabilized solution is computed at a given point in the loading history. Each of the +Figure 6.2.7–1 Elastic stiffness degradation as a function of the cycle number. +solutions along the loading history represents the stabilized response of the structure subjected to the +applied period loads, with a level of material damage at each point in the structure computed from the +previous solution. This process is repeated up to a point in the loading history at which a fatigue life +assessment can be made. +In bulk material, there are two approaches to modeling the progressive damage and failure. One +approach is based on continuum damage mechanics. This approach is more appropriate for ductile +material, in which the cyclic loading leads to stress reversals and the accumulation of plastic strains, +which in turn cause the initiation and propagation of cracks. The damage initiation and evolution are +characterized by the stabilized accumulated inelastic hysteresis strain energy per cycle as illustrated in +Figure 6.2.7–2. The other approach is based on the principles of linear elastic fracture mechanics with the +extended finite element method. This approach is more appropriate for brittle material or material with +small scale yielding, in which the cyclic loading leads to material strength degradation causing fatigue +crack growth along an arbitrary path. The onset and growth of the crack are characterized by the relative +fracture energy release rate at the crack tip based on the Paris law (Paris, 1961). +At interfaces of laminated composites the cyclic loading leads to interface strength degradation +causing fatigue delamination growth. The onset and growth of delamination are also characterized by +the relative fracture energy release rate at the crack tip based on the Paris law (Paris, 1961). +Both the progressive damage mechanism in the bulk material and the progressive delamination +growth mechanism at interfaces can be considered simultaneously, with the failure occurring first at the +weakest link in a model. +Defining a low-cycle fatigue analysis using the direct cyclic approach is similar to defining a direct +cyclic analysis. See “Direct cyclic analysis,” Section 6.2.6, for details on how to specify the number +of Fourier terms, number of iterations, and the increment sizes. You specify the maximum numbers of +cycles, +, when you define the low-cycle fatigue analysis step. +*DIRECT CYCLIC, FATIGUE +first data line +, , +Step module: Create Step: General: Direct cyclic; Fatigue: Include +low-cycle fatigue analysis, Maximum number of cycles: Value: +Abaqus/CAE Usage: +Input File Usage: +time +stabilized +plastic shakedown +Figure 6.2.7–2 Plastic shakedown in a direct cyclic analysis. +Determining whether to use the Fourier coefficients from the previous step +A low-cycle fatigue step using the direct cyclic approach can be the only step in an analysis, can follow a +general or linear perturbation step, or can be followed by a general or linear perturbation step. Multiple +low-cycle fatigue analysis steps can be included in a single analysis. In such a case the Fourier series +coefficients obtained in the previous step can be used as starting values in the current step. By default, +the Fourier coefficients are reset to zero, thus allowing application of cyclic loading conditions that are +very different from those defined in the previous low-cycle fatigue step. +As in a direct cyclic analysis, you can specify that a low-cycle fatigue step in a restart analysis +should use the Fourier coefficients from the previous step, thus allowing continuation of an analysis to +simulate more loading cycles. In a low-cycle fatigue analysis a restart file is written at the end of the +stabilized cycle. Consequently, a restart analysis that is a continuation of a previous low-cycle fatigue +analysis will start with a new loading cycle at +. +Input File Usage: +Use the following option to specify that the current step is a continuation of the +previous low-cycle fatigue step using the direct cyclic approach: +*DIRECT CYCLIC, FATIGUE, CONTINUE=YES +Use the following option to reset the Fourier series coefficients to zero: +*DIRECT CYCLIC, FATIGUE, CONTINUE=NO (default) +Use the following option to specify that the current step is a continuation of the +previous low-cycle fatigue step using the direct cyclic approach: +Abaqus/CAE Usage: +Step module: Create Step: General: Direct cyclic; Basic: Use +displacement Fourier coefficients from previous direct cyclic +step; Fatigue: Include low-cycle fatigue analysis +Use the following option to reset the Fourier series coefficients to zero: +Step module: Create Step: General: Direct cyclic; Fatigue: +Include low-cycle fatigue analysis +Progressive damage and damage extrapolation in bulk ductile material based on continuum +damage mechanics approach +Low-cycle fatigue analysis in Abaqus/Standard allows modeling of progressive damage and failure for +ductile materials in any elements whose response is defined in terms of a continuum-based constitutive +model (“Material library: overview,” Section 21.1.1). This includes cohesive elements modeled using a +continuum approach (“Modeling of an adhesive layer of finite thickness” in “Defining the constitutive +response of cohesive elements using a continuum approach,” Section 32.5.5). The inelastic definition +in a material point must be used in conjunction with the linear elastic material model (“Linear elastic +behavior,” Section 22.2.1), the porous elastic material model (“Elastic behavior of porous materials,” +Section 22.3.1), or the hypoelastic material model (“Hypoelastic behavior,” Section 22.4.1). +After damage initiation the elastic material stiffness is degraded progressively in each cycle (as +shown in Figure 6.2.7–1) based on the accumulated stabilized inelastic hysteresis energy. It is impractical +and computationally expensive to perform a cycle-by-cycle simulation for a low-cycle fatigue analysis; +Instead, to accelerate the low-cycle fatigue analysis, each increment extrapolates the current damaged +state in the bulk material forward over many cycles to a new damaged state after the current loading +cycle is stabilized. +Damage initiation and evolution +Damage initiation refers to the beginning of degradation of the response of a material point. +In a +low-cycle fatigue analysis the damage initiation criterion is characterized by the accumulated inelastic +hysteresis energy per cycle, +and material constants are used to determine the number of the +cycle in which damage is initiated, +, Abaqus/Standard +. At the end of a stabilized loading cycle, +checks to see if the damage initiation criterion +is satisfied in any material point; material +stiffness at a material point will not be degraded unless this criterion is satisfied. The calculations +and output associated with damage initiation are discussed in detail in “Damage initiation for ductile +materials in low-cycle fatigue,” Section 24.4.2. +. +Once the damage initiation criterion is satisfied at a material point, the damage state is calculated +and updated based on the inelastic hysteresis energy for the stabilized cycle. Abaqus/Standard assumes +that the degradation of the elastic stiffness can be modeled using the scalar damage variable, +. The +rate of the damage in a material point per cycle, +, is calculated based on the accumulated inelastic +hysteresis energy, the characteristic length associated with an integration point, and material constants. +For details, see “Damage evolution for ductile materials in low-cycle fatigue,” Section 24.4.3. +Typically, a material has completely lost its load carrying capacity when +. You can remove +an element from the mesh if all of the section points at all integration locations of the element have lost +their load carrying capability. +Damage extrapolation technique in the bulk material +If the damage initiation criterion is satisfied in any material point at the end of a stabilized cycle, +Abaqus/Standard extrapolates the damage variable +increment over a number of cycles, +, +from the current cycle forward to the next +, is given by +. The new damage state, +is the characteristic length associated with an integration point, and +are material +where +constants . +and +You specify the minimum ( +) number of cycles over which +) and maximum ( +the damage is extrapolated forward in any given increment. The default values are 100 and 1000, +respectively. +Input File Usage: +*DIRECT CYCLIC, FATIGUE +first data line +, +Abaqus/CAE Usage: +Step module: Create Step: General: Direct cyclic; Fatigue: +Include low-cycle fatigue analysis, Cycle increment size: +Minimum: +, Maximum: +Discrete crack propagation along an arbitrary path based on the principles of linear elastic +fracture mechanics with the extended finite element method +Low-cycle fatigue analysis in Abaqus/Standard allows the modeling of discrete crack growth along an +arbitrary path based on the principles of linear elastic fracture mechanics with the extended finite element +method. You complete the definition of the crack propagation capability by defining a fracture-based +surface behavior and specifying the fracture criterion in enriched elements. The fracture energy release +rates at the crack tips in enriched elements are calculated based on the modified virtual crack closure +technique (VCCT). VCCT uses the principles of linear elastic fracture mechanics. Therefore, VCCT +is appropriate for problems in which brittle fatigue crack growth occurs, although nonlinear material +deformations can occur somewhere else in the bulk materials. For more information about defining +fracture criteria and VCCT in enriched elements, see “Modeling discontinuities as an enriched feature +using the extended finite element method,” Section 10.7.1. +To accelerate the low-cycle fatigue analysis, the damage extrapolation technique is used, which +advances the crack by at least one element length after each stabilized cycle. +LOW-CYCLE FATIGUE ANALYSIS +; the other criterion is based on the maximum fracture energy release rate, +The onset and growth of fatigue crack at an enriched element are characterized by using the Paris law, +which relates the relative fracture energy release rate, +, to crack growth rates. Two criteria must be +met to initiate fatigue crack growth: one criterion is based on material constants, +, and the current +cycle number, +, which +corresponds to the cyclic energy release rate when the structure is loaded up to its maximum value. Once +the onset of fatigue crack growth criterion is satisfied at the enriched elements, the crack growth rate, +(the Paris law). The criteria for fatigue +crack onset and growth are discussed in detail in “Modeling discontinuities as an enriched feature using +the extended finite element method,” Section 10.7.1. +, is a piecewise function based on material constants and +Damage extrapolation technique +and +, Abaqus/Standard extends the crack length, +If the onset of crack growth criterion is satisfied at any crack tip in the enriched element at the end of a +stabilized cycle, +, from the current cycle forward over +a number of cycles, +by fracturing at least one enriched element ahead of the crack tips. +, to +Given the material constants +(as defined in “Modeling discontinuities as an enriched feature +using the extended finite element method,” Section 10.7.1), combined with the known element length and +likely propagation direction +at the enriched elements ahead of the crack tips, the +number of cycles necessary to fail each enriched element ahead of the crack tip can be calculated as +, +where +represents the enriched element ahead of the th crack tip. The analysis is set up to advance the +crack by at least one enriched element per increment after the loading cycle is stabilized. The element +with the fewest cycles is identified to be fractured, and its +is represented as the +number of cycles to grow the crack equal to its element length, +. The most +critical element is completely fractured with a zero constraint and a zero stiffness at the cracked surfaces +at the end of the stabilized cycle. As the enriched element is fractured, the load is redistributed, and a +new relative fracture energy release rate must be calculated for the enriched elements ahead of the crack +tips for the next cycle. This capability allows at least one enriched element ahead of the crack tips to +be fractured after each stabilized cycle and precisely accounts for the number of cycles needed to cause +fatigue crack growth over that length. +Progressive delamination growth along a pre-defined path at interfaces +Low-cycle fatigue analysis in Abaqus/Standard also allows the modeling of progressive delamination +growth at the interfaces in laminated composites. The interface along which the delamination (or crack) +propagates must be indicated in the model using a fracture criterion definition. The fracture energy +release rates at the crack tips in the interface elements are calculated based on the virtual crack closure +technique (VCCT). VCCT uses the principles of linear elastic fracture mechanics. Therefore, VCCT is +appropriate for problems in which brittle fatigue delamination growth occurs along predefined surfaces, +although nonlinear material deformations can occur in the bulk materials. For more information about +defining fracture criteria and VCCT, see “Crack propagation analysis,” Section 11.4.3. +To accelerate the low-cycle fatigue analysis, the damage extrapolation technique is used, which +releases at least one element length at the crack tip along the interface after each stabilized cycle. When +both brittle fatigue delamination at interfaces and ductile damage or discrete crack growth in bulk +materials are considered in an analysis, failure occurs first at the weakest link. +Onset and growth of fatigue delamination +, and the current cycle number, +The onset and growth of fatigue delamination at a defined crack interface are characterized by using +the Paris law, which relates the relative fracture energy release rate, +, to crack growth rates. Two +criteria must be met to initiate fatigue delamination growth: one criterion is based on material constants, +; the other criterion is based on the maximum fracture energy +release rate, +, which corresponds to the cyclic energy release rate when the structure is loaded up +to its maximum value. Once the onset of delamination growth criterion is satisfied at the interface, the +delamination growth rate, +(the Paris +law). The criteria for fatigue delamination onset and growth are discussed in detail in “Low-cycle fatigue +criterion” in “Crack propagation analysis,” Section 11.4.3. +, is a piecewise function based on material constants and +Damage extrapolation technique at the interface elements +, to +, Abaqus/Standard extends the crack length, +If the onset of delamination growth criterion is satisfied at any crack tip in the interface at the end of +a stabilized cycle, +, from the current cycle forward +over a number of cycles, +by releasing at least one element at the interface. Given the +material constants +(as defined in “Low-cycle fatigue criterion” in “Crack propagation analysis,” +and +Section 11.4.3), combined with the known node spacing +at the interface elements +at the crack tips, the number of cycles necessary to fail each interface element at the crack tip can be +calculated as +, where j represents the node at the jth crack tip. The analysis is set up to release +at least one interface element per increment after the loading cycle is stabilized. The element with the +fewest cycles is identified to be released, and its +is represented as the number of +cycles to grow the crack equal to its element length, +. The most critical element +is completely released with a zero constraint and a zero stiffness at the end of the stabilized cycle. As +the interface element is released, the load is redistributed, and a new relative fracture energy release rate +must be calculated for the interface elements at the crack tips for the next cycle. This capability allows +at least one interface element at the crack tips to be released after each stabilized cycle and precisely +accounts for the number of cycles needed to cause fatigue crack growth over that length. +Controlling the solution accuracy +Low-cycle fatigue analysis utilizes the direct cyclic approach to obtain the stabilized cyclic solution +iteratively by combining a Fourier series approximation with time integration of the nonlinear material +behavior using a modified Newton method. The accuracy of the algorithm depends on the number of +Fourier terms used, the number of iterations taken to obtain the stabilized solution, and the number of +time points within the load period at which the material response and residual vector are evaluated. Some +methods for controlling the solution accuracy in a direct cyclic analysis are described in detail in “Direct +cyclic analysis,” Section 6.2.6. They all remain valid in a low-cycle fatigue analysis using the direct +cyclic approach. In addition, the accuracy of a low-cycle fatigue analysis depends on the number of +cycles over which the damage is extrapolated forward, as described below. +Controlling the accuracy of damage extrapolation in the bulk material when using continuum +damage mechanics approach +To accelerate the low-cycle fatigue analysis, the damage extrapolation technique is used at the end of +a stabilized cycle. In addition to specifying the minimum and maximum number of cycles over which +the damage is extrapolated , you can +specify the damage extrapolation tolerance, +, to control the accuracy of damage extrapolation in +the bulk material. The default is +. +Input File Usage: +Use the following option to specify the damage extrapolation tolerance: +*DIRECT CYCLIC, FATIGUE +first data line +, , , +Abaqus/CAE Usage: +Step module: Create Step: General: Direct cyclic; Fatigue: Include +low-cycle fatigue analysis, Damage extrapolation tolerance: +Determining the increment over which damage is extrapolated forward +Abaqus/Standard uses an adaptive algorithm to determine the number of cycles over which the damage +is extrapolated forward in each increment. By default, Abaqus/Standard starts with 500 cycles (half of +the default value of maximum increment in number of cycles) and determines the maximum damage +increment at any material points based on +If the maximum damage increment, +, is greater than the damage extrapolation tolerance that you +specify, the number of cycles over which the damage is extrapolated forward is reduced accordingly +to ensure the maximum damage increment is less than the damage extrapolation tolerance. On the +other hand, if the maximum damage increment at all material points is less than half of the damage +extrapolation tolerance that you specify, the number of cycles is increased accordingly to ensure the +maximum damage increment is equal to the damage extrapolation tolerance. +Initial conditions +Initial values of stresses, temperatures, field variables, solution-dependent state variables, etc. can be +specified . +Boundary conditions +Boundary conditions can be applied to any of the displacement or rotation degrees of freedom. During +the analysis, prescribed boundary conditions must have an amplitude definition that is cyclic over the +step: the start value must be equal to the end value . If the +analysis consists of several steps, the usual rules apply . At each new step the boundary condition can either be modified +or completely defined. All boundary conditions defined in previous steps remain unchanged unless they +are redefined. +Loads +The following loads can be prescribed in a low-cycle fatigue analysis using the direct cyclic approach: +• Concentrated nodal forces can be applied to the displacement degrees of freedom (1–6); see +“Concentrated loads,” Section 33.4.2. +• Distributed pressure forces or body forces can be applied; see “Distributed loads,” Section 33.4.3. +The distributed load types available with particular elements are described in Part VI, “Elements.” +During the analysis each load must have an amplitude definition that is cyclic over the step where the start +value must be equal to the end value . If the analysis consists +of several steps, the usual rules apply . At each new +step the loading can either be modified or completely defined. All loads defined in previous steps remain +unchanged unless they are redefined. +Predefined fields +The following predefined fields can be specified in a low-cycle fatigue analysis using the direct cyclic +approach, as described in “Predefined fields,” Section 33.6.1: +• Temperature is not a degree of freedom in a low-cycle fatigue analysis using the direct cyclic +approach, but nodal temperatures can be specified as a predefined field. The temperature values +specified must be cyclic over the step: +the start value must be equal to the end value . If the temperatures are read from the results file, you should +specify initial temperature conditions equal to the temperature values at the end of the step . Alternatively, +you can ramp the temperatures back to their initial condition values, as described in “Predefined +fields,” Section 33.6.1. Any difference between the applied and initial temperatures will cause +thermal strain if a thermal expansion coefficient is given for the material (“Thermal expansion,” +Section 26.1.2). The specified temperature also affects temperature-dependent material properties, +if any. +• The values of user-defined field variables can be specified. These values affect only field-variable- +dependent material properties, if any. The field variable values specified must be cyclic over the +step. +Material options +Most ductile material models that describe mechanical behavior are available for use in a low-cycle +fatigue analysis. The inelastic definition in a material point must be used in conjunction with the linear +elastic material model (“Linear elastic behavior,” Section 22.2.1), the porous elastic material model +(“Elastic behavior of porous materials,” Section 22.3.1), or the hypoelastic material model (“Hypoelastic +behavior,” Section 22.4.1). +The following material properties are not active during a low-cycle fatigue analysis: acoustic +properties, thermal properties (except for thermal expansion), mass diffusion properties, electrical +conductivity properties, piezoeletric properties, and pore fluid flow properties. +(“Rate-dependent +creep +23.2.3), +creep and swelling,” Section 23.2.4), and two-layer viscoplasticity +yield +(“Rate-dependent plasticity: +(“Two-layer viscoplasticity,” Section 23.2.11) can also be used during a low-cycle fatigue analysis. +yield,” Section +Rate-dependent +rate-dependent +Elements +Any of the stress/displacement elements in Abaqus/Standard can be used in a low-cycle fatigue analysis +. This includes cohesive +elements with finite thickness (“Modeling of an adhesive layer of finite thickness” in “Defining the +constitutive response of cohesive elements using a continuum approach,” Section 32.5.5). However, +when modeling fatigue crack growth based on the principles of linear elastic fracture mechanics with the +extended finite element method, only first-order continuum stress/displacement elements and second- +order stress/displacement tetrahedron elements can be associated with an enriched feature . +Output +Different types of output are available for postprocessing and for monitoring a low-cycle fatigue analysis +using the direct cyclic approach. +Message file information +As in a direct cyclic analysis, +low-cycle fatigue analysis using the direct cyclic approach in +Abaqus/Standard prints the residual force, time average force, and a flag to indicate if equilibrium was +satisfied in the message (.msg) file at different time increments for each iteration in each loading cycle. +You can control the frequency in increments at which information is printed to the message file, and you +can suppress the output; the default is to print output every 10 increments . +Abaqus/Standard also prints the number of Fourier terms used, the maximum residual coefficient, +the maximum correction to displacement coefficients, and the maximum displacement coefficient in the +Fourier series in the message file at the end of each iteration in each cycle. An example of the output is +shown below: +INC +10 +20 +30 +TIME +INC +0.250 +0.250 +0.250 +CYCLE +5 STARTS +ITERATION +STEP +TIME +2.50 +5.00 +7.50 +26 STARTS +LARG. RESI. +FORCE +1.008E+01 +1.622E+01 +4.622E-02 +6.2.7–11 +TIME AVG. +FORCE +50.9 +76.8 +99.8 +FORCE +EQUV. +ITERATION +26 SUMMARY +NUMBER OF FOURIER TERMS USED 40, TOTAL NUMBER OF INCREMENTS +CYCLE/STEP TIME +AVERAGE FORCE +TOTAL TIME COMPLETED +TIME AVG. FORCE +30.0, +21.2 +31.0 +25.7 +120 +AT NODE 24 DOF 2 +MAX. COEFFICIENT OF DISP. +AT NODE 44 DOF 1 +MAX. COEFF. OF RESI. FORCE ON CONST. TERM +6 DOF 3 +AT NODE +MAX. COEFF. OF RESI. FORCE ON PERI. TERMS +MAX. CORR. TO COEFF. OF DISP. ON CONST. TERM 0.002 AT NODE 50 DOF 3 +MAX. CORR. TO COEFF. OF DISP. ON PERI. TERMS 0.015 AT NODE 50 DOF 3 +0.142 +31.7 +0.82 +Results output +Element and nodal output are written only when the stabilized cycle is reached. If a stabilized cycle has +not been reached at the end of a cycle, output is written for the last iteration of the cycle. All standard +output variables in Abaqus/Standard (“Abaqus/Standard output variable identifiers,” Section 4.2.1) are +In addition, the following variables are available for progressive damage in bulk ductile +available. +material based on the continuum damage mechanics approach: +STATUS +SDEG +CYCLEINI +Status of element (the status of an element is 1.0 if the element is active, 0.0 if the +element is not). +Scalar stiffness degradation, D. +Number of cycles to initialize the damage at the material point. +The following variables are available for discrete crack propagation along an arbitrary path based +on the principles of linear elastic fracture mechanics with the extended finite element method: +STATUSXFEM Status of the enriched element. (The status of an enriched element is 1.0 if the +element is completely cracked, 0.0 if the element is not. If the element is partially +cracked, the value lies between 1.0 and 0.0.) +CYCLEINIXFEM Number of cycles to initialize the crack at the enriched element. +ENRRTXFEM +All components of strain energy release rate range; i.e., the difference between the +energy release rate at the maximum loading and at the minimum loading. +Recovering additional results for a stabilized cycle +You may want to recover additional results for a stabilized cycle. You can extract these results from the +restart data . +Input File Usage: +Abaqus/CAE Usage: +*POST OUTPUT, CYCLE=n +Recovering additional results for a stabilized cycle is not supported in +Abaqus/CAE. +Specifying output at exact times +Output at exact times is not supported for low-cycle fatigue analysis. If output at exact times is requested, +Abaqus will issue a warning message and change the output to an output at approximate times. +Limitations +A low-cycle fatigue analysis using the direct cyclic approach is subject to the following limitations: +• Contact conditions cannot change during a given cycle when direct cyclic analysis is used iteratively +to obtain a stabilized solution. +• Geometric nonlinearity can be included only in any general step prior to a direct cyclic step; +however, only small displacements and strains will be considered during the cyclic step. +Input file template +The following is an example of modeling progressive damage and failure in the bulk material based on +the continuum damage mechanics approach and progressive delamination growth at the interface: +*HEADING +… +*BOUNDARY +Data lines to specify zero-valued boundary conditions +*INITIAL CONDITIONS +Data lines to specify initial conditions +*AMPLITUDE +Data lines to define amplitude variations +** +*MATERIAL +Options to define material properties +*DAMAGE INITIATION, CRITERION=HYSTERESIS ENERGY +Data lines to define material constants for bulk ductile material damage initiation +*DAMAGE EVOLUTION, TYPE=HYSTERESIS ENERGY +Data lines to define material constants for bulk ductile material damage evolution +** +*SURFACE, NAME=slave +Data lines to define slave surface at delamination interface +*SURFACE, NAME=master +Data lines to define master surface at delamination interface +*CONTACT PAIR +slave, master +** +*STEP (,INC=) +Set INC equal to the maximum number of increments in a single loading cycle +*DIRECT CYCLIC, FATIGUE +Data line to define time increment, cycle time, initial number of Fourier terms, +maximum number of Fourier terms, increment in number of Fourier terms, +and maximum number of iterations +Data line to define minimum increment in number of cycles, +maximum increment in number of cycles, total number of cycles, +and damage extrapolation tolerance +*DEBOND, SLAVE=slave, MASTER=master +*FRACTURE CRITERION, TYPE=FATIGUE +Data lines to define material constants used in Paris law and fracture criterion +** +*BOUNDARY, AMPLITUDE= +Data lines to prescribe zero-valued or nonzero boundary conditions +*CLOAD and/or *DLOAD, AMPLITUDE= +Data lines to specify loads +*TEMPERATURE and/or *FIELD, AMPLITUDE= +Data lines to specify values of predefined fields +** +*END STEP +The following is an example of modeling discrete crack growth in the bulk material based on the +principles of linear elastic fracture mechanics with the extended finite element method and progressive +delamination growth at the interface: +*HEADING +… +*ENRICHMENT, TYPE=PROPAGATION CRACK, INTERACTION=INTERACTION, +ELSET=ENRICHED +*BOUNDARY +Data lines to specify zero-valued boundary conditions +*INITIAL CONDITIONS +Data lines to specify initial conditions +*AMPLITUDE +Data lines to define amplitude variations +** +*MATERIAL +Options to define material properties +*SURFACE, INTERACTION=INTERACTION +*SURFACE BEHAVIOR +*FRACTURE CRITERION, TYPE=FATIGUE +Data lines to define material constants used in the Paris law and fracture criterion in the bulk +material for enriched elements +** +*SURFACE, NAME=slave +Data lines to define slave surface at delamination interface +*SURFACE, NAME=master +Data lines to define master surface at delamination interface +*CONTACT PAIR +slave, master +** +*STEP (,INC=) +Set INC equal to the maximum number of increments in a single loading cycle +*DIRECT CYCLIC, FATIGUE +Data line to define time increment, cycle time, initial number of Fourier terms, +maximum number of Fourier terms, increment in number of Fourier terms, +and maximum number of iterations +Data line to define minimum increment in number of cycles, +maximum increment in number of cycles, total number of cycles, +and damage extrapolation tolerance +*DEBOND, SLAVE=slave, MASTER=master +*FRACTURE CRITERION, TYPE=FATIGUE +Data lines to define material constants used in the Paris law and fracture criterion at the interface +** +*BOUNDARY, AMPLITUDE= +Data lines to prescribe zero-valued or nonzero boundary conditions +*CLOAD and/or *DLOAD, AMPLITUDE= +Data lines to specify loads +*TEMPERATURE and/or *FIELD, AMPLITUDE= +Data lines to specify values of predefined fields +** +*END STEP +Additional references +• Coffin, L., “A Study of the Effects of Cyclic Thermal Stresses on a Ductile Metal,” Transactions of +the American Society of Mechanical Engineering, vol. 76, pp. 931–951, 1954. +• Manson, S., “Behavior of Materials under Condition of Thermal Stress,” Heat Transfer Symposium, +University of Michigan Engineering Research Institute, Ann Arbor, MI, pp. 9–75, 1953. +• Paris, P., M. Gomaz, and W. Anderson, “A Rational Analytic Theory of Fatigue,” The Trend in +Engineering, vol. 15, 1961. +6.3 +Dynamic stress/displacement analysis +• “Dynamic analysis procedures: overview,” Section 6.3.1 +• “Implicit dynamic analysis using direct integration,” Section 6.3.2 +• “Explicit dynamic analysis,” Section 6.3.3 +• “Direct-solution steady-state dynamic analysis,” Section 6.3.4 +• “Natural frequency extraction,” Section 6.3.5 +• “Complex eigenvalue extraction,” Section 6.3.6 +• “Transient modal dynamic analysis,” Section 6.3.7 +• “Mode-based steady-state dynamic analysis,” Section 6.3.8 +• “Subspace-based steady-state dynamic analysis,” Section 6.3.9 +• “Response spectrum analysis,” Section 6.3.10 +• “Random response analysis,” Section 6.3.11 +6.3.1 +DYNAMIC ANALYSIS PROCEDURES: OVERVIEW +Overview +Abaqus offers several methods for performing dynamic analysis of problems in which inertia effects +are considered. Direct integration of the system must be used when nonlinear dynamic response is being +studied. Implicit direct integration is provided in Abaqus/Standard; explicit direct integration is provided +in Abaqus/Explicit. Modal methods are usually chosen for linear analyses because in direct-integration +dynamics the global equations of motion of the system must be integrated through time, which makes +direct-integration methods significantly more expensive than modal methods. Subspace-based methods +are provided in Abaqus/Standard and offer cost-effective approaches to the analysis of systems that are +mildly nonlinear. +In Abaqus/Standard dynamic studies of linear problems are generally performed by using the +eigenmodes of the system as a basis for calculating the response. In such cases the necessary modes and +frequencies are calculated first in a frequency extraction step. The mode-based procedures are generally +simple to use; and the dynamic response analysis itself is usually not expensive computationally, +although the eigenmode extraction can become computationally intensive if many modes are required +for a large model. The eigenvalues can be extracted in a prestressed system with the “stress stiffening” +effect included (the initial stress matrix is included if the base state step definition included nonlinear +geometric effects), which may be necessary in the dynamic study of preloaded systems. +It is not +possible to prescribe nonzero displacements and rotations directly in mode-based procedures. The +method for prescribing motion in mode-based procedures is explained in “Base motions in modal-based +procedures,” Section 2.5.9 of the Abaqus Theory Manual. +Density must be defined for all materials used in any dynamic analysis, and damping (both viscous +and structural) can be specified either at the material or step level, as described below in “Damping in +dynamic analysis.” +Implicit versus explicit dynamics +The direct-integration dynamic procedure provided in Abaqus/Standard offers a choice of implicit +operators for integration of the equations of motion, while Abaqus/Explicit uses the central-difference +operator. In an implicit dynamic analysis the integration operator matrix must be inverted and a set of +nonlinear equilibrium equations must be solved at each time increment. In an explicit dynamic analysis +displacements and velocities are calculated in terms of quantities that are known at the beginning +of an increment; therefore, the global mass and stiffness matrices need not be formed and inverted, +which means that each increment is relatively inexpensive compared to the increments in an implicit +integration scheme. The size of the time increment in an explicit dynamic analysis is limited, however, +because the central-difference operator is only conditionally stable; whereas the implicit operator +options available in Abaqus/Standard are unconditionally stable and, thus, there is no such limit on the +size of the time increment that can be used for most analyses in Abaqus/Standard (accuracy governs +the time increment in Abaqus/Standard). +The stability limit for the central-difference method (the largest time increment that can be taken +without the method generating large, rapidly growing errors) is closely related to the time required for a +stress wave to cross the smallest element dimension in the model; thus, the time increment in an explicit +dynamic analysis can be very short if the mesh contains small elements or if the stress wave speed in the +material is very high. The method is, therefore, computationally attractive for problems in which the total +dynamic response time that must be modeled is only a few orders of magnitude longer than this stability +limit; for example, wave propagation studies or some “event and response” applications. Many of the +advantages of the explicit procedure also apply to slower (quasi-static) processes for cases in which it is +appropriate to use mass scaling to reduce the wave speed . +Abaqus/Explicit offers fewer element types than Abaqus/Standard. For example, only first-order, +displacement method elements (4-node quadrilaterals, 8-node bricks, etc.) and modified second-order +elements are used, and each degree of freedom in the model must have mass or rotary inertia associated +with it. However, the method provided in Abaqus/Explicit has some important advantages: +1. The analysis cost rises only linearly with problem size, whereas the cost of solving the nonlinear +equations associated with implicit integration rises more rapidly than linearly with problem size. +Therefore, Abaqus/Explicit is attractive for very large problems. +2. The explicit integration method is often more efficient than the implicit integration method for +solving extremely discontinuous short-term events or processes. +3. Problems involving stress wave propagation can be far more efficient computationally in +Abaqus/Explicit than in Abaqus/Standard. +In choosing an approach to a nonlinear dynamic problem you must consider the length of time for which +the response is sought compared to the stability limit of the explicit method; the size of the problem; and +the restriction of the explicit method to first-order, pure displacement method or modified second-order +elements. In some cases the choice is obvious, but in many problems of practical interest the choice +depends on details of the specific case. Experience is then the only useful guide. +Direct-solution versus modal superposition procedures +Direct solution procedures must be used for dynamic analyses that involve a nonlinear response. Modal +superposition procedures are a cost-effective option for performing linear or mildly nonlinear dynamic +analyses. +Direct-solution dynamic analysis procedures +The following direct-solution dynamic analyses procedures are available in Abaqus: +• Implicit dynamic analysis: +Implicit direct-integration dynamic analysis (“Implicit dynamic +analysis using direct integration,” Section 6.3.2) is used to study (strongly) nonlinear transient +dynamic response in Abaqus/Standard. +• Subspace-based explicit dynamic analysis: The +subspace projection method in +integration of the dynamic equations of equilibrium +Abaqus/Standard uses direct, explicit +written in terms of a vector space spanned by a number of eigenvectors (“Implicit dynamic analysis +using direct integration,” Section 6.3.2). The eigenmodes of the system extracted in a frequency +extraction step are used as the global basis vectors. This method can be very effective for systems +with mild nonlinearities that do not substantially change the mode shapes. It cannot be used in +contact analyses. +• Explicit dynamic analysis: Explicit direct-integration dynamic analysis (“Explicit dynamic +analysis,” Section 6.3.3) is available in Abaqus/Explicit. +• Direct-solution steady-state harmonic response analysis: The steady-state harmonic +response of a system can be calculated in Abaqus/Standard directly in terms of the physical +degrees of freedom of the model (“Direct-solution steady-state dynamic analysis,” Section 6.3.4). +The solution is given as in-phase (real) and out-of-phase (imaginary) components of the solution +variables (displacement, stress, etc.) as functions of frequency. The main advantage of this method +is that frequency-dependent effects (such as frequency-dependent damping) can be modeled. The +direct method is the most accurate but also the most expensive steady-state harmonic response +procedure. The direct method can also be used if nonsymmetric terms in the stiffness are important +or if model parameters depend on frequency. +Modal superposition procedures +Abaqus includes a full range of modal superposition procedures. Modal superposition procedures can be +run using a high-performance linear dynamics software architecture called SIM. The SIM architecture +offers advantages over the traditional linear dynamics architecture for some large-scale analyses, as +discussed below in “Using the SIM architecture for modal superposition dynamic analyses.” +Prior to any modal superposition procedure, the natural frequencies of a system must be extracted +using the eigenvalue analysis procedure (“Natural frequency extraction,” Section 6.3.5). Frequency +extraction can be performed using the SIM architecture. +The following modal superposition procedures are available in Abaqus: +• Mode-based steady-state harmonic response analysis: A steady-state dynamic analysis +based on the natural modes of the system can be used to calculate a system’s linearized response to +harmonic excitation (“Mode-based steady-state dynamic analysis,” Section 6.3.8). This mode-based +method is typically less expensive than the direct method. The solution is given as in-phase (real) +and out-of-phase (imaginary) components of the solution variables (displacement, stress, etc.) as +functions of frequency. Mode-based steady-state harmonic analysis can be performed using the +SIM architecture. +• Subspace-based +of +Abaqus/Standard analysis the steady-state dynamic equations are written in terms of a vector +space spanned by a number of eigenvectors (“Subspace-based steady-state dynamic analysis,” +Section 6.3.9). The eigenmodes of the system extracted in a frequency extraction step are used as +the global basis vectors. The method is attractive because it allows frequency-dependent effects to +be modeled and is much cheaper than the direct analysis method (“Direct-solution steady-state +dynamic analysis,” Section 6.3.4). Subspace-based steady-state harmonic response analysis can be +used if the stiffness is nonsymmetric and can be performed using the SIM architecture. +steady-state +harmonic +response +analysis: +type +this +In +• Mode-based transient response analysis: The modal dynamic procedure (“Transient modal +dynamic analysis,” Section 6.3.7) provides transient response for linear problems using modal +superposition. Mode-based transient analysis can be performed using the SIM architecture. +• Response spectrum analysis: A linear response spectrum analysis (“Response spectrum +analysis,” Section 6.3.10) is often used to obtain an approximate upper bound of the peak significant +response of a system to a user-supplied input spectrum (such as earthquake data) as a function of +frequency. The method has a very low computational cost and provides useful information about +the spectral behavior of a system. Response spectrum analysis can be performed using the SIM +architecture. +• Random response analysis: The linearized response of a model to random excitation can be +calculated based on the natural modes of the system (“Random response analysis,” Section 6.3.11). +This procedure is used when the structure is excited continuously and the loading can be expressed +statistically in terms of a “Power Spectral Density” (PSD) function. The response is calculated in +terms of statistical quantities such as the mean value and the standard deviation of nodal and element +variables. Random response analysis can be performed using the SIM architecture. +• Complex eigenvalue extraction: The complex eigenvalue extraction procedure performs +eigenvalue extraction to calculate the complex eigenvalues and the corresponding complex mode +shapes of a system (“Complex eigenvalue extraction,” Section 6.3.6). The eigenmodes of the +system extracted in a frequency extraction step are used as the global basis vectors. The complex +eigenvalue extraction can be performed using the SIM architecture. +Using the SIM architecture for modal superposition dynamic analyses +SIM is a high-performance software architecture available in Abaqus that can be used to perform modal +superposition dynamic analyses. The SIM architecture is much more efficient than the traditional +architecture for large-scale linear dynamic analyses (both model size and number of modes) with +minimal output requests. +SIM-based analyses can be used to efficiently handle nondiagonal damping generated from element +or material contributions, as discussed below in “Damping in a mode-based steady-state and transient +linear dynamic analysis using the SIM architecture.” Therefore, SIM-based procedures are an efficient +alternative to subspace-based linear dynamic procedures for models with element damping or frequency- +independent materials. +Activating the SIM architecture +To use the SIM architecture for a modal superposition dynamic analysis, activate SIM for the initial +frequency extraction procedure. SIM-based frequency extraction procedures write the mode shapes and +other modal system information to a special linear dynamics data (.sim) file. By default, this data file +is written to the scratch directory and deleted upon job completion; however, if restart is requested, the +file is saved in the user directory. All subsequent mode-based steady-state or transient dynamic steps in +an analysis automatically use this linear dynamics data file (and by extension the SIM architecture). If +you restart an analysis that uses the SIM architecture, you must include the linear dynamics data file. +For more information about frequency extraction procedures, see “Natural frequency extraction,” +Section 6.3.5. +Input File Usage: +*FREQUENCY, SIM +Abaqus/CAE Usage: +Step module: Step→Create: Frequency: Use SIM-based +linear dynamics procedures +Example +The SIM architecture will be used for the entire linear dynamic analysis in the following input file +template: +*STEP +*FREQUENCY, EIGENSOLVER=LANCZOS or AMS, SIM +Data line to control eigenvalue extraction +*END STEP +** +*STEP +*MODAL DYNAMIC +Data line to control time incrementation +*SELECT EIGENMODES +Data lines to define the applicable mode ranges +*END STEP +** +*STEP +*STEADY STATE DYNAMICS +Data lines to specify frequency ranges and bias parameters +*SELECT EIGENMODES +Data lines to define the applicable mode ranges +*END STEP +** +*STEP +*STEADY STATE DYNAMICS, SUBSPACE PROJECTION +Data lines to specify frequency ranges and bias parameters +*SELECT EIGENMODES +Data lines to define the applicable mode ranges +*END STEP +Output in a SIM-based analysis +Output is a fundamental factor in the performance of a linear dynamic analysis. Since it is difficult to +predict the desired output quantities for a linear dynamic analysis, no output is written to the output +database (.odb) file by default during a SIM-based linear dynamic analysis; output requests must be +requested explicitly. Preselected output requests are ignored in SIM-based dynamic analysis procedures. +There are several restrictions on available output requests that apply specifically to SIM-based +analyses: +• You cannot request output to the results (.fil) file. +• Element variables cannot be output to the printed data (.dat) file except for random response +analysis. +• Output of “base motion” is not supported except for random response analysis. +Limitations of the SIM architecture +The SIM architecture cannot be used with frequency extractions using the subspace iteration eigensolver. +Fully coupled structural-acoustic frequency extractions cannot be performed using the +SIM architecture. However, projected coupling operators can be used to perform fully coupled +structural-acoustic steady-state response analyses . +The cyclic symmetry modeling feature cannot be used in SIM-based analyses. +Nonphysical material properties in dynamic analyses +Abaqus relies on user-supplied model data and assumes that the material’s physical properties reflect +experimental results. Examples of meaningful material properties are a positive mass density per volume, +a positive Young’s modulus, and a positive value for any available damping coefficients. However, in +special cases you may want to “adjust” a value of density, mass, stiffness, or damping in a region or +a part of the model to bring the overall mass, stiffness, or damping to the expected required levels. +Certain material options in Abaqus allow you to introduce nonphysical material properties to achieve +this adjustment. +For example, to adjust the mass of the model, you can define a nonstructural mass with a negative +mass value, use mass elements with a negative mass over a region of nodes, or introduce additional +elements with negative density. Similarly, to adjust damping levels, you can use negative damping +coefficients or introduce dashpot elements with a negative dashpot constant to reduce the overall damping +levels. Springs with negative stiffness can be defined to adjust the model stiffness. +If you specify nonphysical but allowed material properties, Abaqus issues a warning message. +However, if you specify nonphysical material properties that are not allowed, Abaqus issues an error +message. When introducing nonphysical material properties, you must be aware that the overall +behavior should be “physical”; for example, the mass values at all nodes must be positive in an +eigenvalue extraction procedure. +There are consequences of using nonphysical material properties that are easy to check and interpret, +and there are others beyond the control of Abaqus. Therefore, you should fully understand the stated +problem and the consequences of using nonphysical material properties before you specify the properties. +This is particularly important in Abaqus/Explicit analyses, where the size of the time increment depends +on material properties. For example, distributed mass-dependent loads are calculated based on the overall +mass density (positive and negative) provided. +Damping in dynamic analysis +Every nonconservative system exhibits some energy loss that is attributed to material nonlinearity, +internal material friction, or to external (mostly joint) frictional behavior. Conventional engineering +materials like steel and high strength aluminum alloys provide small amounts of internal material +damping, not enough to prevent large amplification at or near resonant frequencies. Damping properties +increase in modern composite fiber-reinforced materials, where the energy loss occurs through plastic or +viscoelastic phenomena as well as from friction at the interfaces between the matrix and reinforcement. +Still larger material damping is exhibited by thermoplastics. Mechanical dampers may be added to +models to introduce damping forces to the system. In general, it is difficult to quantify the source of a +system’s damping. It usually comes from several sources simultaneously; e.g., from energy loss during +hysteretic loading, viscoelastic material properties, and external joint friction. +Users that work with a specific system know the source of the energy loss from experience. A +variety of methods are available in Abaqus to specify damping that accurately models the energy loss in +a dynamic system. +Sources of damping +Abaqus has four categories of damping sources: material and element damping, global damping, modal +damping, and damping associated with time integration. If necessary, you can include multiple damping +sources and combine different damping sources in a model. +Material and element damping +Damping may be specified as part of a material definition that is assigned to a model . +In addition, Abaqus has elements such as dashpots, springs with their +complex stiffness matrix, and connectors that serve as dampers, all with viscous and structural damping +factors. Viscous damping can be included in mass, beam, pipe, and shell elements with general +section properties; and it can also be used in substructure elements . +In direct steady-state dynamic analysis you can define the viscous and structural +damping due to the interaction between the contacting surfaces by using user subroutine UINTER . Contact damping is +not applicable for linear perturbation procedures. +In acoustic elements, velocity proportional viscous damping is implemented using the volumetric +drag parameter . Acoustic infinite elements and impedance +conditions also add damping to a model. +Global damping +In situations where material or element damping is not appropriate or sufficient, you can apply abstract +damping factors to an entire model. Abaqus allows you to specify global damping factors for both viscous +(Rayleigh damping) and structural damping (imaginary stiffness matrix). +Modal damping +Modal damping applies only to mode-based linear dynamic analyses. This technique allows you to apply +damping directly to the modes of the system. By definition, modal damping contributes only diagonal +entries to the modal system of equations and can be defined several different ways. +Damping associated with time integration +Marching through a simulation with a finite time increment size causes some damping. This type of +damping applies only to analyses using direct time integration. See “Implicit dynamic analysis using +direct integration,” Section 6.3.2, for further discussion of this source of damping. +Damping in a linear dynamic analysis +Damping can be applied to a linear dynamic system in two forms: +• velocity proportional viscous damping; and +• displacement proportional structural damping, which is for use in frequency domain dynamics. +The exception is SIM-based transient modal dynamic analysis, where the structural damping is +converted to the equivalent diagonal viscous damping . +An additional type of damping known as composite damping serves as a means to calculate a model +average critical damping with the material density as the weight factor and is intended for use in mode- +based dynamics (excluding subspace projection steady-state analysis and SIM-based dynamic analyses). +For additional information, see “Damping options for modal dynamics,” Section 2.5.4 of the Abaqus +Theory Manual. +The types of damping available for linear dynamic analyses depend on the procedure type +and the architecture (traditional or SIM) used to perform the analysis, as outlined in Table 6.3.1–1 +and Table 6.3.1–2. For completeness, Table 6.3.1–1 also includes the damping options for a direct +steady-state dynamic analysis. In addition to directly specified modal damping, global damping can be +used in all linear dynamic procedures. Material and element damping can be used in subspace-based +and SIM-based linear dynamic procedures. +Table 6.3.1–1 Damping sources for traditional architecture. +Damping Source +Modal +Global +Material and Element +6.3.1–8 +Traditional Architecture +Mode-based steady-state dynamics +Subspace-based steady-state dynamics +Transient modal dynamics +Random response analysis +Complex frequency +Response spectrum +Table 6.3.1–2 Damping sources for SIM architecture. +SIM Architecture +Damping Source +Modal +Global +Material and Element +Mode-based steady-state dynamics +Subspace-based steady-state dynamics +Transient modal dynamics +Random response analysis +Complex frequency +Response spectrum +In a subspace-based or SIM-based linear dynamic analysis, material and element damping operators +must first be projected onto the basis of mode shapes. This projection results in a full modal damping +matrix for both viscous and structural damping; therefore, a modal steady-state response analysis requires +the solution of a system of linear equations at each frequency point. The size of this system is equal to +the number of modes used in the response calculation. In a mode-based transient analysis, the projected +damping operator is treated explicitly in time by including it on the right-hand side of the system of +equations. +Frequency-dependent damping is supported only for the subspace-based and direct-integration +steady-state dynamic procedures. +Material and element damping is not supported for the response spectrum or the random response +procedures. In these procedures, only modal and global damping are allowed, and material or element +damping is ignored. +Damping in a mode-based steady-state and transient linear dynamic analysis using the SIM architecture +SIM-based linear dynamic analyses may include material and element damping contributions that +introduce both diagonal and nondiagonal terms in the modal system of equations. The projection of +material and element damping operators onto the basis of mode shapes is performed during the natural +frequency extraction procedure, which enables a high-performance projection operation to be performed +when used with the AMS eigensolver. +If the damping operators depend on frequency, they will be +evaluated at the frequency specified for property evaluation during the frequency extraction procedure. +When the structural and viscous damping operators are projected onto the mode shapes, the full +modal damping matrix is stored in the linear dynamics data (.sim) file. The full modal damping matrix +is combined with any diagonal contributions from global damping or traditional modal damping. The +combined damping operator matrix is included in subsequent mode-based transient or steady-state +dynamics steps. If there are nondiagonal (i.e., projected) damping contributions and a large number of +modes are included, performance of the linear dynamics calculations will be impacted since a direct +solve must be performed at each frequency point. +Acoustic damping due to impedance conditions is projected onto the subspace of acoustic +eigenvectors. These contributions are taken into account in a subspace-based steady-state dynamics +analysis that uses the SIM architecture. +The default behavior for a SIM-based frequency extraction step is to project any element and +material damping onto the mode shapes. You can turn off this damping projection if it is not desired; +however, in this case only diagonal damping is available for subsequent modal superposition steps. +If the projected damping matrices are not desired in a particular mode-based linear dynamic step +for performance reasons, they can be deactivated in that step using the damping control techniques +discussed above in “Damping in dynamic analysis.” +Input File Usage: +Use the following option to project material and element damping operators in +a SIM-based analysis: +Abaqus/CAE Usage: +*FREQUENCY, SIM, DAMPING PROJECTION=ON (default) +Use the following option to turn off damping projection in a SIM-based +analysis: +*FREQUENCY, SIM, DAMPING PROJECTION=OFF +To control the projection of element and material damping in a SIM-based +frequency extraction step that uses the Lanczos eigensolver: +Step module: Step→Create: Frequency: Eigensolver: Lanczos, +Use SIM-based linear dynamics procedures, toggle Project +damping operators +To control the projection of element and material damping in a frequency +extraction step that uses the AMS eigensolver: +Step module: Step→Create: Frequency: Eigensolver: AMS, +toggle Project damping operators +Defining viscous damping +Abaqus allows you to choose a particular source of viscous damping, to add several sources, or to exclude +viscous damping effects. +Defining material/element viscous damping +You can choose to model the viscous damping matrix, +, by using material damping properties +and/or damping elements (such as dashpot or mass elements). The viscous, mass, and/or stiffness +proportional damping matrix will include the material Rayleigh damping factors, +, as +well as the element-oriented damping factor, +(e.g., for mass elements). The material/element-based +viscous damping matrix can be written as +and +where +procedures projection of +Input File Usage: +Abaqus/CAE Usage: +represents the viscous damping matrix for elements such as dashpots. In mode-based +into the eigenmodes results in a non-diagonal matrix. +, BETA= +Use the following option to specify material viscous damping for elements with +mechanical degrees of freedom: +*DAMPING, ALPHA= +Use the following option to specify material viscous damping for acoustic +elements: +*ACOUSTIC MEDIUM, VOLUMETRIC DRAG +Property module: material editor: Mechanical→Damping: +Alpha: +or Beta: +Property module: material editor: Other→Acoustic Medium: +Volumetric Drag +Defining global viscous damping +You can supply global mass and stiffness proportional viscous damping factors, +respectively, to create the global damping matrix using the global model mass and stiffness matrices, +and +, respectively: +and +, +These parameters can be specified for the entire model (default), for the mechanical degree of freedom +field (displacements and rotations) only, or for the acoustic field only. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to specify global viscous damping: +*GLOBAL DAMPING, ALPHA= +Global viscous damping is not supported in Abaqus/CAE. +, BETA= +Defining viscous modal damping +Rayleigh damping introduces a damping matrix, +, defined as +where +factors that you define. +is the mass matrix of the model, +is the stiffness matrix of the model, and +and +are +In Abaqus/Standard you can define +and +independently for each mode, so that the above equation +becomes +(no sum on M) +where the subscript M refers to the mode number and +stiffness terms associated with the Mth mode. +, +, and +are the damping, mass, and +Input File Usage: +Use the following option to define Rayleigh damping by specifying mode +numbers: +Abaqus/CAE Usage: +*MODAL DAMPING, RAYLEIGH, DEFINITION=MODE NUMBERS +Use the following option to define Rayleigh damping by specifying a frequency +range: +*MODAL DAMPING, RAYLEIGH, DEFINITION=FREQUENCY RANGE +Use the following input to define Rayleigh damping by specifying mode +numbers: +Step module: Create Step: Linear perturbation: any valid step +type: Damping: Specify damping over ranges of: Modes, +Rayleigh: Use Rayleigh damping data +Use the following input to define Rayleigh damping by specifying frequency +ranges: +Step module: Create Step: Linear perturbation: any valid step +type: Damping: Specify damping over ranges of: Frequencies, +Rayleigh: Use Rayleigh damping data +Defining viscous modal damping as a fraction of the critical damping +You can also specify the damping in each eigenmode in the model or for the specified frequency as a +fraction of the critical damping. Critical damping is defined as +where m is the mass of the system and k is the stiffness of the system. Typical values of the fraction +of critical damping, +; but Abaqus/Standard accepts any +positive value. The critical damping factors can be changed from step to step. +, are from 1% to 10% of critical damping, +Input File Usage: +Use the following option to define the fraction of critical damping by specifying +mode numbers: +*MODAL DAMPING, MODAL=DIRECT, +DEFINITION=MODE NUMBERS +Use the following option to define the fraction of critical damping by specifying +a frequency range: +*MODAL DAMPING, MODAL=DIRECT, +DEFINITION=FREQUENCY RANGE +Abaqus/CAE Usage: +Use the following input to define the fraction of critical damping by specifying +mode numbers: +Step module: Create Step: Linear perturbation: any valid step +type: Damping: Specify damping over ranges of: Modes, +Direct modal: Use direct damping data +Use the following input to define the fraction of critical damping by specifying +frequency ranges: +Step module: Create Step: Linear perturbation: any valid step +type: Damping: Specify damping over ranges of: Frequencies, +Direct modal: Use direct damping data +Viscous modal damping for uncoupled structural-acoustic frequency extractions +For uncoupled structural-acoustic frequency extractions performed using the AMS eigensolver, you can +apply different damping to the structural and acoustic modes. This technique can be used only when +damping is specified for a range of frequencies. +Input File Usage: +Use the following option to apply the specified damping to only the structural +modes: +*MODAL DAMPING, MODAL=DIRECT, +DEFINITION=FREQUENCY RANGE, FIELD=MECHANICAL +Use the following option to apply the specified damping to only the acoustic +modes: +*MODAL DAMPING, MODAL=DIRECT, +DEFINITION=FREQUENCY RANGE, FIELD=ACOUSTIC +Use the following option to apply the specified damping to both structural and +acoustic modes (default): +*MODAL DAMPING, MODAL=DIRECT, +DEFINITION=FREQUENCY RANGE, FIELD=ALL +Abaqus/CAE Usage: +The ability to specify different damping for structural and acoustic modes is not +supported in Abaqus/CAE. +Controlling the sources of viscous damping +The material/element and global viscous damping sources can be controlled at the step level; controls +are not available for modal damping. If both the material/element and global viscous damping matrices +are supplied, both will be used as a combined damping matrix unless you request that only the element +or global damping factor be used. The combined material/element and global viscous damping is +Input File Usage: +Use the following option to activate only the material/element viscous damping +matrix: +*DAMPING CONTROLS, VISCOUS=ELEMENT +Use the following option to activate only the global viscous damping matrix: +*DAMPING CONTROLS, VISCOUS=FACTOR +Use the following option to activate the combined material/element and global +viscous damping matrix: +Abaqus/CAE Usage: +*DAMPING CONTROLS, VISCOUS=COMBINED +Damping controls are not supported in Abaqus/CAE. +Excluding viscous damping effects +You can choose to exclude the effects of viscous damping altogether at the step level. +Input File Usage: +Use the following option to exclude the viscous damping matrix: +Abaqus/CAE Usage: +*DAMPING CONTROLS, VISCOUS=NONE +Damping controls are not supported in Abaqus/CAE. +Defining structural damping +Abaqus allows you to choose a particular source of structural damping, to add several sources, or to +exclude structural damping effects. +Defining material/element structural damping +The material/element structural damping matrix (that represents the imaginary stiffness and is +proportional to forces or displacements) is defined as +represents the material structural damping, +represents the structural damping coefficient for +where +elements such as springs with complex stiffnesses and connectors, and +is the real element stiffness +matrix. In mode-based procedures the projection of +onto the mode shapes results in a full modal +damping matrix. When using SIM-based modal procedures, the projected material and element damping +matrix may be combined with global and modal damping . Material/element structural damping is not available for acoustic elements. +Input File Usage: +Use the following option to specify material structural damping: +Abaqus/CAE Usage: +*DAMPING, STRUCTURAL= +Property module: material editor: Mechanical→Damping: Structural: +Defining global structural damping +You can define the global structural damping factor, +, to get +Global structural damping can be specified for the entire model (default), for the mechanical degree of +freedom field (displacements and rotations) only, or for the acoustic field only. +Input File Usage: +Use the following option to specify global structural damping: +Abaqus/CAE Usage: +*GLOBAL DAMPING, STRUCTURAL= +Global structural damping is not supported in Abaqus/CAE. +Defining structural modal damping +Structural damping assumes that the damping forces are proportional to the forces caused by stressing +of the structure and are opposed to the velocity . This form of damping can be used only when the displacement +and velocity are exactly 90° out of phase, as in steady-state and random response analyses where the +excitation is purely sinusoidal. +Structural damping can be defined as diagonal modal damping for mode-based steady-state dynamic +and random response analyses. +Input File Usage: +Use the following option to define structural damping by specifying mode +numbers: +*MODAL DAMPING, STRUCTURAL, DEFINITION=MODE NUMBERS +Use the following option to define structural damping by specifying a frequency +range: +*MODAL DAMPING, STRUCTURAL, +DEFINITION=FREQUENCY RANGE +Abaqus/CAE Usage: +Use the following input to define structural damping by specifying mode +numbers: +Step module: Create Step: Linear perturbation: any valid step +type: Damping: Specify damping over ranges of: Modes, +Structural: Use structural damping data +Use the following input to define structural damping by specifying frequency +ranges: +Step module: Create Step: Linear perturbation: any valid step +type: Damping: Specify damping over ranges of: Frequencies, +Structural: Use structural damping data +Controlling the sources of structural damping +The material/element and global structural damping sources can be controlled at the step level; controls +are not available for modal damping. If both the material/element and global structural damping matrices +are supplied, both will be combined unless you request that only the element or global damping factor +be used. The combined structural damping matrix is +Input File Usage: +Use the following option to activate only the material/element structural +damping matrix: +*DAMPING CONTROLS, STRUCTURAL=ELEMENT +Use the following option to activate only the global structural damping matrix: +*DAMPING CONTROLS, STRUCTURAL=FACTOR +Use the following option to activate the combined material/element and global +structural damping matrix: +Abaqus/CAE Usage: +*DAMPING CONTROLS, STRUCTURAL=COMBINED +Damping controls are not supported in Abaqus/CAE. +Excluding structural damping effects +You can choose to exclude the effects of structural damping altogether at the step level. +Input File Usage: +Use the following option to exclude structural damping matrix: +Abaqus/CAE Usage: +*DAMPING CONTROLS, STRUCTURAL=NONE +Damping controls are not supported in Abaqus/CAE. +Defining both viscous and structural damping +The imaginary contribution to the frequency domain dynamics equation, which represents the effect of +damping, may include both viscous and structural damping and can be written as +where +is the forcing frequency. +Defining composite modal damping +Composite modal damping allows you to define a damping factor for each material in the model as a +fraction of critical damping. These factors are then combined into a damping factor for each mode as +weighted averages of the mass matrix associated with each material: +(no sum over +) +where +material m, +is the critical damping fraction used in mode +, +is the mass matrix associated with material m, +is the critical damping fraction defined for +is the eigenvector of mode , and +is the generalized mass associated with mode +: +(no sum on ) +If you specify composite modal damping, Abaqus calculates the damping coefficients +in +the eigenfrequency extraction step from the damping factors +that you defined for each material. +Composite modal damping can be defined only by specifying mode numbers; it cannot be defined by +specifying a frequency range. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options: +*DAMPING, COMPOSITE= +*MODAL DAMPING, MODAL=COMPOSITE +Property module: material editor: Mechanical→Damping: Composite: +Step module: Create Step: Linear perturbation: any valid step type: +Damping: Composite modal: Use composite damping data +Defining global damping for acoustic fields +If your model contains acoustic elements, Abaqus applies any specified global damping to both the +acoustic fields and the structural fields in the model by default. If desired, you can specify that a global +damping definition applies only to the acoustic fields or only to the displacement and rotation fields. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to apply global damping to all of the displacement, +rotation, and acoustic fields in a model: +*GLOBAL DAMPING, FIELD=ALL (default) +Use the following option to apply global damping only to the acoustic fields in +a model: +*GLOBAL DAMPING, FIELD=ACOUSTIC +Use the following option to apply global damping only to the displacement and +rotation fields in a model: +*GLOBAL DAMPING, FIELD=MECHANICAL +Global damping is not supported in Abaqus/CAE. +Defining and using both global and modal diagonal damping +Mode-based procedures—such as steady-state dynamics, transient modal dynamic, response spectrum, +and random response analyses—can also use a step-dependent, modal damping definition that is specified +per eigenmode. When multiple modal damping definitions are used with different damping types, the +damping is additive. If the same damping type is specified more than once, the last specification is used. +If modal damping is used with global damping, both types of damping will contribute to the damping +matrix. +Damping controls have no effect on modal damping. If damping controls are used to exclude certain +global damping effects in a step, all modal damping effects are still included in the step. To exclude modal +damping, the damping definition must be specifically removed from the step definition. +6.3.2 +IMPLICIT DYNAMIC ANALYSIS USING DIRECT INTEGRATION +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “Dynamic analysis procedures: overview,” Section 6.3.1 +• *DYNAMIC +• “Configuring a dynamic, +Section 14.11.1 of the Abaqus/CAE User’s Manual, in the online HTML version of this manual +implicit procedure” in “Configuring general analysis procedures,” +Overview +A direct-integration dynamic analysis in Abaqus/Standard: +• must be used when nonlinear dynamic response is being studied; +• can be fully nonlinear (general dynamic analysis) or can be based on the modes of the linear system +(subspace projection method); and +• can be used to study a variety of applications, including: +– dynamic responses requiring transient fidelity and involving minimal energy dissipation; +– dynamic responses involving nonlinearity, contact, and moderate energy dissipation; and +– quasi-static responses in which considerable energy dissipation provides stability and improved +convergence behavior for determining an essentially static solution. +General dynamic analysis +General nonlinear dynamic analysis in Abaqus/Standard uses implicit time integration to calculate the +transient dynamic or quasi-static response of a system. The procedure can be applied to a broad range of +applications calling for varying numerical solution strategies, such as the amount of numerical damping +required to obtain convergence and the way in which the automatic time incrementation algorithm +proceeds through the solution. Typical dynamic applications fall into three categories: +• Transient fidelity applications, such as an analysis of satellite systems, require minimal energy +In these applications small time increments are taken to accurately resolve the +dissipation. +vibrational response of the structure, and numerical energy dissipation is kept at a minimum. These +stringent requirements tend to degrade convergence behavior for simulations involving contact or +nonlinearities. +• Moderate dissipation applications encompass a more general range of dynamic events in which a +moderate amount of energy is dissipated by plasticity, viscous damping, or other effects. Typical +applications include various insertion, impact, and forming analyses. The response of these +structures can be either monotonic or nonmonotonic. Accurate resolution of high-frequency +vibrations is usually not of interest in these applications. Some numerical energy dissipation +tends to reduce solution noise and improve convergence behavior in these applications without +significantly degrading solution accuracy. +• Quasi-static applications are primarily interested in determining a final static response. These +problems typically show monotonic behavior, and inertia effects are introduced primarily to +the statically unstable behavior may be due to +regularize unstable behavior. +temporarily unconstrained rigid body modes or “snap-through” phenomena. Large time increments +are taken when possible to obtain the final solution at minimal computational cost. Considerable +numerical dissipation may be required to obtain convergence during certain stages of the loading +history. +For example, +An example of a transient fidelity application is available in “Modeling of an automobile +suspension,” Section 2.1.7 of the Abaqus Example Problems Manual. An analysis that includes both +a moderate dissipation step and a quasi-static step is described in “Impact analysis of a pawl-ratchet +device,” Section 2.1.17 of the Abaqus Example Problems Manual. +Specifying the application type +Based on the classifications listed above, you should indicate the type of application you are studying +when performing a general dynamic analysis. Abaqus/Standard assigns numerical settings based on +your classification of the application type, and this classification can significantly affect a simulation. In +some cases accurate results can be obtained with more than one application-type setting, in which case +analysis efficiency should be considered. A general trend is that—among the three classifications—the +high-dissipation quasi-static classification tends to result in the best convergence behavior and the low- +dissipation transient fidelity classification tends to have the highest likelihood of convergence difficulty. +Input File Usage: +Abaqus/CAE Usage: +Use the following option for transient fidelity applications: +*DYNAMIC, APPLICATION=TRANSIENT FIDELITY (default +for models without contact) +Use the following option for moderate dissipation applications: +*DYNAMIC, APPLICATION=MODERATE DISSIPATION +(default for models with contact) +Use the following option for quasi-static applications: +*DYNAMIC, APPLICATION=QUASI-STATIC +Step module: Create Step: General: Dynamic, Implicit +The application type is specified in the Edit Step dialog box: +Basic: Application: Transient fidelity, Moderate dissipation, +Quasi-static, or Analysis product default +Diagnostics for modeling errors associated with mass properties +Accurate representation of inertia properties is necessary for accurate dynamic analyses. In some cases +Abaqus/Standard provides diagnostic messages when it detects likely modeling errors associated with the +specification of inertia properties. The most common way of specifying inertia properties is with material +densities. Abaqus/Standard issues a warning message to the data (.dat) file if a material density is +omitted in a dynamic analysis (this warning is not issued if the density is zero only for certain values of +temperature or field variables). Other methods of specifying inertia properties include: +• point mass and rotary inertia definitions, and +• constraining nodes without inertia themselves to nodes having inertia properties defined. +In some circumstances Abaqus/Standard attempts to solve systems of equations involving effective +inversion of the global mass matrix to directly adjust velocities and accelerations during a general +dynamic analysis as described in “Initial conditions” and “Intermittent contact/impact” below. These +additional velocity and acceleration adjustments occur by default only for transient fidelity application +types as defined above. If the global mass matrix is found to be singular, Abaqus/Standard issues an +error message by default, because singular mass is an indication that the mass properties are not realistic +due to a modeling error. +Diagnostic feedback specific to the global mass matrix being singular is typically not provided for +quasi-static and moderate dissipation application types, although warnings typically are issued regarding +the lack of material density. Singular mass is not necessarily detrimental to a quasi-static analysis. For +example, it would be reasonable to only define inertia properties (such as density) in components or +regions with temporary static instabilities (such as initially unconstrained rigid body modes that become +constrained once contact occurs) in a quasi-static analysis. +You can control the course of action Abaqus/Standard takes upon detecting a singular global mass +matrix. +Input File Usage: +Use the following default option to issue an error message and stop execution +if a singular global mass matrix is detected when calculating velocity and +acceleration adjustments: +*DYNAMIC, SINGULAR MASS=ERROR +Use the following option to issue a warning message and avoid velocity and +acceleration adjustments (i.e., continue time integration using current velocities +and accelerations) if a singular global mass matrix is detected: +*DYNAMIC, SINGULAR MASS=WARNING +Use the following option to adjust velocities and accelerations even if a singular +mass matrix is detected. This setting can result in large, non-physical velocity +and/or acceleration adjustments, which can, in turn, cause poor time integration +solutions and artificial convergence difficulties. This approach is not generally +recommended; it should be used only in special cases when the analyst has a +thorough understanding of how to interpret results obtained in this way. +Abaqus/CAE Usage: +*DYNAMIC, SINGULAR MASS=MAKE ADJUSTMENTS +The default singular mass setting cannot be modified in Abaqus/CAE. +Numerical details +The effect of the application-type classification on numerical aspects of general dynamic analyses +is described below. +In most cases the settings determined by the application type are sufficient to +successfully perform an analysis. However, detailed user controls are provided to override settings on +an individual basis. +Time integration methods +Abaqus/Standard uses the Hilber-Hughes-Taylor time integration by default unless you specify that the +application type is quasi-static. The Hilber-Hughes-Taylor operator is an extension of the Newmark +-method. Numerical parameters associated with the Hilber-Hughes-Taylor operator are tuned +differently for moderate dissipation and transient fidelity applications (as discussed later in this section). +The backward Euler operator is used by default if the application classification is quasi-static. +These time integration operators are implicit, which means that the operator matrix must be +inverted and a set of simultaneous nonlinear dynamic equilibrium equations must be solved at each time +increment. This solution is done iteratively using Newton’s method. The principal advantage of these +operators is that they are unconditionally stable for linear systems; there is no mathematical limit on +the size of the time increment that can be used to integrate a linear system. An unconditionally stable +integration operator is of great value when studying structural systems because a conditionally stable +integration operator (such as that used in the explicit method) can lead to impractically small time steps +and, therefore, a computationally expensive analysis. +Marching through a simulation with a finite time increment size generally introduces some +degree of numerical damping. This damping differs from the material damping discussed in “Material +damping,” Section 26.1.1 (and in many cases these two forms of damping will work well together). +The amount of damping associated with the time integration varies among the operator types (for +example, the backward Euler operator tends to be more dissipative than the Hilber-Hughes-Taylor +operator) and in many cases (such as with the Hilber-Hughes-Taylor operator) depends on settings +of numerical parameters associated with the operator. The ability of the operator to effectively treat +contact conditions is often of considerable importance with respect to their usefulness. For example, +some changes in contact conditions can result in “negative damping” (nonphysical energy source) for +many time integrators, which can be very undesirable. +It is possible to override the time integrator implied by the application-type classification; for +example, you can perform a moderate dissipation dynamic analysis using the backward Euler integrator. +Changing the default integrator is not generally recommended but may be useful in special cases. +Input File Usage: +Use the following option to use the Hilber-Hughes-Taylor integrator with +default integrator parameter settings corresponding to those for transient +fidelity applications: +*DYNAMIC, TIME INTEGRATOR=HHT-TF +Use the following option to use the Hilber-Hughes-Taylor integrator with +default integrator parameter settings corresponding to those for moderate +dissipation applications: +*DYNAMIC, TIME INTEGRATOR=HHT-MD +Abaqus/CAE Usage: +Use the following option to use the backward Euler integrator: +*DYNAMIC, TIME INTEGRATOR=BWE +The default time integrator cannot be modified in Abaqus/CAE. +Additional control over integrator parameters +Additional user controls enable modifications to settings of numerical parameters associated with the +Hilber-Hughes-Taylor operator for descriptions of the numerical +parameters). The default parameter settings depend on the specified application type, as indicated in +Table 6.3.2–1 for the basis of these settings). +Table 6.3.2–1 Default parameters for the Hilber-Hughes-Taylor integrator. +Parameter +Transient Fidelity +Moderate Dissipation +Application +–0.05 +0.275625 +0.55 +–0.41421 +0.5 +0.91421 +These parameters can be adjusted or modified individually if the Hilber-Hughes-Taylor operator is +being used. If the default settings of these parameters correspond to the transient fidelity settings shown +in Table 6.3.2–1 and you explicitly modify the +parameter alone, the other parameters will be adjusted +automatically to +. This relation provides control of the numerical +damping associated with the time integrator while preserving desirable characteristics of the integrator. +The numerical damping grows with the ratio of the time increment to the period of vibration of a mode. +Negative values of +results in no damping (energy preserving) and +is exactly the trapezoidal rule (sometimes called the Newmark -method, with +). +The setting +provides the maximum numerical damping. It gives a damping ratio of about 6% +when the time increment is 40% of the period of oscillation of the mode being studied. Allowable values +of +provide damping; whereas +, and +are: +and +and +, +, +, +Input File Usage: +Abaqus/CAE Usage: +. +*DYNAMIC, ALPHA= , BETA= , GAMMA= +Only the +parameter can be modified in Abaqus/CAE: +Step module: Create Step: General: Dynamic, Implicit: +Other: Alpha: Specify: +Default incrementation schemes +Automatic time incrementation is used by default for nonlinear dynamic procedures. The main +factors used to control adjustments to the time increment size for an implicit dynamic procedure are +the convergence behavior of the Newton iterations and the accuracy of the time integration. The +time increment size may vary considerably during an analysis. Details of the time increment control +algorithm depend on the type of dynamic application you are studying. +The following factors are considered by default in the time increment control algorithm if you +specify a quasi-static–type application (the same factors control the time increment size for purely static +analyses): +• The time increment size is reduced if an increment appears to be diverging or if the convergence +rate is slow. +• The time increment size is fairly aggressively increased if rapid convergence occurs in previous +increments. +Analyses for moderate dissipation-type applications also use these same factors, as well as a default +upper bound on the time increment size equal to one-tenth of the step duration. +The following factors are considered by default in the time increment control algorithm if you +specify a transient fidelity–type application: +• The time increment size is reduced if an increment appears to be diverging or if the convergence +rate is slow. +• The time increment size is reduced if changes in contact status are detected during the first +attempt of processing an increment. The new increment size is set such that the end of the +increment corresponds to the average time of the contact status changes that were detected with the +previous increment size. (In such cases an additional very small time increment is used to enforce +compatibility of velocities and accelerations across active contact interfaces.) +• The time increment size is reduced if the half-increment residual (out-of-balance force) halfway +through a time increment exceeds the half-increment residual tolerance, which is 10,000 times the +time average force for a contact analysis or 1000 times the time average force for an analysis without +contact. +• The time increment is gradually increased if rapid convergence occurs in previous increments. +• The upper bound for the time increment size is equal to 1/100 of the step duration. +Intermittent contact/impact +The second and third factors described in the preceding list often result in very small time increment sizes +for contact simulations that are performed as a transient fidelity application (and the time increment size +tends to remain small due to the fourth factor). This problem can be avoided by specifying a different +application type or by using more detailed user controls, as discussed below. +General settings for the time increment controls +A high level user control over which factors are considered by the time increment control algorithm can +be used to override the defaults implied by the specified application type for the analysis. Regardless of +the application type you have specified, you can enforce time increment controls associated with either +quasi-static applications or transient fidelity applications. +Input File Usage: +Use the following option to obtain the aggressive time increment control +settings associated with quasi-static applications: +*DYNAMIC, INCREMENTATION=AGGRESSIVE +Use the following option to obtain the more conservative time increment control +settings associated with transient fidelity applications: +*DYNAMIC, INCREMENTATION=CONSERVATIVE +The default +Abaqus/CAE. +time incrementation control settings cannot be modified in +Abaqus/CAE Usage: +Controlling the half-increment residual +Controls associated with the half-increment residual tolerance are provided for tuning the time +incrementation. These controls are intended for advanced users and typically do not need to be +modified. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to specify that no check of the half-increment residual +should be performed: +*DYNAMIC, NOHAF +Use the following option to specify the half-increment residual tolerance as a +scale factor of the time average force (moment): +*DYNAMIC, HALFINC SCALE FACTOR=scale factor +Use the following option to directly specify the half-increment residual force +tolerance (the half-increment residual moment tolerance is the half-increment +residual force tolerance times the characteristic element length automatically +calculated): +*DYNAMIC, HAFTOL=tolerance +Use the following option to specify that no check of the half-increment residual +should be performed: +Step module: Create Step: General: Dynamic, Implicit: Incrementation: +toggle on Suppress half-increment residual calculation +Use the following option to specify the half-increment residual tolerance as a +scale factor of the time average force (moment): +Step module: Create Step: General: Dynamic, Implicit: Incrementation: +Half-increment Residual: Specify scale factor: scale factor +Use the following option to specify the half-increment residual force tolerance +directly: +Step module: Create Step: General: Dynamic, Implicit: Incrementation: +Half-increment Residual: Specify value: tolerance +Controlling incrementation involving contact +By default, specifying a transient fidelity application typically results in reduced time increment sizes +upon changes in contact status. An extra time increment with a very small size is subsequently performed +to enforce compatibility of velocities and accelerations across active contact interfaces. Direct user +control over these incrementation aspects is available. +Input File Usage: +Use the following option to avoid automatically cutting back the increment size +and enforcing velocity and acceleration compatibility in the contact region upon +changes in contact status: +*DYNAMIC, IMPACT=NO +Use the following option to automatically cut back the increment size and +enforce velocity and acceleration compatibility in the contact region upon +changes in contact status: +*DYNAMIC, IMPACT=AVERAGE TIME +Use the following option to enforce velocity and acceleration compatibility in +the contact region without automatically cutting back the increment size upon +changes in contact status: +Abaqus/CAE Usage: +*DYNAMIC, IMPACT=CURRENT TIME +The default contact incrementation scheme cannot be modified in Abaqus/CAE. +Direct time incrementation +You may directly specify the time increment size to be used. This approach is not generally recommended +but may be useful in special cases. The analysis will terminate if convergence tolerances are not satisfied +within the maximum number of iterations allowed. +It is possible to ignore convergence tolerances: +the solution to an increment is accepted after +the specified maximum number of iterations allowed even if convergence tolerances are not satisfied. +Ignoring convergence tolerances can result in highly nonphysical results and is not recommended +except by analysts with a thorough understanding of how to interpret results obtained this way. +Input File Usage: +Use the following option to directly specify the time increment: +*DYNAMIC, DIRECT +Use the following option to ignore convergence tolerances after the maximum +number of iterations is reached: +Abaqus/CAE Usage: +*DYNAMIC, DIRECT=NO STOP +Use the following option to specify the time increment directly: +Step module: Create Step: General: Dynamic, Implicit: +Incrementation: Fixed +Use the following option to ignore convergence tolerances after the maximum +number of iterations is reached: +Step module: Create Step: General: Dynamic, Implicit: Other: Accept +solution after reaching maximum number of iterations +Default amplitude for loads +Loads such as applied forces or pressures are ramped on by default if you have selected the quasi-static +application classification; such ramping tends to enhance robustness because the load increment size is +proportional to the time increment size. For example, if the Newton iterations are not able to converge +for a particular time increment size, the automatic time incrementation algorithm will reduce the time +increment size and restart the Newton iterations with a smaller load incremental considered. +For the other application classifications the dynamic procedure applies loads with a step function by +default such that the full load is applied in the first increment of the step (regardless of the time increment +size) and the load magnitude remains constant over each step. Thus, if the first increment is unable to +converge with the original time increment size, reducing the time increment will not reduce the load +increment by default. In some cases the convergence behavior will still improve upon reducing the time +increment because the regularizing effect of inertia on the integration operators is inversely proportional +to the square of the time increment size. See “Defining an analysis,” Section 6.1.2, for more information +on default amplitude types for the various procedures and how to override the default. +The “subspace projection” method +The alternative approach provided in Abaqus/Standard for nonlinear dynamic problems is the “subspace +projection” method. See “Subspace dynamics,” Section 2.4.3 of the Abaqus Theory Manual, for +the theory behind this method. +In this method the modes of the linear system are extracted in an +eigenfrequency extraction step (“Natural frequency extraction,” Section 6.3.5) prior to the dynamic +analysis and are used as a small set of global basis vectors to develop the solution. These modes will +include eigenmodes and, if activated in the eigenfrequency extraction step, residual modes. The method +works well when the system exhibits mildly nonlinear behavior, such as small regions of plastic yielding +or rotations that are not small but not too large. +This method can be very effective. As with the other direct integration methods, it is more expensive +in terms of computer time than the modal methods of purely linear dynamic analysis, but it is often +significantly less expensive than the direct integration of all of the equations of motion of the model. +However, since the subspace projection method is based on the modes of the system, it will not be +accurate if there is extreme nonlinear response that cannot be modeled well by the modes that form the +basis of the solution. +Input File Usage: +Abaqus/CAE Usage: +*DYNAMIC, SUBSPACE +Step module: Create Step: General: Dynamic, Subspace +Selecting the modes on which to project +You can select the modes of the system on which the subspace projection will be performed. The mode +numbers can be listed individually, or they can be generated automatically. If you choose not to select +the modes, all modes extracted in the prior frequency extraction step, including residual modes if they +were activated, are used in the subspace projection. +Input File Usage: +Use one of the following options: +*SELECT EIGENMODES +*SELECT EIGENMODES, GENERATE +Step module: Create Step: General: Dynamic, Subspace: Basic: +Number of modes to use: All or Specify +Abaqus/CAE Usage: +Numerical implementation +The subspace projection method is implemented in Abaqus/Standard using the explicit (central +difference) operator to integrate the equations of motion written in terms of the modes of the linear +system. This integration method is particularly effective here because the modes are orthogonal with +respect to the mass matrix so that the projected system always has a diagonal mass matrix. +for the linear system, where +A fixed time increment is used: this increment is the smaller of the time increment that you specify +or 80% of the stable time increment, which is +is the highest +circular frequency of the modes that are used as the basis of the solution. The 80% factor is intended as +a safety factor so that any increase in this highest frequency caused by nonlinear effects is less likely +to cause the integration to become unstable. The 80% is rather arbitrary; in some cases it may be +nonconservative. You must monitor the response—for example, the energy balance—to ensure that +the time increment is not causing instability. Instability is a concern if the nonlinearities can stiffen +the system significantly, although in many practical cases such stiffening effects are more prominent in +increasing the lower frequencies of the system than in affecting the highest frequencies that are likely to +be retained to represent the dynamic behavior accurately. +Accuracy of the subspace projection method +The effectiveness of the subspace projection method depends on the value of the modes of the linear +system as a set of global interpolation functions for the problem, which is a matter of judgment on your +part—the same sort of judgment as required when deciding if a particular mesh of finite elements is +sufficient. The method is valuable for mildly nonlinear systems and for cases where it is easy to extract +enough modes that you can be confident that they describe the system adequately. +If nonlinear geometric effects are considered in the subspace dynamics step, it is possible to perform +a dynamic simulation for some time, reextract the modes on the current stressed geometry by using +another frequency extraction step, and then continue the analysis with the new modes as the subspace +basis system. This procedure can improve the accuracy of the method in some cases. +Material damping +You can introduce Rayleigh damping, as explained in “Material damping,” Section 26.1.1. This damping +will act in addition to numerical damping associated with the time integrator (discussed previously). +Input File Usage: +Abaqus/CAE Usage: +*DAMPING, ALPHA= +Property module: material editor: Mechanical→Damping: Alpha and Beta +, BETA= +Initial conditions +“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1, describes all of the +available initial conditions. Initial velocities must be defined in global directions regardless of the use +of nodal transformations . +If initial velocities are specified at nodes for which displacement boundary conditions are also +specified, the initial velocities will be ignored at these nodes. However, if a displacement boundary +condition refers to an amplitude curve with an analytically defined time variation (i.e., excluding the +piecewise linear tabular and equally spaced definitions), Abaqus/Standard will compute the initial +velocity for the nodes involved in the boundary condition as the time derivative (evaluated at time zero) +of the analytic variation. +When initial velocities are specified for dynamic analysis, they should be consistent with all of +the constraints on the model, especially time-dependent boundary conditions. Abaqus/Standard will +ensure that initial velocities are consistent with boundary conditions and with multi-point and equation +constraints but will not check for consistency with internal constraints such as incompressibility of the +material. In case of a conflict, boundary conditions and multi-point constraints take precedence over +initial conditions. +Specified initial velocities are used in a dynamic step only if it is the first dynamic step in an analysis. +If a dynamic step is not the first dynamic step and there is an immediately preceding dynamic step, the +velocities from the end of the preceding step are used as the initial velocities for the current step. If a +dynamic step is not the first dynamic step and the immediately preceding step is not a dynamic step, zero +initial velocities are assumed for the current step. +Controlling calculation of accelerations at the beginning of a dynamic step +By default, Abaqus/Standard will calculate accelerations at the beginning of the dynamic step for +transient fidelity applications. You can choose to bypass these acceleration calculations, in which +case Abaqus/Standard will assume that initial accelerations for the current step are zero unless there +is an immediately preceding dynamic step. If the immediately preceding step is also a dynamic step, +bypassing the acceleration calculations will cause Abaqus/Standard to use the accelerations from the end +of the previous step to continue the new step. It is appropriate to bypass the acceleration calculations if +the loading has not changed suddenly at the start of the dynamic step, but it is not correct if the loading +at the beginning of the first increment is significantly different from that at the end of the previous +step. In cases where large loads are applied suddenly, high-frequency noise due to the bypass of the +acceleration calculations may greatly increase the half-increment residual. +Input File Usage: +Abaqus/CAE Usage: +*DYNAMIC, INITIAL=NO +Step module: Create Step: General: Dynamic, Implicit: Other: Initial +acceleration calculations at beginning of step: Bypass +Boundary conditions +Boundary conditions can be applied to any of the displacement or rotation degrees of freedom (1–6), to +warping degree of freedom 7 in open-section beam elements, to fluid pressure degree of freedom 8 for +hydrostatic fluid elements, or to acoustic pressure degree of freedom 8 for acoustic elements (“Boundary +conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1). +Amplitude references can be used to prescribe time-varying boundary conditions in a +direct-integration dynamic step. Default amplitude variations are described in “Defining an analysis,” +Section 6.1.2. +In direct time integration dynamic analysis, when a node with a prescribed motion is used in an +equation constraint or a multi-point constraint to control the motion of another node, the equation or +multi-point constraint will be imposed correctly for the displacement and velocity of the dependent node. +However, the acceleration will not be rigorously transmitted to the dependent node, which may cause +some high-frequency noise. +In the subspace projection method it is not currently possible to specify nonzero boundary +conditions directly. Instead, acceleration boundary conditions can be approximated by using appropriate +combinations of large point masses and concentrated loads. At the node where such a boundary +condition is desired, attach a large point mass that is approximatively 105 –106 times larger than the +mass of the original model. In addition, a concentrated load of magnitude equal to the product between +the large point mass and the desired acceleration must be specified in the direction of the approximated +boundary condition. Since the point mass is significantly larger than the mass of the model, the big +mass–concentrated load combination will approximate the desired acceleration in the specified direction +accurately. Boundary conditions other than accelerations must be converted into acceleration histories +before they can be approximated. +Loads +The following loads can be prescribed in a dynamic analysis: +• Concentrated nodal forces can be applied to the displacement degrees of freedom (1–6); see +“Concentrated loads,” Section 33.4.2. +• Distributed pressure forces or body forces can be applied; see “Distributed loads,” Section 33.4.3. +The distributed load types available with particular elements are described in Part VI, “Elements.” +• Distributed pressure or volumetric accelerations (on acoustic elements) can be applied; these are +described in “Acoustic, shock, and coupled acoustic-structural analysis,” Section 6.10.1. +Predefined fields +The following predefined fields can be specified in a dynamic analysis, as described in “Predefined +fields,” Section 33.6.1: +• Although temperature is not a degree of freedom in stress/displacement elements, nodal +temperatures can be specified as a predefined field. Any difference between the applied and +initial temperatures will cause thermal strain if a thermal expansion coefficient is given for +the material (“Thermal expansion,” Section 26.1.2). The specified temperature also affects +temperature-dependent material properties, if any. +• The values of user-defined field variables can be specified. These values only affect field-variable- +dependent material properties, if any. +Material options +Most material models that describe mechanical behavior are available for use in a dynamic analysis. +The following material properties are not active during a dynamic analysis: thermal properties (except +for thermal expansion), mass diffusion properties, electrical conductivity properties, and pore fluid flow +properties. +Rate-dependent material properties (“Time domain viscoelasticity,” Section 22.7.1; “Hysteresis in +elastomers,” Section 22.8.1; “Rate-dependent yield,” Section 23.2.3; and “Two-layer viscoplasticity,” +Section 23.2.11) can be included in a dynamic analysis. +Elements +Other than generalized axisymmetric elements with twist, any of the stress/displacement elements +in Abaqus/Standard (including those with temperature, pressure, and electrical potential degrees of +freedom) can be used in a dynamic analysis. Inertia effects are ignored in hydrostatic fluid elements, +and the inertia of the fluid in pore pressure elements is not taken into account. +Output +In addition to the usual output variables available in Abaqus/Standard , the following variables are provided specifically for implicit dynamic +analysis: +Variables for a specified element set or for the entire model: +Current coordinates of the center of mass. +Coordinate n of the center of mass ( +). +). +Displacement of the center of mass. +Displacement component n of the center of mass ( +Rotation component n of the center of mass. +Equivalent rigid body velocity components. +Component n of the equivalent rigid body velocity ( +Component n of the equivalent rigid body angular velocity ( +Angular momentum about the center of mass. +Component n of the angular momentum about the center of mass ( +Angular momentum about the origin. +Component n of the angular momentum about the origin ( +Rotary inertia about the origin. +). +-component of the rotary inertia about the origin ( +). +Mass. +Current volume. +6.3.2–13 +). +). +). +XC +XCn +UC +UCn +URCn +VC +VCn +VRCn +HC +HCn +HO +HOn +RI +RIij +MASS +Input file template +*HEADING +… +*BOUNDARY +Data lines to specify zero-valued boundary conditions +*INITIAL CONDITIONS +Data lines to specify initial conditions +*AMPLITUDE, NAME=name +Data lines to define amplitude variations +** +*STEP (,NLGEOM) +Once NLGEOM is specified, it will be active in all subsequent steps. +*DYNAMIC +Data line to control automatic time incrementation +*BOUNDARY +Data lines to describe zero-valued or nonzero boundary conditions +*CLOAD and/or *DLOAD and/or *INCIDENT WAVE +Data lines to specify loads +*TEMPERATURE and/or *FIELD +Data lines to prescribe predefined fields +*CECHARGE and/or *DECHARGE (if electrical potential degrees of +freedom are active) +Data lines to specify charges +*END STEP +Additional references +• Czekanski, A., N. El-Abbasi, and S. A. Meguid, “Optimal Time Integration Parameters for +Elastodynamic Contact Problems,” Communications in Numerical Methods in Engineering, +vol. 17, pp. 379–384, 2001. +• Hilber, H. M., T. J. R. Hughes, and R. L. Taylor, “Improved Numerical Dissipation for Time +Integration Algorithms in Structural Dynamics,” Earthquake Engineering and Structural Dynamics, +vol. 5, pp. 283–292, 1977. +6.3.3 +EXPLICIT DYNAMIC ANALYSIS +Products: Abaqus/Explicit Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• *DYNAMIC +• “Configuring a dynamic, explicit procedure” in “Configuring general analysis procedures,” +Section 14.11.1 of the Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +An explicit dynamic analysis: +• is computationally efficient for the analysis of large models with relatively short dynamic response +times and for the analysis of extremely discontinuous events or processes; +• allows for the definition of very general contact conditions (“Contact +interaction analysis: +overview,” Section 35.1.1); +• uses a consistent, +deformation; +large-deformation theory—models can undergo large rotations and large +• can use a geometrically linear deformation theory—strains and rotations are assumed to be small +; +• can be used to perform an adiabatic stress analysis if inelastic dissipation is expected to generate +heat in the material ; +• can be used to perform quasi-static analyses with complicated contact conditions; and +• allows for either automatic or fixed time incrementation to be used—by default, Abaqus/Explicit +uses automatic time incrementation with the global time estimator. +Explicit dynamic analysis +The explicit dynamics procedure performs a large number of small time increments efficiently. An +explicit central-difference time integration rule is used; each increment is relatively inexpensive +(compared to the direct-integration dynamic analysis procedure available in Abaqus/Standard) because +there is no solution for a set of simultaneous equations. The explicit central-difference operator satisfies +the dynamic equilibrium equations at the beginning of the increment, t; the accelerations calculated at +time t are used to advance the velocity solution to time +and the displacement solution to time +. +Input File Usage: +Abaqus/CAE Usage: +*DYNAMIC, EXPLICIT +Step module: Create Step: General: Dynamic, Explicit +Numerical implementation +The explicit dynamics analysis procedure is based upon the implementation of an explicit integration +rule together with the use of diagonal (“lumped”) element mass matrices. The equations of motion for +the body are integrated using the explicit central-difference integration rule +where +is a degree of freedom (a displacement or rotation component) and the subscript i refers to the +increment number in an explicit dynamics step. The central-difference integration operator is explicit in +the sense that the kinematic state is advanced using known values of +from the previous +increment. +and +The explicit integration rule is quite simple but by itself does not provide the computational +efficiency associated with the explicit dynamics procedure. The key to the computational efficiency +of the explicit procedure is the use of diagonal element mass matrices because the accelerations at the +beginning of the increment are computed by +is the mass matrix, +is the applied load vector, and +where +is the internal force vector. A +lumped mass matrix is used because its inverse is simple to compute and because the vector multiplication +of the mass inverse by the inertial force requires only n operations, where n is the number of degrees +of freedom in the model. The explicit procedure requires no iterations and no tangent stiffness matrix. +The internal force vector, +, is assembled from contributions from the individual elements such that a +global stiffness matrix need not be formed. +Nodal mass and inertia +The explicit integration scheme in Abaqus/Explicit requires nodal mass or inertia to exist at all activated +degrees of freedom unless constraints are applied using boundary +conditions. More precisely, a nonzero nodal mass must exist unless all activated translational degrees +of freedom are constrained and nonzero rotary inertia must exist unless all activated rotational degrees +of freedom are constrained. Nodes that are part of a rigid body do not require mass, but the entire rigid +body must possess mass and inertia unless constraints are used. Nodes that belong to Eulerian elements +also do not require mass, since the surrounding Eulerian elements may be void at some time during the +simulation. +When degrees of freedom at a node are activated by elements with a nonzero mass density (e.g., +solid, shell, beam) or mass and inertia elements, a nonzero nodal mass or inertia occurs naturally from +the assemblage of lumped mass contributions. +When degrees of freedom at a node are activated by elements with no mass (e.g., spring, dashpot, +or connector elements), care must be taken either to constrain the node or to add mass and inertia as +appropriate. +Stability +The explicit procedure integrates through time by using many small time increments. The central- +difference operator is conditionally stable, and the stability limit for the operator (with no damping) +is given in terms of the highest frequency of the system as +With damping, the stable time increment is given by +is the fraction of critical damping in the mode with the highest frequency. Contrary to our +where +usual engineering intuition, introducing damping to the solution reduces the stable time increment. In +Abaqus/Explicit a small amount of damping is introduced in the form of bulk viscosity to control high +frequency oscillations. Physical forms of damping, such as dashpots or material damping, can also be +introduced. Bulk viscosity and material damping are discussed below. +Estimating the stable time increment size +An approximation to the stability limit is often written as the smallest transit time of a dilatational wave +across any of the elements in the mesh +where +of +is the smallest element dimension in the mesh and +, defined below. +and +In general, for beams, conventional shells, and membranes the element thickness or cross-sectional +dimensions are not considered in determining the smallest element dimension; the stability limit is based +upon the midplane or membrane dimensions only. When the transverse shear stiffness is defined for shell +elements , the stable time increment will also be based on +the transverse shear behavior. +is the dilatational wave speed in terms +This estimate for +is only approximate and in most cases is not a conservative (safe) estimate. In +general, the actual stable time increment chosen by Abaqus/Explicit will be less than this estimate by a +factor between +and 1 in a three-dimensional +model. The time increment chosen by Abaqus/Explicit also accounts for any stiffness behavior in a +model associated with penalty contact. For further discussion, see “Computational cost” below. +and 1 in a two-dimensional model and between +Stable time increment report +Abaqus/Explicit writes a report to the status (.sta) file during the data check phase of the analysis that +contains an estimate of the minimum stable time increment and a listing of the elements with the smallest +stable time increments and their values. The initial stable time increments listed do not include damping +(bulk viscosity), mass scaling, or penalty contact effects. +This listing is provided because often a few elements have much smaller stability limits than the +rest of the elements in the mesh. The stable time increment can be increased by modifying the mesh to +increase the size of the controlling element or by using appropriate mass scaling. +Dilatational wave speed +The current dilatational wave speed, +hypoelastic material moduli from the material’s constitutive response. Effective Lamé’s constants, +and +, is determined in Abaqus/Explicit by calculating the effective +, are determined in the following manner. Define +as the increment of volumetric strain, and +as the increment in the mean stress, +as the +as the increment in the deviatoric stress, +deviatoric strain increment. We assume a hypoelastic stress-strain rule of the form +The effective moduli can then be computed as +For shell elements defined by a shell cross-section that requires numerical integration , the effective +moduli for the section are computed by integrating the effective moduli at the section points through the +thickness. These effective moduli represent the element stiffness and determine the current dilatational +wave speed in the element as +where +is the density of the material. +modulus, E, and Poisson’s ratio, +, by +EXPLICIT DYNAMIC ANALYSIS +and +Time incrementation +The time increment used in an analysis must be smaller than the stability limit of the central-difference +operator. Failure to use a small enough time increment will result in an unstable solution. When the +solution becomes unstable, the time history response of solution variables such as displacements will +usually oscillate with increasing amplitudes. The total energy balance will also change significantly. +If the model contains only one material type, the initial time increment is directly proportional to +the size of the smallest element in the mesh. If the mesh contains uniform size elements but contains +multiple material descriptions, the element with the highest wave speed will determine the initial time +increment. +In nonlinear problems—those with large deformations and/or nonlinear material response—the +highest frequency of the model will continually change, which consequently changes the stability limit. +Abaqus/Explicit has two strategies for time incrementation control: fully automatic time incrementation +(where the code accounts for changes in the stability limit) and fixed time incrementation. +Scaling the time increment +To reduce the chance of a solution going unstable, you can adjust the stable time increment computed +by Abaqus/Explicit by a constant scaling factor. This factor can be used to scale the default global time +estimate, the element-by-element estimate, or the fixed time increment based on the initial element-by- +element estimate; it cannot be used to scale a fixed time increment specified directly by you. +Input File Usage: +Use the following option to scale the stable time increment based on the global +time estimate: +*DYNAMIC, EXPLICIT, SCALE FACTOR=f +Use the following option to scale the stable time increment based on the +element-by-element estimate: +*DYNAMIC, EXPLICIT, ELEMENT BY ELEMENT, SCALE FACTOR=f +Use the following option to scale the stable time increment based on the fixed +time increment on the initial element-by-element estimate: +*DYNAMIC, EXPLICIT, FIXED TIME INCREMENTATION, +SCALE FACTOR=f +Abaqus/CAE Usage: +Step module: Create Step: General: Dynamic, Explicit: +Incrementation: Time scaling factor: f +Automatic time incrementation +The default time incrementation scheme in Abaqus/Explicit is fully automatic and requires no user +intervention. Two types of estimates are used to determine the stability limit: element by element and +global. An analysis always starts by using the element-by-element estimation method and may switch +to the global estimation method under certain circumstances, as explained below. +Element-by-element estimation +In an analysis Abaqus/Explicit initially uses a stability limit based on the highest element frequency in +the whole model. This element-by-element estimate is determined using the current dilatational wave +speed in each element. +The element-by-element estimate is conservative; it will give a smaller stable time increment +than the true stability limit that is based upon the maximum frequency of the entire model. In general, +constraints such as boundary conditions and kinematic contact have the effect of compressing the +eigenvalue spectrum, and the element-by-element estimates do not take this into account. +The concept of the stable time increment as the time required to propagate a dilatational wave +across the smallest element dimension is useful for interpreting how the explicit procedure chooses the +time increment when element-by-element stability estimation controls the time increment. As the step +proceeds, the global stability estimate, if used, will make the time increment less sensitive to element +size. +Input File Usage: +Abaqus/CAE Usage: +*DYNAMIC, EXPLICIT, ELEMENT BY ELEMENT +Step module: Create Step: General: Dynamic, Explicit: Incrementation: +Stable increment estimator: Element-by-element +Global estimation +The stability limit will be determined by the global estimator as the step proceeds unless the element-by- +element estimation method is specified, fixed time incrementation is specified, or one of the conditions +explained below prevents the use of global estimation. The switch to the global estimation method occurs +once the algorithm determines that the accuracy of the global estimation method is acceptable. +The adaptive, global estimation algorithm determines the maximum frequency of the entire model +using the current dilatational wave speed. This algorithm continuously updates the estimate for the +maximum frequency. The global estimator will usually allow time increments that exceed the element- +by-element values. +Abaqus/Explicit monitors the effectiveness of the global estimation algorithm. +If the cost for +computing the global time estimate is more than its benefit, the code will turn off the global estimation +algorithm and simply use the element-by-element estimates to save computation time. +Conditions that will prevent the use of the global time estimator +The global estimation algorithm will not be used when any of the following capabilities are included in +the model: +• Fluid elements +• Infinite elements +• Dashpots +• Thick shells (thickness to characteristic length ratio larger than 0.92) +• Thick beams (thickness to length ratio larger than 1.0) +• The JWL equation of state +• Material damping +• Nonisotropic elastic materials with temperature and field variable dependency +• Distortion control +• Adaptive meshing +• Subcycling +“Improved” stable time increment for three-dimensional continuum elements and elements with plane +stress formulations +For three-dimensional continuum elements and elements with plane stress formulations (shell, +membrane, and two-dimensional plane stress elements) an “improved” estimate of the element +characteristic length is used by default. This “improved” method usually results in a larger element +stable time increment than a more traditional method. For analyses using variable mass scaling, the +total mass added to achieve a given stable time increment will be less with the improved estimate. +Input File Usage: +Abaqus/CAE Usage: +Fixed time incrementation +Use the following option to activate the “improved” element time estimation +method: +*DYNAMIC, EXPLICIT, IMPROVED DT METHOD=YES +Use the following option to deactivate the “improved” element time estimation +method: +*DYNAMIC, EXPLICIT, IMPROVED DT METHOD=NO +The ability to deactivate the “improved” element time estimation method is not +supported in Abaqus/CAE. +A fixed time incrementation scheme is also available in Abaqus/Explicit. The fixed time increment size +is determined either by the initial element-by-element stability estimate for the step or by a user-specified +time increment. +Fixed time incrementation may be useful when a more accurate representation of the higher mode +response of a problem is required. In this case a time increment size smaller than the element-by-element +estimates may be used. The element-by-element estimate can be obtained simply by running a data check +analysis . +When fixed time incrementation is used, Abaqus/Explicit will not check that the computed response +is stable during the step. You should ensure that a valid response has been obtained by carefully checking +the energy history and other response variables. +Basing the fixed time increment size on the initial element-by-element stability limit +You can use time increments the size of the initial element-by-element stability limit throughout a step. +The dilatational wave speed in each element at the beginning of the step is used to compute the fixed +time increment size. +Input File Usage: +Abaqus/CAE Usage: +*DYNAMIC, EXPLICIT, FIXED TIME INCREMENTATION +Step module: Create Step: General: Dynamic, Explicit: Incrementation: +Type: Fixed: Use element-by-element time increment estimator +Specifying the fixed time increment size directly +Alternatively, you can specify a time increment size directly. +Input File Usage: +Abaqus/CAE Usage: +*DYNAMIC, EXPLICIT, DIRECT USER CONTROL +Step module: Create Step: General: Dynamic, Explicit: Incrementation: +Type: Fixed: User-defined time increment +Advantages of the explicit method +The use of small increments (dictated by the stability limit) is advantageous because it allows the solution +to proceed without iterations and without requiring tangent stiffness matrices to be formed. +It also +simplifies the treatment of contact. +The explicit dynamics procedure is ideally suited for analyzing high-speed dynamic events, but +many of the advantages of the explicit procedure also apply to the analysis of slower (quasi-static) +processes. A good example is sheet metal forming, where contact dominates the solution and local +instabilities may form due to wrinkling of the sheet. +The results in an explicit dynamics analysis are not automatically checked for accuracy as they are in +Abaqus/Standard (Abaqus/Standard uses the half-increment residual). In most cases this is not of concern +because the stability condition imposes a small time increment such that the solution changes only slightly +in any one time increment, which simplifies the incremental calculations. While the analysis may take +an extremely large number of increments, each increment is relatively inexpensive, often resulting in an +economical solution. It is not uncommon for Abaqus/Explicit to take over 105 increments for an analysis. +The method is, therefore, computationally attractive for problems where the total dynamic response time +that must be modeled is only a few orders of magnitude longer than the stability limit; for example, wave +propagation studies or some “event and response” applications. +Computational cost +The computer time involved in running a simulation using explicit time integration with a given mesh +is proportional to the time period of the event. The time increment based on the element-by-element +stability estimate can be rewritten (ignoring damping) in the form +where the minimum is taken over all elements in the mesh, +element , +of the material in the element, and +element (defined above). +is a characteristic length associated with an +is the density +are the effective Lamé’s constants for the material in the +and +The time increment from the global stability estimate may be somewhat larger, but for this +discussion we will assume that the above inequality always holds (when the inequality does not hold, +the solution time will be somewhat faster). +For linear, nonisotropic elastic materials this stability limit is further scaled down by the square +root of the ratio of the effective material stiffness to the maximum material stiffness in one particular +direction. Since this effectively means that the time increment can be no larger than the time required to +propagate a stress wave across an element, the computer time involved in running a quasi-static analysis +can be very large: the cost of the simulation is directly proportional to the number of time increments +required. +The number of increments, n, required is +remains constant, where T is the +time period of the event being simulated. (Even the element-by-element approximation of +will not +remain constant in general, since element distortion will change +and nonlinear material response will +change the effective Lamé constants. But the assumption is sufficiently accurate for the purposes of this +discussion.) Thus, +if +In a two-dimensional analysis refining the mesh by a factor of two in each direction will increase +the run time in the explicit procedure by a factor of eight—four times as many elements and half the +original time increment size. Similarly, in a three-dimensional analysis refining the mesh by a factor of +two in each direction will increase the run time by a factor of sixteen. +In a quasi-static analysis it is expedient to reduce the computational cost by either speeding up the +simulation or by scaling the mass. In either case the kinetic energy should be monitored to ensure that +the ratio of kinetic energy to internal energy does not get too large—typically less than 10%. +Reducing the computational cost by speeding up the simulation +To reduce the number of increments required, n, we can speed up the simulation compared to the time of +the actual process—that is, we can artificially reduce the time period of the event, T. This will introduce +two possible errors. If the simulation speed is increased too much, the increased inertia forces will change +the predicted response (in an extreme case the problem will exhibit wave propagation response). The +only way to avoid this error is to choose a speed-up that is not too large. +The other error is that some aspects of the problem other than inertia forces—for example, material +behavior—may also be rate dependent. In this case the actual time period of the event being modeled +cannot be changed. +Reducing the computational cost by using mass scaling +Artificially increasing the material density, +, just like decreasing T +to +. This concept, called “mass scaling,” reduces the ratio of the event time to the time for wave +propagation across an element while leaving the event time fixed, which allows rate-dependent behavior +to be included in the analysis. Mass scaling has exactly the same effect on inertia forces as speeding up +the time of simulation. +reduces n to +, by a factor +Mass scaling is attractive because it can be used in rate-dependent problems, but it must be used with +care to ensure that the inertia forces do not dominate and change the solution. Either fixed or variable +mass scaling can be invoked . +Mass scaling can also be accomplished by altering the density; however, the fixed and variable mass +scaling capabilities provide more versatile methods of scaling the mass of the entire model or specific +element sets in the model. +Reducing the computational cost by using selective subcycling +One disadvantage in an explicit dynamic analysis is that a few very small elements will force the entire +model to be integrated with a small time increment. You can use mixed time integration or “subcycling” +methods to reduce this problem. In these methods the equations of motion for the body are still integrated +using the explicit central-difference integration rule as shown above, but the different time increments are +allowed for different groups of nodes in the finite element model. If most nodes are integrated with a large +stable time increment and only a few nodes are integrated with a small time increment, the computational +cost may be reduced significantly. +Selective subcycling can be invoked by defining the subcycling zones. See “Selective subcycling,” +Section 11.7.1 for details. +Bulk viscosity +Bulk viscosity introduces damping associated with volumetric straining. Its purpose is to improve the +modeling of high-speed dynamic events . Abaqus/Explicit contains two forms of bulk viscosity: linear and quadratic. +Linear bulk viscosity is included by default in an Abaqus/Explicit analysis. +The bulk viscosity parameters +defined below can be redefined and can be changed from +step to step. If the default values are changed in a step, the new values will be used in subsequent steps +until they are redefined. Bulk viscosities defined this way apply to the whole model. For an individual +element set the linear and quadratic bulk viscosities can be scaled by a factor by defining section controls +. +and +Input File Usage: +Abaqus/CAE Usage: +Use the following option to define bulk viscosity for the entire model: +*BULK VISCOSITY +Use the following options to define bulk viscosity for an individual element set: +*BULK VISCOSITY +*SECTION CONTROLS +Use the following option to define bulk viscosity for the entire model: +Step module: Create Step: General: Dynamic, Explicit: Other: Linear +bulk viscosity parameter and Quadratic bulk viscosity parameter +Defining bulk viscosity for an individual element set is not supported in +Abaqus/CAE. +Linear bulk viscosity +Linear bulk viscosity is found in all elements and is introduced to damp “ringing” in the highest element +frequency. This damping is sometimes referred to as truncation frequency damping. It generates a bulk +viscosity pressure that is linear in the volumetric strain rate +where +dilatational wave speed, +is a damping coefficient (default=.06), +is the current material density, +is the current +is an element characteristic length, and +is the volumetric strain rate. +For acoustic elements, the bulk viscosity pressure can be obtained from the above equation by +using the relationship of the fluid particle velocity and the pressure rate as +where +and c are the pressure rate and the speed of sound in the fluid, respectively. +Quadratic bulk viscosity +The second form of bulk viscosity pressure is found only in solid continuum elements (except the plane +stress element CPS4R). This form is quadratic in the volumetric strain rate +where +viscosity. Quadratic bulk viscosity is applied only if the volumetric strain rate is compressive. +is a damping coefficient (default=1.2) and all other quantities are as defined for the linear bulk +The quadratic bulk viscosity pressure will smear a shock front across several elements and is +introduced to prevent elements from collapsing under extremely high velocity gradients. Consider a +simple one-element problem in which the nodes on one side of the element are fixed and the nodes on +the other side have an initial velocity in the direction of the fixed nodes. If the initial velocity is equal +to the dilatational wave speed of the material, without the quadratic bulk viscosity, the element would +collapse to zero volume in one time increment (because the stable time increment size is precisely +the transit time of a dilatational wave across the element). The quadratic bulk viscosity pressure will +introduce a resisting pressure that will prevent the element from collapsing. +Fraction of critical damping due to bulk viscosity +The bulk viscosity pressure is not included in the material point stresses because it is intended as a +numerical effect only—it is not considered part of the material’s constitutive response. The bulk viscosity +pressures are based upon the dilatational mode of each element. The fraction of critical damping in the +dilatational mode of each element is given by +Rotational bulk viscosity for shell elements +For the displacement degrees of freedom, bulk viscosity introduces damping associated with volumetric +straining. Linear bulk viscosity or truncation frequency damping is used to damp the high frequency +ringing that leads to unwanted noise in the solution or spurious overshoot in the response amplitude. For +the same reason, in shells the high frequency ringing in the rotational degrees of freedom is damped with +linear bulk viscosity acting on the mean curvature strain rate. This damping generates a bulk viscosity +“pressure moment,” m, which is linear in the mean curvature strain rate +is a damping coefficient (default = 0.06), +where +is the current dilatational wave speed, L is the characteristic length used for rotary inertia and transverse +shear stiffness scaling , and +, +where h is the current thickness, is added to the direct components of the moment resultant. +is twice the mean curvature strain rate. The resultant pressure moment +is the original thickness, +is the mass density, +Material damping +Defining inelastic material behavior, dashpots, etc. will introduce energy dissipation into a model. In +addition to these mechanisms, general (“Rayleigh”) material damping can be introduced . Adding damping to a model, especially stiffness proportional damping, +, +may significantly reduce the stable time increment. +Input File Usage: +Abaqus/CAE Usage: +*DAMPING, ALPHA= +Property module: material editor: Mechanical→Damping: Alpha and Beta +, BETA= +Obtaining diagnostic information about critical elements +Abaqus/Explicit writes critical elements (elements with the smallest stable time increments) and their +stable time increment values to the output database at each summary increment for visualization in +Abaqus/CAE. By default, the number of critical elements written to the output database is 10. +Input File Usage: +Abaqus/CAE Usage: +*DIAGNOSTICS, CRITICAL ELEMENTS=value +The ability to control the number of critical elements written to the output +database is not supported in Abaqus/CAE. +Obtaining diagnostic information about the deformation speed +The deformation speed in an element is defined as the largest absolute value of all the deformation +rate components of an element times the element characteristic length, +. You can request diagnostic +information about the deformation speed within a step definition, as described below. In a multistep +analysis diagnostic requests remain in effect until they are explicitly redefined. +Deformation speed warnings +By default, Abaqus/Explicit will check for a relatively large deformation speed in all the elements since +too high a value may cause the element to deform or collapse unrealistically. A warning message is +issued if the ratio of deformation speed versus dilatational wave speed in an element reaches the value +specified for the “warning ratio.” By default, the warning ratio is 0.3. You can redefine this limit. +The first occurrence of the warning message is written to the status (.sta) file; subsequent +occurrences are written to the message (.msg) file. See “Output,” Section 4.1.1, for a description of +these output files. +Generally when the ratio of deformation speed to dilatational wave speed is greater than 0.3, it is +an indication that the purely mechanical material constitutive relationship is no longer valid and that a +thermo-mechanical equation of state material is required. +Input File Usage: +Abaqus/CAE Usage: +*DIAGNOSTICS, WARNING RATIO=ratio +The ability to redefine the warning ratio limit is not supported in Abaqus/CAE. +Deformation speed errors +An error message is issued and the analysis is terminated when the maximum ratio of deformation speed +versus current dilatational wave speed for any element is greater than the “cutoff ratio.” By default, the +cutoff ratio is 1.0. You can redefine this limit. +The check for this cutoff ratio is not applied to any model that has an equation of state material or a user-defined material . +Input File Usage: +Abaqus/CAE Usage: +*DIAGNOSTICS, CUTOFF RATIO=ratio +The ability to redefine the cutoff ratio limit is not supported in Abaqus/CAE. +Obtaining a summary of the deformation speed information +You can request summary diagnostic information to obtain warning and error messages for only the +element with the largest ratio of deformation speed to dilatational wave speed. +Input File Usage: +Abaqus/CAE Usage: +*DIAGNOSTICS, DEFORMATION SPEED CHECK=SUMMARY +A summary of the deformation speed diagnostic information is output by +default in Abaqus/CAE. +Obtaining detailed deformation speed information +You can request detailed diagnostic information to obtain warning and error messages for all elements +with large deformation speed to dilatational wave speed ratios. +Input File Usage: +Abaqus/CAE Usage: +*DIAGNOSTICS, DEFORMATION SPEED CHECK=DETAIL +You cannot output detailed diagnostic information about the deformation speed +in Abaqus/CAE. +Disabling deformation speed checks +You can choose to completely bypass the checks for large deformation speed. +Input File Usage: +Abaqus/CAE Usage: +*DIAGNOSTICS, DEFORMATION SPEED CHECK=OFF +You cannot disable the deformation speed checks in Abaqus/CAE. +Monitoring output variables for extreme values +There are some analyses in which it is useful to monitor the value of a variable at every increment. For +example, in a force-driven analysis such as hydro-forming, the simulation time that is sufficient to model +the completion of the physical process may depend on the magnitude of the displacement of a node or a +group of nodes in the model. Another example is a drop test simulation where the postfailure response is +not of interest. Monitoring the values of critical variables and halting the analysis when those variables +exceed a given criterion can reduce computational expense and turnaround time. +For such problems Abaqus/Explicit allows output variables to be monitored during an analysis +to verify whether or not their values have exceeded or fallen below user-specified values in specified +element or node sets. Comparisons of specified element integration point variables, element section +variables, or nodal variables with user-specified values are performed at every increment. At the first +occurrence of a variable exceeding the user-specified bounds, the variable name, the associated element +or node number, and the increment number are written to the status (.sta) file. In addition, you can +request that the analysis be stopped and/or the output state be written in the increment following the one +in which the variable has exceeded the user-specified bound. At the end of each step in which variables +are monitored, the maximum, minimum, or absolute maximum value that each variable attains during the +course of the analysis, along with the number of the element or node where the extreme value occurred, +will be written to the status file. +Defining the element and nodal variables to be monitored +The element output variables that can be monitored include all the element integration point variables +and element section point variables that are available for history-type output to the output database. +Similarly, the nodal output variables that can be monitored include all the nodal variables that are +available for history output to the output database. The keys identifying the output variables are defined +in “Abaqus/Explicit output variable identifiers,” Section 4.2.2. +Input File Usage: +Use the first option with one or both of the following options in the history +portion of the input file: +*EXTREME VALUE +*EXTREME ELEMENT VALUE, ELSET=element_set_name +*EXTREME NODE VALUE, NSET=nset_set_name +The *EXTREME VALUE option can be repeated in the same step, and the +*EXTREME ELEMENT VALUE and *EXTREME NODE VALUE options +can be repeated as many times as necessary. +Abaqus/CAE Usage: +Extreme value output monitoring is not supported in Abaqus/CAE. +Halting the analysis when the extreme value criterion is met +You can choose to halt the analysis when the extreme value criterion is met. The analysis will stop at the +end of the increment following the one in which any of the specified element or nodal variables exceeded +the prescribed bounds. +Input File Usage: +Use the following options: +Abaqus/CAE Usage: +*EXTREME VALUE, HALT=YES +*EXTREME ELEMENT VALUE and/or *EXTREME NODE VALUE +Extreme value output monitoring is not supported in Abaqus/CAE. +Obtaining output when the extreme value criterion is met +You can obtain field-type output to the output database and an additional restart state when any of the +selected variables fall outside the specified bounds for the first time during the analysis. The output will +be written in the increment following the one in which such an occurrence took place. Since output is +automatically written when the analysis terminates, this request has an effect only if you have not chosen +to halt the analysis when the extreme value criterion is met as described above. +Input File Usage: +Use either or both of the following options in conjunction with the *EXTREME +VALUE option: +*EXTREME ELEMENT VALUE, ELSET=element_set_name, +OUTPUT=YES +*EXTREME NODE VALUE, NSET=node_set_name, OUTPUT=YES +Extreme value output monitoring is not supported in Abaqus/CAE. +Abaqus/CAE Usage: +Monitoring variables in a multistep analysis +In a multistep analysis the monitoring requests you specify remain in effect until they are redefined. You +must redefine all requests to add or change any variables, element or node sets, or maxima or minima. +Stopping the monitoring of variables in a new step +You can stop monitoring variables in a new step. +Input File Usage: +Abaqus/CAE Usage: +Use the *EXTREME VALUE option without the *EXTREME ELEMENT +VALUE and *EXTREME NODE VALUE options. +Extreme value output monitoring is not supported in Abaqus/CAE. +Initial conditions +“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1, describes all of the initial +conditions that are available for an explicit dynamic analysis. +Boundary conditions +Boundary conditions can be defined as explained in “Boundary conditions in Abaqus/Standard and +Abaqus/Explicit,” Section 33.3.1. Boundary conditions applied during an explicit dynamic response +step should use appropriate amplitude references (“Amplitude curves,” Section 33.1.2). If boundary +conditions are specified for the step without amplitude references, they are applied instantaneously at +the beginning of the step. Since Abaqus/Explicit does not admit jumps in displacement, the value of +a nonzero displacement boundary condition that is specified without an amplitude reference will be +ignored, and a zero velocity boundary condition will be enforced. +Loads +The loading types available for an explicit dynamic analysis are explained in “Applying loads: overview,” +Section 33.4.1. Concentrated nodal forces or moments can be applied to the displacement or rotation +degrees of freedom (1–6). Distributed pressure forces or body forces can also be applied; the distributed +load types available with particular elements are described in Part VI, “Elements.” +As with boundary conditions, loads applied during a dynamic response step should use appropriate +amplitude references (“Amplitude curves,” Section 33.1.2). If loads are specified for the step without +amplitude references, they are applied instantaneously at the beginning of the step. +Predefined fields +The following predefined fields can be specified, as described in “Predefined fields,” Section 33.6.1: +• Although temperature is not a degree of freedom in explicit dynamic analysis, nodal temperatures +can be specified. Any difference between the applied and initial +temperatures will cause +thermal strain if a thermal expansion coefficient is given for the material (“Thermal expansion,” +Section 26.1.2). The specified temperature also affects temperature-dependent material properties, +if any. +• The values of user-defined field variables can be specified. These values affect only field-variable- +dependent material properties, if any. +Material options +Any of the material models in Abaqus/Explicit can be used in a general explicit dynamic analysis . +Elements +All of the elements available in Abaqus/Explicit can be used in an explicit dynamic analysis. The +elements are listed in Part VI, “Elements.” +If coupled temperature-displacement elements are used in an explicit dynamic analysis, +the +temperature degrees of freedom will be ignored. +Output +The element output available for a dynamic analysis includes stress; strain; energies; and the values of +state, field, and user-defined variables. The nodal output available includes displacements, velocities, +accelerations, reaction forces, and coordinates. All of the output variable identifiers are outlined in +“Abaqus/Explicit output variable identifiers,” Section 4.2.2. The types of output available are described +in “Output,” Section 4.1.1. +When an Abaqus/Explicit analysis encounters a fatal error, the preselected variables applicable to +the current procedure are added automatically to the output database as field data for the last increment. +Energy output is particularly important in checking the accuracy of the solution in an explicit +dynamic analysis. In general, the total energy (ETOTAL) should be a constant or close to a constant; the +“artificial” energies, such as the artificial strain energy (ALLAE), the damping dissipation (ALLVD), +and the mass scaling work (ALLMW) should be negligible compared to “real” energies such as the +strain energy (ALLSE) and the kinetic energy (ALLKE). +In a quasi-static analysis the value of the kinetic energy (ALLKE) should not exceed a small fraction +of the value of the strain energy (ALLIE). +It is a good practice to output the constraint penalty work (ALLCW) and the contact penalty work +(ALLPW) in analyses involving constraints (such as ties and fasteners) and contact. The value of these +energies should be close to zero. +Input file template +*HEADING +… +*MATERIAL, NAME=name +*ELASTIC +… +*DENSITY +Data lines to define density +*DAMPING, ALPHA = , BETA= +Data lines to define Rayleigh damping +… +*BOUNDARY +Data lines to specify zero-valued boundary conditions +*INITIAL CONDITIONS, TYPE=type +Data lines to specify initial conditions +*AMPLITUDE, NAME=name +Data lines to define amplitude variations +************************* +*STEP +*DYNAMIC, EXPLICIT +Data line to specify the time period of the step +*DIAGNOSTICS, DEFORMATION SPEED CHECK=SUMMARY +*BOUNDARY, AMPLITUDE=name +Data lines to describe zero-valued or nonzero boundary conditions +*CLOAD and/or *DLOAD +Data lines to specify loading +*TEMPERATURE and/or *FIELD +Data lines to specify predefined fields +*FILE OUTPUT, NUMBER INTERVAL=n +*EL FILE +Data line specifying element output variables +*NODE FILE +Data line specifying node output variables +*ENERGY FILE +*OUTPUT, FIELD, NUMBER INTERVAL=n +*ELEMENT OUTPUT +Data line specifying element output variables +*NODE OUTPUT +Data line specifying node output variables +*OUTPUT, HISTORY, TIME INTERVAL=t +*ELEMENT OUTPUT, ELSET=element set name +Data line specifying element output variables +*NODE OUTPUT, NSET=node set name +Data line specifying node output variables +*ENERGY OUTPUT +Data line specifying energy output variables +*END STEP +************************* +*STEP +*DYNAMIC, EXPLICIT, ELEMENT BY ELEMENT +… +*BULK VISCOSITY +Data line to define linear and/or quadratic bulk viscosity in this step +… +*END STEP +6.3.4 +DIRECT-SOLUTION STEADY-STATE DYNAMIC ANALYSIS +Products: Abaqus/Standard Abaqus/CAE +References +• “Dynamic analysis procedures: overview,” Section 6.3.1 +• “Mode-based steady-state dynamic analysis,” Section 6.3.8 +• “Subspace-based steady-state dynamic analysis,” Section 6.3.9 +• “Defining an analysis,” Section 6.1.2 +• “General and linear perturbation procedures,” Section 6.1.3 +• *STEADY STATE DYNAMICS +• “Configuring a direct-solution steady-state dynamic procedure” in “Configuring linear perturbation +analysis procedures,” Section 14.11.2 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +• “Creating and modifying prescribed conditions,” Section 16.4 of the Abaqus/CAE User’s Manual +Overview +A direct-solution steady-state dynamic analysis: +• is used to calculate the steady-state dynamic linearized response of a system to harmonic excitation; +• is a linear perturbation procedure; +• calculates the response directly in terms of the physical degrees of freedom of the model; +• is an alternative to mode-based steady-state dynamic analysis, in which the response of the system +is calculated on the basis of the eigenmodes; +• is more expensive computationally than mode-based or subspace-based steady-state dynamics; +• is more accurate than mode-based or subspace-based steady-state dynamics, +in particular if +significant frequency-dependent material damping or viscoelastic material behavior is present in +the structure; and +• is able to bias the excitation frequencies toward the approximate values that generate a response +peak. +Introduction +Steady-state dynamic analysis provides the steady-state amplitude and phase of the response of a system +due to harmonic excitation at a given frequency. Usually such analysis is done as a frequency sweep by +applying the loading at a series of different frequencies and recording the response; in Abaqus/Standard +the direct-solution steady-state dynamic procedure conducts this frequency sweep. In a direct-solution +steady-state analysis the steady-state harmonic response is calculated directly in terms of the physical +degrees of freedom of the model using the mass, damping, and stiffness matrices of the system. +When defining a direct-solution steady-state dynamic step, you specify the frequency ranges +of interest and the number of frequencies at which results are required in each range (including the +bounding frequencies of the range). In addition, you can specify the type of frequency spacing (linear or +logarithmic) to be used, as described below (“Selecting the frequency spacing”). Logarithmic frequency +spacing is the default. Frequencies are given in cycles/time. +Those frequency points for which results are required can be spaced equally along the frequency axis +(on a linear or a logarithmic scale), or they can be biased toward the ends of the user-defined frequency +range by introducing a bias parameter (described below). +The direct-solution steady-state analysis procedure can be used in the following cases for which the +eigenvalues cannot be extracted (and, thus, the mode-based steady-state dynamics procedures are not +applicable): +• for nonsymmetric stiffness; +• when any form of damping other than modal damping must be included; and +• when viscoelastic material properties must be taken into account. +While the response in this procedure is linear, the prior response can be nonlinear. Initial stress +effects (stress stiffening) as well as load stiffness effects will be included in the steady-state dynamics +response if nonlinear geometric effects (“General and linear perturbation procedures,” Section 6.1.3) +were included in any general analysis step prior to the direct-solution steady-state dynamic procedure. +Input File Usage: +Abaqus/CAE Usage: +*STEADY STATE DYNAMICS, DIRECT +Step module: Create Step: Linear perturbation: Steady-state +dynamics, Direct +Ignoring damping +If damping terms can be ignored, you can specify that a real, rather than a complex, system matrix be +factored, which can significantly reduce computational time. Damping is discussed below. +Input File Usage: +Abaqus/CAE Usage: +*STEADY STATE DYNAMICS, DIRECT, REAL ONLY +Step module: Create Step: Linear perturbation: Steady-state +dynamics, Direct: Compute real response only +Selecting the type of frequency interval for which output is requested +Three types of frequency intervals are permitted for output from a direct-solution steady-state dynamic +step. If an eigenvalue extraction step precedes the direct-solution steady-state dynamic step, you can +select either the range or the eigenfrequency type of frequency interval; otherwise, only the range type +can be used. +Dividing the specified frequency range using the user-defined number of points and the optional bias +function +For the range type of frequency interval (the default), the specified frequency range of interest is divided +using the user-defined number of points and the optional bias function. +Input File Usage: +Abaqus/CAE Usage: +*STEADY STATE DYNAMICS, DIRECT, INTERVAL=RANGE +Step module: Create Step: Linear perturbation: Steady-state +dynamics, Direct: toggle off Use eigenfrequencies to +subdivide each frequency range +Specifying the frequency ranges by using the system’s eigenfrequencies +If the direct-solution steady-state dynamic analysis is preceded by an eigenfrequency extraction step, +you can select the eigenfrequency type of frequency interval. The following intervals then exist in each +frequency range: +• First interval: extends from the lower limit of the frequency range given to the first eigenfrequency +in the range. +• Intermediate intervals: extend from eigenfrequency to eigenfrequency. +• Last interval: extends from the highest eigenfrequency in the range to the upper limit of the +frequency range. +For each of these intervals the frequencies at which results are calculated are determined using the user- +defined number of points (which includes the bounding frequencies for the interval) and the optional bias +function. Figure 6.3.4–1 illustrates the division of the frequency range for 5 calculation points and a bias +parameter equal to 1. +Input File Usage: +*STEADY STATE DYNAMICS, DIRECT, +INTERVAL=EIGENFREQUENCY +Abaqus/CAE Usage: +Step module: Create Step: Linear perturbation: Steady-state dynamics, +Direct: Use eigenfrequencies to subdivide each frequency range +frequency points +lower end +of the range +mode n +mode n +1 +mode n + 2 +upper end +of the range +Figure 6.3.4–1 Division of range for the eigenfrequency +type of interval and 5 calculation points. +Specifying the frequency ranges by the frequency spread +If the direct-solution steady-state dynamic analysis is preceded by an eigenfrequency extraction +In this case intervals exist around each +step, you can select the spread type of frequency interval. +eigenfrequency in the frequency range. For each of the intervals the equally spaced frequencies at +which results are calculated are determined using the user-defined number of points (which includes +the bounding frequencies for the interval). The minimum number of frequency points is 3. +If the +user-defined value is less than 3 (or omitted), the default value of 3 points is assumed. Figure 6.3.4–2 +illustrates the division of the frequency range for 5 calculation points. +The bias parameter is not supported with the spread type of frequency interval. +Frequency points +Frequency points +fn +fn + 1 +(1 – spread) · fn +(1 + spread) · fn +(1 – spread) · fn + 1 +(1 + spread) · fn + 1 +Figure 6.3.4–2 Division of range for the spread type of interval and 5 calculation +points. +and +are eigenfrequencies of the system. +Input File Usage: +*STEADY STATE DYNAMICS, DIRECT, INTERVAL=SPREAD +lwr_freq, upr_freq, numpts, bias_param, freq_scale_factor, spread +Abaqus/CAE Usage: +You cannot specify frequency ranges by frequency spread in Abaqus/CAE. +Selecting the frequency spacing +Two types of frequency spacing are permitted for a direct-solution steady-state dynamic step. For the +logarithmic frequency spacing (the default), the specified frequency ranges of interest are divided using +a logarithmic scale. Alternatively, a linear frequency spacing can be used if a linear scale is desired. +Input File Usage: +Use either of the following options: +Abaqus/CAE Usage: +*STEADY STATE DYNAMICS, DIRECT, +FREQUENCY SCALE=LOGARITHMIC +*STEADY STATE DYNAMICS, DIRECT, FREQUENCY SCALE=LINEAR +Step module: Create Step: Linear perturbation: Steady-state +dynamics, Direct: Scale: Logarithmic or Linear +Requesting multiple frequency ranges +You can request multiple frequency ranges or multiple single frequency points for a direct-solution +steady-state dynamic step. +Input File Usage: +*STEADY STATE DYNAMICS, DIRECT +lwr_freq1, upr_freq1, numpts1, bias_param1, freq_scale_factor1 +lwr_freq2, upr_freq2, numpts2, bias_param2, freq_scale_factor2 +... +single_freq1 +single_freq2 +... +Repeat the data lines as often as necessary. +Abaqus/CAE Usage: +Step module: Create Step: Linear perturbation: Steady-state dynamics, +Direct: Data: enter data in table, and add rows as necessary +The bias parameter +The bias parameter can be used to provide closer spacing of the results points either toward the middle +or toward the ends of each frequency interval. Figure 6.3.4–3 shows a few examples of the effect of the +bias parameter on the frequency spacing. +frequency points +f1 +Bias parameter = 1 +f2 +Bias parameter = 2 +Bias parameter = 3 +Bias parameter = 5 +Figure 6.3.4–3 Effect of the bias parameter on the frequency +spacing for a number of points +. +The bias formula used in direct-solution steady-state dynamics is +where +; +); +is the number of frequency points at which results are to be given; +is one such frequency point ( +is the lower limit of the frequency range; +is the upper limit of the range; +is the frequency at which the kth results are given; +is the bias parameter value; and +is the frequency or the logarithm of the frequency, depending on the value chosen for the +frequency scale. +A bias parameter, p, that is greater than 1.0 provides closer spacing of the results points toward the ends +of the frequency interval, while values of p that are less than 1.0 provide closer spacing toward the middle +of the frequency interval. The default bias parameter is 1.0 for a range frequency interval and 3.0 for an +eigenfrequency interval. +The frequency scale factor +The frequency scale factor can be used to scale frequency points. All the frequency points, except the +lower and upper limit of the frequency range, are multiplied by this factor. This scale factor can be used +only when the frequency interval is specified by using the system’s eigenfrequencies . +Damping +If damping is absent, the response of a structure will be unbounded if the forcing frequency is equal +to an eigenfrequency of the structure. To get quantitatively accurate results, especially near natural +frequencies, accurate specification of damping properties is essential. The various damping options +available are discussed in “Material damping,” Section 26.1.1. +In direct-solution steady-state dynamics damping can be created by the following: +• dashpots , +• “Rayleigh” damping associated with materials and elements +Section 26.1.1), +, +• structural damping , and +• viscoelasticity included in the material definitions . +When a real-only system matrix is factored, all forms of damping are ignored, including quiet +boundaries on infinite elements and nonreflecting boundaries on acoustic elements. +Contact conditions with sliding friction +Abaqus/Standard automatically detects the contact nodes that are slipping due to velocity differences +imposed by the motion of the reference frame or the transport velocity in prior steps. At those nodes the +tangential degrees of freedom are not constrained and the effect of friction results in an unsymmetric +contribution to the stiffness matrix. At other contact nodes the tangential degrees of freedom are +constrained. +Friction at contact nodes at which a velocity differential is imposed can give rise to damping terms. +There are two kinds of friction-induced damping effects. The first effect is caused by the friction forces +stabilizing the vibrations in the direction perpendicular to the slip direction. This effect exists only in +three-dimensional analysis. The second effect is caused by a velocity-dependent friction coefficient. +If the friction coefficient decreases with velocity (which is usually the case), the effect is destabilizing +and is also known as “negative damping.” For more details, see “Coulomb friction,” Section 5.2.3 of +the Abaqus Theory Manual. Direct-solution steady-state dynamics analysis allows you to include these +friction-induced contributions to the damping matrix. +Input File Usage: +Abaqus/CAE Usage: +*STEADY STATE DYNAMICS, DIRECT, FRICTION DAMPING=YES +Step module: Create Step: Linear perturbation: Steady-state dynamics, +Direct: Include friction-induced damping effects +Initial conditions +The base state is the current state of the model at the end of the last general analysis step prior to the +steady-state dynamic step. If the first step of an analysis is a perturbation step, the base state is determined +from the initial conditions (“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1). +Initial condition definitions that directly define solution variables, such as velocity, cannot be used in a +steady-state dynamic analysis. +Boundary conditions +In a steady-state dynamic analysis the real and imaginary parts of any degree of freedom are either +restrained or unrestrained simultaneously; it is physically impossible to have one part restrained and the +other part unrestrained. Abaqus/Standard will automatically restrain both the real and imaginary parts of +a degree of freedom even if only one part is prescribed specifically. The unspecified part will be assumed +to have a perturbation magnitude of zero. +Boundary conditions can be applied to any of the displacement or rotation degrees of freedom +(1–6) in a direct-solution steady-state analysis. See “Boundary conditions in Abaqus/Standard and +Abaqus/Explicit,” Section 33.3.1. These boundary conditions will vary sinusoidally with time. You +specify the real (in-phase) part of a boundary condition and the imaginary (out-of-phase) part of a +boundary condition separately. +Input File Usage: +Use either of the following options to define the real (in-phase) part of the +boundary condition: +*BOUNDARY +*BOUNDARY, REAL +Abaqus/CAE Usage: +Use the following option to define the imaginary (out-of-phase) part of the +boundary condition: +*BOUNDARY, IMAGINARY +Load module: boundary condition editor: real (in-phase) part + imaginary +(out-of-phase) part i +Frequency-dependent boundary conditions +An amplitude definition can be used to specify the amplitude of a boundary condition as a function of +frequency (“Amplitude curves,” Section 33.1.2). +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options: +*AMPLITUDE, NAME=name +*BOUNDARY, REAL or IMAGINARY, AMPLITUDE=name +Load or Interaction module: Create Amplitude: Name: name +Load module: boundary condition editor: real (in-phase) part + imaginary +(out-of-phase) part i: Amplitude: name +Loads +The following loads can be prescribed in a steady-state dynamic analysis: +• Concentrated nodal forces can be applied to the displacement degrees of freedom (1–6); see +“Concentrated loads,” Section 33.4.2. +• Distributed pressure forces or body forces can be applied; see “Distributed loads,” Section 33.4.3. +The distributed load types available with particular elements are described in Part VI, “Elements.” +• Incident wave loads can be applied; see “Acoustic and shock loads,” Section 33.4.6. +These loads are assumed to vary sinusoidally with time over a user-specified range of frequencies. Loads +are given in terms of their real and imaginary components. +Coriolis distributed loading adds an imaginary antisymmetric contribution to the overall system of +equations. This contribution is currently accounted for in solid and truss elements only and is activated +by using the unsymmetric matrix storage and solution scheme for the step (“Defining an analysis,” +Section 6.1.2). +Incident wave loads can be used to model sound waves from distinct planar or spherical sources or +from diffuse fields. +Fluid flux loading cannot be used in a steady-state dynamic analysis. +Input File Usage: +Use any of the following options to define the real (in-phase) part of the load: +*CLOAD or *DLOAD +*CLOAD or *DLOAD, REAL +Use either of the following options to define the imaginary (out-of-phase) part +of the load: +*CLOAD or *DLOAD, IMAGINARY +Abaqus/CAE Usage: +Load module: +part i +load editor: real (in-phase) part + imaginary (out-of-phase) +Frequency-dependent loading +An amplitude definition can be used to specify the amplitude of a load as a function of frequency +(“Amplitude curves,” Section 33.1.2). +Input File Usage: +Use both of the following options: +*AMPLITUDE, NAME=name +*CLOAD or *DLOAD, REAL or IMAGINARY, AMPLITUDE=name +Load or Interaction module: Create Amplitude: Name: name +Load module: +part i: Amplitude: name +load editor: real (in-phase) part + imaginary (out-of-phase) +Abaqus/CAE Usage: +Predefined fields +Predefined temperature fields can be specified in direct-solution steady-state dynamic analysis and will produce harmonically varying thermal strains if thermal +expansion is included in the material definition (“Thermal expansion,” Section 26.1.2). Other predefined +fields are ignored. +Material options +As in any dynamic analysis procedure, mass or density (“Density,” Section 21.2.1) must be assigned +to some regions of any separate parts of the model where dynamic response is required. If an analysis +is desired in which the inertia effects are neglected, the density should be set to a very small number. +The following material properties are not active during steady-state dynamic analyses: plasticity and +other inelastic effects, thermal properties (except for thermal expansion), mass diffusion properties, +electrical properties (except for the electrical potential, +, in piezoelectric analysis), and pore fluid flow +properties—see “General and linear perturbation procedures,” Section 6.1.3. +Viscoelastic effects can be included in direct-solution steady-state harmonic response analysis. +The linearized viscoelastic response is considered to be a perturbation about a nonlinear preloaded +state, which is computed on the basis of purely elastic behavior (long-term response) in the viscoelastic +components. Therefore, the vibration amplitude must be sufficiently small so that the material response +in the dynamic phase of the problem can be treated as a linear perturbation about the predeformed +state. Viscoelastic frequency domain response is described in “Frequency domain viscoelasticity,” +Section 22.7.2. +Elements +Any of the following elements available in Abaqus/Standard can be used in a steady-state dynamic +procedure: +• stress/displacement elements (other than generalized axisymmetric elements with twist); +• acoustic elements; +• piezoelectric elements; or +• hydrostatic fluid elements. +See “Choosing the appropriate element for an analysis type,” Section 27.1.3. +Output +In direct-solution steady-state dynamic analysis the value of an output variable such as strain (E) or stress +(S) is a complex number with real and imaginary components. In the case of data file output the first +printed line gives the real components while the second lists the imaginary components. Results and +data file output variables are also provided to obtain the magnitude and phase of many variables . In the case of data file output the first +printed line gives the magnitudes while the second lists the phase angle. +The following variables are provided specifically for steady-state dynamic analysis: +Element integration point variables: +PHS +PHE +PHEPG +PHEFL +PHMFL +PHMFT +Magnitude and phase angle of all stress components. +Magnitude and phase angle of all strain components. +Magnitude and phase angles of the electrical potential gradient vector. +Magnitude and phase angles of the electrical flux vector. +Magnitude and phase angle of the mass flow rate in fluid link elements. +Magnitude and phase angle of the total mass flow in fluid link elements. +For connector elements, the following element output variables are available: +PHCTF +PHCEF +PHCVF +PHCRF +PHCSF +PHCU +PHCCU +PHCV +PHCA +Nodal variables: +PU +PPOR +PHPOT +PRF +PHCHG +Magnitude and phase angle of connector total forces. +Magnitude and phase angle of connector elastic forces. +Magnitude and phase angle of connector viscous forces. +Magnitude and phase angle of connector reaction forces. +Magnitude and phase angle of connector friction forces. +Magnitude and phase angle of connector relative displacements. +Magnitude and phase angle of connector constitutive displacements. +Magnitude and phase angle of connector relative velocities. +Magnitude and phase angle of connector relative accelerations. +Magnitude and phase angle of all displacement/rotation components at a node. +Magnitude and phase angle of the fluid, pore, or acoustic pressure at a node. +Magnitude and phase angle of the electrical potential at a node. +Magnitude and phase angle of all reaction forces/moments at a node. +Magnitude and phase angle of the reactive charge at a node. +Element energy densities (such as the elastic strain energy density, SENER) and whole element +energies (such as the total kinetic energy of an element, ELKE) are not available for output in a direct- +solution steady-state dynamic analysis. +Whole model variables such as ALLIE (total strain energy) are available for direct-solution steady- +state dynamic analysis by requesting energy output to the data, results, or output database files . +Input file template +*HEADING +… +*AMPLITUDE, NAME=loadamp +Data lines to define an amplitude curve as a function of frequency (cycles/time) +** +*STEP, NLGEOM +Include the NLGEOM parameter so that stress stiffening effects will +be included in the steady-state dynamic step +*STATIC +**Any general analysis procedure can be used to preload the structure +… +*CLOAD and/or *DLOAD +Data lines to prescribe preloads +*TEMPERATURE and/or *FIELD +Data lines to define values of predefined fields for preloading the structure +*BOUNDARY +Data lines to specify boundary conditions to preload the structure +… +*END STEP +** +*STEP +*STEADY STATE DYNAMICS, DIRECT +Data lines to specify frequency ranges and bias parameters +*BOUNDARY, REAL +Data lines to specify real (in-phase) boundary conditions +*BOUNDARY, IMAGINARY +Data lines to specify imaginary (out-of-phase) boundary conditions +*CLOAD, AMPLITUDE=loadamp +Data lines to specify sinusoidally varying, frequency-dependent, concentrated loads +*CLOAD and/or *DLOAD +Data lines to specify sinusoidally varying loads +… +*END STEP +6.3.5 +NATURAL FREQUENCY EXTRACTION +Products: Abaqus/Standard Abaqus/CAE Abaqus/AMS +References +• “Defining an analysis,” Section 6.1.2 +• “General and linear perturbation procedures,” Section 6.1.3 +• “Dynamic analysis procedures: overview,” Section 6.3.1 +• *FREQUENCY +• “Configuring a frequency procedure” in “Configuring linear perturbation analysis procedures,” +Section 14.11.2 of the Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +The frequency extraction procedure: +• performs eigenvalue extraction to calculate the natural frequencies and the corresponding mode +shapes of a system; +• will include initial stress and load stiffness effects due to preloads and initial conditions if geometric +nonlinearity is accounted for in the base state, so that small vibrations of a preloaded structure can +be modeled; +• will compute residual modes if requested; +• is a linear perturbation procedure; +• can be performed using the traditional Abaqus software architecture or, if appropriate, the high- +performance SIM architecture ; and +• solves the eigenfrequency problem only for symmetric mass and stiffness matrices; the complex +eigenfrequency solver must be used if unsymmetric contributions, such as the load stiffness, are +needed. +Eigenvalue extraction +The eigenvalue problem for the natural frequencies of an undamped finite element model is +where +is the mass matrix (which is symmetric and positive definite); +is the stiffness matrix (which includes initial stiffness effects if the base state +included the effects of nonlinear geometry); +is the eigenvector (the mode of vibration); and +are degrees of freedom. +M and N +is positive definite, all eigenvalues are positive. Rigid body modes and instabilities +When +cause +Instabilities produce +to be indefinite. Rigid body modes produce zero eigenvalues. +negative eigenvalues and occur when you include initial stress effects. Abaqus/Standard solves the +eigenfrequency problem only for symmetric matrices. +Selecting the eigenvalue extraction method +Abaqus/Standard provides three eigenvalue extraction methods: +• Lanczos +• Automatic multi-level substructuring (AMS), an add-on analysis capability for Abaqus/Standard +• Subspace iteration +In addition, you must consider the software architecture that will be used for the subsequent modal +superposition procedures. The choice of architecture has minimal impact on the frequency extraction +procedure, but the SIM architecture can offer significant performance improvements over the traditional +architecture for subsequent mode-based steady-state or transient dynamic procedures . The architecture that you use for the frequency extraction procedure is used +for all subsequent mode-based linear dynamic procedures; you cannot switch architectures during an +analysis. The software architectures used by the different eigensolvers are outlined in Table 6.3.5–1. +Table 6.3.5–1 Software architectures available with different eigensolvers. +Eigensolver +Lanczos +AMS +Subspace +Iteration +Software +Architecture +Traditional +SIM +The Lanczos solver with the traditional architecture is the default eigenvalue extraction method +because it has the most general capabilities. However, the Lanczos method is generally slower than the +AMS method. The increased speed of the AMS eigensolver is particularly evident when you require a +large number of eigenmodes for a system with many degrees of freedom. However, the AMS method +has the following limitations: +• All restrictions imposed on SIM-based linear dynamic procedures also apply to mode-based linear +dynamic analyses based on mode shapes computed by the AMS eigensolver. See “Using the +SIM architecture for modal superposition dynamic analyses” in “Dynamic analysis procedures: +overview,” Section 6.3.1, for details. +• The AMS eigensolver does not compute composite modal damping factors, participation factors, +or modal effective masses. However, if participation factors are needed for primary base motions, +they will be computed but are not written to the printed data (.dat) file. +• You cannot use the AMS eigensolver in an analysis that contains piezoelectric elements. +• You cannot request output to the results (.fil) file in an AMS frequency extraction step. +If your model has many degrees of freedom and these limitations are acceptable, you should use the +AMS eigensolver. Otherwise, you should use the Lanczos eigensolver. The Lanczos eigensolver and the +subspace iteration method are described in “Eigenvalue extraction,” Section 2.5.1 of the Abaqus Theory +Manual. +Lanczos eigensolver +For the Lanczos method you need to provide the maximum frequency of interest or the number of +eigenvalues required; Abaqus/Standard will determine a suitable block size (although you can override +If you specify both the maximum frequency of interest and the number of +this choice, if needed). +eigenvalues required and the actual number of eigenvalues is underestimated, Abaqus/Standard will issue +a corresponding warning message; the remaining eigenmodes can be found by restarting the frequency +extraction. +You can also specify the minimum frequencies of interest; Abaqus/Standard will extract +eigenvalues until either the requested number of eigenvalues has been extracted in the given range or +all the frequencies in the given range have been extracted. +See “Using the SIM architecture for modal superposition dynamic analyses” in “Dynamic analysis +procedures: overview,” Section 6.3.1, for information on using the SIM architecture with the Lanczos +eigensolver. +Input File Usage: +Abaqus/CAE Usage: +*FREQUENCY, EIGENSOLVER=LANCZOS +Step module: Step→Create: Frequency: Basic: Eigensolver: Lanczos +Choosing a block size for the Lanczos method +In general, the block size for the Lanczos method should be as large as the largest expected multiplicity of +eigenvalues (that is, the largest number of modes with the same frequency). A block size larger than 10 +is not recommended. If the number of eigenvalues requested is n, the default block size is the minimum +of (7, n). The choice of 7 for block size proves to be efficient for problems with rigid body modes. The +number of block Lanczos steps within each Lanczos run is usually determined by Abaqus/Standard but +can be changed by you. In general, if a particular type of eigenproblem converges slowly, providing more +block Lanczos steps will reduce the analysis cost. On the other hand, if you know that a particular type +of problem converges quickly, providing fewer block Lanczos steps will reduce the amount of in-core +memory used. The default values are +Block size +Maximum number of +block Lanczos steps +≥ 4 +80 +50 +45 +35 +Automatic multi-level substructuring (AMS) eigensolver +For the AMS method you need only specify the maximum frequency of interest (the global frequency), +and Abaqus/Standard will extract all the modes up to this frequency. You can also specify the minimum +frequencies of interest and/or the number of requested modes. However, specifying these values will not +affect the number of modes extracted by the eigensolver; it will affect only the number of modes that are +stored for output or for a subsequent modal analysis. +, +, and +The execution of the AMS eigensolver can be controlled by specifying three parameters: +. These three parameters multiplied by the maximum +(default value of 5) controls the cutoff +frequency of interest define three cutoff frequencies. +frequency for substructure eigenproblems in the reduction phase, while +(default values of 1.7 and 1.1, respectively) control the cutoff frequencies used to define a starting +subspace in the reduced eigensolution phase. Generally, increasing the value of +and +and +improves the accuracy of the results but may affect the performance of the analysis. +Requesting eigenvectors at all nodes +By default, the AMS eigensolver computes eigenvectors at every node of the model. +Input File Usage: +Abaqus/CAE Usage: +*FREQUENCY, EIGENSOLVER=AMS +Step module: Step→Create: Frequency: Basic: Eigensolver: AMS +Requesting eigenvectors only at specified nodes +Alternatively, you can specify a node set, and eigenvectors will be computed and stored only at the +nodes that belong to that node set. The node set that you specify must include all nodes at which loads +are applied or output is requested in any subsequent modal analysis (this includes any restarted analysis). +If element output is requested or element-based loading is applied, the nodes attached to the associated +elements must also be included in this node set. Computing eigenvectors at only selected nodes improves +performance and reduces the amount of stored data. Therefore, it is recommended that you use this option +for large problems. +Input File Usage: +Abaqus/CAE Usage: +*FREQUENCY, EIGENSOLVER=AMS, NSET=name +Step module: Step→Create: Frequency: Basic: Eigensolver: +AMS: Limit region of saved eigenvectors +Controlling the AMS eigensolver +The AMS method consists of the following three phases: +• Reduction phase: +In this phase Abaqus/Standard uses a multi-level substructuring technique to +reduce the full system in a way that allows a very efficient eigensolution of the reduced system. The +approach combines a sparse factorization based on a multi-level supernode elimination tree and a +local eigensolution at each supernode. +Starting from the lowest level supernodes, we use a Craig-Bampton substructure reduction +technique to successively reduce the size of the system as we progress upward in the elimination +tree. At each supernode a local eigensolution is obtained based on fixing the degrees of freedom +connected to the next higher level supernode (these are the local retained or “fixed-interface” degrees +of freedom). At the end of the reduction phase the full system has been reduced such that the reduced +stiffness matrix is diagonal and the reduced mass matrix has unit diagonal values but contains +off-diagonal blocks of nonzero values representing the coupling between the supernodes. +The cost of the reduction phase depends on the system size and the number of eigenvalues +extracted (the number of eigenvalues extracted is controlled indirectly by specifying the highest +eigenfrequency desired). You can make trade-offs between cost and accuracy during the reduction +phase through the +parameter. This parameter multiplied by the highest eigenfrequency +specified for the full model yields the highest eigenfrequency that is extracted in the local supernode +eigensolutions. Increasing the value of +increases the accuracy of the reduction since +more local eigenmodes are retained. However, increasing the number of retained modes also +increases the cost of the reduced eigensolution phase, which is discussed next. +• Reduced eigensolution phase: +In this phase Abaqus/Standard computes the eigensolution of +the reduced system that comes from the previous phase. Although the reduced system typically is +two orders of magnitude smaller in size than the original system, generally it still is too large to +solve directly. Thus, the system is further reduced mainly by truncating the retained eigenmodes +and then solved using a single subspace iteration step. The two AMS parameters, +and +, define a starting subspace of the subspace iteration step. The default values of these +parameters are carefully chosen and provide accurate results in most cases. When a more accurate +solution is needed, the recommended procedure is to increase both parameters proportionally from +their respective default values. +• Recovery phase: +eigenvectors of the reduced problem and local substructure modes. +specified nodes, the eigenvectors are computed only at those nodes. +In this phase the eigenvectors of the original system are recovered using +If you request recovery at +Subspace iteration method +For the subspace iteration procedure you need only specify the number of eigenvalues required; +If the subspace iteration +Abaqus/Standard chooses a suitable number of vectors for the iteration. +technique is requested, you can also specify the maximum frequency of interest; Abaqus/Standard +extracts eigenvalues until either the requested number of eigenvalues has been extracted or the last +frequency extracted exceeds the maximum frequency of interest. +Input File Usage: +Abaqus/CAE Usage: +*FREQUENCY, EIGENSOLVER=SUBSPACE +Step module: Step→Create: Frequency: Basic: Eigensolver: Subspace +Structural-acoustic coupling +In Abaqus only the +Structural-acoustic coupling affects the natural frequency response of systems. +Lanczos eigensolver fully includes this effect. In Abaqus/AMS and the subspace eigensolver the effect +of coupling is neglected for the purpose of computing the modes and frequencies; these are computed +using natural boundary conditions at the structural-acoustic coupling surface. An intermediate degree of +consideration of the structural-acoustic coupling operator is the default in Abaqus/AMS and the Lanczos +eigensolver, which is based on the SIM architecture: the coupling is projected onto the modal space and +stored for later use. +Structural-acoustic coupling using the Lanczos eigensolver without the SIM architecture +If structural-acoustic coupling is present in the model and the Lanczos method not based on the SIM +architecture is used, Abaqus/Standard extracts the coupled modes by default. Because these modes +fully account for coupling, they represent the mathematically optimal basis for subsequent modal +procedures. The effect is most noticeable in strongly coupled systems such as steel shells and water. +However, coupled structural-acoustic modes cannot be used in subsequent random response or response +spectrum analyses. You can define the coupling using either acoustic-structural interaction elements + or the surface-based tie constraint . It is possible to ignore coupling when +extracting acoustic and structural modes; in this case the coupling boundary is treated as traction-free +on the structural side and rigid on the acoustic side. +Input File Usage: +Use the following option to account for structural-acoustic coupling during the +frequency extraction: +*FREQUENCY, EIGENSOLVER=LANCZOS, +ACOUSTIC COUPLING=ON (default if the SIM architecture is not used) +Use the following option to ignore structural-acoustic coupling during the +frequency extraction: +*FREQUENCY, EIGENSOLVER=LANCZOS, +ACOUSTIC COUPLING=OFF +Abaqus/CAE Usage: +Step module: Step→Create: Frequency: Basic: Eigensolver: Lanczos, +toggle Include acoustic-structural coupling where applicable +Structural-acoustic coupling using the AMS and Lanczos eigensolver based on the SIM +architecture +For frequency extractions that use the AMS eigensolver or the Lanczos eigensolver based on the SIM +architecture, the modes are computed using traction-free boundary conditions on the structural side of +the coupling boundary and rigid boundary conditions on the acoustic side. Structural-acoustic coupling +operators are projected +by default onto the subspace of eigenvectors. Contributions to these global operators, which come from +surface-based tie constraints defined between structural and acoustic surfaces, are assembled into global +matrices that are projected onto the mode shapes and used in subsequent SIM-based modal dynamic +procedures. +User-defined acoustic-structural +interaction elements + cannot be used in an AMS eigenvalue extraction analysis. +Input File Usage: +Use either of the following options to project structural-acoustic coupling +operators onto the subspace of eigenvectors: +Abaqus/CAE Usage: +*FREQUENCY, EIGENSOLVER=AMS, +ACOUSTIC COUPLING=PROJECTION (default for the AMS eigensolver) +or +*FREQUENCY, EIGENSOLVER=LANCZOS, SIM, +ACOUSTIC COUPLING=PROJECTION (default in SIM-based analysis) +Use the following option to disable the projection of structural-acoustic +coupling operators: +*FREQUENCY, ACOUSTIC COUPLING=OFF +Use the following option to project structural-acoustic coupling operators onto +the subspace of eigenvectors: +Step module: Step→Create: Frequency: Basic: Eigensolver: AMS, +toggle on Project acoustic-structural coupling where applicable +Use the following option to disable the projection of structural-acoustic +coupling operators: +Step module: Step→Create: Frequency: Basic: Eigensolver: AMS, +toggle off Project acoustic-structural coupling where applicable +Projection of structural-acoustic coupling operators using the Lanczos +eigensolver based on the SIM architecture is not supported in Abaqus/CAE. +Specifying a frequency range for the acoustic modes +Because structural-acoustic coupling is ignored during the AMS and SIM-based Lanczos eigenanalysis, +the computed resonances will, in principle, be higher than those of the fully coupled system. This may +be understood as a consequence of neglecting the mass of the fluid in the structural phase and vice versa. +For the common metal and air case, the structural resonances may be relatively unaffected; however, +some acoustic modes that are significant in the coupled response may be omitted due to the air’s upward +frequency shift during eigenanalysis. Therefore, Abaqus allows you to specify a multiplier, so that the +maximum acoustic frequency in the analysis is taken to be higher than the structural maximum. +Input File Usage: +Use either of the following options: +*FREQUENCY, EIGENSOLVER=AMS +, , , , , , acoustic range factor +or +*FREQUENCY, EIGENSOLVER=LANCZOS, SIM +, , , , , , acoustic range factor +Abaqus/CAE Usage: +Step module: Step→Create: Frequency: Basic: Eigensolver: AMS, +Acoustic range factor: acoustic range factor +Specifying a frequency range for the acoustic modes when using the SIM-based +Lanczos eigenanalysis is not supported in Abaqus/CAE. +Effects of fluid motion on natural frequency analysis of acoustic systems +To extract natural frequencies from an acoustic-only or coupled structural-acoustic system in which +fluid motion is prescribed using an acoustic flow velocity, either the Lanczos method or the complex +eigenvalue extraction procedure can be used. In the former case Abaqus extracts real-only eigenvalues +and considers the fluid motion’s effects only on the acoustic stiffness matrix. Thus, these results are of +primary interest as a basis for subsequent linear perturbation procedures. When the complex eigenvalue +extraction procedure is used, the fluid motion effects are included in their entirety; that is, the acoustic +stiffness and damping matrices are included in the analysis. +Frequency shift +For the Lanczos and subspace iteration eigensolvers you can specify a positive or negative shifted +squared frequency, S. This feature is useful when a particular frequency is of concern or when the +natural frequencies of an unrestrained structure or a structure that uses secondary base motions (large +mass approach) are needed. In the latter case a shift from zero (the frequency of the rigid body modes) +will avoid singularity problems or round-off errors for the large mass approach; a negative frequency +shift is normally used. The default is no shift. +If the Lanczos eigensolver is in use and the user-specified shift is outside the requested frequency +range, the shift will be adjusted automatically to a value close to the requested range. +Normalization +For the Lanczos and subspace iteration eigensolvers both displacement and mass eigenvector +normalization are available. Displacement normalization is the default. Mass normalization is the only +option available for SIM-based natural frequency extraction. +The choice of eigenvector normalization type has no influence on the results of subsequent modal +dynamic steps . The normalization type determines only the manner in which the eigenvectors +are represented. +In addition to extracting the natural frequencies and mode shapes, the Lanczos and subspace +iteration eigensolvers automatically calculate the generalized mass, the participation factor, the effective +mass, and the composite modal damping for each mode; therefore, these variables are available for use +in subsequent linear dynamic analyses. The AMS eigensolver computes only the generalized mass. +Displacement normalization +If displacement normalization is selected, the eigenvectors are normalized so that the largest displacement +entry in each vector is unity. If the displacements are negligible, as in a torsional mode, the eigenvectors +are normalized so that the largest rotation entry in each vector is unity. In a coupled acoustic-structural +extraction, if the displacements and rotations in a particular eigenvector are small when compared to the +acoustic pressures, the eigenvector is normalized so that the largest acoustic pressure in the eigenvector +is unity. The normalization is done before the recovery of dependent degrees of freedom that have been +previously eliminated with multi-point constraints or equation constraints. Therefore, it is possible that +such degrees of freedom may have values greater than unity. +Input File Usage: +Abaqus/CAE Usage: +*FREQUENCY, NORMALIZATION=DISPLACEMENT +Step module: Step→Create: Frequency: Other: Normalize +eigenvectors by: Displacement +Mass normalization +Alternatively, the eigenvectors can be normalized so that the generalized mass for each vector is unity. +The “generalized mass” associated with mode +is +(no sum on ) +is the structure’s mass matrix and +where +and M refer to degrees of freedom of the finite element model. +is the eigenvector for mode +. The superscripts N +If the eigenvectors are normalized with respect to mass, all the eigenvectors are scaled so that +=1. +For coupled acoustic-structural analyses, an acoustic contribution fraction to the generalized mass is +computed as well. +Input File Usage: +Abaqus/CAE Usage: +*FREQUENCY, NORMALIZATION=MASS +Step module: Step→Create: Frequency: Other: Normalize +eigenvectors by: Mass +Modal participation factors +The participation factor for mode +, is a variable that indicates how strongly motion +in the global x-, y-, or z-direction or rigid body rotation about one of these axes is represented in the +eigenvector of that mode. The six possible rigid body motions are indicated by +, 6. The +participation factor is defined as +in direction i, +, 2, +where +defines the magnitude of the rigid body response of degree of freedom N in the model to +imposed rigid body motion (displacement or infinitesimal rotation) of type i. For example, at a node +with three displacement and three rotation components, +is +(no sum on ) +where +is unity and all other +are zero; x, y, and z are the coordinates of the node; and +, and +represent the coordinates of the center of rotation. The participation factors are, thus, defined for the +translational degrees of freedom and for rotation around the center of rotation. For coupled acoustic- +structural eigenfrequency analysis, an additional acoustic participation factor is computed as outlined in +“Coupled acoustic-structural medium analysis,” Section 2.9.1 of the Abaqus Theory Manual. +, +Modal effective mass +The effective mass for mode +associated with kinematic direction i ( +, 2, +, 6) is defined as +(no sum on ) +If the effective masses of all modes are added in any global translational direction, the sum should give +the total mass of the model (except for mass at kinematically restrained degrees of freedom). Thus, if +the effective masses of the modes used in the analysis add up to a value that is significantly less than +the model’s total mass, this result suggests that modes that have significant participation in a certain +excitation direction have not been extracted. +For coupled acoustic-structural eigenfrequency analysis, an additional acoustic effective mass is +computed as outlined in “Coupled acoustic-structural medium analysis,” Section 2.9.1 of the Abaqus +Theory Manual. +Composite modal damping +You can define composite damping factors for each material (“Material damping,” Section 26.1.1), which +are assembled into fractions of critical damping values for each mode, +, according to +(no sum on ) +where +mass matrix made of material a. +is the critical damping fraction given for material a and +is the part of the structure’s +A composite damping value will be calculated for each mode. These values are weighted damping +values based on each material’s participation in each mode. +Input File Usage: +Abaqus/CAE Usage: +*DAMPING, COMPOSITE +Property module: Material→Create: Mechanical→Damping: Composite +Obtaining residual modes for use in mode-based procedures +Several analysis types in Abaqus/Standard are based on the eigenmodes and eigenvalues of the system. +For example, in a mode-based steady-state dynamic analysis the mass and stiffness matrices and load +vector of the physical system are projected onto a set of eigenmodes resulting in a diagonal system in +terms of modal amplitudes (or generalized degrees of freedom). The solution to the physical system is +obtained by scaling each eigenmode by its corresponding modal amplitude and superimposing the results +(for more information, see “Linear dynamic analysis using modal superposition,” Section 2.5.3 of the +Abaqus Theory Manual). +Due to cost, usually only a small subset of the total possible eigenmodes of the system are +extracted, with the subset consisting of eigenmodes corresponding to eigenfrequencies that are close to +the excitation frequency. Since excitation frequencies typically fall in the range of the lower modes, +it is usually the higher frequency modes that are left out. Depending on the nature of the loading, +the accuracy of the modal solution may suffer if too few higher frequency modes are used. Thus, a +trade-off exists between accuracy and cost. To minimize the number of modes required for a sufficient +degree of accuracy, the set of eigenmodes used in the projection and superposition can be augmented +with additional modes known as residual modes. The residual modes help correct for errors introduced +In Abaqus/Standard a residual mode, R, represents the static response of the +by mode truncation. +structure subjected to a nominal (or unit) load, P, corresponding to the actual load that will be used in +the mode-based analysis orthogonalized against the extracted eigenmodes, +followed by an orthogonalization of the residual modes against each other. +This orthogonalization is required to retain the orthogonality properties of the modes (residual and +eigen) with respect to mass and stiffness. As a consequence of the mass and stiffness matrices being +available, the orthogonalization can be done efficiently during the frequency extraction. Hence, if you +wish to include residual modes in subsequent mode-based procedures, you must activate the residual +mode calculations in the frequency extraction step. If the static responses are linearly dependent on each +other or on the extracted eigenmodes, Abaqus/Standard automatically eliminates the redundant responses +for the purpose of computing the residual modes. +For the Lanczos eigensolver you must ensure that the static perturbation response of the load that +will be applied in the subsequent mode-based analysis (i.e., +) is available by specifying that load in +a static perturbation step immediately preceding the frequency extraction step. If multiple load cases are +specified in this static perturbation analysis, one residual mode is calculated for each load case; otherwise, +it is assumed that all loads are part of a single load case, and only one residual mode will be calculated. +When residual modes are requested, the boundary conditions applied in the frequency extraction step +must match those applied in the preceding static perturbation step. +In addition, in the immediately +preceding static perturbation step Abaqus/Standard requires that (1) if multiple load cases are used, +the boundary conditions applied in each load case must be identical, and (2) the boundary condition +magnitudes are zero. When generating dynamic substructures , residual modes usually +will provide the most benefit if the loading patterns defined in each of the load cases in the preceding +static perturbation step match the loading patterns defined under the corresponding substructure load +cases in the substructure generation step. +If you use the AMS eigensolver, you do not need to specify the loads in a preceding static +perturbation step. Residual modes are computed at all degrees of freedom at which a concentrated +load is applied in the following mode-based procedure. You can request additional residual modes by +specifying degrees of freedom. One residual mode is computed for every requested degree of freedom. +As an outcome of the orthogonalization process, a pseudo-eigenvalue corresponding to each residual +mode, +, is computed and given by +(no sum on ) +Henceforth, and in other Abaqus/Standard documentation, the term eigenvalue is used generally to refer +to actual eigenvalues and pseudo-eigenvalues. All data (e.g., participation factors, etc.; see “Output”) +associated with the modes (eigenmodes and residual modes) are ordered by increasing eigenvalue. +Therefore, both eigenmodes and residual modes are assigned mode numbers. In the printed output file +Abaqus/Standard clearly identifies which modes are eigenmodes and which modes are residual modes +so that you can easily distinguish between them. By default, if you activate residual modes, all the +calculated eigenmodes and residual modes will be used in subsequent mode-based procedures, unless: +• You choose to obtain a new set of eigenmodes and residual modes in a new frequency extraction +step. +• You choose to select a subset of the available eigenmodes and residual modes in the mode-based +procedure (selection of modes is described in each of the mode-based analysis type sections). +Residual modes cannot be calculated if the cyclic symmetric modeling capability is used. In addition, +the Lanczos or AMS eigensolver must be used if you wish to activate residual mode calculations. +Input File Usage: +Abaqus/CAE Usage: +*FREQUENCY, RESIDUAL MODES +Step module: Step→Create: Frequency: Basic: Include residual modes +Evaluating frequency-dependent material properties +When frequency-dependent material properties are specified, Abaqus/Standard offers the option of +choosing the frequency at which these properties are evaluated for use in the frequency extraction +procedure. This evaluation is necessary because the stiffness cannot be modified during the eigenvalue +If you do not choose the frequency, Abaqus/Standard evaluates the stiffness +extraction procedure. +associated with frequency-dependent springs and dashpots at zero frequency and does not consider the +stiffness contributions from frequency domain viscoelasticity. If you do specify a frequency, only the +real part of the stiffness contributions from frequency domain viscoelasticity is considered. +Evaluating the properties at a specified frequency is particularly useful in analyses in which the +eigenfrequency extraction step is followed by a subspace projection steady-state dynamic step . +In these analyses the eigenmodes +extracted in the frequency extraction step are used as global basis functions to compute the steady-state +dynamic response of a system subjected to harmonic excitation at a number of output frequencies. The +accuracy of the results in the subspace projection steady-state dynamic step is improved if you choose +to evaluate the material properties at a frequency in the vicinity of the center of the range spanned by +the frequencies specified for the steady-state dynamic step. +Input File Usage: +Abaqus/CAE Usage: +*FREQUENCY, PROPERTY EVALUATION=frequency +Step module: Step→Create: Frequency: Other: Evaluate +dependent properties at frequency +Initial conditions +If the frequency extraction procedure is the first step in an analysis, the initial conditions form the base +state for the procedure (except for initial stresses, which cannot be included in the frequency extraction if +it is the first step). Otherwise, the base state is the current state of the model at the end of the last general +analysis step (“General and linear perturbation procedures,” Section 6.1.3). Initial stress stiffness effects +(specified either through defining initial stresses or through loading in a general analysis step) will be +included in the eigenvalue extraction only if geometric nonlinearity is considered in a general analysis +procedure prior to the frequency extraction procedure. +If initial stresses must be included in the frequency extraction and there is not a general nonlinear +step prior to the frequency extraction step, a “dummy” static step—which includes geometric +nonlinearity and which maintains the initial stresses with appropriate boundary conditions and +loads—must be included before the frequency extraction step. +“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1, describes all of the +available initial conditions. +Boundary conditions +Nonzero magnitudes of boundary conditions in a frequency extraction step will be ignored; the degrees +of freedom specified will be fixed (“Boundary conditions in Abaqus/Standard and Abaqus/Explicit,” +Section 33.3.1). +Boundary conditions defined in a frequency extraction step will not be used in subsequent general +analysis steps (unless they are respecified). +In a frequency extraction step involving piezoelectric elements, the electric potential degree of +freedom must be constrained at least at one node to remove numerical singularities arising from the +dielectric part of the element operator. +Defining primary and secondary bases for modal superposition procedures +If displacements or rotations are to be prescribed in subsequent dynamic modal superposition +procedures, boundary conditions must be applied in the frequency extraction step; +these degrees +of freedom are grouped into “bases.” The bases are then used for prescribing motion in the modal +superposition procedure—see “Transient modal dynamic analysis,” Section 6.3.7. +Boundary conditions defined in the frequency extraction step supersede boundary conditions defined +in previous steps. Hence, degrees of freedom that were fixed prior to the frequency extraction step will +be associated with a specific base if they are redefined with reference to such a base in the frequency +extraction step. +The primary base +By default, all degrees of freedom listed for a boundary condition will be assigned to an unnamed +“primary” base. If the same motion will be prescribed at all fixed points, the boundary condition is +defined only once; and all prescribed degrees of freedom belong to the primary base. +Unless removed in the frequency extraction step, boundary conditions from the last general analysis +step become fixed boundary conditions for the frequency step and belong to the primary base. +If all rigid body motions are not suppressed by the boundary conditions that make up the primary +base, you must apply a suitable frequency shift to avoid numerical problems. +Input File Usage: +*BOUNDARY +The *BOUNDARY option without the BASE NAME parameter can appear +only once in a frequency extraction step. +Abaqus/CAE Usage: +Load module: Create Boundary Condition +Secondary bases +If the modal superposition procedure will have more than one independent base motion, the driven +nodes must be grouped together into “secondary” bases in addition to the primary base. The secondary +bases must be named. Secondary bases are used only in modal dynamic and steady-state dynamic (not direct) +procedures. +The degrees of freedom associated with secondary bases are not suppressed; instead, a “big” mass +is added to each of them. To provide six digits of numerical accuracy, Abaqus/Standard sets each “big” +mass equal to 106 times the total mass of the structure and each “big” rotary inertia equal to 106 times +the total moment of inertia of the structure. Hence, an artificial low frequency mode is introduced for +every degree of freedom in a secondary base. To keep the requested range of frequencies unchanged, +Abaqus/Standard automatically increases the number of eigenvalues extracted. Consequently, the cost +of the eigenvalue extraction step will increase as more degrees of freedom are included in the secondary +bases. To reduce the analysis cost, keep the number of degrees of freedom associated with secondary +bases to a minimum. This can sometimes be done by reducing several secondary bases that all have the +same prescribed motion to a single node by using BEAM type MPCs (“General multi-point constraints,” +Section 34.2.2). +For the Lanczos and subspace iteration methods a negative shift must be used with either the rigid +body modes or secondary bases. +The “big” masses are not included in the model statistics, and the total mass of the structure and the +printed messages about masses and inertia for the entire model are not affected. However, the presence +of the masses will be noticeable in the output tables printed for the eigenvalue extraction step, as well as +in the information for the generalized masses and effective masses. See “Double cantilever subjected to +multiple base motions,” Section 1.4.12 of the Abaqus Benchmarks Manual, for an example of the use of +the base motion feature. +More than one secondary base can be defined by repeating the boundary condition definition and +assigning different base names. +Input File Usage: +Abaqus/CAE Usage: +*BOUNDARY, BASE NAME=name +Load module; Create Boundary Condition; Step: frequency_step; +Category: Mechanical; Types for Selected Step: Secondary +base; Constrained degrees-of-freedom: Region: select region, +U1, U2, U3, UR1, UR2, and/or UR3 +Loads +Applied loads (“Applying loads: overview,” Section 33.4.1) are ignored during a frequency extraction +analysis. +If loads were applied in a previous general analysis step and geometric nonlinearity +was considered for that prior step, the load stiffness determined at the end of the previous general +analysis step is included in the eigenvalue extraction (“General and linear perturbation procedures,” +Section 6.1.3). +Predefined fields +Predefined fields cannot be prescribed during natural frequency extraction. +Material options +The density of the material must be defined (“Density,” Section 21.2.1). The following material +properties are not active during a frequency extraction: +plasticity and other inelastic effects, +rate-dependent material properties, thermal properties, mass diffusion properties, electrical properties +(although piezoelectric materials are active), and pore fluid flow properties—see “General and linear +perturbation procedures,” Section 6.1.3. +Elements +Other than generalized axisymmetric elements with twist, any of the stress/displacement or acoustic +elements in Abaqus/Standard (including those with temperature, pressure, or electrical degrees of +freedom) can be used in a frequency extraction procedure. +Output +The eigenvalues (EIGVAL), eigenfrequencies in cycles/time (EIGFREQ), generalized masses (GM), +composite modal damping factors (CD), participation factors for displacement degrees of freedom 1–6 +(PF1–PF6) and acoustic pressure (PF7), and modal effective masses for displacement degrees of freedom +1–6 (EM1–EM6) and acoustic pressure (EM7) are written automatically to the output database as history +data. Output variables such as stress, strain, and displacement (which represent mode shapes) are also +available for each eigenvalue; these quantities are perturbation values and represent mode shapes, not +absolute values. +The eigenvalues and corresponding frequencies (in both radians/time and cycles/time) will also +be automatically listed in the printed output file, along with the generalized masses, composite modal +damping factors, participation factors, and modal effective masses. +The only energy density available in eigenvalue extraction procedures is the elastic strain energy +density, SENER. All of the output variable identifiers are outlined in “Abaqus/Standard output variable +identifiers,” Section 4.2.1. +The AMS eigensolver does not compute composite modal damping factors, participation factors, +or modal effective masses. In addition, you cannot request output to the results (.fil) file. +You can restrict output to the results, data, and output database files by selecting the modes for +which output is desired . +Input File Usage: +Use one of the following options: +*EL FILE, MODE, LAST MODE +*EL PRINT, MODE, LAST MODE +*OUTPUT, MODE LIST +Step module: Output→Field Output Requests→Create: +Frequency: Specify modes +Abaqus/CAE Usage: +Input file template +*HEADING +… +*BOUNDARY +Data lines to specify zero-valued boundary conditions +*INITIAL CONDITIONS +Data lines to specify initial conditions +** +*STEP (,NLGEOM) +If NLGEOM is used, initial stress and preload stiffness effects +will be included in the frequency extraction step +*STATIC +… +*CLOAD and/or *DLOAD +Data lines to specify loads +*TEMPERATURE and/or *FIELD +Data lines to specify values of predefined fields +*BOUNDARY +Data lines to specify zero-valued or nonzero boundary conditions +*END STEP +** +*STEP, PERTURBATION +*STATIC +… +*LOAD CASE, NAME=load case name +Keywords and data lines to define loading for this load case +*END LOAD CASE +… +*END STEP** +*STEP +*FREQUENCY, EIGENSOLVER=LANCZOS, RESIDUAL MODES +Data line to control eigenvalue extraction +*BOUNDARY +*BOUNDARY, BASE NAME=name +Data lines to assign degrees of freedom to a secondary base +*END STEP +6.3.6 +COMPLEX EIGENVALUE EXTRACTION +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “General and linear perturbation procedures,” Section 6.1.3 +• *COMPLEX FREQUENCY +• “Configuring a complex frequency procedure” in “Configuring linear perturbation analysis +procedures,” Section 14.11.2 of the Abaqus/CAE User’s Manual, in the online HTML version of +this manual +Overview +The complex eigenvalue extraction procedure: +• performs eigenvalue extraction to calculate the complex eigenvalues and the corresponding complex +mode shapes of a system; +• is a linear perturbation procedure; +• requires that an eigenfrequency extraction procedure (“Natural frequency extraction,” Section 6.3.5) +be performed prior to the complex eigenvalue extraction; +• can use the high-performance SIM software architecture ; +• will include initial stress and load stiffness effects due to preloads and initial conditions if nonlinear +geometric effects are included in the base state step definition (“General and linear perturbation +procedures,” Section 6.1.3); +• can include friction, damping, and unsymmetric load stiffness contributions; +• can include unsymmetric damping and stiffness contributions in acoustic finite elements due to +underlying mean flow (“Acoustic, shock, and coupled acoustic-structural analysis,” Section 6.10.1); +and +• cannot be used in a model defined as a cyclic symmetric structure (“Analysis of models that exhibit +cyclic symmetry,” Section 10.4.3). +Complex eigenvalue extraction +the complex +The complex eigenvalue extraction procedure uses a projection method to extract +eigenvalues of the current system. The eigenvalue problem of the finite element model is formulated in +the following manner: +where +M and N +is the mass matrix (which is symmetric and, in general, is semi-positive definite); +is the damping matrix; +is the stiffness matrix (which can include initial stress stiffness and friction effects +and, therefore, in general is unsymmetric); +is the complex eigenvalue; +is the complex eigenvector (the mode of vibration); and +are degrees of freedom. +The complex eigenvalue extraction procedure in Abaqus/Standard uses a subspace projection +method; thus, the eigenmodes of the undamped system with the symmetrized stiffness matrix must be +extracted using the eigenfrequency extraction procedure prior to the complex eigenvalue extraction step. +By default, the entire subspace is used as the base vector; this subspace can be reduced as described +below. Abaqus/Standard always computes all the complex eigenmodes available in the projection +subspace (taking into account any user-specified modifications to the subspace). The user-specified +number of requested eigenmodes and frequency range for the complex eigenvalue extraction procedure +do not influence the number of computed complex eigenmodes. +It determines only the number of +reported modes, which cannot be higher than the dimension of the projected subspace. To modify the +number of computed eigenmodes, reduce the projection subspace as described below or change the +number of eigenmodes extracted in the prior natural frequency extraction step accordingly. If you do +not specify the number of requested complex modes or the frequency range, all the computed modes +will be reported. +To take into account the unsymmetric effects, the unsymmetric matrix solution and storage scheme +is used automatically for a complex eigenvalue extraction step. The unsymmetric effects will be +disregarded if you specify that the symmetric solution and storage scheme should be used . +Input File Usage: +*COMPLEX FREQUENCY +number of complex eigenmodes, frequency_min, frequency_max +Abaqus/CAE Usage: +Step module: Create Step: Linear perturbation: Complex +frequency: Number of eigenvalues requested: All or Value, +Minimum frequency of interest (cycles/time): value, Maximum +frequency of interest (cycles/time): value +Shift point +You can specify a shift point, S, in cycles per time, for the complex eigenvalue extraction procedure +(S ≥ 0). Abaqus/Standard reports the complex eigenmodes, +so +that the modes with the imaginary part closest to a given shift point are reported first. This feature is +useful when a particular frequency range is of concern. The default is no shift. +, in order of increasing +Input File Usage: +Abaqus/CAE Usage: +*COMPLEX FREQUENCY +, , , S +Step module: Create Step: Linear perturbation: Complex +frequency: Frequency shift (cycles/time): S +Selecting the eigenmodes on which to project +You can select eigenmodes of the undamped system with the symmetrized stiffness matrix on which +the subspace projection will be performed. You can select them by specifying the mode numbers +individually, by requesting that Abaqus/Standard generate the mode numbers automatically, or +If you do not select the +by requesting the eigenmodes that belong to specified frequency ranges. +eigenmodes, all modes extracted in the prior eigenfrequency extraction step are used in the modal +superposition. +Input File Usage: +Use one of the following options to select the eigenmodes by specifying mode +numbers: +*SELECT EIGENMODES, DEFINITION=MODE NUMBERS +*SELECT EIGENMODES, GENERATE, DEFINITION=MODE NUMBERS +Use the following option to define the eigenmodes by specifying a frequency +range: +*SELECT EIGENMODES, DEFINITION=FREQUENCY RANGE +You cannot select the eigenmodes in Abaqus/CAE; all modes extracted are used +in the subspace projection. +Abaqus/CAE Usage: +Evaluating frequency-dependent material properties +When frequency-dependent material properties are specified, Abaqus/Standard offers the option of +choosing the frequency at which these properties are evaluated for use in the complex eigenvalue +extraction procedure. This evaluation is necessary because the operators cannot be modified during the +eigenvalue extraction procedure. If you do not choose the frequency, Abaqus/Standard evaluates the +stiffness and damping associated with frequency-dependent springs and dashpots at zero frequency and +does not consider the stiffness and damping contributions from frequency-domain viscoelasticity. If you +do specify a frequency, the stiffness and damping contributions from frequency-domain viscoelasticity +are considered. +Input File Usage: +Abaqus/CAE Usage: +*COMPLEX FREQUENCY, PROPERTY EVALUATION=frequency +Step module: Create Step: Complex Frequency: Other: Evaluate +dependent properties at frequency: value +Contact conditions with sliding friction +Abaqus/Standard automatically detects the contact nodes that are slipping due to velocity differences +imposed by the motion of the reference frame or the transport velocity in prior steps. At those nodes +the tangential degrees of freedom will not be constrained and the effect of friction will result in an +unsymmetric contribution to the stiffness matrix. At other nodes in contact the tangential degrees of +freedom will be constrained. +Friction at contact nodes at which a velocity differential is imposed can give rise to damping terms. +There are two kinds of friction-induced damping effects. The first effect is caused by the friction forces +stabilizing the vibrations in the direction perpendicular to the slip direction. This effect exists only in +three-dimensional analysis. The second effect is caused by a velocity-dependent friction coefficient. If +the friction coefficient decreases with velocity (which is usually the case), the effect is destabilizing and is +also known as “negative damping.” For more details, see “Coulomb friction,” Section 5.2.3 of the Abaqus +Theory Manual. The complex eigensolver allows you to include these friction-induced contributions to +the damping matrix. +Input File Usage: +Abaqus/CAE Usage: +*COMPLEX FREQUENCY, FRICTION DAMPING=YES +Step module: Create Step: Linear perturbation: Complex frequency: +Include friction-induced damping effects +Damping +In complex eigenvalue extraction analysis damping can be defined by dashpots , by “Rayleigh” damping associated with materials and elements , and by quiet boundaries on infinite elements or acoustic elements. +In +addition, as described in “Contact conditions with sliding friction” above, friction-induced damping +can be included. +Structural damping, damping contributions from frequency-domain viscoelasticity, and all types +of modal damping (except composite modal damping) are supported in complex eigenvalue extraction +using the high-performance SIM architecture. +Prescribing motion, transport velocity, and acoustic flow velocity +Motion, transport velocity, and acoustic flow velocity affect complex frequency analyses. Motion and +transport velocity must be specified in a preceding steady-state transport general step, and their effects +are included in the complex frequency step. The acoustic flow velocity has no effect in steady-state +transport steps, and acoustic flow velocities specified in a steady-state transport step are not propagated +to perturbation steps. The acoustic flow velocity must be specified in each linear perturbation step where +it is desired. +Initial conditions +Initial conditions cannot be specified for complex eigenvalue extraction. +Boundary conditions +Boundary conditions cannot be defined during complex eigenvalue extraction. The boundary conditions +will be the same as in the prior natural frequency extraction analysis. +Loads +Applied loads (“Applying loads: overview,” Section 33.4.1) are ignored during a complex eigenvalue +extraction. If loads were applied in a previous general analysis step in which nonlinear geometric effects +were included, the load stiffness determined at the end of the previous general analysis step is included +in the complex eigenvalue extraction . +Coriolis distributed loading adds an unsymmetric contribution to the damping operator, which is +currently accounted for only in solid and truss elements. +Predefined fields +Predefined fields cannot be prescribed during complex eigenvalue extraction. +Material options +The density of the material must be defined . The following material +properties are not active during complex eigenvalue extraction: +• plasticity and other inelastic effects; +• rate-dependent material properties, excluding friction, which can be rate dependent if the velocity +differential on the contact interface exists; +• thermal properties; +• mass diffusion properties; +• electrical properties (although piezoelectric materials are active); and +• pore fluid flow properties. +Elements +Other than generalized axisymmetric elements with twist, any of the stress/displacement elements in +Abaqus/Standard (including those with temperature or pressure degrees of freedom) can be used in +complex eigenvalue extraction. +Output +); frequencies +The real (EIGREAL) and imaginary (EIGIMAG) parts of the eigenvalues, ( +in cycles/time (EIGFREQ); and effective damping ratios (DAMPRATIO = +) are written +automatically to the data (.dat) file and to the output database (.odb) file as history data. In addition, +you can request that the generalized displacements (GU), which are the modes of the projected system, +be written to the output database file . Output +variables such as stress, strain, and displacement (which represent mode shapes) are also available +for each eigenvalue; these quantities are perturbation values and represent mode shapes, not absolute +values. +and +The only energy density available in eigenvalue extraction procedures is the elastic strain energy +density, SENER. All of the output variable identifiers are outlined in “Abaqus/Standard output variable +identifiers,” Section 4.2.1. +You can restrict output to the data file and output database file by selecting the modes for which +output is desired or “Output to the output +database,” Section 4.1.3). Output to the results (.fil) file is not available for the complex eigenvalue +extraction procedure. +Setting the cutoff value for complex eigenmodes +You can also set the cutoff value for complex eigenmodes, so only complex modes with the real part +of the eigenvalue higher than the cutoff value are written to the output database file. The default cutoff +value is 0.0. If the cutoff value is not set, all complex modes are output. +Input File Usage: +Use one of the following options to select complex eigenmodes for output: +*COMPLEX FREQUENCY, UNSTABLE MODES ONLY +*COMPLEX FREQUENCY, UNSTABLE MODES ONLY=value +The SIM architecture +The complex eigenvalue extraction analysis can be performed using the SIM architecture. The +advantages of performing the complex eigenvalue extraction procedure using the SIM architecture are +as follows: +• structural damping, including damping defined with viscoelastic material, is taken into account; +• modal damping can be specified; +• matrices representing the stiffness, mass, and damping can be defined (both symmetric and +unsymmetric matrices are supported); and +• the AMS eigensolver can be used to generate the projection subspace for the complex eigenvalue +extraction. +When the AMS eigensolver is used for computing the projection subspace, you should increase the +accuracy of the AMS eigensolution by increasing the values of the AMS parameters and by increasing +the highest frequency of interest. The coupled structural-acoustic modes cannot be used in complex +eigenvalue extraction analysis based on the SIM architecture. +Input file template +*HEADING +… +*SURFACE INTERACTION +*FRICTION +Specify zero friction coefficient +*BOUNDARY +Data lines to specify zero-valued boundary conditions +*INITIAL CONDITIONS +Data lines to specify initial conditions +** +*STEP (,NLGEOM) +If NLGEOM is used, initial stress and preload stiffness effects +will be included in the eigenvalue extraction steps +*STATIC +… +*CLOAD and/or *DLOAD +Data lines to specify loads +*TEMPERATURE and/or *FIELD +Data lines to specify values of predefined fields +*BOUNDARY +Data lines to specify zero-valued or nonzero boundary conditions +*END STEP +** +*STEP(,NLGEOM) +*STATIC +Data line to define incrementation +*CHANGE FRICTION +*FRICTION +Data lines to redefine friction coefficient +*MOTION, ROTATION or TRANSLATION +Data lines to define the velocity differential +*END STEP +** +*STEP +*FREQUENCY +Data line to control eigenvalue extraction +*END STEP +** +*STEP +*COMPLEX FREQUENCY +Data line to control complex eigenvalue extraction +*SELECT EIGENMODES +Data lines to define applicable mode ranges +*END STEP +6.3.7 +TRANSIENT MODAL DYNAMIC ANALYSIS +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “General and linear perturbation procedures,” Section 6.1.3 +• “Dynamic analysis procedures: overview,” Section 6.3.1 +• *MODAL DYNAMIC +• “Configuring a modal dynamics procedure” in “Configuring linear perturbation analysis +procedures,” Section 14.11.2 of the Abaqus/CAE User’s Manual, in the online HTML version of +this manual +Overview +A modal dynamic analysis: +• is used to analyze transient linear dynamic problems using modal superposition; +• can be performed only after a frequency extraction procedure since it bases the structure’s response +on the modes of the system; +• can use the high-performance SIM software architecture ; +• can include nondiagonal damping effects (i.e., from material or element damping) only when using +the SIM architecture; and +• is a linear perturbation procedure. +Modal dynamic analysis +Transient modal dynamic analysis gives the response of the model as a function of time based on a given +time-dependent loading. The structure’s response is based on a subset of the modes of the system, which +must first be extracted using an eigenfrequency extraction procedure (“Natural frequency extraction,” +Section 6.3.5). The modes will include eigenmodes and, if activated in the eigenfrequency extraction +step, residual modes. The number of modes extracted must be sufficient to model the dynamic response +of the system adequately, which is a matter of judgment on your part. +The modal amplitudes are integrated through time, and the response is synthesized from these modal +responses. For linear systems the modal dynamic procedure is much less expensive computationally than +the direct integration of the entire system of equations performed in the dynamic procedure (“Implicit +dynamic analysis using direct integration,” Section 6.3.2). +As long as the system is linear and is represented correctly by the modes being used (which are +generally only a small subset of the total modes of the finite element model), the method is also very +accurate because the integration operator used is exact whenever the forcing functions vary piecewise +linearly with time. You should ensure that the forcing function definition and the choice of time increment +are consistent for this purpose. For example, if the forcing is a seismic record in which acceleration +values are given every millisecond and it is assumed that the acceleration varies linearly between these +values, the time increment used in the modal dynamic procedure should be a millisecond. +The user-specified maximum number of increments is ignored in a modal dynamic step. The number +of increments is based on both the time increment and the total time chosen for the step. +While the response in this procedure is for linear vibrations, the prior response can be nonlinear and +stress stiffening (initial stress) effects will be included in the response if nonlinear geometric effects were +included in the step definition for the base state of the eigenfrequency extraction procedure, as explained +in “Natural frequency extraction,” Section 6.3.5. +Selecting the modes and specifying damping +You can select the modes to be used in modal superposition and specify damping values for all selected +modes. +Selecting the modes +You can select modes by specifying the mode numbers individually, by requesting that Abaqus/Standard +generate the mode numbers automatically, or by requesting the modes that belong to specified frequency +ranges. If you do not select the modes, all modes extracted in the prior eigenfrequency extraction step, +including residual modes if they were activated, are used in the modal superposition. +Input File Usage: +Use one of the following options to select the modes by specifying mode +numbers: +*SELECT EIGENMODES, DEFINITION=MODE NUMBERS +*SELECT EIGENMODES, GENERATE, DEFINITION=MODE NUMBERS +Use the following option to select the modes by specifying a frequency range: +*SELECT EIGENMODES, DEFINITION=FREQUENCY RANGE +You cannot select the modes in Abaqus/CAE; all modes extracted are used in +the modal superposition. +Abaqus/CAE Usage: +Specifying modal damping +Damping is almost always specified for a mode-based procedure; see “Material damping,” Section 26.1.1. +You can define a damping coefficient for all or some of the modes used in the response calculation. The +damping coefficient can be given for a specified mode number or for a specified frequency range. When +damping is defined by specifying a frequency range, the damping coefficient for a mode is interpolated +linearly between the specified frequencies. The frequency range can be discontinuous; the average +damping value will be applied for an eigenfrequency at a discontinuity. The damping coefficients are +assumed to be constant outside the range of specified frequencies. +Input File Usage: +Use the following option to define damping by specifying mode numbers: +*MODAL DAMPING, DEFINITION=MODE NUMBERS +Abaqus/CAE Usage: +Use the following option to define damping by specifying a frequency range: +*MODAL DAMPING, DEFINITION=FREQUENCY RANGE +Use the following input to define damping by specifying mode numbers: +Step module: Create Step: Linear perturbation: Modal dynamics: +Damping +Defining damping by specifying frequency ranges is not supported in +Abaqus/CAE. +Example of specifying damping +Figure 6.3.7–1 illustrates how the damping coefficients at different eigenfrequencies are determined for +the following input: +*MODAL DAMPING, DEFINITION=FREQUENCY RANGE +damping values +d = +d +2 d 3 +f i +d i +eigenfrequencies +frequencies +damping values +d 2 d 3 +f 2 +d 3 +f 3 +d 4 +f 4 +frequency +Figure 6.3.7–1 Damping coefficients specified by frequency range. +Rules for selecting modes and specifying damping coefficients +The following rules apply for selecting modes and specifying modal damping coefficients: +• No modal damping is included by default. +• Mode selection and modal damping must be specified in the same way, using either mode numbers +or a frequency range. +• If you do not select any modes, all modes extracted in the prior frequency analysis, including residual +modes if they were activated, will be used in the superposition. +• If you do not specify damping coefficients for modes that you have selected, zero damping values +will be used for these modes. +• Damping is applied only to the modes that are selected. +• Damping coefficients for selected modes that are beyond the specified frequency range are constant +and equal to the damping coefficient specified for the first or the last frequency (depending which +one is closer). This is consistent with the way Abaqus interprets amplitude definitions. +Specifying global damping +For convenience you can specify constant global damping factors for all selected eigenmodes for +mass and stiffness proportional viscous factors, as well as stiffness proportional structural damping. +Structural damping is a commonly used damping model that represents damping as complex stiffness. +This representation causes no difficulty for frequency domain analysis such as steady-state dynamics +for which the solution is already complex. However, the solution must remain real-valued in the time +domain. To allow users to apply their structural damping model in the time domain, a method has +been developed to convert structural damping to an equivalent viscous damping. This technique was +designed so that the viscous damping applied in the frequency domain is identical to the structural +damping if the projected damping matrix is diagonal. For further details, see “Modal dynamic analysis,” +Section 2.5.5 of the Abaqus Theory Manual. +Input File Usage: +*GLOBAL DAMPING, ALPHA=factor, BETA=factor, +STRUCTURAL=factor +Abaqus/CAE Usage: +Defining damping by global factors is not supported in Abaqus/CAE. +Material damping +Structural and viscous material damping is taken into account +in a SIM-based transient modal analysis. Since the projection of damping onto the mode shapes is +performed only one time during the frequency extraction step, significant performance advantages can +be achieved by using the SIM-based transient modal procedure . +If the damping operators depend on frequency, they will be evaluated at the frequency specified for +property evaluation during the frequency extraction procedure. +You can deactivate the structural or viscous damping in a transient modal procedure if desired. +Input File Usage: +Use the following option to deactivate structural and viscous damping in a +specific transient modal dynamic step: +Abaqus/CAE Usage: +*DAMPING CONTROLS, STRUCTURAL=NONE, VISCOUS=NONE +Damping controls are not supported in Abaqus/CAE. +Initial conditions +By default, the modal dynamic step will begin with zero initial displacements. If initial velocities have +been defined (“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1), they will be +used; otherwise, the initial velocities will be zero. +Alternatively, you can force the modal dynamic step to carry over the initial conditions from the +immediately preceding step, which must be either another modal dynamic step or a static perturbation +step: +• In most cases if the immediately preceding step is a modal dynamic step, both the displacements and +velocities are carried over from the end of that step and used as initial conditions for the current step. +For a SIM-based analysis, you should use secondary base motion instead of primary base motion + to carry over the initial conditions; +Abaqus issues a warning message if primary base motion is used. +• If the immediately preceding step is a static perturbation step, the displacements are carried over +from that step. If initial velocities have been defined (“Initial conditions in Abaqus/Standard and +Abaqus/Explicit,” Section 33.2.1), they will be used; otherwise, the initial velocities will be zero. +Input File Usage: +Use the following option to begin the modal dynamic step with zero initial +displacements: +Abaqus/CAE Usage: +*MODAL DYNAMIC, CONTINUE=NO +Use the following option to force the modal dynamic step to carry over the +initial conditions from the immediately preceding step: +*MODAL DYNAMIC, CONTINUE=YES +Use the following option to begin the modal dynamic step with zero initial +displacements: +Step module: Create Step: Linear perturbation: Modal dynamics: +Basic: Zero initial conditions +Use the following option to force the modal dynamic step to carry over the +initial conditions from the immediately preceding step: +Step module: Create Step: Linear perturbation: Modal dynamics: +Basic: Use initial conditions +Boundary conditions +It is not possible to prescribe nonzero displacements and rotations directly as boundary conditions +(“Boundary conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1) in mode-based +dynamic response procedures. In these procedures the motion for nodes can be specified only as base +motion, as described below. Nonzero displacement or acceleration history definitions given as boundary +conditions are ignored in modal superposition procedures, and any changes in the support conditions +from the eigenfrequency extraction step are flagged as errors. +Prescribed motions in modal superposition procedures +Boundary conditions must be applied during the eigenfrequency extraction step to the degrees of freedom +that will be prescribed in the modal dynamic procedure. These degrees of freedom are grouped into one +or more “bases” . The unnamed base is called the +“primary” base. Named “secondary” bases must be defined by specifying boundary conditions in the +frequency extraction step. A different motion can be prescribed for each base. +Specifying the degree of freedom and the time history of the motion +The displacements and rotations that are associated with a base are prescribed during the modal dynamic +response procedure. The base motions are fully defined by at most three global translations and +three global rotations. Thus, at most one base motion can be defined for each translation and rotation +component. Base motions are always specified in global directions, regardless of the use of nodal +transformations. You specify the global direction (1–6) for which the base motion is being defined. +If a rotation is specified about an origin that is not the origin of the coordinates, you must specify the +center of rotation. +The time history of a motion must be defined by an amplitude curve (“Amplitude curves,” +Section 33.1.2). +Input File Usage: +Abaqus/CAE Usage: +*BASE MOTION, DOF=n, AMPLITUDE=name +Load module; Create Boundary Condition; Step: modal_dynamic_step; +Category: Mechanical; Types for Selected Step: Displacement +base motion or Velocity base motion or Acceleration base +motion; Basic tabbed page: Degree-of-freedom: U1, U2, U3, +UR1, UR2, or UR3; Amplitude: name +Scaling the amplitude of the base motion +The amplitude curve used to define the time history of the motion can be scaled. By default, the scaling +factor is 1.0. +Input File Usage: +Abaqus/CAE Usage: +*BASE MOTION, DOF=n, AMPLITUDE=name, SCALE=n +Load module; Create Boundary Condition; Step: modal_dynamic_step; +Category: Mechanical; Types for Selected Step: Displacement +base motion or Velocity base motion or Acceleration base motion; +Basic tabbed page: Degree-of-freedom: U1, U2, U3, UR1, UR2, or +UR3; Amplitude: name; Amplitude scale factor: n +Specifying the type of base motion +Base motions can be defined by a displacement, a velocity, or an acceleration history. If the prescribed +excitation record is given in the form of a displacement or velocity history, Abaqus/Standard +differentiates it to obtain the acceleration history. Furthermore, if the displacement or velocity histories +have nonzero initial values, Abaqus/Standard will make corrections to the initial accelerations as +described in “Modal dynamic analysis,” Section 2.5.5 of the Abaqus Theory Manual. The default is to +give an acceleration history. +Input File Usage: +Use one of the following options: +Abaqus/CAE Usage: +*BASE MOTION, DOF=n, AMPLITUDE=name, TYPE=ACCELERATION +*BASE MOTION, DOF=n, AMPLITUDE=name, TYPE=VELOCITY +*BASE MOTION, DOF=n, AMPLITUDE=name, TYPE=DISPLACEMENT +Load module; Create Boundary Condition; Step: modal_dynamic_step; +Category: Mechanical; Types for Selected Step: Displacement base +motion or Velocity base motion or Acceleration base motion +Specifying secondary base motion +The primary base motion is specified by defining a base motion without referring to a base. +If the +base motion is to be applied to a secondary base, it must refer to the name of the base defined in the +eigenfrequency extraction step. +Input File Usage: +*BASE MOTION, DOF=n, AMPLITUDE=name, BASE +NAME=secondary base +Abaqus/CAE Usage: +Load module; Create Boundary Condition; Step: modal_dynamic_step; +Category: Mechanical; Types for Selected Step: Displacement +base motion or Velocity base motion or Acceleration base motion; +toggle on Secondary base: boundary_condition_name +Example +To illustrate the concept of primary and secondary bases, consider a single-bay frame with supports at +nodes 1 and 4. If the input prior to the eigenfrequency extraction step includes the following boundary +conditions: +• degrees of freedom 1 through 6 constrained at node 1 +• degree of freedom 1 constrained at node 4 +• degrees of freedom 3 through 6 constrained at node 4 +and different base motions are assigned to degree of freedom 2 at nodes 1 and 4, the following step +definitions could be used: +• an eigenfrequency extraction step that includes a boundary condition associated with BASE2 +constraining degree of freedom 2 at node 4; and +• a modal dynamic step that includes two base motion definitions: the primary base motion assigned +to degree of freedom 2 that does not refer to a base and the secondary base motion assigned to +degree of freedom 2 that refers to BASE2. +If boundary conditions were not given prior to the eigenfrequency extraction step, you would have to +define them in the eigenfrequency extraction step. Again, the secondary base would be defined by a +boundary condition with a base name. +Calculating the response of the structure +The degrees of freedom associated with the primary base are set to zero in the eigenfrequency extraction +step, and primary base motions are introduced by multiplying the base acceleration with the modal +participation factors. Hence, Abaqus/Standard calculates the response of the structure with respect to the +primary base. If the rotational degrees of freedom are references in the primary base motion definition, +the rotation is defined, as default, about the origin of the coordinate system unless you provide the center +of rotation. +The degrees of freedom associated with the secondary bases are not set to zero in the eigenfrequency +extraction step; instead, a “big” mass is added to each of them. Any degree of freedom in a secondary +base that was constrained by a regular boundary condition in a previous general step will be released, +and a big mass will be added to that degree of freedom. Secondary base motions are introduced by nodal +forces, obtained by multiplying the base acceleration with the big mass. Although the secondary base +motions are defined in absolute terms, the response calculated at the secondary bases is relative to the +motion of the primary base for the translational degrees of freedom. The rotational secondary bases are +defined about the nodes included in the node sets specified in the base name definition. Therefore, you +cannot change the center of rotation for secondary bases. +For a more detailed description of the base motion procedure, see “Base motions in modal-based +procedures,” Section 2.5.9 of the Abaqus Theory Manual. +Loads +The following loads can be prescribed in modal dynamic analysis, as described in “Concentrated loads,” +Section 33.4.2: +• Concentrated nodal forces can be applied to the displacement degrees of freedom (1–6). +• Distributed pressure forces or body forces can be applied; the distributed load types available with +particular elements are described in Part VI, “Elements.” +Predefined fields +Predefined temperature fields are not allowed in transient modal dynamic analysis. Other predefined +fields are ignored. +Material options +The density of the material must be defined (“Density,” Section 21.2.1). The following material +properties are not active during a modal dynamic analysis: plasticity and other inelastic effects, +rate-dependent material properties, thermal properties, mass diffusion properties, electrical properties +(except for the electrical potential, +, in piezoelectric analysis), and pore fluid flow properties. See +“General and linear perturbation procedures,” Section 6.1.3. +Elements +Other than generalized axisymmetric elements with twist, any of the stress/displacement elements in +Abaqus/Standard (including those with temperature and pressure degrees of freedom) can be used in a +modal dynamic analysis. +Output +All the output variables in Abaqus/Standard are listed in “Abaqus/Standard output variable identifiers,” +Section 4.2.1. The values of nodal solution variables U, V, and A in modal dynamics in the time domain +are relative to the motion of the primary base. Hence, the sum of the relative motion and the base motion +of the primary base yields the total motion; this total motion is available by requesting output variables +TU, TV, and TA. In the absence of primary base motions, the relative and total motions are identical. +The following modal variables can be output to the data or results files : +GU +GV +GA +SNE +KE +BM +Generalized displacements for all modes. +Generalized velocities for all modes. +Generalized accelerations for all modes. +Elastic strain energy for the entire model per each mode. +Kinetic energy for the entire model per each mode. +External work for the entire model per each mode. +Base motion. +Neither element energy densities (such as the elastic strain energy density, SENER) nor whole +element energies (such as the total kinetic energy of an element, ELKE) are available for output in modal +dynamic analysis. However, whole model variables such as ALLIE (total strain energy) are available for +mode-based procedures as output to the data or results files . +The computational expense of a modal dynamic analysis can be decreased significantly by reducing +the amount of output requested. +Input file template +*HEADING +… +*AMPLITUDE, NAME=amplitude +Data lines to define amplitude variations +** +*STEP +*FREQUENCY +Data line to specify the number of modes to be extracted +*BOUNDARY +Data lines to assign degrees of freedom to the primary base +*BOUNDARY, BASE NAME=base +Data lines to assign degrees of freedom to a secondary base +*END STEP +** +*STEP +*MODAL DYNAMIC +Data line to control time incrementation +*SELECT EIGENMODES +Data lines to define the applicable mode ranges +*MODAL DAMPING +Data line to define modal damping +*BASE MOTION, DOF=dof, AMPLITUDE=amplitude +*BASE MOTION, DOF=dof, AMPLITUDE=amplitude, BASE NAME=base +*END STEP +6.3.8 +MODE-BASED STEADY-STATE DYNAMIC ANALYSIS +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “General and linear perturbation procedures,” Section 6.1.3 +• “Dynamic analysis procedures: overview,” Section 6.3.1 +• “Direct-solution steady-state dynamic analysis,” Section 6.3.4 +• “Natural frequency extraction,” Section 6.3.5 +• “Subspace-based steady-state dynamic analysis,” Section 6.3.9 +• *STEADY STATE DYNAMICS +• “Configuring a mode-based steady-state dynamic analysis” in “Configuring linear perturbation +analysis procedures,” Section 14.11.2 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +A mode-based steady-state dynamic analysis: +• is used to calculate the steady-state dynamic linearized response of a system to harmonic excitation; +• is a linear perturbation procedure; +• calculates the response based on the system’s eigenfrequencies and modes; +• requires that an eigenfrequency extraction procedure be performed prior to the steady-state dynamic +analysis; +• can use the high-performance SIM software architecture ; +• can include nondiagonal damping effects (i.e., from material or element damping) only when using +the SIM architecture; +• is an alternative to direct-solution steady-state dynamic analysis, in which the system’s response is +calculated in terms of the physical degrees of freedom of the model; +• is computationally cheaper than direct-solution or subspace-based steady-state dynamics; +• is less accurate than direct-solution or subspace-based steady-state analysis, +in particular if +significant material damping is present, and +• is able to bias the excitation frequencies toward the values that generate a response peak. +Introduction +Steady-state dynamic analysis provides the steady-state amplitude and phase of the response of a system +due to harmonic excitation at a given frequency. Usually such analysis is done as a frequency sweep by +applying the loading at a series of different frequencies and recording the response; in Abaqus/Standard +the steady-state dynamic analysis procedure is used to conduct the frequency sweep. +In a mode-based steady-state dynamic analysis the response is based on modal superposition +techniques; +the modes of the system must first be extracted using the eigenfrequency extraction +procedure. The modes will include eigenmodes and, if activated in the eigenfrequency extraction step, +residual modes. The number of modes extracted must be sufficient to model the dynamic response of +the system adequately, which is a matter of judgment on your part. +When defining a mode-based steady-state dynamic step, you specify the frequency ranges of +interest and the number of frequencies at which results are required in each range (including the +bounding frequencies of the range). In addition, you can specify the type of frequency spacing (linear or +logarithmic) to be used, as described below (“Selecting the frequency spacing”). Logarithmic frequency +spacing is the default. Frequencies are given in cycles/time. +These frequency points for which results are required can be spaced equally along the frequency axis +(on a linear or a logarithmic scale), or they can be biased toward the ends of the user-defined frequency +range by introducing a bias parameter . +While the response in this procedure is for linear vibrations, the prior response can be nonlinear. +Initial stress effects (stress stiffening) will be included in the steady-state dynamics response if nonlinear +geometric effects (“General and linear perturbation procedures,” Section 6.1.3) were included in any +general analysis step prior to the eigenfrequency extraction step preceding the steady-state dynamic +procedure. +Input File Usage: +*STEADY STATE DYNAMICS +The DIRECT and SUBSPACE PROJECTION parameters must be omitted +from the *STEADY STATE DYNAMICS option to conduct a mode-based +steady-state dynamic analysis. +Abaqus/CAE Usage: +Step module: Create Step: Linear perturbation: Steady-state +dynamics, Modal +Selecting the type of frequency interval for which output is requested +Three types of frequency intervals are permitted for output from a mode-based steady-state dynamic step. +Specifying the frequency ranges by using the system’s eigenfrequencies +By default, the eigenfrequency type of frequency interval is used; in this case the following intervals +exist in each frequency range: +• First interval: extends from the lower limit of the frequency range given to the first eigenfrequency +in the range. +• Intermediate intervals: extend from eigenfrequency to eigenfrequency. +• Last interval: extends from the highest eigenfrequency in the range to the upper limit of the +frequency range. +For each of these intervals the frequencies at which results are calculated are determined using the user- +defined number of points (which includes the bounding frequencies for the interval) and the optional bias +function (which is discussed below and allows the sampling points on the frequency scale to be spaced +closer together at eigenfrequencies in the frequency range). Thus, detailed definition of the response +close to resonance frequencies is allowed. Figure 6.3.8–1 illustrates the division of the frequency range +for 5 calculation points and a bias parameter equal to 1. +Input File Usage: +Abaqus/CAE Usage: +*STEADY STATE DYNAMICS, INTERVAL=EIGENFREQUENCY +Step module: Create Step: Linear perturbation: Steady-state +dynamics, Modal: Use eigenfrequencies to subdivide +each frequency range +frequency points +lower end +of the range +mode n +mode n +1 +mode n + 2 +upper end +of the range +Figure 6.3.8–1 Division of range for the eigenfrequency type of interval and 5 calculation points. +Specifying the frequency ranges by the frequency spread +If the spread type of frequency interval is selected, intervals exist around each eigenfrequency in the +frequency range. For each of the intervals the equally spaced frequencies at which results are calculated +are determined using the user-defined number of points (which includes the bounding frequencies for +the interval). The minimum number of frequency points is 3. If the user-defined value is less than 3 (or +omitted), the default value of 3 points is assumed. Figure 6.3.8–2 illustrates the division of the frequency +range for 5 calculation points. +The bias parameter is not supported with the spread type of frequency interval. +Input File Usage: +*STEADY STATE DYNAMICS, INTERVAL=SPREAD +lwr_freq, upr_freq, numpts, bias_param, freq_scale_factor, spread +Abaqus/CAE Usage: +You cannot specify frequency ranges by frequency spread in Abaqus/CAE. +Specifying the frequency ranges directly +If the alternative range type of frequency interval is chosen, there is only one interval in the specified +frequency range spanning from the lower to the upper limit of the range. This interval is divided using +Frequency points +Frequency points +fn +fn + 1 +(1 – spread) · fn +(1 + spread) · fn +(1 – spread) · fn + 1 +(1 + spread) · fn + 1 +Figure 6.3.8–2 Division of range for the spread type of interval and 5 calculation +points. +and +are eigenfrequencies of the system. +the user-defined number of points and the optional bias function, which can be used to space the sampling +frequency points closer to the range limits. For the range type of frequency interval, the peak responses +around the system’s eigenfrequencies may be missed since the sampling frequencies at which output will +be reported will not be biased toward the eigenfrequencies. +Input File Usage: +Abaqus/CAE Usage: +*STEADY STATE DYNAMICS, INTERVAL=RANGE +Step module: Create Step: Linear perturbation: Steady-state +dynamics, Modal: toggle off Use eigenfrequencies to +subdivide each frequency range +Selecting the frequency spacing +Two types of frequency spacing are permitted for a mode-based steady-state dynamic step. For the +logarithmic frequency spacing (the default), the specified frequency ranges of interest are divided using +a logarithmic scale. Alternatively, a linear frequency spacing can be used if a linear scale is desired. +Input File Usage: +Abaqus/CAE Usage: +Use either of the following options: +*STEADY STATE DYNAMICS, FREQUENCY SCALE=LOGARITHMIC +*STEADY STATE DYNAMICS, FREQUENCY SCALE=LINEAR +Step module: Create Step: Linear perturbation: Steady-state +dynamics, Modal: Scale: Logarithmic or Linear +Requesting multiple frequency ranges +You can request multiple frequency ranges or multiple single frequency points for a mode-based steady- +state dynamic step. +Input File Usage: +*STEADY STATE DYNAMICS +lwr_freq1, upr_freq1, numpts1, bias_param1, freq_scale_factor1 +lwr_freq2, upr_freq2, numpts2, bias_param2, freq_scale_factor2 +... +single_freq1 +single_freq2 +... +Repeat the data lines as often as necessary. +Abaqus/CAE Usage: +Step module: Create Step: Linear perturbation: Steady-state dynamics, +Modal: Data: enter data in table, and add rows as necessary +The bias parameter +The bias parameter can be used to provide closer spacing of the results points either toward the middle +or toward the ends of each frequency interval. Figure 6.3.8–3 shows a few examples of the effect of the +bias parameter on the frequency spacing. +frequency points +f1 +Bias parameter = 1 +f2 +Bias parameter = 2 +Bias parameter = 3 +Bias parameter = 5 +Figure 6.3.8–3 Effect of the bias parameter on the frequency +spacing for a number of points +. +The bias formula used to calculate the frequency at which results are presented is as follows: +where +; +is the number of frequency points at which results are to be given within a frequency interval +(discussed above); +is one such frequency point ( +is the lower limit of the frequency interval; +is the upper limit of the frequency interval; +is the frequency at which the kth results are given; +); +is the bias parameter value; and +is the frequency or the logarithm of the frequency, depending on the value used for the +frequency scale parameter. +A bias parameter, p, that is greater than 1.0 provides closer spacing of the results points toward the ends +of the frequency interval, while values of p that are less than 1.0 provide closer spacing toward the middle +of the frequency interval. The default bias parameter is 3.0 for an eigenfrequency interval and 1.0 for a +range frequency interval. +The frequency scale factor +The frequency scale factor can be used to scale frequency points. All the frequency points, except the +lower and upper limit of the frequency range, are multiplied by this factor. This scale factor can be used +only when the frequency interval is specified by using the system’s eigenfrequencies . +Selecting the modes and specifying damping +You can select the modes to be used in modal superposition and specify damping values for all selected +modes. +Selecting the modes +You can select modes by specifying the mode numbers individually, by requesting that Abaqus/Standard +generate the mode numbers automatically, or by requesting the modes that belong to specified frequency +ranges. If you do not select the modes, all modes extracted in the prior eigenfrequency extraction step, +including residual modes if they were activated, are used in the modal superposition. +Input File Usage: +Abaqus/CAE Usage: +Specifying modal damping +Use one of the following options to select the modes by specifying mode +numbers: +*SELECT EIGENMODES, DEFINITION=MODE NUMBERS +*SELECT EIGENMODES, GENERATE, DEFINITION=MODE NUMBERS +Use the following option to select the modes by specifying a frequency range: +*SELECT EIGENMODES, DEFINITION=FREQUENCY RANGE +You cannot select the modes in Abaqus/CAE; all modes extracted are used in +the modal superposition. +Damping is almost always specified for a steady-state analysis . +If damping is absent, the response of a structure will be unbounded if the forcing frequency is equal +to an eigenfrequency of the structure. To get quantitatively accurate results, especially near natural +frequencies, accurate specification of damping properties is essential. The various damping options +available are discussed in “Material damping,” Section 26.1.1. You can define a damping coefficient for +all or some of the modes used in the response calculation. The damping coefficient can be given for +a specified mode number or for a specified frequency range. When damping is defined by specifying +a frequency range, the damping coefficient for a mode is interpolated linearly between the specified +frequencies. The frequency range can be discontinuous; the average damping value will be applied for +an eigenfrequency at a discontinuity. The damping coefficients are assumed to be constant outside the +range of specified frequencies. +Input File Usage: +Use the following option to define damping by specifying mode numbers: +*MODAL DAMPING, DEFINITION=MODE NUMBERS +Use the following option to define damping by specifying a frequency range: +*MODAL DAMPING, DEFINITION=FREQUENCY RANGE +Use the following option to define damping by global factors: +Abaqus/CAE Usage: +Use the following input to define damping by specifying mode numbers: +Step module: Create Step: Linear perturbation: +Steady-state dynamics, Modal: Damping +Defining damping by specifying frequency ranges is not supported in +Abaqus/CAE. +Example of specifying damping +Figure 6.3.8–4 illustrates how the damping coefficients at different eigenfrequencies are determined for +the following input: +*MODAL DAMPING, DEFINITION=FREQUENCY RANGE +Rules for selecting modes and specifying damping coefficients +The following rules apply for selecting modes and specifying modal damping coefficients: +• No modal damping is included by default. +• Mode selection and modal damping must be specified in the same way, using either mode numbers +or a frequency range. +• If you do not select any modes, all modes extracted in the prior frequency analysis, including residual +modes if they were activated, will be used in the superposition. +• If you do not specify damping coefficients for modes that you have selected, zero damping values +will be used for these modes. +• Damping is applied only to the modes that are selected. +• Damping coefficients for selected modes that are beyond the specified frequency range are constant +and equal to the damping coefficient specified for the first or the last frequency (depending which +one is closer). This is consistent with the way Abaqus interprets amplitude definitions. +damping values +d = +d +2 d 3 +f i +d i +eigenfrequencies +frequencies +damping values +d 2 d 3 +f 2 +d 3 +f 3 +d 4 +f 4 +frequency +Figure 6.3.8–4 Damping values specified by frequency range. +Specifying global damping +For convenience you can specify constant global damping factors for all selected eigenmodes for mass +and stiffness proportional viscous factors, as well as stiffness proportional structural damping. For further +details, see “Damping in dynamic analysis” in “Dynamic analysis procedures: overview,” Section 6.3.1. +Input File Usage: +*GLOBAL DAMPING, ALPHA=factor, BETA=factor, +STRUCTURAL=factor +Abaqus/CAE Usage: +Defining damping by global factors is not supported in Abaqus/CAE. +Material damping +Structural and viscous material damping is taken into account +in a SIM-based steady-state dynamic analysis. Since the projection of damping onto the mode shapes is +performed only one time during the frequency extraction step, significant performance advantages can +be achieved by using the SIM-based steady-state dynamic procedure . +If the damping operators depend on frequency, they will be evaluated at the frequency specified for +property evaluation during the frequency extraction procedure. +You can deactivate the structural or viscous damping in a mode-based steady-state dynamic +procedure if desired. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to deactivate structural and viscous damping in a +specific steady-state dynamic step: +*DAMPING CONTROLS, STRUCTURAL=NONE, VISCOUS=NONE +Damping controls are not supported in Abaqus/CAE. +Initial conditions +The base state is the current state of the model at the end of the last general analysis step prior to the +steady-state dynamic step. If the first step of an analysis is a perturbation step, the base state is determined +from the initial conditions (“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1). +Initial condition definitions that directly define solution variables, such as velocity, cannot be used in a +steady-state dynamic analysis. +Boundary conditions +In a mode-based steady-state dynamic analysis both the real and imaginary parts of any degree of freedom +are either restrained or unrestrained; it is physically impossible to have one part restrained and the other +part unrestrained. Abaqus/Standard will automatically restrain both the real and imaginary parts of a +degree of freedom even if only one part is restrained. +Base motion +It is not possible to prescribe nonzero displacements and rotations directly as boundary conditions +(“Boundary conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1) in mode-based +dynamic response procedures. Therefore, in a mode-based steady-state dynamic analysis, the motion of +nodes can be specified only as base motion; nonzero displacement or acceleration history definitions +given as boundary conditions are ignored, and any changes in the support conditions from the +eigenfrequency extraction step are flagged as errors. The method for prescribing base motion in modal +superposition procedures is described in “Transient modal dynamic analysis,” Section 6.3.7. +When secondary bases are used, low frequency eigenmodes will be extracted for each “big” mass +applied in the model. Use care when choosing the frequency lower limit range in such cases. The +“big” mass modes are important in the modal superposition; however, the response at zero or arbitrarily +low frequency level should not be requested since it forces Abaqus/Standard to calculate responses at +frequencies between these “big” mass eigenfrequencies, which is not desirable. +Frequency-dependent base motion +An amplitude definition can be used to specify the amplitude of a base motion as a function of frequency +(“Amplitude curves,” Section 33.1.2). +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*AMPLITUDE, NAME=name +*BASE MOTION, REAL or IMAGINARY, AMPLITUDE=name +Load module; Create Boundary Condition; Step: step_name; Category: +Mechanical; Types for Selected Step: Displacement base motion or +Velocity base motion or Acceleration base motion; Basic tabbed page: +Degree-of-freedom: U1, U2, U3, UR1, UR2, or UR3; Amplitude: name +Loads +The following loads can be prescribed in a mode-based steady-state dynamic analysis, as described in +“Concentrated loads,” Section 33.4.2: +• Concentrated nodal forces can be applied to the displacement degrees of freedom (1–6). +• Distributed pressure forces or body forces can be applied; the distributed load types available with +particular elements are described in Part VI, “Elements.” +These loads are assumed to vary sinusoidally with time over a user-specified range of frequencies. Loads +are given in terms of their real and imaginary components. +Fluid flux loading cannot be used in a steady-state dynamic analysis. +Input File Usage: +Abaqus/CAE Usage: +Use either of the following input lines to define the real (in-phase) part of the +load: +*CLOAD or *DLOAD +*CLOAD or *DLOAD, REAL +Use the following input line to define the imaginary (out-of-phase) part of the +load: +*CLOAD or *DLOAD, IMAGINARY +Load module: +part i +load editor: real (in-phase) part + imaginary (out-of-phase) +Frequency-dependent loading +An amplitude definition can be used to specify the amplitude of a load as a function of frequency +(“Amplitude curves,” Section 33.1.2). +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options: +*AMPLITUDE, NAME=name +*CLOAD or *DLOAD, REAL or IMAGINARY, AMPLITUDE=name +Load or Interaction module: Create Amplitude: Name: name +Load module: +part i: Amplitude: name +load editor: real (in-phase) part + imaginary (out-of-phase) +Predefined fields +Predefined temperature fields are not allowed in mode-based steady-state dynamic analysis. Other +predefined fields are ignored. +Material options +As in any dynamic analysis procedure, mass or density (“Density,” Section 21.2.1) must be assigned to +some regions of any separate parts of the model where dynamic response is required. The following +material properties are not active during mode-based steady-state dynamic analyses: plasticity and other +inelastic effects, viscoelastic effects, thermal properties, mass diffusion properties, electrical properties +(except for the electrical potential, +, in piezoelectric analysis), and pore fluid flow properties—see +“General and linear perturbation procedures,” Section 6.1.3. +Elements +Any of the following elements available in Abaqus/Standard can be used in a steady-state dynamics +procedure: +• stress/displacement elements (other than generalized axisymmetric elements with twist); +• acoustic elements; +• piezoelectric elements; or +• hydrostatic fluid elements. +See “Choosing the appropriate element for an analysis type,” Section 27.1.3. +Output +In mode-based steady-state dynamic analysis the value of an output variable such as strain (E) or stress +(S) is a complex number with real and imaginary components. In the case of data file output the first +printed line gives the real components while the second lists the imaginary components. Results and +data file output variables are also provided to obtain the magnitude and phase of many variables . In this case the first printed line in the +data file gives the magnitude while the second gives the phase angle. +The following variables are provided specifically for steady-state dynamic analysis: +Element integration point variables: +PHS +PHE +PHEPG +PHEFL +PHMFL +PHMFT +Magnitude and phase angle of all stress components. +Magnitude and phase angle of all strain components. +Magnitude and phase angles of the electrical potential gradient vector. +Magnitude and phase angles of the electrical flux vector. +Magnitude and phase angle of the mass flow rate in fluid link elements. +Magnitude and phase angle of the total mass flow in fluid link elements. +For connector elements, the following element output variables are available: +PHCTF +PHCEF +PHCVF +PHCRF +PHCSF +PHCU +PHCCU +Magnitude and phase angle of connector total forces. +Magnitude and phase angle of connector elastic forces. +Magnitude and phase angle of connector viscous forces. +Magnitude and phase angle of connector reaction forces. +Magnitude and phase angle of connector friction forces. +Magnitude and phase angle of connector relative displacements. +Magnitude and phase angle of connector constitutive displacements. +Nodal variables: +PU +PPOR +PHPOT +PRF +PHCHG +Magnitude and phase angle of all displacement/rotation components at a node. +Magnitude and phase angle of the fluid or acoustic pressure at a node. +Magnitude and phase angle of the electrical potential at a node. +Magnitude and phase angle of all reaction forces/moments at a node. +Magnitude and phase angle of the reactive charge at a node. +Element energy densities (such as the elastic strain energy density, SENER) and whole element +energies (such as the total kinetic energy of an element, ELKE) are not available for output in a mode- +based steady-state dynamic analysis. +The standard output variables U, V, A, and the variable PU listed above correspond to motions +relative to the motion of the primary base in a mode-based analysis. Total values, which include the +motion of the primary base, are also available: +TU +TV +TA +PTU +Magnitude of all components of total displacement/rotation at a node. +Magnitude of all components of total velocity at a node. +Magnitude of all components of total acceleration at a node. +Magnitude and phase angle of all total displacement/rotation components at a node. +The following modal variables are also available for mode-based steady-state dynamic analysis and +can be output to the data, results, and/or output database files : +GU +GV +GA +GPU +GPV +GPA +SNE +KE +BM +Generalized displacements for all modes. +Generalized velocities for all modes. +Generalized accelerations for all modes. +Phase angle of generalized displacements for all modes. +Phase angle of generalized velocities for all modes. +Phase angle of generalized acceleration for all modes. +Elastic strain energy for the entire model per mode. +Kinetic energy for the entire model per mode. +External work for the entire model per mode. +Base motion. +Whole model variables such as ALLIE (total strain energy) are available for mode-based steady- +state dynamics as output to the data, results, and/or output database files . +Input file template +*HEADING +… +*AMPLITUDE, NAME=loadamp +Data lines to define an amplitude curve as a function of frequency (cycles/time) +*AMPLITUDE, NAME=base +Data lines to define an amplitude curve to be used to prescribe base motion +** +*STEP, NLGEOM +Include the NLGEOM parameter so that stress stiffening effects will +be included in the steady-state dynamics step +*STATIC +**Any general analysis procedure can be used to preload the structure +… +*CLOAD and/or *DLOAD +Data lines to prescribe preloads +*TEMPERATURE and/or *FIELD +Data lines to define values of predefined fields for preloading the structure +*BOUNDARY +Data lines to specify boundary conditions to preload the structure +*END STEP +** +*STEP +*FREQUENCY +Data line to control eigenvalue extraction +*BOUNDARY +Data lines to assign degrees of freedom to the primary base +*BOUNDARY, BASE NAME=base2 +Data lines to assign degrees of freedom to a secondary base +*END STEP +** +*STEP +*STEADY STATE DYNAMICS +Data lines to specify frequency ranges and bias parameters +*SELECT EIGENMODES +Data lines to define the applicable mode ranges +*MODAL DAMPING +Data lines to define the modal damping factors +*BASE MOTION, DOF=dof, AMPLITUDE=base +*BASE MOTION, DOF=dof, AMPLITUDE=base, BASE NAME=base2 +*CLOAD and/or *DLOAD, AMPLITUDE=loadamp +Data lines to specify sinusoidally varying, frequency-dependent loads +… +*END STEP +6.3.9 +SUBSPACE-BASED STEADY-STATE DYNAMIC ANALYSIS +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “General and linear perturbation procedures,” Section 6.1.3 +• “Dynamic analysis procedures: overview,” Section 6.3.1 +• “Direct-solution steady-state dynamic analysis,” Section 6.3.4 +• “Natural frequency extraction,” Section 6.3.5 +• “Mode-based steady-state dynamic analysis,” Section 6.3.8 +• *STEADY STATE DYNAMICS +• “Configuring a subspace-based steady-state dynamic analysis” in “Configuring linear perturbation +analysis procedures,” Section 14.11.2 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +A subspace-based steady-state dynamic analysis: +• is used to calculate the steady-state dynamic linearized response of a system to harmonic excitation; +• is based on projection of the steady-state dynamic equations on a subspace of selected modes of the +undamped system; +• is a linear perturbation procedure; +• provides a cost-effective way to include frequency-dependent effects (such as frequency-dependent +damping and viscoelastic effects) in the model; +• allows for nonsymmetric stiffness; +• requires that an eigenfrequency extraction procedure be performed prior to the steady-state dynamic +analysis; +• can use the high-performance SIM software architecture ; +• is an alternative to direct-solution steady-state dynamic analysis, in which the system’s response is +calculated in terms of the physical degrees of freedom of the model; +• is computationally cheaper than direct-solution steady-state dynamics but more expensive than +mode-based steady-state dynamics; +• is less accurate than direct-solution steady-state analysis, +damping or viscoelasticity with a high loss modulus is present; and +in particular if significant material +• is able to bias the excitation frequencies toward the values that generate a response peak. +Introduction +Steady-state dynamic analysis provides the steady-state amplitude and phase of the response of a system +subjected to harmonic excitation at a given frequency. Usually such analysis is done as a frequency +In +sweep, by applying the loading at a series of different frequencies and recording the response. +Abaqus/Standard the subspace-based steady-state dynamic analysis procedure is used to conduct the +frequency sweep. +In a subspace-based steady-state dynamic analysis the response is based on direct solution of the +steady-state dynamic equations projected onto a subspace of modes. The modes of the undamped, +symmetric system must first be extracted using the eigenfrequency extraction procedure. The modes +will include eigenmodes and, if activated in the eigenfrequency extraction step, residual modes. The +procedure is based on the assumption that the forced steady-state vibration can be represented accurately +by a number of modes of the undamped system that are in the range of the excitation frequencies of +interest. The number of modes extracted must be sufficient to model the dynamic response of the system +adequately, which is a matter of judgment on your part. The projection of the dynamic equilibrium +equations onto a subspace of selected modes leads to a small system of complex equations that is solved +for modal amplitudes, which are then used to compute nodal displacements, stresses, etc. +When defining a subspace-based steady-state dynamic step, you specify the frequency ranges +of interest and the number of frequencies at which results are required in each range (including the +bounding frequencies of the range). In addition, you can specify the type of frequency spacing (linear or +logarithmic) to be used, as described below (“Selecting the frequency spacing”). Logarithmic frequency +If the +spacing is the default if the frequency ranges are specified directly or by eigenfrequencies. +frequency ranges are specified by the frequency spread, only linear spacing can be used. Frequencies +should be given in cycles/time. +The frequency points for which results are required can be spaced equally along the frequency axis +(on a linear or a logarithmic scale), or they can be biased toward the ends of the user-defined frequency +range by introducing a bias parameter . +The subspace-based steady-state dynamic analysis procedure can be used: +• for nonsymmetric stiffness; +• when any form of damping (except modal damping) is included; and +• when viscoelastic material properties must be taken into account. +While the response in this procedure is for linear vibrations, the prior response can be nonlinear. +Initial stress effects (stress stiffening) will be included in the steady-state dynamic response if nonlinear +geometric effects (“General and linear perturbation procedures,” Section 6.1.3) were included in any +general analysis step prior to the eigenfrequency extraction step preceding the subspace-based steady- +state dynamic procedure. +Input File Usage: +Abaqus/CAE Usage: +*STEADY STATE DYNAMICS, SUBSPACE PROJECTION +Step module: Create Step: Linear perturbation: Steady-state +dynamics, Subspace +Ignoring damping +If damping terms can be ignored, you can specify that a real, rather than a complex, system matrix be +generated and projected, which can significantly reduce computational time, at the cost of ignoring the +damping effects. +Input File Usage: +Abaqus/CAE Usage: +*STEADY STATE DYNAMICS, SUBSPACE PROJECTION, REAL ONLY +Step module: Create Step: Linear perturbation: Steady-state +dynamics, Subspace: Compute real response only +Selecting the type of frequency interval for which output is requested +Three types of frequency intervals are permitted for output from a subspace-based steady-state dynamic +step. +Specifying the frequency ranges by using the system’s eigenfrequencies +By default, the eigenfrequency type of frequency interval is used; in this case the following intervals +exist in each frequency range: +• First interval: extends from the lower limit of the frequency range given to the first eigenfrequency +in the range. +• Intermediate intervals: extend from eigenfrequency to eigenfrequency. +• Last interval: extends from the highest eigenfrequency in the range to the upper limit of the +frequency range. +For each of these intervals the frequencies at which results are calculated are determined using the user- +defined number of points (which includes the bounding frequencies for the interval) and the optional bias +function (which is discussed below and allows the sampling points on the frequency scale to be spaced +closer together at eigenfrequencies in the frequency range). Thus, detailed definition of the response +close to resonance frequencies is allowed. Figure 6.3.9–1 illustrates the division of the frequency range +for 5 calculation points and a bias parameter equal to 1. +frequency points +lower end +of the range +mode n +mode n +1 +mode n + 2 +upper end +of the range +Figure 6.3.9–1 Division of range for the eigenfrequency type of interval and 5 calculation points. +Input File Usage: +*STEADY STATE DYNAMICS, SUBSPACE PROJECTION, +INTERVAL=EIGENFREQUENCY +Abaqus/CAE Usage: +Step module: Create Step: Linear perturbation: Steady-state +dynamics, Subspace: Use eigenfrequencies to subdivide +each frequency range +Specifying the frequency ranges by the frequency spread +If the spread type of frequency interval is selected, intervals exist around each eigenfrequency in the +frequency range. For each of the intervals the equally spaced frequencies at which results are calculated +are determined using the user-defined number of points (which includes the bounding frequencies for +the interval). The minimum number of frequency points is 3. If the user-defined value is less than 3 (or +omitted), the default value of 3 points is assumed. Figure 6.3.9–2 illustrates the division of the frequency +range for 5 calculation points. +The bias parameter is not supported with the spread type of frequency interval. +Frequency points +Frequency points +fn +fn + 1 +(1 – spread) · fn +(1 + spread) · fn +(1 – spread) · fn + 1 +(1 + spread) · fn + 1 +Figure 6.3.9–2 Division of range for the spread type of interval and 5 calculation +points. +and +are eigenfrequencies of the system. +Input File Usage: +*STEADY STATE DYNAMICS, SUBSPACE PROJECTION, +INTERVAL=SPREAD +lwr_freq, upr_freq, numpts, bias_param, freq_scale_factor, spread +Abaqus/CAE Usage: +You cannot specify frequency ranges by frequency spread in Abaqus/CAE. +Specifying the frequency ranges directly +If the alternative range type of frequency interval is chosen, there is only one interval in the specified +frequency range spanning from the lower to the upper limit of the range. This interval is divided using +the user-defined number of points and the optional bias function, which can be used to space the sampling +frequency points closer to the range limits. For the range type of frequency interval, the peak responses +around the system’s eigenfrequencies may be missed since the sampling frequencies at which output will +be reported will not be biased toward the eigenfrequencies. +Input File Usage: +Abaqus/CAE Usage: +*STEADY STATE DYNAMICS, SUBSPACE PROJECTION, +INTERVAL=RANGE +Step module: Create Step: Linear perturbation: Steady-state +dynamics, Subspace: toggle off Use eigenfrequencies to +subdivide each frequency range +Selecting the frequency spacing +Two types of frequency spacing are permitted for a subspace-based steady-state dynamic step. For the +logarithmic frequency spacing (the default), the specified frequency ranges of interest are divided using +a logarithmic scale. Alternatively, a linear frequency spacing can be used if a linear scale is desired. +Input File Usage: +Use the following option to specify logarithmic frequency spacing: +*STEADY STATE DYNAMICS, SUBSPACE PROJECTION, +FREQUENCY SCALE=LOGARITHMIC (default) +Use the following option to specify linear frequency spacing: +*STEADY STATE DYNAMICS, SUBSPACE PROJECTION, +FREQUENCY SCALE=LINEAR +Abaqus/CAE Usage: +Step module: Create Step: Linear perturbation: Steady-state +dynamics, Subspace: Scale: Logarithmic or Linear +Requesting multiple frequency ranges +You can request multiple frequency ranges for a subspace-based steady-state dynamic step. When both +frequency ranges and additional single frequency points are requested, the frequency ranges must be +specified first. +Input File Usage: +Repeat the data lines as often as necessary to request multiple frequency ranges +or multiple single frequency points: +*STEADY STATE DYNAMICS, SUBSPACE PROJECTION +lwr_freq1, upr_freq1, numpts1, bias_param1, freq_scale_factor1 +lwr_freq2, upr_freq2, numpts2, bias_param2, freq_scale_factor2 +... +single_freq1 +single_freq2 +... +Abaqus/CAE Usage: +Step module: Create Step: Linear perturbation: Steady-state dynamics, +Subspace: Data: enter data in table, and add rows as necessary +The bias parameter +The bias parameter can be used to provide closer spacing of the results points either toward the middle +or toward the ends of each frequency interval. Figure 6.3.9–3 shows a few examples of the effect of the +bias parameter on the frequency spacing. +frequency points +f1 +Bias parameter = 1 +f2 +Bias parameter = 2 +Bias parameter = 3 +Bias parameter = 5 +Figure 6.3.9–3 Effect of the bias parameter on the frequency +spacing for a number of points +. +The bias formula used in subspace-based steady-state dynamics is +where +; +is the number of frequency points at which results are to be given within a frequency interval +(discussed above); +is one such frequency point ( +); +is the lower limit of the frequency interval; +is the upper limit of the frequency interval; +is the frequency at which the kth results are given; +is the bias parameter value; and +is the frequency or the logarithm of the frequency, depending on the value chosen for the +frequency scale. +A bias parameter, p, that is greater than 1.0 provides closer spacing of the results points toward the ends +of the frequency interval, while values of p that are less than 1.0 provide closer spacing toward the middle +of the frequency interval. The default bias parameter is 3.0 for an eigenfrequency interval and 1.0 for a +range frequency interval. +The frequency scale factor +The frequency scale factor can be used to scale frequency points. All the frequency points, except the +lower and upper limit of the frequency range, are multiplied by this factor. This scale factor can be used +only when the frequency interval is specified by using the system’s eigenfrequencies . +Damping +If damping is absent, the response of a structure will be unbounded if the forcing frequency is equal +to an eigenfrequency of the structure. To get quantitatively accurate results, especially near natural +frequencies, accurate specification of damping properties is essential. The various damping options +available are discussed in “Material damping,” Section 26.1.1. +In subspace-based steady-state dynamic analysis damping can be created by the following: +• dashpots , +• “Rayleigh” damping associated with materials and elements +Section 26.1.1), +, +• viscoelasticity included in the material definitions , +• contributions from infinite elements or defined impedance +conditions on acoustic elements, and +• “volumetric drag” (viscous Rayleigh damping) in acoustic elements . +If you specify that a real-only system matrix be generated and projected , all forms of damping are ignored, +nonreflecting boundaries on acoustic elements. +Contact conditions with sliding friction +Abaqus/Standard automatically detects the contact nodes that are slipping due to velocity differences +imposed by the motion of the reference frame or the transport velocity in prior steps. At those nodes the +tangential degrees of freedom are not constrained and the effect of friction results in an unsymmetric +contribution to the stiffness matrix. At other contact nodes the tangential degrees of freedom are +constrained. +Friction at contact nodes at which a velocity differential is imposed can give rise to damping terms. +There are two kinds of friction-induced damping effects. The first effect is caused by the friction forces +stabilizing the vibrations in the direction perpendicular to the slip direction. This effect exists only in +three-dimensional analysis. The second effect is caused by a velocity-dependent friction coefficient. If +the friction coefficient decreases with velocity (which is usually the case), the effect is destabilizing and +is also known as “negative damping.” For more details, see “Coulomb friction,” Section 5.2.3 of the +Abaqus Theory Manual. Subspace-based steady-state dynamics analysis allows you to include these +friction-induced contributions to the damping matrix. +Input File Usage: +*STEADY STATE DYNAMICS, SUBSPACE PROJECTION, +FRICTION DAMPING=YES +Abaqus/CAE Usage: +Step module: Create Step: Linear perturbation: Steady-state dynamics, +Subspace: Include friction-induced damping effects +Selecting the modes on which to project +You can select modes by specifying the mode numbers individually, by requesting that Abaqus/Standard +generate the mode numbers automatically, or by requesting the modes that belong to specified frequency +ranges. If you do not select the modes, all modes extracted in the prior eigenfrequency extraction step, +including residual modes if they were activated, are used in the modal superposition. +Input File Usage: +Use the following option to select the modes by specifying mode numbers +individually: +*SELECT EIGENMODES, DEFINITION=MODE NUMBERS +Use the following option to request that Abaqus/Standard generate the mode +numbers automatically: +*SELECT EIGENMODES, GENERATE, DEFINITION=MODE NUMBERS +Use the following option to select the modes by specifying a frequency range: +*SELECT EIGENMODES, DEFINITION=FREQUENCY RANGE +You cannot select the modes in Abaqus/CAE; all modes extracted are used in +the modal superposition. +Abaqus/CAE Usage: +Selecting the subspace projection frequency +You can control the frequency of the subspace projections. By default, the dynamic equations are +projected onto the subspace at each frequency you request. However, considerable computational +savings can be obtained if the projection onto the subspace is performed only at selected frequency +points. +Projecting the subspace at each frequency requested +By default, the dynamic equations are projected onto the subspace at each frequency you requested. This +is the most computationally expensive method. If coupled acoustic-structural modes are extracted in the +preceding eigenfrequency extraction step, this is the only method allowed. +Input File Usage: +Use either of the following options: +*STEADY STATE DYNAMICS, SUBSPACE PROJECTION +*STEADY STATE DYNAMICS, +SUBSPACE PROJECTION=ALL FREQUENCIES +Abaqus/CAE Usage: +Step module: Create Step: Linear perturbation: Steady-state dynamics, +Subspace: Projection: Evaluate at each frequency +Projecting the subspace using model properties at the center frequency of all ranges +You can perform only one projection using model properties evaluated at the center frequency of all +ranges and individual frequency points specified. The center frequency is determined on a logarithmic +or linear scale depending on the spacing requested. +This method is the least expensive. However, it should be chosen only when the material properties +do not depend strongly on frequency. +Input File Usage: +Abaqus/CAE Usage: +*STEADY STATE DYNAMICS, SUBSPACE PROJECTION=CONSTANT +Step module: Create Step: Linear perturbation: Steady-state +dynamics, Subspace: Projection: Constant +Projecting the subspace at each extracted eigenfrequency +You can perform the projections at each extracted eigenfrequency in the requested frequency range and +at eigenfrequencies immediately outside the range. The projected mass, stiffness, and damping matrices +are then interpolated at each frequency point requested. The interpolation is performed on a linear or +logarithmic scale depending on the spacing requested. +Input File Usage: +*STEADY STATE DYNAMICS, +SUBSPACE PROJECTION=EIGENFREQUENCY +Abaqus/CAE Usage: +Step module: Create Step: Linear perturbation: Steady-state dynamics, +Subspace: Projection: Interpolate at eigenfrequencies +Projecting the subspace based on material property changes as a function of frequency +You can select how often subspace projections are performed based on material property changes as +a function of frequency. You specify the relative change in material stiffness and damping properties +allowed before a new projection is performed. +In the beginning of the subspace-based steady-state +dynamic step Abaqus/Standard computes a table of relative changes in material stiffness and damping +properties, and projections are performed based on the strictest of the two criteria. The projections +are then interpolated at each requested frequency point as described above. The default value for the +allowable stiffness or damping change is 0.1. +Input File Usage: +Abaqus/CAE Usage: +*STEADY STATE DYNAMICS, +SUBSPACE PROJECTION=PROPERTY CHANGE, +DAMPING CHANGE=percentage, STIFFNESS CHANGE=percentage +Step module: Create Step: Linear perturbation: Steady-state dynamics, +Subspace: Projection: As a function of property changes, Max. +damping change: percentage, Max. stiffness change: percentage +Projecting the subspace at the limits of each frequency range +You can select how often subspace projections are performed based on the limits of each frequency range. +The projections onto the modal subspace of the dynamic equations are performed at the lower limit of +each frequency range and at the upper limit of the last frequency range. The interpolation of the projected +mass, stiffness, and damping matrices is performed on a linear scale. This method can be used only with +the SIM architecture. +This method should be chosen when the frequency dependence of material properties is close to +linear within a frequency range. +Input File Usage: +Abaqus/CAE Usage: +*STEADY STATE DYNAMICS, SUBSPACE PROJECTION=RANGE +Step module: Create Step: Linear perturbation: Steady-state dynamics, +Subspace: Projection: Interpolate at lower and upper frequency limits +Initial conditions +The base state is the current state of the model at the end of the last general analysis step prior to the +steady-state dynamic step. If the first step of an analysis is a perturbation step, the base state is determined +from the initial conditions (“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1). +Initial condition definitions that directly define solution variables, such as velocity, cannot be used in a +steady-state dynamic analysis. +Boundary conditions +In a subspace-based steady-state dynamic analysis both the real and imaginary parts of any degree of +freedom are either restrained or unrestrained; it is physically impossible to have one part restrained and +the other part unrestrained. Abaqus/Standard will restrain both the real and imaginary parts of a degree +of freedom automatically even if only one part is restrained. +Base motion +It is not possible to prescribe nonzero displacements and rotations directly as boundary conditions +(“Boundary conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1) in subspace-based +Instead, prescribed motion can be specified as base motion; nonzero +steady-state dynamic analysis. +displacement or acceleration history definitions given as boundary conditions are ignored, and any +changes in the support conditions from the eigenfrequency extraction step are flagged as errors. The +method for prescribing base motion in modal superposition procedures is described in “Transient modal +dynamic analysis,” Section 6.3.7. +Frequency-dependent base motion +An amplitude definition can be used to specify the amplitude of a base motion as a function of frequency +(“Amplitude curves,” Section 33.1.2). +Input File Usage: +Use both of the following options: +*AMPLITUDE, NAME=name +*BASE MOTION, REAL or IMAGINARY, AMPLITUDE=name +Abaqus/CAE Usage: +Load module; Create Boundary Condition; Step: step_name; Category: +Mechanical; Types for Selected Step: Displacement base motion or +Velocity base motion or Acceleration base motion; Basic tabbed page: +Degree-of-freedom: U1, U2, U3, UR1, UR2, or UR3; Amplitude: name +Loads +The following loads can be prescribed in a subspace-based steady-state dynamic analysis, as described +in “Concentrated loads,” Section 33.4.2: +• Concentrated nodal forces can be applied to the displacement degrees of freedom (1–6). +• Distributed pressure forces or body forces can be applied; the distributed load types available with +particular elements are described in Part VI, “Elements.” +• Incident wave loads can be applied; see “Acoustic and shock loads,” Section 33.4.6. Incident wave +loads can be used to model sound waves from distinct planar or spherical sources or from diffuse +fields. +These loads are assumed to vary sinusoidally with time over a user-specified range of frequencies. Loads +are given in terms of their real and imaginary components. +Input File Usage: +Use either of the following input lines to define the real (in-phase) part of the +load: +*CLOAD or *DLOAD +*CLOAD or *DLOAD, REAL +Use the following input line to define the imaginary (out-of-phase) part of the +load: +Abaqus/CAE Usage: +*CLOAD or *DLOAD, IMAGINARY +You can only define the real (in phase) part of the load in Abaqus/CAE. +Load module: load editor: real (in-phase) part +Frequency-dependent loading +An amplitude definition can be used to specify the amplitude of a load as a function of frequency +(“Amplitude curves,” Section 33.1.2). +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*AMPLITUDE, NAME=name +*CLOAD or *DLOAD, REAL or IMAGINARY, AMPLITUDE=name +Load or Interaction module: Create Amplitude: Name: name +Load module: load editor: Amplitude: name +Loading limitations +Coriolis distributed loading adds an imaginary antisymmetric contribution to the overall system of +equations. This contribution is currently accounted for in solid and truss elements only and is activated +by requesting the unsymmetric matrix storage and solution scheme for the step. +Fluid flux loading cannot be used in subspace-based steady-state dynamic analysis. +Predefined fields +Predefined temperature fields can be specified in subspace-based steady-state dynamic analysis and will produce harmonically varying thermal strains if thermal +expansion is included in the material definition (“Thermal expansion,” Section 26.1.2). Other predefined +fields are ignored. +Material options +As in any dynamic analysis procedure, mass or density (“Density,” Section 21.2.1) must be assigned +to some regions of any separate parts of the model where dynamic response is required. If an analysis +is desired in which the inertia effects are neglected, the density should be set to a very small number. +Natural damping, as well as individual dashpots, can be included in this procedure. +Viscoelastic effects can be included in subspace-based steady-state dynamic analysis. The +linearized viscoelastic response is considered to be a perturbation about a nonlinear preloaded state, +which is computed on the basis of purely elastic behavior (long-term response) in the viscoelastic +components. Therefore, the vibration amplitude must be sufficiently small so that the material response +in the dynamic phase of the problem can be treated as a linear perturbation about the predeformed +state. Viscoelastic frequency domain response is described in “Frequency domain viscoelasticity,” +Section 22.7.2. +The following material properties are not active during subspace-based steady-state dynamic +analyses: plasticity and other inelastic effects, thermal properties (except for thermal expansion), mass +diffusion properties, electrical properties (except for the electrical potential, +, in piezoelectric analysis), +and pore fluid flow properties—see “General and linear perturbation procedures,” Section 6.1.3. +Numerical investigations show that in general the accuracy of the results in the subspace-based +steady-state dynamic step is improved if in the previous eigenfrequency extraction step the material +properties are evaluated at a frequency in the vicinity of the center of the range spanned by +the frequencies specified for the steady-state dynamic step . In this case the modes extracted in the previous eigenfrequency extraction step for the +undamped system will reflect most accurately the modes of the damped system at frequencies located in +the proximity of the frequency at which the material properties are evaluated. Thus, if the steady-state +dynamic response is sought for a large span of frequencies and the specified material properties vary +significantly over this span, the results will be more accurate if the range is divided into smaller ranges +and several separate analyses are run over these smaller ranges with the material properties evaluated +at appropriate frequencies. +Elements +Any of the following elements available in Abaqus/Standard can be used in a subspace-based steady-state +dynamic analysis: +• stress/displacement elements (other than generalized axisymmetric elements with twist); +• acoustic elements; +• piezoelectric elements; and +• hydrostatic fluid elements. +See “Choosing the appropriate element for an analysis type,” Section 27.1.3. +Output +In subspace-based steady-state dynamic analysis the value of an output variable such as strain (E) or +stress (S) is a complex number with real and imaginary components. In the case of data file output the +first printed line gives the real components while the second lists the imaginary components. Results +and data file output variables are also provided to obtain the magnitude and phase of many variables . In this case the first printed line in the data +file gives the magnitude while the second gives the phase angle. +The following variables are provided specifically for subspace-based steady-state dynamic analysis: +Element integration point variables: +PHS +PHE +PHEPG +PHEFL +PHMFL +PHMFT +Magnitude and phase angle of all stress components. +Magnitude and phase angle of all strain components. +Magnitude and phase angles of the electrical potential gradient vector. +Magnitude and phase angles of the electrical flux vector. +Magnitude and phase angle of the mass flow rate in fluid link elements. +Magnitude and phase angle of the total mass flow in fluid link elements. +For connector elements, the following element output variables are available: +PHCTF +PHCEF +PHCVF +PHCRF +PHCSF +PHCU +PHCCU +PHCV +PHCA +Magnitude and phase angle of connector total forces. +Magnitude and phase angle of connector elastic forces. +Magnitude and phase angle of connector viscous forces. +Magnitude and phase angle of connector reaction forces. +Magnitude and phase angle of connector friction forces. +Magnitude and phase angle of connector relative displacements. +Magnitude and phase angle of connector constitutive displacements. +Magnitude and phase angle of connector relative velocities. +Magnitude and phase angle of connector relative accelerations. +Nodal variables: +PU +PPOR +PHPOT +PRF +PHCHG +Magnitude and phase angle of all displacement/rotation components at a node. +Magnitude and phase angle of the fluid or acoustic pressure at a node. +Magnitude and phase angle of the electrical potential at a node. +Magnitude and phase angle of all reaction forces/moments at a node. +Magnitude and phase angle of the reactive charge at a node. +Neither element energy densities (such as the elastic strain energy density, SENER) nor whole +element energies (such as the total kinetic energy of an element, ELKE) are available for output in a +subspace-based steady-state dynamic analysis. +The standard output variables U, V, A, and the variable PU listed above correspond to motions +relative to the motion of the primary base in a subspace-based steady-state dynamic analysis. Total +values, which include the motion of the primary base, are also available: +TU +TV +TA +PTU +Components of total displacement/rotation at a node. +Components of total velocity at a node. +Components of total acceleration at a node. +Magnitude and phase angle of all total displacement/rotation components at a node. +The specified base motion is available for subspace-based steady-state dynamic analysis and can +be output to the data, results, and/or output database files . +BM +Base motion. +Whole model variables such as ALLIE (total strain energy) are available for subspace-based steady- +state dynamic analysis as output to the data, results, and/or output database files . +Input file template +*HEADING +… +*AMPLITUDE, NAME=loadamp +Data lines to define an amplitude curve as a function of frequency (cycles/time) +*AMPLITUDE, NAME=base +Data lines to define an amplitude curve to be used to prescribe base motion +** +*STEP, NLGEOM +Include the NLGEOM parameter so that stress stiffening effects will +be included in the steady-state dynamics step +*STATIC +**Any general analysis procedure can be used to preload the structure +… +*CLOAD and/or *DLOAD +Data lines to prescribe preloads +*TEMPERATURE and/or *FIELD +Data lines to define values of predefined fields for preloading the structure +*BOUNDARY +Data lines to specify boundary conditions to preload the structure +*END STEP +** +*STEP +*FREQUENCY +Data line to control eigenvalue extraction +*BOUNDARY +Data lines to assign degrees of freedom to the primary base +*BOUNDARY, BASE NAME=base2 +Data lines to assign degrees of freedom to a secondary base +*END STEP +** +*STEP +*STEADY STATE DYNAMICS, SUBSPACE PROJECTION +Data lines to specify frequency ranges and bias parameters +*SELECT EIGENMODES +Data lines to define the applicable mode ranges +*BASE MOTION, DOF=dof, AMPLITUDE=base +*BASE MOTION, DOF=dof, AMPLITUDE=base, BASE NAME=base2 +*CLOAD and/or *DLOAD, AMPLITUDE=loadamp +Data lines to specify sinusoidally varying, frequency-dependent loads +… +*END STEP +6.3.10 +RESPONSE SPECTRUM ANALYSIS +Products: Abaqus/Standard Abaqus/CAE +References +• “Dynamic analysis procedures: overview,” Section 6.3.1 +• “Defining an analysis,” Section 6.1.2 +• “General and linear perturbation procedures,” Section 6.1.3 +• *RESPONSE SPECTRUM +• *SPECTRUM +• “Configuring a response spectrum procedure” in “Configuring linear perturbation analysis +procedures,” Section 14.11.2 of the Abaqus/CAE User’s Manual, in the online HTML version of +this manual +• “Defining a spectrum,” Section 57.11 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +A response spectrum analysis: +• provides an estimate of the peak linear response of a structure to dynamic motion of fixed points +(“base motion”) or dynamic force; +• is typically used to analyze response to a seismic event; +• assumes that the system’s response is linear so that it can be analyzed in the frequency domain using +its natural modes, which must be extracted in a previous eigenfrequency extraction step (“Natural +frequency extraction,” Section 6.3.5); +• can use the high-performance SIM software architecture ; and +• is a linear perturbation procedure and is, therefore, not appropriate if the excitation is so severe that +nonlinear effects in the system are important. +Response spectrum analysis +Response spectrum analysis can be used to estimate the peak response (displacement, stress, etc.) of a +structure to a particular base motion or force. The method is only approximate, but it is often a useful, +inexpensive method for preliminary design studies. +The response spectrum procedure is based on using a subset of the modes of the system, which must +first be extracted by using the eigenfrequency extraction procedure. The modes will include eigenmodes +and, if activated in the eigenfrequency extraction step, residual modes. The number of modes extracted +must be sufficient to model the dynamic response of the system adequately, which is a matter of judgment +on your part. +In cases with repeated eigenvalues and eigenvectors, +the modal summation results must be +interpreted with care. You should add insignificant mass to the structure or perturb the symmetric +geometry such that the eigenvalues become unique. +While the response in the response spectrum procedure is for linear vibrations, the prior response +may be nonlinear. +Initial stress effects (stress stiffening) will be included in the response spectrum +analysis if nonlinear geometric effects (“General and linear perturbation procedures,” Section 6.1.3) were +included in a general analysis step prior to the eigenfrequency extraction step. +The problem to be solved can be stated as follows: given a set of base motions, +), +( +), estimate the peak value +specified in orthogonal directions defined by direction cosines +over all time of the response of any variable in a finite element model that is simultaneously subjected +to these multiple base motions. The peak response is first computed independently for each direction +of excitation for each natural mode of the system as a function of frequency and damping. These +independent responses are then combined to create an estimate of the actual peak response of any +variable chosen for output, as a function of frequency and damping. +( +The acceleration history (base motion) is not given directly in a response spectrum analysis; it must +first be converted into a spectrum. +Specifying a spectrum +, at each mode +The response spectrum method is based on first finding the peak response to each base motion excitation +of a one degree of freedom system that has a natural frequency equal to the frequency of interest. +The single degree of freedom system is characterized by its undamped natural frequency, +, and the +fraction of critical damping present in the system, +. The equations of motion of the +system are integrated through time to find peak values of relative displacement, relative velocity, and +relative or absolute acceleration for the linear, one degree of freedom system. This process is repeated +for all frequency and damping values in the range of interest. Plots of these responses are known +as displacement, velocity, and acceleration spectra: +. The +response spectrum can be obtained directly from measured data, as described in “Defining a spectrum +using values of S as a function of frequency and damping,” below. You can also use a FORTRAN +program to define a spectrum; an example of defining a spectrum from an acceleration record in this way +is provided in “Analysis of a cantilever subject to earthquake motion,” Section 1.4.13 of the Abaqus +Benchmarks Manual. +, and +, +Alternatively, you can create the required spectrum by specifying an amplitude (time history +record), the frequency range, and the damping values for which the spectrum will be built, as described +in “Creating a spectrum from a given time history record,” below. The spectrum can be used in the +subsequent response spectrum analysis, or it can be written to a file for future use. +For each damping value the magnitude of the response spectrum must be given over the entire +range of frequencies needed, in ascending value of frequency. Abaqus/Standard interpolates linearly +between the values given on a log-log scale. Outside the extremes of the frequency range given, +the magnitude is assumed to be constant, corresponding to the end value given. +Any number of spectra can be defined, and each spectrum must be named. The response spectrum +procedure allows up to three spectra to be applied simultaneously to the model in orthogonal physical +directions defined by their direction cosines. +Defining a spectrum using values of S as a function of frequency and damping +You can define a spectrum by specifying values for the magnitude of the spectrum; frequency, in cycles +per time, at which the magnitude is used; and associated damping, given as a ratio of critical damping. +Input File Usage: +To define the spectrum on the data lines: +*SPECTRUM, NAME=spectrum name +Repeat this option to define multiple spectra for an analysis. +Abaqus/CAE Usage: +To define a spectrum, do the following: +Step, Interaction, or Load module: Tools→Amplitude→Create; +Name: spectrum name, Type: Spectrum +To apply a spectrum to the model, do the following: +Step module: Create Step: Linear perturbation: Response +spectrum: Use response spectrum: select spectrum name for each +physical direction in which it should be applied +Specifying the type of spectrum +You can indicate whether a displacement, velocity, or acceleration spectrum is given. The default is an +acceleration spectrum. +Alternatively, an acceleration spectrum can be given in g-units. In this case you must also specify +the value of the acceleration of gravity. +Input File Usage: +Use one of the following options to define a displacement, velocity, or +acceleration spectrum: +Abaqus/CAE Usage: +*SPECTRUM, NAME=name, TYPE=DISPLACEMENT +*SPECTRUM, NAME=name, TYPE=VELOCITY +*SPECTRUM, NAME=name, TYPE=ACCELERATION +Use the following option to define an acceleration spectrum given in g-units: +*SPECTRUM, NAME=name, TYPE=G, G=g +Use one of the following options to define a displacement, velocity, or +acceleration spectrum: +Step, Interaction, or Load module: Tools→Amplitude→Create; Type: +Spectrum; Specification units: Displacement, Velocity, or Acceleration +Use the following option to define an acceleration spectrum given in g-units: +Step, Interaction, or Load module: Tools→Amplitude→Create; Type: +Spectrum; Specification units: Gravity, Gravity: g +Reading the data defining the spectrum from an alternate input file +The data for the spectrum can be specified in an alternate input file and read into the Abaqus/Standard +input file. +Input File Usage: +Abaqus/CAE Usage: +*SPECTRUM, NAME=name, INPUT=file name +Step, Interaction, or Load module: Tools→Amplitude→Create; +Type: Spectrum; click mouse button 3 while holding the cursor +over the data table, and select Read from File +Creating a spectrum from a given time history record +If you have a time history of a dynamic event (e.g., acceleration, velocity, displacement), you can build +your own spectrum by specifying the record type and the amplitude name that this record represents. If +the amplitude record is given with an arbitrarily changing time increment, linear interpolation will be +needed for the implicit integration scheme for the dynamic equation of motion for a single degree of +freedom system subjected to this record. You can specify the frequency range for the integration scheme +and the frequency increment. You can build a spectrum for every fraction of critical damping indicated +in the list of damping values. +Input File Usage: +*SPECTRUM, CREATE, AMPLITUDE=amplitude name, +NAME=spectrum name, TIME INCREMENT=dt +Abaqus/CAE Usage: +Creating a spectrum from a given time history record is not supported in +Abaqus/CAE. +Specifying the type of spectrum to be created +You can indicate whether a displacement, velocity, or acceleration spectrum is to be created. The default +is an acceleration spectrum. +Alternatively, an acceleration spectrum can be created in g-units. In this case you must also specify +the value of the acceleration of gravity. +Input File Usage: +Use one of the following options to create a displacement, velocity, or +acceleration spectrum: +*SPECTRUM, CREATE, TYPE=DISPLACEMENT +*SPECTRUM, CREATE, TYPE=VELOCITY +*SPECTRUM, CREATE, TYPE=ACCELERATION +Use the following option to create an acceleration spectrum in g-units: +Abaqus/CAE Usage: +*SPECTRUM, CREATE, TYPE=G, G=g +Creating a spectrum from a given time history record is not supported in +Abaqus/CAE. +Specifying the record type that the time history represents +You can indicate whether a displacement, velocity, or acceleration amplitude is specified. The default is +an acceleration amplitude. +Alternatively, an acceleration amplitude can be given in g-units. In this case you must also specify +the value of the acceleration of gravity. +Input File Usage: +Use one of the following options to indicate that the amplitude is defined in +displacement, velocity, or acceleration units: +*SPECTRUM, CREATE, EVENT TYPE=DISPLACEMENT +*SPECTRUM, CREATE, EVENT TYPE=VELOCITY +*SPECTRUM, CREATE, EVENT TYPE=ACCELERATION +Use the following option to indicate that an acceleration amplitude is given in +g-units: +*SPECTRUM, CREATE, EVENT TYPE=G, G=g +Creating a spectrum from a given time history record is not supported in +Abaqus/CAE. +Abaqus/CAE Usage: +Creating an absolute or relative acceleration spectrum +When you create an acceleration spectrum from a given time history record, you can create an absolute +or relative response spectrum. The default is an absolute spectrum. +Input File Usage: +Abaqus/CAE Usage: +*SPECTRUM, CREATE, TYPE=ACCELERATION, ABSOLUTE +*SPECTRUM, CREATE, TYPE=ACCELERATION, RELATIVE +Creating a spectrum from a given time history record is not supported in +Abaqus/CAE. +Generating the list of damping values for the fraction of critical damping +You must provide a list of damping values for the fraction of critical damping to create a spectrum. +However, if the damping is evenly spaced between its lower and upper bound, you can automatically +generate the list of damping values by providing the start value, end value, and increment for the fraction +of critical damping. +Input File Usage: +Abaqus/CAE Usage: +*SPECTRUM, CREATE, DAMPING GENERATE +Creating a spectrum from a given time history record is not supported in +Abaqus/CAE. +Writing the generated spectra to an independent file +You can write the generated spectra to an independent file. Otherwise, the generated spectra can be used +only within the currently submitted job in subsequent response spectra procedures. You can inspect the +generated spectra if you request that model definition data be printed to the data file . +Input File Usage: +Abaqus/CAE Usage: +*SPECTRUM, CREATE, FILE=file name +Creating a spectrum from a given time history record is not supported in +Abaqus/CAE. +Estimating the peak values of the modal responses +Since the response spectrum procedure uses modal methods to define a model’s response, the value of any +physical variable is defined from the amplitudes of the modal responses (the “generalized coordinates”), +. The first stage in the response spectrum procedure is to estimate the peak values of these modal +responses. For mode +and spectrum k this is +where +; +; +is the modal amplitude for mode +is a scaling parameter introduced as part of the response spectrum procedure +definition for spectrum +is the user-defined value of the spectrum in +direction k interpolated, if necessary, at natural frequency +and the fraction of +critical damping +in mode +is the jth direction cosine for the kth spectrum; and +is the participation factor for mode +extraction,” Section 6.3.5). +in direction j (see “Natural frequency +; +Similar expressions for +and +can be obtained by substituting velocity or +acceleration spectra in the above equation. +Combining the individual peak responses +The individual peak responses to the excitations in different directions will occur at different times and, +therefore, must be combined into an overall peak response. Two combinations must be performed, and +both introduce approximations into the results: +1. The multidirectional excitations must be combined into one overall response. This combination +is controlled by the directional summation method, as described below in “Directional summation +methods.” +2. The peak modal responses must be combined to estimate the peak physical response. This +combination is controlled by the modal summation method, as described below in “Modal +summation methods.” +Depending on the type of base excitation, either modal responses or directional responses are combined +first. +Directional summation methods +You choose the method for combining the multidirectional excitations depending on the nature of the +excitations. +The algebraic method +If the input spectra in the different directions are components of a base excitation that is approximately +in a single direction in space, then for each mode the peak responses in the different spatial directions +are summed algebraically by +After this summation is performed, the modal responses are summed. (Choosing the method used for +modal summation is described below in “Modal summation methods.”) Since the directional components +are summed first, the subscript k is not relevant and can be ignored in the modal summation equations +that follow. +Input File Usage: +Abaqus/CAE Usage: +*RESPONSE SPECTRUM, COMP=ALGEBRAIC, SUM=sum +Step module: Create Step: Linear perturbation: Response spectrum: +Excitations: Single direction or Multiple direction absolute sum +The square root of the sum of the squares directional summation method +If the spectra in different directions represent independent excitations, the modal summation is performed +first, as explained below in “Modal summation methods.” Then, the responses in different excitation +directions are combined by +Input File Usage: +Abaqus/CAE Usage: +*RESPONSE SPECTRUM, COMP=SRSS, SUM=sum +Step module: Create Step: Linear perturbation: Response spectrum: +Excitations: Multiple direction square root of the sum of squares +The forty-percent method +If the spectra in different directions represent independent excitations, the modal summation is performed +first, as explained below in “Modal summation methods.” Then, the responses in different excitation +directions are combined by the 40% rule recommended by the ASCE 4–98 standard for Seismic Analysis +of Safety-Related Nuclear Structures and Commentary, Section 3.2.7.1.2. This method combines the +response for all possible combinations of the three components, including variations in sign (plus/minus), +assuming that when the maximum response from one component occurs, the response from the other two +components is 40% of their maximum value, using one of the following: +Input File Usage: +Abaqus/CAE Usage: +*RESPONSE SPECTRUM, COMP=R40, SUM=sum +Step module: Create Step: Linear perturbation: Response spectrum: +Excitations: Multiple direction forty percent rule +The thirty-percent method +If the spectra in different directions represent independent excitations, the modal summation is performed +first, as explained below in “Modal summation methods.” Then, the responses in different excitation +directions are combined by the 30% rule recommended by the ASCE 4–98 standard for Seismic Analysis +of Safety-Related Nuclear Structures and Commentary, Section 3.2.7.1.2. This method combines the +response for all possible combinations of the three components, including variations in sign (plus/minus), +assuming that when the maximum response from one component occurs, the response from the other two +components is 30% of their maximum value, using one of the following: +Input File Usage: +Abaqus/CAE Usage: +*RESPONSE SPECTRUM, COMP=R30, SUM=sum +Step module: Create Step: Linear perturbation: Response spectrum: +Excitations: Multiple direction thirty percent rule +Modal summation methods +The peak response of some physical variable +reaction force, etc.) caused by the motion in the +in direction k at frequency +with damping +(a component i of displacement, stress, section force, +th natural mode excited by the given response spectra +is given by +where +the subscript k is not relevant and can be ignored in this equation and in those that follow.) +is the ith component of mode , and there is no sum on . (In the case of algebraic summation +, into estimates of the total peak response, +There are several methods for combining these peak physical responses in the individual modes, +. Most of the methods implemented in +Abaqus/Standard follow the ASCE 4–98 standard for Seismic Analysis of Safety Related Nuclear +Structures and Commentary. The updated documents, “Reevaluation of Regulatory Guidance on +Modal Response Combination Methods for Seismic Response Spectrum Analysis” issued in 1999 +(NUREG/CR-6645, BNL-NUREG-52276) and “Draft Regulatory Guide” (DG-1127) issued in 2005 +contain new recommendations. You are advised to read the new recommendations before choosing a +modal summation method from among those described below. +The absolute value method +The absolute value method is the most conservative method for combining the modal responses. It is +obtained by summing the absolute values resulting from each mode: +This method implies that all of the responses peak simultaneously. It will overpredict the peak response +of most systems; therefore, it may be too conservative to help in design. +Input File Usage: +Abaqus/CAE Usage: +*RESPONSE SPECTRUM, COMP=comp, SUM=ABS +Step module: Create Step: Linear perturbation: Response +spectrum: Summations: Absolute values +The square root of the sum of the squares modal summation method +The square root of the sum of the squares method is less conservative than the absolute value method. +It is also usually more accurate if the natural frequencies of the system are well separated. It uses the +square root of the sum of the squares to combine the modal responses: +Input File Usage: +Abaqus/CAE Usage: +*RESPONSE SPECTRUM, COMP=comp, SUM=SRSS +Step module: Create Step: Linear perturbation: Response spectrum: +Summations: Square root of the sum of squares +The Naval Research Laboratory method +The absolute value and square root of the sum of the squares methods can be combined to yield the +Naval Research Laboratory method. It distinguishes the mode, +, in which the physical variable has its +maximum response and adds the square root of the sum of squares of the peak responses in all other +modes to the absolute value of the peak response of that mode. This method gives the estimate: +Input File Usage: +Abaqus/CAE Usage: +*RESPONSE SPECTRUM, COMP=comp, SUM=NRL +Step module: Create Step: Linear perturbation: Response spectrum: +Summations: Naval Research Laboratory +The ten-percent method +The ten-percent method recommended by Regulatory Guide 1.92 (1976) is no longer recommended +according to the “Reevaluation of Regulatory Guidance on Modal Response Combination Methods +for Seismic Response Spectrum Analysis” document issued in 1999. It is retained here because of its +extensive prior use. The ten-percent method modifies the square root of the sum of the squares method +by adding a contribution from all pairs of modes +and whose frequencies are within 10% of each +other, giving the estimate: +The frequencies of modes +and +are considered to be within 10% of each other whenever +The ten-percent method reduces to the square root of the sum of the squares method if the modes +are well separated with no coupling between them. +Input File Usage: +Abaqus/CAE Usage: +*RESPONSE SPECTRUM, COMP=comp, SUM=TENP +Step module: Create Step: Linear perturbation: Response +spectrum: Summations: Ten percent +The complete quadratic combination method +Like the ten-percent method, the complete quadratic combination method improves the estimation for +structures with closely spaced eigenvalues. The complete quadratic combination method combines the +modal response with the formula +where +frequencies and modal damping between the two modes: +are cross-correlation coefficients between modes +and +, which depend on the ratio of +where +. +If the modes are well spaced, their cross-correlation coefficient will be small ( +method will give the same results as the square root of the sum of the squares method. +) and the +This method is usually recommended for asymmetrical building systems since, in such cases, other +methods can underestimate the response in the direction of motion and overestimate the response in the +transverse direction. +Input File Usage: +Abaqus/CAE Usage: +*RESPONSE SPECTRUM, COMP=comp, SUM=CQC +Step module: Create Step: Linear perturbation: Response spectrum: +Summations: Complete quadratic combination +The grouping method +This method, also known as the NRC grouping method, improves the response estimation for structures +with closely spaced eigenvalues. The modal responses are grouped such that the lowest and highest +frequency modes in a group are within 10% and no mode is in more than one group. The modal responses +are summed absolutely within groups before performing a SRSS combination of the groups. Within the +group responses are summed as +for “n” frequencies within any “gr” group and then performing +The above expression includes all the groups; in addition, the group can consist of just one frequency +response if this frequency does not have another member that is within the 10% limit. +Input File Usage: +The ten-percent method will always produce results higher in value than the grouping method. +*RESPONSE SPECTRUM, COMP=comp, SUM=GRP +Step module: Create Step: Linear perturbation: Response +spectrum: Summations: Grouping method +Abaqus/CAE Usage: +Double sum combination +This method, also known as Rosenblueth’s double sum combination (Rosenblueth and Elorduy, 1969), +is the first attempt to evaluate modal correlation based on random vibration theory. It utilizes the time +duration +, which depend also on +the frequencies and damping coefficient +of strong earthquake motion. The mode correlation coefficients +, lead to the following mode combination: +where +where +Input File Usage: +Abaqus/CAE Usage: +*RESPONSE SPECTRUM, COMP=comp, SUM=DSC +Step module: Create Step: Linear perturbation: Response spectrum: +Summations: Double sum combination +Selecting the modes and specifying damping +You can select the modes to be used in modal superposition and specify damping values for all selected +modes. +Selecting the modes +You can select modes by specifying the mode numbers individually, by requesting that Abaqus/Standard +generate the mode numbers automatically, or by requesting the modes that belong to specified frequency +ranges. If you do not select the modes, all modes extracted in the prior eigenfrequency extraction step, +including residual modes if they were activated, are used in the modal superposition. +Input File Usage: +Use one of the following options to select the modes by specifying mode +numbers: +*SELECT EIGENMODES, DEFINITION=MODE NUMBERS +*SELECT EIGENMODES, GENERATE, DEFINITION=MODE NUMBERS +Use the following option to select the modes by specifying a frequency range: +*SELECT EIGENMODES, DEFINITION=FREQUENCY RANGE +You cannot select the modes in Abaqus/CAE; all modes extracted are used in +the modal superposition. +Abaqus/CAE Usage: +Specifying damping +Damping is almost always specified for a mode-based procedure; see “Material damping,” Section 26.1.1. +You can define a damping coefficient for all or some of the modes used in the response calculation. The +damping coefficient can be given for a specified mode number or for a specified frequency range. When +damping is defined by specifying a frequency range, the damping coefficient for an mode is interpolated +linearly between the specified frequencies. The frequency range can be discontinuous; the average +damping value will be applied for an eigenfrequency at a discontinuity. The damping coefficients are +assumed to be constant outside the range of specified frequencies. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to define damping by specifying mode numbers: +*MODAL DAMPING, DEFINITION=MODE NUMBERS +Use the following option to define damping by specifying a frequency range: +*MODAL DAMPING, DEFINITION=FREQUENCY RANGE +Use the following input to define damping by specifying mode numbers: +Step module: Create Step: Linear perturbation: Response spectrum: +Damping: Specify damping over ranges of: Modes +Use the following input to define damping by specifying a frequency range: +Step module: Create Step: Linear perturbation: Response spectrum: +Damping: Specify damping over ranges of: Frequencies +Example of specifying damping +Figure 6.3.10–1 illustrates how the damping coefficients at different eigenfrequencies are determined for +the following input: +*MODAL DAMPING, DEFINITION=FREQUENCY RANGE +Rules for selecting modes and specifying damping coefficients +The following rules apply for selecting modes and specifying modal damping coefficients: +• No modal damping is included by default. +• Mode selection and modal damping must be specified in the same way, using either mode numbers +or a frequency range. +• If you do not select any modes, all modes extracted in the prior frequency analysis, including residual +modes if they were activated, will be used in the superposition. +• If you do not specify damping coefficients for modes that you have selected, zero damping values +will be used for these modes. +damping values +d = +d +2 d 3 +f i +d i +eigenfrequencies +frequencies +damping values +d 2 d 3 +f 2 +d 3 +f 3 +d 4 +f 4 +frequency +Figure 6.3.10–1 Damping values specified by frequency range. +• Damping is applied only to the modes that are selected. +• Damping coefficients for selected modes that are beyond the specified frequency range are constant +and equal to the damping coefficient specified for the first or the last frequency (depending which +one is closer). This is consistent with the way Abaqus interprets amplitude definitions. +Initial conditions +It is not appropriate to specify initial conditions in a response spectrum analysis. +Boundary conditions +All points constrained by boundary conditions and the ground nodes of connector elements are assumed +to move in phase in any one direction. This base motion can use a different input spectrum in each of +three orthogonal directions (two directions in a two-dimensional model). You define the input spectra, +, as described earlier in +, for different values of critical damping, +, as functions of frequency, +“Specifying a spectrum.” Secondary bases cannot be used in a response spectrum analysis. +Loads +The only “loading” that can be defined in a response spectrum analysis is that defined by the input spectra, +as described earlier. No other loads can be prescribed in a response spectrum analysis. +Predefined fields +Predefined fields, including temperature, cannot be used in response spectrum analysis. +Material options +The density of the material must be defined (“Density,” Section 21.2.1). The following material +properties are not active during a response spectrum analysis: plasticity and other inelastic effects, +rate-dependent material properties, thermal properties, mass diffusion properties, electrical properties, +and pore fluid flow properties—see “General and linear perturbation procedures,” Section 6.1.3. +Elements +Other than generalized axisymmetric elements with twist, any of the stress/displacement elements in +Abaqus/Standard can be used in a response spectrum analysis—see “Choosing the appropriate element +for an analysis type,” Section 27.1.3. +Output +All the output variables in Abaqus/Standard are listed in “Abaqus/Standard output variable identifiers,” +Section 4.2.1. The value of an output variable such as strain, E; stress, S; or displacement, U, is its peak +magnitude. +In addition to the usual output variables available, the following modal variables are available for +response spectrum analysis and can be output to the data and/or results files : +GU +GV +GA +SNE +KE +Generalized displacements for all modes. +Generalized velocities for all modes. +Generalized accelerations for all modes. +Elastic strain energy for the entire model per each mode. +Kinetic energy for the entire model per each mode. +External work for the entire model per each mode. +Neither element energy densities (such as the elastic strain energy density, SENER) nor whole +element energies (such as the total kinetic energy of an element, ELKE) are available for output in +response spectrum analysis. However, whole model variables such as ALLIE (total strain energy) are +available for modal-based procedures as output to the data and/or results files . +Reaction force output is not supported for response spectrum analysis using eigenmodes extracted +using a SIM-based frequency extraction procedure with either the AMS or Lanczos eigensolver. +Reaction force output in response spectrum analysis using eigenmodes extracted with the default +Lanczos eigensolver provides directional combinations of so-called, modal reaction forces weighted +with maximal absolute values of corresponding generalized displacements. Directional and modal +combination rules used for the reaction force calculation are the same as for other nodal output variables. +Modal reaction forces are calculated in the frequency extraction procedure. They represent static +reaction forces calculated for the normal mode shapes. Generally, they cannot adequately represent +reaction force in dynamic analysis. For models with diagonal mass and diagonal damping matrices the +superposition of the modal reaction forces can provide a reasonable approximation of a nodal reaction +force in mode-based analyses other than response spectrum analysis. In response spectrum analysis the +model response can be better represented by requesting section stresses and section forces in structural +elements containing supported nodes. +Input file template +, and +*HEADING +… +*BOUNDARY +Data lines to define points to be excited by the base motion controlled by the input spectra +*SPECTRUM, NAME=name1, TYPE=type +Data lines to define spectrum “name1” as a function of frequency, +fraction of critical damping, +*SPECTRUM, NAME=name2, TYPE=type +Data lines to define spectrum “name2” as a function of frequency, +fraction of critical damping, +** +*STEP +*FREQUENCY +Data line to specify number of modes to be extracted +*END STEP +** +*STEP +*RESPONSE SPECTRUM, COMP=comp, SUM=sum +Data lines referring to response spectra and defining direction cosines +*SELECT EIGENMODES +Data lines to define the applicable mode ranges +*MODAL DAMPING +Data lines to define modal damping +*END STEP +, and +Additional reference +• Rosenblueth, E., and J. Elorduy, “Response of Linear Systems to Certain Transient Disturbances,” +Proceedings of the Fourth World Conference on Earthquake Engineering, Santiago, Chile, 1969. +6.3.11 +RANDOM RESPONSE ANALYSIS +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “General and linear perturbation procedures,” Section 6.1.3 +• “Dynamic analysis procedures: overview,” Section 6.3.1 +• *RANDOM RESPONSE +• *PSD-DEFINITION +• *CORRELATION +• “Configuring a random response procedure” in “Configuring linear perturbation analysis +procedures,” Section 14.11.2 of the Abaqus/CAE User’s Manual, in the online HTML version of +this manual +Overview +A random response analysis: +• is a linear perturbation procedure that gives the linearized dynamic response of a model to user- +defined random excitation; and +• uses the set of modes extracted in a previous eigenfrequency extraction step to calculate the power +spectral densities of response variables (stresses, strains, displacements, etc.) and the corresponding +root mean square (RMS) values of these same variables. +Random response analysis +Random response analysis predicts the response of a system that is subjected to a nondeterministic +continuous excitation that is expressed in a statistical sense by a cross-spectral density matrix. Since the +loading is nondeterministic, it can be characterized only in a statistical sense; Abaqus/Standard assumes +that the excitation is stationary and ergodic. These statistical measures are explained in detail in “Random +response analysis,” Section 2.5.8 of the Abaqus Theory Manual. The random response procedure can, +for example, be used to determine the response of an airplane to turbulence, the response of a car to +road surface imperfections, the response of a structure to jet noise, or the response of a building to an +earthquake. +In the most general case the excitation is defined as a frequency-dependent cross-spectral density +(CSD) matrix. Except in cases involving moving noise or user subroutine UCORR, it is assumed that for +a given load case the CSD matrix can be separated into a product of a frequency-dependent, complex- +valued scalar function and a frequency-independent, complex-valued, spatial correlation matrix. This +assumption helps reduce both the computational time and the amount of required user input but implies +that each element of the CSD matrix in a given load case has the same frequency dependence. You can +define a different frequency dependence for each load case, but the loads in one load case will not be +correlated with loads in another. Consequently, the system CSD matrix is assembled by simply summing +(superimposing) the CSD matrices of the individual load cases. +The frequency-dependent scalar function can be composed of a weighted sum of user-defined, +complex-valued, frequency functions. These user-defined frequency functions are specified in units of +power spectral density. You assign weights to each frequency function as well as specify properties of +the spatial correlation matrix that defines the correlation between excitations at different locations and in +different directions for a particular load case. Frequency functions and correlations are discussed below; +see “Defining the frequency functions,” and “Defining the correlation.” +The loads can be defined as concentrated point loads, as distributed loads, as connector element +loads, or as base motion excitations, as described below in “Boundary conditions,” and “Loads.” +Multiple, uncorrelated load cases can be defined for concentrated point loads, connector loads, and +base motions. Load case 1 is reserved for all distributed loads defined in a particular step. In these +steps load case 1 cannot be used for any concentrated point load, connector load, or base motion. Thus, +there cannot be any correlation between distributed loads and any other load. Moreover, base motion +excitations are assumed to be statistically independent (no correlation) with any other load type even +when the same load case number is used. The concentrated point and connector element loads are +assumed to be correlated if the same load case number is used. +The random response procedure is based on using a subset of the modes of the system, which must +first be extracted by using the eigenfrequency extraction procedure. The modes will include eigenmodes +and, if activated in the eigenfrequency extraction step, residual modes. The number of modes extracted +must be sufficient to model the dynamic response of the system adequately, which is a matter of judgment +on your part. The model can be preloaded prior to the eigenfrequency extraction. Initial stress effects are +included in the stiffness used in the eigenfrequency extraction if geometric nonlinearities are included in +the general analysis procedure used to apply the preloads (“General and linear perturbation procedures,” +Section 6.1.3). +The random response of the model is expressed as power spectral density values of nodal and +element variables, as well as their root mean square values. +Defining the frequency range +You specify the frequency range of interest for the random response procedure. The response is calculated +at multiple points between the lowest frequency of interest and the first eigenfrequency in the range, +between each eigenfrequency in the range, and between the last eigenfrequency in the range and the +highest frequency in the range as illustrated in Figure 6.3.11–1. The default number of calculation points +in each interval is 20; you can change this number when you define the step. Accurate RMS values can +be obtained only if enough points are used so that Abaqus/Standard can integrate accurately over the +frequency range. The bias function allows the points on the frequency scale to be spaced closer together +at the eigenfrequencies, thus allowing detailed definition of the response close to resonant frequencies +and more accurate integration. +Input File Usage: +*RANDOM RESPONSE +lower_freq_limit, upper_freq_limit, num_calc_pts, bias_parameter, freq_scale +frequency points +lower end +of the range +mode n +mode n +1 +mode n + 2 +upper end +of the range +Figure 6.3.11–1 Division of range using modes and 5 calculation points. +Abaqus/CAE Usage: +Step module: Create Step: Linear perturbation: Random response +The bias parameter +The bias parameter can be used to provide closer spacing of the result points either toward the middle or +toward the ends of each frequency interval. Figure 6.3.11–2 shows a few examples of the effect of the +bias parameter on the frequency spacing. +frequency points +f1 +Bias parameter = 1 +f2 +Bias parameter = 2 +Bias parameter = 3 +Bias parameter = 5 +Figure 6.3.11–2 Effect of the bias parameter on the frequency +spacing for a number of points +. +The bias formula used to calculate the frequency at which results are presented is as follows: +where +; +is the number of frequency points at which results are to be given; +is one such frequency point ( +is the lower limit of the frequency interval; +is the upper limit of the interval; +is the frequency at which the kth results are given; +is the bias parameter value; and +is the frequency or the logarithm of the frequency, depending on the chosen frequency scale. +); +A bias parameter, p, that is greater than 1.0 provides closer spacing of the results points toward the ends of +each frequency interval (as shown in the examples above), while values of p that are less than 1.0 provide +closer spacing toward the middle of each frequency interval. The default value of the bias parameter for +random response analysis is 3.0. +Defining the frequency functions +To define the random loading, you specify a frequency function and a cross-correlation definition that +refers to the frequency function. The frequency functions are defined as model data (i.e., they are step +independent) and must be named. A log-log scale is used in interpolating between the given values. +The type of units in the CSD matrix of the excitation are specified as part of the frequency function +definition. The default type is power units. If the CSD matrix of the excitation is due to base motion, +the units must be in g units and you should define the acceleration of gravity. Alternatively, decibel units +can be specified; this type of units is explained below. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options to define the frequency function: +*PSD-DEFINITION, NAME=name, TYPE=FORCE (default; power units) +*PSD-DEFINITION, NAME=name, TYPE=BASE, G=g +*PSD-DEFINITION, NAME=name, TYPE=DB, DB REFERENCE= +Load module: Create Amplitude; Type: PSD Definition; Specification +units: Power, Decibel, or Gravity +Defining the cross-spectral density matrix in decibel units +In Abaqus/Standard the decibel value +full octave band conversion formula: +is related to the frequency function +by the following +where +Hence, the frequency function follows from the function defined in decibel units as +is the user-specified reference power and +is the midband frequency . +Table 6.3.11–1 Standard octave bands. +Band +number +Band center +(frequency, Hz) +10 +11 +12 +13 +14 +15 +1.0 +2.0 +4.0 +8.0 +16.0 +31.5 +63.0 +125.0 +250.0 +500.0 +1000.0 +2000.0 +4000.0 +8000.0 +16000.0 +If you have data in terms of an alternative frequency scale (e.g., one-third octave band), an equivalent +full octave band power reference value can be obtained as described in “Random response analysis,” +Section 2.5.8 of the Abaqus Theory Manual. +in decibels must be specified as a function of the frequency band; the associated midband +frequencies are given in Table 6.3.11–1. +Alternate methods for defining frequency functions +You can define a frequency function in an external file or in a user subroutine. +Defining the frequency function in an external file +The data to define a frequency function can be contained in an external file. +Input File Usage: +Abaqus/CAE Usage: +*PSD-DEFINITION, NAME=name, TYPE=type, INPUT=file name +Load module: Create Amplitude; Type: PSD Definition; Specification +units: Power, Decibel, or Gravity; Real, Imaginary, Frequency +Defining the frequency function in a user subroutine +Complicated frequency functions can be more easily defined by user subroutine UPSD than by entering +data directly. +Input File Usage: +*PSD-DEFINITION, NAME=name, TYPE=type, USER +Any data lines given will be ignored if the USER parameter is specified. +Abaqus/CAE Usage: +Load module: Create Amplitude; Type: PSD Definition; +Specification units: Power or Gravity; toggle on Specify +data in an external user subroutine +Defining the correlation +You define the cross-correlation between the applied nodal loads or base motions. You can also assign +scaling (weight) factors to the frequency functions through the cross-correlation definition. Distributed +loads are converted to equivalent nodal loads, which are treated as individual point loads with respect +to the cross-correlation. The cross-correlation is defined in the random response step and references a +particular load case number and frequency function. +Three types of correlation can be defined: correlated, uncorrelated, and moving noise. As many +correlations as needed to define the random loading can be specified unless the moving noise type is +chosen, in which case only one correlation can appear in the step definition. +• For the correlated type all terms in the cross-spectral density matrix are considered, which implies +that the loads on all degrees of freedom within the load case are fully correlated (statistically +dependent on each other). +• For the uncorrelated type only diagonal terms in the cross-spectral density matrix are considered, +which implies that no correlation exists between the load on one degree of freedom and the load on +another. You should exercise caution when choosing the uncorrelated type with distributed loads +since the equivalent nodal forces would be uncorrelated with each other (statistically independent). +• For the moving noise type the terms in the correlation matrix depend on the relative position of the +points where the loads are applied. This type can be used only in conjunction with concentrated point +loads and distributed loads. In addition, the moving noise formulation assumes that the frequency +function referenced by the cross-correlation defines a reference power spectral density function of +the noise source. (It is a reference power spectral density because it can later be scaled by the +magnitude of the loadings specified as distributed, concentrated point, or connector element loads.) +Since the power spectral density is real-valued for real-valued variables, the frequency function +must not contain imaginary terms when used with the moving noise type of cross-correlation. +Input File Usage: +Use one of the following options to define the correlation: +*CORRELATION, TYPE=CORRELATED, PSD=name +*CORRELATION, TYPE=UNCORRELATED, PSD=name +*CORRELATION, TYPE=MOVING NOISE +For the moving noise type the reference to the power spectral density function +must be given on each data line. +Abaqus/CAE Usage: +Load module; Create Boundary Condition; Step: random_response_step; +Category: Mechanical; Types for Selected Step: Displacement +base motion or Velocity base motion or Acceleration base motion; +Correlation tabbed page: toggle on Specify correlation; Approach: +Correlated or Uncorrelated; PSD: psd_amplitude_name +Specifying whether the correlation matrix is complex +For correlated or uncorrelated cross-correlations you can specify whether or not both real and imaginary +terms will be included in the spatial correlation matrix. This specification does not affect the imaginary +terms given for the power spectral density frequency function. +Input File Usage: +Use one of the following options: +Abaqus/CAE Usage: +*CORRELATION, TYPE=CORRELATED, COMPLEX=YES or NO, +PSD=name +*CORRELATION, TYPE=UNCORRELATED, COMPLEX=YES or NO, +PSD=name +Load module; Create Boundary Condition; Step: random_response_step; +Category: Mechanical; Types for Selected Step: Displacement +base motion or Velocity base motion or Acceleration base motion; +Correlation tabbed page: toggle on Specify correlation; Approach: +Correlated or Uncorrelated; PSD: psd_amplitude_name; Real; Imaginary +Alternate methods for defining a correlation +You can define a correlation in an external input file or in a user subroutine. +Defining the correlation in an external input file +The data to define a correlation can be contained in an external input file. +Input File Usage: +Abaqus/CAE Usage: +*CORRELATION, TYPE=type, PSD=name, INPUT=file_name +You cannot define a correlation in an external file in Abaqus/CAE. +Defining the correlation in a user subroutine +Simple excitations, such as uncorrelated white noise, are easily defined. Excitations involving more +complicated correlations, including cases where the elements of the CSD matrix have different frequency +dependencies, can be defined through user subroutine UCORR. If the user subroutine is specified, only +the load case number must be entered as part of the correlation definition. A user subroutine cannot be +used to define a moving noise correlation. +For uncorrelated cross-correlations only the diagonal terms of the correlation matrix specified in +UCORR will be used. The combination of the cross-correlation with the various kinds of applied loads is +discussed in more detail below. +Input File Usage: +Use one of the following options: +Abaqus/CAE Usage: +*CORRELATION, TYPE=CORRELATED, USER, COMPLEX=YES +or NO, PSD=name +*CORRELATION, TYPE=UNCORRELATED, USER, PSD=name +Load module; Create Boundary Condition; Step: random_response_step; +Category: Mechanical; Types for Selected Step: Displacement +base motion or Velocity base motion or Acceleration base motion; +Correlation tabbed page: toggle on Specify correlation; Approach: User +Selecting the modes and specifying damping +You can select the modes to be used in modal superposition and specify damping values for all selected +modes. +Selecting the modes +You can select modes by specifying the mode numbers individually, by requesting that Abaqus/Standard +generate the mode numbers automatically, or by requesting the modes that belong to specified frequency +ranges. If you do not select the modes, all modes extracted in the prior eigenfrequency extraction step, +including residual modes if they were activated, are used in the modal superposition. +Input File Usage: +Use one of the following options to select the modes by specifying mode +numbers: +*SELECT EIGENMODES, DEFINITION=MODE NUMBERS +*SELECT EIGENMODES, GENERATE, DEFINITION=MODE NUMBERS +Use the following option to select the modes by specifying a frequency range: +*SELECT EIGENMODES, DEFINITION=FREQUENCY RANGE +You cannot select the modes in Abaqus/CAE; all modes extracted are used in +the modal superposition. +Abaqus/CAE Usage: +Specifying damping +Damping is almost always specified for a random response analysis . +If damping is absent, the response of a structure will be unbounded if the forcing +frequency is equal to an eigenfrequency of the structure. To get quantitatively accurate results, +especially near natural frequencies, accurate specification of damping properties is essential. The +various damping options available are discussed in “Material damping,” Section 26.1.1. You can define +a damping coefficient for all or some of the modes used in the response calculation. The damping +coefficient can be given for a specified mode number or for a specified frequency range. When damping +is defined by specifying a frequency range, the damping coefficient for a mode is interpolated linearly +between the specified frequencies. The frequency range can be discontinuous; the average damping +value will be applied for an eigenfrequency at a discontinuity. The damping coefficients are assumed to +be constant outside the range of specified frequencies. +Input File Usage: +Use the following option to define damping by specifying mode numbers: +Abaqus/CAE Usage: +*MODAL DAMPING, DEFINITION=MODE NUMBERS +Use the following option to define damping by specifying a frequency range: +*MODAL DAMPING, DEFINITION=FREQUENCY RANGE +Use the following input to define damping by specifying mode numbers: +Step module: Create Step: Linear perturbation: Random response: +Damping +Defining damping by specifying frequency ranges is not supported in +Abaqus/CAE. +Example of specifying damping +Figure 6.3.11–3 illustrates how the damping coefficients at different eigenfrequencies are determined for +the following input: +*MODAL DAMPING, DEFINITION=FREQUENCY RANGE +damping values +d = +d +2 d 3 +f i +d i +eigenfrequencies +frequencies +damping values +d 2 d 3 +f 2 +d 3 +f 3 +d 4 +f 4 +frequency +Figure 6.3.11–3 Damping values specified by frequency range. +Rules for selecting modes and specifying damping coefficients +The following rules apply for selecting modes and specifying modal damping coefficients: +• No modal damping is included by default. +• Mode selection and modal damping must be specified in the same way, using either mode numbers +or a frequency range. +• If you do not select any modes, all modes extracted in the prior frequency analysis, including residual +modes if they were activated, will be used in the superposition. +• If you do not specify damping coefficients for modes that you have selected, zero damping values +will be used for these modes. +• Damping is applied only to the modes that are selected. +• Damping coefficients for selected modes that are beyond the specified frequency range are constant +and equal to the damping coefficient specified for the first or the last frequency (depending which +one is closer). This is consistent with the way Abaqus interprets amplitude definitions. +Initial conditions +It is not appropriate to specify initial conditions in a random response analysis. +Boundary conditions +It is not possible to prescribe nonzero displacements and rotations directly as boundary conditions +(“Boundary conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1) in mode-based +dynamic response procedures. Therefore, in a random response analysis the motion of nodes can be +specified only as base motion; nonzero displacement, velocity, or acceleration history definitions given +as boundary conditions are ignored, and any changes in the support conditions from the eigenfrequency +extraction step are flagged as errors. In addition, any amplitude definitions are ignored in a random +response analysis. +The method for prescribing motion in modal superposition procedures is described in “Transient +modal dynamic analysis,” Section 6.3.7. In random response analysis only a single (primary) base can +be defined. +Defining multiple load cases +The excitation defined by the base motion is assigned to numbered load cases. These load cases are then +referenced in the cross-correlation definition. The load cases are associated with frequency functions +through the reference in the cross-correlation definition. Any number of load cases can be defined, but +load case number 1 cannot be used if distributed loads are defined in the same step. +Input File Usage: +Abaqus/CAE Usage: +*BASE MOTION, LOAD CASE=n +Base motions with load cases are not supported in Abaqus/CAE. +Converting base motion excitation to a cross-spectral density matrix +When the excitation is provided by a base motion, it is converted directly into a cross-spectral density +matrix projected onto the eigenspace through the modal participation factors , giving +for +for +for +, +, +, +Re +where the superscript * denotes complex conjugate and where +is the modal participation factor for mode +is the frequency function referenced by the Jth cross-correlation and defined as a function +of the frequency f in g units; +is a matrix of weight factors indicating the fraction of +between base motion in directions i and j for load case I, as described below; +to be associated with the correlation +in excitation direction i (i=1–6); +, 1, or 2, depending on whether the base motion corresponding to load case I is defined +in terms of an acceleration spectrum, a velocity spectrum, or a displacement spectrum ; and +is the user-specified acceleration of gravity for the same power spectral density frequency +function that defines +. +If the cross-correlation is defined in user subroutine UCORR, +Otherwise, +is defined in the user subroutine. +for all +if the excitation is correlated or +if the excitation is uncorrelated, +where +in load case I. +is the (complex) value of the weight factor by which to scale the frequency function +used +Loads +, where f is frequency in cycles per time and the subscripts +The loading for random response analysis is defined in general terms by the cross-spectral density matrix +refer to +degree of freedom i at node N and degree of freedom j at node M, respectively. Distributed loads are +converted to equivalent nodal loads, which—for the formulation of the correlation matrix—are treated +are (force)2 or (moment)2 +in the same way as concentrated point loads. The units of +per frequency. In addition, any amplitude references on the concentrated point, connector element, or +distributed load definitions are ignored in a random response analysis. +and +Defining multiple load cases +Distributed loads will be assigned automatically to load case number 1. You assign a concentrated point +load or connector element load to a numbered load case. Any number of concentrated point and connector +element load cases can be specified, but load case number 1 cannot be used for a concentrated point or +connector element load if a distributed load is present in the same step. The concentrated point, connector +element, and distributed load cases are associated with frequency functions through the cross-correlation +definition. +Input File Usage: +Use one or more of the following options: +*CLOAD, LOAD CASE=n +*CONNECTOR LOAD, LOAD CASE=m +*DLOAD +Correlated and uncorrelated loading +For correlated or uncorrelated cross-correlations, the cross-spectral density matrix is defined as +Re +for +for +for +, +, +, +where the superscript * denotes complex conjugate and where +is the load magnitude applied to degree of freedom i at node N for load case I; +is the frequency function referenced by the Jth cross-correlation and defined as a +function of the frequency f in power (force) or decibel units; and +is a matrix of weight factors indicating the fraction of +the +cross-correlation term for load case I, as described below. +to be associated with +If the cross-correlation is defined in user subroutine UCORR, +Otherwise, +is defined in the user subroutine. +for all +if the excitation is correlated or +if the excitation is uncorrelated, +where +in load case I. +is the (complex) value of the weight factor by which to scale the frequency function +used +Moving noise loading +For moving noise cross-correlations, the cross-spectral density matrix is defined as +where +is the load magnitude applied to degree of freedom i at node N for load case I; +is the reference power spectral density function associated with load case I and defined as a +function of the frequency f in power (force) or decibel units; +is the velocity vector of noise propagation given for load case I; and +are the coordinates of node N. +This definition of moving noise implies that the different noise sources have no cross-correlation. +Therefore, it is most generally used with only one noise source ( +is the actual power spectral density of the moving noise source, it must be defined as a real-valued +function. +only). In addition, since +Predefined fields +Predefined fields, including temperature, cannot be used in random response analysis. +Material options +As in any dynamic analysis procedure, mass or density (“Density,” Section 21.2.1) must be assigned +to some regions of any separate parts of the model where dynamic response is required. The following +material properties are not active during a random response analysis: plasticity and other inelastic effects, +rate-dependent properties, thermal properties, mass diffusion properties, electrical properties, and pore +fluid flow properties . +Elements +Other than generalized axisymmetric elements with twist, any of the stress/displacement elements in +Abaqus/Standard can be used in a random response analysis . +Output +In random response analysis the value of a variable is its power spectral density; all of the output variables +in Abaqus/Standard are listed in “Abaqus/Standard output variable identifiers,” Section 4.2.1. Power +spectral density values are not available for concentrated and distributed loads and for SINV. +Options are also provided in random response analysis to obtain root mean square values for certain +variables, as listed below. Total values include base motion, while relative values are measured relative +to the base motion. +Element integration point variables: +RS +RE +Root mean square of all stress components. +Root mean square of all strain components. +Element nodal point variables: +MISES +RMISES +Mises equivalent stress.. +Root mean square of Mises equivalent stress. +For connector elements, the following element output variables are available: +RCTF +Root mean square of connector total forces. +RCEF +RCVF +RCRF +RCSF +RCU +RCCU +Nodal variables: +RU +RTU +RV +RTV +RA +RTA +RRF +Root mean square of connector elastic forces. +Root mean square of connector viscous forces. +Root mean square of connector reaction forces. +Root mean square of connector friction forces. +Root mean square of connector relative displacements. +Root mean square of connector constitutive displacements. +Root mean square values of all components of the relative displacement/rotation +at a node. +Root mean square values of all components of the total displacement/rotation at a +node. +Root mean square values of all components of the relative velocity at a node. +Root mean square values of all components of the total velocity at a node. +Root mean square values of all components of the relative acceleration at a node. +Root mean square values of all components of the total acceleration at a node. +Root mean square values of all components of reaction forces and reaction +moments at a node. +No energy values are available for a random response analysis. +To reduce the computational cost of random response analysis, you should request output only for +selected element and node sets. Abaqus/Standard will calculate the response for only the element and +nodal variables requested. +When MISES or RMISES output is requested, Abaqus/Standard stores the needed data in the +output database (.odb) file and Abaqus/Viewer does the actual computation of the responses. These +computations require element stress output in the frequency step preceding the random response step. +Note that specifying the name of the element set in the output request in the random response step has +no effect on these two output variables. If MISES or RMISES output for a selected set of elements is +desired, the name of that element set needs to be specified for the element stress output request in the +preceding frequency step. Unlike in other procedures, MISES and RMISES output for random response +analysis is computed at the element nodal points and not at the element integration points. +Input file template +*HEADING +… +*PSD-DEFINITION, NAME=name, TYPE=type +Data lines to define a frequency function (or PSD function for moving noise) +** +*STEP +*FREQUENCY +Data line to control eigenvalue extraction +*BOUNDARY +Data lines to assign degrees of freedom to the primary base +*END STEP +*STEP +*RANDOM RESPONSE +Data line to specify frequency range of interest +*SELECT EIGENMODES +Data lines to define the applicable mode ranges +*MODAL DAMPING +Data line to define modal damping +*CORRELATION, PSD=name, TYPE=type +Data lines to specify correlation for various excitation load cases (n, p) +*DLOAD +Data lines to define distributed loads +*CLOAD, LOAD CASE=n +Data lines to define concentrated loads in load case n +*CONNECTOR LOAD, LOAD CASE=m +Data lines to define connector loads in load case m +*BASE MOTION, DOF=dof, LOAD CASE=p +Data lines to define base motion p +*END STEP +6.4 +Steady-state transport analysis +• “Steady-state transport analysis,” Section 6.4.1 +6.4.1 +STEADY-STATE TRANSPORT ANALYSIS +Product: Abaqus/Standard +References +• “Defining an analysis,” Section 6.1.2 +• “Symmetric model generation,” Section 10.4.1 +• *STEADY STATE TRANSPORT +• *SYMMETRIC MODEL GENERATION +• *MOTION +• *TRANSPORT VELOCITY +• *ACOUSTIC FLOW VELOCITY +Overview +A steady-state transport analysis: +• allows for steady-state rolling and sliding solutions including frictional effects and inertia effects; +• allows for steady-state solutions to be obtained directly or by using a quasi-steady-state (pass-by- +pass) technique; +• is used to model the interaction between a deformable rolling object and one or more flat, convex, +or concave surfaces; +• is based on a specialized analysis capability where the rigid body motion is described in a spatial or +Eulerian manner and the deformation in a material or Lagrangian manner; +• allows for one element set in a model to be described in an Eulerian manner while the rest of the +elements in the model are treated in a classical Lagrangian manner; +• can be preceded by a static stress analysis or followed by a natural frequency extraction or a complex +eigenvalue extraction step; +• uses regular stress/displacement elements and special steady-state rolling and sliding contact pairs; +• is currently available only for three-dimensional analysis with an axisymmetric geometry or a +periodic geometry; and +• allows rate-independent, rate-dependent, or history-dependent material behavior. +Steady-state transport analysis +It is cumbersome to model rolling and sliding contact, such as a tire rolling along a rigid surface or a +disc rotating relative to a brake assembly, using a traditional Lagrangian formulation since the frame +of reference in which motion is described is attached to the material. An observer in this reference +frame views even steady-state rolling as a time-dependent process since each point undergoes a repeated +history of deformation. Such an analysis is computationally expensive since a transient analysis must be +performed and fine meshing is required along the entire surface of the cylinder. +The steady-state transport analysis capability in Abaqus/Standard uses a reference frame that is +attached to the axle of the rotating cylinder. An observer in this frame sees the cylinder as points that +are not moving, although the material of which the cylinder is made is moving through those points. +This removes the explicit time dependence from the problem—the observer sees a fixed point anywhere, +with material moving through it. Thus, the finite element mesh describing the cylinder in this frame of +reference does not undergo the large rigid body spinning motion. This means that a fine mesh is required +only near the contact zone. +This description can be viewed as a mixed Lagrangian/Eulerian method, where rigid body rotation +is described in a spatial or Eulerian manner, and deformation, which is now measured relative to the +rotating rigid body, is described in a material or Lagrangian manner. It is this kinematic description that +converts the steady-state moving contact problem into a purely spatially dependent simulation. +The steady-state rolling and sliding analysis capability provides solutions that include frictional +effects, inertia effects, and material convection for most rate-independent, rate-dependent, and history- +dependent material models. +The theory is described in detail in “Steady-state transport analysis,” Section 2.7.1 of the Abaqus +Theory Manual. +Input File Usage: +*STEADY STATE TRANSPORT +Pass-by-pass analysis technique +By default, the steady-state transport analysis procedure in Abaqus/Standard solves for a steady-state +rolling and sliding solution directly as a series of increments, with iterations to obtain equilibrium within +each increment. The solution in each increment is a steady-state solution corresponding to the loads +acting on the structure at that instant. The steady-state transport analysis procedure also provides an +alternative technique to obtain a quasi-steady-state rolling and sliding solution as a series of increments, +with iterations to obtain equilibrium within each increment. However, the solution in each increment +is usually not a steady-state solution corresponding to the loads acting on the structure at that instant. +A steady-state solution is generally obtained in several increments, with each increment corresponding +to a loading pass through the structure. Each loading pass through the structure can have a different +magnitude. +The pass-by-pass analysis technique is relevant only when used with plasticity/creep models. It has +no effect on a viscoelastic material model. +Input File Usage: +*STEADY STATE TRANSPORT, PASS BY PASS +Unstable problems +Local instabilities (e.g., surface wrinkling, material instability, or local buckling), can occur in a steady- +state transport analysis. Abaqus/Standard offers the option to stabilize this class of problems by applying +damping throughout the model in such a way that the viscous forces introduced are sufficiently large to +prevent instantaneous buckling or collapse but small enough not to affect the behavior significantly while +the problem is stable. The available automatic stabilization schemes are described in detail in “Automatic +stabilization of unstable problems” in “Solving nonlinear problems,” Section 7.1.1. +Defining the model +A steady-state transport analysis requires the definition of streamlines. The streamlines are the +trajectories that the material follows during transport through the mesh. To meet this requirement, the +mesh must be generated using the symmetric model generation capability, which is described in detail in +“Symmetric model generation,” Section 10.4.1. The three-dimensional model can be created either by +revolving an axisymmetric model about its axis of revolution or by revolving a single three-dimensional +repetitive sector about its axis of symmetry. +Revolving an axisymmetric cross-section to create a three-dimensional model +You can generate a three-dimensional mesh by revolving a two-dimensional cross-section about +In this case the symmetric model +a symmetry axis, so that the streamlines follow the mesh lines. +generation capability requires a two-dimensional cross-section of the body as a starting point. The +cross-section, which must be discretized with axisymmetric finite elements, is defined in a separate +input file. A data check analysis must be performed to write the model information to a restart file. The +restart file is read in a subsequent run, and a three-dimensional model is generated by Abaqus/Standard +by revolving the cross-section about the symmetry axis, starting at a reference plane. Both the symmetry +axis and reference plane of the new three-dimensional model can be oriented in any direction in the +global coordinate system. The symmetry axis also defines the axis of the spinning body. A nonuniform +discretization in the circumferential direction can be specified to allow a finer mesh in the contact region +than elsewhere in the model. +Input File Usage: +*SYMMETRIC MODEL GENERATION, REVOLVE +Revolving a single three-dimensional sector to create a periodic model +Alternatively, you can generate a periodic three-dimensional mesh by revolving a single +To accurately account for the material +three-dimensional sector about +convection when the streamline integration is performed, +the segment angle for the repetitive +three-dimensional sector must be chosen small enough. +its axis of symmetry. +In this case the symmetric model generation capability requires a single three-dimensional sector +as a starting point. The original three-dimensional sector is defined in a separate input file. A data check +analysis must be performed to write the model information to a restart file. The restart file is read in a +subsequent run, and a three-dimensional periodic model is generated by Abaqus/Standard by revolving +the original three-dimensional sector about the symmetry axis. Both the symmetry axis and the original +three-dimensional repetitive sector can be oriented in any direction in the global coordinate system. The +symmetry axis also defines the axis of the spinning body. There is no restriction that the meshes on the +two symmetry surfaces of the repetitive sector match in any way. If the surface meshes on either side of +the original sector are not matched completely, constraints will be generated automatically to couple the +opposing neighboring surfaces when revolving the original sector to create a periodic model. +Input File Usage: +*SYMMETRIC MODEL GENERATION, PERIODIC +Identifying the elements being treated in an Eulerian manner +By default, the rigid body motion in the whole model will be described in a spatial or Eulerian manner. +In some cases you may want only part of the model to be treated with the Eulerian method while the rest +should be treated with the classical Lagrangian method. One typical example is a disc brake where the +disc itself can be treated with the Eulerian method while the brake assembly (brake pads and caliper) is +treated with the Lagrangian method. In this case you can specify the name of an element set for which +the rigid body motion will be described in an Eulerian manner. The elements that are not included in +the element set will be treated with the classical Lagrangian method. Only one Eulerian element set can +be specified in the whole model. In a new steady-state transport step or upon restart you can respecify a set of elements to be treated with the Eulerian method even +after it has previously been treated with the Lagrangian method and vice versa. Elements treated with the +Eulerian method and elements treated with the Lagrangian method cannot be mixed along a streamline. +*STEADY STATE TRANSPORT, ELSET=name +Input File Usage: +Defining reference frame motions +The deformable and rigid bodies can each be defined in their own moving reference frame in a steady- +state rolling and sliding analysis. The motion of these reference frames can be defined quite generally +and provides modeling of a spinning deformable body traveling along a straight line, or “cornering” +or “precessing” around an axis. It is also possible to define reference frame motions for rigid bodies, +including translations and rotations. The rigid body can be flat, convex, or concave, which allows for +modeling of a deformable body in contact with a rotating drum, such as a tire rolling on a drum, or for +modeling a tire mounted on a rigid rim. +When defining different reference frame motions for bodies that interact, you must make sure that +the interactions are indeed steady. For example, for a planar rigid surface the relative reference frame +motion must be tangential to the rigid surface, and for a body of revolution the relative reference frame +motion must be rotation around its axis. +Spinning motion +The spinning motion of the deformable body around its own axis is described by a user-specified angular +velocity, +. This angular velocity defines the transport of material through the mesh; you define the +magnitude of the spinning rotation, +. The axis of revolution is the symmetry axis used for generating +the mesh as described in “Defining the model.” The transport velocity must be defined for all nodes +on the spinning body. The magnitude of the angular velocity can also be defined with user subroutine +UMOTION. +The transport velocity can also be applied to a rigid body based on a three-dimensional surface of +revolution. In that case the velocity is applied to the rigid body reference node to describe the transport +of the (rigid) material relative to the reference node. Abaqus/Standard assumes that the rigid body spins +around the axis of revolution of the rigid body. This option can, for example, be applied to the rigid body +representing the rim on which a tire is mounted. +Abaqus/Standard will automatically update the position and orientation of the rotation axis to the +current configuration in a large-displacement analysis, such as in the case where a prescribed load applied +to the reference node of a rotating rigid drum maintains the contact pressure between the tire and drum +or the case where a camber angle is applied to the axle of the deformable body. +Input File Usage: +Use either of the following options: +*TRANSPORT VELOCITY +*TRANSPORT VELOCITY, USER +Defining a reference frame for translational or rotational motion +The rotating deformable body is also associated with a reference frame. This reference frame can either +translate or rotate with respect to the fixed global reference frame. Similarly, each rigid body must be +defined in a reference frame that is either fixed, translates, or rotates. For example, to associate straight +line travel at ground velocity, +, with a spinning deformable body, the deformable body can be defined in +a reference frame translating at velocity and the rigid surface can be defined in a fixed reference frame. +Alternatively, the deformable body can be defined in a reference frame that does not translate and the +rigid body can be defined in a frame translating at velocity +. Another example is a deformable body +precessing along a circular path. In such a case a rotating frame is associated with the deformable body +that defines the precession axis and angular velocity, while the rigid body is defined in a fixed reference +frame. +For this purpose you can apply a specified motion of the reference frame to all nodes of the +deformable body or to the reference node of a rigid body. A translating reference frame is defined by +specifying the components of the velocity vector, +. A rotating reference frame is defined by specifying +the magnitude of an angular rotation velocity, +, and the position and orientation of the axis of rotation +in the current configuration. The position and orientation of the axis are applied at the beginning of the +step and remain fixed during the step. +Input File Usage: +Use the following option to define the motion of a translating reference frame: +*MOTION, TRANSLATION +Use the following option to define the motion of a rotating reference frame: +*MOTION, ROTATION +Contact conditions +Abaqus/Standard provides contact between a rigid surface and deformable body moving with different +velocities, such as contact between a rolling tire and the ground, as well as contact between surfaces +moving with the same velocity, such as the contact between the bead and rim in a tire analysis. +Abaqus/Standard also provides contact between two deformable bodies moving with the same velocity, +such as the contact between the tread blocks on a tire surface, as well as contact between two deformable +bodies moving with different velocities, such as the contact between a disc and brake assembly. +Contact between a rigid surface and a deformable body moving with different velocities +The rigid surface can be either an analytical surface or made from rigid elements. When the master and +slave surfaces move with different velocities, you will normally select to use a Coulomb friction law that +assumes that slip occurs if the frictional stress +is equal to the critical stress +the friction coefficient, and p is the contact pressure. No slip occurs when +transport the condition of no slip is approximated in Abaqus/Standard by stiff “viscous” behavior +are the shear stresses on the contact plane, +is +. For steady-state +, where +and +where +are the tangential slip velocities that depend on deformation along a streamline and +is the “stick viscosity,” R is the radius of the cylinder, and +is a user-defined slip tolerance for which +the default is 0.005. Using a larger slip tolerance makes convergence of the solution more rapid at the +expense of solution accuracy. Using a smaller slip tolerance imposes the “no relative motion” constraint +more accurately but may slow convergence. The default value provides a conservative balance between +efficiency and accuracy for rolling contact problems. +Since this frictional model used for steady-state rolling is different from the frictional models used +with other analysis procedures in Abaqus/Standard, discontinuities may arise in the solutions between a +steady-state transport analysis and any other analysis procedure, such as a static footprint analysis. To +ensure a smooth transition in the solution, it is recommended that all analysis steps prior to a steady- +state rolling analysis use a zero coefficient of friction. You can then modify the friction properties in +the steady-state transport analysis step to use the desired friction coefficient . +This frictional model is more relevant in a tire analysis since the velocity of the rotating tire strongly +depends on the deformation gradients along a streamline on the contact surface. The solution state at a +material point depends on the solution of neighboring points, and convective effects must be considered. +However, since the deformation gradients along a streamline on the contact surface are small in a disc +brake analysis, a simplified frictional model, which ignores the convective effect on the contact surface, +can be used. Such a frictional model is discussed in the following section. +Contact between two deformable bodies moving with different velocities +When the slave and master surfaces rotate with different velocities, such as contact between a disc +and brake assembly, slip will develop between the two deformable surfaces. The transport velocity +(“Spinning motion”) and the motion of a reference frame (“Defining a reference frame for translational or +rotational motion”) can be defined in a steady-state transport analysis procedure to model the steady-state +frictional sliding between two deformable bodies that are moving with different velocities. In this case +it is assumed that the slip rate simply follows from the difference in velocities specified by the transport +velocity and the motion of the reference frame and is independent of the deformation gradient along +a streamline or the nodal displacements on the contact surface. No convective effects are considered +between the contact surfaces, and the frictional stress does not depend on any history effects. Hence, the +frictional stress is given by +is the friction coefficient, p is the contact pressure, +are the slip +where +velocities that are defined by the transport velocity and the motion of the reference frame. If no velocity or +the same velocity are defined at contact nodes with friction, sticking conditions are applied automatically. +The friction model is described in detail in “Coulomb friction,” Section 5.2.3 of the Abaqus Theory +Manual. +are the slip directions, and +Such a simplified frictional model is relevant only in a disc brake analysis. It should be used with +care in a rolling tire analysis where deformation gradients on the contact surface are significant. +Since this frictional behavior is different from the frictional models used with other analysis +procedures in Abaqus/Standard, discontinuities may arise in the solutions between a steady-state +transport analysis and any other analysis procedure. An example is the discontinuity that occurs +between the initial preloading of the disc pads in a disc brake system and the subsequent braking +analysis where the disc spins with a prescribed rotation. To ensure a smooth transition in the solution, +it is recommended that all analysis steps prior to a steady-state analysis use a zero coefficient of +friction . You can then increase the friction coefficient to the desired value in the steady-state +transport analysis . +Contact between surfaces spinning with the same angular velocity +When the slave and master surfaces rotate with the same angular velocity, such as the surface between +In such a +the bead and rim in a tire analysis, no relative velocity develops between the surfaces. +case, frictional stresses develop as a reaction between the bodies. Abaqus/Standard will automatically +determine that the slave and master surface rotate with the same speed and apply the standard Coulomb +friction model, which is described in detail in “Frictional behavior,” Section 36.1.5. +When the standard Coulomb friction model is used in a reference frame that implies flow of material +through the mesh, convective effects must be considered. However, Abaqus/Standard assumes that no +convective effects are present between surfaces during steady-state transport analysis. In other words, +Abaqus/Standard assumes that the frictional stress at a point depends on the history of deformation in the +Lagrangian reference frame and ignores any history effects that may occur as a result of the deformation +that the point experiences during the spinning motion. The assumption that the frictional stress does +not depend on history effects during rolling is valid for modeling contact between a tire bead and rim +where relative slip occurs only during rim mounting in a static analysis prior to the steady-state transport +analysis. When slip occurs during the steady-state transport analysis, the solution obtained is no longer +the correct steady-state solution because convective effects are ignored. To ensure that no slip takes +place between the surfaces during steady-state rolling, it is recommended that you modify the friction +properties in the steady-state transport analysis step to activate rough friction . +Incrementation +Abaqus/Standard uses Newton’s method to solve the nonlinear equilibrium equations. The nonlinearities +in a steady-state transport analysis arise from large-displacement effects, material nonlinearity, and +boundary nonlinearities such as contact and friction. If geometrically nonlinear behavior is expected +other than the large rigid body rotation associated with the steady-state motion, the step definition +should include nonlinear geometric effects. +The steady-state rolling and sliding solution must often be obtained as a series of increments, with +iterations to obtain equilibrium within each increment. If the direct steady-state solution technique is +used, the solution in each increment is a steady-state solution corresponding to the loads acting on the +structure at that instant. If the pass-by-pass steady-state solution technique is used, the solution in each +increment is usually not a steady-state solution corresponding to the loads acting on the structure at +that instant. In this case a steady-state solution is generally obtained in several increments, with each +increment corresponding to a loading pass through the structure. +Since Newton’s method has a finite radius of convergence, too large an increment in the applied +load can prevent any solution from being obtained because the current steady-state solution is too far +away from the new steady-state equilibrium solution that is being sought: it is outside the radius of +convergence. Thus, there is an algorithmic restriction on the increment size. +Automatic incrementation +In most cases the default automatic incrementation scheme is preferred because it will select increment +sizes based on computational efficiency. +Input File Usage: +*STEADY STATE TRANSPORT +Direct incrementation +Direct user control of the increment size is also provided because if you have considerable experience +with a particular problem, you may be able to select a more economical approach. +Input File Usage: +*STEADY STATE TRANSPORT, DIRECT +Using the maximum number of iterations to determine the increment size +The solution to an increment can be accepted after the maximum number of iterations allowed has been +completed (as defined in “Commonly used control parameters,” Section 7.2.2), even if the equilibrium +tolerances are not satisfied. This approach is not recommended; it should be used only in special cases +when you have a thorough understanding of how to interpret results obtained in this way. Very small +increments and a minimum of two iterations are usually necessary in this case. +Input File Usage: +*STEADY STATE TRANSPORT, DIRECT=NO STOP +Convergence in a steady-state transport analysis +The steady-state transport procedure may experience convergence difficulties in certain situations that +are described below. +Convergence issues with friction +, and the traveling straight line velocity, +The frictional forces that develop on the contact surface as a result of steady-state rolling are functions +of the spinning angular velocity, +. +When these frictional forces are large, convergence of Newton’s method becomes difficult. Convergence +problems in Abaqus/Standard are usually resolved by taking a smaller load increment. However, contact +forces due to steady-state rolling usually do not reduce when the magnitudes of the velocities are reduced. +For example, if a spinning object is prevented from moving ( +), full slipping conditions will +develop over the entire contact zone for all values of spinning angular velocity +. Consequently, +the frictional force remains constant for all +(provided that the normal force remains constant), +so that smaller increments in the velocities ( +) do not reduce the magnitude of the frictional forces +and, hence, do not overcome convergence difficulties. +, or cornering velocity, +To provide for convergence through the use of smaller increments in such cases, the friction +coefficient can be increased from zero to the desired value over the analysis step. This is accomplished +by setting the initial friction coefficient for the model to zero , then increasing the friction +coefficient to its final value in the steady-state transport analysis step . +Convergence issues with the Mullins effect material model +If the Mullins effect material model is included in the material definition , there could be a strong discontinuity in the response of a structure in transitioning from +a static (non-rolling) state to a steady-state rolling state. This discontinuity is due to the damage that +occurs during the transient response (such as the damage that occurs as the structure undergoes its first +revolution after static preloading). Since the transient response is not modeled during a steady-state +transport analysis, the resulting discontinuity in the response can lead to convergence problems. The +damage associated with the Mullins effect is independent of the angular speed of rotation: as a result, +time increment cutbacks do not resolve the convergence problems. The Mullins effect can be ramped +up over the time period of the step in these situations to obtain a converged solution. In such a case the +change in response due to damage is applied gradually over the step. The solution at the end of the step +corresponds to the fully damaged material; solutions during the step correspond to a partially damaged +material and are, therefore, physically meaningless. Thus, it is recommended that in going from a static +to a steady-state rolling solution, a do-nothing step at a low angular speed of rotation be first carried out +with the Mullins effect ramped on. This facilitates resolution of the discontinuity in a gradual manner. +The do-nothing step can then be followed by the regular steady-state transport step with the Mullins +effect applied instantaneously at the beginning of the step. This approach is illustrated in “Analysis of +a solid disc with Mullins effect and permanent set,” Section 3.1.7 of the Abaqus Example Problems +Manual. +Input File Usage: +*STEADY STATE TRANSPORT, MULLINS=RAMP or STEP (default) +Convergence issues with streamline integration in plasticity/creep models +Although in principle any material point along a streamline can be used as a starting point for the +streamline integration when material convective calculations are performed, Abaqus/Standard always +uses the material points in the original sector or the material points in the original cross-section as +starting points for the streamline integration in a model with periodic geometry or axisymmetric +geometry, respectively. +If the pass-by-pass solution technique is used, after an increment has been performed for all the +streamlines, Abaqus/Standard will automatically use the state obtained at the end of the streamline as the +starting state for the streamline integration in the subsequent increment. This iterative process is repeated +for each increment until a steady-state solution is reached. +If the direct steady-state solution technique is used, several local iterations are usually required for +each streamline, with a local iteration corresponding to an integration over a closed loop streamline. +After a local iteration has been performed for a streamline, Abaqus/Standard will check to see if the +steady-state condition is satisfied for the streamline. This is best measured by ensuring the differences +between the stresses/strains at the starting point of the streamline obtained before and after the iteration +are sufficiently small. If the steady-state condition is not satisfied for the streamline, Abaqus/Standard +will automatically use the state obtained at the end of the previous local iteration as the starting state +for the streamline integration in the subsequent local iteration. This iterative process is repeated until a +steady-state solution is reached for all the streamlines. +To improve the rate of convergence, it is recommended that you apply loads on elements or nodes +away from the starting points of the streamlines. +Initial conditions +Initial values of stresses, temperatures, field variables, solution-dependent state variables, etc. can be +specified. “Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1, describes all of +the available initial conditions. +Boundary conditions +Boundary conditions can be applied to any of the displacement or rotation degrees of freedom (1–6). During the analysis +prescribed boundary conditions can be varied using an amplitude definition . +Loads +Loading in a steady-state transport analysis includes the motion of the structure, inertia (d’Alembert) +forces due to motion, concentrated loads, distributed pressures, and body forces. +Inertia effects +The motion of the deformable body gives rise to inertia (d’Alembert) forces that can be included. These +forces include centrifugal and Coriolis effects. +The density of the material must be defined in the material description. At higher rotational +velocities, inertia forces can give rise to instabilities in the form of standing waves, which are likely +to prevent convergence of the Newton algorithm. +Input File Usage: +Use the following option to include inertia forces: +*STEADY STATE TRANSPORT, INERTIA=YES +Inertia loads for tetrahedral elements +Inertia loads for tetrahedral elements C3D4, C3D10, C3D10I, and C3D10M are not taken into account +in a steady-state transport analysis. Tetrahedral elements will appear only in a periodic model created by +revolving a three-dimensional sector that contains tetrahedral elements. Tetrahedral elements will not +appear in an axisymmetric model created by revolving a two-dimensional cross-section about a symmetry +axis. See “Symmetric model generation,” Section 10.4.1, for details. +Other prescribed loads +The following loads can be prescribed in a steady-state transport analysis, as described in “Concentrated +loads,” Section 33.4.2: +• Concentrated nodal forces can be applied to the displacement degrees of freedom (1–6). +• Distributed pressure forces or body forces can be applied; the distributed load types available with +particular elements are described in Part VI, “Elements.” +In most cases such loads should be applied around the whole circumference of the body; a load on a +single point or element corresponds to a spatially fixed load, which in most cases is not realistic. +Predefined fields +The following predefined fields can be specified in a steady-state transport analysis, as described in +“Predefined fields,” Section 33.6.1: +• Although temperature is not a degree of freedom in a steady-state transport analysis, nodal +temperatures can be specified as a predefined field. Any difference between the applied and +initial temperatures will cause thermal strain if a thermal expansion coefficient is given for +the material (“Thermal expansion,” Section 26.1.2). The specified temperature also affects +temperature-dependent material properties, if any. +• The values of user-defined field variables can be specified. These values only affect field-variable- +dependent material properties, if any. +Material options +Since the steady-state transport capability uses a kinematic description that implies flow of material +through the mesh, convective effects must be considered for the material response. Most material +models that describe mechanical behavior (including user-defined materials) are available for use +in a steady-state transport analysis. In particular, history-dependent viscoelasticity (“Time domain +viscoelasticity,” Section 22.7.1), history-dependent Mullins effect (“Mullins effect,” Section 22.6.1), +classical metal plasticity (“Classical metal plasticity,” Section 23.2.1), +rate-dependent yield +(“Rate-dependent yield,” Section 23.2.3), rate-dependent creep (“Rate-dependent plasticity: creep and +swelling,” Section 23.2.4), and two-layer viscoplasticity (“Two-layer viscoplasticity,” Section 23.2.11) +can all be used during a steady-state transport analysis. +The following material properties are not active during a steady-state transport analysis: thermal +properties (except for thermal expansion), mass diffusion properties, electrical properties, and pore fluid +flow properties. +Abaqus/Standard also provides the ability to obtain the fully relaxed long-term elastic or elastic- +plastic solution during a steady-state transport analysis if the material description includes viscoelastic +or viscoplastic material properties. If the material description includes viscoelastic material properties, +the long-term solution will ignore the material convection calculations. If the two-layer viscoplastic +material model is used, the long-term solution will include only the material convection calculations +based on the long-term response of the elastic-plastic network. +Input File Usage: +*STEADY STATE TRANSPORT, LONG TERM +Choosing an appropriate material model +Since material points in a spinning and sliding body undergo repeated loading/unloading cycles, an +appropriate material model must be chosen to characterize the response correctly under such loading +conditions. The use of plasticity material models with isotropic type hardening is generally not +recommended since they will continue to harden during cyclic loading, which may lead to a large +number of iterations until the steady-state solution is reached. Kinematic hardening plasticity models +should be used to model the inelastic behavior of materials that are subjected to repeated loading. +For rate-dependent creep, +is recommended (“Two-layer +the two-layer viscoplasticity model +viscoplasticity,” Section 23.2.11) for modeling the response of materials with significant time-dependent +behavior as well as plasticity at elevated temperatures. +For history-dependent viscoelasticity, it is more appropriate to use cyclic (frequency domain) test +data to calibrate the time-domain viscoelastic material model for steady-state transport analysis. The +cyclic experiments should be performed in the frequency range anticipated in the rolling simulation. +Abaqus/Standard internally converts the frequency domain storage and loss modulus data into a time- +domain (Prony series) representation. This data conversion capability is described in detail in “Time +domain viscoelasticity,” Section 22.7.1. +Analysis steps prior to a steady-state transport analysis +It is recommended that the solutions in any analysis step prior to a steady-state transport analysis, such +as a static footprint or preloading solution, be based on the long-term elastic moduli or the long-term +elastic-plastic response if viscoelastic or viscoplastic material properties are used (for example, see +“Static stress analysis,” Section 6.2.2). The long-term solution provides a smooth transition between a +static analysis and a slow rolling or sliding steady-state transport analysis. +Material convection in nonlinear analysis +When material convection is included in the steady-state transport solution, Abaqus/Standard uses +an approximate Jacobian matrix in the Newton solution of the nonlinear equilibrium equations. The +rate of convergence in such a case is no longer quadratic but depends strongly on the severity of the +nonlinearities. It is often necessary to adjust the default solution controls (“Commonly used control +parameters,” Section 7.2.2) to obtain a steady-state transport solution when material convection is +considered. +Elements +the three-dimensional stress/displacement elements in Abaqus/Standard can be used +Most of +in a steady-state transport analysis . When the three-dimensional model is generated from an axisymmetric cross-section, the +element type used in the two-dimensional model determines the element type in the three-dimensional +The correspondence between the two-dimensional and three-dimensional element types +model. +is described in “Symmetric model generation,” Section 10.4.1. +If the three-dimensional periodic +model is generated from a single three-dimensional sector, any of the stress/displacement elements in +Abaqus/Standard can be used. +Output +The element output available for a steady-state transport analysis includes stress, strain, energies, and +the values of state, field, and user-defined variables. The nodal output available includes displacements, +velocities, reaction forces, and coordinates. The contact output variable CSLIP contains steady-state slip +rates for the steady-state transport procedure, unlike the usual definition of this variable. All of the output +variable identifiers are outlined in “Abaqus/Standard output variable identifiers,” Section 4.2.1. +Limitations +The steady-state transport analysis capability has several limitations. +• The deformable structure must be a full 360° cylindrical body of revolution. Convective boundary +conditions are not available to model segments of a cylinder. +• The capability is not available in two dimensions. +• Only one deformable spinning body is permitted. The symmetric model generation capability must +be used to generate the deformable body (“Symmetric model generation,” Section 10.4.1). +Input file template +*HEADING +… +*SYMMETRIC MODEL GENERATION, REVOLVE +Data lines to define model generation +*SURFACE INTERACTION +*FRICTION +Specify zero friction coefficient +** +*STEP +*STATIC +Data lines to define analysis steps prior to transport analysis +*END STEP +… +*STEP +*STEADY STATE TRANSPORT +Data line to define incrementation +*CHANGE FRICTION +*FRICTION +Data lines to redefine friction coefficient +*BOUNDARY +Data lines to define boundary conditions +*TRANSPORT VELOCITY +Data lines to define spinning angular velocity +*MOTION, TRANSLATION or ROTATION +Data lines to define traveling velocity or cornering rotational velocity +*EL PRINT and/or *NODE PRINT +Data lines to request output variables +*END STEP +6.5 +Heat transfer and thermal-stress analysis +• “Heat transfer analysis procedures: overview,” Section 6.5.1 +• “Uncoupled heat transfer analysis,” Section 6.5.2 +• “Fully coupled thermal-stress analysis,” Section 6.5.3 +• “Adiabatic analysis,” Section 6.5.4 +6.5.1 +HEAT TRANSFER ANALYSIS PROCEDURES: OVERVIEW +Abaqus can solve the following types of heat transfer problems: +• Uncoupled heat +transfer analysis: Heat +forced +convection, and boundary radiation can be analyzed in Abaqus/Standard. See “Uncoupled heat transfer +analysis,” Section 6.5.2. In these analyses the temperature field is calculated without knowledge of the +stress/deformation state or the electrical field in the bodies being studied. Pure heat transfer problems +can be transient or steady-state and linear or nonlinear. +transfer problems involving conduction, +• Sequentially coupled thermal-stress analysis: +If the stress/displacement solution is dependent on +a temperature field but there is no inverse dependency, a sequentially coupled thermal-stress analysis +can be conducted in Abaqus/Standard. Sequentially coupled thermal-stress analysis is performed by +first solving the pure heat transfer problem, then reading the temperature solution into a stress analysis +as a predefined field. See “Sequentially coupled thermal-stress analysis,” Section 16.1.2. In the stress +analysis the temperature can vary with time and position but is not changed by the stress analysis solution. +Abaqus allows for dissimilar meshes between the heat transfer analysis model and the thermal-stress +analysis model. Temperature values will be interpolated based on element interpolators evaluated at +nodes of the thermal-stress model. +• Fully coupled thermal-stress analysis: A coupled temperature-displacement procedure is used +to solve simultaneously for the stress/displacement and the temperature fields. A coupled analysis +is used when the thermal and mechanical solutions affect each other strongly. For example, in rapid +metalworking problems the inelastic deformation of the material causes heating, and in contact problems +the heat conducted across gaps may depend strongly on the gap clearance or pressure. +Both Abaqus/Standard and Abaqus/Explicit provide coupled temperature-displacement analysis +procedures, but the algorithms used by each program differ considerably. In Abaqus/Standard the heat +transfer equations are integrated using a backward-difference scheme, and the coupled system is solved +using Newton’s method. These problems can be transient or steady-state and linear or nonlinear. In +Abaqus/Explicit the heat transfer equations are integrated using an explicit forward-difference time +integration rule, and the mechanical solution response is obtained using an explicit central-difference +integration rule. Fully coupled thermal-stress analysis in Abaqus/Explicit is always transient. Cavity +radiation effects cannot be included in a fully coupled thermal-stress analysis. See “Fully coupled +thermal-stress analysis,” Section 6.5.3, for more details. +• Fully coupled thermal-electrical-structural analysis: A coupled thermal-electrical-structural +procedure is used to solve simultaneously for the stress/displacement, the electrical potential, and the +temperature fields. A coupled analysis is used when the thermal, electrical, and mechanical solutions +affect each other strongly. An example of such a process is resistance spot welding, where two or more +metal parts are joined by fusion at discrete points at the material interface. The fusion is caused by heat +generated due to the current flow at the contact points, which depends on the pressure applied at these +points. +These problems can be transient or steady-state and linear or nonlinear. Cavity radiation effects +cannot be included in a fully coupled thermal-electrical-structural analysis. This procedure is available +only in Abaqus/Standard. See “Fully coupled thermal-electrical-structural analysis,” Section 6.7.4, for +more details. +• Adiabatic analysis: An adiabatic mechanical analysis can be used in cases where mechanical +deformation causes heating, but the event is so rapid that this heat has no time to diffuse through the +material. Adiabatic analysis can be performed in Abaqus/Standard or Abaqus/Explicit; see “Adiabatic +analysis,” Section 6.5.4. An adiabatic analysis can be static or dynamic and linear or nonlinear. +• Coupled thermal-electrical analysis: A fully coupled thermal-electrical analysis capability is +provided in Abaqus/Standard for problems where heat is generated due to the flow of electrical current +through a conductor. See “Coupled thermal-electrical analysis,” Section 6.7.3. +• Cavity radiation: +In Abaqus/Standard cavity radiation effects can be included (in addition +to prescribed boundary radiation) in uncoupled heat transfer problems. +See “Cavity radiation,” +Section 40.1.1. The cavities can be open or closed. Symmetries and blocking within cavities can +be modeled. Viewfactors are calculated automatically, and motion of objects bounding a cavity can +be prescribed during the analysis. Cavity radiation problems are nonlinear and can be transient or +steady-state. +6.5.2 +UNCOUPLED HEAT TRANSFER ANALYSIS +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “Heat transfer analysis procedures: overview,” Section 6.5.1 +• *HEAT TRANSFER +• “Including volumetric heat generation in heat +Abaqus/CAE User’s Manual, in the online HTML version of this manual +transfer analyses,” Section 12.10.2 of +the +• “Configuring a heat +transfer procedure” in “Configuring general analysis procedures,” +Section 14.11.1 of the Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +Uncoupled heat transfer problems: +• are those in which the temperature field is calculated without consideration of the stress/deformation +or the electrical field in the bodies being studied; +• can include conduction, boundary convection, and boundary radiation; +• can include cavity radiation effects—see “Cavity radiation,” Section 40.1.1; +• can include forced convection through the mesh if forced convection/diffusion heat transfer +elements are used; +• can include thermal interactions such as gap radiation, conductance, and heat generation between +contact surfaces—see “Thermal contact properties,” Section 36.2.1; +• can include thermal material behavior defined in user subroutine UMATHT—see “User-defined +thermal material behavior,” Section 26.7.2; +• can be transient or steady-state; +• can be linear or nonlinear; and +• require the use of heat transfer elements. +Heat transfer analysis +Uncoupled heat transfer analysis is used to model solid body heat conduction with general, temperature- +dependent conductivity, internal energy (including latent heat effects), and quite general convection and +radiation boundary conditions, including cavity radiation. Forced convection of a fluid through the mesh +can be modeled by using forced convection/diffusion elements. +Sources of nonlinearity in a heat transfer analysis +Heat transfer problems can be nonlinear because the material properties are temperature dependent or +because the boundary conditions are nonlinear. Usually the nonlinearity associated with temperature- +dependent material properties is mild because the properties do not change rapidly with temperature. +However, when latent heat effects are included, the analysis may be severely nonlinear . +Boundary conditions are very often nonlinear; for example, film coefficients can be functions of +surface temperature. Again, the nonlinearities are often mild and cause little difficulty. An exception +is the “boiling” film condition, in which the film coefficient can change very rapidly because the +fluid adjacent to the surface boils. A rapidly changing film condition (within a step or from one step +to another) can be modeled easily using temperature-dependent and field-variable-dependent film +coefficients. Radiation effects always make heat transfer problems nonlinear. Nonlinearities in radiation +grow as temperatures increase. +Abaqus/Standard uses an iterative scheme to solve nonlinear heat transfer problems. The scheme +uses the Newton method with some modification to improve stability of the iteration process in the +presence of highly nonlinear latent heat effects. +Steady-state cases involving severe nonlinearities are sometimes more effectively solved as +transient cases because of the stabilizing influence of the heat capacity terms. The required steady-state +solution can be obtained as the very long transient time response; the transient will simply stabilize the +solution for that long time response. +Matrix storage and solution scheme +In heat transfer analyses involving cavity radiation or forced convection/diffusion elements, the system +of equations is unsymmetric. The nonsymmetric matrix storage and solution scheme is invoked +automatically in these cases . +Steady-state analysis +Steady-state analysis means that the internal energy term (the specific heat term) in the governing +heat transfer equation is omitted. The problem then has no intrinsic physically meaningful time scale. +Nevertheless, you can assign an initial time increment, a total time period, and maximum and minimum +allowed time increments to the analysis step, which is often convenient for output identification and for +specifying prescribed temperatures and fluxes with varying magnitudes. +Any fluxes or boundary condition changes to be applied during a steady-state heat transfer step +should be given within the step, using appropriate amplitude references to specify their “time” variations +(“Amplitude curves,” Section 33.1.2). +If fluxes and boundary conditions are specified for the step +without amplitude references, they are assumed to change linearly with “time” during the step, from +their magnitudes at the end of the previous step (or zero, if this is the beginning of the analysis) to their +newly specified magnitudes at the end of the heat transfer step. +Input File Usage: +*HEAT TRANSFER, STEADY STATE +Abaqus/CAE Usage: +Step module: Create Step: General: Heat transfer: Response: +Steady state +Automatic incrementation +When steady-state analysis is chosen, you suggest an initial “time” increment and define a “time” +period for the step; Abaqus/Standard then increments through the step accordingly. By default, +Abaqus/Standard automatically determines a suitable increment size for each increment of the step. +Fixed incrementation +You can also use a fixed incrementation scheme, in which Abaqus/Standard uses the same increment size +for the duration of the step. The suggested initial “time” increment, +, defines the increment size. +Input File Usage: +Set the initial increment, minimum increment size, and maximum increment +size to the same value: +*HEAT TRANSFER, STEADY STATE +, , +, +Abaqus/CAE Usage: +Step module: Create Step: General: Heat transfer: Response: +Steady-state: Incrementation: Type: Fixed: Increment size: +Transient analysis +Time integration in transient problems is done with the backward Euler method (sometimes also +referred to as the modified Crank-Nicholson operator) in the pure conduction elements. This method is +unconditionally stable for linear problems. +The forced convection/diffusion elements use the trapezoidal rule for time integration. They +include numerical diffusion control (the “upwinding” Petrov-Galerkin method) and, optionally, +numerical dispersion control. The elements with dispersion control offer improved solution accuracy +in cases where the transient response of the fluid is important. Artificial dispersion control introduces a +stability limit on the size of the time increment such that the local Courant number +is the time increment, +is the magnitude of the velocity vector, and +must be less than 1, where +is +a characteristic element length in the direction of flow; that is, heat cannot be convected across more than +one element length, +, in a single increment of time. In a uniform velocity field the smallest element +will dictate the stable time increment. Approximate calculation of the Courant number, C, is helpful +during the mesh design stages so that excessively small stable time increments can be avoided. The +elements without dispersion control have no such stability limit; therefore, it may be more economical +to use the elements without this feature in transient cases where transient effects in the fluid itself are not +a critical part of the solution (for example, when the important solution is the temperature field in the +solid bodies that are included in the model, and when characteristic transient times in the fluid are very +much shorter than characteristic transient times in the solids). +Time incrementation in a transient heat transfer analysis can be controlled directly by you or +automatically by Abaqus/Standard. Automatic time incrementation is generally preferred. +Automatic incrementation +The time increments can be selected automatically based on the user-prescribed maximum allowable +nodal temperature change in an increment, +. Abaqus/Standard will restrict the time increments to +ensure that this value is not exceeded at any node (except nodes with boundary conditions) during any +increment of the analysis . +Input File Usage: +Abaqus/CAE Usage: +*HEAT TRANSFER, DELTMX= +Step module: Create Step: General: Heat transfer: Response: +Transient: Incrementation: Type: Automatic: Max. allowable +temperature change per increment: +Fixed incrementation +If you select direct incrementation and do not specify +specified initial time increment, +, will then be used throughout the analysis. +, fixed time increments equal to the user- +Input File Usage: +*HEAT TRANSFER +Abaqus/CAE Usage: +Step module: Create Step: General: Heat transfer: Response: Transient: +Incrementation: Type: Fixed: Increment size: +Spurious oscillations due to small time increments +In transient heat transfer analysis with second-order elements there is a relationship between the +minimum usable time increment and the element size. A simple guideline is +is the time increment, +is the density, c is the specific heat, k is the thermal conductivity, +where +and +is a typical element dimension (such as the length of a side of an element). If time increments +smaller than this value are used in a mesh of second-order elements, spurious oscillations can appear +in the solution, in particular in the vicinity of boundaries with rapid temperature changes. These +oscillations are nonphysical and may cause problems if temperature-dependent material properties +are present. Abaqus/Standard provides no check on the user-defined initial time increment; you must +ensure that the given value does not violate the above criterion. +In transient analyses using first-order elements the heat capacity terms are lumped, which eliminates +such oscillations but can lead to locally inaccurate solutions especially in terms of the heat flux for small +time increments. If smaller time increments are required, a finer mesh should be used in regions where +the temperature changes occur. +Unless you specify a maximum allowable time increment size as part of the heat transfer +step definition, +there is no upper limit on the time increment size (the integration procedure is +unconditionally stable, at least for linear problems). However, if forced convection/diffusion elements +including numerical dispersion control (element types DCCxxD) are included in the model, there is a +numerical stability limit on the allowable time increment. The requirement is that +, where +is a characteristic element length in the direction of +is the magnitude of the fluid velocity and +flow. Abaqus/Standard will adjust the time increment automatically to satisfy this stability limit. +Ending a transient analysis +A transient analysis can be terminated by completing a specified time period, or it can be continued until +steady-state conditions are reached. By default, the analysis will end when the given time period has +been completed. Alternatively, you can specify that the analysis will end when steady state is reached +or after the given time period, whichever comes first. Steady state is defined by the temperature change +rate: when the temperature at every temperature degree of freedom changes at a rate that is less than the +user-specified rate (given as part of the step definition), the analysis terminates. +Input File Usage: +Use the following option to end the analysis when the time period is reached: +*HEAT TRANSFER, END=PERIOD (default) +Use the following option to end the analysis based on the temperature change +rate: +*HEAT TRANSFER, END=SS +Step module: Create Step: General: Heat transfer: Response: Transient: +Incrementation: End step when temperature change is less than +Abaqus/CAE Usage: +Internal heat generation +Volumetric heat generation within a material can be defined either in user subroutine HETVAL or user +subroutine UMATHT. These user subroutines are mutually exclusive. +Defining internal heat generation in user subroutine HETVAL +If user subroutine HETVAL is used to define internal heat generation, heat generation must be included +in the material definition with the other thermal property definitions. +Heat generation might be associated with (relatively low) energy phase changes occurring during +the solution. Such heat generation usually depends on state variables (such as the fraction transformed), +which themselves evolve with the solution and are stored as solution-dependent state variables . The heat generation is computed in user subroutine HETVAL, +where any associated state variables can also be updated. The subroutine will be called at all material +calculation points for which the material definition includes heat generation. +*HEAT GENERATION +Property module: material editor: Thermal: Heat Generation +Abaqus/CAE Usage: +Input File Usage: +Defining internal heat generation in user subroutine UMATHT +If user subroutine UMATHT is used to define internal heat generation, all other thermal properties must +also be defined within the subroutine. +Input File Usage: +Abaqus/CAE Usage: +*USER MATERIAL +Property module: material editor: General: User Material: +User material type: Thermal +Forced convection through the mesh +The velocity of a fluid moving through the mesh can be prescribed if forced convection/diffusion heat +transfer elements are used. Conduction between the fluid and adjacent forced convection/diffusion heat +transfer elements will be affected by the mass flow rate of the fluid. For example, if a pipe is filled with +a fluid with an initial temperature profile that contains a temperature pulse, the initial temperature pulse +will not only diffuse (because of conduction in the fluid and the pipe), but it will also be transported (or +convected) down the pipe. Since the fluid velocity is prescribed, it is called forced convection. +Natural convection occurs when differences in fluid density created by thermal gradients cause +motion of the fluid (bouyancy-driven flow). The forced convection/diffusion elements are not designed +to handle this phenomenon; the flow must be prescribed. +You can specify the mass flow rates per unit area (or through the entire section for one-dimensional +elements) at the nodes. Abaqus/Standard interpolates the mass flow rates to the material points. The +numerical solution of the transient heat transfer equation including convection becomes increasingly +difficult as convection dominates diffusion. The Peclet number, +, is a dimensionless parameter that +indicates the degree of convection dominance over diffusion: +is the magnitude of the velocity vector, +where +conductivity, and +that convection dominates over diffusion on the spatial scale defined by the element size, +Peclet numbers greater than about 1000 should not be used. +is the density, c is the specific heat, k is the thermal +indicate +. In general, +is a characteristic element length in the direction of flow. Large values of +Petrov-Galerkin finite elements are used in Abaqus/Standard to model systems with high Peclet +numbers accurately; +these elements use nonsymmetric, upwinded weighting functions to control +numerical diffusion and dispersion and, thus, stabilize results. The upwinding term is partly a function +of the element Peclet number, as described in “Convection/diffusion,” Section 2.11.3 of the Abaqus +Theory Manual. +If the fluid flows along a boundary along which a rapid change of temperature is prescribed, it is, +in fact, subjected to a thermal transient, even for steady-state analysis. This transient can give rise to +the same kind of spurious temperature oscillations that are observed in transient heat transfer analysis, +as discussed earlier in this section. Since Abaqus/Standard uses first-order elements for convective heat +transfer, the oscillation can be eliminated by lumping the heat capacity terms. However, the upwinded +weighting functions prevent lumping in the direction of the flow. Hence, spurious oscillations may still +occur, in particular if the flow is not precisely tangential to the boundary along which the temperature +change occurs. +Input File Usage: +Use the following option within the heat transfer step definition to prescribe the +fluid velocity: +*MASS FLOW RATE +Abaqus/CAE Usage: Mass flow rate is not supported in Abaqus/CAE. +Modifying or removing mass flow rates +By default, the mass flow rates given are modifications of existing flow rates or are to be applied in +addition to any mass flow rates defined previously. You can remove all previously defined mass flow +rates and, optionally, specify new mass flow rates. +Input File Usage: +Use the following option to modify an existing flow rate or to specify an +additional flow rate: +*MASS FLOW RATE, OP=MOD (default) +Use the following option to release all previously applied flow rates and to +specify new flow rates: +*MASS FLOW RATE, OP=NEW +Abaqus/CAE Usage: Mass flow rate is not supported in Abaqus/CAE. +Specifying time-dependent mass flow rates +Mass flow rates can be given in combination with an amplitude definition, if required, to control the +magnitude of the flow rate as a function of time (“Amplitude curves,” Section 33.1.2). +Input File Usage: +Use both of the following options to define a time-dependent mass flow rate: +*AMPLITUDE, NAME=name +*MASS FLOW RATE, AMPLITUDE=name +Abaqus/CAE Usage: Mass flow rate is not supported in Abaqus/CAE. +Defining mass flow rates in a user subroutine +Mass flow rates can be defined by user subroutine UMASFL. UMASFL will be called for each specified +node. Any mass flow rate values given directly will be ignored. +Input File Usage: +*MASS FLOW RATE, USER +Abaqus/CAE Usage: Mass flow rate is not supported in Abaqus/CAE. +Reading the mass flow rate data from an alternate file +The data for the mass flow rate can be contained in an alternate file. See “Input syntax rules,” +Section 1.2.1, for the syntax of the file name. +Input File Usage: +*MASS FLOW RATE, INPUT=file_name +Abaqus/CAE Usage: Mass flow rate is not supported in Abaqus/CAE. +Cavity radiation +Cavity radiation can be activated in a heat transfer step. This feature involves interacting heat transfer +between all of the facets of the cavity surface, dependent on the facet temperatures, facet emissivities, +and the geometric viewfactors between each facet pair. When the thermal emissivity is a function of +temperature or field variables, you can specify the maximum allowable emissivity change during an +increment in addition to the maximum temperature change to control the time incrementation. See +“Cavity radiation,” Section 40.1.1, for more information. +Input File Usage: +Use the following option in the step definition to activate cavity radiation: +*RADIATION VIEWFACTOR +Use the following option to specify the maximum allowable emissivity change: +*HEAT TRANSFER, MXDEM=max_delta_emissivity +You can specify the maximum allowable emissivity change for a heat transfer +step. +Step module: Create Step: General: Heat transfer: Incrementation: +Max. allowable emissivity change per increment +Abaqus/CAE Usage: +Initial conditions +By default, the initial temperature of all nodes is zero. You can specify nonzero initial temperatures . +Forced convection through the mesh +In a heat transfer analysis involving forced convection through the mesh, you can define nonzero initial +mass flow rates at the nodes of the forced convection/diffusion heat transfer elements in the model, as +described in “Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1. +For element types DCC1D2 and DCC1D2D the mass flow rate is positive from the first to the second +node of the element. For two- and three-dimensional elements the direction of the mass flow rate is +defined by giving the components in the x-, y-, and z-directions. +Input File Usage: +*INITIAL CONDITIONS, TYPE=MASS FLOW RATE +Abaqus/CAE Usage: Mass flow rate is not supported in Abaqus/CAE. +Boundary conditions +Boundary conditions can be used to prescribe temperatures (degree of freedom 11) at nodes in a heat +transfer analysis . +Shell elements have additional temperature degrees of freedom 12, 13, etc. through the thickness . Boundary conditions can be specified as functions of time by referring +to amplitude curves . +For purely diffusive heat transfer elements a boundary without any prescribed boundary conditions +(natural boundary condition) corresponds to an insulated surface. For forced convection/diffusion +elements only the flux associated with conduction is zero; energy is free to convect across an +unconstrained surface. This natural boundary condition correctly models areas where fluid is crossing +a surface (as, for example, at the upstream and downstream boundaries of the mesh) and prevents +spurious reflections of energy back into the mesh. +Loads +The following types of loading can be prescribed in a heat transfer analysis, as described in “Thermal +loads,” Section 33.4.4: +• Concentrated heat fluxes. +• Body fluxes and distributed surface fluxes. +• Average-temperature radiation conditions. +• Convective film conditions and radiation conditions; film properties can be made a function of +temperature. +Cavity radiation effects can also be included, as described in “Cavity radiation,” Section 40.1.1. +Predefined fields +Predefined temperature fields are not allowed in heat transfer analyses. Boundary conditions should be +used instead to specify temperatures, as described earlier. +Other predefined field variables can be specified in a heat transfer analysis. These values will affect +field-variable-dependent material properties, if any. See “Predefined fields,” Section 33.6.1. +Material options +The thermal conductivity of the materials in a heat transfer analysis must be defined. The specific heat +and density of the materials must also be defined for transient heat transfer problems. Latent heat can +be defined for diffusive heat transfer elements if changes in internal energy due to phase changes are +important. Latent heat cannot be defined directly for forced convection/diffusion elements. See “Thermal +properties: overview,” Section 26.2.1, for details on defining thermal properties in Abaqus. +Alternatively, user subroutine UMATHT can be used to define the thermal constitutive behavior of +the material, including internal heat generation. For example, if a material modeled can go through a +complex phase change, the specific heat can be defined in user subroutine UMATHT in sufficient detail to +capture the phase change. +Thermal expansion coefficients are not meaningful in an uncoupled heat transfer analysis problem +since deformation of the structure is not considered. +Elements +The heat transfer element library in Abaqus/Standard includes diffusive heat transfer elements, which +allow for heat storage (specific heat and latent heat effects) and heat conduction. +Forced convection/diffusion heat transfer elements are also available: in addition to heat storage and +heat conduction these elements allow for forced convection caused by fluid flowing through the mesh. +These elements cannot be used with latent heat—see “Solid (continuum) elements,” Section 28.1.1, +for additional details. Forced convection/diffusion elements with dispersion control are available for +problems where the temperature transient in the fluid must be calculated accurately. See “Choosing the +appropriate element for an analysis type,” Section 27.1.3. +Multiple temperatures are available through the thickness of shell heat transfer elements. See +“Choosing a shell element,” Section 29.6.2. +The first-order heat transfer elements (such as the 2-node link, 4-node quadrilateral, and 8-node +brick) use a numerical integration rule with the integration stations located at the corners of the +element for the heat capacitance terms and for the calculations of the distributed surface fluxes. +First-order diffusive elements are preferred in cases involving latent heat effects since they use +such a special integration technique to provide accurate solutions with large latent heats. The forced +convection/diffusion elements cannot use this special integration technique and, therefore, are unsuitable +for problems with latent heat effects. The second-order heat transfer elements use conventional Gaussian +integration. Thus, the second-order elements are to be preferred for problems when the solution will +be smooth (without latent heat effects), and usually give more accurate results for the same number of +nodes in the mesh. +Thermal interactions between adjacent surfaces and thermal gap elements are also provided to model +heat transfer across the boundary layer between a solid and a fluid or between two closely adjacent solids. +See “Thermal contact properties,” Section 36.2.1. +Output +The following heat transfer output variables are available: +Element integration point variables: +HFL +HFLn +HFLM +TEMP +MFR +MFRn +Magnitude and components of the heat flux vector. +Component n of the heat flux vector (n=1, 2, 3). +Magnitude of the heat flux vector. +Integration point temperatures. +User-specified mass flow rates. +Component n of the mass flow rate (n=1, 2, 3). +Whole element variables: +FLUXS +NFLUX +FILM +RAD +Nodal variables: +NT +NTn +RFL +RFLn +CFL +CFLn +Current values of uniform distributed heat fluxes. +Fluxes at the nodes caused by heat conduction (internal fluxes). +Current values of film conditions. +Current values of radiation conditions. +Nodal point temperatures. +Temperature degree of freedom n at a node (n=11, 12, …). +Reaction flux values due to prescribed temperature. +Reaction flux value n at a node (n=11, 12, …). +Concentrated flux values. +Concentrated flux value n at a node (n=11, 12, …). +RFLE +Total flux at a node, +including flux convected through the node in forced +convection/diffusion elements but excluding external fluxes due to user-defined +concentrated fluxes, distributed fluxes, film conditions, radiation conditions, and +cavity radiation. Since RFLE is a scalar nodal output variable, care should be +taken when summing it over on two surfaces with shared nodes. If node sets on +both surfaces include the shared nodes, the output of RFLE on the common nodes +will contribute to the sums of this output quantity on both surfaces. +RFLEn +Total flux value n at a node (n=11, 12, …). +All of the output variables available in Abaqus/Standard are listed in “Abaqus/Standard output variable +identifiers,” Section 4.2.1. +Input file template +*HEADING +… +*PHYSICAL CONSTANTS, ABSOLUTE ZERO= +*INITIAL CONDITIONS, TYPE=TEMPERATURE +Data lines to prescribe initial temperatures at the nodes +*AMPLITUDE, NAME=trefamp +Data lines to define amplitude curve to be used for radiation reference temperature, +*FILM PROPERTY, NAME=film +Data lines to define the convection film coefficient, h, as a function of temperature +** +*STEP +Transient analysis including forced convection through the mesh +*HEAT TRANSFER, END=SS, DELTMX= +Data line to define incrementation and steady state +** +*CFLUX and/or *DFLUX +Data lines to define concentrated and/or distributed fluxes +*FILM +Data lines referring to film property table film +*RADIATE, AMPLITUDE=trefamp +Data lines to define boundary radiation +** +*EL PRINT +TEMP, HFL +NFLUX, FILM, RAD +*NODE PRINT +NT11, RFL +*END STEP +6.5.3 +FULLY COUPLED THERMAL-STRESS ANALYSIS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “Heat transfer analysis procedures: overview,” Section 6.5.1 +• *COUPLED TEMPERATURE-DISPLACEMENT +• *DYNAMIC TEMPERATURE-DISPLACEMENT +• “Specifying an inelastic heat fraction,” Section 12.10.3 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Configuring a fully coupled, simultaneous heat transfer and stress procedure” in “Configuring +general analysis procedures,” Section 14.11.1 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Configuring a dynamic fully coupled thermal-stress procedure using explicit integration” in +“Configuring general analysis procedures,” Section 14.11.1 of the Abaqus/CAE User’s Manual, in +the online HTML version of this manual +Overview +A fully coupled thermal-stress analysis: +• is performed when the mechanical and thermal solutions affect each other strongly and, therefore, +must be obtained simultaneously; +• requires the existence of elements with both temperature and displacement degrees of freedom in +the model; +• can be used to analyze time-dependent material response; +• cannot include cavity radiation effects but may include average-temperature radiation conditions +; and +• takes into account temperature dependence of material properties only for the properties that are +assigned to elements with temperature degrees of freedom. +In Abaqus/Standard a fully coupled thermal-stress analysis: +• neglects inertia effects; and +• can be transient or steady-state. +In Abaqus/Explicit a fully coupled thermal-stress analysis: +• includes inertia effects; and +• models transient thermal response. +Fully coupled thermal-stress analysis +Fully coupled thermal-stress analysis is needed when the stress analysis is dependent on the temperature +distribution and the temperature distribution depends on the stress solution. For example, metalworking +problems may include significant heating due to inelastic deformation of the material which, +in +In addition, contact conditions exist in some problems where +turn, changes the material properties. +the heat conducted between surfaces may depend strongly on the separation of the surfaces or the +pressure transmitted across the surfaces . For such +cases the thermal and mechanical solutions must be obtained simultaneously rather than sequentially. +Coupled temperature-displacement elements are provided for this purpose in both Abaqus/Standard +and Abaqus/Explicit; however, each program uses different algorithms to solve coupled thermal-stress +problems. +Fully coupled thermal-stress analysis in Abaqus/Standard +In Abaqus/Standard the temperatures are integrated using a backward-difference scheme, and the +nonlinear coupled system is solved using Newton’s method. Abaqus/Standard offers an exact as well +as an approximate implementation of Newton’s method for fully coupled temperature-displacement +analysis. +Exact implementation +An exact implementation of Newton’s method involves a nonsymmetric Jacobian matrix as is illustrated +in the following matrix representation of the coupled equations: +and +where +are submatrices of the fully coupled Jacobian matrix, and +residual vectors, respectively. +are the respective corrections to the incremental displacement and temperature, +and +are the mechanical and thermal +Solving this system of equations requires the use of the unsymmetric matrix storage and solution +scheme. Furthermore, the mechanical and thermal equations must be solved simultaneously. The method +provides quadratic convergence when the solution estimate is within the radius of convergence of the +algorithm. The exact implementation is used by default. +Approximate implementation +Some problems require a fully coupled analysis in the sense that the mechanical and thermal solutions +evolve simultaneously, but with a weak coupling between the two solutions. +In other words, the +components in the off-diagonal submatrices +are small compared to the components in +the diagonal submatrices +. An example of such a situation is the disc brake problem +(“Thermal-stress analysis of a disc brake,” Section 5.1.1 of the Abaqus Example Problems Manual). +For these problems a less costly solution may be obtained by setting the off-diagonal submatrices to +zero so that we obtain an approximate set of equations: +, +, +As a result of this approximation the thermal and mechanical equations can be solved separately, +with fewer equations to consider in each subproblem. The savings due to this approximation, measured +as solver time per iteration, will be of the order of a factor of two, with similar significant savings in +solver storage of the factored stiffness matrix. Further, in many situations the subproblems may be fully +symmetric or approximated as symmetric, so that the less costly symmetric storage and solution scheme +can be used. The solver time savings for a symmetric solution is an additional factor of two. Unless +you explicitly choose the unsymmetric matrix storage and solution scheme, selection of the scheme will +depend on other details of the problem . +This modified form of Newton’s method does not affect solution accuracy since the fully coupled +effect is considered through the residual vector +at each increment in time. However, the rate of +convergence is no longer quadratic and depends strongly on the magnitude of the coupling effect, so more +iterations are generally needed to achieve equilibrium than with the exact implementation of Newton’s +method. When the coupling is significant, the convergence rate becomes very slow and may prohibit +obtaining a solution. In such cases the exact implementation of Newton’s method is required. In cases +where it is possible to use this approximation, the convergence in an increment will depend strongly on the +quality of the first guess to the incremental solution, which you can control by selecting the extrapolation +method used for the step . +Input File Usage: +Abaqus/CAE Usage: +Use the following option to specify a separated solution scheme: +*SOLUTION TECHNIQUE, TYPE=SEPARATED +Step module: Create Step: General: Coupled temp-displacement: +Other: Solution technique: Separated +Steady-state analysis +A steady-state coupled temperature-displacement analysis can be performed in Abaqus/Standard. +In +steady-state cases you should assign an arbitrary “time” scale to the step: you specify a “time” period +and “time” incrementation parameters. This time scale is convenient for changing loads and boundary +conditions through the step and for obtaining solutions to highly nonlinear (but steady-state) cases; +however, for the latter purpose, transient analysis often provides a natural way of coping with the +nonlinearity. +Frictional slip heat generation is normally neglected in for the steady-state case. However, it can still +be accounted for if motions are used to specify translational or rotational nodal velocities in disk brake- +type problems or if user subroutine FRIC provides the incremental frictional dissipation through the +variable SFD. If frictional heat generation is present, the heat flux into the two contact surfaces depends +on the slip rate of the surfaces. The “time” scale in this case cannot be described as arbitrary, and a +transient analysis should be performed. +Input File Usage: +Abaqus/CAE Usage: +*COUPLED TEMPERATURE-DISPLACEMENT, STEADY STATE +Step module: Create Step: General: Coupled temp-displacement: +Basic: Response: Steady state +Transient analysis +Alternatively, you can perform a transient coupled temperature-displacement analysis. You can control +the time incrementation in a transient analysis directly, or Abaqus/Standard can control it automatically. +Automatic time incrementation is generally preferred. +Automatic incrementation controlled by a maximum allowable temperature change +The time increments can be selected automatically based on a user-prescribed maximum allowable nodal +temperature change in an increment, +. Abaqus/Standard will restrict the time increments to ensure +that this value is not exceeded at any node (except nodes with boundary conditions) during any increment +of the analysis . +Input File Usage: +Abaqus/CAE Usage: +*COUPLED TEMPERATURE-DISPLACEMENT, DELTMX= +Step module: Create Step: General: Coupled temp-displacement: +Basic: Response: Transient; Incrementation: Type: Automatic, Max. +allowable temperature change per increment: +Fixed incrementation +If you do not specify +, fixed time increments equal to the user-specified initial time increment, +, will be used throughout the analysis. +Input File Usage: +*COUPLED TEMPERATURE-DISPLACEMENT +Abaqus/CAE Usage: +Step module: Create Step: General: Coupled temp-displacement: Basic: +Response: Transient; Incrementation: Type: Fixed: Increment size: +Spurious oscillations due to small time increments +In transient analysis with second-order elements there is a relationship between the minimum usable time +increment and the element size. A simple guideline is +where +is the time increment, +is the density, c is the specific heat, k is the thermal conductivity, and +is a typical element dimension (such as the length of a side of an element). If time increments smaller +than this value are used in a mesh of second-order elements, spurious oscillations can appear in the +solution, in particular in the vicinity of boundaries with rapid temperature changes. These oscillations +are nonphysical and may cause problems if temperature-dependent material properties are present. +In transient analyses using first-order elements the heat capacity terms are lumped, which eliminates +such oscillations but can lead to locally inaccurate solutions for small time increments. If smaller time +increments are required, a finer mesh should be used in regions where the temperature changes rapidly. +There is no upper limit on the time increment size (the integration procedure is unconditionally +stable) unless nonlinearities cause convergence problems. +Automatic incrementation controlled by the creep response +The accuracy of the integration of time-dependent (creep) material behavior is governed by the +user-specified accuracy tolerance parameter, +. This parameter is used +to prescribe the maximum strain rate change allowed at any point during an increment, as described +in “Rate-dependent plasticity: creep and swelling,” Section 23.2.4. The accuracy tolerance parameter +can be specified together with the maximum allowable nodal temperature change in an increment, +(described above); however, specifying the accuracy tolerance parameter activates automatic +incrementation even if +is not specified. +Input File Usage: +*COUPLED TEMPERATURE-DISPLACEMENT, DELTMX= +CETOL=tolerance +, +Abaqus/CAE Usage: +Step module: Create Step: General: Coupled temp-displacement: Basic: +Response: Transient, Include creep/swelling/viscoelastic behavior; +Incrementation: Type: Automatic, Max. allowable temperature +change per increment: +strain error tolerance: tolerance +, Creep/swelling/viscoelastic +Selecting explicit creep integration +Nonlinear creep problems (“Rate-dependent plasticity: creep and swelling,” Section 23.2.4) that exhibit +no other nonlinearities can be solved efficiently by forward-difference integration of the inelastic +strains if the inelastic strain increments are smaller than the elastic strains. This explicit method is +efficient computationally because, unlike implicit methods, iteration is not required as long as no other +nonlinearities are present. Although this method is only conditionally stable, the numerical stability +limit of the explicit operator is in many cases sufficiently large to allow the solution to be developed in +a reasonable number of time increments. +For most coupled thermal-stress analyses, however, the unconditional stability of the backward +difference operator (implicit method) is desirable. In such cases the implicit integration scheme may be +invoked automatically by Abaqus/Standard. +Explicit integration can be less expensive computationally and simplifies implementation of user- +defined creep laws in user subroutine CREEP; you can restrict Abaqus/Standard to using this method +for creep problems (with or without geometric nonlinearity included). See “Rate-dependent plasticity: +creep and swelling,” Section 23.2.4, for further details. +Input File Usage: +*COUPLED TEMPERATURE-DISPLACEMENT, CETOL=tolerance, +CREEP=EXPLICIT +Abaqus/CAE Usage: +Step module: Create Step: General: Coupled temp-displacement: Basic: +Response: Transient, Include creep/swelling/viscoelastic behavior; +Incrementation: Type: Automatic, Creep/swelling/viscoelastic +strain error tolerance: tolerance, Creep/swelling/viscoelastic +integration: Explicit +Excluding creep and viscoelastic response +You can specify that no creep or viscoelastic response will occur during a step even if creep or viscoelastic +material properties have been defined. +Input File Usage: +*COUPLED TEMPERATURE-DISPLACEMENT, DELTMX= +CREEP=NONE +, +Abaqus/CAE Usage: +Step module: Create Step: General: Coupled temp- +displacement: Basic: Response: Transient, toggle off Include +creep/swelling/viscoelastic behavior +Unstable problems +Some types of analyses may develop local instabilities, such as surface wrinkling, material instability, +In such cases it may not be possible to obtain a quasi-static solution, even with +or local buckling. +the aid of automatic incrementation. Abaqus/Standard offers a method of stabilizing this class of +problems by applying damping throughout the model in such a way that the viscous forces introduced +are sufficiently large to prevent instantaneous buckling or collapse but small enough not to affect the +behavior significantly while the problem is stable. The available automatic stabilization schemes are +described in detail in “Automatic stabilization of unstable problems” in “Solving nonlinear problems,” +Section 7.1.1. +Units +In coupled problems where two different fields are active, take care when choosing the units of the +problem. +If the choice of units is such that the terms generated by the equations for each field are +different by many orders of magnitude, the precision on some computers may be insufficient to resolve the +numerical ill-conditioning of the coupled equations. Therefore, choose units that avoid ill-conditioned +matrices. For example, consider using units of Mpascal instead of pascal for the stress equilibrium +equations to reduce the disparity between the magnitudes of the stress equilibrium equations and the +heat flux continuity equations. +Fully coupled thermal-stress analysis in Abaqus/Explicit +In Abaqus/Explicit the heat transfer equations are integrated using the explicit forward-difference time +integration rule +is the temperature at node N and the subscript i refers to the increment number in an explicit +where +dynamic step. The forward-difference integration is explicit in the sense that no equations need to be +solved when a lumped capacitance matrix is used. The current temperatures are obtained using known +are computed at the beginning of the +values of +increment by +from the previous increment. The values of +where +internal flux vector. +is the lumped capacitance matrix, +is the applied nodal source vector, and +is the +The mechanical solution response is obtained using the explicit central-difference integration rule +with a lumped mass matrix as described in “Explicit dynamic analysis,” Section 6.3.3. Since both the +forward-difference and central-difference integrations are explicit, the heat transfer and mechanical +solutions are obtained simultaneously by an explicit coupling. Therefore, no iterations or tangent +stiffness matrices are required. +Explicit integration can be less expensive computationally and simplifies the treatment of contact. +For a comparison of explicit and implicit direct-integration procedures, see “Dynamic analysis +procedures: overview,” Section 6.3.1. +Stability +The explicit procedure integrates through time by using many small time increments. The central- +difference and forward-difference operators are conditionally stable. The stability limit for both operators +(with no damping in the mechanical solution response) is obtained by choosing +where +is the highest frequency in the system of equations of the mechanical solution response and +is the largest eigenvalue in the system of equations of the thermal solution response. +Estimating the time increment size +An approximation to the stability limit for the forward-difference operator in the thermal solution +response is given by +where +material. The parameters k, +heat, respectively. +is the smallest element dimension in the mesh and +is the thermal diffusivity of the +, and c represent the material’s thermal conductivity, density, and specific +In most applications of explicit analysis the mechanical response will govern the stability limit. The +thermal response may govern the stability limit when material parameter values are non-physical or a +very large amount of mass scaling is used. The calculation of the time increment size for the mechanical +solution response is discussed in “Explicit dynamic analysis,” Section 6.3.3. +Stable time increment report +Abaqus/Explicit writes a report to the status (.sta) file during the data check phase of the analysis +that contains an estimate of the minimum stable time increment and a listing of the elements with the +smallest stable time increments and their values. The initial minimum stable time increment accounts +for the stability requirements of both the thermal and mechanical solution responses. The initial stable +time increments listed do not include damping (bulk viscosity), mass scaling, or penalty contact effects +in the mechanical solution response. +This listing is provided because often a few elements have much smaller stability limits than the +rest of the elements in the mesh. The stable time increment can be increased by modifying the mesh to +increase the size of the controlling element or by using appropriate mass scaling. +Time incrementation +The time increment used in an analysis must be smaller than the stability limits of the central- +and forward-difference operators. Failure to use such a time increment will result in an unstable +solution. When the solution becomes unstable, the time history response of solution variables, such +as displacements, will usually oscillate with increasing amplitudes. The total energy balance will also +change significantly. +Abaqus/Explicit has two strategies for time incrementation control: +fully automatic time +incrementation (where the code accounts for changes in the stability limit) and fixed time incrementation. +Scaling the time increment +To reduce the chance of a solution going unstable, the stable time increment computed by Abaqus/Explicit +can be adjusted by a constant scaling factor. This factor can be used to scale the default global time +estimate, the element-by-element estimate, or the fixed time increment based on the initial element-by- +element estimate; it cannot be used to scale a fixed time increment that you specified directly. +Input File Usage: +Use any of the following options: +*DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT, +SCALE FACTOR=f +*DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT, +ELEMENT BY ELEMENT, SCALE FACTOR=f +*DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT, +FIXED TIME INCREMENTATION, SCALE FACTOR=f +Abaqus/CAE Usage: +Step module: Create Step: General: Dynamic, Temp-disp, Explicit: +Incrementation: Time scaling factor: f +Automatic time incrementation +The default time incrementation scheme in Abaqus/Explicit is fully automatic and requires no user +intervention. Two types of estimates are used to determine the stability limit: element-by-element for +both the thermal and mechanical solution responses and global for the mechanical solution response. +An analysis always starts by using the element-by-element estimation method and may switch to the +global estimation method under certain circumstances, as explained in “Explicit dynamic analysis,” +Section 6.3.3. +In an analysis Abaqus/Explicit initially uses a stability limit based on the thermal and mechanical +solution responses in the whole model. This element-by-element estimate is determined using the +smallest time increment size due to the thermal and mechanical solution responses in each element. +The element-by-element estimate is conservative; it will give a smaller stable time increment than +the true stability limit, which is based upon the maximum frequency of the entire model. In general, +constraints such as boundary conditions and kinematic contact have the effect of compressing the +eigenvalue spectrum, and the element-by-element estimates do not take this into account +The stable time increment size due to the mechanical solution response will be determined by +the global estimator as the step proceeds unless the element-by-element estimator is chosen, fixed +time incrementation is specified, or one of the conditions explained in “Explicit dynamic analysis,” +Section 6.3.3, prevents the use of global estimation. The stable time increment size due to the thermal +solution response will always be determined by using an element-by-element estimation method. The +switch to the global estimation method in mechanical solution response occurs once the algorithm +determines that the accuracy of the global estimation method is acceptable. For details, see “Explicit +dynamic analysis,” Section 6.3.3 +For three-dimensional continuum elements and elements with plane stress formulations (shell, +membrane, and two-dimensional plane stress elements) an “improved” estimate of the element +characteristic length is used by default. This “improved” method usually results in a larger element +stable time increment than a more traditional method. For analyses using variable mass scaling, the +total mass added to achieve a given stable time increment will be less with the improved estimate. +Input File Usage: +Use the following option to specify the element-by-element estimation method: +*DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT, +ELEMENT BY ELEMENT +Use the following option to activate the “improved” element time estimation +method: +*DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT, +IMPROVED DT METHOD=YES +Use the following option to deactivate the “improved” element time estimation +method: +*DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT, +IMPROVED DT METHOD=NO +Step module: Create Step: General: Dynamic, Temp-disp, +Explicit: Incrementation: Type: Automatic, Stable increment +estimator: Element-by-element +The ability to deactivate the “improved” element time estimation method is not +supported in Abaqus/CAE. +Abaqus/CAE Usage: +Fixed time incrementation +A fixed time incrementation scheme is also available in Abaqus/Explicit. The fixed time increment size +is determined either by the initial element-by-element stability estimate for the step or by a user-specified +time increment. +Fixed time incrementation may be useful when a more accurate representation of the higher mode +response of a problem is required. In this case a time increment size smaller than the element-by-element +estimates may be used. The element-by-element estimate can be obtained simply by running a data check +analysis . +When fixed time incrementation is used, Abaqus/Explicit will not check that the computed response +is stable during the step. You should ensure that a valid response has been obtained by carefully checking +the energy history and other response variables. +If you choose to use time increments the size of the initial element-by-element stability limit +throughout a step, the dilatational wave speed and the thermal diffusivity in each element at the +beginning of the step are used to compute the fixed time increment size. To reduce the chance of a +solution going unstable, the initial stable time increment that Abaqus/Explicit computes can be adjusted +by a constant scaling factor, as described above in “Scaling the time increment.” Alternatively, you can +specify a time increment size directly. +Input File Usage: +Use the following option to request time increments the size of the element-by- +element stability limit: +*DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT, +FIXED TIME INCREMENTATION +Use the following option to specify the time increment size directly: +*DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT, +DIRECT USER CONTROL +Abaqus/CAE Usage: +Step module: Create Step: General: Dynamic, Temp-disp, Explicit: +Incrementation: Type: Fixed, Use element-by-element time increment +estimator or User-defined time increment: +Reducing the computational cost by using selective subcycling +The selective subcycling method can be used in a coupled thermal-stress analysis exactly as in a +pure mechanical analysis, as described in “Explicit dynamic analysis,” Section 6.3.3 and “Selective +subcycling,” Section 11.7.1. +Monitoring output variables for extreme values +The extreme values defined as the element and nodal variables in a coupled thermal-stress analysis can +be monitored exactly as described in “Explicit dynamic analysis,” Section 6.3.3, for a pure mechanical +analysis. +Initial conditions +By default, the initial temperature of all nodes is zero. You can specify nonzero initial temperatures. +Initial stresses, field variables, etc. can also be defined; “Initial conditions in Abaqus/Standard and +Abaqus/Explicit,” Section 33.2.1, describes all of the initial conditions that are available for a fully +coupled thermal-stress analysis. +Boundary conditions +Boundary conditions can be used to prescribe both temperatures (degree of freedom 11) and +displacements/rotations (degrees of freedom 1–6) at nodes in fully coupled thermal-stress analysis . Shell elements in +Abaqus/Standard have additional temperature degrees of freedom 12, 13, etc. through the thickness +. +Boundary conditions can be specified as functions of time by referring to amplitude curves +(“Amplitude curves,” Section 33.1.2). +Boundary conditions applied during a dynamic coupled temperature-displacement response +step should use appropriate amplitude references (“Amplitude curves,” Section 33.1.2). If boundary +conditions are specified for the step without amplitude references, they are applied instantaneously at +the beginning of the step. Since Abaqus/Explicit does not admit jumps in displacement, the value of +a nonzero displacement boundary condition that is specified without an amplitude reference will be +ignored, and a zero velocity boundary condition will be enforced. +Loads +The following types of thermal loads can be prescribed in a fully coupled thermal-stress analysis, as +described in “Thermal loads,” Section 33.4.4: +• Concentrated heat fluxes. +• Body fluxes and distributed surface fluxes. +• Node-based film and radiation conditions. +• Average-temperature radiation conditions. +• Element and surface-based film and radiation conditions. +The following types of mechanical loads can be prescribed: +• Concentrated nodal forces can be applied to the displacement degrees of freedom (1–6); see +“Concentrated loads,” Section 33.4.2. +• Distributed pressure forces or body forces can be applied; see “Distributed loads,” Section 33.4.3. +The distributed load types available with particular elements are described in Part VI, “Elements.” +Predefined fields +Predefined temperature fields are not allowed in a fully coupled thermal-stress analysis. Boundary +conditions should be used instead to prescribe temperature degree of freedom 11 (and 12, 13, etc. in +Abaqus/Standard shell elements), as described earlier. +Other predefined field variables can be specified in a fully coupled thermal-stress analysis. These +values will affect only field-variable-dependent material properties, if any. See “Predefined fields,” +Section 33.6.1. +Material options +The materials in a fully coupled thermal-stress analysis must have both thermal properties, such as +conductivity, and mechanical properties, such as elasticity, defined. See Part V, “Materials,” for details +on the material models available in Abaqus. +In Abaqus/Standard internal heat generation can be specified; see “Uncoupled heat transfer +analysis,” Section 6.5.2. +Thermal strain will arise if thermal expansion (“Thermal expansion,” Section 26.1.2) is included in +the material property definition. +In Abaqus/Standard a fully coupled temperature-displacement analysis can be used to analyze static +creep and swelling problems, which generally occur over fairly long time periods (“Rate-dependent +plasticity: creep and swelling,” Section 23.2.4); viscoelastic materials (“Time domain viscoelasticity,” +Section 22.7.1); or viscoplastic materials (“Rate-dependent yield,” Section 23.2.3). +Inelastic energy dissipation as a heat source +You can specify an inelastic heat fraction in a fully coupled thermal-stress analysis to provide for inelastic +energy dissipation as a heat source. Plastic straining gives rise to a heat flux per unit volume of +where +constant), +is the heat flux that is added into the thermal energy balance, +is a user-defined factor (assumed +is the stress, and +is the rate of plastic straining. +Inelastic heat fractions are typically used in the simulation of high-speed manufacturing processes +involving large amounts of inelastic strain, where the heating of the material caused by its deformation +significantly influences temperature-dependent material properties. The generated heat is treated as a +volumetric heat flux source term in the heat balance equation. +An inelastic heat fraction can be specified for materials with plastic behavior that use the Mises +or Hill yield surface (“Inelastic behavior,” Section 23.1.1). +It cannot be used with the combined +isotropic/kinematic hardening model. The inelastic heat fraction can be specified for user-defined +material behavior in Abaqus/Explicit and will be multiplied by the inelastic energy dissipation coded in +the user subroutine to obtain the heat flux. In Abaqus/Standard the inelastic heat fraction cannot be used +with user-defined material behavior; in this case the heat flux that must be added to the thermal energy +balance is computed directly in the user subroutine. +In Abaqus/Standard an inelastic heat fraction can also be specified for hyperelastic material +definitions that include time-domain viscoelasticity (“Time domain viscoelasticity,” Section 22.7.1). +The default value of the inelastic heat fraction is 0.9. If you do not include the inelastic heat fraction +behavior in the material definition, the heat generated by inelastic deformation is not included in the +analysis. +Input File Usage: +*INELASTIC HEAT FRACTION +Abaqus/CAE Usage: +Property module: material editor: Thermal: Inelastic Heat Fraction: +Fraction: +Elements +Coupled temperature-displacement elements that have both displacements and temperatures as +nodal variables are available in both Abaqus/Standard and Abaqus/Explicit . +In Abaqus/Standard simultaneous +temperature/displacement solution requires the use of such elements; pure displacement elements can be +used in part of the model in the fully coupled thermal-stress procedure, but pure heat transfer elements +cannot be used. In Abaqus/Explicit any of the available elements, except Eulerian elements, can be +used in the fully coupled thermal-stress procedure; however, the thermal solution will be obtained only +at nodes where the temperature degree of freedom has been activated (i.e., at nodes attached to coupled +temperature-displacement elements). +The first-order coupled temperature-displacement elements in Abaqus use a constant temperature +over the element to calculate thermal expansion. The second-order coupled temperature-displacement +elements in Abaqus/Standard use a lower-order interpolation for temperature than for displacement +(parabolic variation of displacements and linear variation of temperature) to obtain a compatible +variation of thermal and mechanical strain. +Output +See “Abaqus/Standard output variable identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable +identifiers,” Section 4.2.2, for a complete list of output variables. The types of output available are +described in “Output,” Section 4.1.1. +Input file template +*HEADING +… +** Specify the coupled temperature-displacement element type +*ELEMENT, TYPE=CPS4T +… +** +*STEP +*COUPLED TEMPERATURE-DISPLACEMENT or +*DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT +Data line to define incrementation +*BOUNDARY +Data lines to define nonzero boundary conditions on displacement or +temperature degrees of freedom +*CFLUX and/or *CFILM and/or +*CRADIATE and/or *DFLUX and/or +*DSFLUX and/or *FILM and/or +*SFILM and/or *RADIATE and/or +*SRADIATE +Data lines to define thermal loads +*CLOAD and/or *DLOAD and/or *DSLOAD +Data lines to define mechanical loads +*FIELD +Data lines to define field variable values +*END STEP +6.5.4 +ADIABATIC ANALYSIS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “Heat transfer analysis procedures: overview,” Section 6.5.1 +• *DYNAMIC +• *STATIC +• *DENSITY +• *INELASTIC HEAT FRACTION +• *SPECIFIC HEAT +• “Configuring general analysis procedures,” Section 14.11.1 of the Abaqus/CAE User’s Manual, in +the online HTML version of this manual +• “Defining thermal material models,” Section 12.10 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +An adiabatic stress analysis: +• is used in cases where mechanical deformation causes heating but the event is so rapid that this heat +has no time to diffuse through the material—for example, a very high-speed forming process; +• can be conducted as part of a dynamic analysis (“Implicit dynamic analysis using direct integration,” +Section 6.3.2, or “Explicit dynamic analysis,” Section 6.3.3) or as part of a static analysis (“Static +stress analysis,” Section 6.2.2); +• in Abaqus/Standard is available only for the isotropic hardening metal plasticity models with a +Mises yield surface (“Classical metal plasticity,” Section 23.2.1); +• in Abaqus/Explicit is relevant only for the metal plasticity models (including both Mises and Hill +yield surfaces); +• can be conducted if parts of the model are elastic only—no change in temperature occurs in the +elastic regions; and +• requires that a material’s density, specific heat, and inelastic heat fraction (fraction of inelastic +dissipation rate that appears as heat flux) be specified. +Adiabatic analysis +Adiabatic thermal-stress analysis is typically used to simulate high-speed manufacturing processes +involving large amounts of inelastic strain, where the heating of the material caused by its deformation +is an important effect because of temperature-dependent material properties. The temperature increase +is calculated directly at the material integration points according to the adiabatic thermal energy +increases caused by inelastic deformation; temperature is not a degree of freedom in the problem. No +allowance is made for conduction of heat in an adiabatic analysis. For problems where both inelastic +heating and conduction of the heat are important, a fully coupled temperature-displacement analysis +must be performed (“Fully coupled thermal-stress analysis,” Section 6.5.3). +In an adiabatic analysis plastic straining gives rise to a heat flux per unit volume of +is the heat flux that is added into the thermal energy balance, +where +heat fraction (assumed constant; discussed below), +The heat equation solved at each integration point is +is the stress, and +is the user-specified inelastic +is the rate of plastic straining. +is the material density and +where +heat,” Section 26.2.3). +is the specific heat . In this case the temperatures +at the end of the adiabatic analysis must be written to the Abaqus/Standard results file as element +variables averaged at the nodes. Since temperature values in an adiabatic analysis can be written to +the results file as element quantities only by using the TEMP output variable identifier, they cannot +be read directly into a subsequent thermal diffusion analysis as initial conditions. However, if you +postprocess the results file to produce a second results file in which the temperature data are provided +as nodal quantities, a subsequent heat transfer analysis can be performed with these temperatures as +initial conditions. See “Predefined fields,” Section 33.6.1, and “Accessing the results file information,” +Section 5.1.3, for details. Alternatively, you could postprocess the results file to produce a data list +containing data pairs consisting of nodes and temperatures. +The temperatures, NT, obtained from the heat transfer analysis can then be used to drive a +continuation of the previous stress analysis. This stress analysis should be restarted from the end of the +adiabatic analysis and will provide the response to the change of the temperature field obtained during +the heat transfer analysis. In this case Abaqus/Standard will automatically read the temperatures from +the results file that was obtained from the heat transfer analysis and apply them in the restarted analysis. +Example +The following input options could be used to perform a heat transfer analysis using the temperatures +from an adiabatic analysis and then continue the stress analysis: +**Static adiabatic analysis +… +*STEP +*STATIC, ADIABATIC +… +**Write the temperatures to the results file as element +**variables averaged at the nodes +*EL FILE, POSITION=AVERAGED AT NODES +TEMP +*END STEP +**Heat transfer analysis using the temperatures from the +**static analysis as initial conditions +… +*INITIAL CONDITIONS, TYPE=TEMPERATURE, FILE=new results file, +STEP=step, INC=increment +*STEP +*HEAT TRANSFER +… +*NODE FILE +NT +*END STEP +**Restart from the adiabatic analysis using temperatures +**obtained from the heat transfer analysis +*RESTART, WRITE, READ, STEP=k, INC=i, END STEP +… +*STEP +*STATIC +… +*TEMPERATURE, FILE=heat_transfer_results_file +… +*END STEP +Fully coupled temperature-displacement analysis +If the continuation of the analysis into thermal diffusion requires a fully coupled temperature- +displacement analysis , the simplest (but +more expensive) approach is to use coupled temperature-displacement elements throughout +the +adiabatic analysis. At the end of the static or the dynamic adiabatic calculations, the temperatures +must be written to the results file as element variables averaged at the nodes. In addition, you must +constrain all temperature degrees of freedom since they are not used in the adiabatic analysis. The +adiabatic analysis can then be restarted to apply the correct temperature distribution obtained from the +adiabatic analysis to the temperature degree of freedom of each node in the model. To create the input +for the boundary conditions, you must postprocess the results file obtained from the adiabatic analysis +and extract the value of TEMP at each node in the model . The temperature boundary conditions can be released as needed in subsequent coupled +temperature-displacement analysis steps. +Example +The following input options could be used to perform a coupled temperature-displacement analysis using +the temperatures from an adiabatic analysis: +**Static adiabatic analysis, coupled temperature-displacement +**plane stress elements +… +*ELEMENT, TYPE=CPS4T, ELSET=EALL +… +*BOUNDARY +nodes, 11, 11, 0.0 +*STEP +*STATIC, ADIABATIC +… +**Write the temperatures to the results file as element +**variables averaged at the nodes +*EL FILE, POSITION=AVERAGED AT NODES +TEMP +*END STEP +**Restart from the adiabatic analysis +*RESTART, WRITE, READ, STEP=k, INC=i, END STEP +… +*STEP +*STATIC +**Dummy step to associate the temperature variable TEMP with +**the temperature degree of freedom at each node +1.0, 1.0 +… +*BOUNDARY, OP=NEW +node, 11, 11, temperature +… +*END STEP +**Coupled temperature displacement run for cool down of +**structure: continuation of the restart analysis +… +*STEP +*COUPLED TEMPERATURE-DISPLACEMENT +0.1, 1.0 +… +*BOUNDARY, OP=NEW +**no temperature boundary condition specified +*END STEP +Initial conditions +Initial temperatures can be prescribed at nodes as initial conditions. +Initial values of stresses, field +variables, solution-dependent state variables, etc. can also be specified . +Boundary conditions +Boundary conditions can be applied to displacement degrees of freedom in an adiabatic analysis in the +same way that they are applied in nonadiabatic dynamic, explicit dynamic, or static analysis steps . Temperature is not a +degree of freedom in an adiabatic analysis. +Loads +The loading options available for an adiabatic analysis are the same as those available for nonadiabatic +dynamic, explicit dynamic, or static analysis steps . +The following types of mechanical loads can be prescribed: +• Concentrated nodal forces can be applied to the displacement degrees of freedom (1–6); see +“Concentrated loads,” Section 33.4.2. +• Distributed pressure forces or body forces can be applied; see “Distributed loads,” Section 33.4.3. +The distributed load types available with particular elements are described in Part VI, “Elements.” +Predefined fields +Predefined temperature fields cannot be used during an adiabatic analysis step. +The values of user-defined field variables can be specified; these values affect only field-variable- +dependent material properties, if any. See “Predefined fields,” Section 33.6.1. +Material options +In Abaqus/Standard only Mises plasticity with isotropic elasticity and isotropic hardening (“Inelastic +behavior,” Section 23.1.1) is allowed in adiabatic stress analysis. Kinematic or combined hardening +is not available, but rate effects can be included. However, portions of the model can include only +elastic material; no change in temperature occurs in the elastic regions, since there is no source of heat +generation. In Abaqus/Explicit both Mises and Hill plasticity are allowed in adiabatic stress analysis. +You must specify the density, the inelastic heat fraction, and the specific heat as part of the material +definition for the material in which heat will be generated by plastic dissipation. You can also specify +latent heat if necessary (“Latent heat,” Section 26.2.4). +The inelastic heat fraction is the amount of inelastic dissipation used to calculate the increase in +temperature. The default value of the inelastic heat fraction is 0.9. If the inelastic heat fraction is not +included in the material definition, the heat generated by inelastic deformation is not included in the +analysis. +In Abaqus/Standard adiabatic analyses can also be carried out with user subroutine UMAT. In this +case the temperature must be defined as a solution-dependent state variable, and all coupling terms must +be included in the user subroutine. If conductivity (“Conductivity,” Section 26.2.2) is defined for the +material, it will be ignored during adiabatic analysis steps. +Input File Usage: +All of the following options must be included in the material definition: +*DENSITY +*INELASTIC HEAT FRACTION +*SPECIFIC HEAT +The following option can be included if latent heat effects are important: +Abaqus/CAE Usage: +*LATENT HEAT +All of the following must be included in the material definition: +Property module: +Material editor: General→Density +Material editor: Thermal→Inelastic Heat Fraction +Material editor: Thermal→Specific Heat +The following can be included if latent heat effects are important: +Property module: material editor: Thermal→Latent Heat +Temperature-dependent material properties +Material properties can be temperature dependent. Since the only source of temperature change in +adiabatic analysis is inelastic deformation, the temperature can only rise. This temperature rise may +cause thermal expansion (usually a small effect) and localization of the deformation if the flow stress is +reduced by the temperature rise. Since the adiabatic assumption applies only in rapid events and inelastic +deformation usually causes significant temperature rises only if the deformation is substantial, the strain +rates are often large in adiabatic analysis. The softening of the material caused by the temperature rise +may, thus, be offset somewhat by strengthening associated with rate dependence if the material is rate +sensitive. +Elements +Any of the stress/displacement or coupled temperature-displacement elements in Abaqus can be used in +an adiabatic analysis . Mass +or spring elements will not contribute to the heating of the material since they cannot generate plastic +strains. +If coupled temperature-displacement elements are used in an adiabatic analysis, the temperature +degrees of freedom will be ignored. +Output +Since temperatures are updated at the material calculation points, output of temperature is available with +output variable TEMP, not with output variable NT. +The element output available for an adiabatic analysis includes stress; strain; energies; the values +of state, field, and user-defined variables; and composite failure measures. The nodal output available +includes displacements, reaction forces, and coordinates. All of the output variable identifiers are +outlined in “Abaqus/Standard output variable identifiers,” Section 4.2.1, and “Abaqus/Explicit output +variable identifiers,” Section 4.2.2. +Input file template +*HEADING +… +*MATERIAL, NAME=name +*ELASTIC, TYPE=ISOTROPIC +Data lines to define isotropic linear elasticity +*PLASTIC +Data lines to define metal plasticity +*DENSITY +Data lines to define density +*INELASTIC HEAT FRACTION +Data line to define inelastic heat fraction +*SPECIFIC HEAT +Data lines to define specific heat +… +*BOUNDARY +Data lines to specify zero-valued boundary conditions +*INITIAL CONDITIONS, TYPE=type +Data lines to specify initial conditions +*AMPLITUDE, NAME=name +Data lines to define amplitude variations +** +*STEP, NLGEOM +The NLGEOM parameter is used in Abaqus/Standard to include geometric nonlinearity +*DYNAMIC, ADIABATIC or *DYNAMIC, EXPLICIT, ADIABATIC or +*STATIC, ADIABATIC +Data line to control time incrementation or to specify the time period of the step +*BOUNDARY, AMPLITUDE=name +Data lines to describe nonzero or zero-valued boundary conditions +*CLOAD and/or *DLOAD and/or *DSLOAD +Data lines to specify loads +*FIELD +Data lines to specify field variable values +*END STEP +6.6 +Fluid dynamic analysis +• “Fluid dynamic analysis procedures: overview,” Section 6.6.1 +• “Incompressible fluid dynamic analysis,” Section 6.6.2 +6.6.1 +FLUID DYNAMIC ANALYSIS PROCEDURES: OVERVIEW +Overview +Abaqus/CFD provides advanced computational fluid dynamics capabilities with extensive support for +preprocessing and postprocessing provided in Abaqus/CAE. These scalable parallel CFD simulation +capabilities address a broad range of nonlinear coupled fluid-thermal and fluid-structural problems. +Abaqus/CFD can solve the following types of incompressible flow problems: +• Laminar and turbulent: +Internal or external flows that are steady-state or transient, span a broad +Reynolds number range, and involve complex geometry may be simulated with Abaqus/CFD. This +includes flow problems induced by spatially varying distributed body forces. +• Thermal convective: Problems that involve heat transfer and require an energy equation and that +may involve buoyancy-driven flows (i.e., natural convection) can also be solved with Abaqus/CFD. +This type of problem includes turbulent heat transfer for a broad range of Prandtl numbers. +• Deforming-mesh ALE: Abaqus/CFD includes the ability to perform deforming-mesh analyses +using an arbitrary Lagrangian-Eulerian (ALE) description of the equations of motion, heat transfer, +and turbulent transport. Deforming-mesh problems may include prescribed boundary motion that +induces fluid flow or FSI problems where the boundary motion is relatively independent of the fluid +flow. +For more details, see “Incompressible fluid dynamic analysis,” Section 6.6.2. +Activation of fields in Abaqus/CFD +In Abaqus/CFD the active fields (degrees of freedom) are determined by the analysis procedure and the +options specified, such as turbulence models and auxiliary transport equations. For example, using the +energy equation in conjunction with the incompressible flow procedure activates the velocity, pressure, +and temperature degrees of freedom. For a complete listing of the available degrees of freedom, see +“Active degrees of freedom” in “Boundary conditions in Abaqus/CFD,” Section 33.3.2. +6.6.2 +INCOMPRESSIBLE FLUID DYNAMIC ANALYSIS +Products: Abaqus/CFD Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “Fluid dynamic analysis procedures: overview,” Section 6.6.1 +Overview +An incompressible fluid dynamics analysis: +• is one where the velocity field is divergence-free and the pressure does not contain a thermodynamic +component; +• is one where the energy contained in acoustic waves is small relative to the energy transported by +advection (i.e., when the Mach number is in the range +); +• can be either laminar or turbulent, steady or time-dependent; +• can be used to study either internal or external flows; +• can include energy transport and buoyancy forces; +• can be used with a deforming mesh for ALE calculations; and +• can be performed with conjugate heat transfer or fluid-structure interaction. +Incompressible fluid dynamic analysis +Incompressible flow is one of the most frequently encountered flow regimes encompassing a diverse set +of problems that include: atmospheric dispersal, food processing, aerodynamic design of automobiles, +biomedical flows, electronics cooling, and manufacturing processes such as chemical vapor deposition, +mold filling, and casting. +Input File Usage: +Abaqus/CAE Usage: +*CFD, INCOMPRESSIBLE NAVIER STOKES +Step module: Create Step: General: Flow; Flow type: Incompressible +Governing equations +The momentum equations in integral form for an arbitrary control volume can be written as +where +is an arbitrary control volume with surface area +is the outward normal to , +, +is the fluid density, +is the pressure, +is the velocity vector, +is the velocity of the moving mesh, +is the body force, and +is the viscous shear stress. +The viscous shear stress, +information, see “Viscosity,” Section 26.1.4. +, is also referred to as the deviatoric stress, +Incompressibility requires a solenoidal velocity field expressed by +, where +. For more +Numerical implementation +The solution of the incompressible Navier-Stokes equations poses a number of algorithmic issues +due to the divergence-free velocity condition and the concomitant spatial and temporal resolution +required to achieve solutions in complex geometries for engineering applications. The Abaqus/CFD +incompressible solver uses a hybrid discretization built on the integral conservation statements for +an arbitrary deforming domain. For time-dependent problems, an advanced second-order projection +method is used with a node-centered finite-element discretization for the pressure. This hybrid approach +guarantees accurate solutions and eliminates the possibility of spurious pressure modes while retaining +the local conservation properties associated with traditional finite volume methods. An edge-based +implementation is used for all transport equations permitting a single implementation that spans a broad +variety of element topologies ranging from simple tetrahedral and hexahedral elements to arbitrary +polyhedral. In Abaqus/CFD tetrahedral, wedge, and hexahedral elements are supported. +Projection method +The basic concept for projection methods is the legitimate segregation of pressure and velocity fields for +efficient solution of the incompressible Navier-Stokes equations. Over the past two decades, projection +methods have found broad application for problems involving laminar and turbulent fluid dynamics, +large density variations, chemical reactions, free surfaces, mold filling, and non-Newtonian behavior. +In practice, the projection is used to remove the part of the velocity field that is not divergence- +free (“div-free”). The projection is achieved by splitting the velocity field into div-free and curl-free +components using a Helmholtz decomposition. The projection operators are constructed so that they +satisfy prescribed boundary conditions and are norm-reducing, resulting in a robust solution algorithm +for incompressible flows. +Least-squares gradient estimation +The solution methods in Abaqus/CFD use a linearly complete second-order accurate least-squares +gradient estimation. This permits accurate evaluation of dual-edge fluxes for both advective and +diffusive processes. All transport equations in Abaqus/CFD make use of the second-order least-squares +operators. +Advection methods +The advection treatment +in Abaqus/CFD is edge-based, monotonicity-preserving, and preserves +smooth variations to second order in space. The advection algorithm relies on a least-squares gradient +estimation with unstructured-grid slope limiters that are topology independent. Sharp gradients are +captured within approximately 2–3 elements; i.e., +, and the use of slope limiting in conjunction +with a local diffusive limiter precludes over-/under-shoots in advected fields. The advection terms in +the momentum and transport equations can be treated either explicitly or implicitly . +Energy equation +The energy transport equation is optionally activated in Abaqus/CFD for non-isothermal flows. For +small density variations, the Boussinesq approximation provides the coupling between momentum and +energy equations. In turbulent flows, the energy transport includes a turbulent heat flux based on the +turbulent eddy viscosity and turbulent Prandtl number. Abaqus/CFD provides a temperature-based +energy equation. +The energy equation, in temperature form, can be obtained from the first law of thermodynamics +and is given by +is the constant pressure specific heat, +where +is heat flux due to conduction +defined by Fourier’s law, and is the heat supplied externally into the body per unit volume. The energy +equation is solved in terms of temperature in Abaqus/CFD. +is the temperature, +Input File Usage: +Use the following option to specify an isothermal flow problem (default): +*CFD, ENERGY EQUATION=NO ENERGY +Use the following option to specify a thermal (heat) transport problem with +temperature as the primary transport scalar variable: +Abaqus/CAE Usage: +*CFD, ENERGY EQUATION=TEMPERATURE +Use the following option to specify an isothermal flow problem: +Step module: Create Step: General: Flow; Basic tabbed +page: Energy equation: None +Use the following option to specify a thermal (heat) transport problem with +temperature as the primary transport scalar variable: +Step module: Create Step: General: Flow; Basic tabbed page: +Energy equation: Temperature +Turbulence models +Turbulence modeling is a pacing technology for computational fluid dynamics. There is no single +universal turbulence model that can adequately handle all possible flow conditions and geometrical +configurations. This is complicated by the plethora of turbulence models and modeling approaches that +are currently available; e.g., Reynolds Averaged Navier-Stokes (RANS), Unsteady Reynolds Averaged +Navier-Stokes (URANS), Large-Eddy Simulation (LES), Implicit Large-Eddy Simulation (ILES), and +hybrid RANS/LES (HRLES). Ultimately, you must ensure that the approximations made in a given +turbulence model are consistent with the physical problem being modeled. +The following turbulent flow models are available: ILES, Spalart-Allmaras (SA), and RNG k– . +These models span a relatively broad set of flow problems that include time-dependent flows, fluid- +structure interaction (FSI), and conjugate heat transfer (CHT). +Implicit Large-Eddy Simulation (ILES) +Large-eddy simulation relies on a segregation of length and time scales in turbulent flows and a +modeling approach that permits the direct simulation of grid-resolved flow structures and the modeling +of unresolved subgrid features. Implicit LES is a methodology for modeling high Reynolds number +flows that combines computational efficiency and ease of implementation with predictive calculations +and flexible application. +In Abaqus/CFD ILES relies on the discrete monotonicity-preserving form +of the advective operator to implicitly define the subgrid-scale model. This model is inherently +time-dependent requiring time-accurate solutions to the incompressible Navier-Stokes equations where +the time scale is approximately that of an eddy-turnover time for resolve-scale flow features. In addition, +this model must be run in full three dimensions, which typically imposes larger grid densities and +stringent grid resolution criteria relative to more traditional steady-state RANS simulations. However, +this approach is extremely flexible and can be applied to a broad range of flows and FSI problems. +There are no user settings required for ILES. +Input File Usage: +Abaqus/CAE Usage: +Use the *CFD option without the *TURBULENCE MODEL option. +Step module: Create Step: General: Flow; Turbulence tabbed page: None +Spalart-Allmaras (SA) turbulence model +The Spalart-Allmaras (SA) model is a one-equation turbulence model that uses an eddy-viscosity +variable with a nonlinear transport equation. +The model was developed based on empiricism, +dimensional analysis, and a requirement for Galilean invariance. The model has found broad use and +has been calibrated for two-dimensional mixing layers, wakes, and flat-plate boundary layers. The +model produces reasonably accurate predictions of turbulent flows in the presence of adverse pressure +gradients and may be used for flows where separation occurs. This model is spatially local and requires +only moderate resolution in boundary layers. Although initially designed for external and free-shear +flows, the Spalart-Allmaras model can also be used for internal flows. +The basic form of the one-equation Spalart-Allmaras model consists of one transport equation +for the turbulent eddy viscosity, +. The model requires the normal distance from the wall used in the +damping functions needed to control the turbulent viscosity in the near-wall region. Abaqus/CFD +automatically computes the normal distance function, permitting simple specification of the model +boundary conditions. The turbulent viscosity transport equation for the Spalart-Allmaras model is given +by +where the damping functions and model coefficients are defined as: +where +is the normal distance from the wall, and the effective turbulent viscosity is defined as +The Spalart-Allmaras model coefficients are shown in Table 6.6.2–1. In addition, a turbulent Prandtl +number ( +) can be specified. +Table 6.6.2–1 Spalart-Allmaras model coefficients. +0.1355 +0.622 +7.1 +0.6667 +0.3 +0.41 +The Spalart-Allmaras model can provide very accurate boundary layer results if the near-wall +region is resolved (near-wall resolution such that the nondimensional wall distance is approximately 3). +However, the implementation of boundary conditions for the Spalart-Allmaras model in Abaqus/CFD +permits the use of coarser meshes as well. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options: +*CFD +*TURBULENCE MODEL, TYPE=SPALART ALLMARAS +Step module: Create Step: General: Flow; Turbulence +tabbed page: Spalart-Allmaras +RNG k–epsilon turbulence model +The RNG k– model is a two-equation turbulence model that evolves an equation for the turbulent +kinetic energy, k, and the energy dissipation rate, +. The model equations are developed from +fundamental physical principles and dimensional analysis. +In general, the coefficients of the model +are usually calibrated using canonical flows and experimental data. However, the RNG version of the +model computes the coefficients using Renormalization Group theory (Yakhot et al., 1992). The model +equations are +where +the turbulent viscosity +is +and +The second and third terms on the right-hand-side of the k– transport equations above represent the +production and dissipation of k and , respectively. +The RNG k– model coefficients are shown in Table 6.6.2–2. In addition, a turbulent Prandtl number +) can be specified. +( +Table 6.6.2–2 RNG k– model coefficients. +0.085 +1.42 +1.68 +0.72 +0.72 +0.012 +4.38 +Input File Usage: +Use both of the following options: +*CFD +*TURBULENCE MODEL, TYPE=RNG KEPSILON +Step module: Create Step: General: Flow; Turbulence tabbed +page: k-epsilon renormalization group (RNG) +Abaqus/CAE Usage: +Wall functions +It is well known that the k– model has limitations, especially on wall-bounded flows where high values +of eddy viscosity in the near-wall region are usually reproduced. For high Reynolds number flows often +encountered in many industrial applications, a full resolution of the thin viscous sub-layer that occurs +near a wall using a fine mesh may not be economical. Consequently, for meshes that cannot resolve the +viscous sub-layer, wall functions are used to represent the effects of the viscous sub-layer on the transport +processes. In Abaqus/CFD wall functions are used to avoid the need for highly resolved boundary layer +meshes. This approach relies on the law of the wall to obtain the wall shear stress. +The law of the wall is a universal velocity profile that wall-bounded flows develop in the absence +of pressure gradients. The law of the wall is +where +if +if +, +is the wall tangent velocity, +is the kinematic viscosity, +is the density, +is the shear stress at the +wall, and +and +are constants. +The standard law of the wall profile is limited in its usage. For example, in recirculating flows the +turbulent kinetic energy k becomes zero at separation and reattachment points, where, by definition, +is +zero. This singular behavior causes the predicted results to be erroneous. To overcome this, the standard +law of the wall is modified based on a new scale for the friction velocity following the method proposed +by Launder and Spalding (1974). The modified friction velocity is given by +which does not suffer from a singular behavior at flow reattachment, separation, and at points of flow +impingement. Correspondingly, the wall distances are re-scaled as follows: +The modified law of the wall reduces to the standard law of the wall under the conditions of uniform +wall shear stress, and when the generation and dissipation of turbulent kinetic energy are in balance (i.e., +when the turbulence structure is in equilibrium). Under such conditions, +and thus, +. +The wall shear stress for the modified law of the wall can be evaluated as (Albets-Chico, et al., +2008) +if +if +, +where the subscript p denotes the wall element center at which all the quantities of interest are evaluated. +The use of the wall function requires the modification of the transport equations for k and for the wall +layer of elements. Specifically, the production and dissipation terms in the governing transport equation +for the turbulent kinetic energy k are modified to account for the presence of the wall. +Following the procedure outlined in (Craft et al., 2002), an average value of the production of k as +given below is used in the transport equation. Such an average is obtained based on a two-layer model +of the wall element (i.e., the wall element is divided into a partly viscous sub-layer region and a partly +turbulent log-layer or inertial layer region). +if +if +, +where +is the maximum of the wall normal distances of all the vertices of a given wall element, and +is the wall normal distance of the edge of the viscous sub-layer, where +Similarly, an average value of the dissipation rate for k is also prescribed for the wall elements based +on a two-layer integration and is given by +The transport equation for +is not solved for the wall layer elements. Instead, the value of +is +directly prescribed at the point p as follows: +if +if +. +if +if +. +Therefore, integration of the k and transport equations is performed with a zero-flux (i.e., homogeneous +Neumann boundary conditions) at the walls. +Guidelines on wall functions +The main advantage of wall functions is the relaxed requirement on mesh resolution at walls. However, +the main disadvantage of using wall functions is the dependence on the near-wall mesh resolution. Wall +functions based on the law of the wall approach usually work best for wall elements whose centers lie +in the fully turbulent layer (inertial or log layer) for which such functions are designed. This effectively +imposes a lower limit on the value of the scaled wall coordinate, +. For complex geometries, ensuring +that all the near wall cells are outside the viscous sublayer is difficult. The precise location of the +logarithmic region is solution dependent and may vary with time. To accommodate a more flexible +mesh, a resolution-insensitive wall function (Durbin, 2009) has been implemented. Briefly, this wall +function is based on limiting the minimum value of +such that the value of the velocity gradient at +the first wall-attached element is the same as if it was located on the edge of the viscous sub-layer. A +best practice for wall-bounded flows is to have at least 8–10 points in the boundary layer region where +. +Deforming-mesh ALE +Many industrial CFD/FSI/CHT problems involve moving boundaries or deforming geometries. This +class of problem includes prescribed boundary motion that induces fluid flow or where the boundary +motion is relatively independent of the fluid flow. Abaqus/CFD uses an arbitrary Lagrangian-Eulerian +(ALE) formulation and automated mesh deformation method that preserves element size in boundary +layers. The ALE and deforming-mesh algorithms are activated automatically for problems that involve +a moving boundary prescribed by the user or identified as a moving boundary in an FSI co-simulation. +Abaqus/CFD offers distortion control to prevent elements from inverting or distorting excessively in +fluid mesh movement . +To properly control the mesh motion during a simulation, it is the user’s responsibility to prescribe +appropriate displacement boundary conditions on the computational mesh. +Porous media flows +Flows through fluid-saturated porous media occur in a wide range of industrial and environmental +applications. Such flows can be isothermal (no heat transfer) or non-isothermal in nature. Examples +include packed-bed heat exchangers, heat pipes, thermal insulation, petroleum reservoirs, nuclear waste +repositories, geothermal engineering, thermal management of electronic devices, metal alloy casting, +and flow past porous scaffolds in bioreactors. +Isothermal flows +For isothermal flows in porous media, many studies are usually carried out using the Darcy flow model, +which is an empirical law for creeping flow through an infinitely extended uniform medium. However, +non-Darcian effects such as fluid inertial effects are quite important for certain applications. The model +implemented in Abaqus/CFD is based on the volume-averaged Darcy-Brinkman-Forchheimer equations +that account for both Darcian and inertial non-Darcian effects. The following assumptions are made in +deriving the governing equations: +• the porosity of the medium does not vary with time or the time scale of variation of the porosity is +considered to be much larger than the dominant time scales of the fluid motion; and +• the permeability of the porous medium is isotropic and dependent only on the porosity of the +medium. +Based on the above assumptions, the volume-averaged mass conservation and the Darcy-Brinkman- +Forchheimer momentum equations governing the flow of an incompressible fluid in a fluid-saturated +porous media can be written as follows (Nield and Bejan, 2010): +where +is the extrinsic average or the superficial velocity vector, where the average is taken over a +representative volume incorporating both the solid (matrix) and the fluid phases; +is the intrinsic average of the pressure (average taken only over the fluid-phase); +is the density of the fluid; +is the viscosity of the fluid; +is the porosity (volume fraction of the fluid phase) of the porous medium; and +is the permeability of the porous medium. +The second term on the right-hand side of the momentum equation is the Brinkman term accounting for +the presence of solid boundaries, the third term represents the Darcy drag term (linear in velocity), and the +last term represents the inertial (quadratic in velocity) or the Forchheimer drag. The parameter +is the +inertial drag coefficient (also referred to as the form drag coefficient). Based on Ergun’s equation (Nield +and Bejan, 2010), +. +The porous drag forces (namely, the Darcy and Forchheimer drag forces) are activated for a prescribed +element set by specifying them as distributed loads . +is a constant that is set to a default value of +, where +Thus, +, of the porous medium. The default value of +the porous media flow problem requires the specification of the porosity, +, and the +permeability, +can also be changed in the material +property definition . For the case of turbulent flow within a porous +medium, the fluid viscosity +includes the contribution of both the molecular and the turbulent eddy +viscosities. +For conjugate flows involving domains consisting of both pure fluid regions and fluid-saturated +porous media, the pure fluid porosity is set to a value of 1 by default. +Permeability-Porosity relationships +The permeability of a porous medium is generally a function of the physical properties of the +interconnected pore system such as porosity and tortuosity. Determination of the appropriate +permeability-porosity relationship requires a detailed knowledge of the size distribution and spatial +arrangement of the pore channels in the porous medium. The permeability-porosity relation can be +specified directly in Abaqus/CFD using the material property definition. +Another permeability-porosity relation supported in Abaqus/CFD is the widely accepted Carman- +Kozeny model. This relation is given as follows: +where +particles/fibers. +represents the Carman-Kozeny constant and +represents the average radius of the porous +Limitations +• While turbulence can be activated for a porous media flow problem, a rigorous volume-averaging +procedure has not been implemented in Abaqus/CFD to account for turbulence transport within +the porous media. The equations governing the transport of the turbulence variables are solved +by neglecting the effects of the presence of porous medium. In other words, the porous medium +remains transparent (fully open) to the transport of turbulence variables. +• When the arbitrary Lagrangian-Eulerian (ALE) and deforming mesh algorithms are activated for a +porous flow problem, changes in the porosity of the medium associated with large mesh/domain +deformations are not taken into account. The model is strictly valid only for the case of +undeformable porous media. +Non-isothermal flows (heat transfer) +The following assumptions are made in the implementation of the volume-averaged energy equation for +porous media in Abaqus/CFD: +• The medium is isotropic. +• Radiative effects, viscous dissipation, and work done by the changes in pressure are negligible. +• Local thermal equilibrium is valid (i.e., solid and fluid phase temperatures are the same). +• No net heat transfer takes place between the different phases in the porous media. +Based on the above assumptions, the effective energy equation for the porous medium can be given as +follows (Nield and Bejan, 2010): +where +and +Here, +, +, and +is the extrinsic average or the superficial velocity vector, and +denote the fluid phase, solid (matrix) phase, and effective medium, respectively. +the specific heat capacity at constant pressure, +heat production per unit volume or the heat source ( +heat transfer within a porous medium, the fluid conductivity +molecular and turbulent eddy conductivities. +is the thermal conductivity, and +is the temperature. The subscripts +is +is the effective +). For the case of turbulent +includes the contribution of both the +As seen from the above equation, the porous media heat transfer problem requires the specification +of the following input: +• The thermal properties of the solid (matrix) phase: the density, +; and +specific heat capacity, +; the conductivity, +; and the +• The thermal properties of the fluid (matrix) phase: the molecular conductivity, +capacity, +, apart from the specification of other fluid properties such as the density, +; and specific heat +, viscosity, +, and permeability, +. +Linear equation solvers +The solution methods for the momentum and auxiliary transport equations in Abaqus/CFD rely on +scalable parallel preconditioned Krylov solvers. The pressure, pressure-increment, and distance +function equations are solved with user-selectable Krylov solvers and a robust algebraic multigrid +preconditioner. A set of preselected default convergence criteria and iteration limits are prescribed for +all linear equation solvers. The default solver settings should provide computationally efficient and +robust solutions across a spectrum of CFD problems. However, full access to diagnostic information, +In practice, the pressure-increment equation +convergence criteria, and optional solvers is provided. +may be the most sensitive linear system and could require user intervention based on knowledge of the +specific flow problem. +Input File Usage: +Use the following option to specify parameters for solving the momentum +transport equations: +*MOMENTUM EQUATION SOLVER +Use the following option to specify parameters for solving other transport +equations, such as the energy or turbulence transport equations: +*TRANSPORT EQUATION SOLVER +Use the following option to specify parameters for solving the pressure +equation: +*PRESSURE EQUATION SOLVER +Convergence criteria and diagnostics +Iterative solvers compute an approximate solution to a given set of equations; therefore, convergence +criteria are required to determine if the solution is acceptable. While default settings should be adequate +for most problems, you can modify the convergence criteria. +In addition to the option of setting +convergence criteria, convergence history output is available that may be useful for some advanced +users to tune the solvers for performance or robustness. For the algebraic multigrid preconditioner, +diagnostic information such as the number of grids, grid sparsity, and largest eigenvalue and condition +number estimates are available upon request. The diagnostic information for the algebraic multigrid +preconditioner is printed every time the preconditioner is computed. +Specifying convergence criteria +The linear convergence limit (also commonly referred to as the convergence tolerance), the frequency +of convergence checking, and the maximum number of iterations can be set. The iterative solver will +stop when the relative residual norm of the system of equations and the relative correction of the solution +norm fall below the convergence limit. +Input File Usage: +Abaqus/CAE Usage: +Use the following options to specify convergence criteria for the momentum +and auxiliary transport equations: +*MOMENTUM EQUATION SOLVER +max iterations, frequency check, convergence limit +*TRANSPORT EQUATION SOLVER +max iterations, frequency check, convergence limit +*PRESSURE EQUATION SOLVER +max iterations, frequency check, convergence limit +Step module: Create Step: General: Flow; Solvers tabbed page: +Momentum Equation, Pressure Equation, or Transport Equation +tabbed page; enter values for Iteration limit, Convergence checking +frequency, and Linear convergence limit +Accessing convergence output +You can monitor the convergence of the iterative solver by accessing convergence output. When you +activate the convergence output, the current relative residual norm and the relative solution correction +norm are output each time the convergence is checked. +Input File Usage: +Abaqus/CAE Usage: +Use the following options to write convergence output to the log file for the +linear equation solvers: +*MOMENTUM EQUATION SOLVER, CONVERGENCE=ON +*TRANSPORT EQUATION SOLVER, CONVERGENCE=ON +*PRESSURE EQUATION SOLVER, CONVERGENCE=ON +Step module: Create Step: General: Flow; Solvers tabbed page: +Momentum Equation, Pressure Equation, or Transport Equation +tabbed page; toggle on Include convergence output +Accessing diagnostic information +Diagnostic output is useful only for the algebraic multigrid preconditioner. For other preconditioners, +only a solver initialization message is printed for diagnostic output. For the algebraic multigrid +preconditioner, +the number of grids, grid sparsity, and largest eigenvalue and condition number +estimates are output each time the preconditioner is computed. +Input File Usage: +Use the following option to write diagnostic output to the log file for the +pressure equation solver using the algebraic multigrid preconditioner: +*PRESSURE EQUATION SOLVER, TYPE=AMG, DIAGNOSTICS=ON +Abaqus/CAE Usage: +Step module: Create Step: General: Flow; Solvers tabbed page: Pressure +Equation tabbed page; toggle on Include diagnostic output +Specifying a solver for the pressure equation +Three solver types are available for the solving the pressure equation. The default AMG solver uses +an algebraic multigrid preconditioner and offers the choice of three Krylov solvers: conjugate gradient, +bi-conjugate gradient stabilized, and flexible generalized minimal residual. The SSORCG solver uses a +symmetric successive over-relaxation preconditioner and conjugate gradient Krylov solver. The DSCG +solver uses a diagonally scaled preconditioner and conjugate gradient Krylov solver. The AMG solver +provides many additional options that are intended for advanced usage and in cases where convergence +difficulties are encountered. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options to specify the solver type: +*PRESSURE EQUATION SOLVER, TYPE=AMG (default) +*PRESSURE EQUATION SOLVER, TYPE=SSORCG +*PRESSURE EQUATION SOLVER, TYPE=DSCG +Use the following option to specify the AMG solver: +Step module: Create Step: General: Flow; Solvers tabbed page: Pressure +Equation tabbed page: Solver options: Use analysis defaults +Use the following option to specify the SSORCG solver: +Step module: Create Step: General: Flow; Solvers tabbed page: Pressure +Equation tabbed page: Solver options: Specify, Preconditioner +Type: Symmetric successive over-relaxation +The DSCG solver is not supported in Abaqus/CAE. +Specifying the complexity level +For the AMG solver, you can choose from three preset levels or you can specify the Krylov solver and +smoother settings directly. The presets are provided for convenience. Preset level 1 is primarily intended +for use with meshes with good element aspect ratios and in some cases may provide a performance +benefit over the default preset level 2. Preset level 3 is intended for problems that encounter convergence +difficulties, which typically have elements with high aspect ratios or highly distorted elements. +Input File Usage: +Preset level 1 corresponds to the following: +*PRESSURE EQUATION SOLVER, TYPE=AMG +250, 2, 10−5 +CHEBYCHEV, 2, 2, CG +Preset level 2 (default) corresponds to the following: +*PRESSURE EQUATION SOLVER, TYPE=AMG +250, 2, 10−5 +ICC, 1, 1, CG +Abaqus/CAE Usage: +Preset level 3 corresponds to the following: +*PRESSURE EQUATION SOLVER, TYPE=AMG +250, 2, 10−5 +ICC, 2, 2, BCGS +Step module: Create Step: General: Flow; Solvers tabbed page: +Pressure Equation tabbed page: Solver options: Specify, +Preconditioner Type: Algebraic multi-grid +Use one of the following options to choose a preset complexity level: +Complexity Level: Preset: 1, 2, or 3 +Use the following option to specify the Krylov solver and smoother settings +directly: +Complexity Level: User defined +Specifying the solver type +Three Krylov solver options are provided for the AMG solver. The default conjugate gradient solver is +the fastest; however, in some cases where convergence difficulties are observed, the bi-conjugate gradient +stabilized or flexible generalized minimal residual solvers are recommended. These two solvers are more +robust but computationally more expensive than the conjugate gradient solver. +Input File Usage: +Use the following option to specify the Krylov solver type: +*PRESSURE EQUATION SOLVER, TYPE=AMG +first data line +, , , solver type +Abaqus/CAE Usage: +where solver type is CG for the conjugate gradient solver (default), BCGS +for the bi-conjugate gradient squared solver, and FGMRES for the flexible +generalized minimum residual solver. +Step module: Create Step: General: Flow; Solvers tabbed page: +Pressure Equation tabbed page: Solver options: Specify, +Preconditioner Type: Algebraic multi-grid +Use one of the following options to specify the Krylov solver: +Solver Type: Conjugate gradient, Bi-conjugate gradient, stabilized, +or Flexible generalized minimal residual +Specifying the residual smoother settings +You can choose between incomplete factorization and polynomial residual smoothers that are used +within the AMG preconditioner. While incomplete factorization is computationally more expensive +than polynomial smoothing, in many cases this cost is amortized by fast convergence and robustness. +Polynomial smoothing is recommended for problems with a very good mesh quality (i.e., no skewed or +large aspect ratio elements). The number of pre- and post-smoothing sweeps can also be specified. It is +recommended that you apply the same number of pre- and post-sweeps. For the polynomial smoother, +a minimum of two pre- and post-sweeps are recommended. +Input File Usage: +Use the following option to specify the residual smoother settings: +*PRESSURE EQUATION SOLVER, TYPE=AMG +first data line +smoother, pre-smoothing sweeps, post-smoothing sweeps +Abaqus/CAE Usage: +Step module: Create Step: General: Flow; Solvers tabbed page: Pressure +Equation tabbed page: Solver options: Specify, Preconditioner Type: +Algebraic multi-grid, Residual Smoother: Incomplete factorization or +Polynomial, Pre-sweeps: select number, Post-sweeps: select number +Time incrementation +Abaqus/CFD uses second-order time-accurate integration by default, where all diffusive terms, +advective terms, and body forces are integrated with the trapezoidal rule (Crank-Nicolson method). +The default method is “second-order accurate” in that truncation errors within a time increment are +proportional to the time increment squared, thus they decrease by a factor of four if the time increment +is halved. You can individually select alternative time integrators for each of these terms. A fully +implicit advection treatment is also available, which is particularly useful for quickly advancing toward +steady-state solutions. +Time increment size control +By default, Abaqus/CFD uses an automatic time incrementation algorithm that continually adjusts the +time increment size to satisfy the Courant-Friedrichs-Lewy (CFL) stability condition for advection. The +default value, CFL=0.45, guarantees the solution’s stability. You can further limit the automatically +computed time increment size by specifying a maximum value. You can also specify an initial time +increment size. This value is automatically decreased as necessary to satisfy a maximum initial CFL +value of 0.45 based on the starting conditions of the flow. +Alternatively, you can select fixed time incrementation and specify the time increment size. In this +case the time increment size remains constant throughout the step, but stability is not guaranteed. +Input File Usage: +Use the following option to specify automatic time incrementation (default): +*CFD, INCREMENTATION=FIXED CFL +time increment, time period, scale factor, suggested CFL, check increment, +max allowable time increment +divergence tolerance, +, +, , +Use the following option to specify fixed time step incrementation: +*CFD, INCREMENTATION=FIXED STEP SIZE +time increment, time period, +divergence tolerance, +, , +, +For both options above, +can be set to 0.5 for the Crank-Nicolson method +(default), 0.6667 for the Galerkin method, or 1 for the first-order backward- +Euler method. +Abaqus/CAE Usage: +Use the following options to specify automatic time incrementation: +Step module: Create Step: General: Flow; Basic tabbed page: +enter a value for Time period; Incrementation tabbed page: Type: +Automatic (Fixed CFL); enter values for Initial time increment, +Maximum CFL number, Increment adjustment frequency, Time +step growth scale factor, Divergence tolerance +Use the following option to specify fixed time step incrementation: +Step module: Create Step: General: Flow; Basic tabbed page: enter a +value for Time period; Incrementation tabbed page: Type: Fixed, enter +values for Time increment and Divergence tolerance +Use the following options to specify the time integration method for +viscous/diffusive terms, boundary conditions, and advective terms: +Viscous, Load/Boundary condition, or Advective: Trapezoid +(1/2), Galerkin (2/3), or Backward-Euler (1) +Time-accurate analysis +The time integration parameters are all set by default to +, which produces a second order–accurate +semi-implicit method suitable for time-accurate transient analysis. When automatic time incrementation +is used, you should specify CFL +to maintain stability and time accuracy. +Steady-state analysis +In analyses where the goal is to reach a steady-state solution, the fully implicit (backward-Euler) method +can be activated by setting all time integration parameters to +. This method is unconditionally +stable, allowing you to specify large CFL values to significantly increase the time increment size. Strict +guidelines for selecting the maximum allowable CFL number are not available, and this maximum value +may vary for different flows and meshes. CFL values of 10 or more have been used successfully for +some analyses where only the final result is of interest. +Monitoring output variables +Abaqus/CFD provides a number of output variables that are useful for monitoring the health of a +calculation and are good indicators for situations where the flow has reached a steady-state condition. +These variables are written to the status (.sta) file and can be examined as the analysis job is executing. +The RMS divergence output variable is useful for determining if a calculation is proceeding normally. +Values of the RMS divergence output variable that are O(1) can indicate that the problem is incorrectly +specified or that the calculation has become unstable. The global kinetic energy (KE) provides a good +indicator for when the flow has reached a steady state; i.e., when the kinetic energy asymptotically +approaches a constant value, the flow is typically achieving a steady-state condition where the velocities +and pressure do not vary in time. Alternatively, the global kinetic energy can indicate a steady-periodic +or chaotic flow situation as well. +Initial conditions +Initial conditions for the density, velocity, temperature, turbulent eddy viscosity, turbulent kinetic energy, +and dissipation rate can be specified . If the +density is omitted, the specified material density is used for incompressible flow simulations. +For a well-posed incompressible flow problem, the initial velocity must satisfy the boundary +conditions and also the imposed divergence-free condition; i.e., the solvability conditions. Abaqus/CFD +automatically uses the user-defined boundary conditions and tests the specified velocity initial conditions +to be sure the solvability conditions are satisfied. If they are not, the initial velocity is projected onto +a divergence-free subspace, yielding initial conditions that define a well-posed incompressible +Navier-Stokes problem. Therefore, in some circumstances, user-specified velocity initial conditions +may be overridden with velocity conditions that satisfy solvability. +Boundary conditions +temperature, pressure, and eddy viscosity can be defined . During the analysis prescribed boundary +conditions can be varied using an amplitude definition . All +amplitude definitions except smooth step and solution-dependent amplitudes are available. By default, +all boundary conditions are applied instantaneously. Velocity and pressure boundary conditions can +be specified via user subroutines . +Displacement and velocity boundary conditions at FSI interfaces are prescribed automatically +by the definition of a co-simulation region; therefore, you should not prescribe these conditions at an +FSI interface. Similarly, you should not define the temperature at a CHT interface; the temperature +is automatically prescribed by the definition of a co-simulation region. For more information, see +“Preparing an Abaqus analysis for co-simulation,” Section 17.2.1. +The specification of no-slip/no-penetration boundary conditions at walls requires the specification +of the turbulent eddy viscosity and normal-distance function, which is handled automatically by +Abaqus/CFD. +Hydrostatic pressure condition +In incompressible flows, the pressure is only known within an arbitrary additive constant value or the +hydrostatic pressure. In many practical situations, the pressure at an outflow boundary may be prescribed, +which, in effect, sets the hydrostatic pressure level. In cases where there is no pressure prescribed, it is +necessary to set the hydrostatic pressure level at a minimum of one node in the mesh. +The fluid reference pressure can be used to specify the hydrostatic pressure level. When there are +no prescribed pressure boundary conditions, the fluid reference pressure establishes the hydrostatic +pressure level and makes the pressure-increment equation non-singular. If pressure boundary conditions +are prescribed in addition to the reference pressure level, the reference pressure simply adjusts the +output pressures according to the specified pressure level. For more information, see “Specifying a fluid +reference pressure” in “Concentrated loads,” Section 33.4.2. +Loads +The loading types for Abaqus/CFD include applied heat flux, volumetric heat-generation sources, +general body forces, and gravity loading. Gravity loading defines the gravity vector used with a +Boussinesq-type body force in buoyancy driven flow . Gravity loading can be used only in conjunction with the energy equation and +will be ignored if used without the energy equation. During the analysis prescribed loads can be varied +using an amplitude definition . All amplitude definitions +except smooth step and solution-dependent amplitudes are available. +Material options +Material definitions in Abaqus/CFD follow the Abaqus conventions but also present several material +properties specific to fluid dynamics. In Abaqus/CFD the typical material properties include viscosity, +constant-pressure specific heat, density, and coefficient of thermal expansion. The thermal expansion is +used with a Boussinesq-type body force in buoyancy driven flow. +In contrast to Abaqus/Standard and Abaqus/Explicit, which use the constant-volume specific +heat, the constant-pressure specific heat is required when the energy equation is used for thermal-flow +problems. For problems involving an ideal gas, the user may optionally specify constant-volume +specific heat and the ideal gas constant. +Elements +Abaqus/CFD supports three element types: the 8-node hexahedral element, FC3D8; the 6-node triangular +prism element, FC3D6; and the 4-node tetrahedral element, FC3D4 elements,” +Section 28.2.1). These elements cannot be mixed in a single connected fluid domain. However, a single +flow model can contain multiple domains, each with a different element type. +Output +The output available from Abaqus/CFD for an incompressible fluid dynamic analysis includes both nodal +and surface field data and element and surface time-history data. For the nodal and element output, the +preselected field and history data include velocity (V), temperature (TEMP), pressure (PRESSURE), +and turbulent eddy viscosity (TURBNU). In addition, preselected field data include displacement (U). +Preselected data are not available for surface output. +In addition to the preselected output, you can request several derived and auxiliary variables. All of +the output variable identifiers are outlined in “Abaqus/CFD output variable identifiers,” Section 4.2.3. +Input file template +*HEADING +… +*NODE +… +*ELEMENT, TYPE=FC3D4 +… +*MATERIAL, NAME=matname +*CONDUCTIVITY +Data lines to define the thermal conductivity +*DENSITY +Data lines to define the fluid density +*SPECIFIC HEAT, TYPE=CONSTANT PRESSURE +Data lines to define the specific heat +*VISCOSITY +Data lines to define the fluid viscosity +*INITIAL CONDITIONS, TYPE=TEMPERATURE, ELEMENT AVERAGE +Data lines to prescribe initial temperatures at the elements +*INITIAL CONDITIONS, TYPE=VELX, ELEMENT AVERAGE +Data lines to prescribe initial x-velocity at the elements +*INITIAL CONDITIONS, TYPE=VELY, ELEMENT AVERAGE +Data lines to prescribe initial y-velocity at the elements +*INITIAL CONDITIONS, TYPE=VELY, ELEMENT AVERAGE +Data lines to prescribe initial y-velocity at the elements +… +*AMPLITUDE, NAME=velxamp, DEFINITION=TABULAR +Data lines to define amplitude curve to be used for inlet x-velocity +** +*STEP +** Incompressible flow example +*CFD, INCOMPRESSIBLE NAVIER STOKES, INCREMENTATION=FIXED CFL +Data lines to define incrementation +** +** Boundary conditions +** +*FLUID BOUNDARY, TYPE=SURFACE +inlet_surface, VELX, value for x-velocity +inlet_surface, VELY, value for y-velocity +inlet_surface, VELZ, value for z-velocity +** +*FLUID BOUNDARY, TYPE=SURFACE +temperature_surface, TEMP, value for temperature +** +*FLUID BOUNDARY, TYPE=SURFACE +outlet_surface, P, value for pressure +** +** Field output +** +*OUTPUT, FIELD, TIME INTERVAL=interval for field output +*ELEMENT OUTPUT +PRESSURE, TEMP, TURBNU, V +*NODE OUTPUT +PRESSURE, TEMP, TURBNU, V +** +** History output +** +*OUTPUT, HISTORY, FREQUENCY=interval for history output +*ELEMENT OUTPUT, ELSET=element set for history output, FREQUENCY=SURFACE +… +*END STEP +Additional references +• Albets-Chico, X., C. D. Perez-Segarra, A. Olivia, and J. Bredberg, “Analysis of Wall-Function +Approaches using Two-Equation Turbulence Models,” International Journal of Heat and Mass +Transfer, vol. 51, p. 4940–4957, 2008. +• Casey, M., and T. Wintergerste, ERCOFTAC Special Interest Group on “Quality and Trust +in Industrial CFD”, European Research Community on Flow, Turbulence and Combustion +(ERCOFTAC), 2000. +• Craft, T. J., A. V. Gerasimov, H. Iacovides, and B. E. Launder, “Progress in the Generalization +of Wall-Function Treatments,” International Journal of Heat and Fluid Flow, vol. 23, p. 148–160, +2002. +• Durbin, P. A., “Limiters and wall treatments in applied turbulence modeling,” Fluid Dynamics +research, vol. 41, p. 1–17, 2009. +• Launder, B. E., and D. B. Spalding, “The Numerical Computation of Turbulent Flows,” Computer +Methods in Applied Mechanics and Engineering, vol. 3, p. 269–289, 1974. +• Nield, D.A., and A. Bejan, Convection in Porous Media, Springer, New York, Third edition, 2010. +• Yakhot, V., S. A. Orszag, S. Thangam, T. B. Gatski, and C. G. Speziale, “Development of +Turbulence Models for Shear Flows by a Double Expansion Technique,” Physics of Fluids A, +vol. 4, no. 7, p. 1510–1520, 1992. +6.7 +Electromagnetic analysis +• “Electromagnetic analysis procedures,” Section 6.7.1 +• “Piezoelectric analysis,” Section 6.7.2 +• “Coupled thermal-electrical analysis,” Section 6.7.3 +• “Fully coupled thermal-electrical-structural analysis,” Section 6.7.4 +• “Eddy current analysis,” Section 6.7.5 +• “Magnetostatic analysis,” Section 6.7.6 +6.7.1 +ELECTROMAGNETIC ANALYSIS PROCEDURES +Overview +Abaqus/Standard offers several analysis procedures to model piezoelectric, electrical conduction, +and electromagnetic phenomena. The distinct electrical phenomena modeled by these procedures is +described first, followed by a brief overview of each procedure. +Electrostatic, electrical conduction, magnetostatic, and electromagnetic analyses +Piezoelectric effect is the electromechanical interaction exhibited by some materials. This coupled +electrostatic-structural response is modeled using piezoelectric analysis in Abaqus/Standard. +In this +procedure the electric potential is a degree of freedom and its conjugate is the electric charge. +Coupled thermal-electrical conduction, with or without structural coupling, is modeled using +electrical procedures. In these procedures the electric potential is a degree of freedom and its conjugate +is the electric current. While transient effects are ignored in electrical conduction, thus making it steady +state, thermal fields can be modeled either as transient or steady state. +Magnetostatic analysis is used to compute the magnetic fields due to direct currents. +It solves +the magnetostatic approximation to Maxwell’s equations. The magnetic vector potential is a degree +of freedom in a magnetostatic analysis, and its conjugate is the surface current. +Electromagnetic analysis is used to model the full coupling between time-varying electric and +magnetic fields by solving Maxwell’s equations. In such an analysis the magnetic vector potential is a +degree of freedom and its conjugate is the surface current. +Electrostatic procedure +The following electrostatic analysis procedure is available in Abaqus/Standard: +• Piezoelectric analysis: +In a piezoelectric material an electric potential gradient causes straining, +while stress causes an electric potential in the material (“Piezoelectric analysis,” Section 6.7.2). This +coupling is provided by defining the piezoelectric and dielectric coefficients of a material and can +be used in natural frequency extraction, transient dynamic analysis, both linear and nonlinear static +stress analysis, and steady-state dynamic analysis procedures. In all procedures, including nonlinear +statics and dynamics, the piezoelectric behavior is always assumed to be linear. +Steady electrical conduction procedures +The following electrical conduction analyses procedures are available in Abaqus/Standard: +• Coupled thermal-electrical analysis: The electric potential and temperature fields can +be solved simultaneously by performing a coupled thermal-electrical analysis (“Coupled +In these problems the energy dissipated by an +thermal-electrical analysis,” Section 6.7.3). +electrical current flowing through a conductor is converted into thermal energy, and the electrical +conductivity can, in turn, be temperature dependent. Thermal loads can be applied, but deformation +of the structure is not considered. Coupled thermal-electrical problems can be linear or nonlinear. +• Fully coupled thermal-electrical-structural analysis: A coupled thermal-electrical-structural +analysis is used to solve simultaneously for the stress/displacement, the electric potential, and the +temperature fields. A coupled analysis is used when the thermal, electrical, and mechanical solutions +affect each other strongly. An example of such a process is resistance spot welding, where two or +more metal parts are joined by fusion at discrete points at the material interface. The fusion is caused +by heat generated due to the current flow at the contact points, which depends on the pressure applied +at these points. +These problems can be transient or steady state and linear or nonlinear. Cavity radiation effects +cannot be included in a fully coupled thermal-electrical-structural analysis. See “Fully coupled +thermal-electrical-structural analysis,” Section 6.7.4, for more details. +Magnetostatic procedure +The following magnetostatic analysis procedure is available in Abaqus/Standard: +• Magnetostatic analysis: A magnetostatic analysis is used to solve for the magnetic vector +potential, from which the magnetic field is computed in the entire domain. For example, the +magnetic field due to the flow of direct current can be modeled. The procedure supports linear as +well as nonlinear magnetic material properties. See “Magnetostatic analysis,” Section 6.7.6, for +more details. +Electromagnetic procedures +Electromagnetic analyses are used to solve for the magnetic vector potential, from which both electric and +magnetic fields are computed in the entire domain. The following electromagnetic analysis procedures +are available in Abaqus/Standard: +• Time-harmonic eddy current analysis: This procedure assumes time-harmonic excitation and +It supports linear electrical conductivity and linear magnetic material behavior. For +response. +example, eddy currents induced in a workpiece that is in the vicinity of a source of excitation (such +as a coil carrying alternating current) can be modeled. See “Time-harmonic analysis” in “Eddy +current analysis,” Section 6.7.5, for more details. +• Transient eddy current analysis: This procedure assumes general time variation of the +excitation and response. It supports linear electrical conductivity and both linear and nonlinear +magnetic material behavior. For example, eddy currents induced in a workpiece that is in the +vicinity of a source of excitation (such as a coil carrying time-varying current) can be modeled. +See “Transient analysis” in “Eddy current analysis,” Section 6.7.5, for more details. +6.7.2 +PIEZOELECTRIC ANALYSIS +Products: Abaqus/Standard Abaqus/CAE +References +• “Piezoelectric behavior,” Section 26.5.2 +• “Defining an analysis,” Section 6.1.2 +• “Electromagnetic analysis procedures,” Section 6.7.1 +• “Defining a concentrated charge,” Section 16.9.30 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Defining a surface charge,” Section 16.9.31 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Defining a body charge,” Section 16.9.32 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +Coupled piezoelectric problems: +• are those in which an electric potential gradient causes straining, while stress causes an electric +potential gradient in the material; +• are solved using an eigenfrequency extraction, modal dynamic, static, dynamic, or steady-state +dynamic procedure; +• require the use of piezoelectric elements and piezoelectric material properties; +• can be performed for continuum problems in one, two, and three dimensions; and +• can be used in both linear and nonlinear analysis (however, in nonlinear analysis the piezoelectric +part of the constitutive behavior is assumed to be linear). +Piezoelectric response +The electrical response of a piezoelectric material is assumed to be made up of piezoelectric and dielectric +effects: +where +is the electrical potential, +is the component of the electric flux vector (also known as the electric displacement) in the +ith material direction, +is the piezoelectric stress coupling, +is a small-strain component, +is the material’s dielectric matrix for a fully constrained material, and +is the gradient of the electrical potential along the ith material direction, +. +Defining piezoelectric and dielectric properties is discussed in “Piezoelectric behavior,” Section 26.5.2. +The theoretical basis of the piezoelectric analysis capability in Abaqus is defined in “Piezoelectric +analysis,” Section 2.10.1 of the Abaqus Theory Manual. +Procedures available for piezoelectric analysis +Piezoelectric analysis can be carried out with the following procedures: +• “Static stress analysis,” Section 6.2.2 +• “Implicit dynamic analysis using direct integration,” Section 6.3.2 +• “Direct-solution steady-state dynamic analysis,” Section 6.3.4 +• “Natural frequency extraction,” Section 6.3.5 +• “Transient modal dynamic analysis,” Section 6.3.7 +• “Mode-based steady-state dynamic analysis,” Section 6.3.8 +• “Subspace-based steady-state dynamic analysis,” Section 6.3.9 +Initial conditions +Initial conditions of piezoelectric quantities cannot be specified. +See “Initial conditions in +Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1, for a description of the initial conditions that +can be applied in static or dynamic procedures. +Boundary conditions +The electric potential at a node (degree of freedom 9) can be prescribed using a boundary condition +. Displacement +and rotation degrees of freedom can also be prescribed by using boundary conditions as described in the +relevant static and dynamic analysis procedure sections. See “Boundary conditions in Abaqus/Standard +and Abaqus/Explicit,” Section 33.3.1. +Boundary conditions can be prescribed as functions of time by referring to amplitude curves +(“Amplitude curves,” Section 33.1.2). +In an eigenfrequency extraction step (“Natural frequency extraction,” Section 6.3.5 ) involving +piezoelectric elements, the electric potential degree of freedom must be constrained at least at one node +to remove singularities from the dielectric part of the element operator. +Loads +Both mechanical and electrical loads can be applied in a piezoelectric analysis. +Applying mechanical loads +The following types of mechanical loads can be prescribed in a piezoelectric analysis: +• Concentrated nodal forces can be applied to the displacement degrees of freedom (1–6); see +“Concentrated loads,” Section 33.4.2. +• Distributed pressure forces or body forces can be applied; see “Distributed loads,” Section 33.4.3. +Applying electrical loads +The following types of electrical loads can be prescribed, as described in “Electromagnetic loads,” +Section 33.4.5: +• Concentrated electric charge. +• Distributed surface electric charge and body electric charge. +Loading in mode-based and subspace-based procedures +Electrical charge loads should be used only in conjunction with residual modes in the eigenvalue +extraction step, due to the “massless” mode effect. Since the electrical potential degrees of freedom do +not have any associated mass, these degrees of freedom are essentially eliminated (similar to Guyan +reduction or mass condensation) during the eigenvalue extraction. The residual modes represent +the static response corresponding to the electrical charge loads, which will adequately represent the +potential degree of freedom in the eigenspace. +Predefined fields +The following predefined fields can be specified in a piezoelectric analysis, as described in “Predefined +fields,” Section 33.6.1: +• Although temperature is not a degree of freedom in piezoelectric elements, nodal temperatures can +be specified. The specified temperature affects only temperature-dependent material properties, if +any. +• The values of user-defined field variables can be specified. These values affect only field-variable- +dependent material properties, if any. +Material options +The piezoelectric coupling matrix and the dielectric matrix are specified as part of the material definition +for piezoelectric materials, as described in “Piezoelectric behavior,” Section 26.5.2. They are relevant +only when the material definition is used with coupled piezoelectric elements. +The mechanical behavior of the material can include linear elasticity only (“Linear elastic behavior,” +Section 22.2.1). +Elements +Piezoelectric elements must be used in a piezoelectric analysis . The electric potential, +, is degree of freedom 9 at each node of +these elements. In addition, regular stress/displacement elements can be used in parts of the model where +piezoelectric effects do not need to be considered. +Output +The following output variables are applicable to the electrical solution in a piezoelectric analysis: +Element integration point variables: +EENER +EPG +EPGM +EPGn +EFLX +EFLXM +EFLXn +Electrostatic energy density. +Magnitude and components of the electrical potential gradient vector, +Magnitude of the electrical potential gradient vector. +Component n of the electrical potential gradient vector (n=1, 2, 3). +Magnitude and components of the electrical flux (displacement) vector, +Magnitude of the electrical flux (displacement) vector. +Component n of the electrical flux (displacement) vector (n=1, 2, 3). +. +. +Whole element variables: +CHRGS +ELCTE +Values of distributed electrical charges. +Total electrostatic energy in the element, +. +Nodal variables: +EPOT +RCHG +CECHG +Input file template +Electrical potential degree of freedom at a node. +Reactive electrical nodal charge (conjugate to prescribed electrical potential). +Concentrated electrical nodal charge. +*HEADING +… +*MATERIAL, NAME=matl +*ELASTIC +Data lines to define linear elasticity +*PIEZOELECTRIC +Data lines to define piezoelectric behavior +*DIELECTRIC +Data lines to define dielectric behavior +… +*AMPLITUDE, NAME=name +Data lines to define amplitude curve for defining concentrated electric charge +** +*STEP, (optionally NLGEOM) +*STATIC +** or *DYNAMIC, *FREQUENCY, *MODAL DYNAMIC, +** *STEADY STATE DYNAMICS (, DIRECT or , SUBSPACE PROJECTION) +*BOUNDARY +Data lines to define boundary conditions on electrical potential and +displacement (rotation) degrees of freedom +*CECHARGE, AMPLITUDE=name +Data lines to define time-dependent concentrated electric charges +*DECHARGE and/or *DSECHARGE +Data lines to define distributed electric charges +*CLOAD and/or *DLOAD and/or *DSLOAD +Data lines to define mechanical loading +*END STEP +6.7.3 +COUPLED THERMAL-ELECTRICAL ANALYSIS +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “Electromagnetic analysis procedures,” Section 6.7.1 +• “Electrical conductivity,” Section 26.5.1 +• *COUPLED THERMAL-ELECTRICAL +• *JOULE HEAT FRACTION +• “Specifying a joule heat fraction,” Section 12.10.4 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Configuring a fully coupled, simultaneous heat transfer and electrical procedure” in “Configuring +general analysis procedures,” Section 14.11.1 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +Coupled thermal-electrical problems: +• are those in which coupling between the electrical potential and temperature fields make it necessary +to solve both fields simultaneously; +• require the use of coupled thermal-electrical elements, although pure heat transfer elements can also +be used in the model; +• can include a specification of the fraction of electrical energy that will be released as heat; +• can include thermal interactions such as gap radiation, gap conductance, and heat generation +between surfaces ; +• can include cavity radiation effects ; +• can include electrical interactions such as electrical current flowing across surfaces ; +• allow for transient or steady-state thermal solutions and for steady-state electrical solutions; and +• can be linear or nonlinear. +Coupled thermal-electrical analysis +Joule heating arises when the energy dissipated by an electrical current flowing through a conductor is +converted into thermal energy. Abaqus/Standard provides a fully coupled thermal-electrical procedure +for analyzing this type of problem: the coupled thermal-electrical equations are solved simultaneously +for both temperature and electrical potential at the nodes. +The capability includes the analysis of the electrical problem, the thermal problem, and the +temperature-dependent +coupling between the two problems. Coupling arises from two sources: +electrical conductivity and internal heat generation, which is a function of the electrical current density. +The thermal part of the problem can include heat conduction and heat storage (“Thermal properties: +overview,” Section 26.2.1) as well as cavity radiation effects (“Cavity radiation,” Section 40.1.1). +Forced convection caused by fluid flowing through the mesh is not considered. +The thermal-electrical equations are unsymmetric; therefore, the unsymmetric solver is invoked +automatically if you request coupled thermal-electrical analysis. For problems where coupling between +the thermal and electrical solutions is weak or where a pure electrical conduction analysis is required +for the entire model, the unsymmetric terms resulting from the interfield coupling may be small or zero. +In these problems you can invoke the less costly symmetric storage and solution scheme by solving +the thermal and electrical equations separately. The separated technique uses the symmetric solver by +default. The thermal-electrical solution schemes are discussed below. +The theoretical basis of coupled thermal-electrical analysis is described in detail in “Coupled +thermal-electrical analysis,” Section 2.12.1 of the Abaqus Theory Manual. +Governing electric field equation +The electric field in a conducting material is governed by Maxwell’s equation of conservation of charge. +Assuming steady-state direct current, the equation reduces to +where V is any control volume whose surface is S, +density (current per unit area), and +is the outward normal to S, +is the electrical current +is the internal volumetric current source per unit volume. +The flow of electrical current is described by Ohm’s law: +where +) +, +is the electrical field intensity, defined as the negative of the gradient of the +electrical potential +is the electrical potential, +is the electrical conductivity matrix, +is the temperature, and +are predefined field variables. +Using Ohm’s law in the conservation equation, written in variational form, provides the governing +equation of the finite element model: +where +is the current density entering the control volume across S. +Defining the electrical conductivity +The electrical conductivity, +, can be isotropic, orthotropic, or fully anisotropic . Ohm’s law assumes that the electrical conductivity is independent of the +electrical field, +. The coupled thermal-electrical problem is nonlinear when the electrical conductivity +depends on temperature. +Specifying the amount of thermal energy generated due to electrical current +Joule’s law describes the rate of electrical energy, +as +, dissipated by current flowing through a conductor +The amount of this energy released as internal heat within the body is +conversion factor. You specify +is converted into heat ( +The fraction given can include a unit conversion factor, if required. +is an energy +in the material definition. It is assumed that all the electrical energy +) if you do not include the joule heat fraction in the material description. +, where +Input File Usage: +Abaqus/CAE Usage: +*JOULE HEAT FRACTION +Property module: material editor: Thermal→Joule Heat Fraction +Steady-state analysis +Steady-state analysis provides the steady-state solution directly. Steady-state thermal analysis means that +the internal energy term (the specific heat term) in the governing heat transfer equation is omitted. Only +direct current is considered in the electrical problem, and it is assumed that the system has negligible +capacitance. (Electrical transient effects are so rapid that they can be neglected.) +Input File Usage: +Abaqus/CAE Usage: +*COUPLED THERMAL-ELECTRICAL, STEADY STATE +Step module: Create Step: General: Coupled thermal-electric: +Basic: Response: Steady state +Assigning a “time” scale to the analysis +A steady-state analysis has no intrinsic physically meaningful time scale. Nevertheless, you can assign +a “time” scale to the analysis step, which is often convenient for output identification and for specifying +prescribed temperatures, electrical potential, and fluxes (heat flux and current density) with varying +magnitudes. Thus, when steady-state analysis is chosen, you specify a “time” period and “time” +incrementation parameters for the step; Abaqus/Standard then increments through the step accordingly. +Any fluxes or boundary condition changes to be applied during a steady-state step should be +given using appropriate amplitude references to specify their “time” variations (“Amplitude curves,” +If fluxes and boundary conditions are specified for the step without amplitude +Section 33.1.2). +references, they are assumed to change linearly with “time” during the step—from their magnitudes at +the end of the previous step (or zero, if this is the beginning of the analysis) to their newly specified +magnitudes at the end of this step . +Transient analysis +Alternatively, +the thermal portion of the coupled thermal-electrical problem can be considered +transient. As in steady-state analysis, electrical transient effects are neglected. See “Uncoupled heat +transfer analysis,” Section 6.5.2, for a more detailed description of the heat transfer capability in +Abaqus/Standard. +Input File Usage: +Abaqus/CAE Usage: +*COUPLED THERMAL-ELECTRICAL +Step module: Create Step: General: Coupled thermal-electric: +Basic: Response: Transient +Time incrementation +Time integration in the transient heat transfer problem is done with the same backward Euler method +used in uncoupled heat transfer analysis. This method is unconditionally stable for linear problems. +You can specify the time increments directly, or Abaqus can select them automatically based on a user- +prescribed maximum nodal temperature change in an increment. Automatic time incrementation is +generally preferred. +Automatic incrementation +The time increment size can be selected automatically based on a user-prescribed maximum allowable +nodal temperature change in an increment, +. Abaqus/Standard will restrict the time increments to +ensure that these values are not exceeded at any node (except nodes with boundary conditions) during +any increment of the analysis . +Input File Usage: +Abaqus/CAE Usage: +*COUPLED THERMAL-ELECTRICAL, DELTMX= +Step module: Create Step: General: Coupled thermal-electric: Basic: +Response: Transient; Incrementation: Type: Automatic: Max. +allowable temperature change per increment: +Fixed incrementation +If you select fixed time incrementation and do not specify +user-specified initial time increment, +, will then be used throughout the analysis. +, fixed time increments equal to the +Input File Usage: +*COUPLED THERMAL-ELECTRICAL +Abaqus/CAE Usage: +Step module: Create Step: General: Coupled thermal-electric: Basic: +Response: Transient; Incrementation: Type: Fixed: Increment size: +Spurious oscillations due to small time increments +In transient heat transfer analysis with second-order elements there is a relationship between the +minimum usable time increment and the element size. A simple guideline is +where +is the time increment, +is the density, c is the specific heat, k is the thermal conductivity, and +is a typical element dimension (such as the length of a side of an element). If time increments smaller +than this value are used in a mesh of second-order elements, spurious oscillations can appear in the +solution, in particular in the vicinity of boundaries with rapid temperature changes. These oscillations +are nonphysical and may cause problems if temperature-dependent material properties are present. +In transient analyses using first-order elements the heat capacity terms are lumped, which eliminates +such oscillations but can lead to locally inaccurate solutions for small time increments. If smaller time +increments are required, a finer mesh should be used in regions where the temperature changes rapidly. +There is no upper limit on the time increment size (the integration procedure is unconditionally +stable) unless nonlinearities cause convergence problems. +Ending a transient analysis +By default, a transient analysis will end when the specified time period has been completed. Alternatively, +you can specify that the analysis should continue until steady-state conditions are reached. Steady state +is defined by the temperature change rate; when the temperature changes at a rate that is less than the +user-specified rate (given as part of the step definition), the analysis terminates. +Input File Usage: +Use the following option to end the analysis when the time period is reached: +*COUPLED THERMAL-ELECTRICAL, END=PERIOD (default) +Use the following option to end the analysis based on the temperature change +rate: +*COUPLED THERMAL-ELECTRICAL, END=SS +Step module: Create Step: General: Coupled thermal-electric: +Basic: Response: Transient; Incrementation: End step when +temperature change is less than +Abaqus/CAE Usage: +Fully coupled solution schemes +Abaqus/Standard offers an exact as well as an approximate implementation of Newton’s method for +coupled thermal-electrical analysis. +Exact implementation +An exact implementation of Newton’s method involves a nonsymmetric Jacobian matrix as is illustrated +in the following matrix representation of the coupled equations: +where +and +are submatrices of the fully coupled Jacobian matrix, and +are the respective corrections to the incremental electrical potential and temperature, +are the electrical and thermal +and +residual vectors, respectively. +Solving this system of equations requires the use of the unsymmetric matrix storage and solution +scheme. Furthermore, the electrical and thermal equations must be solved simultaneously. The method +provides quadratic convergence when the solution estimate is within the radius of convergence of the +algorithm. The exact implementation is used by default. +Approximate implementation +Some problems require a fully coupled analysis in the sense that the electrical and thermal solutions +In other words, the +evolve simultaneously, but with a weak coupling between the two solutions. +components in the off-diagonal submatrices +are small compared to the components in the +diagonal submatrices +. For these problems a less costly solution may be obtained by setting +the off-diagonal submatrices to zero, so that we obtain an approximate set of equations: +, +, +As a result of this approximation the electrical and thermal equations can be solved separately, with +fewer equations to consider in each subproblem. The savings due to this approximation, measured as +solver time per iteration, will be of the order of a factor of two, with similar significant savings in solver +storage of the factored stiffness matrix. Further, in situations without strong thermal loading due to cavity +radiation, the subproblems may be fully symmetric or approximated as symmetric, so that the less costly +symmetric storage and solution scheme can be used. The solver time savings for a symmetric solution is +an additional factor of two. Unless you explicitly select the unsymmetric solver for the step (“Defining +an analysis,” Section 6.1.2), the symmetric solver will be used with this separated technique. +This modified form of Newton’s method does not affect solution accuracy since the fully coupled +effect is considered through the residual vector +at each increment in time. However, the rate of +convergence is no longer quadratic and depends strongly on the magnitude of the coupling effect, so more +iterations are generally needed to achieve equilibrium than with the exact implementation of Newton’s +method. When the coupling is significant, the convergence rate becomes very slow and may prohibit +the attainment of a solution. In such cases the exact implementation of Newton’s method is required. +In cases where it is possible to use this approximation, the convergence in an increment will depend +strongly on the quality of the first guess to the incremental solution, which you can control by selecting +the extrapolation method used for the step . +Input File Usage: +Abaqus/CAE Usage: +Use the following option to specify a separated solution scheme: +*SOLUTION TECHNIQUE, TYPE=SEPARATED +Step module: Create Step: General: Coupled thermal-electric: +Other: Solution technique: Separated +Uncoupled electric conduction and heat transfer analysis +The coupled thermal-electrical procedure can also be used to perform uncoupled electric conduction +analysis for the whole model or just part of the model (using coupled thermal-electrical elements). +Uncoupled electrical analysis is available by omitting the thermal properties from the material +description, in which case only the electric potential degrees of freedom are activated in the element and +all heat transfer effects are ignored. If heat transfer effects are ignored in the entire model, you should +invoke the separated solution technique described above. Use of this technique will then invoke the +symmetric storage and solution scheme, which is an exact representation of a purely electrical problem. +Similarly, coupled thermal-electrical elements can be used in an uncoupled heat transfer analysis +(“Uncoupled heat transfer analysis,” Section 6.5.2), in which case all electric conduction effects are +ignored. This feature is useful if a thermal-electrical analysis is followed by a pure heat conduction +analysis. A typical example is a welding process, where the electric current is applied instantaneously, +followed by a cooldown period during which no electrical effects need to be considered. The symmetric +solver is activated by default in an uncoupled heat transfer analysis. +Cavity radiation +Cavity radiation can be activated in a heat transfer step. This feature involves interacting heat transfer +between all of the facets of the cavity surface, dependent on the facet temperatures, facet emissivities, +and the geometric viewfactors between each facet pair. When the thermal emissivity is a function of +temperature or field variables, you can specify the maximum allowable emissivity change during an +increment in addition to the maximum temperature change to control the time incrementation. See +“Cavity radiation,” Section 40.1.1, for more information. +Input File Usage: +Use the following option in the step definition to activate cavity radiation: +*RADIATION VIEWFACTOR +Use the following option to specify the maximum allowable emissivity change: +*HEAT TRANSFER, MXDEM=max_delta_emissivity +You can specify the maximum allowable emissivity change for a heat transfer +step. +Step module: Create Step: General: Heat transfer: Incrementation: +Max. allowable emissivity change per increment +Abaqus/CAE Usage: +Initial conditions +By default, the initial temperature of all nodes is zero. You can specify nonzero initial temperatures +or field variables . +Since only steady-state electrical currents are considered, the initial value of the electrical potential is +not relevant. +Boundary conditions +Boundary conditions can be used to prescribe the electrical potential, +9), and the temperature, +Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1. +(degree of freedom +(degree of freedom 11), at the nodes. See “Boundary conditions in +Boundary conditions can be specified as functions of time by referring to amplitude curves . +A boundary without any prescribed boundary conditions corresponds to an insulated surface. +Loads +Both thermal and electrical loads can be applied in a coupled thermal-electrical analysis. +Applying thermal loads +The following types of thermal loads can be prescribed in a coupled thermal-electrical analysis, as +described in “Thermal loads,” Section 33.4.4: +• Concentrated heat fluxes. +• Body fluxes and distributed surface fluxes. +• Average-temperature radiation conditions. +• Convective film conditions and radiation conditions. +Applying electrical loads +The following types of electrical loads can be prescribed, as described in “Electromagnetic loads,” +Section 33.4.5: +• Concentrated current. +• Distributed surface current densities and body current densities. +Predefined fields +Predefined temperature fields are not allowed in coupled thermal-electrical analyses. Boundary +conditions should be used instead to specify temperatures, as described above. +Other predefined field variables can be specified in a coupled thermal-electrical analysis. These +See “Predefined fields,” +values affect only field-variable-dependent material properties, +Section 33.6.1. +if any. +Material options +Both thermal and electrical properties are active in coupled thermal-electrical analyses. +properties are omitted, an uncoupled electrical analysis will be performed. +If thermal +All mechanical behavior material models (such as elasticity and plasticity) are ignored in a coupled +thermal-electrical analysis. +Thermal material properties +For the heat transfer portion of the analysis, the thermal conductivity must be defined . The specific heat must also be defined for transient heat transfer problems . If changes in internal energy due to phase changes are important, latent heat can +be defined . Thermal expansion coefficients (“Thermal expansion,” +Section 26.1.2) are not meaningful in a coupled thermal-electrical analysis since deformation of the +structure is not considered. +Internal heat generation can be specified . +Electrical material properties +For the electrical portion of the analysis, the electrical conductivity must be defined . The electrical conductivity can be a function of temperature and +user-defined field variables. The fraction of electrical energy dissipated as heat can also be defined, as +explained above. +Elements +The simultaneous solution in a coupled thermal-electrical analysis requires the use of elements that have +both temperature (degree of freedom 11) and electrical potential (degree of freedom 9) as nodal variables. +The finite element model can also include pure heat transfer elements (so that a pure heat transfer analysis +is provided for that part of the model) and coupled thermal-electrical elements for which no thermal +properties are given (so that a pure electrical conduction solution is provided for that part of the model). +Coupled thermal-electrical elements are available in Abaqus/Standard in one dimension, two +dimensions (planar and axisymmetric), and three dimensions. See “Choosing the appropriate element +for an analysis type,” Section 27.1.3. +Output +The following output variables can be used to request output relating to the electric conduction solution: +Element integration point variables: +EPG +EPGM +EPGn +ECD +JENER +Magnitude and components of the electrical potential gradient vector, +Magnitude of the electrical potential gradient vector. +Component n of the electrical potential gradient vector (n=1, 2, 3). +Magnitude and components of the electrical current density vector, J. +Electrical energy dissipated due to flow of current, +. +. +Whole element variables: +ECURS +NCURS +ELJD +Distributed applied electrical current. +Electrical current at nodes due to electric conduction. +Total electrical energy dissipated due to flow of current, +. +Nodal variables: +EPOT +RECUR +CECUR +Electrical potential, +Reactive electrical current. +Concentrated applied electrical current. +. +Whole model variables: +ALLJD +Electrical energy summed over the model. +Surface interaction variables : +ECD +ECDA +ECDT +ECDTA +SJD +SJDA +SJDT +SJDTA +WEIGHT +Electrical current density. +ECD multiplied by area. +Time integrated ECD. +Time integrated ECDA. +Heat flux per unit area generated by the electrical current. +SJD multiplied by area. +Time integrated SJD. +Time integrated SJDA. +Heat distribution between interface surfaces, f. +Considerations for steady-state coupled thermal-electrical analysis +In a steady-state coupled thermal-electrical analysis the electrical energy dissipated due to flow of +electrical current at an integration point (output variable JENER) is computed using the following +relationship: +denotes the electrical energy dissipated due to flow of electrical current and +where +step time. In the above relationship it is assumed that the rate of the electrical energy dissipation, +has a constant value in the step that is equal to the value currently computed. +is the current +, +The output variable JENER and the derived output variables ELJD and ALLJD contain the values +of electrical energies dissipated in the current step only. Similarly, the contribution from the electrical +current flow to the output variable ALLWK includes only the external work performed in the current +step. +Input file template +*HEADING +… +*MATERIAL, NAME=mat1 +*CONDUCTIVITY +Data lines to define thermal conductivity +*ELECTRICAL CONDUCTIVITY +Data lines to define electrical conductivity +* HEAT FRACTION +Data lines to define the fraction of electric energy released as heat +** +*STEP +*COUPLED THERMAL-ELECTRICAL +Data line to define incrementation and steady state +*BOUNDARY +Data lines to define boundary conditions on electrical potential and +temperature degrees of freedom +*CECURRENT +Data lines to define concentrated currents +*DECURRENT and/or *DSECURRENT +Data lines to define distributed current densities +*CFLUX and/or *DFLUX and/or *DSFLUX +Data lines to define thermal loading +*FILM and/or *SFILM and/or *RADIATE and/or *SRADIATE +Data lines to define convective film and radiation conditions +… +*CONTACT PRINT or *CONTACT FILE +Data lines to request output of surface interaction variables +*END STEP +6.7.4 +FULLY COUPLED THERMAL-ELECTRICAL-STRUCTURAL ANALYSIS +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “Fully coupled thermal-stress analysis,” Section 6.5.3 +• “Coupled thermal-electrical analysis,” Section 6.7.3 +• *COUPLED TEMPERATURE-DISPLACEMENT +• “Configuring a fully coupled, simultaneous heat transfer, electrical, and structural procedure” in +“Configuring general analysis procedures,” Section 14.11.1 of the Abaqus/CAE User’s Manual, in +the online HTML version of this manual +Overview +A fully coupled thermal-electrical-structural analysis: +• is performed when coupling between the displacement, temperature, and electrical potential fields +makes it necessary to obtain solutions for all three fields simultaneously; +• requires the existence of elements with displacement, temperature, and electrical potential degrees +of freedom in the model; +• allows for transient or steady-state thermal solutions, static displacement solutions, and steady-state +electrical solutions; +• can include thermal interactions such as gap radiation, gap conductance, and gap heat generation +between surfaces ; +• can include electrical interactions such as gap electrical conductance ; +• cannot include cavity radiation effects but may include radiation boundary conditions ; +• takes into account temperature dependence of material properties only for the properties that are +assigned to elements with temperature degrees of freedom; +• neglects inertia effects; and +• can be transient or steady state. +Fully coupled thermal-electrical-structural analysis +A fully coupled thermal-electrical-structural analysis is the union of a coupled thermal-displacement +analysis and a coupled thermal-electrical +analysis . +Coupling between the temperature and electrical degrees of freedom arises from temperature- +dependent electrical conductivity and internal heat generation (Joule heating), which is a function of the +electrical current density. The thermal part of the problem can include heat conduction and heat storage +(“Thermal properties: overview,” Section 26.2.1). Forced convection caused by fluid flowing through +the mesh is not considered. +Coupling between the temperature and displacement degrees of +from +and internal heat generation, +temperature-dependent material properties, +which is a function of inelastic deformation of the material. +In addition, contact conditions exist in +some problems where the heat conducted between surfaces may depend strongly on the separation of +the surfaces and/or the pressure transmitted across the surfaces as well as friction . +thermal expansion, +freedom arises +Coupling between the electrical and displacement degrees of freedom arises in problems where +electricity flows between contact surfaces. The electrical conduction may depend strongly on the +separation of the surfaces and/or the pressure transmitted across the surfaces . +An example of a simulation that requires a fully coupled thermal-electrical-structural analysis is +resistance spot welding. In a typical spot welding process two or more thin metal sheets are pinched +between two electrodes. A large current is passed between the electrodes, which melts the metal between +the electrodes and forms a weld. The integrity of the weld depends on many parameters including the +electrical conductance between the sheets (which can be a function of contact pressure and temperature). +Steady-state analysis +Steady-state analysis provides the steady-state solution directly. Steady-state thermal analysis means +that the internal energy term (the specific heat term) in the governing heat transfer equation is omitted. +A static displacement solution is assumed. Only direct current is considered in the electrical problem, +and it is assumed that the system has negligible capacitance. Electrical transient effects are so rapid that +they can be neglected. +Input File Usage: +*COUPLED TEMPERATURE-DISPLACEMENT, ELECTRICAL, +STEADY STATE +Abaqus/CAE Usage: +Step module: Create Step: General: Coupled thermal-electrical- +structural: Basic: Response: Steady state +Assigning a “time” scale to the analysis +In steady-state cases you should assign an arbitrary “time” scale to the step: you specify a “time” +period and “time” incrementation parameters. This time scale is convenient for changing loads and +boundary conditions through the step and for obtaining solutions to highly nonlinear (but steady-state) +cases; however, for the latter purpose, transient analysis often provides a natural way of coping with +the nonlinearity. +Accounting for frictional slip heat generation +Frictional slip heat generation is normally neglected in the steady-state case. However, it can still be +accounted for if motions are used to specify translational or rotational nodal velocities in disk brake-type +problems or if user subroutine FRIC provides the incremental frictional dissipation through the variable +SFD. If frictional heat generation is present, the heat flux into the two contact surfaces depends on the +slip rate of the surfaces. The “time” scale in this case cannot be described as arbitrary, and a transient +analysis should be performed. +Transient analysis +Alternatively, you can perform a transient coupled thermal-electrical-structural analysis. As in steady- +state analysis, electrical transient effects are neglected and a static displacement solution is assumed. +You can control the time incrementation in a transient analysis directly, or Abaqus/Standard can control +it automatically. Automatic time incrementation is generally preferred. +Automatic incrementation controlled by a maximum allowable temperature change +The time increments can be selected automatically based on a user-prescribed maximum allowable nodal +temperature change in an increment, +. Abaqus/Standard will restrict the time increments to ensure +that this value is not exceeded at any node (except nodes with boundary conditions) during any increment +of the analysis . +Input File Usage: +Abaqus/CAE Usage: +*COUPLED TEMPERATURE-DISPLACEMENT, ELECTRICAL, +DELTMX= +Step module: Create Step: General: Coupled thermal-electrical- +structural: Basic: Response: Transient; Incrementation: Type: +Automatic: Max. allowable temperature change per increment: +Fixed incrementation +If you do not specify +, fixed time increments equal to the user-specified initial time increment, +, will be used throughout the analysis. +Input File Usage: +*COUPLED TEMPERATURE-DISPLACEMENT, ELECTRICAL +Abaqus/CAE Usage: +Step module: Create Step: General: Coupled thermal-electrical- +structural: Basic: Response: Transient; Incrementation: +Type: Fixed: Increment size: +Spurious oscillations due to small time increments +In transient analysis with second-order elements there is a relationship between the minimum usable time +increment and the element size. A simple guideline is +where +is the time increment, +is the density, c is the specific heat, k is the thermal conductivity, and +is a typical element dimension (such as the length of a side of an element). If time increments smaller +than this value are used in a mesh of second-order elements, spurious oscillations can appear in the +solution, in particular in the vicinity of boundaries with rapid temperature changes. These oscillations +are nonphysical and may cause problems if temperature-dependent material properties are present. +In transient analyses using first-order elements the heat capacity terms are lumped, which eliminates +such oscillations but can lead to locally inaccurate solutions for small time increments. If smaller time +increments are required, a finer mesh should be used in regions where the temperature changes rapidly. +There is no upper limit on the time increment size (the integration procedure is unconditionally +stable) unless nonlinearities cause convergence problems. +Automatic incrementation controlled by the creep response +The accuracy of the integration of time-dependent (creep) material behavior is governed by the +user-specified accuracy tolerance parameter, +. This parameter is used +to prescribe the maximum strain rate change allowed at any point during an increment, as described +in “Rate-dependent plasticity: creep and swelling,” Section 23.2.4. The accuracy tolerance parameter +can be specified together with the maximum allowable nodal temperature change in an increment, +(described above); however, specifying the accuracy tolerance parameter activates automatic +incrementation even if +is not specified. +Input File Usage: +Abaqus/CAE Usage: +*COUPLED TEMPERATURE-DISPLACEMENT, ELECTRICAL, +DELTMX= +, CETOL=tolerance +Step module: Create Step: General: Coupled thermal-electrical- +structural: Basic: Response: Transient, toggle on Include +creep/swelling/viscoelastic behavior; Incrementation: Type: +Automatic: Max. allowable temperature change per increment: +Creep/swelling/viscoelastic strain error tolerance: tolerance +, +Selecting explicit creep integration +Nonlinear creep problems (“Rate-dependent plasticity: creep and swelling,” Section 23.2.4) that exhibit +no other nonlinearities can be solved efficiently by forward-difference integration of the inelastic +strains if the inelastic strain increments are smaller than the elastic strains. This explicit method is +efficient computationally because, unlike implicit methods, iteration is not required as long as no other +nonlinearities are present. Although this method is only conditionally stable, the numerical stability +limit of the explicit operator is in many cases sufficiently large to allow the solution to be developed in +a reasonable number of time increments. +For most coupled thermal-electrical-structural analyses, however, the unconditional stability of the +backward difference operator (implicit method) is desirable. In such cases the implicit integration scheme +may be invoked automatically by Abaqus/Standard. +Explicit integration can be less expensive computationally and simplifies implementation of user- +defined creep laws in user subroutine CREEP; you can restrict Abaqus/Standard to using this method +for creep problems (with or without geometric nonlinearity included). See “Rate-dependent plasticity: +creep and swelling,” Section 23.2.4, for further details. +Input File Usage: +Abaqus/CAE Usage: +*COUPLED TEMPERATURE-DISPLACEMENT, ELECTRICAL, +CETOL=tolerance, CREEP=EXPLICIT +Step module: Create Step: General: Coupled thermal-electrical- +structural: Basic: Response: Transient, toggle on Include +creep/swelling/viscoelastic behavior; Incrementation: +Creep/swelling/viscoelastic strain error tolerance: tolerance, +Creep/swelling/viscoelastic integration: Explicit +Excluding creep and viscoelastic response +You can specify that no creep or viscoelastic response will occur during a step even if creep or viscoelastic +material properties have been defined. +Input File Usage: +Abaqus/CAE Usage: +*COUPLED TEMPERATURE-DISPLACEMENT, ELECTRICAL, +DELTMX= +, CREEP=NONE +Step module: Create Step: General: Coupled thermal-electrical- +structural: Basic: Response: Transient, toggle off Include +creep/swelling/viscoelastic behavior +Unstable problems +Some types of analyses may develop local instabilities, such as surface wrinkling, material instability, +or local buckling. +In such cases it may not be possible to obtain a quasi-static solution, even with +the aid of automatic incrementation. Abaqus/Standard offers a method of stabilizing this class of +problems by applying damping throughout the model in such a way that the viscous forces introduced +are sufficiently large to prevent instantaneous buckling or collapse but small enough not to affect the +behavior significantly while the problem is stable. The available automatic stabilization schemes are +described in detail in “Automatic stabilization of unstable problems” in “Solving nonlinear problems,” +Section 7.1.1. +Units +In coupled problems where two or three different fields are active, take care when choosing the units of +the problem. If the choice of units is such that the terms generated by the equations for each field are +different by many orders of magnitude, the precision on some computers may be insufficient to resolve the +numerical ill-conditioning of the coupled equations. Therefore, choose units that avoid ill-conditioned +matrices. For example, consider using units of Mpascal instead of pascal for the stress equilibrium +equations to reduce the disparity between the magnitudes of the stress equilibrium equations, the heat +flux continuity equations, and the conservation of charge equations. +Initial conditions +By default, the initial temperature of all nodes is zero. You can specify nonzero initial temperatures. +Initial stresses, field variables, etc. can also be defined; “Initial conditions in Abaqus/Standard and +Abaqus/Explicit,” Section 33.2.1, describes all of the initial conditions that are available for a fully +coupled thermal-electrical-structural analysis. +Boundary conditions +can be used to prescribe +freedom 11), +Boundary conditions +displacements/rotations (degrees of freedom 1–6), or electrical potentials (degree of freedom 9) at nodes +in a fully coupled thermal-electrical-structural analysis . +temperatures +(degree of +Boundary conditions can be specified as functions of time by referring to amplitude curves +(“Amplitude curves,” Section 33.1.2). +Loads +The following types of thermal loads can be prescribed in a fully coupled thermal-electrical-structural +analysis, as described in “Thermal loads,” Section 33.4.4: +• Concentrated heat fluxes. +• Body fluxes and distributed surface fluxes. +• Node-based film and radiation conditions. +• Average-temperature radiation conditions. +• Element and surface-based film and radiation conditions. +The following types of mechanical loads can be prescribed: +• Concentrated nodal forces can be applied to the displacement degrees of freedom (1–6); see +“Concentrated loads,” Section 33.4.2. +• Distributed pressure forces or body forces can be applied; see “Distributed loads,” Section 33.4.3. +The following types of electrical loads can be prescribed, as described in “Electromagnetic loads,” +Section 33.4.5: +• Concentrated current. +• Distributed surface current densities and body current densities. +Predefined fields +Predefined temperature fields are not allowed in a fully coupled thermal-electrical-structural analysis. +Boundary conditions should be used instead to prescribe temperature degree of freedom 11, as described +earlier. +Other predefined field variables can be specified in a fully coupled thermal-electrical-structural +analysis. These values will affect only field-variable-dependent material properties, if any. See +“Predefined fields,” Section 33.6.1. +Material options +The materials in a fully coupled thermal-electrical-structural analysis must have thermal properties (such +as conductivity), mechanical properties (such as elasticity), and electrical properties (such as electrical +conductivity) defined. See Part V, “Materials,” for details on the material models available in Abaqus. +Internal heat generation can be specified; see “Uncoupled heat transfer analysis,” Section 6.5.2. +Thermal strain will arise if thermal expansion (“Thermal expansion,” Section 26.1.2) is included in +the material property definition. +A fully coupled thermal-electrical-structural analysis can be used to analyze static creep +and swelling problems, which generally occur over fairly long time periods (“Rate-dependent +plasticity: creep and swelling,” Section 23.2.4); viscoelastic materials (“Time domain viscoelasticity,” +Section 22.7.1); or viscoplastic materials (“Rate-dependent yield,” Section 23.2.3). +Inelastic energy dissipation as a heat source +You can specify an inelastic heat fraction in a fully coupled thermal-electrical-structural analysis to +provide for inelastic energy dissipation as a heat source. Plastic straining gives rise to a heat flux per unit +volume of +where +constant), +is the heat flux that is added into the thermal energy balance, +is a user-defined factor (assumed +is the stress, and +is the rate of plastic straining. +Inelastic heat fractions are typically used in the simulation of high-speed manufacturing processes +involving large amounts of inelastic strain, where the heating of the material caused by its deformation +significantly influences temperature-dependent material properties. The generated heat is treated as a +volumetric heat flux source term in the heat balance equation. +An inelastic heat fraction can be specified for materials with plastic behavior that use the Mises +or Hill yield surface (“Inelastic behavior,” Section 23.1.1). +It cannot be used with the combined +isotropic/kinematic hardening model. The inelastic heat fraction can be specified for user-defined +material behavior in Abaqus/Explicit and will be multiplied by the inelastic energy dissipation coded in +the user subroutine to obtain the heat flux. In Abaqus/Standard the inelastic heat fraction cannot be used +with user-defined material behavior; in this case the heat flux that must be added to the thermal energy +balance is computed directly in the user subroutine. +In Abaqus/Standard an inelastic heat fraction can also be specified for hyperelastic material +definitions that include time-domain viscoelasticity (“Time domain viscoelasticity,” Section 22.7.1). +The default value of the inelastic heat fraction is 0.9. If you do not include the inelastic heat fraction +behavior in the material definition, the heat generated by inelastic deformation is not included in the +analysis. +Input File Usage: +*INELASTIC HEAT FRACTION +Specifying the amount of thermal energy generated due to electrical current +Joule’s law describes the rate of electrical energy, +as +, dissipated by current flowing through a conductor +The amount of this energy released as internal heat within the body is +conversion factor. You specify +is converted into heat ( +The fraction given can include a unit conversion factor, if required. +is an energy +in the material definition. It is assumed that all the electrical energy +) if you do not include the joule heat fraction in the material description. +, where +Input File Usage: +*JOULE HEAT FRACTION +Elements +Coupled thermal-electrical-structural elements that have displacements, temperatures, and electrical +potentials as nodal variables are available. Simultaneous temperature/electrical potential/displacement +solution requires the use of such elements; pure displacement and temperature-displacement elements +can be used in part of the model in a fully coupled thermal-electrical-structural analysis, but pure heat +transfer elements cannot be used. +The first-order coupled thermal-electrical-structural elements in Abaqus use a constant temperature +over the element to calculate thermal expansion. The second-order coupled thermal-electrical-structural +elements in Abaqus use a lower-order interpolation for temperature than for displacement (parabolic +variation of displacements and linear variation of temperature) to obtain a compatible variation of thermal +and mechanical strain. +Output +See “Abaqus/Standard output variable identifiers,” Section 4.2.1, for a complete list of output variables. +The types of output available are described in “Output,” Section 4.1.1. +Considerations for steady-state coupled thermal-electrical-structural analysis +In a steady-state coupled thermal-electrical-structural analysis the electrical energy dissipated due to flow +of electrical current at an integration point (output variable JENER) is computed using the following +relationship: +denotes the electrical energy dissipated due to flow of electrical current and +where +step time. In the above relationship it is assumed that the rate of the electrical energy dissipation, +has a constant value in the step that is equal to the value currently computed. +is the current +, +The output variable JENER and the derived output variables ELJD and ALLJD contain the values +of electrical energies dissipated in the current step only. Similarly, the contribution from the electrical +current flow to the output variable ALLWK includes only the external work performed in the current +step. +Input file template +*HEADING +… +** Specify the coupled thermal-electrical-structural element type +*ELEMENT, TYPE=Q3D8 +… +** +*STEP +*COUPLED TEMPERATURE-DISPLACEMENT, ELECTRICAL +Data line to define incrementation +*BOUNDARY +Data lines to define nonzero boundary conditions on displacement, +temperature or electrical potential degrees of freedom +*CFLUX and/or *CFILM and/or +*CRADIATE and/or *DFLUX and/or +*DSFLUX and/or *FILM and/or +*SFILM and/or *RADIATE and/or +*SRADIATE +Data lines to define thermal loads +*CLOAD and/or *DLOAD and/or *DSLOAD +Data lines to define mechanical loads +*CECURRENT +Data lines to define concentrated currents +*DECURRENT and/or *DSECURRENT +Data lines to define distributed current densities +*FIELD +Data lines to define field variable values +*END STEP +6.7.5 +EDDY CURRENT ANALYSIS +Products: Abaqus/Standard Abaqus/CAE +References +• “Mapping thermal and magnetic loads,” Section 3.2.22 +• “Electromagnetic analysis procedures,” Section 6.7.1 +• “Electrical conductivity,” Section 26.5.1 +• “Magnetic permeability,” Section 26.5.3 +• “Electromagnetic loads,” Section 33.4.5 +• “Predefined loads for sequential coupling,” Section 16.1.3 +• *ELECTROMAGNETIC +• *D EM POTENTIAL +• *DECURRENT +• *DSECURRENT +• “UDECURRENT,” Section 1.1.23 of the Abaqus User Subroutines Reference Manual +• “UDEMPOTENTIAL,” Section 1.1.24 of the Abaqus User Subroutines Reference Manual +• “UDSECURRENT,” Section 1.1.26 of the Abaqus User Subroutines Reference Manual +• “Configuring a time-harmonic electromagnetic analysis” in “Configuring linear perturbation +analysis procedures,” Section 14.11.2 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +• “Defining a magnetic vector potential boundary condition,” Section 16.10.17 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +Eddy current problems: +• involve coupling between electric and magnetic fields, which are solved for simultaneously; +• solve Maxwell’s equations describing electromagnetic phenomena under the low-frequency +assumption that neglects the effects of displacement currents; +• require the use of electromagnetic elements in the whole domain; +• require that magnetic permeability is specified in the whole domain and electrical conductivity is +specified in the conducting regions; +• allows for both time-harmonic and transient electromagnetic solutions; +• calculate as output variables, rate of Joule heating and intensity of magnetic body forces +associated with eddy currents, and these output variables can be transferred from a time-harmonic +electromagnetic solution to drive a subsequent heat transfer, coupled temperature-displacement, +or stress/displacement analysis, thereby allowing for the coupling of electromagnetic fields with +thermal and/or mechanical fields in a sequentially coupled manner; and +• can be solved using continuum elements in two- and three-dimensional space. +Eddy current analysis +Eddy currents are generated in a metal workpiece when it is placed within a time-varying magnetic field. +Joule heating arises when the energy dissipated by the eddy currents flowing through the workpiece is +converted into thermal energy. This heating mechanism is usually referred to as induction heating; the +induction cooker is an example of a device that uses this mechanism. The time-varying magnetic field is +usually generated by a coil that is placed close to the workpiece. The coil carries either a known amount +of total current or an unknown amount of current under a known potential (voltage) difference. The +current in the coil is assumed to be alternating at a known frequency for a time-harmonic eddy current +analysis but may have an arbitrary variation in time for a transient eddy current analysis. +The time-harmonic eddy current analysis procedure is based on the assumption that a time-harmonic +excitation with a certain frequency results in a time-harmonic electromagnetic response with the same +frequency everywhere in the domain. In other words, both the electric and the magnetic fields oscillate at +the same frequency as that of the alternating current in the coil. The transient eddy current analysis does +not make any assumption regarding the time-variation of the current in the coil; in fact any arbitrary time +variation can be specified, and the electric and magnetic fields follow from the solution to Maxwell’s +equations in the time domain. +The eddy current analysis provides output, such as Joule heat dissipation or magnetic body +force intensity, that can be transferred, from a time-harmonic eddy current analysis only, to drive a +subsequent heat transfer, coupled temperature-displacement, or stress/displacement analysis. This +allows for modeling the interactions of the electromagnetic fields with thermal and/or mechanical fields +in a sequentially coupled manner. See “Mapping thermal and magnetic loads,” Section 3.2.22, and +“Predefined loads for sequential coupling,” Section 16.1.3, for details. +Electromagnetic elements must be used to model the response of all the regions in an eddy current +analysis including the coil, the workpiece, and the space in between and surrounding them. To obtain +accurate solutions, the outer boundary of the space (surrounding the coil and the workpiece) being +modeled must be at least a few characteristic length scales away from the device on all sides. +The electromagnetic elements use an element edge-based interpolation of the fields instead of the +standard node-based interpolation. The user-defined nodes only define the geometry of the elements; +and the degrees of freedom of the element are not associated with these nodes, which has implications +for applying boundary conditions . +Governing field equations +The electric and magnetic fields are governed by Maxwell’s equations describing electromagnetic +phenomena. +The formulation is based on the low-frequency assumption, which neglects the +displacement current correction term in Ampere’s law. This assumption is appropriate when the +wavelength of the electromagnetic waves corresponding to the excitation frequency is large compared +to typical length scales over which the response is computed. In the following discussion, the governing +equations are written for a linear medium. +Time-harmonic analysis +It is convenient to introduce a magnetic vector potential, +. The solution procedure seeks a time-harmonic electromagnetic response, +, such that the magnetic flux density vector +, +radians/sec when the system is subjected to a time-harmonic excitation of the same +. In the +represent the amplitudes of the magnetic vector potential +) +with frequency +frequency; for example, through an impressed oscillating volume current density, +preceding expressions the vectors +and +and applied volume current density vector, respectively, while the exponential factors (with +represent the corresponding phases. Under these assumptions, Maxwell’s equations reduce to +in terms of the amplitudes of the field quantities, +the electrical conductivity tensor, +to the magnetic field, +conductivity relates the volume current density, +, through a constitutive equation of the form: +and +; the magnetic permeability tensor, +. The magnetic permeability relates the magnetic flux density, +; and +, +, while the electrical +. +, and the electric field, +, by Ohm’s law: +The variational form of the above equation is +where +tangential surface current density, if any, at the external surfaces. +represents the variation of the magnetic vector potential, and +represents the applied +Abaqus/Standard solves the variational form of Maxwell’s equations for the in-phase (real) and +out-of-phase (imaginary) components of the magnetic vector potential. The other field quantities are +derived from the magnetic vector potential. +Transient analysis +It is convenient to introduce a magnetic vector potential, +and time, such that the magnetic flux density vector +time-dependent electromagnetic response, +excitation; for example, through an impressed distribution of volume current density, +these assumptions, Maxwell’s equations reduce to +, assumed to be a function of spatial position +. The solution procedure seeks a +, when the system is subjected to a time-dependent +. Under +in terms of the field quantities, +conductivity tensor, +and +; the magnetic permeability tensor, +. The magnetic permeability relates the magnetic flux density, +; and the electrical +, to the +magnetic field, +conductivity relates the volume current density, +, through a constitutive equation of the form: +, and the electric field, +, while the electrical +. +, by Ohm’s law: +The variational form of the above equation is +where +tangential surface current density, if any, at the external surfaces. +represents the variation of the magnetic vector potential, and +represents the applied +Abaqus/Standard solves the variational form of Maxwell’s equations for the components of the +magnetic vector potential. The other field quantities are derived from the magnetic vector potential. +Defining the magnetic behavior +The magnetic behavior of the electromagnetic medium can be linear or nonlinear. However, only linear +magnetic behavior is available for time-harmonic eddy current analysis. Linear magnetic behavior is +characterized by a magnetic permeability tensor that is assumed to be independent of the magnetic field. +It is defined through direct specification of the absolute magnetic permeability tensor, +, which can be +isotropic, orthotropic, or fully anisotropic . The magnetic +permeability can also depend on temperature and/or predefined field variables. For a time-harmonic eddy +current analysis, the magnetic permeability can also depend on frequency. +Nonlinear magnetic behavior, which is available only for transient eddy current analysis, +is characterized by magnetic permeability that depends on the strength of the magnetic field. The +nonlinear magnetic material model in Abaqus is suitable for ideally soft magnetic materials characterized +by a monotonically increasing response in B–H space, where B and H refer to the strengths of the +magnetic flux density vector and the magnetic field vector, respectively. Nonlinear magnetic behavior +is defined through direct specification of one or more B–H curves that provide B as a function of H and, +optionally, temperature and/or predefined field variables, in one or more directions. Nonlinear magnetic +behavior can be isotropic, orthotropic, or transversely isotropic (which is a special case of the more +general orthotropic behavior). +Defining the electrical conductivity +The electrical conductivity, +, can be isotropic, orthotropic, or fully anisotropic . The electrical conductivity can also depend on temperature and/or +predefined field variables. For a time-harmonic eddy current analysis, the electrical conductivity can +also depend on frequency. Ohm’s law assumes that the electrical conductivity is independent of the +electrical field, +. +Time-harmonic analysis +The eddy current analysis procedure provides the time-harmonic solution directly at a given excitation +frequency. You can specify one or more excitation frequencies, one or more frequency ranges, or a +combination of excitation frequencies and ranges. +Input File Usage: +*ELECTROMAGNETIC, LOW FREQUENCY, TIME HARMONIC +lower_freq1, upper_freq1, num_pts1 +lower_freq2, upper_freq2, num_pts2 +... +single_freq1 +single_freq2 +... +For example, the following input illustrates the simplest case of specifying +excitation at a single frequency: +*ELECTROMAGNETIC, LOW FREQUENCY, TIME HARMONIC +single_freq1 +Abaqus/CAE Usage: +Step module: Create Step: Linear perturbation: Electromagnetic, +Time harmonic; enter data in table, and add rows as necessary +Transient analysis +The eddy current analysis procedure provides the transient solution to a given arbitrary time-dependent +excitation. +Input File Usage: +Abaqus/CAE Usage: +*ELECTROMAGNETIC, LOW FREQUENCY, TRANSIENT +A transient eddy current analysis is not supported in Abaqus/CAE. +Tme incrementation +Time integration in the transient eddy current analysis is done with the backward Euler method. This +method is unconditionally stable for linear problems but may lead to inaccuracies if time increments +are too large. The resulting system of equations can be nonlinear in general, and Abaqus/Standard uses +Newton’s method to solve the system. The solution usually is obtained as a series of increments, with +iterations to obtain equilibrium within each increment. Increments must sometimes be kept small to +ensure accuracy of the time integration procedure. The choice of increment size is also a matter of +computational efficiency: if the increments are too large, more iterations are required. Furthermore, +Newton’s method has a finite radius of convergence; too large an increment can prevent any solution from +being obtained because the initial state is too far away from the equilibrium state that is being sought—it +is outside the radius of convergence. Thus, there is an algorithmic restriction on the increment size. +Automatic incrementation +In most cases the default automatic incrementation scheme is preferred because it will select increment +sizes based on computational efficiency. However, you must ensure that the time increments are such that +the time integration results in an accurate solution. Abaqus/Standard does not have any built in checks +to ensure integration accuracy. +Input File Usage: +Abaqus/CAE Usage: +*ELECTROMAGNETIC, LOW FREQUENCY, TRANSIENT +A transient eddy current analysis is not supported in Abaqus/CAE. +Direct incrementation +Direct user control of the increment size is also provided; if you have considerable experience with a +particular problem, you may be able to select a more economical approach. +Input File Usage: +Abaqus/CAE Usage: +*ELECTROMAGNETIC, LOW FREQUENCY, TRANSIENT, DIRECT +A transient eddy current analysis is not supported in Abaqus/CAE. +Ill-conditioning in eddy current analyses with electrically nonconductive regions +In an eddy current analysis it is very common that large portions of the model consist of electrically +nonconductive regions, such as air and/or a vacuum. In such cases it is well known that the associated +stiffness matrix can be very ill-conditioned; i.e., it can have many singularities (Bíró, 1999). Abaqus +uses a special iterative solution technique to prevent the ill-conditioned matrix from negatively +impacting the computed electric and magnetic fields. The default implementation works well for many +problems. However, there can be situations in which the default numerical scheme fails to converge or +results in a noisy solution. In such cases adding a “small” amount of artificial electrical conductivity to +the nonconductive domain may help regularize the problem and allow Abaqus to converge to the correct +solution. The artificial electrical conductivity should be chosen such that the electromagnetic waves +propagating through these regions undergo little modification and, in particular, do not experience +the sharp exponential decay that is typical when such fields impinge upon a real conductor. +It is +recommended that you set the artificial conductivity to be about five to eight orders of magnitude less +than that of any of the conductors in the model. +As an alternative to specifying electrical conductivity in the nonconductive domain, Abaqus also +provides a stabilization scheme to help mitigate the effects of the ill-conditioning. You can provide input +to this stabilization algorithm by specifying the stabilization factor, which is assumed to be 1.0 by default +if the stabilization scheme is used. Higher values of the stabilization factor lead to more stabilization, +while lower values of the stabilization factor lead to less stabilization. +Input File Usage: +Use the following to use stabilization in a time-harmonic procedure: +*ELECTROMAGNETIC, LOW FREQUENCY, TIME HARMONIC, +STABILIZATION=stabilization factor +Use the following to use stabilization in a transient procedure: +*ELECTROMAGNETIC, LOW FREQUENCY, TRANSIENT, +STABILIZATION=stabilization factor +Initial conditions +Initial values of temperature and/or predefined field variables can be specified. These values affect only +temperature and/or field-variable-dependent material properties, if any. Initial conditions on the electric +and/or magnetic fields cannot be specified in an eddy current analysis. +Boundary conditions +Electromagnetic elements use an element edge-based interpolation of the fields. The degrees of freedom +of the element are not associated with the user-defined nodes, which only define the geometry of the +element. Consequently, the standard node-based method of specifying boundary conditions cannot +be used with electromagnetic elements. The method used for specifying boundary conditions for +electromagnetic elements is described in the following paragraphs. +Boundary conditions in Abaqus typically refer to what are traditionally known as Dirichlet-type +boundary conditions in the literature, where the values of the primary variable are known on the whole +boundary or on a portion of the boundary. The alternative, Neumann-type boundary conditions, refer +to situations where the values of the conjugate to the primary variable are known on portions of the +boundary. In Abaqus Neumann-type boundary conditions are represented as surface loads in the finite- +element formulation. +For electromagnetic boundary value problems, Dirichlet boundary conditions on an enclosing +surface must be specified as +is the outward normal to the surface, as discussed in +this section. Neumann boundary conditions must be specified as the surface current density vector, +, where +, as discussed in “Loads” below. +for the representative surfaces. +In Abaqus Dirichlet boundary conditions are specified as magnetic vector potential, +, on +(element-based) surfaces that represent symmetry planes and/or external boundaries in the model; +Abaqus computes +In applications where the electromagnetic +fields are driven by a current-carrying coil that is close to the workpiece, the model may span a domain +that is up to 10 times the characteristic length scale associated with the coil/workpiece assembly. In +such cases, the electromagnetic fields are assumed to have decayed sufficiently in the far-field, and the +value of the magnetic vector potential can be set to zero in the far-field boundary. On the other hand, in +applications such as one where a conductor is embedded in a uniform (but varying time-harmonically +in a time-harmonic eddy current analysis or with a more general time variation in a transient eddy +current analysis) far-field magnetic field, it may be necessary to specify nonzero values of the magnetic +vector potential on some portions of the external boundary. In this case an alternative method to model +the same physical phenomena is to specify the corresponding unique value of surface current density, +can be computed based on known values of the +, on the far-field boundary . +far-field magnetic field. +A surface without any prescribed boundary condition corresponds to a surface with zero surface +currents, or no loads. +Nonuniform boundary conditions can be defined with user subroutine UDEMPOTENTIAL. +Prescribing boundary conditions in a time-harmonic eddy current analysis +In a time-harmonic eddy current analysis the boundary conditions are assumed to be time harmonic and +are applied simultaneously to both the real and imaginary parts of the magnetic vector potential. It is not +possible to specify Dirichlet boundary conditions on the real parts and Neumann boundary conditions +on the imaginary parts and vice versa. Abaqus automatically restrains both the real and imaginary parts +even if only one part is prescribed explicitly. The unspecified part is assumed to have a magnitude of +zero. +When you prescribe the boundary condition on an element-based surface for a time-harmonic +eddy current analysis , you must specify the +surface name, the region type label (S), the boundary condition type label, an optional orientation name, +the magnitude of the real part of the boundary condition, the direction vector for the real part of the +boundary condition, the magnitude of the imaginary part of the boundary condition, and the direction +vector for the imaginary part of the boundary condition. The optional orientation name defines the local +coordinate system in which the components of the magnetic vector potential are defined. By default, the +components are defined with respect to the global directions. The specified direction vector components +are normalized by Abaqus and, thus, do not contribute to the magnitude of the boundary condition. +During a time-harmonic eddy current analysis, frequency-dependent boundary conditions can be +prescribed as described in “Frequency-dependent boundary conditions in a time-harmonic eddy current +analysis” below. +Input File Usage: +Use the following option in a time-harmonic eddy current analysis to define +both the real (in-phase) and imaginary (out-of-phase) parts of the boundary +condition on element-based surfaces: +*D EM POTENTIAL +surface name, S, bc type label, orientation, magnitude of real +part, direction vector of real part, magnitude of imaginary part, +direction vector of imaginary part +where the boundary condition type label (bc type label) can be MVP for a +uniform boundary condition or MVPNU for a nonuniform boundary condition. +Load module: Create Boundary Condition: choose Electrical/Magnetic +for the Category and Magnetic vector potential for the Types +for Selected Step; Distribution: Uniform or User-defined; +real components + imaginary components +Abaqus/CAE Usage: +Prescribing boundary conditions in a transient eddy current analysis +The method of specification of the boundary condition for a transient eddy current analysis is substantially +similar to that of the time-harmonic eddy current analysis, except that the concepts of real and imaginary +are not relevant any more. +In this case you specify the magnitude of the magnetic vector potential, +followed by its direction vector. The specified direction vector components are normalized by Abaqus +and, thus, do not contribute to the magnitude of the boundary condition. +During a transient eddy current analysis, prescribed boundary conditions can be varied using an +amplitude definition . +Input File Usage: +Use the following option in a transient eddy current analysis to define the +boundary condition on element-based surfaces: +*D EM POTENTIAL +surface name, S, bc type label, orientation, magnitude, direction vector +where the boundary condition type label (bc type label) can be MVP for a +uniform boundary condition or MVPNU for a nonuniform boundary condition. +Abaqus/CAE Usage: +Transient eddy current analysis is not supported in Abaqus/CAE. +Frequency-dependent boundary conditions in a time-harmonic eddy current analysis +An amplitude definition can be used to specify the amplitude of a boundary condition as a function of +frequency (“Amplitude curves,” Section 33.1.2). +Input File Usage: +Use both of the following options: +*AMPLITUDE, NAME=name +*D EM POTENTIAL, AMPLITUDE=name +Load or Interaction module: Create Amplitude: Name: amplitude_name +Load module: Create Boundary Condition: choose Electrical/Magnetic +for the Category and Magnetic vector potential for the Types for +Selected Step; Amplitude: amplitude_name +Abaqus/CAE Usage: +Loads +The following types of electromagnetic loads can be applied in an eddy current analysis : +analysis, and +• Element-based distributed volume current density vector: +in a transient eddy current analysis +• Surface-based distributed surface current density vector: +in a transient eddy current analysis +analysis, and +in a time-harmonic eddy current +in a time-harmonic eddy current +All loads in a time-harmonic eddy current analysis are assumed to be time-harmonic with the excitation +frequency. During a transient eddy current analysis all loads can be varied using an amplitude definition +. +Nonuniform loads can be specified using user subroutines UDECURRENT and UDSECURRENT. +Frequency-dependent loading in a time-harmonic eddy current analysis +In a time-harmonic eddy current analysis, an amplitude definition can be used to specify the amplitude +of a load as a function of frequency (“Amplitude curves,” Section 33.1.2). +Predefined fields +Predefined temperature and field variables can be specified in an eddy current analysis. These values +affect only temperature and/or field-variable-dependent material properties, if any. See “Predefined +fields,” Section 33.6.1. +Material options +Magnetic material behavior must be specified everywhere +in the model. Only linear magnetic behavior is supported in a time-harmonic eddy current analysis, but +nonlinear magnetic behavior is also supported in a transient eddy current analysis. Linear magnetic +behavior can be defined by specifying the magnetic permeability directly, while nonlinear magnetic +behavior is defined in terms of one or more B–H curves. Electrical conductivity must be specified in conductor regions. All other material properties are +ignored in an eddy current analysis. +Both magnetic permeability and electrical conductivity can be functions of frequency, predefined +temperature, and field variables in a time-harmonic eddy current analysis. In a transient eddy current +analysis, all material behavior can be functions of predefined temperature and/or field variables. +Elements +Electromagnetic elements must be used to model all regions in an eddy current analysis. Unlike +conventional finite elements, which use node-based interpolation, +these elements use edge-based +interpolation with the tangential components of the magnetic vector potential along element edges +serving as the primary degrees of freedom. +Electromagnetic elements are available in Abaqus/Standard in two dimensions (planar only) and +three dimensions . The +planar elements are formulated in terms of an in-plane magnetic vector potential, thereby the magnetic +flux density and magnetic field vectors only have an out-of-plane component. The electric field and the +current density vectors are in-plane for the planar elements. +Output +Eddy current analysis provides output only to the output database (.odb) file . Output to the data (.dat) file and to the results (.fil) file is not available. +For the first four vector quantities listed below (which are derived from the magnetic vector potential and +the constitutive equations), the magnitude and components of the real and imaginary parts are output in +a time-harmonic eddy current procedure. +Element centroidal variables: +EMB +EMH +EME +EMCD +Magnitude and components of the magnetic flux density vector, +Magnitude and components of the magnetic field vector, +. +. +Magnitude and components of the electric field vector, +Magnitude and components of the eddy current vector, +. +, in conducting regions. +EMBF +EMBFC +EMJH +Magnetic body force intensity vector (force per unit volume per unit time) due to +flow of current. +Complex magnetic body force intensity vector (real and imaginary parts of the +force per unit volume) due to flow of current. Only available in a time-harmonic +eddy current analysis. +Rate of Joule heating (amount of heat per unit volume per unit time) due to flow +of current. +Whole element variables: +ELJD +Total rate of Joule heating (amount of heat per unit time) due to flow of current in +an element. +Whole model variables: +ALLJD +Rate of Joule heating (amount of heat per unit time) summed over the model or an +element set. +Input file template +The following is an input file template that makes use of linear magnetic material behavior in a time- +harmonic eddy current analysis: +*HEADING +… +*MATERIAL, NAME=mat1 +*MAGNETIC PERMEABILITY +Data lines to define magnetic permeability +*ELECTRICAL CONDUCTIVITY +Data lines to define electrical conductivity in the conductor region +** +*STEP +*ELECTROMAGNETIC, LOW FREQUENCY, TIME HARMONIC +Data line to specify excitation frequencies +*D EM POTENTIAL +Data lines to define boundary conditions on magnetic vector potential +*DECURRENT +Data lines to define element-based distributed volume current density vector +*DSECURRENT +Data lines to define surface-based distributed surface current density vector +*OUTPUT, FIELD or HISTORY +Data lines to request element-based output +*ENERGY OUTPUT +Data line to request whole model Joule heat dissipation output +*END STEP +The following is an input file template that makes use of nonlinear magnetic material behavior in a +transient eddy current analysis: +*HEADING +… +*MATERIAL, NAME=mat1 +*MAGNETIC PERMEABILITY, NONLINEAR +*NONLINEAR BH, DIR=direction +Data lines to define nonlinear B-H curve +*ELECTRICAL CONDUCTIVITY +Data lines to define electrical conductivity in the conductor region +** +*STEP +*ELECTROMAGNETIC, LOW FREQUENCY, TRANSIENT +*D EM POTENTIAL +Data lines to define boundary conditions on magnetic vector potential +*DECURRENT +Data lines to define element-based distributed volume current density vector +*DSECURRENT +Data lines to define surface-based distributed surface current density vector +*OUTPUT, FIELD or HISTORY +Data lines to request element-based output +*ENERGY OUTPUT +Data line to request whole model Joule heat dissipation output +*END STEP +Additional reference +• Bíró, O., “Edge Element Formulation of Eddy Current Problems,” Computer Methods in Applied +Mechanics and Engineering, vol. 169, pp. 391–405, 1999. +6.7.6 +MAGNETOSTATIC ANALYSIS +Product: Abaqus/Standard +References +• “Electromagnetic analysis procedures,” Section 6.7.1 +• “Magnetic permeability,” Section 26.5.3 +• “Electromagnetic loads,” Section 33.4.5 +• *MAGNETOSTATIC +• *D EM POTENTIAL +• *DECURRENT +• *DSECURRENT +• “UDECURRENT,” Section 1.1.23 of the Abaqus User Subroutines Reference Manual +• “UDEMPOTENTIAL,” Section 1.1.24 of the Abaqus User Subroutines Reference Manual +• “UDSECURRENT,” Section 1.1.26 of the Abaqus User Subroutines Reference Manual +Overview +Magnetostatic problems: +• solve the magnetostatic approximation of Maxwell’s equations describing electromagnetic +phenomena and compute the magnetic fields due to direct currents; +• involve only magnetic fields, which are assumed to be vary slowly in time such that electromagnetic +coupling can be neglected; +• require the use of electromagnetic elements in the whole domain; +• require that magnetic permeability is specified in the whole domain; +• can be solved with nonlinear magnetic behavior; and +• can be solved using continuum elements in two- and three-dimensional space. +Magnetostatic analysis +A direct current creates a static magnetic field in the space surrounding the current carrying region. +For applications where the magnitude of the direct current can be assumed to be a constant or to vary +slowly with time, coupling between magnetic and electric fields can be neglected. The magnetostatic +approximation to Maxwell’s equations involves the magnetic fields only. Magnetostatic analysis +provides a solution for applications where the above assumptions are valid. +Electromagnetic elements must be used to model the response of all the regions in a magnetostatic +analysis, including regions such as current carrying coils and the surrounding space. To obtain accurate +solutions, the outer boundary of the space being modeled must be at least a few characteristic length +scales away from the region of interest on all sides. +Electromagnetic elements use an element edge-based interpolation of the fields instead of the +standard node-based interpolation. The user-defined nodes only define the geometry of the elements; +and the degrees of freedom of the element are not associated with these nodes, which has implications +for applying boundary conditions . +Governing field equations +The magnetic fields are governed by the magnetostatic approximation to Maxwell’s equations describing +electromagnetic phenomena. +It is convenient to introduce a magnetic vector potential, +, such that the magnetic flux density +. The solution procedure seeks a static magnetic response due to, for example, an +in some regions of the model. The magnetostatic +vector +impressed direct volume current density distribution, +approximation to Maxwell’s equations is given by +in terms of the field quantities, +permeability relates the magnetic flux density, +equation of the form: +and +. +and the magnetic permeability tensor, +, to the magnetic field, +. The magnetic +, through a constitutive +The variational form of the above equation is +where +tangential surface current density, if any, at the external surfaces. +represents the variation of the magnetic vector potential, and +represents the applied +Abaqus/Standard solves the variational form of Maxwell’s equations for the components of the +magnetic vector potential. The other field quantities are derived from the magnetic vector potential. In +the following discussion, the governing equations are written for a linear medium. +Defining the magnetic behavior +The magnetic behavior of the electromagnetic medium can be linear or nonlinear. Linear magnetic +behavior is characterized by a magnetic permeability tensor that is assumed to be independent of the +magnetic field. It is defined through direct specification of the absolute magnetic permeability tensor, +, +which can be isotropic, orthotropic, or fully anisotropic . +The magnetic permeability can also depend on temperature and/or predefined field variables. +Nonlinear magnetic behavior is characterized by magnetic permeability that depends on the strength +of the magnetic field. The nonlinear magnetic material model in Abaqus is suitable for ideally soft +magnetic materials characterized by a monotonically increasing response in B–H space, where B and +H refer to the strengths of the magnetic flux density vector and the magnetic field vector, respectively. +Nonlinear magnetic behavior is defined through direct specification of one or more B–H curves that +provide B as a function of H and, optionally, temperature and/or predefined field variables, in one or +more directions. Nonlinear magnetic behavior can be isotropic, orthotropic, or transversely isotropic +(which is a special case of the more general orthotropic behavior). +Magnetostatic analysis +Magnetostatic analysis provides the magnetic flux density and the magnetic field at a given value of the +impressed direct current. +Input File Usage: +*MAGNETOSTATIC +Ill-conditioning in magnetostatic analyses +In magnetostatic analysis the stiffness matrix can be very ill-conditioned; +i.e., it can have many +singularities. Abaqus uses a special iterative solution technique to prevent the ill-conditioned matrix +from negatively impacting the computed magnetic fields. The default implementation works well +for many problems. However, there can be situations in which the default numerical scheme fails to +converge. Abaqus provides a stabilization scheme to help mitigate the effects of the ill-conditioning. +You can provide input to this stabilization algorithm by specifying the stabilization factor, which is +assumed to be 1.0 by default if the stabilization scheme is used. Higher values of the stabilization factor +lead to more stabilization, while lower values of the stabilization factor lead to less stabilization. +Input File Usage: +*MAGNETOSTATIC, STABILIZATION=stabilization factor +Initial conditions +Initial values of temperature and/or predefined field variables can be specified. These values affect only +temperature and/or field-variable-dependent material properties, if any. Initial conditions on magnetic +fields cannot be specified in a magnetostatic analysis. +Boundary conditions +Electromagnetic elements use an element edge-based interpolation of the fields. The degrees of freedom +of the element are not associated with the user-defined nodes, which only define the geometry of the +element. Consequently, the standard node-based method of specifying boundary conditions cannot be +used with electromagnetic elements. +Boundary conditions in Abaqus typically refer to what are traditionally known as Dirichlet-type +boundary conditions in the literature, where the values of the primary variable are known on the whole +boundary or on a portion of the boundary. The alternative, Neumann-type boundary conditions, refer +to situations where the values of the conjugate to the primary variable are known on portions of the +boundary. In Abaqus, Neumann-type boundary conditions are represented as surface loads in the finite +element formulation. +For electromagnetic boundary value problems, +including magnetostatic problems, Dirichlet +boundary conditions on an enclosing surface must be specified as +is the outward +, where +normal to the surface, as discussed in this section. Neumann boundary conditions must be specified as +the surface current density vector, +, as discussed in “Loads” below. +In Abaqus, Dirichlet boundary conditions are specified as magnetic vector potential, +, on +(element-based) surfaces that represent symmetry planes and/or external boundaries in the model; +Abaqus computes +for the representative surfaces. The model may span a domain that is up to 10 +times some characteristic length scale for the problem. In such cases the magnetic fields are assumed +to have decayed sufficiently in the far-field, and the value of the magnetic vector potential can be set to +zero in the far-field boundary. On the other hand, in applications such as one where a magnetic material +is embedded in a uniform far-field magnetic field, it may be necessary to specify nonzero values of the +magnetic vector potential on some portions of the external boundary. In this case an alternative method +to model the same physical phenomena is to specify the corresponding unique value of surface current +density, +can be computed based on known values +of the far-field magnetic field. +, on the far-field boundary . +In a magnetostatic analysis the boundary conditions are assumed to be either constant or varying +slowly with time. The time variation can be specified using an amplitude definition (“Amplitude curves,” +Section 33.1.2) +A surface without any prescribed boundary condition corresponds to a surface with zero surface +currents or no loads. +When you prescribe the boundary condition on an element-based surface , you must specify the surface name, the region type label (S), the +boundary condition type label, an optional orientation name, the magnitude of the magnetic vector +potential, and the direction vector for the magnetic vector potential. The optional orientation name +defines the local coordinate system in which the components of the magnetic vector potential are +defined. By default, the components are defined with respect to the global directions. +The specified vector components are normalized by Abaqus and, thus, do not contribute to the +magnitude of the boundary condition. +Nonuniform boundary conditions can be defined with user subroutine UDEMPOTENTIAL. +Input File Usage: +Use the following option to define both the real (in-phase) and imaginary (out- +of-phase) parts of the boundary condition on element-based surfaces: +*D EM POTENTIAL +surface name, S, bc type label, orientation, magnitude, direction vector +where the boundary condition type label (bc type label) can be MVP for a +uniform boundary condition or MVPNU for a nonuniform boundary condition. +Loads +The following types of electromagnetic loads can be applied in a magnetostatic analysis : +• Element-based distributed volume current density vector, +• Surface-based distributed surface current density vector, +During the analysis the prescribed load can be varied using an amplitude definition (“Amplitude curves,” +Section 33.1.2). +Predefined fields +Predefined temperature and field variables can be specified in a magnetostatic analysis. These values +affect only temperature and/or field-variable-dependent material properties, if any. See “Predefined +fields,” Section 33.6.1. +Material options +The magnetic behavior must be defined everywhere in the +model, either by specifying the absolute magnetic permeability tensor for linear magnetic behavior or by +specifying the B–H curve-based response for nonlinear magnetic behavior. All other material properties, +including electrical conductivity, are ignored in a magnetostatic analysis. The magnetic behavior can be +functions of predefined temperature and/or field variables. +Elements +Electromagnetic elements must be used to model all regions in a magnetostatic analysis. Unlike +conventional finite elements, which use node-based interpolation, +these elements use edge-based +interpolation with the tangential components of the magnetic vector potential along element edges +serving as the primary degrees of freedom. +Electromagnetic elements are available in Abaqus/Standard in two dimensions (planar only) and +three dimensions . The +planar elements are formulated in terms of an in-plane magnetic vector potential, thereby the magnetic +flux density and magnetic field vectors have only an out-of-plane component. +Output +Magnetostatic analysis provides output only to the output database (.odb) file . Output to the data (.dat) file and to the results (.fil) file is not available. +Element centroidal variables: +EMB +EMH +Magnitude and components of the magnetic flux density vector, +Magnitude and components of the magnetic field vector, +. +. +Input file template +*HEADING +… +*MATERIAL, NAME=mat1 +*MAGNETIC PERMEABILITY, NONLINEAR +Data lines to define magnetic permeability for linear magnetic behavior; no data required here for +nonlinear magnetic behavior +*NONLINEAR BH, DIR=direction +Data lines to define nonlinear B-H curve +** +*STEP +*MAGNETOSTATIC +Data line to define time incrementation +*D EM POTENTIAL +Data lines to define boundary conditions on magnetic vector potential +*DECURRENT +Data lines to define element-based distributed volume current density vector +*DSECURRENT +Data lines to define surface-based distributed surface current density vector +*OUTPUT, FIELD or HISTORY +Data lines to request element-based output +*END STEP +6.8 +Coupled pore fluid flow and stress analysis +• “Coupled pore fluid diffusion and stress analysis,” Section 6.8.1 +• “Geostatic stress state,” Section 6.8.2 +6.8.1 +COUPLED PORE FLUID DIFFUSION AND STRESS ANALYSIS +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “Pore fluid flow properties,” Section 26.6.1 +• *SOILS +• “Defining pore fluid expansion” in “Defining a fluid-filled porous material,” Section 12.12.3 of the +Abaqus/CAE User’s Manual, in the online HTML version of this manual +• “Configuring an effective stress analysis for fluid-filled porous media” in “Configuring general +analysis procedures,” Section 14.11.1 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +A coupled pore fluid diffusion/stress analysis: +• is used to model single phase, partially or fully saturated fluid flow through porous media; +• can be performed in terms of either total pore pressure or excess pore pressure by including or +excluding the pore fluid weight; +• requires the use of pore pressure elements with associated pore fluid flow properties defined; +• can, optionally, also model heat transfer due to conduction in the soil skeleton and the pore fluid, and +convection due to the flow of the pore fluid, through the use of coupled temperature–pore pressure +displacement elements; +• can be transient or steady-state; +• can be linear or nonlinear; and +• can include pore pressure contact between bodies . +Typical applications +Some of the more common coupled pore fluid diffusion/stress (and, optionally, thermal) analysis +problems that can be analyzed with Abaqus/Standard are: +• Saturated flow: Soil mechanics problems generally involve fully saturated flow, since the solid +is fully saturated with ground water. Typical examples of saturated flow include consolidation of +soils under foundations and excavation of tunnels in saturated soil. +• Partially saturated flow: Partially saturated flow occurs when the wetting liquid is absorbed +into or exsorbed from the medium by capillary action. Irrigation and hydrology problems generally +include partially saturated flow. +• Combined flow: Combined fully saturated and partially saturated flow occurs in problems such +as seepage of water through an earth dam, where the position of the phreatic surface (the boundary +between fully saturated and partially saturated soil) is of interest. +• Moisture migration: Although not normally associated with soil mechanics, moisture migration +problems can also be solved using the coupled pore fluid diffusion/stress procedure. These problems +may involve partially saturated flow in polymeric materials such as paper towels and sponge-like +materials; in the biomedical industry they may also involve saturated flow in hydrated soft tissues. +In some applications, such as a source of heat +buried in soil, it is important to model the coupling between the mechanical deformation, pore +fluid flow, and heat transfer. In such problems the difference in the thermal expansion coefficients +between the soil and the pore fluid often plays an important role in determining the rate of diffusion +of the pore fluid and heat from the source. +• Combined heat transfer and pore fluid flow: +Flow through porous media +A porous medium is modeled in Abaqus/Standard by a conventional approach that considers the medium +as a multiphase material and adopts an effective stress principle to describe its behavior. The porous +medium modeling provided considers the presence of two fluids in the medium. One is the “wetting +liquid,” which is assumed to be relatively (but not entirely) incompressible. Often the other is a gas, +which is relatively compressible. An example of such a system is soil containing ground water. When +the medium is partially saturated, both fluids exist at a point; when it is fully saturated, the voids are +completely filled with the wetting liquid. The elementary volume, +, is made up of a volume of grains +of solid material, +, that is free +; a volume of voids, +to move through the medium if driven. In some systems (for example, systems containing particles that +absorb the wetting liquid and swell in the process) there may also be a significant volume of trapped +wetting liquid, +; and a volume of wetting liquid, +. +The porous medium is modeled by attaching the finite element mesh to the solid phase; fluid can +flow through this mesh. The mechanical part of the model is based on the effective stress principle +defined in “Effective stress principle for porous media,” Section 2.8.1 of the Abaqus Theory Manual. +The model also uses a continuity equation for the mass of wetting fluid in a unit volume of the +medium. This equation is described in “Continuity statement for the wetting liquid phase in a porous +medium,” Section 2.8.4 of the Abaqus Theory Manual. It is written with pore pressure (the average +pressure in the wetting fluid at a point in the porous medium) as the basic variable (degree of freedom 8 +at the nodes). The conjugate flux variable is the volumetric flow rate at the node, +. The porous medium +is partially saturated when the pore liquid pressure, +, is negative. +Coupled flow and heat transfer through porous media +Optionally, heat transfer due to conduction in the soil skeleton and pore fluid, as well as convection in +the pore fluid, can also be modeled. This capability represents an enhancement to the basic pore fluid +flow capabilities discussed in the earlier paragraphs and requires the use of coupled temperature–pore +pressure elements that have temperature as an additional degree of freedom (degree of freedom 11 +at the nodes) in addition to the pore pressure and the displacement components. When you use the +coupled temperature–pore pressure elements, Abaqus solves the heat transfer equation in addition to +and in a fully coupled manner with the continuity equation and the mechanical equilibrium equations. +Only linear brick, first-order axisymmetric, and second-order modified tetrahedrons are available +for modeling coupled heat transfer with pore fluid flow and mechanical deformation. Coupled +temperature–pore pressure elements are not supported in Abaqus/CAE. +Total and excess pore fluid pressure +The coupled pore fluid diffusion/stress analysis capability can provide solutions either in terms of total +or “excess” pore fluid pressure. The excess pore fluid pressure at a point is the pore fluid pressure in +excess of the hydrostatic pressure required to support the weight of pore fluid above the elevation of the +material point. The difference between total and excess pore pressure is relevant only for cases in which +gravitational loading is important; for example, when the loading provided by the hydrostatic pressure +in the pore fluid is large or when effects like “wicking” (transient capillary suction of liquid into a dry +column) are being studied. Total pore pressure solutions are provided when the gravity distributed load +is used to define the gravity load on the model. Excess pore pressure solutions are provided in all other +cases; for example, when gravity loading is defined with body force distributed loads. +Steady-state analysis +Steady-state coupled pore pressure/effective stress analysis assumes that there are no transient effects in +the wetting liquid continuity equation; that is, the steady-state solution corresponds to constant wetting +liquid velocities and constant volume of wetting liquid per unit volume in the continuum. Thus, for +example, thermal expansion of the liquid phase has no effect on the steady-state solution: it is a transient +effect. Therefore, the time scale chosen during steady-state analysis is relevant only to rate effects in the +constitutive model used for the porous medium (excluding creep and viscoelasticity, which are disabled +in steady-state analysis). +Mechanical loads and boundary conditions can be changed gradually over the step by referring to +an amplitude curve to accommodate possible geometric nonlinearities in the response. +The steady-state coupled equations are strongly unsymmetric; therefore, the unsymmetric matrix +solution and storage scheme is used automatically for steady-state analysis steps . +If heat transfer is modeled using the coupled temperature–pore pressure elements, the steady-state +solution neglects all transient effects in the heat transfer equation and provides only the steady-state +temperature distribution. +Input File Usage: +Abaqus/CAE Usage: +*SOILS +Step module: Create Step: General: Soils: Basic: Pore +fluid response: Steady state +Incrementation +You can specify a fixed time increment size in a coupled pore fluid diffusion/stress analysis, or +Abaqus/Standard can select the time increment size automatically. Automatic incrementation is +recommended because the time increments in a typical diffusion analysis can increase by several +orders of magnitude during the simulation. If you do not activate automatic incrementation, fixed time +increments will be used. +Input File Usage: +Use the following option to activate automatic incrementation in steady-state +analysis: +*SOILS, UTOL=any arbitrary nonzero value +The solution does not depend on the value specified for UTOL; this value is +simply a flag for automatic incrementation. +Abaqus/CAE Usage: +Step module: Create Step: General: Soils: Basic: Pore fluid response: +Steady state; Incrementation: Type: Automatic +Transient analysis +In a transient coupled pore pressure/effective stress analysis the backward difference operator is used to +integrate the continuity equation and the heat transfer equation (if heat transfer is modeled): this operator +provides unconditional stability so that the only concern with respect to time integration is accuracy. You +can provide the time increments, or they can be selected automatically. +The coupled partially saturated flow equations are strongly unsymmetric, so the unsymmetric solver +is used automatically if you request partially saturated analysis (by including absorption/exsorption +behavior in the material definition). The unsymmetric solver is also activated automatically when +gravity distributed loading is used during a soils consolidation analysis. +For fully saturated flow analyses in which finite-sliding coupled pore pressure-displacement contact +is modeled using contact pairs, certain contributions to the model’s stiffness matrix are unsymmetric. +Using the unsymmetric solver can sometimes improve convergence in such cases since Abaqus does not +automatically do so. +For fully saturated flow analyses in which heat transfer is also modeled, the contributions to the +model’s stiffness matrix arising from convective heat transfer due to pore fluid flow are unsymmetric. +Using the unsymmetric solver can sometimes improve convergence in such cases since Abaqus does not +automatically do so. +Spurious oscillations due to small time increments +The integration procedure used in Abaqus/Standard for consolidation analysis introduces a relationship +between the minimum usable time increment and the element size, as shown below for fully saturated and +partially saturated flows. If time increments smaller than these values are used, spurious oscillations may +appear in the solution (except for partially saturated cases when linear elements or modified triangular +elements are used; in these cases Abaqus/Standard uses a special integration scheme for the wetting liquid +storage term to avoid the problem). These nonphysical oscillations may cause problems if pressure- +sensitive plasticity is used to model the porous medium and may lead to convergence difficulties in +partially saturated analyses. +If the problem requires analysis with smaller time increments than the +relationships given below allow, a finer mesh is required. Generally there is no upper limit on the time +step except accuracy, since the integration procedure is unconditionally stable unless nonlinearities cause +convergence problems. +Fully saturated flow +A simple guideline that can be used for the minimum usable time increment in the case of fully saturated +flow is +where +is the time increment, +is the specific weight of the wetting liquid, +is the Young’s modulus of the soil, +is the permeability of the soil , +is the magnitude of the velocity of the pore fluid, +is the velocity coefficient in Forchheimer’s flow law ( +in the case of Darcy flow), +is the bulk modulus of the solid grains , and +is a typical element dimension. +Partially saturated flow +In partially saturated flow cases the corresponding guideline for the minimum time increment is +where +is the saturation; +is the permeability-saturation relationship; +is the rate of change of saturation with respect +Section 26.6.4); +is the initial porosity of the material; and the other parameters are as defined for the case of +fully saturated flow. +to pore pressure (see “Sorption,” +Fixed incrementation +If you choose fixed time incrementation, fixed time increments equal to the size of the user-specified +initial time increment, +, will be used. Fixed incrementation is not generally recommended because +the time increments in a typical diffusion analysis can increase over several orders of magnitude during +the simulation; automatic incrementation is usually a better choice. +Input File Usage: +*SOILS, CONSOLIDATION +Abaqus/CAE Usage: +Step module: Create Step: General: Soils: Basic: Pore fluid +response: Transient consolidation; Incrementation: Type: +Fixed, Increment size: +Automatic incrementation +If you choose automatic time incrementation, you must specify two (three if heat transfer is also modeled) +tolerance parameters. +The accuracy of the time integration of the flow continuity equations is governed by the maximum +wetting liquid pore pressure change, +, allowed in an increment. Abaqus/Standard restricts the time +increments to ensure that this value is not exceeded at any node (except nodes with boundary conditions) +during any increment in the analysis. +If heat transfer is modeled, the accuracy of time integration is also governed by the maximum +temperature change, +, allowed in an increment. Abaqus/Standard restricts the time increments to +ensure that this value is not exceeded at any node (except nodes with boundary conditions) during any +increment of the analysis. +The accuracy of the integration of the time-dependent (creep) material behavior is governed by the +, as +maximum strain rate change allowed at any point during an increment, +described in “Rate-dependent plasticity: creep and swelling,” Section 23.2.4. +Input File Usage: +If heat transfer is not modeled: +Abaqus/CAE Usage: +*SOILS, CONSOLIDATION, UTOL= +, , CETOL=errtol +If heat transfer is modeled: +*SOILS, CONSOLIDATION, UTOL= +CETOL=errtol +, DELTMX= +, +Step module: Create Step: General: Soils: Basic: Pore fluid +response: Transient consolidation; Incrementation: Type: +Automatic, Max. pore pressure change per increment: +Creep/swelling/viscoelastic strain error tolerance: errtol +, +Specifying the maximum temperature change per increment is not supported in +Abaqus/CAE. +Ending a transient analysis +Transient soils analysis can be terminated by completing a specified time period, or it can be continued +until steady-state conditions are reached. By default, the analysis will end when the given time period has +been completed. Alternatively, you can specify that the analysis will end when steady state is reached or +the time period ends, whichever comes first. When heat transfer is not modeled, steady state is defined by +a maximum permitted rate of change of pore pressure with time: when all pore pressures are changing at +less than the user-defined rate, the analysis terminates. However, with heat transfer included, the analysis +terminates only when both the pore pressure and temperature are changing at less than the user-defined +rates. +Input File Usage: +Use the following option to end the analysis when the time period is reached: +Abaqus/CAE Usage: +*SOILS, CONSOLIDATION, END=PERIOD (default) +Use the following option to end the analysis based on the pore pressure and, if +heat transfer is modeled, temperature change rate: +*SOILS, CONSOLIDATION, END=SS +Step module: Create Step: General: Soils: Basic: Pore fluid +response: Transient consolidation; Incrementation: End step +when pore pressure change rate is less than +If heat transfer is modeled, directly specifying the temperature change rate to +define steady state is not supported in Abaqus/CAE. +Neglecting creep during a transient analysis +You can specify that creep or viscoelastic response should be neglected during a consolidation analysis, +even if creep or viscoelastic material properties have been defined. +Input File Usage: +Abaqus/CAE Usage: +*SOILS, CONSOLIDATION, CREEP=NONE +Step module: Create Step: General: Soils: Basic: Pore +fluid response: Transient consolidation, toggle off Include +creep/swelling/viscoelastic behavior +Unstable problems +Some types of analyses may develop local instabilities, such as surface wrinkling, material instability, +or local buckling. In such cases it may not be possible to obtain a quasi-static solution, even with the aid +of automatic incrementation. Abaqus/Standard offers the option to stabilize this class of problems by +applying damping throughout the model in such a way that the viscous forces introduced are sufficiently +large to prevent instantaneous buckling or collapse but small enough not to affect the behavior +significantly while the problem is stable. The available automatic stabilization schemes are described in +detail in “Automatic stabilization of unstable problems” in “Solving nonlinear problems,” Section 7.1.1. +Optional modeling of coupled heat transfer +When coupled temperature–pore pressure elements are used, heat transfer is modeled in these elements +by default. However, you may optionally choose to switch off heat transfer within these elements during +some steps in the analysis. This feature may be helpful in reducing computation time during certain +phases in the analysis when heat transfer is not an important part of the overall physics of the problem. +Input File Usage: +Use the following option either during a transient or a steady-state procedure +to suppress heat transfer modeling: +*SOILS, CONSOLIDATION, HEAT=NO +Abaqus/CAE Usage: +Switching off the heat +Abaqus/CAE. +transfer part of the physics is not supported in +Units +In coupled problems where two or more different fields are being solved, you must be careful when +choosing the units of the problem. +If the choice of units is such that the numbers generated by the +equations for the different fields differ by many orders of magnitude, the precision on some computers +may be insufficient to resolve the numerical ill-conditioning of the coupled equations. Therefore, choose +units that avoid badly conditioned matrices. For example, consider using units of Mpascal instead of +pascal for the stress equilibrium equations to reduce the disparity between the magnitudes of the stress +equilibrium equations and the pore flow continuity equations. +Initial conditions +Initial conditions can be applied as defined in “Initial conditions in Abaqus/Standard and +Abaqus/Explicit,” Section 33.2.1. +Defining initial pore fluid pressures +Initial values of pore fluid pressures, +, can be defined at the nodes. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=PORE PRESSURE +Load module: Create Predefined Field: Step: Initial: choose Other for the +Category and Pore pressure for the Types for Selected Step +Defining initial void ratios +Initial values of the void ratio, e, can be given at the nodes. The void ratio is defined as the ratio +of the volume of voids to the volume of solid material . The evolution of void ratio is governed by the +deformation of the different phases of the material, as discussed in detail in “Constitutive behavior in a +porous medium,” Section 2.8.3 of the Abaqus Theory Manual. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=RATIO +Load module: Create Predefined Field: Step: Initial: choose Other for +the Category and Void ratio for the Types for Selected Step +Defining initial saturation +Initial saturation values, s, can be given at the nodes. Saturation is defined as the ratio of wetting fluid +volume to void volume . +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=SATURATION +Load module: Create Predefined Field: Step: Initial: choose Other for +the Category and Saturation for the Types for Selected Step +Defining initial stresses +An initial (effective) stress field can be specified . +Most geotechnical problems begin from a geostatic state, which is a steady-state equilibrium +configuration of the undisturbed soil or rock body under geostatic loading and usually includes both +horizontal and vertical components. +It is important to establish these initial conditions correctly so +that the problem begins from an equilibrium state. The geostatic procedure can be used to verify that +the user-defined initial stresses are indeed in equilibrium with the given geostatic loads and boundary +conditions . +Input File Usage: +Use one of the following options: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=STRESS +*INITIAL CONDITIONS, TYPE=STRESS, GEOSTATIC +Load module: Create Predefined Field: Step: Initial: choose +Mechanical for the Category and Stress or Geostatic stress +for the Types for Selected Step +Defining initial temperature +Initial temperature values can be defined at the nodes. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=TEMPERATURE +Load module: Create Predefined Field: Step: Initial: choose Other for +the Category and Temperature for the Types for Selected Step +Boundary conditions +Boundary conditions can be applied to displacement degrees of freedom 1–6 and to pore pressure degree +of freedom 8 (“Boundary conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1). +In +addition, boundary conditions can also be applied to temperature degree of freedom 11 if heat transfer +is modeled using coupled temperature–pore pressure elements. During the analysis prescribed boundary +conditions can be varied by referring to an amplitude curve (“Amplitude curves,” Section 33.1.2). If +no amplitude reference is given, the default variation of a boundary condition in a coupled pore fluid +diffusion/stress analysis step is as defined in “Defining an analysis,” Section 6.1.2. +If the pore pressure is prescribed with a boundary condition, fluid is assumed to enter and leave +through the node as needed to maintain the prescribed pressure. Likewise, if the temperature is prescribed +with a boundary condition, heat is assumed to enter and leave through the node as needed to maintain +the prescribed temperature. +Loads +The following loading types can be prescribed in a coupled pore fluid diffusion/stress analysis: +• Concentrated nodal forces can be applied to the displacement degrees of freedom (1–6); see +“Concentrated loads,” Section 33.4.2. +• Distributed pressure forces or body forces can be applied; see “Distributed loads,” Section 33.4.3. +The distributed load types available with particular elements are described in Part VI, “Elements.” +The magnitude and direction of gravitational loading are usually defined by using the gravity +distributed load type. +• Pore fluid flow is controlled as described in “Pore fluid flow,” Section 33.4.7. +If heat transfer is modeled, the following types of thermal loading can also be prescribed (“Thermal +loads,” Section 33.4.4). These loads are not supported in Abaqus/CAE during a coupled thermal pore +pressure/stress analysis. +• Concentrated heat fluxes. +• Body fluxes and distributed surface fluxes. +• Convective film conditions and radiation conditions; film properties can be made a function of +temperature. +Predefined fields +The following predefined fields can be prescribed, as described in “Predefined fields,” Section 33.6.1: +• For a coupled pore fluid diffusion/stress analysis that does not model heat transfer and uses regular +pore pressure elements, temperature is not a degree of freedom and nodal temperatures can be +specified. Any difference between the applied and initial temperatures will cause thermal strain +if a thermal expansion coefficient is given for the material (“Thermal expansion,” Section 26.1.2). +The specified temperature also affects temperature-dependent material properties, if any. +• Predefined temperature fields are not allowed in coupled pore fluid diffusion/stress analysis that +also models heat transfer. Boundary conditions should be used instead to specify temperatures, as +described earlier. +• The values of user-defined field variables can be specified; these values affect only field-variable- +dependent material properties, if any. +Material options +Any of the mechanical constitutive models available in Abaqus/Standard can be used to model the porous +material. +In problems formulated in terms of total pore pressure, you must include the density of the dry +material in the material definition . +You can use a permeability material property to define the specific weight of the wetting liquid, +; +the permeability, +. +, and its dependence on the void ratio, e, and saturation, +; and the flow velocity, +You can define the compressibility of the solid grains and of the permeating fluid in both fully and +partially saturated flow problems . If you do +not specify the porous bulk moduli, the materials are assumed to be fully incompressible. +For partially saturated flow you must define the porous medium’s absorption/exsorption behavior +. +Gel swelling (“Swelling gel,” Section 26.6.5) and volumetric moisture swelling of the solid +skeleton (“Moisture swelling,” Section 26.6.6) can be included in partially saturated cases. These +effects are usually associated with modeling of moisture migration in polymeric systems rather than +with geotechnical systems. +Thermal properties if heat transfer is modeled +In problems that model heat transfer, the thermal conductivity for either the solid material or the +permeating fluid, or more commonly for both phases, must be defined. Only isotropic conductivity +can be specified for the pore fluid. The specific heat and density of the phases must also be defined +for transient heat transfer problems. Latent heat for the phases can be defined if changes in internal +energy due to phase changes are important. See “Thermal properties: overview,” Section 26.2.1, for +details on defining thermal properties in Abaqus. Examples of problems that model fully coupled heat +transfer along with pore fluid diffusion and mechanical deformation can be found in “Consolidation +around a cylindrical heat source,” Section 1.15.7 of the Abaqus Benchmarks Manual, and “Permafrost +thawing–pipeline interaction,” Section 10.1.6 of the Abaqus Example Problems Manual. +The thermal properties can be defined separately for the solid material and the permeating fluid. +Input File Usage: +To define the conductivity, specific heat, density, and latent heat of the +permeating fluid, use the following options: +*CONDUCTIVITY, TYPE=ISO, PORE FLUID +*SPECIFIC HEAT, PORE FLUID +*LATENT HEAT, PORE FLUID +*DENSITY, PORE FLUID +To define the conductivity, specific heat, density, and latent heat of the solid +material, use the following options: +*EXPANSION, TYPE=ISO or ORTHO or ANISO +*SPECIFIC HEAT +*DENSITY +*LATENT HEAT +Defining the thermal properties and the density of the permeating fluid is not +supported in Abaqus/CAE. +To define the conductivity, specific heat, density, and latent heat of the solid +material, use the following options: +Property module: material editor: +Thermal→Conductivity: Type: Isotropic +Thermal→Specific Heat +General→Density +Thermal→Latent Heat +6.8.1–11 +Thermal expansion +Thermal expansion can be defined separately for the solid material and for the permeating fluid. In such +a case you should repeat the expansion material property, with the necessary parameters, to define the +different thermal expansion effects . Thermal expansion will +be active only in a consolidation (transient) analysis. +Input File Usage: +Abaqus/CAE Usage: +To define the thermal expansion of the permeating fluid: +*EXPANSION, TYPE=ISO, PORE FLUID +To define the thermal expansion of the solid material: +*EXPANSION, TYPE=ISO or ORTHO or ANISO +To define the thermal expansion of the permeating fluid: +Property module: material editor: Other→Pore Fluid→Pore +Fluid Expansion +To define the thermal expansion of the solid material: +Property module: material editor: Mechanical→Expansion +Elements +The analysis of flow through porous media in Abaqus/Standard is available for plane strain, +axisymmetric, and three-dimensional problems. The modeling of coupled heat transfer effects is +available only for axisymmetric and three-dimensional problems. Continuum pore pressure elements +are provided for modeling fluid flow through a deforming porous medium in a coupled pore fluid +diffusion/stress analysis. These elements have pore pressure degree of freedom 8 in addition to +displacement degrees of freedom 1–3. Heat transfer through the porous medium can also be modeled +using continuum coupled temperature–pore pressure elements. These elements have temperature degree +of freedom 11 in addition to pore pressure degree of freedom 8 and displacement degrees of freedom +1–3. Stress/displacement elements can be used in parts of the model without pore fluid flow. See +“Choosing the appropriate element for an analysis type,” Section 27.1.3, for more information. +Output +The element output available for a coupled pore fluid diffusion/stress analysis includes the usual +mechanical quantities such as (effective) stress; strain; energies; and the values of state, field, and +user-defined variables. In addition, the following quantities associated with pore fluid flow are available: +. +Void ratio, e. +Pore pressure, +Saturation, s. +Gel volume ratio, +Total fluid volume ratio, +Magnitude and components of the pore fluid effective velocity vector, +. +. +. +6.8.1–12 +VOIDR +POR +SAT +GELVR +FLUVR +FLVELM +FLVELn +Magnitude, +, of the pore fluid effective velocity vector. +Component n of the pore fluid effective velocity vector (n=1, 2, 3). +If heat transfer is modeled, the following element output variables associated with heat transfer are +also available: +HFL +HFLn +HFLM +TEMP +Magnitude and components of the heat flux vector. +Component n of the heat flux vector (n=1, 2, 3). +Magnitude of the heat flux vector. +Integration point temperatures. +The nodal output available includes the usual mechanical quantities such as displacements, reaction +forces, and coordinates. In addition, the following quantities associated with pore fluid flow are available: +CFF +POR +RVF +RVT +Concentrated fluid flow at a node. +Pore pressure at a node. +Reaction fluid volume flux due to prescribed pressure. This flux is the rate at which +fluid volume is entering or leaving the model through the node to maintain the +prescribed pressure boundary condition. A positive value of RVF indicates that +fluid is entering the model. +Reaction total fluid volume (computed only in a transient analysis). This value is +the time integrated value of RVF. +If heat transfer is modeled, the following nodal output variables associated with heat transfer are +also available: +NT +RFL +RFLn +CFL +CFLn +Nodal point temperatures. +Reaction flux values due to prescribed temperature. +Reaction flux value n at a node (n=11, 12, …). +Concentrated flux values. +Concentrated flux value n at a node (n=11, 12, …). +All of the output variable identifiers are outlined in “Abaqus/Standard output variable identifiers,” +Section 4.2.1. +Input file template +*HEADING +… +*********************************** +** +** Material definition +** +*********************************** +, as a function of the void ratio, e +*MATERIAL, NAME=soil +Data lines to define mechanical properties of the solid material +… +*EXPANSION +Data lines to define the thermal expansion coefficient of the solid grains +*EXPANSION, TYPE=ISO, PORE FLUID +Data lines to define the thermal expansion coefficient of the permeating fluid +*PERMEABILITY, SPECIFIC= +Data lines to define permeability, +*PERMEABILITY, TYPE=SATURATION +Data lines to define the dependence of permeability on saturation, +*PERMEABILITY, TYPE=VELOCITY +Data lines to define the velocity coefficient, +*POROUS BULK MODULI +Data line to define the bulk moduli of the solid grains and the permeating fluid +*SORPTION, TYPE=ABSORPTION +Data lines to define absorption behavior +*SORPTION, TYPE=EXSORPTION +Data lines to define exsorption behavior +*SORPTION, TYPE=SCANNING +Data lines to define scanning behavior (between absorption and exsorption) +*GEL +Data line to define gel behavior in partially saturated flow +*MOISTURE SWELLING +Data lines to define moisture swelling strain as a function of saturation +in partially saturated flow +*CONDUCTIVITY +Data lines to define thermal conductivity of the solid grains if heat transfer is modeled +*CONDUCTIVITY,TYPE=ISO, PORE FLUID +Data lines to define thermal conductivity of the permeating fluid if heat transfer is modeled +*SPECIFIC HEAT +Data lines to define specific heat of the solid grains if transient heat transfer is modeled +*SPECIFIC HEAT,PORE FLUID +Data lines to define specific heat of the permeating fluid if transient heat transfer is modeled +*DENSITY +Data lines to define density of the solid grains if transient heat transfer is modeled +*DENSITY,PORE FLUID +Data lines to define density of the permeating fluid if transient heat transfer is modeled +*LATENT HEAT +Data lines to define latent heat of the solid grains if phase change due to temperature change +is modeled +*LATENT HEAT,PORE FLUID +Data lines to define latent heat of the permeating fluid if phase change due to temperature change +is modeled +… +*********************************** +** +** Boundary conditions and initial conditions +** +*********************************** +*BOUNDARY +Data lines to specify zero-valued boundary conditions +*INITIAL CONDITIONS, TYPE=STRESS, GEOSTATIC +Data lines to specify initial stresses +*INITIAL CONDITIONS, TYPE=PORE PRESSURE +Data lines to define initial values of pore fluid pressures +*INITIAL CONDITIONS, TYPE=RATIO +Data lines to define initial values of the void ratio +*INITIAL CONDITIONS, TYPE=SATURATION +Data lines to define initial saturation +*INITIAL CONDITIONS, TYPE=TEMPERATURE +Data lines to define initial saturation +*AMPLITUDE, NAME=name +Data lines to define amplitude variations +*********************************** +** +** Step 1: Optional step to ensure an equilibrium +** geostatic stress field +** +*********************************** +*STEP +*GEOSTATIC +*CLOAD and/or *DLOAD and/or *TEMPERATURE and/or *FIELD +Data lines to specify mechanical loading +*FLOW and/or *SFLOW and/or *DFLOW and/or *DSFLOW +Data lines to specify pore fluid flow +*CFLUX and/or *DFLUX +Data lines to define concentrated and/or distributed heat fluxes if heat transfer is modeled +*BOUNDARY +Data lines to specify displacements or pore pressures +*END STEP +*********************************** +** +** Step 2: Coupled pore diffusion/stress analysis step +** +*********************************** +*STEP (,NLGEOM) +** Use NLGEOM to include geometric nonlinearities +*SOILS +Data line to define incrementation +*CLOAD and/or *DLOAD and/or *DSLOAD +Data lines to specify mechanical loading +*FLOW and/or *SFLOW and/or *DFLOW and/or *DSFLOW +Data lines to specify pore fluid flow +*CFLUX and/or *DFLUX +Data lines to define concentrated and/or distributed heat fluxes if heat transfer is modeled +*FILM +Data lines referring to film property table if heat transfer is modeled +*BOUNDARY +Data lines to specify displacements, pore pressures, or temperatures +*END STEP +6.8.2 +GEOSTATIC STRESS STATE +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “Coupled pore fluid diffusion and stress analysis,” Section 6.8.1 +• *GEOSTATIC +• “Configuring a geostatic stress field procedure” in “Configuring general analysis procedures,” +Section 14.11.1 of the Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +A geostatic stress field procedure: +• is used to verify that the initial geostatic stress field is in equilibrium with applied loads and boundary +conditions and to iterate, if necessary, to obtain equilibrium; +• accounts for pore pressure degrees of freedom when pore pressure elements are used, and accounts +for temperature degrees of freedom when coupled temperature–pore pressure elements are used; +• is usually the first step of a geotechnical analysis, followed by a coupled pore fluid diffusion/stress +(with or without heat transfer) or static analysis procedure; and +• can be linear or nonlinear. +Establishing geostatic equilibrium +The geostatic procedure is normally used as the first step of a geotechnical analysis; in such cases gravity +loads are applied during this step. Ideally, the loads and initial stresses should exactly equilibrate and +produce zero deformations. However, in complex problems it may be difficult to specify initial stresses +and loads that equilibrate exactly. +Abaqus/Standard provides two procedures for establishing the initial equilibrium. The first +procedure is applicable to problems for which the initial stress state is known at least approximately. +The second, enhanced, procedure is also applicable for cases in which the initial stresses are not known; +it is supported for only a limited number of elements and materials. +Establishing equilibrium when the initial stress state is approximately known +The geostatic procedure requires that the initial stresses are close to the equilibrium state; otherwise, +the displacements corresponding to the equilibrium state might be large. Abaqus/Standard checks for +equilibrium during the geostatic procedure and iterates, if needed, to obtain a stress state that equilibrates +the prescribed boundary conditions and loads. This stress state, which is a modification of the stress +field defined by the initial conditions (“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” +Section 33.2.1), is then used as the initial stress field in a subsequent static or coupled pore fluid +diffusion/stress (with or without heat transfer) analysis. +If the stresses given as initial conditions are far from equilibrium under the geostatic loading and +there is some nonlinearity in the problem definition, this iteration process may fail. Therefore, you should +ensure that the initial stresses are reasonably close to equilibrium. +If the deformations produced during the geostatic step are significant compared to the deformations +caused by subsequent loading, the definition of the initial state should be reexamined. +If heat transfer is modeled during the geostatic step through the use of coupled temperature–pore +pressure elements, the initial temperature field and thermal loads, if specified, must be such that the +system is relatively close to a state of thermal equilibrium. Steady-state heat transfer is assumed during +a geostatic step. +Input File Usage: +Abaqus/CAE Usage: +*GEOSTATIC +Step module: Create Step: General: Geostatic +Establishing equilibrium when the initial stress state is unknown +To obtain equilibrium in cases when the initial stress state is unknown or is known only approximately, +you can invoke an enhanced procedure. Abaqus automatically computes the equilibrium corresponding +to the initial loads and the initial configuration, allowing only small displacements within user-specified +tolerances. (The default tolerance is +.) The procedure is available with a limited number of elements +and materials and is intended to be used in analyses in which the material response is primarily elastic; +that is, inelastic deformations are small. +The procedure is supported for both geometrically linear and geometrically nonlinear analyses. +However, in general, the performance in the geometrically linear case will be better. Therefore, it +might be advantageous to obtain the initial equilibrium in a geometrically linear step, even though a +geometrically nonlinear analysis is performed in subsequent steps. +Input File Usage: +Use the following option to invoke the enhanced procedure: +Abaqus/CAE Usage: +*GEOSTATIC, UTOL=displacement tolerance +Step module: Create Step: General: Geostatic: Incrementation +tabbed page: Automatic: Max. displacement change +Limitations +The following limitations apply to the enhanced procedure: +• It is supported only for a limited number of elements and materials . When the procedure is used with nonsupported elements or material +models, Abaqus issues a warning message. In this case it is the user’s responsibility to ensure that the +displacement tolerances are larger than the displacements in the analysis; otherwise, convergence +problems may occur. +• It can be used in a restart analysis only if it had been used in the previous analysis. +Optional modeling of coupled heat transfer +When coupled temperature–pore pressure elements are used, heat transfer is modeled in these elements +by default. However, you may optionally choose to switch off heat transfer within these elements during +a geostatic step. This feature may be helpful in reducing computation time if temperature and associated +heat flow effects are not important. +Input File Usage: +Use the following option to suppress heat transfer modeling: +Abaqus/CAE Usage: +*GEOSTATIC, HEAT=NO +Switching off the heat +Abaqus/CAE. +transfer part of the physics is not supported in +Vertical equilibrium in a porous medium +Most geotechnical problems begin from a geostatic state, which is a steady-state equilibrium +configuration of the undisturbed soil or rock body under geostatic loading. The equilibrium state +usually includes both horizontal and vertical stress components. It is important to establish these initial +conditions correctly so that the problem begins from an equilibrium state. Since such problems often +involve fully or partially saturated flow, the initial void ratio of the porous medium, +, the initial pore +pressure, +, and the initial effective stress must all be defined. +If the magnitude and direction of the gravitational loading are defined by using the gravity +distributed load type, a total, rather than excess, pore pressure solution is used . This discussion is based on the total pore pressure +formulation. +The z-axis points vertically in this discussion, and atmospheric pressure is neglected. We assume +that the pore fluid is in hydrostatic equilibrium during the geostatic procedure so that +where +is the user-defined specific weight of the pore fluid . (The +pore fluid is not in hydrostatic equilibrium if there is significant steady-state flow of pore fluid through the +porous medium: in that case a steady-state coupled pore fluid diffusion/stress analysis must be performed +to establish the initial conditions for any subsequent transient calculations—see “Coupled pore fluid +diffusion and stress analysis,” Section 6.8.1.) If we also take +to be independent of z (which is usually +the case, since the fluid is almost incompressible), this equation can be integrated to define +where +fluid is only partially saturated. +is the height of the phreatic surface, at which +and above which +and the pore +We usually assume that there are no significant shear stresses +, +. Then, equilibrium in the +vertical direction is +is the dry density of the porous solid material (the dry mass per unit volume), g is the +where +gravitational acceleration, +. Since porosity is the ratio of pore volume to total volume and the +void ratio is the ratio of pore volume to solids volume, +is the initial porosity of the material, and s is the saturation, +is defined from the initial void ratio by +Abaqus/Standard requires that the initial value of the effective stress, +, be given as an initial +condition (“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1). Effective stress +is defined from the total stress, +, by +is a unit matrix. Combining this definition with the equilibrium statement in the z-direction and +where +hydrostatic equilibrium in the pore fluid gives +again using the assumption that +the dry soil from the partially saturated soil. The soil is assumed to be dry ( +assumed to be partially saturated for +and fully saturated for +is independent of z. +In many cases s is constant. For example, in fully saturated flow +phreatic surface. If we further assume that the initial porosity, +medium, +, are also constant, the above equation is readily integrated to give +is the position of the surface that separates +, and it is +) for +. +everywhere below the +, and the dry density of the porous +where +is the position of the surface of the porous medium, +. +In more complicated cases where s, +, and/or +vary with height, the equation must be integrated +in the vertical direction to define the initial values of +. +Horizontal equilibrium in a porous medium +In many geotechnical applications there is also horizontal stress, typically caused by tectonic action. +If the pore fluid is under hydrostatic equilibrium and +, equilibrium in the horizontal +directions requires that the horizontal components of effective stress do not vary with horizontal position: +only, where +is any horizontal component of effective stress. +Initial conditions +The initial effective geostatic stress field, +, is given by defining initial stress conditions. Unless +the enhanced procedure is used, the initial state of stress must be close to being in equilibrium +with the applied loads and boundary conditions. See “Initial conditions in Abaqus/Standard and +Abaqus/Explicit,” Section 33.2.1. +You can specify that the initial stresses vary only with elevation, as described in “Initial conditions +in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1. In this case the horizontal stress is typically +assumed to be a fraction of the vertical stress: those fractions are defined in the x- and y-directions. +In problems involving partially or fully saturated porous media, initial pore fluid pressures, +, void +, and saturation values, s, must be given . +In partially saturated cases the initial pore pressure and saturation values must lie on or between +the absorption and exsorption curves . A partially saturated problem is +illustrated in “Wicking in a partially saturated porous medium,” Section 1.9.3 of the Abaqus Benchmarks +Manual. +You may also specify initial temperatures in the model if heat transfer is modeled during the geostatic +procedure. +Boundary conditions +Boundary conditions can be applied to displacement degrees of freedom 1–6 and to pore pressure +degree of freedom 8 (“Boundary conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1). +If coupled temperature–pore pressure elements are used, boundary conditions on temperature degree +of freedom 11 can also be applied to nodes belonging to these elements. If the enhanced procedure +is used and nonzero boundary conditions are applied, it is the user’s responsibility to ensure that the +displacements corresponding to the tolerances specified are larger than the displacements in the analysis; +otherwise, the displacements at the nonzero boundary nodes will be reset to zero with the tolerances +specified. +The boundary conditions should be in equilibrium with the initial stresses and applied loads. If the +horizontal stress is nonzero, horizontal equilibrium must be maintained by fixing the boundary conditions +on any nonhorizontal edges of the finite element model in the horizontal direction or by using infinite +elements (“Infinite elements,” Section 28.3.1). If heat transfer is modeled, the temperature boundary +conditions should be in equilibrium with the initial temperature field and applied thermal loads. +Loads +The following loading types can be prescribed in a geostatic stress field procedure: +• Concentrated nodal forces can be applied to the displacement degrees of freedom (1–6); see +“Concentrated loads,” Section 33.4.2. +• Distributed pressure forces or body forces can also be applied; +see “Distributed loads,” +Section 33.4.3. The distributed load types available with particular elements are described in +Part VI, “Elements.” The magnitude and direction of gravitational loading are defined by using +the gravity or body force distributed load types. +• Pore fluid flow is controlled as described in “Pore fluid flow,” Section 33.4.7. +If heat transfer is modeled, the following types of thermal loading can also be prescribed (“Thermal +loads,” Section 33.4.4). These loads are not supported in Abaqus/CAE during a geostatic analysis. +• Concentrated heat fluxes. +• Body fluxes and distributed surface fluxes. +• Convective film conditions and radiation conditions; film properties can be made a function of +temperature. +Predefined fields +The following predefined fields can be specified in a geostatic stress field procedure, as described in +“Predefined fields,” Section 33.6.1: +• For a geostatic analysis that does not model heat transfer and uses regular pore pressure elements, +temperature is not a degree of freedom and nodal temperatures can be specified. +• Predefined temperature fields are not allowed in a geostatic analysis that also models heat transfer. +Boundary conditions should be used instead to specify temperatures, as described earlier. +• The values of user-defined field variables can be specified; these values affect only field-variable- +dependent material properties, if any. +Material options +Any of the mechanical constitutive models available in Abaqus/Standard can be used to model the porous +solid material. However, the enhanced procedure can be used only with the elastic, porous elastic, +extended Cam-clay plasticity, and Mohr-Coulomb plasticity models. Use of a nonsupported material +model with this procedure may lead to poor convergence or no convergence if displacements are larger +than the displacements corresponding to the tolerances specified. Abaqus will issue a warning message +if the procedure is used with a nonsupported material model. +If a porous medium will be analyzed subsequent to the geostatic procedure, pore fluid flow quantities +such as permeability and sorption should be defined . +If heat transfer is modeled, thermal properties such as conductivity, specific heat, and density should +be defined for both the solid and the pore fluid phases (see “Thermal properties if heat transfer is modeled” +in “Coupled pore fluid diffusion and stress analysis,” Section 6.8.1, for details on how to specify separate +thermal properties for the two phases). +Elements +Any of the stress/displacement elements in Abaqus/Standard can be used in a geostatic procedure. +Continuum pore pressure elements can also be used for modeling fluid in a deforming porous medium. +These elements have pore pressure degree of freedom 8 in addition to displacement degrees of freedom +1–3. However, the enhanced procedure can be used only with continuum and cohesive elements +with pore pressure degrees of freedom and the corresponding stress/displacements elements. Use +of nonsupported elements with this procedure may lead to poor convergence or no convergence if +displacements are larger than the displacements corresponding to the tolerances specified. Abaqus will +issue a warning message if the procedure is used with a nonsupported element. +Continuum elements that couple temperature, pore pressure, and displacement can be used if heat +transfer needs to be modeled. These elements have temperature degree of freedom 11 in addition to pore +pressure degree of freedom 8 and displacement degrees of freedom 1–3. See “Choosing the appropriate +element for an analysis type,” Section 27.1.3, for more information. +Output +The element output available for a coupled pore fluid diffusion/stress analysis includes the usual +mechanical quantities such as (effective) stress; strain; energies; and the values of state, field, and +user-defined variables. In addition, the following quantities associated with pore fluid flow are available: +VOIDR +POR +SAT +GELVR +FLUVR +FLVEL +FLVELM +FLVELn +. +Void ratio, e. +Pore pressure, +Saturation, s. +Gel volume ratio, +Total fluid volume ratio, +Magnitude and components of the pore fluid effective velocity vector, +, of the pore fluid effective velocity vector. +Magnitude, +Component n of the pore fluid effective velocity vector (n=1, 2, 3). +. +. +. +If heat transfer is modeled, the following element output variables associated with heat transfer are +also available: +HFL +HFLn +HFLM +TEMP +Magnitude and components of the heat flux vector. +Component n of the heat flux vector (n=1, 2, 3). +Magnitude of the heat flux vector. +Integration point temperatures. +The nodal output available includes the usual mechanical quantities such as displacements, reaction +forces, and coordinates. In addition, the following quantities associated with pore fluid flow are available: +POR +RVF +Pore pressure at a node. +Reaction fluid volume flux due to prescribed pressure. This flux is the rate at which +fluid volume is entering or leaving the model through the node to maintain the +prescribed pressure boundary condition. A positive value of RVF indicates fluid is +entering the model. +If heat transfer is modeled, the following nodal output variables associated with heat transfer are +also available: +NT +RFL +RFLn +CFL +CFLn +Nodal point temperatures. +Reaction flux values due to prescribed temperature. +Reaction flux value n at a node (n=11, 12, …). +Concentrated flux values. +Concentrated flux value n at a node (n=11, 12, …). +All of the output variable identifiers are outlined in “Abaqus/Standard output variable identifiers,” +Section 4.2.1. +Input file template +, as a function of the void ratio, e +*HEADING +… +*MATERIAL, NAME=mat1 +Data lines to define mechanical properties of the solid material +… +*DENSITY +Data lines to define the density of the dry material +*PERMEABILITY, SPECIFIC= +Data lines to define permeability, +*CONDUCTIVITY +Data lines to define thermal conductivity of the solid grains if heat transfer is modeled +*CONDUCTIVITY,TYPE=ISO, PORE FLUID +Data lines to define thermal conductivity of the permeating fluid if heat transfer is modeled +*SPECIFIC HEAT +Data lines to define specific heat of the solid grains if transient heat transfer is modeled in a +subsequent step +*SPECIFIC HEAT,PORE FLUID +Data lines to define specific heat of the permeating fluid if transient heat transfer is modeled in a subsequent step +*DENSITY +Data lines to define density of the solid grains if transient heat transfer is modeled in a subsequent +step +*DENSITY,PORE FLUID +Data lines to define density of the permeating fluid if transient heat transfer is modeled in a +subsequent step +*LATENT HEAT +Data lines to define latent heat of the solid grains if phase change due to temperature change is modeled +*LATENT HEAT,PORE FLUID +Data lines to define latent heat of the permeating fluid if phase change due to temperature change +is modeled +… +*INITIAL CONDITIONS, TYPE=STRESS, GEOSTATIC +Data lines to define the initial stress state +*INITIAL CONDITIONS, TYPE=PORE PRESSURE +Data lines to define initial values of pore fluid pressures +*INITIAL CONDITIONS, TYPE=RATIO +Data lines to define initial values of the void ratio +*INITIAL CONDITIONS, TYPE=SATURATION +Data lines to define initial saturation +*INITIAL CONDITIONS, TYPE=TEMPERATURE +Data lines to define initial temperature +*BOUNDARY +Data lines to define zero-valued boundary conditions +** +*STEP +*GEOSTATIC +*CLOAD and/or *DLOAD and/or *DSLOAD +Data lines to specify mechanical loading +*FLOW and/or *SFLOW and/or *DFLOW and/or *DSFLOW +Data lines to specify pore fluid flow +*CFLUX and/or *DFLUX +Data lines to define concentrated and/or distributed heat fluxes if heat transfer is modeled +*BOUNDARY +Data lines to specify displacements or pore pressures +*END STEP +6.9 +Mass diffusion analysis +• “Mass diffusion analysis,” Section 6.9.1 +6.9.1 +MASS DIFFUSION ANALYSIS +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• *MASS DIFFUSION +• “Configuring a mass diffusion procedure” in “Configuring general analysis procedures,” +Section 14.11.1 of the Abaqus/CAE User’s Manual, in the online HTML version of this manual +• “Creating and modifying prescribed conditions,” Section 16.4 of the Abaqus/CAE User’s Manual +• “Defining a concentrated concentration flux,” Section 16.9.33 of the Abaqus/CAE User’s Manual, +in the online HTML version of this manual +• “Defining a body concentration flux,” Section 16.9.35 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Defining a surface concentration flux,” Section 16.9.34 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +A mass diffusion analysis: +• models the transient or steady-state diffusion of one material through another, such as the diffusion +of hydrogen through a metal; +• requires the use of mass diffusion elements; and +• can be used to model temperature and/or pressure-driven mass diffusion. +Governing equations +The governing equations for mass diffusion are an extension of Fick’s equations: +they allow for +nonuniform solubility of the diffusing substance in the base material and for mass diffusion driven by +gradients of temperature and pressure. The basic solution variable (used as the degree of freedom at +the nodes of the mesh) is the “normalized concentration” (often also referred to as the “activity” of the +diffusing material), +, where c is the mass concentration of the diffusing material and s is its +solubility in the base material. Therefore, when the mesh includes dissimilar materials that share nodes, +the normalized concentration is continuous across the interface between the different materials. +For example, a diatomic gas that dissociates during diffusion can be described using Sievert’s law: +, where p is the partial pressure of the diffusing gas. Combining Sievert’s law with the definition +of normalized concentration given earlier, +. Equilibrium requires the partial pressure to be +continuous across an interface, so normalized concentration will be continuous as well. If an expression +other than Sievert’s law defines the relationship between concentration and partial pressure for a diffusing +material, solubility should be defined accordingly. +The diffusion problem is defined from the requirement of mass conservation for the diffusing phase: +where V is any volume whose surface is S, +of the diffusing phase, and +is the concentration flux leaving S. +is the outward normal to S, +is the flux of concentration +Diffusion is assumed to be driven by the gradient of a general chemical potential, which gives the +behavior +is the solubility; +where +is the diffusivity; +providing diffusion because of temperature gradient; +zero on the temperature scale being used; +driven by the gradient of the equivalent pressure stress, +predefined field variables. +, or +is the temperature; +is the “Soret effect” factor, +is the value of absolute +is the pressure stress factor, providing diffusion +are any +is stress; and +; +Whenever D, +depends on concentration, the problem becomes nonlinear and the system +of equations becomes nonsymmetric. In practical cases the dependence on concentration is quite strong, +so the nonsymmetric matrix storage and solution scheme is invoked automatically when a mass diffusion +analysis is performed . +Fick’s law +Mass diffusion behavior is often described by Fick’s law (Crank, 1956): +Fick’s law is offered in Abaqus/Standard as a special case of the general chemical potential relation. To +establish the relationship between Fick’s law and the general chemical potential, we write Fick’s law as +In most practical cases +, and we can write +The two terms in this equation describe the normalized concentration and temperature-driven +diffusion, respectively. The normalized concentration-driven diffusion term is identical to that given in +relation if +MASS DIFFUSION +This conversion is done automatically in Abaqus/Standard when you request Fick’s law . +An extended form of Fick’s law can also be chosen by specifying a nonzero value for +: +In this case Abaqus/Standard will still define +automatically as discussed earlier. +Units +The units of concentration are commonly given as parts per million (P). On the basis of the applicability +of Sievert’s law to the mass diffusion, the units of solubility are +, where F is force and L is +length. The units of the Soret effect factor are +. The units of the pressure stress factor are +, +; and the concentration volumetric +, and the units of equivalent pressure stress are +, then has units of +. The diffusivity, +, has units of +where T is time. The concentration flux, +flux, +, has units of +. +Steady-state analysis +Steady-state mass diffusion analysis provides the steady-state solution directly: the rate of change of +concentration with respect to time is omitted from the governing diffusion equation in steady-state +analysis. In nonlinear cases iteration may be necessary to achieve a converged solution. +Since the rate term is removed from the governing equations, the steady-state problem has no +intrinsic physically meaningful time scale; nevertheless, you may assign a “time” scale to the analysis +step. This time scale is often convenient for output identification and for specifying prescribed +normalized concentrations and fluxes with varying magnitudes. Thus, when steady-state analysis +is chosen, you specify a “time” increment and a “time” period for the step; Abaqus/Standard then +increments through the step accordingly. If a steady-state analysis step is to be followed by a transient +analysis step and total time is used in amplitude definitions (“Amplitude curves,” Section 33.1.2), the +time period should be defined to be negligibly small in the steady-state step. For more details on time +scales and time stepping, see “Defining an analysis,” Section 6.1.2. +*MASS DIFFUSION, STEADY STATE +Step module: Create Step: General: Mass diffusion: Basic: +Response: Steady state +Abaqus/CAE Usage: +Input File Usage: +Transient analysis +Time integration in transient diffusion analysis is done with the backward Euler method (also referred to +as the modified Crank-Nicholson operator). This method is unconditionally stable for linear problems. +Automatic or fixed time incrementation can be used for transient analysis. The automatic time +incrementation scheme is generally preferred because the response is usually simple diffusion: the rate of +change of normalized concentration varies widely during the step and requires different time increments +to maintain accuracy in the time integration. +Spurious oscillations due to small time increments +In transient mass diffusion analysis with second-order elements there is a relationship between the +minimum usable time step and the element size. A simple guideline is +is the time increment, D is the diffusivity, and +where +is a typical element dimension (such as the +length of a side of an element). If time increments smaller than this value are used, spurious oscillations +can appear in the solution. Abaqus/Standard provides no check on the initial time increment defined for +a mass diffusion analysis; you must ensure that the given value does not violate the above criterion. +In transient analysis using first-order elements the solubility terms are lumped, which eliminates +such oscillations but can lead to locally inaccurate solutions for small time increments. If smaller time +increments are required, a finer mesh should be used in regions where the normalized concentration +changes occur. +Generally there is no upper limit on the time increment because the integration procedure is +unconditionally stable unless nonlinearities cause numerical problems. +Automatic incrementation +Input File Usage: +The automatic time incrementation scheme for mass diffusion problems is based on the user-specified +maximum normalized concentration change allowed at any node during an increment, +*MASS DIFFUSION, DCMAX= +Step module: Create Step: General: Mass diffusion: Basic: Response: +Transient; Incrementation: Type: Automatic: Max. allowable +normalized concentration change: +Abaqus/CAE Usage: +. +Fixed time incrementation +If you choose fixed time incrementation, fixed time increments equal to the size of the user-specified +initial time increment, +, will be used. +Input File Usage: +*MASS DIFFUSION +Abaqus/CAE Usage: +Step module: Create Step: General: Mass diffusion: Basic: Response: +Transient; Incrementation: Type: Fixed, Increment size: +Ending a transient analysis +Transient mass diffusion analysis can be terminated by completing a specified time period, or it can be +continued until steady-state conditions are reached. By default, the analysis will end when the given time +period has been completed. Alternatively, you can specify that the analysis will end when steady state is +reached or the time period ends, whichever comes first. Steady state is defined as the point in time when +all normalized concentrations change at less than a user-defined rate. +Input File Usage: +Abaqus/CAE Usage: +Initial conditions +Use the following option to end the analysis when the time period is reached: +*MASS DIFFUSION, END=PERIOD (default) +Use the following option to end the analysis based on the concentration change +rate: +*MASS DIFFUSION, END=SS +Step module: Create Step: General: Mass diffusion: Basic: Response: +Transient; Incrementation: Type: Automatic: End step when +normalized concentration change rate is less than +An initial normalized concentration of the diffusing material at specific nodes that belong to mass +diffusion elements can be defined (“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” +Section 33.2.1). For an analysis in which mass diffusion is driven by gradients of temperature and/or +pressure (“Diffusivity,” Section 26.4.1), the initial temperature and pressure stress fields in a model can +also be defined. +Input File Usage: +Use the following options: +*INITIAL CONDITIONS, TYPE=CONCENTRATION for initial +concentrations +*INITIAL CONDITIONS, TYPE=TEMPERATURE for initial temperatures +*INITIAL CONDITIONS, TYPE=PRESSURE STRESS for initial equivalent +pressure stress +Abaqus/CAE Usage: +Load module: Create Predefined Field: Step: Initial: choose Other for +the Category and Temperature for the Types for Selected Step +Initial concentration and equivalent pressure stress are not supported in +Abaqus/CAE. +Boundary conditions +Boundary conditions can be applied to nodal degree of freedom 11 in any mass diffusion element +to prescribe values of normalized concentration (“Boundary conditions in Abaqus/Standard and +Abaqus/Explicit,” Section 33.3.1). Such values can be specified as functions of time. +Any boundary condition changes to be applied during a mass diffusion step should be given in the +respective step using appropriate amplitude definitions to specify their “time” variations (“Amplitude +curves,” Section 33.1.2). If boundary conditions are specified for the step without amplitude references, +they are assumed to change either linearly with “time” during the step or instantly at the start of the +step, according to the user-specified or default time variation associated with the step . +Loads +Concentration fluxes are the only loads that can be applied in a mass diffusion analysis step. +Input File Usage: +Use the following option to specify a concentrated concentration flux at a node: +*CFLUX +node number or node set name, degree of freedom, concentrated flux magnitude +Use the following option to specify a distributed concentration flux acting on +entire elements (body flux) or just on element faces (surface flux): +*DFLUX +element number or element set name, BF or Sn, distributed flux magnitude +Abaqus/CAE Usage: +Use the following input to define a concentrated concentration flux at a node: +Load module: Create Load: choose Mass diffusion for the Category +and Concentrated concentration flux for the Types for Selected +Step: select region: Magnitude: concentrated flux magnitude +Use the following input to define a distributed concentration flux acting on +entire elements (body flux) or just on element faces (surface flux): +Load module: Create Load: choose Mass diffusion for the Category +and Body concentration flux or Surface concentration flux for +the Types for Selected Step: Distribution: Uniform or select an +analytical field, Magnitude: distributed flux magnitude +Modifying or removing concentration fluxes +Concentrated or distributed concentration fluxes can be added, modified, or removed as described in +“Applying loads: overview,” Section 33.4.1. +Specifying time-dependent concentration fluxes +The magnitude of a concentrated or a distributed concentration flux can be controlled by referring to an +amplitude curve . If different magnitude variations are needed +for different fluxes, the flux definitions can be repeated, with each referring to its own amplitude curve. +Defining nonuniform distributed concentration fluxes in a user subroutine +To define nonuniform distributed concentration fluxes, the variation of the flux magnitude throughout a +step can be defined in user subroutine DFLUX. If a reference flux magnitude is specified directly, it will +be ignored. As a result, any amplitude reference in the flux definition is also ignored. +Input File Usage: +Use the following option to define a nonuniform distributed concentration body +flux: +*DFLUX +element number or element set, BFNU +Use the following option to define a nonuniform distributed concentration +surface flux: +*DFLUX +element number or element set, SnNU +Abaqus/CAE Usage: +Use the following input to define a nonuniform distributed concentration body +flux: +Load module: Create Load: choose Mass diffusion for the Category +and Body concentration flux for the Types for Selected Step: +select region: Distribution: User-defined +Use the following input to define a nonuniform distributed concentration +surface flux: +Load module: Create Load: choose Mass diffusion for the Category +and Surface concentration flux for the Types for Selected Step: +select region: Distribution: User-defined +Predefined fields +Predefined temperatures, equivalent pressure stresses, and field variables can be specified in a mass +diffusion analysis. +Prescribing temperatures +Temperatures are applied to nodes in temperature-driven mass diffusion analyses by defining a +temperature field; absolute zero on the temperature scale used is defined as described in “Specifying the +value of absolute zero” in “Thermal loads,” Section 33.4.4. Alternatively, the temperature field can be +obtained from a previous heat transfer analysis. Time-dependent temperature variations are possible +with either approach. +A simple interface is provided that uses the Abaqus/Standard results file from the heat transfer +analysis to define the temperature field at different times in the mass diffusion analysis. Abaqus/Standard +assumes that the nodes in the mass diffusion analysis have the same numbers as the nodes in the previous +heat transfer analysis. Values in the results file are ignored at nodes that exist in the heat transfer analysis +but not in the mass diffusion analysis, and the temperatures at nodes that did not exist in the heat transfer +analysis will not be set by reading the results file. +For specific details on prescribing temperatures, see “Predefined temperature” in “Predefined +fields,” Section 33.6.1. +Prescribing equivalent pressure stresses +Equivalent pressure stress values can be given at nodes by specifying them directly as a predefined field +in the mass diffusion analysis or indirectly by reading the equivalent pressure stresses from the results +file of a previous stress/displacement, fully coupled temperature-displacement, or fully coupled thermal- +electrical-structural analysis. Regardless of the manner in which they are specified, pressures should be +entered according to the Abaqus convention that equivalent pressure stresses are positive when they are +compressive. +A simple interface is provided that uses the Abaqus/Standard results file from a mechanical +analysis to define the equivalent pressure stresses at different times in the mass diffusion analysis. +Abaqus/Standard assumes that the nodes in the mass diffusion analysis have the same numbers as the +nodes in the previous mechanical analysis. Values in the results file are ignored at nodes that exist in the +mechanical analysis but not in the mass diffusion analysis, and the pressures at nodes that did not exist +in the mechanical analysis will not be set by reading the results file. +For specific details on prescribing equivalent pressure stresses, see “Predefined pressure stress” in +“Predefined fields,” Section 33.6.1. +Specifying predefined field variables +You can specify values of predefined field variables during a mass diffusion analysis. These values affect +only field-variable-dependent material properties, if any. See “Predefined field variables” in “Predefined +fields,” Section 33.6.1. +Material options +Both diffusivity (“Diffusivity,” Section 26.4.1) and solubility (“Solubility,” Section 26.4.2) must be +defined in a mass diffusion analysis. Optionally, a Soret effect factor and a pressure stress factor can be +defined to introduce mass diffusion caused by temperature and pressure gradients, respectively. The use +of Fick’s law also introduces temperature-driven mass diffusion since a Soret effect factor is calculated +automatically. +Elements +Mass diffusion analysis can be performed using only the two-dimensional, three-dimensional, and +axisymmetric solid elements that are included in the Abaqus/Standard heat transfer/mass diffusion +element library. +Output +In addition to the standard output identifiers available in Abaqus/Standard (“Abaqus/Standard output +variable identifiers,” Section 4.2.1), the following variables have special meaning in mass diffusion +analyses: +Element integration point variables: +CONC +ISOL +MFL +MFLM +MFLn +TEMP +Mass concentration. +Amount of solute at the integration point, calculated as the product of the mass +concentration and the integration point volume. +Magnitude and components of the concentration flux vector (excluding the terms +due to pressure and temperature gradients). +Magnitude of the concentration flux vector. +Component n of the concentration flux vector (n = 1, 2, 3). +Magnitude of the applied temperature field. +Whole element variables: +ESOL +NFLUX +FLUXS +Amount of solute in the element, calculated as the sum of ISOL over all the element +integration points. +Fluxes at the nodes of the element caused by mass diffusion in the element. +Distributed mass flux applied to an element. +Whole or partial model variables: +SOL +Amount of solute in the model or specified element set, calculated as the sum of +ESOL over all the elements in the model or set. +Nodal variables: +CFL +CFLn +NNC +NNCn +RFL +RFLn +Input file template +All concentrated flux values. +Concentrated flux value n at a node (n = 11). +All normalized concentration values at a node. +Normalized concentration degree of freedom n at a node (n = 11). +All reaction flux values (conjugate to normalized concentration). +Reaction flux value n at a node (n = 11) (conjugate to normalized concentration). +The following template is representative of a three-step mass diffusion analysis. The first step +establishes an initial steady-state concentration distribution of a diffusing material. In the second step +equivalent pressure stresses are read from a fully coupled temperature-displacement analysis and the +transient mass diffusion response is obtained for the case of mechanical loading of the body. In the final +step a temperature field is read from a fully coupled temperature-displacement analysis and the transient +mass diffusion response is calculated for the case of heating and cooling the body in which diffusion +occurs. An example problem that follows this template is “Thermo-mechanical diffusion of hydrogen +in a bending beam,” Section 1.10.1 of the Abaqus Benchmarks Manual. +*HEADING +… +*MATERIAL,NAME=mat1 +*SOLUBILITY +Data lines to define solubility +*DIFFUSIVITY +Data lines to define diffusivity +*KAPPA,TYPE=TEMP +Data lines to define diffusion driven by temperature gradients +*KAPPA,TYPE=PRESS +Data lines to define diffusion driven by gradients of equivalent pressure stress +*INITIAL CONDITIONS,TYPE=TEMPERATURE +Data lines to define an initial temperature field +*INITIAL CONDITIONS,TYPE=CONCENTRATION +Data lines to define initial nodal values of normalized concentration +*INITIAL CONDITIONS,TYPE=PRESSURE STRESS +Data lines to define initial nodal values of equivalent pressure stress +*AMPLITUDE,NAME=name +Data lines to define amplitude variations +** +*STEP +Step 1 - steady-state solution +*MASS DIFFUSION,STEADY STATE +Data line to define incrementation +*BOUNDARY +Data lines to prescribe nodal values of normalized concentration +*EL FILE +Data lines to define element integration output to the results file +*NODE FILE +Data lines to define nodal output to the results file +*END STEP +** +*STEP +Step 2 - transient analysis driven by pressure stress gradients +*MASS DIFFUSION,DCMAX=dcmax,END=SS +Data line to define incrementation +*BOUNDARY +Data lines to prescribe nodal values of normalized concentration +*PRESSURE STRESS,FILE=name +*EL FILE +Data lines to define element integration output to the results file +*NODE FILE +Data lines to define nodal output to the results file +*END STEP +** +*STEP +Step 3 - transient analysis driven by temperature gradients +*MASS DIFFUSION,DCMAX=dcmax,END=SS +Data line to define incrementation +*BOUNDARY +Data lines to prescribe nodal values of normalized concentration +*TEMPERATURE,FILE=name +*EL FILE +Data lines to define element integration output to the results file +*NODE FILE +Data lines to define nodal output to the results file +*END STEP +Additional reference +• Crank, J., The Mathematics of Diffusion, Clarendon Press, Oxford, 1956. +6.10 +Acoustic and shock analysis +• “Acoustic, shock, and coupled acoustic-structural analysis,” Section 6.10.1 +6.10.1 +ACOUSTIC, SHOCK, AND COUPLED ACOUSTIC-STRUCTURAL ANALYSIS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Acoustic medium,” Section 26.3.1 +• “Acoustic and shock loads,” Section 33.4.6 +• “Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1 +• “ALE adaptive meshing: overview,” Section 12.2.1 +• “Steady-state transport analysis,” Section 6.4.1 +• *ACOUSTIC FLOW VELOCITY +• *ACOUSTIC WAVE FORMULATION +• *ADAPTIVE MESH +• *BEAM FLUID INERTIA +• *CONWEP CHARGE PROPERTY +• *IMPEDANCE +• *IMPEDANCE PROPERTY +• *INCIDENT WAVE +• *INCIDENT WAVE INTERACTION +• *INITIAL CONDITIONS +• *SIMPEDANCE +• *TIE +• “Defining an acoustic pressure boundary condition,” Section 16.10.19 of the Abaqus/CAE User’s +Manual, in the online HTML version of this manual +• “Creating the submodel boundary condition,” Section 38.4 of the Abaqus/CAE User’s Manual +Overview +Analyses performed using acoustic elements, an acoustic medium, and a dynamic procedure can simulate +a variety of engineering phenomena including low-amplitude wave phenomena involving fluids such as +air and water and “shock” analysis involving higher amplitude waves in fluids interacting with structures. +An acoustic analysis: +• is used to model sound propagation, emission, and radiation problems; +• can include incident wave loading to model effects such as underwater explosion (UNDEX) on +structures interacting with fluids, airborne blast loading on structures, or sound waves impinging on +a structure; +• in Abaqus/Explicit can include fluid undergoing cavitation when the absolute pressure drops to a +limit value; +• is performed using one of the dynamic analysis procedures (“Dynamic analysis procedures: +overview,” Section 6.3.1); +• can be used to model an acoustic medium alone, as in the study of the natural frequencies of vibration +of a cavity containing an acoustic fluid; +• can be used to model a coupled acoustic-structural system, as in the study of the noise level in a +vehicle; +• can be used to model the sound transmitted through a coupled acoustic-structural system; +• requires the use of acoustic elements and, for coupled acoustic-structural analysis, a surface-based +interaction using a tie constraint or, in Abaqus/Standard, acoustic interface elements; +• can be used to obtain the scattered wave solution directly under incident wave loading when the +mechanical behavior of the fluid is linear; +• can be used to obtain a total wave solution (sum of the incident and the scattered waves) by selecting +the total wave formulation, particularly when nonlinear fluid behavior such as cavitation is present +in the acoustic medium; +• can be used to model problems where the acoustic medium interacts with a structure subjected to +large static deformation; +• in Abaqus/Standard can be used with symmetric model generation (“Symmetric model generation,” +Section 10.4.1) and symmetric results transfer (“Transferring results from a symmetric mesh or a +partial three-dimensional mesh to a full three-dimensional mesh,” Section 10.4.2); +• in Abaqus/Standard can be used with steady-state transport (“Steady-state transport analysis,” +Section 6.4.1) and an acoustic flow velocity (“*ACOUSTIC FLOW VELOCITY,” Section 1.1 of +the Abaqus Keywords Reference Manual) to model acoustic perturbations of a moving fluid; +• in Abaqus/Standard can include a coupled structural-acoustic substructure that was previously +defined (“Defining substructures,” Section 10.1.2); +• can be used to model both interior problems, where a structure surrounds one or more acoustic +cavities, and exterior problems, where a structure is located in a fluid medium extending to infinity; +and +• is applicable to any vibration or dynamic problem in a medium where the effects of shear stress are +negligible. +A shock analysis: +• is used to model blast effects on structures; +• often requires double precision to avoid roundoff error when Abaqus/Explicit is used; +• may include acoustic elements to model the effects of fluid inertia and compressibility; +• may include virtual mass effects to model the effect of an incompressible fluid interacting with a +pipe structure; +• is performed using one of the dynamic analysis procedures (“Dynamic analysis procedures: +overview,” Section 6.3.1); +• can be used to model both interior problems, where a structure surrounds one or more fluid cavities, +and exterior problems, where a structure is located in a fluid medium extending to infinity; and +• in Abaqus/Explicit can include air blast loading on structures using the CONWEP model. +Procedures available for acoustic analysis +Acoustic elements model the propagation of acoustic waves and are active only in dynamic analysis +procedures. They are most commonly used in the following procedures: +• Direct solution, steady-state, harmonic analysis. +analysis,” Section 6.3.4. +See “Direct-solution steady-state dynamic +• Frequency analysis. See “Natural frequency extraction,” Section 6.3.5. +• Subspace-based steady-state dynamic analysis. +See “Subspace-based steady-state dynamic +analysis,” Section 6.3.9. +• Explicit dynamic analysis. See “Explicit dynamic analysis,” Section 6.3.3. +Acoustic analysis can also be performed using: +• Direct time integration analysis. +Section 6.3.2. +See “Implicit dynamic analysis using direct integration,” +• Complex frequency analysis. See “Natural frequency extraction,” Section 6.3.5. +• Mode-based transient dynamic analysis. See “Transient modal dynamic analysis,” Section 6.3.7. +• Mode-based steady-state dynamic analysis. See “Mode-based steady-state dynamic analysis,” +Section 6.3.8. +• Dynamic fully coupled temperature-displacement analysis. See “Fully coupled thermal-stress +analysis,” Section 6.5.3. +In general, analysis with acoustic elements should be thought of as small-displacement linear +perturbation analysis, in which the strain in the acoustic elements is strictly (or overwhelmingly) +volumetric and small. In many applications the base state for the linear perturbation is simply ignored: +for solid structures interacting with air or water, the initial stress (if any) in the air or water has negligible +physical effect on the acoustic waves. Most engineering acoustic analyses, transient or steady state, are +of this type. +An important exception is when the acoustic perturbation occurs in a gas or liquid with high-speed +underlying flow. If the magnitude of the flow velocity is significant compared to the speed of sound in +the fluid (i.e., the Mach number is much greater than zero), the propagation of waves is facilitated in +the direction of flow and impeded in the direction against the flow. This phenomenon is the source of +the well-known “Doppler effect.” In Abaqus/Standard underlying flow effects are prescribed for nodes +making up acoustic elements by specifying an acoustic flow velocity. +Acoustic elements can be used in a static analysis, but all acoustic effects will be ignored. A +typical example is the air cavity in a tire/wheel assembly. In such a simulation the tire is subjected +to inflation, rim mounting, and footprint loads prior to the coupled acoustic-structural analysis in which +the acoustic response of the air cavity is determined. See “Defining ALE adaptive mesh domains in +Abaqus/Standard,” Section 12.2.6, and “ALE adaptive meshing and remapping in Abaqus/Standard,” +Section 12.2.7, for more information. +Acoustic elements also can be used in a substructure generation procedure to generate coupled +structural-acoustic substructures. Only structural degrees of freedom can be retained. The retained +eigenmodes must be selected when an acoustic-structural substructure is generated. In a static analysis +involving a substructure containing acoustic elements, the results will differ from the results obtained in +an equivalent static analysis without substructures. The reason is that the acoustic-structural coupling is +taken into account in the substructure (leading to hydrostatic contributions of the acoustic fluid), while the +coupling is ignored in a static analysis without substructures. More details on coupled structural-acoustic +substructures can be found in “Defining substructures,” Section 10.1.2. +A volumetric drag coefficient, +, can be defined to simulate fluid velocity-dependent pressure +amplitude losses. These occur, for example, when the acoustic medium flows through a porous matrix +that causes some resistance , such as a sound-deadening +material like fiberglass insulation. For direct time integration dynamic analysis we assume there are +no significant spatial discontinuities in the quantity +is the density of the fluid (acoustic +medium), and that the volumetric drag is small at acoustic-structural boundaries. These assumptions, +which can limit the applicability of the analysis, are discussed further in “Coupled acoustic-structural +medium analysis,” Section 2.9.1 of the Abaqus Theory Manual. +, where +The direct-solution steady-state dynamic harmonic response procedure is advantageous for +acoustic-structural sound propagation problems, because the gradient of +need not be small and +because acoustic-structural coupling and damping are not restricted in this formulation. If there is no +damping or if damping can be neglected, factoring a real-only matrix can reduce computational time +significantly; see “Direct-solution steady-state dynamic analysis,” Section 6.3.4, for details. +Some fluid-solid interaction analyses involve long-duration dynamic effects that more closely +resemble structural dynamic analysis than wave propagation; that is, the important dynamics of the +structure occur at a time scale that is long compared to the compressional wave speed of the solid +medium and the acoustic wave speed of the fluid. Equivalently, in such cases, disturbances of interest in +the structure propagate very slowly in comparison to waves in the fluid and compressional waves in the +structure. In such instances, modeling of the structure using beams is common. When these structural +elements interact with a surrounding fluid, the important fluid effect is due to motions associated with +incompressible flow . These motions result in a perceived inertia added to the structural beam; +therefore, this case is usually referred to as the “virtual mass approximation.” For this case Abaqus +allows you to modify the inertia properties of beam and pipe elements, as described below. Loads on +the structure associated with incident waves in the fluid can be accommodated under this approximation +as well. +Natural frequency extraction +Abaqus can compute both real and complex eigensolutions for purely acoustic or structural-acoustic +systems, with or without damping. Exterior acoustic problems may also be solved. +Selecting an eigensolver +In a coupled acoustic-structural model, real-valued coupled modes are extracted by default using the +Lanczos eigenfrequency extraction procedure. Coupling may be suppressed in the frequency extraction +step; in this case the structural elements behave as though the interface with the acoustic elements were +free (as though this surface were “in vacuo”), and the acoustic elements behave as though the boundary +with the structural elements were rigid. +Structural-acoustic coupling is ignored if the subspace iteration eigensolver is used. +When applying the AMS eigensolver or the Lanczos eigensolver based on the SIM architecture to +a coupled structural-acoustic model, Abaqus by default projects and stores the acoustic coupling matrix +during the natural frequency extraction, for later use in coupled forced response analyses. The structural +and acoustic regions are not actually coupled during the eigenanalysis; Abaqus solves the two regions +separately but computes and stores the projected coupling operator for use in subsequent steady-state +dynamic steps. Only structural-acoustic coupling defined using tied contact is supported. You can +suppress this coupling if desired. Damping due to acoustic volumetric drag is also projected by default +during an eigenanalysis and is restored by default in subsequent steady-state dynamic steps. +Damping and inertia effects in an acoustic natural frequency extraction +Since damping is not taken into account in real-valued modal extraction, the volumetric drag effect is +not considered, except for its small contribution to any nonreflecting boundaries . The damping contributions +due to any impedance boundary conditions (element-based or surface-based) or acoustic infinite elements +are not included in an eigenfrequency extraction step, but the contributions to the acoustic element mass +and stiffness matrices are included. Similarly, the (symmetrized) stiffness and mass contributions of +acoustic infinite elements are included in an eigenfrequency extraction step, but the damping effects are +neglected. +Modal analysis of damped and radiating acoustic systems can be performed in Abaqus as well. +Using the complex eigenvalue extraction procedure, the damping contributions of acoustic infinite +elements, nonreflecting impedance conditions, and general impedance layers are restored to the element +operators. +If an underlying flow field is defined for the acoustic region by specifying an acoustic flow velocity, +the natural frequencies and modes are affected. However, in real-valued frequency extraction only +the acoustic element mass and stiffness matrices contribute to the solution. Since the formulation for +acoustics in the presence of a flow field requires a complex part in the element operator (damping matrix), +the real-valued procedure can include the effects of flow only to a limited degree. The complex frequency +procedure in Abaqus/Standard includes the damping matrix contribution and is, therefore, required when +modes of a system with moving fluid are sought. The complex frequency procedure can be used only +following the Lanczos real-valued frequency procedure. +Virtual mass effects defined for beams by adding inertia (“Additional inertia due to immersion in +fluid” in “Beam section behavior,” Section 29.3.5) are included in modal analysis: their effect is simply +to add inertia to a beam element. +Interpreting the extracted modes in a coupled structural-acoustic natural frequency analysis +While all the modes extracted in a coupled Lanczos structural-acoustic natural frequency analysis include +the effects of fluid-solid interaction, some of them may have predominantly structural contributions while +others may have predominantly acoustic contributions. Coupled structural-acoustic eigenmodes can be +categorized as follows: +• Most generally, an individual mode may exhibit participation in both the fluid and the solid media; +this is referred to as a “coupled mode.” +• Second, there are the “structural resonance” modes. These are modes corresponding to the +eigenmodes of the structure without the presence of the acoustic fluid. The presence of the acoustic +fluid has a relatively small effect on these eigenfrequencies and the mode shapes. +• Third, there are the “acoustic cavity resonance” modes. These are nonzero eigenfrequency coupled +modes that have a significant contribution in the resulting dynamics of the acoustic pressure in +mode-based dynamic procedures. +• Fourth, +if insufficient boundary conditions are specified on the structural part of a model, +the frequency extraction procedure will extract rigid body modes. These modes have zero +eigenfrequencies (sometimes they appear as either small positive or even negative eigenvalues). +However, if sufficient structural degrees of freedom are constrained, these rigid body modes +disappear. +• Finally, there are the singular acoustic modes, which have zero eigenfrequencies and constant +acoustic pressure; they are mathematically analogous to structural rigid body modes. The structural +part of the singular acoustic modes corresponds to the quasi-static structural response to constant +pressure in unconstrained acoustic regions. These eigenmodes are predominantly acoustic and +are important in representing the (low-frequency) acoustic response in mode-based analysis +in the presence of acoustic loads, in the same way that rigid body modes are important in the +representation of structural motion. As is true for the structural rigid body modes, if a sufficient +number of constrained acoustic degrees of freedom is specified (one degree of freedom 8 per +acoustic region is enough), the singular acoustic modes will disappear. In models with only one +unconstrained acoustic region (the most common case) only one singular acoustic mode will +In general there are as many singular acoustic modes as there are independent +be computed. +unconstrained acoustic regions. If these modes are present, they are always reported first by the +Lanczos eigensolver; and a note at the bottom of the eigenfrequency table in the data file provides +information about the number of singular acoustic modes. +The generalized masses and effective masses can help distinguish between the various types of +modes and can be used to assess which modes are important for subsequent mode-based analyses. In +addition, the acoustic contribution to the generalized masses is reported as a fraction for each eigenmode. +The closer the value of this fraction is to unity, the more pronounced is the acoustic component of this +eigenmode. An acoustic effective mass is also computed for each eigenmode. This scalar quantity is +scaled such that when all eigenmodes in a model are extracted, the sum of all acoustic effective masses +is equal to 1.0 (minus the contributions from nodes with restrained acoustic degrees of freedom). The +the higher the acoustic effective +acoustic effective mass can be compared between different modes: +mass, the more important (typically) the mode is for accurate representation of the acoustic pressure. For +example, the fluid cavity acoustic resonance modes will have larger acoustic effective masses compared +to the other modes. +Modal superposition procedures +In Abaqus acoustic domains are handled quite similarly to solid and structural domains. Real-valued +eigenmodes, resulting from a previous real-valued eigenfrequency extraction procedure with or without +coupling effects included, are used as a basis for modal solutions. The mode-based steady-state dynamic +procedure is the most computationally efficient alternative to compute the steady-state response of +structural-acoustic systems. Structural-acoustic coupling and damping effects in these analyses depend +on the type of modal procedure and the eigensolver that was used to compute the eigenfrequencies. +Structural-acoustic coupling in modal analyses using the Lanczos eigensolver without the SIM +architecture +If coupled modes are computed using the Lanczos eigensolver, both the mode-based and subspace +projection steady-state dynamic procedures will +If +uncoupled Lanczos modes are computed, coupling can be restored only by using subspace projection. +It is sufficient to project at a single frequency (constant subspace) to resolve the acoustic coupling for +all frequencies. +include structural-acoustic coupled effects. +Acoustic medium damping in modal analyses using the Lanczos eigensolver without the SIM +architecture +In subspace-based steady-state dynamic analysis, acoustic medium damping and structural material +infinite element, and impedance +damping are considered, and the structural-acoustic interaction, +boundary terms are also included. +Acoustic medium damping is not considered in the procedures that base the response prediction +directly on the system’s eigenmodes, such as transient modal dynamic analysis or the mode-based steady- +state dynamic procedure. These methods should, therefore, be used with caution for problems with +impedance boundary conditions. Modal damping can be used in these procedures (“Material damping,” +Section 26.1.1) to model material damping and volumetric drag effects; however, modal damping usually +cannot be used to model the fluid-solid coupling or the impedance boundary effects accurately. +Structural-acoustic coupling and damping in modal analyses using the subspace iteration eigensolver +The subspace iteration eigensolver neglects the effects of structural-acoustic coupling; +coupling effects are not included in subsequent modal procedures. +therefore, +As with analyses using the Lanczos eigensolver, acoustic medium damping and structural material +damping are considered in subsequent subspace-based steady-state dynamic procedures, but these +damping effects are not considered in subsequent transient modal or mode-based steady-state dynamic +procedures. +Structural-acoustic coupling and damping in modal analyses using the AMS eigensolver or the Lanczos +eigensolver based on the SIM architecture +When modes are computed using the AMS eigensolver or the Lanczos eigensolver based on the SIM +architecture, the structural-acoustic coupling and acoustic damping operators are projected and stored +by default during the natural frequency extraction. Subsequent coupled forced response analyses +using modal steady-state dynamics automatically restore the effects of structural-acoustic coupling +and damping by automatically using these projected matrices; if the matrices were not projected, the +steady-state dynamic step would not include these effects. A mode-based steady-state dynamic step +cannot use nonsymmetric damping, such as from acoustic flow velocity or infinite element effects. To +take these effects into account, a subspace-based steady-state dynamic analysis should be used. +Defining translational or rotational underlying flow velocity in Abaqus/Standard +As described above, acoustic analysis in Abaqus/Standard can be performed as a linear perturbation +of a high-speed flow field. The flow velocity field affects the propagation of acoustic waves in the +medium through the effect of the flow velocity on the speed of the wave propagation. Waves travel faster +along the direction of the local flow vector and are correspondingly impeded in the direction against the +flow direction. It is sufficient for you to define the velocity field in the affected acoustic region; the +accelerations do not play a role in the formulation. +You specify the flow in the acoustic finite element region as history data within a dynamic linear +perturbation step. The flow field can be described either by direct input of the velocity components or by +defining rotating motion associated with a reference frame. In the former case, each node in the acoustic +region where flow occurs is assigned a Cartesian velocity defined by specifying the components of the +velocity vector, +. In the latter case, the rotational velocity for the nodes in the acoustic region is defined +by specifying the magnitude of an angular rotation velocity, +, and the position and orientation of the +axis of rotation in the current configuration. The position and orientation of the axis are applied at the +beginning of the step and remain fixed during the step. +The specified underlying flow is active only for acoustic finite elements; other elements with +acoustic degrees of freedom, such as acoustic infinite and interface elements, are unaffected by the +specified flow velocity. The effect of underlying flow on the acoustic finite elements depends also +on the procedure used: +the effects are present only in frequency-domain dynamic procedures and +natural frequency extraction. For complex-valued procedures, such as complex frequency extraction +and steady-state dynamics, the presence of underlying flow affects the acoustic finite element stiffness +matrices and adds a significant contribution to the element damping matrix. For real-valued procedures, +such as eigenfrequency extraction and steady-state dynamics analysis in which a real-only system +matrix is factored, the presence of underlying flow affects only the acoustic finite element stiffness +matrices; the damping matrix is ignored. Consequently, the effect of flow on the acoustic field is fully +realized only in complex-valued procedures. +For rotating systems, solid and acoustic materials are treated differently in Abaqus. Flow of +solid material through a mesh may induce significant deformation and is handled by using steady-state +transport; subsequent linear perturbation steps are analyzed about this deformed state . Flow of material through an acoustic mesh is handled entirely within +linear perturbation steps by specifying an acoustic flow velocity; a preliminary nonlinear steady-state +transport analysis is not required. For coupled acoustic-structural systems undergoing rotation, such +as tires, the model may be subjected to a steady-state transport step, which deforms the solid medium, +followed by linear perturbation dynamic steps. The effect of the rotation of the solid is included in the +linear perturbation steps in this case; to include the effect of the rotation of the acoustic fluid, specify an +acoustic flow velocity in the linear perturbation steps. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to define a translating fluid velocity: +*ACOUSTIC FLOW VELOCITY, TRANSLATION +Use the following option to define a rotating fluid velocity: +*ACOUSTIC FLOW VELOCITY, ROTATION +Acoustic flow velocity is not supported in Abaqus/CAE. +Updating the acoustic domain during a large-displacement Abaqus/Standard analysis +By default, the acoustic-structural coupling calculations are based on the original configuration of the +fluid domain. However, acoustic elements can also be used in an analysis where the structural domain +experiences large deformation prior to the coupled analysis. A typical example is the interior cavity of a +tire subjected to structural loads such as inflation, rim mounting, and footprint pressure. +the deformation of +The acoustic elements in Abaqus do not have displacement degrees of freedom and, therefore, +cannot model +the fluid when the structure undergoes large deformation. +Abaqus/Standard solves the problem of computing the current configuration of the acoustic domain +by periodically creating a new acoustic mesh. The new mesh uses the same topology (elements and +connectivity) throughout the simulation, but the nodal locations are adjusted so that the acoustic domain +conforms to the structural domain on the boundary. +A new acoustic mesh is computed when adaptive meshing is specified and nonlinear geometric +effects are considered in any non-perturbation Abaqus/Standard analysis procedure in which acoustic +effects are ignored. +The adaptive meshing features for acoustic analysis are described in detail in “Defining ALE +adaptive mesh domains in Abaqus/Standard,” Section 12.2.6, and “ALE adaptive meshing and +remapping in Abaqus/Standard,” Section 12.2.7. +Initial conditions +In Abaqus/Standard the initial acoustic static pressure (hydrostatic or ambient) is not modeled by the +acoustic formulation and cannot be specified as an initial condition. +In Abaqus/Explicit the initial acoustic pressure corresponding to the initial static equilibrium +(hydrostatic or ambient) can be specified and is meaningful only when the acoustic fluid is capable of +undergoing cavitation. In problems with possible fluid cavitation the initial acoustic static pressure is +taken into account in the cavitation condition; i.e., the sum of the dynamic and static acoustic pressures +needs to drop to the cavitation pressure limit for the cavitation to occur. The specified acoustic static +pressure is used only in the cavitation condition and does not apply any static loads to the acoustic +or structural meshes at their common wetted interface. In addition, the acoustic static pressure is not +included in the nodal acoustic pressure degree of freedom. +The initial +temperature and field variable values can be specified (“Initial conditions in +Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1) for the direct time integration dynamic, explicit +dynamic, dynamic fully coupled temperature-displacement, and mode-based transient dynamic analysis +procedures. Changes in these variables during the analysis will affect any temperature-dependent or +field-variable-dependent acoustic medium properties. +Boundary conditions +The various boundary conditions that can be applied to an acoustic medium are described below. These +include acoustic domain boundaries with stationary rigid walls or symmetry planes, prescribed pressure +values such as a free surface with zero dynamic pressure, specified impedance , and structural interfaces such as the interface with a ship or a submarine. +The radiating (nonreflecting) boundary condition for exterior problems (such as a structure vibrating +in an acoustic medium of infinite extent) is implemented as a special case of the impedance boundary +condition . On any given part of the acoustic domain +boundary only one boundary condition type should be applied, except for the combination of the +impedance boundary condition and the acoustic-structural interface condition. +Boundary with a stationary rigid wall or a symmetry plane +The default boundary condition for an acoustic medium is a boundary with a stationary rigid wall or a +symmetry plane. The “force” conjugate to pressure in the acoustics formulation in Abaqus is the normal +pressure gradient at the surface divided by the mass density; dimensionally this is equal to a force per +unit mass. In the absence of volumetric drag this force per unit mass is equal to the inward acceleration of +the acoustic medium. The conjugate variable at a node on the surface is the inward volume acceleration, +which is the integral of the inward acceleration of the acoustic medium evaluated over the surface area +associated with the node. A “traction-free” surface (one with no boundary conditions, no applied loads, +no surface impedance conditions, and no interface elements) is a surface normal to which the acoustic +medium undergoes no motion and, thus, corresponds to a rigid, stationary surface adjacent to the fluid. +A symmetry plane for the acoustic medium is another “traction-free” surface. +Prescribed pressure +The basic variable in the acoustic medium is pressure (degree of freedom 8). Therefore, this variable can +be prescribed at any node in the acoustic model by applying a boundary condition (“Boundary conditions +in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1). Setting the pressure to zero represents a “free +surface,” where the pressure does not vary because of the motion of the surface (to account for surface +motion effects, see the discussion of impedance below). Prescribing a nonzero value for the pressure +represents a sound source. +An amplitude variation can be used to specify the value of the pressure. In a steady-state analysis +you can specify both the in-phase (real) part of the pressure (default) and the out-of-phase (imaginary) +part of the pressure. +Input File Usage: +Abaqus/CAE Usage: +Boundary with a structure +Use either of the following options to define the real (in-phase) part of the +boundary condition: +*BOUNDARY +*BOUNDARY, REAL +Use the following option to define the imaginary (out-of-phase) part of the +boundary condition: +*BOUNDARY, IMAGINARY +Load module: Create Boundary Condition: choose Other for the +Category and Acoustic pressure for the Types for Selected Step: +select regions: Magnitude: real (in-phase) part + imaginary (out-of-phase) +part i +If the acoustic medium is adjacent to a structure, there will be a transfer of momentum and energy +between the media at the boundary. The pressure field modeled with acoustic elements creates a normal +surface traction on the structure, and the acceleration field modeled with structural elements creates the +natural forcing term at the fluid boundary (for details, see “Coupled acoustic-structural medium analysis,” +Section 2.9.1 of the Abaqus Theory Manual). +The surface-based coupling procedure and the user-defined acoustic interface elements differ +slightly in their theoretical implementation. In essence, the interface elements computed internally by +the surface-based procedure are discrete point elements computed at the nodes of the slave surface. A +user-defined acoustic interface element, on the other hand, distributes coupling effects across all of its +nodes. Generally, the results obtained using the two coupling methods will be very similar, but the +difference in discretization at the coupling boundary may create small differences in results. +Defining acoustic-structural coupling with user-defined acoustic interface elements +In Abaqus/Standard, if the structural and acoustic meshes share nodes at the boundary, lining this +boundary with acoustic-structural +library,” +Section 32.13.2) will enforce the required physical coupling condition. The interface element normals +must point into the acoustic medium, which forces continuity of the normal accelerations of the acoustic +medium and of the structure at the boundary and ensures that the pressure of the acoustic elements is +applied to the structure. Displacements can also be prescribed at such a boundary. +interface elements . No additional element definitions are required. +The slave surface, the first of the two surfaces specified for the tie constraint, must be element-based; +whereas the master surface can be either element- or node-based. A surface based on rigid element types +(R3D4, etc.) or an analytical rigid surface cannot be used as a master surface; instead, use a deformable +surface made rigid. +For surface-based tie constraints Abaqus automatically computes the region of influence for +each internally generated acoustic-structural interface element. +If the user-defined slave surface +overhangs the master surface significantly, the regions of influence may include parts of the overhang. +Consequently, the overhanging part of the slave surface may exhibit nonphysical coupled degrees of +freedom: displacements if the slave surface is acoustic and acoustic pressures if the slave surface is solid +or structural. These nonphysical results on the overhang do not affect the remainder of the solution, and +it should be understood that they are not meaningful. +Input File Usage: +Use the following option in an analysis with the fluid mesh surface as the slave: +*TIE, NAME=fluidslave +fluid_surf, struct_surface +Use the following option in an analysis with the solid mesh surface as the slave: +*TIE, NAME=solidslave +struct_surf, fluid_surf +Abaqus/CAE Usage: +Interaction module: Create Constraint: Tie +Coupling surfaces to structures using acoustic infinite elements +Acoustic infinite elements may form surfaces that can be coupled to structures by using a tie constraint +in two different ways. The acoustic infinite element surface may consist of the base (first) facets +of the acoustic infinite elements; in this case this surface should be tied to a topologically similar +structural surface. The acoustic infinite element edges may also be used to define surfaces , which can be tied to solid elements. This approach couples the +semi-infinite sides of acoustic infinite elements to solid elements. +Mesh refinement +Although the meshes may be nodally nonconforming at the tied surfaces, mesh refinement affects the +accuracy of the coupled solution. In acoustic-solid problems the mesh refinement depends on the wave +speeds in the two media. The mesh for the medium with the lower wave speed should generally be more +refined and, therefore, should be the slave surface. If the details of the wave field in the vicinity of the +fluid-solid interface are important, the meshes should be of equally high refinement, with the refinement +corresponding to the lower wave speed medium. In this case the choice of the master surface is arbitrary. +An exception is the case where the acoustic medium must be updated to follow the structure during a +large-deformation analysis. In such a case the slave surface must be defined on the acoustic domain. +Another exception is the case of fluids coupled to both sides of shell or beam elements (as described +below). +Solving the structural system sequentially using the submodeling technique +In some applications the normal surface traction on the structure created by the acoustic fluid may +be negligible compared to other forces in the structural system. For example, a metal motor housing +may radiate sound into the surrounding air, but the reaction pressure of the air on the motor may +be insignificant to the dynamics of the housing. +In these cases the submodeling technique can be used to solve the system sequentially; that is, the +structural analysis (uncoupled from the fluid) is followed by the acoustic analysis (driven by the +structure). Usually, this decoupling of the analysis reduces computational cost. The structural system +plays the role of the “global” model, and the acoustic fluid is the submodel. The structural displacements +on the boundary of the acoustic fluid must be saved to the results file in the global analysis. Since +Abaqus interpolates the fields between the global and submodels, acoustic-structural interface elements +can be used. They should be applied to the fluid boundary to be driven by the global structural model. +Input File Usage: +Use the following options in the global (structural) analysis to be followed by +a submodeling analysis: +*NSET, NSET=solid_boundary_driving_the_fluid +*NODE FILE, NSET=solid_boundary_driving_the_fluid +Use the following options in the subsequent submodeling (fluid) analysis that +uses acoustic interface elements on the fluid boundary to be driven: +*NSET, NSET=fluid_boundary_to_be_driven +*SUBMODEL, EXTERIOR TOLERANCE=tolerance +fluid_boundary_to_be_driven +*BOUNDARY, SUBMODEL, STEP=1 +fluid_boundary_to be_driven, 1, 3, +Abaqus/CAE Usage: +Use the following input in the submodeling (fluid) analysis that uses an acoustic +interface on the fluid boundary to be driven: +Load module: Create Boundary Condition: choose Other for the +Category and Submodel for the Types for Selected Step: +select regions for fluid_boundary_to _be_driven: Exterior tolerance: +relative: tolerance; Degrees of freedom: 1, 3; Global step number: 1 +Defining acoustic-structural coupling on both sides of a beam or shell +In Abaqus/Standard there are two alternatives available for modeling a beam (in two dimensions) or +shell interacting with fluid on both sides: a surface-based procedure and an element-based procedure. In +Abaqus/Explicit the surface-based procedure must be used. +Use of the surface-based procedure is straightforward. Two surfaces must be defined on the beam +or shell: one on the SPOS side and one on the SNEG side. Each surface is then coupled to the fluid using +a tie constraint. At least one of the two surfaces on the beam or shell must be a master surface. +In Abaqus/Standard, if the same nodes are used for the fluid and the beam or shell, acoustic interface +elements must be used in the following manner to define acoustic-structural coupling on both sides of a +beam or shell element: +1. Define a second set of nodes coincident with the beam or shell nodes, and constrain the motions +of the two sets of nodes together using a PIN-type MPC (“General multi-point constraints,” +Section 34.2.2). +2. Use the first set of nodes to line one side of the beam or shell elements with acoustic interface +elements (with the normals of the acoustic interface elements pointing into the fluid). +3. Use the second set of nodes to line the other side of the beam or shell elements with acoustic interface +elements (with the normals pointing into the fluid on the opposite side of the structure, as in Step 2). +4. The acoustic elements on the first side of the beam or shell elements should be defined using the +first set of nodes, and the acoustic elements on the second side of the beam or shell elements should +be defined using the second set of nodes. +Defining the virtual mass effect (fluid-structural coupling) for beam and pipe elements +In Abaqus virtual mass effects on submerged Timoshenko beam elements can be modeled by specifying +additional inertia for the beam. The virtual mass effects are specified as part of the section definition of +the beam. +1. Define the beam section (“Using a beam section integrated during the analysis to define the section +behavior,” Section 29.3.6, or “Using a general beam section to define the section behavior,” +Section 29.3.7), any additional internal inertia (“Adding inertia to the beam section behavior for +Timoshenko beams” in “Beam section behavior,” Section 29.3.5), and the beam material properties. +2. Define the virtual mass effect (“Additional inertia due to immersion in fluid” in “Beam section +behavior,” Section 29.3.5). +3. If the model is to be loaded using an incident wave (“Incident wave loading due to external sources” +in “Acoustic and shock loads,” Section 33.4.6), define a surface or surfaces on the beam elements. +Loads +The following types of loading can be prescribed in an acoustic analysis, as described in “Acoustic and +shock loads,” Section 33.4.6: +• Concentrated pressure-conjugate loading. +• An impedance condition that specifies the relationship between the pressure of the acoustic medium +and the normal motion at the boundary (either element-based or surface-based). Such a condition +is applied, for example, to include the effect of small-amplitude “sloshing” in a gravity field or +to include the effect of a compressible, possibly dissipative, lining (such as a carpet) between the +acoustic medium and a fixed, rigid wall or a structure. This type of condition can also be applied to +edge facets of acoustic infinite elements. +• Nonreflecting radiation conditions on acoustic boundaries (either element-based or surface-based). +An impedance can be defined to select the appropriate radiating boundary condition taking the +radiating surface shape into consideration. +• Incident wave loading such as that caused by an underwater explosion or a sound field. Since this +type of loading is usually applied in conjunction with semi-infinite acoustic regions, two alternative +modeling formulations are available in Abaqus. A total pressure-based formulation is provided +when the incident wave loading is applied to the exterior of a semi-infinite acoustic mesh. This +formulation must be used to handle the incident wave loading when the acoustic medium is capable +of cavitation, rendering the fluid material behavior nonlinear. The scattered pressure formulation is +typically used when cavitation is not part of the fluid mechanical behavior and when the loads are +applied to fluid-solid interfaces. Sound transmission loss and acoustic scattering problems usually +fall into the latter category. +For both formulations, when incident wave loading is applied to a given surface, a +mathematical jump occurs between the pressures on both sides of the surface because the side +from which the incident pressure arrives is implicitly a region of scattered pressure. This jump is +handled automatically when the incident wave load is applied to a surface with a nonreflecting +impedance condition and when the incident wave load is applied to a fluid-solid interface. +However, if the incident wave load is applied to a surface lying between acoustic finite or infinite +elements, the jump will not be modeled properly because pressures are continuous between +acoustic elements. For this case, low-mass and low-stiffness membrane, shell, or surface elements +should be interposed between the acoustic elements to permit the jump in pressure to exist. +Incident wave loading can be applied in time-harmonic problems, using the direct solution +steady-state dynamics and the subspace-based, steady-state dynamic procedures. You can define +individual spherical or planar sources emitting waves, or you can use the deterministic diffuse +field model in Abaqus. In the former case, usage is quite similar to transient analysis: the defined +sources correspond to distinct sound sources. The latter case models the sound field incident on a +surface exposed to a reverberant chamber: the field is assumed to be equivalent to a number of plane +waves arriving from directions distributed on a hemisphere. Only the scattered wave formulation +is supported when using incident wave loading in steady-state dynamics. +See “Acoustic and shock loads,” Section 33.4.6, for several examples of incident wave loading. +• Loading due to an incident shock wave caused by an air explosion. Although this type of wave +is highly nonlinear and complex, the pressure loading due to the shock wave can be calculated +readily from empirical data provided by the CONWEP model available in Abaqus/Explicit. The +main advantage of this model is that the loading is applied directly to the structure subject to the +blast; there is no need to include the fluid medium in the computational domain. In the CONWEP +model, empirical data for two types of waves are available: spherical waves for explosions in mid- +air and hemispherical waves for explosions at ground level in which ground effects are included. +The CONWEP model does not account for effects of shadowing by intervening objects. In +addition, it does not account for effects due to confinement and, thereby, excludes incorporation of +any reflecting surfaces in the analysis. The model does account for the angle of incident of the blast +wave; see “Acoustic and shock loads,” Section 33.4.6, for incorporation of the incident angle in the +pressure load calculation. +Predefined fields +The following predefined fields can be specified in an acoustic analysis, as described in “Predefined +fields,” Section 33.6.1: +• Although temperature is not a degree of freedom in acoustic elements, nodal temperatures can be +specified. The specified temperature affects temperature-dependent material properties. +• The values of user-defined field variables can be specified. These values affect field-variable- +dependent material properties. +Material options +Only the acoustic medium material model (“Acoustic medium,” Section 26.3.1) is valid for use in an +acoustic analysis. The structure in a coupled acoustic-structural analysis can be modeled using any +material model. Since acoustic analyses are always performed using a dynamic procedure, the structure’s +density (“Density,” Section 21.2.1) should usually be defined. +Porous materials are often modeled using an acoustic formulation when the dilatational waves in +the porous medium dominate the shear effects. A large number of models exist for this category of +phenomenon. In Abaqus, two categories of models are available for porous media modeled with acoustic +elements: phenomenological models and general frequency-dependent models. Phenomenological +models describe the dynamic characteristics using material data related to the porous structure, such +as porosity itself, tortuosity, etc. Alternatively, you can specify the dynamic properties directly for +the material; usually, this is done using a table of frequency-dependent data. See “Acoustic medium,” +Section 26.3.1, for details on specifying acoustic materials in Abaqus. +When the acoustic medium is capable of cavitation and the analysis includes incident wave loading, +a total pressure-based formulation must be used. Either the default scattered wave formulation or the total +wave formulation can be used if the cavitation is absent or the problem has no incident wave loading. +For beam elements using the virtual mass approximation, the relevant data are specified as part of +the beam section definition. +Elements +Abaqus provides a set of elements for modeling an acoustic medium undergoing small pressure changes. +In addition, Abaqus/Standard provides interface elements to couple these acoustic elements to a structural +model . If interface elements +are used, only direct-solution steady-state harmonic (linear) response analysis (“Direct-solution steady- +state dynamic analysis,” Section 6.3.4) and transient response analysis (“Implicit dynamic analysis using +direct integration,” Section 6.3.2) can be performed. +In Abaqus/Standard the second-order acoustic elements are generally considerably more accurate +than first-order acoustic elements for a given number of degrees of freedom. The acoustic elements in +Abaqus/Explicit are limited to first-order interpolations. +Acoustic elements cannot be used together with hydrostatic fluid elements. +With the CONWEP model provided in Abaqus/Explicit, the analysis must be three-dimensional. +In addition, +The loading surface must be comprised of solid, shell, or membrane elements only. +CONWEP loading cannot be applied to acoustic elements. +Exterior problems +We often need to model an exterior problem, such as a structure vibrating in an acoustic medium of +infinite extent. Impedance-type radiation boundary conditions can be used to model the motions of waves +out of the mesh. In addition, Abaqus provides acoustic infinite elements for this class of problems. +Impedance-type radiation conditions +In this case acoustic elements are used to model the region between the structure and a simple geometric +surface (located away from the structure), and a radiating (nonreflecting) boundary condition is applied at +that surface. The radiating boundary conditions are approximate, so that the error in an exterior acoustic +analysis is controlled not only by the usual finite element discretization error but also by the error in +the approximate radiation condition. In Abaqus the radiation boundary conditions converge to the exact +condition in the limit as they become infinitely distant from the radiating structure. In practice, these +radiation conditions provide accurate results when the distance between the surface and the structure is +at least one-half of the longest characteristic or responsive structural wavelength. +For details, see “Acoustic and shock loads,” Section 33.4.6. +Acoustic infinite elements +Acoustic infinite elements are provided for modeling exterior problems (“Infinite elements,” +Section 28.3.1). These elements have surface topology: line and quadratic segments in two-dimensional +and axisymmetric problems and triangles and quadrilaterals in three-dimensional problems. Generally, +the acoustic infinite elements are defined on a terminating surface of a region of acoustic finite +elements. The infinite element formulation is considerably more accurate than the impedance-type +radiation boundary conditions in cases where the wave field impinging on the terminating surface +has many complex features. The radiation boundary conditions are relatively simple, equivalent to a +“zeroth-order” infinite element; the acoustic infinite elements implemented in Abaqus are of variable +order, up to ninth. +Acoustic infinite elements can be coupled directly to structural surfaces by using a surface-based +tie constraint: this may provide adequate accuracy in some applications. In general cases the acoustic +infinite elements are defined on the terminating surface of the acoustic finite element mesh. The diameter +of the acoustic finite element mesh can be considerably smaller, for a given solution accuracy, than is the +case when using radiation boundary conditions. +The nodal connectivity on the acoustic infinite element defines the element’s surface topology. To +complete the element formulation, the surface topology must be mapped into the infinite domain. This +mapping requires a reference point, given in the element section property definition. The reference point +serves to define a characteristic length used in the coordinate mapping. In the ideal case of acoustic +radiation from a spherical surface, the correct placement of the reference point is the center of the sphere. +In general, the acoustic infinite elements produce the most accurate results when the reference node is +located near the center of the region enclosed by the infinite elements. +Nodal normal vectors are required for an accurate mapping of the infinite domain. The nodal normal +vectors must point into the infinite domain and are used to define the portion of the infinite domain treated +by a particular infinite element. To cover the infinite domain without overlap, each node attached to an +infinite element must have a unique normal. The nodal normal vectors are specified or calculated as +follows. +User-specified alternative nodal normals (“Normal definitions at nodes,” Section 2.1.4) are ignored +for acoustic infinite elements and, therefore, cannot be used to define normal directions for acoustic +elements. Over the element’s surface topology, the normal vectors must be divergent; that is, the area +mapped (in two dimensions) or the volume mapped (in three dimensions) must increase with distance +into the infinite domain. To ensure this criteria, the normal vectors at each acoustic infinite element node +are defined to lie along the vector between that node and the reference point given in the element section +property definition. See “Infinite elements,” Section 28.3.1, for more information. +Mesh refinement +Inadequate mesh refinement is the most common source of difficulties in acoustic and vibration analysis. +For reasonable accuracy, at least six representative internodal intervals of the acoustic mesh should fit +into the shortest acoustic wavelength present in the analysis; accuracy improves substantially if ten +or more internodal intervals are used at the shortest wavelength. In steady-state analyses the shortest +wavelength will occur in the medium with the lowest speed of sound, at the highest frequency analyzed. +In transient analyses the shortest wavelength present is more difficult to determine before an analysis: it +is reasonable to estimate this wavelength using the highest frequency present in the loads or prescribed +boundary conditions. +An “internodal interval” is defined as the distance from a node to its nearest neighbor in an element; +that is, the element size for a linear element or half of the element size for a quadratic element. At a fixed +internodal interval, quadratic elements are more accurate than linear elements. The level of refinement +chosen for the acoustic medium should be reflected in the solid medium as well: the solid mesh should +be sufficiently refined to accurately model flexural, compressional, and shear waves. +The level of mesh refinement required depends on the application. Any finite element discretization +of a domain in which waves propagate introduces a certain amount of error per wavelength. In meshes +that are small in terms of wavelengths, relatively coarse (for example, six internodal intervals per +wavelength) meshes may be adequate. For meshes that contain many wavelengths at the frequency +of interest, the per-wavelength finite element discretization error accumulates, generally necessitating +In these larger meshes the accumulated per-wavelength error may be +greater levels of refinement. +present throughout the mesh if refinement is inadequate. +The acoustic wavelength decreases with increasing frequency, so there is an upper frequency limit +for a given mesh. Let +the number of internodal intervals we desire per acoustic wavelength ( +represent the maximum internodal interval of an element in a mesh, +the cyclical frequency of excitation, and +the speed of sound, where +is recommended), +is the bulk +modulus of the acoustic medium and +is its density. The requirements are then expressed as +The above expressions can be used to estimate the maximum allowable element length if the frequency +is given or the maximum frequency for which a given mesh size is valid. For example, in air at room +temperature, +meters per second. The following table gives some values for maximum internodal +distances to model given maximum frequencies +accurately: +Maximum Frequency of +Interest, +Maximum Internodal +Interval, +, +Maximum Internodal +Interval, +, +100 Hz +500 Hz +1000 Hz +20 kHz +< 430 mm +< 86 mm +< 43 mm +< 2.1 mm +< 286 mm +< 57 mm +<29mm +< 1.4mm +For exterior problems the accuracy of an analysis also depends on the accuracy of the absorbing +boundary condition. As mentioned above, the absorbing boundary impedance conditions implemented +in Abaqus are used with a standoff thickness +of acoustic finite elements between the acoustic sources +and the radiating boundary. Since the approximate radiation conditions converge to the exact condition +in the limit of infinite standoff, a greater standoff thickness improves the accuracy of the solution. The +standoff thickness +wavelengths at the minimum frequency to be analyzed: +is expressed as +Continuing the example using the properties of air, we can calculate the recommended minimum standoff +thicknesses corresponding to a specified minimum frequency of interest, using +: +Minimum Frequency of Interest, +Radiation Boundary Standoff, +100 Hz +500 Hz +1000 Hz +20 kHz +> 1140 mm +> 230 mm +> 114 mm +> 5.7 mm +The computational requirements for an exterior problem thus depend on both the radiation boundary +standoff and the internodal distance. The number of nodes N in a model depends on the volume of the +mesh, controlled by +. The exact +number of nodes depends on the details of the model, but the expression +and the spatial dimension d, and the mesh density, controlled by +indicates the size of the model with respect to the ratio of the maximum to minimum frequencies in a +given analysis. Because the mesh size for an exterior problem exhibits such strong dependence on the +bandwidth, +, you can control the size of an analysis by splitting the band. For example, if +the overall frequency range of interest is 100 to 10000 Hz, a single spherical mesh covering this band in +three dimensions has size +However, splitting the problem into two bands, +mesh for each band, results in two analyses of size +and +, and creating an exterior +In coupled acoustic-structural systems there usually exist different wave speeds for the fluid and +solid media. In the region of the acoustic-structural interface, the wave phenomena in both media may +exhibit length scales characteristic of the slower medium; that is, the length scale of the wave dynamics +may be as short as the shorter wavelength, corresponding to the lower wave speed. This result follows +from the fact that the two media are coupled at the boundary. The region near the acoustic-structural +interface where these effects are important is usually no thicker than the shorter wavelength. +For example, in an analysis involving water interacting with rubber, the wave speed in the rubber +may be much lower than that of water. A finite element mesh used to model this problem in detail would +require refinement down to six (or more) nodes per shorter wavelength, on both sides of the interface. +On the water side (faster, longer wavelength) accuracy will probably not be compromised significantly +if this region of high refinement extends no further into the water than one short wavelength. Of course, +in some analyses the effects in the vicinity of the interface may be unimportant. Then, the two meshes +can be refined only so far as to represent their own characteristic wavelengths accurately. +Output +Nodal output variable POR (pressure magnitude at the nodes of the acoustic elements) is available for +an acoustic medium (in Abaqus/CAE this output variable is called PAC). When the scattered wave +formulation (default) is used with incident wave loading, output variable POR represents only the +scattered pressure response of the model and does not include the incident wave loading itself. When +the total wave formulation is used, output variable POR represents the total dynamic acoustic pressure, +which includes contributions from both incident and scattered waves as well as the dynamic effects of +fluid cavitation. For either formulation output variable POR does not include the acoustic static pressure. +In Abaqus/Explicit an additional nodal output variable PABS (the absolute pressure, equal to the +sum of POR and the acoustic static pressure) is available. When the dynamic effects of fluid cavitation +are of interest, you can specify the acoustic static pressure in an acoustic analysis that uses the total wave +formulation. If the acoustic static pressure is not specified in an acoustic region, it is assumed to be large; +thus precluding cavitation in that region. +For general steps, including implicit and explicit dynamic steps, no energy quantities are computed +for acoustic elements. Consequently, these elements will not contribute to the total energy balance. +Steady-state dynamic output +For steady-state dynamic analysis POR is complex and can be displayed in several forms in the +Visualization module of Abaqus/CAE. The phase angle (PPOR) is available as output to the data +(.dat) and results (.fil) files. +in direct-solution steady-state dynamic or subspace-based steady-state dynamic analysis. The “sound +pressure level” is defined as: +ACOUSTIC ANALYSIS +where +and the +is defined as a physical constant in the model , +at any point using the formula: +is computed from the complex-valued acoustic pressure +The acoustic particle velocity at any material point is +The acoustic intensity vector, a measure of the rate of flow of energy at a material point, is +In an acoustic medium the stress tensor is simply the acoustic pressure times the identity tensor, so this +expression simplifies to +The hats denote complex conjugation. The real part of the intensity is referred to as the “active intensity,” +and the imaginary part is the “reactive intensity.” The acoustic pressure gradient is also available for +acoustic finite elements in steady-state dynamic analysis. +In steady-state dynamic analysis, additional nodal output quantities are available for acoustic infinite +elements. +PINF denotes the complex pressure coefficients of the infinite element shape functions. These +coefficients can be used to visualize the exterior acoustic field (i.e., within the volume of the acoustic +infinite elements) using scripting in the Visualization module of Abaqus/CAE; see “Using infinite +elements to compute and view the results of an acoustic far-field analysis,” Section 9.10.11 of the +INFN is the normal vector used by the acoustic infinite element +Abaqus Scripting User’s Manual. +to define the element volume. INFR denotes the radius used for the element at that node, and INFC +denotes the element cosine; that is, the minimum dot product between the nodal normal vector and the +acoustic infinite element facet normal vectors attached to that node. See “Acoustic infinite elements,” +Section 3.3.2 of the Abaqus Theory Manual, for more complete descriptions of these quantities. INFN, +INFR, INFC are useful in debugging a model using acoustic infinite elements; consequently, it is +sometimes valuable to perform a steady-state dynamics, direct analysis on a model to visualize this +information. +For steady-state dynamic steps, energy quantities are available for acoustic elements. These +elements contribute to the total energy balance in steady-state dynamics. +Defining the reference pressure +You must define the reference pressure, +default value for the reference pressure. +, used to compute the sound pressure level; there is no +Input File Usage: +Abaqus/CAE Usage: +*PHYSICAL CONSTANTS, SPL REFERENCE PRESSURE= +You cannot define a reference pressure in Abaqus/CAE. +Input file template +The following is an example of the step definition for a direct-solution steady-state dynamic acoustic +analysis that looks for the response of a model at six frequencies ranging linearly from +to +cycles/time. The pressure at node set INPUT (nodes at the boundary) is prescribed to have an in- +). An +phase component of 3.0 and an out-of-phase component of −4.0 (i.e., a complex value of +in-phase inward volume acceleration of 40.0 is specified at node 10. +On the surface LINER1 an impedance is defined based on the impedance property named +CARPET1. On the second face of all of the elements in element set PAD, another surface impedance +based on CARPET1 is defined. On the fourth face of all of the elements in element set END, the default +plane wave boundary condition is specified. +Printed output of pressure magnitude and phase is requested for node set OUTPUT. Acoustic pressure +and displacement are written to the output database. All output is written once for each of the six +excitation frequencies. +*HEADING +… +*SURFACE, NAME=LINER1 +10, S3 +*IMPEDANCE PROPERTY, NAME=CARPET1 +Data describing impedance properties as a function of frequency +** +*STEP +*STEADY STATE DYNAMICS, DIRECT +10, 100, 6 +*SIMPEDANCE, PROPERTY=CARPET1 +LINER1, +** +*IMPEDANCE, PROPERTY=CARPET1 +PAD, I2 +*IMPEDANCE +END, I4 +** Apply complex pressure at node set INPUT +*BOUNDARY, REAL +INPUT, 8, 8, 3. +*BOUNDARY, IMAGINARY +INPUT, 8, 8, -4. +** Apply an in-phase inward volume acceleration at node 10 +*CLOAD +10, 8, 40. +** Output requests +*NODE PRINT, NSET=OUTPUT, TOTALS=YES +POR, PPOR +*OUTPUT, FIELD +*NODE OUTPUT +U, PU, POR +*END STEP +The following is a template of the step definition for an Abaqus/Explicit acoustic analysis. On the +surface SURF an impedance is defined based on the impedance property named IPROP. In addition, +impedance is defined on elements or element sets. +*HEADING +… +*ELEMENT, TYPE=AC2D4R +… +** +*SURFACE, NAME=SURF +Data line to define surface +*IMPEDANCE PROPERTY, NAME=IPROP +Data describing impedance properties +** +*STEP +*DYNAMIC, EXPLICIT or *DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT +Data line to define incrementation +*SIMPEDANCE, PROPERTY=IPROP +SURF, +** +*IMPEDANCE +Data lines to define impedance on elements or element sets +*CLOAD +Data line to define acoustic loads +*FIELD +Data line to define field variable values +*END STEP +The following template is representative of a coupled acoustic-structural shock problem using +the preferred interface for applying incident wave loading : +*HEADING +… +*ELEMENT, TYPE=…, ELSET=ACOUSTIC +Data lines to define acoustic elements +*ELEMENT, TYPE=…, ELSET=SOLID +Data lines to define solid elements +*ELEMENT, TYPE=…, ELSET=BEAM +Data lines to define beam elements +*BEAM SECTION,ELSET=BEAM,MATERIAL=... +Data lines to define the beam stiffness section properties +*BEAM FLUID INERTIA +Data line to define the beam virtual mass property +*SURFACE, NAME=IW_LOAD_ACOUSTIC +Data lines to define the acoustic surface loaded by the incident wave +*SURFACE, NAME=IW_LOAD_SOLID +Data lines to define the solid surface loaded by the incident wave +*SURFACE, NAME=IW_LOAD_BEAM +Data lines to define the beam surface loaded by the incident wave +*SURFACE, NAME=TIE_ACOUSTIC +Data lines to define the acoustic surface interface with the solid mesh +*SURFACE, NAME=TIE_SOLID +Data lines to define the solid surface interface with the acoustic mesh +*INCIDENT WAVE INTERACTION PROPERTY, NAME=IWPROP, TYPE=SPHERE +Data lines to define a spherical incident wave field +*UNDEX CHARGE PROPERTY +Data lines to define the underwater explosion parameters +** Tie the acoustic mesh to the solid mesh +*TIE, NAME=COUPLING +TIE_ACOUSTIC, TIE_SOLID +*STEP +*DYNAMIC, EXPLICIT or *DYNAMIC +** Load the acoustic surface +*INCIDENT WAVE INTERACTION, PROPERTY=IWPROP +IW_LOAD_ACOUSTIC, source node, standoff node, reference magnitude +** Load the solid surface +*INCIDENT WAVE INTERACTION, PROPERTY=IWPROP +IW_LOAD_SOLID, source node, standoff node, reference magnitude +** Load the beam surface +*INCIDENT WAVE INTERACTION, PROPERTY=IWPROP +IW_LOAD_BEAM, source node, standoff node, reference magnitude +*END STEP +The following template is representative of a coupled acoustic-structural shock problem using the +alternative interface for applying incident wave loading: +*HEADING +… +*ELEMENT, TYPE=…, ELSET=ACOUSTIC +Data lines to define acoustic elements +*ELEMENT, TYPE=…, ELSET=SOLID +Data lines to define solid elements +*ELEMENT, TYPE=…, ELSET=BEAM +Data lines to define beam elements +*BEAM SECTION,ELSET=BEAM,MATERIAL=... +Data lines to define the beam stiffness section properties +*BEAM FLUID INERTIA +Data line to define the beam virtual mass property +*SURFACE, NAME=IW_LOAD_ACOUSTIC +Data lines to define the acoustic surface loaded by the incident wave +*SURFACE, NAME=IW_LOAD_SOLID +Data lines to define the solid surface loaded by the incident wave +*SURFACE, NAME=IW_LOAD_BEAM +Data lines to define the beam surface loaded by the incident wave +*SURFACE, NAME=TIE_ACOUSTIC +Data lines to define the acoustic surface interface with the solid mesh +*SURFACE, NAME=TIE_SOLID +Data lines to define the solid surface interface with the acoustic mesh +*INCIDENT WAVE PROPERTY, NAME=IWPROP, TYPE=SPHERE +Data lines to define a spherical incident wave field +*INCIDENT WAVE FLUID PROPERTY +Data lines to define the fluid properties for the incident wave field +*AMPLITUDE, DEFINITION=BUBBLE, NAME=PRESSUREVTIME +Data lines to define the underwater explosion parameters +** Tie the acoustic mesh to the solid mesh +*TIE, NAME=COUPLING +TIE_ACOUSTIC, TIE_SOLID +*STEP +*DYNAMIC or *DYNAMIC, EXPLICIT +** Load the acoustic surface +*INCIDENT WAVE, PRESSURE AMPLITUDE=PRESSUREVTIME, +PROPERTY=IWPROP +IW_LOAD_ACOUSTIC, {amplitude} +** Load the solid surface and the beam surface +*INCIDENT WAVE, PRESSURE AMPLITUDE=PRESSUREVTIME, +PROPERTY=IWPROP +IW_LOAD_SOLID, {amplitude} +IW_LOAD_BEAM, {amplitude} +*END STEP +The following template is representative of a coupled acoustic-structural sound transmission +problem using the preferred interface for applying incident wave loading : +*HEADING +… +*ELEMENT, TYPE=…, ELSET=ACOUSTIC +Data lines to define acoustic elements +*ELEMENT, TYPE=…, ELSET=SOLID +Data lines to define solid elements +*SURFACE, NAME=IW_LOAD_ACOUSTIC +Data lines to define the acoustic surface loaded by the incident wave +*SURFACE, NAME=IW_LOAD_SOLID +Data lines to define the solid surface loaded by the incident wave +*SURFACE, NAME=TIE_ACOUSTIC +Data lines to define the acoustic surface interface with the solid mesh +*SURFACE, NAME=TIE_SOLID +Data lines to define the solid surface interface with the acoustic mesh +*INCIDENT WAVE INTERACTION PROPERTY, NAME=FIRST, TYPE=SPHERE +Data lines to define a spherical incident wave field +*INCIDENT WAVE INTERACTION PROPERTY, NAME=SECOND, TYPE=PLANE +Data lines to define a planar incident wave field +** Tie the acoustic mesh to the solid mesh +*TIE, NAME=COUPLING +TIE_ACOUSTIC, TIE_SOLID +*STEP +*STEADY STATE DYNAMICS, DIRECT or SUBSPACE PROJECTION +** Define the load on the acoustic and solid surfaces due to +** the first loading case: +*LOAD CASE, NAME=FIRST_SOURCE +** Load the acoustic surface: define the real part at the +** standoff point +*INCIDENT WAVE INTERACTION, PROPERTY=FIRST, REAL +IW_LOAD_ACOUSTIC, first source node, first standoff node, reference magnitude +** Load the acoustic surface: define the imaginary part at the +** standoff point +*INCIDENT WAVE INTERACTION, PROPERTY=FIRST, IMAGINARY +IW_LOAD_ACOUSTIC, first source node, first standoff node, reference magnitude +** Load the solid surface: define the real part at the +** standoff point +*INCIDENT WAVE INTERACTION, PROPERTY=FIRST, REAL +IW_LOAD_SOLID, first source node, first standoff node, reference magnitude +** Load the solid surface: define the imaginary part at the +** standoff point +*INCIDENT WAVE INTERACTION, PROPERTY=FIRST, IMAGINARY +IW_LOAD_SOLID, first source node, first standoff node, reference magnitude +*END LOAD CASE +** Define the load on the acoustic and solid surfaces due to +** the next loading case: +*LOAD CASE, NAME=SECOND_SOURCE +** Load the acoustic surface: define the real part at the +** standoff point +*INCIDENT WAVE INTERACTION, PROPERTY=SECOND, REAL +IW_LOAD_ACOUSTIC, second source node, second standoff node, reference magnitude +** Load the acoustic surface: define the imaginary part at the +** standoff point +*INCIDENT WAVE INTERACTION, PROPERTY=SECOND, IMAGINARY +IW_LOAD_ACOUSTIC, second source node, second standoff node, reference magnitude +** Load the solid surface: define the real part at the +** standoff point +*INCIDENT WAVE INTERACTION, PROPERTY=SECOND, REAL +IW_LOAD_SOLID, second source node, second standoff node, reference magnitude +** Load the solid surface: define the imaginary part at the +** standoff point +*INCIDENT WAVE INTERACTION, PROPERTY=SECOND, IMAGINARY +IW_LOAD_SOLID, second source node, second standoff node, reference magnitude +*END LOAD CASE +*END STEP +6.11 +Abaqus/Aqua analysis +• “Abaqus/Aqua analysis,” Section 6.11.1 +6.11.1 +Abaqus/AQUA ANALYSIS +Product: Abaqus/Aqua +References +• “UWAVE,” Section 1.1.54 of the Abaqus User Subroutines Reference Manual +• “Defining an analysis,” Section 6.1.2 +• *AQUA +• *CLOAD +• *C ADDED MASS +• *DLOAD +• *D ADDED MASS +• *WAVE +• *WIND +Overview +An Abaqus/Aqua analysis: +• is used to apply steady current, wave, and wind loading to submerged or partially submerged +structures in problems such as the modeling of offshore piping installations or the analysis of +marine risers; +• can be performed using the static (“Static stress analysis,” Section 6.2.2), direct-integration dynamic +(“Implicit dynamic analysis using direct integration,” Section 6.3.2), explicit dynamics (“Explicit +dynamic analysis,” Section 6.3.3), or eigenfrequency extraction (“Natural frequency extraction,” +Section 6.3.5) procedures; +• will calculate drag, buoyancy, and inertia loading only for beam, pipe, elbow, truss, and certain rigid +elements; +• can include elements that model spud cans for jack-up foundation analysis in Abaqus/Standard; and +• can be linear or nonlinear. +Procedures available for Aqua analysis +Aqua loading can be applied in static steps (“Static stress analysis,” Section 6.2.2), direct-integration +dynamic steps (“Implicit dynamic analysis using direct integration,” Section 6.3.2), and explicit dynamic +steps (“Explicit dynamic analysis,” Section 6.3.3). During these steps fluid particle velocity is assumed +to consist of two superposed effects: steady currents, which can vary with elevation and location, and +gravity waves. Fluid particle accelerations are associated with gravity waves only. +The fluid particle velocities and accelerations are used to calculate drag and inertia loading on the +immersed body. Abaqus/Aqua also computes the fluid surface elevation and allows for partial immersion; +drag and buoyancy loadings are omitted for those parts of the structure that are above the fluid surface +or below the seabed level. +An eigenfrequency extraction step (“Natural frequency extraction,” Section 6.3.5) can be +used to extract the natural frequencies of a structure prestressed by the Aqua loading in a static or +direct-integration dynamic step (if that step included the effects of nonlinear geometry). The added-mass +effect due to fluid inertia loads can be included in an eigenfrequency extraction step. +Defining an Abaqus/Aqua problem +Aqua loads are applied in the following manner: +1. The fluid properties and steady current velocity are defined for the model. +2. Gravity waves and wind velocity are defined for the model. +3. Drag, buoyancy, and fluid inertia loads are applied to elements and nodes of the structure using +distributed or concentrated load definitions within the static or direct-integration dynamic step +definition. The magnitudes of the loads applied are determined by the fluid properties, steady +current, wave, and wind definitions. +4. In an eigenfrequency extraction step concentrated and distributed added mass definitions are used +(instead of concentrated and distributed loads) to include the effects of fluid inertia. +The load-stiffness terms from Abaqus/Aqua loads, which are important in geometrically nonlinear +analysis, are fundamentally unsymmetric. Therefore, the unsymmetric matrix solution and storage +scheme should be used for the step when nonlinear geometric effects are included (“Defining an +analysis,” Section 6.1.2). It is essential to use the unsymmetric solver when the structure being analyzed +is flexible (see, for example, “Slender pipe subject to drag: the “reed in the wind”,” Section 1.13.3 of +the Abaqus Benchmarks Manual). +On the other hand, if a relatively stiff structure is subject to Aqua loads or if a dynamic step uses +small time increments, the unsymmetric load-stiffness terms may not be dominant and you may be +able to obtain a convergent solution with the symmetric solver (see, for example, “Riser dynamics,” +Section 12.1.2 of the Abaqus Example Problems Manual). +Coordinate system +The z-coordinate axis must point vertically for three-dimensional cases, and the y-coordinate axis must +point vertically for two-dimensional cases. For the three-dimensional case the still fluid surface (when +there is no wave motion) lies in a plane that is parallel to the x–y plane. For the two-dimensional case it +lies parallel to the x-axis. The position of the still fluid surface is specified as part of the fluid property +data. +Defining the fluid properties +Aqua loadings require the definition of fluid density, seabed and free surface elevation, and the +gravitational constant. +Input File Usage: +*AQUA +seabed elevation, free surface elevation, gravitational constant, fluid density +The *AQUA option must be included in the model data portion of the input file. +Defining a steady current +Steady currents are defined by giving steady fluid velocity as a function of elevation and location. +Elevation is defined in the positive z-direction for three-dimensional models and in the positive +y-direction for two-dimensional models. For two-dimensional cases the z-component of the steady +current velocity is ignored. See “Input syntax rules,” Section 1.2.1, for an explanation of how to define +one property (in this case steady current velocity) as a function of multiple independent variables. +If the fluid velocity is not a function of elevation or location (for example, when modeling a problem +in a coordinate system that moves uniformly through the still fluid, such as a tow-out analysis), only one +fluid velocity need be specified. +The steady current velocities can be scaled by referring to an amplitude curve (“Amplitude curves,” +Section 33.1.2) from the concentrated or distributed load definitions used to apply drag loads, as described +later. +Input File Usage: +*AQUA +fluid properties on first data line (described above) +X-velocityfluid, Y-velocityfluid , Z-velocityfluid , elevation, X-coord, Y-coord +... +Defining gravity waves +Gravity waves are defined by specifying a wave theory. The wave theory determines fluid acceleration, +velocity, and pressure field fluctuations. The fluid acceleration and velocity field fluctuations contribute +to the drag loads. The fluid pressure field fluctuations contribute to the buoyancy loads. +Choosing the type of wave theory to be used +Using Abaqus/Aqua in an Abaqus/Standard analysis, you can choose Airy linear wave theory, Stokes +fifth-order wave theory, wave data read from a gridded mesh, or fluid kinematics defined in user +subroutine UWAVE. For Airy and Stokes waves the fluid surface elevation and the fluid particle velocities +and accelerations will be calculated as functions of time and location based on the wave definition. +If wave data are provided in the form of a gridded mesh, you must specify these quantities. If user +subroutine UWAVE is used, the fluid kinematics must be defined in that routine. +Similarly, using Abaqus/Aqua in an Abaqus/Explicit analysis, you can choose Airy linear wave +theory, Stokes fifth-order wave theory, or fluid kinematics defined in user subroutine VWAVE. +All of the built-in wave theories assume a series of waves in the horizontal plane (the plane of +the fluid surface) that are unaffected by any fluid-structural interaction. The Airy and Stokes theories +are based on irrotational flow of an inviscid, incompressible fluid, where the wave height H is small +compared to the still water depth d. The bottom of the fluid is assumed to be flat (the still water depth is +constant). +The Ursell parameter, +is the wavelength, should be much less than 1.0 for Airy wave theory to be applicable and should +where +be less than 10.0 for Stokes theory to be applicable. For ratios of H/ greater than 0.142, the crest of +the wave is predicted to break. The assumed boundary conditions on the free surface are then no longer +valid in either theory, which limits the maximum wave amplitude for either theory. +Airy wave theory +, is less +Linear Airy wave theory is generally used when the ratio of wave height to water depth, +than 0.03, provided that the water is deep (ratio of water depth to wavelength, +, is greater than 20). +Convective acceleration terms are neglected in the Airy theory as part of the linearization. The Airy +wave theory is described in detail in “Airy wave theory,” Section 6.2.2 of the Abaqus Theory Manual. +Since the Airy wave theory is linear, any number of wave trains traveling in different directions +across the water can be defined; the fluid particle velocities and accelerations sum by linear superposition. +The direction of each wave component is given by specifying the direction cosines of a vector, +, lying +in the plane defined by the still fluid surface. +By default, Airy waves are defined in terms of wavelength, +. Alternatively, you can define the +. For Airy wave theory the wavelength and period of each component +waves in terms of wave period, +are related by +where +is the period of this component, +is the gravitational acceleration, +is the wavelength, and +is the undisturbed (still) water depth. +Input File Usage: +Use the following option to define an Airy wave in terms of wavelength: +*WAVE, TYPE=AIRY +amplitude, wavelength, phase angle, x-direction cosine, y-direction cosine +Use the following option to define an Airy wave in terms of wave period: +*WAVE, TYPE=AIRY, WAVE PERIOD +amplitude, wave period, phase angle, x-direction cosine, y-direction cosine +In either case repeat the data line to define multiple wave trains. +Stokes fifth-order wave theory +The Stokes fifth-order wave theory is a deep-water wave theory that is valid for relatively large +wavelengths. Convective terms are included in the fluid particle acceleration calculations for Stokes +fifth-order theory and can be significant for larger +ratios. The Stokes wave theory is described in +detail in “Stokes wave theory,” Section 6.2.3 of the Abaqus Theory Manual. +Because the Stokes fifth-order wave theory is nonlinear, only one wave train is allowed in an +analysis. The relationship between wavelength and period of the waves in Stokes fifth-order theory is +not as simple as that for the Airy theory, although the formula given above is a first-order approximation. +Stokes waves can be defined only in terms of the wave period, +. +Input File Usage: +*WAVE, TYPE=STOKES +wave height, wave period, phase angle, direction of travel cosines +Gridded wave data +You can choose to provide wave surface elevations, particle velocities and accelerations, and the +dynamic pressure at points in a user-defined grid through a binary data file. The binary file contains +information about the wave definition, the location of the grid points where wave information is +specified, and the wave kinematics at user-defined times. At spatial locations within the user-defined +grid, Abaqus/Aqua will interpolate the wave kinematics from the nearest grid points, using either linear +or quadratic interpolation. When a point on the structure is above the user-defined grid, Abaqus/Aqua +assumes that the point is above the free surface elevation. Hence, no fluid loads are applied. If a point +on the structure falls outside the user-defined spatial grid without being above the grid, Abaqus/Aqua +finds the wave kinematics at the nearest point within the grid and uses those values at the point on the +structure. +Input File Usage: +*WAVE, TYPE=GRIDDED, DATA FILE=file_name +Binary data file requirements for gridded wave data +The data file must contain the following unformatted (binary) records . The data for the FORTRAN WRITE statement are +given for each record: +First record: +NCOMP, DTG, NWGX, NWGY, NWGZ, IPDYN +where +NCOMP is the number of wave components to be read in the data file; +DTG +is the time increment at which wave data are given on the grid; +NWGX +NWGY +is the number of grid points in the grid’s x-direction; +is the number of grid points in the grid’s y-direction—if this number is one, Abaqus/Aqua +assumes that the wave data are constant with respect to the local y-direction; +NWGZ +is the number of grid points in the grid’s z-direction—if this number is zero or one, the +analysis is two-dimensional and the y-direction is vertical; and +IPDYN is an integer flag indicating whether dynamic pressure information is stored (IPDYN=1) or +not stored (IPDYN=0) in the gridded wave file. +Second record: +(AMP(K1), WXL(K1), PHI(K1), K1=1,NCOMP) +where +NCOMP is read on the first record, above; +AMP +WXL +PHI +contains the wave component amplitude, +contains the wavelength of this component, +contains the phase angle of this component, +; +; and +(in degrees). +The second record of this file contains the wave component data used to generate the gridded wave data; +it is not used by Abaqus/Aqua. This record is provided only for information in user subroutine UEL +by using the GETWAVE interface . The meaning of the arrays AMP and +WXL is left to you; however, PHI is converted to radians. +Third record: +(WGX(K1),K1=1,NWGX), (WGY(K1),K1=1,NWGY), (WGZ(K1),K1=1,NWGZ) +where +NWGi +WGX +WGY +WGZ +are read on the first record, above; +contains the local x-coordinates of the grid points; +contains the local y-coordinates of the grid points; and +contains the local z-coordinates of the grid points (not included in the gridded wave file for +two-dimensional analyses). +Remaining records if IPDYN=0: +For three dimensions: +(((WGVX(K1,K2,K3), WGVY(K1,K2,K3), WGVZ(K1,K2,K3), +WGAX(K1,K2,K3), WGAY(K1,K2,K3), WGAZ(K1,K2,K3), K3=1,NWGZ), +WZCRST(K1,K2), NCRST(K1,K2), K1=1,NWGX), K2=1,NWGY) +For two dimensions: +((WGVX(K1,K2), WGVY(K1,K2), WGAX(K1,K2), WGAY(K1,K2), +K2=1,NWGY), WZCRST(K1), NCRST(K1), K1=1,NWGX) +Remaining records if IPDYN=1: +For three dimensions: +(((WGVX(K1,K2,K3), WGVY(K1,K2,K3), WGVZ(K1,K2,K3), +WGAX(K1,K2,K3), WGAY(K1,K2,K3), WGAZ(K1,K2,K3), +P(K1,K2,K3), DPDZ(K1,K2,K3), K3=1,NWGZ), +WZCRST(K1,K2), NCRST(K1,K2), K1=1,NWGX), K2=1,NWGY) +For two dimensions: +((WGVX(K1,K2), WGVY(K1,K2), WGAX(K1,K2), WGAY(K1,K2), +P(K1,K2), DPDZ(K1,K2), K2=1,NWGY), +WZCRST(K1), NCRST(K1), K1=1,NWGX) +where +WGVX +WGVY +WGVZ +WGAX +WGAY +WGAZ +WZCRST +NCRST +DPDZ +contains the local x-components of the wave particle velocity, +contains the local y-components of the wave particle velocity, +contains the local z-components of the wave particle velocity, +contains the local x-components of the wave particle acceleration, +contains the local y-components of the wave particle acceleration, +contains the local z-components of the wave particle acceleration, +contains the wave surface elevation, +contains the index for the vertical grid level just above the instantaneous water +surface, +contains the dynamic pressure, and +contains the gradient of the dynamic pressure in the vertical direction. +User-defined wave theory in Abaqus/Standard +A user-defined wave theory can be coded in user subroutine UWAVE in an Abaqus/Aqua analysis in +Abaqus/Standard. You can define the fluid particle velocity, acceleration, free surface elevation, and +fluid pressure field in the user subroutine. +For stochastic analysis, you can specify a random number seed, r, and define frequency/amplitude +pairs that define the wave spectrum. During the analysis Abaqus/Aqua stores an intermediate +configuration that can be used in the user subroutine to compute the stochastic description of the waves. +The intermediate configuration is initialized as the reference configuration and is replaced by the current +configuration only when requested by the user subroutine. In this way the stochastic description of the +wave field can be stored in an external database and recalculated only when necessary. +Input File Usage: +Use the following option to specify the wave kinematics in user subroutine +UWAVE: +*WAVE, TYPE=USER +Use the following option for stochastic analysis to make the intermediate +configuration available in user subroutine UWAVE: +*WAVE, TYPE=USER, STOCHASTIC=r +frequency, amplitude +... +User-defined wave theory in Abaqus/Explicit +A user-defined wave theory can be coded in user subroutine VWAVE in an Abaqus/Aqua analysis in +Abaqus/Explicit. You can define the fluid particle velocity, acceleration, free surface elevation, and fluid +pressure field in the user subroutine. +The quantities required to define the wave kinematics can be specified as properties and passed into +the user subroutine. For example, in the case of stochastic wave kinematics, any required seed variable +and/or frequency-amplitude data pairs can be specified as properties. +You can also declare and use state variables for user-defined wave calculations, which will be +provided at the nodes and initialized to zero at the beginning of the step. You have to update the +state variables within the user subroutine. For example, the state variables can be used to store any +intermediate configuration of the structure that is used to describe a stochastic wave field. +Input File Usage: +Use the following option to specify the wave kinematics in user subroutine +VWAVE: +*WAVE, TYPE=USER +Use the following option to specify properties available as a real-array argument +PROPS of size NPROPS in user subroutine VWAVE: +*WAVE, TYPE=USER, PROPERTIES=nprops +prop_1, prop_2, ..., prop_8 +..., prop_nprops +Use the following option to specify state variables available as a real-array +argument STATEVAR of size NSTATEVAR in user subroutine VWAVE: +*WAVE, TYPE=USER, DEPVAR=nstatevar +Wave position as a function of time +can be chosen by specifying the phase +For Airy and Stokes waves the position of the wave at time +angle +of the wave (or wave components for Airy waves). By default, the waves are chosen such that +they have a trough (vertical displacement of the fluid surface is a minimum) at the origin of the horizontal +axes at time +for the waves. A positive +phase angle shifts the waves backward in their travel direction . +. You can change this trough by introducing a phase angle +The time t used in the wave theory is the total time in the analysis. Therefore, if the direct-integration +dynamic steps in which Airy or Stokes waves are applied are preceded by any steps other than direct- +integration dynamic steps (such as static steps), it is usually convenient to make the time period in these +steps very small compared to the period of the wave. +Because total time is used, the phase of the wave will be continuous from the end of one dynamic +step to the beginning of the next dynamic step. +Defining a minimum wave trough elevation +For computational efficiency Abaqus/Aqua uses a minimum wave trough elevation below which the +structure is assumed to be immersed. Below this elevation no calculation of the fluid surface need be done +Vertical axis +(Z-direction in 3-D cases, +Y-direction in 2-D cases) +Direction of wave travel +H, wave height +Wave of zero phase angle has a trough at the +origin of the horizontal axis at time t=0. +λ, wavelength +Figure 6.11.1–1 Wave of zero phase angle. +horizontal position +to determine if the point of interest is above the instantaneous free surface. Similarly, a maximum wave +elevation is used: any point above the maximum wave elevation is assumed to have no fluid loading. +For Airy and Stokes waves the minimum and maximum wave elevations are calculated from the +wave theory. +For gridded waves Abaqus/Aqua allows the definition of a minimum wave trough elevation: +in two-dimensional analysis. The structure is always assumed to +in three-dimensional analysis or +be immersed below this elevation. The maximum wave elevation is calculated as the still water elevation +plus the difference between this elevation and the minimum wave trough elevation. If the minimum wave +trough elevation is not specified for gridded waves, Abaqus/Aqua will compare the elevation of every +point on the structure with the instantaneous fluid surface as defined by the gridded data. When defining +this elevation, make sure that no wave trough ever drops below the minimum wave trough elevation +specified. +Input File Usage: +*WAVE, TYPE=GRIDDED, DATA FILE=file_name, MINIMUM=elevation +Wave kinematics, dynamic pressure, and extrapolation for Airy waves +A spatial (Eulerian) description of the wave field is used for all wave types; therefore, a structural point’s +coordinates are used to evaluate the wave kinematics. In geometrically nonlinear analysis the structural +point’s coordinates are its current coordinates. In geometrically linear analysis the wave kinematics are +evaluated using the structural point’s reference coordinates. +In both geometrically linear and nonlinear analysis for both static and direct-integration dynamic +procedures, submergence is calculated to the instantaneous water level at the current value of total time +for the analysis. Fluid loading is applied only to those points on the structure below the instantaneous +water level. +When buoyancy loading is applied in conjunction with a gravity wave, the dynamic pressure due to +the disturbance of the still surface is added to the hydrostatic pressure (measured to the still water level) +to obtain the total buoyancy loading, except when the buoyancy loading described by a distributed or +concentrated load definition overrides the fluid properties given for the Abaqus/Aqua analysis. Dynamic +pressure is included for both static and dynamic procedures for Airy, Stokes, and gridded wave types; +however, with gridded wave data you can choose to suppress this effect. See “Airy wave theory,” +Section 6.2.2 of the Abaqus Theory Manual, and “Stokes wave theory,” Section 6.2.3 of the Abaqus +Theory Manual, for a definition of dynamic pressure. +Although the linearized Airy wave theory assumes that the fluid displacements are small with +respect to the wavelength and the fluid depth, these displacements may not be small with respect to +the dimensions of the structure immersed in the fluid. As a result of the linearizing approximations +special treatment is necessary to calculate the wave kinematics for points below the instantaneous +water level but above the still water line. Abaqus/Aqua uses extrapolation with Airy wave theory: the +wave velocity, acceleration, and dynamic pressure for points above the still water level but below the +instantaneous free surface are taken to be the values evaluated from the wave theory at the still water +level. See “Airy wave theory,” Section 6.2.2 of the Abaqus Theory Manual, for more details. +Reading the data that define gravity waves from an alternate file +The data for the gravity wave can be contained in an alternate file. See “Input syntax rules,” Section 1.2.1, +for the syntax of the file name. +Input File Usage: +*WAVE, INPUT=file_name +Defining a wind velocity profile +You can define a wind velocity profile. Wind loading is applied only to elements above the still water +surface elevation (defined in the fluid properties). If an element is above the still water depth but is +submerged due to a wave, the wind loading will still be applied. +The wind profile is assumed to vary with height (the positive z-direction in three-dimensional +models, the positive y-direction in two-dimensional models) according to the power law wind profile +and has no variation in the horizontal plane. The power law wind velocity profile is given by +where +is the local wind velocity ( is a unit vector along the local x-axis of +the wind field, and is a unit vector along the local y-axis of the wind field); +is the time-varying wind velocity at the reference height, +is a user-defined constant (default value 1/7); +is the distance above the still water surface (i.e., +, as described below; +is the still water surface); and +is the reference distance above the still water surface where the time variation of the wind +velocity is given. +The wind local system is defined by giving the direction cosines of the unit vector . +Input File Usage: +*WIND +air density, +, +, +, x-direction cosine for , y-direction cosine for , +Prescribing the time variation of wind velocity at the reference height +The variation in time of the wind profile is defined by +reference height +: +, the wind velocity vector time history at a +The wind velocity component time histories +and +are given by +and +are user-defined as described above (with default values of 1.0) and +where +are +time-dependent functions defined by referring to amplitude curves from the concentrated or distributed +load definitions used to apply the wind loading to the model. If no amplitude curve is referenced, the +wind velocity components are the constant values +and +and +. +Geometrically linear versus geometrically nonlinear analysis +In geometrically linear analysis wind velocities are calculated based on the original coordinates of the +structure. In geometrically nonlinear analysis the current coordinates of a point on the structure are used +to calculate the wind velocity at that point. +Initial conditions +Initial conditions can be applied to the structure in an Abaqus/Aqua analysis in the same way as in +static and dynamic analyses without Aqua loads. See “Initial conditions in Abaqus/Standard and +Abaqus/Explicit,” Section 33.2.1. +Boundary conditions +Boundary conditions can be applied to the structure in an Abaqus/Aqua analysis in the same way as in +static and dynamic analyses without Aqua loads. See “Boundary conditions in Abaqus/Standard and +Abaqus/Explicit,” Section 33.3.1. +Defining contact at the seabed +Aqua loads are applied only above the seabed. To model the bottom of the sea using a contact plane, the +elevation of the contact plane must be slightly higher than the seabed level to avoid ambiguity between +the contact condition and applied loading. If the contact plane is at the same level as the seabed, there is a +risk that round-off problems will cause Aqua loads not to be applied to nodes in contact with the seabed. +Loads +Steady current, wave, and wind loads are applied to nodes or elements of the structure using concentrated +and/or distributed load definitions. Wind loads are applied only if the point is currently above the still +fluid surface; fluid loads are applied only if the point is currently below the instantaneous fluid surface +and above the seabed. Distributed loads are applied to partly immersed elements. +Concentrated and distributed load definitions cannot be used in eigenfrequency extraction steps, so +the loads described below can be applied only in static and direct-integration dynamic steps. +Controlling the time variation and magnitude of Aqua loading +You have three ways to control the magnitude of an Aqua load as a function of time: +1. You can reference a user-defined amplitude curve (“Amplitude curves,” Section 33.1.2) from the +concentrated or distributed load definition to scale the entire load. +2. You can specify a magnitude factor, M, for the concentrated or distributed load definition, which is +used to scale all the load. This magnitude factor allows normalized amplitude curves to be defined +and used for multiple loads. The default magnitude factor is always +. +3. You can reference individual user-defined amplitude curves to scale different components of the +loading separately. For example, steady current velocity and wave velocity can be scaled separately +by referencing different amplitude curves. +All of these scaling factors are cumulative. +Buoyancy loads +The calculated buoyancy of a structure depends on the orientation of the exposed surface area with respect +to the vertical direction. This surface area is calculated automatically by Abaqus/Aqua for distributed +buoyancy loading; however, you must specify the exposed area and direction cosines of the outward +normal at a node for concentrated buoyancy loading. +Abaqus/Aqua uses a closed-end loading condition while computing the distributed buoyancy forces +on all line elements. To obtain an open-end loading condition, concentrated buoyancy loading can be +used to counteract the buoyancy load applied to the ends of the elements. +The buoyancy loads require the definition of fluid density, seabed and free surface elevation, and +the gravitational constant. The default external fluid properties are defined for the model as described in +“Defining the fluid properties.” You can override some of these properties by specifying them directly +in the distributed or concentrated load definition. This provides for modeling situations where different +parts of the structure are subjected to different buoyancy loads, such as a pipe inside another pipe +where the static fluid surrounding the inner pipe is different from the fluid surrounding the outer pipe. +Gravity waves (“Wave kinematics, dynamic pressure, and extrapolation for Airy waves”) do not affect +the buoyancy loading when any external fluid property is overridden. +Specifying distributed buoyancy loads +To apply distributed buoyancy loads to elements immersed in a fluid, the effective outer diameter of +beam, truss, and one-dimensional rigid elements must be specified. Provide the external fluid density, free +surface elevation, and additional pressure to override the default fluid properties to model the situations +described above. For situations where it is necessary to model the fluid inside an element, the effective +inner diameter of the element must also be given, along with the density and free surface elevation of +the fluid inside the element. +Distributed buoyancy loading can be applied to rigid surface elements. However, the effects of +waves are ignored for these elements; the buoyancy loading is calculated to the still water level only. For +proper application of a positive buoyancy force, the positive normal of R3D3 and R3D4 elements must +point into the fluid. +Input File Usage: +*DLOAD +element number or set, PB, M, effective outer diameter, internal fluid +density, effective inner diameter, internal free surface elevation, external +fluid density, external free surface elevation, additional pressure +Specifying concentrated buoyancy loads +For concentrated buoyancy loads applied to nodes immersed in a fluid, the load is calculated based on +the sum of the hydrostatic pressure (measured to the still water level) and the dynamic pressure due to +wave action. The total pressure is multiplied by the exposed area associated with the node. The loading +is automatically considered to be a follower force in geometrically nonlinear analysis (for elements that +have rotational degrees of freedom); therefore, it is not necessary to specify that the load is a follower +force. Provide the external fluid density, free surface elevation, and additional pressure to override the +default fluid properties to model the situations described above. +Input File Usage: +*CLOAD +node number or set, TSB, M, exposed area, local coordinate system data, +external fluid density, external free surface elevation, additional pressure +Drag loads +Both waves and wind can cause drag loading on a structure. Fluid drag refers to drag caused by the +structural member being immersed in the fluid defined by the fluid properties and the gravity waves and, +thus, subject to steady current and wave loading. Fluid drag loading is provided by Morison’s equation. +Fluid drag loads must be specified in terms of a normal (transverse) load and a tangential load. +Wind drag is generated on the portions of a structure that are above the still fluid surface defined by +the fluid properties because these portions are exposed to the user-defined wind velocity profile. +Specifying distributed transverse fluid or wind drag loads +Distributed transverse drag is defined as follows : +where +is the force per unit length, transverse to the member; +is the current value of the amplitude curve referred to by the distributed load definition, +multiplied by the user-defined magnitude factor, M; +is the mass density of the fluid (given in the fluid properties) for fluid distributed drag or is +the mass density of the air (given in the wind velocity profile) for wind distributed drag; +is the drag coefficient; and +is the effective outer diameter of the member. +The relative fluid particle velocity in the normal direction, +, is given by +where +is the fluid particle velocity ; +is the velocity of this point on the structure (zero during static steps); +is the structural velocity factor; and +is the unit vector along the axis of the element. +The effective outer diameter of the element, D; the drag coefficient, +factor, +distributed drag or wind distributed drag). +; and the structural velocity +, must be defined in the distributed load definition together with the distributed load type (fluid +The velocities due to steady current and waves can be scaled individually for fluid distributed drag +by referring to different amplitude curves. Thus, the fluid particle velocity, +, at any time is +where +is the current value of the first amplitude curve listed in the load definition or 1.0 if the +amplitude reference is omitted, +is the steady current velocity defined in the fluid properties, +is the current value of the second amplitude curve listed in the load definition or 1.0 if the +amplitude reference is omitted, and +is the user-defined wave velocity. +The wind velocity is defined in components relative to the local axes +and defined for the wind +velocity profile. Each velocity component can be scaled independently by referring to different amplitude +curves. The total wind velocity at any time, +, is +and +where +components in the local x- and y-directions, respectively. The values of +, +the wind velocity profile; and z is the distance above the still fluid surface. +are the amplitude references provided in the load definition for the velocity +are defined by +, and +, +Input File Usage: +Use the following option to define fluid distributed drag: +*DLOAD +element number or set, FDD, M, D, +, +, +, +Use the following option to define wind distributed drag: +*DLOAD +element number or set, WDD, M, D, +, +, +, +Specifying distributed tangential fluid drag loads +Distributed tangential fluid loading is a load in the tangential direction of an element due to skin friction. +This type of loading is defined as follows : +where +is the force per unit length, tangent to the member; +is the amplitude curve referred to by the distributed load definition, multiplied by the user- +defined magnitude factor, M; +is the mass density of the fluid (given in the fluid properties); +is the tangential drag coefficient; +is the effective outer diameter of the member; and +is a constant (by default, +, for quadratic dependence of force on velocity). +The relative fluid particle velocity in the tangential direction, +, is given by +where +is the fluid particle velocity (as defined above for distributed transverse fluid drag loading), +is the velocity of this point on the structure (zero during static steps), +is the structural velocity factor, and +is the unit vector along the axis of the element. +The effective outer diameter of the element, D; the drag coefficient, +; the structural velocity factor, +; and the exponent, h, must be defined in the distributed load definition together with the distributed +load type (fluid drag tangential). +As with distributed transverse fluid loading, the velocities due to steady current and waves ( +and +) can be scaled individually by referring to different amplitude curves. +Input File Usage: +Use the following option to define fluid drag tangential: +*DLOAD +element number or set, FDT, M, D, +, +, h, +, +Specifying concentrated fluid or wind drag loads using a concentrated load definition +Concentrated fluid or wind drag loading applies a load normal to the end of an element. Such loading +is automatically considered to be a follower force in geometrically nonlinear analysis (for elements that +have rotational degrees of freedom). +The drag theory uses Morison’s equation . The drag force is nonzero when the net flow is in the opposite direction +of the outward normal to the exposed area and is zero when the net flow is in the direction of the normal: +drag +where +for +for +is the amplitude curve referenced by the concentrated load definition multiplied by the user- +defined magnitude factor, M; +is the mass density of the fluid (given in the fluid properties) for transition section fluid drag +or is the mass density of the air (given in the wind velocity profile) for transition section +wind drag; +is the drag coefficient; +is the exposed area; and +is the relative velocity between the structural member and the fluid particle along +is given by +, where +tangential fluid drag loading. +and +as defined above for distributed +The exposed area, +, must be +defined in the concentrated load definition together with the concentrated load type (transition section +fluid drag or transition section wind drag). +; and the structural velocity factor, +; the drag coefficient, +As with distributed transverse fluid loading, the velocities due to steady current and waves ( +) and the velocity components of the wind in the +and +individually by referring to different amplitude curves. +and directions ( +and +) can be scaled +Input File Usage: +Use the following option to define transition section fluid drag: +*CLOAD +node number or set, TFD, M, +, +, +, +, +Use the following option to define transition section wind drag: +*CLOAD +node number or set, TWD, M, +, +, +, +, +Specifying concentrated fluid or wind drag loads using a distributed load definition +You can apply concentrated fluid or wind drag loading on the ends of elements. These loads have the same +effect as specifying a concentrated load at a node using a concentrated load definition with concentrated +load type transition section fluid drag or transition section wind drag, except that the normal to the +exposed area cannot be specified when a distributed load definition is used; the normal to the end of +the element is defined by the tangent to the element. +The load can be applied to the first end (node) of the element or to the second end (node 2 or 3, as +appropriate) of the element. These loads are nonzero only when the net flow is in the opposite direction +of the outward normal to the exposed area. +The loading is exactly the same as that described for the concentrated fluid or wind drag loading +applied with a concentrated load definition. The “distributed” form of the loading is provided for +convenience. +Input File Usage: +Use the following option to define fluid drag on the first end of the element: +*DLOAD +element number or set, FD1, M, +, C, +, +, +Use the following option to define fluid drag on the second end of the element: +*DLOAD +element number or set, FD2, M, +, C, +, +, +Use the following option to define wind drag on the first end of the element: +*DLOAD +element number or set, WD1, M, +, C, +, +, +Use the following option to define wind drag on the second end of the element: +*DLOAD +element number or set, WD2, M, +, C, +, +, +Neglecting the wave’s contribution to drag and inertia loading during a step +If the wave’s contribution to the drag and inertia loading should not be applied during a step, the +concentrated or distributed load component definition must explicitly refer to an amplitude curve with +a value of zero. This is the only way to prevent waves from contributing to the fluid velocities and +accelerations used in the calculation of these concentrated or distributed load types. +Fluid inertia loads (added-mass effects) +Fluid inertia loading causes a structure to have increased inertial resistance to acceleration. This fluid +“added-mass” effect is included automatically in a direct-integration dynamic step when fluid inertia +loading is applied. Concentrated or distributed added mass must be defined to include the added-mass +effect in an eigenfrequency extraction step. +Specifying distributed fluid inertia loads in a direct-integration dynamic step +Distributed fluid inertia loading is defined as follows : +where +is the force per unit length, transverse to the member, caused by fluid inertia; +is the amplitude curve referred to by the distributed load definition multiplied by the user- +defined magnitude factor, M; +is the mass density of the fluid (given in the fluid properties); +is the effective outer diameter of the member; +is the transverse fluid inertia coefficient; +is the transverse added-mass coefficient; +is the transverse component of the fluid acceleration; and +is the transverse component of the beam acceleration (zero during static steps). +The effective outer diameter, D; transverse fluid inertia coefficient, +coefficient, +(distributed fluid inertia). +; and transverse added-mass +, must be defined in the distributed load definition together with the distributed load type +The fluid acceleration, +scaled by the amplitude curve, +, is calculated according to the user-defined gravity wave and is further +, referred to by the distributed load definition. +Input File Usage: +Use the following option to define distributed fluid inertia in a dynamic step: +*DLOAD +element number or set, FI, M, D, +, +, +Specifying distributed fluid inertia loads in an eigenfrequency extraction step +The added mass contribution due to distributed fluid inertia loading is +per unit length of the member in the directions transverse to the axis of the member only, where +is the mass density of the fluid (given in the fluid properties), +is the effective outer diameter of the member, and +is the transverse added-mass coefficient. +Input File Usage: +*D ADDED MASS +element number or set, FI, D, +Specifying concentrated fluid inertia loads in a direct-integration dynamic step using a concentrated +load definition +Concentrated fluid inertia loading is automatically considered to be a follower force (for elements that +have rotational degrees of freedom). +The inertia term is calculated as a force in the current direction of the outward normal to the exposed +surface area: +where +is the point force caused by fluid inertia; +is the amplitude curve referenced by the concentrated load definition multiplied by the user- +defined magnitude factor, M; +is the mass density of the fluid (given in the fluid properties); +is the tangential inertia coefficient; +is the fluid acceleration shape factor (of dimension +); +is the tangential added-mass coefficient; +is the structural acceleration shape factor (of dimension +); +is the fluid acceleration in the direction of the outward normal to the exposed surface; and +is the structural acceleration in the direction of the outward normal to the exposed surface +(zero during static steps). +The tangential inertia coefficient, +coefficient, +; and the structural acceleration shape factor, +definition together with the concentrated load type (transition section inertia). +; the fluid acceleration shape factor, +; the tangential added-mass +, are given in the concentrated load +The fluid acceleration, +scaled by the amplitude curve, +, is calculated according to the user-defined gravity wave and is further +, referred to by the concentrated load definition. +Input File Usage: +Use the following option to define transition section inertia in a dynamic step: +*CLOAD +node number or set, TSI, M, +, +, +, +, +Specifying concentrated fluid inertia loads in a direct-integration dynamic step using a distributed +load definition +You can apply concentrated fluid inertia loading at the ends of elements. These loads have the same +effect as specifying a concentrated fluid added-inertia loading using a concentrated load definition with +concentrated load type transition section inertia, except that the normal to the exposed area cannot be +specified when a distributed load definition is used; the normal to the end of the element is defined by +the tangent to the element. +The inertia loading can be applied to the first end (node) of the element or to the second end (node 2 +or 3, as appropriate) of the element. +The loading is exactly the same as that described for the concentrated fluid inertia loading applied +with a concentrated load definition. The “distributed” form of the loading is provided for convenience. +Input File Usage: +Use the following option to define fluid inertia on the first end of the element +in a dynamic step: +*DLOAD +element number or set, FI1, M, +, +, +, +, +Use the following option to define fluid inertia on the second end of the element +in a dynamic step: +*DLOAD +element number or set, FI2, M, +, +, +, +, +Specifying concentrated fluid inertia effects in an eigenfrequency extraction step using a concentrated +added mass definition +The added mass contribution due to concentrated fluid inertia loading in an eigenfrequency extraction +step is +in the direction normal to the transition section area, where +is the mass density of the fluid (given in the fluid properties), +is the tangential added-mass coefficient, and +is the structural acceleration shape factor (of dimension +). +Input File Usage: +*C ADDED MASS +node number or set, TSI, +direction cosines defining the outward normal of the exposed area +, +Specifying concentrated fluid inertia effects in an eigenfrequency extraction step using a distributed +added mass definition +You can apply concentrated fluid inertia effects at the ends of elements. These loads have the same +effect as specifying concentrated fluid inertia effects using a concentrated added mass definition with +concentrated load type transition section inertia, but in this case the normal to the exposed area cannot +be specified; the normal to the end of the element is defined by the tangent to the element. +The added mass can be applied to the first end (node) of the element or to the second end (node 2 +or 3, as appropriate) of the element. +The effect is exactly the same as that described for the concentrated fluid inertia effects applied with +a concentrated added mass definition. The “distributed” form of the loading is provided for convenience. +Input File Usage: +Use the following option to define fluid inertia on the first end of the element +in an eigenfrequency extraction step: +*D ADDED MASS +element number or set, FI1, +, +Use the following option to define fluid inertia on the second end of the element +in an eigenfrequency extraction step: +*D ADDED MASS +element number or set, FI2, +, +Applying non-Aqua loads to the structure +Concentrated and distributed load definitions can also be used to apply concentrated and distributed +forces that are not associated with wind, waves, or steady current to the structure. See “Concentrated +loads,” Section 33.4.2, and “Distributed loads,” Section 33.4.3. +Predefined fields +The following predefined fields can be specified for the structure (not the fluid) in an Abaqus/Aqua +analysis, as described in “Predefined fields,” Section 33.6.1: +• Temperatures of nodes in the structure can be specified. Any difference between the applied and +initial temperatures will cause thermal strain if a thermal expansion coefficient is given for the +material (“Thermal expansion,” Section 26.1.2). The specified temperature also affects temperature- +dependent material properties, if any. +• The values of user-defined field variables can be specified. These values affect only field-variable- +dependent material properties, if any. +Material options +Any of the mechanical constitutive models in Abaqus can be used for modeling the structure in +an Abaqus/Aqua analysis . +Elements +The fluid loads in an Abaqus/Aqua analysis cannot be applied to all element types. Only the beam, +pipe, elbow, truss, and rigid beam elements in Abaqus/Standard and linear beam and pipe elements in +Abaqus/Explicit can be used to subject a structure to general Abaqus/Aqua loading. The only load that +can be applied to two-dimensional rigid surfaces (R3D3 and R3D4 elements) is hydrostatic buoyancy; +and this loading can be applied only in Abaqus/Standard. Current, wave, and wind loading have no effect +on rigid surfaces. +Jack-up foundation analysis +Abaqus/Standard provides element types JOINT2D and JOINT3D, which can be used to model elastic- +plastic interaction between spud cans and the sea floor . +Output +In addition to the usual output variables available in Abaqus/Standard and in Abaqus/Explicit , element section output variable ESF1 can be used to request output +of the effective axial force in a beam subjected to pressure loading . The velocities and accelerations of the fluid cannot be output. +Input file template +*HEADING +… +*AQUA +Data lines defining the fluid properties and steady current velocity +*WAVE, TYPE=wave theory +Data lines defining gravity waves +** +*STEP (, NLGEOM) +Use the NLGEOM parameter to include nonlinear geometric effects +*DYNAMIC (or *STATIC or *DYNAMIC, EXPLICIT) +… +*CLOAD +Data lines defining concentrated buoyancy, fluid/wind drag, and fluid inertia loads +*DLOAD +Data lines defining distributed buoyancy, fluid/wind drag, and fluid inertia loads +*END STEP +** +*STEP +The NLGEOM parameter must have been included in the previous step to obtain +the natural frequencies of the prestressed structure +*FREQUENCY +… +*C ADDED MASS +Data lines to define concentrated added-mass effects +*D ADDED MASS +Data lines to define distributed added-mass effects +*END STEP +6.12 +Annealing +• “Annealing procedure,” Section 6.12.1 +6.12.1 +ANNEALING PROCEDURE +Products: Abaqus/Explicit Abaqus/CAE +References +• *ANNEAL +• “Configuring an annealing procedure” +Section 14.11.1 of the Abaqus/CAE User’s Manual, +manual +in “Configuring general +analysis procedures,” +in the online HTML version of this +Overview +The anneal procedure: +• is used to anneal a structure by setting all appropriate state variables and velocities to zero; and +• is intended only for metal plasticity and user-defined material models; it has no effect on other +material models. +The annealing process +The anneal procedure is intended to simulate the relaxation of stresses and plastic strains that occurs +as metals are heated to high temperatures. Physically, annealing is the process of heating a metal part +to a high temperature to allow the microstructure to recrystallize, removing dislocations caused by cold +working of the material. During the anneal procedure Abaqus/Explicit sets all appropriate state variables +to zero. These variables include stresses, backstresses, plastic strains, and velocities. In the case of metal +porous plasticity, the void volume fraction is also set to zero, such that the material becomes fully dense. +There is no time scale in an annealing step; therefore, time does not advance. The annealing process +occurs instantaneously. No data are required for the anneal procedure. +Input File Usage: +Abaqus/CAE Usage: +*ANNEAL +Step module: Create Step: General: Anneal +Temperatures +Thermal strains are set to zero, and the temperature at all nodes in the model will be set to a uniform +temperature or will be maintained at the current temperature during the anneal procedure. By default, +the temperature at all nodes is maintained at the current temperature. You can specify a different final +temperature, +. +Input File Usage: +Abaqus/CAE Usage: +*ANNEAL, TEMPERATURE= +Step module: Create Step: General: Anneal: Post-anneal +reference temperature: Value +Initial conditions +The initial state for the anneal step is the state of the model at the end of the last explicit dynamic analysis +step. +Boundary conditions +It is not appropriate to specify new boundary conditions or to modify boundary conditions in an anneal +procedure; all boundary conditions in effect prior to this procedure will remain fixed. +Loads +It is not meaningful to specify loads in an anneal procedure. +Predefined fields +It is not meaningful to specify predefined fields in an anneal procedure. +Material options +The annealing procedure is intended only for metal plasticity models (“Classical metal plasticity,” +Section 23.2.1) and user-defined materials modeled with user subroutines VFABRIC and VUMAT. +The metal plasticity models in Abaqus/Explicit include Mises, Johnson-Cook, Hill, and metal porous +plasticity. Abaqus/Explicit also allows annealing of elastic materials (“Linear elastic behavior,” +Section 22.2.1), including isotropic, orthotropic, and anisotropic elasticity. The annealing procedure +has no effect on other material models. +Elements +All of the elements that are available in Abaqus/Explicit can be used in an anneal procedure. The elements +are listed in Part VI, “Elements.” +Output +There is no output associated with an anneal step. +Input file template +*HEADING +… +** +*STEP +*DYNAMIC, EXPLICIT (,ADIABATIC) or +*DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT +Data line to specify the time period of the step +*BOUNDARY, AMPLITUDE=name +Data lines to describe zero-valued or nonzero boundary conditions +*CLOAD and/or *DLOAD +Data lines to specify loads +*TEMPERATURE and/or *FIELD +Data lines to specify values of predefined fields +*END STEP +** +*STEP +*ANNEAL (,TEMPERATURE= ) +*END STEP +** +*STEP +*DYNAMIC, EXPLICIT (,ADIABATIC) +Data line to specify the time period of the step +*BOUNDARY, AMPLITUDE=name +Data lines to describe zero-valued or nonzero boundary conditions +*CLOAD and/or *DLOAD and/or *DSLOAD +Data lines to specify loads +*TEMPERATURE and/or *FIELD +Data lines to specify values of predefined fields +*END STEP +7. +Analysis Solution and Control +Solving nonlinear problems +Analysis convergence controls +7.1 +7.1 +Solving nonlinear problems +• “Solving nonlinear problems,” Section 7.1.1 +7.1.1 +SOLVING NONLINEAR PROBLEMS +Products: Abaqus/Standard Abaqus/CAE +References +• “Convergence and time integration criteria: overview,” Section 7.2.1 +• “Commonly used control parameters,” Section 7.2.2 +• “Convergence criteria for nonlinear problems,” Section 7.2.3 +• “Time integration accuracy in transient problems,” Section 7.2.4 +• “Configuring general analysis procedures,” Section 14.11.1 of the Abaqus/CAE User’s Manual, in +the online HTML version of this manual +Overview +Solving nonlinear problems in Abaqus/Standard involves: +• a combination of incremental and iterative procedures; +• using the Newton method to solve the nonlinear equations; +• determining convergence; +• defining loads as a function of time; and +• choosing suitable time increments automatically. +Some static problems may become unstable because of severe nonlinearity. Abaqus/Standard offers a +set of automatic stabilization mechanisms to handle such problems. +The solution of nonlinear problems +The nonlinear load-displacement curve for a structure is shown in Figure 7.1.1–1. +Load +Displacement +Figure 7.1.1–1 Nonlinear load-displacement curve. +The objective of the analysis is to determine this response. In a nonlinear analysis the solution cannot be +calculated by solving a single system of linear equations, as would be done in a linear problem. Instead, +the solution is found by specifying the loading as a function of time and incrementing time to obtain the +nonlinear response. Therefore, Abaqus/Standard breaks the simulation into a number of time increments +and finds the approximate equilibrium configuration at the end of each time increment. Using the Newton +method, it often takes Abaqus/Standard several iterations to determine an acceptable solution to each +time increment. +Steps, increments, and iterations +• The time history for a simulation consists of one or more steps. You define the steps, which generally +consist of an analysis procedure, loading, and output requests. Different loads, boundary conditions, +analysis procedures, and output requests can be used in each step. For example: +Step 1: Hold a plate between rigid jaws. +Step 2: Add loads to deform the plate. +Step 3: Find the natural frequencies of the deformed plate. +• An increment is part of a step. In nonlinear analyses each step is broken into increments so that +the nonlinear solution path can be followed. You suggest the size of the first increment, and +Abaqus/Standard automatically chooses the size of the subsequent increments. At the end of each +increment the structure is in (approximate) equilibrium and results are available for writing to the +restart, data, results, or output database files. +• An iteration is an attempt at finding an equilibrium solution in an increment. If the model is not in +equilibrium at the end of the iteration, Abaqus/Standard tries another iteration. With every iteration +the solution that Abaqus/Standard obtains should be closer to equilibrium; however, sometimes the +iteration process may diverge—subsequent iterations may move away from the equilibrium state. +In that case Abaqus/Standard may terminate the iteration process and attempt to find a solution with +a smaller increment size. +Convergence +Consider the external forces, P, and the internal (nodal) forces, I, acting on a body +and Figure 7.1.1–2(b), respectively). The internal loads acting on a node are caused by the stresses in +the elements that are attached to that node. +For the body to be in equilibrium, the net force acting at every node must be zero. Therefore, the +basic statement of equilibrium is that the internal forces, I, and the external forces, P, must balance each +other: +The nonlinear response of a structure to a small load increment, +Abaqus/Standard uses the structure’s tangent stiffness, +, which is based on its configuration at +, is shown in Figure 7.1.1–3. +, and +, the structure’s configuration +to calculate a displacement correction, +, for the structure. Using +is updated to +. +Id +Ia +Ic +Ib +(a) External loads in a simulation. +(b) Internal forces acting at a node. +Figure 7.1.1–2 Internal and external loads on a body. +Load +Ra +Ia +ΔP +K0 +Ka +ca +u0 +ua +Displacement +Figure 7.1.1–3 First iteration in an increment. +Abaqus/Standard then calculates the structure’s internal forces, +, in this updated configuration. +The difference between the total applied load, P, and +can now be calculated as +where +If +is the force residual for the iteration. +is zero at every degree of freedom in the model, point a in Figure 7.1.1–3 would lie on the +load-deflection curve and the structure would be in equilibrium. In a nonlinear problem +will never be +exactly zero, so Abaqus/Standard compares it to a tolerance value. If +is less than this force residual +tolerance at all nodes, Abaqus/Standard accepts the solution as being in equilibrium. By default, this +tolerance value is set to 0.5% of an average force in the structure, averaged over time. Abaqus/Standard +automatically calculates this spatially and time-averaged force throughout the simulation. You can +change this, and all other such tolerances, by specifying solution controls . +If +is less than the current tolerance value, P and +are considered to be in equilibrium and +is a valid equilibrium configuration for the structure under the applied load. However, before +Abaqus/Standard accepts the solution, it also checks that the last displacement correction, +, is +small relative to the total incremental displacement, +is greater than a fraction +(1% by default) of the incremental displacement, Abaqus/Standard performs another iteration. Both +convergence checks must be satisfied before a solution is said to have converged for that time increment. +If the solution from an iteration is not converged, Abaqus/Standard performs another iteration to try +to bring the internal and external forces into balance. First, Abaqus/Standard forms the new stiffness, +. This stiffness, together with the residual +, that brings the system closer to equilibrium (point +, for the structure based on the updated configuration, +, determines another displacement correction, +. If +b in Figure 7.1.1–4). +Ia +ΔP +K0 +u0 +ua +Ka +Load +Rb +Ib +Ia +K0 +cb +ua +ub +Displacement +Figure 7.1.1–4 Second iteration. +Abaqus/Standard calculates a new force residual, +. Again, the largest force residual at any degree of freedom, +, using the internal forces from the structure’s +new configuration, +, is compared against +the force residual tolerance, and the displacement correction for the second iteration, +, is compared to +the increment of displacement, +. If necessary, Abaqus/Standard performs further iterations. For +more details on convergence in Abaqus/Standard, see “Convergence criteria for nonlinear problems,” +Section 7.2.3. +For each iteration in a nonlinear analysis Abaqus/Standard forms the model’s stiffness matrix +and solves a system of equations. Therefore, the computational cost of each iteration is close to +the cost of conducting a complete linear analysis, making the computational expense of a nonlinear +analysis potentially many times greater than the cost of a linear analysis. Since it is possible with +Abaqus/Standard to save results at each converged increment, the amount of output data available from +a nonlinear simulation can also be much greater than that available from a linear analysis of the same +geometry. +Automatic incrementation control +By default, Abaqus/Standard automatically adjusts the size of the time increments to solve nonlinear +problems efficiently. You need to suggest only the size of the first increment in each step of the simulation, +after which Abaqus/Standard automatically adjusts the size of the increments. If you do not provide a +suggested initial increment size, Abaqus/Standard will attempt to apply all of the loads defined in the +step in a single increment. For highly nonlinear problems Abaqus/Standard will have to reduce the +increment size repeatedly to obtain a solution, resulting in wasted CPU time. +It is advantageous to +provide a reasonable initial increment size because only in mildly nonlinear problems can all of the +loads in a step be applied in a single increment. +The number of iterations needed to find a converged solution for a time increment will vary +depending on the degree of nonlinearity in the system. With the default incrementation control, the +procedure works as follows. If the solution has not converged within 16 iterations or if the solution +appears to diverge, Abaqus/Standard abandons the increment and starts again with the increment size +set to 25% of its previous value. It then attempts to find a converged solution with this smaller time +increment. If the solution still fails to converge, Abaqus/Standard reduces the increment size again. +This process is continued until a solution is found. +If the time increment becomes smaller than the +minimum you defined or more than 5 attempts are needed, Abaqus/Standard stops the analysis. +If the increment converges in fewer than 5 iterations, this indicates that the solution is being +found fairly easily. Therefore, Abaqus/Standard automatically increases the increment size by 50% if +2 consecutive increments require fewer than 5 iterations to obtain a converged solution. +While the default automatic incrementation control is suitable for most analyses, you can change all +the defaults when necessary by specifying solution controls; see “Commonly used control parameters,” +Section 7.2.2, and “Time integration accuracy in transient problems,” Section 7.2.4. +Automatic stabilization of unstable problems +Nonlinear static problems can be unstable. Such instabilities may be of a geometrical nature, such +as buckling, or of a material nature, such as material softening. If the instability manifests itself in a +global load-displacement response with a negative stiffness, the problem can be treated as a buckling or +collapse problem as described in “Unstable collapse and postbuckling analysis,” Section 6.2.4. However, +if the instability is localized, there will be a local transfer of strain energy from one part of the model to +neighboring parts, and global solution methods may not work. This class of problems has to be solved +either dynamically or with the aid of (artificial) damping; for example, by using dashpots. +Abaqus/Standard provides an automatic mechanism for stabilizing unstable quasi-static problems +through the automatic addition of volume-proportional damping to the model. The applied damping +factors can be constant over the duration of a step, or they can vary with time to account for changes over +the course of a step. The latter, adaptive approach is typically preferred. +Automatic stabilization of static problems with a constant damping factor +Automatic stabilization with a constant damping factor is triggered by including automatic stabilization +in any nonlinear quasi-static procedure. Viscous forces of the form +are added to the global equilibrium equations +is an artificial mass matrix calculated with unity density, c is a damping factor, +where +is the vector of nodal velocities, and +meaning in the context of the problem being solved). +is the increment of time (which may or may not have a physical +For the case of static stabilization the mass matrix for Timoshenko beams is always calculated +assuming isotropic rotary inertia, regardless of the type of rotary inertia specified for the beam section +definition (“Rotary inertia for Timoshenko beams” in “Beam section behavior,” Section 29.3.5). +Automatic stabilization does not carry over automatically to subsequent steps. +It needs to be +declared for any step in which you want it to be active. Abaqus/Standard recalculates new values for +the damping factor, based on the declared damping intensity and on the solution of the first increment of +the step. Therefore, unless you specify the same damping factor directly , an analysis with an unstable step may produce slightly different results from +the same analysis with the original step split into two steps. Moreover, if the instabilities in the model +have not subsided by the end of a step, viscous forces may be terminated abruptly or modified at the +beginning of subsequent steps, potentially causing convergence difficulties if automatic stabilization +is not used in the subsequent step. If such a situation arises, it is recommended that the problem be +restarted with the damping factor set equal to the value chosen by Abaqus/Standard (or to the value you +specified) in the previous step. This value is printed in the message (.msg) file for the previous step. If +it is necessary to have an accurate static equilibrium solution after an instability has occurred (and the +model’s behavior has returned to a stable regime), the step with automatic stabilization can be followed +by a step without such stabilization. +Calculating the damping factor based on the dissipated energy fraction +It is assumed that the problem is stable at the beginning of the step and that instabilities may develop in the +course of the step. While the model is stable, viscous forces and, therefore, the viscous energy dissipated +are very small. Thus, the additional artificial damping has no effect. If a local region goes unstable, the +local velocities increase and, consequently, part of the strain energy then released is dissipated by the +applied damping. Abaqus/Standard can, if necessary, reduce the time increment to permit the process to +occur without the unstable response causing very large displacements. Abaqus/Standard calculates and +prints to the message file the damping factor, c, based on the solution of the first increment of a step. +In most applications the first increment of the step is stable without the need to apply damping. The +damping factor is then determined in such a way that the dissipated energy for a given increment with +characteristics similar to the first increment is a small fraction of the extrapolated strain energy. The +fraction is called the dissipated energy fraction and has a default value of 2.0 × 10−4 . If the default value +for the dissipated energy fraction is used, the adaptive automatic stabilization scheme discussed in the +next section will be activated automatically by default in the step. +Alternatively, you can specify the non-default dissipated energy fraction for automatic stabilization +directly. +Input File Usage: +Abaqus/CAE Usage: +Use any of the following options to specify a nondefault dissipated energy +fraction: +*COUPLED TEMPERATURE-DISPLACEMENT, +STABILIZE=dissipated energy fraction +*SOILS, STABILIZE=dissipated energy fraction +*STATIC, STABILIZE=dissipated energy fraction +*STEADY STATE TRANSPORT, STABILIZE=dissipated energy fraction +*VISCO, STABILIZE=dissipated energy fraction +Step module: Create Step: General: any valid step type: Basic: select +Specify dissipated energy fraction from the Automatic stabilization field +Considerations when the first increment is unstable or singular +There are cases where the first increment is either unstable or singular (due to a rigid body mode). In +such cases it is not possible to obtain a solution to the first increment without applying some damping. +Therefore, some damping is already applied during the first increment. The damping factor used for +the initial increment is chosen such that the average element damping matrix component, divided by +the step time, is equal to the average element stiffness matrix component multiplied by the dissipated +energy fraction. If the calculated strain energy change in this increment indicates that the solution without +damping is stable, the damping factor is recalculated based upon the energy method described previously. +However, if the strain energy change indicates that the solution is unstable or singular, the initially +calculated damping factor is maintained, and a warning message is issued indicating that the amount of +damping applied may not be appropriate. In many cases the amount of damping may actually be rather +large, which can affect the solution in ways that are not desirable. Therefore, if the above mentioned +warning message is issued, check the viscous forces (VF) and compare them with the expected nodal +forces to make sure that the viscous forces do not dominate the solution. If necessary, follow the stabilized +step with another step in which stabilization is not used or with a step in which a much smaller damping +factor is used. +Directly specifying the damping factor +You can also specify the damping factor directly. Unfortunately, it is generally quite difficult to make a +reasonable estimate for the damping factor unless a value is known from the output of previous runs; the +damping factor depends not only on the amount of damping but also on mesh size and material behavior. +Input File Usage: +Use any of the following options to specify the damping factor directly: +*COUPLED TEMPERATURE-DISPLACEMENT, STABILIZE, +FACTOR=damping factor +*SOILS, STABILIZE, FACTOR=damping factor +Abaqus/CAE Usage: +*STATIC, STABILIZE, FACTOR=damping factor +*STEADY STATE TRANSPORT, STABILIZE, FACTOR=damping factor +*VISCO, STABILIZE, FACTOR=damping factor +Step module: Create Step: General: Coupled temp-displacement, +Soils, Static, General, or Visco: Basic: select Specify damping +factor from the Automatic stabilization field +Adaptive automatic stabilization scheme +As discussed above, the automatic stabilization scheme with a constant damping factor typically works +well to subside instabilities and to eliminate rigid body modes without having a major effect on the +solution. However, there is no guarantee that the value of the damping factor is optimal or even suitable +in some cases. This is particularly true for thin shell models, in which the damping factor may be too +high when a poor estimation of the extrapolated strain energy is made during the first increment. For +such models you may have to increase the damping factor if the convergence behavior is problematic or +to decrease the damping factor if it distorts the solution. The former case would require you to rerun the +analysis with a larger damping factor, while the latter case would require you to perform post-analysis +comparison of the energy dissipated by viscous damping (ALLSD) to the total strain energy (ALLIE). +Therefore, obtaining an optimal value for the damping factor is a manual process requiring trial and error +until a converged solution is obtained and the dissipated stabilization energy is sufficiently small. +The adaptive automatic stabilization scheme, in which the damping factor can vary spatially and +with time, provides an effective alternative approach. +In this case the damping factor is controlled +by the convergence history and the ratio of the energy dissipated by viscous damping to the total +strain energy. If the convergence behavior is problematic because of instabilities or rigid body modes, +Abaqus/Standard automatically increases the damping factor. For example, the damping factor may +increase if an analysis takes extra severe discontinuity or equilibrium iterations per increment or +requires time increment cutbacks. On the other hand, Abaqus/Standard may reduce the damping factor +automatically if instabilities and rigid body modes subside. +The ratio of the energy dissipated by viscous damping to the total strain energy is limited by an +accuracy tolerance that you specify. Such an accuracy tolerance is imposed on the global level for the +whole model. If the ratio of the energy dissipated by viscous damping to the total strain energy for the +whole model exceeds the accuracy tolerance, the damping factor at each individual element is adjusted to +ensure that the ratio of the stabilization energy to the strain energy is less than the accuracy tolerance on +both the global and local element level. The stabilization energy always increases, while the strain energy +may decrease. Therefore, Abaqus/Standard restricts the ratio of the incremental value of the stabilization +energy to the incremental value of the strain energy for each increment to ensure that this value has not +exceeded the accuracy tolerance if the ratio of the total stabilization energy to the total strain energy +exceeds the accuracy tolerance. The accuracy tolerance is a targeted value and can be exceeded in some +situations, such as when there is rigid body motion or when significant non-local instability occurs. +The default accuracy tolerance used by the adaptive automatic stabilization scheme is 0.05. The +default tolerance is suitable for most applications, but you have the option of specifying a nondefault +accuracy tolerance if necessary. If the accuracy tolerance is set equal to zero, the adaptive automatic +stabilization scheme is not activated and the automatic stabilization scheme with a constant damping +factor will be used in the step. +If the accuracy tolerance is not specified but the dissipated energy fraction with the default value +of 2.0 × 10−4 is used, the adaptive automatic damping algorithm will be activated automatically with an +accuracy tolerance of 0.05. +Input File Usage: +Use any of the following options to activate adaptive automatic stabilization +with the default stabilization energy tolerance: +*COUPLED TEMPERATURE-DISPLACEMENT, STABILIZE +*SOILS, STABILIZE +*STATIC, STABILIZE +*STEADY STATE TRANSPORT, STABILIZE +*VISCO, STABILIZE +Use any of the following options to activate adaptive automatic stabilization +with a nondefault stabilization energy tolerance: +*COUPLED TEMPERATURE-DISPLACEMENT, STABILIZE, +ALLSDTOL=accuracy tolerance +*SOILS, STABILIZE, ALLSDTOL=accuracy tolerance +*STATIC, STABILIZE, ALLSDTOL=accuracy tolerance +*STEADY STATE TRANSPORT, STABILIZE, +ALLSDTOL=accuracy tolerance +*VISCO, STABILIZE, ALLSDTOL=accuracy tolerance +Step module: Create Step: General: Coupled temp-displacement, Soils, +Static, General, or Visco: Basic: select an Automatic stabilization +method: toggle on Use adaptive stabilization with max. ratio of +stabilization to strain energy: accuracy tolerance +Abaqus/CAE Usage: +Default value of the initial damping factor +By default, the initial value of the damping factor is typically equal to the value that would be used for +automatic stabilization with a constant damping factor . In some cases additional factors that are considered with adaptive +automatic stabilization cause some differences in the initial damping factor. +Specifying the initial damping factor directly +Alternatively, you can specify the initial damping factor directly. The damping factor is adjusted based +on the convergence history and the accuracy tolerance through the step. +Input File Usage: +Use any of the following options to specify the initial damping factor directly +with the default stabilization energy tolerance: +*COUPLED TEMPERATURE-DISPLACEMENT, STABILIZE, +FACTOR=damping factor, ALLSDTOL +*SOILS, STABILIZE, FACTOR=damping factor, ALLSDTOL +Abaqus/CAE Usage: +*STATIC, STABILIZE, FACTOR=damping factor, ALLSDTOL +*STEADY STATE TRANSPORT, STABILIZE, FACTOR=damping factor, +ALLSDTOL +*VISCO, STABILIZE, FACTOR=damping factor, ALLSDTOL +Step module: Create Step: General: Coupled temp-displacement, +Soils, Static, General, or Visco: Basic: from the Automatic +stabilization field, select Specify damping factor: damping +factor: toggle on Use adaptive stabilization with max. ratio of +stabilization to strain energy: maximum ratio +Propagating the damping factors from the immediately preceding general step into the current step +Adaptive automatic stabilization provides an option to propagate the damping factors from the +immediately preceding general step to the subsequent steps. The default is to not propagate the +damping factors from the results of the preceding general step. In this case Abaqus recalculates the +initial damping factors based on the declared dissipated energy faction and on the solution of the first +increment of the step, or you can specify the initial damping factors directly. +Input File Usage: +Use any of the following options to indicate that the damping factors in the +current step are propagated from the immediately preceding general step: +*COUPLED TEMPERATURE-DISPLACEMENT, STABILIZE, +ALLSDTOL, CONTINUE=YES +*SOILS, STABILIZE, ALLSDTOL, CONTINUE=YES +*STATIC, STABILIZE, ALLSDTOL, CONTINUE=YES +*STEADY STATE TRANSPORT, STABILIZE, ALLSDTOL, +CONTINUE=YES +*VISCO, STABILIZE, ALLSDTOL, CONTINUE=YES +Step module: Create Step: General: Coupled temp-displacement, +Soils, Static, General, or Visco: Basic: select Use damping factors +from previous general step from the Automatic stabilization +field: Use adaptive stabilization with max. ratio of stabilization +to strain energy: accuracy tolerance +Abaqus/CAE Usage: +Ensuring that an accurate solution is obtained with automatic stabilization +Whenever automatic stabilization is applied to a problem, check the following to ensure that accurate +solutions are obtained: +• For a damping factor calculated using the dissipated energy fraction, check the factor printed to the +message (.msg) file at the end of the first increment to ensure that a reasonable amount of damping +is applied. Unfortunately, the damping factor is problem dependent; therefore, you must rely on +experience from previous runs. +• Compare the viscous forces (VF) with the overall forces in the analysis, and ensure that the viscous +forces are relatively small compared with the overall forces in the model. +• Compare the viscous damping energy (ALLSD) with the total strain energy (ALLIE), and ensure +that the ratio does not exceed the dissipated energy fraction or any reasonable amount. The viscous +damping energy may be large if the structure undergoes a large amount of motion. +The automated procedure of computing damping factors works well for many applications. However, +there are cases where the computed damping factor is either too small, thus not controlling the instability, +or too high, thus leading to inaccurate results. These problems are more likely to occur when using +a constant damping factor—the damping factor is computed in the first increment, which may not be +representative of behavior in the rest of the step. For example, consider a sequentially coupled thermal- +stress analysis in which a mechanical analysis reads temperatures from a previous transient thermal +analysis. Typically the thermal analysis exhibits a diffusive process, where rapid changes in temperature +occurs early in the analysis and minor changes in temperature occur once steady state is reached. In such +a case Abaqus will compute the extrapolated strain energy based on the temperatures corresponding to +the time of the first increment (in this case there may be a significant change in temperature for the +first increment), thus yielding a larger then expected extrapolated strain energy. This in turn leads to a +damping factor that is too large, resulting in inaccurate results. +If one of the automatic stabilization methods is not working appropriately, you can try using the other +automatic stabilization method; the adaptive stabilization scheme is generally preferred. Alternatively, +you can try directly specifying the damping factor. +7.2 +Analysis convergence controls +• “Convergence and time integration criteria: overview,” Section 7.2.1 +• “Commonly used control parameters,” Section 7.2.2 +• “Convergence criteria for nonlinear problems,” Section 7.2.3 +• “Time integration accuracy in transient problems,” Section 7.2.4 +7.2.1 +CONVERGENCE AND TIME INTEGRATION CRITERIA: OVERVIEW +Numerous control parameters are associated with the convergence and integration accuracy algorithms in +Abaqus/Standard. These parameters are assigned default values that are chosen to optimize the accuracy and +efficiency of the solution for a wide spectrum of nonlinear problems. You can change the solution control +parameters, as described in the following sections: +• A brief synopsis of the more important solution control parameters, together with a description of the +circumstances in which they can be used effectively, is provided in “Commonly used control parameters,” +Section 7.2.2. This section is likely to be the most useful for the general user and should be read first. +• Abaqus/Standard incorporates an empirical algorithm designed to solve the equilibrium equations of +nonlinear systems accurately and economically. The criteria used to establish convergence of nonlinear +increments and the automatic adjustment of increment size based on the convergence rate are described +in “Convergence criteria for nonlinear problems,” Section 7.2.3. +• Abaqus/Standard allows you to choose “time integration accuracy parameters” in problems that have +a physical time scale. The algorithms that use these parameters for automatically controlling time +increment sizes are described in “Time integration accuracy in transient problems,” Section 7.2.4. +• Abaqus/CFD allows you to choose the control parameters used in an Abaqus/CFD to Abaqus/Standard +or to Abaqus/Explicit co-simulation to alleviate instability and mesh distortion during the analysis. +Modifying the default solution controls +The default values for the solution control parameters need not be adjusted for most cases. You can reset +them, however, within a step definition. +Values given for the solution control parameters remain in effect for the remainder of the analysis +or until they are reset. +Input File Usage: +*CONTROLS +The *CONTROLS option can be repeated, +parameters. +if necessary, with different +Abaqus/CAE Usage: +Step module: Other→General Solution Controls→Edit: toggle on Specify +Resetting all default solution controls +You can restore all solution control parameters to their default values. +Input File Usage: +Abaqus/CAE Usage: +*CONTROLS, RESET +Step module: Other→General Solution Controls→Edit: toggle on +Reset all parameters to their system-defined defaults +7.2.2 +COMMONLY USED CONTROL PARAMETERS +Products: Abaqus/Standard Abaqus/CFD Abaqus/CAE +References +• “Convergence and time integration criteria: overview,” Section 7.2.1 +• *CONTROLS +• “Customizing general solution controls,” Section 14.15.1 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +Solution control parameters can be used to control: +• nonlinear equation solution accuracy; +• time increment adjustment; and +• FSI stabilization and mesh distortion in an Abaqus/CFD to Abaqus/Standard or to Abaqus/Explicit +co-simulation. +These solution control parameters need not be changed for most analyses. In difficult cases, however, +the solution procedure may not converge with the default controls or may use an excessive number of +increments and iterations. After it has been established that such problems are not due to modeling errors, +it may be useful to change certain control parameters. +This section presents a brief synopsis of the more important solution control parameters, together +with a description of the circumstances in which they can be used effectively. +Values given for the solution control parameters remain in effect for the remainder of the analysis +or until they are reset. You can restore all solution control parameters to their default values . +Terminology +In this section the word “flux” means the variable whose discretized equilibrium is being sought and for +which the equilibrium equations may be nonlinear: force, moment, heat flux, concentration volumetric +flux, or pore liquid volumetric flux. The word “field” refers to the basic variables of the system, such +as the components of the displacement in a continuum stress analysis or temperature in a heat transfer +analysis. The superscript +refers to one such type of equation. The fields and corresponding fluxes +available in Abaqus/Standard are listed in “Convergence criteria for nonlinear problems,” Section 7.2.3. +Defining tolerances for field equations +Solution control parameters can be used to define tolerances for field equations. You can select the type +of equation for which the solution control parameters are being defined, as shown in Table 7.2.2–1. The +default tolerances can be reset if the analysis does not require high accuracy in the convergence criteria. +Table 7.2.2–1 Selecting the field equation. +Equilibrium equation +Input file +Abaqus/CAE +All active fields +FIELD=GLOBAL +Apply to all applicable +fields +Force and bimoment +FIELD=DISPLACEMENT +Displacement +Moment +Heat transfer +Hydrostatic fluid +Pore fluid pressure +FIELD=ROTATION +Rotation +FIELD=TEMPERATURE +Temperature +11, 12, 13, ... +FIELD=HYDROSTATIC +FLUID PRESSURE +Hydrostatic Fluid +Pressure +FIELD=PORE FLUID +PRESSURE +Pore Fluid Pressure +Mass diffusion +FIELD=CONCENTRATION Concentration +Electrical conduction +FIELD=ELECTRICAL +POTENTIAL +Electrical Potential +FIELD=MATERIAL FLOW Unsupported +DOF +all +1, 2, 3, 7 +4, 5, 6 +11 +10 +FIELD=PRESSURE +LAGRANGE MULTIPLIER +Unsupported +N/A +FIELD=VOLUMETRIC +LAGRANGE MULTIPLIER +Unsupported +N/A +7.2.2–2 +Mechanism analysis +(connector elements with +material flow degree of +freedom) +Analysis containing +C3D4H elements +(all materials, except +compressible hyperelastic +elastomers and +elastomeric foams). +Analysis containing +C3D4H elements with +compressible hyperelastic +The most significant solution control parameters for field equation tolerances— , +, and +—may have to be modified in cases where the residuals are large relative to the fluxes or in cases +, +where the incremental solution is essentially zero. +Input File Usage: +Abaqus/CAE Usage: +*CONTROLS, PARAMETERS=FIELD, FIELD=field +Step module: Other→General Solution Controls→Edit: toggle +on Specify: Field Equations: Apply to all applicable fields +or Specify individual fields: field +Modifying the residual control +is the convergence criterion for the ratio of the largest residual to the corresponding average flux norm, +is defined in “Convergence criteria for nonlinear problems,” Section 7.2.3. The +, for convergence. += 5 × 10−3, which is rather strict by engineering standards but in all but exceptional +default value is +cases will guarantee an accurate solution to complex nonlinear problems. The value for this ratio can be +increased to a larger number if some accuracy can be sacrificed for computational speed. +Modifying the solution correction control +is the convergence criterion for the ratio of the largest solution correction to the largest corresponding += 10−2. In addition to sufficiently small residuals, +incremental solution value. The default value is +Abaqus/Standard requires that the largest correction to the solution value be small in comparison to the +largest corresponding incremental solution value. Some analyses may not require such accuracy, thus +permitting this ratio to be increased. +Specifying the average flux +is the value of average flux used by Abaqus/Standard for checking residuals. The default value is +the time average flux calculated by Abaqus/Standard, as defined in “Convergence criteria for nonlinear +problems,” Section 7.2.3. You may, however, define a constant value, +, for the average flux, in which +case +throughout the step. +You may wish to use absolute tolerances for your residual checks. The absolute tolerance value is +. To avoid testing the magnitude of the +, and the ratio +then equal to the product of the average flux, +solution correction, you can set +to 1.0. +Modifying the initial time average flux +is the initial value of the time average flux for the current step. The default value is the time average +flux from the previous step or 10−2 if this is Step 1. Redefining +is sometimes helpful when a coupled +problem is analyzed and some of the fields in the problem are not active in the first step; for example, if +a static step is carried out before a fully coupled thermal-stress step. +Redefinition of +can also be useful if the first step is essentially a null step; for example, in a +contact problem before any contact occurs, the initial fluxes (forces) generated are zero. In such cases +should be given as a typical flux magnitude that will occur when field +first becomes active. +The initial value of +is retained until an iteration is completed for which +time we redefine +criteria for nonlinear problems,” Section 7.2.3). +. The criterion for zero flux compared to +is +If you specify the average flux, +, directly, the value given for +is ignored. +, at which + and message (.msg) files. Nondefault +controls are marked by ***. For example, specifying the following controls: +Field +Equation +Displacement +Rotation +0.01 +0.02 +1.0 +2.0 +10.0 +20.0 +– +2.E3 +– +– +1.E−4 +– +would result in the following output: +CONVERGENCE TOLERANCE PARAMETERS FOR FORCE +*** CRIT. FOR RESIDUAL FORCE FOR A NONLINEAR PROBLEM +*** CRITERION FOR DISP. CORRECTION IN A NONLINEAR PROBLEM +*** INITIAL VALUE OF TIME AVERAGE FORCE +AVERAGE FORCE IS TIME AVERAGE FORCE +ALT. CRIT. FOR RESIDUAL FORCE FOR A NONLINEAR PROBLEM +*** CRIT. FOR ZERO FORCE RELATIVE TO TIME AVRG. FORCE +CRIT. FOR DISP. CORRECTION WHEN THERE IS ZERO FLUX +CRIT. FOR RESIDUAL FORCE WHEN THERE IS ZERO FLUX +FIELD CONVERSION RATIO +CONVERGENCE TOLERANCE PARAMETERS FOR MOMENT +*** CRIT. FOR RESIDUAL MOMENT FOR A NONLINEAR PROBLEM +*** CRIT. FOR ROTATION CORRECTION IN A NONLINEAR PROBLEM +*** INITIAL VALUE OF TIME AVERAGE MOMENT +*** USER DEFINED VALUE OF AVERAGE MOMENT NORM +ALT. CRIT. FOR RESID. MOMENT FOR A NONLINEAR PROBLEM +CRIT. FOR ZERO MOMENT RELATIVE TO TIME AVRG. MOMENT +CRIT. FOR ROTATION CORRECTION WHEN ZERO FLUX +CRIT. FOR RESIDUAL MOMENT WHEN ZERO FLUX +FIELD CONVERSION RATIO +1.000E-02 +1.00 +10.0 +2.000E-02 +1.000E-04 +1.000E-03 +1.000E-08 +1.00 +2.000E-02 +2.00 +20.0 +2.000E+03 +2.000E-02 +1.000E-05 +1.000E-03 +1.000E-08 +1.00 +Controlling the time incrementation scheme +Solution control parameters can be used to alter both the convergence control algorithm and the time +incrementation scheme. The time incrementation parameters +are the most significant since +they have a direct effect on convergence. They may have to be modified if convergence is (initially) +nonmonotonic or if convergence is nonquadratic. +and +Nonmonotonic convergence may occur if various nonlinearities interact; +the +combination of friction, nonlinear material behavior, and geometric nonlinearity may lead to +nonmonotonically decreasing residuals. +for example, +Nonquadratic convergence will occur if the Jacobian is not exact, which may occur for complex +material models. It may also occur if the Jacobian is nonsymmetric but the symmetric equation solver +is used. In that case the unsymmetric equation solver should be specified for the step . +Input File Usage: +Abaqus/CAE Usage: +*CONTROLS, PARAMETERS=TIME INCREMENTATION +Step module: Other→General Solution Controls→Edit: toggle +on Specify: Time Incrementation +Specifying the equilibrium iteration for a residual check +is the number of equilibrium iterations after which the check is made that the residuals are not +If the initial convergence is +increasing in two consecutive iterations. The default value is +nonmonotonic, it may be necessary to increase this value. +. +Specifying the equilibrium iteration for a logarithmic rate of convergence check +is the number of equilibrium iterations after which the logarithmic rate of convergence check begins. +The default value is +. In cases where convergence is nonquadratic and this cannot be corrected +by using the unsymmetric equation solver for the step, the logarithmic convergence check should be +eliminated by setting this parameter to a high value. +Avoiding premature cutbacks in difficult analyses +. For example, in a difficult analysis involving both +Sometimes it is useful to increase both +friction and the concrete material model, it may be helpful to set +to avoid premature +cutbacks of the time increment. These two parameters can be raised to more appropriate values for +severely discontinuous problems by increasing them individually. +and +and +Automatically setting the time incrementation parameters +. In this +You can automatically set the parameters described above to the values +case any values that you specified previously for +are +specified multiple times in a step with different solution control settings, the last definition will be used. +*CONTROLS, ANALYSIS=DISCONTINUOUS +Step module: Other→General Solution Controls→Edit: toggle on +Specify: Time Incrementation: Discontinuous analysis +are overridden. However, if +Abaqus/CAE Usage: +Input File Usage: +and +and +and +Improving solution efficiency in a problem that involves a high coefficient of friction +The solution efficiency can sometimes be improved in an analysis that involves a high coefficient of +friction by automatically setting the time incrementation parameters and using the unsymmetric equation +solver. +Abaqus/Standard output +The controls in effect for an analysis are listed in the data (.dat) and message (.msg) files. Nondefault +controls are marked by **. For example, specifying the time incrementation parameters =7 and +=10 +would result in the following output: +TIME INCREMENTATION CONTROL PARAMETERS: +*** FIRST EQUIL. ITERATION FOR CONSECUTIVE DIVERGENCE CHECK +*** EQUIL. ITER. AT WHICH LOG. CONVERGENCE RATE CHECK BEGINS +EQUIL. ITER. AFTER WHICH ALTERNATE RESIDUAL IS USED +MAXIMUM EQUILIBRIUM ITERATIONS ALLOWED +EQUIL. ITERATION COUNT FOR CUT-BACK IN NEXT INCREMENT +MAX EQUIL. ITERS IN TWO INCREMENTS FOR TIME INC. INCREASE +MAXIMUM ITERATIONS FOR SEVERE DISCONTINUITIES +MAXIMUM CUT-BACKS ALLOWED IN AN INCREMENT +MAX DISCON. ITERS IN TWO INCS FOR TIME INC. INCREASE +CUT-BACK FACTOR AFTER DIVERGENCE +CUT-BACK FACTOR FOR TOO SLOW CONVERGENCE +CUT-BACK FACTOR AFTER TOO MANY EQUILIBRIUM ITERATIONS +10 +16 +10 +12 +0.250 +0.500 +0.750 +Activating the “line search” algorithm +In strongly nonlinear problems the Newton algorithms used in Abaqus/Standard may sometimes +diverge during equilibrium iteration. The line search algorithm (discussed in “Improving the efficiency +of the solution by using the line search algorithm” in “Convergence criteria for nonlinear problems,” +Section 7.2.3) detects these situations automatically and applies a scale factor to the computed solution +correction, which helps to prevent divergence. The line search algorithm is particularly useful when +the quasi-Newton method is used. +By default, the line search algorithm is enabled only during steps where the quasi-Newton method +, to a reasonable value (such as 5) to +is used. Set the maximum number of line search iterations, +activate the line search procedure or to zero to forcibly deactivate the line search. +Input File Usage: +*CONTROLS, PARAMETERS=LINE SEARCH +Abaqus/CAE Usage: +Step module: Other→General Solution Controls→Edit: toggle +on Specify: Line Search Control: +Defining tolerances for constraint equations +Solution control parameters can be used to set tolerances for constraint equations. You can set strain +compatibility tolerances for hybrid elements, displacement and rotation compatibility tolerances for +distributing coupling constraints (specified as surface-based constraints or using DCOUP2D/DCOUP3D +elements), and compatibility tolerances for softened contact. See “Convergence criteria for nonlinear +problems,” Section 7.2.3, for details. +Controlling the solution accuracy in direct cyclic analysis +Solution control parameters can be used in direct cyclic analysis to specify when to impose the periodicity +conditions and to set tolerances for stabilized state and plastic ratchetting detections. +Input File Usage: +*CONTROLS, TYPE=DIRECT CYCLIC +, +, +, +, +Abaqus/CAE Usage: +Step module: Other→General Solution Controls→Edit: toggle on +Specify: Direct Cyclic: +, +, +, +, +Imposing the periodicity condition +You can specify the iteration number at which the periodicity condition is first imposed, +value is +of an analysis. This solution control parameter rarely needs to be reset from its default value. +. The default += 1, in which case the periodicity condition is imposed for all iterations from the beginning +Defining tolerances for stabilized state and plastic ratchetting detections +You can specify the stabilized state detection criteria, +is the maximum allowable +ratio of the largest residual coefficient on any terms in the Fourier series to the corresponding average flux +norm, and +is the maximum allowable ratio of the largest correction to the displacement coefficient +on any terms in the Fourier series to the largest displacement coefficient. The default values are += 5 × 10−3 and +satisfied. += 5 × 10−3 . The solution converges to a stabilized state if both these criteria are +and +. +If plastic ratchetting occurs, the shape of the stress-strain curves remains unchanged but the mean +value of the plastic strain over a cycle continues to shift from one iteration to the next. In that case +it is desirable to use separate tolerances for the constant term in the Fourier series to detect the plastic +ratchetting. +You can also specify the plastic ratchetting detection criteria, +is the +maximum allowable ratio of the largest residual coefficient on the constant term in the Fourier series to +the corresponding average flux norm, and +is the maximum allowable ratio of the largest correction +to the displacement coefficient on the constant term in the Fourier series to the largest displacement += 5 × 10−3 . Plastic ratchetting is expected +coefficient. The default values are +if the residual coefficients and the corrections to the displacement coefficients on any of the periodic +terms are within the tolerances set by +, respectively, but the maximum residual coefficient +on the constant term and the maximum correction to the displacement coefficient on the constant term +exceed the tolerances set by +, respectively. += 5 × 10−3 and +and +and +and +. +Abaqus/Standard output +The controls in effect for an analysis are listed in the data (.dat) and message (.msg) files. Nondefault +controls are marked by **. For example, specifying the following controls: +1.0E−4 1.0E−4 1.0E−4 1.E−4 +would result in the following output: +STABILIZED STATE AND PLASTIC RATCHETTING DETECTION +PARAMETERS FOR FORCE +1.0E-04 +** CRIT. FOR RESI. COEFF. ON ANY FOURIER TERMS +1.0E-04 +** CRIT. FOR CORR. TO DISP. COEFF. ON ANY FOURIER TERMS +1.0E-04 +** CRIT. FOR RESI. COEFF. ON CONSTANT FOURIER TERM +** CRIT. FOR CORR. TO DISP. COEFF. ON CONST. FOURIER TERM 1.0E-04 +PERIODICITY CONDITION CONTROL PARAMETER: +** ITERATION NUMBER AT WHICH PERIODICITY CONDITION +** STARTS TO IMPOSE +Controlling the solution accuracy in an Abaqus/CFD to Abaqus/Standard or to Abaqus/Explicit +co-simulation +Solution control parameters can be used in an Abaqus/CFD to Abaqus/Standard or to Abaqus/Explicit +co-simulation to control the FSI stabilization and the mesh distortion. +Controlling FSI stabilization +You can specify the minimum number of remesh increments, maximum number of remesh increments, +FSI penalty scale factor, and solid/fluid density ratio to control the FSI stabilization. +The minimum and maximum number of remesh increments controls the number of mesh smoothing +steps taken during the ALE process for FSI or deforming mesh problems. Reducing the minimum and +maximum number of mesh smoothing increments can help reduce the computational time. Similarly, +increasing the minimum/maximum number of smoothing increments helps to ensure that the mesh quality +remains good and avoids potential element collapse during the evolution of an FSI problem. +The FSI penalty scale factor has a default value of 1.0. Increasing this parameter in increments of 0.1 +may be necessary for extremely flexible structures in high density fluids when the structural accelerations +are high. +When multiple solid-fluid interfaces are present, you should choose the smallest solid/fluid density +ratio. +Input File Usage: +Use the following option to control the FSI stabilization: +*CONTROLS, TYPE=FSI +minimum number of remesh increments, maximum number of remesh +increments, FSI penalty scale factor, solid/fluid density ratio +Abaqus/CAE Usage: +Controlling FSI stabilization in an Abaqus/CFD to Abaqus/Standard or to +Abaqus/Explicit co-simulation is not supported in Abaqus/CAE. +Controlling mesh distortion +Similar to the distortion control used in Abaqus/Explicit , Abaqus/CFD offers distortion control to prevent elements from inverting or distorting +excessively in fluid mesh movement. By default, distortion control is turned off during the co-simulation. +Input File Usage: +Use the following option to deactivate distortion control (default): +*CONTROLS, TYPE=FSI, DISTORTION CONTROL=OFF +Use the following option to activate distortion control: +Abaqus/CAE Usage: +*CONTROLS, TYPE=FSI, DISTORTION CONTROL=ON +Controlling mesh distortion in an Abaqus/CFD to Abaqus/Standard or to +Abaqus/Explicit co-simulation is not supported in Abaqus/CAE. +7.2.3 +CONVERGENCE CRITERIA FOR NONLINEAR PROBLEMS +Products: Abaqus/Standard Abaqus/CAE +WARNING: The information in this section is provided for users who may wish to +adjust the convergence criteria for the solution of nonlinear systems. In most cases +these criteria need not be adjusted. +References +• “Convergence and time integration criteria: overview,” Section 7.2.1 +• *CONTROLS +• “Customizing general solution controls,” Section 14.15.1 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +In nonlinear problems the governing balance equations must be solved iteratively. This section describes: +• the solution method for nonlinear problems (Newton’s method); +• the field equations that can be solved by Abaqus/Standard; +• the criteria used to establish convergence of each iteration during the solution; +• “severe discontinuity” iterations; and +• the line search algorithm, which can be used to improve the robustness of the Newton method. +Solution method +Where possible, Abaqus/Standard uses Newton’s method to solve nonlinear problems. In some cases +it uses an exact implementation of Newton’s method, in the sense that the Jacobian of the system is +defined exactly, and quadratic convergence is obtained when the estimate of the solution is within the +radius of convergence of the algorithm. In other cases the Jacobian is approximated so that the iterative +method is not an exact Newton method. For example, some material and surface interface models (such +as nonassociated flow plasticity models or Coulomb friction) create a nonsymmetric Jacobian matrix, +but you may choose to approximate this matrix by its symmetric part. +Many problems exhibit discontinuous behavior. A common example is contact: at a particular point +on a surface, the contact constraint is either present or absent. Another (usually less severe) example is +strain reversal in plasticity at a point where the material is yielding. +Specifying the quasi-Newton method +You can choose to use the quasi-Newton technique for a particular step (described in “Quasi-Newton +solution technique,” Section 2.2.2 of the Abaqus Theory Manual) instead of the standard Newton method +for solving nonlinear equations. +The quasi-Newton technique can save substantial computational cost in some cases by reducing +the number of times the Jacobian matrix is factorized. Generally it is most successful when the system +is large and many iterations are needed per increment or when the stiffness matrix is not changing +much from iteration to iteration (such as in a dynamic analysis using implicit time integration or in +a small-displacement analysis with local plasticity). +It can be used only for symmetric systems of +equations; therefore, it cannot be used when the unsymmetric solver is specified for a step , nor can it be used for procedures that always produce an unsymmetric +system of equations, such as “Fully coupled thermal-stress analysis,” Section 6.5.3, and “Abaqus/Aqua +analysis,” Section 6.11.1. +In addition, it cannot be used for a static Riks procedure . +The quasi-Newton method works well in combination with the line search method . Line searches help to prevent divergence +of equilibrium iterations resulting from the inexact Jacobian produced by the quasi-Newton method. The +line search method is activated by default for steps that use the quasi-Newton method. You can override +this action by specifying line search controls. +You can specify the number of quasi-Newton iterations allowed before the kernel matrix is reformed. +The default number of iterations is 8. Additional matrix reformations may occur automatically during the +iteration process depending on the convergence behavior. Since quadratic convergence is not expected +during quasi-Newton iterations, the logarithmic rate of convergence check is not applied during the time +incrementation. Furthermore, the iteration count used in the time incrementation is a weighted sum of +quasi-Newton iterations, with the weight factor depending on whether or not a kernel matrix has been +reformed. +Input File Usage: +*SOLUTION TECHNIQUE, TYPE=QUASI-NEWTON, +REFORM KERNEL=n +Abaqus/CAE Usage: +Step module: step editor: Other: Solution technique: Quasi-Newton, +Number of iterations allowed before the kernel matrix is reformed: n +Specifying the separated method +Alternatively, you can choose to use the separated technique instead of the standard Newton method for +solving nonlinear equations for fully coupled thermal-stress and coupled thermal-electrical procedures. +The separated technique (described in “Fully coupled thermal-stress analysis,” Section 6.5.3, +and “Coupled thermal-electrical analysis,” Section 6.7.3) approximates the Jacobian by eliminating +interfield coupling terms and can save substantial computational cost in cases where there is relatively +weak coupling between the fields. +Input File Usage: +Abaqus/CAE Usage: +*SOLUTION TECHNIQUE, TYPE=SEPARATED +Step module: step editor: Other: Solution technique: Separated +Field equations +Field equations can be modeled separately or fully coupled. Some fields in Abaqus/Standard can only +have linear response. Each field is discretized by using basic nodal variables (the degrees of freedom at +the nodes of the finite element model) such as the components of the displacement in a continuum stress +analysis problem. Each field has a conjugate “flux.” +Available fields and their conjugate fluxes +The fields and conjugate fluxes available in Abaqus/Standard are as follows: +Basic problem +Stress analysis: +Force equilibrium +Structural stress analysis: +Moment equilibrium +Field +Conjugate flux +Displacement, +; +Force, +; +Warping, w +Rotation, +Bimoment, W +Moment, +Heat transfer analysis +Temperature, +Heat flux, q +Acoustic analysis (linear only) +Acoustic pressure, u +Rate of change of fluid +volumetric flux +Pore liquid flow analysis +Pore liquid pressure, u +Pore liquid volumetric flux, q +Hydrostatic fluid modeling +Fluid pressure, p +Fluid volume, V +Mass diffusion analysis +Normalized +concentration, +Mass concentration volumetric +flux, Q +Piezoelectric analysis +Electrical potential, +Electrical charge, q +Electric conduction analysis +Electrical potential, +Electrical current, J +Mechanism analysis (connector +elements with material flow degree of +freedom) +Analysis containing C3D4H +elements (all materials, except +compressible hyperelastic elastomers +and elastomeric foams). +Analysis containing C3D4H elements +with compressible hyperelastic or +hyperfoam materials. +Material flow +Material flux +Pressure Lagrange +multiplier +Volumetric flux +Volumetric Lagrange +multiplier +Pressure flux +Constraint equations +In some cases the problem also involves constraint equations. +constraints are included by using Lagrange multipliers: +In Abaqus/Standard the following +Problem +Constraint variable +Constraint +Hybrid solid (except C3D4H +elements) +Hybrid beam +Hybrid beam +Distributing coupling +Distributing coupling +Contact +Pressure stress +Volumetric strain compatibility +Axial force +Axial strain compatibility +Transverse shear force +Transverse shear strain compatibility +Force +Moment +Coupling displacement compatibility +Coupling rotation compatibility +Normal pressure +Surface penetration +Contact with Lagrange friction +Shear stress +Relative shear sliding +If the penalty method is used, the contact Lagrange multipliers may not be present. +Solving coupled field equations +In a general problem several (possibly nonlinear) coupled field equations of types +be solved and several different (possibly nonlinear) constraints of type +simultaneously. For example, in a structural problem in which hybrid beam elements are used, +might represent the displacement field and the equilibrium equations for the conjugate force and +might represent the rotation field and the equilibrium equations for the conjugate moment, while +represents axial strain compatibility and +represents transverse shear strain compatibility. +must +must be satisfied +Controlling the accuracy of the solution +The default solution control parameters defined in Abaqus/Standard are designed to provide reasonably +optimal solution of complex problems involving combinations of nonlinearities as well as efficient +solution of simpler nonlinear cases. However, the most important consideration in the choice of the +control parameters is that any solution accepted as “converged” is a close approximation to the exact +solution of the nonlinear equations. In this context “close approximation” is interpreted rather strictly +by engineering standards when the default value is used, as described below. +You can reset many solution control parameters related to the tolerances used for field equations. +If you define less strict convergence criteria, results may be accepted as converged when they are +not sufficiently close to the exact solution of the system. Use caution when resetting solution control +parameters. Lack of convergence is often due to modeling issues, which should be resolved before +changing the accuracy controls. +You can select the type of equation for which the solution control parameters are being defined; for +example, you can redefine the default controls for the displacement field and warping degree of freedom +equilibrium equations only. By default, the solution control parameters will apply to all active fields +in the model. See “Defining tolerances for field equations” in “Commonly used control parameters,” +Section 7.2.2, for details. +Input File Usage: +*CONTROLS, PARAMETERS=FIELD, FIELD=field +, +, +, +, +, +, +, +, +, +Abaqus/CAE Usage: +Step module: Other→General Solution Controls→Edit: toggle +on Specify: Field Equations: Apply to all applicable fields +or Specify individual fields: field +Terminology +Each field, +measures are used in deciding if an increment has converged: +, that is active in the problem is tested for convergence of the field equations. The following +The largest residual in the balance equation for field . +The largest change in a nodal variable of type +The largest correction to any nodal variable of type +iteration. +The largest error in a constraint of type j. +The instantaneous magnitude of the flux for field +at time t, averaged over the entire model +(spatial average flux). This average is by default defined by the fluxes that the elements +apply to their nodes and any externally defined fluxes: +provided by the current Newton +in the increment. +at its +th node at time t, +Here, E is the number of elements in the model, +is the number of degrees of freedom of type +is the number of nodes in element e, +is the +of element e, +at node +magnitude of the total flux component that element e applies at its ith degree of freedom of +type +(depends +is the number of external fluxes for field +on element type, loading type, and number of loads applied to an element), and +is the +magnitude of the ith external flux for field . +An overall time-averaged value of the typical flux for field +the current increment. Normally, +the step in which +iteration of the current increment. +so far during this step including +is defined as +averaged over all the increments in +for the current increment is recalculated after every +is nonzero. The +where +in which +number. The default for +is the total number of increments so far in the step, including the current increment, +is a small +is the value of +. Here +is 10−5, but in rare cases, you can change this default. +at increment i and +Alternatively, you can define a value for the average flux in the step, +. In this case, +throughout the step. +At the start of the step, +is normally the value from the previous step (except for +by default). Alternatively, you can define an initial value for +, as described in “Modifying the initial time average flux” in +retains its initial value until an +is +Step 1, when +the time average flux, +“Commonly used control parameters,” Section 7.2.2. +iteration is completed for which +defined, the value defined for +The time-averaged value of the largest flux corresponding to the field +excluding the current increment. +The largest flux corresponding to the field +during the current iteration. +, at which time we redefine +during this step, +is ignored.) +. (If +Average flux +) is computed from the spatial average of the flux ( +The time-averaged value of the flux ( +) at +various instants in time. In some situations where only a small part of the model is active (the fluxes +over the rest of the model are zero or very small), the spatial average of a flux over the entire model can +be very small when compared to the spatial average over the active part of the model. Over a period +of time this can result in a small value for the time-averaged value of the flux and in turn may lead to +a convergence criterion that is very strict by engineering standards. To avoid such an excessively strict +convergence criterion, Abaqus/Standard uses an algorithm to determine the active parts of a model at +any given instant. +During an iteration any flux +freedom is also marked inactive. +the current step. The default value of +is treated as inactive, and the corresponding degree of +is the time-averaged value of the largest flux in the model during +is 10−5; you can redefine this parameter. +At the end of an iteration the largest flux in the model during the current iteration ( +) is compared +with the time-averaged value of the largest flux ( +, the spatial average is +computed over only the active parts of the model; if +, all inactive parts of the model +are reclassified as active and the spatial average is computed over the entire model. The appropriate +spatial average of the flux obtained in this manner is then used to compute the time-averaged flux +that is used in the convergence criterion. Setting +computed over the entire model. +forces the spatial averages of a flux to be always +If +). +If you specify a value for the average flux in the step, +, +throughout the step. +Residuals +Most nonlinear engineering calculations will be sufficiently accurate if the error in the residuals is less +than %. Therefore, Abaqus/Standard normally uses +as the residual check, where you can define +convergence is accepted if the largest correction to the solution, +largest incremental change in the corresponding solution variable, +(it is 0.005 by default). If this inequality is satisfied, +, is also small compared to the +, +estimated as +CONVERGENCE CRITERIA +satisfies the same criterion: +You can define +; the default value is 10−2. +, and +The superscripts i, +residual in field +parameters,” Section 7.2.2, for more details on specifying +refers to the largest +at the start of the first iteration of the increment. See “Commonly used control +. +refer to the iteration number, and +Zero flux +In some cases there may be zero flux in the equations of type +increments. Zero flux is defined as +10−5 and the solution for field +convergence for field +redefine this parameter. +is accepted when +is accepted if +, where, as discussed earlier, +anywhere in the model during some +has a default value of +, and +is 10−3 ; you can +. If not, +. The default value of +is compared to +Negligible response in some fields +Cases may arise where more than one field is active in the model yet there is negligible response in some +of the fields in some increments. If some type of physical conversion factor, +, exists between active +for those particular increments +fields +) to be used realistically as part of the convergence +where +criteria for field . An example of +is a characteristic length to convert between force and moment. +in the above paragraph can be replaced by +is deemed too small ( +and , +Here, +is a factor calculated by Abaqus/Standard based on the problem definition and the fields +involved and +is 1.0. Currently, +this concept is used only for converting between the fields associated with forces and moments, when +is a field conversion ratio that you can define. The default value for +represents a characteristic element length. +Linear increments +Linear cases do not require more than one equilibrium iteration per increment. If +for all +, the increment is considered to be linear. +You can define +is 10−8 . Any case that +passes such a stringent comparison of the largest residual with the average flux magnitude in each field is +; it is intended to be very small. The default value of +considered linear and does not require further iteration. If this requirement is satisfied at some iteration +after the first, the solution is accepted without any check on the size of the correction to the solution. +Nonquadratic convergence +In some cases quadratic convergence of the iterations is not possible because the Jacobian of the Newton +scheme is approximated. If after +iterations the convergence rate is only linear, Abaqus/Standard uses +a looser tolerance, +as the residual check. This tolerance modification is not applied when the quasi-Newton method is used, +since it is normal for this method to require a larger number of iterations to converge. +You can define +“Controlling iteration”). +, which is 2 × 10−2 by default. You can also define +(by default, +; see +Convergence also requires that +Iteration continues until both criteria are satisfied for all active fields or the increment is abandoned. +When the active field is the displacement, +the convergence criterion requiring the largest +displacement correction to be small relative to the maximum displacement increment ( +) is ignored when the maximum displacement increment itself is very small, as defined by +is 10−8; you +is the characteristic element length. The default value for +, where +can redefine this parameter. +Controlling iteration +Each increment of a nonlinear solution will usually be solved by multiple equilibrium iterations. The +number of iterations may become excessive, in which case the increment size should be reduced +and the increment attempted again. On the other hand, if successive increments are solved with a +minimum number of iterations, the increment size may be increased. You can specify a number of time +incrementation control parameters; some of them are described in this section, while the remainder are +described in “Time integration accuracy in transient problems,” Section 7.2.4. +Input File Usage: +*CONTROLS, PARAMETERS=TIME INCREMENTATION +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +, +Abaqus/CAE Usage: +Step module: Other→General Solution Controls→Edit: toggle on +Specify: Time Incrementation; click More to see additional data tables +CONVERGENCE CRITERIA +Abaqus/Standard may have trouble with the element calculations because of excessive distortion in large- +displacement problems or because of very large plastic strain increments. If this occurs and automatic +time incrementation has been chosen, the increment will be attempted again with a time increment of +. If fixed time +times the current time increment, where you can define +. By default, +stepping has been chosen, the analysis will terminate with an error message. +Reattempting a diverging increment +Sometimes the increment is too large for the solution to converge at all—the initial state is outside the +“radius of convergence” of the Newton method. This condition can be detected by observing the behavior +of the largest residuals, +. In some cases these will not decrease from iteration to iteration throughout +an iteration sequence that leads to convergence, but we assume that, if they fail to decrease over two +consecutive iterations, the iterations should be abandoned. Thus, if +where i is the iteration counter, the iterations are abandoned. This check is first made after +following a solution discontinuity. You can define +If fixed time stepping has been chosen, the analysis will terminate with an error message. +With automatic time stepping the increment is begun again, using a time increment of +times the +previous attempt, where you can define +. This subdivision continues until a +successful time increment is found or the minimum time increment allowed has failed, in which case the +job ends with an error message. Using the line search algorithm with +sometimes helps in such +cases . +; it must be at least 3. The default value of +iterations +is 4. +. By default, +Reattempting an increment when too many equilibrium iterations are required +In case quadratic convergence cannot be obtained, the logarithmic rate of convergence, +will often be maintained throughout the iteration process. This rate can be established during the +early iterations. If convergence has not been achieved after +or more iterations following a solution +discontinuity, if automatic time incrementation has been selected, and if the slowest convergence rate +over all fields +total iterations subsequent to the last solution discontinuity +are expected to be required, the increment is begun again with a time increment of +times the +If fixed time incrementation has been chosen, the iterations are continued; but if +one abandoned. +convergence is not achieved within +iterations after the last solution discontinuity in the increment, +the analysis will terminate with an error message. +suggests that more than +You can define the values of +, +, and +. By default, +, +, and +=0.5. +Increasing or reducing the size of the time increment for efficiency +When automatic time incrementation is chosen, the effectiveness of the nonlinear equation solution is +used in the selection of the next time increment (in addition to the time integration accuracy criteria +discussed in “Time integration accuracy in transient problems,” Section 7.2.4). +iterations are required in two consecutive increments, the time increment may be increased by a factor +of +iterations, the next time increment is reduced +to +. By default, +. If an increment converges but takes more than +times the current time increment. You can define the values of +, +If no more than +, and +, and +, +, +. +, +Extrapolation +At each increment after the first increment of a nonlinear analysis step Abaqus/Standard estimates the +solution to the increment by extrapolating the solution from the previous increment (or increments). By +default, 100% linear extrapolation is used (1% for the Riks method). Extrapolation is abandoned if +where +define the value of +; it is 0.1 by default. +is the proposed new time increment, and +is the last successful time increment. You can +You can turn this extrapolation scheme off for a particular step—see “Defining an analysis,” +Section 6.1.2. +Convergence of strain constraints in hybrid elements +, with an absolute tolerance for the corresponding error, +Strain constraint convergence in “hybrid” elements is checked by comparing the largest error in each +strain constraint, +. The magnitudes of these +errors are reported in the message (.msg) file after each iteration as “compatibility errors.” For example, +the volumetric compatibility error is a measure of the accuracy with which the incompressibility +constraint is satisfied. Since nonlinearity in constraint equations is generally reflected in the field +equations in the same problem, no attempt is made to estimate convergence rates in these constraint +equations: we assume that the measures of convergence rate in the field equations are sufficient. +You can define the +Input File Usage: +, +( +). By default, all of the +*CONTROLS, PARAMETERS=CONSTRAINTS +, and += 10−5. +, +, +Abaqus/CAE Usage: +Step module: Other→General Solution Controls→Edit: toggle +on Specify: Constraint Equations +Severe discontinuity iterations +Abaqus/Standard distinguishes between regular, equilibrium iterations (in which the solution varies +smoothly) and severe discontinuity iterations (SDIs) in which abrupt changes in stiffness occur. By +default, Abaqus/Standard will continue to iterate until the severe discontinuities are sufficiently small (or +no severe discontinuities occur) and the equilibrium (flux) tolerances are satisfied. For more information +on the criteria used for the severe discontinuity checks, see “Severe discontinuities in Abaqus/Standard” +in “Defining an analysis,” Section 6.1.2. Alternatively, Abaqus/Standard will continue to iterate until +no severe discontinuities occur and the equilibrium (flux) tolerances are satisfied. This more traditional +method can cause convergence difficulties if the contact conditions are only weakly determined and +contact “chattering” occurs or if a large number of severe discontinuity iterations are required to settle +the contact conditions. +You can define the contact and slip compatibility tolerance, the soft contact compatibility tolerance +for low pressure, and the contact force error tolerance. +Input File Usage: +*CONTROLS, PARAMETERS=CONSTRAINTS +, , , +, , , +, +Abaqus/CAE Usage: +Step module: Other→General Solution Controls→Edit: toggle +on Specify: Constraint Equations +Defining the contact force error tolerance is not supported in Abaqus/CAE. +Severe discontinuity iterations in implicit dynamic analysis +In implicit dynamic analysis, the average time of all contact changes in the increment is estimated and +the time incrementation is interrupted to solve impact equations at that time. With augmented Lagrange +or penalty constraint enforcement methods or with softened contact, no contact constraints are imposed +when impact equations are solved. However, if the contact constraints are not satisfied within given +tolerances, a severe discontinuity iteration is forced. See “Intermittent contact/impact,” Section 2.4.2 of +the Abaqus Theory Manual, for details on intermittent contact in dynamic problems. +Controlling the number of severe discontinuity iterations +By default, Abaqus applies sophisticated criteria involving changes in penetration, changes in the residual +force, and the number of severe discontinuities from one iteration to the next to determine whether +iteration should be continued or terminated. Hence, it is in principle not necessary to limit the number of +severe discontinuity iterations. This makes it possible to run contact problems that require large numbers +of contact changes without having to change the control parameters. It is still possible to set a limit, +, +for the maximum number of severe discontinuity iterations; by default, +, which in practice should +always be more than the actual number of iterations in an increment. +Input File Usage: +*CONTROLS, PARAMETERS=TIME INCREMENTATION +, , , , , , , , , , +Abaqus/CAE Usage: +Step module: Other→General Solution Controls→Edit: toggle on +Specify: Time Incrementation; click More to see additional data tables +Controlling the number of severe discontinuity iterations when severe discontinuities always +force iterations +In this case a limit, +an increment. +If more than +started over with a time increment size of +, is placed on the number of iterations caused by severe discontinuities in +iterations are required for severe discontinuities, the increment is +times the abandoned increment size (for automatic +time incrementation). If fixed time incrementation was chosen, the analysis terminates with an error +message. You can define the values of +. +and +. By default, +*CONTROLS, PARAMETERS=TIME INCREMENTATION +, , , , , , +, , , , +and +Input File Usage: +Abaqus/CAE Usage: +Step module: Other→General Solution Controls→Edit: toggle on +Specify: Time Incrementation; click More to see additional data tables +Improving the efficiency of the solution by using the line search algorithm +Abaqus/Standard provides the option of including a “line search” algorithm. The purpose of the line +search is to improve the robustness of the Newton or quasi-Newton methods. By default, the line search +is active only for steps that use the quasi-Newton method. During equilibrium iterations where residuals +are large, the line search algorithm scales the correction to the solution by a line search scale factor, +. +An iterative process is used to find the value of +that minimizes the component of the residual vector +in the direction of the correction vector; this component is called +, where j is the line search iteration +number. Each line search iteration requires one pass through the Abaqus/Standard element loop but does +not require any operations using the global stiffness matrix. +It is usually sufficient to determine +limit this accuracy. A maximum of +allowable range of +: +The line search ceases when +only to modest accuracy. There are several controls used to +line search iterations are performed. There is a limit on the +where +line search ceases, +cease when the change in +is evaluated before the first equilibrium iteration. The residual reduction factor at which the +, is typically set to a rather loose tolerance. The line search algorithm will also +provided by a line search iteration is less than +, +, and +, +times +. += 1.0, +You can define the values of +, +=5 with the quasi-Newton method. Set +. By default, += 0 with the Newton +method, and +to a nonzero value to activate the line +search algorithm or to zero to forcibly deactivate line search. Default values for the additional line search +parameters are += 0.10. These defaults are chosen to +achieve modest accuracy for the line search scale factor, while minimizing the additional cost of line +search iterations. More agressive line searching can be beneficial in some simulations, especially when +many nonlinear iterations and/or cutbacks are needed to resolve sharp discontinuities in the solution. In +these cases you could try allowing more line search iterations ( +=10) and requiring more accuracy in +the line search scale factor ( +=0.01). This may result in more line search iterations but fewer nonlinear +iterations and cutbacks and an overall reduction in solution cost. += 0.25, and += 0.0001, +Input File Usage: +*CONTROLS, PARAMETERS=LINE SEARCH +, +, +, +, +Abaqus/CAE Usage: +Step module: Other→General Solution Controls→Edit: toggle +on Specify: Line Search Control +TIME INTEGRATION ACCURACY IN TRANSIENT PROBLEMS +TIME INTEGRATION ACCURACY +Products: Abaqus/Standard Abaqus/CAE +References +• “Convergence and time integration criteria: overview,” Section 7.2.1 +• “Implicit dynamic analysis using direct integration,” Section 6.3.2 +• “Uncoupled heat transfer analysis,” Section 6.5.2 +• “Coupled pore fluid diffusion and stress analysis,” Section 6.8.1 +• “Rate-dependent plasticity: creep and swelling,” Section 23.2.4 +• *CONTROLS +• “Customizing general solution controls,” Section 14.15.1 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +Abaqus/Standard usually uses automatic time stepping schemes for the solution of transient problems. +Factors influencing the increment size for transient problems include convergence aspects related to the +degree of geometric, material, and contact nonlinearity (which also influence non-transient problems and +are discussed in “Convergence criteria for nonlinear problems,” Section 7.2.3) and the ability of the time +integration operator to accurately resolve variations in the accelerations, velocities, and displacements +over an increment. This section discusses tolerance parameters and adjustments to the time increment +size related to the latter aspect. +Time incrementation parameters and adjustment criteria +Table 7.2.4–1 lists tolerance parameters available for specific analysis procedures. Descriptions of time +integrators for the transient procedure types and, in the case of implicit dynamics, discussion of additional +factors influencing the time increment size related to accuracy of time integration are provided in the +respective sections referenced in Table 7.2.4–1. +Table 7.2.4–1 Time integration accuracy measures for various procedures. +Procedure +Accuracy measure +Tolerance +Implicit dynamics (“Implicit +dynamic analysis using direct +integration,” Section 6.3.2) +Half-increment residual +Half-increment residual tolerance +Transient heat transfer analysis +(“Uncoupled heat transfer +analysis,” Section 6.5.2) +Consolidation analysis (“Coupled +pore fluid diffusion and stress +analysis,” Section 6.8.1) +Creep and viscoelastic material +behavior (“Rate-dependent +plasticity: creep and swelling,” +Section 23.2.4) +Temperature increment, +Pore pressure increment, +Creep tolerance +, will be active. Corresponding measures of the integration accuracy, +In any transient analysis where automatic time incrementation is used, some of these tolerances, +, +, will be calculated +for each increment in the step. Abaqus/Standard will use these values to adjust the time incrementation +using the criteria described in this section. The smallest time increment required by all criteria is used if +more than one accuracy measure is active. +Reducing the time increment size +for any control, J, that is active in the step, the time increment +If +is too large to satisfy that +time integration accuracy requirement. The increment is, therefore, begun again with a time increment +of +where you can define the value of +. By default, += 0.85. +Input File Usage: +Abaqus/CAE Usage: +*CONTROLS, PARAMETERS=TIME INCREMENTATION +first data line +, , , +Step module: Other→General Solution Controls→Edit: toggle on +Specify: Time Incrementation; click More to see additional data tables +Increasing the time increment size +If at the current time increment, +, +for all J in each of +because of nonlinearity, the next time increment will be increased to +consecutive increments, i, and if no cut-back has occurred within those increments += 3, += 0.75, and += 0.8. +is +You can define the values of +the proposed new time increment, which is defined as +, and +. By default, +, +for transient heat transfer and transient mass diffusion problems and which is defined as +for other transient problems. +A limit, +, is placed on the time increment increase factor. The default value of +depends on +the type of analysis: +• +• +• += 1.25 for dynamic analysis += 2.0 for diffusion-dominated processes: creep, transient heat transfer, coupled temperature- +displacement, soils consolidation, and transient mass diffusion += 1.5 for all other cases +You can redefine +for each analysis type. +If the problem is nonlinear, the time increment may be restricted by the rate of convergence of the +nonlinear equations. The time incrementation controls used with nonlinear problems are described in +“Convergence criteria for nonlinear problems,” Section 7.2.3. +Input File Usage: +*CONTROLS, PARAMETERS=TIME INCREMENTATION +, , , , , , , , , +, , , , , , , +, +, +, +Abaqus/CAE Usage: +Step module: Other→General Solution Controls→Edit: toggle on +Specify: Time Incrementation; click More to see additional data tables +Avoiding small changes to the time increment size during implicit integration procedures +In linear transient problems when Abaqus/Standard uses implicit integration, the system of equations +must be reformed and decomposed whenever the time increment changes even though the stiffness matrix +does not change. Therefore, to reduce the number of increments at which the system matrix changes, +Abaqus/Standard makes use of the factor +, where +The definition of +increments: +results in the following inequality between the proposed and the current time +Based on this inequality the time increment is allowed to increase only when its value computed by the +criteria described earlier in this section, or computed using the value of PNEWDT specified in certain user +subroutines (UMAT, for example), is greater than or equal to +is 1.0, +but you can redefine it to be a smaller number. Reducing +to a value less than 1.0 allows the time +increment to increase by a factor that is smaller than +, thereby forcing a time increment change, even +if the change is small. Otherwise, the solution continues with the same +. The default value of +. +Input File Usage: +Abaqus/CAE Usage: +*CONTROLS, PARAMETERS=TIME INCREMENTATION +first data line +second data line +, , , , +Step module: Other→General Solution Controls→Edit: toggle on +Specify: Time Incrementation; click More to see additional data tables +• Chapter 8, “Analysis Techniques: Introduction” +• Chapter 9, “Analysis Continuation Techniques” +• Chapter 10, “Modeling Abstractions” +• Chapter 11, “Special-Purpose Techniques” +• Chapter 12, “Adaptivity Techniques” +• Chapter 13, “Optimization Techniques” +• Chapter 14, “Eulerian Analysis” +• Chapter 15, “Particle Methods” +• Chapter 16, “Sequentially Coupled Multiphysics Analyses” +• Chapter 17, “Co-simulation” +• Chapter 18, “Extending Abaqus Analysis Functionality” +• Chapter 19, “Design Sensitivity Analysis” +8. +Analysis Techniques: Introduction +Introduction +8.1 +Introduction +• “Analysis techniques: overview,” Section 8.1.1 +8.1.1 +ANALYSIS TECHNIQUES: OVERVIEW +Abaqus provides an extensive selection of analysis techniques. These techniques provide powerful tools for +performing your analysis more efficiently and effectively. +Analysis continuation techniques +In many cases your analysis results represent a significant investment of computational effort. As a result, +you will often want to reduce computation costs by utilizing results from an analysis that has already been +performed. In other cases your overall analysis history will be comprised of distinct Abaqus jobs, each +representing a portion of the response history of the model. Abaqus provides the following analysis +continuation techniques: +• Abaqus allows you to restart an analysis, as long as you request that certain files containing model +and state data be saved in the original analysis. See “Restarting an analysis,” Section 9.1.1. +• You can perform part of an analysis with Abaqus/Standard or Abaqus/Explicit and continue the +analysis with the other product. You can transfer results from Abaqus/Standard to Abaqus/Explicit, +from Abaqus/Explicit to Abaqus/Standard, and from Abaqus/Standard to Abaqus/Standard. See +“Transferring results between Abaqus analyses: overview,” Section 9.2.1. +Modeling abstractions +All Abaqus models involve certain abstractions. In addition to the traditional abstractions associated +with the finite element method, you can include techniques in your model to obtain more cost-effective +solutions. Abaqus provides the following techniques for modeling abstractions: +• You can create substructures by grouping a number of elements together and retaining only the +degrees of freedom needed to interface with adjacent structures. This technique is particularly +useful when a substructure is to be reused in the same analysis, in different analyses, or by different +analysts. See “Using substructures,” Section 10.1.1. +• You can analyze local regions of a model in greater detail and interpolate the solution results from +a larger coarser global model. See “Submodeling: overview,” Section 10.2.1. +• You can allow for the mathematical abstraction of model data such as mesh and material +information by generating global or element matrices representing the stiffness, mass, viscous +See “Generating matrices,” +damping, structural damping, and load vectors in a model. +Section 10.3.1. +• You can create a three-dimensional model in Abaqus/Standard by revolving various forms of +axisymmetric and three-dimensional model sectors about an axis of symmetry . You can also transfer the solution obtained in an original +axisymmetric model to the new model . In addition, for models +that exhibit cyclic symmetry you can extract eigenmodes and perform mode-based steady-state +dynamic analysis by modeling only a single repetitive sector of the model . +• Using the periodic media analysis technique, you can effectively model systems that are repetitive in +nature, such as manufacturing processes involving conveyor belts or continuous forming operations. +See “Periodic media analysis,” Section 10.5.1. +• You can define a complex beam cross-section, +including multiple materials and complex +geometry, and automatically generate beam element cross-section properties. See “Meshed beam +cross-sections,” Section 10.6.1. +• Using the extended finite element method, you can model discontinuities, such as cracks, as an +enriched feature without creating a mesh to match the geometry of the discontinuity. See “Modeling +discontinuities as an enriched feature using the extended finite element method,” Section 10.7.1. +Special-purpose techniques +Certain analysis techniques do not fall into a general classification and are grouped here as special- +purpose techniques. Abaqus provides the following special-purpose techniques: +• You can use the inertia relief technique as an inexpensive alternative to performing a full dynamic +analysis on a free or partially constrained body subjected to loads derived from rigid body +accelerations. See “Inertia relief,” Section 11.1.1. +• You can selectively remove, and later reintroduce, parts of a model. See “Element and contact pair +removal and reactivation,” Section 11.2.1. +• You can introduce small imperfections into a model, typically for postbuckling analysis. See +“Introducing a geometric imperfection into a model,” Section 11.3.1. +• You can evaluate fracture performance through contour integral evaluation, +through crack +propagation modeling techniques, or by using line spring elements in conjunction with shell +elements. See “Fracture mechanics: overview,” Section 11.4.1. +• You can model coupling between the deformation of a fluid-filled structure and the pressure exerted +by a contained fluid . +• In Abaqus/Explicit you can use the mass scaling technique to control the stable time increment and +increase computational efficiency. See “Mass scaling,” Section 11.6.1. +• You can use selective subcycling to allow different time increments to be used for different groups +of elements, which can reduce the run time for an analysis when a small region of elements in the +model controls the stable time increment. See “Selective subcycling,” Section 11.7.1. +• You can use steady-state detection to detect the time in a quasi-static uni-directional Abaqus/Explicit +simulation when a steady-state condition has been reached and then terminate the simulation. See +“Steady-state detection,” Section 11.8.1. +Adaptivity techniques +Adaptivity techniques enable modification of your mesh to obtain a better solution. Abaqus provides the +following adaptivity techniques: +• You can use ALE adaptive meshing to control mesh distortion or to model material loss. See “ALE +adaptive meshing: overview,” Section 12.2.1. +• You can use adaptive remeshing with Abaqus/Standard and Abaqus/CAE to iteratively improve +your mesh to obtain a more accurate solution. See “Adaptive remeshing: overview,” Section 12.3.1. +• You can use mesh-to-mesh solution mapping as part of a mesh replacement strategy for distortion +control. See “Mesh-to-mesh solution mapping,” Section 12.4.1. +See “Adaptivity techniques,” Section 12.1.1, for a comparison of the adaptivity methods. +Optimization techniques +You can use structural optimization, an iterative process that helps you refine your designs, +to +perform topology and shape optimization. In Abaqus/CAE you create the model to be optimized and +define, configure, and execute the structural optimization. See “Structural optimization: overview,” +Section 13.1.1. +Eulerian analysis +You can use Abaqus/Explicit to simulate extreme deformation, up to and including fluid flow, in an +Eulerian analysis. Eulerian materials can be coupled to Lagrangian structures to analyze fluid-structure +interactions. See “Eulerian analysis,” Section 14.1.1. +Particle methods +Using the smoothed particle hydrodynamics technique, you can model violent free-surface fluid flow +(such as wave impact) and extremely high deformation/obliteration of solid structures (such as ballistics). +See “Smoothed particle hydrodynamic analysis,” Section 15.1.1. +Sequentially coupled multiphysics analyses +In Abaqus/Standard you can perform sequentially coupled multiphysics analyses when the coupling +between one or more of the physical fields in a model is only important in one direction. See “Sequentially +coupled multiphysics analyses,” Section 16.1. +Co-simulation +You can use the co-simulation technique for run-time coupling of two Abaqus analyses or of Abaqus +with third-party analysis programs to perform multiphysics simulation. See “Co-simulation: overview,” +Section 17.1.1. +Extending Abaqus analysis functionality +You can use the flexibility of user subroutines to increase the functionality of Abaqus. See “User +subroutines and utilities,” Section 18.1. +Design sensitivity analysis +You can use design sensitivity analysis (DSA) techniques to determine sensitivities of responses +with respect to specified design parameters. You can use these techniques for design studies within +Abaqus/Standard or in conjunction with third-party design optimization tools. See “Design sensitivity +analysis,” Section 19.1.1. +Parametric studies +You can use parametric studies to perform multiple analyses in which you can systematically +vary modeling parameters that you define. See “Scripting parametric studies,” Section 20.1.1, and +“Parametric studies: commands,” Section 20.2. +Availability of analysis techniques +The availability of the analysis techniques provided in Abaqus is summarized in Table 8.1.1–1. +In +addition, optimization techniques are available in Abaqus/CAE . +Table 8.1.1–1 Availability of analysis techniques in Abaqus. +Technique +Abaqus/Standard Abaqus/Explicit Abaqus/CFD +“Restarting an analysis,” Section 9.1 +“Importing and transferring results,” +Section 9.2 +“Substructuring,” Section 10.1 +“Submodeling,” Section 10.2 +“Generating global matrices,” Section 10.3 +“Symmetric model generation, results +transfer, and analysis of cyclic symmetry +models,” Section 10.4 +“Periodic media analysis,” Section 10.5 +“Meshed beam cross-sections,” +Section 10.6 +“Modeling discontinuities as an enriched +feature using the extended finite element +method,” Section 10.7 +“Inertia relief,” Section 11.1 +Abaqus/Standard Abaqus/Explicit Abaqus/CFD +ANALYSIS TECHNIQUES OVERVIEW +“Mesh modification or replacement,” +Section 11.2 +“Geometric imperfections,” Section 11.3 +“Fracture mechanics,” Section 11.4 +“Surface-based fluid modeling,” +Section 11.5 +“Mass scaling,” Section 11.6 +“Selective subcycling,” Section 11.7 +“Steady-state detection,” Section 11.8 +“ALE adaptive meshing,” Section 12.2 +“Adaptive remeshing,” Section 12.3 +“Analysis continuation after mesh +replacement,” Section 12.4 +“Eulerian analysis,” Section 14.1 +“Smoothed particle hydrodynamic +analyses,” Section 15.1 +“Sequentially coupled multiphysics +analyses,” Section 16.1 +“Co-simulation,” Section 17.1 +“User subroutines and utilities,” +Section 18.1 +“Design sensitivity analysis,” Section 19.1 +“Scripting parametric studies,” +Section 20.1 +9. +Analysis Continuation Techniques +Restarting an analysis +Importing and transferring results +9.1 +9.1 +Restarting an analysis +• “Restarting an analysis,” Section 9.1.1 +9.1.1 +RESTARTING AN ANALYSIS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD Abaqus/CAE +References +• “Output,” Section 4.1.1 +• *RESTART +• “Restarting an analysis,” Section 19.6 of the Abaqus/CAE User’s Manual +Overview +When you run an analysis, you can write the model definition and state to the files required for restart. +Scenarios for using the restart capability include: +• Continuing an interrupted run: +If an analysis is interrupted by a computer malfunction, the +Abaqus restart analysis capability allows the analysis to complete as originally defined. +• Continuing with additional steps: After viewing results from a successful analysis, you may +decide to append steps to the load history. +• Changing an analysis: Sometimes, having viewed the results of the previous analysis, you may +want to restart the analysis from an intermediate point and change the remaining load history data in +some manner. In addition, you may want to add additional steps to the load history if the previous +analysis completed successfully. +“Output,” Section 4.1.1, describes the process of obtaining results output from an Abaqus/Standard +restart file. +Writing restart files +If you want to be able to restart an analysis, you must request restart output. This output will be written +to files that can be used to restart the analysis. If you do not request that restart data be written, restart +files will not be created in Abaqus/Standard, while in Abaqus/Explicit and Abaqus/CFD a state file will +be created with results at only the beginning and end of each step. +In Abaqus/Standard these files are the restart (job-name.res; file size limited to 16 gigabytes), +analysis database (.mdl and .stt), part (.prt), output database (.odb), and linear dynamics and +substructure database (.sim) files. In Abaqus/Explicit these files are the restart (job-name.res; file +size limited to 16 gigabytes), analysis database (.abq, .mdl, .pac, and .stt), part (.prt), selected +results (.sel), and output database (.odb) files. In Abaqus/CFD these files are the restart and analysis +database (job-name.sim) and output database (.odb) files. These files, collectively referred to as the +restart files, allow an analysis to be completed up to a certain point in a particular run and restarted and +continued in a subsequent run. The output database file only needs to contain the model data; results +data are not required and can be suppressed. +You can control the amount of data written to the restart files, as described below. The amount of +data written to the restart file can be changed from step to step if you include the restart request in each +step definition. +Restart information is not written during the following linear perturbation steps: +• “Static stress analysis,” Section 6.2.2 (perturbation) +• “Eigenvalue buckling prediction,” Section 6.2.3 +• “Direct-solution steady-state dynamic analysis,” Section 6.3.4 +• “Complex eigenvalue extraction,” Section 6.3.6 +• “Transient modal dynamic analysis,” Section 6.3.7 +• “Mode-based steady-state dynamic analysis,” Section 6.3.8 +• “Subspace-based steady-state dynamic analysis,” Section 6.3.9 +• “Response spectrum analysis,” Section 6.3.10 +• “Random response analysis,” Section 6.3.11 +• “Eddy current analysis,” Section 6.7.5 +Input File Usage: +Use the following option to request that restart data be written for an analysis: +*RESTART, WRITE +The *RESTART, WRITE option can be used as either model data or history +data. +Abaqus/CAE Usage: +Step module: Output→Restart Requests +In Abaqus/CAE restart requests are always associated with a particular step; +you cannot define a restart request for the entire analysis. Restart requests +are created by default for every step; restart requests for Abaqus/Standard and +Abaqus/CFD steps have a default frequency of 0, while restart requests for +Abaqus/Explicit steps have a default number of intervals of 1. +Controlling the frequency of output to the restart files +You can specify the frequency at which data will be written to the Abaqus/Standard restart file and +the Abaqus/Explicit and Abaqus/CFD state files. The variables to be written cannot be specified; a +complete set of data is written each time. Therefore, the restart files can be quite large unless you +control the frequency with which restart information is written. If restart information is requested for an +Abaqus/Standard analysis at exact time intervals, Abaqus/Standard will obtain a solution each time data +are written. In this case if the frequency of output to the restart file is high, the number of increments +and, consequently, the computational cost of the analysis may increase considerably. +Specifying the frequency of output to the Abaqus/Standard restart file in increments +By default, Abaqus/Standard will write data to the restart file after each increment at which the increment +number is exactly divisible by a user-specified frequency value, N, and at the end of each step of the +analysis (regardless of the increment number at that time). +In a direct cyclic or a low-cycle fatigue +analysis Abaqus/Standard will write data to the restart file only at the end of a loading cycle; therefore, +Abaqus/Standard will write data to the restart file after each iteration (or cycle in a low-cycle fatigue +analysis) at which the iteration number (or cycle number in a low-cycle fatigue analysis) is exactly +divisible by N and at the end of each step of the analysis. +Input File Usage: +Abaqus/CAE Usage: +*RESTART, WRITE, FREQUENCY=N +By default, N=1. +Step module: Output→Restart Requests: enter N in the +Frequency column for each step +By default, N=0 (no restart information is written). +Specifying the frequency of output to the Abaqus/Standard restart file in time intervals +Abaqus/Standard can divide the step into a user-specified number of time intervals, n, and write the +results at the end of each interval, for a total of n points for the step. If n is specified, by default data +will be written to the results file at the exact times calculated by dividing the step into n equal intervals. +Alternatively, you can choose to write the information at the increment ending immediately after the time +dictated by each interval. +You can specify the frequency of restart output in time intervals only for the procedures listed in +Table 9.1.1–1. In addition, this capability is not supported for linear perturbation analyses. +Input File Usage: +Use the following option to request results at the exact time intervals: +*RESTART, WRITE, NUMBER INTERVAL=n, TIME MARKS=YES +Use the following option to request +immediately after each time interval: +results at +the increments ending +Abaqus/CAE Usage: +*RESTART, WRITE, NUMBER INTERVAL=n, TIME MARKS=NO +Step module: Output→Restart Requests: enter n in the Intervals +column; toggle on the Time Marks column for each step if you want +the results written at the exact time intervals +Table 9.1.1–1 List of Abaqus/Standard procedures that support restart at time intervals. +Procedure +Time +incrementation +Restart at +exact time +intervals +Restart at +approximate +time intervals +“Static stress analysis,” Section 6.2.2 +(except if the Riks method is used) +“Implicit dynamic analysis using direct +integration,” Section 6.3.2 +Automatic +Fixed +Automatic +Fixed +9.1.1–3 +— +Procedure +Time +incrementation +Restart at +exact time +intervals +Restart at +approximate +time intervals +“Uncoupled heat transfer analysis,” +Section 6.5.2 (except if you specify that +the analysis end when steady state is +reached) +“Mass diffusion analysis,” Section 6.9.1 +(except if you specify that the analysis end +when steady state is reached) +“Coupled pore fluid diffusion and stress +analysis,” Section 6.8.1 (except if you +specify that the analysis end when steady +state is reached) +“Fully coupled thermal-stress analysis,” +Section 6.5.3 +“Fully coupled thermal-electrical- +structural analysis,” Section 6.7.4 +“Coupled thermal-electrical analysis,” +Section 6.7.3 (except if you specify that +the analysis end when steady state is +reached) +“Steady-state transport analysis,” +Section 6.4.1 +“Subspace-based steady-state dynamic +analysis,” Section 6.3.9 +“Quasi-static analysis,” Section 6.2.5 +Automatic +Fixed +Automatic +Fixed +Automatic +Fixed +Automatic +Fixed +Automatic +Fixed +Automatic +Fixed +Automatic +Fixed +Fixed +Automatic +Fixed +— +— +— +— +— +— +— +— +— +Time incrementation +If the output frequency is specified in terms of the number of intervals, Abaqus/Standard will adjust the +time increments to ensure that data are written at the exact time points specified. In some cases Abaqus +may use a time increment smaller than the minimum time increment allowed in the step in the increment +directly before a time point. However, Abaqus will not violate the minimum time increment allowed +for consolidation, transient mass diffusion, transient heat transfer, transient couple thermal-electrical, +transient coupled temperature-displacement, and transient coupled thermal-electrical-structural analyses. +For these procedures if a time increment smaller than the minimum time increment is required, Abaqus +will use the minimum time increment allowed in the step and will write restart data at the first increment +after the time point. +When the output frequency is specified in terms of the number of intervals, the number of increments +necessary to complete the analysis might increase, which might adversely affect performance. +Specifying the frequency of output to the Abaqus/Explicit state file +Abaqus/Explicit will divide the step into a user-specified number of time intervals, n, and write the results +at the beginning of the step and at the end of each interval, for a total of n+1 points for the step. By default, +the results will be written to the state file at the increment ending immediately after the time dictated by +each interval. Alternatively, you can choose to write the results at the exact times calculated by dividing +the step into n equal intervals. Results are always written at the end of the step, so it is not necessary to +request results at the exact time intervals if results are required only at the end of a step. +If a problem precludes the analysis from continuing to completion, such as if an element becomes +excessively distorted, Abaqus/Explicit will attempt to save the last completed increment in the state file. +Input File Usage: +Use the following option to request +immediately after each time interval: +results at +the increments ending +*RESTART, WRITE, NUMBER INTERVAL=n, TIME MARKS=NO +Use the following option to request results at the exact time intervals: +*RESTART, WRITE, NUMBER INTERVAL=n, TIME MARKS=YES +By default, n=1. +Abaqus/CAE Usage: +Step module: Output→Restart Requests: enter n in the Intervals +column; toggle on the Time Marks column for each step if you want +the results written at the exact time intervals +By default, n=1. +Specifying the frequency of output to the Abaqus/CFD state file in increments +Abaqus/CFD will write data to the restart file after each increment at which the increment number is +exactly divisible by a user-specified frequency value, N, and at the end of each step of the analysis +(regardless of the increment number at that time). +Input File Usage: +*RESTART, WRITE, FREQUENCY=N +Abaqus/CAE Usage: +By default, N=1. +Step module: Output→Restart Requests: enter N in the +Frequency column for each step +By default, N=0 (no restart information is written). +Specifying the frequency of output to the Abaqus/CFD state file in time intervals +Abaqus/CFD will divide the step into a user-specified number of time intervals, n, and write the results at +the beginning of the step and at the end of each interval, for a total of n+1 points for the step. By default, +the results will be written to the state file at the increment ending immediately after the time dictated by +each interval. +If a problem precludes the analysis from continuing to completion, such as if the solution does not +converge, Abaqus/CFD will attempt to save the last completed increment in the state file. +Input File Usage: +Abaqus/CAE Usage: +*RESTART, WRITE, NUMBER INTERVAL=n +Step module: Output→Restart Requests: enter n in the Intervals column +By default, n=0. +Synchronizing restart information written in a co-simulation +Restart output must be synchronized between co-simulation analyses for a co-simulation restart to be +successful. To achieve this synchronization, it is recommended that you request that restart data are +written at a specified number of time intervals, n. In this case Abaqus/Standard, Abaqus/Explicit, and +Abaqus/CFD will write restart information at the co-simulation target time immediately after the time +dictated by each interval. If you specify the frequency of output for restart data in increments, it is very +difficult to synchronize the writing of restart information, and the restart analysis may start from two +different time points, possibly leading to an imbalance. +Input File Usage: +Use the following option to synchronize restart information written in a co- +simulation: +*RESTART, WRITE, NUMBER INTERVAL=n +When using the NUMBER INTERVAL parameter for a co-simulation, the +TIME MARKS parameter on the *RESTART option is always set to NO. +Step module: Output→Restart Requests: enter n in the Intervals column +Abaqus/CAE Usage: +Controlling the precision of output to the Abaqus/Explicit state file +By default, Abaqus/Explicit writes to the state file in double precision when the analysis is run in double +precision. Alternatively, you can choose to write data to the state file in single precision if you want +to reduce the size of the state file. This option may cause noisy results between step boundaries or for +the first step of a restart analysis. If Abaqus/Explicit is run in single precision, this control parameter is +ignored and single precision is always used. +Input File Usage: +Abaqus/CAE Usage: +*RESTART, WRITE, SINGLE +Single precision state file output is not supported by Abaqus/CAE. +Overlaying results in the restart files +For an Abaqus/Standard or Abaqus/Explicit analysis, you can specify that only one increment (or one +iteration in the case of a direct cyclic analysis) per step should be retained in the Abaqus/Standard restart +file or Abaqus/Explicit state file, thus minimizing the size of the files. As the data are written, they +overlay the data from the previous increment (or iteration), if any, written for the same step. You can +specify whether or not the data should be overlaid for each step individually. Since in Abaqus/Explicit +the results are written by default only at the end of the step, it is recommended to overlay the data in +conjunction with specifying a number of time intervals at which data are written; in this way the data in +the restart file are advanced as dictated by the number of intervals used. +To protect you from losing data if your system crashes, when Abaqus/Standard writes a frame from +a given increment, it does not strictly overwrite the frame from the last saved increment. Instead, it +always keeps a reserve frame and only frees a given saved frame for overwriting when the next frame +is secured on the file. This reserve frame is not deleted unless the space is required for later increments. +This process produces a bonus frame in the last step of an analysis if overlaying is occurring in that step +and if the analysis completes successfully; users will observe that the penultimate restart frame is also +retained for the last step, even though overlay is being used. +The advantage of overlaying the restart data is that it minimizes the space required to store the restart +files. +Input File Usage: +Abaqus/CAE Usage: +Restarting an analysis +Use the following option in Abaqus/Standard: +*RESTART, WRITE, OVERLAY +Use the following option in Abaqus/Explicit: +*RESTART, WRITE, OVERLAY, NUMBER INTERVAL=n +Step module: Output→Restart Requests: click to check the +Overlay column for each step +You restart (continue) an analysis by specifying that the restart or state, analysis database, and part files +created by the original analysis be read into the new analysis. The restart files must be saved upon +completion of the first job. In Abaqus/Explicit the package (.pac) file and the selected results (.sel) +file are also used for restarting an analysis and must be saved upon completion of the first job. Since +restart files can be very large, sufficient disk space must be provided (in Abaqus/Standard the analysis +input file processor estimates the space that is required for the restart file). +You can specify the point at which the analysis is continued in the new run, as discussed below. +An analysis cannot be restarted from the linear perturbation steps listed in “Writing restart files.” +In addition, if an Abaqus/Standard or Abaqus/Explicit analysis is terminated abruptly by an +operating system command or due to a power failure, it is unlikely that the job can be recovered or +restarted. In this situation, files that are open during the analysis process are not closed properly, which +may result in loss of data and incomplete files. +Input File Usage: +Use the following option to restart an analysis: +*RESTART, READ +When the READ parameter is included, the *RESTART option must appear as +model data. It is normally the first option in the input file after the *HEADING +option. +Abaqus/CAE Usage: +Job module: job editor: toggle on Restart as the Job Type +Identifying the analysis to be restarted +In an Abaqus/Standard restart analysis you must specify the name of the restart file that contains the +specified step and increment, iteration (for a direct cyclic analysis), or cycle (for a low-cycle fatigue +analysis). In an Abaqus/Explicit or an Abaqus/CFD restart analysis you must specify the name of the +state file that contains the specified step and interval. +Abaqus issues an error message if the step and increment, iteration, cycle, or interval number at +which restart is requested do not exist in the specified restart or state file. +Input File Usage: +Enter the following input on the command line: +abaqus job=job-name oldjob=oldjob-name +Abaqus/CAE Usage: +Any module: Model→Edit Attributes→model_name: Restart: toggle +on Read data from job and enter the oldjob-name +Specifying the restart point +You can specify the point (step and increment, iteration, cycle, or interval) in the previous analysis from +which to restart. Truncating a step in the previous analysis when you restart is discussed below. +Specifying the restart point for an Abaqus/Standard analysis (except when restarting from a direct +cyclic or a low-cycle fatigue analysis) +An Abaqus/Standard analysis restarted from any analysis other than a direct cyclic or a low-cycle fatigue +analysis will continue the analysis immediately after the user-specified step and increment. If you do not +specify a step or increment, the analysis will restart at the last available step and increment found in the +restart file. +Input File Usage: +Abaqus/CAE Usage: +*RESTART, READ, STEP=step, INC=increment +Any module: Model→Edit Attributes→model_name: Restart: toggle +on Read data from job, Step name: step, toggle on Restart from +increment, interval, iteration, or cycle, and enter the increment +Specifying the restart point for an Abaqus/Standard analysis restarted from a direct cyclic analysis +An Abaqus/Standard analysis restarted from a previous direct cyclic analysis can be restarted only from +the end of a loading cycle. In this case you should specify the step and iteration number at which the +new analysis will be resumed. +In a direct cyclic analysis that has not reached a stabilized cycle upon restart, you can increase +the number of iterations or Fourier terms, thus allowing continuation of an analysis . +Input File Usage: +Abaqus/CAE Usage: +*RESTART, READ, STEP=step, ITERATION=iteration +Any module: Model→Edit Attributes→model_name: Restart: toggle +on Read data from job, Step name: step, toggle on Restart from +increment, interval, iteration, or cycle, and enter the iteration +Specifying the restart point for an Abaqus/Standard analysis restarted from a low-cycle fatigue analysis +An Abaqus/Standard analysis restarted from a previous low-cycle fatigue analysis can be restarted only +from the end of a loading cycle. In this case you should specify the step and cycle number at which the +new analysis will be resumed. +Input File Usage: +Abaqus/CAE Usage: +*RESTART, READ, STEP=step, CYCLE=cycle +Any module: Model→Edit Attributes→model_name: Restart: toggle +on Read data from job, Step name: step, toggle on Restart from +increment, interval, iteration, or cycle, and enter the cycle +Specifying the restart point for an Abaqus/Explicit analysis +An Abaqus/Explicit restart analysis will continue the analysis immediately after the user-specified step +and interval. You must specify the step from which an Abaqus/Explicit restart analysis will continue. +If you do not specify an interval from which to restart or that the current step should be terminated at a +specified interval, the analysis is restarted from the last interval available in the state file for the specified +step. +Input File Usage: +Abaqus/CAE Usage: +*RESTART, READ, STEP=step, INTERVAL=interval +Any module: Model→Edit Attributes→model_name: Restart: toggle +on Read data from job, Step name: step, toggle on Restart from +increment, interval, iteration, or cycle, and enter the interval +Specifying the restart point for an Abaqus/CFD analysis +An Abaqus/CFD restart analysis will continue the analysis immediately after the user-specified step and +increment. You must specify the step and increment from which an Abaqus/CFD restart analysis will +continue. If you do not specify a step or increment, an error message will be issued. +Input File Usage: +Abaqus/CAE Usage: +*RESTART, READ, STEP=step, INC=increment +Any module: Model→Edit Attributes→model_name: Restart: toggle +on Read data from job, Step name: step, toggle on Restart from +increment, interval, iteration, or cycle, and enter the increment +Continuing an analysis without changes +To continue an analysis without changes, only the steps subsequent to the step at which restart is being +made should be defined in the restart analysis. All other information has been saved to the restart files. +This feature cannot be used for an Abaqus analysis that uses the co-simulation technique and cannot be +used for an Abaqus/CFD analysis. +Continuing an Abaqus/Standard analysis without changes +In Abaqus/Standard, in cases where restart is being performed simply to continue a long step (which +might have been terminated because the time limit for the job was exceeded, for example), the data for +the restart run may simply consist of the request to read restart data from another analysis. +Input File Usage: +Abaqus/CAE Usage: +*RESTART, READ +Any module: Model→Edit Attributes→model_name: Restart: +toggle on Read data from job +Continuing an Abaqus/Explicit analysis without changes +In Abaqus/Explicit, in cases where restart is being performed simply to continue a long step (which might +have been terminated because a CPU time limit was exceeded, for example), do not use a restart analysis; +instead, use a recover analysis. In this case no data are needed (unless user subroutines are being used). +Input File Usage: +Enter the following input on the command line: +abaqus job=job-name recover +Abaqus/CAE Usage: +Job module: job editor: toggle on Recover (Explicit) as the Job Type +Truncating a step +You can truncate an analysis step prior to its completion when you restart the analysis. For example, by +default, if the previous analysis is an Abaqus/Standard procedure and you specify that the restart point +is Step p, the restart analysis will restart from the last saved increment of Step p and continue the step +to completion. However, if you specify that the restart point is increment n of Step p and that the step +should be terminated before restart, the restart analysis will restart from increment n of Step p, end Step p +at that point, and continue with newly defined steps. In this case the step from which the analysis is being +restarted will be truncated at the time of restart, regardless of the step end time that had been given in the +previous analysis. Thus, the step is considered to be completed even though all of the loading may not +have been applied. Continuation of the analysis will be defined by history data provided in the restart +run. +When you truncate an analysis step in an Abaqus/Explicit restart analysis, you must specify +the interval after which the analysis should be restarted. When you truncate an analysis step in an +Abaqus/CFD restart analysis, you must specify the increment after which the analysis should be +restarted. +If the step from which the restart is being made completed normally, you can truncate the step to +restart within the step so that you can request additional output, write to the restart file with a higher +frequency, etc. In Abaqus/Explicit it may be necessary to truncate an analysis step when an unforeseen +event occurs within a step; for example, if contact surface definitions require modification due to +unforeseen displacements. If the step from which the restart is being made completed normally and +the restart is being made from the last increment, iteration, or interval, truncating the analysis step will +have no effect. +If the restart is being made from a job that was truncated by the operating system (for example, +because of insufficient disk space, run-time limit exceeded, etc.), you will usually not choose to truncate +the analysis step, so that the old step will first be completed before a new step—if any exists—is started. +If restart is being made from the end of a step that terminated prematurely inside Abaqus (for example, +because it ran out of increments or it failed to converge), you must truncate the step and include a new +step definition. If you do not truncate the step, Abaqus will try to continue the old step upon restart and +will terminate the analysis in the same manner as before. +Use the following option in Abaqus/Standard to restart from any analysis step +other than a direct cyclic step: +RESTART +*RESTART, READ, STEP=p, INC=n, END STEP +Use the following option in Abaqus/Standard to restart from a direct cyclic +analysis step: +*RESTART, READ, STEP=p, ITERATION=n, END STEP +Use the following option in Abaqus/Standard to restart from a low-cycle fatigue +analysis step: +*RESTART, READ, STEP=p, CYCLE=n, END STEP +Use the following option in Abaqus/Explicit: +*RESTART, READ, STEP=p, INTERVAL=n, END STEP +Any module: Model→Edit Attributes→model_name: Restart: toggle on +Read data from job; Step name: step; toggle on Restart from increment, +interval, iteration, or cycle, enter the increment, interval, iteration, or +cycle; and toggle on and terminate the step at this point +Abaqus/CAE Usage: +Amplitude references +Care should be taken if loads and boundary conditions refer to amplitude curves (“Amplitude curves,” +Section 33.1.2). If the amplitude is given in terms of total time, the loads and boundary conditions will +continue to be applied according to the amplitude definition. However, if the amplitude is given in terms +of step time (default), the loads and boundary conditions will be held constant at their values at the time +the step is terminated. +Temperatures, field variables, and mass flow rates applied in the old step will remain in the new +step if they are not redefined. If an amplitude curve was not specified, these quantities will continue to +be applied according to the default amplitude for the procedure. +Automatic stabilization in Abaqus/Standard +In Abaqus/Standard care should be exercised when automatic stabilization is active at the point at which +a step is truncated. This may happen either in the middle of quasi-static procedures using automatic +stabilization or during contact analyses using +automatic viscous damping . +In such cases viscous forces may be present, which will not be carried over to the subsequent step, +therefore causing convergence difficulties. +In the case of quasi-static procedures using automatic stabilization it is recommended that the +stabilization continue to be enforced during the following step and that you specify the damping factor +directly, using the last value printed out by Abaqus/Standard in the message file. In the case of automatic +viscous damping in a contact pair when contact has not yet been fully established, it is recommended +that the damping be applied again, although there is no guarantee that the amount of damping applied +will be the same as in the original step. +Choosing the initial time increment for an Abaqus/Standard restart analysis +In Abaqus/Standard take care in choosing the time period and initial time increment for the new step if +the previous step was truncated. In transient analyses the initial time increment for the new step should be +similar to the time increment that was used at the point of restart in the old step. In quasi-static analyses +choose the initial time increment of the new step so that the increments in loads or prescribed boundary +conditions are similar to those at the point of restart in the old step. +In a nonlinear analysis the increment of load applied in the first increment of the restart run should +be similar to that applied in the last converged increment of the previous run. Let += the load to be applied in the first increment of the restart run, += the remaining load to be applied in the restart run, += the initial time increment for the restart run, and += the total step time for the first step of the restart run. +The following equation can then be used to determine the initial time increment for the restart run: +Example +Suppose an Abaqus/Standard job stopped running because it reached the maximum number of increments +specified for the step. The original input file was as follows: +*HEADING +… +*STEP, INC=4 +*STATIC, DIRECT +0.1, 1.0 +*CLOAD +1, 2, 20.0 +*RESTART, WRITE, FREQUENCY=2 +*END STEP +This run ended at Step 1, increment 4 with a load of 8.0 applied. The following input file could be used +to restart this job and to complete the loading: +*HEADING +*RESTART, READ, STEP=1, INC=4, END STEP +*STEP, INC=120 +*STATIC, DIRECT +0.1, 0.6 +*CLOAD +1, 2, 20.0 +*END STEP +Notice that the concentrated load applied is the same as in the previous step. +In this example assume that a load increment of 2.0 was applied in the last converged increment +of the previous run. Therefore, the initial time increment for the restart run is chosen such that the load +increment applied during the first increment is also 2.0. The remaining load to be applied in the restart +run is 12.0 (20.0 total − 8.0 applied in the previous run). Substitution into the equation for the initial time +increment yields +, is chosen to be +0.6 so that the total accumulated time is 1.0 when the applied load is 20.0 (at the end of the step). Thus, +the initial time increment for the restart run, +/6. The step time for the first step of the restarted job, +, is set equal to 0.1. += +Supplying additional data in the restart analysis +It is possible to define steps subsequent to the step at which restart is being made. It is also possible to +supply new amplitude definitions, new surfaces, new node sets, and new element sets during the restart +analysis. Existing sets cannot be modified. +In Abaqus/Standard additional surfaces defined in the model part of a restart analysis have the +restriction that they can be referenced only from surface-based loading definitions or output requests for user-defined surface sections . +Example +For example, suppose a one-step Abaqus/Explicit job stopped prior to completion because a CPU time +limit was exceeded and you have decided that a second step should be added with new boundary condition +definitions. The following input file could be used to restart this job, complete the remaining part of +Step 1, and complete Step 2: +*HEADING +*RESTART, READ, STEP=1 +** +** This defines Step 2 +** +*STEP +*DYNAMIC, EXPLICIT +, .003 +*BOUNDARY, OP=NEW +… +*END STEP +Continuation of optional history data in restart analyses +The rules governing the continuation of optional analysis history data—loading, boundary conditions, +output controls, and auxiliary controls —are the +same for the steps defined in the restart analysis and the original analysis. For a discussion of the rules +governing the continuation of optional history data, see “Defining an analysis,” Section 6.1.2. +Prescribing predefined fields in the restart analysis +It is possible to prescribe predefined fields in the restart analysis. +To specify predefined temperatures or field variables in an Abaqus/Standard restart analysis, the +corresponding predefined field must have been specified in the original analysis as initial temperatures +or field variables (“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1) or as +predefined temperatures or field variables (“Predefined fields,” Section 33.6.1). +Restarting with user subroutines +User subroutines are not written to the Abaqus/Standard restart file or to the Abaqus/Explicit state file. +Therefore, if the original analysis contained any user subroutines, these subroutines must be included +again in the restart run or when recovering additional results output from restart data . These +subroutines can be modified on restart; however, modifications should be made with caution because +they may invalidate the solution from which the restart is being made. +Simultaneously reading and writing a restart file +You can continue a previous analysis as a restart analysis and write the results from the restart analysis +to a new restart file or state file. For example, if the previous analysis is an Abaqus/Explicit procedure +and in the current analysis you specify that the restart point is Step p and the restart output frequency is +n, the analysis will be restarted from the last saved interval of Step p and restart states will be written in +subsequent steps based on the new value of n. +To discontinue the writing of a restart file in Abaqus/Standard when you are restarting a previous +analysis, specify a restart output frequency of 0; if you do not specify a frequency, the file will continue +to be written at the frequency defined for the previous analysis. +The new restart file +Restart files can be very large for large models or for jobs involving many restart increments (unless +you choose to overlay the restart data—see “Overlaying results in the restart files”). Therefore, the +previous restart file is not copied to the beginning of the new restart file when a job is restarted: only the +data at restart increments requested in the current run are saved to the new restart file. However, if an +eigenfrequency extraction step (“Natural frequency extraction,” Section 6.3.5) is restarted and additional +eigenvalues are requested, the new restart file will contain those eigenvalues that converged during the +first run as well as the additional eigenvalues. +Example: Abaqus/Standard +Suppose an Abaqus/Standard job stopped running because it ran out of disk space. The last complete +information for an increment in the restart file is from Step 2, increment 4. The following two-line input +file could be used to restart this job and continue writing the restart file: +*HEADING +*RESTART, READ, STEP=2, INC=4, WRITE +Example: Abaqus/Explicit +Suppose you stopped an Abaqus/Explicit job because too much output was being generated. The last +information in the state file is from Step 2, Interval 4 at a time of .004. Step 2 has a time period of .010 +and restart results were requested at 10 intervals. The following input file could be used to restart this +job and redefine the remainder of the step with reduced output requests: +*HEADING +*RESTART, READ, END STEP, STEP=2, INTERVAL=4 +*STEP +*DYNAMIC, EXPLICIT +, .006 +*RESTART, WRITE, NUMBER INTERVAL=2 +*END STEP +Continuation of output upon restart +When you restart an analysis, Abaqus creates a new output database file (job-name.odb) and a new +results file (job-name.fil; this file is not created in Abaqus/CFD) and writes output data to those files +according to the criteria described below. +Output database (.odb) files +The Abaqus output database file (job-name.odb) contains results that can be used for postprocessing in +Abaqus/CAE. By default, the output database file is not made continuous across restarts; Abaqus creates +a new output database file each time a job is run. You can combine X–Y data extracted from multiple +output database files in the Visualization module of Abaqus/CAE. Alternatively, you can also join field +and history results from an original analysis and a restart analysis by running the abaqus restartjoin +execution procedure. For more information, see “Joining output database (.odb) files from restarted +analyses,” Section 3.2.18. +Results (.fil) files +The Abaqus results file created in Abaqus/Standard and Abaqus/Explicit (job-name.fil) contains +user-specified results that can be used for postprocessing in external postprocessing packages. +In +Abaqus/Explicit results are also written to the selected results file (job-name.sel), which is then +converted to the results file for postprocessing. See “Output,” Section 4.1.1, for details. +Upon restart Abaqus/Standard will copy the information from the old results file into the results file +for the new job up to the restart point and begin writing the new results to the new file following that +point. Abaqus/Explicit will copy the information from the old selected results file into the selected results +file for the new job up to the restart point and begin writing the new results to the new file following that +point. +If the old results file is not provided, Abaqus/Standard will continue the analysis, writing the results +of the restart analysis only to the new results file. Therefore, you will have segments of the analysis +results in different files, which should be avoided in most cases since postprocessing programs assume +that the results are in a single continuous file. You can merge such segmented results files, if necessary, +by using the abaqus append execution procedure (“Joining results (.fil) files,” Section 3.2.12). +Restart compatibility +A restart analysis in Abaqus/Standard can use the restart files generated from the same or any previous +maintenance delivery of the same general release. For example, if the original analysis is executed with +the Abaqus 6.12-3 maintenance delivery, all subsequent Abaqus 6.12 maintenance deliveries can be used +to launch the restart analysis. Restart is not compatible between general releases (for example, between +Abaqus 6.11 and Abaqus 6.12). +In Abaqus/Explicit and Abaqus/CFD the original analysis and the restart analysis must use precisely +the same release. For example, if the original analysis is executed with the Abaqus 6.12-3 maintenance +delivery, only this exact release can be used to launch the restart analysis. +A restart analysis in Abaqus and a recover analysis in Abaqus/Explicit must be run on a computer +that is binary compatible with the computer used to generate the restart files. +9.2 +Importing and transferring results +• “Transferring results between Abaqus analyses: overview,” Section 9.2.1 +• “Transferring results between Abaqus/Explicit and Abaqus/Standard,” Section 9.2.2 +• “Transferring results from one Abaqus/Standard analysis to another,” Section 9.2.3 +• “Transferring results from one Abaqus/Explicit analysis to another,” Section 9.2.4 +TRANSFERRING RESULTS BETWEEN Abaqus ANALYSES: OVERVIEW +TRANSFERRING RESULTS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Transferring results between Abaqus/Explicit and Abaqus/Standard,” Section 9.2.2 +• “Transferring results from one Abaqus/Standard analysis to another,” Section 9.2.3 +• “Transferring results from one Abaqus/Explicit analysis to another,” Section 9.2.4 +• *IMPORT +• *IMPORT ELSET +• *IMPORT NSET +• *IMPORT CONTROLS +• *INSTANCE +• “Transferring results between Abaqus analyses,” Section 16.6 of the Abaqus/CAE User’s Manual +Overview +Abaqus provides the capability to import a deformed mesh and its associated material state from +Abaqus/Standard into Abaqus/Explicit and vice versa. +in +manufacturing problems; for example, the entire sheet metal forming process (which requires an initial +preloading, forming, and subsequent springback) can be analyzed. In this case the initial preloading +can be simulated with Abaqus/Standard using a static procedure and the subsequent forming process +can be simulated with Abaqus/Explicit. Finally, +the springback analysis can be performed with +Abaqus/Standard. +This capability is particularly useful +Abaqus also provides the capability to transfer desired results and model information from an +Abaqus/Standard analysis to a new Abaqus/Standard analysis or from an Abaqus/Explicit analysis +to a new Abaqus/Explicit analysis, where additional model definitions may be specified before the +analysis is continued. For example, during an assembly process an analyst may first be interested in +the local behavior of a particular component but later is concerned with the behavior of the assembled +product. In this case the local behavior can first be analyzed in an Abaqus/Standard or Abaqus/Explicit +analysis. Subsequently, the model information and results from this analysis can be transferred to a +second Abaqus/Standard or Abaqus/Explicit analysis, where additional model definitions for the other +components can be specified, and the behavior of the entire product can then be analyzed. +For this capability to work, the same release of Abaqus/Explicit and Abaqus/Standard must be run +on computers that are binary compatible. In addition, you can transfer model and results only from one +previous analysis; transfer from multiple analyses is not supported. +Saving the analysis results +The restart files from the original analysis contain the analysis results that are transferred from +Abaqus/Standard or Abaqus/Explicit. Obtaining restart files is described in more detail in “Writing +restart files” in “Restarting an analysis,” Section 9.1.1; brief summaries are provided below. By default, +Abaqus/Standard does not write any restart information and Abaqus/Explicit writes results at the +beginning and end of each step. +Saving results from Abaqus/Standard +If the results are to be imported from an Abaqus/Standard analysis, the results from the original +Abaqus/Standard job must be written to the restart (.res), analysis database (.mdl and .stt), part +(.prt), and output database (.odb) files. You can specify the increments at which restart information +will be written. Restart information is always written at the end of a step in addition to the requested +increments whenever you request restart data in Abaqus/Standard. +*RESTART, WRITE, FREQUENCY=n +Step module: Output→Restart Requests: enter n in the +Frequency column for each step +Abaqus/CAE Usage: +Input File Usage: +Saving results from Abaqus/Explicit +If the results are to be imported from an Abaqus/Explicit analysis, the results from the original +Abaqus/Explicit job must be written to the state (.abq) file at the time when transfer of the state of +the deformed body is required. The state (.abq), restart (.res), analysis database (.stt), package +(.pac), part (.prt), and output database (.odb) files will be used for importing the results from +Abaqus/Explicit. +You can specify whether the results are to be written at the exact time dictated by the specified time +interval, n, during a step of an Abaqus/Explicit analysis or at the increment ending after the time dictated +by the specified time interval. Results are always written at the end of a step, so it is not necessary to +request results at the exact time intervals if results will be read only from the end of a step. +Input File Usage: +Use the following option to request +immediately after each time interval: +results at +the increments ending +Abaqus/CAE Usage: +*RESTART, WRITE, NUMBER INTERVAL=n, TIME MARKS=NO +Use the following option to request results at the exact time intervals: +*RESTART, WRITE, NUMBER INTERVAL=n, TIME MARKS=YES +Step module: Output→Restart Requests: enter n in the Number +Interval column; click to check the Time Marks column for each step +if you want the results written at the exact time intervals +Specifying the transfer of model data and results +The import capability is used to transfer model data and results from one analysis to another. The +following sections describe how to specify the import request. You can import element sets from models +that are not defined as assemblies of part instances, or you can import part instances from models that +are defined as assemblies of part instances. In Abaqus/CAE you can import model data and results only +from models that are defined as assemblies of part instances. +Specifying the transfer of model data and results for models that are not defined as assemblies +of part instances +You can import element sets from a previous analysis to specify the transfer of model data and results +for models that are not defined as assemblies of part instances. This import capability is illustrated in +“Springback of two-dimensional draw bending,” Section 1.5.1 of the Abaqus Example Problems Manual, +and “Axisymmetric forming of a circular cup,” Section 1.3.7 of the Abaqus Example Problems Manual. +Input File Usage: +Use the following option to import element sets from a previous analysis: +*IMPORT +list of element sets that are to be imported +To prevent any ambiguity regarding element and node definitions, +the +*IMPORT option must be specified before any options that define additional +model data in the input file. In addition, the *IMPORT option can be specified +only once. +Each element set name specified on the data line of the *IMPORT option must +have been used in a section definition option (e.g., *SOLID SECTION) in the +original analysis. An element set can contain no more than three different types +of elements. +Abaqus/CAE Usage: +In Abaqus/CAE you can import model data and results only from models that +are defined as assemblies of part instances. +Specifying the transfer of model data and results for models that are defined as assemblies of +part instances +You can import part instances from a previous analysis to specify the transfer of model data and results +for models that are defined as assemblies of part instances. If you import more than one part instance, +the part instances must be from the same output database (.odb) file and all import parameters must be +the same for each imported part instance. Each instance name that you specify must be the same as the +instance name in the original analysis. Only sets that are defined within the imported instance will be +imported. Sets defined at the assembly level must be redefined in the import analysis. New set definitions +and surface definitions can be added upon import. You cannot assign new sections, material orientations, +normals, or beam orientations to the imported part instance. +Input File Usage: +Use the following options to import a part instance from a previous analysis: +*INSTANCE, INSTANCE=instance-name +Abaqus/CAE Usage: +Additional set and surface definitions (optional) +*IMPORT +*END INSTANCE +In Abaqus/CAE you can import model data and results only from models that +are defined as assemblies of part instances. +Load module: Create Predefined Field: Step: Initial: choose Other for +the Category and Initial State for the Types for Selected Step: select +the instances to which the initial state should be assigned +Identifying the analysis from which the data will be obtained +You must specify the name of the job from which the model and results data will be obtained. +Input File Usage: +For all models you can enter the following input on the command line: +abaqus job=job-name oldjob=oldjob-name +If the oldjob parameter is omitted, Abaqus will prompt for the job name + even if the current job is an Abaqus/Explicit analysis that uses +the recover option to restart from the last available step and increment in the +state file. +Alternatively, for models defined as assemblies of part instances, you can use +the following option: +*INSTANCE, LIBRARY=oldjob-name +If you import more than one part instance, the oldjob-name specified by the +LIBRARY parameter must be the same for each imported part instance. +If the job name is specified on the command line using the oldjob option, the +command line specification will take precedence over the LIBRARY parameter. +Abaqus/CAE Usage: +In Abaqus/CAE you can import model data and results only from models that +are defined as assemblies of part instances. +Load module: Create Predefined Field: Step: Initial: choose Other +for the Category and Initial State for the Types for Selected +Step: Job name: output-database-name +Importing model data +Element property definitions of imported elements can be redefined only if the reference configuration +is updated and the material state is not imported . +In this case the material orientation definitions (“Orientations,” +Section 2.2.5), hourglass stiffness but not hourglass control definitions, and transverse shear stiffness +definitions (in the case of shell elements) of the imported elements can also be redefined. +For other reference configuration and material state combinations, the information required to +define the section for each imported element will be imported from the original analysis. Material +orientations cannot be redefined in the import analysis; orientation names cannot be reused in the +import analysis. For imported elements, the material orientations will be transferred from the original +analysis. Transverse shear stiffness for imported shell elements cannot be redefined; the values will +be transferred from the original analysis. Hourglass stiffness for the imported elements cannot be +redefined in an Abaqus/Standard import analysis; the default values will be used. The section control +definitions (kinematic formulation, order of accuracy in the element formulation, and hourglass control +approach) to be used for imported elements cannot be redefined . +Only nodes associated with the imported elements are imported. New nodes can be defined in the +import analysis. +Nodes or elements that use the same numbers as nodes or elements being imported can be defined +provided that the reference configuration is updated, the material state is not imported, and the import +is not done from an instance library. The new definitions will overwrite the imported definitions. If the +reference configuration is not updated, new nodes or elements cannot use the imported node and element +numbers irrespective of whether or not the material state is imported. +During results transfer from an Abaqus/Standard analysis to another Abaqus/Standard analysis or +from an Abaqus/Explicit to another Abaqus/Explicit analysis, the coordinates of imported nodes can be +modified from their imported values by respecifying the nodal definitions if the reference configuration +is updated and the material state is not imported. This modification of the coordinates of imported nodes +is not allowed during transfer of results from Abaqus/Explicit to Abaqus/Standard or vice versa. +Importing model data defined by a distribution +While transferring results from one Abaqus/Standard analysis to another Abaqus/Standard analysis, most +element or material properties defined by a distribution are +imported along with the elements. The only exceptions are spatially varying thicknesses and orientation +angles defined on the layers of composite shells and solids; in this case Abaqus issues an error message +during input file preprocessing. +While transferring results from an Abaqus/Explicit analysis to an Abaqus/Standard analysis, +the only spatially varying element properties defined by a distribution that can be imported are shell +thicknesses and section orientations for shell and solid elements. +If any other element or material +properties are defined with a distribution, Abaqus issues an error message during input file preprocessing. +While transferring results from an Abaqus/Standard analysis to an Abaqus/Explicit analysis or from +an Abaqus/Explicit analysis to another Abaqus/Explicit analysis, the only spatially varying element +properties defined by a distribution that can be imported are shell thicknesses, section orientations for +shell and solid elements, orientation angles defined for shell sections on the layers of composite shells, +and section stiffness matrices specified directly for general shell sections. If any other element or material +properties are defined with a distribution, Abaqus issues an error message during input file preprocessing. +Section and material properties of imported elements can be redefined with distributions only if the +reference configuration is updated and the material state +is not imported . +In this case the material orientation definitions +(“Orientations,” Section 2.2.5), hourglass stiffness but not hourglass control definitions, and transverse +shear stiffness definitions (in the case of shell elements) of the imported elements can also be redefined. +Importing results from an Abaqus/Standard analysis (other than a direct cyclic analysis) +If the results are imported from an Abaqus/Standard analysis, you can specify the step and increment in +the restart file for which the results are to be imported. By default, the results written at the end of the +analysis are imported. +Input File Usage: +*IMPORT, STEP=step, INCREMENT=increment +For models that are defined as assemblies of part instances, the *IMPORT +option must appear within a part instance definition. +Abaqus/CAE Usage: +In Abaqus/CAE you can import model data and results only from models that +are defined as assemblies of part instances. +Load module: Create Predefined Field: Step: Initial: choose Other for +the Category and Initial State for the Types for Selected Step: select +instances: Step: select Specify: step and Frame: select Specify: increment +Importing results from an Abaqus/Standard direct cyclic analysis +If the results are imported from a direct cyclic analysis, you can specify the step and iteration number in +the restart file for which the results are to be imported. By default, the results written at the end of the +analysis are imported. +Input File Usage: +*IMPORT, STEP=step, ITERATION=iteration +For models that are defined as assemblies of part instances, the *IMPORT +option must appear within a part instance definition. +Abaqus/CAE Usage: +In Abaqus/CAE you can import model data and results only from models that +are defined as assemblies of part instances. +Load module: Create Predefined Field: Step: Initial: choose Other for +the Category and Initial State for the Types for Selected Step: select +instances: Step: select Specify: step and Frame: select Specify: iteration +Importing results from an Abaqus/Explicit analysis +If the results are imported from an Abaqus/Explicit analysis, you can specify the step and interval in the +state file for which the results are to be imported. By default, the results written at the end of the analysis +are imported. +Input File Usage: +*IMPORT, STEP=step, INTERVAL=interval +For models that are defined as assemblies of part instances, the *IMPORT +option must appear within a part instance definition. +Abaqus/CAE Usage: +In Abaqus/CAE you can import model data and results only from models that +are defined as assemblies of part instances. +Load module: Create Predefined Field: Step: Initial: choose Other for +the Category and Initial State for the Types for Selected Step: select +instances: Step: select Specify: step and Frame: select Specify: interval +Updating the reference configuration +Once the current model configuration of an Abaqus analysis is imported into Abaqus/Explicit or +Abaqus/Standard, the analysis can be continued with or without updating the reference configuration +If the reference configuration is not updated to be the imported +to be the imported configuration. +configuration, the displacements and strains are reported as total values relative to the original reference +configuration and will, hence, be continuous. If the reference configuration is updated to be the imported +configuration, displacements and strains reported in the import analysis are the total values relative to +the updated reference configuration. This choice is useful if results need to be displayed relative to the +imported configuration, such as may be desirable in springback analysis. The reference configuration +cannot be updated if the imported analysis is geometrically linear. +The choice of whether or not to update the reference configuration can influence strain-free nodal +adjustments associated with contact initialization in Abaqus/Standard. Strain-free adjustments can +be used to resolve penetrations or gaps that exist in the reference configuration in Abaqus/Standard, +so prior displacements are not considered by the strain-free adjustment algorithm upon import if +the reference configuration is not updated. Strain-free nodal adjustments in Abaqus/Explicit are +based on the current configuration rather than the reference configuration, so these adjustments +are not sensitive to whether the reference configuration is updated in Abaqus/Explicit. +Further +details on strain-free adjustments are provided in “Default contact +initialization method” in +“Controlling initial contact status in Abaqus/Standard,” Section 35.2.4; “Controlling initial contact +status in Abaqus/Standard,” Section 35.2.4; “Controlling initial contact status for general contact +in Abaqus/Explicit,” Section 35.4.4; and “Adjusting initial surface positions and specifying initial +clearances for contact pairs in Abaqus/Explicit,” Section 35.5.4. +If connector elements are imported, the configuration can be updated provided that the state is not +imported. +Input File Usage: +Use the following option to specify that the reference configuration is to be +updated to the imported configuration: +*IMPORT, STEP=step, UPDATE=YES +Use the following option to specify that the reference configuration should not +be updated to the imported configuration: +*IMPORT, STEP=step, UPDATE=NO +For models that are defined as assemblies of part instances, the *IMPORT +option must appear within a part instance definition. +Abaqus/CAE Usage: +In Abaqus/CAE you can import model data and results only from models that +are defined as assemblies of part instances. +Load module: Create Predefined Field: Step: Initial: choose Other +for the Category and Initial State for the Types for Selected Step: +toggle Update reference configuration on or off +Importing the material state +You can specify whether or not the associated material state should be imported. If you choose to import +the material state, the following are imported: +• stresses; +• equivalent plastic strains; +• back stresses for the kinematic hardening models; +• user-defined state variables; +• damage-related state variables for the concrete damaged plasticity model; +• damage-related state-variables for traction-separation response with cohesive elements; +• damage-related state variables for ductile metals; +• damage-related state variables for fiber-reinforced composites; +• maximum deviatoric strain energy density during deformation history for Mullins effect; +• internal strains and stresses for viscoelastic material models; and +• connector state variables such as plastic strains, frictional slip, and damage state. +Thus, the state is imported correctly for further analysis only for the following: +• linear elasticity, +• Mises plasticity (including the kinematic hardening models), +• extended Drucker-Prager plasticity, +• crushable foam plasticity, +• Mohr-Coulomb plasticity, +• critical state (clay) plasticity, +• cast iron plasticity, +• concrete damaged plasticity, +• hyperelasticity (including Mullins effect), +• hyperfoam, +• viscoelasticity, +• traction-separation response with damage for cohesive elements, +• damage for ductile metals, +• damage for fiber-reinforced composites, +• connector behavior, and +• materials defined in user subroutines UMAT and VUMAT. +For all other material models only stresses will be imported. No other state variables will be imported. +If the material behavior is defined in a user subroutine, you must ensure that the UMAT and VUMAT +are consistent. +If connector elements are imported, the state can be imported provided that the configuration is not +updated. +Input File Usage: +Use the following option to specify that the material state should be imported: +Abaqus/CAE Usage: +*IMPORT, STATE=YES +Use the following option to specify that the material state should not be +imported: +*IMPORT, STATE=NO +For models that are defined as assemblies of part instances, the *IMPORT +option must appear within a part instance definition. +In Abaqus/CAE you can import model data and results only from models that +are defined as assemblies of part instances. Abaqus/CAE always imports the +material state. If you want to import only the deformed mesh, you can import +an orphan mesh from a selected step and increment of an output database; +see “What kinds of files can be imported and exported from Abaqus/CAE?,” +Section 10.1.1 of the Abaqus/CAE User’s Manual. +Defining constraints upon import +Most constraints (such as multi-point constraints and surface-based tie constraints) are not imported from +the original analysis and must be redefined in the import analysis. Using the reference configuration of +the original analysis without update ensures identical reproduction of these constraints in the import +analysis. +If a new constraint is defined in the import analysis, it is important to ensure that the constraint +is not in violation either in the reference configuration or in the starting configuration of the import +analysis. These two configurations are one and the same for newly introduced nodes. If a new constraint +involves nodes of the original analysis, it is appropriate to update the reference configuration for the +import analysis . +In an Abaqus/Standard analysis with adaptive meshing and acoustic-to-structure tie constraints, +the structural as well as the acoustic nodes may move from their initial positions. When such acoustic +and structure meshes are imported from Abaqus/Standard into Abaqus/Explicit without updating the +reference configuration, the acoustic elements at the interface may appear distorted when viewed in the +undeformed plot mode in the Visualization module of Abaqus/CAE. This distortion appears because the +reference configuration for the acoustic nodes is updated automatically while the configuration for the +non-acoustic nodes is not. The deformed plot at time=0 displays the correct mesh. +Importing element set and node set definitions +All element set and node set definitions associated with the imported elements are imported by default. +For models that are not defined as assemblies of part instances, you can also selectively import only +specified element set or node set definitions. This capability provides a convenient way of selectively +reusing the element or node sets defined in the original analysis. However, any members of such sets +that do not belong to the imported elements are removed from the specified sets. +For example, suppose three element sets—SHELL3D, MEMB, and ALL—are defined in the original +analysis. Element set ALL contains all of the elements in element sets SHELL3D and MEMB, as well +as other elements. You choose to import only the element sets SHELL3D and MEMB (i.e., the elements +in these sets as well as the element set definitions). In addition, you selectively import the element set +definition ALL (but not the elements in this set). If element 100 belongs to element set ALL but not to +either element set SHELL3D or element set MEMB, it will not be imported and will be removed from the +list of elements belonging to element set ALL. The imported element set definitions are processed before +any node or element definitions; therefore, even if element 100 is subsequently redefined in the import +analysis, it will not belong to element set ALL (unless it is explicitly assigned to element set ALL in the +import analysis). +Only node and element sets defined in the original or previous import analysis are available for +importing. New sets defined during a restart run cannot be imported. +Input File Usage: +Abaqus/CAE Usage: +Use either or both of the following options immediately following the +*IMPORT option to import selected element or node set definitions: +*IMPORT ELSET +*IMPORT NSET +For models that are defined as assemblies of part instances, you cannot +selectively import element and node set definitions. All element and node set +definitions are imported automatically. +In Abaqus/CAE you can import model data and results only from models that +are defined as assemblies of part instances. You cannot selectively import +element and node set definitions in Abaqus/CAE. All element and node set +definitions are imported automatically. +Specifying a tolerance for shell normals in the updated configuration +When the imported configuration is updated upon import, the mesh discretization may not satisfy the +mesh geometry checks imposed in Abaqus/Explicit or Abaqus/Standard to evaluate whether or not a +mesh is reasonable. In the case of highly warped shell elements it is possible that the normal at the +center of the element that is calculated from the midsurface interpolation may differ from the normal that +is interpolated from the rotated normals at the nodes. If the difference exceeds the tolerance specified, the +analysis will terminate. This suggests that a fine mesh may be required to model areas of high curvature +change to achieve a successful analysis. +The unit normal computed from the midsurface interpolation, +, and that predicted by the +interpolation of the rotated normals at the nodes, +, must satisfy the condition: +where you can specify the tolerance, += 0.1 is used. +. If you do not specify a tolerance value, a default value of +Input File Usage: +If you update the reference configuration to be the imported configuration, you +can specify a tolerance for error checking on shell normals: +Abaqus/CAE Usage: +*IMPORT CONTROLS, NORMAL TOL= +The shell normal tolerance is not supported in Abaqus/CAE. +9.2.2 +TRANSFERRING RESULTS BETWEEN Abaqus/Explicit AND Abaqus/Standard +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Transferring results between Abaqus analyses: overview,” Section 9.2.1 +• *IMPORT +• *IMPORT ELSET +• *IMPORT NSET +• *IMPORT CONTROLS +• *INSTANCE +• “Transferring results between Abaqus analyses,” Section 16.6 of the Abaqus/CAE User’s Manual +Overview +Abaqus provides the capability to import a deformed mesh and its associated material state from +Abaqus/Standard into Abaqus/Explicit and vice versa. +In addition, new model information can be +specified during the import analysis. This capability is useful for problems that involve several analysis +stages. For example, in manufacturing processes the preloading can be analyzed using Abaqus/Standard +and the subsequent forming operation can be simulated using Abaqus/Explicit. Finally, the springback +of the material can be performed in Abaqus/Standard. +For this capability to work, the same release of Abaqus/Explicit and Abaqus/Standard must be run +on computers that are binary compatible. +Information about how to transfer results between Abaqus analyses is provided in “Transferring +results between Abaqus analyses: overview,” Section 9.2.1. +Specifying new data in an import analysis +Additional model definitions such as new elements, nodes, surfaces, etc. can be defined during the import +analysis. Initial conditions can also be specified during the import analysis. +New model definitions +New nodes, elements, and material properties can be added to the model in an import analysis once import +has been specified. Nodal coordinates must be defined in the updated configuration, regardless of whether +or not the reference configuration is updated on import . The usual Abaqus input can +be used. Imported material definitions can be used with the new elements (which will need new section +property definitions). +Nodal transformation +transformations +(“Transformed coordinate systems,” Section 2.1.5) are not +Nodal +imported; +transformations can be defined independently in the import analysis. Continuous displacements, +velocities, etc. are obtained only if the nodal transformations in the import analysis are the same as those +in the original analysis. Use of the same transformations is also recommended for nodes with boundary +conditions or point loads defined in a local system. +Specifying geometric nonlinearity in an import analysis +By default, Abaqus/Standard uses a small-strain formulation (i.e., geometric nonlinearity is ignored) and +Abaqus/Explicit uses a large-deformation formulation (i.e., geometric nonlinearity is included). For each +step of an analysis you can specify which formulation should be used; see “Geometric nonlinearity” in +“General and linear perturbation procedures,” Section 6.1.3, for details. +The default value for the formulation in an import analysis is the same as the value at the time +of import. Once the large-displacement formulation is used during a given step in any analysis, it will +remain active in all the subsequent steps, whether or not the analysis is imported. +If the small-displacement formulation is used at the time of import, the reference configuration +cannot be updated. +Specifying initial conditions for imported elements and nodes +Initial conditions (“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1) can be +specified on the imported elements or nodes only under certain conditions. Table 9.2.2–1 lists the initial +conditions that are allowed depending on whether or not the material state is imported . The +reference configuration can be updated or not, as desired. +Table 9.2.2–1 Valid initial conditions. +Initial condition +Hardening +Relative density +Rotational velocity +Solution-dependent state +variables +Stress +Velocity +Void ratio +Material state +imported? +No +No +Yes or No +No +No +Yes or No +No +Procedures +Results can be imported into Abaqus/Explicit only from a general analysis step involving static stress +analysis, dynamic stress analysis, or steady-state transport analysis in Abaqus/Standard. Results transfer +from linear perturbation procedures (“General and linear perturbation procedures,” Section 6.1.3) is not +allowed. +Abaqus/Standard offers several analysis procedures that can be used in an import analysis. These +procedures can be used to perform an eigenvalue analysis, static or dynamic stress analysis, buckling +analysis, etc. See “Solving analysis problems: overview,” Section 6.1.1, for a discussion of the available +procedures. +For springback analysis of a formed component the first step in the Abaqus/Standard analysis usually +consists of a static analysis procedure so that the initial out-of-balance forces can be removed gradually +from the system. The removal of these forces is performed automatically by Abaqus/Standard during +the first static analysis step, as described below. If the first step in the Abaqus/Standard analysis is not +a static step (such as a dynamic step), the analysis proceeds directly from the state imported from the +Abaqus/Explicit analysis. +Achieving static equilibrium when importing into Abaqus/Standard +When the current state of a deformed body in an explicit dynamic analysis is imported into a static +analysis, the model will not initially be in static equilibrium. +Initial out-of-balance forces must be +applied to the deformed body in dynamic equilibrium to achieve static equilibrium. Both dynamic forces +(inertia and damping) and boundary interaction forces contribute to the initial out-of-balance forces. The +boundary forces are the result of interactions from fixed boundary and contact conditions. Any changes +in the boundary and contact conditions from the Abaqus/Explicit analysis to the Abaqus/Standard +analysis will contribute to the initial out-of-balance forces. +In general the instantaneous removal of the initial out-of-balance forces in a static analysis will +lead to convergence problems. Hence, these forces need to be removed gradually until complete static +equilibrium is achieved. During this process of removing the out-of-balance forces, the body will deform +further and a redistribution of internal forces will occur, resulting in a new stress state. (This is essentially +what occurs during “springback,” when a formed product is removed from the worktools.) +When the first step in the Abaqus/Standard import analysis is a static procedure, the following +algorithm is used to remove the initial out-of-balance forces automatically: +1. The imported stresses are defined at the start of the analysis as the initial stresses in the material. +2. An additional set of artificial stresses is defined at each material point. These stresses are equal in +magnitude to the imported stresses but are of opposite sign. The sum of the material point stresses +and these artificial stresses, thus, creates zero internal forces at the beginning of the step. +3. The internal artificial stresses are ramped off linearly in time during the first step. Thus, at the end +of the step the artificial stresses have been removed completely and the remaining stresses in the +material will be the residual stress state associated with static equilibrium. +Once static equilibrium has been obtained, subsequent steps can be defined using any analysis procedure +that would normally follow a static analysis in Abaqus. +When the first step is not a static analysis, no artificial stress state is applied and the imported stresses +are used in the internal force computations for the element. +Boundary conditions +Boundary conditions, including any connector motion, specified in the original analysis are not imported. +They must be defined again in the import analysis. In some cases nonzero boundary conditions imposed +in the original analysis need to be maintained at the same values in the import analysis when the +imported configuration is not updated. +In such cases you can prescribe a constant (step function) +amplitude variation for the analysis step so that the newly applied boundary conditions are applied instantaneously +and held at that value for the duration of the step. Alternatively, you can refer to an amplitude curve +in the boundary condition definition . If boundary conditions +in the original analysis are applied in a transformed coordinate system , the same coordinate system should be defined and used in the import analysis. +For a discussion of applying boundary conditions, see “Boundary conditions in Abaqus/Standard +and Abaqus/Explicit,” Section 33.3.1. +Loads +Loads, including those applied for connector actuation, defined in the original analysis are not imported. +Loads may, therefore, need to be redefined in the import analysis. There are no restrictions on the loads +that can be applied when results are imported from one analysis to the other. In cases when the loads +need to be maintained at the same values as in the original analysis, you can prescribe a constant (step +function) amplitude variation for the analysis step to apply the loads instantaneously at the start of the step and +hold them for the duration of the step. Alternatively, you can refer to an amplitude curve in the load +definition . If point loads in the original analysis are applied in +a transformed coordinate system and the loads +must be maintained in the import analysis, the load application is simplified if the same coordinate system +is defined and used in the import analysis. +See “Applying loads: overview,” Section 33.4.1, for an overview of the loading types available in +Abaqus. +Predefined fields +The field variables at nodes are not imported. If the elements being imported are coupled temperature- +displacement elements, the temperature is imported if the associated material state is imported. The +temperature is also imported for an adiabatic analysis if the associated material state is imported. For all +other cases the temperatures at nodes are not imported. +If the original analysis uses predefined temperature fields (“Predefined temperature” in “Predefined +fields,” Section 33.6.1) to vary the temperatures at nodes, the import analysis will not be allowed to +continue. If the original analysis uses predefined field variable definitions (“Predefined field variables” +in “Predefined fields,” Section 33.6.1) to vary the field variables at nodes, the import analysis will +be allowed to continue only if all the elements being imported are coupled temperature-displacement +elements; however, the field variables are not imported. If the original analysis uses initial temperature +(“Defining initial +temperatures” in “Initial conditions in Abaqus/Standard and Abaqus/Explicit,” +Section 33.2.1) and field variable (“Defining initial values of predefined field variables” in “Initial +conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1) conditions, the import analysis +will be allowed to continue only if all the elements being imported are coupled temperature-displacement +elements. +In addition, specification of initial conditions for temperatures and field variables is not allowed in an +import analysis, unless all the elements being imported are coupled temperature-displacement elements. +In this case initial conditions for temperatures and field variables can be specified on the imported nodes +if the reference configuration is updated and the material state is not imported. Initial temperatures can +be specified in the import analysis if it is an adiabatic analysis. +Material options +All material property definitions and the orientations associated with imported elements are imported +by default. Material properties can be changed by respecifying the material property definitions with +the same material name. All relevant material properties must be redefined since the old definitions that +were imported by default will be overwritten. Material orientations associated with imported elements +can be changed only if the reference configuration is updated and the material state is not imported; the +material orientations associated with imported elements cannot be redefined for other combinations of +the reference configuration and material state. +When connector elements are imported, any associated connector behavior definitions are imported +by default. The imported connector behavior definitions can be modified only if the state is not imported. +If mass scaling (“Mass scaling,” Section 11.6.1) is used in Abaqus/Explicit, the scaled masses will +not be transferred to the subsequent import analysis in Abaqus/Standard. The mass of the model for the +Abaqus/Standard analysis will be based on either the imported or the redefined density definitions. +The material model must be redefined in the import analysis if changes to material damping are +required. +When material definitions are changed, care must be taken to ensure that a consistent material state +is maintained. It may sometimes be possible to simplify the material definition. For example, if a Mises +plasticity model was used in the Abaqus/Explicit analysis and no further plastic yielding is expected +in the Abaqus/Standard analysis (as is generally the case for springback simulations), a linear elastic +material can be used for the Abaqus/Standard analysis. However, if further nonlinear material behavior +is expected, no changes to the existing material definitions should be made. The history of the state +variables will not be maintained if the material models are not the same in both the original analysis and +the import analysis. +Elements +The import capability is available for first-order continuum, modified triangular and tetrahedral elements, +conventional shell, continuum shell, membrane, beam (both linear and quadratic), pipe (linear), truss, +connector, rigid, and surface elements that are common to both Abaqus/Explicit and Abaqus/Standard, +as defined in Table 9.2.2–2. +Table 9.2.2–2 Common element types that can be transferred +between Abaqus/Explicit and Abaqus/Standard. +Common element types +CPS3, CPS3T, CPS4R, CPS4RT, CPS6M, CPS6MT +CPE3, CPE3T, CPE4R, CPE4RT, CPE6M, CPE6MT +CAX3, CAX3T, CAX4R, CAX4RT, CAX6M, CAX6MT +C3D4, C3D4T, C3D6, C3D6T, C3D8, C3D8R, C3D8T, C3D8RT, +C3D10M, C3D10MT +M3D3, M3D4, M3D4R +R2D2 +R3D3, R3D4 +RAX2 +S4, S4R, S3R, S4RT, S3RT +SC8R, SC8RT, SC6R, SC6RT +SAX1 +SFM3D3, SFM3D4R +T2D2 +T3D2 +B21, B22, PIPE21 +B31, B32, PIPE31 +CONN2D21 , CONN3D21 +AC2D3, AC2D4R, AC2D4, ACIN2D2 +AC3D4, AC3D6, AC3D8R, AC3D8, ACIN3D3, ACIN3D4 +ACAX3, ACAX4R, ACAX4, ACINAX2 +COH2D4, COHAX4, COH3D6, COH3D8 +1 Connector elements can be imported from Abaqus/Standard to +Abaqus/Explicit; but not vice versa. +When S3R shell elements are imported from Abaqus/Explicit into Abaqus/Standard, they are converted +into degenerated S4R elements automatically. However, when S3R shell elements are imported from +Abaqus/Standard into Abaqus/Explicit, they remain S3R elements. When C3D6 and C3D6T solid +elements are imported from Abaqus/Explicit into Abaqus/Standard, the results at the single point +integration are applied to both integration points in Abaqus/Standard and the full integration is used +automatically. However, when C3D6 and C3D6T solid elements are imported from Abaqus/Standard +into Abaqus/Explicit, only the results at the first integration point are imported and are used in the +reduced integration. When quadrilateral and hexahedral acoustic finite elements are imported between +Abaqus/Explicit and Abaqus/Standard, they are converted to or from reduced-integration types, as +required. +The following restrictions apply to the import capability: +• Connector elements can be imported from Abaqus/Standard to Abaqus/Explicit but not vice versa. +Further, if connector elements are imported, the configuration can be updated provided that the state +is not imported and the state can be imported provided that the configuration is not updated. +• Rebars defined using rebar layers (“Defining reinforcement,” Section 2.2.3) are imported provided +the underlying elements are also imported. Rebar reinforcements defined using the embedded +element technique (“Embedded elements,” Section 34.4.1) are imported if the host and embedded +elements used in this definition are also imported. Rebars defined as an element property (“Defining +rebar as an element property,” Section 2.2.4) cannot be imported. +• Infinite elements and fluid elements cannot be imported. +• Rigid elements for which the thickness is interpolated from the nodes in an Abaqus/Explicit analysis +will not be imported into Abaqus/Standard. +• A rigid body containing both deformable and rigid elements cannot be imported. A rigid body that +includes rigid elements is imported when the element set used to define the rigid body is specified for +import. A rigid body that includes deformable elements is imported into Abaqus/Explicit when the +element set used to define the rigid body is specified for import. The imported rigid body definition +is overwritten if it is respecified using the same element set. When the model is defined in terms +of an assembly of part instances, the reference node of an imported rigid body must belong to an +imported instance. +• When a rigid body is imported, any associated data such as pin node sets and tie node sets are +part of the imported definition. However, these sets as imported contain only those nodes that are +connected to the imported elements. +• Failed elements in Abaqus/Explicit will not be imported into Abaqus/Standard. +• Elements that are being removed or are inactive in Abaqus/Standard will not be imported into Abaqus/Explicit. +• Rigid surfaces will not be imported. +When importing results from an Abaqus/Explicit analysis to an Abaqus/Standard analysis, each +element set specified can contain only compatible element types listed in Table 9.2.2–3 and can contain +at most three different element types. +Table 9.2.2–3 Compatible element types. +ACINAX2, ACIN2D2, ACIN3D3, ACIN3D4 +CPE4R, CPE3, AC2D3, AC2D4 +CPS4R, CPS3 +CAX4R, CAX3, ACAX3, ACAX4 +AC3D4, AC3D6, AC3D8, C3D8, C3D8R, C3D4, C3D6 +M3D4R, M3D3, M3D4 +R3D3, R3D4 +S4R, S3R, SC6R, SC8R, S4 +SFM3D3, SFM3D4R +CAX6M, C3D10M +C3D8T, C3D4T, C3D6T +SC6RT, SC8RT, S4T, S4RT, S3T, S3RT +Using section controls in an import analysis +it is important that the +When transferring results between Abaqus/Standard and Abaqus/Explicit, +hourglass forces are computed consistently. +The enhanced hourglass control formulation is recommended for computing hourglass forces in the original as well as all subsequent +import analyses. +Once section controls have been defined in the original analysis, they cannot be modified in any +subsequent Abaqus/Standard or Abaqus/Explicit analysis. Therefore, if section controls are to be used +in any one analysis in a series of import analyses, they must be specified in the very first analysis. +The section controls specified for an element set in the original analysis will be used for the elements +belonging to that element set in all subsequent import analyses. +Section controls other than the hourglass control formulation have appropriate defaults depending +on the type of analysis and, generally, do not need to be changed. Nondefault values can be chosen +subject to certain restrictions. +In an Abaqus/Standard analysis only the average strain kinematic formulation and second-order +accurate element formulation are available; other kinematic formulations, element formulations, +or section controls that are relevant only in an Abaqus/Explicit analysis can be specified in the +Abaqus/Standard analysis. Such controls will be ignored in the Abaqus/Standard analysis but retained +for the subsequent Abaqus/Explicit import analysis. +If a kinematic formulation other than average strain is used for solid elements in the Abaqus/Explicit +analysis, the differences in the kinematic formulations may lead to errors in Abaqus/Standard if the +elements are distorted or undergo large rotations. +Using the first-order accurate element +in Abaqus/Explicit and the +second-order accurate element formulation (the only available formulation) in Abaqus/Standard is not +expected to cause significant errors, since the time increment size in Abaqus/Explicit is inherently small. +One exception to this is when the Abaqus/Explicit analysis involves components undergoing several +revolutions, in which case it is recommended that the second-order accurate element formulation be +used in Abaqus/Explicit. +formulation (default) +Input File Usage: +Use the following options in the original analysis: +*MEMBRANE SECTION, CONTROLS=name1, ELSET=elset1 +*SHELL SECTION, CONTROLS=name2, ELSET=elset2 +*SHELL GENERAL SECTION, CONTROLS=name3, ELSET=elset3 +*SOLID SECTION, CONTROLS=name4, ELSET=elset4 +Use options similar to the following one in the original analysis: +*SECTION CONTROLS, NAME=name1 +Define section controls when you assign the element type in the original +analysis: +Mesh module: Mesh→Element Type: Element Controls +Abaqus/CAE Usage: +Membrane and shell element thickness computation +The computations for membrane and shell element thicknesses are described below. +Shell elements defined using a general shell section +For shells defined using a general shell section, the current thickness is computed based on the effective +Poisson’s ratio, which is 0.5 by default, in both Abaqus/Explicit and Abaqus/Standard. +Input File Usage: +Abaqus/CAE Usage: +*SHELL GENERAL SECTION, POISSON= +Property module: homogeneous or composite shell section editor: Section +integration: Before analysis: Advanced: Section Poisson's ratio +Shell elements defined using shell sections integrated during analysis and membrane elements +For shells defined using shell sections integrated during analysis and for membranes in Abaqus/Standard, +the current thickness is computed based on the effective Poisson’s ratio, which is 0.5 by default. In +Abaqus/Explicit, on the other hand, the computation of the thickness could be based either on the effective +Poisson’s ratio or the through-thickness strains, with the computation based on the through-thickness +strains used by default. +If you do not specify a section Poisson’s ratio for shell sections integrated during analysis or +for membrane sections in an original Abaqus/Explicit or Abaqus/Standard analysis, the thickness +computations in the original and all subsequent import analyses are carried out using the default +methods. +In other words, the thicknesses in all Abaqus/Standard analyses are computed using the +default effective Poisson’s ratio of 0.5, while the thicknesses in all Abaqus/Explicit analyses are +computed using the through-thickness strains. +When the section Poisson’s ratio is assigned a numerical value in an original Abaqus/Standard or +Abaqus/Explicit analysis, the thickness computations in the original analysis and all subsequent import +analyses are performed using the specified value for the effective Poisson’s ratio. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options: +*SHELL SECTION, POISSON= +*SHELL SECTION, POISSON=MATERIAL +*MEMBRANE SECTION, POISSON= +*MEMBRANE SECTION, POISSON=MATERIAL +Property module: +Homogeneous or composite shell section editor: Section integration: +During analysis: Advanced: Section Poisson's ratio +Membrane section editor: Section Poisson's ratio +Contact angle computation in SLIPRING-type connector elements +The contact angle, +, made by the belt wrapping around node b is computed automatically in Abaqus/Explicit, ignoring the value specified within the +Abaqus/Standard analysis. +Constraints +Most types of kinematic constraints (including multi-point constraints and surface-based tie constraints) +specified in the original analysis are not imported and must be defined again in the import analysis; +however, embedded element constraints are imported by default. See “Kinematic constraints: overview,” +Section 34.1.1, for a discussion of the various types of kinematic constraints. +Interactions +Contact definitions specified in the original analysis and the contact state are not imported. Contact +can be defined again in the import analysis by specifying the surfaces and contact pairs; however, you +may not be able to use the exact contact definitions that were used in the original analysis because of +differences in the contact capabilities between Abaqus/Standard and Abaqus/Explicit. +The contact constraint enforcement may be different in Abaqus/Standard and Abaqus/Explicit. +Examples of potential causes for differences include: +• Abaqus/Standard typically uses a “pure master-slave” approach, whereas Abaqus/Explicit typically +uses a “balanced master-slave” approach. +• Depending on the contact formulations used, Abaqus/Standard and Abaqus/Explicit sometimes treat +shell thicknesses and midsurface offsets differently. +Thus, when the contact conditions are defined in the import analysis, the contact state that existed in the +previous analysis may not be reproduced at the beginning of the import analysis. This could lead to a +redistribution of stresses and an analysis that differs from what you desire. In some cases this problem can +be mitigated by using nondefault options, such as ignoring shell thicknesses in the contact calculations, +to match behaviors in Abaqus/Standard and Abaqus/Explicit. +For a detailed description of the contact capabilities in Abaqus and the differences in the +contact capabilities between Abaqus/Standard and Abaqus/Explicit, see “Contact interaction analysis: +overview,” Section 35.1.1. +Output +Output can be requested for an import analysis in the same way as for an analysis in which the results +are not imported. The output variables available in Abaqus/Standard are listed in “Abaqus/Standard +output variable identifiers,” Section 4.2.1. The output variables available in Abaqus/Explicit are listed +in “Abaqus/Explicit output variable identifiers,” Section 4.2.2. +The values of the following material point output variables will be continuous in an import analysis +when the material state is imported: stress, equivalent plastic strain (PEEQ), and solution-dependent +state variables (SDV) for UMAT and VUMAT. Similarly, for a connector behavior, the plastic relative +displacement (CUP), kinematic hardening shift force (CALPHAF), overall damage (CDMG), damage +initiation criteria (CDIF, CDIM, CDIP), friction accumulated slip (CASU), and connector status (CSLST, +CFAILST) will be continuous. +If the reference configuration is not updated, the displacements, strains, whole element variables, +section variables, and energy quantities will be reported relative to the original configuration. +Accelerations are recomputed at the start of an import analysis in Abaqus/Explicit and may be different +from those obtained at the end of an Abaqus/Standard analysis. The differences in accelerations arise +from the recalculation of the internal forces created by the imported stresses using the Abaqus/Explicit +element formulation algorithms. +If the reference configuration is updated, displacements, strains, whole element variables, section +variables, and energy quantities will not be continuous in an import analysis and will be reported relative +to the updated reference configuration. +Time and step number will not be continuous between the original and the import analyses if the +reference configuration is updated. Time and step number will be continuous only if the reference +configuration is not updated. +Limitations +The import capability has the following known limitations. Where applicable, details are given in the +relevant sections. +• The same release of Abaqus/Explicit and Abaqus/Standard must be run on computers that are binary +compatible. +• The capability is not available for fluid elements; infinite elements; and spring, mass, dashpot, +and rotary inertia elements. Connector elements can be imported from Abaqus/Standard to +Abaqus/Explicit but not vice versa. See the discussion on “Elements” earlier in this section for +further details. +• If connector elements are imported, the configuration can be updated provided that the state is not +imported and the state can be imported provided that the configuration is not updated. +• All elements and nodes must be included in at least one set in the original analysis when importing +part instances. +• Node sets that are generated from existing element sets must +be defined in the original analysis. +• Surface definitions, contact pair definitions, and general contact definitions are not imported. +Analytical rigid surfaces will not be imported. +• If the material state is imported, only stresses will be imported for material models other than +those defined by linear elasticity, hyperelasticity, Mullins effect, hyperfoam, viscoelasticity, +Mises plasticity (including the kinematic hardening models), extended Drucker-Prager plasticity, +crushable foam plasticity, Mohr-Coulomb plasticity, critical state (clay) plasticity, cast iron +plasticity, concrete damaged plasticity, damage for cohesive elements, damage for ductile metals, +or damage for fiber-reinforced composites. See “Importing the material state” in “Transferring +results between Abaqus analyses: overview,” Section 9.2.1, for details. +• If the state is imported for connector elements with behavior defined, the plastic displacements, the +frictional slip, and the damage state are imported and the connector forces are recomputed. Some +of the connector output variables, such as CU, are also recomputed on import. The recomputed +variables may differ slightly at the point of import due to precision and algorithmic differences +between the two solvers across import. See “Importing the material state” in “Transferring results +between Abaqus analyses: overview,” Section 9.2.1, for details. +• Temperatures and field variables at nodes are not imported. If the temperature is a state variable (as +in an adiabatic analysis where temperature is an integration point quantity), it will be imported if +the material state is imported. See the discussion on “Predefined fields” for details. +• Loads, boundary conditions, multi-point constraints, and equations are not imported. +• Kinematic and distributing coupling constraints are not imported. In addition, the reference node +of a coupling constraint will not be imported unless the reference node is part of another element +definition that is imported. +• Element and contact pair +removal and +reactivation,” Section 11.2.1) cannot be used in the first step of an import analysis in +Abaqus/Standard. It can be used in the subsequent steps. +removal/reactivation (“Element and contact pair +• In a series of Abaqus/Standard and Abaqus/Explicit import analyses in the order Abaqus/Explicit(1) +→ Abaqus/Standard(1) → Abaqus/Explicit(2) →Abaqus/Standard(2), if elements in an element +set are removed in the Abaqus/Standard(1) analysis, the subsequent Abaqus/Standard(2) import +analysis does not recognize that this element set was removed in a previous analysis and fails with +an error message stating that the element set is not found in the restart file. Such failures can be +avoided by using flattened input files and requesting only the active element sets for import. +• Section controls must be defined in the original analysis if any of a series of import analyses uses +nondefault element formulations since section controls cannot be changed in an import analysis. +See the discussion on “Using section controls in an import analysis” earlier in this section. +• The symmetric model generation capability (“Symmetric model generation,” Section 10.4.1) cannot +be used in an import analysis in Abaqus/Standard. +• The results file, restart file, or output database file generated during the import analysis is not +appended to the results file, restart file, or output database file of the original analysis. +• An Abaqus/Standard import analysis where the reference configuration is not updated is not allowed +if the adaptive meshing capability (“ALE adaptive meshing: overview,” Section 12.2.1) was used +in the previous Abaqus/Explicit analysis. +• Mesh-independent spot welds and tie +constraints are not imported. These constraints can +be redefined in the import analysis and are formed using the reference configuration of the import +model. +If the reference configuration is updated, the redefined constraints may not match the +old constraints exactly due to the differences in geometry. If new constraints are defined and the +reference configuration of the import model is not updated, they may not initially be in compliance +if the nodes involved in the constraint have nonzero displacements. This may cause numerical +difficulty and potential abort of the import analysis. In this case it is recommended that you update +the reference configuration upon import. +• The first step after an import when the reference conference is updated should not be used to generate +a substructure. +• For beam structures that have acute curvatures and undergo large permanent changes in curvatures, +slightly different equilibrated configurations will be seen when using import depending on whether +or not the reference configuration is to be updated to the imported configuration . This configuration difference is due to beam element formulation differences +between Abaqus/Standard and Abaqus/Explicit. +Input file template +Transferring results between Abaqus/Explicit and Abaqus/Standard using models that are +not defined as assemblies of part instances: +Abaqus/Explicit analysis: +*HEADING +… +*MATERIAL, NAME=mat1 +*ELASTIC +Data lines to define linear elasticity +*PLASTIC +Data lines to define Mises plasticity +*DENSITY +Data line to define the density of the material +… +*BOUNDARY +Data lines to define boundary conditions +*STEP +*DYNAMIC, EXPLICIT +… +*RESTART, WRITE, NUMBER INTERVAL=n +*END STEP +Abaqus/Standard analysis: +*HEADING +*IMPORT, STEP=step, INTERVAL=interval, STATE=YES, UPDATE=NO +Data lines to specify element sets to be imported +*IMPORT ELSET +Data lines to specify element set definitions to be imported +*IMPORT NSET +Data lines to specify node set definitions to be imported +** +*** Optionally redefine the material block +** +*MATERIAL, NAME=mat1 +*ELASTIC +Data lines to redefine linear elasticity +*PLASTIC +Data lines to redefine Mises plasticity +… +*BOUNDARY +Data lines to redefine boundary conditions +*STEP, NLGEOM=YES +*STATIC +… +*END STEP +Transferring results between Abaqus/Standard and Abaqus/Explicit using models that are +not defined as assemblies of part instances: +Abaqus/Standard analysis: +*HEADING +… +*MATERIAL, NAME=mat1 +*ELASTIC +Data lines to define linear elasticity +*PLASTIC +Data lines to define Mises plasticity +*DENSITY +Data line to define the density of the material +… +*BOUNDARY +Data lines to define boundary conditions +*STEP +*STATIC +… +*RESTART, WRITE, FREQUENCY=n +*END STEP +Abaqus/Explicit analysis: +*HEADING +*IMPORT, STEP=step, INCREMENT=increment, STATE=YES, UPDATE=NO +Data lines to specify element sets to be imported +*IMPORT ELSET +Data lines to specify element set definitions to be imported +*IMPORT NSET +Data lines to specify node set definitions to be imported +** +*** Optionally redefine the material block +** +*MATERIAL, NAME=mat1 +*ELASTIC +Data lines to redefine linear elasticity +*PLASTIC +Data lines to redefine Mises plasticity +… +*BOUNDARY +Data lines to redefine boundary conditions +*STEP +*DYNAMIC, EXPLICIT +… +*END STEP +Transferring results between Abaqus/Explicit and Abaqus/Standard using models defined +as assemblies of part instances: +Abaqus/Explicit analysis: +*HEADING +*PART, NAME=Part-1 +Node, element, section, set, and surface definitions +*END PART +*ASSEMBLY, NAME=Assembly-1 +*INSTANCE, NAME=i1, PART=Part-1 + +Additional set and surface definitions (optional) +*END INSTANCE +Assembly level set and surface definitions +… +*END ASSEMBLY +*MATERIAL, NAME=mat1 +*ELASTIC +Data lines to define linear elasticity +*PLASTIC +Data lines to define Mises plasticity +*DENSITY +Data line to define the density of the material +… +*BOUNDARY +Data lines to define boundary conditions +*STEP +*DYNAMIC, EXPLICIT +… +*RESTART, WRITE, NUMBER INTERVAL=n +*END STEP +Abaqus/Standard analysis: +*HEADING +Part definitions (optional) +*ASSEMBLY, NAME=Assembly-1 +*INSTANCE, INSTANCE=i1, LIBRARY=oldjob-name +Additional set and surface definitions (optional) +*IMPORT, STEP=step, INTERVAL=interval, STATE=YES, UPDATE=NO +*END INSTANCE +Additional part instance definitions (optional) +Assembly level set and surface definitions +… +*END ASSEMBLY +** +*** Optionally redefine the material block +** +*MATERIAL, NAME=mat1 +*ELASTIC +Data lines to define linear elasticity +*PLASTIC +Data lines to define Mises plasticity +*DENSITY +Data line to define the density of the material +… +*BOUNDARY +Data lines to define boundary conditions +*STEP, NLGEOM=YES +*STATIC +… +*END STEP +Transferring results between Abaqus/Standard and Abaqus/Explicit using models defined +as assemblies of part instances: +Abaqus/Standard analysis: +*HEADING +*PART, NAME=Part-1 +Node, element, section, set, and surface definitions +*END PART +*ASSEMBLY, NAME=Assembly-1 +*INSTANCE, NAME=i1, PART=Part-1 + +Additional set and surface definitions (optional) +*END INSTANCE +Assembly level set and surface definitions +… +*END ASSEMBLY +*MATERIAL, NAME=mat1 +*ELASTIC +Data lines to define linear elasticity +*PLASTIC +Data lines to define Mises plasticity +*DENSITY +Data line to define the density of the material +… +*BOUNDARY +Data lines to define boundary conditions +*STEP +*STATIC +… +*RESTART, WRITE, FREQUENCY=n +*END STEP +Abaqus/Explicit analysis: +*HEADING +Part definitions (optional) +*ASSEMBLY, NAME=Assembly-1 +*INSTANCE, INSTANCE=i1, LIBRARY=oldjob-name +Additional set and surface definitions (optional) +*IMPORT, STEP=step, INCREMENT=increment, STATE=YES, UPDATE=NO +*END INSTANCE +Additional part instance definitions (optional) +Assembly level set and surface definitions +*END ASSEMBLY +** +*** Optionally redefine the material block +** +*MATERIAL, NAME=mat1 +*ELASTIC +Data lines to redefine linear elasticity +*PLASTIC +Data lines to redefine Mises plasticity +… +*BOUNDARY +Data lines to redefine boundary conditions +*STEP +*DYNAMIC, EXPLICIT +… +*END STEP +9.2.3 +TRANSFERRING RESULTS FROM ONE Abaqus/Standard ANALYSIS TO ANOTHER +Products: Abaqus/Standard Abaqus/CAE +References +• “Transferring results between Abaqus analyses: overview,” Section 9.2.1 +• *IMPORT +• *IMPORT ELSET +• *IMPORT NSET +• *IMPORT CONTROLS +• *INSTANCE +• “Transferring results between Abaqus analyses,” Section 16.6 of the Abaqus/CAE User’s Manual +Overview +information from an +Abaqus provides the capability to transfer desired results and model +Abaqus/Standard analysis to a new Abaqus/Standard analysis, where additional model definitions may +be specified before the analysis is continued. For example, during an assembly process an analyst may +first be interested in the local behavior of a particular component but later is concerned with the behavior +of the assembled product. In this case the local behavior can first be analyzed in an Abaqus/Standard +analysis. Subsequently, the model information and results from this analysis can be transferred to a +second Abaqus/Standard analysis, where additional model definitions for the other components can be +specified, and the behavior of the entire product can then be analyzed. +For this capability to work, the same release of Abaqus/Standard must be run on computers that are +binary compatible. +Information about how to transfer results between Abaqus analyses is provided in “Transferring +results between Abaqus analyses: overview,” Section 9.2.1. +Comparison with the restart capability +Both the import and restart capabilities in Abaqus/Standard allow for the transfer of results and model +information from one Abaqus/Standard analysis to another Abaqus/Standard analysis. However, the two +capabilities have been designed for different applications. +The restart capability allows a completed Abaqus/Standard analysis to be restarted and continued. +The entire model and results from the original analysis are transferred to the restart run, where additional +analysis steps can be defined. Not much new model data can be specified in the restarted analysis; only +model information such as new amplitude definitions, new node sets, and new element sets are allowed. +Detailed information on the restart capability is given in “Restarting an analysis,” Section 9.1.1. +The import capability also allows a completed Abaqus/Standard analysis to be continued. +In +addition, this capability allows for the analysis to be continued with only desired components from the +original analysis; the entire model need not be transferred. New model data—such as elements, nodes, +surfaces, contact pairs, etc.—can be specified during the import analysis. During the import analysis it +is possible to choose whether only model information from the previous analysis is to be transferred or +if the results associated with that model also are to be transferred. +For situations where the goal is to continue the original analysis with no change to the model +information, it is recommended that the restart capability be used. For situations where the model +information requires changes, or for cases where you require control over the transfer of results, the +import capability should be used. +Specifying new data in an import analysis +Additional model definitions such as new elements, nodes, surfaces, etc. can be defined during the import +analysis. Initial conditions can also be specified during the import analysis. +New model definitions +New nodes, elements, and material properties can be added to the model in an import analysis once import +has been specified. Nodal coordinates must be defined in the updated configuration, regardless of whether +or not the reference configuration is updated on import . The usual Abaqus/Standard +input can be used. Imported material definitions can be used with the new elements (which will need +new section property definitions). +Nodal transformation +transformations +(“Transformed coordinate systems,” Section 2.1.5) are not +Nodal +imported; +transformations can be defined independently in the import analysis. Continuous displacements, +velocities, etc. are obtained only if the nodal transformations in the import analysis are the same as those +in the original analysis. Use of the same transformations is also recommended for nodes with boundary +conditions or point loads defined in a local system. +Specifying geometric nonlinearity in an import analysis +By default, Abaqus/Standard uses a small-strain formulation (i.e., geometric nonlinearity is ignored). +For each step of an analysis you can specify whether or not geometric nonlinearity should be included; +see “Geometric nonlinearity” in “General and linear perturbation procedures,” Section 6.1.3, for details. +The default value for the formulation in an import analysis is the same as the value at the time +of import. Once the large-displacement formulation is used during a given step in any analysis, it will +remain active in all the subsequent steps, whether or not the analysis is imported. +If the small-displacement formulation is used at the time of import, the reference configuration +cannot be updated. +Specifying initial conditions for imported elements and nodes +Initial conditions can be specified on the imported elements or nodes only under certain conditions. +Table 9.2.3–1 lists the initial conditions that are allowed depending on whether or not the material +state is imported . The reference configuration can be updated or not, as desired, with one +exception: +for initial temperature or field variable conditions, the reference configuration must be +updated. +Table 9.2.3–1 Valid initial conditions. +Initial condition +Field variable +Hardening +Relative density +Rotational velocity +Solution-dependent state +variables +Stress +Temperature +Velocity +Void ratio +Material state +imported? +No +No +No +Yes or No +No +No +No +Yes or No +No +Procedures +Results can be imported only from a general analysis step involving static stress analysis, dynamic +stress analysis, steady-state transport analysis, coupled temperature-displacement analysis, or thermal- +electrical-structural analysis in Abaqus/Standard. Results transfer from linear perturbation procedures +(“General and linear perturbation procedures,” Section 6.1.3) is not allowed. +Abaqus/Standard offers several analysis procedures that can be used in an import analysis. These +procedures can be used to perform an eigenvalue analysis, static or dynamic stress analysis, buckling +analysis, etc. See “Solving analysis problems: overview,” Section 6.1.1, for a discussion of the available +procedures. +When results are transferred from an Abaqus/Standard dynamic analysis +to another +Abaqus/Standard analysis where the first step is a static procedure, +the initial out-of-balance +forces must be removed gradually from the system. The removal of these forces is performed +automatically by Abaqus/Standard during the first static analysis step, as described below. If the first +step in the Abaqus/Standard analysis is not a static step (such as a dynamic step), the analysis proceeds +directly from the state imported from the previous Abaqus/Standard analysis. +Achieving static equilibrium when importing from a dynamic analysis to a static analysis +When the current state of a deformed body in a dynamic analysis is imported into a static analysis, the +model will not initially be in static equilibrium. Initial out-of-balance forces must be applied to the +deformed body in dynamic equilibrium to achieve static equilibrium. Both dynamic forces (inertia and +damping) and boundary interaction forces contribute to the initial out-of-balance forces. The boundary +forces are the result of interactions from fixed boundary and contact conditions. Any changes in the +boundary and contact conditions will contribute to the initial out-of-balance forces. +In general, the instantaneous removal of the initial out-of-balance forces in a static analysis will +lead to convergence problems. Hence, these forces need to be removed gradually until complete static +equilibrium is achieved. During this process of removing the out-of-balance forces, the body will deform +further and a redistribution of internal forces will occur, resulting in a new stress state. (This is essentially +what occurs during “springback,” when a formed product is removed from the worktools.) +When the first step in the Abaqus/Standard import analysis is a static procedure, the following +algorithm is used to remove the initial out-of-balance forces automatically: +1. The imported stresses are defined at the start of the analysis as the initial stresses in the material. +2. An additional set of artificial stresses is defined at each material point. These stresses are equal in +magnitude to the imported stresses but are of opposite sign. The sum of the material point stresses +and these artificial stresses, thus, creates zero internal forces at the beginning of the step. +3. The internal artificial stresses are ramped off linearly in time during the first step. Thus, at the end +of the step the artificial stresses have been removed completely and the remaining stresses in the +material will be the residual stress state associated with static equilibrium. +Once static equilibrium has been obtained, subsequent steps can be defined using any analysis procedure +that would normally follow a static analysis. +When the first step is not a static analysis, no artificial stress state is applied and the imported stresses +are used in the internal force computations for the element. +Boundary conditions +Boundary conditions specified in the original analysis are not imported; they must be redefined in the +import analysis. +In some cases nonzero boundary conditions imposed in the original analysis need to be maintained +at the same values in the import analysis when the imported configuration is not updated. In such cases +you can prescribe a constant (step function) amplitude variation for the analysis step so that the newly applied +boundary conditions are applied instantaneously and held at that value for the duration of the step. +Alternatively, you can refer to an amplitude curve in the boundary condition definition . If boundary conditions in the original analysis are applied in a transformed +coordinate system , the same coordinate system +should be defined and used in the import analysis. +For discussions on applying boundary conditions and multi-point constraints, see “Boundary +conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1, and “Kinematic constraints: +overview,” Section 34.1.1. +Loads +Loads defined in the original analysis are not imported. Therefore, loads may need to be redefined in +the import analysis. There are no restrictions on the loads that can be applied when results are imported +from one analysis to the other. In cases when the loads need to be maintained at the same values as in the +original analysis, you can prescribe a constant (step function) amplitude variation for the analysis step + to apply the +loads instantaneously at the start of the step and hold them for the duration of the step. Alternatively, +you can refer to an amplitude curve in the load definition . If +point loads in the original analysis are applied in a transformed coordinate system and the loads must be maintained in the import analysis, the load +application is simplified if the same coordinate system is defined and used in the import analysis. +See “Applying loads: overview,” Section 33.4.1, for an overview of the loading types available in +Abaqus/Standard. +Predefined fields +Temperatures, whether they are prescribed or are degrees of freedom (as in a coupled thermal-stress +analysis), and field variables at nodes are imported if the material state is imported. +If the reference configuration is updated and the material state is imported, the initial conditions +for temperatures and field variables at the imported nodes will be reset to the imported values; for +example, the thermal strains will now be measured relative to the imported temperatures. If the reference +configuration is updated but the material state is not imported, the initial conditions are reset to zero. In +this case you can respecify the initial conditions on the imported nodes. +If the temperature is a state variable (as in an adiabatic analysis where temperature is an integration +point quantity), it will be imported if the material state is imported. +Material options +All material property definitions and orientations associated with imported elements are imported by +default. Material properties can be changed by respecifying the material property definitions with +the same material name. In this case all relevant material properties must be redefined since the old +definitions that were imported by default will be overwritten. Material orientations associated with +imported elements can be changed only if the reference configuration is updated and the material state +is not imported; the material orientations associated with imported elements cannot be redefined for +other combinations of the reference configuration and material state. +The material model must be redefined in the import analysis if changes to material damping are +required. +When material definitions are changed, care must be taken to ensure that a consistent material state +is maintained. It may sometimes be possible to simplify the material definition. For example, if a Mises +plasticity model was used in the first Abaqus/Standard analysis and no further plastic yielding is expected +in a subsequent Abaqus/Standard analysis, a linear elastic material can be used for the Abaqus/Standard +analysis. However, if further nonlinear material behavior is expected, no changes to the existing material +definitions should be made. The history of the state variables will not be maintained if the material +models are not the same in both the original analysis and the import analysis. +Elements +The import capability is available for thermal-electrical-structural elements and a subset of the +stress/displacement and coupled temperature-displacement continuum, shell, membrane, truss, rigid, +and surface elements available in Abaqus/Standard. The complete list of supported elements is provided +in Table 9.2.3–2. If elements that are removed are imported, they become active in the import analysis and should be removed in the +first step of the import analysis. +Table 9.2.3–2 Element types that can be transferred from one Abaqus/Standard analysis to another. +Element Type +Supported Elements +Plane strain continuum +CPE3, CPE3H, CPE3T, CPE4, CPE4H, CPE4HT, CPE4I, CPE4IH, +CPE4R, CPE4RHT, CPE4RT, CPE4T +CPE6, CPE6H, CPE6M, CPE6MH, CPE6MHT, CPE6MT, CPE8, +CPE8H, CPE8HT, CPE8R, CPE8RH, CPE8RHT, CPE8RT, CPE8T +Plane stress continuum +CPS3, CPS3T, CPS4, CPS4I, CPS4R, CPS4T +CPS6, CPS6M, CPS6MT, CPS8, CPS8R, CPS8RT, CPS8T +Three-dimensional +continuum +Axisymmetric continuum +C3D4, C3D4H, C3D4T, C3D6, C3D6H, C3D6T, C3D8, C3D8H, +C3D8HT, C3D8I, C3D8IH, C3D8R, C3D8RH, C3D8RHT, C3D8RT, +C3D8T, Q3D4, Q3D6, Q3D8, Q3D8H, Q3D8R, Q3D8RH +C3D10, C3D10H, C3D10I, C3D10M, C3D10MH, C3D10MHT, +C3D10MT, C3D15, C3D15H, C3D15V, C3D15VH, C3D20, +C3D20H, C3D20HT, C3D20R, C3D20RHT, C3D20RT, C3D20T, +C3D27, C3D27H, C3D27RH, Q3D10M, Q3D10MH, Q3D20, +Q3D20H, Q3D20R, Q3D20RH +CAX3, CAX3H, CAX3T, CAX4, CAX4H, CAX4HT, CAX4I, +CAX4IH, CAX4R, CAX4RH, CAX4RHT, CAX4RT, CAX4T +CAX6, CAX6M, CAX6MH, CAX6MHT, CAX6MT, CAX8, +CAX8H, CAX8HT, CAX8R, CAX8RH, CAX8RHT, CAX8RT, +CAX8T +Membrane +M3D3, M3D4R +Element Type +Supported Elements +Two-dimensional rigid +R2D2 +Three-dimensional rigid +R3D3, R3D4 +Axisymmetric rigid +RAX2 +Three-dimensional shell +S4R, S3R, S4RT, S3RT, S4T, S3T +Axisymmetric shell +SAX1 +Continuum shell +SC6RT, SC8RT +Surface +SFM3D3, SFM3D4R +Two-dimensional truss +T2D2, T2D2T +Three-dimensional truss +T3D2, T3D2T +Cohesive +COH2D4, COHAX4, COH3D6, COH3D8 +The following element types cannot be imported: +• Acoustic elements +• Axisymmetric-asymmetric continuum and shell elements +• Beam elements +• Connector elements +• Coupled thermal-electrical elements +• Diffusive heat transfer/mass diffusion elements and forced convection/diffusion elements +• Generalized plane strain elements +• Gasket elements +• Heat capacitance elements +• Inertial elements (mass and rotary inertia) +• Infinite elements +• Piezoelectric elements +• Special-purpose elements +• Substructures +• User-defined elements +In addition, the following restrictions apply to the import capability: +• Rebars defined using rebar layers (“Defining reinforcement,” Section 2.2.3) are imported provided +the underlying elements are also imported. Rebar reinforcements defined using the embedded +element technique (“Embedded elements,” Section 34.4.1) are imported if the host and embedded +elements used in this definition are also imported. Rebars defined as an element property (“Defining +rebar as an element property,” Section 2.2.4) cannot be imported. +• A rigid body containing both deformable and rigid elements cannot be imported. A rigid body that +includes rigid elements is imported when the element set used to define the rigid body is specified +for import. A rigid body that includes deformable elements is imported when the element set used +to define the rigid body is specified for import. The imported rigid body definition is overwritten if +it is respecified using the same element set. When the model is defined in terms of an assembly of +part instances, the reference node of an imported rigid body must belong to an imported instance. +• When a rigid body is imported, any associated data such as pin node sets and tie node sets are +part of the imported definition. However, these sets as imported contain only those nodes that are +connected to the imported elements. +Constraints +Most types of kinematic constraints specified in the original analysis are not imported and must be +defined again in the import analysis; however, surface-based tie constraints are imported by default. See +“Kinematic constraints: overview,” Section 34.1.1, for a discussion of the various types of kinematic +constraints. +Interactions +The various aspects of most surface-based mechanical contact definitions (including the surface, +contact pair, and contact property definitions) can be imported. Thermal interactions, electrical +interactions, and pore fluid surface interactions cannot be imported. Certain types of mechanical +contact aspects—pressure, penetration loads, and debonded surfaces—cannot be imported. The most +commonly used mechanical contact aspects—pressure-overclosure behavior, frictional behavior, and +damping—can be imported. +The ability to import element-based and node-based surfaces is determined by whether or not the +underlying elements and nodes defining these surfaces are imported. If the underlying elements or nodes +of a surface are not imported, that surface will not be imported. If only some of the underlying nodes +or elements used in the original definition of the surface are imported, only that part of the surface +corresponding to the imported elements will be imported. Rigid surface definitions are imported when +the associated slave surface is also imported. Contact pair definitions are imported provided that all the +slave and master surfaces used in the original definition of the contact pair are also imported. +Contact conditions modeled with contact elements will be ignored during the transfer process. +The contact state associated with a stress/displacement analysis is imported if the material state is +imported. If the reference configuration is updated, the accumulated contact strains will be set to zero. +The contact state associated with thermal, electrical, or pore fluid surface interactions is not imported. +The contact state associated with a crack propagation analysis is not imported; initially bonded contact +surface definitions are not transferred. If a contact pair was inactive in the step from which the import was +done due to the use of contact pair removal , it must be deactivated again in the first step of the +import analysis. +Additional contact information can be defined in the import analysis by specifying new surfaces, +contact pairs, and interactions. New contact pair definitions can use the imported surface interaction +definitions. +For a detailed description of the contact capabilities in Abaqus/Standard, refer to “Contact +interaction analysis: overview,” Section 35.1.1. +Output +Output can be requested for an import analysis in the same way as for an analysis in which the results are +not imported. Output requests in the original analysis are not transferred to the import analysis; output +requests in the import analysis have to be respecified. The output variables available in Abaqus/Standard +are listed in “Abaqus/Standard output variable identifiers,” Section 4.2.1. +The values of the following material point output variables will be continuous in an import analysis +when the material state is imported: stress, equivalent plastic strain (PEEQ), and solution-dependent +state variables (SDV) for UMAT. +If the reference configuration is not updated, the displacements, strains, whole element variables, +section variables, and energy quantities will be reported relative to the original configuration. +If the reference configuration is updated, displacements, strains, whole element variables, section +variables, and energy quantities will not be continuous in an import analysis and will be reported relative +to the updated reference configuration. +Time and step number will not be continuous between the original and the import analyses if the +reference configuration is updated. Time and step number will be continuous only if the reference +configuration is not updated. +Limitations +The import capability has the following known limitations. Where applicable, details are given in the +relevant sections. +• The same release of Abaqus/Standard must be run on computers that are binary compatible. +• The capability is not available for fluid elements; infinite elements; and spring, mass, dashpot, rotary +inertia, and connector elements. See the discussion on “Elements” earlier in this section for further +details. +• Surfaces are not imported when the model is defined as an assembly of part instances. +• All elements and nodes must be included in at least one set in the original analysis when importing +part instances. +• The contact state associated with thermal, electrical, and pore fluid surface interactions is not +imported; the contact state associated with crack propagation is not imported. +• General contact definitions are not imported. +• If the material state is imported, only stresses will be imported for material models other than those +defined by linear elasticity, hyperelasticity, hyperfoam, viscoelasticity, Mises plasticity, and damage +for cohesive elements. See “Importing the material state” in “Transferring results between Abaqus +analyses: overview,” Section 9.2.1, for details. +• Loads, boundary conditions, multi-point constraints, and equations are not imported. +• Kinematic and distributing coupling constraints are not imported. In addition, the reference node +of a coupling constraint will not be imported unless the reference node is part of another element +definition that is imported. +• When you import part instances individually from a previous analysis that was defined as an +assembly of part instances, reference nodes associated with rigid body or coupling constraints +defined on the imported instances will not be available in the import analysis for load or boundary +condition application. +• Pre-tension section definitions are not imported; they have to be redefined in the import analysis. +• The capability is not available for elements with composite solid section definitions. +• If the elements that are removed in the original analysis are imported, they become active in the import analysis and should +be removed in the first step of the import analysis. +• The symmetric model generation capability cannot be used in an import analysis in +Abaqus/Standard. +• The results file, restart file, or output database file generated during the import analysis is not +appended to the results file, restart file, or output database file of the original analysis. +• There may be a slight discontinuity during the transfer of state variables for analyses using fully +integrated, first-order continuum elements if the elements are significantly deformed and the +reference configuration is updated. +• Mesh-independent spot welds are not imported. +However, the spot weld reference nodes are imported and can be used to redefine spot welds in +the import analysis. The locations of the spot weld reference nodes and projection points are +computed based upon the reference configuration of the import analysis. Therefore, if the deformed +configuration of the imported model is significantly different from its reference configuration, it is +recommended that the reference configuration be updated. +• If the value of the friction coefficient is changed from the value given in the model data of the original +analysis, the changed value must be respecified in the first step of the import analysis . +• The capability is not available if adaptive meshing is used in the original analysis. +• Enriched features are not imported. +• Restart files from the original analysis are used in the analysis preprocessor and in the +Abaqus/Standard execution in the import analysis. When the import job is run in parallel on +computer clusters by using MPI-based parallelization, these restart files are copied to each host +machine. The original job restart files are not decomposed to match the import analysis parallel +domain and may be large relative to the local disk space available on the host machines. You can +minimize this file size by requesting restart output only for the increment from which import will +occur. +Input file template +Transferring results using models that are not defined as assemblies of part instances: +First Abaqus/Standard analysis: +*HEADING +… +*MATERIAL, NAME=mat1 +*ELASTIC +Data lines to define linear elasticity +*PLASTIC +Data lines to define Mises plasticity +*DENSITY +Data line to define the density of the material +… +*BOUNDARY +Data lines to define boundary conditions +*STEP, NLGEOM=YES +*STATIC +… +*RESTART, WRITE +*END STEP +Abaqus/Standard import analysis: +*HEADING +*IMPORT, STEP=step, INCREMENT=increment, STATE=YES, UPDATE=NO +Data lines to specify element sets to be imported +*IMPORT ELSET +Data lines to specify element set definitions to be imported +*IMPORT NSET +Data lines to specify node set definitions to be imported +** +*** Optionally define additional model information +** +*BOUNDARY +Data lines to redefine boundary conditions +*STEP, NLGEOM=YES +*STATIC +… +*END STEP +Transferring results using models defined as assemblies of part instances: +First Abaqus/Standard analysis: +*HEADING +*PART, NAME=Part-1 +Node, element, section, set, and surface definitions +*END PART +*ASSEMBLY, NAME=Assembly-1 +*INSTANCE, NAME=i1, PART=Part-1 + +Additional set and surface definitions (optional) +*END INSTANCE +Assembly level set and surface definitions +… +*END ASSEMBLY +*MATERIAL, NAME=mat1 +*ELASTIC +Data lines to define linear elasticity +*PLASTIC +Data lines to define Mises plasticity +*DENSITY +Data line to define the density of the material +… +*BOUNDARY +Data lines to define boundary conditions +*STEP +*STATIC +… +*RESTART, WRITE, FREQUENCY=n +*END STEP +Abaqus/Standard import analysis: +*HEADING +Part definitions (optional) +*ASSEMBLY, NAME=Assembly-1 +*INSTANCE, INSTANCE=i1, LIBRARY=oldjob-name +Additional set and surface definitions (optional) +*IMPORT, STEP=step, INCREMENT=increment, STATE=YES, UPDATE=NO +*END INSTANCE +Additional part instance definitions (optional) +Assembly level set and surface definitions +… +*END ASSEMBLY +** +*** Optionally define additional model information +** +*BOUNDARY +Data lines to define boundary conditions +*STEP, NLGEOM=YES +*STATIC +… +*END STEP +9.2.4 +TRANSFERRING RESULTS FROM ONE Abaqus/Explicit ANALYSIS TO ANOTHER +Products: Abaqus/Explicit Abaqus/CAE +References +• “Transferring results between Abaqus analyses: overview,” Section 9.2.1 +• *IMPORT +• *IMPORT ELSET +• *IMPORT NSET +• *IMPORT CONTROLS +• *INSTANCE +• “Transferring results between Abaqus analyses,” Section 16.6 of the Abaqus/CAE User’s Manual +Overview +Abaqus provides the capability to transfer desired results and model information from an Abaqus/Explicit +analysis to a new Abaqus/Explicit analysis, where additional model definitions may be specified before +the analysis is continued. For example, during an assembly process an analyst may first be interested +in the local behavior of a particular component but later is concerned with the behavior of the +assembled product. In this case the local behavior can first be analyzed in an Abaqus/Explicit analysis. +Subsequently, the model information and results from this analysis can be transferred to a second +Abaqus/Explicit analysis, where additional model definitions for the other components can be specified, +and the behavior of the entire product can then be analyzed. +For this capability to work, the same release of Abaqus/Explicit must be run on computers that are +binary compatible. +Information about how to transfer results between Abaqus analyses is provided in “Transferring +results between Abaqus analyses: overview,” Section 9.2.1. +Comparison with the restart capability +Both the import and restart capabilities in Abaqus/Explicit allow for the transfer of results and model +information from one Abaqus/Explicit analysis to another Abaqus/Explicit analysis. However, the two +capabilities have been designed for different applications. +The restart capability allows a completed Abaqus/Explicit analysis to be restarted and continued. +The entire model and results from the original analysis are transferred to the restart run, where additional +analysis steps can be defined. Not much new model data can be specified in the restarted analysis; only +model information such as new amplitude definitions, new node sets, and new element sets are allowed. +Detailed information on the restart capability is given in “Restarting an analysis,” Section 9.1.1. +The import capability also allows a completed Abaqus/Explicit analysis to be continued. In addition, +this capability allows for the analysis to be continued with only desired components from the original +analysis; the entire model need not be transferred. New model data—such as elements, nodes, surfaces, +contact pairs, etc.—can be specified during the import analysis. During the import analysis it is possible +to choose whether only model information from the previous analysis is to be transferred or if the results +associated with that model also are to be transferred. +For situations where the goal is to continue the original analysis with no change to the model +information, it is recommended that the restart capability be used. For situations where the model +information requires changes, or for cases where you require control over the transfer of results, the +import capability should be used. +Specifying new data in an import analysis +Additional model definitions such as new elements, nodes, surfaces, etc. can be defined during the import +analysis. Initial conditions can also be specified during the import analysis. +New model definitions +New nodes, elements, and material properties can be added to the model in an import analysis once import +has been specified. Nodal coordinates must be defined in the updated configuration, regardless of whether +or not the reference configuration is updated on import . The usual Abaqus/Explicit +input can be used. Imported material definitions can be used with the new elements (which will need +new section property definitions). +Nodal transformation +transformations +(“Transformed coordinate systems,” Section 2.1.5) are not +Nodal +imported; +transformations can be defined independently in the import analysis. Continuous displacements, +velocities, etc. are obtained only if the nodal transformations in the import analysis are the same as those +in the original analysis. Use of the same transformations is also recommended for nodes with boundary +conditions or point loads defined in a local system. +Specifying geometric nonlinearity in an import analysis +By default, Abaqus/Explicit uses a large-strain formulation. For each step of an analysis you can specify +whether or not geometric nonlinearity should be included; see “Geometric nonlinearity” in “General and +linear perturbation procedures,” Section 6.1.3, for details. +The default value for the formulation in an import analysis is the same as the value at the time +of import. Once the large-displacement formulation is used during a given step in any analysis, it will +remain active in all the subsequent steps, whether or not the analysis is imported. +If the small-displacement formulation is used at the time of import, the reference configuration +cannot be updated. +Specifying initial conditions for imported elements and nodes +Initial conditions can be specified on the imported elements or nodes only under certain conditions. +Table 9.2.4–1 lists the initial conditions that are allowed depending on whether or not the material +state is imported . The reference configuration can be updated or not, as desired, with one +exception: +for initial temperature or field variable conditions, the reference configuration must be +updated. +Table 9.2.4–1 Valid initial conditions. +Initial condition +Field variable +Hardening +Relative density +Rotational velocity +Solution-dependent state +variables +Stress +Temperature +Velocity +Void ratio +Material state +imported +No +No +No +Yes or No +No +No +No +Yes or No +No +Boundary conditions +Boundary conditions (including connector motion) specified in the original analysis are not imported. +They must be redefined in the import analysis. +In some cases nonzero boundary conditions imposed in the original analysis need to be maintained +at the same values in the import analysis when the imported configuration is not updated. In such cases +you can prescribe a constant (step function) amplitude variation for the analysis step so that the newly applied +boundary conditions are applied instantaneously and held at that value for the duration of the step. +Alternatively, you can refer to an amplitude curve in the boundary condition definition . If boundary conditions in the original analysis are applied in a transformed +coordinate system , the same coordinate system +should be defined and used in the import analysis. +For discussions on applying boundary conditions and multi-point constraints, see “Boundary +conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1, and “Kinematic constraints: +overview,” Section 34.1.1. +Loads +Loads, including those applied for connector actuation, defined in the original analysis are not imported. +Therefore, loads may need to be redefined in the import analysis. There are no restrictions on the loads +that can be applied when results are imported from one analysis to the other. In cases when the loads +need to be maintained at the same values as in the original analysis, you can prescribe a constant (step +function) amplitude variation for the analysis step to apply the loads instantaneously at the start of the step and +hold them for the duration of the step. Alternatively, you can refer to an amplitude curve in the load +definition . If point loads in the original analysis are applied in +a transformed coordinate system and the loads +must be maintained in the import analysis, the load application is simplified if the same coordinate system +is defined and used in the import analysis. +See “Applying loads: overview,” Section 33.4.1, for an overview of the loading types available in +Abaqus/Explicit. +Predefined fields +Temperatures, whether they are prescribed or are degrees of freedom (as in a coupled thermal-stress +analysis), and field variables at nodes are imported if the material state is imported. +If the reference configuration is updated and the material state is imported, the initial conditions +for temperatures and field variables at the imported nodes will be reset to the imported values; for +example, the thermal strains will now be measured relative to the imported temperatures. If the reference +configuration is updated but the material state is not imported, the initial conditions are reset to zero. In +this case you can respecify the initial conditions on the imported nodes. +If the temperature is a state variable (as in an adiabatic analysis where temperature is an integration +point quantity), it will be imported if the material state is imported. +Material options +All material property definitions and orientations associated with imported elements are imported by +default. Material properties can be changed by respecifying the material property definitions with +the same material name. In this case all relevant material properties must be redefined since the old +definitions that were imported by default will be overwritten. Material orientations associated with +imported elements can be changed only if the reference configuration is updated and the material state +is not imported; the material orientations associated with imported elements cannot be redefined for +other combinations of the reference configuration and material state. +When connector elements are imported, any associated connector behavior definitions are imported +by default. The imported connector behavior definitions can be modified only if the state is not imported. +The material model must be redefined in the import analysis if changes to material damping are +required. +When material definitions are changed, care must be taken to ensure that a consistent material state +It may sometimes be possible to simplify the material definition. For example, if a +is maintained. +Mises plasticity model was used in the first Abaqus/Explicit analysis and no further plastic yielding is +expected in a subsequent Abaqus/Explicit analysis, a linear elastic material can be used for the subsequent +Abaqus/Explicit analysis. However, if further nonlinear material behavior is expected, no changes to the +existing material definitions should be made. The history of the state variables will not be maintained if +the material models are not the same in both the original analysis and the import analysis. +Elements +The import capability is available for a subset of the stress/displacement and coupled temperature- +displacement continuum, shell, membrane, truss, connector, rigid, and surface elements available in +Abaqus/Explicit. The complete list of supported elements is provided in Table 9.2.4–2. If elements that +are removed are imported, +they become active in the import analysis and should be removed in the first step of the import analysis. +Table 9.2.4–2 Element types that can be transferred from one Abaqus/Explicit analysis to another. +Element Type +Supported Elements +Plane strain continuum +CPE3, CPE4R, CPE4RT, CPE6M, CPE6MT, CPE3T +Plane stress continuum +CPS3, CPS4R, CPS4RT, CPS6M, CPS6MT, CPS3T +Three-dimensional +continuum +C3D4, C3D4T, C3D6, C3D6T, C3D8R, C3D8RT, C3D10M, +C3D10MT, C3D8, C3D8T, C3D8I +Axisymmetric continuum +CAX3, CAX4R, CAX3T, CAX4RT, CAX6M, CAX6MT +Membrane +M3D3, M3D4 M3D4R +Two-dimensional rigid +R2D2 +Three-dimensional rigid +R3D3, R3D4 +Axisymmetric rigid +RAX2 +Three-dimensional shell +S4R, S3R, S3, S4, S4RS, S4RSW, S3RS, S3T, S3RT, S4T, S4RT +Continuum shell elements +SC6R, SC8R, SC6RT, SC8RT +Axisymmetric shell +SAX1 +Surface +SFM3D3, SFM3D4R +Two-dimensional truss +Three-dimensional truss +T2D2 +T3D2 +Two-dimensional beam +B21, B22 +Three-dimensional beam +B31, B32 +Connector elements +CONN2D2, CONN3D2 +Element Type +Supported Elements +Cohesive +COH2D4, COHAX4, COH3D6, COH3D8 +Infinite elements +CINPS4, CINPE4, CINAX4, CIN3D8, ACIN2D2, ACIN3D3, +ACINAX2 +Acoustic elements +AC2D3, AC2D4R, AC3D4, AC3D6, ACAX3, ACAX4R, AC3D8R +The following element types cannot be imported: +• Heat capacitance elements +• Inertial elements (mass and rotary inertia) +• Eulerian elements (EC3D8R and EC3D8RT) +In addition, the following restrictions apply to the import capability: +• Rebars defined using rebar layers (“Defining reinforcement,” Section 2.2.3) are imported provided +the underlying elements are also imported. Rebar reinforcements defined using the embedded +element technique (“Embedded elements,” Section 34.4.1) are imported if the host and embedded +elements used in this definition are also imported. Rebars defined as an element property (“Defining +rebar as an element property,” Section 2.2.4) cannot be imported. +• If connector elements are imported, the configuration can be updated provided that the state is not +imported and the state can be imported provided that the configuration is not updated. +• A rigid body containing both deformable and rigid elements cannot be imported. A rigid body that +includes rigid elements is imported when the element set used to define the rigid body is specified +for import. A rigid body that includes deformable elements is imported when the element set used +to define the rigid body is specified for import. The imported rigid body definition is overwritten if +it is respecified using the same element set. When the model is defined in terms of an assembly of +part instances, the reference node of an imported rigid body must belong to an imported instance. +• When a rigid body is imported, any associated data such as pin node sets and tie node sets are +part of the imported definition. However, these sets as imported contain only those nodes that are +connected to the imported elements. +Constraints +Kinematic constraints (including multi-point constraints and surface-based tie constraints) specified in +the original analysis are not imported and must be defined again in the import analysis. See “Kinematic +constraints: overview,” Section 34.1.1, for a discussion of the various types of kinematic constraints. +Interactions +For general contact, the contact state is imported if general contact is defined in both analyses. +For contact defined by contact pairs, contact definitions specified in the original analysis and the +contact state are not imported. Contact can be defined again in the import analysis by specifying the +surfaces and contact pairs. +Additional contact information can be defined in the import analysis by specifying new surfaces, +contact pairs, and interactions. +For a detailed description of the contact capabilities in Abaqus/Explicit, refer to “Contact interaction +analysis: overview,” Section 35.1.1. +Output +Output can be requested for an import analysis in the same way as for an analysis in which the results are +not imported. Output requests in the original analysis are not transferred to the import analysis; output +requests in the import analysis have to be respecified. The output variables available in Abaqus/Explicit +are listed in “Abaqus/Explicit output variable identifiers,” Section 4.2.2. +The values of the following material point output variables will be continuous in an import analysis +when the material state is imported: stress, equivalent plastic strain (PEEQ), and solution-dependent +state variables (SDV) for VUMAT. Similarly, for a connector behavior, the plastic relative displacement +(CUP), kinematic hardening shift force (CALPHAF), overall damage (CDMG), damage initiation criteria +(CDIF, CDIM, CDIP), friction accumulated slip (CASU), and connector status (CSLST, CFAILST) will +be continuous. +If the reference configuration is not updated, the displacements, strains, whole element variables, +section variables, and energy quantities will be reported relative to the original configuration. +If the reference configuration is updated, displacements, strains, whole element variables, section +variables, and energy quantities will not be continuous in an import analysis and will be reported relative +to the updated reference configuration. +Time and step number will not be continuous between the original and the import analyses if the +reference configuration is updated. Time and step number will be continuous only if the reference +configuration is not updated. +Limitations +The import capability has the following known limitations. Where applicable, details are given in the +relevant sections. +• The same release of Abaqus/Explicit must be run on computers that are binary compatible. +• The capability is not available for spring, mass, dashpot, and rotary inertia. See the discussion on +“Elements” earlier in this section for further details. +• If connector elements are imported, the configuration can be updated provided that the state is not +imported and the state can be imported provided that the configuration is not updated. +• Surfaces are not imported when the model is defined as an assembly of part instances. +• All elements and nodes must be included in at least one set in the original analysis when importing +part instances. +• The contact state for contact pairs is not imported. +• If the material state is imported, only stresses will be imported for material models other than those +defined by linear elasticity, hyperelasticity, hyperfoam, viscoelasticity, Mises plasticity, and damage +for cohesive elements. See “Importing the material state” in “Transferring results between Abaqus +analyses: overview,” Section 9.2.1, for details. For a connector behavior, the plastic displacements, +the frictional slip, and the damage state are imported and the connector forces are recomputed. +See “Importing the material state” in “Transferring results between Abaqus analyses: overview,” +Section 9.2.1, for details. +• Loads, boundary conditions, multi-point constraints, equations, and surface-based tie constraints +are not imported. +• Kinematic and distributing coupling constraints are not imported. In addition, the reference node +of a coupling constraint will not be imported unless the reference node is part of another element +definition that is imported. +• The results file, restart file, or output database file generated during the import analysis is not +appended to the results file, restart file, or output database file of the original analysis. +• Mesh-independent spot welds and tie +constraints are not imported. These constraints can +be redefined in the import analysis and are formed using the reference configuration of the import +model. +If the reference configuration is updated, the redefined constraints may not match the +old constraints exactly due to the differences in geometry. If new constraints are defined and the +reference configuration of the import model is not updated, they may not initially be in compliance +if the nodes involved in the constraint have nonzero displacements. This may cause numerical +difficulty and potential abort of the import analysis. In this case it is recommended that you update +the reference configuration upon import. +Input file template +Transferring results using models that are not defined as assemblies of part instances: +First Abaqus/Explicit analysis: +*HEADING +… +*MATERIAL, NAME=mat1 +*ELASTIC +Data lines to define linear elasticity +*PLASTIC +Data lines to define Mises plasticity +*DENSITY +Data line to define the density of the material +… +*BOUNDARY +Data lines to define boundary conditions +*STEP +*DYNAMIC, EXPLICIT +… +*RESTART, WRITE, NUMBER INTERVAL=n +*END STEP +Abaqus/Explicit import analysis: +*HEADING +*IMPORT, STEP=step, INTERVAL=interval, STATE=YES, UPDATE=NO +Data lines to specify element sets to be imported +*IMPORT ELSET +Data lines to specify element set definitions to be imported +*IMPORT NSET +Data lines to specify node set definitions to be imported +** +*** Optionally define additional model information +** +*BOUNDARY +Data lines to redefine boundary conditions +*STEP +*DYNAMIC, EXPLICIT +… +*END STEP +Transferring results using models defined as assemblies of part instances: +First Abaqus/Explicit analysis: +*HEADING +*PART, NAME=Part-1 +Node, element, section, set, and surface definitions +*END PART +*ASSEMBLY, NAME=Assembly-1 +*INSTANCE, NAME=i1, PART=Part-1 + +Additional set and surface definitions (optional) +*END INSTANCE +Assembly level set and surface definitions +… +*END ASSEMBLY +*MATERIAL, NAME=mat1 +*ELASTIC +Data lines to define linear elasticity +*PLASTIC +Data lines to define Mises plasticity +*DENSITY +Data line to define the density of the material +… +*BOUNDARY +Data lines to define boundary conditions +*STEP +*DYNAMIC, EXPLICIT +… +*RESTART, WRITE, NUMBER INTERVAL=n +*END STEP +Abaqus/Explicit import analysis: +*HEADING +Part definitions (optional) +*ASSEMBLY, NAME=Assembly-1 +*INSTANCE, INSTANCE=i1, LIBRARY=oldjob-name +Additional set and surface definitions (optional) +*IMPORT, STEP=step, INTERVAL=interval, STATE=YES, UPDATE=NO +*END INSTANCE +Additional part instance definitions (optional) +Assembly level set and surface definitions +… +*END ASSEMBLY +** +*** Optionally define additional model information +** +*BOUNDARY +Data lines to define boundary conditions +*STEP +*DYNAMIC, EXPLICIT +… +*END STEP +10. +Modeling Abstractions +Substructuring +Submodeling +Generating global matrices +Symmetric model generation, results transfer, and analysis of cyclic symmetry models +Periodic media analysis +Meshed beam cross-sections +Modeling discontinuties as an enriched figure using extended finite element method +10.1 +10.2 +10.3 +10.4 +10.5 +10.6 +10.1 +Substructuring +• “Using substructures,” Section 10.1.1 +• “Defining substructures,” Section 10.1.2 +10.1.1 +USING SUBSTRUCTURES +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining substructures,” Section 10.1.2 +• *SLOAD +• *SUBSTRUCTURE PATH +• *SUBSTRUCTURE PROPERTY +Overview +Substructures: +• allow a collection of elements to be grouped together and all but the retained degrees of freedom +eliminated on the basis of linear response within the group; +• are used in the same manner as any of the standard element types in the Abaqus element library +once created as described in “Defining substructures,” Section 10.1.2; +• can be used in stress/displacement and in coupled acoustic-structural analyses; +• have linear response but allow for large translations and large rotations; +• are particularly useful in cases where identical pieces appear several times in a structure (such as +the teeth of a gear) since a single substructure can be used repeatedly; +• can be translated, rotated with respect to the global system, and reflected in a plane when they are +used; +• are connected to the rest of the model by the retained degrees of freedom at the retained nodes; +• may contain a set of internal load cases and boundary conditions that can be activated and scaled; +• can include dynamic effects by including retained eigenmodes; and +• appear to the rest of the model as a stiffness, optional mass, damping, and a set of scalable load +vectors. +Substructures +Substructures are collections of elements from which the internal degrees of freedom have been +eliminated. Retained nodes and degrees of freedom are those that will be recognized externally at the +usage level (when the substructure is used in an analysis), and they are defined during generation of +the substructure. Factors that determine how many and which nodes and degrees of freedom should be +retained are discussed below and in “Defining substructures,” Section 10.1.2. +Substructures versus superelements +In the finite element literature substructures are also referred to as superelements. In earlier releases of +Abaqus a distinction was made between substructures and superelements. The term “substructure” was +used when it was needed to make clear that results were recovered within the substructure. Otherwise, +both terms were used interchangeably. To avoid confusion, the term “superelement” will no longer be +used. +Why use substructures? +There are a number of good reasons to use substructures. +Computational advantages +• System matrices (stiffness, mass) are small as a result of substructuring. Subsequent to the creation +of the substructure, only the retained degrees of freedom and the associated reduced stiffness (and +mass) matrix are used in the analysis until it is necessary to recover the solution internal to the +substructure. +• Efficiency is improved when the same substructure is used multiple times. The stiffness calculation +and substructure reduction are done only once; however, the substructure itself can be used many +times, resulting in a significant savings in computational effort. +• Substructuring can isolate possible changes outside substructures to save time during reanalysis. +During the design process large portions of the structure will often remain unchanged; these portions +can be isolated in a substructure to save the computational effort involved in forming the stiffness +of that part of the structure. +• In a problem with local nonlinearities, such as a model that includes interfaces with possible +separation or contact, the iterations to resolve these local nonlinearities can be made on a very +much reduced number of degrees of freedom if the substructure capability is used to condense the +model down to just those degrees of freedom involved in the local nonlinearity. +Organizational advantages +• Substructuring provides a systematic approach to complex analyses. The design process often +begins with independent analyses of naturally occurring substructures. Therefore, it is efficient to +perform the final design analysis with the use of substructure data obtained during these independent +analyses. +• Substructure libraries allow analysts to share substructures. In large design projects large groups of +engineers must often conduct analyses using the same structures. Substructure libraries provide a +clean and simple way of sharing structural information. +• Many practical structures are so large and complex that a finite element model of the complete +structure places excessive demands on available computational resources. Such a large linear +problem can be solved by building the model, substructure by substructure, and stacking these +level by level until the whole structure is complete and then recovering the displacements and +stresses locally, as required. +Valid procedures +Substructures can be used without restriction in the following procedures: +• “Static stress analysis,” Section 6.2.2 +• “Implicit dynamic analysis using direct integration,” Section 6.3.2 +• “Direct-solution steady-state dynamic analysis,” Section 6.3.4 +• “Natural frequency extraction,” Section 6.3.5 +• “Complex eigenvalue extraction,” Section 6.3.6 +• “Mode-based steady-state dynamic analysis,” Section 6.3.8 +Substructures can also be used in the following procedures, but recovery of eliminated degrees of freedom +is not supported: +• “Transient modal dynamic analysis,” Section 6.3.7 +• “Response spectrum analysis,” Section 6.3.10 +• “Random response analysis,” Section 6.3.11 +Using substructures in static analysis +Substructuring introduces no additional approximation in linear static structural analysis: +the +substructure is an exact representation of the linear, static behavior of its members. The principal +drawback to the use of substructures in stress/displacement analyses is that a substructure’s stiffness +matrix is fully populated (no zero terms) and, therefore, may be very large if the substructure has a large +number of retained degrees of freedom. This, in turn, may mean that the wavefront of the model within +which substructures are used may be large, thus leading to long computer times to solve the equations. +This difficulty can often be avoided by choosing the substructure’s boundaries carefully or by +reusing several smaller substructures rather than a single larger substructure. In some cases it is possible +to take advantage of the fact that Abaqus/Standard allows individual degrees of freedom to be retained, +rather than the whole set of degrees of freedom at a node. For example, in contact problems without +friction only the displacement component normal to the surface need be retained for the contact solution. +Nodal transformations can be helpful in orienting the displacement components at surface nodes for +this purpose . +In a static analysis involving a substructure containing acoustic elements, the results will differ +from the results obtained in an equivalent static analysis without substructures. The acoustic-structural +coupling is taken into account in the substructure (leading to hydrostatic contributions of the acoustic +fluid), while the coupling is ignored in a static analysis without substructures. +Using substructures in dynamic analysis +Substructures introduce approximations in dynamic analysis. The default approach to the dynamic +representation of a substructure is to reduce its mass and damping matrix with the same transformation +as is used for its stiffness matrix, which is known as “Guyan reduction.” This approach assumes that the +response between the eliminated and retained degrees of freedom is correctly represented by the static +modes only. This representation may not be accurate if dynamic modes within the substructure are +important. The dynamic representation may be improved for Guyan reduction by retaining additional +physical degrees of freedom that are not required to connect the substructure to the rest of the model. +For example, if the substructure is a plate or a beam, some transverse displacements (and, perhaps, +in-surface rotation components) might be included as retained degrees of freedom for this purpose. For +more details regarding Guyan reduction, see “Substructuring and substructure analysis,” Section 2.14.1 +of the Abaqus Theory Manual. +“Dynamic mode addition” can be used as an alternative to Guyan reduction. This approach +involves adding generalized degrees of freedom associated with the eigenmodes extracted for the +substructure, with all of the physical retained degrees of freedom automatically constrained. This +improves dynamic behavior, but it introduces the additional cost of extracting the eigenmodes for the +constrained substructure. For more details regarding dynamic mode addition, see “Substructuring and +substructure analysis,” Section 2.14.1 of the Abaqus Theory Manual. +The reduction methods can be applied simultaneously to different substructures within the same +structure. Definition of the reduced mass matrix is discussed further in “Defining substructures,” +Section 10.1.2. +Using substructures in geometrically nonlinear stress/displacement analysis +Substructures may undergo large motions if geometric nonlinearities are considered in a particular +overview,” Section 6.2.1). +stress/displacement analysis deformations at all times during +the geometrically nonlinear analysis. An equivalent rigid body rotation for each substructure is computed +during each equilibrium iteration using the retained nodes of the substructure. The substructure’s +mass, damping, stiffness matrix (including the retained eigenmodes), and force vectors are then +rotated appropriately using the equivalent rigid body rotation. Appropriate (rotated) linear perturbation +displacements (strain-inducing displacements relative to the rotating reference configuration) are used +to compute the internal force associated with the substructure. Degrees of freedom at a node should not +be retained selectively if the substructure is to be used in geometrically nonlinear analysis. Coupled +acoustic-structural substructures should not be used in geometrically nonlinear analyses. +Comparison with component mode synthesis +The component mode synthesis method (also known as the Craig-Bampton method) has been developed +to permit the structure to be subdivided into components (substructures), with most of the analysis being +done on the smaller components to develop an approximate model for the entire structure. +The substructures in Abaqus/Standard are, in fact, a particular case of the Craig-Bampton method +extended to allow for large rotations and translations of the substructure (component). The component +mode synthesis method is based on the assumption that the small deformations of a substructure can be +modeled using a collection of modes. The most frequently used modes in the literature are typically +referred to as follows: +• constraint modes, which are static shapes obtained by giving each retained degree of freedom in the +substructure a unit displacement while holding all other retained degrees of freedom fixed; and +• fixed-interface normal modes, which are obtained by fixing the retained degrees of freedom and +computing the eigenmodes of the substructure. +The constraint modes are precisely the static modes used by Abaqus/Standard. You include these modes in the +substructure’s representation by specifying the degrees of freedom that are to be retained . The fixed-interface +normal modes are the eigenmodes extracted in the eigenfrequency extraction step at the generation +level, and these modes represent a particular case of substructure dynamic modes allowed in Abaqus +. You +include the dynamic modes in the substructure’s representation by specifying the eigenmodes to be +retained. +Including substructures in a model +When a substructure is used in a model, it is assigned an element number and defined by nodes just like +any other element. +Use an element definition (“Element definition,” Section 2.2.1) with a substructure identifier to +include substructures in the definition of another substructure (nested substructure) or in an analysis +model. The substructure can be read from a substructure library. A maximum of 500 libraries can be +accessed to read substructure data within a given analysis. +In the element definition you define the substructure’s element number at the usage level and assign +node numbers to the substructure’s retained nodes. More than one substructure can be defined per element +definition. +Once a substructure has been introduced by an element definition, it is treated like any other element +in the model, except that its response can be linear only (although it can be used as a part of a model that +includes nonlinear effects, including large displacements). +Using substructures requires that the substructure database be available. All the files generated for +a substructure including the .sup and .sim files and/or the .prt, .stt, and .mdl files must be +available. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to include one or more substructures in a model: +*ELEMENT, TYPE=Zn +Use the following option to include one substructure in a model: +All modules: File→Import→Part: File Filter: Substructure +Repeat the import process for each substructure that you want to include in the +model. +Ordering of the substructure nodes on the usage level +The node numbers that are used when a substructure is created and the node numbers that are associated +with the substructure when it is used are entirely independent. The ordering of the retained nodes when +the substructure is used can be defined in two different ways: +1. The nodes can be provided in the same order that they were listed in the substructure definition. In +this case you must prevent the sorting of the retained nodes when you specify the retained degrees +of freedom (see “Preventing the degrees of freedom from being sorted” in “Defining substructures,” +Section 10.1.2). Duplicate nodes are not combined if the retained nodes are not sorted. Therefore, +if the same nodes are specified more than once in the list of retained degrees of freedom to retain +different degrees of freedom, the corresponding nodes at the usage level must appear the same +number of times. +2. The substructure nodes must be specified in the same order as the retained nodes sorted into +ascending numerical order according to their numbers used within the substructure. This approach +is the default when you specify the retained degrees of freedom. +In either case you must ensure that the nodes match up properly whenever a substructure is used. +Reading the substructure definition from a substructure library +You can read the substructure definition from a substructure library. +Input File Usage: +Abaqus/CAE Usage: +*ELEMENT, TYPE=Zn, FILE=substructure_library_name +Substructure libraries are not supported in Abaqus/CAE. +Interpreting the model output in the data file +If model definition data are written to the data file (“Controlling the amount of analysis input file processor +information written to the data file” in “Output,” Section 4.1.1), substructure instances are identified in +the data (.dat) file by the substructure identifier followed by an F and two digits that indicate the +substructure library number. The full name of the substructure library associated with this number is +also contained in the model output. +Defining the substructure’s properties +You associate a property definition with each substructure in the model. The property definition serves +the following purposes: +1. It defines any translation, rotation, and reflection of the substructure at the usage level. +2. It allows a tolerance to be set to ensure that the coordinates of the usage level nodes match the +coordinates of the nodes used to generate the substructure. +3. It controls using various sources of substructure damping in the dynamic analysis at the usage level. +Input File Usage: +Abaqus/CAE Usage: +*SUBSTRUCTURE PROPERTY, ELSET=name +Use the following options to define translation and rotation of the substructure: +Assembly module: Instance→Translate or Instance→Rotate +Reflection of the substructure is not supported in Abaqus/CAE. +Use the following option to apply constraints that connect the retained nodes +with the usage level nodes: +Interaction module: Constraint→Create +Translating, rotating, and reflecting a substructure +Translation, rotation, and/or reflection (in that order) of a substructure can be specified in a substructure +property definition. +Specify a translation by giving a translation vector. Specify a rotation by giving two points, a and +b, defining a rotation axis plus a right-handed angular rotation around that axis. Specify a reflection by +giving three non-colinear points in the reflection plane. +A translation does not affect the substructure’s stiffness or mass: the principal reason to apply a +translation is to enable the tolerance check on nodal coordinates as discussed later. Rotation and/or +reflection of a substructure affect the substructure’s stiffness and mass. The substructure load case +definitions are rotated and/or reflected in the same way as the substructure’s stiffness and mass; +therefore, all loads within substructure load cases are applied in the local directions associated with the +substructure when it was created. +For distributed loads (for example, pressure loading of a surface) this application is precisely what +is desired. However, distributed body forces in coordinate directions (BX, BY, BZ) are applied in the +substructure’s local directions instead of in the global directions, which may not be what is needed. +Similarly, distributed loadings that depend on position (for example, hydrostatic pressure or centrifugal +loads) are based on the substructure’s local coordinates and not on the substructure position during usage. +Be careful to ensure that loading of a rotated or shifted substructure is correct for its usage. +Whenever a substructure is translated, rotated, and/or reflected, the degrees of freedom at any +retained nodes are with respect to the coordinate directions at the usage level. Therefore, if all of +the degrees of freedom of a node are not retained or if a two-dimensional substructure is used in a +three-dimensional model with rotation out of the x–y plane, additional degrees of freedom may be +activated due to rotation and/or reflection. Be careful to check the validity of the substructure usage +in such cases. +Setting a tolerance on the substructure nodes +One difficulty with using large substructures is ensuring that the retained nodes in the substructure +are connected to the correct nodes on the usage level (after substructure translation, rotation, and/or +reflection, if applicable). Therefore, Abaqus/Standard checks that the coordinates of the retained nodes +match the coordinates of the corresponding nodes on the usage level. A substructure does not require +any coordinates on the usage level because it consists only of a stiffness matrix, a mass matrix, and a +number of load cases. Nevertheless, it is usually a good check of a model’s validity to verify that the +substructure and the model into which it is introduced are geometrically consistent. +To check the coordinates, you can set a tolerance on the distance between usage level nodes and +the corresponding substructure nodes. This tolerance indicates the largest deviation allowable before a +warning is issued. If you do not specify this tolerance, the default is to use a tolerance of 10−4 times the +largest overall dimension within the substructure. If you specify a tolerance of 0.0, the position of the +retained nodes is not checked. +The geometric check is based on the coordinates of the retained nodes after translation, rotation, +and/or reflection of the substructure at the usage level; motions of these nodes that occur as a result of +geometrically nonlinear preloading during generation of the substructure are not considered in this check. +Input File Usage: +Abaqus/CAE Usage: +*SUBSTRUCTURE PROPERTY, ELSET=name, POSITION TOL=tolerance +Assembly module: Instance→Translate and Instance→Rotate +Defining substructure damping +Abaqus allows you to choose a particular source of damping for a substructure, to add several sources, +or to exclude the damping effects for a substructure at the usage level. +Sources of substructure damping +You can choose to model the damping of a substructure at the usage stage by using the condensed viscous +damping matrix, +, computed during the +, and the condensed structural damping matrix, +generation stage and stored on the substructure data base. Alternatively, you can use stiffness and mass +proportional damping factors to create a substructure damping matrix using the condensed stiffness and +mass matrices, +, respectively. You can also request that both damping sources be combined or +exclude the effects of damping altogether at the usage level. +and +Input File Usage: +Use the following option to control the sources of the substructure damping: +*DAMPING CONTROLS, VISCOUS=viscousDampingSource, +STRUCTURAL=structuralDampingSource +Abaqus/CAE Usage: +Use the following option to control the sources of the substructure damping: +Step module: Create Step: Linear perturbation: Substructure +generation: Damping tabbed page +Controlling the sources of viscous damping +In the general case the substructure viscous damping is defined by the following matrix: +Input File Usage: +To activate only the generated condensed viscous damping matrix of the +substructure (the first term on the right hand side), use the following option: +*DAMPING CONTROLS, VISCOUS=ELEMENT +To activate only the Rayleigh viscous damping, use the following option: +*DAMPING CONTROLS, VISCOUS=FACTOR +To activate the combined generated and Rayleigh viscous damping matrix, use +the following option: +*DAMPING CONTROLS, VISCOUS=COMBINED +To exclude the effects of viscous damping altogether at the usage level, use the +following option: +*DAMPING CONTROLS, VISCOUS=NONE +To activate only the generated condensed viscous damping matrix of the +substructure (the first term on the right hand side), use the following option: +USING SUBSTRUCTURES +Step module: Create Step: Linear perturbation: Substructure +generation: Damping tabbed page: Viscous damping: Element +To activate only the Rayleigh viscous damping, use the following option: +Step module: Create Step: Linear perturbation: Substructure +generation: Damping tabbed page: Viscous damping: Factor +To activate the combined generated and Rayleigh viscous damping matrix, use +the following option: +Step module: Create Step: Linear perturbation: Substructure +generation: Damping tabbed page: Viscous damping: Combined +To exclude the effects of viscous damping altogether at the usage level, use the +following option: +Step module: Create Step: Linear perturbation: Substructure +generation: Damping tabbed page: Viscous damping: None +Controlling the sources of structural damping +In the general case the substructure structural damping is defined by the following matrix: +Input File Usage: +Abaqus/CAE Usage: +To activate only the generated condensed structural damping matrix of the +substructure (the first term on the right hand side), use the following option: +*DAMPING CONTROLS, STRUCTURAL=ELEMENT +To activate only the stiffness proportional structural damping matrix, use the +following option: +*DAMPING CONTROLS, STRUCTURAL=FACTOR +To activate the combined generated and stiffness proportional structural +damping matrix, use the following option: +*DAMPING CONTROLS, STRUCTURAL=COMBINED +To exclude the structural damping matrix, use the following option: +*DAMPING CONTROLS, STRUCTURAL=NONE +To activate only the generated condensed structural damping matrix of the +substructure (the first term on the right hand side), use the following option: +Step module: Create Step: Linear perturbation: Substructure +generation: Damping tabbed page: Structural damping: Element +To activate only the stiffness proportional structural damping matrix, use the +following option: +Defining damping ratios +Step module: Create Step: Linear perturbation: Substructure +generation: Damping tabbed page: Structural damping: Factor +To activate the combined generated and stiffness proportional structural +damping matrix, use the following option: +Step module: Create Step: Linear perturbation: Substructure +generation: Damping tabbed page: Structural damping: Combined +To exclude the structural damping matrix, use the following option: +Step module: Create Step: Linear perturbation: Substructure +generation: Damping tabbed page: Structural damping: None +By default, the Rayleigh damping ratios, +stiffness proportional and mass proportional damping for a substructure are zeros. +, and the structural damping ratio, +and +, used to define +Input File Usage: +Abaqus/CAE Usage: +Use the following options to define the values of the substructure damping ratios +at the usage level: +*DAMPING, ALPHA= +Use the following option to define the values of the substructure damping ratios +at the usage level: +, STRUCTURAL= +, BETA= +Step module: Create Step: Linear perturbation: Substructure +generation: Damping tabbed page: Alpha: +: Beta: +: Structural: +Defining damping for modal dynamic analysis +To define damping for linear dynamic analysis based on the structure’s modes, specify modal damping +when using the substructure. The damping in each eigenmode can be given as a fraction of the critical +damping. Alternatively, Rayleigh damping can be defined. Composite modal damping cannot be used +inside substructures. +See “Transient modal dynamic analysis,” Section 6.3.7, for more information about the modal +damping procedure. +Input File Usage: +Use the following option to define the damping in each eigenmode as a fraction +of the critical damping: +*MODAL DAMPING, MODAL=DIRECT +Use the following option to define Rayleigh damping: +*MODAL DAMPING, RAYLEIGH +Abaqus/CAE Usage: Modal damping for substructures is not supported in Abaqus/CAE. +Defining kinematic constraints and transformations +All kinematic boundary conditions, MPCs, and transformations can be applied to retained degrees of +freedom at the usage level. These specifications can be changed from step to step in the usual way. In +this respect substructures and their retained nodes act in an identical manner to regular elements and their +nodes. +Defining transformations at retained nodes +If a nodal transformation (“Transformed coordinate systems,” Section 2.1.5) is used during substructure +generation at a retained node, +the transformations are built into the substructure. This creates +an inconsistency when the substructure node is attached to a standard Abaqus element since +Abaqus/Standard uses the retained degrees of freedom directly without checking their directions. +Therefore, it is suggested that this situation be avoided. +If a nodal transformation must be used, the resulting inconsistency can be resolved by retaining all +degrees of freedom at the node and applying a linear constraint equation (“Linear constraint equations,” +Section 34.2.1) as follows. At any point where such a transformed substructure node is attached to a +global model, define two coincident nodes on the usage level, P and Q, for example. Use node P for the +substructure at the usage level (defined with an element definition); the local directions of the degrees +of freedom are already built in at this node. Use node Q for all standard Abaqus elements attached to +this point. Use a local transformation at node Q to transform the degrees of freedom to the same local +directions that are built-in for node P. Now use a linear constraint equation to equate the individual +degrees of freedom at nodes P and Q. +Applying loads to a substructure +Loads or boundary conditions that are to be applied to a substructure within an analysis (at the usage +level) must be specified during the substructure generation step by defining a substructure load case or +by requesting that the substructure’s gravity load vectors be calculated . A load case +can be made up of any combination of loadings and nonzero boundary conditions, and multiple load +cases can be defined for any given substructure. +When you activate load cases created for a substructure, you specify the element number or element +set name of the substructures, the associated substructure load case names, and the scaling multipliers +for the specified substructure load case loads and/or boundary conditions. To reproduce the loading +conditions defined during substructure generation exactly, use a magnitude of 1.0. +Boundary conditions specified during a substructure’s generation are always present, whether the +substructure load case that they are part of is active or not. They are effectively built into the substructure +and can only be scaled if desired but not removed. See “Defining substructures,” Section 10.1.2, for +further information about defining boundary conditions in substructures. +Input File Usage: +Use the following option to activate a substructure load case: +Abaqus/CAE Usage: +*SLOAD +Use the following option to activate a substructure load case: +Load module: load editor: Category: Mechanical: Types for +Selected Step: Substructure load +Modifying or removing load cases +By default, substructure loads are applied as modifications of existing loads or in addition to any loads +previously defined. You can remove all previously defined loads and, optionally, specify new loads when +you activate a load case. Boundary conditions cannot be removed. +Input File Usage: +Use the following option to modify load cases: +Abaqus/CAE Usage: +*SLOAD, OP=MOD +Use the following option to remove load cases: +*SLOAD, OP=NEW +Use the following option to modify load cases: +Load module: Load Case Manager: click Edit +Use the following option to remove load cases: +Load module: Load Case Manager: click Delete +Specifying time-dependent load cases +The magnitude of substructure loads can be varied with time by referring to an amplitude definition +(“Amplitude curves,” Section 33.1.2). +Input File Usage: +Use the following options to define time-dependent load cases: +Abaqus/CAE Usage: +*AMPLITUDE, NAME=amplitude +*SLOAD, AMPLITUDE=amplitude +Use the following options to define time-dependent load cases: +Load module: amplitude editor: Create Amplitude: Amplitude: amplitude +Load module: load editor: Category: Mechanical: Types for Selected +Step: Substructure load: Amplitude: amplitude +Load cases in geometrically nonlinear analyses +All substructure loads and boundary conditions are applied in a local system associated with the +substructure. Since this local system rotates with the substructure when large motions are present, these +loads and boundary conditions will rotate as well. As a consequence, you should be careful when using +substructure loads in geometrically nonlinear analyses to ensure that the loading is in the appropriate +direction at the usage level. This situation is similar to rotating the substructure via a substructure +property definition. +Gravity loading +A distributed load definition can be used to apply gravity loading to a substructure with a user-defined +magnitude, scaled by an amplitude definition, and acting in a specifed direction. To enable gravity +the calculation of the substructure’s gravity load +loading for a substructure, you must request +vectors during the substructure generation step . In this case gravity loading should not be defined as part of a substructure load case. +Input File Usage: +Use the following option to define gravity loading: +*DLOAD, AMPLITUDE=amplitude +element set or element number, GRAV, magnitude, direction +Abaqus/CAE Usage: +Load module: Create Load: choose Mechanical for the Category +and Gravity for the Types for Selected Step +Obtaining output of results within a substructure +You can obtain output within substructures used in static, dynamic, eigenfrequency extraction, +and steady-state and transient modal dynamic analyses. The recovery of output is not possible for +substructures used in response spectrum and random response analyses. Output within a substructure +does not +include the displacements, stresses, etc. resulting from the preload deformation of a +substructure. +Output within substructures is available in the data (.dat) file, in the results (.fil) file, and in +output database (.odb) files. Separate output database files are created for each substructure using +the naming convention inputfile-name_substructure-number.odb. If a substructure contains a nested +substructure, a file called inputfile-name_substructure-number_nested-substructure-number.odb is +created containing the output for the nested substructure. The abaqus substructurecombine execution +procedure can combine model and results data from two substructure output databases into a single +output database. For more information, see “Combining output from substructures,” Section 3.2.19. +Recovery of the solution within substructures requires that the information for recovering the data +within a substructure be available from the .sup, .sim, .prt, .stt, and .mdl files. +Output is organized substructure by substructure: you direct Abaqus/Standard to go inside a +particular substructure and then request output for that substructure. Results can be recovered within +nested multilevel substructures only if the substructure libraries for all substructures in the chain are +available. +Substructure output requests are most easily pictured by thinking of substructures as “levels” of +detailed modeling. At the global (top) level we have the analysis model (for example, an airplane). +Dropping down from this level to the first substructure level, we have the main components of the model +defined as substructures (wings, stabilizer, fuselage, etc.). Dropping down to the second substructure +level, we have other substructures (flaps, tanks, floors, etc.), which, in turn, may contain third level +substructures (spars, stringers, etc.), and so on. To obtain output, you move down and back up through +these various levels using substructure paths, similar to the way you navigate a tree structure for file +directories. Each substructure path definition consists of entering into a substructure at the next level +down or leaving the current substructure and moving up one level in the tree. +At the start of the output requests, Abaqus/Standard is at the global model level. You must +always enter and leave a substructure consistently, so that after a set of substructure output requests +Abaqus/Standard is left at the global model level. You must return to the global level (outside all +substructures) before the end of the step definition. +If you enter and leave in the same substructure path definition, the effect is to leave the substructure +and enter another substructure at the same level. +Entering a substructure for output +To enter a particular substructure for output, you identify the substructure by the element number n +chosen for it in the model. All subsequent output requests are for output within that substructure and +must be given in terms of its internal node and element numbers (the node and element numbers used +when the substructure was created). +Input File Usage: +Abaqus/CAE Usage: +*SUBSTRUCTURE PATH, ENTER ELEMENT=n +Step module: field output request editor: Domain: Substructure: +click +and select substructure sets +Leaving a substructure after obtaining output +After you have obtained output for a substructure, you must return to the level of the model of which +the substructure forms a part, thus indicating the end of the output requests for variables within that +substructure. +Input File Usage: +Abaqus/CAE Usage: +*SUBSTRUCTURE PATH, LEAVE +Step module: field output request editor: Domain: Substructure: +click +and select substructure sets +Obtaining output if substructures are nested +You must enter several substructures if substructures are used at multiple levels and output is required +several levels down. Nesting of substructures is not supported in Abaqus/CAE. +Example: obtaining output within nested substructures +For example, suppose that a model includes several substructures at two levels. Printed output of stress +components is required in some elements within two substructures at the second level, as well as printed +output of the displacements at some of the nodes of one of the first-level substructures. (Recall that +“first-level” refers to substructures used directly in the analysis model; “second-level” substructures are +used as components of first-level substructures.) +The data might be as follows: +*SUBSTRUCTURE PATH, ENTER ELEMENT=N +** This option takes us into element number N, which must be a substructure. +*SUBSTRUCTURE PATH, ENTER ELEMENT=M +** We now drop down into element number M of this substructure. +** M is the element number used for this substructure when N was created. +** M must refer to a substructure.*EL PRINT, ELSET=A1 +** This option requests stress output in element set A1 of this substructure. +** This element set must have been defined during the creation of substructure M. +*SUBSTRUCTURE PATH, LEAVE +** This option takes us back up into first-level substructure N. +*SUBSTRUCTURE PATH, ENTER ELEMENT=P +** This option takes us down into element P, which must again be a substructure in element N. +*EL PRINT, ELSET=A1 +** This option requests the printing of stress output in element set A1. It is possible that +** this is the same set of elements in the same substructure as was used in the request above +** because substructures M and P may both be copies of the same substructure. +** However, the stresses will presumably be different because they represent the same +** component in different locations in the model. +*SUBSTRUCTURE PATH, LEAVE +** Back to N. +*SUBSTRUCTURE PATH, LEAVE +** We are now back at the global level. +*SUBSTRUCTURE PATH, ENTER ELEMENT=R +** Enter element R at the global level: this element is the substructure in which we want +** to print the displacements. +*NODE PRINT, NSET=FLANGE +** This option prints the displacements at all nodes in node set +** FLANGE of the substructure. +** Again, FLANGE must have been defined when the substructure was +** created. +*SUBSTRUCTURE PATH, LEAVE +** Back to the global level. +Interpreting nodal variable output +The nodal displacements within the substructure do not include the displacements resulting from the +preload deformation if it exists. +If a substructure is rotated and/or reflected, nodal variables are output relative to the global +coordinate system of the analysis. In a geometrically nonlinear analysis, the nodal displacements will +include the large motions associated with the translation and rotation of the substructure in addition +If a nodal transformation (“Transformed coordinate systems,” +to the small-strain displacements. +Section 2.1.5) has been used, nodal output will be in either the local or the global directions, depending +on the nodal output request . +If a nodal +transformation has been used during substructure generation, the transformed directions are rotated +with the substructure. +Interpreting element variable output +Element output variables within a substructure do not include the values of the variable resulting from +the preload deformation if it exists. +Element variables in continuum elements are output relative to the global coordinate system of +the analysis model or in the local (material) coordinate system if one has been used (“Orientations,” +Section 2.2.5). Element output for structural elements is always given with respect to the element +coordinate system used during substructure generation. Integration point coordinates and local material +directions are given with respect to the global +coordinate system. +Element quantities associated with nonlinear preload response (plastic strains, creep strains, etc.) +can be output during a substructure recovery. Since the response in a substructure during its usage is +entirely linear, these quantities, which are part of the base state, do not change from the values computed +during the preload. +If a substructure was reflected, the element connectivities of continuum elements written to the +substructure instance output database are adjusted so as not to violate the Abaqus convention for +counterclockwise element numbering. +You cannot directly obtain the element output for the element centroidal values or the element output +at the element nodes when you recover results within substructures. This output data can be calculated +from the substructure-related data in the output database file using commands in the Abaqus Scripting +Interface. +Interpreting results written to the results file +Results within substructures can be written to the results file. Substructure path records are inserted in +the results file to indicate the switch into a substructure: all records following such a record belong to +the substructure defined on that record until the next substructure path record appears in the file. +Requests for output to the results file will cause Abaqus/Standard to write the definitions of elements +and nodes at the global level and within all substructures in the model to the file. As with the results +records themselves, these records for nodes and elements within substructures will be preceded and +followed by substructure path records to indicate that they belong to that substructure. +Node and element numbers within each substructure are local to that substructure, so that the same +node and element numbers may appear in several substructures and in the global level model. In such a +case the substructure path records must be used to identify the location of a particular node or element +within the model. If you can ensure that node and element numbers are unique throughout the entire +model, including all substructures, the substructure path records in the results file can be ignored. +Visualizing substructure results +While Abaqus/CAE does not support substructures directly, you can view substructure results by +combining all of the substructure instance output database (.odb) files into a single file. +See +“Combining output from substructures,” Section 3.2.19, for details. +You can also load and view each individual substructure instance output database (.odb) file +separately in Abaqus/CAE. +Substructure library compatibility +A substructure usage analysis can use the substructure libraries generated from the same or any previous +maintenance delivery of the same general release. For example, if a substructure is generated with +the Abaqus 6.12-3 maintenance delivery, it can be used in all subsequent Abaqus 6.12 maintenance +deliveries. The substructure library is not compatible between general releases (for example, between +Abaqus 6.11 and Abaqus 6.12). +A substructure usage analysis must be run on a computer that is binary compatible with the computer +used to generate the substructure library. +Input file template +The following template can be used to generate a substructure: +*HEADING +… +*NODE,NSET=N1 +Data lines to define the nodes. +… +*NSET,NSET=N3 +Data lines to define the node set members. +… +*ELEMENT, TYPE=CPE8, ELSET=E1 +Data lines to define the elements that make up the substructure. +… +*ELSET,ELSET=E3 +Data lines to define the element set members. +… +*SOLID SECTION, ELSET=E1, MATERIAL=M1 +*MATERIAL, NAME=M1 +*ELASTIC +30.E6, 0.3 +*DENSITY +0.0007324 +*STEP +*FREQUENCY +Data line to specify the number of modes ( m). The *FREQUENCY option +is required if modes are requested using the *SELECT EIGENMODES option. +*END STEP +*STEP +*STATIC +… +Options to define a linear or nonlinear static preload. +… +*END STEP +*STEP +*SUBSTRUCTURE GENERATE, TYPE=Z101, OVERWRITE, MASS MATRIX=YES, +VISCOUS DAMPING MATRIX=YES, STRUCTURAL DAMPING MATRIX=YES, +RECOVERY MATRIX=YES, NSET=N3, ELSET=E3 +*RETAINED NODAL DOFS +Data lines to define the retained degrees of freedom. +*SELECT EIGENMODES, GENERATE +1, m, 1 +*SUBSTRUCTURE LOAD CASE, NAME=BOUND +*BOUNDARY +Data lines to define the boundary conditions. +*SUBSTRUCTURE LOAD CASE, NAME=LOADS +*CLOAD +Data lines to define concentrated loading. +*DLOAD +Data lines to define distributed loading. +*END STEP +The following template can be used to define substructure instances: +*HEADING +… +*ELEMENT, TYPE=Z101, ELSET=E2 +Data line to define the element. +*SUBSTRUCTURE PROPERTY, ELSET=E2 +*BOUNDARY +… +*RESTART, WRITE +*STEP +*STATIC +… +*BOUNDARY +… +*SLOAD +E2, LOADS, scale factor +*SUBSTRUCTURE PATH, ENTER ELEMENT=n +*EL PRINT +S, +*NODE PRINT +U, +*SUBSTRUCTURE PATH, LEAVE +*END STEP +*STEP +*DYNAMIC +… +*BOUNDARY +… +*SUBSTRUCTURE PATH, ENTER ELEMENT=n +*EL PRINT +S, +*NODE PRINT +U, V +*SUBSTRUCTURE PATH, LEAVE +*END STEP +10.1.2 +DEFINING SUBSTRUCTURES +Products: Abaqus/Standard Abaqus/CAE +References +• “Using substructures,” Section 10.1.1 +• *RETAINED NODAL DOFS +• *SELECT EIGENMODES +• *SUBSTRUCTURE COPY +• *SUBSTRUCTURE DELETE +• *SUBSTRUCTURE DIRECTORY +• *SUBSTRUCTURE GENERATE +• *SUBSTRUCTURE LOAD CASE +• *SUBSTRUCTURE MATRIX OUTPUT +Overview +This section describes how individual substructures are defined. +Section 10.1.1, for information regarding how they are used in a model. +See “Using substructures,” +Substructures are defined using the substructure generation procedure. The substructure creation +and usage cannot be included in the same analysis. Multiple substructures can be generated in an analysis. +Any substructure can consist of one or more other substructures; if this is the case, the nested-level +substructures must be defined first. The substructure library is not organized in terms of part instances; +therefore, substructures cannot be generated from models that have an assembly defined. None of the +substructure options are supported in models that have an assembly defined. +To define a typical substructure generation step, do the following: +• Invoke the substructure generation procedure. +• Define the nodes and degrees of freedom that are to be retained as external degrees of freedom when +the substructure is used. +• Optionally, retain extra dynamic modes to improve the dynamic behavior of the substructure during +usage. +• Optionally, specify substructure load cases. +• Optionally, write the recovery matrix, substructure’s stiffness matrix, mass matrix, and/or load case +vectors to a file. +Generating a substructure +When you generate a substructure, you specify an identifier that will be assigned to this substructure in a +substructure library. The identifier must begin with the letter Z followed by a number that cannot exceed +9999. +Substructure identifiers must be unique within a library. If a substructure with this same identifier +already exists in the library, the analysis will terminate with an error message unless you have specified +that the existing substructure should be overwritten, as described below. +*SUBSTRUCTURE GENERATE, TYPE=Zn +Step module: Create Step: Linear perturbation: +Substructure generation: n +Abaqus/CAE Usage: +Input File Usage: +Substructure database +A substructure database is the set of files that describe the geometry of a substructure, and Abaqus writes +all substructure data to the substructure database during the analysis. The substructure database can +include files with the following extensions: .sup, .sim, .prt, .mdl, and .stt; the .sup file is +called the substructure library. By default, substructure data are written to a substructure database named +jobname, and the substructure files are named jobname.sup, jobname_Zn.sim, jobname_Zn.prt, +jobname_Zn.mdl, and jobname_Zn.stt. Files with the extensions .sup and .sim are generated for +all substructures. Files with the extensions .prt, .mdl, and .stt are generated only if the solution +within the substructure can be fully or partially recovered. Several substructures can share a substructure +library file, but other files are individual for each substructure. +It is strongly recommended that the +substructure library name be different for different substructures. +You can choose to write the data to a user-specified substructure database. +If you specify the substructure library name, the files will be named library_name_Zn.sim, +library_name_Zn.prt, library_name_Zn.mdl, and library_name_Zn.stt. +Input File Usage: +Abaqus/CAE Usage: +*SUBSTRUCTURE GENERATE, TYPE=Zn, LIBRARY=library_name +Definition of substructure libraries is not supported in Abaqus/CAE. +Overwriting the substructure data in a library +If a substructure generation analysis is rerun using the same jobname without deleting the substructure +library and one substructure or more will be regenerated, you must specify that the existing substructures +can be overwritten. This requirement also holds true if the jobname is different for the second analysis +but the same library_name is specified. +Input File Usage: +Abaqus/CAE Usage: +*SUBSTRUCTURE GENERATE, TYPE=Zn, LIBRARY=library_name, +OVERWRITE +Definition of substructure libraries is not supported in Abaqus/CAE. +Recovery within a substructure +By default, the solution at any degree of freedom in the substructure can be recovered. Abaqus must +have access to the substructure’s .mdl, .prt, and .stt files to perform a full recovery. These files all +reside in the substructure database. +You can specify that a recovery of element or nodal information will not be required within this +substructure. This reduces the size of the substructure database significantly for a large substructure +because the information that is needed to recover eliminated variables is not stored. However, this +information cannot be recreated at a later time except by regenerating the entire substructure with +recovery enabled. +Input File Usage: +Use the following option to enable recovery for a substructure: +*SUBSTRUCTURE GENERATE, TYPE=Zn, RECOVERY +MATRIX=YES (default) +Use the following option to disable recovery for a substructure: +Abaqus/CAE Usage: +*SUBSTRUCTURE GENERATE, TYPE=Zn, RECOVERY MATRIX=NO +Use the following option to enable recovery for a substructure: +Step module: Create Step: Linear perturbation: Substructure +generation: Basic tabbed page: toggle on Evaluate recovery +matrix for: select Whole model +Use the following option to disable recovery for a substructure: +Step module: Create Step: Linear perturbation: Substructure +generation: Basic tabbed page: toggle off Evaluate recovery matrix for +Using the selective recovery method +If results recovery is desired only at a subset of the internal degrees of freedom, disk usage can be reduced +substantially by using the selective recovery method. To enable selective recovery, the region where +recovery is desired can be specified directly. +Input File Usage: +Use the following option to define the node set for selective recovery: +*SUBSTRUCTURE GENERATE, RECOVERY MATRIX=YES, +NSET=Node set name +Use the following option to define the element set for selective recovery: +*SUBSTRUCTURE GENERATE, RECOVERY MATRIX=YES, +ELSET=Element set name +Abaqus/CAE Usage: +Use the following option to define the node set for selective recovery: +Step module: Create Step: Linear perturbation: Substructure +generation: Basic tabbed page: toggle on Evaluate recovery +matrix for: select Region: Node set name +Use the following option to define the element set for selective recovery: +Step module: Create Step: Linear perturbation: Substructure +generation: Basic tabbed page: toggle on Evaluate recovery +matrix for: select Region: Element set name +Evaluating frequency-dependent material properties +When frequency-dependent material properties are specified, Abaqus/Standard offers the option of +choosing the frequency at which these properties are evaluated for use in substructure generation. If +you do not choose the frequency, Abaqus/Standard evaluates the stiffness at zero frequency and does +not consider the stiffness contributions from frequency-domain viscoelasticity. +If you do specify a +frequency, only the real part of the stiffness contributions from frequency-domain viscoelasticity is +considered. +Input File Usage: +Abaqus/CAE Usage: +*SUBSTRUCTURE GENERATE, PROPERTY EVALUATION=frequency +Step module: Step editor: Substructure generate: Options +tabbed page: toggle on Evaluate frequency-dependent +properties at frequency: frequency +Defining the retained degrees of freedom +The degrees of freedom at a node can be divided into retained degrees of freedom (for use at the +usage level of the substructure) and eliminated degrees of freedom (internal to the substructure). +Abaqus/Standard allows any of the degrees of freedom at any of the nodes of a substructure to be +retained with one exception: if an acoustic-structural substructure is generated, based on coupled or +uncoupled modes, only structural degrees of freedom can be retained. You must make sure that the +choice of retained degrees of freedom is reasonable so that the substructure can be connected correctly +to the rest of the model. +Any degrees of freedom where kinematic constraints may have to be respecified during usage of +the substructure should be kept as retained degrees of freedom. +If any degrees of freedom of nodes used to define distributing coupling elements are retained, the +degrees of freedom of an internal node associated with the Lagrange multipliers are added automatically +to the list of the retained degrees of freedom of the substructure. +To define the retained degrees of freedom, specify the node number or node set label and, optionally, +the first and the last degree of freedom to be retained. +By default, the nodes associated with the retained degrees of freedom will be sorted into ascending +numerical order. +Input File Usage: +Abaqus/CAE Usage: +*RETAINED NODAL DOFS +Load module: boundary condition editor: Category: Mechanical: +Types for Selected Step: Retained nodal dofs +Preventing the degrees of freedom from being sorted +You can prevent the degrees of freedom from being sorted. The ordering of the nodes when using a +substructure is then the same as the ordering used when specifying the retained nodes. +Input File Usage: +Abaqus/CAE Usage: +*RETAINED NODAL DOFS, SORTED=NO +You cannot prevent retained nodes from being sorted in Abaqus/CAE. +Retaining degrees of freedom when the substructure is intended for geometrically nonlinear +analysis at the usage level +When the substructure is intended for use in geometrically nonlinear analyses, it is recommended to +retain all translational and/or all rotational degrees of freedom from a particular node. Even in the case +when only a single translational/rotational degree of freedom of a particular node is deemed as needed +at the usage level, you should retain all translational/rotational degrees of freedom associated with that +node. Otherwise, as the substructure rotates during a geometrically nonlinear analysis, local numerical +instabilities (negative eigenvalues) may occur since the rotated substructure may have no stiffness in +particular degrees of freedom. +You must choose an appropriate number of nodes that will allow for the computation of an equivalent +rigid body motion of the substructure. In two-dimensional or axisymmetric analyses, retaining two nodes +with all translational degrees of freedom or one node with all translational and rotational degrees of +freedom is sufficient to compute an equivalent rigid body motion of the substructure at the usage level. +In three-dimensional analysis, three non-colinear nodes with all translational degrees of freedom retained +or one node with all translations and rotations are needed. If the retained nodes are colinear or fewer +than three nodes are retained, you must retain at least one node with all rotational degrees of freedom. +When Abaqus/Standard cannot compute an equivalent rigid body motion for the substructure during +the analysis at the usage level because the number of retained degrees of freedom is not appropriate, a +warning message is issued and any geometrically nonlinear effects associated with the substructure are +ignored. +Defining kinematic constraints +Kinematic constraints are defined as described in “Kinematic constraints: overview,” Section 34.1.1. +The following rules apply: +• All kinematic boundary conditions associated with degrees of freedom that are not retained must +be specified when the substructure is generated. The conditions are built into the substructure and +remain imposed any time that it is used. Once the substructure is generated, kinematic constraints +on internal variables cannot be respecified; they can be modified or removed only by erasing and +recreating the substructure in the library. The magnitude of a prescribed boundary condition applied +to an internal degree of freedom can be associated with a substructure load case and can be changed +at the usage level. The restraint itself is built into the substructure and cannot be removed by omitting +a reference to the load case. +• During substructure generation, multi-point constraints in which some of the substructure’s retained +degrees of freedom are eliminated in favor of internal degrees of freedom must be avoided. If it +is desirable to retain certain degrees of freedom that are eliminated by the multi-point constraints, +you must reassign all of the variables appearing in the multi-point constraints as retained degrees +of freedom and impose the constraints at the usage level. +Defining the generalized degrees of freedom +An effective technique for modeling the dynamic behavior of a substructure is to augment the response +within the substructure by including some generalized degrees of freedom associated with the dynamic +modes. You can select the modes to retain, which must be calculated in a previous frequency extraction +step (“Natural frequency extraction,” Section 6.3.5). The selected modes have to be fully recovered: +if they were computed with the AMS eigensolver and only partially recovered, an error message will +be issued. The modes will include eigenmodes and, if activated in the eigenfrequency extraction step, +residual modes. If all retained degrees of freedom of the substructure are constrained in the frequency +extraction step, this technique is commonly referred to as the Craig-Bampton method. If all retained +degrees of freedom of the substructure are not constrained in the frequency extraction step, this technique +is commonly referred to as the Craig-Chang method. The substructure dynamic modes in the Craig- +Bampton method are commonly referred to as the fixed-interface modes, and the substructure dynamic +modes in the Craig-Chang method are commonly referred to as the free-interface modes. If some retained +degrees of freedom of the substructure are constrained and other retained degrees of freedom are not +constrained in the frequency extraction step, the dynamic modes are called mixed-interface modes. If +the free-interface or mixed-interface dynamic modes are selected, the substructure generation time can +increase substantially compared to the case when the same number of fixed-interface dynamic modes is +used. Abaqus issues a warning message in this case. However, better solution accuracy can sometimes +be achieved with a significantly smaller number of free- or mixed-interface dynamic modes than by using +fixed-interface modes. +A sufficient number of the dynamic modes should be selected to provide adequate dynamic +representation of the substructure. Examine loading frequencies and frequency content of the structure +to determine this range. Specify a shift point and/or a cutoff frequency in the eigenfrequency extraction +step definition to obtain modes in the desired frequency range only. Inclusion of generalized degrees +of freedom adds the cost of the frequency extraction to the substructure generation step but greatly +improves the accuracy of the solution if the substructure is used in a subsequent dynamic (“Implicit +dynamic analysis using direct integration,” Section 6.3.2), steady-state dynamic (“Direct-solution +steady-state dynamic analysis,” Section 6.3.4), or frequency extraction (“Natural frequency extraction,” +Section 6.3.5) analysis. +In the case of the displacement normalization of the eigenvectors in a frequency extraction analysis, +a substructure must have at least one physical degree of freedom active on the usage level; otherwise, the +modes cannot be normalized properly. See “Substructuring and substructure analysis,” Section 2.14.1 of +the Abaqus Theory Manual, for additional details. +The retained eigenmodes must be selected when an acoustic-structural substructure is generated. +The effect of acoustic-structural coupling can be included in the retained eigenmodes during the +natural frequency extraction procedure. To calculate the coupled structural-acoustic eigenmodes, use a +frequency extraction analysis with the default Lanczos eigensolver and include the effect of acoustic- +structural coupling during the natural frequency extraction procedure (“Natural frequency extraction,” +Section 6.3.5). +Abaqus can also use uncoupled eigenmodes, generated from either SIM-based Lanczos or +AMS eigensolver, to generate a coupled acoustic-structural substructure. +In this case the effect of +acoustic-structural coupling is included during the substructure generation. Both structural and acoustic +eigenmodes have to be retained for the substructure generation, and the selection of the acoustic +zero-frequency modes, if such modes are present, is required to get an accurate substructure. +Selecting the modes to be used in a substructure generation analysis by their mode numbers +You can directly specify the eigenmodes to be used in a substructure generation analysis by their mode +numbers. +Input File Usage: +*SELECT EIGENMODES +eigenmode 1, eigenmode 2, etc. +Abaqus/CAE Usage: +Use the following option to generate the list of eigenmodes by mode range, +with each row in the data table specifying a single mode number. The starting +mode number and ending mode number in each row should be equal, and the +increment value should be zero. +Step module: Create Step: Linear perturbation: Substructure generation: +Options tabbed page: toggle on Specify retained eigenmodes by: +Mode range: +Start Mode: eigenmode 1: End Mode: eigenmode 1: Increment: 0 +Start Mode: eigenmode 2: End Mode: eigenmode 2: Increment: 0 +etc. +Generating a list of the eigenmodes by mode range +Instead of listing all the retained eigenmode numbers, you can generate the list of eigenmodes. +Input File Usage: +Use the following option to generate the list of eigenmodes by mode range, +with each data line specifying the start mode number, the end mode number, +and the increment in mode numbers between these two values: +*SELECT EIGENMODES, GENERATE +first mode number, last mode number, increment +Abaqus/CAE Usage: +Use the following option to generate the list of eigenmodes by mode range, +with each row in the data table specifying the start mode number, the end mode +number, and the increment in mode numbers between these two values: +Step module: Create Step: Linear perturbation: Substructure +generation: Options tabbed page: toggle on Specify retained +eigenmodes by: Mode range: Start Mode: first mode number: End +Mode: last mode number: Increment: increment +Generating a list of the eigenmodes by frequency range +You can select all the modes from the specified frequency range including frequency boundaries. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to generate the list of eigenmodes by frequency range, +with each data line specifying the lower boundary of the frequency range and +the upper boundary of the frequency range: +*SELECT EIGENMODES, DEFINITION=FREQUENCY RANGE +lower boundary of the frequency range, upper boundary of the frequency range +Use the following option to generate the list of eigenmodes by frequency range, +with each row in the data table specifying the lower boundary of the frequency +range and the upper boundary of the frequency range: +Step module: Create Step: Linear perturbation: Substructure +generation: Options tabbed page: toggle on Specify retained eigenmodes +by: Frequency range: Lower Frequency: lower boundary of the frequency +range: Upper Frequency: upper boundary of the frequency range +Preloading a substructure +Substructures can be used in models that exhibit nonlinear response (associated with standard Abaqus +elements or with contact definitions), but the response within a substructure assumes linear small +deformations. However, a substructure’s response may be a linear perturbation about a predeformed +(possibly rotating and translating) base state, defined on the basis of nonlinear response within the +substructure during its preload history. +When the substructure is intended for use in geometrically nonlinear analyses, the substructure +preloading should be limited to loads that generate self-equilibrating stresses only (such as thermal +stresses or interference fits). In most cases, preload stresses are not self-equilibrating (such as stresses +from specified boundary conditions or applied loads). +If non-self-equilibrating prestress exists and +the substructure undergoes a rigid body motion at the usage level, additional stress is generated in +the substructure. Such usage level stresses are non-physical and will lead to convergence problems +and results that are difficult to interpret. Therefore, you should use extreme care when preloading a +substructure intended for use in geometrically nonlinear analyses. +This preloading concept allows such effects as stress stiffening to be included in a substructure. +Preloading is a part of the state of the substructure: the preload is self-equilibrating and so does not +generate a load vector when the substructure is used. Any loading of the substructure during its use in a +model is in addition to the preload. +It is important to distinguish the difference between a preload and a load case. Both are allowed +during a substructure generation analysis, but only the preloads are actually applied to the substructure +during generation. Load cases, defined during substructure generation, can only be applied at the usage +level . Load cases are +discussed in more detail later. +Computation of the total response of a variable +Any recovered response variable within a substructure (such as stress or displacement) is defined to +be a perturbation (with some exceptions for geometrically nonlinear analyses) from the preloaded base +state. For geometrically nonlinear analyses, the displacement output includes both the equivalent rigid +body rotation and translation associated with the substructure and the strain-inducing small-displacement +perturbation. If the total response of a variable is desired, it can be computed by adding the perturbation +result to the final result computed during the substructure preload. +Computation of the tangent stiffness of a preloaded substructure +The rules for calculating the stiffness matrix of a preloaded substructure are the same as those for a static +linear perturbation step. See “General and linear perturbation procedures,” Section 6.1.3, for a detailed +description of the rules. +Defining a preloading history +Specify the loading history that defines the preload state for a substructure. +Input File Usage: +Abaqus/CAE Usage: +Use the following options: +*STEP +Options to define the preloading history. +*END STEP +Any number of steps can be defined. +*STEP +*SUBSTRUCTURE GENERATE +Options to define the substructure. +*END STEP +The Substructure generation step must be defined after the +preloading steps in an Abaqus/CAE analysis. +Prescribing boundary conditions at retained degrees of freedom during preloading steps +During substructure preloading, boundary conditions can be prescribed at retained degrees of freedom. +When the preloaded substructure is subsequently created in a substructure generation step, you must +release all the retained degrees of freedom . An error message will be issued if some of the retained +degrees of freedom are not released. The reaction forces at the released degrees of freedom become +concentrated loads that are in equilibrium with the stresses within the substructure. These concentrated +loads cannot be removed without changing the preload. +The preloaded substructure is, thus, in equilibrium. If the preload in a substructure must effectively +apply loading to other parts of the structure, a substructure load case corresponding to the loads applied +in the preload history must be created. +The technique is demonstrated in “Analysis of a rotating fan using substructures and cyclic +symmetry,” Section 2.2.1 of the Abaqus Example Problems Manual. +Generating a reduced mass matrix for a substructure +You can generate a reduced mass matrix for a substructure. +A reduced mass matrix is calculated by projecting the global mass matrix to the subspace of the +substructure modes. This technique is known as Guyan reduction if only the static modes associated +with the nodal retained degrees of freedom are used. Using only the static modes may not be sufficient +to define the dynamic response of the substructure accurately. Additional dynamic modes must be used +to improve the response inside the substructure. +Input File Usage: +Abaqus/CAE Usage: +*SUBSTRUCTURE GENERATE, TYPE=Zn, MASS MATRIX=YES +Step module: Create Step: Linear perturbation: Substructure +generation: Options tabbed page: toggle on Compute +reduced mass matrix +Generating a reduced viscous damping matrix for a substructure +You can generate a reduced viscous damping matrix for a substructure. +The reduced viscous damping matrix is calculated in a manner similar to that used for the reduced +mass matrix. +Input File Usage: +Abaqus/CAE Usage: +*SUBSTRUCTURE GENERATE, TYPE=Zn, VISCOUS +DAMPING MATRIX=YES +Step module: Create Step: Linear perturbation: Substructure +generation: Options tabbed page: toggle on Compute reduced +viscous damping matrix +Generating a reduced structural damping matrix for a substructure +You can generate a reduced structural damping matrix for a substructure. +The reduced structural damping matrix is calculated in a manner similar to that used for the reduced +mass matrix. +Input File Usage: +Abaqus/CAE Usage: +*SUBSTRUCTURE GENERATE, TYPE=Zn, STRUCTURAL +DAMPING MATRIX=YES +Step module: Create Step: Linear perturbation: Substructure +generation: Options tabbed page: toggle on Compute reduced +structural damping matrix +Generating substructures with unsymmetric damping matrices +When a coupled acoustic-structural substructure, generated from coupled or uncoupled modes, is +generated from a model with damping specified on the acoustic domain, the substructure damping +matrices are unsymmetric. The substructure viscous damping matrix will be unsymmetric if a +substructure is generated from the rolling tire. +Abaqus does not automatically generate an unsymmetric substructure in these cases. You must +explicitly select the unsymmetric solver for the substructure +generation step to obtain correct substructure damping matrices with unsymmetric contributions. +Defining substructure load cases for subsequent loading in an analysis +The load cases defined during the generation of a substructure and activated at the usage level are the +equivalent of the elemental loading types available for the regular elements in Abaqus. They can be made +up of any combination of loadings (distributed loads, concentrated nodal loads, thermal expansion, and +load cases defined for any substructures that may be used as part of the definition of this substructure). +The load cases are needed so that, when the substructure is subsequently used in a model, the +consistent loads on the retained degrees of freedom need be scaled only by the appropriate magnitudes of +the particular loads applied: it is not necessary to go inside the substructure and repeat the basic element +calculations to distribute the loads. +Each such load case can be applied when the substructure is used by associating it with an +amplitude/time curve and a magnitude (“Amplitude curves,” Section 33.1.2). When a substructure +is used, the substructure load case loadings that were created when the substructure was generated +are the only loads that can be used in that substructure. Except for gravity loading, when using the +substructure, you cannot apply distributed loads, temperature loads, etc. to the elements that make up +any substructure. These loads must be built into the substructure during its creation. +You can define multiple substructure load cases during the substructure generation to define different +loadings for the substructure. Each load case is assigned a name that will be used when the load case is +applied on the usage level. +You can use any combination of concentrated load, distributed load, substructure load, and +temperature fields (“Concentrated loads,” Section 33.4.2; and “Distributed loads,” Section 33.4.3) to +define each load case. +You assign each basic loading a reference magnitude, which will then be scaled by the actual +magnitude specified when the substructure load is applied. The reference magnitude assigned to each +basic loading must be defined as the change in load or boundary condition from the base state, not the +total of the base state plus the perturbation value. +Initial conditions applied within the substructure +generation are not included as part of a load case definition. +For temperature loads, +the load vector for the substructure load case will contain only the +contributions due to thermal expansion. +If temperature-dependent properties are present, they are +evaluated at the temperatures specified in the preloaded state. Consequently, to take into account +nonzero initial temperature fields prescribed as initial conditions (“Initial conditions in Abaqus/Standard +and Abaqus/Explicit,” Section 33.2.1), it is necessary to preload the structure before creating the +substructure. When using temperature loading in a substructure load case, the data cannot be read from +a results file. The temperatures specified must be defined as the change in the temperatures from the +base state. +Abaqus/Standard currently has a limitation when a substructure load case definition includes +acoustic loading during a substructure generation procedure in which retained modes are specified: +the contribution of the singular (constant pressure) acoustic modes (“Acoustic, shock, and coupled +acoustic-structural analysis,” Section 6.10.1) is not taken into account in the generated load case. +Since the contribution of this mode is significant for low frequency response, the generated load case +will inadequately represent the specified acoustic load in these cases. If there are no singular acoustic +regions in the coupled acoustic-structure substructure, the acoustic loads are represented accurately. +It is important to distinguish the difference between a load case and a preload. Both are defined +during substructure generation, but only the preloads are actually applied to the substructure on the +generation level; load cases, defined on the generation level, can only be applied on the usage level, +and they act on a preloaded base state if one has been specified. (Preloads were discussed earlier.) +In general analysis steps and perturbation steps substructure loads are treated in the same way as +other loads, such as concentrated loads and distributed loads (“Concentrated loads,” Section 33.4.2, and +“Distributed loads,” Section 33.4.3). For example, if a general analysis step is followed by another +general analysis step, the substructure loads will be retained in the second step with their magnitude +equal to that at the end of the previous general analysis step, unless the substructure load is modified or +removed. In a linear perturbation step the substructure load represents an incremental load. +If a substructure load is used to apply Coriolis loading in a direct-solution steady-state dynamic +analysis, the unsymmetric load stiffness contribution is not taken into account. +Input File Usage: +Use the following options: +*SUBSTRUCTURE LOAD CASE, NAME=name +*CLOAD and/or +*DLOAD and/or +*DSLOAD and/or +*TEMPERATURE +The load case defined via the *SUBSTRUCTURE LOAD CASE option +ends when an option other +than *CLOAD, *DLOAD, *DSLOAD, or +*TEMPERATURE is encountered. The load definitions can be specified in +any order. +Abaqus/CAE Usage: +Use the following option to define a substructure load case and the loads +included in it: +Load module: Create Load Case: click +: select loads +Defining boundary conditions +All boundary conditions to be built into the substructure matrices must be specified using a boundary +condition definition. These cannot be part of a substructure load case specification. Once a kinematic +boundary condition is specified on a particular nodal degree of freedom, it is built into the substructure +matrices, is in effect for all load cases, and cannot be removed (or redefined at the usage level). The +boundary conditions specified as part of the preloading history are built into the substructure matrices. +If there is any doubt whether a restraint is permanent or not, it is better to make the degree of freedom +a retained degree of freedom and not specify any restraint in the substructure definition. The restraint +can then be included as needed in each analysis step. +Load cases when the substructure is used in geometrically nonlinear analyses +All loads and boundary conditions included in a substructure load case at the generation level and applied +as a substructure load at the usage level are applied in a local system associated with the substructure. +Since this system rotates with the substructure when large motions are present, these loads and boundary +conditions will rotate as well. As a consequence, you should be careful when using substructure load +cases in geometrically nonlinear analyses to ensure that the loading is in the appropriate direction at the +usage level. This situation is similar to rotating the substructure using a substructure property definition. +Gravity loading +To apply gravity loading, density must be defined for at least some of the elements included in the +substructure. A gravity load can be applied to a substructure in two different ways with two different +interpretations. +If a distributed load definition is used as a part of a substructure load case during +substructure generation (as described in “Defining substructure load cases for subsequent loading in +an analysis” above), the gravity loading becomes part of the substructure load case and, hence, rotates +to follow the substructure’s local system during usage (the local system may rotate by rotating the +substructure via a substructure property definition or due to geometrically nonlinear response). +To define gravity loading that acts in a fixed global direction during usage, you can request that +the substructure’s gravity load vectors be calculated during substructure generation. In this case gravity +loading should not be defined as part of a substructure load case. When the gravity load vectors +are calculated, Abaqus/Standard generates a gravity load vector for each global direction (three for +three-dimensional analyses and two for two-dimensional/axisymmetric analyses). At the usage level, a +distributed load definition can be used +to specify gravity loading on the substructure that acts in a fixed global direction with the specified +magnitude. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to calculate the substructure’s gravity load vectors +during substructure generation: +*SUBSTRUCTURE GENERATE, GRAVITY LOAD=YES +Step module: Create Step: Linear perturbation: Substructure +generation: Options tabbed page: toggle on Compute gravity load vectors +Writing the recovery matrix, reduced stiffness matrix, mass matrix, load case vectors, and +gravity vectors to a file +You can write a substructure’s recovery matrix, reduced stiffness matrix, mass matrix, and load case +vectors to a file. This output is useful when the substructure is to be used in another program. +The output records can be written either to the Abaqus/Standard results file, to a user-defined file, or +to the output database file . In each case you must specify which output to write out: the mass +matrix, the recovery matrix, the load case vectors, the stiffness matrix, and/or the gravity load vectors. +By default, no output will be generated. +Repeat the substructure matrix output request in the substructure generation file of each substructure +for which the substructure matrix output is required. +If substructure load case vector output is requested for a preloaded substructure, the output will +contain a record with a load case number that is equal to zero. This load vector contains the forces that +were necessary to equilibrate any stresses that were generated during the previous steps. +Input File Usage: +*SUBSTRUCTURE MATRIX OUTPUT, MASS=YES, RECOVERY +MATRIX=YES, SLOAD=YES, STIFFNESS=YES, GRAVITY LOAD=YES +Abaqus/CAE Usage: +Step module: Create Step: Linear perturbation: Substructure +generation: Basic tabbed page: toggle on Evaluate recovery +matrix for: select Whole model or Region +Writing the records to the Abaqus/Standard results file +By default, the requested matrices are written to the Abaqus/Standard results file corresponding to the +substructure generation input file name. The record formats for the results file are described in “Results +file output format,” Section 5.1.2. The file can be written in either binary or ASCII format (“Output,” +Section 4.1.1). +Input File Usage: +Abaqus/CAE Usage: +*SUBSTRUCTURE MATRIX OUTPUT, OUTPUT FILE=RESULTS FILE +Abaqus/CAE automatically writes the requested matrices to the Abaqus +results file when you run an analysis with a Substructure generation step. +Writing the records to the output database file +You can specify that the matrices should be written to the output database (.odb) file. +Input File Usage: +Abaqus/CAE Usage: +*SUBSTRUCTURE MATRIX OUTPUT, OUTPUT FILE=ODB +Abaqus/CAE automatically writes the requested matrices to the output +database file when you run an analysis with a Substructure generation step. +Writing the records to a user-defined file +You can specify the name of the file (without an extension) to which the data will be written. The records +are written to be compatible with a linear user-defined element. The record formats are described in +“User-defined elements,” Section 32.15.1. An .mtx extension will be added to the file name specified. +Input File Usage: +*SUBSTRUCTURE MATRIX OUTPUT, +OUTPUT FILE=USER DEFINED, FILE NAME=file_name +Abaqus/CAE Usage: +Job module: job editor: Name +Managing substructures inside libraries +Substructures are stored in a collection of libraries. Housekeeping functions are provided to help maintain +extensive libraries; for example, substructures can be deleted from a library or moved to a different +library. +Once a substructure library has been generated, the disk files can be made read-only to protect +the library from accidental deletion or modification. A substructure library must be write-accessible +during a substructure’s generation and when substructures are added or deleted from a library using the +substructure housekeeping functions. +When multiple analyses are used to generate a substructure library, these analyses must be run one +after another; they cannot be run simultaneously. Abaqus may not be able to provide any indication +that the substructure library being written may already be in use by another Abaqus analysis. If several +analyses write to the same library simultaneously, the library may get corrupted. If this occurs and the +library is used in a subsequent analysis, the result may be a large preprocessor memory demand. +Input File Usage: +Use any of the following options (described in detail below) to perform +housekeeping functions on substructure libraries: +*SUBSTRUCTURE COPY +*SUBSTRUCTURE DELETE +*SUBSTRUCTURE DIRECTORY +The housekeeping options can appear anywhere within the model portion of +the input file (“Defining a model in Abaqus,” Section 1.3.1). An input file can +consist of merely the *HEADING option and one or more of the housekeeping +options. +In this case the files and substructures to which the housekeeping +options refer must exist at the start of the analysis. +Abaqus/CAE Usage: +Substructure libraries are not supported in Abaqus/CAE. +Listing the substructures stored in a substructure library +You can obtain a summary of information about the substructures stored in a substructure library. If +necessary, you can identify a nondefault name for the library (the default name is jobname). +Input File Usage: +Abaqus/CAE Usage: +*SUBSTRUCTURE DIRECTORY, LIBRARY=substructure_library_name +Substructure libraries are not supported in Abaqus/CAE. +Removing a substructure from a substructure library +You can remove a specified substructure from a substructure library. If necessary, you can identify the +name of the library. +Input File Usage: +*SUBSTRUCTURE DELETE, TYPE=Zn, +LIBRARY=substructure_library_name +Abaqus/CAE Usage: +Substructure libraries are not supported in Abaqus/CAE. +Copying or moving a substructure definition +You can copy a substructure definition from one library to another or from one substructure to another +within the same library. You must identify the substructure being copied and assign a name to the +substructure being created. +When copying substructures from library to library, you can identify the name of the library +containing the substructure being copied. Similarly, you can identify the name of the new library to +which the substructure will be copied. This new library need not exist prior to the substructure being +copied; it will be created in this case. +If the original substructure is to be deleted, you can follow the copy with a delete . +Input File Usage: +*SUBSTRUCTURE COPY, OLD TYPE=Zn, NEW TYPE=Zn, +OLD LIBRARY=substructure_library_name, +NEW LIBRARY=substructure_library_name +Abaqus/CAE Usage: +Substructure libraries are not supported in Abaqus/CAE. +Renaming substructure libraries +Once a substructure library has been generated, the disk file should not be renamed manually. To rename +a substructure library, copy the existing substructures to a new library. The new library need not exist +prior to the first substructure being copied. You can then delete the original disk file manually if you do +not need it anymore. +10.2 +Submodeling +• “Submodeling: overview,” Section 10.2.1 +• “Node-based submodeling,” Section 10.2.2 +• “Surface-based submodeling,” Section 10.2.3 +10.2.1 +SUBMODELING: OVERVIEW +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Node-based submodeling,” Section 10.2.2 +• “Surface-based submodeling,” Section 10.2.3 +• *SUBMODEL +• Chapter 38, “Submodeling,” of the Abaqus/CAE User’s Manual +Overview +The submodeling technique: +• is used to study a local part of a model with a refined mesh based on interpolation of the solution +from an initial (undeformed), relatively coarse, global model; +• is most useful when it is necessary to obtain an accurate, detailed solution in a local region and the +detailed modeling of that local region has negligible effect on the overall solution; +• can be used to drive a local part of the model by nodal results, such as displacements , or by the element stress results from the global mesh; +• can be used to analyze an acoustic model driven by displacements from a structural, global model +when the acoustic fluid has negligible effect on the structural solution; +• can be used for the analysis of a structure driven by acoustic pressures from an acoustic or coupled +acoustic-structural, global model; +• can use a combination of Abaqus/Explicit and Abaqus/Standard procedures; +• can use a combination of linear and nonlinear procedures; and +• cannot be used in an import analysis. +Terminology +The model whose solution is interpolated onto the relevant parts of the boundary of the submodel is +referred to as the “global” model (even though it may itself be a submodel of a larger “global” model). +Driven variables are defined as those variables in the submodel that are constrained to match results from +the global model. Driven variables can be degrees of freedom at nodes in the node-based technique, or +they can be components of stress tensor at the integration points of element faces in the surface-based +technique. +Submodeling techniques +Submodeling can be applied quite generally in Abaqus. The material response defined for the submodel +may be different from that defined for the global model. Both the global model and the submodel can +have nonlinear response. See “Shell-to-solid submodeling and shell-to-solid coupling of a pipe joint,” +Section 1.1.10 of the Abaqus Example Problems Manual, for an example application of the submodeling +technique. +Submodeling is classified first according to which of two basic techniques is used. The most +common, and more general technique, is node-based submodeling, which uses a nodal results field +(including displacement, temperature, or pressure degrees of freedom) to interpolate global model +results onto the submodel nodes. The alternative surface-based technique uses the stress field to +interpolate global model results onto the submodel integration points on the driven element-based +surface facets. +You can choose either the node-based or surface-based technique or a combination of the two in +your submodel. The following factors should be considered in deciding on the technique to be used: +• Whether you are performing solid-to-solid submodeling in a general static analysis in +Abaqus/Standard: +– Surface-based submodeling is available only for solid models and static analyses. +– For all other procedures use the node-based technique. +• Whether the global model and submodel differ significantly in their average stiffness in the region +of the submodel: +– When the stiffness of the models is comparable, node-based submodeling of displacements will +provide comparable results to the surface-based technique with a lesser likelihood of numerical +issues associated with rigid-body modes. +– When the stiffness of the models differs and the global model is exposed primarily to +a load-controlled environment, +the surface-based technique will generally provide more +accurate stress results. Stiffness differences may arise due to additional detail in the submodel, +such as explicit modeling of a fillet or a hole. In other cases stiffness changes may result from +minor geometry changes for which a reanalysis of the global model is not warranted. +• Whether your model is subjected to large deformations or rotations: +– Node-based submodeling of displacements will result in more accurate transmission of large +deformation and rotation to the submodel. +• Whether the displacement response of the global model corresponds to the displacement response +of the submodel: +– When the displacements in the global model correspond closely with the expected +displacements in the submodel, node-based submodeling is generally preferable. +– Surface-based submodeling should be used when the submodel displacement response is +expected to differ from the global model response. This situation can occur when thermal +strains are modeled and the temperature history of the submodel differs from that of the global +model; for example, when heat transfer submodeling is performed as part of a sequential +thermal-structural analysis. +• The stiffness of the structure: +– Surface-based submodeling may provide more accurate results for very stiff structures. When +the structure is so stiff that only a small component of the global model displacement field +contributes to the stress response, numerical roundoff in the displacement results can become +significant; for example, when the global model displacement is dominated by a rigid-body +motion component. +• The type of output you are interested in from the submodel: +– Node-based submodeling of displacements will result in more accurate transmission of a +displacement field. +– Surface-based submodeling will result in more accurate transmission of a stress field, and +determination of reaction forces in the submodel. +You can use both node-based submodeling and stress-based submodeling in the same model. +Node-based submodeling +Node-based submodeling is the more general +combinations and procedures in both Abaqus/Explicit and Abaqus/Standard. +technique, supporting a variety of element +type +Input File Usage: +Abaqus/CAE Usage: +*SUBMODEL, TYPE=NODE +Load module: Create Boundary Condition: choose Other for the Category +and Submodel for the Types for Selected Step: Driving region: Specify +Element types supported +Different element types can be used in the submodel than those used to model the corresponding region +in the global model. +The following types of submodeling are provided for the node-based approach (global-to- +submodel): +• Two-dimensional models: +– Solid-to-solid +– Acoustic-to-structure +• Three-dimensional models: +– Solid-to-solid +– Shell-to-shell +– Membrane-to-membrane +– Shell-to-solid +– Acoustic-to-structure +A global or submodel +is meshed with continuum shell elements constitutes a +three-dimensional solid region in the submodeling technique. Hence, the use of the submodeling +technique for models involving continuum shell elements is the same as with models involving +continuum solid elements such as C3D8R or C3D6. +region that +Procedures supported +Both the global model and the submodel can have nonlinear response and can be analyzed for any +sequence of analysis procedures. These procedures do not have to be the same for both models. For +example, the linear or nonlinear dynamic response of the global model can be used to drive the static, +nonlinear response of the submodel on the grounds that the submodel is too small for dynamic effects to +be significant in that local region. The global procedure can be performed in Abaqus/Standard to drive a +submodeling procedure in Abaqus/Explicit and vice versa. For example, a static analysis performed in +Abaqus/Standard can drive a quasi-static Abaqus/Explicit analysis in the submodel. The step time used +in these analyses can be different; the time variable of the amplitude functions generated at the driven +nodes can be scaled to the step time used in the submodel. +Your submodel cannot refer to a global model step that includes multiple load cases . You must perform the global analysis with a single load definition +for the step that will drive the submodel. +Surface-based submodeling +Surface-based submodeling is provided as a complement to the node-based technique, enabling you to +drive the submodel with stresses from the global model. +Input File Usage: +Abaqus/CAE Usage: +*SUBMODEL, TYPE=SURFACE +Load module: Create Load: choose Mechanical for the Category and +Submodel for the Types for Selected Step: Driving region: Specify +Element types supported +The following types of submodeling are provided for the surface-based approach (global-to-submodel): +• Two-dimensional models: +– Solid-to-solid +• Three-dimensional models: +– Solid-to-solid +Different element types can be used in the submodel than those used to model the corresponding +region in the global model. Continuum elements supported for the static analysis procedure are supported +for surface-based submodeling, with the following exceptions: +• Cylindrical elements are not supported. +• Continuum shell elements are not supported. +Procedures supported +The surface-based technique is implemented only for static analysis in Abaqus/Standard. +Your submodel cannot refer to a global model step that includes multiple load cases . You must perform the global analysis with a single load definition +for the step that will drive the submodel. +Performing a submodeling analysis +A submodeling analysis consists of: +• running a global analysis and saving the results in the vicinity of the submodel boundary; +• defining the total set of driven nodes or driven surfaces in the submodel; +• defining the time variation of the driven variables in the submodel analysis by specifying the actual +nodes and degrees of freedom or element-based surfaces to be driven in each step; and +• running the submodel analysis using the “driven variables” to drive the solution. +Linking the global model and the submodel +The submodel is run as a separate analysis from the global analysis. The only link between the submodel +and the global model is the transfer of the time-dependent values of variables saved in the global analysis +to the relevant boundary nodes of the submodel or to the relevant boundary surfaces. This transfer is +accomplished by saving the results from the global model either in the results (.fil) file or in the output +database (.odb) for the node-based technique or in the output database (.odb) for the stress-based +technique, then reading these results into the submodel analysis. If the global model is defined in terms +of an assembly of part instances, the part (.prt) file from the global model is required for the submodel +analysis. Since the submodel is a separate analysis, submodeling can be used to any number of levels; a +submodel can be used as the global model for a subsequent submodel. +Accuracy +The global model in a submodeling analysis must define the submodel boundary response with sufficient +accuracy. It is your responsibility to ensure that any particular use of the submodeling technique provides +physically meaningful results. In general, the solution at the boundary of the submodel must not be +altered significantly by the different local modeling. There is no built-in check of this criterion in Abaqus; +it is a matter of judgment on your part. In general, accuracy can be checked by comparing contour plots +of important variables near the boundaries of the submodeled region. +Specifying the global elements used to drive the submodel +By default, the global model in the vicinity of the submodel is searched for elements that encompass +the locations of driven nodes or driven surfaces’ faces; the submodel is then driven by the response of +these elements. In some cases more than one element can encompass the location of a driven node. For +example, adjacent bodies in the global model may have temporarily coincident nodes or surfaces, as +depicted in Figure 10.2.1–1. +Global model +Local model +A B +contact +interface +driven +node +Figure 10.2.1–1 A global model with coincident surfaces in +the area of the local model’s driven nodes. +In this case the location of the driven node in the corresponding global model is touching both element A +and element C; however, only the results from element A should drive the node in the submodel. +To preclude certain elements from driving the submodel, you have the option of specifying a global +element set to limit the search to an appropriate subset of the global model. +Input File Usage: +*SUBMODEL, GLOBAL ELSET=name +If the global model is defined in terms of an assembly of part instances, give +the complete name—including the assembly and part instance names—when +specifying the global element set. For example, an element set named top +in part instance I-1 of assembly Assembly-1 must be referred to by +Assembly-1.I-1.top. +If the submodel is not defined in terms of an assembly of part instances, the dots +in the global element set name must be replaced by underscores: Assembly- +1_I-1_top. +If the global element set is defined at the assembly level, you may provide the +element set name without qualifying it with the assembly name in a submodel +analysis. +Abaqus/CAE Usage: +Load module: Create Boundary Condition: choose Other for the Category +and Submodel for the Types for Selected Step: Driving region: Specify +Minimizing file sizes +The size of the results file or the output database can be minimized for a submodeling analysis by +requesting output for only those global nodes and global elements that are used to drive the submodel. +To determine which global nodes and/or elements are used to drive the submodel, do the following: +1. Run a data check analysis on the global model with any combination of results file or output database +file output requests. A data check analysis is performed by using the datacheck parameter in the +command for running Abaqus (“Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD execution,” +Section 3.2.2). +2. Run a data check analysis on the submodel. +A listing of the global nodes and/or elements that will be used to drive the submodel is output to the data +file during the submodeling data check analysis. +Frequency of output +Pay special attention to the frequency at which you request output in the global model . It is +possible to define the results file output or nodal and element output to the output database file such that +the information is written at different frequencies for different nodes and elements, although that should +not be done for nodes and elements involved in the interpolation to define values at driven variables +since Abaqus will take values at the coarsest frequency only. To avoid this problem, write the nodal and +elemental output to the output database or the results file using the same frequency for all nodes and +elements involved in the interpolation and choose a frequency that will allow the history in the submodel +to be reproduced accurately. +Input File Usage: +To control the output frequency to the Abaqus/Standard results file, use the +following option: +*NODE FILE, FREQUENCY +To control the output frequency to the Abaqus/Explicit results file, use the +following option: +*FILE OUTPUT, NUMBER INTERVAL +To control the output frequency to the output database, use the following option: +Abaqus/CAE Usage: +*OUTPUT, FIELD, FREQUENCY +Step module: Output→Field Output Requests→Create: Frequency +Material options +Any of the material models described in Part V, “Materials,” can be used in the global and submodel +analyses. The material response defined for the submodel may be different from that defined for the +global model. +Elements +The dimensionality of the submodel must be the same as that of the global model: both models must be +either two-dimensional or three-dimensional. The following limitations apply: +• The boundary nodes of the submodel must lie within regions of the global model where Abaqus +is able to perform spatial interpolation to define the values of the driven variables. Therefore, +they must lie within (or, as allowed by the exterior tolerance, near to) two- or three-dimensional +geometrically defined elements in the global model. Such geometrically defined elements are: +– first- or second-order triangles or quadrilaterals in two dimensions; +– first- or second-order triangular or quadrilateral shells; and +– first- or second-order tetrahedra, wedges, or bricks in three dimensions. +• The boundary nodes cannot lie in regions of the global model where there are only one-dimensional +elements (beams, trusses, links, axisymmetric shells) since Abaqus does not provide the necessary +interpolation of results for such elements. +• The boundary nodes cannot lie in regions of the global model where there are only user elements, +substructures, springs, dashpots, cohesive elements, etc. since those element types do not allow for +geometric interpolation. +• The boundary nodes cannot lie in regions of the global model where there are only axisymmetric +solid elements with nonlinear, asymmetric deformation (CAXA elements). The submodeling +capability is currently not supported for these elements. +• The reference node associated with generalized plane strain elements (CPEG) cannot be used as a +driven boundary node in a submodeling analysis. +Output +Any of the output normally available within a particular procedure is also available during a submodeling +analysis . +As described above, nodal output requests to the results file or output database file must be used in +the global analysis to save the values of the driven variables at the submodel boundary. +10.2.2 +NODE-BASED SUBMODELING +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Submodeling: overview,” Section 10.2.1 +• *SUBMODEL +• *BOUNDARY +• Chapter 38, “Submodeling,” of the Abaqus/CAE User’s Manual +Overview +The following types of node-based submodeling are available: +• Same-to-same (e.g., solid-to-solid, shell-to-shell); +• Shell-to-solid; and +• Acoustic-to-structure. +These submodel types support the following nodal-driven variables: +• Displacement, +• Rotation, +• Temperature, +• Pore pressure, and +• Acoustic pressure. +Performing a node-based submodeling analysis +For an overview of submodeling that includes some details common to both node-based and surface- +based submodeling, see “Submodeling: overview,” Section 10.2.1. +Your submodel analysis is driven, either partly or completely, from the results obtained from a global +model analysis. The results from the global model are interpolated onto the nodes on the appropriate parts +of the boundary of the submodel . Thus, the response at the boundary of the local +region is defined by the solution for the global model. The driven nodes and any loads applied to the +local region determine the solution in the submodel. +Different types of node-based submodeling +Three different techniques are available for nodal-based submodeling. +Solid-to-solid submodeling +The linear or nonlinear response of a global solid model can be used to drive the submodel response of +a solid submodel. The driven variables can be displacements or temperatures. +symmetry +submodel boundaries +nodes where global model +solution must be stored for +interpolation +Figure 10.2.2–1 The global model. +Shell-to-solid submodeling +The linear or nonlinear response of a global shell model can be used to drive the submodel response +of a solid submodel. The driven variables are displacements, which are determined from global model +displacements and rotations. +Acoustic submodeling +The linear or nonlinear response of a global, structural model can be used to drive the acoustic response +of a fluid region of any size if the forces exerted on the structure by the fluid are small. This is often the +case for metal structures in air, building interiors, or for sound propagation from a liquid to air. In the case +of a liquid and a gas, no special procedures need be followed; the pressure degrees of freedom couple +straightforwardly. In the case of a structure driving a fluid, you must ensure that the degrees of freedom +to be driven in the submodel exist among the global model results. Several alternatives exist. A thin layer +of fluid elements, with the same properties as the submodel fluid, can be added to the global model; this +element set and its nodes can then be used to drive the submodel in the usual manner. Alternatively, you +can create acoustic interface elements on the surface of the submodel and drive the corresponding nodes +with the structural nodes . +In problems where the fluid exerts large pressures on the structure, the mechanical response of the +structure may be of interest. Acoustic-to-structure submodeling can be used in such problems. The +submodel in these problems is a part of the structural component of the global model. The acoustic +pressure obtained from solving a coupled acoustic-structural global analysis is used to drive the submodel +on the surface it shares with the fluid medium. Other boundaries of the submodel may be driven using +the displacements of the structural component of the global model via solid-to-solid submodeling. The +acoustic-to-structure submodel analysis solves an uncoupled structural force-displacement problem. +The acoustic pressure from the global model is interpolated to the submodel driven nodes. The tributary +area and the outward normal associated with the driven node are used to convert the interpolated +acoustic pressure to a concentrated load acting at that location . +Saving the results from the global model +The results from the global analysis must be saved at all nodes required for the interpolation of the driven +variables to the boundary of the submodel . The results (.fil) file or the output +database (.odb) file can be used for this purpose. +Saving the results to the results file +In each step of the global model whose solution will be used to drive the submodel, write the nodal results +for all driven variables to the results file . These +results must be written in the global coordinate system of the model. The submodel can refer only to a +global model results file that is from a binary compatible platform. +When the global model is run in Abaqus/Explicit and results file output is requested, the results +are written to the selected results (.sel) file; this file needs to be converted into a results (.fil) +file using the convert option . +Input File Usage: +Abaqus/CAE Usage: +*NODE FILE +(In Abaqus/Standard GLOBAL=NO should not be used on +the *NODE FILE option.) +You cannot write output to the results file in Abaqus/CAE. +Saving the results to the output database +In each step of the global model whose solution will be used to drive the submodel, write the nodal results +for all driven variables to the output database . Unlike +the results file, nodal output to the output database is always written in the global directions. The output +database can be transferred to any platform since it is binary neutral. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options: +*OUTPUT, FIELD +*NODE OUTPUT +Step module: Output→Field Output Requests→Create +Saving results with higher precision +By default, the nodal output to the output database is written using single precision, which may not +be sufficient for certain classes of problems; for example, submodels undergoing large rigid body +motions (consider also surface-based submodeling in these cases—see “Surface-based submodeling,” +Section 10.2.3). For such analyses request the nodal output to the fullest possible precision . +Input File Usage: +Abaqus/CAE Usage: +abaqus job=global_model_input_file output_precision=full +Job module: Create Job: Precision: Nodal output precision: Full +Saving results from a global model with a physical time scale +If the global analysis in Abaqus/Standard involves a physical time scale and the results file is to be used in +the submodel analysis, request that the results file output be written at the beginning of the step (the zero +increment) for all steps in the global analysis . Abaqus will then have the +complete solution history (including the solution state at the beginning of a step) from which a submodel +may be driven. If the zero increment results are not requested, incorrect results will be obtained if the +step time in the submodel is less than the step time of the first increment on the results file. Instead of +interpolating between the results at the start of the step and the results of the first increment on the results +file, Abaqus will simply use the results of the first increment as long as the submodel step time is less +than the step time of the first increment on the results file. The zero increment request is not required in +Abaqus/Explicit, because the results are always written to the results file at the beginning of each step. +Similarly, the results will always be correctly interpolated when using the output database to transfer the +results from the global model to the submodel, because the zero increment is always written to the output +database. +Input File Usage: +Abaqus/CAE Usage: +*FILE FORMAT, ZERO INCREMENT +You cannot write output to the results file in Abaqus/CAE. +Referring to the global model results from the submodel analysis +You must define the source of the global solution results. Provide the name of the global results file or +output database file; the file extension is optional. If the file extension is omitted, Abaqus will correctly +choose the extension if only the results file or the output database file exists. If the file extension is +omitted and both results and output database files exist, the results file will be used. +Input File Usage: +abaqus job=submodel_input_file globalmodel=global_results_file or +global_output_database +Abaqus/CAE Usage: +Any module: Model→Edit Attributes→submodel: Submodel: Read +data from job: global_results_file or global_output_database +Specifying the driven nodes in the submodel +Specifying the driven nodes does not activate the driven variables: they must be activated by specifying +the appropriate submodel boundary conditions. +All nodes of the submodel where variables will be driven in any step must be +specified as driven nodes since the list of nodes cannot be extended subsequent to its initial definition +(even at restart). However, variables at the nodes given do not have to be driven in all steps: the choice +of which variables are driven in a particular step is made as part of a submodel boundary condition +definition, as discussed later. +NODE-BASED SUBMODELING +boundary nodes of the submodel +driven by global model solution +Figure 10.2.2–2 The magnified submodel. +Input File Usage: +*SUBMODEL +list of nodes or node set labels or, for acoustic-to-structure submodeling, +the name of an element-based structural surface +The *SUBMODEL option must be included in the model definition portion of +the input file for the submodel analysis. Multiple *SUBMODEL options are +allowed; however, in this case you must ensure that the driven nodes specified +on the data line of one option are separate and distinct from the nodes specified +on the data lines of all the other options. +Abaqus/CAE Usage: +Load module: Create Boundary Condition: choose Other for the Category +and Submodel for the Types for Selected Step: select region +Specifying the driven nodes in shell-to-solid submodeling +In shell-to-solid submodeling, the submodel is made up of solid elements and replaces a region where +conventional shell elements are used in the global model. In this case Abaqus expects that all the driven +nodes on the submodel belong to solid elements and are driven from a global model region that is entirely +made up of shell elements. The boundary where the submodel is driven is a set of surfaces in the submodel +but is a set of lines in the shell reference surface in the global model, as shown in Figure 10.2.2–3. The +dashed line +on the shell model is replaced by the shaded surfaces of the solid element +submodel. +a) Shell global model with submodel boundaries +A, B, C - shell reference surface + - driven nodes +b) Magnified solid element submodel +Figure 10.2.2–3 Shell-to-solid submodeling. +Whenever shell-to-solid submodeling is used, you must define the maximum shell thickness in the +global model, given in the units used for the models. If a shell offset is defined in the global model, the +shell thickness must be set equal to twice the maximum distance from the top or bottom shell surface to +the shell reference surface. +Input File Usage: +Abaqus/CAE Usage: +*SUBMODEL, SHELL TO SOLID, SHELL THICKNESS=thickness +If more than one *SUBMODEL option is used, +parameter must be included on every option. +the SHELL TO SOLID +Any module: Model→Edit Attributes→submodel: Submodel: +Shell global model drives a solid submodel +Load module: Create Boundary Condition: choose Other for +the Category and Submodel for the Types for Selected Step: +select region: Shell thickness: thickness +Specifying the driven nodes in acoustic-to-structure submodeling +The global analysis for acoustic-to-structure submodeling problems is performed as a coupled acoustic- +structural analysis. The acoustic nodal pressures from the global analysis must be written to the results +file for the acoustic mesh in contact with the structural surface of interest. In the submodel analysis +acoustic pressures from the global analysis drive the user-specified structural surface of interest. The +driven nodes for the submodel are the nodes lying on the specified surface. Only element-based surfaces +are allowed in acoustic-to-structure submodeling. +Input File Usage: +*SUBMODEL, ACOUSTIC TO STRUCTURE, +ABSOLUTE EXTERIOR TOLERANCE=value +Abaqus/CAE Usage: +Acoustic-to-structure submodeling is not supported in Abaqus/CAE. +Specifying driven nodes for shells with acoustic pressures on both sides +In certain problems the acoustic pressure may act on both sides of a shell structure. Figure 10.2.2–4 +shows a section of a global model consisting of a shell structure that is sandwiched between two acoustic +media. +acoustic region 1 +SPOS +SNEG +acoustic region 2 +ELSET = Acoustic_SPOS +ELSET = Acoustic_SNEG +shell +structure +Figure 10.2.2–4 A cross-section of the acoustic-to-structure global +model with acoustic regions on both sides of the shell. +Separate element sets consisting of acoustic elements on the positive and negative sides of the shell are +defined, respectively. The nodal pressures for nodes attached to elements in these sets are written to the +selected results file. Figure 10.2.2–5 shows the submodel that consists only of the refined shell structure. +surface Shell_SPOS +surface Shell_SNEG +driven node +shell structure +Figure 10.2.2–5 The acoustic-to-structure submodel with acoustic pressure on both sides of the shell. +Two separate surfaces are defined on the SPOS and SNEG sides, respectively. To apply the acoustic +pressure from the global analysis on each side of the shell correctly, you must specify the surface name +along with the corresponding acoustic element set. +Input File Usage: +*SUBMODEL, ACOUSTIC TO STRUCTURE, GLOBAL +ELSET=Acoustic_SPOS +Shell_SPOS +*SUBMODEL, ACOUSTIC TO STRUCTURE, GLOBAL +ELSET=Acoustic_SNEG +Shell_SNEG +Abaqus/CAE Usage: +Acoustic-to-structure submodeling is not supported in Abaqus/CAE. +Defining geometric tolerances +A geometric tolerance is used to define how far a boundary node in the submodel can lie outside the +exterior surface of the global model, as that surface is interpolated in the global, undeformed finite +element model. By default, nodes in the submodel must lie within a distance calculated by multiplying +the average element size in the global model by 0.05. You can change the tolerance, which is useful +in cases where submodel driven nodes lie to a greater extent outside the global model exterior surface. +Tolerances larger than this default value, however, may result in significantly greater computation times +and lower accuracy in the driven solution for driven nodes significantly outside the global model exterior +surface. +You can define the geometric tolerance as a fraction of the size of the average element in the global +model or as an absolute distance in the length units chosen for the model. If both tolerances are defined, +Abaqus uses the tighter tolerance. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to define the geometric tolerance as an absolute +distance: +*SUBMODEL, ABSOLUTE EXTERIOR TOLERANCE=tolerance +Use the following option to define the geometric tolerance as a fraction of the +size of the average element in the global model: +*SUBMODEL, EXTERIOR TOLERANCE=tolerance +Load module: Create Boundary Condition: choose Other for the +Category and Submodel for the Types for Selected Step: select region: +Exterior tolerance: absolute: or relative: tolerance +The exterior tolerance in solid-to-solid submodeling +The exterior tolerance for a solid-to-solid submodel analysis is indicated by the shaded region in +If the distance between the driven nodes and the free surface of the global model +Figure 10.2.2–6. +falls within the specified tolerance, the solution variables from the global model are extrapolated to the +submodel. +The exterior tolerance in shell-to-shell submodeling +In a shell-to-shell submodel analysis Abaqus checks whether the driven nodes of the submodel lie +sufficiently close to the reference surface of the shell elements in the global model. To simplify +calculations, the closest point in the global model is calculated as the intersection of a line drawn +exterior surface in global model +exterior surface in submodel +nodes in global model +nodes in submodel +actual geometric +surface +Figure 10.2.2–6 The exterior tolerance in solid-to-solid submodeling. +through the node on the submodel with the reference surface of the shell in the global model. The +direction of the line is normal to a flat surface approximation to each shell element. The normal to the +flat surface is the average of the normals at the nodes of the shell element. The distance checked against +the specified exterior tolerance is shown in Figure 10.2.2–7. +The exterior tolerance in shell-to-solid submodeling +For shell-to-solid submodeling Abaqus uses two kinds of tolerances to determine the relationship +between the submodel and the global model. First, the closest point on the shell reference surface +of the global model is determined. This point, the “image node,” is shown in Figure 10.2.2–8. The +user-specified exterior tolerance is used to check if the image node lies within the domain of the global +model. Then the distance, +, between the driven node and its image is checked; if the distance is less +than half the value of the specified shell thickness plus the exterior tolerance, it is accepted. This check +is only approximate if the global model has varying shell thickness or if the shell reference surface is +offset from the midsurface. +interpolated position +on shell reference surface +plane approximation +global model +shell reference surface +submodel's driven +node +distance checked +against exterior tolerance +Figure 10.2.2–7 Flat surface approximation in shell-to-shell submodeling. +exterior +tolerance +AI +global model shell elements +shell +reference surface +t = shell thickness + A - driven node +AI - driven node image + on the shell reference + surface +solid element +submodel mesh +Figure 10.2.2–8 The exterior tolerance in shell-to-solid submodeling. +Permitting driven nodes to be excluded from submodeling +In some cases (such as when your submodel geometry is more detailed than the global model in regions +near a free surface) you may specify driven nodes that Abaqus will find, even when accounting for the +search tolerance, to be outside the region of the global model elements. By default, these cases result +in an error message. In solid-to-solid submodeling you can, however, specify that Abaqus ignore driven +nodes that cannot be found. Use this option with caution and always evaluate the list of nodes that are +labeled as not found. Most cases where Abaqus finds driven nodes to lie outside the global model reflect +a modeling error and use of the intersection only option may lead to incorrect results in these cases. +Input File Usage: +Use the following option to specify that Abaqus ignore driven nodes that cannot +be found in the global model elements: +*SUBMODEL, INTERSECTION ONLY +list of nodes or node set labels +The driven nodes ignored through the use of the INTERSECTION ONLY +parameter are then ignored in all subsequent submodel boundary condition +references. +Defining the driven variables in the submodel +The actual driven variables are defined in any step as a submodel boundary condition. The boundary +conditions are “driven variables” obtained from the results or output database file of the global analysis. +The degrees of freedom on the driven nodes of the submodel must exist at the forcing nodes of the +global model. In a problem involving an acoustic fluid submodel driven by a structural global model, +for example, acoustic interface elements should be created on the submodel’s driven boundary with the +structure. +For solid-to-solid and shell-to-shell submodeling specify the individual degrees of freedom to be +driven. In most cases all components of the solution variables (displacements, rotations, temperatures, +etc.) at these nodes are driven by the global solution, although you may choose to drive only some +components at any of the driven nodes. For shell-to-solid submodeling the driven degrees of freedom +are chosen automatically based on a user-specified zone around the shell reference surface, as explained +later. +Abaqus/Explicit does not admit jumps in displacement and rotation boundary conditions ; any jumps in the driven displacements and rotations will be ignored. +It is not recommended to have all the variables at all the nodes in the submodel driven by the global +solution. +For acoustic-to-structure submodeling, the loads due to acoustic pressure acting at the driven nodes +of the submodel are activated by specifying pressure (degree of freedom 8) along with the driven node +set. +Only one submodel boundary condition can be specified in each step of the analysis. +Input File Usage: +Abaqus/CAE Usage: +*BOUNDARY, SUBMODEL +Load module: Create Boundary Condition: choose Other for the +Category and Submodel for the Types for Selected Step: select +region: Degrees of freedom: degrees of freedom +Specifying the step number from the global analysis +You specify the step of the global model history that is to be used for the driven variables in the current +submodel analysis step. When the global solution is obtained from the results file, the zero increment is +included if it was requested in the global analysis . +In a general analysis step or a direct-solution steady-state dynamic analysis step, Abaqus calculates +the amplitudes for the driven variables as functions of time or frequency from the results of the global +model. +Input File Usage: +Abaqus/CAE Usage: +*BOUNDARY, SUBMODEL, STEP=step +Load module: Create Boundary Condition: choose Other for +the Category and Submodel for the Types for Selected Step: +select region: Global step number: step +Scaling the global time period to the submodel time period +The global analysis and submodel analysis can have different time steps. You can scale the time variable +of the driven nodes from the global analysis to the step time of the submodel analysis. This technique is +useful when the analyses are static or quasi-static in nature; the use of this technique in dynamic analyses +with significant inertial effects is not recommended. If the same step time is used in both the global model +and the submodel, the time scale has no effect. The time scale cannot be specified in frequency domain +analyses or in linear perturbation steps. +Abaqus will determine the values that the driven variables will follow throughout the step in the +submodel analysis by using the points in time at which the global solution results or output database file +was written. When the time variable of the driven nodes of the global analysis is scaled and if the step +time is different from the submodel step time, the points in time of the driven variables are scaled to the +submodel step time. +Input File Usage: +Abaqus/CAE Usage: +*BOUNDARY, SUBMODEL, STEP=step, TIMESCALE +Load module: Create Boundary Condition: choose Other for the Category +and Submodel for the Types for Selected Step: select region: Scale +time period of global step to time period of submodel step +Scaling the magnitude of driven variables +For displacement-based submodeling the magnitude values of driven variables are obtained by +multiplying the displacement history as obtained from the global analysis by a scaling parameter. You +can scale the driven variables by setting the scaling parameter in the definition of the submodel boundary +conditions. This technique is useful in scaling the submodel boundary conditions in a multiple-step +analysis without rerunning the global model. It can be used in Abaqus/Standard and Abaqus/Explicit +for the same-to-same and shell-to-solid cases except for acoustic-to-structure submodeling. +*BOUNDARY, SUBMODEL, STEP=step, SCALE=scalarValue +Load module: Create Boundary Condition: choose Other for the Category +and Submodel for the Types for Selected Step: select region: Scale: scale +Abaqus/CAE Usage: +Input File Usage: +Modifying the set of driven variables +You can modify the submodel boundary condition to add new variables to the list of driven variables, you +can remove variables from the driven variable set, and you can reintroduce them later . New nodes cannot be added to +the total set of driven nodes defined for the submodel; this set of driven nodes is a fixed part of the model +definition. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options: +*BOUNDARY, SUBMODEL, OP=MOD +*BOUNDARY, SUBMODEL, OP=NEW +Load module: boundary condition editor: Degrees of freedom +Automatically selecting the driven variables in shell-to-solid submodeling +For shell-to-solid submodeling the driven degrees of freedom at +the driven nodes are chosen +automatically, depending on the distance between the driven node and the global model shell reference +surface. All displacement components are driven at nodes that lie on the reference surface or within +a “center zone,” as shown in Figure 10.2.2–9. The size of the center zone is specified as part of the +submodel boundary condition definition, as described below. For nodes that lie further away from the +reference surface, only the displacement components parallel to the shell reference surface are driven. +At least one layer of nodes in the submodel must be within the center zone; if no nodes are found this +close to the reference surface, Abaqus issues an error message. +Specifying the size of the center zone in shell-to-solid submodeling +The center zone method of prescribing driven variables usually provides a reasonable transfer of the +plane stress assumption in the shell model. The width of this zone around the reference surface where +all displacement components are driven may be different for various driven nodes or node sets. If you +do not provide values for the center zone size, a default value of 10% of the maximum of the specified +shell thicknesses is assumed. +For complicated geometries it can be advantageous to assign a different center zone size to different +nodes or node sets. +You can view the driven nodes lying inside and outside the center zone in Abaqus/CAE by displaying +Input File Usage: +the model boundary conditions (View→ODB Display Options) in the Visualization module. +*BOUNDARY, SUBMODEL, STEP=step +nodes, center zone size +Load module: Create Boundary Condition: choose Other for the +Category and Submodel for the Types for Selected Step: select +region: Center zone size: center zone size +Abaqus/CAE Usage: +Transferring transverse shear stresses in shell-to-solid submodeling +Usually it is enough for the layer of nodes closest to the shell reference surface to lie inside the center +zone. If a very fine solid mesh is used in the thickness direction and substantial transverse shear stresses +If this distance is small +enough, all displacement +components are driven. +center +zone +shell nodes +boundary nodes on solid submodel +(driven nodes) +For most solid nodes only +tangential displacement +components are driven +u t +tangent to +shell +reference +surface +Figure 10.2.2–9 Center zone choice in shell-to-solid submodeling. +are transferred, it may be necessary to make the center zone size large enough that multiple layers of +nodes lie inside the zone. However, if the transverse shear stresses at the submodel boundary are high +and the submodel is highly refined in the thickness direction, high local stresses may develop since the +shear force at the submodel boundary is transferred only at the driven nodes within the center zone. High +transverse shear stresses occur only in regions where bending moments vary rapidly; it is better not to +locate the submodel boundary in such regions. It is best to locate the submodel boundary in areas of low +transverse shear stress in the global model. +Special considerations +There are several special considerations that are worth noting. +Specifying the shell thickness in shell-to-shell submodeling +For shell-to-shell submodeling the shell thickness generally is not changed between the models. You +can specify different shell thicknesses if, for example, a local thickness change is being investigated; +however, Abaqus does not check the validity of these differences. +Limitations in shell-to-solid submodeling +The following limitations and special cases apply to the shell-to-solid capability: +• The global model can contain both solid and shell elements; however, when the shell-to-solid +capability is used, all driven nodes must lie within shell elements in the global model. If the driven +boundary lies at the border between a solid and a shell region, the driven nodes must be moved a +small distance away from the solid region . +• Corners or kinks may exist in global models made of shell elements. At such corners or kinks the +shell elements only approximate the distribution of the material away from the midsurface of the +shell . Because of such approximations, it is not possible to drive a submodel +correctly if the driven nodes of the submodel lie within a shell thickness from a corner or a kink. If +necessary, use the approach shown in Figure 10.2.2–11. A better approach is to include the corner +or kink as part of the submodel and drive it from nodes well away from corners or kinks since they +are a source of stress concentration and high stress gradients . +• Temperature degrees of freedom cannot be driven in shell-to-solid submodeling. +Alternative to shell-to-solid submodeling +An alternative to shell-to-solid submodeling is the surface-based shell-to-solid coupling capability +discussed in “Shell-to-solid coupling,” Section 34.3.3. +Procedures +Neither the coupled thermal-electrical procedure nor any of the mode-based dynamics procedures can +be used on the submodel level. In addition, submodeling cannot be used in conjunction with symmetric +model generation or symmetric results transfer. Adaptive meshes should not be used in the global model. +However, they can be used in the submodel analysis; Abaqus will always treat the driven nodes in the +submodel as Lagrangian nodes. +Both general (possibly nonlinear) and linear perturbation steps can be used in submodeling . +Submodeling in dynamic procedures +The submodeling capability can be used in the dynamic procedures using explicit integration (in +Abaqus/Explicit) and in the dynamic procedures using direct integration (in Abaqus/Standard). The +following combinations of procedures between the global model and the submodel can be considered: +explicit dynamic, implicit dynamic, dynamic coupled thermal-stress, and coupled thermal-stress. +In +dynamic problems in which inertial forces are significant, the global model and the submodel need to +be run for the same step time intervals. +In Abaqus/Explicit a quasi-static analysis is performed as a dynamic procedure. For this case and +for the static analyses performed in Abaqus/Standard, the time step of the global model and submodel +can be different. The time variable of the driven nodes from the global analysis must be scaled to the +step time of the submodel analysis to match the time variable of the amplitude functions generated at the +driven nodes to the step time used in the submodel. +For significantly dynamic problems in Abaqus/Explicit, a sufficiently large number of intervals need +to be written to the results or output database file for the global model. Preferably the displacement results +solid elements +shell elements +Global model +=driven node +(1) +(2) +Two possible submodels +Incorrect submodel (driven nodes in +both shell and solid regions of the +global model) +Figure 10.2.2–10 A limitation of shell-to-solid submodeling. +=driven node +solid submodel +overlap of material in submodel +shell reference surface +ε << thickness +global model +Figure 10.2.2–11 Shell-to-solid submodeling around corners. +driven nodes away +from kinks or corners +Figure 10.2.2–12 Solid submodel of a shell intersection. +shell reference surface +for the nodes that are used to drive the submodel should be saved for each increment. This caution is +necessary in particular for problems with elastic material properties to avoid possible aliasing (under +sampling), which can cause solution distortion in the submodel. These requirements do not apply to +quasi-static problems. +Interpreting acceleration results +When you drive a submodel boundary with global model displacement results, the displacements +are interpreted as a smoothed piecewise linear function in time, similar to how you would apply +a displacement boundary condition using a tabular amplitude definition . This smoothed function +typically results in displacements and velocities at the driven nodes that agree reasonably with the global +model. Acceleration results at the driven boundary, however, are generally not in good agreement with +the global model as they reflect the shape of the displacement history smoothing rather than the global +model acceleration results (information that is not available from a piecewise linear global-model +displacement history). The submodel acceleration results away from the submodel driven nodes are less +affected by this smoothing and are typically in good agreement with the global model response. +Obtaining a solution at a particular point in time using linear perturbation analysis +In Abaqus/Standard it is possible to study the submodel’s linearized response corresponding to a +particular point in time in the global solution by using a static, linear perturbation procedure in the +submodel analysis. You can select the increment in the global analysis step that is to be used as the basis +for calculating the values for the driven variables. If you do not select an increment in a static linear +perturbation step, the last increment of the selected step in the global analysis is used as the basis for +calculating the values for the driven variables. You cannot select an increment in a general submodel +step. +Input File Usage: +Abaqus/CAE Usage: +*BOUNDARY, SUBMODEL, STEP=step, INC=increment +Load module: Create Boundary Condition: choose Other for the +Category and Submodel for the Types for Selected Step: select region: +Global step number: step, Global increment: increment +Submodeling in the frequency domain +The submodeling capability can be used in the frequency domain by using the direct-solution steady-state +dynamics procedure. Mode-based steady-state dynamics cannot be used at the submodel level. +The only restriction on the specification of the frequency range in the submodel is that the minimum +and maximum frequency should lie within the range of calculated frequencies in the global model. +Abaqus will interpolate the solution variables from the global model in the frequency domain, as well +as spatially, before applying them to the submodel. The results will be most accurate if the frequencies +at which the response in the submodel is requested match the frequencies at which the response was +calculated in the global model. This is particularly true in the vicinity of the eigenfrequencies of the +global model. +In the global model you must write both the amplitude and the phase of the nodal displacements to +the results file so that Abaqus can apply the real and imaginary parts of the solution at the driven nodes in +the submodel. If you are using the output database to drive the submodel, you need to request only nodal +displacement output since displacement output to the output database includes both real and imaginary +parts. +Mixing general and linear perturbation steps +It is possible to mix general steps and linear perturbation steps in both the global and the submodel +analyses. Abaqus allows general analysis steps to be treated as linear perturbation steps during +submodeling, and vice versa. +Example: Submodeling with general and linear perturbation steps +For an example of submodeling that uses both general and linear perturbation steps, consider the +following situation. The global analysis consists of a static preload—done as a general, nonlinear, +5 seconds of modal dynamic response analysis: +NODE-BASED SUBMODELING +*STEP +** Apply preload +*STATIC +0.1, 1.0 +… +** Write out results for nodes needed to +** interpolate to the submodel's boundary +*NODE FILE, NSET=DETAIL +*END STEP +*STEP +** Calculate modes and frequencies +*FREQUENCY +… +** The *NODE FILE option is repeated because +** this is the first linear perturbation step +*NODE FILE, NSET=DETAIL +*END STEP +*STEP +** Dynamic response of preloaded system +*MODAL DYNAMIC +0.01, 5.0 +… +*END STEP +We wish to study the local, possibly nonlinear, response of a part of this model that is so small that we +do not need to model dynamic effects locally and can, thus, perform two steps of static analysis: +** Define submodel boundary (driven nodes) +*SUBMODEL +PERIM +*STEP +** Preload +*STATIC +0.1, 1.0 +*BOUNDARY, SUBMODEL, STEP=1 +… +*END STEP +*STEP +** Local static response to global dynamic step +*STATIC +0.01, 5.0 +*BOUNDARY, SUBMODEL, STEP=3 +… +*END STEP +It is perfectly acceptable that the submodel analysis requests general, possibly nonlinear, analysis for +both steps, while in the global analysis the dynamic step was a linear perturbation step (modal dynamics +is always a linear perturbation analysis). It is your responsibility to judge that this use of the submodeling +feature is reasonable. For example, suppose that the global analysis were continued with a fourth step +of general, nonlinear static response: +*RESTART, READ, STEP=3 +** Read state at end of initial preload +** (could equally well use *RESTART, READ, STEP=1) +*STEP +** Add more preload +*STATIC +0.2, 1.0 +… +*END STEP +This fourth general analysis step starts with the state at the end of general analysis Step 1 because the +frequency extraction and the modal dynamic steps are both linear perturbation steps. However, if we +restart the submodel analysis in the same way, the solution may not be comparable with the global model +solution: +*RESTART, READ, STEP=2 +** Read state at end of step 2 +*STEP +** Add more preload +*STATIC +0.2, 1.0 +*BOUNDARY, SUBMODEL, STEP=4 +… +*END STEP +The second step in the submodel is a general analysis step, to which the response may be nonlinear, +thus changing the state of the model. A valid alternative would be to apply the Step 4 response to the +submodel immediately after the first step: +*RESTART, READ, STEP=1 +** Read state at end of preload step +*STEP +** Add more preload +*STATIC +0.2, 1.0 +*BOUNDARY, SUBMODEL, STEP=4 +… +*END STEP +Reinterpreting solution variables in the submodel analysis +During general analysis steps Abaqus works in terms of total solution variables such as the displacements, +, about a base +. When general analysis steps and linear perturbation steps are reinterpreted in the submodel +. In linear perturbation steps Abaqus works in terms of the displacement perturbation, +state, +analysis, the global analysis results are treated as defined in Table 10.2.2–1. +Table 10.2.2–1 Reinterpreting solution variables in the submodel analysis. +Driven variable +basis +Global increment +specified in +definition of +submodel boundary +condition +none +none +Global analysis +step basis +Submodel step +basis +General +Linear perturbation +General +Linear perturbation +General +General +Static, linear +perturbation +Static, linear +perturbation +In this table +is the current value of a driven variable in the submodel at any time during a +general, nonlinear, analysis step; +is the value of the perturbation of a driven variable in the submodel during a linear +perturbation step; +and +are the corresponding values of the same (geometrically interpolated) variable in +the global model; +is the “base state” value of the variable during a linear perturbation step in the +global analysis; +is the “base state” value of the variable during a linear perturbation step in the +submodel analysis; +is the value of +at increment i of the global analysis step; and +is the value of +at increment i of the global analysis step. +Mixing general and linear perturbation steps in shell-to-solid submodeling +Additional assumptions must be made for the shell-to-solid case when a general procedure on the global +model drives a linear perturbation procedure on the submodel and vice versa. The assumptions depend on +the geometric formulation used (linear or nonlinear) and on the procedure combination. For details and +governing equations for these cases, see “Submodeling analysis,” Section 2.15.1 of the Abaqus Theory +Manual. +Initial conditions +The definition of initial conditions should be consistent between the global model and the submodel. +Boundary conditions +Boundary conditions (other than submodel boundary conditions) prescribed on the degrees of freedom +that are driven will replace those prescribed using submodel boundary conditions. When this replacement +occurs, Abaqus reports the change in the data file. +A node can be driven from the global model in some steps and have user-prescribed boundary +In these cases all relevant boundary conditions must be respecified . +Any other boundary conditions that are applied in the submodel region should be imposed in the +submodel analysis in the usual way. It is your responsibility to apply such prescribed boundary conditions +to the submodel correctly so that they correspond to the loading of the global model. +Be careful with submodel boundary nodes that are also on planes of symmetry, where both forms +of boundary conditions can be applied. It may be helpful in such cases to apply boundary conditions in +a local coordinate system . The local coordinate +system should be applied only to the boundary conditions that are intended to override the submodel +boundary conditions, since the submodel boundary conditions are always output in the global coordinate +directions by the global model. +Loads +Any loads that are applied in the submodel region must be imposed in the submodel analysis in the usual +way. It is your responsibility to apply such loads to the submodel correctly so that they correspond to +the loading of the global model. See “Applying loads: overview,” Section 33.4.1, for an overview of the +loads available in Abaqus. +Predefined fields +The following predefined fields can be specified in a submodeling analysis, as described in “Predefined +fields,” Section 33.6.1: +• Nodal temperatures can be specified. Any difference between the applied and initial temperatures +will cause thermal strain if a thermal expansion coefficient is given for the material (“Thermal +expansion,” Section 26.1.2). The specified temperature also affects temperature-dependent material +properties, if any. +• The values of user-defined field variables can be specified. These values affect only field-variable- +dependent material properties, if any. +Abaqus interpolates solution variables onto the submodel driven nodes. +It can also interpolate +temperatures as field variables . Other predefined fields will not be interpolated to the nodes of the submodel; +they must be available from the input data for all nodes of the submodel where they are required. +Abaqus/Standard provides multiple approaches for cases where a submodel thermal-stress analysis +must be performed using temperature solutions from a global heat transfer analysis. +• Run a heat transfer analysis of the global model, and write the nodal temperatures to the results or +output database file. Run a sequentially coupled thermal-stress analysis of the global model. The +temperatures obtained from the results or output database file of the global heat transfer analysis +are field variables in this case. If the mesh used in the thermal-stress analysis is different from the +mesh in the heat transfer analysis, specify that Abaqus/Standard should interpolate the temperature +field from the heat transfer analysis mesh to the thermal-stress analysis mesh. Run a thermal- +stress analysis of the submodel using the results or output database file for the global thermal-stress +analysis to read the driven variables (displacement field) and using the results or output database +file from either the global heat transfer analysis or the global thermal-stress analysis to read the +temperatures as field variables. In either case the temperature field will have to be interpolated to +the current submodel nodes. If interpolation between dissimilar meshes is necessary, the global +output database file must be used to read the temperatures. For details, see Figure 10.2.2–13 and +Figure 10.2.2–14. +Global model (mesh1) +Heat transfer analysis +Field variables +Global.odb +Interpolate from +mesh1 to mesh 3 +Field variables +Global.odb +Interpolate from +mesh1 to mesh4 +Global model (mesh3) +Static analysis +Read temperatures from Global.odb +Driven variables +Global_u.fil or Global_u.odb +Submodel (mesh4) +Static analysis +Read temperatures from Global.odb +Figure 10.2.2–13 Sequentially coupled thermal-stress analysis for +the global model with only a thermal-stress analysis for the submodel. +• Run a heat transfer analysis of the global model, and write the nodal temperatures to the results or +output database file. Run a sequentially coupled thermal-stress analysis (the global thermal-stress +Global model (mesh1) +Heat transfer analysis +Field variable +Global_1.odb +Interpolate from +mesh1 to mesh2 +Global model (mesh2) +Static analysis +Read temperatures from Global_1.odb +Driven variable +Global_2.fil or Global_2.odb +Field variable +Global_2.odb +Interpolate from +mesh2 to mesh3 +Submodel (mesh3) +Static analysis +Read temperatures from Global_2.odb +Figure 10.2.2–14 Sequentially coupled thermal-stress analysis for +the global model with only a thermal-stress analysis for the submodel. +analysis) using the same mesh (mesh1) as the global heat transfer analysis and the temperatures +from the results or output database file for the global heat transfer analysis. Next, run a submodel +heat transfer analysis using the mesh (mesh2) that is required for the final submodel thermal-stress +analysis, and write the nodal temperatures to the results or output database file. Use the temperature +solution from the global heat transfer analysis to drive the solution of the submodel heat transfer +analysis. Finally, run the submodel thermal-stress analysis using the temperatures (as field +variables) obtained from the results or output database file for the submodel heat transfer analysis +and the displacements (as driven variables) obtained from the global thermal-stress analysis. See +the detailed flow chart in Figure 10.2.2–15. +Material options +Any of the material models described in Part V, “Materials,” can be used in the global and submodel +analyses. The material response defined for the submodel may be different from that defined for the +global model. +Elements +The dimensionality of the submodel must be the same as that of the global model: both models must be +either two-dimensional or three-dimensional. The following limitations apply: +Submodel (mesh2) +Submodel +Heat transfer analysis +Field variables +Submodel_heat.fil +or +Submodel_heat.odb +Global model (mesh1) +Heat transfer analysis +Driven variables +Global.fil +Global.odb +Field variables +Global.fil or Global.odb +Global model (mesh1) +Static analysis +Read temperatures from +Global.fil or Global.odb +Driven variables +Global_u.fil +Global_u.odb +Submodel (mesh2) +Static analysis +Read temperatures from +Submodel_heat.fil or Submodel_heat.odb +Figure 10.2.2–15 Sequentially coupled thermal-stress analysis +for both the global model and submodel. +• The boundary nodes of the submodel must lie within regions of the global model where Abaqus +is able to perform spatial interpolation to define the values of the driven variables. Therefore, +they must lie within (or, as allowed by the exterior tolerance, near to) two- or three-dimensional +geometrically defined elements in the global model. Such geometrically defined elements are: +– first- or second-order triangles or quadrilaterals in two dimensions; +– first- or second-order triangular or quadrilateral shells; and +– first- or second-order tetrahedra, wedges, or bricks in three dimensions. +• When shell elements with five degrees of freedom per node (S4R5, S8R5, STRI65, etc.) are used +in the global model, the rotations are not written to the results file or the output database; therefore, +only the displacement degrees of freedom can be driven. This restriction suggests that submodeling +should not be used with these elements or that the submodel should include a set of narrow elements +around its driven edges so that the interpolated displacements at these nodes effectively transfer the +rotation. Five degree of freedom shells cannot be used in shell-to-solid submodeling. +• The boundary nodes cannot lie in regions of the global model where there are only one-dimensional +elements (beams, trusses, links, axisymmetric shells) since Abaqus does not provide the necessary +interpolation of results for such elements. +• The boundary nodes cannot lie in regions of the global model where there are only user elements, +substructures, springs, dashpots, etc. since those element types do not allow for geometric +interpolation. +• The boundary nodes cannot lie in regions of the global model where there are only axisymmetric +solid elements with nonlinear, asymmetric deformation (CAXA elements). The submodeling +capability is currently not supported for these elements. +• The reference node associated with generalized plane strain elements (CPEG) cannot be used as a +driven boundary node in a submodeling analysis. +Output +Any of the output normally available within a particular procedure is also available during a submodeling +analysis . +As described above, nodal output requests to the results file or output database file must be used in +the global analysis to save the values of the driven variables at the submodel boundary. +Input file template +Global analysis: +*HEADING +… +*STEP +Step 1 +*STATIC (or *DYNAMIC, etc.) +Data line to define step time and control incrementation +… +*NODE FILE +List of solution variables to be used to drive the submodel +*OUTPUT, FIELD +*NODE OUTPUT +List of solution variables to be used to drive the submodel +*END STEP +Submodel analysis: +*HEADING +… +*SUBMODEL, EXTERIOR TOLERANCE=tolerance +List of all nodes to be driven +** +*STEP +*STATIC (or any other allowable procedure) +Data line to define step time (must be the same as the step time in the global analysis unless the +TIMESCALE parameter is used on the *BOUNDARY option) and control incrementation +… +*BOUNDARY, SUBMODEL, STEP=1 +Data lines listing nodes and degrees of freedom to be driven in this step +… +*END STEP +10.2.3 +SURFACE-BASED SUBMODELING +Products: Abaqus/Standard +References +• “Submodeling: overview,” Section 10.2.1 +• *SUBMODEL +• *DSLOAD +• Chapter 38, “Submodeling,” of the Abaqus/CAE User’s Manual +Overview +The surface-based submodeling technique: +• may not provide the same level of accuracy as node-based submodeling; +• should be used only when the node-based technique cannot provide adequate results; +• is limited to stress-based solid-to-solid submodeling for general static procedures in Abaqus/Standard; +• applies surface tractions to submodel surfaces based on a stress field interpolated from the global +model; and +• can be combined with node-based submodeling of displacements . +Performing a surface-based submodeling analysis +Your submodel analysis is driven, either partly or completely, from the results obtained from a global +model analysis. The results from the global model are interpolated onto the surfaces on the appropriate +parts of the boundary of the submodel. Thus, the response at the boundary of the local region is defined +by the solution for the global model. The driven surfaces and any loads applied to the local region +determine the solution in the submodel. +Surface-based submodeling should be used only when the node-based technique cannot provide +adequate results. For a comparison of the two submodeling techniques and recommendations for their +application, refer to “Submodeling: overview,” Section 10.2.1. +Saving the results from the global model +The results from the global analysis must be saved at all elements required for the interpolation of the +driven variables to the boundary surface of the submodel. Only the output database can be used for this +purpose. +In each step of the global model whose solution will be used to drive the submodel, write the stress +results to the output database . +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*OUTPUT, FIELD +*ELEMENT OUTPUT +Step module: Output→Field Output Requests→Create +Referring to the global model results from the submodel analysis +You must define the source of the global solution results and provide the name of the output database file; +the file extension is optional. If the file extension is omitted, Abaqus will correctly choose the extension +if the output database file exists. +Input File Usage: +abaqus job=submodel_input_file globalmodel= global_output_database +Abaqus/CAE Usage: +Any module: Model→Edit Attributes→submodel: Submodel: +Read data from job: global_output_database +Specifying the driven surfaces in the submodel +Specifying the driven element-based surfaces does not activate the driven surface loads: they must be +activated by specifying the appropriate submodel distributed surface loads. +All surface facets of the submodel to be driven by stresses in any step must be specified as driven +surfaces since the list of surfaces cannot be extended subsequent to its initial definition (even at restart). +However, variables at the surfaces given do not have to be driven in all steps: +the choice of which +surfaces are driven in a particular step is made as part of a submodel distributed surface load definition, +as discussed in “Defining the driven surface tractions in the submodel,” later in this section. +boundary surface of the submodel +driven by the global model solution +Figure 10.2.3–1 The magnified submodel. +Input File Usage: +*SUBMODEL +list of element-based structural surfaces +The *SUBMODEL option must be included in the model definition portion +of the input file for the submodel analysis. Multiple *SUBMODEL options are +allowed; however, in this case you must ensure that the driven surfaces specified +on the data line of one option are separate and distinct from the other surfaces +specified on the data lines of all the other options. +Abaqus/CAE Usage: +Load module: Create Load: choose Other for the Category and Submodel +for the Types for Selected Step: Driving region: select region +Defining geometric tolerances +A geometric tolerance is used to define how far driven element-based surface nodes in the submodel +can lie outside the exterior surface of the global model, as that surface is interpolated in the global, +undeformed finite element model. By default, surface nodes in the submodel must lie within a distance +calculated by multiplying the average element size in the global model by 0.05. You can change the +tolerance, which is useful in cases where submodel driven surfaces lie to a greater extent outside +the global model exterior surface. Tolerances larger than this default value, however, can result in +significantly greater computation times and lower accuracy in the driven solution for driven surface +regions significantly outside the global model exterior surface. +You can define the geometric tolerance as a fraction of the size of the average element in the global +model or as an absolute distance in the length units chosen for the model. If both tolerances are defined, +Abaqus uses the tighter tolerance. +Input File Usage: +Use the following option to define the geometric tolerance as an absolute +distance: +*SUBMODEL, TYPE=SURFACE, ABSOLUTE EXTERIOR +TOLERANCE=tolerance +Use the following option to define the geometric tolerance as a fraction of the +size of the average element in the global model: +*SUBMODEL, TYPE=SURFACE, EXTERIOR TOLERANCE=tolerance +Load module: Create Load choose Other for the Category and +Submodel for the Types for Selected Step: select region: Exterior +tolerance: absolute: or relative: tolerance +Abaqus/CAE Usage: +The exterior tolerance in solid-to-solid submodeling +The exterior tolerance for a solid-to-solid submodel analysis is indicated by the shaded region in +Figure 10.2.3–2. If the distance between the driven surface nodes and the free surface of the global +model falls within the specified tolerance, the solution variables from the global model are extrapolated +to the submodel. +exterior surface in global model +driven surface in submodel +nodes in global model +nodes in submodel +actual geometric +surface +Figure 10.2.3–2 The exterior tolerance in surface-based submodeling. +Defining the driven surface tractions in the submodel +The actual driven surface tractions are defined in any step as submodel distributed surface loads. The +stresses resulting in these tractions are “driven variables” obtained from the output database file of the +global analysis. +All stress components from the global model elements that will drive the submodel boundary surface +must have been written to the output database. They will be used to create traction, shear, and normal +stresses at integration points of driven surfaces (as non-uniform distributed surface loads). All applicable +stress components are calculated and applied to the surface integration points at each time increment. +Input File Usage: +Abaqus/CAE Usage: +*DSLOAD, SUBMODEL +Load module: Create load: choose Other for the Category and +Submodel for the Types for Selected Step +Specifying the step number from the global analysis +You specify the step of the global model history that is to be used for the driven variables in the current +submodel analysis step. +Input File Usage: +Abaqus/CAE Usage: +*DSLOAD, SUBMODEL, STEP=step +Load module: Create load: choose Other for the Category and Submodel +for the Types for Selected Step: select region: Global step number: step +Modifying the set of driven surface tractions +You can modify the submodel distributed surface load definitions from step to step to change the +global step reference, you can remove surface load definitions, and you can reintroduce them later . New surfaces cannot be added to the total set of driven +surface defined for the submodel; this set of driven surfaces is a fixed part of the model definition. +Input File Usage: +Use one of the following options: +*DSLOAD, SUBMODEL, OP=MOD +*DSLOAD, SUBMODEL, OP=NEW +Guidelines for obtaining adequate solution accuracy +Unlike node-based submodeling, surface-based submodeling can in many cases provide incorrect or +misleading submodel results. This risk follows from the methods used to interpolate stresses from the +global model to the submodel: +• The global model material point stresses are smoothed and associated with the global model nodes. +• These global model node-located stresses are then interpolated to the submodel surface integration +points and applied as tractions. +This process is generally nonconservative, resulting in a submodel traction field that is not equivalent to +the global model stress field in an equilibrium sense. +Modeling guidelines +You can improve accuracy and achieve reasonable submodel solutions by observing the following +guidelines: +• Design your models so that your submodel surface intersects the global model in regions of +relatively low stress gradients. +• Design your models so that your submodel surface intersects the global model in regions of uniform +element size. A warning message is provided in the data (.dat) file in cases where significant +nonuniform element size distributions are seen. +Checking your results +To understand whether your modeling approach results in a reasonably accurate solution, the following +guidelines are recommended: +• Compare the stress distributions on the submodel-driven surfaces with the stress distributions in +the global model. You can view the stress distributions in the global model by using tools such as +cutting planes and path plots in the Visualization module of Abaqus/CAE. The degree to which the +global model’s stress distributions agree with those in the submodel-driven surface is generally an +indication of the level of accuracy of your submodel solution. +• When using inertia relief in the submodel for cases where submodeling does not remove all rigid +body modes, compare the inertia relief forces to the prevailing force level in your submodel. If the +inertia relief force is large compared to the prevailing force level, your submodel results may be +inaccurate. +Special considerations +There are several special considerations that are worth noting. +Handling of rigid-body modes +When you use surface-based submodeling exclusively to drive your submodel response, your +displacement solution will not be unique; you will generally encounter rigid-body modes and +accompanying numerical issues. You can address these rigid-body modes by +• providing sufficient node-based submodel displacement boundary condition definitions in the +submodel analysis, +• providing sufficient boundary condition definitions in the submodel analysis, or +• providing an inertia relief load definition in the submodel analysis . +You can combine these definitions, as necessary and appropriate to your model, to address all rigid body +modes. +Cases of finite rotation +Global model stress results are stored in the output database in the global coordinate system. Submodel +tractions are calculated from these stresses and the current configuration surface normal in the +submodel. Hence, when your global model result involves significant finite rotation, your submodel +results will generally be inaccurate unless you provide sufficient node-based submodel displacement +boundary condition definitions to impart similar rigid-body rotations to the submodel; exclusive use of +surface-based submodeling definitions is not adequate to provide these rigid-body motions. You may +also experience convergence difficulties in the submodel when it is not properly rotated. +Inelastic behavior +When surface-based submodeling is used to drive a submodel region with an inelastic material +definition, you may encounter rigid-body modes and accompanying numerical issues. For example, +numerical issues will prevent convergence if the submodel material definition includes plasticity and +the submodel loading results in a shear band formation beyond the material hardening definition, such +that unconstrained motion can occur (i.e., if the submodel loads exceed the limit load capacity). In these +cases node-based submodeling should be used. +Procedures +Only the static procedure is allowed. Both general (possibly nonlinear) and linear perturbation steps can +be used in submodeling . +Obtaining a solution at a particular point in time using linear perturbation analysis +In Abaqus/Standard it is possible to study the submodel’s linearized response corresponding to a +particular point in time in the global solution by using a static, linear perturbation procedure in the +submodel analysis. You can select the increment in the global analysis step that is to be used as the basis +for calculating the values for the driven variables. If you do not select an increment in a static linear +perturbation step, the last increment of the selected step in the global analysis is used as the basis for +calculating the values for the driven variables. You cannot select an increment in a general submodel +step. +Input File Usage: +Abaqus/CAE Usage: +*DSLOAD, SUBMODEL, STEP=step, INC=increment +Selection of a specific global model increment is not supported in Abaqus/CAE. +Mixing general and linear perturbation steps +It is possible to mix general steps and linear perturbation steps in both the global and the submodel +analyses. Abaqus allows general analysis steps to be treated as linear perturbation steps during +submodeling, and vice versa. +Example: Submodeling with general and linear perturbation steps +For an example of submodeling that uses both general and linear perturbation steps, consider the +following situation. The global analysis consists of a static preload—done as a general, nonlinear, +analysis step—followed by extraction of the eigenmodes of the preloaded structure, then a step of +5 seconds of modal dynamic response analysis: +*STEP +** Apply preload +*STATIC +0.1, 1.0 +… +** Write out stress results for elements needed to +** interpolate to the submodel's surfaces +*ELEMENT OUTPUT, ELSET=DETAIL +*END STEP +*STEP +** Calculate modes and frequencies +*FREQUENCY +… +** The *ELEMENT OUTPUT option is repeated because +** this is the first linear perturbation step +*ELEMENT OUTPUT, ELSET=DETAIL +*END STEP +*STEP +** Dynamic response of preloaded system +*MODAL DYNAMIC +0.01, 5.0 +… +*END STEP +We wish to study the local, possibly nonlinear, response of a part of this model that is so small that we +do not need to model dynamic effects locally and can, thus, perform two steps of static analysis: +** Define submodel surfaces (driven surfaces) +*SUBMODEL,TYPE=SURFACE +PERIM +*STEP +** Preload +*STATIC +0.1, 1.0 +*DSLOAD, SUBMODEL, STEP=1 +… +*END STEP +*STEP +** Local static response to global dynamic step +*STATIC +0.01, 5.0 +*DSLOAD, SUBMODEL, STEP=3 +… +*END STEP +It is perfectly acceptable that the submodel analysis requests general, possibly nonlinear, analysis for +both steps, while in the global analysis the dynamic step was a linear perturbation step (modal dynamics +is always a linear perturbation analysis). It is your responsibility to judge that this use of the submodeling +feature is reasonable. For example, suppose that the global analysis were continued with a fourth step +of general, nonlinear static response: +*RESTART, READ, STEP=3 +** Read state at end of initial preload +** (could equally well use *RESTART, READ, STEP=1) +*STEP +** Add more preload +*STATIC +0.2, 1.0 +… +*END STEP +This fourth general analysis step starts with the state at the end of general analysis Step 1 because the +frequency extraction and the modal dynamic steps are both linear perturbation steps. However, if we +restart the submodel analysis in the same way, the solution may not be comparable with the global model +solution: +*RESTART, READ, STEP=2 +** Read state at end of step 2 +*STEP +** Add more preload +*STATIC +0.2, 1.0 +*DSLOAD, SUBMODEL, STEP=4 +… +*END STEP +The second step in the submodel is a general analysis step, to which the response may be nonlinear, +thus changing the state of the model. A valid alternative would be to apply the Step 4 response to the +submodel immediately after the first step: +*RESTART, READ, STEP=1 +** Read state at end of preload step +*STEP +** Add more preload +*STATIC +0.2, 1.0 +*DSLOAD, SUBMODEL, STEP=4 +… +*END STEP +Loads +Any loads that are applied in the submodel region of the global analysis must be imposed in the submodel +analysis in the usual way. It is your responsibility to apply such loads to the submodel correctly so that +they correspond to the loading of the global model. See “Applying loads: overview,” Section 33.4.1, for +an overview of the loads available in Abaqus. +Output +Any of the output normally available within a particular procedure is also available during a submodeling +analysis . +As described above, element stress output requests to the output database file must be used in the +global analysis to save the values of the driven variables at the submodel boundary. +Input file template +Global analysis: +*HEADING +… +*STEP +Step 1 +*STATIC (or *STATIC, etc.) +Data line to define step time and control incrementation +… +*ELEMENT OUTPUT +*OUTPUT, FIELD +*ELEMENT OUTPUT +*END STEP +Submodel analysis: +*HEADING +… +*SUBMODEL,TYPE=SURFACE, EXTERIOR TOLERANCE=tolerance +List of all surfaces to be driven +** +*STEP +*STATIC (or any other allowable procedure) +Data line to define step time and control incrementation. +…*DSLOAD, SUBMODEL, STEP=1 +Data lines listing surfaces to be driven in this step +… +*END STEP +10.3 +Generating global matrices +• “Generating matrices,” Section 10.3.1 +10.3.1 +GENERATING MATRICES +Product: Abaqus/Standard +References +• “Defining matrices,” Section 2.11.1 +• “Defining an analysis,” Section 6.1.2 +• *MATRIX GENERATE +• *MATRIX OUTPUT +• *MATRIX INPUT +• *CLOAD +Overview +Matrix generation: +• is a linear perturbation procedure; +• allows for the mathematical abstraction of model data such as mesh and material information by +generating global or element matrices representing the stiffness, mass, viscous damping, structural +damping, and load vectors in a model; +• generally creates matrices identical to those used in a subspace-based steady-state dynamic +procedure . +• includes initial stress and load stiffness effects due to preloads and initial conditions if nonlinear +geometric effects are included in the analysis; +• writes matrix data to a binary .sim file that can be read as input by Abaqus; and +• can output matrix data to text files that can be read as input in other analyses by Abaqus or other +simulation software. +Generating global matrices +A linearized finite element model can be summarized in terms of matrices representing the stiffness, mass, +damping, and loads in the model. Using these matrices, you can exchange model data between other +users, vendors, or software packages without exchanging mesh or material data. Matrix representations +of a model prevent the transfer of proprietary information and minimize the need for data manipulation. +The matrix generation procedure is a linear perturbation step that accounts for all current boundary conditions, loads, and material +response in a model. You can also specify new boundary conditions, loads, and predefined fields within +the matrix generation step. The generated matrices are input to a matrix usage model. +The matrix generation procedure uses SIM, which is a high-performance database available in +Abaqus. The generated matrices are stored in a file named jobname_Xn.sim, where jobname is the +name of the input file or analysis job and n is the number of the Abaqus step that generates the matrices. +Specifying the matrix type +You can generate matrices representing the following model features: +• stiffness, +• mass, +• viscous damping, +• structural damping, and +• loads. +The load matrix contains integrated nodal load vectors (right-hand sides) for the load cases defined in the +matrix generation step. Load cases can be made up of any combination of loadings—distributed loads, +concentrated nodal loads, thermal expansion, and load cases defined for any substructures that may be +used as part of the model. +Input File Usage: +Use the following option to generate the stiffness matrix: +*MATRIX GENERATE, STIFFNESS +Use the following option to generate the mass matrix: +*MATRIX GENERATE, MASS +Use the following option to generate the viscous damping matrix: +*MATRIX GENERATE, VISCOUS DAMPING +Use the following option to generate the structural damping matrix: +*MATRIX GENERATE, STRUCTURAL DAMPING +Use the following option to generate the load matrix: +*MATRIX GENERATE, LOAD +Generating element matrices +By default, the matrix generation procedure generates global matrices for a model in assembled form. +The generated global matrices are assembled from the local element matrices and include contributions +from matrix input data. Abaqus/Standard offers an option to generate global matrices in element-by- +element form. Instead of global (assembled) matrices, local element matrices are generated. If you +choose to generate local element matrices for a model containing matrix input data, Abaqus/Standard +calculates and stores only element matrices; the matrix input data are ignored. +Input File Usage: +*MATRIX GENERATE, ELEMENT BY ELEMENT +Generating matrices for a part of the model +By default, the matrix generation procedure generates matrices for a whole model. Abaqus/Standard can +generate matrices for a part of the model defined by an element set. +Input File Usage: +*MATRIX GENERATE, ELSET=element set name +Evaluating frequency-dependent material properties +When frequency-dependent material properties are specified in the model definition, Abaqus/Standard +offers the option of choosing the frequency at which these properties are evaluated for use in global +matrix generation. If you do not choose the frequency, Abaqus/Standard evaluates the matrices at zero +frequency and does not consider the contributions from frequency-domain viscoelasticity. +Input File Usage: +*MATRIX GENERATE, PROPERTY EVALUATION=frequency +Specifying public nodes +An Abaqus/Standard model may contain user-defined nodes and internal nodes. +Internal nodes are +nodes with internal degrees of freedom associated with them (for example, Lagrange multipliers and +generalized displacements) that are created internally by Abaqus/Standard. +You can use the matrix generation procedure to specify some of the user-defined nodes as “public +nodes.” These nodes will be visible in the matrix usage model. The remaining user-defined nodes in +the matrix data are designated as internal nodes and are effectively hidden in the matrix usage model +. By default, all user-defined +nodes in the matrix data are public nodes. +By specifying public nodes, you can reduce the number of user-defined nodes in the matrix usage +analysis, which simplifies the remapping process . For example, you may want to identify the nodes +for attaching a subcomponent (matrix) to the matrix usage model or the nodes for the output of results +as public nodes. +Input File Usage: +*MATRIX GENERATE, PUBLIC NODES=node set name +Initial conditions +Matrix generation is a linear perturbation procedure. Therefore, the initial state for the matrix generation +step is the state of the model at the end of the last general analysis step. The generated matrix includes +initial stress and load stiffness effects due to preloads and initial conditions if nonlinear geometric effects +are included in the analysis. +Boundary conditions +Boundary conditions can be defined or modified in a matrix generation step. For more information +on defining boundary conditions, see “Boundary conditions in Abaqus/Standard and Abaqus/Explicit,” +Section 33.3.1. Any boundary conditions that are defined in a matrix generation step will not be used in +subsequent general analysis steps (unless they are respecified). +Loads +All types of loads can be applied in the load cases for a matrix generation step. Real and imaginary parts +of the load vectors will be generated for the complex loads. For more information on applying loads, see +“Applying loads: overview,” Section 33.4.1. Any loads that are defined in a matrix generation step will +not be used in subsequent general analysis steps (unless they are respecified). +Predefined fields +All types of predefined fields can be specified in a matrix generation procedure. For more information +on specifying predefined fields, see “Predefined fields,” Section 33.6.1. Any predefined fields that are +defined in a matrix generation step will not be used in subsequent general analysis steps (unless they are +respecified). +Material options +All types of materials that are available in Abaqus/Standard can be used in a matrix generation procedure. +Elements +All types of elements that are available in Abaqus/Standard can be used in the matrix generation +procedure. +Generating matrices for models containing solid continuum infinite elements +Solid continuum infinite elements (CIN-type elements) have different formulations in static and dynamic +analyses. Therefore, when generating matrices for a model containing solid continuum infinite elements, +you must specify whether to use the static or dynamic formulation. +Input File Usage: +Use the following option to select the static formulation for solid infinite +elements: +*MATRIX GENERATE, SOLID INFINITE FORMULATION=STATIC +Use the following option to select the dynamic formulation for solid infinite +elements: +*MATRIX GENERATE, SOLID INFINITE FORMULATION=DYNAMIC +Output +In a matrix generation analysis, you can output the stiffness, mass, viscous damping, structural damping, +and load matrices to text files. Several formats are available for the matrix output, as discussed below. +Matrices are copied from the .sim file and output in text files that use the following naming convention: +jobname_matrixN.mtx +where jobname is the name of the input file or analysis job, matrix is a four-letter identifier indicating +the matrix type (as outlined in Table 10.3.1–1), and N is the number associated with the Abaqus analysis +step generating the matrices. +Table 10.3.1–1 Identifiers used in the generated matrix file name. +Identifier Matrix Type +STIF +MASS +DMPV +DMPS +LOAD +Stiffness matrix +Mass matrix +Viscous damping matrix +Structural damping matrix +Load matrix +For example, if a stiffness matrix generation is performed in the third step of an analysis job named +VehicleFrame, the matrix is output to a file named VehicleFrame_STIF3.mtx. +Input File Usage: +Use the following option to output the stiffness matrix: +*MATRIX OUTPUT, STIFFNESS +Use the following option to output the mass matrix: +*MATRIX OUTPUT, MASS +Use the following option to output the viscous damping matrix: +*MATRIX OUTPUT, VISCOUS DAMPING +Use the following option to output the structural damping matrix: +*MATRIX OUTPUT, STRUCTURAL DAMPING +Use the following option to output the load matrix: +*MATRIX OUTPUT, LOAD +Matrix input text format +This default text format creates matrix files consistent with the format used by the matrix definition +technique in Abaqus/Standard . This format does not convert +any of the internal Abaqus node labels. A negative number or zero can be used as a label for an internal +node. +Input File Usage: +*MATRIX OUTPUT, FORMAT=MATRIX INPUT +Format of the operator matrix +The assembled sparse matrix operator data are written to the text file as a series of comma-separated lists. +Each row in the file represents a single matrix entry; a row is written as a comma-separated list with the +following elements: +1. Row node label +2. Degree of freedom for row node +3. Column node label +4. Degree of freedom for column node +5. Matrix entry +Format of the load matrix +Nonzero entries in load matrices, which represent right-hand-side vector data, are written to the text file +as a comma-separated list with the following elements: +1. Node label +2. Degree of freedom +3. Right-hand-side vector entry +The format of the load vectors and heading labels is based on the Abaqus keyword interface, which allows +the generated loads to be easily applied in other Abaqus analyses. Each load vector uses the following +headings to indicate the real and imaginary portions of the load: +*CLOAD, REAL +*CLOAD, IMAGINARY +If the matrix generation step has multiple load cases, the load matrices for each load case are +wrapped by the following labels in the generated text file: +*LOAD CASE +… +*END LOAD CASE +Including generated matrix data and generated loads in another Abaqus model +The generated sparse matrix data and generated loads that are output in matrix input text format can be +included in another Abaqus model. +Input File Usage: +Use the following options: +*MATRIX INPUT +*INCLUDE, INPUT=matrix or load file +Labeling text format +You can generate text files in which the matrix is formatted according to the standard labeling format. +Internal Abaqus node labels are converted into large positive numbers that are acceptable for Abaqus +matrix input data. This is the only difference between the labeling text format and the default matrix +input text format. All nodes of the matrix generated in the labeling text format are treated as user-defined +nodes if the matrix is used in an Abaqus/Standard analysis. +Input File Usage: +*MATRIX OUTPUT, FORMAT=LABELS +Coordinate text format +You can generate text files in which the matrix is formatted according to the common mathematical +coordinate format. This format is commonly used in mathematics programs such as MATLAB. +separated list with the following elements: +GENERATING MATRICES +1. Row number +2. Column number +3. Matrix entry +For load matrices, which represent right-hand-side vector data, each row in the text file is written with +the following elements: +1. Equation (row) number +2. Right-hand-side vector entry +Commented load case options are written to the output file to indicate the load cases. +Input File Usage: +*MATRIX OUTPUT, FORMAT=COORDINATE +Outputting matrices in element-by-element form +If matrices are generated in element-by-element form, you can write them in element-by-element form. +When you generate text files using the matrix input or labeling format, each row in the file represents a +single matrix entry; a row is written as a comma-separated list with the following elements: +1. Element label +2. Row node label +3. Degree of freedom for row node +4. Column node label +5. Degree of freedom for column node +6. Matrix entry +For load matrices, which represent right-hand-side vector data, each row in the text file is written +with the following elements: +1. Element label +2. Node label +3. Degree of freedom +4. Right-hand-side vector entry +Coordinate format is also available for element-by-element global matrix generation. Each row in a +coordinate-formatted file corresponds to a matrix entry; a row is written as a comma-separated list with +the following elements: +1. Element number +2. Row number +3. Column number +4. Matrix entry +For load matrices each row in the text file is written with the following elements: +1. Element number +2. Equation (row) number +3. Right-hand-side vector entry +Input file template +*HEADING +… +** +*STEP +Options to define the preloading history for the model. +*END STEP +** +*STEP +*MATRIX GENERATE, STIFFNESS, MASS, VISCOUS DAMPING, +STRUCTURAL DAMPING, LOAD +*MATRIX OUTPUT, STIFFNESS, MASS, VISCOUS DAMPING, +STRUCTURAL DAMPING, LOAD, FORMAT=MATRIX INPUT +*BOUNDARY +Options to define the boundary conditions for the matrix generation step. +** +*LOAD CASE, NAME=LC1 +Options to define the loading for the first load case. +*END LOAD CASE +** +*LOAD CASE, NAME=LC2 +Options to define the loading for the second load case. +*END LOAD CASE +Any number of load cases can be defined. +*END STEP +OF CYCLIC SYMMETRY MODELS +10.4 +Symmetric model generation, results transfer, and analysis of +cyclic symmetry models +• “Symmetric model generation,” Section 10.4.1 +• “Transferring results from a symmetric mesh or a partial three-dimensional mesh to a full three- +dimensional mesh,” Section 10.4.2 +• “Analysis of models that exhibit cyclic symmetry,” Section 10.4.3 +10.4.1 +SYMMETRIC MODEL GENERATION +Product: Abaqus/Standard +Reference +• *SYMMETRIC MODEL GENERATION +Overview +A three-dimensional model can be created in Abaqus/Standard by: +• revolving an axisymmetric model about its axis of revolution; +• revolving a single three-dimensional sector about its axis of symmetry; or +• combining two parts of a symmetric three-dimensional model, where one of the parts is the original +model and the other part is obtained by reflecting the original model through either a symmetry line +or a symmetry plane. +Abaqus/Standard also provides for the transfer of the solution obtained in the original analysis onto the +new model . +Only stress/displacement, heat transfer, coupled temperature-displacement, and acoustic elements +can be used to generate a new model. +Model generation +The symmetric model generation capability can be used to create a three-dimensional model by revolving +an axisymmetric model about its axis of revolution, by revolving a single three-dimensional sector about +its axis of symmetry, or by combining two parts of a symmetric model, where one part is the original +model and the other part is the original model reflected through a line or a plane. The original model +must have been saved to a restart file. The symmetric model generation capability is not available for +models defined in terms of an assembly of part instances. Therefore, an element set name or a node set +name containing quotation marks is not supported. +An entire three-dimensional model—including nodes, elements, section definitions, material +and orientation definitions, rebar, and contact pair definitions—is generated from the original model. +Symmetric model generation from a model with general contact is not allowed. You must redefine +most types of kinematic constraints (“Kinematic constraints: overview,” Section 34.1.1). However, +surface-based constraints (“Mesh tie constraints,” Section 34.3.1) and embedded element constraints +(“Embedded elements,” Section 34.4.1) defined in the original model will be generated automatically in +the new three-dimensional model. Changes made to the model as part of the history data—element or +contact pair removal/reactivation (“Element and contact pair removal and reactivation,” Section 11.2.1) +or changes to friction properties (“Changing friction properties during an Abaqus/Standard analysis” in +“Frictional behavior,” Section 36.1.5)—will not be transferred to the new model. Such changes will +have to be redefined in the history data of the new model. All element and node sets defined in the +original model will be used in the new model. These sets will contain all of the new elements and nodes +that originated from the original sets. +Additional nodes, elements, contact surfaces, etc. can also be defined to create parts of the model +that were not specified in the original model. You must ensure that the numbering of these nodes and +elements does not conflict with those used by the symmetric model generation capability. You can control +the node and element numbering in the new model (as described below for each type of revolved model) +so that you can define additional parts of the model without the risk of conflicting element and node +labels. The smallest node/element number used in defining additional parts of the new model should be +greater than the largest node/element number generated by the symmetric model generation capability. +Eliminating duplicate nodes +Duplicate nodes will be generated in certain situations. Such nodes can be eliminated to ensure that the +mesh is connected properly. Duplicate nodes can be generated on the axis of revolution of a revolved +model, on the connection planes between sectors of a periodic model, and on the connection plane +between the two parts of a reflected model. You can specify the tolerance distance, d, to be used in +the search for duplicate nodes. The default distance is 1.0% of the average element dimension. In some +cases a tolerance distance that is smaller than the default value needs to be specified if, for example, +the distance between two nodes on one of the connection planes in the original sector of a periodic +model is smaller than the default tolerance distance. Closely spaced nodes elsewhere in the model, such +as between interface surfaces or on parts of the model that are generated with any of the other model +definition options, will not be eliminated. +Input File Usage: +Use one of the following options to specify the tolerance to be used in the search +for duplicate nodes: +*SYMMETRIC MODEL GENERATION, PERIODIC, TOLERANCE=d +*SYMMETRIC MODEL GENERATION, REVOLVE, TOLERANCE=d +*SYMMETRIC MODEL GENERATION, REFLECT, TOLERANCE=d +Writing the new model definition to an external file +You can specify the name of an external file (without an extension) to which the data for the new model +definition will be written. The extension .axi will be added to the file name provided. The file can be +edited to modify or to extend the model generated by Abaqus/Standard. +Input File Usage: +Use one of the following options: +*SYMMETRIC MODEL GENERATION, PERIODIC, FILE NAME=name +*SYMMETRIC MODEL GENERATION, REVOLVE, FILE NAME=name +*SYMMETRIC MODEL GENERATION, REFLECT, FILE NAME=name +Identifying the restart files +The symmetric model generation capability uses the restart (.res), analysis database (.stt and .mdl), +and part (.prt) files from the old model to generate the new model. The name of the restart files +from the old model must be specified when the new analysis is executed by using the oldjob parameter +in the command for running Abaqus or by answering a request made by the command procedure . +Verifying the new model +It is recommended that you verify the new model carefully before an analysis is performed. The +symmetric model generation capability requires only information stored in the restart file during a data +check run to generate the new model, which allows you to verify the new model before the analysis of +the original model is performed. A data check analysis is performed by using the datacheck parameter +in the command for running Abaqus . +Revolving an axisymmetric cross-section +You can create a three-dimensional model by revolving the cross-section of a two-dimensional +axisymmetric model about a symmetry axis starting at a prescribed reference plane, +. Both the +symmetry axis and reference plane of the new three-dimensional model can be oriented in any direction +with respect to the global coordinate system . A nonuniform discretization in the +circumferential direction can be specified. +reference +cross-section +at θ = 0 +Figure 10.4.1–1 Revolving an axisymmetric cross-section. +Specify the coordinates of points a, b, and c shown in Figure 10.4.1–1, followed by a list that defines +the discretization in the circumferential direction containing the segment angle, number of elements per +segment, and the bias ratio of the segment. Several segment angles, each with a different number of +element subdivisions and a different bias ratio, can be used to define the complete discretization around +the circumference of the revolved model. The endpoint of a cross-section revolved through 360.0° will +always be connected to the origin of revolution, +, regardless of the value specified for the +duplicate node tolerance. +Input File Usage: +*SYMMETRIC MODEL GENERATION, REVOLVE +Local orientation system +A local cylindrical orientation system is always used for element output of stress, strain, etc. A default +local orientation definition is provided if the material in the original axisymmetric model does not contain +an orientation definition. This default orientation is defined with the polar axis of the system along the +axis of revolution, with an additional 90.0° rotation about the local 1-direction so that the local axes are +1=radial, 2=axial, and 3=circumferential. If shells or membranes are used, the projections of the local +2- and 3-axes onto the surface of the shell or membrane are taken as the local directions on the surface. +This orientation system is always provided, even if an orientation is specified in the original axisymmetric +model. However, if the results of the axisymmetric analysis are mapped onto the new three-dimensional +model and an orientation definition is associated with the material +in the original model, the original orientation revolved about the axis of symmetry replaces this default +orientation definition. +Controlling the new node and element numbering +You can define the increments in numbers between each node and element around the circumference +of the three-dimensional model. The numbering starts at the reference cross-section +. The +reference cross-section uses the same numbering as the original axisymmetric model. The defaults are the +largest node and element numbers used in the original axisymmetric model. Control over the numbering +allows you to define additional parts of the model without the risk of conflicting element and node labels. +Each offset value should be greater than or equal to the maximum node or element label, respectively, +used in the original model. When specifying the offset value, care must be taken that the generated node +or element does not exceed the maximum value allowed, which is 999,999,999. +Input File Usage: +*SYMMETRIC MODEL GENERATION, REVOLVE, NODE +OFFSET=offset, ELEMENT OFFSET=offset +Correspondence between axisymmetric and three-dimensional elements +The element type used in the original two-dimensional model determines the element type in the new +three-dimensional model. You can specify whether the new element should be either a general three- +dimensional element or a cylindrical element. General and cylindrical elements can be used in the same +model. +Input File Usage: +*SYMMETRIC MODEL GENERATION, REVOLVE +coordinates of points a and b +coordinates of point c +segment angle, number of elements per segment, bias ratio, +CYLINDRICAL or GENERAL +For example, the following input specifies 4 cylindrical elements in a 300° +segment and 10 general elements in a 60° segment: +*SYMMETRIC MODEL GENERATION, REVOLVE +ax , ay , az , bx , by , bz +cx , cy , cz +300.0, 4, 1.0, CYLINDRICAL +60.0, 10, 1.0, GENERAL +Regular axisymmetric elements (CAX), axisymmetric elements with twist (CGAX), shell elements, +membrane elements, rigid elements, and surface elements can be used in the two-dimensional model; +however, nonlinear axisymmetric elements (CAXA) cannot be used. A two-dimensional model that +contains incompatible mode elements; first-order, reduced-integration, continuum elements; shell +elements; or rigid elements cannot be used to generate cylindrical elements. The correspondence +between the axisymmetric element type and the equivalent three-dimensional element type (general or +cylindrical) is shown in Table 10.4.1–1. +Table 10.4.1–1 Correspondence between axisymmetric and +three-dimensional (general and cylindrical) element types. +Axisymmetric +element +General three- +dimensional element +Cylindrical element +ACAX3 +CAX3 +CAX3H +CGAX3 +CGAX3H +CGAX3T +DCAX3 +ACAX4 +CAX4 +CAX4H +CAX4I +CAX4R +CAX4RH +CGAX4 +AC3D6 +C3D6 +C3D6H +C3D6 +C3D6H +C3D6T +DC3D6 +AC3D8 +C3D8 +C3D8H +C3D8I +C3D8R +C3D8RH +C3D8 +10.4.1–5 +CCL9 +CCL9H +CCL9 +CCL9H +CCL12 +CCL12H +Axisymmetric +element +General three- +dimensional element +Cylindrical element +CGAX4H +CGAX4R +CGAX4RH +CAX4T +CAX4RT +CAX4HT +CAX4RHT +CGAX4T +CGAX4RT +CGAX4HT +CGAX4RHT +DCAX4 +DCCAX4 +DCCAX4D +ACAX6 +CAX6 +CAX6H +CGAX6 +CGAX6H +DCAX6 +ACAX8 +CAX8 +CAX8H +CAX8R +CAX8RH +CGAX8 +CGAX8H +CGAX8R +CCL12H +CCL18 +CCL18H +CCL18 +CCL18H +CCL24 +CCL24H +CCL24R +CCL24RH +CCL24 +CCL24H +CCL24R +C3D8H +C3D8R +C3D8RH +C3D8T +C3D8RT +C3D8HT +C3D8RHT +C3D8T +C3D8RT +C3D8HT +C3D8RHT +DC3D8 +DCC3D8 +DCC3D8D +AC3D15 +C3D15 +C3D15H +C3D15 +C3D15H +DC3D15 +AC3D20 +C3D20 +C3D20H +C3D20R +C3D20RH +C3D20 +C3D20H +C3D20R +Axisymmetric +element +General three- +dimensional element +Cylindrical element +CGAX8RH +CAX8T +CAX8RT +CAX8HT +CAX8RHT +CGAX8T +CGAX8RT +CGAX8HT +CGAX8RHT +DCAX8 +SAX1 +DSAX1 +SAX2 +DSAX2 +MAX1 +MGAX1 +MAX2 +MGAX2 +RAX2 +SFMAX1 +SFMGAX1 +SFMAX2 +SFMGAX2 +C3D20RH +C3D20T +C3D20RT +C3D20HT +C3D20RHT +C3D20T +C3D20RT +C3D20HT +C3D20RHT +DC3D20 +S4R +DS4 +S8R +DS8 +M3D4R +M3D4R +M3D8R +M3D8R +R3D4 +SFM3D4R +SFM3D4R +SFM3D8R +SFM3D8R +CCL24RH +MCL6 +MCL6 +MCL9 +MCL9 +SFMCL6 +SFMCL6 +SFMCL9 +SFMCL9 +Limitations +• First- and second-order elements cannot be used together in the axisymmetric model. +• Nonaxisymmetric elements such as springs, dashpots, beams, and trusses will be ignored in the +model generation. +• Only surface-based contact pairs can be revolved. Models using general contact cannot be revolved. +Contact conditions modeled with contact elements will be ignored in the model generation. +• A two-dimensional model +reduced- +integration, continuum elements; shell elements; or rigid elements cannot be used to generate +cylindrical elements. +includes incompatible mode elements; first-order, +that +• Rebar with nonuniform spacing in the radial direction of an axisymmetric element cannot be +revolved. +• Most types of kinematic constraints cannot be revolved. However, surface-based constraints +(“Mesh tie constraints,” Section 34.3.1) and embedded element constraints (“Embedded elements,” +Section 34.4.1) defined in the original model will be generated automatically in the new +three-dimensional model. +• Only stress/displacement, heat transfer, coupled temperature-displacement, and acoustic elements +can be revolved. +Revolving a three-dimensional sector to create a periodic model +You can create a three-dimensional periodic model by revolving a single three-dimensional sector +about a symmetry axis. Each generated sector in the periodic model can span the same angle in the +circumferential direction, such as in a vented disc, or alternatively, can have a variable angle, such as in +a treaded tire. In both cases, each sector always has the same geometry and mesh. Both the symmetry +axis and the original three-dimensional sector can be oriented in any direction with respect to the global +coordinate system . Mismatched surface meshes can be used between sectors. +Both open (the structure has end edges) or closed loop periodic structures can be generated. If a closed +loop periodic structure needs to be created, the sum of the segment angles over all the sectors must be +equal to 360°. +Defining a periodic model with a constant angle +To define a periodic model with a constant angle, you must specify the coordinates of points a and b +shown in Figure 10.4.1–2 to define the symmetry axis. You then define the segment angle, +(in degrees), +of the original sector and the number of three-dimensional repetitive sectors, N, including the original +sector, in the generated periodic model. +Input File Usage: +*SYMMETRIC MODEL GENERATION, PERIODIC=CONSTANT +coordinates of points a and b +θ, N +Defining a periodic model with a variable angle +To define a periodic model with a variable angle, the surfaces on both sides of the original sector must be +completely planar. You specify the coordinates of points a and b shown in Figure 10.4.1–2 to define the +symmetry axis. You then define the segment angle, +(in degrees), of the original sector and the number +of three-dimensional repetitive sectors, N, including the original sector, in the generated periodic model. +Next, you specify an additional number of three-dimensional sectors to be generated, M, and the angular +Figure 10.4.1–2 Revolving a three-dimensional sector to form a periodic model. +scaling factor, f, in the circumferential direction with respect to the original sector to be applied to these +additional sectors. You can define pairs of additional sectors and scaling factors as needed. +Input File Usage: +*SYMMETRIC MODEL GENERATION, PERIODIC=VARIABLE +coordinates of points a and b +θ, N +M1 , f1 +M2 , f2 +Etc. +For example, the following input creates a 210° three-dimensional model with +7 sectors with the angles of 20°, 20°, 30°, 30°, 30°, 40°, and 40°, respectively: +*SYMMETRIC MODEL GENERATION, PERIODIC=VARIABLE +ax , ay , az , bx , by , bz +20.0,2 +3,1.5 +2,2.0 +Applying constraints to symmetric surfaces with mismatched meshes +If the symmetric surfaces in the original sector have precisely matched meshes, as shown in +Figure 10.4.1–3, any duplicate nodes that are generated will be eliminated automatically to ensure that +the mesh is connected properly between the neighboring sectors when revolving the original sector +about the symmetry axis to create a periodic model. +Figure 10.4.1–3 Surfaces with precisely matching meshes on the original sector. +In all other cases you must define one or more pairs of corresponding surfaces on each side of the +original sector in the original model and specify the pairs +of corresponding surfaces in the symmetric model generation definition. +Optionally, you can also specify the tolerance distance within which nodes on one surface of a +sector must lie from the corresponding surface of the neighboring sector to be constrained. Nodes on +the surface of the sector that are further away from the corresponding surface of the neighboring sector +than this distance are not constrained. The default value for the tolerance distance is 5% or 10% of +the typical element size in the surfaces of the original sector, depending on whether node-to-surface or +surface-to-surface type constraints are used, respectively. +You can also specify whether surface-to-surface (default) or node-to-surface constraints should be +used. Constraints between the automatically generated neighboring pairs of corresponding surfaces +are then applied with an automatically generated surface-based tie constraint (“Mesh tie constraints,” +Section 34.3.1) when revolving the original sector about the symmetry axis to create a periodic model. +The first surface of each specified pair is the slave surface, and all degrees of freedom of the nodes in the +surface will be eliminated by internally generated multi-point constraints. +MODEL GENERATION +Use the following options in the original model: +*SURFACE, NAME=master +*SURFACE, NAME=slave +Use the following option in the new model with a constant angle for each sector: +*SYMMETRIC MODEL GENERATION, PERIODIC=CONSTANT +ax , ay , az , bx , by , bz +θ, N +slave, master, tolerance distance, SURFACE or NODE +Use the following option in the new model with a variable angle for each sector: +*SYMMETRIC MODEL GENERATION, PERIODIC=VARIABLE +ax , ay , az , bx , by , bz +θ, N +M, f +slave, master, tolerance distance, SURFACE or NODE +Local orientation system +If an +A local cylindrical orientation system is always used for element output of stress, strain, etc. +orientation is specified in the original three-dimensional sector , the +orientation system in the new model is defined by revolving the original orientation system about the +symmetry axis. If shells or membranes are used, the projections of the local 2- and 3-axes onto the +surface of the shell or membrane are taken as the local directions on the surface. If the material in the +original three-dimensional sector does not contain an orientation definition, a default local orientation +definition is provided. This default orientation is defined by revolving the global coordinate system in +the original model about the axis of symmetry in the new model. +Controlling the new node and element numbering +You can define the increments in numbers between each node and element around the circumference of +the three-dimensional model. The numbering starts at the original three-dimensional repetitive sector. +The original three-dimensional repetitive sector uses the same numbering as the original model. The +defaults are the largest node and element numbers used in the original model. Control over the numbering +allows you to define additional parts of the model without the risk of conflicting element and node labels. +Each offset value should be greater than or equal to the maximum node or element label, respectively, +used in the original model. When specifying the offset value, care must be taken that the generated node +or element does not exceed the maximum value allowed, which is 999,999,999. +*SYMMETRIC MODEL GENERATION, PERIODIC, +NODE OFFSET=offset, ELEMENT OFFSET=offset +Input File Usage: +Limitations +• Only surface-based contact pairs can be revolved. Models using general contact cannot be revolved. +Contact conditions modeled with contact elements will be ignored in the model generation. +• Most types of kinematic constraints cannot be revolved. However, surface-based constraints +(“Mesh tie constraints,” Section 34.3.1) and embedded element constraints (“Embedded elements,” +Section 34.4.1) defined in the original model will be generated automatically in the new +three-dimensional model. One exception is that surface-based ties for enforcing cyclic symmetric +constraints are not revolved. +• Surface-based distributed coupling constraints—e.g., +(“Coupling constraints,” +Section 34.3.2), shell-to-solid couplings (“Shell-to-solid coupling,” Section 34.3.3), and fasteners +(“Mesh-independent fasteners,” Section 34.3.4)—cannot be revolved and must be redefined. +• Only stress/displacement, heat transfer, coupled temperature-displacement, and acoustic elements +couplings +can be revolved. Beam and frame elements cannot be revolved. +Reflecting a partial three-dimensional model +You can create a three-dimensional model by combining two parts of a symmetric three-dimensional +model. One of the parts is the original model, and the other part is obtained by reflecting the original +model through a symmetry line (Figure 10.4.1–4) or plane (Figure 10.4.1–5). +Specify the coordinates of points a, b, and (if required) c shown in Figure 10.4.1–4 and +Figure 10.4.1–5. +reflection line +6 + n +5 + n +7 + n +8 + n +2 + n +1 + n +3 + n +4 + n +Figure 10.4.1–4 Reflecting a three-dimensional model through line +with node offset n. +reflection plane +7 + n +8 + n +6 + n +5 + n +3 + n +4 + n +2 + n +1 + n +Figure 10.4.1–5 Reflecting a three-dimensional model through a plane +with node offset n. +Input File Usage: +Use one of the following options: +*SYMMETRIC MODEL GENERATION, REFLECT=LINE +*SYMMETRIC MODEL GENERATION, REFLECT=PLANE +Controlling the new node and element numbering +You can specify constants that must be added to the original node and element numbers for numbering the +reflected part of the three-dimensional model. The defaults are the maximum node and element numbers +used in the original model. Control over the numbering allows you to define additional parts of the model +without the risk of conflicting element and node labels. +Input File Usage: +*SYMMETRIC MODEL GENERATION, REFLECT, +NODE OFFSET=offset, ELEMENT OFFSET=offset +Limitations +• Only surface-based contact pairs can be reflected. Models using general contact cannot be reflected. +Contact conditions modeled with contact elements will be ignored in the model generation. +• You must ensure that master surfaces remain continuous after reflection. A discontinuous surface +is created when the surface in the original model does not intersect the connection plane between +the two parts of the symmetric structure. +• Rigid surfaces cannot be reflected. The rigid surface definition of the original model is simply +repeated in the new model. You must, therefore, specify the complete rigid surface in the original +model. +• Most types of kinematic constraints cannot be reflected. However, surface-based constraints +(“Mesh tie constraints,” Section 34.3.1) and embedded element constraints (“Embedded elements,” +Section 34.4.1) defined in the original model will be generated automatically in the new +three-dimensional model. +• Only stress/displacement, heat transfer, coupled temperature-displacement, and acoustic elements +can be reflected. +• Nonaxisymmetric elements such as springs, dashpots, beams, and trusses cannot be reflected. +TRANSFERRING RESULTS FROM A SYMMETRIC MESH OR A PARTIAL THREE- +DIMENSIONAL MESH TO A FULL THREE-DIMENSIONAL MESH +SYMMETRIC RESULTS TRANSFER +Product: Abaqus/Standard +References +• “Symmetric model generation,” Section 10.4.1 +• *SYMMETRIC RESULTS TRANSFER +Overview +Symmetric results transfer: +• reduces the analysis cost of structures that may first undergo symmetric deformation followed by +nonsymmetric deformation later during the loading history; +• can be used to transfer the solution of an axisymmetric model to a three-dimensional model; +• can be used to transfer the solution of the symmetric part of a three-dimensional model to a full +three-dimensional model; +• must be used in conjunction with the symmetric model generation capability ; and +• can be used only to transfer the solution of a stress/displacement, heat transfer, coupled temperature- +displacement, or coupled acoustic-structural analysis to a new model. +Transferring the solution from a symmetric mesh or a partial three-dimensional mesh to a +full three-dimensional mesh +The symmetric results transfer capability can be used to transfer the solution of an axisymmetric model to +a three-dimensional model or to transfer the solution of the symmetric part of a three-dimensional model +to a full three-dimensional model. The symmetric model generation capability described in “Symmetric +model generation,” Section 10.4.1, must be used to generate the three-dimensional model. +The symmetric results transfer capability is not available for models defined in terms of an assembly +of part instances. +The solution that is transferred to the new model consists of the deformed configuration and +corresponding material state, which includes strains and all state variables. The nodes are imported +with their original coordinates. This solution becomes the initial or base state in the new analysis. +Specifying the time at which the solution obtained in the original model must be read +You specify the time at which the solution obtained in the original model must be read. The required +step and increment or iteration must have been written to the restart files during the original analysis. +Input File Usage: +Use the following option if the solution is transferred from any analysis other +than a direct cyclic procedure: +*SYMMETRIC RESULTS TRANSFER, STEP=step, INC=increment +Use the following option if the solution is transferred from a previous direct +cyclic analysis: +*SYMMETRIC RESULTS TRANSFER, STEP=step, ITERATION=iteration +Obtaining equilibrium +You must ensure that the model is in equilibrium at the beginning of the analysis. It is recommended +that an initial step definition be included using boundary conditions and loading that match the state of +the model from which the results are transferred. An initial time increment equal to the total time should +be used for this step to allow Abaqus/Standard to try and achieve the equilibrium in one increment. If +needed, Abaqus/Standard can resolve the stress unbalance linearly over the step such that more than one +increment is used. You can choose to have the stress unbalance resolved in the first increment of the step +instead. +Input File Usage: +Use the following option to have Abaqus/Standard resolve the stress unbalance +linearly over the step: +*SYMMETRIC RESULTS TRANSFER, UNBALANCED STRESS=RAMP +Use the following option to have Abaqus/Standard resolve the stress unbalance +in the first increment of the step: +*SYMMETRIC RESULTS TRANSFER, UNBALANCED STRESS=STEP +Identifying the restart files +The symmetric results transfer capability uses the restart (.res), analysis database (.stt and .mdl), +part (.prt), and output database (.odb) files from the old analysis to transfer the solution data to the +new mesh. The name of the restart files from the old analysis must be specified when the new analysis is +executed by using the oldjob parameter in the command for running Abaqus or by answering a request +made by the command procedure . +Verifying the new model +It is recommended that you verify that the new model is generated correctly before results are transferred +or any analysis is performed. The model generation capability requires only information stored in the +restart files during a data check run to generate the new model, which allows you to verify the new model +before the analysis of the original model is performed. A data check analysis is performed by using the +datacheck parameter in the command for running Abaqus . +Once the model has been verified, the analysis of the original model can be performed and the results +can be transferred to the new model. +The transferred solution can be written to the results files by requesting output at the beginning of a +step (the zero increment; see “Output,” Section 4.1.1). This solution can also be viewed in Abaqus/CAE. +Orientation system +When results are transferred from an axisymmetric model to a three-dimensional model, a local +cylindrical orientation system is used for element output of stress, strain, etc. A default local orientation +definition (“Orientations,” Section 2.2.5) is provided if the material in the original axisymmetric model +does not contain an orientation definition. This default orientation is defined with the polar axis of the +system along the axis of revolution with an additional 90° rotation about the local 1-direction so that the +local axes are 1=radial, 2=axial, and 3=circumferential. If shells or membranes are used, the projections +of the local 2- and 3-axes onto the surface of the shell or membrane are taken as the local directions on +the surface. It is assumed that the material properties are specified in this system. If, on the other hand, +an orientation definition is associated with the material in the original model, the orientation in the new +three-dimensional model will be that orientation definition revolved about the axis of symmetry. +When results are transferred from a partial three-dimensional model to a full three-dimensional +model by reflecting the partial three-dimensional model, a local material orientation is created in +the full three-dimensional model based on the corresponding orientation definition in the partial +three-dimensional model. However, if the material does not contain an orientation definition in the +partial three-dimensional model and the partial three-dimensional model is not created by revolving an +axisymmetric model, no local orientation definition is created in the full three-dimensional model. The +full three-dimensional model uses a global coordinate system. +When results are transferred from a three-dimensional sector to a periodic three-dimensional model +by revolving the three-dimensional sector about its symmetry axis, a local cylindrical orientation system +is always used for element output of stress, strain, etc. +If an orientation is specified in the original +three-dimensional sector, the orientation system in the new model is defined by revolving the original +orientation system about the symmetry axis. If shells or membranes are used, the projections of the +local 2- and 3-axes onto the surface of the shell or membrane are taken as the local directions on the +surface. If the material in the original three-dimensional sector does not contain an orientation definition, +a default local orientation definition is provided. This default orientation is defined by revolving the +global coordinate system in the original model about the axis of symmetry in the new model. +Coordinate system at nodes +The displacement and rotational components obtained from the original model are first transformed into a +global, rectangular Cartesian axis system before the results are transferred. If local coordinate directions +are required in the new model, a nodal transformation (“Transformed coordinate systems,” Section 2.1.5) +must be specified in the new model to define this coordinate system. +Limitations +The following limitations exist for result transfer from an axisymmetric model to a 3-D model: +• Result transfer is not available from 8-node reduced-integration axisymmetric elements (CAX8R +and CAX8RH) to the corresponding 20-node brick elements (C3D20R and C3D20RH) when the +elements are underlying the slave surface in a contact pair. +• SAX2 is a finite-strain shell, while S8R is a small-strain shell. Do not use this combination when +deformations are large in the original analysis. +The following limitation exists for result transfer from a symmetric 3-D model to a full 3-D model: +• Result transfer is not supported for shells with five degrees of freedom per node (STRI65, S8R5, +and S9R5). +Initial conditions +Initial conditions can +be specified on all nodes and elements, including the part of the model generated using symmetric model +generation . However, in most cases the symmetric +results transfer capability will overwrite the initial condition values with the solution obtained from the +original model. An exception is initial temperatures and field variables. Initial temperatures and field +variables are overwritten only when temperatures and field variables are specified in the original model. +If only part of the original model contains a specification for temperatures or field variables, the remaining +part of the model is assumed to have initial conditions with a magnitude of zero. This distribution of the +field will be transferred to the new model. If temperatures and/or field variables are not defined anywhere +in the original model, the initial conditions specified in the new model are applied. +Boundary conditions +All boundary conditions must be redefined; +the symmetric result transfer capability ignores the +boundary conditions specified in the original model. You must ensure that the model is in equilibrium +at the beginning of the analysis; therefore, an initial step definition should be included using boundary +conditions and loading that match the state of the model from which the results are transferred. +Loads +All loads must be redefined; the symmetric result transfer capability ignores the loads specified in the +original model. You must ensure that the model is in equilibrium at the beginning of the analysis; +therefore, an initial step definition should be included using boundary conditions and loading that match +the state of the model from which the results are transferred. +Material options +All of the material definitions defined in the original model will be transferred to the new model. +Elements +Any element or contact pair removal/reactivation definition that was active in the original model should be respecified. +Output +All of the standard output variables available for stress/displacement elements can be used with the +symmetric results transfer capability. +The solution that is transferred to the new model can be written to the results (.fil) file by +requesting output at the beginning of a step (the zero increment; see “Output,” Section 4.1.1). It can +also be displayed in Abaqus/CAE. +10.4.3 +ANALYSIS OF MODELS THAT EXHIBIT CYCLIC SYMMETRY +Products: Abaqus/Standard Abaqus/CAE +References +• “Natural frequency extraction,” Section 6.3.5 +• “Mode-based steady-state dynamic analysis,” Section 6.3.8 +• *CYCLIC SYMMETRY MODEL +• *SELECT CYCLIC SYMMETRY MODES +• *SURFACE +• *TIE +• “Defining cyclic symmetry,” Section 15.13.19 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +The cyclic symmetry analysis technique in Abaqus/Standard: +• makes it possible to analyze the behavior of a 360° structure with cyclic symmetry based on a model +of a repetitive sector; +• can determine the response to cyclic symmetric loading in static, quasi-static, and heat transfer +analyses; +• can calculate all eigenfrequencies and eigenmodes of the 360° structure with the block Lanczos +eigenfrequency extraction procedure; +• can determine the response to loading corresponding to a given cyclic symmetry mode in modal- +based steady-state dynamic analysis; and +• does not require that matched meshes be used on the symmetry surfaces. +Introduction +Structures that exhibit cyclic symmetry provide the analyst with an opportunity to model an entire 360° +structure at considerably reduced computational expense by analyzing only a single repetitive sector of +the model. Typically, this is the smallest sector that can be identified, although this is not necessary. +For example, if a structure consists of 16 repetitive sectors it is possible to use a 45° model containing +two repetitive sectors. The sectors are numbered in the counterclockwise direction to the axis of cyclic +symmetry (as described further below). Of course this is less efficient than using a 22.5° model with one +sector. There is no restriction that the meshes on the two symmetry surfaces of a repetitive sector match +in any way. +There are two basic cases that must be considered in such an analysis: a model that has a cyclic +symmetric initial state and a cyclic symmetric response, and a model with a cyclic symmetric initial state +but a nonsymmetric response. The cyclic symmetry capability in Abaqus/Standard provides for linear +and nonlinear analysis of cyclic symmetric structures with cyclic symmetric response. The condition +that the structure be cyclic symmetric holds throughout the analysis, so in a loading step it is not possible +to have any nonsymmetric deformation in the structure at any time. Therefore, only cyclic symmetric +loads can be applied for this situation. +Analysis of cyclic symmetric structures that exhibit nonsymmetric response requires additional +consideration. +Such an analysis can be performed only in a linear perturbation step, since the +nonsymmetric deformation invalidates the assumption of a cyclic symmetric “base state” for any +subsequent step in a general nonlinear analysis. The full response of an entire cyclic symmetric +structure, such as the structure illustrated in Figure 10.4.3–1, can be represented as a linear combination +of several independent basic responses, each of which corresponds to some k-fold cyclic symmetry +mode. +Finite element model +of this sector only +Figure 10.4.3–1 Cyclic symmetric structure. +The cyclic symmetry mode number, which is sometimes also referred to as the “nodal diameter,” indicates +the number of waves along the circumference in a basic response. Figure 10.4.3–2, Figure 10.4.3–3, and +Figure 10.4.3–4 illustrate basic responses corresponding to the 0-, 1-, and 2-fold modes (nodal diameters +0, 1, and 2) in a cyclic symmetric structure containing four repetitive sectors. A full linear perturbation +analysis can be performed by solving a sequence of corresponding linear analyses for a symmetric single +sector. Cyclic symmetric boundary conditions (associated with various cyclic symmetry modes) on the +single sector give rise to Hermitian stiffness and mass matrices (complex matrices with symmetric real +parts and skew-symmetric imaginary parts). The kth linear analysis in the sequence is performed using +symmetry conditions that correspond to the k-fold cyclic symmetry mode of the structural response. +For a structure exhibiting N-fold cyclic symmetry, only +(N odd) such +analyses are required. This results in a solution for the response of the entire structure at a relatively low +computational expense. +(N even) or +Figure 10.4.3–2 Response corresponding to the 0-fold cyclic symmetry mode. +Figure 10.4.3–3 Response corresponding to the 1-fold cyclic symmetry mode. +Figure 10.4.3–4 Response corresponding to the 2-fold cyclic symmetry mode. +To perform a general linear analysis of a cyclic symmetric structure, the external forces should be +represented as a linear combination of basic loads, each of which corresponds to a symmetry mode and +excites a structural response corresponding to the same mode. In static analysis a capability to define +loads on any mode other than the 0-fold mode has not yet been implemented. As the response of the 0-fold +mode preserves cyclic symmetry, analysis of this type of structure can be done in a general nonlinear +step, as well as in a linear perturbation step (as described above). For the same reason, such a step can +be used as a preload step for a cyclic symmetric linear perturbation step. +Extraction of a nonsymmetrical response for a cyclic symmetric structure is currently available +only for eigenfrequency extraction analysis (“Natural frequency extraction,” Section 6.3.5) using +the block Lanczos method and for frequency domain, modal-based steady-state dynamic analysis +(“Mode-based steady-state dynamic analysis,” Section 6.3.8). Natural frequencies corresponding to +both symmetric and nonsymmetric eigenmodes can be extracted for a specific cyclic symmetry mode, +for a group of cyclic symmetry modes, or for all cyclic symmetry modes. They can be used within the +subsequent steady-state dynamic analysis. The eigenmodes onto which the solution is projected are +chosen as described in “Selecting the modes and specifying damping” in “Mode-based steady-state +dynamic analysis,” Section 6.3.8. +In a steady-state modal-based dynamic analysis, concentrated, distributed, and surface loads can be +defined as projected onto a specific cyclic symmetry mode. Within the same steady-state dynamics step +all applied loads have to be given as projected onto the same cyclic symmetry mode. This limitation +implies that the specified cyclic symmetry mode must be the same for all loads within the given steady- +state dynamics step. +Defining a cyclic symmetric model +Define the mesh for a single sector of the model, the so called “datum sector.” Specify the number of +sectors, n, in the 360° model. Define the axis of symmetry by specifying the coordinates (in the global +coordinate system) of two points lying on the axis. The axis direction is from the first point to the second +point, and the sectors are numbered counterclockwise around the axis, with the datum sector as sector +number 1. For a two-dimensional model only a single point needs to be given on the axis. The axis +direction is assumed to be in the positive z-direction; hence, the sectors are numbered counterclockwise +in the x–y plane. +Input File Usage: +*CYCLIC SYMMETRY MODEL, N=n +In a model defined in terms of an assembly of part instances, the *CYCLIC +SYMMETRY MODEL option must appear within the model definition . +Abaqus/CAE Usage: +Interaction module: Interaction→Create: Cyclic symmetry: +Total number of sectors: n +Applying cyclic symmetry constraints +To apply the cyclic symmetry constraints, you must define one or more pairs of corresponding surfaces +on each side of the datum sector . You can then apply the cyclic +symmetry constraints between the pairs of corresponding surfaces using a cyclic symmetry surface-based +tie constraint . The first surface of each +pair specified in the tie constraint definition is the slave surface, and all degrees of freedom of the nodes +in the surface will be eliminated by internally generated multi-point constraints. The second surface +of each pair is a master surface. If more than one pair of slave/master surfaces is defined, the rotation +direction from the slave surface to the master surface must be the same for all pairs (i.e., clockwise or +counterclockwise). +Input File Usage: +Use the following options to apply a cyclic symmetry constraint between two +surfaces: +*SURFACE, NAME=master +*SURFACE, NAME=slave +*TIE, CYCLIC SYMMETRY, NAME=cyclic +slave, master +Abaqus/CAE Usage: +Interaction module: Interaction→Create: Cyclic symmetry: +click Surface in the prompt area +Using mismatched surface meshes +In the case of mismatched surface meshes, as shown in Figure 10.4.3–5, the finer mesh should typically +be the slave surface. Mismatched meshes may cause some local inaccuracies in the stress field. The +magnitude of the inaccuracies depends on the degree of mismatch between the meshes as well as on +the element type used: +the inaccuracies are typically most pronounced for second-order (modified) +tetrahedral elements. Hence, if mismatched surface meshes are used, it is recommended that the sector +boundaries be chosen in areas where accuracy of the local stress field is not critical. +datum sector +symmetry axis +symmetry surfaces +Figure 10.4.3–5 Cyclic symmetry surfaces with mismatched nodes. +For shells the cyclic symmetry condition has to be applied to the nodes on the edges of the shell +elements. Currently cyclic symmetry is not supported for element-based surfaces defined on the edges +of shells. Therefore, if mismatched meshes are used for shell elements, an element-based surface should +be defined on the top or bottom of the shell elements adjacent to the edges that form the master surface. +A node-based surface can be defined on the edge that forms the slave surface. +Applying node-to-node cyclic symmetry constraints +In the case of matched meshes, either surface can be chosen as the slave surface. If the surfaces have +matched meshes, as shown in Figure 10.4.3–6, it is possible to use a node-based master surface to obtain +node-to-node cyclic symmetry constraints. The advantage of this is that Abaqus/Standard will adjust the +positions of the nodes on the slave surface so that they precisely match the positions of the nodes on the +master surface. This yields the most accurate results and minimizes the computational cost. In this case +the slave surface will typically be chosen as a node-based surface as well, although computationally it +does not matter since in either case a strict node-to-node constraint is applied. +datum sector +symmetry axis +corresponding nodes on +the symmetry surfaces +symmetry surfaces +Figure 10.4.3–6 Cyclic symmetry surfaces with node-to-node matching. +For discrete members (such as trusses or beams) the cyclic symmetry condition can be enforced +only using node-based surfaces. +Input File Usage: +Use the following options to apply a cyclic symmetry constraint between two +node-based surfaces: +*SURFACE, TYPE=NODE, NAME=master +*SURFACE, TYPE=NODE, NAME=slave +*TIE, CYCLIC SYMMETRY, NAME=cyclic +slave, master +Abaqus/CAE Usage: +Interaction module: Interaction→Create: Cyclic symmetry: +click Node Region in the prompt area +Applying cyclic symmetry conditions on the symmetry axis +If a node is located on the symmetry axis, special cyclic symmetry constraints must be applied for the +0-fold and 1-fold cyclic symmetry modes; whereas all degrees of freedom must be constrained for the +other cyclic symmetry modes. For the 0-fold cyclic symmetry mode the degrees of freedom in the +plane orthogonal to the symmetry axis are constrained; for the 1-fold cyclic symmetry mode the degrees +of freedom along the symmetry axis are constrained. Abaqus/Standard will create these constraints +automatically as long as the node is included in the definition of the slave surface, the master surface, or +both the slave and master surfaces. +Obtaining all eigenfrequencies of a cyclic symmetric structure +The natural frequencies and corresponding eigenmodes of a cyclic symmetric structure can be extracted +using the eigenfrequency extraction procedure with the Lanczos eigensolver . No additional information is required for the eigenfrequency extraction +procedure. All the natural frequencies are sorted in the conventional (ascending) order. For each natural +frequency the cyclic symmetry mode number is reported. +The eigenmodes are written in the order corresponding to natural frequencies to the data (.dat), +results (.fil), and output database (.odb) files for the user-specified datum sector only. These modes +can be expanded in Abaqus/CAE to the entire structure depending on the cyclic symmetry mode number. +There are two different types of eigenmodes: single and paired. The eigenmodes for 0-fold cyclic +symmetry are always single. For even N the eigenmodes for the +-fold cyclic symmetry are also +single. The eigenmodes for the remaining +(odd N) cyclic symmetry +modes are paired. The natural frequencies corresponding to the paired eigenmodes are equal and always +appear together in the table of the natural frequencies in the data file. The expansion of the eigenmodes +with k-fold cyclic symmetry ( +can be done in the following manner: +) to the sector +(even N) or +where +Here +(datum) sector and on the ith sectors, respectively; and +and +are paired eigenmodes corresponding to double natural frequencies on the first +. +From the expressions above it is clear that eigenmodes with 0-fold cyclic symmetry are always +-fold cyclic symmetry are +. Similarly, for even N the eigenmodes with +symmetric; i.e., +single, since +. +Selecting the cyclic symmetry modes +You can select the cyclic symmetry modes for which the eigenfrequency analysis will be performed by +specifying the lowest cyclic symmetry mode to be used in the analysis, nmin, and the highest cyclic +symmetry mode to be used in the analysis, nmax. By default, nmin is 0. By default, nmax is +(even +N) or +(odd N). The value of nmin cannot be greater than the value of nmax, and the value +of nmax cannot be greater than the default value. If you do not select the cyclic symmetry modes, all +possible cyclic symmetry modes are considered in the analysis. You can choose to use only the even +cyclic symmetry modes. +Input File Usage: +Use the following option to specify the cyclic symmetry modes: +Abaqus/CAE Usage: +*SELECT CYCLIC SYMMETRY MODES, NMIN=nmin, NMAX=nmax +Use the following option to request only the even cyclic symmetry modes: +*SELECT CYCLIC SYMMETRY MODES, EVEN +Use the following option to specify the cyclic symmetry modes: +Interaction module: Interaction→Create: Cyclic symmetry: +toggle on Specified range and specify the Lowest nodal +diameter and Highest nodal diameter +You cannot request only the even cyclic symmetry modes in Abaqus/CAE. +Selecting the cyclic symmetry mode for a steady-state dynamic step +Only a single cyclic mode can be excited in a steady-state dynamic step. You specify the cyclic symmetry +mode associated with the loading in the load definition. +Input File Usage: +Use one of the following options: +Abaqus/CAE Usage: +*CLOAD, CYCLIC MODE=k, REAL or IMAGINARY +*DLOAD, CYCLIC MODE=k, REAL or IMAGINARY +*DSLOAD, CYCLIC MODE=k, REAL or IMAGINARY +Interaction module: Interaction→Create: Cyclic symmetry: +Excited nodal diameter +Comparison of the cyclic symmetry analysis technique and MPC type CYCLSYM +MPC type CYCLSYM (“General multi-point constraints,” Section 34.2.2) provides a subset of the +functionality provided by the cyclic symmetry analysis capability. For an eigenvalue analysis MPC type +CYCLSYM will allow extraction of the symmetric (0-fold) modes only. The cyclic symmetry analysis +capability allows the use of surfaces (“Surfaces: overview,” Section 2.3.1) to define the symmetry +surfaces for the model, which enables the use of mismatched meshes on the symmetry surfaces, whereas +MPC type CYCLSYM can be applied only on a node-to-node basis. +Limitations +The following limitations exist: +• A continuation capability is not available for the cyclic symmetry eigenvalue extraction procedure. +Each eigenvalue extraction step will not reuse any eigenmodes obtained in the previous eigenvalue +extraction steps. +• The specified cyclic symmetry mode must be the same for all loads defined within a given steady- +state dynamic step. +• Base motion is not implemented for cyclic symmetry models. +• Cyclic symmetry conditions are applied to the mechanical degrees of freedom in stress/displacement +analysis and temperature degrees of freedom in heat transfer analysis. Cyclic symmetry conditions +are not applied to acoustic pressure, pore pressure, and electrical degrees of freedom. +• Cavity radiation cannot be used in cyclic symmetric models. +Initial conditions +All applied initial conditions must be cyclic symmetric. +Boundary conditions +Only cyclic symmetric boundary conditions can be applied. Boundary conditions cannot be applied to +the nodes on the slave cyclic symmetry surface. +Loads +In static analysis only cyclic symmetric loads can be applied. Coriolis loads cannot be applied, and the +effect of the Coriolis load stiffness is not considered in the frequency analysis. +In modal-based steady-state dynamic analysis the loads are defined on the datum sector for a specific +cyclic symmetry mode, which is indicated in the loading definition. For the k-fold cyclic symmetry +mode +(corresponding to real and imaginary components, +respectively) on the sector +are obtained in the following manner: +the complex loads +and +where +and F and G are real and imaginary components of loads specified for the datum +sector, respectively. For the 0-fold cyclic symmetry mode ( +) this type of loading corresponds to a +cyclic symmetric load pattern with +this type of loading is generated when +. For +a spatially constant load pattern is applied to a rotating structure (or when a constant load pattern rotates +around the structure). For the +and +-fold mode the complex loads on the sector i are: +and +. +Predefined fields +Only cyclic symmetric predefined fields can be applied. Hence, the predefined fields should have the +same values at each side of the datum sector. +Material options +No specific restrictions apply to material models for cyclic symmetry models of general procedures. For +the frequency analysis procedure, see the remarks in “Natural frequency extraction,” Section 6.3.5. +Elements +Axisymmetric elements should not be used in cyclic symmetry models. +Output +Nodal displacements and element output variables such as stress, strain, and section force are only +available for the datum sector. The mass listed in the data file is computed for the whole model. +In the eigenvalue extraction procedure the following special conditions apply: +• If displacement eigenvector normalization is chosen (the default), the largest displacement entry +in each eigenvector on the datum sector is unity. If mass eigenvector normalization is chosen, the +eigenvectors are normalized so that the generalized mass computed on the datum sector is unity. +See “Natural frequency extraction,” Section 6.3.5, for details. +• The eigenvalue numbers, cyclic symmetry mode numbers, and corresponding frequencies (in both +radians/time and cycles/time) are listed in the data file, along with the generalized masses, composite +modal damping factors, participation factors, and modal effective masses. The generalized masses +are calculated on the datum sector; composite modal damping factors, participation factors, and +modal effective masses are calculated for the entire model. +• You can restrict output to the results and data files by selecting the modes for which output is desired +. +• With Abaqus/CAE static displacements and eigenmodes can be displayed for any sector. The results +of steady-state, modal-based dynamic analysis can also be animated for any number of sectors, +including the entire model. +Input file template +*HEADING +… +** +*CYCLIC SYMMETRY MODEL, N=integer +N denotes the number of sectors in the entire 360° model. +… +** +*SURFACE, NAME=name, TYPE=ELEMENT +*SURFACE, NAME=name, TYPE=NODE +Surface description for the slave and master nodes that will be referenced in the *TIE option. +… +** +*TIE, CYCLIC SYMMETRY +Indicates the internal MPCs that tie the master and slave surfaces +using the cyclic symmetry condition in the cyclic symmetry models only. +Data lines to specify surface names that will be tied with this option. +… +** +*STEP (,NLGEOM) +If NLGEOM is used, initial stress and preload stiffness effects +will be included in subsequent linear perturbation steps, including the +frequency extraction step +*STATIC +... +*DLOAD +Data lines to specify element or element set, load type, value, (direction). +... +** +*END STEP +*STEP +*FREQUENCY, EIGENSOLVER=LANCZOS +… +*SELECT CYCLIC SYMMETRY MODES, NMAX=integer, NMIN=integer, EVEN +… +** +*END STEP +*STEP +*STEADY STATE DYNAMICS +… +*SELECT EIGENMODES +Use this option to specify the list of eigenmodes used in the response. +*MODAL DAMPING +Data lines to specify damping coefficients associated with eigenmodes. +… +*CLOAD, CYCLIC MODE=integer, REAL or IMAGINARY +Data lines to specify node or node set, degree of freedom, value +*DLOAD, CYCLIC MODE=integer, REAL or IMAGINARY +Data lines to specify element or element set, load type, value, (direction) +… +*DSLOAD, CYCLIC MODE=integer, REAL or IMAGINARY +Data lines to specify element or element set, load type, value, (direction) +… +** +*END STEP +10.5 +Periodic media analysis +• “Periodic media analysis,” Section 10.5.1 +10.5.1 +PERIODIC MEDIA ANALYSIS +Product: Abaqus/Explicit +References +• *PERIODIC MEDIA +• *MEDIA TRANSPORT +Overview +The periodic media analysis technique in Abaqus/Explicit: +• is a Lagrangian technique that offers an Eulerian-like view into a moving structure; +• can be used to effectively model systems that are repetitive in nature, such as manufacturing +processes involving conveyor belts or continuous forming operations; +• leads to significant analysis time speedup when compared to traditional modeling techniques that +may require excessively large meshes; and +• requires topologically identical meshed parts to create the model, which can be accomplished via +the parts and instances modeling paradigm. +Introduction +Quite often industrial processes that need to be analyzed involve sections that repeat in a simple pattern +and move through a process zone. A prominent example is a conveyor belt with regularly spaced +packages, as illustrated schematically in Figure 10.5.1–1 and exemplified with a finite element mesh in +Figure 10.5.1–2. Continuous forming operations such as metal rolling are also good examples because +the deforming material can be broken up into an arbitrary number of identical sections. +Trigger plane +Moving belt direction +Re-instantiate exiting building block +Figure 10.5.1–1 Schematic representation of periodic media. +Step: Step−1, pre−tensioning of belt +Increment 0: Step Time = 0.0 +Figure 10.5.1–2 Conveyor belt with packages on top. +For the sake of clarity we will use the conveyor belt example throughout this discussion to illustrate +many of the concepts associated with the periodic media analysis technique. Figure 10.5.1–1 shows a +conceptual decomposition of the conveyor belt; in reality, the belt is a continuous entity. +Conceptually, the overall model can be decomposed into blocks (topologically identical meshed +structures) that are connected together and span the process zone. You create a part that defines a +“building block” (the meshed structure that is repeated to model the entire periodic media) and then +construct the whole model via a chain of appropriately positioned instances. The periodic media +analysis technique provides a simple way to automatically connect these instances together at the front +and back ends of adjacent blocks. This technique also provides a convenient way to define loads and +boundary conditions that represent the physical system at the unconnected ends of the first and last +blocks in the chain. The first block of the chain is referred to as the inlet, and the last block is referred +to as the outlet. Finally, when the periodic media moves through the process zone, blocks from the +outlet are automatically shuffled to the inlet. The blocks (meshed structures) defined with this technique +can interact via contact with other modeling features that are not periodic in nature, such as the rollers +depicted in Figure 10.5.1–1. +At the core of the periodic media analysis technique lies the concept of shuffling blocks from +the outlet back to the inlet. A dedicated algorithm is used to detect when the inlet has moved too far +into the process zone and to shuffle a block from the outlet directly to the inlet. The dashed arrow in +Figure 10.5.1–1 illustrates the shuffling process. To ensure a smooth transition, the necessary nodal and +element state data from the inlet block are stored at the beginning of the current step. When shuffling +occurs, the stored nodal and element state data are mapped to the new inlet block and any inlet/outlet +loads or boundary conditions are transferred to the newly exposed block ends. +Thus, the periodic media analysis technique offers a convenient way for an Eulerian-like view into +the moving repetitive structure. For example, you may be interested in assessing the package dynamics +on the belt at a location somewhere between the rollers in both transient and steady-state conditions. +You define several blocks around that location, you define contact with the rollers as necessary, and you +provide appropriate inlet and outlet loading conditions. The periodic media analysis technique provides +a convenient and economical way to create and analyze this system. By re-using elements that have left +the process zone via this shuffling process, you can avoid the large meshes at the inlet end required for +purely Lagrangian simulations. +Constructing a periodic media model +The first step in constructing a periodic media model is to identify the portion of the model that constitutes +the building block of the repetitive structure. In Figure 10.5.1–2 one square belt patch together with one +asymmetrically shaped package on top constitute such a building block. If you string together several +blocks, the entire belt with packages can be modeled as shown. +Defining a building block +The following requirements must be observed when defining each building block: +• an unsorted element set must be defined to include all elements in the building block, and +• an unsorted node set must be defined to include all nodes in the building block. +To ensure the proper transfer of information as the periodic media advances, these unsorted sets must +be topologically identical between all blocks. The easiest way to achieve this requirement is to use the +parts and instances modeling paradigm. You define one part corresponding to the building block and +define unsorted element and node sets as discussed above. You then instantiate the part as many times as +needed with the appropriate translations and rotations to generate the periodic media mesh. Constraints +such as ties, couplings, and rigid bodies are allowed within a building block. You must ensure that these +constraints are defined in a topologically identical fashion in all blocks. +The periodic media analysis technique connects together these otherwise unconnected blocks to +create a continuous model. If structural elements (e.g., shells) are used in the connecting regions of the +blocks, the nodes on the edges of these regions are connected to the adjacent regions. If continuum +elements are used, the nodes on the faces of these regions are connected. For these constraints to be +constructed reliably, the following additional requirements must be observed: +• the nodal arrangements at the front and back connecting ends of blocks must be topologically +identical, +• the front and back end nodes of adjacent blocks must be coincident, +• the nodal arrangements at the front and back end of the initial inlet block must have coordinates that +differ only by a rigid body translation, and +• two node-based surfaces created using unsorted node sets at the front and back end of each block +must be defined. +The node-based surfaces are used to automatically generate node-to-node tie constraints between +adjacent blocks such that the whole assembly behaves as a continuous entity. +Input File Usage: +Use the following option to define the sequence of blocks using unsorted sets +and surfaces as described above: +*PERIODIC MEDIA, NAME=name +elset1, nodeset1, frontsurf1, backsurf1 +elset2, nodeset2, frontsurf2, backsurf2 +... +elsetn, nodesetn, frontsurfn, backsurfn +Each data line provides the set and surface names associated with a given block. +Applying loads and boundary conditions at media ends +In the schematic belt shown in Figure 10.5.1–1, you usually need to apply loads or boundary conditions +at both ends of the assembly. At the inlet point I it is often useful to apply a pre-tension load that keeps +the belt taut, while at the outlet point O the belt velocity is usually prescribed. As the belt advances and +exiting blocks are being shuffled from the outlet to the inlet, the nodes requiring the boundary conditions +will change. Therefore, these boundary conditions and loads cannot be prescribed directly at nodes +belonging to the block. +The periodic media analysis technique allows for the application of such loading features via two +control nodes that are associated with the current inlet and outlet node-based surfaces. The control +nodes are similar to reference nodes used in other features (such as kinematic couplings) and impose +automatically defined rigid body–like constraints on the nodes at the extreme ends of the assembly. You +apply loads and boundary conditions at these control nodes. A rigid body–like constraint is also imposed +on the front end nodes of the inlet block, but no loads or boundary conditions can be applied. When +exiting blocks are being shuffled back to the inlet, the control points will enforce these rigid body–like +constraints on the new extreme end surfaces and remove the rigid body–like constraints from the previous +locations. The process is automatic and fully managed by the periodic media analysis technique. +Input File Usage: +Use the following option to define control nodes for the inlet and outlet +conditions: +*PERIODIC MEDIA, INLET CONTROL NODE=node, +OUTLET CONTROL NODE=node +Defining the process zone +When the inlet block moves completely into the process zone, the outlet block is shuffled back to the +inlet, as the dashed arrow indicates in Figure 10.5.1–1. A trigger plane controls the precise timing for +when the shuffling occurs. When the nodes located at the current inlet point I cross the trigger plane, the +shuffling process is launched. The trigger plane is defined using the coordinates of a (usually) stationary +node and the z-axis of a user-defined orientation. The local z-axis direction points from the inlet toward +the process zone. +Input File Usage: +Use the following option to define the trigger plane via a trigger node and +orientation: +*PERIODIC MEDIA, TRIGGER NODE=node, +ORIENTATION=orientation +Activating a periodic media +The shuffling process can be activated on a step-by-step basis. By default, the shuffling process is +inactive. +In many cases the configuration of the periodic media in the operating condition can be +determined only via simulation. This allows any number of analysis steps to be carried out prior to +activating the shuffling process. +The example illustrated in Figure 10.5.1–2 and in “Media transport,” Section 3.25.1 of the Abaqus +Verification Manual, shows a conveyor belt transporting asymmetrical packages placed initially at regular +intervals. In its operating condition the belt will be tensioned. You can pre-stretch the belt assembly in +either Abaqus/Standard or Abaqus/Explicit. If the pre-stretch analysis is conducted in Abaqus/Standard, +all ties between adjacent blocks as well as boundary conditions at the inlet and outlet ends nodes need to +be defined explicitly as the periodic media analysis technique is available only in Abaqus/Explicit. If the +pre-stretching step is conducted in Abaqus/Explicit, the shuffling process should remain inactive during +the pre-stretching step. +Input File Usage: +Use the following option to activate or deactivate the periodic media shuffling +process: +*MEDIA TRANSPORT +periodic_media_name1, ACTIVE +periodic_media_name2, INACTIVE +... +Modeling tips +The periodic media analysis technique is a powerful feature; however, you must exercise good +engineering judgement when using it. The following comments and recommendations will help you +avoid common pitfalls when using this technique: +• The block shuffling process is inherently noisy as chunks of elements are detached at one end and +reattached at the other. Although the process uses appropriate material and kinematic states, small +shocks are inherent to the process. A small amount of mass proportional damping is recommended +to dampen out this excitation. +• The combination of boundary conditions at the inlet control node and any loads applied in the +process zone should ensure that the inlet block moves across the trigger plane without a change in +direction. In the conveyor belt example, a good modeling practice would be to place a fixed guide +roller at least two blocks away from the trigger plane. +• For more complex geometries (such as belts that change direction between rollers or package +wrapping analyses when the belt is the wrapping material itself), it may be necessary to start with +a straight sequence of blocks and move the belt rollers (which are not part of the periodic media +definition) into the desired locations. Contact interaction between the belt and the rollers would +deform the belt in the desired configuration. This additional analysis step can greatly simplify the +definition of the initial mesh. +• Sometimes it may be necessary to model the process of threading a belt wrapping through rollers, +just as in physical reality at the start of a manufacturing process. If this leading segment is followed +by periodic blocks that include actual packages, you can attach the periodic media mesh to a regular +mesh to execute the threading. The periodic media part of the mesh can then be imported into a +separate model without the leading mesh, and the analysis of the periodic media consisting only of +the wrapper and packages can be executed. +Initial conditions +Initial conditions can be specified at all nodes in the periodic media mesh. Velocity initial boundary +conditions can be used to minimize the solution time needed to reach a steady-state operating condition. +In cases where pre-stretching is required, importing from the prior analysis rather than performing a +multistep analysis allows for initial conditions to be applied to the stretched configuration. Since periodic +media definitions are not imported, they must be respecified in every analysis in which they are required. +Boundary conditions +The inlet and outlet control nodes are the only two nodes associated with a periodic media definition +at which boundary conditions can be specified. Furthermore, only velocity boundary conditions are +permitted. You must not specify boundary conditions at any other node associated with the periodic +media mesh. While the periodic media is active and if a steady-state solution is sought, these boundary +conditions should be kept constant in both direction and magnitude to mitigate solution noise. +Loads +Only concentrated loads can be applied to the inlet and outlet control nodes to either drive or stretch the +periodic media. While the periodic media is active, these loads should be kept constant in both direction +and magnitude. Gravity loads can be applied as desired. Other distributed loads can also be specified; +however, you must keep in mind that the loads will travel with the blocks as they are shuffled. +Material options +Only the following material models can be used in association with a periodic media: +• elasticity, +• viscoelasticity, +• Mises plasticity, +• lamina elasticity, +• hyperfoams, +• crushable foams, and +• user-defined materials. +Limitations +Periodic media analyses are subject to the following limitations: +• Only membranes, shells, trusses, continuum elements, and rigid elements are allowed within blocks. +Rebar layers can also be used, if applicable. +• No explicitly defined constraints are allowed between nodes belonging to different blocks. +• Mass scaling must be defined in the same fashion for all blocks. +The periodic media should not be involved in +• general contact that defines thermal contact properties or coupled Eulerian-Lagrangian contact or +• contact defined via the contact pair algorithm. +Input file template +The following example illustrates a model with two periodic media defined: +*HEADING +… +*PERIODIC MEDIA, NAME=belt1, CONTROL NODE=10, +OUTLET CONTROL NODE=110, ORIENTATION=ori1, TRIGGER NODE=210 +elset1, nodeset1, frontedgesurf1, backedgesurf1 +elset2, nodeset1, frontedgesurf2, backedgesurf2 +elset3, nodeset1, frontedgesurf3, backedgesurf3 +*PERIODIC MEDIA, NAME=belt2, CONTROL NODE=11, +OUTLET CONTROL NODE=111, ORIENTATION=ori2, TRIGGER NODE=211 +elset1, nodeset1, frontedgesurf1, backedgesurf1 +elset2, nodeset1, frontedgesurf2, backedgesurf2 +elset3, nodeset1, frontedgesurf3, backedgesurf3 +*STEP +*DYNAMIC, EXPLICIT +*MEDIA TRANSPORT +belt1, ACTIVE +belt2, INACTIVE +*END STEP +10.6 +Meshed beam cross-sections +• “Meshed beam cross-sections,” Section 10.6.1 +10.6.1 +MESHED BEAM CROSS-SECTIONS +Products: Abaqus/Standard Abaqus/Explicit +References +• *BEAM GENERAL SECTION +• *BEAM SECTION GENERATE +• *SECTION ORIGIN +• *SECTION POINTS +Overview +Meshed cross-sections: +• allow for the description of a beam cross-section including multiple materials and complex +geometry; +• are meshed in Abaqus/Standard with two-dimensional warping elements, which have an out-of- +plane warping displacement as the only degree of freedom; +• generate beam cross-section properties that can be used in a subsequent beam element analysis in +either Abaqus/Standard or Abaqus/Explicit; +• allow only isotropic linear elastic material behavior (“Defining isotropic elasticity” in “Linear +elastic behavior,” Section 22.2.1) or orthotropic linear elastic material behavior for warping +elements (“Defining orthotropic elasticity for warping elements” in “Linear elastic behavior,” +Section 22.2.1); and +• allow stress and strain postprocessing on the beam element model or the two-dimensional warping +element model. +Introduction +The response of some structures is beam-like, yet the beam cross-section geometry or multi-material +makeup of the cross-section do not permit the use of a predefined library beam cross-section. In these +cases a meshed cross-section can be used to model the beam cross-section and to generate beam cross- +section properties appropriate for subsequent use in a Timoshenko beam analysis. The beam properties +are generated assuming a thick-walled (solid) cross-section with unconstrained out-of-plane warping, so +open-section beam elements cannot use the beam cross-section properties generated from the meshed +section . The generated beam cross-section properties +include axial, bending, torsional, and transverse shear stiffnesses; mass, rotary inertia, and damping +properties; and the centroid and shear center of the cross-section. +In addition, the equivalent beam +cross-section properties include information on stress recovery, such as the warping function and its +derivatives. +A typical example of a structure that requires a meshed cross-section is the hull of a ship for +whipping analysis, where the ship’s hull has a multi-cell and multi-material construction. Other +examples include an airfoil-shaped rotor blade or wing, a layered composite I-beam (with fibers running +along the length of the beam axis or perpendicular to it), etc. +Modeling approach +As shown in Figure 10.6.1–1, a meshed cross-section allows for a complex description of a beam cross- +section: one which may include an arbitrary shape, multiple materials, multiple cells, and non-structural +mass. The basic idea is to create a two-dimensional finite element model of the beam cross-section. +The meshed cross-section is used in Abaqus/Standard to numerically calculate the properties required to +characterize the structural response of the cross-section in a subsequent beam element analysis. The two- +dimensional Abaqus/Standard analysis writes the cross-sectional properties to an input-file-ready text +file (jobname.bsp). In the subsequent Abaqus/Standard or Abaqus/Explicit beam element analysis +the beam elements requiring the meshed cross-section properties include the text file jobname.bsp as +the general beam section data. Once the beam element analysis is complete, the Visualization module +of Abaqus/CAE is used to visualize results at preselected points along the beam length or to examine +detailed stress and strain results displayed directly on the two-dimensional meshed cross-section. +Y global +foam +fluid +steel or composite media +X global +Figure 10.6.1–1 An example of a meshed section profile. +In summary, the procedure for analyzing and postprocessing a beam analysis using a meshed cross- +section is as follows: +1. Mesh and analyze a two-dimensional Abaqus/Standard model of the beam cross-section. +2. Use the generated cross-sectional properties in an Abaqus/Standard or Abaqus/Explicit beam +analysis. +3. Using the beam analysis results, postprocess from the beam model or the two-dimensional cross- +section model. +Meshing and analyzing a two-dimensional model of the beam cross-section +The cross-section is meshed using special-purpose two-dimensional elements: WARP2D3 (3-node +triangular) and WARP2D4 (4-node quadrilateral). These elements have one degree of freedom per +node representing the value of the out-of-plane warping function and use a solid section definition; no section data are required. Adjacent elements in +the cross-sectional mesh must share common nodes; mesh refinement using multi-point constraints is +not allowed. +Each element in the cross-sectional mesh can refer to a different elastic material, using either +isotropic linear elastic material behavior or orthotropic linear elastic material behavior for warping elements . Alternatively, +density (“Density,” Section 21.2.1) can be the only material property specified, which is useful for +modeling non-structural masses such as fuel in a tank. +The model is then analyzed by using the beam section property generation procedure within +the step definition. This cross-section analysis will numerically calculate geometric, stiffness, and +inertial properties of the section, including the warping function and shear center and will write the calculated properties +to the jobname.bsp text file. The contents of this text file, which can be used in a subsequent +Abaqus/Standard or Abaqus/Explicit beam analysis, are described in detail below. +Input File Usage: +Use the following option to generate beam section properties for a meshed +cross-section: +*BEAM SECTION GENERATE +Defining the origin of the cross-section +By default, the origin of the cross-section is the origin of the coordinate system used to define the mesh. +You can override this default and input the coordinates of the origin directly or specify that the origin +coincides with the shear center or centroid of the cross-section. A nondefault origin is particularly +useful when the beam node to be used in the actual analysis does not coincide with the origin of the +two-dimensional coordinate system. +Input File Usage: +Use both of the following options to input the coordinates of the origin directly: +*BEAM SECTION GENERATE +*SECTION ORIGIN +Use both of the following options to locate the origin at either the centroid or +shear center: +*BEAM SECTION GENERATE +*SECTION ORIGIN, ORIGIN=CENTROID or SHEAR CENTER +Requesting output at particular integration points +Output to the output database can be recovered during the actual analysis at particular integration +points on the cross-section. Requesting output at a large number of cross-sectional points may degrade +performance. +Input File Usage: +Use both of the following options to request output at particular integration +points: +*BEAM SECTION GENERATE +*SECTION POINTS +Contents of the jobname.bsp text file +After the analysis to generate the cross-sectional properties completes, the jobname.bsp text file +contains the following lines of data: +, +, +, +, +, +, +, +, +, +*TRANSVERSE SHEAR STIFFNESS +, +, +*CENTROID +, +*SHEAR CENTER +, +*DAMPING, ALPHA= +, BETA= +, COMPOSITE= +The first two lines of data in the jobname.bsp text file correspond to the section property data for +an arbitrarily shaped solid general beam cross-section meshed with warping elements . +If you requested output at particular integration points in the two-dimensional cross-section model +generation, the jobname.bsp text file contains the following additional lines: +*SECTION POINTS +section point label, 2-D element number, integration point number +E, +, +... +, +, +, +, +, +where the set of two data lines is repeated for as many section points as requested. +The cross-sectional property information written to the jobname.bsp text file will be read into the +general beam section definition in the subsequent beam analysis as described below. +Using the generated cross-section properties in a beam analysis +the section properties calculated and stored in the jobname.bsp text file +As discussed above, +can be used in an actual beam analysis to define cross-sections for beam elements. The data stored +in jobname.bsp correspond to the section property data for an arbitrarily shaped solid general +beam cross-section meshed with warping elements . +Consequently, a simple method of inserting these data is to include the jobname.bsp text file in the +beam analysis. +Input File Usage: +Use the following options to generate section properties in a beam analysis: +*BEAM GENERAL SECTION, SECTION=MESHED +, +, +(direction cosines for +) +*INCLUDE, INPUT=jobname.bsp +Postprocessing from the beam model or the two-dimensional cross-section model +A tickmark contour plot can be used to visualize stress and strain output along the length of the +beam model. All stress and strain components requested for the two-dimensional cross-section model +generation will be available. Contour plots of stress and strain on the two-dimensional cross-section are +also available. The section geometry is read from the output database generated by the two-dimensional +cross-section analysis, while the generalized section results are read from the output database generated +by the beam analysis. +Initial conditions +Initial conditions are not meaningful when generating beam section properties and are ignored. +Boundary conditions +Boundary conditions are not meaningful when generating beam section properties and are ignored. +Loads +Loads are not meaningful when generating beam section properties and are ignored. +Predefined fields +Temperature and field variables are not allowed for meshed sections. +Material options +Only the following material behaviors are allowed for meshed sections: +• isotropic linear elasticity (“Defining isotropic elasticity” in “Linear elastic behavior,” +Section 22.2.1) +• orthotropic linear elasticity for warping elements (“Defining orthotropic elasticity for warping +elements” in “Linear elastic behavior,” Section 22.2.1) +• density (“Density,” Section 21.2.1) +Elements +Warping elements must be used to mesh the two-dimensional cross-section. See “Warping elements,” +Section 28.4.1, for details. +Output +Element output is calculated during the actual beam analysis at the integration points on the meshed +cross-section that are selected in the property generation analysis as described above. Output from +the property generation analysis is available only on the output database. The Visualization module of +Abaqus/CAE can be used to generate contour plots of element output on the cross-section, which requires +the output databases from both the section property generation analysis (the cross-section model) and the +actual beam analysis. For more information, see the example Python script in “Viewing the analysis of +a meshed beam cross-section,” Section 9.10.10 of the Abaqus Scripting User’s Manual. +Input file template +Generating the cross-section properties in an Abaqus/Standard analysis +*HEADING +Meshed cross section +... +*NODE, NSET=ALL +... +*ELEMENT, TYPE=WARP2D3, ELSET=TRI +... +*ELEMENT, TYPE=WARP2D4, ELSET=QUAD +... +*SOLID SECTION, MATERIAL=COMPOSITE, ELSET=TRI +*MATERIAL,NAME=COMPOSITE +*ELASTIC, TYPE=TRACTION +E, G1, G2 +*DENSITY +... +*SOLID SECTION, MATERIAL=MASS_ONLY, ELSET=QUAD +*MATERIAL, NAME=MASS_ONLY +*DENSITY +... +*STEP +*BEAM SECTION GENERATE +*SECTION ORIGIN +X, Y +*SECTION POINTS +section point label, element number, integration point number +*END STEP +Using the generated cross-section properties in a subsequent Abaqus/Standard or +Abaqus/Explicit beam analysis +*HEADING +Beam analysis +) +, +, +... +*NODE, NSET=NALL +... +*ELEMENT, TYPE=B31, ELSET=BEAM1 +... +*BEAM GENERAL SECTION, SECTION=MESHED +(direction cosines for +*INCLUDE, INPUT=jobname.bsp +... +*STEP +*DYNAMIC +... +*BOUNDARY +... +*CLOAD +... +*OUTPUT +*ELEMENT OUTPUT +... +*END STEP +EXTENDED FINITE ELEMENT METHOD +10.7 +Modeling discontinuities as an enriched feature using the +extended finite element method +• “Modeling discontinuities as an enriched feature using the extended finite element method,” +Section 10.7.1 +10.7.1 +MODELING DISCONTINUITIES AS AN ENRICHED FEATURE USING THE +EXTENDED FINITE ELEMENT METHOD +Products: Abaqus/Standard Abaqus/CAE Abaqus/Viewer +References +• *ENRICHMENT +• *ENRICHMENT ACTIVATION +• “Using the extended finite element method to model fracture mechanics,” Section 31.3 of the +Abaqus/CAE User’s Manual +Overview +Modeling discontinuities, such as cracks, as an enriched feature: +• is commonly referred to as the extended finite element method (XFEM); +• is an extension of the conventional finite element method based on the concept of partition of unity; +• allows the presence of discontinuities in an element by enriching degrees of freedom with special +displacement functions; +• does not require the mesh to match the geometry of the discontinuities; +• is a very attractive and effective way to simulate initiation and propagation of a discrete crack along +an arbitrary, solution-dependent path without the requirement of remeshing in the bulk materials; +• can be simultaneously used with the surface-based cohesive behavior approach or the Virtual Crack Closure Technique , which are best suited for modeling interfacial delamination; +• can be performed using the static procedure , the implicit +dynamic procedure , or the +low-cycle fatigue analysis using the direct cyclic approach ; +• can also be used to perform contour integral evaluations for an arbitrary stationary surface crack +without the need to refine the mesh around the crack tip; +• allows contact interaction of cracked element surfaces based on a small-sliding formulation; +• allows both material and geometrical nonlinearity; and +• is currently available only for first-order stress/displacement solid continuum elements and second- +order stress/displacement tetrahedron elements. +Modeling approach +Modeling stationary discontinuities, such as a crack, with the conventional finite element method +requires that the mesh conforms to the geometric discontinuities. Therefore, considerable mesh +refinement is needed in the neighborhood of the crack tip to capture the singular asymptotic fields +adequately. Modeling a growing crack is even more cumbersome because the mesh must be updated +continuously to match the geometry of the discontinuity as the crack progresses. +The extended finite element method (XFEM) alleviates the shortcomings associated with meshing +crack surfaces. The extended finite element method was first introduced by Belytschko and Black +(1999). It is an extension of the conventional finite element method based on the concept of partition of +unity by Melenk and Babuska (1996), which allows local enrichment functions to be easily incorporated +into a finite element approximation. The presence of discontinuities is ensured by the special enriched +functions in conjunction with additional degrees of freedom. However, the finite element framework +and its properties such as sparsity and symmetry are retained. +Introducing nodal enrichment functions +For the purpose of fracture analysis, the enrichment functions typically consist of the near-tip asymptotic +functions that capture the singularity around the crack tip and a discontinuous function that represents the +jump in displacement across the crack surfaces. The approximation for a displacement vector function +with the partition of unity enrichment is +where +are the usual nodal shape functions; the first term on the right-hand side of the above +equation, +, is the usual nodal displacement vector associated with the continuous part of the finite +element solution; the second term is the product of the nodal enriched degree of freedom vector, +, +and the associated discontinuous jump function +across the crack surfaces; and the third term is +the product of the nodal enriched degree of freedom vector, +, and the associated elastic asymptotic +crack-tip functions, +. The first term on the right-hand side is applicable to all the nodes in the +model; the second term is valid for nodes whose shape function support is cut by the crack interior; and +the third term is used only for nodes whose shape function support is cut by the crack tip. +Figure 10.7.1–1 illustrates the discontinuous jump function across the crack surfaces, +, which +is given by +where +normal to the crack at +is a sample (Gauss) point, +. +is the point on the crack closest to , and +is the unit outward +Figure 10.7.1–1 illustrates the asymptotic crack tip functions in an isotropic elastic material, +, +which are given by +Crack tip +X* +X* +Figure 10.7.1–1 Illustration of normal and tangential coordinates for a smooth crack. +where +at the tip. +is a polar coordinate system with its origin at the crack tip and +is tangent to the crack +These functions span the asymptotic crack-tip function of elasto-statics, and +takes into +account the discontinuity across the crack face. The use of asymptotic crack-tip functions is not +restricted to crack modeling in an isotropic elastic material. The same approach can be used to represent +a crack along a bimaterial interface, impinged on the bimaterial interface, or in an elastic-plastic +power law hardening material. However, in each of these three cases different forms of asymptotic +crack-tip functions are required depending on the crack location and the extent of the inelastic material +deformation. The different forms for the asymptotic crack-tip functions are discussed by Sukumar +(2004), Sukumar and Prevost (2003), and Elguedj (2006), respectively. +Accurately modeling the crack-tip singularity requires constantly keeping track of where the crack +propagates and is cumbersome because the degree of crack singularity depends on the location of the +crack in a non-isotropic material. Therefore, we consider the asymptotic singularity functions only +when modeling stationary cracks in Abaqus/Standard. Moving cracks are modeled using one of the +two alternative approaches described below. +Modeling moving cracks with the cohesive segments method and phantom nodes +One alternative approach within the framework of XFEM is based on traction-separation cohesive +behavior. This approach is used in Abaqus/Standard to simulate crack initiation and propagation. +This is a very general interaction modeling capability, which can be used for modeling brittle or +ductile fracture. The other crack initiation and propagation capabilities available in Abaqus/Standard +are based on cohesive elements (“Defining the constitutive response of cohesive elements using a +traction-separation description,” Section 32.5.6) or on surface-based cohesive behavior (“Surface-based +cohesive behavior,” Section 36.1.10). Unlike these methods, which require that the cohesive surfaces +align with element boundaries and the cracks propagate along a set of predefined paths, the XFEM-based +cohesive segments method can be used to simulate crack initiation and propagation along an arbitrary, +solution-dependent path in the bulk materials, since the crack propagation is not tied to the element +boundaries in a mesh. +In this case the near-tip asymptotic singularity is not needed, and only the +displacement jump across a cracked element is considered. Therefore, the crack has to propagate across +an entire element at a time to avoid the need to model the stress singularity. +Phantom nodes, which are superposed on the original real nodes, are introduced to represent the +discontinuity of the cracked elements, as illustrated in Figure 10.7.1–2. When the element is intact, each +phantom node is completely constrained to its corresponding real node. When the element is cut through +by a crack, the cracked element splits into two parts. Each part is formed by a combination of some real +and phantom nodes depending on the orientation of the crack. Each phantom node and its corresponding +real node are no longer tied together and can move apart. +original nodes +phantom nodes +Ω− +crack +crack +Ω+ +Ω− +crack +Ω+ +Ω− ++ +Ω− +Ω− +Ω− +Ω− +Figure 10.7.1–2 The principle of the phantom node method. +The magnitude of the separation is governed by the cohesive law until the cohesive strength of the +cracked element is zero, after which the phantom and the real nodes move independently. To have a set of +full interpolation bases, the part of the cracked element that belongs in the real domain, +, is extended +to the phantom domain, +, can be interpolated by using +the degrees of freedom for the nodes in the phantom domain, +. The jump in the displacement field is +realized by simply integrating only over the area from the side of the real nodes up to the crack; i.e., +and +. This method provides an effective and attractive engineering approach and has been used for +simulation of the initiation and growth of multiple cracks in solids by Song (2006) and Remmers (2008). +It has been proven to exhibit almost no mesh dependence if the mesh is sufficiently refined. +. Then the displacement in the real domain, +Modeling moving cracks based on the principles of linear elastic fracture mechanics (LEFM) +and phantom nodes +Another alternative approach to modeling moving cracks within the framework of XFEM is based on the +principles of linear elastic fracture mechanics (LEFM). Therefore, it is more appropriate for problems +in which brittle crack propagation occurs. Similar to the XFEM-based cohesive segments method +described above, the near-tip asymptotic singularity is not considered, and only the displacement jump +across a cracked element is considered. Therefore, the crack has to propagate across an entire element +at a time to avoid the need to model the stress singularity. The strain energy release rate at the crack +tip is calculated based on the modified Virtual Crack Closure Technique (VCCT), which has been used +to model delamination along a known and partially bonded surface (see “Crack propagation analysis,” +Section 11.4.3). However, unlike this method, the XFEM-based LEFM approach can be used to +simulate crack propagation along an arbitrary, solution-dependent path in the bulk material without the +requirement of a pre-existing crack in the model. +The modeling technique is very similar to the XFEM-based cohesive segment approach described +above where phantom nodes are introduced to represent the discontinuity of the cracked element when +the fracture criterion is satisfied. The real node and the corresponding phantom node will separate when +the equivalent strain energy release rate exceeds the critical strain energy release rate at the crack tip in an +enriched element. The traction is initially carried as equal and opposite forces on the two surfaces of the +cracked element. The traction is ramped down linearly over the separation between the two surfaces with +the dissipated strain energy equal to either the critical strain energy required to initiate the separation or +the critical strain energy required to propagate the crack depending on whether the VCCT or the enhanced +VCCT criterion is specified. +Modeling low-cycle fatigue crack propagation based on the principles of LEFM +The XFEM-based LEFM approach can also be used to simulate a discrete crack growth subjected to sub- +critical cyclic loading in a low-cycle fatigue analysis using the direct cyclic approach (“Low-cycle fatigue +analysis using the direct cyclic approach,” Section 6.2.7). The fracture energy release rates at the crack +tips in the enriched elements are calculated based on the above mentioned modified VCCT technique. +The onset and crack growth are characterized by using the Paris law, which relates the relative fracture +energy release rates to crack growth rates as illustrated in Figure 10.7.1–3. This approach has been used +to model progressive delamination under a sub-critical cyclic loading along a known and partially bonded +surface . However, +unlike this method, the XFEM-based LEFM approach can be used to simulate fatigue crack propagation +along an arbitrary, solution-dependent path in the bulk material. +Using the level set method to describe discontinuous geometry +A key development that facilitates treatment of cracks in an extended finite element analysis is the +description of crack geometry, because the mesh is not required to conform to the crack geometry. The +level set method, which is a powerful numerical technique for analyzing and computing interface motion, +fits naturally with the extended finite element method and makes it possible to model arbitrary crack +growth without remeshing. The crack geometry is defined by two almost-orthogonal signed distance +functions, as illustrated in Figure 10.7.1–4. The first, +, describes the crack surface, while the second, +, is used to construct an orthogonal surface so that the intersection of the two surfaces gives the crack +front. +indicates the positive normal to the +crack front. No explicit representation of the boundaries or interfaces is needed because they are entirely +described by the nodal data. Two signed distance functions per node are generally required to describe +a crack geometry. +indicates the positive normal to the crack surface; +da +dN +Paris +Regime +Gthresh +Gpl +GC +Figure 10.7.1–3 Fatigue crack growth governed by the Paris law. +crack surface ( = 0) + φ +orthogonal surface ( = 0) + Ψ ++ ++ +crack front (intersection of and ) + Ψ φ +Figure 10.7.1–4 Representation of a nonplanar crack in three dimensions by two +signed distance functions +and +. +Defining an enriched feature and its properties +You must specify an enriched feature and its properties. One or multiple pre-existing cracks can be +associated with an enriched feature. In addition, during an analysis one or multiple cracks can initiate +in an enriched feature without any initial defects. However, multiple cracks can nucleate in a single +enriched feature only when the damage initiation criterion is satisfied in multiple elements in the same +time increment. Otherwise, additional cracks will not nucleate until all the pre-existing cracks in an +enriched feature have propagated through the boundary of the given enriched feature. If several crack +nucleations are expected to occur at different locations sequentially during an analysis, multiple enriched +features can be specified in the model. Enriched degrees of freedom are activated only when an element +is intersected by a crack. Only stress/displacement solid continuum elements can be associated with an +enriched feature. +Input File Usage: +Abaqus/CAE Usage: +*ENRICHMENT +Interaction module: Special→Crack→Create→XFEM +Defining the type of enrichment +You can choose to model an arbitrary stationary crack or a discrete crack propagation along an arbitrary, +solution-dependent path. The former requires that the elements around the crack tips are enriched with +asymptotic functions to catch the singularity and that the elements intersected by the crack interior are +enriched with the jump function across the crack surfaces. The latter infers that crack propagation is +modeled with either the cohesive segments method or the linear elastic fracture mechanics approach in +conjunction with phantom nodes. However, the options are mutually exclusive and cannot be specified +simultaneously in a model. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to specify a crack propagation analysis (default): +*ENRICHMENT, TYPE=PROPAGATION CRACK +Use the following option to specify an analysis with stationary cracks: +*ENRICHMENT, TYPE=STATIONARY CRACK +Use the following input to specify a crack propagation analysis: +Interaction module: crack editor: toggle on Allow crack growth +Use the following input to specify an analysis with stationary cracks: +Interaction module: crack editor: toggle off Allow crack growth +Assigning a name to the enriched feature +You must assign a name to an enriched feature, such as a crack. This name can be used in defining the +initial location of the crack surfaces, in identifying a crack for contour integral output, and in activating +or deactivating the crack propagation analysis. +Input File Usage: +Abaqus/CAE Usage: +*ENRICHMENT, NAME=name +Interaction module: Special→Crack→Create: XFEM: Name: name +Identifying an enriched region +You must associate the enrichment definition with a region of your model. Only degrees of freedom in +elements within these regions are potentially enriched with special functions. The region should consist +of elements that are presently intersected by cracks and those that are likely to be intersected by cracks +as the cracks propagate. +Input File Usage: +Abaqus/CAE Usage: +*ENRICHMENT, ELSET=element set name +Interaction module: Special→Crack→Create→: XFEM: Select +the crack domain: select region +Defining contact of cracked element surfaces using a small-sliding formulation +When an element is cut by a crack, the compressive behavior of the crack surfaces has to be considered. +The formulae that govern behavior are very similar to those used for surface-based small-sliding penalty +contact (“Mechanical contact properties: overview,” Section 36.1.1). +For an element intersected by a stationary crack or a moving crack with the linear elastic fracture +mechanics approach, it is assumed that the elastic cohesive strength of the cracked element is zero. +Therefore, compressive behavior of the crack surfaces is fully defined with the above options when the +crack surfaces come into contact. For a moving crack with the cohesive segments method, the situation +is more complex; traction-separation cohesive behavior as well as compressive behavior of the crack +surfaces are involved in a cracked element. In the contact normal direction, the pressure-overclosure +relationship governing the compressive behavior between the surfaces does not interact with the cohesive +behavior, since they each describe the interaction between the surfaces in a different contact regime. The +pressure-overclosure relationship governs the behavior only when the crack is “closed”; the cohesive +behavior contributes to the contact normal stress only when the crack is “open” (i.e., not in contact). +If the elastic cohesive stiffness of an element is undamaged in the shear direction, it is assumed +that the cohesive behavior is active. Any tangential slip is assumed to be purely elastic in nature and +is resisted by the elastic cohesive strength of the element, resulting in shear forces. If damage has been +defined, the cohesive contribution to the shear stresses starts degrading with damage evolution. Once +maximum degradation has been reached, the cohesive contribution to the shear stresses is zero. The +friction model activates and begins contributing to the shear stresses. +Input File Usage: +Use the following options to define contact of crack surfaces using a small- +sliding formulation: +*ENRICHMENT, INTERACTION=interaction_property_name +*SURFACE INTERACTION, NAME=interaction_property_name +*SURFACE BEHAVIOR +Interaction module: crack editor: toggle on Specify contact property +Abaqus/CAE Usage: +Applying cohesive material concepts to XFEM-based cohesive behavior +The formulae and laws that govern the behavior of XFEM-based cohesive segments for a crack +propagation analysis are very similar to those used for cohesive elements with traction-separation +constitutive behavior (“Defining the constitutive response of cohesive elements using a traction- +separation description,” Section 32.5.6) and those used for surface-based cohesive behavior +(“Surface-based cohesive behavior,” Section 36.1.10). The similarities extend to the linear elastic +traction-separation model, damage initiation criteria, and damage evolution laws. +Linear elastic traction-separation behavior +The available traction-separation model in Abaqus assumes initially linear elastic behavior followed by +the initiation and evolution of damage. The elastic behavior is written in terms of an elastic constitutive +matrix that relates the normal and shear stresses to the normal and shear separations of a cracked element. +, and (in three- +, which represent the normal and the two shear tractions, respectively. The +, consists of the following components: +The nominal traction stress vector, +, +dimensional problems) +corresponding separations are denoted by +, +, and +. The elastic behavior can then be written as +The normal and tangential stiffness components will not be coupled: pure normal separation by +itself does not give rise to cohesive forces in the shear directions, and pure shear slip with zero normal +separation does not give rise to any cohesive forces in the normal direction. +The terms +are calculated based on the elastic properties for an enriched element. +Specifying the elastic properties of the material in an enriched region is sufficient to define both the elastic +stiffness and the traction-separation behavior. +, and +, +Damage modeling +Damage modeling allows you to simulate the degradation and eventual failure of an enriched element. +The failure mechanism consists of two ingredients: a damage initiation criterion and a damage evolution +law. The initial response is assumed to be linear as discussed in the previous section. However, once a +damage initiation criterion is met, damage can occur according to a user-defined damage evolution law. +Figure 10.7.1–5 shows a typical linear and a typical nonlinear traction-separation response with a failure +mechanism. The enriched elements do not undergo damage under pure compression. +Damage of the traction-separation response for cohesive behavior in an enriched element is defined +within the same general framework used for conventional materials . However, unlike cohesive elements with traction-separation behavior, you do +not have to specify the undamaged traction-separation behavior in an enriched element. +Crack initiation and direction of crack extension +Crack initiation refers to the beginning of degradation of the cohesive response at an enriched element. +The process of degradation begins when the stresses or the strains satisfy specified crack initiation criteria. +Crack initiation criteria are available based on the following Abaqus/Standard built-in models: +• the maximum principal stress criterion, +• the maximum principal strain criterion, +Tmax +Tmax +max +max +Crack opening +(a) +Crack opening +(b) +Figure 10.7.1–5 Typical linear (a) and nonlinear (b) traction-separation response. +• the maximum nominal stress criterion, +• the maximum nominal strain criterion, +• the quadratic traction-interaction criterion, and +• the quadratic separation-interaction criterion. +In addition, a user-defined damage initiation criterion can be specified in user subroutine UDMGINI. +An additional crack is introduced or the crack length of an existing crack is extended after an +equilibrium increment when the fracture criterion, f, reaches the value 1.0 within a given tolerance: +You can specify the tolerance +initiation criterion is satisfied. The default value of +. If +, the time increment is cut back such that the crack +is 0.05. +Input File Usage: +Abaqus/CAE Usage: +*DAMAGE INITIATION, TOLERANCE= +Property module: material editor: Mechanical: Damage for Traction +Separation Laws: Quade Damage, Maxe Damage, Quads Damage, +Maxs Damage, Maxpe Damage, or Maxps Damage: Tolerance: +Specifying the crack direction +When the maximum principal stress or the maximum principal strain criterion is specified, the newly +introduced crack is always orthogonal to the maximum principal stress/strain direction when the fracture +criterion is satisfied. However, when one of the other Abaqus/Standard built-in crack initiation criteria +is used, you have to specify if the newly introduced crack will be orthogonal to the element local 1- +direction or orthogonal to the element local 2-direction when the +fracture criterion is satisfied. By default, the crack is orthogonal to the element local 1-direction. If a +user-defined damage initiation criterion is specified, the normal direction to the crack plane or the crack +line can be defined in user subroutine UDMGINI. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options to specify the crack direction when the +maximum nominal stress, +the quadratic +traction-interaction, or +the quadratic separation-interaction criterion is +specified: +the maximum nominal strain, +*DAMAGE INITIATION, NORMAL DIRECTION=1 (default) +*DAMAGE INITIATION, NORMAL DIRECTION=2 +Property module: material editor: Mechanical→Damage for Traction +Separation Laws: Quade Damage, Maxe Damage, Quads Damage, +or Maxs Damage: Direction relative to local 1-direction (for XFEM): +Normal or Parallel +Maximum principal stress criterion +The maximum principal stress criterion can be represented as +represents the maximum allowable principal stress. The symbol +represents the Macaulay +Here, +bracket with the usual interpretation (i.e., +). +if +The Macaulay brackets are used to signify that a purely compressive stress state does not initiate damage. +Damage is assumed to initiate when the maximum principal stress ratio (as defined in the expression +above) reaches a value of one. +and +if +Input File Usage: +Abaqus/CAE Usage: +*DAMAGE INITIATION, CRITERION=MAXPS +Property module: material editor: Mechanical: Damage for Traction +Separation Laws: Maxps Damage +Maximum principal strain criterion +The maximum principal strain criterion can be represented as +Here, +represents the maximum allowable principal strain, and the Macaulay brackets signify that a +purely compressive strain does not initiate damage. Damage is assumed to initiate when the maximum +principal strain ratio (as defined in the expression above) reaches a value of one. +Input File Usage: +Abaqus/CAE Usage: +*DAMAGE INITIATION, CRITERION=MAXPE +Property module: material editor: Mechanical: Damage for Traction +Separation Laws: Maxpe Damage +Maximum nominal stress criterion +The maximum nominal stress criterion can be represented as +The nominal traction stress vector, +is the component normal to the likely cracked surface, and +, consists of three components (two in two-dimensional problems). +are the two shear components +on the likely cracked surface. Depending on what you specify , the likely cracked surface will be orthogonal either to the element local 1-direction or to the +element local 2-direction. Here, +represent the peak values of the nominal stress. The +symbol +represents the Macaulay bracket with the usual interpretation. The Macaulay brackets are +used to signify that a purely compressive stress state does not initiate damage. Damage is assumed to +initiate when the maximum nominal stress ratio (as defined in the expression above) reaches a value of +one. +, and +and +, +Input File Usage: +Abaqus/CAE Usage: +*DAMAGE INITIATION, CRITERION=MAXS +Property module: material editor: Mechanical: Damage for Traction +Separation Laws: Maxs Damage +Maximum nominal strain criterion +The maximum nominal strain criterion can be represented as +Damage is assumed to initiate when the maximum nominal strain ratio (as defined in the expression +above) reaches a value of one. +Input File Usage: +Abaqus/CAE Usage: +*DAMAGE INITIATION, CRITERION=MAXE +Property module: material editor: Mechanical: Damage for Traction +Separation Laws: Maxe Damage +Quadratic nominal stress criterion +The quadratic nominal stress criterion can be represented as +Damage is assumed to initiate when the quadratic interaction function involving the stress ratios (as +defined in the expression above) reaches a value of one. +Input File Usage: +*DAMAGE INITIATION, CRITERION=QUADS +Abaqus/CAE Usage: +Property module: material editor: Mechanical: Damage for Traction +Separation Laws: Quads Damage +Quadratic nominal strain criterion +The quadratic nominal strain criterion can be represented as +Damage is assumed to initiate when the quadratic interaction function involving the nominal strain ratios +(as defined in the expression above) reaches a value of one. +Input File Usage: +Abaqus/CAE Usage: +*DAMAGE INITIATION, CRITERION=QUADE +Property module: material editor: Mechanical: Damage for Traction +Separation Laws: Quade Damage +User-defined damage initiation criterion +User subroutine UDMGINI provides a general capability for implementing a user-defined damage +initiation criterion. +You can define several damage initiation mechanisms in user subroutine UDMGINI. You represent +each damage initiation mechanism by a fracture criterion, +, and its associated normal direction +to the crack plane or the crack line. Although you can define several damage initiation mechanisms, +the actual damage initiation for an enriched element is governed by the most severe damage initiation +mechanism: +Damage is assumed to initiate when f, as defined in the expression above, reaches a value of one. +You must specify any material constants that are needed in user subroutine UDMGINI as part of a +user-defined damage initiation criterion definition. +Input File Usage: +Use the following option to define a user-defined damage initiation criterion: +*DAMAGE INITIATION, CRITERION=USER +Use the following option to specify the total number of failure mechanisms in +the user-defined damage initiation criterion: +*DAMAGE INITIATION, CRITERION=USER, FAILURE +MECHANISMS= +Use the following option to define properties for a user-defined damage +initiation criterion: +*DAMAGE INITIATION, CRITERION=USER, +PROPERTIES=number_of_constants +Abaqus/CAE Usage: +Defining a user-defined damage initiation criterion is not supported in +Abaqus/CAE. +Damage evolution +The damage evolution law describes the rate at which the cohesive stiffness is degraded once the +corresponding initiation criterion is reached. The general framework for describing the evolution of +damage is conceptually similar to that used for damage evolution in surface-based cohesive behavior +(“Surface-based cohesive behavior,” Section 36.1.10). +A scalar damage variable, D, represents the averaged overall damage at the intersection between +the crack surfaces and the edges of cracked elements. It initially has a value of 0. If damage evolution is +modeled, D monotonically evolves from 0 to 1 upon further loading after the initiation of damage. The +normal and shear stress components are affected by the damage according to +otherwise (no damage to compressive stiffness); +where +separation behavior for the current separations without damage. +, and +, +are the normal and shear stress components predicted by the elastic traction- +To describe the evolution of damage under a combination of normal and shear separations across +the interface, an effective separation is defined as +Input File Usage: +Use the following option to specify a damage evolution law: +Abaqus/CAE Usage: +*DAMAGE EVOLUTION +Property module: +editor: +for +Traction Separation Laws: Maxpe Damage or Maxps Damage: +Suboptions→Damage Evolution +Mechanical→Damage +material +Use in conjunction with user-defined damage initiation criterion +A separate damage evolution law should be specified for each damage initiation criterion defined in +user subroutine UDMGINI. Each combination of a damage initiation criterion and a corresponding +damage evolution law is referred to as a failure mechanism. Damage will accumulate for only one +failure mechanism per element, corresponding to the mechanism whose damage initiation criterion was +achieved first. +Input File Usage: +Abaqus/CAE Usage: +Use the following options to specify damage evolution laws for multiple user- +defined damage initiation criteria: +*DAMAGE INITIATION, CRITERION=USER, FAILURE +MECHANISMS= +*DAMAGE EVOLUTION, FAILURE INDEX=1 +*DAMAGE EVOLUTION, FAILURE INDEX=2 +... +*DAMAGE EVOLUTION, FAILURE INDEX= +Defining a user-defined damage initiation criterion is not supported in +Abaqus/CAE. +Viscous regularization in Abaqus/Standard +Models exhibiting various forms of softening behavior and stiffness degradation often lead to severe +convergence difficulties in Abaqus/Standard. Viscous regularization of the constitutive equations +defining cohesive behavior in an enriched element can be used to overcome some of these convergence +difficulties. Viscous regularization damping causes the tangent stiffness matrix to be positive definite +for sufficiently small time increments. +The approximate amount of energy associated with viscous regularization over the whole model is +available using output variable ALLVD. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to specify viscous regularization: +*DAMAGE STABILIZATION +Property module: material editor: Mechanical→Damage for Traction +Separation Laws: +Quade Damage, Maxe Damage, Quads +Damage, Maxs Damage, Maxpe Damage, or Maxps Damage: +Suboptions→Damage Stabilization Cohesive +Applying the VCCT technique to the XFEM-based LEFM approach +The formulae and laws that govern the behavior of the XFEM-based linear elastic fracture mechanics +approach for crack propagation analysis are very similar to those used for modeling delamination along a +known and partially bonded surface , where the strain +energy release rate at the crack tip is calculated based on the modified Virtual Crack Closure Technique +(VCCT). However, unlike this method, the XFEM-based LEFM approach can be used to simulate crack +propagation along an arbitrary, solution-dependent path in the bulk material with or without an initial +crack. You complete the definition of the crack propagation capability by defining a fracture-based +surface behavior and specifying the fracture criterion in enriched elements. +Crack nucleation and direction of crack extension +By definition, the XFEM-based LEFM approach inherently requires the presence of a crack in the model +since it is based on the principles of linear elastic fracture mechanics. The crack can be pre-existing, or it +can nucleate during the analysis. If there is no pre-existing crack for a given enriched region, the XFEM- +based LEFM approach is not activated until a crack nucleates. The crack nucleation is governed by one +of the six built-in stress- or strain-based crack initiation criteria or a user-defined crack initiation criterion +discussed in “Crack initiation and direction of crack extension,” above. After a crack is nucleated in an +enriched region, subsequent propagation of the crack is governed by the XFEM-based LEFM criterion. +Input File Usage: +Use the following option to specify the crack nucleation criterion as part of the +material definition when there is no pre-existing crack in an enriched region: +Abaqus/CAE Usage: +*DAMAGE INITIATION, TOLERANCE= +Property module: material editor: Mechanical: Damage for Traction +Separation Laws: Quade Damage, Maxe Damage, Quads Damage, +Maxs Damage, Maxpe Damage, or Maxps Damage: +Specifying when a pre-existing crack will extend +If there is a pre-existing crack in an enriched region, the crack extends after an equilibrium increment +when the fracture criterion, f, reaches the value 1.0 within a given tolerance: +You can specify the tolerance +extension criterion is satisfied. The default value of +. If +is 0.2. +, the time increment is cut back such that the crack +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +Interaction→Property→Create, +Contact, +*SURFACE BEHAVIOR +*FRACTURE CRITERION, TOLERANCE= +Interaction module: +Mechanical→Fracture Criterion, Tolerance: +, TYPE=VCCT +Specifying the crack propagation direction +You must specify the crack propagation direction when the fracture criterion is satisfied. The crack can +extend at a direction normal to the direction of the maximum tangential stress, orthogonal to the element +local 1-direction , or orthogonal to the element local 2-direction. By +default, the crack propagates normal to the direction of the maximum tangential stress. +Input File Usage: +Use one of the following options to specify the crack direction when the fracture +criterion is satisfied: +Abaqus/CAE Usage: +*FRACTURE CRITERION, NORMAL DIRECTION=MTS (default) +*FRACTURE CRITERION, NORMAL DIRECTION=1 +*FRACTURE CRITERION, NORMAL DIRECTION=2 +Interaction module: +contact property editor: Mechanical→Fracture +Criterion: Direction of crack growth relative to local 1-direction: +Maximum tangential stress, Normal, or Parallel +Mixed mode behavior +Abaqus provides three common mode-mix formulae for computing the equivalent fracture energy release +rate +: the BK law, the power law, and the Reeder law models. The choice of model is not always +clear in any given analysis; an appropriate model is best selected empirically. +BK law +The BK law model is described in Benzeggagh and Kenane (1996) by the following formula: +To define this model, you must provide +and . This model provides a power law +relationship combining energy release rates in Mode I, Mode II, and Mode III into a single scalar fracture +criterion. +Input File Usage: +*FRACTURE CRITERION, TYPE=VCCT, MIXED MODE +BEHAVIOR=BK +Abaqus/CAE Usage: +contact property editor: Mechanical→Fracture +Interaction module: +Criterion: Mixed mode behavior: BK, and enter the critical energy release +rates in the data table +Power law +The power law model is described in Wu and Reuter (1965) by the following formula: +To define this model, you must provide +and +. +Input File Usage: +*FRACTURE CRITERION, TYPE=VCCT, MIXED MODE +BEHAVIOR=POWER +Abaqus/CAE Usage: +contact property editor: Mechanical→Fracture +Interaction module: +Criterion: Mixed mode behavior: Power, and enter the critical energy +release rates in the data table +Reeder law +The Reeder law model is described in Reeder et al. (2002) by the following formula: +To define this model, you must provide +; when +when +applies only to three-dimensional problems. +and . The Reeder law is best applied +, the Reeder law reduces to the BK law. The Reeder law +Input File Usage: +*FRACTURE CRITERION, TYPE=VCCT, MIXED MODE +BEHAVIOR=REEDER +Abaqus/CAE Usage: +contact property editor: Mechanical→Fracture +Interaction module: +Criterion: Mixed mode behavior: Reeder, and enter the critical energy +release rates in the data table +Defining variable critical energy release rates +You can define a VCCT criterion with varying energy release rates by specifying the critical energy +release rates at the nodes. +If you indicate that the nodal critical energy rates will be specified, any constant critical energy +release rates you specify are ignored and the critical energy release rates are interpolated from the nodes. +The critical energy release rates must be defined at all nodes in the enriched region. +Input File Usage: +Use both of the following options: +*FRACTURE CRITERION, TYPE=VCCT, NODAL ENERGY RATE +*NODAL ENERGY RATE +Defining a VCCT criterion with varying energy release rates is not supported +in Abaqus/CAE. +Abaqus/CAE Usage: +Enhanced VCCT criterion +The formulae and laws governing the behavior of the enhanced VCCT criterion are very similar to those +used for the VCCT criterion. However, unlike the VCCT criterion, the onset and growth of a crack +can be controlled by two different critical fracture energy release rates: +. In a general case +and +involving Mode I, II, and III fracture, when the fracture criterion is satisfied; i.e, +the traction on the two surfaces of the cracked element is ramped down over the separation with the +dissipated strain energy equal to the critical equivalent strain energy required to propagate the crack, +. +, rather than the critical equivalent strain energy required to initiate the separation, +for different mixed-mode +are identical to those used for +The formulae for calculating +fracture criteria. +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*SURFACE BEHAVIOR +*FRACTURE CRITERION, TYPE=ENHANCED VCCT +Specifying the enhanced VCCT criterion is not supported in Abaqus/CAE. +Low-cycle fatigue criterion based on the principles of LEFM +If you specify the low-cycle fatigue criterion, progressive crack growth at the enriched elements subjected +to sub-critical cyclic loading can be simulated. This criterion can be used only in a low-cycle fatigue +analysis using the direct cyclic approach (“Low-cycle fatigue analysis using the direct cyclic approach,” +Section 6.2.7). A low-cycle fatigue step can be the only step, can follow a general static step, or can be +followed by a general static step. You can include multiple low-cycle fatigue analysis steps in a single +analysis. If you perform a fatigue analysis in a model without a pre-existing crack, you must precede the +fatigue step with a static step that nucleates a crack, as discussed in “Crack nucleation and direction of +crack extension.” +The onset and fatigue crack growth are characterized by using the Paris law, which relates the +relative fracture energy release rate to crack growth rates as illustrated in Figure 10.7.1–3. The fracture +energy release rates at the crack tips in the enriched elements are calculated based on the above mentioned +VCCT technique. +The Paris regime is bounded by the energy release rate threshold, +, below which there is no +consideration of fatigue crack initiation or growth, and the energy release rate upper limit, +, above +which the fatigue crack will grow at an accelerated rate. +is the critical equivalent strain energy +release rate calculated based on the user-specified mode-mix criterion and the fracture strength of the +bulk material. The formulae for calculating +have been provided above for different mixed mode +fracture criteria. You can specify the ratio of +. The default +values are +. +and the ratio of +over +over +and +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*SURFACE BEHAVIOR +*FRACTURE CRITERION, TYPE=FATIGUE +Specifying a low-cycle fatigue criterion is not supported in Abaqus/CAE. +Onset of fatigue crack growth +The onset of fatigue crack growth refers to the beginning of fatigue crack growth at the crack tip in +the enriched elements. In a low-cycle fatigue analysis the onset of the fatigue crack growth criterion +is characterized by +, which is the relative fracture energy release rate when the structure is loaded +between its maximum and minimum values. The fatigue crack growth initiation criterion is defined as +and +are material constants and +is the cycle number. The enriched elements ahead of the +where +crack tips will not be fractured unless the above equation is satisfied and the maximum fracture energy +release rate, +, which corresponds to the cyclic energy release rate when the structure is loaded up +to its maximum value, is greater than +. +Fatigue crack growth using the Paris law +Once the onset of the fatigue crack growth criterion is satisfied at the enriched element, the crack growth +rate, +. The rate of the +crack growth per cycle is given by the Paris law if +, can be calculated based on the relative fracture energy release rate, +where +and +are material constants. +and +At the end of cycle +, from the current cycle +, Abaqus/Standard extends the crack length, +forward over an incremental number of cycles, +by fracturing at least one enriched element +to +ahead of the crack tips. Given the material constants +, combined with the known element length +and the likely crack propagation direction +at the enriched elements ahead of +the crack tips, the number of cycles necessary to fail each enriched element ahead of the crack tip can +be calculated as +, where j represents the enriched element ahead of the th crack tip. The analysis +is set up to advance the crack by at least one enriched element after the loading cycle is stabilized. The +element with the fewest cycles is identified to be fractured, and its +is represented +as the number of cycles to grow the crack equal to its element length, +. The +most critical element is completely fractured with a zero constraint and a zero stiffness at the end of the +stabilized cycle. As the enriched element is fractured, the load is redistributed and a new relative fracture +energy release rate must be calculated for the enriched elements ahead of the crack tips for the next cycle. +This capability allows at least one enriched element ahead of the crack tips to be fractured completely +after each stabilized cycle and precisely accounts for the number of cycles needed to cause fatigue crack +growth over that length. +If +, the enriched elements ahead of the crack tips will be fractured by increasing the +cycle number count, +, by one only. +Viscous regularization for the XFEM-based LEFM approach +The simulation of structures with unstable propagating cracks is challenging and difficult. +Nonconvergent behavior may occur from time to time. Localized damping is included for the +XFEM-based LEFM approach by using the viscous regularization technique. Viscous regularization +damping causes the tangent stiffness matrix of the softening material to be positive for sufficiently small +time increments. +Input File Usage: +Use one of the following options +Abaqus/CAE Usage: +*FRACTURE CRITERION, TYPE=VCCT, VISCOSITY= +*FRACTURE CRITERION, TYPE=ENHANCED VCCT, VISCOSITY= +Interaction module: +Criterion: Viscosity: +contact property editor: Mechanical→Fracture +Specifying the initial location of an enriched feature +Because the mesh is not required to conform to the geometric discontinuities, the initial location of a +pre-existing crack must be specified in the model. The level set method is provided for this purpose. Two +signed distance functions per node are generally required to describe a crack geometry. The first describes +the crack surface, while the second is used to construct an orthogonal surface so that the intersection of +the two surfaces gives the crack front . +The first signed distance function must be either greater or less than zero and cannot be equal to +zero. If an initial crack has to be defined at the boundaries of an element, a very small positive or negative +value for the first signed distance function must be specified. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to specify the initial location of an enriched feature: +*INITIAL CONDITIONS, TYPE=ENRICHMENT +Interaction module: crack editor: Crack location: Select: select region +Activating and deactivating the enriched feature +The crack propagation capability can be activated or deactivated within the step definition. +Input File Usage: +Abaqus/CAE Usage: +Contour integral +Use the following option to activate the crack propagation capability within the +step definition: +*ENRICHMENT ACTIVATION, NAME=name, ACTIVATE=ON (default) +Use the following option to deactivate the crack propagation capability within +the step definition: +*ENRICHMENT ACTIVATION, NAME=name, ACTIVATE=OFF +Use the following option to deactivate the crack propagation capability +automatically once all the pre-existing cracks (or if there are no pre-existing +cracks, all the allowable newly nucleated cracks) have propagated through the +boundary of the given enriched feature within the step definition: +*ENRICHMENT ACTIVATION, NAME=name, ACTIVATE=AUTO OFF +To modify the status of the crack propagation capability in a step, you must first +create an XFEM crack growth interaction: +Interaction module: Create Interaction: select initial step: XFEM Crack +Growth: select crack: Interaction manager: select interaction in step: +Edit: toggle on/off Allow crack growth in this step +When you evaluate the contour integrals using the conventional finite element method (“Contour integral +evaluation,” Section 11.4.2), you must define the crack front explicitly and specify the virtual crack +extension direction in addition to matching the mesh to the cracked geometry. Detailed focused meshes +are generally required and obtaining accurate contour integral results for a crack in a three-dimensional +curved surface can be cumbersome. The extended finite element in conjunction with the level set method +alleviates these shortcomings. The adequate singular asymptotic fields and the discontinuity are ensured +by the special enrichment functions in conjunction with additional degrees of freedom. In addition, the +crack front and the virtual crack extension direction are determined automatically by the level set signed +distance functions. +Input File Usage: +Use the following option to obtain contour integral for a named enriched feature +with the extended finite element method: +Abaqus/CAE Usage: +*CONTOUR INTEGRAL, XFEM, CRACK NAME=name +Step module: history output request editor: Domain: Crack: crack name +Specifying the enrichment radius +Although XFEM has alleviated the shortcomings associated with refining the mesh in the neighborhood +of the crack front due to the added asymptotic fields, you must generate a sufficient number of elements +around the crack front to obtain path-independent contours. The group of elements within a small radius +from the crack front are enriched and become involved in the contour integral calculations. The default +enrichment radius is three times the typical element characteristic length in the enriched area. You must +include the elements inside the enrichment radius in the element set used to define the enriched region. +Input File Usage: +Use the following option to specify an enrichment radius: +Abaqus/CAE Usage: +*ENRICHMENT, ENRICHMENT RADIUS +Interaction module: crack editor: Enrichment radius: Analysis +default or Specify +Procedures +Modeling discontinuities as an enriched feature can be performed using any of the following: +• static analysis ; +• implicit dynamic analysis ; +or +• low-cycle fatigue analysis using the direct cyclic approach (“Low-cycle fatigue analysis using the +direct cyclic approach,” Section 6.2.7). +Initial conditions +Initial conditions to identify initial boundaries or interfaces of an enriched feature can be specified . +Boundary conditions +Boundary conditions can be applied to any of the displacement degrees of freedom . +Loads +The following types of loading can be prescribed in a model with an enriched feature: +• Concentrated nodal forces can be applied to the displacement degrees of freedom (1–3); see +“Concentrated loads,” Section 33.4.2. +• Distributed pressure forces or body forces can be applied; see “Distributed loads,” Section 33.4.3. +The distributed load types available with particular elements are described in Part VI, “Elements.” +Predefined fields +The following predefined fields can be specified in a model with an enriched feature, as described in +“Predefined fields,” Section 33.6.1: +• Nodal temperatures (although temperature is not a degree of freedom in stress/displacement +elements). The specified temperature affects temperature-dependent critical stress and strain +failure criteria. +• The values of user-defined field variables. The specified value affects field-variable-dependent +material properties. +Material options +Any of the mechanical constitutive models in Abaqus/Standard, including user-defined materials (defined +using user subroutine “UMAT,” Section 1.1.40 of the Abaqus User Subroutines Reference Manual) can +be used to model the mechanical behavior of the enriched element in a crack propagation analysis. See +Part V, “Materials.” The inelastic definition at a material point must be used in conjunction with the +linear elastic material model (“Linear elastic behavior,” Section 22.2.1) or the hypoelastic material model +(“Hypoelastic behavior,” Section 22.4.1). Only isotropic elastic materials are supported when evaluating +the contour integral for a stationary crack. +Elements +Only first-order solid continuum stress/displacement elements and second-order stress/displacement +tetrahedron elements can be associated with an enriched feature. For propagating cracks these include +bilinear plane strain and plane stress elements, bilinear axisymmetric elements, linear brick elements, +linear tetrahedron elements, and second-order tetrahedron elements. For stationary cracks, these include +linear brick elements, linear tetrahedron elements, and second-order tetrahedron elements. +For an incompatible mode element, Abaqus/Standard discards the contribution due to the +incompatible deformation mode immediately after the element is fractured under a tensile loading. +Therefore, the stress level at the cracked element may not return completely to its originally unloaded +state even when this cracked element is unloaded completely and the contact of the cracked element +surfaces is reestablished. +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Standard output variable +identifiers,” Section 4.2.1), the following variables have special meaning for a model with an enriched +feature: +PHILSM +PSILSM +STATUSXFEM +ENRRTXFEM +Signed distance function to describe the crack surface. +Signed distance function to describe the initial crack front. +Status of the enriched element. (The status of an enriched element is 1.0 if the +element is completely cracked and 0.0 if the element contains no crack. If the +element is partially cracked, the value of STATUSXFEM lies between 1.0 and +0.0.) +All components of strain energy release rate when linear elastic fracture +mechanics with the extended finite element method is used. +Visualization +A crack can be visualized through the iso-surface for the signed distance function PHILSM. +If a crack cuts through a very tiny corner of an enriched element, the displacements along the crack +front in the enriched element may be distorted in rare cases in the Visualization module of Abaqus/CAE +(Abaqus/Viewer) when displaying the contours. The distortion, however, is not present when viewing +only the deformed shape. +Limitations +The following limitations exist with an enriched feature: +• An enriched element cannot be intersected by more than one crack. +• A crack is not allowed to turn more than 90° in one increment during an analysis. +• Only asymptotic crack-tip fields in an isotropic elastic material are considered for a stationary crack. +• Adaptive remeshing is not supported. +Input file template +The following is an example of modeling crack propagation with the XFEM-based cohesive segments +method: +*HEADING +... +*NODE, NSET=ALL +... +*ELEMENT, TYPE=C3D8, ELSET=REGULAR +*ELEMENT, TYPE=C3D8, ELSET=ENRICHED +... +*SOLID SECTION, MATERIAL=STEEL1, ELSET=REGULAR +*SOLID SECTION, MATERIAL=STEEL12, ELSET=ENRICHED +*ENRICHMENT, TYPE=PROPAGATION CRACK, ELSET=ENRICHED, +NAME=ENRICHMENT, INTERACTION=INTERACTION +*MATERIAL, NAME=STEEL1 +... +*MATERIAL, NAME=STEEL2 +*DAMAGE INITIATION, CRITERION=MAXPS, TOLERANCE=0.05 +*DAMAGE EVOLUTION, TYPE=ENERGY +Data lines to specify the failure mechanism +... +*SURFACE INTERACTION, NAME=INTERACTION +*SURFACE BEHAVIOR +Data lines to specify the contact of cracked element surfaces +... +*STEP +*STATIC +... +*END STEP +*STEP +*STATIC +... +*ENRICHMENT ACTIVATION, TYPE=PROPAGATION CRACK, +NAME=ENRICHMENT, ACTIVATE=OFF +... +*END STEP +The following is an example of modeling crack propagation with the XFEM-based LEFM approach: +*HEADING +... +*NODE, NSET=ALL +... +*ELEMENT, TYPE=C3D8, ELSET=REGULAR +*ELEMENT, TYPE=C3D8, ELSET=ENRICHED +... +*SOLID SECTION, MATERIAL=STEEL1, ELSET=REGULAR +*SOLID SECTION, MATERIAL=STEEL12, ELSET=ENRICHED +*ENRICHMENT, TYPE=PROPAGATION CRACK, ELSET=ENRICHED, +NAME=ENRICHMENT, INTERACTION=INTERACTION +*MATERIAL, NAME=STEEL1 +... +*MATERIAL, NAME=STEEL2 +*DAMAGE INITIATION, CRITERION=MAXPS, TOLERANCE=0.05 +Data lines to specify the crack nucleation mechanism +... +*SURFACE INTERACTION, NAME=INTERACTION +*SURFACE BEHAVIOR +*FRACTURE CRITERION, TYPE=VCCT, TOLERANCE=0.05,VISCOSITY=0.00001 +Data lines to specify the crack propagation criterion +... +*END STEP +The following is an example of calculating contour integrals in stationary cracks with the extended +finite element method: +*HEADING +... +*NODE, NSET=ALL +... +*ELEMENT, TYPE=C3D8, ELSET=REGULAR +*ELEMENT, TYPE=C3D8, ELSET=ENRICHED +... +*SOLID SECTION, MATERIAL=STEEL1, ELSET=REGULAR +*SOLID SECTION, MATERIAL=STEEL12, ELSET=ENRICHED +*ENRICHMENT, TYPE=STATIONARY CRACK, ELSET=ENRICHED, +NAME=ENRICHMENT, ENRICHMENT RADIUS +*MATERIAL, NAME=STEEL1 +... +*MATERIAL, NAME=STEEL2 +... +*STEP +*STATIC +... +*CONTOUR INTEGRAL, CRACK NAME=ENRICHMENT, XFEM +*END STEP +Additional references +• Belytschko, T., and T. Black, “Elastic Crack Growth in Finite Elements with Minimal Remeshing,” +International Journal for Numerical Methods in Engineering, vol. 45, pp. 601–620, 1999. +• Benzeggagh, M., and M. Kenane, “Measurement of Mixed-Mode Delamination Fracture +Toughness of Unidirectional Glass/Epoxy Composites with Mixed-Mode Bending Apparatus,” +Composite Science and Technology, vol. 56, p. 439, 1996. +• Elguedj, T., A. Gravouil, and A. Combescure, “Appropriate Extended Functions for X-FEM +Simulation of Plastic Fracture Mechanics,” Computer Methods in Applied Mechanics and +Engineering, vol. 195, pp. 501–515, 2006. +• Melenk, J., and I. Babuska, “The Partition of Unity Finite Element Method: Basic Theory and +Applications,” Computer Methods in Applied Mechanics and Engineering, vol. 39, pp. 289–314, +1996. +• Reeder, +“Postbuckling and +and D. R.. Ambur, +Growth of Delaminations +in Composite Plates Subjected to Axial Compression” 43rd +AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, +Denver, Colorado, vol. 1746, p. 10, 2002. +P. B. Chunchu, +S. Kyongchan, +J., +• Remmers, J. J. C., R. de Borst, and A. Needleman, “The Simulation of Dynamic Crack Propagation +using the Cohesive Segments Method,” Journal of the Mechanics and Physics of Solids, vol. 56, +pp. 70–92, 2008. +• Song, J. H., P. M. A. Areias, and T. Belytschko, “A Method for Dynamic Crack and Shear Band +Propagation with Phantom Nodes,” International Journal for Numerical Methods in Engineering, +vol. 67, pp. 868–893, 2006. +• Sukumar, N., Z. Y. Huang, J.-H. Prevost, and Z. Suo, “Partition of Unity Enrichment for +Bimaterial Interface Cracks,” International Journal for Numerical Methods in Engineering, +vol. 59, pp. 1075–1102, 2004. +• Sukumar, N., and J.-H. Prevost, “Modeling Quasi-Static Crack Growth with the Extended Finite +Element Method Part I: Computer Implementation,” International Journal for Solids and Structures, +vol. 40, pp. 7513–7537, 2003. +• Wu, E. M., and R. C. Reuter Jr., “Crack Extension in Fiberglass Reinforced Plastics,” T and M +Report, University of Illinois, vol. 275, 1965. +11. +Special-Purpose Techniques +Inertia relief +Mesh modification or replacement +Geometric imperfections +Fracture mechanics +Surface-based fluid modeling +Mass scaling +Selective subcycling +Steady-state detection +11.1 +11.2 +11.3 +11.4 +11.5 +11.6 +11.7 +11.1 +Inertia relief +• “Inertia relief,” Section 11.1.1 +11.1.1 +INERTIA RELIEF +Products: Abaqus/Standard Abaqus/CAE +References +• “Distributed loads,” Section 33.4.3 +• “Defining an analysis,” Section 6.1.2 +• *INERTIA RELIEF +• “Defining an inertia relief load,” Section 16.9.16 of the Abaqus/CAE User���s Manual, in the online +HTML version of this manual +Overview +Inertia relief: +• involves balancing externally applied forces on a free or partially constrained body with loads +derived from constant rigid body accelerations; +• requires material density or mass and/or rotary inertia values to be specified for computing inertia +relief loads; +• can be performed for static, dynamic, and buckling analyses in Abaqus/Standard; +• varies the inertia relief loading with the applied loading in static analysis; +• applies inertia relief load corresponding to the static preload in dynamic analysis; +• can be used to balance applied perturbation loads when used with buckling analysis; +• uses rigid body accelerations consistent with the specified boundary conditions to compute the +inertia relief loads; +• can be geometrically linear or nonlinear; +• may require the use of the unsymmetric solver if there are large inertia relief moments in a +geometrically nonlinear analysis; +• is an inexpensive alternative to doing a full dynamic free body analysis when applied loads vary +slowly compared to the eigenfrequencies of the body; and +• can be used with multiple load cases. +Typical applications +Inertia relief loading can be applied in static (“Static stress analysis,” Section 6.2.2), dynamic (“Implicit +dynamic analysis using direct integration,” Section 6.3.2), and eigenvalue buckling prediction steps +(“Eigenvalue buckling prediction,” Section 6.2.3). +In a static step the inertia relief loading varies with the applied external loading. An example of +using an inertia relief load is modeling a rocket undergoing constant or slowly varying acceleration during +lift-off (i.e., a free body subjected to a constant or slowly varying external force) with a static analysis +procedure. The inertia forces experienced by the body are included in the static solution through inertia +relief loading that balances the external loading. +In a dynamic step the inertia relief loading is calculated based on the static preload and is held +constant during the step. The following is an example of using an inertia relief load in a dynamic analysis +procedure: Consider a free body submerged in water and subjected to shock wave loading due to an +explosion. A dynamic analysis is needed to compute the transient solution. If it is known that initially the +body is stationary under gravity and hydrostatic pressure from the fluid, the gravity load should exactly +balance the buoyancy force. However, if the finite element model does not include all the mass existing +in the body (for example, ballast), without additional loading, the body would accelerate due to out-of- +balance external forces. Applying inertia relief loading exactly balances these unbalanced external loads, +placing the body in static equilibrium. The dynamic analysis then provides the transient response of the +body to the shock wave loading as deformation of the body relative to its static equilibrium position. +In a buckling analysis the inertia relief load can be applied in the static preload step, in the eigenvalue +buckling prediction step, or in both steps. In the eigenvalue buckling prediction step the inertia relief +load is calculated based on the perturbation loads. Consider the static analysis rocket example. If we use +inertia relief in a buckling analysis of the rocket with the rocket thrust as the perturbation load, we can +predict the critical thrust that causes the rocket to buckle. +Basic formulation +In inertia relief the total response, +due to rigid body motion of a reference point, +, of the body is written as a combination of a rigid body response +, and a relative response, +: +with corresponding expressions for velocities and accelerations. The reference point is the center of +mass except when you must specify the reference point. Then, the finite element approximation to the +dynamic equilibrium equation becomes +is the mass matrix, +where +is the external force vector. The +is the internal force vector, and +response of interest in a static analysis involving inertia relief is the rigid body response corresponding +to the dynamic motion of the reference point and the static response relative to the rigid body motion. +Hence, the relative acceleration term +drops from the equilibrium equation. +The rigid body response can be expressed in terms of the acceleration of the reference point, +, and +rigid body mode vectors, +, +(in three dimensions): +represents the acceleration vector corresponding to a unit imposed acceleration +(displacement or rotation) in the j-direction at the reference point. For example, at a node with the +usual three displacements and three rotations +is +INERTIA RELIEF +is unity; all other +where +represent the coordinates of the reference point that is the center of rotation. If the system undergoes +finite changes in geometry, +are zero; x, y, and z are the coordinates of the node; and +will both be functions of time. +, and +and +, +Projecting the dynamic equilibrium equation onto the rigid body modes, we have +where +is the rigid body acceleration associated +with the rigid body mode j. The actual number of rigid body modes will be less than 6 in the presence +of symmetry planes as well as for two-dimensional and axisymmetric analyses. Thus, the rigid body +response can be evaluated directly from the external loads. +is the “rigid body inertia” and +The relative response of the body can be obtained by solving the equilibrium equation with the +moved to the right hand side; that is, applied as a body force. The static +known inertial term +equilibrium equation then becomes +where +. +In a dynamic analysis involving inertia relief the rigid body mode vectors +are calculated in the +configuration at the start of the dynamic analysis, and the reference point accelerations +are calculated +to balance the static preloads in this configuration. The relative acceleration term is not dropped, so the +dynamic equilibrium equation becomes +where +. In a geometrically nonlinear analysis the rigid body mode vectors +are recomputed during the analysis using the current configuration but the reference point accelerations +are kept constant. This keeps the total magnitude of inertia relief loads constant during the analysis but +allows the loads to be proportional to the spatial mass distribution, which changes with geometry. +Input File Usage: +*INERTIA RELIEF +Abaqus/CAE Usage: +Load module: Create Load: choose Mechanical for the Category +and Inertia relief for the Types for Selected Step +Inertia relief loading directions +By default, all rigid body motion directions in a model can be loaded by inertia relief loading (in this +discussion we use the word “direction” to mean any rigid body translation or rotation). In models with +symmetry planes or models that are allowed to move freely in only specific directions, the free directions +for which inertia relief loading is applied can be specified. For example, in a three-dimensional analysis +with one symmetry plane only three free directions exist—two translations and one rotation. Add an +additional symmetry plane and only one free translation remains. A cylinder-piston arrangement is an +example where the only free direction considered is motion along the cylinder’s axis. In these situations +you specify the free directions that are loaded by inertia relief loading by indicating the degrees of +freedom. +The case of two free rotation directions is not permitted. For cyclic symmetric models with inertia +relief only translation in the Z-direction and rotation about the Z-direction are considered for computing +inertia relief loading. +Input File Usage: +*INERTIA RELIEF +integer list of global degrees of freedom identifying the free directions +Abaqus/CAE Usage: +For example, the list 1, 3, 5 implies that translations in the X- and Z-directions +and rotation about the Y-axis are free directions. +Load module: Create Load: choose Mechanical for the Category and +Inertia relief for the Types for Selected Step: toggle on the degrees +of freedom to define the Free Directions (the degrees of freedom +displayed are dependent on the modeling space) +Defining the free directions in a local coordinate system +If the free directions are not global directions, an orientation can be used to define the local coordinate +system to which the integer list of degree of freedom identifiers refers. +Input File Usage: +*INERTIA RELIEF, ORIENTATION=orientation_name +integer list of local degrees of freedom identifying the free directions +Abaqus/CAE Usage: +Load module: Create Load: choose Mechanical for the Category and Inertia +relief for the Types for Selected Step: click Edit, and choose a local CSYS +Defining free direction combinations that require a user-specified reference point +Not all user-chosen combinations of free directions admit unconstrained rigid body motion; that is, there +are certain combinations of free directions for which an additional point is required to define the rigid +body motion vectors. For example, in three dimensions the choice 4, 5, 6 corresponds to free rotations +about a fixed point. The fixed point must be given to define the rigid body motion vectors. In other +examples the free directions include rotation about a fixed axis. Consider a turbine blade rotating about +its axis, as shown in Figure 11.1.1–1. +turbine blade +surfaces with +cyclic symmetry +constraints +rigid body rotation +chosen as free direction +hub +reference point on +axis of rotation +Figure 11.1.1–1 Inertia relief for a turbine blade with rotation +about the axis as the only free direction. +To find the angular acceleration of the blade as it rotates under an applied force couple or moment, +you should specify the coordinates of the point on the shaft about which the blade is rotating. The free +direction combinations for which you must specify a reference point are given in Table 11.1.1–1. +Input File Usage: +Abaqus/CAE Usage: +*INERTIA RELIEF, ORIENTATION=orientation_name +integer list of local degrees of freedom identifying the free directions +X, Y, Z coordinates of the reference point for defining the rigid body vectors +Load module: Create Load: choose Mechanical for the Category and +Inertia relief for the Types for Selected Step: toggle on Global position +of reference point, and enter the X, Y, and (if available) Z coordinates +Table 11.1.1–1 Free direction combinations requiring a reference point. +Degree of freedom identifiers +defining free directions +Reference point definition +Fixed +rotation point +Point on +rotation axis +Point on +symmetry line +4, 5, 6 +1, 4, 5, 6 +2, 4, 5, 6 +3, 4, 5, 6 +1, 2, 4, 5, 6 +1, 3, 4, 5, 6 +2, 3, 4, 5, 6 +2, 4 +3, 4 +1, 5 +3, 5 +1, 6 +2, 6 +1, 2, 4 +1, 2, 5 +1, 3, 4 +1, 3, 6 +2, 3, 5 +2, 3, 6 +1, 4 +2, 5 +3, 6 +Initial conditions +Initial conditions can be specified in the same way as in static and dynamic analyses without inertia relief +loads. If inertia relief is used in the first step in the analysis, these initial conditions form the base state +of the body. See “Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1. +Boundary conditions +Boundary conditions are specified in the same way as in analyses without inertia relief loads . In theory, a statically +determinate set of restraints is needed when inertia relief is used in a static step. By “statically +determinate” we mean a set of restraints that restrain all rigid body modes but no deformation modes. +Such a set provides a unique displacement solution and ensures that the inertia relief loading exactly +balances the user-specified external loading: zero reaction forces with no rigid body motion of the +center of mass. Table 11.1.1–2 summarizes the restraint requirements for various cases. +Table 11.1.1–2 Necessary and sufficient statically determinate restraints. +Problem +dimensionality +Free directions +Number of required +restraints +2-D +2 Translations and 1 Rotation +Axisymmetric +Axisymmetric +with twist +1 Translation +1 Translation and 1 Rotation +3-D +3 Translations and 3 Rotations +However, it is not necessary for the user to explicitly specify boundary conditions (“Boundary +conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1) with inertia relief except in the +case of buckling analysis. If no boundary conditions or insufficient boundary conditions are specified, a +warning message will be issued and boundary conditions necessary to restrain the rigid body modes will +be imposed internally at the point in the model that corresponds to the original location of the reference +point. On the other hand, if too many boundary conditions are specified in certain directions, a warning +message will be issued to indicate that the reaction forces may be nonzero at the nodes with overspecified +boundary conditions. If there are insufficient boundary conditions in certain directions and too many +boundary conditions in other directions, the problem will be treated as a combination of these cases. +If a model has no boundary conditions or insufficient boundary conditions, a particular number +of numerical singularity warnings can be issued during each equilibrium iteration in the analysis. The +displacement solution is postprocessed to remove unconstrained rigid body motion. However, the +number of numerical singularities should not exceed the number of unconstrained rigid body modes; +any extra numerical singularity messages may indicate other problems. +Similarly, a model with no boundary conditions or insufficient boundary conditions may produce +negative eigenvalue messages. If the number of negative eigenvalues at each equilibrium iteration in +the analysis does not exceed the maximum reasonable number of numerical singularities associated with +the boundary conditions for inertia relief, the results can be trusted, but extra negative eigenvalues may +indicate other problems. +If a model contains symmetry planes or is constrained to move freely in specific directions, inertia +relief loading should be applied only in those free directions. No boundary conditions should be specified +in the free directions; however, sufficient boundary conditions must be specified in the other directions. +Any boundary conditions that violate the above requirements will be flagged as an error. An error will +also be issued if the combination of free directions includes only two free rotations or if a reference point +is required but not specified. +In a buckling analysis, proper boundary conditions are important for getting the correct mode shape. +Sufficient boundary conditions must be specified when inertia relief loading is applied in such an analysis. +See “Eigenvalue buckling prediction,” Section 6.2.3, for details on how to apply boundary conditions in +a buckling analysis. +Loads +An analysis that uses inertia relief can include concentrated nodal forces at displacement degrees of +freedom (1–6), distributed pressure forces or body forces, and user-defined loading. +Inertia relief loads are used to balance the external loads. They are computed and applied when +inertia relief is included in the step definition. The rules for propagating load definitions between steps +hold for inertia relief loads. See “Applying loads: overview,” Section 33.4.1. The inertia relief loads +will not be propagated to steps where inertia relief is not valid for the specified procedure. +If there are large inertia relief moments in a geometrically nonlinear analysis, their contribution to +the stiffness matrix may be unsymmetric. In such cases unsymmetric equation solution may improve the +computational efficiency . +Computing inertia relief loads +The nodal force vector corresponding to the inertia relief loads is calculated as follows. The applied loads +are projected onto the rigid body modes, +. These force and moment components (six components +in three dimensions) are used with the “rigid body inertia” to solve for the rigid body accelerations, +. +Only the rigid body acceleration components corresponding to the inertia relief loading directions are +nonzero. The nodal force vector is calculated using the assembled mass matrix +as +Fixed inertia relief loads +You can specify that the inertia relief loads should be held fixed in magnitude and direction at the values +calculated at the end of the previous step. +Input File Usage: +Abaqus/CAE Usage: +*INERTIA RELIEF, FIXED +Load module: Create Load: choose Mechanical for the Category and Inertia +relief for the Types for Selected Step: Method: Fix at current loading +Removing inertia relief loads +You can specify that the inertia relief loads that were applied in the previous general analysis step should +be removed in the current step. +Input File Usage: +Abaqus/CAE Usage: +*INERTIA RELIEF, REMOVE +Load module: Load Manager: Deactivate +Predefined fields +User-defined field variables can be specified in the same way as in static and dynamic analyses without +inertia relief loads. See “Predefined fields,” Section 33.6.1. +Material options +Any of the mechanical constitutive models that are available in Abaqus/Standard for use in static, +dynamic, or buckling analyses can be used with inertia relief . Since inertia relief loading is calculated using the +inertia properties of the model, the density must be specified to define +the model’s inertia properties. +Elements +Most of the stress/displacement elements that are available in Abaqus/Standard for use in static, +dynamic, and buckling analyses (including mass and rotary inertia elements and user elements) can be +used. A warning will be issued when the model contains elements that do not have associated mass or +inertia (for example, hydrostatic fluid elements and pore pressure elements). An error will be issued +if the model contains elements that do not allow finite boundaries (for example, infinite elements and +elastic element foundations). Although five degree of freedom shell elements can be used in a step with +inertia relief loads, they may cause convergence difficulties if the model has no boundary conditions +or insufficient boundary conditions. To improve convergence, these elements should be replaced with +other conventional shell elements. +In the case of a substructure you must generate a reduced mass matrix for the substructure . The reduced mass matrix is included in the global mass matrix of the entire model +to compute rigid body accelerations and inertia relief loads. +Inertia relief can be used only with +substructures in a geometrically linear analysis. An error message is issued if inertia relief is used with +substructures in a geometrically nonlinear analysis. +Output +In addition to the usual output variables available in Abaqus/Standard , the following variables are provided specifically for inertia relief: +Variables for the entire model: +IRX +IRXn +IRA +IRAn +IRARn +IRF +IRFn +IRMn +IRRI +IRRIij +IRMASS +). +Current coordinates of the reference point. +Coordinate n of the reference point ( +Equivalent rigid body acceleration components. +Component n of the equivalent rigid body acceleration ( +Component n of the equivalent rigid body angular acceleration with respect to the +reference point ( +Inertia relief load corresponding to the equivalent rigid body acceleration. +Component n of the inertia relief load corresponding to the equivalent rigid body +acceleration ( +Component n of the inertia relief moment corresponding to the equivalent rigid +body angular acceleration with respect to the reference point ( +Rotary inertia about the reference point. +). +). +). +). +-component of the rotary inertia about the reference point ( +). +Whole model mass. +For most cases inertia relief loads correspond to the product of “rigid body inertia” and the +equivalent rigid body acceleration vector. However, when only a few rigid body directions are chosen +as free directions for inertia relief, inertia relief loads are computed in all rigid body directions for +output purposes, but equivalent rigid body accelerations are computed in only the free directions with +the equivalent rigid body angular accelerations computed from the diagonal entries of the “rigid body +inertia.” +Limitations +You need to be aware of limitations that may be encountered in analyses with inertia relief loads. +Internal boundary conditions and convergence in geometrically linear and nonlinear analysis +In a model containing internal boundary conditions that generate unbalanced internal forces or +moments, such as is possible from certain elements (for example, SPRING1, DASHPOT1, SPRING2, +DASHPOT2, or GAPUNI elements) or kinematic constraints (for example, coupling constraints, linear +constraint equations, multi-point constraints, or surface-based tie constraints), inertia relief loads will +If the model contains sufficient boundary conditions, +not balance these internal forces or moments. +these internal forces or moments will appear as nonzero reaction forces or moments. If the model does +not contain sufficient boundary conditions, these internal forces or moments will appear as unconverged +residual fluxes in the message file for geometrically linear as well as nonlinear analyses. The model +should be treated as having internal boundary conditions, with the unconverged residuals representing +the reaction forces or moments needed to impose the internal boundary conditions. Ideally, the internal +boundary conditions should be removed or sufficient boundary conditions should be added to the model. +Unconnected regions and analyses with contact +Inertia relief is not supported for models consisting of multiple unconnected regions, even if contact is +defined between them. An exception is when tied contact is defined between the regions. In this case it +is the user’s responsibility to ensure that different parts are tied in such a way that no rigid body motion +is possible between them. +In addition, models involving contact with inertia relief loads may show poor convergence or fail +to converge in cases when the surfaces are not in contact or when contact stabilization is used. +Mass and stiffness defined using matrices +Mass and stiffness cannot be defined using matrices in analyses with inertia relief loads. +Input file template +*HEADING +… +*DENSITY +Data line to specify material density +*BOUNDARY +Data lines to specify zero-valued boundary conditions +** +*STEP (, NLGEOM) (, PERTURBATION) +Use the NLGEOM parameter to include nonlinear geometric effects; +it will remain active in all subsequent steps. +*STATIC (or *DYNAMIC) +… +*CLOAD and/or *DLOAD +Data lines to specify loads +*INERTIA RELIEF, ORIENTATION=orientation_name +Data lines to specify global (or local, if the ORIENTATION parameter is used) degrees +of freedom that define free directions and to provide coordinates of a reference point +*END STEP +** +*STEP +*STATIC(or *DYNAMIC) +… +*INERTIA RELIEF, FIXED or REMOVE +Include the FIXED parameter to keep inertia relief loads fixed at their current +values from the beginning of the step; include the REMOVE parameter to +remove inertia relief loads from the beginning of the step. +*END STEP +11.2 +Mesh modification or replacement +• “Element and contact pair removal and reactivation,” Section 11.2.1 +11.2.1 +ELEMENT AND CONTACT PAIR REMOVAL AND REACTIVATION +Products: Abaqus/Standard Abaqus/CAE +References +• “Removing and reactivating contact pairs” in “Defining contact pairs in Abaqus/Standard,” +Section 35.3.1 +• *MODEL CHANGE +• “Defining a model change interaction,” Section 15.13.13 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +Element and contact pair removal/reactivation: +• can be used to simulate removal of part of the model, either temporarily or for the remainder of the +analysis; +• allows reactivation of elements strain-free or with strain; +• can be used to save computational time when a contact pair is not needed; +• can be used only in general analysis steps; and +• can be used in a restart analysis only if it was used or activated in the original analysis. +Removing elements +You can remove specified elements from the model in a general analysis step. Just prior to the removal +step, Abaqus/Standard stores the forces/fluxes that the region to be removed is exerting on the remaining +part of the model at the nodes on the boundary between them. These forces are ramped down to zero +during the removal step; therefore, the effect of the removed region on the rest of the model is completely +absent only at the end of the removal step. The forces are ramped down gradually to ensure that element +removal has a smooth effect on the model. +No further element calculations are performed for elements being removed, starting from the +beginning of the step in which they are removed. The removed elements remain inactive in subsequent +steps unless you reactivate them as described below. +Input File Usage: +Use the following option to remove elements from the model: +Abaqus/CAE Usage: +*MODEL CHANGE, TYPE=ELEMENT, REMOVE +Interaction module: Create Interaction: Model Change: Definition: +Region, Activation state of region elements: Deactivated in this step +Removing elements in transient procedures +Care must be taken in removing elements in transient procedures. The nodal flux that the removed +elements apply at the boundary with the rest of the model is ramped down over the step. In transient heat +transfer, fully coupled temperature-displacement, or fully coupled thermal-electrical-structural analysis +if the fluxes are high and the step is long, this ramping down may have the effect of cooling down or +heating up the rest of the body. In dynamic analysis if the forces are high and the step is long, kinetic +energy can be imparted to the remaining portion of the model. This problem can be avoided by removing +the elements in a very short transient step prior to the rest of the analysis. This step can be done in a +single increment. +Reactivating stress/displacement elements +types of +reactivation are provided for stress/displacement elements (including +Two distinct +substructures): strain-free reactivation and reactivation with strain. Strain-free reactivation resets the +initial configuration; reactivation with strain does not. +Although elements cannot be created within an analysis, a similar effect can be achieved by creating +elements in the model definition, removing them in the first step, and subsequently reactivating them. +Strain-free reactivation +When stress/displacement elements are reactivated in a strain-free state, they become fully active +immediately at the moment of reactivation (the start of the step in which they are reactivated). They +are reset to an “annealed” state (zero stress, strain, plastic strain, etc.) in the configuration in which +they lie at the start of the reactivation step. This configuration depends on whether a small- or +large-displacement analysis is being conducted. Alternatively, reactivation in a nonvirgin state can be +specified, as described below. +Since these elements are reactivated in a virgin state (i.e., with zero stress), they exert zero nodal +forces on the rest of the model. This result allows reactivation to be done immediately, without an adverse +effect on the smoothness of the solution. +After reactivation the strains and the deformation gradients are based on the displacements +subsequent to the moment of reactivation, rather than on their total displacements. Thus, the current +configuration at the start of the reactivation step is the new initial configuration for the element. +This kind of reactivation usually is used to model the creation of an undeformed and unstrained +region of the model that is sharing a boundary with another, possibly stressed, deformed region. For +example, in tunnel excavation an unstressed tunnel liner is added to line the walls of an already deformed +tunnel . +Input File Usage: +Use the following option to reactivate elements in a strain-free state: +Abaqus/CAE Usage: +*MODEL CHANGE, ADD=STRAIN FREE (default) +Interaction module: Create Interaction: Model Change: Definition: +Region, Activation state of region elements: Reactivated in this step +Small-displacement analysis +In small-displacement analysis the displacements at reactivation are considered to be small; therefore, +volume, mass, initial length, and orientation directions do not change. +Large-displacement analysis +In large-displacement analysis the new configuration can be significantly different from the original +configuration specified in the model definition. The change in configuration may result from large +deformation or rigid body motion. For the nodes of the reactivated elements to be in the correct position +upon reactivation, these nodes must be shared by elements that are not removed. Otherwise, the nodes +of the removed elements remain at the location occupied at the time of removal. For cases where an +enclosed region of material is reactivated, the shared-node restriction may require that a duplicate set +of elements whose material properties do not influence the stress solution be defined on top of the +removed elements. These duplicate elements provide a means of tracking the position of the nodes of +the removed elements. +Upon reactivation an element can have a significantly different volume or mass, so the mass matrix +is reformed for the element. Any local orientations applicable to the element are redefined on the new +configuration. For shell and membrane elements, however, the thickness of the reactivated elements is +the thickness as specified at the start of the analysis by the element’s section definition, a nodal thickness +definition (“Nodal thicknesses,” Section 2.1.3), or an import definition (“Transferring results between +Abaqus analyses: overview,” Section 9.2.1). +The current normals on structural elements at the moment of reactivation become new initial +normals for that element. The current normal is the element’s original normal (as specified in the +model definition) rotated by the nodal rotation at the moment of reactivation. This scheme preserves +the angle between the normals of reactivated elements and those of the elements with which they +share nodes. (Usually, this angle should be zero and the normals should be identical, such as when a +strain-free layer is added to an already deformed shell or beam. This can be achieved by ensuring that +the normals are identical in the model definition.) If the reactivated structural elements share nodes with +only non-structural elements (elements that do not provide stiffness to rotational degrees of freedom), +duplicate structural elements are required so that the rotational degrees of freedom at the shared nodes +will follow the deformation and rigid body motion before reactivation. +In a large-displacement analysis an element that is being reactivated strain free fits into whatever +configuration is given by its nodes at the moment of reactivation. You must ensure that this +configuration is meaningful and is not severely distorted. Abaqus/Standard will apply geometry checks +on the reactivated elements; these checks are the same as the checks that are done in the analysis +input file processor. Warnings are printed in the message file if the elements seem inappropriately +distorted; and error messages are given if the distortion is severe, in which case the analysis will +be stopped. If a geometry check on an element produces a warning or an error message, its current +coordinates—and normals if applicable—are printed to the message file for your inspection. The current +coordinates can be printed for all elements being reactivated by requesting detailed printout for element +removal/reactivation, as explained in “The Abaqus/Standard message file” in “Output,” Section 4.1.1. +Reactivating axisymmetric elements +Abaqus/Standard will not stop the analysis if an axisymmetric element has a very small negative radial +coordinate at reactivation (if the magnitude of the radial coordinate is less than 10−4 times the average +element length). In this case a warning is printed, and a radial coordinate of zero is assumed. If the radial +coordinate is negative and larger than 10−4 times the average element length in magnitude, the analysis +will stop. +For axisymmetric-asymmetric elements (SAXA and CAXA) the displacements at reactivation are +considered small even in large-displacement analysis because these elements require an axisymmetric +original configuration, but the configuration given by the nodes of these elements at reactivation would +not, in general, be axisymmetric. Therefore, the original configuration is assumed not to change for these +elements. +Reactivating coupled temperature-displacement and coupled thermal-electrical-structural elements +In a fully coupled temperature-displacement analysis and a fully coupled thermal-electrical-structural +analysis, continuum elements attain their full mechanical stiffness immediately upon strain-free +reactivation; however, to ensure smoothness of the solution, thermal conductivity is ramped up from +zero over the step. +Reactivating spring elements and substructures +If spring elements or substructures are reactivated “without strain,” the configuration at the moment of +reactivation represents the zero-displacement state of the element; the forces in the spring or substructures +are based on relative displacements subsequent to the moment of reactivation. +Reactivation with strain +Elements reactivated with strain start in an annealed state unless reactivation in a nonvirgin state is +specified, as described below. +The following scheme is implemented for the elements during the reactivation step: Let +represent +the displacements of the nodes of this element, which are the displacements as shared by the rest of the +model or as specified by boundary conditions. In general, these displacements can vary with time over +the reactivation step. At any time in the reactivation step Abaqus/Standard enforces displacements, +, +for the element: +where +is a parameter that ramps linearly from 0 to 1 during the step. Thus, during the step the +displacements felt by the reactivated elements ramp up to their actual values. To produce a consistent +stiffness matrix, the element stiffness is also multiplied by +therefore, the rest of the model +experiences the reactivated elements as though their stiffnesses were ramped up during the step. +; +This ramping up of displacements instead of direct ramping up of element forces ensures that the +strain in the element ramps up from zero to the strain given by the displacement of its nodes. This gradual +ramping up of strains is desirable so that the response of history-dependent materials can be integrated +gradually. +Subsequent to the end of the reactivation step, the strains in reactivated elements correspond to the +displacements of their nodes from their initial configuration, rather than to their displacements since the +moment of reactivation. This is appropriate, for example, in the refueling of a nuclear reactor, where the +new fuel assembly must conform to the distortion of its old neighbors. +This reactivation scheme does not work for the rotations of shell elements that have five degrees of +freedom per node because a total rotation is not stored at those nodes. Consequently, reactivation with +strain is not allowed for these elements. +If an element is reactivated with strain after having been previously reactivated strain free, the strains +are based on the displacements from the configuration in which the element was reactivated strain free +(because this defined the new initial configuration for the element). In this case the +in the formula +above should be interpreted as the displacement of the node relative to the position in which the element +was reactivated strain free. +Input File Usage: +Use the following option to reactivate elements with strain: +Abaqus/CAE Usage: +*MODEL CHANGE, ADD=WITH STRAIN +Interaction module: Create Interaction: Model Change: Definition: +Region, Activation state of region elements: Reactivated in this step; +toggle on Reactivated elements with strain (when applicable) +Reactivating elements with rebar +Rebars are reactivated strain free or with strain exactly like the element in which they are defined. The +annealing that takes place upon reactivation is also applied to rebars in the model. Reactivation of rebars +can also be done in a nonvirgin state. +Reactivating other element types +During reactivation of all element types other than stress/displacement elements, substructures, and +contact elements, the nodal forces caused by stress in the element and by distributed loads are scaled by a +value that ramps from zero to one during the reactivation step. (The nodal fluxes are scaled similarly for +heat transfer elements.) In effect this scaling ramps the element stiffness up from zero during the step; +for elements with mass or damping this scaling also ramps up the mass or damping during the step. +During the reactivation step the thermal conductivity of heat transfer elements and the permeability +of pore pressure elements are ramped up from zero over the step. +User-defined elements can be removed and reactivated. User subroutine UEL is not called in steps +in which the element is being removed or has already been removed. +Input File Usage: +Abaqus/CAE Usage: +*MODEL CHANGE, ADD +Interaction module: Create Interaction: Model Change: Definition: +Region, Activation state of region elements: Reactivated in this step +Removing and reactivating contact pairs +You can remove specified slave and master surfaces from the model in a general analysis step. Contact +pair removal and reactivation is explained in “Removing and reactivating contact pairs” in “Defining +contact pairs in Abaqus/Standard,” Section 35.3.1. +Input File Usage: +Abaqus/CAE Usage: +*MODEL CHANGE, TYPE=CONTACT PAIR, REMOVE or ADD +Use the following option to remove contact pairs: +Interaction module: Create Interaction: Surface-to-surface contact +(Standard) or Self-contact (Standard): toggle off Active in this step +Use the following option to reactivate contact pairs: +Interaction module: Create Interaction: Surface-to-surface contact +(Standard) or Self-contact (Standard): toggle on Active in this step +Removing and reactivating contact elements +Contact elements are removed and reactivated by Abaqus/Standard in the same way as contact pairs, as +described in “Removing and reactivating contact pairs” in “Defining contact pairs in Abaqus/Standard,” +Section 35.3.1. +Input File Usage: +Abaqus/CAE Usage: +*MODEL CHANGE, TYPE=ELEMENT, REMOVE or ADD +Use the following option to remove contact elements: +Interaction module: Create Interaction: Model Change: Definition: +Region, Activation state of region elements: Deactivated in this step +Use the following option to reactivate contact elements: +Interaction module: Create Interaction: Model Change: Definition: +Region, Activation state of region elements: Reactivated in this step +Modeling issues +In some cases element removal/reactivation may cause numerical problems. The following guidelines +can be used to reduce the chance of difficulty: +• If elements are removed in a static stress analysis and this removal leaves a region of the model with +an unconstrained rigid body mode, solver problems will occur and the analysis most likely will fail +to converge. Therefore, ensure that the remainder of the model is constrained sufficiently. +• If elements that are connected to a contact pair are removed, the contact pair should also be removed +to avoid solver problems. +• If all elements attached to a node constrained with a multi-point constraint or a linear constraint +equation are being removed, this node should be the dependent node of the multi-point constraint +or linear constraint equation. +In some cases element removal may cause Abaqus/Standard to report extra unconnected regions in the +message file. These messages can be safely ignored. +Removing or reactivating elements and contact pairs in a restart analysis +Elements or contact pairs can be removed or reactivated in a restart analysis (“Restarting an analysis,” +Section 9.1.1) only if elements or contact pairs were removed or reactivated in the original analysis. In +situations where it is expected that the addition or removal of elements or contact pairs will be required in +a restart analysis, but there is no such need in the original analysis, you must activate element or contact +pair removal/reactivation in the original analysis. Activating this capability does not add or remove any +elements or contact pairs; it only prepares Abaqus/Standard to allow for these changes in a subsequent +restart analysis. +Input File Usage: +the +Use +following +removal/reactivation: +option +to +activate +element +or +contact +pair +Abaqus/CAE Usage: +*MODEL CHANGE, ACTIVATE +Interaction module: Create Interaction: Model Change: +Definition: Restart +Procedures +Elements or contact pairs cannot be removed or reactivated in a linear perturbation step or in a static Riks step . For elements to be absent in such steps, they must have been +inactive at the end of the previous general analysis (nonperturbation) step. +Initial conditions +When elements are added back into the model, they are usually assumed to be “annealed”; that is, +they have zero plastic strain, creep strain, etc. and zero stress at the start of the step in which they are +reactivated. It is possible to reactivate an element so that it starts with a nonzero stress, equivalent plastic +strain, and, if relevant, backstress (in a nonvirgin state). +Reactivation in a nonvirgin state +To reactivate elements with nonzero stress, define initial stress conditions to specify the required stress in the model +definition. Then the elements must be removed in the first step of the analysis. When reactivated, they +will have the initial stress specified. The reactivation is done immediately, so the initial stress (which is +applied in full during the first increment) must be self-equilibrating to avoid convergence issues. +If the elements were not removed in the first step, if they were removed again after the first step, or +if initial conditions were not specified for them, they will have zero stresses when reactivated. +In a similar manner a material can be reactivated with a nonzero initial equivalent plastic strain and, +if relevant, backstress. +When elements are reactivated, any applied initial stress is not displayed in the zero increment +frame. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to specify initial stress conditions: +*INITIAL CONDITIONS, TYPE=STRESS +Use the following option to specify initial equivalent plastic strain and +backstress: +*INITIAL CONDITIONS, TYPE=HARDENING +Use the following options to specify the initial stress conditions: +Load module: Create Predefined Field: Step: Initial, choose Mechanical +for the Category and Stress for the Types for Selected Step +Use the following options to specify the initial equivalent plastic strain and +backstress: +Load module: Create Predefined Field: Step: Initial, choose Mechanical +for the Category and Hardening for the Types for Selected Step +Boundary conditions +The nodal variables of removed elements are not changed when the elements are removed. You can +reset these variables by defining a boundary condition while the elements are inactive . +Loads +Distributed and concentrated loads that are applied in an area where elements are removed or reactivated +may need to be modified. +Distributed loads +Any distributed loads, fluxes, flows, and foundations specified for inactive elements are also inactive. +However, unless you explicitly remove them, records of these loads are still kept and are listed in the data +(.dat) file as though the elements were still present. Continuation of loads across steps is not affected +by removal; on element reactivation unremoved distributed loads are also reactivated. +By default, if a distributed load is applied to an element that is being reactivated in a step, the +distributed load magnitude is scaled up linearly from zero to its end-of-step value during the step. If +such a load is applied with an amplitude reference, the magnitude value given by the amplitude reference +is scaled again by a value that ramps from zero to one throughout the step. This scheme ensures that +reactivation has a smooth effect on the solution, even in cases where a distributed load with an amplitude +reference on a reactivated element is carried over from a previous step. +Concentrated loads +Concentrated loads or fluxes are not removed when the surrounding elements are removed; therefore, +you must ensure that any concentrated loads or fluxes that are carried solely by removed elements are +also removed. Otherwise, a solver problem will occur during the removal step (a force is applied to a +degree of freedom with zero stiffness). Concentrated loads or fluxes should be ramped up when they are +reintroduced along with reactivated elements. +Predefined fields +The nodal variables of removed elements are not changed directly when the elements are removed. You +can reset these variables by defining temperature or other predefined field variables while the elements +are inactive . For example, elements that are removed in a +stress/displacement analysis can be reintroduced at a different temperature by setting the temperatures +at the nodes on these elements to the desired value while the elements are inactive due to removal. +Temperatures +The temperatures at the start of the reactivation step become the initial temperatures for reactivated +elements; thermal strains (and, thus, also the thermal stresses) are based on the temperature change +subsequent to the instant of reactivation . +Material options +On annealing, compaction-related quantities—such as the yield stress in hydrostatic compression, +, +in crushable foam plasticity (“Crushable foam plasticity models,” Section 23.3.5); the yield stress in +hydrostatic compression, +, in cap plasticity (“Modified Drucker-Prager/Cap model,” Section 23.3.2); +and the void volume fraction, f, in porous metal plasticity (“Porous metal plasticity,” Section 23.2.9)—are +reset to the values they had at the start of the analysis. +For porous materials the porosity, n, is reset to its initial value and the saturation, s, retains its value +from the instant of removal . +Elements with a user-defined material type can be removed and reactivated; user subroutines UMAT +and UMATHT are not called while the elements are inactive. On reactivation the stresses and strains in +user subroutine UMAT are set to zero, and conductivity and heat fluxes defined in user subroutine UMATHT +are ramped up from zero during the reactivation step. Solution-dependent state variables must be reset +in user subroutine UMAT, UMATHT, or SDVINI, which will be called on reactivation. +Elements +Removal is not currently supported for rigid, cohesive, gasket, and piezoelectric elements. All other +element types in Abaqus/Standard can be removed and reactivated. See “Choosing the appropriate +element for an analysis type,” Section 27.1.3. +Output +Output is not available for elements or contact surfaces that have been removed. Inactive elements and +contact surfaces are visible in Abaqus/CAE. +Input file template +*HEADING +… +*STEP +*STATIC +… +** Remove all elements in element set SIDE +*MODEL CHANGE, REMOVE +SIDE, +** Remove contact pair (SLAVE1, MASTER1) +*MODEL CHANGE, TYPE=CONTACT PAIR, REMOVE +SLAVE1, MASTER1 +… +*END STEP +** +*STEP +*STATIC +… +** Reactivate elements in element set SIDE +*MODEL CHANGE, ADD=STRAIN FREE +SIDE, +** Reactivate contact pair (SLAVE1, MASTER1) +*MODEL CHANGE, TYPE=CONTACT PAIR, ADD +SLAVE1, MASTER1 +… +*END STEP +11.3 +Geometric imperfections +• “Introducing a geometric imperfection into a model,” Section 11.3.1 +INTRODUCING A GEOMETRIC IMPERFECTION INTO A MODEL +GEOMETRIC IMPERFECTIONS +Products: Abaqus/Standard Abaqus/Explicit +References +• “Unstable collapse and postbuckling analysis,” Section 6.2.4 +• *IMPERFECTION +Overview +A geometric imperfection pattern: +• is generally introduced in a model for a postbuckling load-displacement analysis; +• can be defined as a linear superposition of buckling eigenmodes obtained from a previous eigenvalue +buckling prediction or eigenfrequency extraction analysis performed with Abaqus/Standard; +• can be based on the solution obtained from a previous static analysis performed with +Abaqus/Standard; or +• can be specified directly. +General postbuckling analysis +In Abaqus/Standard the Riks method (“Unstable collapse and postbuckling analysis,” Section 6.2.4) can +be used to solve postbuckling problems, both with stable and unstable postbuckling behavior. However, +the exact postbuckling problem often cannot be analyzed directly due to the discontinuous response +(bifurcation) at the point of buckling. To analyze a postbuckling problem, you must turn it into a problem +with continuous response instead of bifurcation, which can be accomplished by introducing a geometric +imperfection pattern in the “perfect” geometry so that there is some response in the buckling mode before +the critical load is reached. +Introducing geometric imperfections +Imperfections are usually introduced by perturbations in the geometry. Abaqus offers three ways to +define an imperfection: as a linear superposition of buckling eigenmodes, from the displacements +of a static analysis, or by specifying the node number and imperfection values directly. Only the +translational degrees of freedom are modified. Abaqus will then calculate the normals using the usual +algorithm based on the perturbed coordinates. Unless the precise shape of an imperfection is known, +an imperfection consisting of multiple superimposed buckling modes can be introduced (“Eigenvalue +buckling prediction,” Section 6.2.3). +The usual approach involves two analysis runs with the same model definition, using +Abaqus/Standard to establish the probable collapse modes and either Abaqus/Standard or +Abaqus/Explicit to perform the postbuckling analysis: +1. In the first analysis run perform an eigenvalue buckling analysis with Abaqus/Standard on the +“perfect” structure to establish probable collapse modes and to verify that the mesh discretizes those +modes accurately. Write the eigenmodes in the default global system to the results file as nodal data +(“Output to the data and results files,” Section 4.1.2). +2. In the second analysis run use Abaqus/Standard or Abaqus/Explicit to introduce an imperfection +in the geometry by adding these buckling modes to the “perfect” geometry. The lowest buckling +modes are frequently assumed to provide the most critical imperfections, so usually these are scaled +and added to the perfect geometry to create the perturbed mesh. The imperfection thus has the form +where +is the +mode shape and +is the associated scale factor. +You must choose the scale factors of the various modes; usually (if the structure is not +imperfection sensitive) the lowest buckling mode should have the largest factor. The magnitudes +of the perturbations used are typically a few percent of a relative structural dimension such as a +beam cross-section or shell thickness. +3. Use either Abaqus/Standard or Abaqus/Explicit to perform the postbuckling analysis. +• In Abaqus/Standard perform a geometrically nonlinear load-displacement analysis of the +structure containing the imperfection using the Riks method. In this way the Riks method can +be used to perform postbuckling analyses of “stiff” structures that show linear behavior prior +to buckling, if perfect. By performing a load-displacement analysis, other important nonlinear +effects, such as material inelasticity or contact, can be included. +• In Abaqus/Explicit perform a postbuckling analysis on the perturbed structure. +Abaqus imports imperfection data through the user node labels. Abaqus does not check model +compatibility between both analysis runs. Node set definitions in the original model and the model with +the imperfection may be different. Care must be taken for models in which Abaqus generates additional +nodes (for example, the nodes generated for contact surfaces on 20-node brick elements). In such cases +you have to ensure that the models for both analysis runs are identical and that the nodal information for +the generated nodes is written to the results file. +If the model is defined in terms of an assembly of part instances, the part (.prt) file from the +original analysis is required to read the eigenmodes from the results file. Both the original model and the +subsequent model must be defined consistently in terms of an assembly of part instances. +Defining an imperfection based on eigenmode data +To define an imperfection based on the superposition of weighted mode shapes, specify the results file and +step from a previous eigenfrequency extraction or eigenvalue buckling prediction analysis. Optionally, +you can import eigenmode data for a specified node set. +Input File Usage: +*IMPERFECTION, FILE=results_file, STEP=step, NSET=name +Defining an imperfection based on static analysis data +To define an imperfection based on the deformed geometry of a previous static analysis (“Unstable +collapse and postbuckling analysis,” Section 6.2.4), specify the results file and step (and, optionally, +the increment number) from a previous static analysis. (If the increment number is not specified, Abaqus +will read data from the last increment available for the specified step in the results file.) Optionally, you +can import modal data for a specified node set. +Input File Usage: +*IMPERFECTION, FILE=results_file, STEP=step, INC=inc, NSET=name +Defining an imperfection directly +You can specify the imperfection directly as a table of node numbers and coordinate perturbations in the +global coordinate system or, optionally, in a cylindrical or spherical coordinate system. Alternatively, +you can read the imperfection data from a separate input file. +Input File Usage: +*IMPERFECTION, SYSTEM=name, INPUT=input file +If no input file is specified, Abaqus assumes that the data follow the option. +Imperfection sensitivity +The response of some structures depends strongly on the imperfections in the original geometry, +particularly if the buckling modes interact after buckling occurs. Hence, imperfections based on a single +buckling mode tend to yield nonconservative results. By adjusting the magnitude of the scaling factors +of the various buckling modes, the imperfection sensitivity of the structure can be assessed. Normally, +a number of analyses should be conducted to investigate the sensitivity of a structure to imperfections. +Structures with many closely spaced eigenmodes tend to be imperfection sensitive, and imperfections +with shapes corresponding to the eigenmode for the lowest eigenvalue may not give the worst case. +The imperfect structure will be easier to analyze if the imperfection is large. If the imperfection +is small, the deformation will be quite small (relative to the imperfection) below the critical load. The +response will grow quickly near the critical load, introducing a rapid change in behavior. +On the other hand, if the imperfection is large, the postbuckling response will grow steadily before +the critical load is reached. In this case the transition into postbuckled behavior will be smooth and +relatively easy to analyze. +Input file template +The following example illustrates a postbuckling analysis of a structure with an imperfection defined by +a linear superposition of the buckling eigenmodes and involves two analysis runs with the same model +definition. +The initial analysis run performs an eigenvalue buckling analysis with Abaqus/Standard to establish +the probable collapse modes and writes them to the results file. +*HEADING +Initial analysis run to write the buckling modes to the results file +*NODE +Data lines to define initial “perfect” geometry +… +** +*STEP +*BUCKLE +Data lines to define the number of buckling eigenmodes +*CLOAD and/or *DLOAD and/or *DSLOAD and/or *TEMPERATURE +Data lines to specify the reference load, +*NODE FILE, GLOBAL=YES, LAST MODE=n +*END STEP +The second analysis run introduces the imperfection and performs a postbuckling analysis +employing the modified Riks method in Abaqus/Standard. +*HEADING +Second analysis run to define the imperfection and perform the postbuckling analysis +*NODE +Data lines to define initial “perfect” geometry +… +*IMPERFECTION, FILE=results_file, STEP=step +Data lines specifying the mode number and its associated scale factor +… +** +*STEP, NLGEOM +*STATIC, RIKS +Data line to define incrementation and stopping criteria +*CLOAD and/or *DLOAD and/or *DSLOAD and/or *TEMPERATURE +Data lines to specify reference loading, +*END STEP +An alternative second analysis run introduces the imperfection and performs a postbuckling analysis +with Abaqus/Explicit. +*HEADING +Second analysis run to define the imperfection and perform the postbuckling analysis +*NODE +Data lines to define initial “perfect” geometry +… +*IMPERFECTION, FILE=results_file, STEP=step +Data lines specifying the mode number and its associated scale factor +… +** +*STEP +*DYNAMIC, EXPLICIT +Data line to define the time period of the step. +*CLOAD and/or *DLOAD and/or *DSLOAD and/or *TEMPERATURE +*END STEP +11.4 +Fracture mechanics +• “Fracture mechanics: overview,” Section 11.4.1 +• “Contour integral evaluation,” Section 11.4.2 +• “Crack propagation analysis,” Section 11.4.3 +11.4.1 +FRACTURE MECHANICS: OVERVIEW +Abaqus/Standard provides the following methods for performing fracture mechanics studies: +• Onset of cracking: The onset of cracking can be studied in quasi-static problems by using contour +integrals (“Contour integral evaluation,” Section 11.4.2). The J-integral, the +-integral (for creep), +the stress intensity factors for both homogeneous materials and interfacial cracks, the crack propagation +direction, and the T-stress are calculated by Abaqus/Standard. Contour integrals can be used in two- or +three-dimensional problems. In these types of problems focused meshes are generally required and the +propagation of a crack is not studied. +• Crack propagation: The crack propagation capability allows quasi-static, +including low-cycle +fatigue, crack growth along predefined paths to be studied (“Crack propagation analysis,” Section 11.4.3). +Cracks debond along user-defined surfaces. Several crack propagation criteria are available, and +multiple cracks can be included in the analysis. Contour integrals can be requested in crack propagation +problems. +• Line spring elements: Part-through cracks in shells can be modeled inexpensively by using line +spring elements in a static procedure, as explained in “Line spring elements for modeling part-through +cracks in shells,” Section 32.9.1. +• Extended finite element method (XFEM): XFEM models a crack as an enriched feature by adding +degrees of freedom in elements with special displacement functions (“Modeling discontinuities as an +enriched feature using the extended finite element method,” Section 10.7.1). XFEM does not require the +mesh to match the geometry of the discontinuities. It can be used to simulate initiation and propagation +of a discrete crack along an arbitrary, solution-dependent path without the requirement of remeshing. +XFEM can also be used to perform contour integral evaluation without the need to refine the mesh around +the crack tip. +11.4.2 +CONTOUR INTEGRAL EVALUATION +Products: Abaqus/Standard Abaqus/CAE +References +• “Fracture mechanics: overview,” Section 11.4.1 +• *CONTOUR INTEGRAL +• “Using contour integrals to model fracture mechanics,” Section 31.2 of the Abaqus/CAE User’s +Manual +Overview +Abaqus/Standard offers the evaluation of several parameters for fracture mechanics studies based +on either the conventional finite element method or the extended finite element method (XFEM, +see “Modeling discontinuities as an enriched feature using the extended finite element method,” +Section 10.7.1): +• the J-integral, which is widely accepted as a quasi-static fracture mechanics parameter for linear +material response and, with limitations, for nonlinear material response; +• the +-integral, which has an equivalent role to the J-integral in the context of time-dependent +creep behavior (“Rate-dependent plasticity: creep and swelling,” Section 23.2.4) in a quasi-static +step (“Quasi-static analysis,” Section 6.2.5); +• the stress intensity factors, which are used in linear elastic fracture mechanics to measure the strength +of the local crack-tip fields; +• the crack propagation direction—i.e., the angle at which a preexisting crack will propagate; and +• the T-stress, which represents a stress parallel to the crack faces and is used as an indicator of the +extent to which parameters like the J-integral are useful characterizations of the deformation field +around the crack. +Contour integrals: +• are output quantities—they do not affect the results; +• can be requested only in general analysis steps; +• can be used only with two-dimensional quadrilateral elements or three-dimensional brick elements +when used with the conventional finite element method; +• can be evaluated without requiring a detailed refined mesh around the crack tips when used with +XFEM; and +• are currently available only for first-order or second-order tetrahedron and first-order brick elements +with isotropic elastic material when used with XFEM. +Contour integral evaluation +Abaqus/Standard offers two different ways to evaluate the contour integral. The first approach is based +on the conventional finite element method, which typically requires you to conform the mesh to the +cracked geometry, to explicitly define the crack front, and to specify the virtual crack extension direction. +Detailed focused meshes are generally required, and obtaining accurate contour integral results for a +crack in a three-dimensional curved surface can be quite cumbersome. The extended finite element +method (XFEM) alleviates these shortcomings. XFEM does not require the mesh to match the cracked +geometry. The presence of a crack is ensured by the special enriched functions in conjunction with +additional degrees of freedom. This approach also removes the requirement for explicitly defining the +crack front or specifying the virtual crack extension direction when evaluating the contour integral. The +data required for the contour integral are determined automatically based on the level set signed distance +functions at the nodes in an element . +Several contour integral evaluations are possible at each location along a crack. In a finite element +model each evaluation can be thought of as the virtual motion of a block of material surrounding the crack +tip (in two dimensions) or surrounding each node along the crack line (in three dimensions). Each block +is defined by contours, where each contour is a ring of elements completely surrounding the crack tip or +the nodes along the crack line from one crack face to the opposite crack face. These rings of elements +are defined recursively to surround all previous contours. +Abaqus/Standard automatically finds the elements that form each ring from the regions defined as +the crack tip or crack line. Each contour provides an evaluation of the contour integral. The possible +number of evaluations is the number of such rings of elements. You must specify the number of contours +to be used in calculating contour integrals. In addition, you must specify the type of contour integral to +be calculated, as described below. By default, Abaqus/Standard calculates the J-integral. +You can assign a name to a crack that is used to identify the contour integral values in the data +file and in the output database file. The name is also used by Abaqus/CAE to request contour integral +output. If you are using the conventional finite element method and do not specify a crack name, by +default Abaqus/Standard generates crack numbers that follow the order in which the cracks are defined. +If you are using XFEM, you must set the crack name equal to the name assigned to the enriched feature. +Input File Usage: +Use the follow option to evaluate the contour integral with the conventional +finite element method: +*CONTOUR INTEGRAL, CRACK NAME=crack name, +CONTOURS=n, TYPE=integral_type +Abaqus/CAE Usage: +Use the following option to evaluate the contour integral with XFEM: +*CONTOUR INTEGRAL, CRACK NAME=crack name, XFEM, +CONTOURS=n, TYPE=integral_type +Interaction module: Special→Crack→Create: Name: crack +name, Type: Contour integral or XFEM +Step module: history output request editor: Domain: Crack: crack +name, Number of contours: n, Type: integral_type +The domain integral method +Using the divergence theorem, the contour integral can be expanded into an area integral in two +dimensions or a volume integral in three dimensions, over a finite domain surrounding the crack. This +domain integral method is used to evaluate contour integrals in Abaqus/Standard. The method is quite +robust in the sense that accurate contour integral estimates are usually obtained even with quite coarse +meshes. The method is robust because the integral is taken over a domain of elements surrounding the +crack and because errors in local solution parameters have less effect on the evaluated quantities such +as J, +, the stress intensity factors, and the T-stress. +Requesting multiple contour integrals +Contour integrals at several different crack tips in two dimensions or along several different crack lines in +three dimensions can be evaluated at any time by repeating the contour integral request as often as needed +in the step definition. When you are using the conventional finite element method, you must specify the +crack front and the direction of virtual crack extension (or the normal to the crack plane if this normal +is constant) for each crack tip or crack line, as described below. When you are using XFEM, you do not +need to specify the crack front or the virtual crack extension direction because they will be determined by +Abaqus/Standard. However, you must set each crack name equal to the corresponding enriched feature, +with each enriched feature consisting of only one crack. In addition, regardless of whether you are using +either the conventional finite element method or XFEM, you must specify the number of contours to be +calculated for each integral. +The J -integral +The J-integral is usually used in rate-independent quasi-static fracture analysis to characterize the energy +release associated with crack growth. It can be related to the stress intensity factor if the material response +is linear. +The J-integral is defined in terms of the energy release rate associated with crack advance. For a +in the plane of a three-dimensional fracture, the energy release rate is given +virtual crack advance +by +where +line, +is a surface element along a vanishing small tubular surface enclosing the crack tip or crack +is given by +is the local direction of virtual crack extension. +is the outward normal to +, and +For elastic material behavior W is the elastic strain energy; for elastic-plastic or elasto-viscoplastic +material behavior W is defined as the elastic strain energy density plus the plastic dissipation, thus +representing the strain energy in an “equivalent elastic material.” Therefore, the J-integral calculated +is suitable only for monotonic loading of elastic-plastic materials. +Input File Usage: +Abaqus/CAE Usage: +*CONTOUR INTEGRAL, CONTOURS=n, TYPE=J +Step module: history output request editor: Domain: Crack: crack +name, Number of contours: n, Type: J-integral +Domain dependence +The J-integral should be independent of the domain used provided that the crack faces are parallel to +each other, but J-integral estimates from different rings may vary because of the approximate nature of +the finite element solution. Strong variation in these estimates, commonly called domain dependence +or contour dependence, typically indicates an error in the contour integral definition. Gradual variation +in these estimates may indicate that a finer mesh is needed or, if plasticity is included, that the contour +integral domain does not completely include the plastic zone. If the “equivalent elastic material” is not a +good representation of the elastic-plastic material, the contour integrals will be domain independent only +if they completely include the plastic zone. Since it is not always possible to include the plastic zone in +three dimensions, a finer mesh may be the only solution. +If the first contour integral is defined by specifying the nodes at the crack tip, the first few contours +may be inaccurate. To check the accuracy of these contours, you can request more contours and determine +the value of the contour integral that appears approximately constant from one contour to the next. The +contour integral values that are not approximately equal to this constant should be discarded. In linear +elastic problems the first and second contours typically should be ignored as inaccurate. +For some three-dimensional models with an open crack front, the J-integral estimates may be +inaccurate from the node sets (or elements in the case with XFEM) at the crack front ends. The +resolution difficulty is compounded by the skewness of the outmost layer of elements. This accuracy +loss is confined only to the contour integrals at the front ends and has no effect on the accuracy of the +contour integral values at the neighboring node sets (or elements in the case with XFEM) along the +crack front. +Including the effect of a residual stress field on J-integral evaluation +A residual stress field often occurs in a structure; for example, as a result of service loads that produce +plasticity, a metal forming process in the absence of an anneal treatment, thermal effects, or swelling +effects. When the residual stresses are significant, the standard definition of the J-integral as described +above may lead to a path-dependent value. To ensure its path independence, the J-integral evaluation +must include an additional term that accounts for the residual stress field. +In Abaqus/Standard the +problem with a residual stress field is treated as an initial strain problem. If the total strain is written as +the sum of mechanical strain, +, and initial strain, +; i.e., +a path-independent energy release rate in the presence of a residual stress field is given by +where V is the domain volume enclosing the crack tip or crack line, W is defined as the mechanical strain +energy density only, +and +remains constant during the entire deformation. +The residual stress field can be specified by reading the stress data from a previous analysis step or +by defining an initial condition . You specify the step number from which the stress data in the +last available increment of the specified step will be considered as residual stresses. If the step number +is set equal to zero (default), the residual stress field is defined by the initial condition definition. When +XFEM is used, the residual stress field can be defined only with an initial condition definition. +*CONTOUR INTEGRAL, RESIDUAL STRESS STEP=n, TYPE=J +Step module: history output request editor: Domain: Crack: +crack name, Number of contours: n, Step for residual stress +initialization values: step, Type: J-integral +Abaqus/CAE Usage: +Input File Usage: +The Ct -integral +The Ct -integral is supported with the conventional finite element method; however, it is not supported +with XFEM. +The +-integral can be used for time-dependent creep behavior, where it characterizes creep crack +deformation under certain creep conditions, including transient crack growth. +is, for example, +proportional to the rate of growth of the crack-tip/crack-line creep zone for a stationary crack under +small-scale creep conditions. Under steady-state creep conditions, when creep dominates throughout +the specimen, +-integrals should be requested only +in a quasi-static step. +becomes path independent and is known as +. +The +-integral is obtained by replacing the displacements with velocities and the strain energy +density with the strain energy rate density in the J-integral expansion. The strain energy rate density is +defined as +is not uniquely defined if multiple deformation mechanisms contribute to the strain rate. However, the +creep mechanism will dominate within a zone surrounding a crack tip or crack line, so elastic and plastic +contributions to +are negligible. The size of that zone depends on the extent of creep relaxation: the +zone is initially small but eventually encompasses the entire specimen when steady-state creep is reached. +Abaqus/Standard considers only creep in the calculation of +. Neglecting elastic and plastic strain rates, +the strain energy density for the power law creep model with time hardening form in Abaqus/Standard is +where n is the power law exponent, q is the equivalent Mises stress, and is the equivalent uniaxial strain +rate. +For the hyperbolic-sine law an analytical expression of +is +obtained by numerical integration; a five-point Gauss quadrature scheme gives reasonable accuracy in +the range of realistic creep strain rates. +is not available. For this law +The domain integral method is used for +For user-defined creep laws the strain energy rate density must be defined in user subroutine CREEP. +*CONTOUR INTEGRAL, CONTOURS=n, TYPE=C +Step module: history output request editor: Domain: Crack: crack +name, Number of contours: n, Type: Ct-integral +-integrals as described above for J-integrals. +Abaqus/CAE Usage: +Input File Usage: +Domain dependence +Prior to steady state +-integral estimates will exhibit domain dependence, even if the finite element mesh +is sufficiently refined, because of the assumption of creep dominance within the domain specified. These +estimate corresponding to a +contour shrunk onto the crack tip or crack line . +estimates should be extrapolated to zero radius to obtain an improved +Including the effect of a residual stress field on +-integral evaluation +An additional term is included to account for the residual stress field when calculating the +as described in “Including the effect of a residual stress field on J-integral evaluation.” +-integral, +Input File Usage: +Abaqus/CAE Usage: +*CONTOUR INTEGRAL, RESIDUAL STRESS STEP=n, TYPE=C +Step module: history output request editor: Domain: Crack: +crack name, Number of contours: n, Step for residual stress +initialization values: step, Type: Ct-integral +The stress intensity factors +The stress intensity factors +are usually used in linear elastic fracture mechanics to +characterize the local crack-tip/crack-line stress and displacement fields. They are related to the energy +release rate (the J-integral) through +, and +, +where +factor matrix. For homogeneous, isotropic materials +are the stress intensity factors and +is called the pre-logarithmic energy +is diagonal, and the above equation simplifies to +where +For an interfacial crack between two dissimilar isotropic materials, +for plane stress and +for plane strain, axisymmetry, and three dimensions. +where +for plane strain, axisymmetry, and three dimensions; and +for plane +stress. Unlike their analogues in a homogeneous material, +are no longer the pure Mode I +and Mode II stress intensity factors for an interfacial crack. They are simply the real and imaginary parts +of a complex stress intensity factor. +and +Although the energy release rate is calculated directly in Abaqus/Standard, it is usually not +straightforward to compute stress intensity factors from a known J-integral for mixed-mode problems. +Abaqus/Standard provides an interaction integral method to compute the stress intensity factors directly +for a crack under mixed-mode loading. This capability is available for linear isotropic and anisotropic +materials. The theory is described in detail in “Stress intensity factor extraction,” Section 2.16.2 of the +Abaqus Theory Manual. +In this case the J-integrals calculated from the stress intensity factors will also be output. These +J-integral values may be slightly different from those estimated by requesting the J-integral directly, due +to the different algorithms used for the calculations. +Input File Usage: +Abaqus/CAE Usage: +*CONTOUR INTEGRAL, CONTOURS=n, TYPE=K FACTORS +Step module: history output request editor: Domain: Crack: crack name, +Number of contours: n, Type: Stress intensity factors +Domain dependence +The stress intensity factors have the same domain dependence features as the J-integral. +Including the effect of a residual stress field on stress intensity factor evaluation +An additional term is included to account for the residual stress field when calculating the stress intensity +factors, as described in “Including the effect of a residual stress field on J-integral evaluation.” +Input File Usage: +*CONTOUR INTEGRAL, RESIDUAL STRESS STEP=n, +TYPE=K FACTORS +Abaqus/CAE Usage: +Step module: history output request editor: Domain: Crack: crack name, +Number of contours: n, Step for residual stress initialization +values: step, Type: Stress intensity factors +The crack propagation direction +For homogeneous, isotropic elastic materials the direction of cracking initiation can be calculated using +one of the following three criteria: the maximum tangential stress criterion, the maximum energy release +rate criterion, or the +is not taken into account in any of these criteria. +criterion. +The maximum tangential stress criterion +Using either the condition +(where r and +crack tip in a plane orthogonal to the crack line), we can obtain +or +are polar coordinates centered at the +where the crack propagation angle +the crack propagation in the “straight-ahead” direction. +The crack propagation angle is measured from to ; i.e., it is measured about the direction +counterclockwise measured from in Figure 11.4.2–1. +The crack propagation angle will be output. +is measured with respect to the crack plane and +, while +if +if +represents +. +, or +Input File Usage: +*CONTOUR INTEGRAL, CONTOURS=n, TYPE=K FACTORS, +DIRECTION=MTS +Abaqus/CAE Usage: +Step module: history output request editor: Domain: Crack: crack name, +Number of contours: n, Type: Stress intensity factors, Crack +initiation criterion: Maximum tangential stress +The maximum energy release rate criterion +This criterion postulates that a crack initially propagates in the direction that maximizes the energy release +rate. +The crack propagation angle will be output. +Input File Usage: +*CONTOUR INTEGRAL, CONTOURS=n, TYPE=K FACTORS, +DIRECTION=MERR +Abaqus/CAE Usage: +Step module: history output request editor: Domain: Crack: crack name, +Number of contours: n, Type: Stress intensity factors, Crack +initiation criterion: Maximum energy release rate +The KII = 0 criterion +This criterion assumes that a crack initially propagates in the direction that makes +. +The crack propagation angle will be output. +Input File Usage: +*CONTOUR INTEGRAL, CONTOURS=n, TYPE=K FACTORS, +DIRECTION=KII0 +Abaqus/CAE Usage: +Step module: history output request editor: Domain: Crack: crack +name, Number of contours: n, Type: Stress intensity factors, +Crack initiation criterion: K11=0 +The T -stress +The T-stress component represents a stress parallel to the crack faces at the crack tip. Its magnitude can +alter not only the size and shape of the plastic zone but also the stress triaxiality ahead of the crack tip. +It is, therefore, a useful indicator of whether measures of the strength of the crack-tip singularity (such +as the J-integral or the stress intensity factors) are useful in characterizing a crack under a particular +loading. In a linear elastic analysis the T-stress should be calculated using loads equal to the loads in +the elastic-plastic analysis. See “T -stress extraction,” Section 2.16.3 of the Abaqus Theory Manual, for +more information. +Input File Usage: +Abaqus/CAE Usage: +*CONTOUR INTEGRAL, CONTOURS=n, TYPE=T-STRESS +Step module: history output request editor: Domain: Crack: crack +name, Number of contours: n, Type: T-stress +Domain dependence +In general, the T-stress has larger domain dependence or contour dependence than the J-integral and the +stress intensity factors. Numerical tests suggest that the estimates from the first two rings of elements +abutting the crack tip or crack line generally do not provide accurate results. Sufficient contours +extending from the crack tip or crack line should be chosen so that the T-stress can be determined to +be independent of the number of contours, within engineering accuracy. Particularly for axisymmetric +models, the closer the crack tip is to the symmetry axis, the more refined the mesh in the domain should +be to achieve path independence of the contour integral. +Including the effect of a residual stress field on T -stress evaluation +An additional term is included to account for the residual stress field when calculating the T -stress, as +described in “Including the effect of a residual stress field on J-integral evaluation.” +Input File Usage: +Abaqus/CAE Usage: +*CONTOUR INTEGRAL, RESIDUAL STRESS STEP=n, TYPE=T-STRESS +Step module: history output request editor: Domain: Crack: +crack name, Number of contours: n, Step for residual stress +initialization values: step, Type: T-stress +Defining the data required for a contour integral with the conventional finite element method +To request contour integral output with the conventional finite element method, you must define the crack +front and specify the virtual crack extension direction. +Defining the crack front +You must specify the crack front; i.e., the region that defines the first contour. Abaqus/Standard uses this +region and one layer of elements surrounding it to compute the first contour integral. An additional layer +of elements is used to compute each subsequent contour. +The crack front can be equivalent to the crack tip in two dimensions or the crack line in three +dimensions; or it can be a larger region surrounding the crack tip or crack line, in which case it must +include the crack tip or crack line. +If blunted crack tips are modeled, the crack front should include all the nodes going from one crack +face to the other that would collapse onto the crack tip if the radius of the blunted tip were reduced to +zero. Otherwise, the contour integral value will depend on the path until the contour region reaches the +parallel crack faces. +Input File Usage: +*CONTOUR INTEGRAL, CONTOURS=n +Specify the crack front node set name on the data line; the format depends +on the method you use to specify the virtual crack extension direction. +For two-dimensional cases only one crack front node set (the crack front at the +crack tip) must be specified. For three-dimensional cases you must repeat the +data line to specify the crack front for each node (or cluster of focused nodes) +along the crack line in order from one end of the crack to the other, including +the midside nodes of second-order elements; it is not permissible to skip nodes +along the crack line. +Abaqus/CAE Usage: +Interaction module: Special→Crack→Create: select the crack front +Defining the crack tip or crack line +By default, Abaqus/Standard defines the crack tip as the first node specified for the crack front and the +crack line as the sequence of first nodes specified for the crack front. The first node is the node with the +smallest node number, unless the node set is generated as unsorted. Alternatively, you can specify the +crack-tip node or crack-line nodes directly. This specification plays a critical role for a three-dimensional +crack with a blunt crack tip. +Abaqus/CAE cannot determine the crack tip or crack line automatically based on the specified crack +front. However, if you select a point to define the crack front in two dimensions, the same point defines +the crack tip; likewise, if you select edges to define the crack front in three dimensions, the same edges +define the crack line. For all other cases you must define the crack tip or crack line directly. +Input File Usage: +Use the following option to specify the crack-tip nodes directly: +*CONTOUR INTEGRAL, CONTOURS=n, CRACK TIP NODES +Specify the crack front node set name and the crack tip node number +or node set name on the data line; the format depends on the method +you use to specify the virtual crack extension direction. +Repeat the data line for three-dimensional cases. +Abaqus/CAE Usage: +Interaction module: Special→Crack→Create: select the crack front, then +select the crack tip (in two dimensions) or crack line (in three dimensions) +Defining a closed-loop crack line +Sometimes a crack line may form a closed loop (for example, when modeling a full penny-shaped crack +without invoking symmetry conditions). In such cases the finite element mesh in the crack-tip region +can be created with or without seams; i.e., linear constraint equations (“Linear constraint equations,” +Section 34.2.1) or multi-point constraints (“General multi-point constraints,” Section 34.2.2) may or may +not be used to tie two layers of nodes together. +If a crack line forms a closed loop, the starting node set of the crack front can be chosen arbitrarily +and the other node sets defining the crack front must go around the crack front sequentially. The last node +set defining the crack front must be the same as the first node set. If a closed loop is formed by creating +coincident nodes that are then tied together by linear constraint equations and multi-point constraints, the +node sets must be specified in order starting from one of the node sets involved in the constraint equation +or multi-point constraint and terminating with the other node set. +Specifying the virtual crack extension direction +You must specify the direction of virtual crack extension at each crack tip in two dimensions or at each +node along the crack line in three dimensions by specifying either the normal to the crack plane, +, or +the virtual crack extension direction, +. +If the virtual crack extension direction is specified to point into the material (parallel to the crack +faces), the J-integral values calculated will be positive. Negative J-integral values are obtained when +the virtual crack extension direction is specified in the opposite direction. +Specifying the normal to the crack plane +The virtual crack extension direction can be defined by specifying the normal, +this case Abaqus/Standard will calculate a virtual crack extension direction, +crack front tangent, +crack; for a two-dimensional crack, we simply have +implies that the crack plane is flat since only one value of +. As shown in Figure 11.4.2–1, +and +, and the normal, +, to the crack plane. In +, that is orthogonal to the +for a three-dimensional +. Specifying the normal +can be given per contour integral. +Input File Usage: +Abaqus/CAE Usage: +*CONTOUR INTEGRAL, CONTOURS=n, NORMAL +), +), +-direction cosine (or +-direction cosine (or +-direction cosine +(or blank) +crack front node set name (2-D) or names (3-D) +Interaction module: Special→Crack→Create: select the crack front: +Specify crack extension direction using: Normal to crack plane +Specifying the virtual crack extension direction +, can be specified directly. In three dimensions the +Alternatively, the virtual crack extension direction, +virtual crack extension direction, +, will be corrected to be orthogonal to any normal defined at a node +or in other cases to the tangent to the crack line itself. The tangent, +, to the crack line at a particular +point is obtained by parabolic interpolation through the crack front for which the virtual crack extension +1/4 point nodes +crack plane +Crack front +node set +Crack front node set. +See section A-A below. +Figure 11.4.2–1 Typical focused mesh for fracture mechanics evaluation. +vector is defined and the nearest node sets on either side of this region. Abaqus/Standard will normalize +the virtual crack extension direction, +. +Section A-A +*CONTOUR INTEGRAL, CONTOURS=n +crack front node set name, +cosine (or +), +-direction cosine (or blank) +-direction cosine (or +), +-direction +11.4.2–12 +Repeat the data line for three-dimensional cases to specify the crack front and +virtual crack extension vector for each node (or cluster of focused nodes) along +the crack line. +Abaqus/CAE Usage: +Interaction module: Special→Crack→Create: select the crack front: +Specify crack extension direction using: q vectors +Defining surface normals +In a case where the crack front intersects the external surface of a three-dimensional solid, where there +is a surface of material discontinuity in the model, or where the crack is in a curved shell, the virtual +crack extension direction, +, must lie in the plane of the surface for accurate contour integral evaluation. +Surface normals should be specified at all nodes that lie on such surfaces within the contours requested for +this purpose (these nodes are printed out under the “Contour Integral” information in the data file). For +shell element models the normals can be specified with the nodal coordinates if the normals calculated by +Abaqus/Standard are not adequate. For solid element models the normals can be specified either directly + or using the nodal coordinates +(the fourth–sixth coordinates). If surface normals are not specified for the nodes on the crack surfaces and +the external surfaces at the ends of a crack line, Abaqus/Standard will calculate the normals automatically +for these nodes to correct any inadequate virtual crack extension directions, +. +Defining the data required for a contour integral with XFEM +If you are using XFEM to evaluate the contour integral, both the crack front and the virtual crack +extension direction are determined by Abaqus/Standard. +Symmetry with the conventional finite element method +If the crack is defined on a symmetry plane, only half the structure needs to be modeled. The change +in potential energy calculated from the virtual crack front advance is doubled to compute the correct +contour integral values. +Input File Usage: +Use the following option to indicate that the crack is defined on a symmetry +plane: +Abaqus/CAE Usage: +*CONTOUR INTEGRAL, CONTOURS=n, SYMM +Interaction module: Special→Crack→Create: select the crack front and +crack tip or crack line, and specify the crack extension direction: General: +toggle on On symmetry plane (half-crack model) +Constructing a fracture mechanics mesh for small-strain analysis with the conventional finite +element method +Sharp cracks (where the crack faces lie on top of one another in the undeformed configuration) are +usually modeled using small-strain assumptions. Focused meshes, as shown in Figure 11.4.2–1, should +normally be used for small-strain fracture mechanics evaluations. However, for a sharp crack the strain +field becomes singular at the crack tip. This result is obviously an approximation to the physics; however, +the large-strain zone is very localized, and most fracture mechanics problems can be solved satisfactorily +using only small-strain analysis. +The crack-tip strain singularity depends on the material model used. Linear elasticity, perfect +plasticity, and power-law hardening are commonly used in fracture mechanics analysis. Power-law +hardening has the form +is the equivalent total strain, +where +stress, n is the power-law hardening exponent (typically in the range of 3 to 8; +perfect plasticity for large ), and +is a reference strain, +is a material constant (typically in the range 0.5 to 1.0). +is the Mises stress, +is the initial yield +is very close to +Results for pure power-law nonlinear elastic materials in a body under traction loading are +proportional to the load to some power. Therefore, the fracture parameters for one geometry under a +particular load can be scaled to any other load of the same distribution but different magnitude. +If the loading is proportional (the direction of the stress increase in stress space is approximately +constant) and monotonically increasing, power-law hardening deformation plasticity and incremental +plasticity are essentially equivalent. However, deformation plasticity is a nonlinear elastic material for +which more analytical results are available. Abaqus uses the Ramberg-Osgood form of deformation +plasticity ; this model is not a pure power law model, +which must be considered. +Creating the singularity +In most cases the singularity at the crack tip should be considered in small-strain analysis (when +geometric nonlinearities are ignored). +Including the singularity often improves the accuracy of the +J-integral, the stress intensity factors, and the stress and strain calculations because the stresses and +strains in the region close to the crack tip are more accurate. If r is the distance from the crack tip, the +strain singularity in small-strain analysis is +for linear elasticity, +for perfect plasticity, and +for power-law hardening. +Modeling the crack-tip singularity in two dimensions +The square root and +crack tip is modeled with a ring of collapsed quadrilateral elements, as shown in Figure 11.4.2–2. +singularity can be built into a finite element mesh using standard elements. The +-1 +-1 +a, b, c +isoparametric space +physical space +Figure 11.4.2–2 Collapsed two-dimensional element. +To obtain a mesh singularity, generally second-order elements are used and the elements are +collapsed as follows: +1. Collapse one side of an 8-node isoparametric element (CPE8R, for example) so that all three +nodes—a, b, and c—have the same geometric location (on the crack tip). +2. Move the midside nodes on the sides connected to the crack tip to the 1/4 point nearest the crack +tip. You can create “quarter point” spacing with second-order isoparametric elements when you +generate nodes for a region of a mesh; see “Creating quarter-point spacing” in “Node definition,” +Section 2.1.1. +This procedure will create the strain singularity +The +singularity cannot be created using Abaqus elements, but the combination of the +and +terms can provide a reasonable approximation for +. +collapsed, and the two coincident nodes are free to displace independently, a +If 4-node isoparametric elements (for example, CPE4R) are used, one side of the element is +singularity is created. +If the crack region is meshed with linear elements, the position specified for the midside nodes is +ignored. +Creating a square root singularity +If nodes a, b, and c are constrained to move together, +singular (suitable for linear elasticity). +and the strains and stresses are square root +Input File Usage: +*NFILL, SINGULAR +Constrain the collapsed nodes to move together by specifying the same node +number in the list of nodes forming the element or by using a linear constraint +equation or multi-point constraint to tie them together. +Interaction module: Special→Crack→Create: select the crack front and +crack tip, and specify the crack extension direction: Singularity: Midside +node parameter: 0.25, Collapsed element side, single node +Abaqus/CAE Usage: +Creating a 1/r singularity +If the midside nodes remain at the midside points rather than being moved to the 1/4 points and nodes +a, b, and c are allowed to move independently, only the +singularity in strain is created (suitable for +perfect plasticity). +Input File Usage: +Abaqus/CAE Usage: +*NFILL +Interaction module: Special→Crack→Create: select the crack front and +crack tip, and specify the crack extension direction: Singularity: Midside +node parameter: 0.5, Collapsed element side, duplicate nodes +Creating a combined square root and 1/r singularity +If the midside nodes are moved to the 1/4 points but nodes a, b, and c are allowed to move independently, +the singularity created is a combination of the square root and +singularities. This combination is +usually best for a power-law hardening material. However, since the +singularity dominates, moving +the midside nodes to the 1/4 points gives only slightly better results than if the nodes are left at the midside +points. Since creating a mesh with the midside nodes moved to the quarter points can be difficult, it is +often best to simply use the +singularity. +Input File Usage: +Abaqus/CAE Usage: +*NFILL, SINGULAR +Interaction module: Special→Crack→Create: select the crack front and +crack tip, and specify the crack extension direction: Singularity: Midside +node parameter: 0.25, Collapsed element side, duplicate nodes +Modeling the crack-tip singularity in three dimensions +To create singular fields, 20-node bricks and 27-node bricks can be used with a collapsed face .The planes of the three-dimensional elements perpendicular to the crack line should be +planar for the best accuracy. If they are not planar, the element Jacobian may become negative at some +integration points when the midside nodes are moved to the 1/4 points. To correct this problem, move +the midside nodes slightly away from the 1/4 points toward the midpoint position (the distance moved +is not critical). +See “Meshing the crack region and assigning elements,” Section 31.2.7 of the Abaqus/CAE User’s +Manual, for information on creating a three-dimensional fracture mechanics mesh in Abaqus/CAE. +C3D20(RH) +midplane +edge plane +2 nodes collapsed +to the same location +crack line +3 nodes collapsed +to the same location +midside nodes +moved to 1/4 pts. +Figure 11.4.2–3 Collapsed three-dimensional element. +Creating a square root singularity +To obtain a square root singularity, constrain the nodes on the collapsed face of the edge planes to move +together and move the nodes to the 1/4 points. +If the nodes at the midplane of a collapsed 20-node brick are constrained to move together, +; +therefore, the singularity is not the same on the midplane as on an edge plane. This difference causes local +oscillations in the solution about the crack tip along the crack line, although normally the oscillations are +not significant. +If all midface nodes and the centroid node are included in a 27-node brick and the midside and +midface nodes are moved to the 1/4 points closest to the crack line, the oscillation in the local stress and +strain fields can be reduced. +Input File Usage: +Abaqus/CAE Usage: +*NFILL, SINGULAR +Constrain the collapsed nodes to move together by specifying the same node +number in the list of nodes forming the element or by using a linear constraint +equation or multi-point constraint to tie them together. +Interaction module: Special→Crack→Create: select the crack front and +crack line, and specify the crack extension direction: Singularity: Midside +node parameter: 0.25, Collapsed element side, single node +Creating a 1/r singularity +To obtain a +keep the midside nodes at the midpoints. +singularity, allow the three nodes on the collapsed face to displace independently and +Input File Usage: +Abaqus/CAE Usage: +*NFILL +Interaction module: Special→Crack→Create: select the crack front and +crack line, and specify the crack extension direction: Singularity: Midside +node parameter: 0.5, Collapsed element side, duplicate nodes +Creating a combined square root and 1/r singularity +To obtain a combined square root and +singularity, allow the nodes on the collapsed face to displace +independently and move the midside nodes to the 1/4 points. As in the two-dimensional case, if it is +difficult to create the mesh with the nodes moved to the 1/4 points, simply use the +singularity. +Input File Usage: +Abaqus/CAE Usage: +*NFILL, SINGULAR +Interaction module: Special→Crack→Create: select the crack front and +crack line, and specify the crack extension direction: Singularity: Midside +node parameter: 0.25, Collapsed element side, duplicate nodes +Mesh refinement +the smaller the radial +The size of the crack-tip elements influences the accuracy of the solutions: +dimension of the elements from the crack tip, the better the stress, strain, etc. results will be and, +therefore, the better the contour integral calculations will be. +The angular strain dependence is not modeled with the singular elements. Reasonable results are +obtained if typical elements around the crack tip subtend angles in the range of 10° (accurate) to 22.5° +(moderately accurate). +Since the crack tip causes a stress concentration, the stress and strain gradients are large as the crack +tip is approached. Path dependence in the evaluation of the J-integral may be an indication that the mesh +is not sufficiently refined, but path independence does not prove mesh convergence. The finite element +mesh must be refined in the vicinity of the crack to get accurate stresses and strains; however, accurate +J-integral results can frequently be obtained even with a relatively coarse mesh. +In many cases if sufficiently fine meshes are used, accurate contour integral values can be obtained +without using singular elements. +Modeling the crack-tip region in shells +Focused meshes can be used, but not all of the three-dimensional shell elements in Abaqus/Standard can +be collapsed. Elements S8R and S8RT cannot be degenerated into triangles; element types S4, S4R, +S4R5, S8R5, and S9R5 can. +The quarter-point technique (moving the midside nodes to the quarter points to give a +singularity for elastic fracture mechanics applications) can be used with S8R5 and S9R5 elements but +not with S8R(T) elements. When the quarter-point technique is used with S9R5 elements, the midface +node should be moved to the quarter-point position along with the two midside nodes. +If S8R(T) elements are used, a keyhole should be introduced at the crack tip. +Flaws lying in the plane through the thickness of a shell can be modeled using line spring elements; +see “Line spring elements for modeling part-through cracks in shells,” Section 32.9.1. In many cases line +spring elements provide accurate J-integral and stress intensity values, but these elements are limited to +modeling small strain and rotations. Limited modeling of plasticity is also allowed with line springs. +Constructing a fracture mechanics mesh for finite-strain analysis with the conventional finite +element method +In large-strain analysis (when geometric nonlinearities are included) singular elements should not +normally be used. The mesh must be sufficiently refined to model the very high strain gradients around +the crack tip if details in this region are required. Even if only the J-integral is required, the deformation +around the crack tip may dominate the solution and the crack-tip region will have to be modeled with +sufficient detail to avoid numerical problems. +, where +Physically, the crack tip is not perfectly sharp. Therefore, it is normally modeled as a blunted notch +with a radius of +is a characteristic dimension of the plastic zone ahead of the crack +tip. The notch must be small enough that, at the loads of interest, the deformed shape of the notch no +longer depends on the original geometry. Typically, the notch must blunt out to more than four times +its original radius for the deformed shape to be independent of the original geometry. The size of the +elements around the notch should be about 1/10 the notch-tip radius to obtain accurate results. +If a crack is modeled as sharp, the finite elements near the crack tip may not be able to approximate +the high gradients, resulting in convergence problems. The stress and strain results around the crack tip +will probably be inaccurate even if convergence is achieved. However, if the solution converges, the +contour integral results should be reasonably accurate. The convergence difficulties will probably be +greater in three dimensions than in two dimensions. +In situations involving finite rotations but small strains, such as bending of slender structures, a +small “keyhole” around the crack tip should be modeled. If the hole is small, the results will not be +affected significantly and problems in dealing with the singular strains at the crack tip will be avoided. +Using constraints with the conventional finite element method +General multi-point constraints and linear constraint equations (“Kinematic constraints: overview,” +Section 34.1.1) should not be used on nodes in the mesh regions where contour integrals are calculated +unless the nodes involved in the constraint are located at the same point. The nodes at the crack +tip of a focused mesh can be tied together using multi-point constraints without adversely affecting +the contour integral calculations. Tying these nodes will change the singularity at the crack tip, but +path independence of the contour integral will be maintained. In addition, path independence of the +contour integrals will not be affected if two faces of a model are joined using MPC type TIE or a +linear constraint equation, provided that all nodes of the two faces are coincident. Using multi-point +constraints for mesh refinement or for applying symmetry/antisymmetry boundary conditions within +the contour integral region will result in path dependence of the contour integrals. No warning or error +messages are provided if this rule is violated. +Procedures +You can request contour integrals in fracture mechanics problems that were modeled using the following +procedures: +• static (“Static stress analysis,” Section 6.2.2) with both XFEM and the conventional finite element +methods; +• quasi-static (“Quasi-static analysis,” Section 6.2.5) with the conventional finite element method +only; +• steady-state transport (“Steady-state transport analysis,” Section 6.4.1) with the conventional finite +element method only; +• coupled thermal-stress procedures (“Fully coupled thermal-stress analysis,” Section 6.5.3) with the +conventional finite element method only; and +• crack propagation (“Crack propagation analysis,” Section 11.4.3) with the conventional finite +element method only. +Contour integrals can be requested only in general analysis steps: they are not calculated in linear +perturbation analyses (“General and linear perturbation procedures,” Section 6.1.3). +A crack analysis with pressure applied on the crack surfaces may give inaccurate contour integral +values if geometric nonlinearity is included in a step. +Loads +Contour integral calculations include the following distributed load types: +• thermal loads; +• distributed loads, including crack face pressure and traction loads on continuum elements as well +as those applied using user subroutine DLOAD and UTRACLOAD; +• distributed loads, including surface traction loads and crack face edge loads on shell elements as +well as those applied using user subroutine UTRACLOAD; +• uniform and nonuniform body forces; and +• centrifugal loads on continuum and shell elements. +Contributions to the contour integral due to concentrated loads in the domain are not included; +instead, the mesh must be modified to include a small element and a distributed load must be applied to +this element. +Contributions due to contact forces are not included. +Material options +J-integral calculations are valid for linear elastic, nonlinear elastic, and elastic-plastic materials. Plastic +behavior can be modeled as nonlinear elastic (“Deformation plasticity,” Section 23.2.13), but the results +are generally best if the material is modeled by incremental plasticity and is subject to proportional, +monotonic traction loading. +If unloading has taken place in the plastic zone around the crack tip, the J-integral will not be valid +except in very limited cases. +The +-integral is valid for problems involving creep (“Rate-dependent plasticity: creep and +swelling,” Section 23.2.4). +The stress intensity factor calculation is valid for cracks in homogeneous, linear elastic materials. +It is also valid for an interfacial crack between two different isotropic linear elastic materials. It is not +valid for any other types of materials, including user-defined materials. +The crack propagation direction is valid only for homogeneous, isotropic linear elastic materials. +The T-stress is valid only for homogeneous, isotropic linear elastic materials. Although the T-stress +is calculated using the linear elastic material properties of the body with a crack, it is usually used with the +J-integral calculated using the elastic-plastic material properties of the body . +If there is material discontinuity, the normal to the material discontinuity line must be specified for +all nodes on the material discontinuity that will lie in a contour integral domain. The normal can be +specified by defining user-specified normals for the +elements on both sides of the discontinuity or by using nodal normal coordinates for the nodes on the +discontinuity. Contour integral calculations cannot be performed for a crack with a material discontinuity +line passing through its tip (except for an interfacial crack between two different materials). Therefore, +you should be careful when specifying a normal that is not perpendicular to the virtual crack extension +direction, +, for the nodes at the crack tip. +Elements +When used with XFEM, the contour integral can be evaluated only in first-order or second-order +tetrahedron and first-order brick elements. The following paragraphs apply only to the conventional +finite element method. +The contour integral evaluation capability in Abaqus/Standard assumes that the elements that lie +within the domain used for the calculations are quadrilaterals in two-dimensional or shell models or bricks +in continuum three-dimensional models. Triangles, tetrahedra, or wedges should not be used in the mesh +that is included in the contour integral regions. When the elements around the crack tip are generated +in Abaqus/CAE, triangular elements (in two dimensions) or wedge elements (in three dimensions) are +converted to collapsed quadrilateral or hexahedral elements. The elements within the contour domain +should be of the same type. +In shell structures the contour integrals calculated by Abaqus/Standard will be contour independent +only if the deformation mode around the crack tip is primarily membrane. If there are significant bending +or transverse shear effects in the domain, the contour integrals may not be contour independent and +contour integral values should be obtained directly from the displacements and/or the stresses. +Generalized plane strain elements, generalized axisymmetric elements with twist, asymmetric- +axisymmetric elements, membrane elements, and cylindrical elements should not be used in the contour +integral regions. +The contribution of rebar is included only in the calculations of the J-integral and the +-integral +for shell elements defined with a shell section integrated during the analysis . +Output +The domain associated with each contour is calculated automatically. The nodes belonging to each +domain can be printed in the data file; see “Controlling the amount of analysis input file processor +information written to the data file” in “Output,” Section 4.1.1. If you are using the conventional contour +integral method, for each domain Abaqus/Standard creates a new node set in the output database to +In addition, new node sets are +include these nodes; you can view these node sets in Abaqus/CAE. +created in the output database for nodes on crack surfaces and on free surfaces whose nodal normals are +calculated by Abaqus/Standard. +Contour integrals cannot be recovered from the restart file as described in “Output,” Section 4.1.1. +You should not request element output extrapolated to the nodes (“Element output” in “Output +to the data and results files,” Section 4.1.2) for second-order elements with one collapsed side in two +dimensions or one collapsed face in three dimensions. +Default contour integral output +By default, the contour integral values are written to the data file and to the output database file. The +following naming convention is used for contour integrals written to the output database: +integral-type: abbrev-integral-type at history-output-request-name_crack-name_internal- +crack-tip-node-set-name__Contour_contour-number +where integral-type can be +• Crack propagation direction (Cpd) +• J-integral (J) +• J-integral estimated from Ks (JKs) +• Stress intensity factor K1 (K1) +• Stress intensity factor K2 (K2) +• T-stress (T) +For example, +J-integral: J at JINT_CRACK_CRACKTIP-1__Contour_1 +Writing the contour integrals to the results file +You can choose to write the contour integral values to the results file in addition to the data file. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to write the contour integrals to the results file instead +of the data file: +*CONTOUR INTEGRAL, CONTOURS=n, OUTPUT=FILE +Use the following option to write the contour integrals to the results file in +addition to the data file: +*CONTOUR INTEGRAL, CONTOURS=n, OUTPUT=BOTH +You cannot write contour integrals to the results file from Abaqus/CAE. +Controlling the output frequency +You can control the output frequency, in increments, of contour integrals. By default, the crack-tip +location and associated quantities will be printed every increment. Specify an output frequency of 0 to +suppress contour integral output. +The output frequency for contour integral output to the output database is controlled by the larger +of the frequency values specified for history output to the output database (see “Output to the output +database,” Section 4.1.3) or for contour integral output. If you specify an output frequency of 0 for the +history output to the output database, contour integral values will not be written to the output database. +Input File Usage: +*CONTOUR INTEGRAL, CRACK NAME=crack name, +CONTOURS=n, FREQUENCY=f +Abaqus/CAE Usage: +Step module: history output request editor: Domain: Crack: crack +name, Number of contours: n, Save output at +11.4.3 +CRACK PROPAGATION ANALYSIS +Products: Abaqus/Standard Abaqus/Explicit +References +• “Defining an analysis,” Section 6.1.2 +• “Fracture mechanics: overview,” Section 11.4.1 +• “Low-cycle fatigue analysis using the direct cyclic approach,” Section 6.2.7 +• “Surface-based cohesive behavior,” Section 36.1.10 +• *COHESIVE BEHAVIOR +• *CONTACT CLEARANCE +• *DEBOND +• *DIRECT CYCLIC +• *FRACTURE CRITERION +• *NODAL ENERGY RATE +• “Defining surface-to-surface contact in an Abaqus/Standard analysis” in “Defining surface-to- +surface contact,” Section 15.13.7 of the Abaqus/CAE User’s Manual +Overview +Crack propagation analysis: +• allows for six types of fracture criteria in Abaqus/Standard—critical stress at a certain distance +ahead of the crack tip, critical crack opening displacement, crack length versus time, VCCT (the +Virtual Crack Closure Technique), enhanced VCCT, and the low-cycle fatigue criterion based on +the Paris law; +• allows for the VCCT fracture criterion in Abaqus/Explicit; +• in Abaqus/Standard models quasi-static crack growth in two dimensions (planar and axisymmetric) +for all types of fracture criteria and in three dimensions (solid, shells, and continuum shells) for +VCCT, enhanced VCCT, and the low-cycle fatigue criteria; and +• in Abaqus/Explicit models crack growth in three dimensions (solid, shells, and continuum shells) +for VCCT criterion; and +• requires that you define two distinct initially bonded contact surfaces between which the crack will +propagate. +Defining initially bonded crack surfaces in Abaqus/Standard +Potential crack surfaces are modeled as slave and master contact surfaces . Any contact formulation except the finite-sliding, surface-to-surface +formulation can be used. The predetermined crack surfaces are assumed to be initially partially bonded +so that the crack tips can be identified explicitly by Abaqus/Standard. Initially bonded crack surfaces +cannot be used with self-contact. +Define an initial condition to identify which part of the crack is initially bonded. You specify the +slave surface, the master surface, and a node set that identifies the initially bonded part of the slave +surface. The unbonded portion of the slave surface will behave as a regular contact surface. Either the +slave surface or the master surface must be specified; if only the master surface is given, all of the slave +surfaces associated with this master surface that have nodes in the node set will be bonded at these nodes. +If a node set is not specified, the initial contact conditions will apply to the entire contact pair; in +this case, no crack tips can be identified, and the bonded surfaces cannot separate. +If a node set is specified, the initial conditions apply only to the slave nodes in the node set. +Abaqus/Standard checks to ensure that the node set defined includes only slave nodes belonging to the +contact pair specified. +By default, the nodes in the node set are considered to be initially bonded in all directions. +*INITIAL CONDITIONS, TYPE=CONTACT +Input File Usage: +Bonding only in the normal direction +For fracture criteria based on the critical stress, critical crack opening displacement, or crack length +versus time, it is possible to bond the nodes in the node set (or the contact pair if a node set is not defined) +only in the normal direction. In this case the nodes are allowed to move freely tangential to the contact +surfaces. Friction (“Frictional behavior,” Section 36.1.5) cannot be specified if the nodes are bonded +only in the normal direction. +Bonding only in the normal direction is typically used to model bonded contact conditions in Mode I +crack problems where the shear stress ahead of the crack along the crack plane is zero. +Input File Usage: +*INITIAL CONDITIONS, TYPE=CONTACT, NORMAL +Activating the crack propagation capability in Abaqus/Standard +The crack propagation capability must be activated within the step definition to specify that crack +propagation may occur between the two surfaces that are initially partially bonded. You specify the +surfaces along which the crack propagates. +If the crack propagation capability is not activated for partially bonded surfaces, the surfaces will not +separate; in this case the specified initial contact conditions would have the same effect as that provided +by the tied contact capability, which generates a permanent bond between two surfaces during the entire +analysis . +Input File Usage: +*DEBOND, SLAVE=slave_surface_name, MASTER=master_surface_name +Propagation of multiple cracks +Cracks can propagate from either a single crack tip or multiple crack tips. The crack propagation +capability in Abaqus/Standard requires that the surfaces be initially partially bonded so that the crack +tips can be identified. A contact pair can have crack propagation from multiple crack tips. However, +only one crack propagation criterion is allowed for a given contact pair. Crack propagation along +several contact pairs can be modeled by specifying multiple crack propagation definitions. +Defining and activating crack propagation in Abaqus/Explicit +In Abaqus/Explicit potential crack surfaces are modeled as bonded general contact surfaces . Hence, the +capability is available in three-dimensional analyses only and is implemented using a pure master-slave +formulation. As is the case in Abaqus/Standard, the predetermined crack surfaces are assumed to be +initially partially bonded so that the crack tips can be identified explicitly. +interactions in Abaqus/Explicit,” Section 35.4.1) +To identify which pair of surfaces determine the crack and which part of the crack is initially bonded, +you must define and assign a contact clearance . You first define a contact clearance to specify the node set that is +initially bonded, and then you assign this contact clearance to a pair of two single-sided surfaces that +define the crack. The unbonded portion behaves as a regular contact surface. The nodes in the node set +are considered to be initially bonded in all directions. +The crack tip is identified only from the specified two surfaces and the node set. No attempt is made +to determine a crack tip from all surfaces included in the general contact domain. Consequently, to be +able to identify the crack tip, the surface including the specified node set must extend past the node set. +Otherwise, the surfaces will not debond, and the crack cannot propagate. +You complete the definition of the crack propagation capability by defining a fracture-based +cohesive behavior surface interaction. You activate the crack propagation by assigning it to the pair of +surfaces that are initially partially bonded. +If the fracture criterion is met, crack propagation occurs +between these two surfaces. Cohesive behavior is also used to specify the elastic behavior of the bonds +. +If a fracture-based surface interaction is not assigned to a pair of surfaces, the crack definition +is incomplete. Unlike Abaqus/Standard where the identified nodes will stay bonded if the crack is not +activated, in Abaqus/Explicit the nodes identified by the contact clearance definition will separate without +generating any interface stress. +Similar to Abaqus/Standard, cracks can propagate from single or multiple crack tips for the same +pair of surfaces. +Input File Usage: +Use the following options: +*CONTACT CLEARANCE, NAME=clearance_name, +SEARCH NSET=bonded_nset_name +** +*SURFACE INTERACTION, NAME=interaction_name +*COHESIVE BEHAVIOR +*FRACTURE CRITERION +..** +*CONTACT +*CONTACT CLEARANCE ASSIGNMENT +slave_surface, master_surface, clearance_name +*CONTACT PROPERTY ASSIGNMENT +slave_surface, master_surface, interaction_name +Specifying a fracture criterion +You can specify the crack propagation criteria, as discussed below. Table 11.4.3–1 shows which criteria +are supported by Abaqus/Standard and Abaqus/Explicit. Only one crack propagation criterion is allowed +per contact pair even if multiple cracks are present. +Table 11.4.3–1 +Crack propagation criterion +Abaqus/Standard +Abaqus/Explicit +Critical stress +Critical crack opening +displacement +Crack length versus time +VCCT +Enhanced VCCT +Low-cycle fatigue +Yes +Yes +Yes +Yes +Yes +Yes +No +No +No +Yes +No +No +Crack propagation analysis is carried out on a nodal basis. The crack-tip node debonds when the +fracture criterion, f, reaches the value 1.0 within a given tolerance: +and +where +for other fracture criteria. You can specify the tolerance +for VCCT, enhanced VCCT, and low-cycle fatigue criteria or +. In Abaqus/Standard, if +, the time increment is cut back such that the crack propagation criterion is satisfied except +in the case of an unstable crack growth problem where multiple nodes at and ahead of a crack tip are +allowed to debond without the cut back of increment size in one increment. The default value of +is +0.1 for the critical stress, critical crack opening displacement, and crack length versus time criteria and +is 0.2 for the VCCT, enhanced VCCT, and low-cycle fatigue criteria. +Input File Usage: +*FRACTURE CRITERION, TOLERANCE= +, TYPE=type +Critical stress criterion +This criterion is available only in Abaqus/Standard. +If you specify a critical stress criterion at a critical distance ahead of the crack tip, the crack-tip node +debonds when the local stress across the interface at a specified distance ahead of the crack tip reaches a +critical value. +This criterion is typically used for crack propagation in brittle materials. The critical stress criterion +is defined as +is the normal component of stress carried across the interface at the distance specified; +are the shear stress components in the interface; and +where +and +stresses, which you must specify. The second component of the shear failure stress, +a two-dimensional analysis; therefore, the value of +when the fracture criterion, f, reaches the value 1.0. +are the normal and shear failure +, is not relevant in +need not be specified. The crack-tip node debonds +and +If the value of +is not given or is specified as zero, it will be taken to be a very large number so +that the shear stress has no effect on the fracture criterion. +The distance ahead of the crack tip is measured along the slave surface, as shown in Figure 11.4.3–1. +The stresses at the specified distance ahead of the crack tip are obtained by interpolating the values at +the adjacent nodes. The interpolation depends on whether first-order or second-order elements are used +to define the slave surface. +unbonded portion +bonded portion +slave surface +master surface +current +crack tip +distance ahead +of the crack tip +Figure 11.4.3–1 Distance specification for the critical stress criterion. +Input File Usage: +*FRACTURE CRITERION, TYPE=CRITICAL STRESS, DISTANCE=n +Critical crack opening displacement criterion +This criterion is available only in Abaqus/Standard. +If you base the crack propagation analysis on the crack opening displacement criterion, the crack-tip +node debonds when the crack opening displacement at a specified distance behind the crack tip reaches +a critical value. This criterion is typically used for crack propagation in ductile materials. +The crack opening displacement criterion is defined as +is the measured value of crack opening displacement and +where +is the critical value of the crack +opening displacement (user-specified). The crack-tip node debonds when the fracture criterion reaches +the value 1.0. +You must supply the crack opening displacement versus cumulative crack length data. +In +Abaqus/Standard the cumulative crack length is defined as the distance between the initial crack tip and +the current crack tip measured along the slave surface in the current configuration. The crack opening +displacement is defined as the normal distance separating the two faces of the crack at the given distance. +You specify the position, n, behind the crack tip where the critical crack opening displacement is +calculated. The value of this position must be specified as the length of the straight line joining the +current crack tip and points on the slave and master surfaces (Figure 11.4.3–2). +Distance, n, from crack tip +to point x on the slave surface +Measured +crack opening +displacement +value, δ +crack tip +Figure 11.4.3–2 Distance specification for the critical +crack opening displacement criterion. +Abaqus/Standard computes the crack opening displacement at that point by interpolating the values +at the adjacent nodes. The interpolation depends on whether first-order or second-order elements are +used to define the slave surface. An error message will be issued if the value of n is not within the end +points of the contact pair. +Input File Usage: +*FRACTURE CRITERION, TYPE=COD, DISTANCE=n +Modeling symmetry +In problems where the debonding surfaces lie on a symmetry plane, you can specify that Abaqus/Standard +should consider only half of the user-specified crack opening displacement values. In this case the initial +bonding must be in the normal direction only . +*FRACTURE CRITERION, TYPE=COD, DISTANCE=n, SYMMETRY +Input File Usage: +Crack length versus time criterion +This criterion is available only in Abaqus/Standard. +To specify the crack propagation explicitly as a function of total time, you must provide a crack +length versus time relationship and a reference point from which the crack length is measured. This +reference point is defined by specifying a node set. Abaqus/Standard finds the average of the current +positions of the nodes in the set to define the reference point. During crack propagation the crack length is +measured from this user-specified reference point along the slave surface in the deformed configuration. +The time specified must be total time, not step time. +The fracture criterion, f, is stated in terms of the user-specified crack length and the length of the +current crack tip. The length of the current crack tip from the reference point is measured as the sum +of the straight line distance of the initial crack tip from the reference point and the distance between the +initial crack tip and the current crack tip measured along the slave surface. +Referring to Figure 11.4.3–3, let node 1 be the initial location of the crack tip and node 3 be the +current location of the crack tip. The distance of the current crack tip located at node 3 is given by +where +between nodes 1 and 2, and +is the length of the straight line joining node 1 and the reference point, +is the distance +is the distance between nodes 2 and 3 measured along the slave surface. +The fracture criterion, f, is given by +where l is the length at the current time obtained from the user-specified crack length versus time curve. +Crack-tip node 3 will debond when the failure function f reaches the value of 1.0 (within the user-defined +tolerance). +If geometric nonlinearity is considered in the step (“Defining an analysis,” Section 6.1.2), the +reference point may move as the body deforms; you must ensure that this movement does not invalidate +the crack length versus time criterion. +Abaqus/Standard does not extrapolate beyond the end points of your crack data. Therefore, if +the first crack length specified is greater than the distance from the crack reference point to the first +slave +surface +master +surface +length +±ftol +Δl23 +Δl23 +Δl12 +l1 +reference point +reference node set +Figure 11.4.3–3 Crack propagation as a function of time. +time +bonded node, the first bonded node will never debond and the crack will not propagate. In this case +Abaqus/Standard will print warning messages in the message (.msg) file. +Input File Usage: +*FRACTURE CRITERION, TYPE=CRACK LENGTH, NSET=name +VCCT criterion +This criterion is available in both Abaqus/Standard and Abaqus/Explicit. +The Virtual Crack Closure Technique (VCCT) criterion uses the principles of linear elastic fracture +mechanics (LEFM) and, therefore, is appropriate for problems in which brittle crack propagation occurs +along predefined surfaces. +VCCT is based on the assumption that the strain energy released when a crack is extended by a +certain amount is the same as the energy required to close the crack by the same amount. For example, +Figure 11.4.3–4 illustrates the similarity between crack extension from i to j and crack closure at j. +In Figure 11.4.3–5 nodes 2 and 5 will start to release when +is the Mode I energy release rate, +where +is the length of the elements at the crack front, +is the vertical displacement between nodes 1 and 6. Assuming that the crack closure is governed by linear +elastic behavior, the energy to close the crack (and, thus, the energy to open the crack) is calculated from +the previous equation. Similar arguments and equations can be written in two dimensions for Mode II +and for three-dimensional crack surfaces including Mode III. +is the critical Mode I energy release rate, b is the width, d +is the vertical force between nodes 2 and 5, and +δ a +crack closed +i j +δ a +i + j +Figure 11.4.3–4 Mode I: The energy released when a crack is extended by a certain +amount is the same as the energy required to close the crack. +In the general case involving Mode I, II, and III the fracture criterion is defined as +is the equivalent strain energy release rate calculated at a node, and +is the critical +where +equivalent strain energy release rate calculated based on the user-specified mode-mix criterion and the +bond strength of the interface. The crack-tip node will debond when the fracture criterion reaches the +value of 1.0. +v1,6 +y, v +1 +x, u +Fv,2,5 crit +Load +Fv,2,5 +Load +Fv,2,5 +5 + 4 +2 + 3 +Area = G dbIC +V2,5 crit +Displacement +V2,5 +Figure 11.4.3–5 Pure Mode I modified. +Abaqus provides three common mode-mix formulae for computing +: the BK law, the power +law, and the Reeder law models. The choice of model is not always clear in any given analysis; an +appropriate model is best selected empirically. +BK law +The BK law model is described in Benzeggagh (1996) by the following formula: +To define this model, you must provide +and . This model provides a power law +relationship combining energy release rates in Mode I, Mode II, and Mode III into a single scalar fracture +criterion. +Input File Usage: +*FRACTURE CRITERION, TYPE=VCCT, MIXED MODE +BEHAVIOR=BK +Power law +The power law model is described in Wu (1965) by the following formula: +To define this model, you must provide +and +. +Input File Usage: +*FRACTURE CRITERION, TYPE=VCCT, MIXED MODE +BEHAVIOR=POWER +Reeder law +The Reeder law model is described in Reeder (2002) by the following formula: +To define this model, you must provide +when +applies only to three-dimensional problems. +. When +and . The Reeder law is best applied +, the Reeder law reduces to the BK law. The Reeder law +Input File Usage: +*FRACTURE CRITERION, TYPE=VCCT, MIXED MODE +BEHAVIOR=REEDER +Releasing multiple nodes in one increment in Abaqus/Standard +For an unstable crack growth problem, sometimes it is more efficient to allow multiple nodes at and +ahead of a crack tip to debond in one increment without cutting back the increment size when the VCCT +fracture criterion is satisfied. This capability is activated automatically if you specify an unstable growth +tolerance, +. In this case if the fracture criterion, f, is within the given unstable growth tolerance: +where +is the tolerance described earlier in this section, rather than cut back the increment size, more +nodes at and ahead of the crack tip are allowed to debond in one increment until +for all the nodes +ahead of the crack tip. The forces at those debonded nodes are completely released immediately during +the following increment. If you do not specify a value for the unstable growth tolerance, the default +value is infinity. In this case the fracture criterion, f, for unstable crack growth is not limited by any +upper-bound value in the above equation. +Input File Usage: +*FRACTURE CRITERION, TYPE=VCCT, +UNSTABLE GROWTH TOLERANCE= +Defining variable critical energy release rates +You can define a VCCT criterion with varying energy release rates by specifying the critical energy +release rates at the nodes. +If you indicate that the nodal critical energy rates will be specified, any constant critical energy +release rates you specify are ignored, and the critical energy release rates are interpolated from the nodes. +The critical energy release rates must be defined at all nodes on the slave surface. +Input File Usage: +Use both of the following options: +*FRACTURE CRITERION, TYPE=VCCT, NODAL ENERGY RATE +*NODAL ENERGY RATE +Enhanced VCCT criterion +This criterion is available only in Abaqus/Standard. +The enhanced VCCT criterion is very similar to the original VCCT criterion described above. As +in the original VCCT criterion, the fracture criterion in the general case involving Mode I, II, and III is +defined as +The crack-tip node debonds when the fracture criterion reaches the value of 1.0. However, unlike the +original VCCT criterion, you can specify two different critical fracture energy release rates: +for the +onset of a crack and +for the growth of a crack. When the enhanced VCCT criterion is used in the +general case involving Mode I, II, and III fracture, the amount of energy dissipated associated with the +release of the debonding force is controlled by the critical equivalent strain energy release rate required to +propagate the crack, +, rather than by the critical equivalent strain energy release rate required to +initiate the crack, +for different mixed-mode fracture criteria. +are identical to those used for +The formulae for calculating +Input File Usage: +*FRACTURE CRITERION, TYPE=ENHANCED VCCT +Low-cycle fatigue criterion +This criterion is available only in Abaqus/Standard. +If you specify the low-cycle fatigue criterion, progressive delamination growth at the interfaces in +laminated composites subjected to sub-critical cyclic loadings can be simulated. This criterion can be +used only in a low-cycle fatigue analysis using the direct cyclic approach (“Low-cycle fatigue analysis +using the direct cyclic approach,” Section 6.2.7). The onset and delamination growth are characterized +by using the Paris law, which relates the relative fracture energy release rate to crack growth rates as +illustrated in Figure 11.4.3–6. The fracture energy release rates at the crack tips in the interface elements +are calculated based on the above mentioned VCCT technique. +The Paris regime is bounded by the energy release rate threshold, +, below which there is no +consideration of fatigue crack initiation or growth, and the energy release rate upper limit, +, above +which the fatigue crack will grow at an accelerated rate. +is the critical equivalent strain energy release +rate calculated based on the user-specified mode-mix criterion and the bond strength of the interface. +The formulae for calculating +have been provided above for different mixed mode fracture criteria. +You can specify the ratio of +. The default values are +and the ratio of +over +over +and +. +Input File Usage: +*FRACTURE CRITERION, TYPE=FATIGUE +Onset of delamination growth +The onset of delamination growth refers to the beginning of fatigue crack growth at the crack tip along the +interface. In a low-cycle fatigue analysis the onset of the fatigue crack growth criterion is characterized by +, which is the relative fracture energy release rate when the structure is loaded between its maximum +and minimum values. The fatigue crack growth initiation criterion is defined as +da +dN +Paris +Regime +Gthresh +Gpl +GC +Figure 11.4.3–6 Fatigue crack growth govern by Paris law. +and +are material constants and +where +is the cycle number. The interface elements at the crack +tips will not be released unless the above equation is satisfied and the maximum fracture energy release +rate, +, which corresponds to the cyclic energy release rate when the structure is loaded up to its +maximum value, is greater than +. +Fatigue delamination growth using the Paris law +Once the onset of delamination growth criterion is satisfied at the interface, the delamination growth +rate, +. The rate of the +delamination growth per cycle is given by the Paris law if +, can be calculated based on the relative fracture energy release rate, +where +and +are material constants. +At the end of cycle +, Abaqus/Standard extends the crack length, +, from the current cycle +by releasing at least one element at +forward over an incremental number of cycles, +to +the interface. Given the material constants +and +, combined with the known node spacing +at the interface elements at the crack tips, the number of cycles necessary to fail each +interface element at the crack tip can be calculated as +, where j represents the node at the jthe crack +tip. The analysis is set up to release at least one interface element after the loading cycle is stabilized. The +element with the fewest cycles is identified to be released, and its +is represented +as the number of cycles to grow the crack equal to its element length, +. The +most critical element is completely released with a zero constraint and a zero stiffness at the end of the +stabilized cycle. As the interface element is released, the load is redistributed and a new relative fracture +energy release rate must be calculated for the interface elements at the crack tips for the next cycle. This +capability allows at least one interface element at the crack tips to be released after each stabilized cycle +and precisely accounts for the number of cycles needed to cause fatigue crack growth over that length. +, the interface elements at the crack tips will be released by increasing the cycle +If +number count, +, by one only. +Specifying how a debonding force is released after a fracture criterion is met in Abaqus/Standard +After debonding, the traction between two surfaces is initially carried as equal and opposite forces at +the slave node and the corresponding point on the master surface. The debonding force is released as +the crack opens and advances. Once complete debonding has occurred at a point, the bond surfaces act +like standard contact surfaces with associated interface characteristics. There are two different ways to +release the debonding force, depending on the fracture criterion that you specify. +Specifying a debonding amplitude curve +When you use the critical stress, critical crack opening displacement, or crack length versus time fracture +criteria, you can define how this force is to be reduced to zero with time after debonding starts at a +particular node on the bonded surface. You specify a relative amplitude, a, as a function of time after +debonding starts at a node. Thus, suppose the force transmitted between the surfaces at slave node N is +. Then, for any time +the force +. The relative amplitude must be 1.0 at +when that node starts to debond, which occurs at time +transmitted between the surfaces at node N is +the relative time 0.0 and must reduce to 0.0 at the last relative time point given. +The best choice of the amplitude curve depends on the material properties, specified loading, and +the crack propagation criterion. +If the stresses are removed too rapidly, the resulting large changes +in the strains near the crack tip can cause convergence difficulties. For large-strain problems severe +mesh distortion can also occur. For problems with rate-independent materials a linear amplitude curve is +normally adequate. For problems with rate-dependent materials the stresses should be ramped off more +slowly at the beginning of debonding to avoid convergence and mesh distortion difficulties. To reduce +the likelihood of convergence and mesh distortion difficulties, you can reduce the value of the debond +stress by 25% in 50% of the time to debond. The solution should not be strongly influenced by the details +of the unloading procedure; if it is, this usually indicates that the mesh should be refined in the debond +region. +Input File Usage: +*DEBOND, SLAVE=slave, MASTER=master +Data lines to define debonding amplitude curve +Ramping down debonding force for the VCCT and the enhanced VCCT criteria +For the VCCT and the enhanced VCCT criteria, when the energy release rate exceeds the critical value +at a crack tip, you can either release the traction between the two surfaces at the crack tip immediately +during the following increment or release the traction gradually during succeeding increments with the +reduction of the magnitude of the debonding force being governed by the critical fracture energy release +rate. The latter approach is sometimes recommended to avoid sudden loss of stability when the crack +tip is advanced. The enhanced VCCT criterion is meaningful only when used in conjunction with the +latter approach. When the former approach is used, the results obtained by using the enhanced VCCT +criterion are identical to those obtained by using the original VCCT criterion. +Input File Usage: +Use the following option to release the traction immediately: +*DEBOND, SLAVE=slave, MASTER=master, +DEBONDING FORCE=STEP +Use the following option to release the traction gradually: +*DEBOND, SLAVE=slave, MASTER=master, +DEBONDING FORCE=RAMP +Procedures +Crack propagation analysis can be performed for static or dynamic overloadings using the following +procedures: +• “Static stress analysis,” Section 6.2.2 +• “Quasi-static analysis,” Section 6.2.5 +• “Implicit dynamic analysis using direct integration,” Section 6.3.2 +• “Explicit dynamic analysis,” Section 6.3.3 +• “Fully coupled thermal-stress analysis,” Section 6.5.3 +It can also be performed for sub-critical cyclic fatigue loadings using the following procedure: +• “Low-cycle fatigue analysis using the direct cyclic approach,” Section 6.2.7 +Controlling time incrementation during debonding in Abaqus/Standard +When automatic incrementation is used for any criteria other than VCCT, enhanced VCCT, or low-cycle +fatigue, you can specify the size of the time increment used just after debonding starts. By default, the +time increment is equal to the last relative time specified. However, if a fracture criterion is met at the +beginning of an increment, the size of the time increment used just after debonding starts will be set +equal to the minimum time increment allowed in this step. +For fixed time incrementation the specified time increment value will be used as the time increment +size after debonding starts if Abaqus/Standard finds it needs a smaller time increment than the fixed time +increment size. The time increment size will be modified as required until debonding is complete. +*DEBOND, SLAVE=slave, MASTER=master, TIME INCREMENT=t +Input File Usage: +Viscous regularization for VCCT in Abaqus/Standard +The simulation of structures with unstable propagating cracks is challenging and difficult. +Nonconvergent behavior may occur from time to time. While the usual stabilization techniques (such as +contact pair stabilization and static stabilization) can be used to overcome some convergence difficulties, +localized damping is included for VCCT or enhanced VCCT by using the viscous regularization +technique. Viscous regularization damping causes the tangent stiffness matrix of the softening material +to be positive for sufficiently small time increments. +Input File Usage: +Use one of following options: +*FRACTURE CRITERION, TYPE=VCCT, VISCOSITY= +*FRACTURE CRITERION, TYPE=ENHANCED VCCT, VISCOSITY= +Linear scaling to accelerate convergence for VCCT in Abaqus/Standard +For most crack propagation simulations using VCCT or the enhanced VCCT criterion, the deformation +can be nearly linear up to the point of the onset of crack growth; past this point the analysis becomes +very nonlinear. In this case a linear scaling method can be used to effectively reduce the solution time +to reach the onset of crack growth. +Suppose that an applied “trial” load at increment +is just a fraction of the critical load at the +. The following algorithm is used in Abaqus/Standard to quickly +onset time of crack growth, +converge to the critical load state: +where initially would be set between 0.7 and 0.9 depending on the degree of nonlinearity (the default +value is 0.9). When +becomes smaller than 0.5% (indicating that the load is within 0.5% of its +critical value), the next +is automatically set to 1.0 to cause the most critical crack-tip node to precisely +reach the critical value at the next increment. After the first crack-tip node releases, the linear scaling +calculations are no longer valid and the time increment is set to the default value. Cutback is then allowed. +*CONTROLS, TYPE=VCCT LINEAR SCALING +Input File Usage: +Tips for using the VCCT or enhanced VCCT criterion in Abaqus/Standard +Crack propagation problems using the VCCT or enhanced VCCT criterion are numerically challenging. +The following tips will help you create a successful Abaqus/Standard model: +• An analysis with the VCCT or enhanced VCCT criterion requires small +time increments. +Abaqus/Standard tracks the location of the active crack front node by node when the VCCT or +enhanced VCCT criterion is used. Therefore, the crack front is allowed to advance only a single +node forward in any single increment (although such an advance may take place across the entire +crack front in three-dimensional problems). Because an analysis using the VCCT or enhanced +VCCT criterion provides detailed results of the growth of the crack, you will need small time +increments, especially if the mesh is highly refined. +• Three different types of damping can be used to aid convergence for a model using the VCCT +or enhanced VCCT criterion: contact stabilization, automatic or static stabilization, and viscous +regularization. Contact and automatic stabilization are not specific to VCCT; they are built into +Abaqus/Standard and are compatible with VCCT. Setting the value of the damping parameters +is often an iterative procedure. +If your VCCT model fails to converge due to unstable crack +propagation, set the damping parameters to relatively high values and rerun the analysis. If the +parameters are high enough, stable incrementation should return. However, the crack propagation +behavior may have been modified by the damping forces and may not be physically correct. To +monitor the energy absorbed by viscous damping, plot the damping energy and compare the results +to the total strain energy in the model (ALLSE). When set properly, the value of the damping +energy should be a small fraction of the total energy. Monitor the damping energy to ensure that +the results of the VCCT simulation are reasonable in the presence of damping. When you use +contact or automatic stabilization, Abaqus writes the damping energy to the variable ALLSD in +the output database (.odb) file. When you use viscous regularization, Abaqus writes the damping +energy to the variable ALLVD. +• To maximize the accuracy of the debonding simulation, try to use matched meshes between the +slave and master surfaces of the debonding contact pair. +• If you do use a mismatched mesh, you can maximize the accuracy of the simulation by using +the small-sliding, surface-to-surface formulation for the contact pair . +• Printing contact constraint information to the data (.dat) file allows you to review the status of +the debonding contact pair at the beginning of the analysis. By printing detailed contact conditions +to the message (.msg) file, you can track the incremental behavior of the advancing crack front +during the analysis. For more information about these output requests, see “Output,” Section 4.1.1. +• You can add a small clearance to the initially unbonded portion of the debonding contact pair +(“Adjusting initial surface positions and specifying initial clearances in Abaqus/Standard contact +pairs,” Section 35.3.5). The small clearance will help to eliminate unnecessary severe discontinuity +iterations during incrementation as the crack begins to progress. +• Do not use tie MPCs (“General multi-point constraints,” Section 34.2.2) for the slave surface in a +debonding contact pair. Abaqus is unable to resolve the overconstraint presented by the MPC and +the debonded contact state. +• You must have continuous master debonding surfaces. +• You may be able to help the analysis converge by adding geometric nonlinearity (even if small- +sliding is used for the debonding contact pair). For more information, see “Geometric nonlinearity” +in “General and linear perturbation procedures,” Section 6.1.3. +• For two-dimensional models with contact pairs involving higher-order underlying elements, the +initially unbonded portion must extend over complete element faces. In other words, the crack tip +in a two-dimensional, higher-order model must start at a corner node on the quadratic slave surfaces. +The crack tip must not start at a midside node. +Tips for using the VCCT criterion in Abaqus/Explicit +Crack propagation problems using the VCCT criterion analyzed in Abaqus/Explicit benefit from the +robustness of the general contact algorithm in the context of an explicit time integrator. Nevertheless, as +is the case in Abaqus/Standard, these analyses remain challenging given the discontinuous nature of the +fracture phenomenon. The following tips will help you create a successful Abaqus/Explicit model: +• Dynamic effects are of utmost relevance when assessing the results from a debonding analysis using +the VCCT criterion. In most cases experimental and/or theoretical data are available in quasi-static +settings. You must ensure that the Abaqus/Explicit analysis generates low ratios of kinetic energy +to internal energy (1% or less). In practical terms this requirement often translates into avoiding the +use of mass scaling in the model. Use smooth amplitudes to drive the loading to help reduce the +kinetic energy in the model. Running the analysis over a longer period of time will not help in most +cases because bond breakage is an inherently fast and localized process. +• If appropriate, use damping-like behavior in the materials associated with the debonding plates to +reduce dynamic vibrations. Unlike Abaqus/Standard, where a pure static equilibrium is achieved +at the end of a converged increment, in Abaqus/Explicit the bond breakage at a given location is +associated with a dynamic overshoot beyond the static equilibrium position. If the vibrations are +significant (kinetic energy is clearly observable), the dynamic overshoot at nodes behind the crack +tip may lead to premature debonding of the crack tip. +• To maximize the accuracy of the debonding simulation, use quad meshes between the slave and +master surfaces of the debonding surfaces. Avoid using elements with aspect ratios greater than 2. +In most cases mesh refinement will help with obtaining a realistic result. +• Highly mismatched critical energy values between modes tend to induce crack propagation in +continuously changing directions in a manner that may be unstable and unrealistic, particularly for +modes II and III. Do not use such values unless experimental data suggest so. +• Use frequent field output requests to evaluate the debonding evolution as the analysis progresses. +In some cases this can point to nontrivial modeling deficiencies that are difficult to identify from a +simple data check analysis. +• Avoid the use of other constraints involving nodes on both surfaces of the debonding interface +because the cohesive contact forces will compete with the constraint forces to achieve global +equilibrium. Bond breakage might be hard to interpret in these cases. +Comparing VCCT and cohesive elements +Using VCCT to solve delamination problems is very similar to using cohesive elements in Abaqus. +Table 11.4.3–2 describes the advantages and disadvantages of the two approaches. +For an example of the use of cohesive elements, see “Delamination analysis of laminated +composites,” Section 2.7.1 of the Abaqus Benchmarks Manual. This example also shows the effect of +viscous regularization on the predicted force-displacement response. +Table 11.4.3–2 Comparing VCCT and cohesive elements. +VCCT +Cohesive Elements +Simulation (mechanics)-driven +crack propagation along a known +crack surface. +Models brittle fracture using +LEFM only. +Uses a surface-based framework. +Does not require additional +elements. +Requires a pre-existing flaw at the +beginning of the crack surface. +Cannot model crack initiation +from a surface that is not already +cracked. +Crack propagates when strain +energy release rate exceeds +fracture toughness. +Multiple crack fronts/surfaces +can be included. +In Abaqus/Standard crack +surfaces are rigidly bonded when +uncracked. +Requires user-specified fracture +toughness of the bond. +Simulation (mechanics)-driven crack propagation +along a known crack surface. However, cohesive +elements can also be placed between element faces +as a mechanism for allowing individual elements +to separate. +Model brittle or ductile fracture for LEFM +or EPFM. Very general interaction modeling +capability is possible. +Require definition of the connectivity and +interconnectivity of cohesive elements with the +rest of the structure. For accuracy, the mesh of +cohesive elements may need to be smaller than +the surrounding structural mesh and the associated +“cohesive zone.” As a result, cohesive elements +may be more expensive. +Can model crack initiation from initially uncracked +surfaces. The crack initiates when the cohesive +traction stress exceeds a critical value. +Crack propagates according to cohesive damage +model, usually calibrated so that the energy +released when the crack is fully open equals the +critical strain energy release rate. +Multiple crack fronts/surfaces can be included. +Crack surfaces are joined elastically when +uncracked in Abaqus/Standard. +Require user-specified critical traction value and +fracture toughness of the bond, as well as elasticity +of the bonded surface. +Measuring the critical strain energy release properties for VCCT +You must obtain the critical strain energy release properties of the bonded surfaces for VCCT. The +procedure to obtain the critical strain energy release properties is beyond the scope of this manual; +however, you can refer to the following ASTM test specifications for guidance: +• ASTM D 5528-94a, “Standard Test Method for Mode I Interlaminar Fracture Toughness of +Unidirectional Fiber-Reinforced Polymer Matrix Composites” +• ASTM D 6671-01, “Standard Test Method for Mixed Mode I-Mode II Interlaminar Fracture +Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites” +• ASTM D 6115-97, “Standard Test Method for Mode I Fatigue Delamination Growth Onset of +Unidirectional Fiber-Reinforced Polymer Matrix Composites” +These test specifications can be found in the Annual Book of ASTM Standards, American Society for +Testing and Materials, vol. 15.03, 2000. +Initial conditions +Initial contact conditions are used to identify which part of the slave surface is initially bonded, as +explained earlier. +Boundary conditions +Boundary conditions should not be applied to any of the nodes on the master or slave crack surfaces, but +they can be used to load the structure and cause crack propagation. Boundary conditions can be applied +to any of the displacement degrees of freedom in a crack propagation analysis (“Boundary conditions +in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1). In a low-cycle fatigue analysis, prescribed +boundary conditions must have an amplitude definition that is cyclic over the step: the start value must +be equal to the end value . +Loads +The following types of loading can be prescribed in a crack propagation analysis: +• Concentrated nodal forces can be applied to the displacement degrees of freedom (1–6); see +“Concentrated loads,” Section 33.4.2. +• Distributed pressure forces or body forces can be applied; see “Distributed loads,” Section 33.4.3. +The distributed load types available with particular elements are described in Part VI, “Elements.” +For a low-cycle fatigue analysis each load must have an amplitude definition that is cyclic over the step: +the start value must be equal to the end value . +Predefined fields +The following predefined fields can be specified in a crack propagation analysis, as described in +“Predefined fields,” Section 33.6.1: +• Although temperature is not a degree of freedom in stress/displacement elements, nodal +The specified temperature affects +if +temperatures can be specified as predefined fields. +temperature-dependent critical stress and crack opening displacement +specified. +failure criteria, +• The values of user-defined field variables can be specified. These values affect field-variable- +dependent critical stress and crack opening displacement failure criteria, if specified. +The temperatures and user-defined field variables on slave and master surfaces are averaged to determine +the critical stresses and crack opening displacements. +In a low-cycle fatigue analysis, the temperature values specified must be cyclic over the step: the +start value must be equal to the end value . If the temperatures +are read from the results file, you should specify initial temperature conditions equal to the temperature +values at the end of the step . Alternatively, you can ramp the temperatures back to their initial condition values, as +described in “Predefined fields,” Section 33.6.1. +Material options +Any of the mechanical constitutive models in Abaqus/Standard can be used to model the mechanical +behavior of the cracking material. See Part V, “Materials.” +Elements +Regular, rectangular meshes give the best results in crack propagation analyses. Results with nonlinear +materials are more sensitive to meshing than results with small-strain linear elasticity. +First-order elements generally work best for crack propagation analysis. +Line spring elements cannot be used in crack propagation analysis. +The VCCT, enhanced VCCT, and low-cycle fatigue criteria not only support two-dimensional +models (planar and axisymmetric) but also three-dimensional models with contact pairs involving +first-order underlying elements (solids, shells, and continuum shells). +In Abaqus/Standard use of +the VCCT or enhanced VCCT criterion in two-dimensional models with contact pairs involving +higher-order underlying elements is limited to crack fronts that are aligned with the corner nodes of +the higher-order element faces. Use of the low-cycle fatigue criterion with contact pairs involving +higher-order underlying elements is not supported. +Output +Unless otherwise stated, the following discussions in this section are applied only to the critical stress, +critical crack opening displacement, and crack length versus time criteria. +At the start of an analysis Abaqus/Standard will scan the partially bonded surfaces and identify all +of the crack tips that are present in the model. The initial contact status of all of the slave surface nodes +is printed in the data (.dat) file. At this stage Abaqus/Standard will explicitly identify all the crack +tips and mark them as crack 1, crack 2, etc. The slave and master surfaces that are associated with these +cracks are also identified. +The initial contact status of all of the slave surface nodes is also printed in the data (.dat) file for +the VCCT, enhanced VCCT, and low-cycle fatigue criteria. +Printing crack propagation information to the data file +By default, crack propagation information will be printed to the data file during the analysis. For each +crack that is identified Abaqus/Standard will print out the initial and current crack-tip node numbers, +accumulated incremental crack length (distance from the initial crack tip to the current crack tip, +measured along the slave surface), and the current value of the user-specified fracture criterion used. +Crack propagation information cannot be printed to the data file in Abaqus/Explicit. +Input File Usage: +*DEBOND, SLAVE=slave, MASTER=master +For example, if the crack opening displacement criterion is used, the printed output during the +analysis will appear as follows in the data file: +CRACK TIP LOCATION AND ASSOCIATED QUANTITIES +INITIAL +CRACK +NUMBER SURFACE SURFACE CRACKTIP CRACKTIP INCREMENTAL COD +CUMULATIVE +CURRENT +MASTER +SLAVE +CRITICAL +... +... +... +NODE # +... +NODE # +... +LENGTH +... +... +Writing crack propagation information to the results file +In Abaqus/Standard you can choose to write the crack propagation information to the results (.fil) file. +Input File Usage: +*DEBOND, SLAVE=slave, MASTER=master, OUTPUT=FILE +Writing crack propagation information to both the data file and the results file +In Abaqus/Standard you can write the crack propagation information to both the data and the results files. +Input File Usage: +*DEBOND, SLAVE=slave, MASTER=master, OUTPUT=BOTH +Controlling the output frequency +In Abaqus/Standard you can control the output frequency in increments. By default, the crack-tip location +and associated quantities will be printed every increment. Specify an output frequency of 0 to suppress +crack propagation output. +Input File Usage: +*DEBOND, SLAVE=slave, MASTER=master, FREQUENCY=f +Output variables +The following bond failure quantities can be requested as surface output for all fracture criteria: +DBT +DBSF +The time when bond failure occurred. For the VCCT, enhanced VCCT, and low- +cycle fatigue criteria, this is the time when debonding initiates. +Fraction of stress at bond failure that still remains. +DBS +DBS1i +All components of remaining stress in the failed bond. +1i component of stress in the failed bond that remains ( +). +For the VCCT, enhanced VCCT, and low-cycle fatigue criteria, the following additional variables can +be also requested as surface output : +CSDMG +BDSTAT +OPENBC +CRSTS +CRSTS1i +ENRRT +ENRRT1i +EFENRRTR +Overall value of the scalar damage variable. +Bond state. The bond state varies between 1.0 (fully bonded) and 0.0 (fully +unbonded). +Relative displacement behind crack when the fracture criterion is met. +All components of critical stress at failure +1i component of critical stress at failure ( +All components of strain energy release rate. +1i component of strain energy release rate ( +. +Effective energy release rate ratio, +). +). +Surface output requests provide the usual output of contact variables in addition to the above quantities. +The bond failure quantities must be requested explicitly; otherwise, only the default output for contact +will be given. +Abaqus/CAE provides support for the visualization of time-history plots and X–Y plots of the +variables that are written to the output database. +Contour integrals +Contour integrals can be requested for two-dimensional crack propagation analyses performed using the +critical stress, critical crack opening displacement, or crack length versus time fracture criteria. If the +contours are chosen so that the crack tip passes through the contour, the contour value will go to zero +(as it should). Therefore, in crack propagation analysis contour integrals should be requested far enough +from the crack tip that the crack tip does not pass through the contour, which is easily done by including +all nodes along the bond surface in the crack-tip node set specified. See “Contour integral evaluation,” +Section 11.4.2, for details on contour integral output. +Input file template +Abaqus/Standard analysis +*HEADING +… +*BOUNDARY +Data lines to specify zero-valued boundary conditions +*INITIAL CONDITIONS, TYPE=CONTACT (, NORMAL) +Data lines to specify initial conditions +*SURFACE, NAME=slave +Data lines to define slave surface +*SURFACE, NAME=master +Data lines to define master surface +** +*CONTACT PAIR +slave, master +** +*STEP (, NLGEOM) +*STATIC or *VISCO or *COUPLED TEMPERATURE-DISPLACEMENT +*DEBOND, SLAVE=slave, MASTER=master +Data lines to define debonding amplitude curve +*FRACTURE CRITERION, TYPE=type, DISTANCE or NSET +Data lines to define fracture criterion +*BOUNDARY +Data lines to define zero-valued or nonzero boundary conditions +*CLOAD and/or *DLOAD and/or *TEMPERATURE and/or *FIELD +Data lines to define loading +** +*CONTOUR INTEGRAL, CONTOURS=n, TYPE=type +**Contour integrals can be requested in a two-dimensional crack propagation analysis +*CONTACT PRINT +DBT, DBSF, DBS +*EL PRINT +JK, +*END STEP +** +*STEP +*DIRECT CYCLIC, FATIGUE +*DEBOND, SLAVE=slave, MASTER=master +*FRACTURE CRITERION, TYPE=FATIGUE +Data lines to define material constants used in Paris law and fracture criterion +*BOUNDARY +Data lines to define zero-valued or nonzero cyclic boundary conditions +*CLOAD and/or *DLOAD and/or *TEMPERATURE and/or *FIELD +Data lines to define cyclic loading +** +*END STEP +** +Abaqus/Explicit analysis +*HEADING +… +*BOUNDARY +Data lines to specify zero-valued boundary conditions +*SURFACE, NAME=slave +Data lines to define slave surface +*SURFACE, NAME=master +Data lines to define master surface +** +*CONTACT CLEARANCE, NAME=clearance_name, +SEARCH NSET=initially_bonded_nodeset_name +*SURFACE INTERACTION, NAME=interaction_name +*COHESIVE BEHAVIOR +Data lines to specify elastic behavior +*FRACTURE CRITERION, TYPE=VCCT, MIXED MODE BEHAVIOR=BK +** +*STEP +*DYNAMIC, EXPLICIT +*CONTACT +*CONTACT CLEARANCE ASSIGNMENT +Data lines to assign a clearance name to a surface pair +*CONTACT PROPERTY ASSIGNMENT +Data lines to assign a surface interaction to a surface pair +*END STEP +** +Additional references +• Benzeggagh, M., and M. Kenane, “Measurement of Mixed-Mode Delamination Fracture +Toughness of Unidirectional Glass/Epoxy Composites with Mixed-Mode Bending Apparatus,” +Composite Science and Technology, vol. 56, p. 439, 1996. +• Reeder, +J., +S. Kyongchan, +“Postbuckling and +and D. R.. Ambur, +Growth of Delaminations +in Composite Plates Subjected to Axial Compression” 43rd +AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, +Denver, Colorado, vol. 1746, p. 10, 2002. +P. B. Chunchu, +• Wu, E. M., and R. C. Reuter Jr., “Crack Extension in Fiberglass Reinforced Plastics,” T and M +Report, University of Illinois, vol. 275, 1965. +11.5 +Surface-based fluid modeling +• “Surface-based fluid cavities: overview,” Section 11.5.1 +• “Fluid cavity definition,” Section 11.5.2 +• “Fluid exchange definition,” Section 11.5.3 +• “Inflator definition,” Section 11.5.4 +11.5.1 +SURFACE-BASED FLUID CAVITIES: OVERVIEW +Products: Abaqus/Standard Abaqus/Explicit +References +• “Fluid cavity definition,” Section 11.5.2 +• “Fluid exchange definition,” Section 11.5.3 +• “Inflator definition,” Section 11.5.4 +Overview +Surface-based fluid-filled cavities are modeled by: +• using standard finite elements to model the fluid-filled structure; +• using a surface definition to provide the coupling between the deformation of the fluid-filled +structure and the pressure exerted by the contained fluid on the cavity boundary of the structure; +• defining the fluid behavior; +• using fluid exchange definitions to model the transfer of fluid between a cavity and the environment +or between multiple cavities; and +• using inflator definitions to infuse a gas mixture into a fluid cavity to simulate the inflation of an +automotive airbag. +The surface-based fluid cavity capability can be used to model a liquid or gas-filled structure. +It +supersedes the element-based hydrostatic fluid cavity capability in functionality and does not require +the user to define fluid or fluid link elements. +Introduction +In certain applications it may be necessary to predict the mechanical response of a liquid-filled or a +gas-filled structure. Examples include pressure vessels, hydraulic or pneumatic driving mechanisms, +and automotive airbags. A primary difficulty in addressing such applications is the coupling between +the deformation of the structure and the pressure exerted by the contained fluid on the structure. +Figure 11.5.1–1 illustrates a simple example of a fluid-filled structure subjected to a system of external +loads. The response of the structure depends not only on the external loads but also on the pressure +exerted by the fluid, which, in turn, is affected by the deformation of the structure. The surface-based +fluid cavity capability provides the coupling needed to analyze situations in which the cavity can be +assumed completely filled by fluid with uniform properties and state. Applications with significant +spatial variation within cavities cannot be modeled with this feature. For example, consider the +fluid-structure interaction and coupled Eulerian-Lagrangian capabilities for applications involving +sloshing and wave propagation through a fluid . +fluid +Figure 11.5.1–1 Fluid-filled structure. +Discretizing the fluid cavity +The boundary of the fluid cavity is defined by an element-based surface with normals pointing to the +inside of the cavity. The underlying elements can be standard solid or structural elements as well as +surface elements. Surface elements can be used to model holes in the structure or to fill in rigid regions +where rigid or other load-carrying elements do not exist . Care +must be taken when using surface elements such that nodes completely surrounded by only surface +elements have proper boundary conditions. +Consider the example presented in Figure 11.5.1–1. Solid elements are defined on the top and side of +the cavity as indicated in Figure 11.5.1–2. A surface element is defined on the bottom rigid boundary of +the cavity where no standard elements exist. The node located at the intersection of the axis of symmetry +and the lower rigid boundary of the cavity must be restrained in the r- and z-directions because it is +connected only to a surface element. The surface defining the cavity is based on the underlying solid and +surface elements. +In Abaqus/Explicit an additional user-defined volume can be added to the actual or geometric +volume of the cavity. If the boundary of the cavity is not defined by an element-based surface, the fluid +cavity is assumed to have a fixed volume that is equal to the added volume. +axis of +symmetry +standard +elements +cavity +reference +node +surface to +define cavity +surface element +Figure 11.5.1–2 Axisymmetric model of fluid-filled structure. +Defining the location of the cavity reference node +A single node, known as the cavity reference node, is associated with a fluid cavity. This cavity reference +node has a single degree of freedom representing the pressure inside the fluid cavity. The cavity reference +node is also used in calculating the cavity volume. +If the cavity is not bounded by symmetry planes, the surface defining the cavity must completely +enclose the cavity to ensure proper calculation of its volume. In this case the location of the cavity +reference node is arbitrary and does not have to lie inside the cavity. +If, as a result of symmetry, only a portion of the cavity boundary is modeled with standard elements, +the cavity reference node must be located on the symmetry plane or axis (Figure 11.5.1–2). If multiple +symmetry planes exist, the cavity reference node must be located on the intersection of the symmetry +planes (Figure 11.5.1–3). For an axisymmetric analysis the cavity reference node must be located on the +axis of symmetry. These requirements are a consequence of the fluid cavity not being fully enclosed by +the surface defining the cavity. +Finite element calculations +The finite element calculations for surface-based cavities are performed using volume elements as +described in “Hydrostatic fluid calculations,” Section 3.8.1 of the Abaqus Theory Manual. The volume +elements for a cavity are created internally by Abaqus using the surface facet geometry and the +cavity reference node that you define. In Abaqus/Standard the surface facets are represented with the +following element types: FAX2 and F2D2 (which are linear, 2-node, axisymmetric and planar elements, +respectively) and F3D3 and F3D4 (which are linear, 3-node and 4-node three-dimensional elements, +axis of +symmetry +cavity +reference +node +symmetry +plane +Figure 11.5.1–3 Axisymmetric model with additional symmetry plane. +respectively). Second-order facets in Abaqus are subdivided further into multiple linear facets or +elements. +Fluid cavity behavior +The behavior of the fluid within the fluid-filled cavity can be based either on a hydraulic or a +pneumatic model. The hydraulic model can simulate nearly incompressible fluid behavior and fully +incompressible behavior in Abaqus/Standard. The compressibility is introduced by defining a bulk +modulus. The pneumatic model is based on an ideal gas. The gas can be defined by multiple species +in Abaqus/Explicit, and you can specify the temperature of the gas or have it calculated based on the +assumption of adiabatic behavior. A multi-species ideal gas with an adiabatic temperature update is an +appropriate model for automotive airbags. +Modeling flow into or out of a cavity +There are many ways in Abaqus to model the transfer of fluid into or out of a cavity. The flow can be +specified as a prescribed mass or volume flux history or can model physical mechanisms due to a pressure +differential such as venting through an exhaust orifice or leakage through a porous fabric. Fluid exchange +definitions are used for this purpose and can model flow between a fluid cavity and its environment or +between two fluid cavities . In addition, +Abaqus/Explicit has the capability to model inflators used for the deployment of automotive airbags. +Conditions at the inflator can be specified directly, or tank test data can be used . +Modeling multiple chambers +Many fluid-filled systems such as airbags have multiple chambers with fluid flowing between chambers +through holes or fabric leakage. In other cases it is advantageous to divide a single physical chamber +into multiple chambers with fictitious walls to model a gradient in pressure across the physical chamber. +Some fictitious leakage mechanisms through inter-chamber walls can be defined to obtain reasonable +behavior. This can be a useful modeling technique when simulating the complex unfolding of an airbag. +To model multiple chambers, define a fluid cavity for each chamber and link the fluid cavities together +with the appropriate fluid exchange definitions. Averaged properties for the multi-chambered model can +be output if requested . +Defining the fluid inertia in a dynamic procedure +The inertia of the fluid inside a fluid cavity or fluid exchanged between cavities is not automatically +taken into account. To add the effect of inertia, use MASS elements on the boundary of the cavity. You +should make sure that the total added mass corresponds to the mass of the fluid in the cavity and that +the distribution of the MASS elements is a reasonable representation of the distributed fluid mass for +the type of loading to which the structure is subjected. Only the overall effect of the fluid inertia can +be modeled; the uniform pressure assumption in the cavity makes it impossible to model any pressure +gradient-driven fluid motions. Thus, the approach assumes that the time scale of the excitation is very +long compared to typical response times for the fluid. +Modeling contact involving the cavity boundary +If a large amount of fluid is removed from a cavity or the material surrounding the cavity is very flexible, +the cavity may partially collapse and portions of the cavity walls may contact each other. Self-contact +of the cavity walls and contact with surrounding structures can be handled effectively by using the +standard techniques available in Abaqus for modeling contact. Abaqus/Explicit can also account for +the blockage of flow out of a cavity due to contacting surfaces . +Interpreting negative eigenvalue messages +In some applications in Abaqus/Standard, negative eigenvalues may be encountered during the solution. +These negative eigenvalues do not necessarily indicate that a bifurcation or buckling load has been +exceeded. If the predicted response otherwise appears to be reasonable, these messages can be ignored. +A detailed description of how negative eigenvalues can develop during the solution of hydrostatic fluid +element problems is presented in “Hydrostatic fluid calculations,” Section 3.8.1 of the Abaqus Theory +Manual. +Procedures +The surface-based fluid cavity capability can be used in all procedures except coupled pore fluid +diffusion/stress analysis . +Initial conditions +The initial fluid pressure and temperature can be specified . For an ideal gas the initial pressure represents the gauge pressure +over and above the ambient pressure. The initial temperature should be given in the temperature scale +used. Absolute zero in that temperature scale is specified separately for an ideal gas . +If membrane elements are used as the underlying elements for the fluid cavity, the reference mesh +(initial metric) can also be specified . +Boundary conditions +The pressure degree of freedom at the cavity reference node (degree of freedom number 8) is a primary +variable in the problem. Thus, it can be prescribed by defining a boundary condition , similar to the way displacements +of structural nodes can be prescribed. Prescribing the pressure at the cavity reference node is equivalent +to applying a uniform pressure to the cavity boundary using a distributed load definition . +If the pressure is prescribed with a boundary condition, the fluid volume is adjusted automatically to +fill the cavity (that is, fluid is assumed to enter and leave the cavity as needed to maintain the prescribed +pressure). This behavior is useful in situations where a cavity is deformed prior to the introduction of +the effect of the fluid. In a subsequent step you can remove the boundary condition on the pressure +degree of freedom , thus “sealing” the cavity with the current fluid volume. +Loads +Distributed pressures and body forces, as well as concentrated nodal forces, can be applied to the +fluid-filled structure, as described in “Concentrated loads,” Section 33.4.2, and “Distributed loads,” +Section 33.4.3. +Predefined fields +Predefined temperature fields and user-defined field variables can be defined for both fluid-filled +structures and the enclosed fluids, as described in “Predefined fields,” Section 33.6.1. +Temperatures +Fluid temperatures can be specified at all cavity reference nodes as predefined fields , unless an adiabatic process is specified or a +coupled temperature-displacement procedure is used. Any difference between the applied and initial +temperatures will cause thermal expansion for a pneumatic fluid and for a hydraulic fluid if a thermal +expansion coefficient is given. A specified temperature field can also affect temperature-dependent +material properties, if any exist, for both fluid-filled structures and enclosed fluids. +Field variables +The values of user-defined field variables can be specified at all cavity reference nodes . These values will affect field-variable-dependent +material properties for the enclosed fluid. +Output +The state of the fluid inside the cavity is available for history output using the nodal output variables +PCAV and CVOL, which represent the gauge fluid pressure and cavity volume, respectively. In steady- +state dynamic procedures the magnitude and phase angle of the fluid pressure can be obtained as nodal +variable PPOR. +Abaqus/Explicit also provides output for the cavity temperature, cavity surface area, and mass of the +fluid (nodal output variables CTEMP, CSAREA, and CMASS, respectively). Output variable CTEMP +is available only when an ideal gas model is used under adiabatic conditions. If the node set for which +the output request is made contains more than one fluid cavity, the time histories of the average fluid +pressure, total volume, average fluid temperature, sum of all the external cavity surface areas, and total +mass of these cavities will also be output by using the nodal output variables APCAV, TCVOL, ACTEMP, +TCSAREA, and TCMASS, respectively. +In Abaqus/Explicit, when the model includes fluid exchange definitions, use nodal output variables +CMFL and CMFLT to obtain history output of the total mass flow rate and total accumulated mass flow +out of a cavity and CEFL and CEFLT to obtain history output of the total heat energy flow rate and total +accumulated heat energy flow out of a cavity. If more than one fluid exchange is defined for a cavity, +time histories of the mass or heat energy flow rate and accumulated mass or heat energy flow out of the +cavity for each fluid exchange will also be output. +If the fluid cavity is modeled by a mixture of ideal gases, time histories of the molecular mass +fraction of each fluid species inside the fluid cavity can be obtained by using nodal output variable CMF. +If inflators are used, use nodal output variables MINFL, MINFLT, and TINFL to obtain time +histories of mass flow rate, accumulated mass flow, and inflator temperature for each inflator definition +. +Input file template +An analysis with hydrostatic fluid: +*HEADING +… +*FLUID CAVITY, NAME=cavity_name, BEHAVIOR=behavior_name, +REF NODE=cavity_reference_node, SURFACE=surface_name +*FLUID BEHAVIOR, NAME=behavior_name +*FLUID DENSITY +Data line to define density +*FLUID BULK MODULUS +Data line to define bulk modulus +*FLUID EXPANSION +Data line to define thermal expansion +** +*FLUID EXCHANGE, NAME=exchange_name, PROPERTY=exchange_property_name +cavity_reference_node +*FLUID EXCHANGE PROPERTY, NAME=exchange_property_name, TYPE=MASS FLUX +Data line to define mass flow rate per unit area +** +*INITIAL CONDITIONS, TYPE=TEMPERATURE +Data line to define initial temperature +*INITIAL CONDITIONS, TYPE=FLUID PRESSURE +Data line to define initial pressure +** +*STEP +** +*TEMPERATURE +Data line to define temperature +*FLUID EXCHANGE ACTIVATION +exchange_name +** +*END STEP +An airbag analysis with a mixture of ideal gases: +*HEADING +… +*FLUID CAVITY, NAME=chamber_1, MIXTURE=MOLAR FRACTION, ADIABATIC, +REF NODE=chamber_1_reference_node, SURFACE=surface_name_1 +blank line +Oxygen, 0.2 +Nitrogen, 0.75 +Carbon_dioxide, 0.05 +** +*FLUID CAVITY, NAME=chamber_2, BEHAVIOR=Air, ADIABATIC, +REF NODE=chamber_2_reference_node, SURFACE=surface_name_2 +blank line +** +*FLUID BEHAVIOR, NAME=Air +*CAPACITY, TYPE=POLYNOMIAL +Data line to define heat capacity coefficient +*MOLECULAR WEIGHT +Data line to define molecular weight +** +*FLUID BEHAVIOR, NAME=Oxygen +*CAPACITY, TYPE=POLYNOMIAL +Data line to define heat capacity coefficient +*MOLECULAR WEIGHT +Data line to define molecular weight +** +*FLUID BEHAVIOR, NAME=Nitrogen +*CAPACITY, TYPE=POLYNOMIAL +Data line to define heat capacity coefficient +*MOLECULAR WEIGHT +Data line to define molecular weight +** +*FLUID BEHAVIOR, NAME=Carbon_dioxide +*CAPACITY, TYPE=POLYNOMIAL +Data line to define heat capacity coefficient +*MOLECULAR WEIGHT +Data line to define molecular weight +** +*FLUID INFLATOR, NAME=inflator, PROPERTY=inflator_property +chamber_1_reference_node +*FLUID INFLATOR PROPERTY, NAME=inflator_property, +TYPE=TEMPERATURE AND MASS +Data lines to define mass flow rate and gas temperature +*FLUID INFLATOR MIXTURE, TYPE=MOLAR FRACTION, NUMBER SPECIES=2 +Carbon_dioxide, Nitrogen +Table to define molecular mass fraction +** +*FLUID EXCHANGE, NAME=exhaust, PROPERTY=exhaust_behavior +chamber_1_reference_node +*FLUID EXCHANGE PROPERTY, NAME=exhaust_behavior, TYPE=ORIFICE +Data line to specify orifice behavior +*FLUID EXCHANGE, NAME=leakage_1, PROPERTY=fabric_behavior +chamber_1_reference_node +*FLUID EXCHANGE, NAME=leakage_2, PROPERTY=fabric_behavior +chamber_2_reference_node +*FLUID EXCHANGE PROPERTY, NAME=fabric_behavior, TYPE=FABRIC LEAKAGE +Data line to specify fabric leakage behavior +** +*FLUID EXCHANGE, NAME=chamber_wall, PROPERTY=wall_behavior, +EFFECTIVE AREA= +chamber_1_reference_node, chamber_2_reference_node +*FLUID EXCHANGE PROPERTY, NAME=wall_behavior, TYPE=ORIFICE +Data line to specify orifice behavior +** +*AMPLITUDE, NAME=amplitude_name +Data line to define amplitude variations +*PHYSICAL CONSTANTS, UNIVERSAL GAS CONSTANT= +** +*INITIAL CONDITIONS, TYPE=FLUID PRESSURE +Data line to define initial pressure +*INITIAL CONDITIONS, TYPE=TEMPERATURE +Data line to define initial temperature +** +*STEP +** +*FLUID EXCHANGE ACTIVATION +exhaust, leakage_1, leakage_2, chamber_wall +*FLUID INFLATOR ACTIVATION, INFLATION TIME AMPLITUDE=amplitude_name +inflator +** +*END STEP +11.5.2 +FLUID CAVITY DEFINITION +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Surface-based fluid cavities: overview,” Section 11.5.1 +• “Fluid exchange definition,” Section 11.5.3 +• *CAPACITY +• *FLUID BEHAVIOR +• *FLUID BULK MODULUS +• *FLUID CAVITY +• *FLUID DENSITY +• *MOLECULAR WEIGHT +• “Defining a fluid cavity interaction,” Section 15.13.11 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Defining a fluid cavity interaction property,” Section 15.14.4 of the Abaqus/CAE User’s Manual, +in the online HTML version of this manual +Overview +A surface-based fluid cavity: +• can be used to model a liquid-filled or gas-filled structure; +• is associated with a node known as the cavity reference node; +• is defined by specifying a surface that fully encloses the cavity; +• is applicable only for situations where the pressure and temperature of the fluid in a particular cavity +are uniform at any point in time; +• can be used to model an airbag using the assumptions of an ideal gas mixture under adiabatic +conditions; and +• has a name that can be used to identify history output associated with the cavity. +Defining the fluid cavity +You must associate a name with each fluid cavity. +Input File Usage: +Abaqus/CAE Usage: +*FLUID CAVITY, NAME=name +Interaction module: Create Interaction: Fluid cavity, Name: name +Specifying the cavity reference node +Every fluid cavity must have an associated cavity reference node. Along with the fluid cavity name, the +reference node is used to identify the fluid cavity. In addition, it may be referenced by fluid exchange +and inflator definitions. The reference node should not be connected to any elements in the model. +Input File Usage: +Abaqus/CAE Usage: +*FLUID CAVITY, REF NODE=n +Interaction module: Create Interaction: Fluid cavity: select +the fluid cavity reference node +Specifying the boundary of the fluid cavity +The fluid cavity must be completely enclosed by finite elements unless symmetry planes are modeled . Surface elements can be used for portions of +the cavity surface that are not structural. The boundary of the cavity is specified using an element-based +surface covering the elements that surround the cavity with surface normals pointing inward. By default, +an error message is issued if the underlying elements of the surface do not have consistent normals. +Alternatively, you can skip the consistency checking for the surface normals. +Input File Usage: +Use the following option to define the surface with consistent normal checking: +*FLUID CAVITY, SURFACE=surface_name, CHECK NORMALS=YES +Use the following option to define the surface without consistent normal +checking: +*FLUID CAVITY, SURFACE=surface_name, CHECK NORMALS=NO +Interaction module: Create Interaction: Fluid cavity: select the fluid cavity +boundary surface; toggle on or off Check surface normals +Abaqus/CAE Usage: +Specifying additional volume in a fluid cavity +An additional volume can be specified for a fluid cavity in Abaqus/Explicit. The additional volume will +be added to the actual volume when the boundary of the cavity is defined by a specified surface. If you +do not specify a surface forming the boundary of the fluid cavity, the fluid cavity is assumed to have a +fixed volume that is equal to the added volume. +Input File Usage: +Abaqus/CAE Usage: +*FLUID CAVITY, ADDED VOLUME=r +Specification of additional volume is not supported in Abaqus/CAE. +Specifying the minimum volume +When the volume of a fluid cavity is extremely small, transients in an explicit dynamic procedure +can cause the volume to go to zero or even negative causing the effective cavity stiffness values to +tend to infinity. To avoid numerical problems, you can specify a minimum volume for the fluid in +Abaqus/Explicit. +If the volume of the cavity (which is equal to the actual volume plus the added +volume) drops below the minimum, the minimum value is used to evaluate the fluid pressure. +You can specify the minimum volume either directly or as the initial volume of the fluid cavity. +If the latter method is used and the initial volume of the fluid cavity is a negative value, the minimum +volume is set equal to zero. +Input File Usage: +Use the following option to specify the minimum volume directly: +*FLUID CAVITY, MINIMUM VOLUME=minimum volume +Use the following option to specify the minimum volume to be equal to the +initial volume: +Abaqus/CAE Usage: +*FLUID CAVITY, MINIMUM VOLUME=INITIAL VOLUME +Specification of a minimum volume is not supported in Abaqus/CAE. +Defining the fluid cavity behavior +The fluid cavity behavior governs the relationship between cavity pressure, volume, and temperature. A +fluid cavity in Abaqus/Standard can contain only a single fluid. In Abaqus/Explicit a cavity can contain +a single fluid or a mixture of ideal gases. +Fluid behavior with a homogeneous fluid +To define a fluid cavity behavior made of a single fluid, specify a single fluid behavior to define the fluid +properties. You must associate the fluid behavior with a name. This name can then be used to associate +a certain behavior with a fluid cavity definition. +Input File Usage: +Use the following options: +Abaqus/CAE Usage: +*FLUID CAVITY, NAME=fluid_cavity_name, BEHAVIOR=behavior_name +*FLUID BEHAVIOR, NAME=behavior_name +Interaction module: Create Interaction Property: Fluid +cavity, Name: behavior_name +Fluid behavior with a mixture of ideal gases in Abaqus/Explicit +In Abaqus/Explicit you can define a fluid cavity behavior made of multiple gas species. To define a fluid +cavity behavior made of multiple gas species, you specify multiple fluid behaviors to define the fluid +properties. Specify the names of the fluid behaviors and the initial mass or molar fractions defining the +mixture to associate a certain group of behaviors with a fluid cavity definition. +Input File Usage: +Use the following options to define the fluid cavity mixture in terms of the initial +mass fraction: +*FLUID BEHAVIOR, NAME=behavior_name +*FLUID CAVITY, NAME=fluid_cavity_name, +MIXTURE=MASS FRACTION +out-of-plane surface thickness (if required; otherwise, blank) +behavior_name, initial mass fraction +... +Use the following options to define the fluid cavity mixture in terms of the initial +molar fraction: +*FLUID BEHAVIOR, NAME=behavior_name +*FLUID CAVITY, NAME=fluid_cavity_name, +MIXTURE=MOLAR FRACTION +out-of-plane surface thickness (if required; otherwise, blank) +behavior_name, initial molar fraction +... +Abaqus/CAE Usage: +Specification of ideal gas mixtures is not supported in Abaqus/CAE. +User-defined fluid behavior in Abaqus/Standard +In Abaqus/Standard the fluid behavior can be defined in user subroutine UFIELD. +*FLUID BEHAVIOR, USER +User subroutine UFIELD is not supported in Abaqus/CAE. +Abaqus/CAE Usage: +Input File Usage: +Defining the ambient pressure for a fluid cavity +For pneumatic fluids the equilibrium problem is generally expressed in terms of the “gauge” pressure +in the fluid cavity (that is, ambient atmospheric pressure does not contribute to the loading of the solid +and structural parts of the system). You can choose to convert gauge pressure to absolute pressure +as +used in the constitutive law. For hydraulic fluids you can define the ambient pressure, which can be used +to calculate the pressure difference in the fluid exchange between a fluid cavity and its environment. +The pressure value given as degree of freedom 8 at the cavity reference node is the value of the gauge +pressure. The ambient pressure, +, is assumed to be zero if you do not specify it. +Input File Usage: +Abaqus/CAE Usage: +*FLUID CAVITY, AMBIENT PRESSURE= +Interaction module: Create Interaction: Fluid cavity: toggle +on Specify ambient pressure: +Isothermal process +For hydraulic fluids and pneumatic fluids in problems of long time duration, it is reasonable to assume +that the temperature is constant or a known function of the environment surrounding the cavity. +In +this case the temperature of the fluid can be defined by specifying initial conditions +and predefined temperature fields +at the cavity reference node. For a pneumatic fluid the pressure and density of the gas are calculated +from the ideal gas law, conservation of mass, and the predefined temperature field. +Defining the ambient temperature for a fluid cavity +For pneumatic fluids with adiabatic behavior the ambient temperature is needed when the heat energy +flow is defined between a single cavity and its environment and the flow definition is based on analysis +conditions. The ambient temperature, +, is assumed to be zero if you do not specify it. +Input File Usage: +Abaqus/CAE Usage: +*FLUID CAVITY, AMBIENT TEMPERATURE= +Specification of ambient temperature is not supported in Abaqus/CAE. +Hydraulic fluids +The hydraulic fluid model is used to model nearly incompressible fluid behavior and fully incompressible +fluid behavior in Abaqus/Standard. Compressibility is introduced by assuming a linear pressure-volume +relationship. The required parameters for compressible behavior are the bulk modulus and the reference +density. You omit the bulk modulus to specify fully incompressible behavior in Abaqus/Standard. +Temperature dependence of the density can be modeled as a thermal expansion of the fluid. +Input File Usage: +Abaqus/CAE Usage: +*FLUID CAVITY, BEHAVIOR=behavior_name +Interaction module: Create Interaction Property: Fluid +cavity: Definition: Hydraulic +Defining the reference fluid density +The reference fluid density, +, is specified at zero pressure and the initial temperature, +: +Input File Usage: +Abaqus/CAE Usage: +*FLUID DENSITY +Interaction module: Create Interaction Property: Fluid cavity: +Definition: Hydraulic: Fluid density: density +Defining the fluid bulk modulus for compressibility +The compressibility is described by the bulk modulus of the fluid: +where +is the current pressure, +is the current temperature, +is the fluid bulk modulus, +is the current fluid volume, +is the density at current pressure and temperature, +is the fluid volume at zero pressure and current temperature, +is the fluid volume at zero pressure and initial temperature, and +is the density at zero pressure and current temperature. +It is assumed that the bulk modulus is independent of the change in fluid density. However, the bulk +Input File Usage: +modulus can be specified as a function of temperature or predefined field variables. +*FLUID BULK MODULUS +Interaction module: Create Interaction Property: Fluid cavity: Definition: +Hydraulic: Fluid Bulk Modulus tabbed page: toggle on Specify fluid +bulk modulus, and enter the modulus value in the table +Abaqus/CAE Usage: +Use the following options to include temperature and field variable dependence: +Toggle on Use temperature-dependent data, Number of field variables: n +Defining the fluid expansion +The thermal expansion coefficients are interpreted as total expansion coefficients from a reference +temperature, which can be specified as a function of temperature or predefined field variables. The +change in fluid volume due to thermal expansion is determined as follows: +where +(secant) coefficient of thermal expansion. +is the reference temperature for the coefficient of thermal expansion and +is the mean +of +If the coefficient of thermal expansion is not a function of temperature or field variables, the value +is not needed. +Thermal expansion can also be expressed in terms of the fluid density: +Input File Usage: +Abaqus/CAE Usage: +*FLUID EXPANSION, ZERO= +Interaction module: Create Interaction Property: Fluid cavity: +Definition: Hydraulic: Fluid Expansion tabbed page: toggle on +Specify fluid thermal expansion coefficients, and enter the mean +coefficient of thermal expansion in the table +Use the following options to include temperature and field variable dependence: +Toggle on Use temperature-dependent data, Reference temperature: +, Number of field variables: n +Pneumatic fluids +Compressible or pneumatic fluids are modeled as an ideal gas . +The equation of state for an ideal gas (or the ideal gas law) is given as +where the absolute (or total) pressure +is defined as +is the ambient pressure, p is the gauge pressure, R is the gas constant, +is the current temperature, +is absolute zero on the temperature scale being used. The gas constant, R, can also be determined +and +and +from the universal gas constant, +, and the molecular weight, +, as follows: +Conservation of mass gives the change of mass in the fluid cavity as +where m is the mass of the fluid, +flow rate out of the fluid cavity. +Defining the molecular weight +is the mass flow rate into the fluid cavity, and +is the mass +You must specify the value of the molecular weight of the ideal gas, +. +Input File Usage: +*MOLECULAR WEIGHT +Abaqus/CAE Usage: +Interaction module: Create Interaction Property: Fluid cavity: Definition: +Pneumatic, Ideal gas molecular weight: +Specifying the value of the universal gas constant +You can specify the value of the universal gas constant, +. +*PHYSICAL CONSTANTS, UNIVERSAL GAS CONSTANT= +All modules: Model→Edit attributes→model name: Physical +Constants: toggle on Universal gas constant: +Input File Usage: +Abaqus/CAE Usage: +Specifying the value of absolute zero +You can specify the value of absolute zero temperature, +. +Input File Usage: +Abaqus/CAE Usage: +*PHYSICAL CONSTANTS, ABSOLUTE ZERO= +All modules: Model→Edit attributes→model name: Physical +Constants: toggle on Absolute zero temperature: +Adiabatic process +By default, the fluid temperature is defined by the predefined temperature field at the cavity reference +node. However, for rapid events the fluid temperature in Abaqus/Explicit can be determined from the +conservation of energy assumed in an adiabatic process. With this assumption, no heat is added or +removed from the cavity except by transport through fluid exchange definitions or inflators. An adiabatic +process is typically well suited for modeling the deployment of an airbag. During deployment, the gas +jets out of the inflator at high pressure and cools as it expands at atmospheric pressure. The expansion is +so quick that no significant amount of heat can diffuse out of the cavity. +The energy equation can be obtained from the first law of thermodynamics. By neglecting the +kinetic and potential energy, the energy equation for a fluid cavity is given by +where the work done by the fluid cavity expansion is given as +is the heat energy flow rate due to the heat transfer through the surface of the fluid cavity. A +will generate the heat energy flow out of the primary fluid cavity. The specific +and +positive value for +energy is given by +is the initial specific energy at the initial temperature +where +is the specific heat at constant +volume (or the constant volume heat capacity), which depends only upon temperature for an ideal gas, +is the specific enthalpy, and V is the volume occupied by the gas. By definition, the specific enthalpy +, +is +is the initial specific enthalpy at the initial (or reference) temperature +where +is the +specific heat at constant pressure, which depends only upon temperature for an ideal gas. The pressure, +temperature, and density of the gas are obtained by solving the ideal gas law, the energy balance, and +mass conservation. +and +Adiabatic behavior will always be used for the fluid cavity if an adiabatic or coupled procedure is +used. +Input File Usage: +Abaqus/CAE Usage: +*FLUID CAVITY, ADIABATIC +Interaction module: Create Interaction: Fluid cavity: Property definition: +Pneumatic, toggle on Use adiabatic behavior +Defining the heat capacity at constant pressure +The heat capacity at constant pressure must be specified when modeling an adiabatic process for the ideal +gas. It can be defined either in polynomial or tabular form. The polynomial form is based on the Shomate +equation according to the National Institute of Standards and Technology. The constant pressure molar +heat capacity can be expressed as +are gas constants. These gas constants together with molecular +where the coefficients +weight are listed in Table 11.5.2–1 for some gases that are often used in airbag simulations. The constant +pressure heat capacity can then be obtained by +, and +, +, +, +The constant volume heat capacity, +, can be determined by +Table 11.5.2–1 Properties of some commonly used gases (SI units). +Gas +MW +(× 10−3 ) +(× 10−6) +(× 10−9 ) +(× 106 ) +(kelvin) +Air +0.0289 +28.110 +Nitrogen +0.028 +26.092 +Oxygen +0.032 +29.659 +1.967 +8.218 +6.137 +Hydrogen +0.00202 +33.066 +−11.36 +0.028 +25.567 +6.096 +4.802 +–1.976 +–1.186 +11.432 +4.054 +−1.966 +0.1592 +0.0957 +–2.772 +−2.671 +0.0 +273–1800 +0.0444 +298–6000 +–0.219 +298–6000 +–0.158 +273–1000 +0.131 +298–1300 +0.044 +24.997 +55.186 +−33.691 +7.948 +–0.136 +298–1200 +0.0180 +32.240 +1.923 +0.105 +−3.595 +0.0 +273–1800 +Carbon +monoxide +Carbon +dioxide +Water +vapor +You can use the polynomial form for specifying the heat capacity at constant pressure, in which +, and . Alternatively, you can define a table of constant pressure +case you enter the coefficients , +, +heat capacity versus temperature and any predefined field variables. +, +Input File Usage: +Use the following option to specify the heat capacity in polynomial form: +*CAPACITY, TYPE=POLYNOMIAL +, +, +, +, +Use the following option to specify the heat capacity in tabular form: +*CAPACITY, TYPE=TABULAR, DEPENDENCIES=n +, temperature, field_variable_1, etc... +... +Abaqus/CAE Usage: +Use the following option to specify the heat capacity in polynomial form: +Interaction module: Create Interaction Property: Fluid cavity: +Definition: Pneumatic, toggle on Specify molar heat capacity: +Polynomial, Polynomial Coefficients: +, +, +, +, +Use the following option to specify the heat capacity in tabular form: +Interaction module: Create Interaction Property: Fluid cavity: +Definition: Pneumatic: toggle on Specify molar heat capacity: +Tabular: enter the molar heat capacity +Use the following options to include temperature and field variable dependence +in the table: +Toggle on Use temperature-dependent data, Number of field variables: n +A mixture of ideal gases +Abaqus/Explicit can model a mixture of ideal gases in the fluid cavity. For ideal gas mixtures the Amagat- +Leduc rule of partial volumes is used to obtain an estimate of the molar-averaged thermal properties (Van +Wylen and Sonntag, 1985). Let each species have constant pressure and volume heat capacities, +and +. The constant pressure and volume heat capacities +; and mass fraction, +; molecular weight, +for the mixed gas are then given by +and the molecular weight is given by +The specific energy and enthalpy for the mixed gas are then given by +The energy flow entering the fluid cavity is given by +and the energy flow out of the fluid cavity is given by +Using the properties of a mixture of ideal gases as given above, the pressure and temperature can be +obtained from the ideal gas law and the energy equation. +Averaged properties for multiple fluid cavities +If the output of the state of the fluid inside the cavity is requested for a node set that contains more than +one fluid cavity, the averaged properties of the multiple fluid cavities will also be output automatically. +The average pressure is calculated by volume weighting cavity pressure contributions. The average +temperature for an adiabatic ideal gas is obtained by mass weighting cavity temperature contributions. +Let each fluid cavity have pressure +. The +average pressure of the fluid cavity cluster is then defined as +, gas constant +, temperature +, and mass +, volume +and the average temperature is +Additional reference +• Van Wylen, G. J., and R. E. Sonntag, Fundamentals of Classical Thermodynamics, Wiley, New +York, 1985. +11.5.3 +FLUID EXCHANGE DEFINITION +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Surface-based fluid cavities: overview,” Section 11.5.1 +• “Fluid cavity definition,” Section 11.5.2 +• *FLUID EXCHANGE +• *FLUID EXCHANGE PROPERTY +• *FLUID EXCHANGE ACTIVATION +• “VUFLUIDEXCH,” Section 1.2.12 of the Abaqus User Subroutines Reference Manual +• “VUFLUIDEXCHEFFAREA,” Section 1.2.13 of the Abaqus User Subroutines Reference Manual +• “Defining a fluid exchange interaction,” Section 15.13.12 of the Abaqus/CAE User’s Manual, in +the online HTML version of this manual +• “Defining a fluid exchange interaction property,” Section 15.14.5 of the Abaqus/CAE User’s +Manual, in the online HTML version of this manual +Overview +A fluid exchange definition: +• can be used to model flow between a single fluid cavity and its environment or flow between two +fluid cavities; +• can be used to prescribe mass- or volume-based flux into or out of a cavity; +• can model the venting of a cavity through an exhaust orifice; +• can model flow through cavity walls such as leakage through a porous fabric; +• can be used to prescribe heat loss through a cavity surface due to heat transfer; +• can take the local material state into account; +• can account for blockage due to contacting boundary surfaces; and +• has a name that can be used to identify history output of mass flow rates out of a cavity. +Defining fluid exchange +The fluid exchange capability is very general and can be used to define flow in and out of a cavity either +as a prescribed function or based on the pressure difference arising from analysis conditions. The flow +behavior in Abaqus/Standard is based on mass fluid flow, and the behavior in Abaqus/Explicit can be +based on mass fluid flow or heat energy flow. You must associate the fluid exchange definition with a +name. +Input File Usage: +*FLUID EXCHANGE, NAME=name +Abaqus/CAE Usage: +Interaction module: Create Interaction: Fluid exchange, Name: name +Flow between a single cavity and its environment +To define flow between a fluid cavity and its environment, specify the single reference node associated +with the fluid cavity. In the discussion that follows this fluid cavity is referred to as the primary cavity. +When the flow is defined as a prescribed function, the flow can either be into or out of the primary +cavity. If the flow is into the cavity, the properties of the material flowing in are assumed to be the +instantaneous properties of the material in the cavity itself. When the flow behavior is based on analysis +conditions, the mass flow can occur only out of the primary cavity but the heat energy flow can be either +into or out of the primary cavity. For the case of mass flow Abaqus will use the fluid cavity pressure and +the specified constant ambient pressure to calculate the pressure difference used to determine the mass +flow rate. For the case of heat energy flow Abaqus/Explicit will use the fluid cavity temperature and +the specified constant ambient temperature to calculate the temperature difference used to determine the +heat energy flow rate. +Input File Usage: +Use the following options: +*FLUID CAVITY, NAME=primary_cavity_name, +REF NODE=primary_cavity_reference_node +*FLUID EXCHANGE, NAME=fluid_exchange_name +primary_cavity_reference_node +Abaqus/CAE Usage: +Interaction module: Create Interaction: Fluid exchange: +Definition: To environment, Fluid cavity interaction: name, +Fluid exchange property: name +Flow between two fluid cavities +To define flow between two fluid cavities, specify the reference nodes associated with the primary and +secondary fluid cavities. When the flow is based on analysis conditions, the fluid will flow from the high +pressure or upstream cavity to the low pressure or downstream cavity and the heat energy will flow from +the high temperature to the low temperature. +Input File Usage: +Use the following options: +*FLUID CAVITY, NAME=primary_cavity_name, +REF NODE=primary_cavity_reference_node +*FLUID CAVITY, NAME=secondary_cavity_name, +REF NODE=secondary_cavity_reference_node +*FLUID EXCHANGE, NAME=fluid_exchange_name +primary_cavity_reference_node, secondary_cavity_reference_node +Abaqus/CAE Usage: +Interaction module: Create Interaction: Fluid exchange: Definition: +Between cavities, Fluid cavity interaction 1: name, Fluid cavity +interaction 2: name, Fluid exchange property: name +Specifying the effective area +The flow rate from the primary cavity for any fluid exchange property is proportional to the effective +leakage area. The leakage area may represent the size of an exhaust orifice, the area of a porous fabric +enclosing the cavity, or the size of a pipe between cavities. +You can specify the value of the effective leakage area directly. Alternatively, in Abaqus/Explicit +you can define a surface that represents the leakage area by specifying the name of the surface on the +boundary enclosing the primary fluid cavity. The effective area for fluid exchange is based on the area +of the surface unless you specify the area directly or define the effective area with user subroutine +VUFLUIDEXCHEFFAREA. If both the effective area and a surface are specified, the area of the surface +is used only to determine blockage; see “Accounting for blockage due to contacting boundary surfaces,” +below. If neither area is specified, the effective area defaults to 1.0. +You can also define the effective leakage area with user subroutine VUFLUIDEXCHEFFAREA if +leakage needs to be modeled as a function of the material state in the underlying elements of the specified +surface. For example, this subroutine can be used to define the leakage area at an element level for +modeling fabric permeability in uncoated airbags where the leakage can vary locally depending on the +strains in the yarn directions and the angle between the fabric yarns. Only membrane elements are +supported for use with VUFLUIDEXCHEFFAREA. +Input File Usage: +Use the following option to specify the effective leakage area directly and to +specify a surface that represents the leakage area: +*FLUID EXCHANGE, EFFECTIVE AREA=effective_area, +SURFACE=surface_name +Use the following option to define the effective leakage area with a user +subroutine: +*FLUID EXCHANGE, EFFECTIVE AREA=USER, +SURFACE=surface_name +Abaqus/CAE Usage: +Interaction module: Create Interaction: Fluid exchange: +Effective exchange area: effective_area +User subroutine VUFLUIDEXCHEFFAREA is not supported in Abaqus/CAE. +Application of fluid cavity pressure on a fluid exchange surface +You can control how the effect of the cavity pressure on a fluid exchange surface is accounted for in +Abaqus/Explicit. By default, the cavity pressure generates forces at all of the fluid exchange surface +nodes, using the same method as for other portions of the fluid cavity. Optionally, the resultant force of +the cavity pressure on the fluid exchange surface can be distributed only among the perimeter nodes of +the fluid exchange surface; this option can be used to avoid local bulging of a vent surface that can cause +inaccurate computation of the leakage area. +Input File Usage: +Use the following option (default) to indicate that the fluid pressure should +generate forces on all nodes of a fluid exchange surface: +*FLUID EXCHANGE, CAVITY PRESSURE=SURFACE, +SURFACE=surface_name +Use the following option to indicate that the fluid pressure should generate force +only on perimeter nodes of a fluid exchange: +*FLUID EXCHANGE, CAVITY PRESSURE=PERIMETER, +SURFACE=surface_name +Abaqus/CAE Usage: +You cannot change the default pressure application in Abaqus/CAE. The +pressure is always applied to all of the fluid exchange surface nodes. +Defining the fluid exchange property +There are several different types of fluid exchange properties available in Abaqus to define the rate flow +from a fluid cavity to the environment or between two cavities. The fluid exchange property can be as +simple as prescribing the mass or volume flow rate directly. More complex leakage mechanisms such +as those found on automotive airbags can be modeled by defining the mass or volume leakage rate as a +function of the pressure difference, +. The heat loss +; the absolute pressure, +due to heat transfer through the surface of the cavity can be modeled in Abaqus/Explicit by prescribing +the heat energy flow rate directly or by defining the heat energy flow rate as a function of the temperature +difference, +. Alternatively, in Abaqus/Explicit the +; and the temperature, +mass flow rate and/or heat energy flow rate can be specified in user subroutine VUFLUIDEXCH. +; the absolute pressure, +; and the temperature, +For the purposes of evaluating the mass flow rate between two cavities, the absolute pressure and +temperature are taken from the high pressure or upstream cavity. The mass flow is always in the direction +from the high pressure cavity to the low pressure or downstream cavity, and the heat energy flow is always +in the direction from the high temperature cavity to the low temperature cavity. The cavity absolute +pressure and temperature are always used to calculate the flow between a cavity and the environment. +You must associate the fluid exchange property with a name. This name can then be used to associate +a certain property with a fluid exchange definition. +Input File Usage: +Use the following options: +Abaqus/CAE Usage: +*FLUID EXCHANGE, NAME=fluid_exchange_name, +PROPERTY=property_name +*FLUID EXCHANGE PROPERTY, NAME=property_name +Interaction module: Create Interaction Property: Fluid +exchange, Name: property_name +Specifying a mass or volume flux +Fluid flux into or out of the primary fluid cavity can be defined directly by prescribing the mass flow rate +per unit area, +. The mass flow rate is +where A is the effective area. +. The mass flow +rate is +FLUID EXCHANGE +where +is the density. +A negative value for +or will generate flux into the primary fluid cavity. When a second fluid +cavity is not defined, the state of the fluid flowing into the primary cavity is assumed to be that of the +fluid already present in the primary cavity. +Input File Usage: +Abaqus/CAE Usage: +To prescribe a flux based on mass flow rate: +*FLUID EXCHANGE PROPERTY, TYPE=MASS FLUX +To prescribe a flux based on volumetric flow rate: +*FLUID EXCHANGE PROPERTY, TYPE=VOLUME FLUX +Interaction module: Create Interaction Property: Fluid exchange: +Definition: Mass flux or Volume flux +Specifying the flow rate using the viscous and hydrodynamic resistance coefficients +The mass flow rate, +coefficients such as +, can be related to pressure difference by both viscous and hydrodynamic resistance +where +is the pressure difference, A is the effective area, +is the viscous resistance coefficient, and +is the hydrodynamic resistance coefficient. The resistance coefficients can be functions of the average +absolute pressure, average temperature, and average of any user-defined field variables. A positive value +of +corresponds to flow out of the first cavity. +Input File Usage: +*FLUID EXCHANGE PROPERTY, TYPE=BULK VISCOSITY, +DEPENDENCIES=n +viscous resistance coefficient ( +), hydrodynamic resistance coefficient ( +) +Abaqus/CAE Usage: +Interaction module: Create Interaction Property: Fluid +exchange: Definition: Bulk viscosity: Viscous coefficient: +: Hydrodynamic coefficient: +Use the following options to include pressure, temperature, and field variable +dependence: +Toggle on Use pressure-dependent data, toggle on Use +temperature-dependent data, Number of field variables: n +Specifying the flow rate through a vent or exhaust orifice +The mass flow rate through a vent or exhaust orifice that can be approximated by one-dimensional, quasi- +steady, and isentropic flow is given (Bird, Stewart and Lightfoot, 2002) by +where C is the dimensionless discharge coefficient, A is the vent or exhaust orifice area, +temperature in the upstream fluid cavity, +and +is the +is the absolute zero on the temperature scale being used, +is the absolute pressure in the upstream fluid cavity. The pressure ratio, q, is defined as +is the absolute pressure in the orifice. The critical pressure, +where +occurs is defined as +, at which choked or sonic flow +where +is the ratio of the constant pressure heat capacity, +, and the constant volume heat capacity, +: +The orifice pressure, +, is then given by +where +pressure for flow between two fluid cavities. +is equal to the ambient pressure for flow out of a single fluid cavity or the downstream cavity +The value of the discharge coefficient can be a function of the absolute upstream pressure, upstream +temperature, and any user-defined field variables. Fluid exchange through a vent or exhaust orifice is +valid only for pneumatic fluids. +Input File Usage: +*FLUID EXCHANGE PROPERTY, TYPE=ORIFICE, DEPENDENCIES=n +discharge coefficient +Abaqus/CAE Usage: +Fluid exchange through vents or orifices is not supported in Abaqus/CAE. +Specifying the flow rate due to fabric leakage +The mass flow rate due to leakage through fabric can be expressed as +where C is the dimensionless fabric leakage or discharge coefficient and A is the effective fabric leakage +area. +The value of the discharge coefficient can be a function of absolute upstream pressure, upstream +temperature, and any user-defined field variables. +Input File Usage: +*FLUID EXCHANGE PROPERTY, TYPE=FABRIC LEAKAGE, +DEPENDENCIES=n +discharge coefficient +Abaqus/CAE Usage: +Defining fluid exchange due to fabric leakage is not supported in Abaqus/CAE. +Specifying a table of mass flow rate versus pressure difference +The overall mass flow rate can be calculated from a specified mass flow rate per unit area, +, by +where A is the effective area. +In this case you can define the mass flow rate per unit area in a table depending on the absolute +value of pressure difference and, optionally, on the average absolute pressure, average temperature, and +average value of any user-defined field variables. Values for +must be positive and start from +zero. +and +Input File Usage: +*FLUID EXCHANGE PROPERTY, TYPE=MASS RATE LEAKAGE, +DEPENDENCIES=n +0, 0 +, +... +Abaqus/CAE Usage: +Interaction module: Create Interaction Property: Fluid +exchange: Definition: Mass rate leakage: Mass Flow Rate: +, Pressure Difference: +Use the following options to include pressure, temperature, and field variable +dependence: +Toggle on Use pressure-dependent data, toggle on Use +temperature-dependent data, Number of field variables: n +Specifying a table of volumetric flow rate versus pressure difference +The overall mass flow rate can be calculated from a specified volumetric flow rate per unit area, +, by +where A is the effective area and +is the density. +In this case you can define the volumetric flow rate per unit area in a table depending on the absolute +value of pressure difference and, optionally, on the average absolute pressure, average temperature, and +average value of any user-defined field variables. Values for +must be positive and start from +zero. +and +Input File Usage: +*FLUID EXCHANGE PROPERTY, TYPE=VOLUME RATE LEAKAGE, +DEPENDENCIES=n +0, 0 +, +... +Abaqus/CAE Usage: +Interaction module: Create Interaction Property: Fluid exchange: +Definition: Volume rate leakage: Volumetric Flow Rate: +, Pressure Difference: +Use the following options to include pressure, temperature, and field variable +dependence: +Toggle on Use pressure-dependent data, toggle on Use +temperature-dependent data, Number of field variables: n +Specifying a heat energy flux +In Abaqus/Explicit heat energy flux into or out of the primary fluid cavity can be defined directly by +prescribing the heat energy flow rate per unit area, +. The heat energy flow rate is +where A is the effective area. A positive value for +generates heat flux out of the primary fluid cavity. +Input File Usage: +Abaqus/CAE Usage: +*FLUID EXCHANGE PROPERTY, TYPE=ENERGY FLUX +Defining fluid exchange by specifying the heat energy flow rate explicitly is not +supported in Abaqus/CAE. +Specifying a table of heat energy flow rate versus temperature difference +The overall heat energy flow rate can be calculated from a specified heat energy flow rate per unit area, +, by +where A is the effective area. +In this case in Abaqus/Explicit you can define the heat energy flow rate per unit area in a table +depending on the absolute value of temperature difference and, optionally, on the average absolute +pressure, average temperature, and average value of any user-defined field variables. Values for +and +must be positive and start from zero. +Input File Usage: +*FLUID EXCHANGE PROPERTY, TYPE=ENERGY RATE LEAKAGE, +DEPENDENCIES=n +0, 0 +, +... +Abaqus/CAE Usage: +Defining fluid exchange by specifying the heat energy flow rate as a function +of temperature difference and pressure is not supported in Abaqus/CAE. +Specifying mass flow rate and/or heat energy flow rate with a user subroutine +The mass flow rate, +, can be defined in Abaqus/Explicit using +user subroutine VUFLUIDEXCH . +, or the overall heat energy flow rate, +Input File Usage: +*FLUID EXCHANGE PROPERTY, TYPE=USER +Abaqus/CAE Usage: +User subroutine VUFLUIDEXCH is not supported in Abaqus/CAE. +Activating the fluid exchange definition +Fluid exchange will not occur in Abaqus/Explicit unless the fluid exchange definition is activated in an +analysis step. +Input File Usage: +Use the following options to activate a fluid exchange for a given analysis step: +*FLUID EXCHANGE, NAME=fluid_exchange_name +*FLUID EXCHANGE ACTIVATION +fluid_exchange_name +Abaqus/CAE Usage: +Fluid exchange is activated automatically for Abaqus/Explicit steps in +Abaqus/CAE. +Varying the magnitude of the flow +By default, the magnitude of the flow is based on the specified flow behavior. A time variation of flow +magnitude during a step can be introduced by an amplitude curve. The magnitude based on the specified +flow behavior is multiplied by the amplitude value to obtain the actual mass or heat energy flow rate. For +example, a time variation of prescribed mass or volumetric flux can be defined. +An amplitude curve may be used to trigger an event for fluid exchange in the middle of a step. For +example, an airbag may deploy at some predetermined time during a step, and it may be desirable to +close off all exhaust orifices until the actual deployment. A step amplitude curve that starts at zero and +steps up at deployment time could be used for this purpose. +Input File Usage: +Use the following options: +Abaqus/CAE Usage: +*AMPLITUDE, NAME=amplitude_name +*FLUID EXCHANGE ACTIVATION, AMPLITUDE=amplitude_name +The use of an amplitude to activate a fluid exchange is not supported in +Abaqus/CAE. +Accounting for blockage due to contacting boundary surfaces +Abaqus/Explicit can account for the blockage of flow out of a cavity due to an obstruction caused by +contacting surfaces. For example, flow out of an exhaust orifice may be fully or partially blocked because +it is covered by another contacting surface. +Blockage can be considered for any fluid exchange property. However, a surface must be defined +on the boundary of the fluid cavity to be checked for contact obstruction. Abaqus/Explicit will calculate +the area fraction of the surface not blocked by contacting surfaces and apply this fraction to the mass or +energy flow rate out of the cavity. You can control the combination of surfaces that can cause blockage. +Abaqus/Explicit will not consider contacting surfaces to cause blockage unless you specify that they can +potentially cause blockage . +Input File Usage: +Abaqus/CAE Usage: +*FLUID EXCHANGE ACTIVATION, BLOCKAGE=YES +Accounting for blockage due to contacting boundary surfaces is not supported +in Abaqus/CAE. +Limiting the flow direction +By default, flow can occur both in and out of the primary fluid cavity when a second node is included +in the fluid exchange definition. In addition, heat energy flow can occur in both directions when flow is +defined between a single cavity and its environment. You can limit the flow direction in Abaqus/Explicit +in these cases such that fluid or heat energy flows only out of the primary fluid cavity. This method is +relevant only for a fluid exchange definition based on analysis conditions and not on prescribed mass, +volume, or heat energy flux. +Input File Usage: +Abaqus/CAE Usage: +*FLUID EXCHANGE ACTIVATION, OUTFLOW ONLY +Limiting the flow direction is not supported by Abaqus/CAE. +Activating the fluid exchange based on the change in the leakage area +The flow between cavities can be activated in Abaqus/Explicit based on a change in the area of the surface +defining the effective area. You need to specify the ratio of the actual surface area to the initial effective +area, which represents the threshold value for triggering the fluid exchange. The effective area used for +the fluid exchange between the cavities (or between the cavity and the ambient) is the area difference +between the actual area and the initial area. +Input File Usage: +Use the following options: +*FLUID EXCHANGE, SURFACE=surface_name +*FLUID EXCHANGE ACTIVATION, DELTA LEAKAGE +AREA=surface_ratio +Abaqus/CAE Usage: +Activating the fluid exchange based on the change in the leakage area is not +supported by Abaqus/CAE. +Activation in multiple steps +By default, when you modify the activation of a fluid exchange definition or activate a new fluid +exchange definition, all existing fluid exchange activations in the step remain. When modifying an +existing activation, all applicable data must be respecified. +Activated fluid exchange definitions remain active in subsequent steps unless deactivated. You can +choose to deactivate all fluid exchange definitions in the model and optionally reactivate new ones. If +you deactivate any fluid exchange definition in a step, all fluid exchange definitions must be respecified. +Input File Usage: +Use the following option to modify an existing fluid exchange activation or to +specify an additional fluid exchange activation (default): +*FLUID EXCHANGE ACTIVATION, OP=MOD +Use the following option to deactivate all fluid exchange definitions in the +model and optionally reactivate new ones: +*FLUID EXCHANGE ACTIVATION, OP=NEW +Fluid exchange activation is automatic for all fluid exchange interactions in all +steps in Abaqus/CAE. No modifications or additions are allowed. +Abaqus/CAE Usage: +Additional reference +• Bird, R. B., W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, Wiley, New York, 2002. +11.5.4 +INFLATOR DEFINITION +Product: Abaqus/Explicit +References +• “Surface-based fluid cavities: overview,” Section 11.5.1 +• “Fluid cavity definition,” Section 11.5.2 +• “Fluid exchange definition,” Section 11.5.3 +• *FLUID INFLATOR +• *FLUID INFLATOR PROPERTY +• *FLUID INFLATOR ACTIVATION +Overview +An inflator definition: +• can be used to inflate a fluid cavity to simulate actual inflators used for airbag supplemental restraint +systems; +• can inflate a fluid cavity with an ideal gas mixture different from that present in the fluid cavity; +• can be specified directly or by defining data from a tank test; +• has a name that can be used to identify history output of mass flow rates; and +• can be activated at any time during the analysis. +Defining an inflator +The inflator capability in Abaqus/Explicit is suited for modeling the flow characteristics of inflators used +for airbag systems. You must associate the inflator definition with a name. You specify the reference +node of the fluid cavity that the inflator will fill with gas. A single fluid cavity can have any number of +inflators. +Input File Usage: +*FLUID INFLATOR, NAME=name +fluid_cavity_reference_node +Defining the inflator property +The inflator property defines the mass flow rate and temperature as a function of inflation time either +directly or by entering tank test data. It also defines the mixture of gases entering the fluid cavity. You +must associate the inflator property with a name. This name can then be used to associate a certain +property with an inflator definition. +Input File Usage: +Use the following options: +*FLUID INFLATOR, NAME=fluid_inflator_name, +PROPERTY=property_name +*FLUID INFLATOR PROPERTY, NAME=property_name +Specifying the gas temperature and mass flow rate directly +The temperature and the mass flow rate of the gas entering the fluid cavity can be given directly as +functions of inflation time. Enter a table of mass flow rate and temperature versus inflation time. +Input File Usage: +*FLUID INFLATOR PROPERTY, TYPE=TEMPERATURE AND MASS +inflation time, inflator gas temperature, inflator mass flow rate +... +Using tank test data +The mass flow rate and the temperature of the gas entering the fluid cavity can be determined by the +results of a tank test. In the test the inflator is discharged into a closed, fixed volume tank, and the time +history of pressure in the tank is measured. The inflator mass flow rate can then be calculated from the +pressure history using the equations of gas dynamics. For an ideal gas, conservation of energy for an +adiabatic process is given by +where +and +is the temperature, +is the absolute zero on the temperature scale being used, and the subscripts +refer to quantities in the inflator and the rigid tank, respectively. Using mass balance +and the equation of state for an ideal gas with constant volume gives +The mass flow rate can be found by combining the above equations +where +is the ratio of the constant pressure heat capacity, +, and the constant volume heat capacity, +: +To calculate the mass flow rate using the results of a tank test, enter a table of tank pressure and inflator +temperature versus inflation time, and specify the volume of the tank. +Input File Usage: +*FLUID INFLATOR PROPERTY, TYPE=TANK TEST, TANK +VOLUME= +inflation time, inflator gas temperature, tank pressure +... +Using the dual pressure method +If both the inflator pressure, +, time history curves can be measured during +a tank test, the inflator mass flow rate and temperature can then be calculated using the assumption of +isentropic flow (Wang and Nefske, 1988). The mass flow rate through the inflator orifice can be described +by +, and tank pressure, +where C is the discharge coefficient, A is the effective area, and the coefficient +assuming choked or sonic flow as +is determined by +Comparing the expression for inflator mass flow rate obtained in a rigid tank with that given above, the +inflator temperature is given by +and the inflator mass flow rate is +To calculate the inflator mass flow rate and temperature using the dual pressure method, enter a +table of tank pressure and inflator pressure versus inflation time; and specify the volume of the tank, the +effective area, and the discharge coefficient. The tank volume and effective area must be specified. The +discharge coefficient has a default value of 0.4. +Input File Usage: +*FLUID INFLATOR PROPERTY, TYPE=DUAL PRESSURE, +TANK VOLUME= +DISCHARGE COEFFICIENT=C +inflation time, inflator pressure, tank pressure +... +, EFFECTIVE AREA=A, +Specifying the inflator pressure and mass flow rate directly +You can enter a table of the mass flow rate and inflator pressure versus inflation time and specify the +effective area and discharge coefficient. The gas temperature in the inflator will be calculated by using +the assumption of isentropic flow. The effective area must be specified. The discharge coefficient has a +default value of 0.4. +Input File Usage: +*FLUID INFLATOR PROPERTY, TYPE=PRESSURE AND MASS, +EFFECTIVE AREA=A, DISCHARGE COEFFICIENT=C +inflation time, inflator pressure, inflator mass flow rate +... +Specifying the gas mixture +To define the inflator gas mixture, specify the number of gas species used for the inflator, and enter a +list of names of fluid behaviors and a table of the mass fraction or molar fraction of the species. The +mass fraction or molar fraction of the species may be a function of inflation time. The sum of the mass +fractions or molar fractions for the species should be equal to one at any given time. +Input File Usage: +Use the following options to specify the gas mixture in terms of the mass +fractions: +*FLUID INFLATOR PROPERTY +*FLUID INFLATOR MIXTURE, NUMBER SPECIES=k, +TYPE=MASS FRACTION +fluid_behavior_name_1, fluid_behavior_name_2, etc. +inflation time, mass fraction 1, mass fraction 2, etc. +... +Use the following options to specify the gas mixture in terms of the molar +fractions: +*FLUID INFLATOR PROPERTY +*FLUID INFLATOR MIXTURE, NUMBER SPECIES=k, +TYPE=MOLAR FRACTION +fluid_behavior_name_1, fluid_behavior_name_2, etc. +inflation time, molar fraction 1, molar fraction 2, etc. +... +Activating the inflator definition +Inflation will not occur unless the inflation definition is activated in an analysis step. +Input File Usage: +Use the following options to activate a fluid inflator for a given analysis step: +*FLUID INFLATOR, NAME=fluid_inflator_name +*FLUID INFLATOR ACTIVATION +fluid_inflator_name +Relating inflation time to analysis time +Inflator property definition consists of specifying tables of gas variables versus inflation time. +Abaqus/Explicit the inflation time, +, is related to the value of an amplitude curve +by +In +Typically the amplitude variation is a step function stepping from zero to one at the time the airbag should +be deployed. This amplitude variation has the effect of offsetting the inflation time from the analysis time. +Input File Usage: +Use the following options: +*AMPLITUDE, NAME=amplitude_name +*FLUID INFLATOR ACTIVATION, INFLATION TIME +AMPLITUDE=amplitude_name +Modifying the mass flow rate +If the mass flow rate is prescribed directly in the inflator property definition, you can modify it by +specifying an amplitude definition during a step. However, if the mass flow rate is calculated by using +tank test data or the dual pressure method, the amplitude definition will be ignored. +Input File Usage: +Use the following options: +*AMPLITUDE, NAME=amplitude_name +*FLUID INFLATOR ACTIVATION, MASS FLOW +AMPLITUDE=amplitude_name +Activation in multiple steps +By default, when you modify the activation of a fluid inflator definition or activate a new fluid inflator +definition, all existing fluid inflator activations in the step remain. When modifying an existing activation, +all applicable parameters must be respecified. +Activated inflator definitions remain active in subsequent steps unless deactivated. You can choose +If you +to deactivate all fluid inflator definitions in the model and optionally reactivate new ones. +deactivate any fluid inflator definition in a step, all fluid inflator definitions must be respecified. +Input File Usage: +Use the following option to modify an existing fluid inflator activation or to +specify an additional fluid inflator activation (default): +*FLUID INFLATOR ACTIVATION, OP=MOD +Use the following option to deactivate all fluid inflator definitions in the model +and optionally reactivate new ones: +*FLUID INFLATOR ACTIVATION, OP=NEW +Additional reference +• Wang, J. T., and O. J. Nefske, “A New CAL3D Airbag Inflation Model,” SAE paper 880654, 1988. +11.6 +Mass scaling +• “Mass scaling,” Section 11.6.1 +11.6.1 +MASS SCALING +Products: Abaqus/Explicit Abaqus/CAE +References +• “Explicit dynamic analysis,” Section 6.3.3 +• “Adjust and/or redistribute mass of an element set,” Section 2.6.1 +• “Output,” Section 4.1.1 +• *FIXED MASS SCALING +• *VARIABLE MASS SCALING +• “Configuring a dynamic, explicit procedure” in “Configuring general analysis procedures,” +Section 14.11.1 of the Abaqus/CAE User’s Manual, in the online HTML version of this manual +• “Configuring a dynamic fully coupled thermal-stress procedure using explicit integration” in +“Configuring general analysis procedures,” Section 14.11.1 of the Abaqus/CAE User’s Manual, in +the online HTML version of this manual +Overview +Mass scaling is often used in Abaqus/Explicit for computational efficiency in quasi-static analyses and +in some dynamic analyses that contain a few very small elements that control the stable time increment. +Mass scaling can be used to: +• scale the mass of the entire model or scale the masses of individual elements and/or element sets; +• scale the mass on a per step basis in a multistep analysis; and +• scale the mass at the beginning of the step and/or throughout the step. +Mass scaling can be performed by: +• scaling the masses of all specified elements by a user-supplied constant factor; +• scaling the masses of all specified elements by the same value so that the minimum stable time +increment for any element in the element set is equal to a user-supplied time increment; +• scaling the masses of only the elements in the element set whose element stable time increments are +less than a user-supplied time increment so that the element stable time increment for these elements +becomes equal to the user-supplied time increment; +• scaling the masses of all specified elements so that their element stable time increments each become +equal to the user-supplied time increment; and +• scaling automatically based on mesh geometry and initial conditions for bulk metal rolling analyses. +Introduction +The explicit dynamics procedure is typically used to solve two classes of problems: transient dynamic +response calculations and quasi-static simulations involving complex nonlinear effects (most commonly +problems involving complex contact conditions). Because the explicit central difference method is +used to integrate the equations in time , the discrete +mass matrix used in the equilibrium equations plays a crucial role in both computational efficiency +and accuracy for both classes of problems. When used appropriately, mass scaling can often improve +the computational efficiency while retaining the necessary degree of accuracy required for a particular +problem class. However, the mass scaling techniques most appropriate for quasi-static simulations may +be very different from those that should be used for dynamic analyses. +Quasi-static analysis +For quasi-static simulations incorporating rate-independent material behavior, the natural time scale is +generally not important. To achieve an economical solution, it is often useful to reduce the time period +of the analysis or to increase the mass of the model artificially (“mass scaling”). Both alternatives +yield similar results for rate-independent materials, although mass scaling is the preferred means of +reducing the solution time if rate dependencies are included in the model because the natural time scale +is preserved. +Mass scaling for quasi-static analysis is usually performed on the entire model. However, when +different parts of a model have different stiffness and mass properties, it may be useful to scale only +selected parts of the model or to scale each of the parts independently. In any case, it is never necessary +to reduce the mass of the model from its physical value, and it is generally not possible to increase +the mass arbitrarily without degrading accuracy. A limited amount of mass scaling is usually possible +for most quasi-static cases and will result in a corresponding increase in the time increment used by +Abaqus/Explicit and a corresponding reduction in computational time. However, you must ensure that +changes in the mass and consequent increases in the inertial forces do not alter the solution significantly. +Although mass scaling can be achieved by modifying the densities of the materials in the model, +the methods described in this section offer much more flexibility, especially in multistep analyses. +See “Rolling of thick plates,” Section 1.3.6 of the Abaqus Example Problems Manual, for a +discussion of using mass scaling in a quasi-static analysis. +Dynamic analysis +The natural time scale is always important in dynamic analysis, and an accurate representation of the +physical mass and inertia in the model is required to capture the transient response. However, many +complex dynamic models contain a few very small elements, which will force Abaqus/Explicit to use a +small time increment to integrate the entire model in time. These small elements are often the result of +a difficult mesh generation task. By scaling the masses of these controlling elements at the beginning of +the step, the stable time increment can be increased significantly, yet the effect on the overall dynamic +behavior of the model may be negligible. +During an impact analysis, elements near the impact zone typically experience large amounts +of deformation. The reduced characteristic lengths of these elements result in a smaller global time +increment. Scaling the mass of these elements as required throughout the simulation can significantly +decrease the computation time. For cases in which the compressed elements are impacting a stationary +rigid body, increases in mass for these small elements during the simulation will have very little effect +on the overall dynamic response. +Mass scaling for truly dynamic events should almost always occur only for a limited number of +elements and should never significantly increase the overall mass properties of the model, which would +degrade the accuracy of the dynamic solution. +See “Impact of a copper rod,” Section 1.3.10 of the Abaqus Benchmarks Manual, for a discussion +of using mass scaling in a dynamic analysis. +Stable time increments +Throughout this section the term “element stable time increment” refers to the stable time increment of +a single element. The term “element-by-element stable time increment” refers to the minimum element +stable time increment within a specific element set. The term “stable time increment” refers to the stable +time increment of the entire model, regardless of whether the global estimator or the element-by-element +estimator is used. +Introducing mass scaling into a model +Two types of mass scaling are available in Abaqus/Explicit: fixed mass scaling and variable mass +scaling. These two types of mass scaling can be applied separately, or they can be applied together to +define an overall mass scaling strategy. The mass scaling can also apply globally to the entire model or, +alternatively, on an element set by element set basis. +Fixed mass scaling +Fixed mass scaling is performed once at the beginning of the step for which it is specified. Two basic +approaches are available for fixed mass scaling: you can define a mass scaling factor directly, or you can +define a desired minimum stable time increment for which the mass scaling factors are determined by +Abaqus/Explicit. +If both variable mass scaling and fixed mass scaling are specified in a step, the element original +mass is scaled once at beginning of that step based on the specified fixed mass scaling. It is then further +scaled at the beginning and periodically during that step based on the specified variable mass scaling. +Fixed mass scaling provides a simple means to modify the mass properties of a quasi-static model at +the beginning of an analysis or to modify the masses of a few small elements in a dynamic model so that +they do not control the stable time increment size. Since the scaling operation is performed only once +at the beginning of the step for which the mass scaling is defined, fixed mass scaling is computationally +efficient. +Input File Usage: +Abaqus/CAE Usage: +*FIXED MASS SCALING +Step module: Create Step: General, Dynamic, Explicit or Dynamic, +Temp-disp, Explicit: Mass scaling: Use scaling definitions below: +Create: Semi-automatic mass scaling, Scale: At beginning of step +Variable mass scaling +Variable mass scaling is used to scale the mass of elements at the beginning of a step and periodically +during that step. When using this type of mass scaling, you define a desired minimum stable time +increment: mass scaling factors will be calculated automatically and applied, as required, throughout +the step. +If both variable mass scaling and fixed mass scaling are specified in a step, the element original +mass is scaled once at beginning of that step based on the specified fixed mass scaling. It is then further +scaled at the beginning and periodically during that step based on the specified variable mass scaling. +Variable mass scaling is most useful when the stiffness properties that control the stable time +increment change drastically during a step. This situation can occur in both quasi-static bulk forming +and dynamic simulations in which elements are highly compressed or crushed. +Input File Usage: +Abaqus/CAE Usage: +*VARIABLE MASS SCALING +Step module: Create Step: General, Dynamic, Explicit or Dynamic, +Temp-disp, Explicit: Mass scaling: Use scaling definitions below: +Create: Semi-automatic mass scaling, Scale: Throughout step +Defining a scale factor directly +Defining a scale factor directly is useful for quasi-static analyses in which the kinetic energy in the model +should remain small. You can define a fixed mass scaling factor that is applied to the original mass of +all elements in a specified element set. The masses of the elements will be scaled at the beginning of the +step and held fixed throughout the step unless further modified by variable mass scaling. +Input File Usage: +Abaqus/CAE Usage: +*FIXED MASS SCALING, FACTOR=scale_factor +For example, the following option scales the masses of elements contained in +element set elset by a factor of 10: +*FIXED MASS SCALING, FACTOR=10., ELSET=elset +Step module: Create Step: General, Dynamic, Explicit or Dynamic, +Temp-disp, Explicit: Mass scaling: Use scaling definitions below: +Create: Semi-automatic mass scaling, Scale: At beginning +of step, Scale by factor: scale_factor +Defining a desired element-by-element stable time increment +You can define a desired element-by-element stable time increment for an element set for fixed or variable +mass scaling. Abaqus/Explicit will then determine the necessary mass scaling factors. There are three +mutually exclusive methods available to scale the mass of the model when a desired element-by-element +stable time increment is defined. Each method is described in detail later in this section. +To determine the stable time increment used during an increment, Abaqus/Explicit first determines +the smallest stable time increment on an element-by-element basis. Then, a global estimation algorithm +determines a stable time increment based on the highest frequency of the model. The larger of the two +estimates determines the stable time increment used. In general, the stable time increment determined +by the global estimator will be greater than the stable time increment determined by the element-by- +element estimator. When fixed or variable mass scaling is used with a specified element-by-element +stable time increment to scale the mass of a set of elements, the element-by-element stable time increment +estimate is being affected directly. If all of the elements in the model are being scaled by a single mass +scaling definition, the element-by-element estimate will equal the value assigned to the element-by- +element stable time increment unless the penalty method is being used to enforce contact constraints. +Penalty contact can cause the element-by-element estimate to be slightly below the value assigned to the +element-by-element stable time increment . The +actual stable time increment used may be greater than the value assigned to the element-by-element stable +time increment because of the use of the global estimator. If mass scaling is performed on only a portion +of the model, the elements that are not scaled may have element stable time increments that are less +than the value assigned to the element-by-element stable time increment and in that case will control the +element-by-element stable time increment estimate. As a result, if only portions of the model are being +scaled, the time increment used will generally not equal the value assigned to the element-by-element +stable time increment. +If the fixed time increment size for the explicit dynamic step is based on the initial element-by- +element stability limit or is specified directly, the time increment used will be calculated according to the +rules described in “Explicit dynamic analysis,” Section 6.3.3. +Scaling the mass uniformly +Scaling the mass uniformly is useful for quasi-static analyses in which the kinetic energy in the model +should remain small. This approach is similar to defining a scale factor directly. In both cases the masses +of all the elements specified are scaled uniformly by a single factor. However, with this method the mass +scaling factor is determined by Abaqus/Explicit instead of being user specified. A single mass scaling +factor is applied uniformly to all the elements so that the minimum stable time increment within these +elements is equal to the value assigned to the element-by-element stable time increment, dt. +Input File Usage: +Use either of the following options: +Abaqus/CAE Usage: +*FIXED MASS SCALING, TYPE=UNIFORM, DT=dt +*VARIABLE MASS SCALING, TYPE=UNIFORM, DT=dt +Step module: Create Step: General, Dynamic, Explicit or Dynamic, +Temp-disp, Explicit: Mass scaling: Use scaling definitions below: +Create: Semi-automatic mass scaling, Scale: At beginning of +step or Throughout step, Scale to target time increment of: dt, +Scale element mass: Uniformly to satisfy target +Scaling only elements with element stable time increments below the specified element-by-element +stable time increment +Scaling elements with element stable time increments below a user-specified value is appropriate for +both quasi-static and dynamic analyses. It is useful for increasing the element stable time increment of +the most critical elements. +When the mesh at the beginning of an analysis or a step contains a few very small elements that +control the stable time increment size, use fixed mass scaling to scale the masses of those elements and +start the step with a desired time increment value. Increasing the mass of only these controlling elements +means that the stable time increment can be increased significantly, yet the effect on the overall behavior +of the model may be negligible. +For analyses in which evolving deformation creates a limited number of small elements, use variable +mass scaling to scale the masses of those elements, thereby limiting the reduction in the stable time +increment. +Input File Usage: +Abaqus/CAE Usage: +Use either of the following options: +*FIXED MASS SCALING, TYPE=BELOW MIN, DT=dt +*VARIABLE MASS SCALING, TYPE=BELOW MIN, DT=dt +Step module: Create Step: General, Dynamic, Explicit or Dynamic, +Temp-disp, Explicit: Mass scaling: Use scaling definitions below: +Create: Semi-automatic mass scaling, Scale: At beginning of +step or Throughout step, Scale to target time increment of: dt, +Scale element mass: If below minimum target +Scaling all elements to have equal element stable time increments +Scaling all elements such that they have the same stable time increment effectively contracts the +eigenspectrum of the model; +that is, it reduces the range between the lowest and highest natural +frequency of the model. Because of the drastic change in mass properties, this approach is appropriate +only for quasi-static analyses. It implies that some elements may have mass scaling factors that are less +than one. +Input File Usage: +Abaqus/CAE Usage: +Use either of the following options: +*FIXED MASS SCALING, TYPE=SET EQUAL DT, DT=dt +*VARIABLE MASS SCALING, TYPE=SET EQUAL DT, DT=dt +Step module: Create Step: General, Dynamic, Explicit or Dynamic, +Temp-disp, Explicit: Mass scaling: Use scaling definitions below: +Create: Semi-automatic mass scaling, Scale: At beginning of +step or Throughout step, Scale to target time increment of: dt, +Scale element mass: Nonuniformly to equal target +Global and local mass scaling +Specifying an element set for either fixed or variable mass scaling scales the mass of a localized region +of the model. Omitting an element set implies that mass scaling will be performed for all elements. A +global definition can be overwritten by a local definition for a given element set by repeating the mass +scaling definition with an element set specified. +Input File Usage: +Use either of the following options: +*FIXED MASS SCALING, ELSET=elset +*VARIABLE MASS SCALING, ELSET=elset +Abaqus/CAE Usage: +Step module: Create Step: General, Dynamic, Explicit or Dynamic, +Temp-disp, Explicit: Mass scaling: Use scaling definitions below: +Create: Semi-automatic mass scaling, Scale: At beginning of +step or Throughout step, Region: Set: elset +Example 1 +Different mass scaling factors may be useful when materials with vastly different wave speeds or mesh +refinements are present in an analysis. In this example a scale factor of 50 may be desirable for the masses +of all elements in a quasi-static analysis, except for a few elements for which a mass scaling factor of +500 is used. +*FIXED MASS SCALING, FACTOR=50.0 +*FIXED MASS SCALING, FACTOR=500.0, ELSET=elset1 +The first fixed mass scaling definition scales the masses of all elements in the model by a factor of 50. The +second fixed mass scaling definition overrides the first definition for the elements contained in element +set elset1 by scaling their masses by a factor of 500. +Example 2 +An alternative method of scaling the masses of elements in elset1 is to assign a stable time increment to +them and allow Abaqus/Explicit to determine the mass scaling factors. +*FIXED MASS SCALING, FACTOR=50.0 +*FIXED MASS SCALING, DT=.5E-6, TYPE=BELOW MIN, ELSET=elset1 +The first fixed mass scaling definition scales the masses in the entire model by a factor of 50. The +second fixed mass scaling definition overrides the first definition by scaling the masses of any elements +in elset1 whose stable time increments are less than .5 × 10−6 . +Mass scaling at the beginning of the step +Fixed mass scaling is used to prescribe mass scaling only at the beginning of a step and always scales +the original element masses. When the scale factor is defined directly, the mass is scaled by the value +assigned to the scale factor. If the element-by-element stable time increment, dt, is specified, the mass +scaling is based on this value. If both the scale factor and the element-by-element stable time increment +are specified, the mass is first scaled by the value assigned to the scale factor and then possibly scaled +again, depending on the value assigned to the element-by-element stable time increment and the type of +fixed mass scaling chosen. +Local mass scaling can be defined for a specific element set. If no element set is specified, the fixed +mass scaling definition will apply to all elements in the model. Only one fixed mass scaling definition +is permitted per element set. Multiple fixed mass scaling definitions cannot contain overlapping element +sets. Local mass scaling definitions will overwrite global definitions for the specified element sets. +Input File Usage: +*FIXED MASS SCALING, FACTOR=factor, DT=dt, +TYPE=type, ELSET=elset +Abaqus/CAE Usage: +Example +Step module: Create Step: General, Dynamic, Explicit or Dynamic, +Temp-disp, Explicit: Mass scaling: Use scaling definitions below: +Create: Semi-automatic mass scaling, Scale: At beginning of step, +Scale by factor: factor, Scale to target time increment of: dt +Assume that for a quasi-static analysis a mass scaling factor of 50 is applied to all the elements in the +model. Furthermore, assume that even after being scaled by a factor of 50, a few extremely small or +poorly shaped elements are causing the stable time increment to be less than a desired minimum. To +increase the stable time increment, the following option is used: +*FIXED MASS SCALING, FACTOR=50., TYPE=BELOW MIN, DT=.5E-6 +The specified scale factor causes the masses of all the elements in the model to be scaled by a factor +of 50. If any element’s stable time increment is still below 0.5 × 10−6 after being scaled by a factor of +50.0, its mass will be scaled such that its stable time increment is equal to 0.5 × 10−6 . +Mass scaling throughout the step +Variable mass scaling with a specified element-by-element stable time increment is used to define +mass scaling that is to be performed at the beginning and throughout the step. Either the frequency in +increments or the number of intervals must be specified to define how frequently mass scaling is to be +performed. In increments other than those in which mass scaling is performed, the time increment used +will generally be different from the value assigned to the element-by-element stable time increment. +Local mass scaling can be defined for a specific element set. If no element set is specified, the +variable mass scaling definition will apply to all elements in the model. Only one variable mass scaling +definition is permitted per element set. Multiple variable mass scaling definitions cannot contain +overlapping element sets. Local mass scaling definitions will overwrite global definitions for the +specified element sets. +Input File Usage: +Abaqus/CAE Usage: +*VARIABLE MASS SCALING, DT=dt, TYPE=type, ELSET=elset +Step module: Create Step: General, Dynamic, Explicit or Dynamic, +Temp-disp, Explicit: Mass scaling: Use scaling definitions +below: Create: Semi-automatic mass scaling, Scale: Throughout +step, Scale to target time increment of: dt +Calculating the mass scaling at equally spaced increments +You can specify the number of increments between mass scaling calculations. For example, specifying +a frequency of 5 will cause mass scaling to be performed at the beginning of the step and at increments +5, 10, 15, etc. +Care should be taken when choosing the value of the frequency, since performing mass scaling every +few increments during an analysis may result in noticeable additional computational cost per increment. +Input File Usage: +*VARIABLE MASS SCALING, TYPE=type, DT=dt, FREQUENCY=n +Abaqus/CAE Usage: +Step module: Create Step: General, Dynamic, Explicit or Dynamic, +Temp-disp, Explicit: Mass scaling: Use scaling definitions below: +Create: Semi-automatic mass scaling, Scale: Throughout step, Scale +to target time increment of: dt, Scale: Every n increments +Calculating the mass scaling at equally spaced time intervals +Alternatively, you can specify the number of equally spaced time intervals at which the mass scaling +calculations are to be performed. For example, specifying 5 intervals in a step with a duration of one +second will cause mass scaling to be performed at the beginning of the step and at times of .2 , .4, .6, .8, +and 1.0 seconds. +Input File Usage: +*VARIABLE MASS SCALING, TYPE=type, DT=dt, +NUMBER INTERVAL=n +Abaqus/CAE Usage: +Step module: Create Step: General, Dynamic, Explicit or Dynamic, +Temp-disp, Explicit: Mass scaling: Use scaling definitions below: +Create: Semi-automatic mass scaling, Scale: Throughout step, Scale +to target time increment of: dt, Scale: At n equal intervals +Different mass scaling at the beginning and during the step +There are cases where it is desirable to include mass scaling at the beginning of a step that may be +modified further throughout the step. +Input File Usage: +Use both of the following options: +*FIXED MASS SCALING, FACTOR=factor, TYPE=type, DT=dt_init +*VARIABLE MASS SCALING, TYPE=type, DT=dt_min, FREQUENCY=n +or NUMBER INTERVAL=n +Abaqus/CAE Usage: +Create both of the following mass scaling definitions: +Step module: Create Step: General, Dynamic, Explicit or +Dynamic, Temp-disp, Explicit: Mass scaling: Use scaling +definitions below: Create: +Semi-automatic mass scaling, Scale: At beginning of step +Semi-automatic mass scaling, Scale: Throughout step +Example +Assume that in a dynamic impact analysis, a few extremely small or poorly shaped elements exist in the +mesh and consequently control the stable time increment. To prevent these elements from controlling +the stable time increment, it is desirable to scale their masses at the beginning of the step. In addition, +elements in a region of the mesh will develop severe distortions as a result of impact with a fixed rigid +surface. Consequently, elements in the impact zone may eventually control the stable time increment. +Since the elements in the impact zone are essentially stationary against the rigid surface, selectively +scaling their masses will guarantee that the overall dynamic response is not adversely affected. Mass +scaling these elements by prescribing a time increment to limit the reduction in the element-by-element +stable time increment may decrease run time substantially. +For example, specify fixed mass scaling for all elements in the model with stable time increments +below a value of 1.0 × 10−6 . In addition, specify variable mass scaling for the elements in the impact +zone (elset1) with stable time increments below a value of 0.5 × 10−6. In this case all the elements in the +model are checked at the beginning of the step. If any have stable time increments less than 1.0 × 10−6 , +their masses are scaled (independently) such that the element-by-element stable time increment equals +1.0 × 10−6 . This scaling remains in effect throughout the step and is not further modified, except for +those elements in elset1. The variable mass scaling definition causes the elements contained in elset1 to +be scaled throughout the step so that their stable time increments do not become less than 0.5 × 10−6 . +Because only elements in elset1 are scaled during the step, it is possible that a stable time increment less +than 0.5 × 10−6 may result. +Mass scaling in a multiple step analysis +The scaled element masses at the end of one step and any variable mass scaling methods specified in that +step are carried forward automatically to the subsequent step, ensuring continuity in the mass matrix at +the step boundaries and continued application of the variable mass scaling methods. However, you can +reset the element masses to their original values or recompute the element masses by using a new fixed +mass scaling method at the beginning of the subsequent step. You can also remove the variable mass +scaling methods inherited from the prior step or replace an inherited method with a new variable mass +scaling method. +To reset the initial mass matrix, specify a fixed mass scaling method in the subsequent step. +Similarly, specify a variable mass scaling method in the subsequent step to discontinue all of the +variable mass scaling methods of the prior step. The examples below illustrate the following special +cases: (a) continuous mass matrix with no further mass scaling, and (b) reverting the mass matrix to the +original state with no further mass scaling. +Very large changes in element mass across the steps due to mass scaling may lead to precision +problems in the mass calculations. These precision problems may give rise to erroneous or misleading +results. When large changes in element masses are desired in such situations, it is recommended that +fixed mass scaling be used in the new step to reset the element masses to their original values before +using additional mass scaling definitions, as required, to scale the element masses to their desired values. +Continuous mass matrix with no further scaling +To define a continuous mass matrix with no further scaling, remove any variable mass scaling definitions +inherited from the prior step by redefining a new variable mass scaling definition. +Input File Usage: +Abaqus/CAE Usage: +Example +Use the following option without any parameters in a new step: +*VARIABLE MASS SCALING +Step module: Create Step: General, Dynamic, Explicit or Dynamic, +Temp-disp, Explicit: Mass scaling: Use scaling definitions below: +Create: Disable mass scaling throughout step +Assume that during the first step of a quasi-static analysis, elements will experience distortions that will +cause the stable time increment to decrease dramatically. Furthermore, assume that the deformation +during the second step will not be large enough to have any further effect on the stable time increment. +*HEADING +… +*STEP +… +*FIXED MASS SCALING, FACTOR=1.1 +*VARIABLE MASS SCALING, TYPE=BELOW MIN, DT=1.E-5, FREQUENCY=10 +… +*END STEP +*STEP +… +*VARIABLE MASS SCALING +… +*END STEP +During the first step the fixed mass scaling increases the element mass by the factor 1.1. The variable +mass scaling definition scales the mass of the entire model at the beginning of the step and every tenth +increment such that the element-by-element stable time increment equals at least 1 × 10−5 . The variable +mass scaling definition in the second step replaces the one continued from the first step. This particular +definition of variable mass scaling without any parameters in the second step also prevents any further +mass scaling during the second step. The scaled mass matrix from the first step is carried over to be used +during the entire second step. +Reverting the mass matrix to the original state +You can introduce a fixed mass scaling method in the subsequent step to discontinue all of the mass +scaling methods of the prior step. Further, if the default specification of fixed mass scaling is used, +element masses revert to their original values at the beginning of the subsequent step. Thus, specify just +the default fixed mass scaling method to prevent the scaled mass of the previous step from being used in +a new step. This is useful going from a quasi-static simulation step where mass scaling is appropriate to +a dynamic step in which no scaling is desired. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options without any parameters: +*FIXED MASS SCALING +*VARIABLE MASS SCALING +Create both of the following mass scaling definitions: +Step module: Create Step: General, Dynamic, Explicit or +Dynamic, Temp-disp, Explicit: Mass scaling: Use scaling +definitions below: Create: +Reinitialize mass +Disable mass scaling throughout step +Example +Assume that an analysis contains a quasi-static step followed by a dynamic step. Mass scaling can be +performed during the quasi-static step but turned off during the dynamic step. +*HEADING +*STEP +… +*FIXED MASS SCALING, FACTOR=1.1 +*VARIABLE MASS SCALING, TYPE=BELOW MIN, DT=1.E-5, FREQUENCY=10 +*END STEP +*STEP +*FIXED MASS SCALING +*VARIABLE MASS SCALING +*END STEP +During the first step the fixed mass scaling increases the element mass by the factor 1.1. The variable +mass scaling definition scales the mass of the entire model at the beginning of the step and every tenth +increment such that the element-by-element stable time increment equals at least 1 × 10−5 . The new fixed +mass scaling definition without any parameters in the second step then reverts the mass matrix back to the +original state. The new variable mass scaling definition replaces all the variable mass scaling definitions +inherited from the first step. Further, since the new variable mass scaling definition has no parameters, +no mass scaling is applied during the second step. Thus, the mass matrix for the second step reverts to +that of the original state. +Mass contribution from external programs connected to Abaqus via co-simulation +Co-simulation can lead to mass and/or rotary inertia from external programs being added to the Abaqus +model during a step. However, that contribution along with other quantities imported from the external +program must be removed once the co-simulation step is completed. If co-simulation is expected to add +mass and/or rotary inertia to the Abaqus model, Abaqus automatically reverts the mass matrix back to +the original state once such a co-simulation step is completed. You need to respecify any mass scaling +that must be continued beyond the co-simulation step. +When mass scaling is or is not used +The following entities are not affected by mass scaling: +• Thermal solution response in a fully coupled thermal-stress analysis +• Gravity loads, viscous pressure loads +• Adiabatic heat calculations +• Equation of state materials +• Fluid and fluid link elements +• Surface-based fluid cavities +• Spring and dashpot elements +Densities associated with any of the relevant items in this list will remain unscaled. Mass, rotary inertia, +infinite, and rigid elements can be scaled. However, because none of the elements has an associated +stable time increment, they can be scaled only using either a user-specified scale factor or an element- +by-element stable time increment applied uniformly. If the element-by-element stable time increment +is specified, at least one element with a stable time increment must be included in the mass scaling +definition. Rotary inertia in shell, beam, and pipe elements is based on the scaled mass. +The mass of infinite elements can be scaled; however, the infinite elements will not act as quiet +boundaries unless the densities of each adjacent deformable element are scaled by the same factor. The +mass of both elements will be scaled by the same factor if they are both included in the same fixed or +variable mass scaling definition. +Automatic mass scaling for analysis of bulk metal rolling +Bulk metal rolling is generally considered a quasi-static process, but the process is often modeled with +Abaqus/Explicit because of its ability to handle the contact problem well. To achieve an economical +solution with Abaqus/Explicit, it is often useful to increase the mass of the product artificially. However, +the mass scaling factor must be chosen such that the changes in the mass and the corresponding changes +in the inertial forces do not alter the solutions significantly. Choosing too high a scaling factor will not +produce quasi-static results. Choosing too low a scaling factor, while conservative, will result in long +run times. Rolling variable mass scaling can be used to make the choice of the optimal scaling factor +automatic for this process. +The automatic strategy is based on the semi-automatic method of scaling all elements to have equal +element stable time increments. The method is made automatic by determining the appropriate value +for the target stable time increment from several parameters of the rolling process. The value used for +the target stable time increment, +; +the feed rate, V; and the number of nodes in the cross-section of the product, n. The feed rate is defined +as the average velocity of the product in the rolling direction during steady-state conditions. The value +of +is adjusted during the analysis to account for the actual value of the feed rate. You must specify +estimated values for the average velocity, the average element length in the rolling direction, and the +number of nodes in the cross-section of the product. +, is based on the average element length in the rolling direction, +The mass of any element will never drop below its original mass. This is different from the method +of scaling all elements to have equal element stable time increments. Imposing this restriction means +that rolling problems that have significant inertial effects will not have their mass adjusted automatically +when they are analyzed as quasi-static. +To achieve a good result, it is recommended that: +• the product be meshed by extruding a two-dimensional cross-section of the product; +• the average element length in the rolling direction not vary significantly along the length of the +product; +• the product have an initial velocity in the rolling direction approximately equal to the steady-state +feed rate; +• the element size in the cross-section be equal to or less than the size in the rolling direction; and +• no other mass scaling be used on elements scaled with rolling automatic variable mass scaling. +Input File Usage: +*VARIABLE MASS SCALING, ELSET=elset1, FREQUENCY=n, +TYPE=ROLLING, FEED RATE=V, EXTRUDED LENGTH= +CROSS SECTION NODES=n +, +Abaqus/CAE Usage: +Output +Step module: Create Step: General, Dynamic, Explicit or Dynamic, +Temp-disp, Explicit: Mass scaling: Use scaling definitions +below: Create: Automatic mass scaling, Feed rate: V, Extruded +, Nodes in cross section: n +element length: +Output variable EMSF provides the element mass scaling factor. Abaqus/CAE can be used to obtain +contour and history plots of EMSF. Output variable DMASS provides the total percent change in mass +of the model as a result of mass scaling and is available for history plotting in Abaqus/CAE. Output +variable DMASS is not available on an element set basis. +Output variable EDT provides the element stable time increment. The element stable time increment +includes the effect of mass scaling. Abaqus/CAE can be used to obtain history plots of EDT. +11.7 +Selective subcycling +• “Selective subcycling,” Section 11.7.1 +11.7.1 +SELECTIVE SUBCYCLING +Product: Abaqus/Explicit +References +• “Explicit dynamic analysis,” Section 6.3.3 +• “Fully coupled thermal-stress analysis,” Section 6.5.3 +• *SUBCYCLING +Overview +Selective subcycling: +• allows different time increments to be used for different groups of elements; +• reduces run time for an analysis when a small region of elements in the model controls the stable +time increment; and +• is invoked by defining the subcycling zones. +Introduction +The selective subcycling method in Abaqus/Explicit is based on domain decomposition. +In this +method subcycling zones are defined that remain unchanged during the analysis. The domain-level +parallelization method (“Parallel execution in Abaqus/Explicit,” Section 3.5.3) is invoked automatically +when subcycling zones are defined. Each subcycling zone, as well as the non-subcycling zone, is +independently decomposed into the user-specified number of parallel domains. The “master” domains +are defined as the parallel domains that are derived from the non-subcycling zone and are integrated +with the largest stable time increment. The remaining parallel domains derived from the subcycling +zones are integrated using smaller time increments, or “subcycles.” +The subcycle time increment sizes are chosen as integer divisors of the time increment used in +the master parallel domains. Therefore, all parallel domains exactly reach the same time points as the +master parallel domains. During subcycling, nodes that lie on the interface with the non-subcycling zone +require special treatment. The velocity at the interface nodes is taken from the non-subcycling zone +and is constant during subcycles. This produces an interface node displacement field that varies linearly +during the subcycles. +Defining subcycling zones +Subcycling zones are defined by element sets. You can include all element types in these sets except +Eulerian element types EC3D8R and EC3D8RT. However, all parallel domains must have at least one +deformable element to provide the stable time increment. Abaqus/Explicit issues an error message if +there is no deformable element in a parallel domain. You can define an arbitrary number of subcycling +zones. However, some modeling features cannot be split between subcycling zones. Abaqus/Explicit +automatically merges subcycling zones that contain features that cannot be split. Subcycling zones are +merged together when: +• the zones overlap; +• the zones share the same nodes; +• a node is in one subcycling zone, but its adjacent nodes are in a different subcycling zone; +• subcycling zones are involved in the same constraint equation, connector, or rigid body; or +• general contact is specified in the analysis. +When subcycling zones are merged, the smallest stable time increment among the merged zones +is used. The constraint, connector, or rigid body is always assigned to the subcycling zone if any one +of its nodes is involved in that subcycling zone. Since the domain-level parallelization method is used, +all restrictions on parallel domain decomposition apply to subcycling zones. These restrictions prevent +certain features from being split across master parallel domains, as well as parallel domains that contain +the subcycling zones . Analytical rigid +surfaces cannot be included in the general contact domain when a subcycling zone is defined. +Efficient selective subcycling requires proper choice of subcycling zones. For each subcycling zone, +the time increment size should be small compared to the non-subcycling zone, producing a large number +of subcycles. The number of subcycles is the ratio of the stable time increment size in the non-subcycling +zone to the stable time increment sizes in the subcycling zones. In addition to a large number of subcycles, +the number of elements in a subcycling zone should generally be small compared to the total number +of elements in the model for optimal performance benefit. If a majority of elements in the model are in +subcycling zones, there will not be much performance benefit. +Input File Usage: +Use the following option to define a subcycling zone: +*SUBCYCLING, ELSET=element_set_name +Accuracy of results +The subcycling algorithm used in Abaqus/Explicit provides sufficient accuracy for most complex +dynamic models. However, because of the relatively large time increment size used in the non-subcycling +zone and the interpolation used on zone interface nodes, subcycling solutions can introduce a truncation +error, which may slightly alter results compared with traditional solutions. This error should not affect +the overall dynamic behavior of the model. Special attention should be given to the interface between +the subcycling zone and non-subcycling zone when general contact is involved. +surfaces that have the potential for contacting each other within the same zone. However, to minimize +truncation errors, it is highly recommended that a single surface that has the potential for contacting +others not be split across the zones. +Output and mass scaling +Output and mass scaling are always +performed at the same time points reached by all parallel domains. +Input file template +*HEADING +… +*ELSET, ELSET=ZONE1 +… +*SUBCYCLING, ELSET=ZONE1 +************************* +*STEP +*DYNAMIC, EXPLICIT +Data line to specify the time period of the step +... +*END STEP +11.8 +Steady-state detection +• “Steady-state detection,” Section 11.8.1 +11.8.1 +STEADY-STATE DETECTION +Product: Abaqus/Explicit +References +• “Output,” Section 4.1.1 +• *STEADY STATE DETECTION +• *STEADY STATE CRITERIA +Overview +Steady-state detection: +• can be used to detect the time in a quasi-static uni-directional Abaqus/Explicit simulation when a +steady-state condition has been reached and then terminate the simulation; +• can be used to output quantities that are useful in tracking the progress of a uni-directional +Abaqus/Explicit simulation; and +• is available only for three-dimensional analysis. +Introduction +Many types of uni-directional processes are used to transform preformed shapes into forms more suitable +for further processing. The most common examples are rolling, wire drawing, and extrusion processes. +Since the processes are usually carried out at low speeds, explicit dynamic procedures such as those in +Abaqus/Explicit are often used to model the processes as quasi-static. The analyses usually consist of a +workpiece that is formed into a desired shape by any number of rollers or other forming surfaces along +a primary direction. The forming surfaces are usually modeled as rigid bodies. For rolling simulations +the rigid body reference node is usually defined at the center of the roller. The mesh of the workpiece +is often extruded and may be constructed of multiple layers of material. As the workpiece progresses +through the forming surfaces, the shape eventually reaches a constant state. The position where the +workpiece exits the final forming surface is referred to as the exit plane and is usually aligned with the +rigid body reference node of the final forming surface. As soon as this constant shape is reached, the +analysis is considered to have reached steady state. The force and torque on the final forming surfaces +at this steady-state condition have also reached constant values or oscillate about constant values. A +significant computational savings can be achieved by detecting the steady-state condition and halting the +analysis either immediately or as soon as the steady-state cross-section progresses beyond the exit plane +to a position referred to as the cutting plane. +Mesh requirements +The workpiece mesh is required to meet certain conditions for use with the steady-state detection +capability. First, the mesh must be topologically regular in the primary direction. In other words, the +mesh should consist of multiple planes of elements with each plane being similar to its adjacent leading +and trailing planes in that it contains the same number of elements and the same element topology +in the cross-section. Furthermore, each element in a plane is connected to elements in leading and +trailing planes that reference the same material and section properties. Therefore, meshes with multiple +materials and section properties are permitted, but any row of elements in the primary direction must be +of the same type and must reference the same material and section properties . +rolling direction +exit plane +cutting plane +Figure 11.8.1–1 Acceptable multiple-material extruded mesh for a rolling analysis. +material 1 +material 2 +Steady-state detection criteria sampling +To determine if steady state has been reached, steady-state detection “norms” are calculated, which +represent an averaged value of a variable of interest over the cross-section of the workpiece as material +passes through a given position along the primary direction. This position is referred to as the exit plane +and usually coincides with the position of the last rigid forming tool (e.g., roller) that the workpiece +passes through. The normal of the exit plane is by definition coincident with the primary direction. The +time intervals at which the norms are sampled vary depending on whether the rolling analysis is modeled +in an Eulerian or Lagrangian manner. +Sampling in a Lagrangian analysis +In a Lagrangian-based analysis (which may include adaptive meshing employed on a Lagrangian domain) +the steady-state norms are calculated as the trailing control node of each plane of elements passes the +exit plane. Figure 11.8.1–2 illustrates the control node definitions. +first steady-state +rolling plane +trailing control +node of the first plane +leading control +node of the first plane +Figure 11.8.1–2 Control node positioning. +The time period of norm sampling is, therefore, based on the frequency at which the planes of elements +cross the exit plane. For output purposes the values of the norms are assumed to remain constant between +the times at which successive control nodes pass the exit plane. +Sampling in an Eulerian analysis +An Eulerian analysis employs a control volume approach in which material is drawn from an inflow +Eulerian boundary and is pushed or pulled out through an outflow boundary. Adaptive mesh domains +are defined on the workpiece, and sliding boundary regions are defined to model contact between the +workpiece and forming tools such as rollers. See “ALE adaptive meshing: overview,” Section 12.2.1, +for details of adaptive meshing techniques. The mesh remains relatively stationary while the material +moves through the exit plane. The time period between sampling is, therefore, based on the progress of +the material moving through the exit plane. To determine a time period in a manner consistent with the +Lagrangian case, the sampling period is determined by dividing the characteristic element length of the +workpiece by the speed of the material flow. This period is roughly the time it takes for material to pass +through an element of typical size. +Steady-state detection norm definitions +An individual norm is considered to have achieved steady state if its relative change in value over three +consecutive planes does not exceed a tolerance. You can provide the norm tolerances when you define +the steady-state criteria, or default values of tolerances can be chosen by Abaqus/Explicit. The norms +can be output by requesting their identifiers listed in the definitions below. +Equivalent plastic strain norm +The plastic strain norm of a plane of elements is defined by summing the product of the equivalent plastic +strain and the element volume of each element on the plane, then dividing by the total volume of the +elements on the plane. This norm provides a weighted average of the equivalent plastic strain for the +plane. The identifier for the equivalent plastic strain norm is SSPEEQ. +Spread norm +The spread norm of a plane of elements is computed as the largest of the area moments of inertia of the +cross-section of the plane. In determining the spread norm, the cross-section of the plane of elements +is determined by projecting the element faces whose normals originally coincided with the primary +direction onto the exit plane. The area moments of inertia are then determined about the centroid of +the section in the directions of the original principal axes of the cross-section. The identifier for the +spread norm is SSSPRD. +Force norm +The force norm is computed by averaging the magnitude of the force at the rigid body reference node of +a forming tool, such as the exit roller, over the time period between sampling points. You provide the +rigid body reference node and force direction. The identifier for the force norm is SSFORC. +Torque norm +The torque norm is computed by averaging the magnitude of the torque at the rigid body reference node +of a forming tool, such as the exit roller, over the time period between sampling points. You provide the +rigid body reference node and torque direction. The identifier for the torque norm is SSTORQ. +Requesting steady-state detection during an analysis +You must define the criteria that are used to determine if steady state has been reached. Abaqus/Explicit +will halt the analysis based on the achievement of steady state. +Steady-state detection +A steady-state detection definition is used to define the elements in the workpiece, the primary direction +of the workpiece, the cutting position, and the type of sampling used. The primary direction is defined +by specifying the direction cosines with respect to the global Cartesian coordinate system. The cutting +position is defined by specifying the global coordinates of a point lying in the cutting plane. The normal to +the cutting plane is assumed to coincide with the primary direction. Once steady state has been detected, +the analysis is terminated when the plane of the workpiece that was first detected to have reached steady +state has progressed to the cutting plane. You can choose the sampling method used, as described below. +Requesting sampling as elements pass the exit plane for a Lagrangian analysis +You can request that all steady-state norms be calculated as each plane of elements crosses the exit plane. +*STEADY STATE DETECTION, ELSET=elset, +SAMPLING=PLANE BY PLANE +Input File Usage: +Requesting sampling at uniform intervals for an Eulerian analysis +Alternatively, you can request that all steady-state norms be calculated at an interval based on the time +required for material to progress the length of an average element. +Input File Usage: +*STEADY STATE DETECTION, ELSET=elset, SAMPLING=UNIFORM +Steady-state criteria +Any number of steady-state criteria definitions can be specified. Only when all of the criteria specified +under any one steady-state criteria definition have been satisfied will the analysis be considered to have +reached steady state. +To define the criteria, you specify the norm type identifier, the norm tolerance, and the global +coordinates of a point on the exit plane. For force and torque norms, you also specify the rigid body +reference node of the forming tool at the exit plane and the direction cosines of the force or torque. Exit +planes can be defined separately for each norm definition. +Input File Usage: +Use the following options to define the criteria needed to achieve steady state: +*STEADY STATE DETECTION, ELSET=elset, +SAMPLING=PLANE BY PLANE or UNIFORM +*STEADY STATE CRITERIA +*STEADY STATE CRITERIA +... +6.0, 0.0, 0.0 +For example, assume that two sets of criteria are of interest and that the analysis +can be terminated as soon as either is satisfied. The input might be as follows: +*STEADY STATE DETECTION, ELSET=sheet, +SAMPLING=PLANE BY PLANE +1.0, 0.0, 0.0, +*STEADY STATE CRITERIA +SSPEEQ,.002, +SSSPRD,.002, +SSFORC,.005, +SSFORC,.005, +SSTORQ,.005, +*STEADY STATE CRITERIA +SSPEEQ,.001, +SSSPRD,.001, +SSFORC,.010, +5.0, 0.0, 0.0 +5.0, 0.0, 0.0 +5.0, 0.0, 0.0, 1000, 1.0, 0.0, 0.0 +5.0, 0.0, 0.0, 1000, 0.0, 1.0, 0.0 +5.0, 0.0, 0.0, 1000, 0.0, 0.0, 1.0 +5.0, 0.0, 0.0 +5.0, 0.0, 0.0 +5.0, 0.0, 0.0, 1000, 0.0, 1.0, 0.0 +Materials +Steady-state detection is intended to be used with plasticity-based materials since the equivalent plastic +strain norm would be zero for nonplasticity-based material models. +Procedures +One steady-state detection definition is allowed per analysis. The definition can be entered in any step +and is continued through subsequent steps in an analysis. A steady-state detection definition cannot be +entered in an annealing step or continued through an annealing step. +Elements +The current steady-state detection capabilities support the use of C3D8R and C3D8RT elements only. +Output +The output variables SSPEEQn, SSSPRDn, SSFORCn, and SSTORQn are used to output the equivalent +plastic strain, spread, force, and torque norms, respectively. Abaqus/CAE can be used to obtain history +plots of each of the steady-state detection norm variables. Individual norms can be output by requesting +the norm number n, which is based on the order in which the norms are specified. Referring to the +example above, if the force norm of the second steady-state criteria definition were to be requested, the +output identifier would be SSFORC3. If a steady-state detection norm is requested that does not include +a norm number, SSFORC for example, all norms of that type are output. +Once steady state has been detected, an element set is created automatically by Abaqus/Explicit +and written to the output database consisting of the plane of elements that first satisfied the steady-state +criteria. The element set created is named SteadyStatePlane and can be viewed with Abaqus/CAE. If no +output requests are made to the output database, the element set SteadyStatePlane will not be created. +Input file template +*HEADING +… +*ELSET, ELSET=WORKPIECE +************************* +*STEP +*DYNAMIC, EXPLICIT +Data line to specify the time period of the step +... +*STEADY STATE DETECTION, ELSET=WORKPIECE, SAMPLING=PLANE BY PLANE +Data line specifying rolling direction and cutting plane position +*STEADY STATE CRITERIA +Data lines specifying steady-state detection norm criteria +... +*OUTPUT, HISTORY, TIME INTERVAL=1.E-6 +*INCREMENTATION OUTPUT +SSPEEQ, SSSPRD, SSFORC, SSTORQ +... +*END STEP +Adaptivity Techniques +Adaptivity techniques: overview +ALE adaptive meshing +Adaptive remeshing +Analysis continuation after mesh replacement +ADAPTIVITY TECHNIQUES +12.1 +12.2 +12.3 +12.1 +Adaptivity techniques: overview +• “Adaptivity techniques,” Section 12.1.1 +12.1.1 +ADAPTIVITY TECHNIQUES +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “ALE adaptive meshing: overview,” Section 12.2.1 +• “Adaptive remeshing: overview,” Section 12.3.1 +• “Mesh-to-mesh solution mapping,” Section 12.4.1 +• *ADAPTIVE MESH +• “Understanding adaptive remeshing,” Section 17.13 of the Abaqus/CAE User’s Manual +Overview +The finite element discretization that results from suboptimal meshing of models can limit your ability +to obtain adequate analysis results at a reasonable CPU cost. This section provides an overview of the +adaptivity techniques available in Abaqus that help you optimize a mesh and, therefore, obtain quality +solutions while controlling the cost of your analysis. The term “adaptivity” reflects the adaptive, or +solution-dependent, processes that Abaqus uses to adapt your mesh to meet your analysis goals. +Selecting an adaptivity technique +Three adaptivity techniques are available in Abaqus: Arbitrary Lagrangian-Eulerian (ALE) adaptive +meshing; varying topology adaptive remeshing (this functionality is not applicable to V6); and mesh-to- +mesh solution mapping, to enable rezoning analysis. Table 12.1.1–1 shows that the adaptivity techniques +can be classified according to +• their applicability to achieving particular goals, either accuracy or control of mesh distortion; +• their impact on mesh definitions, either through smoothing a single mesh or through generating +multiple dissimilar meshes; and +• when adaptivity occurs with respect to analysis steps. +Table 12.1.1–1 The characteristics of the adaptivity techniques. +Accuracy +Distortion +control +Single +mesh +Multiple +meshes +Adaptivity occurs +ALE adaptive +meshing +Adaptive remeshing +(not applicable to V6) +Mesh-to-mesh +solution mapping +ALE adaptive meshing +Throughout a step +Separately from +analysis steps +Between analysis +steps +Arbitrary Lagrangian-Eulerian (ALE) adaptive meshing provides control of mesh distortion. ALE +adaptive meshing uses a single mesh definition that is gradually smoothed within analysis steps. +ALE adaptive meshing is available for limited applications in Abaqus/Standard and is more generally +applicable in Abaqus/Explicit. The term ALE implies a broad range of analysis approaches, from +purely Lagrangian analysis, in which the node motion corresponds to material motion, to purely +Eulerian analysis, in which the nodes remain fixed in space and material “flows” through the elements. +Typically ALE analyses use an approach between these two extremes. The ALE feature is distinct +from the Eulerian analysis capability in Abaqus/Explicit, which is described in “Eulerian analysis,” +Section 14.1.1. +You can use adaptive meshing to control element distortion in cases where large deformation or loss +of material occurs. Figure 12.1.1–1 illustrates a case where adaptive meshing limits mesh distortion in a +bulk forming simulation. +rigid die +rigid die +symmetry plane +without +ALE adaptive +meshing +with +ALE adaptive +meshing +Figure 12.1.1–1 Use of ALE adaptive meshing to control element distortion. +Unlike other adaptivity techniques, adaptive meshing operates on your original mesh definition and +is, therefore, useful only when a single mesh can be effective for the duration of a simulation. The mesh +is adapted through smoothing of the mesh nodes. This smoothing is typically applied frequently within +analysis steps. ALE adaptive meshing requires only one analysis job. See “ALE adaptive meshing: +overview,” Section 12.2.1, for details. +Adaptive remeshing (varying topology adaptivity) +Adaptive remeshing is typically used for accuracy control, although it can also be used for distortion +control in some situations. The adaptive remeshing process involves the iterative generation of multiple +dissimilar meshes to determine a single, optimized mesh that is used throughout an analysis. Adaptive +remeshing is available only for Abaqus/Standard analyses submitted from Abaqus/CAE. The goal of +adaptive remeshing is to obtain a solution that satisfies mesh discretization error indicator targets that +you set, while minimizing the number of elements and, hence, the cost of your analysis. You can use +adaptive remeshing to obtain a mesh that provides a balance between solution cost and desired accuracy. +Figure 12.1.1–2 illustrates a case where adaptive remeshing improves the quality of the stress result +around a fillet with targeted mesh refinement. +Figure 12.1.1–2 Use of adaptive remeshing to improve the quality of a stress result. +Adaptive remeshing involves an iterative process to determine a single, optimized mesh that is used +through an analysis. The iterative process and the remeshing are controlled in Abaqus/CAE. Each +successive analysis job covers the same simulation history time period but uses a different mesh. Once +the adaptive remeshing process is complete, a single mesh and a single analysis job represent your entire +analysis history. See “Adaptive remeshing: overview,” Section 12.3.1, and “Understanding adaptive +remeshing,” Section 17.13 of the Abaqus/CAE User’s Manual. +Mesh-to-mesh solution mapping +Mesh-to-mesh solution mapping is available only in Abaqus/Standard. You can use this technique to +control element distortion in cases where large deformation occurs by replacing the mesh and continuing +the analysis. Figure 12.1.1–3 illustrates a case where solution mapping is used in conjunction with a new +mesh to overcome difficulties associated with element distortion. +Figure 12.1.1–3 Use of mesh-to-mesh solution mapping +as a component of a rezoning technique. +Mesh replacement, or rezoning, involves the creation of multiple Abaqus jobs, each of which represents +the configuration of the model in distinct, sequential periods of the simulation history. You use mesh +replacement when a single mesh cannot be effective for the duration of a simulation. Each mesh +subsequent to the initial configuration reflects a solution-dependent deformed configuration of the +model. Therefore, analyses that use mesh replacement are sequentially dependent, and Abaqus uses +In +mesh-to-mesh solution mapping to propagate solution variables from one analysis to the next. +contrast to adaptive remeshing, each mesh replacement job represents a component of the overall +analysis history—no single mesh and no single analysis job represent your entire analysis. See +“Mesh-to-mesh solution mapping,” Section 12.4.1, for details. +12.2 +ALE adaptive meshing +• “ALE adaptive meshing: overview,” Section 12.2.1 +• “Defining ALE adaptive mesh domains in Abaqus/Explicit,” Section 12.2.2 +• “ALE adaptive meshing and remapping in Abaqus/Explicit,” Section 12.2.3 +• “Modeling techniques for Eulerian adaptive mesh domains in Abaqus/Explicit,” Section 12.2.4 +• “Output and diagnostics for ALE adaptive meshing in Abaqus/Explicit,” Section 12.2.5 +• “Defining ALE adaptive mesh domains in Abaqus/Standard,” Section 12.2.6 +• “ALE adaptive meshing and remapping in Abaqus/Standard,” Section 12.2.7 +ALE ADAPTIVE MESHING: OVERVIEW +ALE ADAPTIVE MESHING: OVERVIEW +The adaptive meshing technique in Abaqus combines the features of pure Lagrangian analysis and pure +Eulerian analysis. This type of adaptive meshing is often referred to as Arbitrary Lagrangian-Eulerian (ALE) +analysis. The Abaqus documentation often refers to “ALE adaptive meshing” simply as “adaptive meshing.” +ALE adaptive meshing is a tool that makes it possible to maintain a high-quality mesh throughout an +analysis, even when large deformation or loss of material occurs, by allowing the mesh to move independently +of the material. ALE adaptive meshing does not alter the topology (elements and connectivity) of the mesh, +which implies some limitations on the ability of this method to maintain a high-quality mesh upon extreme +deformation. Refer to “Adaptivity techniques,” Section 12.1.1, for a comparison between ALE adaptive +meshing and other Abaqus adaptivity methods. +ALE adaptive meshing is distinct from the pure Eulerian analysis capability in Abaqus/Explicit. The +pure Eulerian capability supports multiple materials and voids within a single element, which allows effective +handling of analyses involving extreme deformation (such as fluid flow). In contrast, ALE elements are always +100% full of a single material; while this formulation limits the deformation of material in the model to the +deformation of the elements, it allows more precise definitions of material boundaries and more complex +contact interactions. For more information on pure Eulerian analysis, see ���Eulerian analysis,” Section 14.1.1. +Although the adaptive meshing techniques and the user interface are similar in Abaqus/Explicit +and Abaqus/Standard, the use-cases and the level of functionality are different. Adaptive meshing in +Abaqus/Explicit is intended to model large-deformation problems. +It does not attempt to minimize +discretization errors in small-deformation analyses. Adaptive meshing in Abaqus/Standard is intended for +use in acoustic domains and for modeling the effects of ablation, or wear, of material. A comparison between +the adaptive remeshing functionality in Abaqus/Explicit and Abaqus/Standard is provided in this section. +Features of ALE adaptive meshing +ALE adaptive meshing: +• can often maintain a high-quality mesh under severe material deformation by allowing the mesh to +move independently of the underlying material; and +• maintains a topologically similar mesh throughout the analysis (i.e., elements are not created or +destroyed). +In Abaqus/Explicit ALE adaptive meshing: +• can be used to analyze Lagrangian problems (in which no material leaves the mesh) and Eulerian +problems (in which material flows through the mesh); +• can be used as a continuous adaptive meshing tool for transient analysis problems undergoing large +deformations (such as dynamic impact, penetration, and forging problems); +• can be used as a solution technique to model steady-state processes (such as extrusion or rolling); +• can be used as a tool to analyze the transient phase in a steady-state process; and +• can be used in explicit dynamics (including adiabatic thermal analysis) and fully coupled thermal- +stress procedures. +In Abaqus/Standard ALE adaptive meshing: +• can be used to solve Lagrangian problems (in which no material leaves the mesh) and to model +effects of ablation, or wear (in which material is eroded at the boundary); +• can be used to update the acoustic mesh when structural preloading causes significant geometric +changes in the acoustic domain; and +• can be used in geometrically nonlinear static, steady-state transport, coupled pore fluid flow and +stress, and coupled temperature-displacement procedures. +Activating ALE adaptive meshing +Adaptive meshing can be applied to an entire model or to individual parts of a model. A Lagrangian +adaptive mesh domain will be created, so that the domain as a whole will follow the material originally +inside it, which is the proper physical interpretation for most structural analyses. Additional options are +provided for controlling the mesh. In Abaqus/Explicit analyses you can define Eulerian boundaries to +allow material to flow into or out of the domain modeled. +The subsequent sections of “ALE adaptive meshing,” Section 12.2, describe the various options +that can be used with adaptive meshing. Although these options give you the ability to exercise detailed +control over adaptive meshing, they are not necessary for many Lagrangian problems. +• To take full advantage of all the adaptive mesh features in Abaqus, it is important to understand +the concepts of adaptive mesh domains, boundary regions, boundary edges, geometric features, +and mesh constraints. These concepts are explained in “Defining ALE adaptive mesh domains in +Abaqus/Explicit,” Section 12.2.2, and “Defining ALE adaptive mesh domains in Abaqus/Standard,” +Section 12.2.6. Instructions for applying boundary conditions, loads, and surfaces to adaptive mesh +boundaries are also provided in those sections. +• “ALE adaptive meshing and remapping in Abaqus/Explicit,” Section 12.2.3, and “ALE adaptive +meshing and remapping in Abaqus/Standard,” Section 12.2.7, outline the methods used to move +the mesh and to remap solution variables to the new mesh. These sections also present options +for controlling these algorithms. Although the default methods have been chosen to work well for +a wide variety of problems, you may wish to override the defaults to balance the robustness and +efficiency of adaptive meshing or to extend the use of adaptive meshing to relatively difficult or +unusual applications. +• Various output and diagnostics are available for verifying the formation of adaptive mesh domains +and for interpreting the results of an analysis. These options are explained in “Output and +diagnostics for ALE adaptive meshing in Abaqus/Explicit,” Section 12.2.5. +• “Modeling techniques for Eulerian adaptive mesh domains in Abaqus/Explicit,” Section 12.2.4, +gives advice, in the form of examples and modeling hints, on setting up and interpreting Eulerian +problems in Abaqus/Explicit using adaptive meshing. +Input File Usage: +Abaqus/CAE Usage: +*ADAPTIVE MESH, ELSET=elset_name +Step module: Other→ALE Adaptive Mesh Domain→Edit: toggle on Use +the ALE adaptive mesh domain below, and click Edit to select the region +Uses for ALE adaptive meshing +Adaptive meshing is of great value in a variety of problems. Abaqus/Explicit and Abaqus/Standard each +employ adaptive meshing in ways that provide the greatest value within the particular solver. +Uses in Abaqus/Explicit +In problems where large deformation is anticipated the improved mesh quality resulting from adaptive +meshing can prevent the analysis from terminating as a result of severe mesh distortion. +In these +situations you can use adaptive meshing to obtain faster, more accurate, and more robust solutions than +with pure Lagrangian analyses. +Adaptive meshing is particularly effective for simulations of metal forming processes such as +forging, extrusion, and rolling because these types of problems usually involve large amounts of +nonrecoverable deformation. Because the final shape of the product can be drastically different from +the original shape, a mesh that is optimal for the original product geometry can become unsuitable +in later stages of the process when large material deformation leads to severe element distortion and +entanglement. Element aspect ratios can also degrade in zones with high strain concentrations. Both of +these factors can lead to a loss of accuracy, a reduction in the size of the stable time increment, or even +termination of the problem. +Uses in Abaqus/Standard +You can use adaptive meshing to enable acoustic domain meshes to follow the large deformations of the +bounding structure. In other applications you can use adaptive meshing and adaptive mesh constraints +to model arbitrarily large amounts of ablation of material away from the domain. +Adaptive meshing of acoustic regions greatly extends the utility of acoustic analysis procedures. +Abaqus can be used to model the response of a coupled structural-acoustic system subjected to structural +preloads. By default, the structural-acoustic calculations are based on the original configuration of +the acoustic domain. This approximation is adequate as long as the boundary between the fluid and +structure does not experience large deformation during application of the preload. However, when the +geometry of the acoustic domain changes significantly as a result of structural loading, the original +acoustic configuration must be updated. An example is the interior cavity of a tire subjected to inflation, +rim mounting, and footprint pressure loads. +The acoustic elements in Abaqus do not have mechanical behavior and, therefore, cannot model the +deformation of the fluid when the structure undergoes large deformation. Abaqus/Standard solves the +problem of computing the current configuration of the acoustic domain by periodically creating a new +acoustic mesh that uses the same topology as the original mesh but with the nodal locations adjusted so +that the deformation of the structural-acoustic boundary does not lead to severe distortion of the acoustic +elements. +The geometric changes associated with the new acoustic mesh are then taken into account in a +subsequent coupled structural-acoustic analysis. However, it is assumed that the material properties of +the fluid, such as the density, do not change as a result of mesh smoothing. +Adaptive meshing can also model effects of ablation, or wear, by enabling you to define boundary +mesh motions independent of the underlying material motion. An example is the wearing of a tire during +its life, an effect that can significantly affect the performance of the structure. +Comparison of ALE adaptive meshing in Abaqus/Explicit and Abaqus/Standard +Adaptive meshing in Abaqus/Explicit is generally more robust and provides more features for controlling +the mesh than does adaptive meshing in Abaqus/Standard. +ALE adaptive meshing in Abaqus/Explicit +Adaptive meshing in Abaqus/Explicit is designed to handle a large variety of problem classes, and +employs a variety of smoothing methods, with controls that you can use to tailor the adaptivity to +specific problems. The Abaqus/Explicit implementation allows you to do the following: +• to create entirely Eulerian models; +• to improve the quality of the mesh initially, before deformation begins; and +• to define tracer particles, which enable tracking and output of material-based results quantities. +ALE adaptive meshing in Abaqus/Standard +Adaptive meshing in Abaqus/Standard uses a single smoothing algorithm that works well for structural +acoustic analyses and the modeling of ablation processes. The Abaqus/Standard implementation of +adaptive meshing has the following limitations: +• Initial mesh sweeps cannot be used to improve the quality of the initial mesh definition. +• The method is not intended to be used in general classes of large-deformation problems, such as +bulk forming. +• Diagnostics capabilities are currently limited. +Illustrative examples +To illustrate the value of adaptive meshing, simple examples of transient and steady-state forming +applications follow. For simplicity, two-dimensional cases are shown. In each case Abaqus/Explicit is +used in the simulation. +Axisymmetric forging +In this example a well-lubricated rigid die of sinusoidal shape moves down to deform a blank of +rectangular cross-section . The indentation depth is 80% of the original blank +thickness. Material extrudes upward and outward (radially) as the blank is indented. The die is modeled +with an analytical rigid surface, and the blank is modeled with axisymmetric continuum elements in a +regular mesh configuration. The blank is assumed to have elastic-plastic material properties. +A pure Lagrangian analysis of this problem does not run to completion because of excessive +distortion in several elements, as shown in Figure 12.2.1–2. The contact surface cannot be treated +correctly because of the gross distortion of the elements at the troughs of the sinusoidal rigid surface. +rigid die +plane of symmetry +Figure 12.2.1–1 A blank and a sinusoidal die. +Figure 12.2.1–2 Eventually, the purely Lagrangian analysis will +terminate because of excessive element distortion. +Adaptive meshing allows the problem to run to completion. A Lagrangian adaptive mesh domain +is created for the entire blank. Abaqus/Explicit automatically chooses suitable defaults for adaptive +meshing; hence, the adaptive mesh approach requires only two additional input lines: +*HEADING +... +*ELSET, ELSET=BLANK +*************************** +*STEP +*DYNAMIC, EXPLICIT +... +*ADAPTIVE MESH, ELSET=BLANK +... +*END STEP +Figure 12.2.1–3 and Figure 12.2.1–4 show the deformed mesh at various stages of the forming +analysis. Because the mesh refinement is maintained on the areas of the slave surface that contact the die +troughs as the material flows radially, contact conditions are resolved correctly throughout the analysis. +Figure 12.2.1–3 Deformed configuration at an intermediate stage of the analysis. +Figure 12.2.1–4 Deformed configuration upon completion of the analysis. +Steady-state rolling example +This example shows how adaptive meshing can be used in a steady-state simulation to allow the flow of +material through Eulerian boundaries on the problem domain. A steel plate is passed through a symmetric +roll stand to reduce its height by 50%. This simulation is run until it reaches steady-state conditions. +Figure 12.2.1–5 and Figure 12.2.1–6 show the initial and final (steady-state) configurations in a +purely Lagrangian model of this problem. +rigid +roller +plane of symmetry +Figure 12.2.1–5 The initial configuration of the roller and the +undeformed blank in the pure Lagrangian model. +Figure 12.2.1–6 The final steady-state configuration in the pure Lagrangian model. +Figure 12.2.1–7 shows this problem modeled using an Eulerian adaptive mesh domain, where +material flows through the mesh. Only the region near the roller is modeled. The exact location of the +free surface does not need to be known to set up the problem: it is created in a likely location, and the +final steady-state position is found as part of the solution. Although not shown, a focused mesh can be +free surface +100 +INFLOW +OUTFLOW +Figure 12.2.1–7 The initial Eulerian adaptive mesh domain. +used to capture steep strain gradients directly beneath the roller. The Eulerian domain reaches the same +steady-state solution as obtained with the Lagrangian approach. +The Eulerian adaptive mesh domain is created by defining an inflow and an outflow boundary on +the adaptive mesh domain. Adaptive mesh constraints are applied normal to these boundaries so that +material will flow through the mesh . Frictional contact between the roller and the blank pulls material through the adaptive +mesh domain. +The problem is set up by making the following modifications to the input file for the pure Lagrangian +analysis: +*HEADING +... +*ELSET, ELSET=BILLET +... +*ELSET, ELSET=INFLOW +... +*ELSET, ELSET=OUTFLOW +... +*NSET, NSET=INFLOW +... +*NSET, NSET=OUTFLOW +... +*SURFACE, NAME=INFLOW, REGION TYPE=EULERIAN +INFLOW, S1 +*SURFACE, NAME=OUTFLOW, REGION TYPE=EULERIAN +OUTFLOW, S2 +*************************** +*STEP +*DYNAMIC, EXPLICIT +Data line to specify the time period of the step +... +*ADAPTIVE MESH, ELSET=BILLET, CONTROLS=ADAPT +*ADAPTIVE MESH CONTROLS, NAME=ADAPT +*ADAPTIVE MESH CONSTRAINT, TYPE=DISPLACEMENT +INFLOW, 1, 1, 0.0 +100, 2, 2, 0.0 +OUTFLOW, 1, 1, 0.0 +... +*END STEP +Adaptive mesh controls were not required to solve this problem; they were included for illustrative +purposes . +12.2.2 +DEFINING ALE ADAPTIVE MESH DOMAINS IN Abaqus/Explicit +Products: Abaqus/Explicit Abaqus/CAE +References +• “ALE adaptive meshing: overview,” Section 12.2.1 +• “ALE adaptive meshing and remapping in Abaqus/Explicit,” Section 12.2.3 +• *ADAPTIVE MESH +• “Understanding ALE adaptive meshing,” Section 14.6 of the Abaqus/CAE User’s Manual +Overview +Arbitrary Lagrangian-Eulerian (ALE) adaptive mesh domains: +• define the portions of a finite element model where mesh movement is independent of material +deformation; +• can be used to analyze Lagrangian or Eulerian problems; +• can contain only first-order, reduced-integration, solid elements (4-node quadrilaterals, 3-node +triangles, 8-node hexahedra, 6-node wedges, and 4-node tetrahedra); +• can be used in planar, axisymmetric, and three-dimensional geometries; +• have boundary regions where loads, boundary conditions, and surfaces can be defined; and +• are active only for geometrically nonlinear steps. +Defining an ALE adaptive mesh domain +ALE adaptive meshing is performed in adaptive mesh domains, which can be either Lagrangian +or Eulerian. Within either type of adaptive mesh domain the mesh will move independently of the +material. Lagrangian adaptive mesh domains are usually used to analyze transient problems with +large deformations. On the boundary of a Lagrangian domain the mesh will follow the material in +the direction normal to the boundary, so that the mesh covers the same material domain at all times. +Eulerian adaptive mesh domains are usually used to analyze steady-state processes involving material +flow. On certain user-defined boundaries of an Eulerian domain, material can flow into or out of the +mesh. By default, the mesh is not fixed spatially on these boundaries; mesh constraints must be applied +to prevent the mesh from moving with the material, as described in “Mesh constraints,” presented later +in this section. There can never be any “empty” elements; all elements in the domain must be filled +completely with material at all times. +You must specify the region of the original mesh that will be subject to adaptive meshing. +Input File Usage: +*ADAPTIVE MESH, ELSET=name +Multiple adaptive mesh domains can be defined in a step by reusing the +*ADAPTIVE MESH option (for example, to prevent material from flowing +from one domain to another or to apply adaptive meshing to unconnected +domains). The element sets used to create adaptive mesh domains cannot +overlap. +Abaqus/CAE Usage: +Step module: Other→ALE Adaptive Mesh Domain→Edit: toggle on Use +the ALE adaptive mesh domain below, and click Edit to select the region +Only one adaptive mesh domain can be defined in Abaqus/CAE for any +particular step. +Modifying an ALE adaptive mesh domain +By default, all adaptive mesh domains defined in the previous analysis step remain unchanged in +the subsequent step. You define the adaptive mesh domains in effect for a given step relative to the +preexisting adaptive mesh domains. At each new step the existing adaptive mesh domains can be +modified and additional adaptive mesh domains can be specified (except in Abaqus/CAE, where only +one adaptive mesh domain can be in effect for a given step). +Input File Usage: +Use either of the following options to modify an existing adaptive mesh domain +or to specify an additional adaptive mesh domain: +Abaqus/CAE Usage: +*ADAPTIVE MESH, ELSET=name +*ADAPTIVE MESH, ELSET=name, OP=MOD +Step module: Other→ALE Adaptive Mesh Domain→Edit +Removing an ALE adaptive mesh domain +If you choose to remove any adaptive mesh domain in a step, no adaptive mesh domains will be +propagated from the previous step. Therefore, all adaptive mesh domains that are in effect during this +step must be respecified. +Input File Usage: +Use the following option to remove all previously defined adaptive mesh +domains and to specify new adaptive mesh domains: +Abaqus/CAE Usage: +*ADAPTIVE MESH, ELSET=name, OP=NEW +If the OP=NEW parameter is used on any *ADAPTIVE MESH option within +a step, it must be used on all *ADAPTIVE MESH options in the step. +Step module: Other→ALE Adaptive Mesh Domain→Edit: toggle +on No adaptive mesh domain for this step +Splitting ALE adaptive mesh domains +User-defined adaptive mesh domains are examined by Abaqus/Explicit. The user-defined domain will +be modeled using a single adaptive mesh if the domain: +• consists of a single element type; +• consists of a single connected region; +• consists of a single material; +• is subject to a uniform body force (including zero body force); and +• has identical section controls. +The user-defined domain will be split into multiple adaptive mesh domains, separated by boundary +regions, if the domain: +• consists of multiple element types; +• spans part instances; +• consists of multiple regions (including regions that are connected by less than a single element face, +only by contact conditions, or only by connectors such as MPCs); +• consists of multiple materials; +• is subject to multiple body force definitions; or +• is subject to multiple section control definitions. +In this documentation the term “adaptive mesh domain” refers to a single domain after splitting by +Abaqus/Explicit. On the rare occasion that a reference is made to an adaptive mesh domain prior to +the automatic splitting, it is referred to as a “user-defined adaptive mesh domain.” Since adaptive mesh +domains are split across element types, degenerate elements should be used for mixed domains that +include both triangles and quadrilaterals (or tetrahedron and bricks). For example, when defining a +mixed plane strain domain with quadrilateral and triangular elements, the CPE4R element type should +be used to define both quadrilaterals and degenerated quadrilaterals. Using the CPE3 element will result +in split domains, which is generally not desirable. +ALE adaptive mesh boundary regions +Each ALE adaptive mesh domain has a boundary, which can consist of one or more regions. (Regions, +in this context, are surfaces in three-dimensional models or lines in two-dimensional or axisymmetric +models.) A boundary region can be either Lagrangian, sliding, or Eulerian. Some boundary regions are +created automatically by Abaqus/Explicit; others can be created by defining boundary conditions, loads, +and surfaces. Adaptive mesh boundary regions are separated by edges in three dimensions and by corners +in two dimensions. Both edges and corners are referred to as “boundary region edges” throughout this +documentation. +Boundary region edges +Two types of boundary region edges can exist: Lagrangian and sliding. Lagrangian edges are always +associated with a material line. Material can never flow past a Lagrangian edge, and nodes can move +only along a Lagrangian edge (like beads on a string). Sliding edges are associated only with the mesh. +Material can flow past a sliding edge (that is, sliding edges are free to slide over the underlying material). +Lagrangian edges can be viewed with Abaqus/CAE; see “Output and diagnostics for ALE adaptive +meshing in Abaqus/Explicit,” Section 12.2.5. +Lagrangian boundary regions +Lagrangian boundary regions are the most common boundary regions in structural finite element analysis; +therefore, with the exception of contact surfaces, they are always the default in Abaqus/Explicit. A +Lagrangian boundary region has the most constraints of all the boundary region types. The mesh is +constrained to move with the material in the direction normal to the surface of the boundary region and +in the directions perpendicular to the boundary region edges. +Lagrangian boundary regions have Lagrangian edges: the edges follow the material. On the interior +of a Lagrangian boundary region, the mesh can move independently of the material in the surface of the +boundary region. Thus, a Lagrangian boundary region can be thought of as a “mesh patch” that follows +the material. Nodes are free to move within and along the edges of the patch but cannot leave the patch. +Lagrangian corners +A Lagrangian corner is formed where two Lagrangian edges meet. The node at a Lagrangian corner is +constrained to move with the material in all directions; it is nonadaptive. +Sliding boundary regions +A sliding boundary region is the same as a Lagrangian boundary region except that it has a sliding edge. +Sliding boundary regions are created by default when you define a surface on the boundary of an adaptive +mesh domain . +The mesh is constrained to move with the material in the direction normal to the boundary region, +but it is completely unconstrained in the directions tangential to the boundary region. Thus, a sliding +boundary region can be thought of as a “mesh patch” that moves independently of the underlying material. +Sliding boundary regions can be created by defining a surface, boundary condition, or load +on the boundary of an adaptive mesh domain (as explained later in this section). Since the mesh +is totally unconstrained in the directions tangential to a sliding boundary region, the location of an +applied boundary condition or load may not be physically meaningful as the mesh moves over the +material. Therefore, to retain the spatial meaning of an applied boundary condition or load, spatial +mesh constraints (described in “Mesh constraints,” presented later in this section) are usually applied +tangential to sliding boundary regions. +Eulerian boundary regions +Eulerian boundary regions can be defined on the exterior of a model where it makes physical sense to let +material flow across the boundary (for example, at the inlet and outlet of a steady-state extrusion or rolling +problem). This flow across the boundary distinguishes Eulerian boundary regions from Lagrangian or +sliding boundary regions. +Eulerian boundary regions have sliding edges and must lie completely on an exterior surface of a +model. It makes no physical sense to allow material flow to originate on an interior surface. You must +explicitly define Eulerian boundary regions since, by default, Abaqus/Explicit assumes that no material +flows into or out of an adaptive mesh domain. +Eulerian boundary regions are created by defining a surface, a boundary condition, or a load on the +boundary of an adaptive mesh domain. On Eulerian boundary regions the mesh motion usually should +be constrained in the direction normal to the material motion; therefore, the surface mesh should be fixed +in space using spatial mesh constraints (described in “Mesh constraints,” presented later in this section). +Applying these constraints normal to an Eulerian boundary region allows material to flow into or out +of the mesh, as in a fluid flow problem, while allowing adaptive meshing to occur on the surface of the +boundary region to maximize mesh quality. +The material flowing into an Eulerian boundary region is assumed to have the same properties as +the material that is inside the adaptive mesh domain. +Techniques for modeling Eulerian domains are presented in “Modeling techniques for Eulerian +adaptive mesh domains in Abaqus/Explicit,” Section 12.2.4. +Creation of boundary regions +Abaqus/Explicit will create adaptive mesh boundary regions automatically on +• the exterior of a model, +• the boundary between different adaptive mesh domains, or +• the boundary between an adaptive mesh domain and a nonadaptive domain. +By default, a boundary region on the exterior of a model will be Lagrangian, so that the boundary region +follows the material, and loads, boundary conditions, etc. will retain their Lagrangian interpretation. A +boundary region between different adaptive mesh domains is always Lagrangian: no material can flow +through such a boundary region. An additional constraint is applied when the model contains multiple +parallel domains . In this case the boundary +region is nonadaptive: no material can flow through the boundary region, and the nodes on this boundary +are constrained to move exactly with the underlying material in all directions. A boundary region between +an adaptive mesh domain and a nonadaptive domain is always nonadaptive. The only exception to this +occurs if an Eulerian boundary region is defined on the boundary between an adaptive mesh domain +and a nonadaptive domain that comprises displacement-based infinite elements. In this case the nodes +on the boundary behave as in Eulerian boundary regions , and the mesh motion at the boundary nodes can be constrained +using spatial mesh constraints. +The boundary between two different materials can never “flow” through the mesh; such a physical +boundary is always associated with a Lagrangian boundary region or a nonadaptive mesh boundary. +Figure 12.2.2–1 shows +that will be created automatically by +Abaqus/Explicit. +In the model shown in this figure Abaqus/Explicit splits the user-defined +adaptive mesh domain into two adaptive mesh domains because the original domain is composed of +two different materials. +some boundary regions +In addition to the boundary regions created automatically by Abaqus/Explicit, Lagrangian, sliding, +and Eulerian boundary regions can be created by the definition of surfaces, boundary conditions, and +loads, as described later in this section. +Geometric features +Many models include distinct geometric kinks that take the form of geometric edges or corners. It is +usually not desirable to perform adaptive meshing across such geometric features unless they flatten. +nonadaptive +domain +adaptive mesh +domain +material 1 +nonadaptive boundary region +Lagrangian boundary region +adaptive mesh +domain +material 2 +user-defined adaptive mesh domain: right half of box +Figure 12.2.2–1 Automatic splitting of mesh domains and creation of boundary regions. +Once a geometric feature does flatten, it is usually best if the feature is deactivated so that adaptive +meshing will occur across it. This is especially true when adaptive mesh domains are subject to large +deformation. +The adaptive meshing algorithm in Abaqus/Explicit will respect geometric features on Lagrangian +and sliding boundaries. +In three dimensions geometric features consist of edges and corners , while in two dimensions they consist of only corners. If a geometric edge coincides +with the edge of a Lagrangian boundary region, the presence of the geometric feature has no effect on +the treatment of the edge: material cannot flow perpendicular to a Lagrangian edge. +Geometric features are not detected or tracked on Eulerian boundary regions because they generally +are not physically meaningful. +Output options are available for viewing the formation of geometric edges and corners—see “Output +and diagnostics for ALE adaptive meshing in Abaqus/Explicit,” Section 12.2.5. +Controlling the detection of geometric edges and corners +Geometric features are identified initially as edges on boundary regions where the angle between the +normals on adjacent element faces is greater than the initial geometric feature angle, +). See Figure 12.2.2–3. The default value for the initial geometric feature angle is +( +. +z-symmetry +crack front +x-symmetry +geometric corner +Lagrangian corner plus +geometric corner +geometric edge +Lagrangian edge +y-symmetry +Figure 12.2.2–2 Geometric features formed on a solid block with a crack. +θ > θ +θ ≤ θ +Initial mesh with a geometric +feature: no mesh flow is +permitted past the corner. +The geometric feature +is deactivated during +simulation. +Figure 12.2.2–3 Detection and deactivation of geometric features. +You can change the value of the angle that will be used to recognize geometric features. Setting +will ensure that no geometric edges or corners are formed on the boundary of the adaptive +mesh domain. +Input File Usage: +*ADAPTIVE MESH CONTROLS, NAME=name, +INITIAL FEATURE ANGLE= +Abaqus/CAE Usage: +Step module: Other→ALE Adaptive Mesh Controls→Create: +Name: name, Initial feature angle: +Controlling the deactivation of geometric edges and corners +Geometric features affect only Lagrangian and sliding boundary regions, where they act as temporary +Lagrangian edges. During each mesh sweep in an adaptive mesh increment, nodes along a geometric +edge are positioned by applying the basic smoothing methods . The nodes are constrained to lie along the discrete +geometric edge unless the angle forming the geometric edge becomes less than the transition geometric +feature angle, +. +If the angle across the geometric edge becomes less than +, the boundary surface is considered to be +flattened sufficiently for the feature to be deactivated, and the mesh is allowed to slide freely over the +material (unconstrained by the deactivated geometric edge). Geometric corners are allowed to flatten +in a similar fashion. This logic allows great flexibility in mesh adaptation while preserving geometric +features in the model. +). The default value for the transition feature angle is +( +You can change the transition feature angle. Setting +will ensure that no geometric edges +or corners are ever deactivated. +Input File Usage: +*ADAPTIVE MESH CONTROLS, NAME=name, +TRANSITION FEATURE ANGLE= +Abaqus/CAE Usage: +Step module: Other→ALE Adaptive Mesh Controls→Create: +Name: name, Transition feature angle: +Mesh constraints +In most adaptive mesh problems the motion of nodes in the mesh is determined by the meshing algorithm, +with constraints imposed by the domain boundary and the boundary region edges. However, there are +cases when you must explicitly define the motion of the nodes. As explained earlier, Eulerian and sliding +boundary regions generally require mesh constraints for the regions to be physically meaningful. In +some problems you may wish to keep certain nodes fixed, to move nodes in a particular direction, or to +force certain nodes to move with the material. In other problems you may desire a node or particular +set of nodes to follow the material motion. Adaptive mesh constraints allow full control over the mesh +movement and act independently of any boundary conditions or loads applied to the underlying material. +Applying spatial mesh constraints +Use a spatial mesh constraint (the default) to prescribe spatial mesh motion that is independent of the +material motion. You specify the nodes to which the constraint is applied, the directions of the prescribed +motion, and the amplitude of the prescribed motion. You can prescribe either a displacement or a velocity +for the spatial mesh motion. +Input File Usage: +Use the following option to define the mesh constraints explicitly: +*ADAPTIVE MESH CONSTRAINT, CONSTRAINT TYPE=SPATIAL, +TYPE=DISPLACEMENT or VELOCITY +Abaqus/CAE Usage: +To define the mesh constraints explicitly: +Step module: Other→ALE Adaptive Mesh Constraint→Create: Types +for selected step: Displacement/Rotation or Velocity/Angular velocity: +select region: Motion: Independent of underlying material +Rules for applying spatial mesh constraints +Spatial mesh constraints can be applied without restriction to nodes on an Eulerian boundary region or +in the interior of an adaptive mesh domain. +In both two and three dimensions nodes at Lagrangian and active geometric corners are fully +constrained to move with the underlying material. No mesh constraints can be applied at such corners. +Adaptive mesh constraints must not conflict with other mesh constraints inherent to Lagrangian +and sliding boundary regions; therefore, adaptive mesh constraints can be applied only tangentially to +a Lagrangian or sliding boundary region. This restriction implies that adaptive mesh constraints can +be applied only in two directions in a three-dimensional boundary region, in one direction in a two- +dimensional boundary region, or in one direction on a Lagrangian or active geometric edge. It may +not always be feasible to adhere to this rule, particularly if the boundary experiences finite rotation. +Therefore, if the normal to a boundary region is not perpendicular to a prescribed mesh constraint at a +node, it is always moved along the current surface of the boundary region so that the projection of the +mesh motion in the direction of the prescribed constraint is correct . +If the normal to the boundary region approaches the direction of the applied mesh constraint, large +mesh motions will be required to satisfy the constraint. By default, an analysis is terminated if the angle +between the normal to the boundary region and the direction of the prescribed constraint becomes less +than +. This cutoff angle is referred to as the mesh constraint angle, and its default value is 60°. +The mesh constraint angle, +, is also used when adaptive mesh constraints are applied to nodes +along a Lagrangian or active geometric edge. Since independent mesh motion cannot be prescribed +perpendicular to these edges, an analysis is terminated if the angle between the prescribed constraint and +the plane perpendicular to the edge falls below the specified mesh constraint angle. +You can change the value of the mesh constraint angle ( +is +not recommended because it may cause errors in determining the free surface geometry, especially for +curved surfaces. +). Setting +Input File Usage: +Abaqus/CAE Usage: +*ADAPTIVE MESH CONTROLS, MESH CONSTRAINT ANGLE= +Step module: Other→ALE Adaptive Mesh Controls→Create: +Mesh constraint angle: +Defining mesh constraints that vary with time +The prescribed magnitude of a nonzero mesh constraint can vary with time during a step according to an +amplitude definition . +Input File Usage: +Use both of the following options: +*AMPLITUDE, NAME=name +*ADAPTIVE MESH CONSTRAINT, AMPLITUDE=name +t = t1 +zero-displacement adaptive mesh constraint applied +at node 3 in direction 1 +direction of +applied constraint +Θ < Θ +c, analysis is terminated +movement of node 3 +without mesh constraint +motion of node 3 along +surface to satisfy constraint +boundary +region +t = t0 +projection of +mesh motion +in prescribed +direction +Figure 12.2.2–4 Enforcing a spatial mesh constraint. +Abaqus/CAE Usage: +Step module: Other→ALE Adaptive Mesh Constraint→Create: Types +for selected step: Displacement/Rotation or Velocity/Angular +velocity: select region: Motion: Independent of underlying +material: Amplitude: amplitude +Applying spatial mesh constraints in local directions +Spatial mesh constraints are applied in local directions if a local coordinate system is defined at a node +; otherwise, they are applied in global directions. +Applying Lagrangian mesh constraints +Lagrangian mesh constraints on a node are used to indicate that mesh smoothing should not be applied; +i.e., the node must follow the material. +Input File Usage: +*ADAPTIVE MESH CONSTRAINT, +CONSTRAINT TYPE=LAGRANGIAN +Abaqus/CAE Usage: +Step module: Other→ALE Adaptive Mesh Constraint→Create: Types +for selected step: Displacement/Rotation or Velocity/Angular velocity: +select region: Motion: Follow underlying material +Modifying ALE adaptive mesh constraints +By default, all adaptive mesh constraints defined in the previous analysis step remain unchanged in +the subsequent step. You define the adaptive mesh constraints in effect for a given step relative to the +preexisting adaptive mesh constraints. At each new step the existing adaptive mesh constraints can be +modified and additional adaptive mesh constraints can be specified. +Input File Usage: +Use either of the following options to modify an existing adaptive mesh +constraint or to specify an additional adaptive mesh constraint: +Abaqus/CAE Usage: +*ADAPTIVE MESH CONSTRAINT, +*ADAPTIVE MESH CONSTRAINT, OP=MOD +Step module: Other→ALE Adaptive Mesh Constraint→Manager: +select the desired step and mesh constraint: Edit +Removing ALE adaptive mesh constraints +If you choose to remove any adaptive mesh constraint in a step, no adaptive mesh constraints will be +propagated from the previous step. Therefore, all adaptive mesh constraints that are in effect during this +step must be respecified. +Input File Usage: +Use the following option to remove all previously defined adaptive mesh +constraints and to specify new adaptive mesh constraints: +*ADAPTIVE MESH CONSTRAINT, OP=NEW +If the OP=NEW parameter is used on any *ADAPTIVE MESH CONSTRAINT +option within a step, +it must be used on all *ADAPTIVE MESH +CONSTRAINT options in the step. +Abaqus/CAE Usage: +Step module: Other→ALE Adaptive Mesh Constraint→Manager: +select the desired step and mesh constraint: Deactivate +Initial conditions +There are no initial conditions specific to adaptive meshing; initial conditions can be defined in the +same way as in nonadaptive problems. If initial mesh sweeps are performed to smooth the mesh at the +beginning of a step , +all initial conditions (except temperatures and field variables, which are discussed in “Predefined fields,” +presented later in this section) are remapped to the new mesh. Initial temperatures are remapped during +adaptive meshing in an adiabatic analysis. +Initial conditions prescribed near an inflow Eulerian boundary region will affect the state of the +material flowing into the domain throughout the analysis. See “Modeling techniques for Eulerian +adaptive mesh domains in Abaqus/Explicit,” Section 12.2.4, for a discussion of the proper treatment +of inflow boundaries. +Defining surfaces on ALE adaptive mesh boundaries +When you define a surface on the boundary of an adaptive mesh domain , Abaqus creates a boundary region coinciding with the surface. By default, a sliding +boundary region is created. You can choose to create a Lagrangian or Eulerian boundary region instead. +A surface defined in the interior of an adaptive mesh domain will move independently of the material +(unless constrained by mesh constraints). +Defining a sliding boundary region using a surface +By default, the boundary region created by a surface definition will be sliding (the surface edge will slide +freely over the material). +Input File Usage: +Abaqus/CAE Usage: +*SURFACE, REGION TYPE=SLIDING +Boundary regions defined using surfaces are not supported in Abaqus/CAE. +Defining a Lagrangian boundary region using a surface +To force the surface edge to follow the material, create a Lagrangian boundary region. +Input File Usage: +Abaqus/CAE Usage: +*SURFACE, REGION TYPE=LAGRANGIAN +Boundary regions defined using surfaces are not supported in Abaqus/CAE. +Defining an Eulerian boundary region using a surface +To decouple the surface from the material motion, create an Eulerian boundary region and apply spatial +mesh constraints normal to the surface. If no mesh constraints are applied, the surface will behave like +a sliding boundary region (no material will flow through the surface). +As an example, it is often assumed that there is no normal or shear stress in the material at the outflow +boundary of an Eulerian domain. This condition can be modeled by defining an Eulerian boundary +region using a surface and applying spatial mesh constraints perpendicular to the surface, as shown in +Figure 12.2.2–5. +Input File Usage: +Abaqus/CAE Usage: +*SURFACE, REGION TYPE=EULERIAN +Boundary regions defined using surfaces are not supported in Abaqus/CAE. +Contact +Lagrangian and sliding boundary regions created using surfaces can be used in contact pairs; they have +the same meaning as surfaces defined on nonadaptive regions. Since contact generally involves relative +sliding between bodies, sliding boundary regions are typically appropriate for contact surfaces. +Surfaces defined on Eulerian boundary regions cannot be used in contact pairs. +free surface +Lagrangian boundary +region (automatic) +flow +node set OUT +Eulerian boundary region +(defined using a surface) +symmetry +Lagrangian boundary +region (automatic) +zero-displacement adaptive mesh constraint +applied to node set OUT in direction 1 +Figure 12.2.2–5 Modeling the outflow boundary of an Eulerian adaptive mesh domain. +If the small-sliding formulation is used for a contact pair, all the nodes on both surfaces are +nonadaptive . The nodes of an element-based surface in +a no-separation contact pair are nonadaptive . All nodes in a general contact domain are nonadaptive . Similarly, the nodes at which spot welds are defined +are nonadaptive +Distributed loads +When a distributed pressure load is applied to the boundary of an adaptive mesh domain, Abaqus/Explicit +creates a boundary region that coincides with the area of the load application. The characteristics of +boundary regions created in this way are identical to those of boundary regions created by defining +surfaces. If a pressure load is applied to a surface in the interior of an adaptive mesh domain, the nodes +on the surface will move with the material in all directions (i.e., they will be nonadaptive). +Boundary regions created by different pressure loads may overlap. +If pressure loads with the +same magnitude and amplitude definition are applied to adjacent regions, the regions will be merged +into a single boundary region to minimize the number of Lagrangian edges and corners formed . +If a nonuniform pressure is applied (for example, a pressure that varies linearly over a surface) or +if a pressure load is defined in user subroutine VDLOAD, each element face or edge becomes a separate +Lagrangian boundary region. Since Lagrangian corners are formed where Lagrangian edges meet, all +If these distributed loads +have identical magnitudes +and amplitude definitions, +they will be combined into +one Lagrangian boundary +region. +Overlapping distributed loads +result in three Lagrangian +boundary regions. +This node is adaptive +because the sliding +boundary region does not +create a Lagrangian corner. +L = Lagrangian boundary region created by pressure load +S = Sliding boundary region created by pressure load + = Lagrangian corner +Figure 12.2.2–6 Applying distributed pressure loads to an adaptive mesh domain. +nodes will follow the material in every direction, and each region becomes nonadaptive. Likewise, if a +nonuniform body force is applied to an adaptive mesh domain, the domain is split into multiple domains, +each with a uniform body force. If this splitting results in one-element domains, the region becomes +nonadaptive. +Defining a Lagrangian boundary region with a pressure load +By default, the boundary region created to coincide with a pressure load will be Lagrangian. Pressure +loads applied to Lagrangian regions are identical to pressure loads applied to nonadaptive regions, except +that the mesh can move inside the boundary region. +Input File Usage: +Abaqus/CAE Usage: +*DLOAD, REGION TYPE=LAGRANGIAN +Boundary regions defined using pressure loads are not supported in +Abaqus/CAE. +Defining a sliding boundary region with a pressure load +A pressure load can be applied to a sliding boundary region to simulate a load that is fixed in space while +material moves past it . A sliding edge is unconstrained in the direction tangential +to the boundary region; therefore, unless adaptive mesh constraints are applied, the area of the load +application will move according to the adaptive meshing algorithm, which is probably not physically +meaningful. +To allow a pressure load to slide over the material, create a sliding boundary region. +Input File Usage: +Abaqus/CAE Usage: +*DLOAD, REGION TYPE=SLIDING +Boundary regions defined using pressure loads are not supported in +Abaqus/CAE. +P0 +flow +flow +flow +Lagrangian +interpretation +Spatial (sliding) +interpretation +t = t0 +t = t1 +t = t1 += sliding boundary region created by pressure load += zero-displacement adaptive mesh constraints + applied to nodes 1 and 4 in direction 1 +Figure 12.2.2–7 Applying a sliding distributed pressure load to an adaptive mesh domain. +Defining an Eulerian boundary region with a pressure load +To decouple the area of pressure application from the material motion, create an Eulerian boundary region +and apply spatial mesh constraints normal to the surface. If no mesh constraints are applied, the mesh +will behave like a sliding boundary region (no material will flow through the surface). +As an example, it is often assumed that a uniform ambient pressure exists at the outflow boundary +of an Eulerian domain. This condition can be modeled by defining the pressure at an Eulerian boundary +region using a distributed load and applying spatial mesh constraints perpendicular to the surface, as +shown in Figure 12.2.2–8. +Input File Usage: +Abaqus/CAE Usage: +*DLOAD, REGION TYPE=EULERIAN +Boundary regions defined using pressure loads are not supported in +Abaqus/CAE. +Distributed surface fluxes and thermal conditions +In coupled thermal-stress analysis Abaqus/Explicit also creates boundary regions for distributed surface +fluxes, convective film conditions, and radiation conditions. The rules governing boundary regions for +free surface +flow +node set OUT +symmetry += Eulerian boundary region created by pressure load += zero-displacement adaptive mesh constraint + applied to node set OUT in direction 1 +Figure 12.2.2–8 Modeling an ambient pressure at the outflow +boundary of an Eulerian adaptive mesh domain. +these loads are identical to those discussed for distributed loads. The ability to specify the boundary +region type is also the same. +Concentrated loads +When a concentrated load is applied to the boundary of an adaptive mesh domain, Abaqus/Explicit +creates a boundary region to coincide with the load. Every node to which a concentrated load is applied +will be considered its own boundary region because it is not possible to identify a surface area associated +with a concentrated load. However, you can control the behavior of each one-node region. +If concentrated loads are applied to nodes in the interior of an adaptive mesh domain, those nodes +will move with the material in all directions (i.e., they will be nonadaptive). +Defining a Lagrangian boundary region with a concentrated load +By default, the boundary region created by a concentrated load will be Lagrangian. Each one-node +Lagrangian boundary region will follow the material in every direction (the nodes will be nonadaptive). +Input File Usage: +Abaqus/CAE Usage: +*CLOAD, REGION TYPE=LAGRANGIAN +Boundary regions defined using concentrated loads are not supported in +Abaqus/CAE. +Defining a sliding boundary region with a concentrated load +A concentrated load can be applied to a sliding boundary region to simulate a load that is fixed in space +while material moves past it . A sliding node is unconstrained in the direction +Lagrangian +interpretation +material slides past this node +zero-displacement adaptive mesh +constraint applied to node N in +direction 1 +Sliding +interpretation +t = t0 +flow +t = t1 +flow +t = t1 +flow +Figure 12.2.2–9 Applying a concentrated sliding load to an adaptive mesh domain. +tangential to the boundary region; therefore, unless adaptive mesh constraints are applied, the point of +load application will move according to the adaptive meshing algorithm, which is probably not physically +meaningful. +To allow the concentrated load to slide freely over the material, create a sliding boundary region. +Input File Usage: +Abaqus/CAE Usage: +*CLOAD, REGION TYPE=SLIDING +Boundary regions defined using concentrated loads are not supported in +Abaqus/CAE. +Defining an Eulerian boundary region with a concentrated load +To decouple the concentrated load from the material motion, create an Eulerian boundary region and +apply spatial mesh constraints normal to the surface. If no mesh constraints are applied, each one-node +boundary region will behave like a sliding boundary region. +Input File Usage: +*CLOAD, REGION TYPE=EULERIAN +Abaqus/CAE Usage: +Boundary regions defined using concentrated loads are not supported in +Abaqus/CAE. +Concentrated fluxes and thermal conditions +In coupled thermal-stress analysis Abaqus/Explicit also creates boundary regions for concentrated heat +fluxes, film conditions, and radiation conditions. The rules governing boundary regions for these loads +are identical to those discussed for concentrated loads. The ability to specify the boundary region type +is also the same. +Boundary conditions +Lagrangian, sliding, and Eulerian boundary regions can be created by applying kinematic constraints to +the boundary of an adaptive mesh domain. If kinematic boundary conditions are applied to nodes in the +interior of an adaptive mesh domain, those nodes will move with the material in all directions (i.e., they +will be nonadaptive), regardless of the specified boundary region type. +Defining a Lagrangian boundary region using a boundary condition +By default, +the boundary region created by a kinematic boundary condition will be Lagrangian. +Abaqus/Explicit will recognize surface-type and point or edge constraints automatically and will create +an appropriate Lagrangian boundary region for each type, as explained in the following subsections. +*BOUNDARY, REGION TYPE=LAGRANGIAN +Boundary regions defined using boundary conditions are not supported in +Abaqus/CAE. +Abaqus/CAE Usage: +Input File Usage: +Surface-type constraints applied using boundary conditions +Although boundary conditions are always applied to individual nodes in Abaqus/Explicit, they often +represent physical constraints on surfaces. For example, symmetry conditions, where nodes are +constrained to move in a plane, are actually surface constraints. A fully clamped (ENCASTRE) +condition along a boundary can also be considered a surface constraint. (During adaptive meshing it is +meaningful to allow nodes to move along a fully clamped edge.) +Abaqus/Explicit will examine an adaptive mesh boundary and try to create regions that are +coincident with the applied boundary conditions. Currently, Abaqus/Explicit can create boundary +regions for surface-based constraints on: +• symmetry planes, +• fully clamped planes, and +• planes on which a uniform motion is prescribed. +Figure 12.2.2–2 shows an example in which boundary regions are created by applying surface-type +boundary conditions. This figure shows a block of material with a crack and three symmetry planes +(therefore, three Lagrangian boundary regions). Material will not flow across any symmetry plane, yet +adaptive meshing can be performed within each Lagrangian boundary region. This flexibility is often +helpful in problems that have significant deformation. +Point or edge constraints applied using boundary conditions +Some boundary conditions represent point or edge constraints. For example, a displacement can be +prescribed at a node. The boundary regions associated with such nodes are exactly the same as those +created by concentrated loads. +Defining a sliding boundary region using a boundary condition +A sliding boundary region associated with a boundary condition can move according to the adaptive +meshing algorithm. Since this behavior is probably not physically meaningful, the edges of a sliding +boundary region are usually fixed in the direction tangential to the surface using adaptive mesh +constraints. This approach can be used, for example, to simulate frictionless contact between a rigid +punch and a deformable body, as shown in Figure 12.2.2–10. += +node set CONTACT +zero-displacement adaptive mesh constraint applied to +node N in direction 1 +sliding boundary region created by velocity-type boundary +condition applied to node set CONTACT +material flows past node N +(a) effect of punch + modeled with contact +(b) effect of punch modeled + with boundary conditions applied + to sliding boundary region +Figure 12.2.2–10 Contact simulation using a sliding boundary region. +In this example the punch is replaced by a sliding boundary region with a constant velocity boundary +condition applied in the area of “contact.” A tangential mesh constraint is applied to the edge of +the boundary region at node N (the other edge is constrained by the Lagrangian boundary region +created automatically on the symmetry plane). This problem definition allows material to flow radially +underneath the “punch” while retaining the original size and location of the “contact” area. +Abaqus/Explicit makes no distinction between surface-type constraints and point or edge constraints +for sliding boundary regions. +To allow the boundary condition to slide freely over the material, create a sliding boundary region. +Input File Usage: +Abaqus/CAE Usage: +*BOUNDARY, REGION TYPE=SLIDING +Boundary regions defined using boundary conditions are not supported in +Abaqus/CAE. +Defining an Eulerian boundary region using a boundary condition +To decouple the boundary region from the material motion, create an Eulerian boundary region and apply +spatial mesh constraints normal to the surface. If no mesh constraints are applied, the mesh will behave +like a sliding boundary region (no material will flow through the surface). +As an example, the mass flow rate at an Eulerian inflow boundary can be prescribed by defining an +Eulerian boundary region using a boundary condition. +Abaqus/Explicit makes no distinction between surface-type constraints and point or edge constraints +for Eulerian boundary regions. +Input File Usage: +Abaqus/CAE Usage: +*BOUNDARY, REGION TYPE=EULERIAN +Boundary regions defined using boundary conditions are not supported in +Abaqus/CAE. +Overlapping boundary regions +A Lagrangian boundary region can overlap any number of other Lagrangian or sliding boundary +regions . If two boundary regions partially overlap, three regions are formed: the +overlapping region and the two initial regions minus the overlapping region. A sliding boundary region +is formed when a Lagrangian and a sliding boundary region overlap. +An Eulerian boundary region can never overlap a Lagrangian or sliding boundary region. +Furthermore, an Eulerian boundary region can never share a boundary with or overlap a nonadaptive +region. Because infinite elements are nonadaptive, this latter restriction implies that infinite elements +cannot be used to simulate ambient conditions at an outflow boundary. +Coincident edges +Edges shared by different types of boundary regions are subject to the following rules: +• An edge shared between a Lagrangian and a sliding boundary region will be Lagrangian. +• An edge shared between a Lagrangian and an Eulerian boundary region will be sliding. +• An edge shared between a Lagrangian and a nonadaptive boundary region will be nonadaptive. +• An edge shared between a sliding and a nonadaptive boundary region will be nonadaptive. +• An edge of an Eulerian boundary region can never be coincident with an edge of a nonadaptive +region. +Predefined fields +There are no restrictions on applying prescribed temperatures or field variables in an adaptive mesh +domain, but these nodal values are not remapped when adaptive meshing is performed. Therefore, +predefined fields that are not spatially uniform may not be meaningful within an adaptive mesh domain. +Lagrangian edge +Sliding edge +Lagrangian corner +L = Lagrangian boundary region +S = Sliding boundary region +E = Eulerian boundary region +Figure 12.2.2–11 Overlapping boundary regions. +(Time-varying, spatially uniform predefined fields are acceptable, since adaptive meshing is applied at +discrete instances in time.) However, if temperature or field variable data are collected from a spatial +frame of reference, it may make physical sense to apply a spatially varying field for an Eulerian domain +in which the mesh does not move. Abaqus/Explicit does not perform any checks or calculations on +predefined fields for adaptive meshing; you must ensure that the predefined fields are meaningful. +Materials +All material models and behaviors, except brittle cracking (“Cracking model +Section 23.6.2), +(“Low-density foams,” Section 22.9.1) materials, can be used in an adaptive mesh domain. +fabric (“Fabric material behavior,” Section 23.4.1), +for concrete,” +and low-density foam +For domains modeled with hyperelastic or hyperfoam materials the usefulness of adaptive meshing +is limited. The recommended enhanced hourglass method (“Section controls,” Section 27.1.4), which +will generally predict a much better return to the original configuration for these materials when loading is +removed, cannot be used in an adaptive mesh domain. Therefore, for hyperelastic or hyperfoam materials +it is recommended that the analysis be run without adaptive meshing but with enhanced hourglass control. +If the porous failure model (“Failure criteria in Abaqus/Explicit” in “Porous metal plasticity,” +Section 23.2.9), shear failure model (“Shear failure model” in “Dynamic failure models,” Section 23.2.8), +tensile failure model (“Tensile failure model” in “Dynamic failure models,” Section 23.2.8), or one of +the progressive damage models (Chapter 24, “Progressive Damage and Failure”) is specified within +an adaptive mesh domain, Abaqus/Explicit will continuously monitor the status of elements while +performing adaptive meshing. When elements within the domain fail, the nodes along the interface +between the failed and unfailed elements will become nonadaptive. This has the effect of creating a +material boundary between the failed and unfailed zones. +When failure occurs in elements that use the shear failure, the tensile failure, or the progressive +damage models without element deletion, elements in the failure zone will not be deleted; they can carry +some states of stress. Adaptive meshing will occur within the failure zone but not along the interface +with the unfailed material. +Elements +An adaptive mesh domain can contain only first-order, reduced-integration, solid elements. All +elements within an adaptive mesh domain must have the same geometry (all +two-dimensional, +three-dimensional, axisymmetric, or plane strain, etc.). Since adaptive mesh domains are split across +element types, degenerate elements should be used for mixed domains that include both triangles and +quadrilaterals (or tetrahedron and bricks). All elements other than first-order, reduced-integration, solid +elements—including mass, rotary inertia, and infinite elements—are nonadaptive. These elements can +be connected to an adaptive mesh domain, but their nodes are nonadaptive. All nodes and elements on +a rigid body are nonadaptive. Rebar are not supported within an adaptive mesh domain. +Multi-point constraints and equations +As with boundary conditions, multi-point constraints (“General multi-point constraints,” Section 34.2.2) +and equations (“Linear constraint equations,” Section 34.2.1) are always applied to nodes but sometimes +represent constraints on surfaces. Abaqus/Explicit will recognize surface-type constraints when the +following conditions are satisfied: +• an equation, PIN MPC, or TIE MPC ties a node set to a single node; and +• all the nodes involved in the MPC or equation are coplanar and lie within the boundary region. +If these conditions are satisfied, a boundary region will be associated with the node set in the MPC or +equation. If the MPC is applied within a Lagrangian or sliding boundary region, a Lagrangian edge will +be created. If the MPC is applied within an Eulerian boundary region, no edge will be created. If the +above conditions are not satisfied, all nodes connected to the MPC or equation will be nonadaptive. +As an example, a constraint can be applied to force a plane section to remain plane in a Lagrangian +adaptive mesh domain, as shown in Figure 12.2.2–12(a). In this case all nodes are constrained by an +equation to lie in the same plane throughout the analysis, but adaptive meshing is allowed within the +plane. +As another example, consider the outflow boundary of an Eulerian domain, as shown in +Figure 12.2.2–12(b). The outflow boundary of an Eulerian domain is often assumed to be far enough +downstream that the velocity is uniform but unknown. To model this condition, an Eulerian boundary +region is created at the outflow boundary using a surface. An adaptive mesh constraint is used to fix the +mesh perpendicular to the boundary, and all nodes on the plane are constrained by an equation to have +the same velocity orthogonal to the plane. +For surface-based tie constraints , all nodes on the tied +surfaces will be nonadaptive. +Lagrangian +boundary +region +node set PLANE +Linear constraint equation +1.0u 1.0u = 0 +PLANE +(a) Using an equation to force a plane section to remain a plane. +zero-displacement adaptive mesh constraints +applied to node 1 and to node set OUTFLOW +in direction 1 +material +flow +element set +OUTFLOW +node set OUTFLOW +Linear constraint equation + 1.0u = 0 +1.0u +OUTFLOW +Eulerian boundary region created using a surface defined on the +S4 faces of element set OUTFLOW +(b) Using an equation to prescribe a uniform velocity outflow condition. +Figure 12.2.2–12 Using equations with adaptive meshing. +Procedures +During an adiabatic analysis temperatures will be remapped properly in adaptive mesh domains. +Adaptive meshing is not used during annealing procedures or during geometrically linear analyses. +The definitions of adaptive mesh domains, boundary regions, mesh constraints, and controls (as +explained in “ALE adaptive meshing and remapping in Abaqus/Explicit,” Section 12.2.3) will propagate +from step to step. +User subroutines +Solution-dependent state variables defined in user subroutine VUMAT will be remapped to the new mesh +when adaptive meshing is performed. +Solution-dependent state variables that are defined on a slave surface in user subroutines VFRIC, +VUINTER, VFRICTION, and VUINTERACTION will not be remapped to the new mesh when adaptive +meshing is performed. Therefore, to ensure physically meaningful results, a Lagrangian adaptive mesh +constraint should be used for nodes on the contact slave surfaces with solution-dependent state variables +where the contact constraint is defined using these user subroutines. +Output +Since the mesh is no longer constrained to the material when adaptive meshing is performed, output at +elements and nodes must be interpreted differently than in a pure Lagrangian problem. See “Output and +diagnostics for ALE adaptive meshing in Abaqus/Explicit,” Section 12.2.5, for details. +Input file template +To create a Lagrangian adaptive mesh domain: +*HEADING +… +*ELSET, ELSET=ADAPT +************************* +*STEP +*DYNAMIC, EXPLICIT +Data line to specify the time period of the step +*ADAPTIVE MESH, ELSET=ADAPT +... +*END STEP +To create an Eulerian adaptive mesh domain with a prescribed velocity inflow condition and a prescribed +pressure outflow condition (both in the global x-direction): +*HEADING... +*ELSET, ELSET=ADAPT +... +*ELSET, ELSET=OUT +... +*NSET, NSET=INFLOW +... +*NSET, NSET=OUTFLOW +... +*SURFACE, NAME=INSURF, REGION TYPE=EULERIAN +Data lines to define the surface +*SURFACE, NAME=OUTSURF, REGION TYPE=EULERIAN +Data lines to define the surface +... +*EQUATION +Data lines specifying uniform velocity at the inflow +************************* +*STEP +*DYNAMIC, EXPLICIT +Data line to specify the time period of the step +*ADAPTIVE MESH, ELSET=ADAPT +*ADAPTIVE MESH CONSTRAINT +INFLOW, +1, 1, 0 +OUTFLOW, 1, 1, 0 +*BOUNDARY, TYPE=VELOCITY, REGION TYPE=EULERIAN +INFLOW, 1, 1, 10.0 +*DLOAD, REGION TYPE=EULERIAN +OUT, P2, 15.0 +... +*END STEP +12.2.3 +ALE ADAPTIVE MESHING AND REMAPPING IN Abaqus/Explicit +Products: Abaqus/Explicit Abaqus/CAE +References +• “ALE adaptive meshing: overview,” Section 12.2.1 +��� “Defining ALE adaptive mesh domains in Abaqus/Explicit,” Section 12.2.2 +• “Output and diagnostics for ALE adaptive meshing in Abaqus/Explicit,” Section 12.2.5 +• *ADAPTIVE MESH +• *ADAPTIVE MESH CONSTRAINT +• *ADAPTIVE MESH CONTROLS +• “Customizing ALE adaptive meshing,” Section 14.14 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +ALE adaptive meshing consists of two fundamental tasks: +• creating a new mesh, and +• remapping solution variables from the old mesh to the new mesh with a process called advection. +The success of the adaptive meshing technique depends on the choice of the methods used for each of +these tasks. The default methods for creating a new mesh and for remapping solution variables have been +chosen carefully to work for a wide variety of problems. However, you may wish to override the default +choices to balance the robustness and efficiency of adaptive meshing or to extend the use of adaptive +meshing to more difficult or unusual applications. +Meshing +A new mesh: +• is created at a specified frequency for each adaptive domain; +• is found by sweeping iteratively over the adaptive mesh domain and moving nodes to smooth the +mesh; and +• can retain the initial gradation of the original mesh. +Remapping +The methods used for advecting solution variables to the new mesh: +• are consistent, monotonic, and (by default) accurate to the second order; and +• conserve mass, momentum, and energy. +Controlling the frequency of ALE adaptive meshing +In most cases the frequency of adaptive meshing is the parameter that most affects the mesh quality and +the computational efficiency of adaptive meshing. A typical adaptive mesh application without Eulerian +boundaries will require adaptive meshing every 5–100 increments. In contrast, adaptive meshing should +generally be performed much more frequently in a steady-state process simulation using Eulerian +boundaries. Thus, if a spatial adaptive mesh constraint or an Eulerian boundary region is defined on an +adaptive mesh domain, the default frequency is 1; otherwise, the default frequency is 10. +Input File Usage: +Use the following option to change the frequency of adaptive meshing: +Abaqus/CAE Usage: +*ADAPTIVE MESH, FREQUENCY=number of increments +Step module: Other→ALE Adaptive Mesh Domain→Edit: toggle on Use +the ALE adaptive mesh domain below, Frequency: number of increments +Controlling the intensity of ALE adaptive meshing +During each adaptive meshing increment, the new mesh is created by performing one or more mesh +sweeps and then advecting the solution variables to the new mesh. +Mesh sweeps +In an adaptive meshing increment, a new, smoother mesh is created by sweeping iteratively over the +adaptive mesh domain. During each mesh sweep, nodes in the domain are relocated—based on the +current positions of neighboring nodes and elements—to reduce element distortion. In a typical sweep +a node is moved a fraction of the characteristic length of any element surrounding the node. Increasing +the number of sweeps increases the intensity of adaptive meshing in each adaptive meshing increment. +The default number of mesh sweeps is one. +Input File Usage: +Use the following option to change the number of mesh sweeps to be performed +in each adaptive mesh increment: +Abaqus/CAE Usage: +*ADAPTIVE MESH, MESH SWEEPS=number of sweeps +Step module: Other→ALE Adaptive Mesh Domain→Edit: toggle +on Use the ALE adaptive mesh domain below, Remeshing +sweeps per increment: number of sweeps +Advection sweeps +The process of mapping solution variables from an old mesh to a new mesh is referred to as an advection +sweep. At least one advection sweep is performed in every adaptive mesh increment. +Ideally, an +advection sweep will be performed only once, after all mesh sweeps for the increment are complete. +However, numerical stability of the advection sweep is maintained only if the difference between the +old mesh and the new mesh is small. Therefore, if after a mesh sweep the total accumulated movement +of any node in the domain is greater than 50% of the characteristic length of any adjacent element, an +advection sweep is performed to remap the solution variables from the old mesh to the intermediate +mesh. Mesh sweeps will continue until the specified number is reached or until the movement of any +node again exceeds the 50% threshold. At this time an advection sweep is performed again to map +variables from the last intermediate mesh to the new intermediate mesh. The cycle will continue until +the number of mesh sweeps reaches the specified number. +The number of advection sweeps per adaptive mesh increment required for each adaptive mesh +domain is determined automatically by Abaqus/Explicit; you cannot override this automatic calculation. +The number of advection sweeps is printed by default to the message (.msg) file . +The computational cost of ALE adaptive meshing +The cost of adaptive meshing depends on the frequency of remeshing, the number of mesh and advection +sweeps performed, and the size of the adaptive mesh domains. When compared to a purely Lagrangian +analysis, additional computational cost is incurred only within adaptive mesh increments. +Generally, the cost of one advection sweep is several times greater than the cost of one mesh sweep. +Multiple advection sweeps are triggered when adaptive meshing is performed too infrequently and/or +a high number of mesh sweeps is specified. Performing adaptive meshing more frequently and doing +1–5 mesh sweeps in each adaptive mesh increment will usually generate only one advection sweep, +minimizing the computational cost. +The relatively smooth mesh and improved element aspect ratios that result from adaptive meshing +may increase the stable time increment compared to a similar pure Lagrangian analysis. In some cases +this increase can offset the cost of adaptive meshing completely. +Although computational cost can vary greatly with the type of application, performing adaptive +meshing on the entire problem domain in every increment will typically increase the cost of the analysis +by 3–5 times that of a similar Lagrangian analysis. Defining adaptive mesh domains that cover only a +fraction of the entire problem domain will reduce the cost proportionally. Changing the frequency to +every 10–25 increments will result in CPU times that are only moderately higher than those for a pure +Lagrangian analysis. +Guidelines for controlling ALE adaptive meshing frequency and intensity +Although the default values work well for many problems, difficult analyses may require a more frequent +adaptive meshing frequency or meshing with a higher intensity. +Guidelines for transient analysis +For problems without spatial adaptive mesh constraints or Eulerian boundary regions, the default +frequency for adaptive meshing is 10, and the default number of mesh sweeps is 1. The default +values are usually adequate for low- to moderate-rate dynamic problems and for quasi-static process +If the frequency or number of mesh sweeps is too +simulations undergoing moderate deformation. +low, excess element distortion may cause the analysis to terminate before the mesh is adapted; or, +if a solution can be obtained, it may not be as accurate as the solution that could be obtained with a +higher quality mesh. In virtually all cases, however, performing adaptive meshing at any frequency will +reduce the distortion of elements (and, thus, improve the quality of the solution) compared to a pure +Lagrangian analysis. +For high-rate impact problems undergoing large amounts of deformation, it may be necessary to +increase the frequency of adaptive meshing or the number of mesh sweeps. It is generally less expensive +to increase the number of mesh sweeps slightly before increasing the frequency, as long as the number +of advection sweeps remains small. +For problems involving explosions taking place over just a few hundred increments, adaptive +meshing is usually required at every increment. It may also be necessary to increase the frequency of +adaptive meshing for quasi-static process simulations that involve large amounts of flow per increment. +For problems in which the deformation per increment is small, a high-quality mesh can be +maintained by performing adaptive meshing only every 25–100 increments. For these problems the +additional cost of adaptive meshing is negligible. +Guidelines for steady-state analysis +When an adaptive mesh domain contains Eulerian boundary regions or has spatial adaptive mesh +constraints, the default frequency of adaptive meshing is 1. This default frequency is conservative and +is chosen primarily because spatial mesh constraints are applied only during adaptive mesh increments. +Thus, between adaptive mesh increments the mesh may drift from its prescribed location, which may +affect the solution. However, drift from adaptive mesh constraints will always be eliminated in the next +adaptive mesh increment: it will not accumulate. +For problems in which the speed of deformation or the speed of material flow from element to +element is much less than the material wave speed, the frequency typically can be increased to 5 or +higher. This class of problems includes most steady-state process simulations, where the drift of the +mesh from the prescribed location is negligible over a few increments. By performing adaptive meshing +less often, steady-state simulations become competitive with their corresponding transient simulations. +For Eulerian domains in which the speed of the deformation or material flow is high, such as in dynamic +shock problems, the default frequency of 1 should be used. +Mesh smoothing methods +The determination of the new mesh in Abaqus/Explicit is based on four aspects. You can control each of +these aspects by defining adaptive mesh controls. Defaults have been chosen so that the overall algorithm +works well for most problems. +First, the calculation of the new mesh in Abaqus/Explicit is based on some combination of three +basic smoothing methods: volume smoothing, Laplacian smoothing, and equipotential smoothing. The +smoothing methods are applied at each node in the adaptive mesh domain to determine the new location +of the node based on the locations of surrounding nodes or elements. Although all the smoothing methods +tend to smooth the mesh and reduce element distortion, the resulting meshes will differ depending on the +methods used. +Second, initial element gradation can be maintained at the expense of element distortion if desired. +Third, optimal positioning of the nodes before the basic smoothing methods are applied can improve +mesh quality and minimize the frequency of adaptive meshing required. +Finally, solution-dependent meshing is used to concentrate mesh refinement near areas of evolving +boundary curvature. This counteracts the tendency of the basic smoothing methods to reduce the mesh +refinement near concave boundaries where solution accuracy is important. +Volume smoothing +Volume smoothing relocates a node by computing a volume-weighted average of the element centers in +the elements surrounding the node. In Figure 12.2.3–1 the new position of node M is determined by a +volume-weighted average of the positions of the element centers, C, of the four surrounding elements. +The volume weighting will tend to push the node away from element center C1 and toward element +center C3, thus reducing element distortion. +L3 +C4 +C3 +L4 +C1 +C2 +L1 +L2 +Figure 12.2.3–1 Relocation of a node during a mesh sweep. +Volume smoothing is very robust and is the default method in Abaqus/Explicit. It works well for +both structured and highly unstructured domains. (A structured domain is one that contains no degenerate +elements and where every node is surrounded by four elements in two dimensions or eight elements in +three dimensions.) +Laplacian smoothing +Laplacian smoothing relocates a node by calculating the average of the positions of each of the adjacent +nodes connected by an element edge to the node in question. In Figure 12.2.3–1 the new position of node +M is determined by averaging the positions of the four nodes, L, connected to M by element edges. The +locations of nodes L2 and L3 will pull node M up and to the right to reduce element distortion. +Laplacian smoothing is the least expensive smoothing algorithm and is commonly used in mesh +preprocessors. For low to moderately distorted mesh domains, the results of Laplacian smoothing are +similar to volume smoothing. For domains with boundaries of complex curvature, volume smoothing +generally results in a more balanced mesh. +Equipotential smoothing +Equipotential smoothing is a higher-order method that relocates a node by calculating a higher-order, +weighted average of the positions of the node’s eight nearest neighbor nodes in two dimensions (or its +eighteen nearest neighbor nodes in three dimensions). In Figure 12.2.3–1 the new position of node M is +based on the position of all the surrounding nodes, L and E. +The weighted averaging for the equipotential smoothing method is fairly complex and is based on +the solution of the Laplace equation. Equipotential smoothing tends to minimize the local curvature of +lines running across a mesh over several elements. Although this tendency can be desirable for gently +curving domains, it can inhibit the ability of equipotential smoothing to reduce element distortion in +highly deformed and locally curved domains. +Equipotential smoothing can be performed only for nodes that are surrounded by a locally structured +mesh. Nodes that are surrounded by an unstructured mesh are moved with an equivalent amount of +volume smoothing when equipotential smoothing is chosen. +Combining smoothing methods +The default smoothing method in Abaqus/Explicit is volume smoothing. To choose an alternate +smoothing method or to combine smoothing methods, you specify the weighting factor for each method. +When more than one smoothing method is used, a node is relocated by computing a weighted average +of the locations predicted by each chosen method. All weights must be positive, and their sum should +typically be 1.0. If the sum of the chosen weights is less than 1.0, the mesh smoothing algorithm will be +less aggressive at each adaptive mesh increment. If the sum of the chosen weights is greater than 1.0, +their values are normalized so that their sum is 1.0. +Input File Usage: +*ADAPTIVE MESH CONTROLS, NAME=name +volume smoothing weight, Laplacian smoothing weight, +equipotential smoothing weight +Abaqus/CAE Usage: +For example, the following option could be used to define an equal blend of +volume and equipotential smoothing, with no Laplacian smoothing: +*ADAPTIVE MESH CONTROLS, NAME=name +0.5, 0.0, 0.5 +Step module: Other→ALE Adaptive Mesh Controls→Create: Name: +name, Volumetric: volume smoothing weight, Laplacian: Laplacian +smoothing weight, Equipotential: equipotential smoothing weight +Geometric enhancements to the basic smoothing methods +The conventional forms of the basic smoothing methods do not perform well in highly distorted domains. +To ensure the robustness of adaptive meshing, Abaqus/Explicit uses geometrically enhanced forms of +the basic smoothing algorithms by default. The enhanced forms are recommended for all adaptive +mesh applications. However, since the basic smoothing algorithms are used by many finite element +preprocessors, their conventional forms are provided as an option. +Input File Usage: +Use the following option to use the conventional forms of the volume, +Laplacian, or equipotential smoothing algorithms: +*ADAPTIVE MESH CONTROLS, NAME=name, +GEOMETRIC ENHANCEMENT=NO +Abaqus/CAE Usage: +Step module: Other→ALE Adaptive Mesh Controls→Create: +Name: name, toggle off Use enhanced algorithm based on +evolving element geometry +Specifying a uniform mesh smoothing objective +For adaptive mesh domains without any Eulerian boundary regions, the default objective of the mesh +smoothing methods is to minimize mesh distortion while improving element aspect ratios, at the expense +of diffusing initial mesh gradation. The uniform mesh smoothing objective is recommended for problems +with moderate to large overall deformation. +Input File Usage: +Use the following option to specify the uniform mesh smoothing objective: +*ADAPTIVE MESH CONTROLS, NAME=name, +SMOOTHING OBJECTIVE=UNIFORM +Abaqus/CAE Usage: +Step module: Other→ALE Adaptive Mesh Controls→Create: +Name: name, Priority: Improve aspect ratio +Specifying a graded mesh smoothing objective +Alternatively, the smoothing methods can attempt to preserve initial mesh gradation while reducing +element distortion as the analysis evolves. This objective is the default for adaptive mesh domains with +one or more Eulerian boundary regions. The graded mesh smoothing objective is recommended only for +adaptive mesh domains with reasonably structured graded meshes undergoing low to moderate overall +deformation. Element distortion will be minimized, but the aspect ratios of adjacent elements will be +maintained approximately. Mesh gradation is particularly useful in steady-state problems where overall +deformations are small and a focused mesh is used in a specific area to capture high solution gradients. +Input File Usage: +Use the following option to specify the graded mesh smoothing objective: +*ADAPTIVE MESH CONTROLS, NAME=name, +SMOOTHING OBJECTIVE=GRADED +Abaqus/CAE Usage: +Step module: Other→ALE Adaptive Mesh Controls→Create: Name: +name, Priority: Preserve initial mesh grading +Positioning nodes in Lagrangian domains +If an adaptive mesh domain has no Eulerian boundary regions, then, by default, the mesh sweeps are +based on current nodal locations, which account for material motion accumulated since the last adaptive +mesh increment. This approach is generally the best for Lagrangian problems that undergo large overall +deformation. +Input File Usage: +Use the following option to request that the current deformed positions of nodes +be used as the starting locations for mesh smoothing: +*ADAPTIVE MESH CONTROLS, NAME=name, +MESHING PREDICTOR=CURRENT +Abaqus/CAE Usage: +Step module: Other→ALE Adaptive Mesh Controls→Create: Name: +name, Meshing predictor: Current deformed position +Positioning nodes in Eulerian domains +Mesh sweeps can be based on the locations of nodes at the end of the previous adaptive mesh increment. +This technique is recommended for problems that are Eulerian in nature, where material flow is +significant compared to overall deformation. Therefore, it is the default for adaptive mesh domains with +one or more Eulerian boundary regions. This approach will result in a virtually stationary mesh. +Input File Usage: +Use the following option to use the position of the nodes at the end of the +previous adaptive mesh increment as a starting location for mesh smoothing: +*ADAPTIVE MESH CONTROLS, NAME=name, +MESHING PREDICTOR=PREVIOUS +Abaqus/CAE Usage: +Step module: Other→ALE Adaptive Mesh Controls→Create: +Name: name, Meshing predictor: Position from previous +adaptive mesh increment +Solution-dependent meshing based on concave boundary curvature +Mesh smoothing algorithms based only on minimizing element distortion tend to reduce the mesh +refinement in areas of concave curvature, especially as the curvature evolves. Having sufficient mesh +refinement near highly curved boundaries is often important to model both the shape and volume +of the domain. To prevent the natural reduction in mesh refinement of areas near evolving concave +curvature, Abaqus/Explicit uses solution-dependent meshing to focus mesh gradation toward these +areas automatically. +Although solution-dependent meshing may “pull” more elements into areas of high curvature, its +primary purpose is to retain the nominal refinement in these zones. Therefore, a fine mesh should always +be used when and where highly curved boundaries are expected and solution-dependent meshing should +generally not be used as a direct substitute for more elements. +. By default, +The aggressiveness of the solution-dependent meshing is governed by the curvature refinement +weight, +, which correponds to an aggressivity level that has been chosen to +work well on a wide variety of problems. You can change the curvature refinement weight. A value of +zero indicates no solution dependence due to evolving boundary curvature, and a value greater than one +increases the aggressivity from the default. +Input File Usage: +*ADAPTIVE MESH CONTROLS, NAME=name, +CURVATURE REFINEMENT= +Abaqus/CAE Usage: +Step module: Other→ALE Adaptive Mesh Controls→Create: +Name: name, Curvature refinement: +Smoothing a distorted mesh at the beginning of a step +When an adaptive mesh domain contains a structured mesh of uniform density, the mesh will move +independently from the material only when the domain deforms. If the mesh is initially nonuniform, +the meshing algorithms in Abaqus/Explicit will smooth the mesh even in the absence of deformation or +material transport. +When the initial mesh contains highly distorted elements, it is often useful to smooth the mesh before +the step begins so that the best possible mesh is used throughout the step. When a uniform smoothing +objective is used, five mesh sweeps are performed by default at the beginning of the step in which the +adaptive mesh domain is defined. For a graded smoothing objective, two mesh sweeps are performed +by default at the beginning of the step without acccounting for gradation. The aspect ratios used for +gradation in all subsequent mesh sweeps are based on this locally smoothed mesh. +Initial conditions are advected to the new mesh when initial mesh sweeps are performed. +Input File Usage: +Use the following option to change the number of mesh sweeps that will be +performed at the beginning of the first step in which the adaptive mesh definition +is active: +*ADAPTIVE MESH, INITIAL MESH SWEEPS=number of initial sweeps +For example, the following option would smooth a badly distorted mesh with 15 +mesh sweeps at the beginning of the step, before performing adaptive meshing +with three mesh sweeps every 20 increments throughout the step: +*ADAPTIVE MESH, FREQUENCY=20, MESH SWEEPS=3, +INITIAL MESH SWEEPS=15 +Abaqus/CAE Usage: +Step module: Other→ALE Adaptive Mesh Domain→Edit: toggle +on Use the ALE adaptive mesh domain below, Initial remeshing +sweeps: Value: number of initial sweeps +Meshing on boundary regions +Adaptive meshing on Lagrangian and sliding boundary regions is subject to the constraint that the mesh +and material must move together in the direction normal to the boundary. Nodes on the interior of such +a boundary are allowed to slide freely over the material within the boundary region, which maximizes +the amount of mesh smoothing that can be performed. Nodes are positioned in each mesh sweep by +applying the basic smoothing methods while constraining the nodes to lie on the boundary region. In +three dimensions some nodes on Lagrangian boundary regions will be on a Lagrangian edge. In each +mesh sweep these nodes are positioned by applying the basic smoothing methods while constraining the +node to lie along the discrete Lagrangian edge. +For problems in which the flow of material from element to element along the boundary is significant +compared to the deformation, oscillations in the boundary mesh can result if these constraints are applied +symmetrically with respect to the upstream and downstream directions of material flow. Abaqus/Explicit +uses a Petrov-Galerkin weighting of the free boundary constraint to suppress any oscillations. The +algorithm is volume preserving, and the degree of upwinding is chosen automatically. +Advecting solution variables to the new mesh +The framework for adaptive meshing in Abaqus/Explicit is the Arbitrary Lagrangian-Eulerian method, +which introduces advective terms into the momentum balance and mass conservation equations to +account for independent mesh and material motion. There are two basic ways to solve these modified +equations: solve the nonsymmetric system of equations directly, or decouple the Lagrangian (material) +motion from the additional mesh motion using an operator split. The operator split method is used in +Abaqus/Explicit because of its computational efficiency. Furthermore, this technique is appropriate in +an explicit setting because small time increments limit the amount of motion within a single increment. +In an adaptive meshing increment the element formulations, boundary conditions, external loads, +contact conditions, etc. are handled first in a manner consistent with a pure Lagrangian analysis. Once +the Lagrangian motion is updated and mesh sweeps have been performed to find the new mesh, the +solution variables are remapped by performing an advection sweep. The advection sweep accounts for +the advective terms in the momentum balance and continuity equations. +Advection methods for element variables +Element and material state variables must be transferred from the old mesh to the new mesh in each +advection sweep. The number of variables to be advected depends on the material model and element +formulation; however, stress, history variables, density, and internal energy are always solution variables. +Two methods are available for the advection of element variables: the default second-order method based +on the work of Van Leer (Van Leer, 1977) and a first-order method based on donor cell differencing. +Both advection methods incorporate the concept of upwinding. They also conserve the element +variables in an integral sense when mapping from the old mesh to the new mesh (that is, the value of any +solution variable integrated over the domain is unchanged by adaptive meshing). Using a conservative +algorithm to advect the element density and the internal energy automatically ensures conservation of +mass and energy for an adaptive mesh domain without Eulerian boundary regions. +Both advection methods are also monotonic and consistent. A method is monotonic if an element +quantity with a monotonic, increasing spatial distribution over a portion of the old mesh remains as such +in the new mesh. A method is consistent if, when solution variables are advected to a new mesh that is +identical to the old mesh, all element quantities remain unchanged. +Second-order advection +Second-order advection is used by default for all adaptive mesh domains. It is recommended for all +problems, ranging from quasi-static to transient dynamic shock. An element variable, +, is remapped +from the old mesh to the new mesh by first determining a linear distribution of the variable in each old +element, as illustrated in Figure 12.2.3–2 for a simple one-dimensional mesh. The linear distribution of +in the two adjacent elements. To construct the linear +in the middle element depends on the values of +distribution: +constant +quadratic +trial +limited +element 1 +element 2 +element 3 +Figure 12.2.3–2 Second-order advection. +1. A quadratic interpolation is constructed from the constant values of +at the integration points of +the middle element and in its adjacent elements. +2. A trial linear distribution, +, is found by differentiating the quadratic function to find the slope +at the integration point of the middle element. +3. The trial linear distribution in the middle element is limited by reducing its slope until its minimum +and maximum values are within the range of the original constant values in the adjacent elements. +This process is referred to as flux-limiting and is essential to ensure that the advection is monotonic. +Once the flux-limited linear distributions are determined for all elements in the old mesh, these +distributions are integrated over each new element. The new value of the variable is found by dividing +the value of each integral by the new element volume. +Input File Usage: +Use the following option to specify that the second-order advection method +should be used to remap element variables: +*ADAPTIVE MESH CONTROLS, NAME=name, +ADVECTION=SECOND ORDER +old mesh +new mesh +φnew = φold +φnew +φold +value on old mesh +value on new mesh +φnew += +φold +φold +la 1 +la +lb ++ +lb+ +la +lb +Figure 12.2.3–3 First-order advection. +Abaqus/CAE Usage: +Step module: Other→ALE Adaptive Mesh Controls→Create: +Name: name, toggle on Second order +First-order advection +First-order advection is simple and computationally efficient; however, it tends to diffuse sharp gradients +over time, especially in transient dynamic analyses or other problems that require fairly frequent adaptive +meshing. Therefore, this technique should be used only as a computationally efficient alternative for +quasi-static simulations that do not require frequent adaptive meshing. +Figure 12.2.3–3 illustrates the first-order method for a portion of a one-dimensional mesh. An +element variable, +, is remapped from the old mesh to the new mesh by first assuming a constant value +of the variable for each old element. These values are then integrated over each new element. The new +value of the variable is found by dividing the value of each integral by the new element volume. +Input File Usage: +Use the following option to specify that the first-order advection method should +be used to remap element variables: +*ADAPTIVE MESH CONTROLS, NAME=name, +ADVECTION=FIRST ORDER +Abaqus/CAE Usage: +Step module: Other→ALE Adaptive Mesh Controls→Create: +Name: name, toggle on First order +Momentum advection +Nodal velocities are computed on a new mesh by first advecting momentum, then using the mass +distribution on the new mesh to calculate the velocity field. Advecting momentum directly ensures that +momentum is conserved properly in the adaptive mesh domain during remapping. Two methods are +available for advecting momentum: the default element center projection method and the half-index +shift method (Benson, 1992). Both methods are applicable for all adaptive mesh applications. +Element center projection method +The element center projection method is the default method used to advect momentum and requires the +fewest numerical operations. The element momentum is calculated first for the old mesh based on the +mass and velocity of the element nodes. The element momentum is then advected from the old mesh to +the new mesh by the same first- or second-order algorithms used for advecting element variables. Finally, +the element momentum on the new mesh is assembled at the nodes using a projection. The element center +projection method requires the advection of only two or three extra variables in two dimensions or three +dimensions, respectively. +Input File Usage: +Use the following option to request +momentum advection method: +the most computationally efficient +*ADAPTIVE MESH CONTROLS, NAME=name, +MOMENTUM ADVECTION=ELEMENT CENTER PROJECTION +Abaqus/CAE Usage: +Step module: Other→ALE Adaptive Mesh Controls→Create: Name: +name, Momentum advection: Element center projection +Half-index shift method +The half-index shift method is computationally more intensive than the element center projection +method, but it may result in less wave dispersion for some problems. This method first shifts each +of the nodal momentum variables from the nodes surrounding an element to the element center. The +shifted momentum variables are then advected from the old mesh to the new mesh by the same first- +or second-order algorithms used for advecting element variables, providing momentum variables at +the center of the new elements. Finally, the momentum variables at the element centers in the new +mesh are shifted back to the nodes. The half-index shift method requires the advection of 8 or 24 extra +variables in two or three dimensions, respectively, which can increase the cost of each advection sweep +significantly. +Input File Usage: +Use the following option to specify that the half-index shift method should be +used for momentum advection: +*ADAPTIVE MESH CONTROLS, NAME=name, +MOMENTUM ADVECTION=HALF INDEX SHIFT +Abaqus/CAE Usage: +Step module: Other→ALE Adaptive Mesh Controls→Create: Name: +name, Momentum advection: Half-index shift +Additional references +• Benson, D. J., “Momentum Advection on a Staggered Mesh,” Journal of Computational Physics, +vol. 100, pp. 143–162, 1992. +• Van Leer, B., “Towards the Ultimate Conservative Difference Scheme III. Upstream-centered +Finite-Difference Schemes for Ideal Compressible Flow,” Journal of Computational Physics, +vol. 23, pp. 263–275, 1977. +• Van Leer, B., “Towards the Ultimate Conservative Difference Scheme IV. A New Approach to +Numerical Convection,” Journal of Computational Physics, vol. 23, pp. 276–299, 1977. +12.2.4 +MODELING TECHNIQUES FOR EULERIAN ADAPTIVE MESH DOMAINS IN +Abaqus/Explicit +Products: Abaqus/Explicit Abaqus/CAE +References +• “ALE adaptive meshing: overview,” Section 12.2.1 +• “Defining ALE adaptive mesh domains in Abaqus/Explicit,” Section 12.2.2 +• *ADAPTIVE MESH CONSTRAINT +• “Understanding ALE adaptive meshing,” Section 14.6 of the Abaqus/CAE User’s Manual +Overview +An Eulerian adaptive mesh domain: +• is used to model material flowing through the mesh; and +• typically has two Eulerian boundary regions, one inflow and one outflow, connected by Lagrangian +and/or sliding boundary regions. +The correct combination of mesh constraints and material boundary conditions applied to an Eulerian +boundary region depends on whether the region acts as an inflow or an outflow boundary. The region +types and mesh constraints assigned to the boundary regions that are connected to the Eulerian boundary +regions must be chosen to simulate the correct physical behavior as well. +The adaptive meshing technique in Abaqus/Explicit is robust if the mesh is underconstrained: the +modeling techniques presented in this section are intended to provide guidance in properly defining +Eulerian models. +ALE adaptive mesh constraints on Eulerian boundaries +ALE adaptive mesh constraints should be applied normal to an Eulerian boundary region; otherwise, +the motion of the mesh on the boundary is ambiguous. If no mesh constraints are applied normal to the +boundary, Abaqus/Explicit will treat the region as if it were sliding, and the mesh will follow the material +normal to the boundary. +Although there are no restrictions on specifying adaptive mesh constraints at nodes on an Eulerian +boundary region, the following guidelines should be followed in most cases: +• Mesh constraints should be applied to every node on the Eulerian boundary region, including the +corners and edges. +• Mesh constraints should be applied either only normal to the Eulerian boundary region or in every +direction. Mesh constraints should not be specified in only the direction tangential to an Eulerian +boundary region; such constraints are ambiguous and may result in undesirable motion of the mesh +at the boundary. +Loads and boundary conditions on Eulerian boundaries act on the material that instantaneously +coincides with the mesh at the surface. When used in combination with spatial adaptive mesh constraints, +physically meaningful Eulerian flow conditions can be defined. +Defining inflow Eulerian boundaries +The material flowing into an adaptive mesh domain through an Eulerian boundary will have the same +stress and material state as the material in the elements immediately adjacent to the boundary. Therefore, +it is important to maintain the stress and material state in those elements at the desired values (which in +many cases will be zero, to simulate stress-free material entering the Eulerian domain). To accomplish +this goal: +• position the inflow boundary far enough upstream from high solution gradients to ensure that the +response at the inflow boundary is smooth, and +• apply sufficient mesh and material constraints at the boundary (as described later in this section). +To be physically meaningful, the size and shape of the inflow boundary region must be maintained. +For example, applying sufficient constraints is crucial for steady-state process simulations where the +cross-section of the workpiece entering the adaptive mesh domain is known and affects the response +downstream. The types of constraints appropriate for an inflow boundary depend on whether the precise +location of the inflow boundary region is known or whether it is part of the solution. +Known inflow boundary location +In many problems the area, shape, and position of the inflow boundary are known a priori. For example, +in the steady-state analysis of a forward extrusion process, an inflow Eulerian boundary can be used to +model the flow of material into the adaptive mesh domain. The size of the inflow boundary is based on +the known billet cross-section, and the location of the inflow boundary is fixed because of the confined +conditions on the material. +When the area, shape, and location of the inflow boundary are known, both material and mesh +constraints should be applied. Figure 12.2.4–1 shows a typical model setup for a two-dimensional +forward extrusion problem where either a prescribed mass flow rate or a prescribed uniform pressure is +applied to a known inflow boundary. Apply boundary conditions at all nodes on the inflow boundary +region to prescribe material constraints in the directions tangential to the boundary surface. Preventing +motion of the material tangential to the inflow boundary helps to maintain the stress and material state +of the elements adjacent to the Eulerian boundary. +Apply adaptive mesh constraints in the normal direction at all nodes on the inflow boundary. In +addition, apply mesh constraints in all tangential directions at the edges and corners surrounding the +Eulerian boundary region. These constraints fix the location and size of the cross-sectional area at the +inflow boundary. +If a nonuniform boundary condition or load is applied to the material at the inflow boundary or if the +initial material state in the elements adjacent to the boundary is nonuniform in the tangential direction, +apply tangential mesh constraints to the nodes strictly in the interior of the Eulerian boundary region. +node set TOP +contact surface +node set INFLOW +element set INFLOW +flow +node set BOTTOM +symmetry +, +zero-displacement adaptive mesh constraints +applied to node set INFLOW in direction 1 +and to node sets TOP and BOTTOM in +direction 2 +Eulerian boundary region defined by a +zero-displacement boundary condition +applied to node set INFLOW in direction 2 +Prescribed inflow velocity: +or +Prescribed inflow pressure: + Eulerian boundary region defined by a + Eulerian boundary region defined by a +velocity-type boundary condition applied to +node set INFLOW in direction 1 +pressure load applied to element set +INFLOW in direction 1 +Figure 12.2.4–1 Known inflow boundary. +Although the application of mesh and material constraints tangential to and along the edges and +corners of an inflow Eulerian boundary may appear to be redundant, they are actually independent. For +example, consider a long billet with a variable cross-section, as shown in Figure 12.2.4–2. +v0 +symmetry +outflow +boundary; +node set +OUTFLOW; +element set +OUTFLOW +inflow +boundary; +node set +INFLOW +Eulerian boundary region created by a surface +defined on the S3 faces of element set OUTFLOW +zero-displacement adaptive mesh constraints +applied to node sets INFLOW and OUTFLOW +in direction 1 +velocity-type adaptive mesh constraint with +amplitude INCOMING applied to node N +in direction 2 +Eulerian boundary region defined by a +zero-displacement boundary condition applied +to node set INFLOW in direction 2 + Eulerian boundary region defined by a velocity-type +boundary condition with a variable amplitude applied +to node set INFLOW in direction 1 +Figure 12.2.4–2 Modeling a billet with a variable cross-section. +The adaptive mesh domain, with its inflow and outflow Eulerian boundary regions, is assumed to +represent a portion of the billet along its length. The entire billet moves with a rigid body velocity along +its length (x-direction) so that material flows into one Eulerian boundary and out the other. Boundary +conditions are applied to the material at the inflow boundary to maintain this velocity. Mesh constraints +are applied normal to the inflow and outflow boundary regions. The mesh constraint applied in the +y-direction at node N is used to prescribe the known variable incoming cross-section of the material. +The motion of this node does not affect the velocity field of the material entering the domain. +Unknown inflow boundary location +Sometimes, the location of the inflow boundary region is known only approximately; +its precise +location will be determined from the solution. For these problems, apply adaptive mesh constraints +In the absence of tangential mesh +only in the direction normal to the Eulerian boundary region. +constraints at the edges and corners of the Eulerian boundary region, Abaqus/Explicit will move these +edges and corners with the material in the tangential direction but with the mesh constraints in the +normal direction. Therefore, material constraints should be applied using multi-point constraints or linear constraint equations to preserve the cross-sectional area of the inflow boundary. +For example, consider a steady-state rolling simulation with multiple rollers in an asymmetric +configuration, as shown in Figure 12.2.4–3. +billet is +free to +move +node set +INFLOW +free surface +flow of material +free surface +zero-displacement adaptive mesh +constraints applied to node 1 +and node set INFLOW in direction 1 +PIN-type multi-point constraints +applied to node set INFLOW +and node 1 +Figure 12.2.4–3 Unknown inflow boundary location. +It may be impractical to extend the analysis domain as far as the guides on the upstream side, but spatially +fixing the inflow boundary at an arbitrary position in the y- and z-directions may cause unrealistic stress +on the workpiece as it finds an equilibrium position between the rollers. Mesh constraints are applied +normal to the Eulerian boundary region to fix the position of the inflow boundary relative to the rollers +in the x-direction. Material constraints (applied with a PIN MPC) are used to ensure that material enters +the domain at a uniform velocity and that the cross-section does not rotate. The material constraints +will maintain the cross-sectional shape of the section while allowing it to move laterally to the correct +equilibrium position. Since tangential mesh constraints are not used, the mesh will follow the material +in the directions tangential to the Eulerian boundary region. +Defining outflow Eulerian boundaries +Typically, adaptive mesh constraints should be applied only in the direction normal to the surface on an +Eulerian boundary region that acts as an outflow boundary. No tangential mesh constraints should be +applied to the edges or corners of an outflow boundary adjacent to a Lagrangian (or sliding) boundary +region acting as a free surface. In contrast to inflow boundaries, the cross-section of an outflow boundary +adjacent to a free surface is determined by the solution in the domain. At the edge or corner where an +Eulerian boundary region meets a Lagrangian or sliding boundary region, Abaqus/Explicit will satisfy the +applied mesh constraint normal to the Eulerian boundary region and the inherent mesh constraint normal +to the Lagrangian or sliding boundary region simultaneously, thus correctly handling the evolution of +the free surface adjacent to the outflow boundary. Figure 12.2.4–4 shows the evolution of an outflow +boundary from to +, where material continues to flow through the outflow boundary. +free surface +v0 +symmetry +position of free surface at time t0 +position of free surface at time t1 +Eulerian boundary region created by +a surface defined on the S2 faces of +element set OUTFLOW +zero-displacement adaptive mesh +constraint applied to node set +OUTFLOW in direction 1 +motion of node N to satisfy +constraint +Figure 12.2.4–4 Abaqus/Explicit will respect the free surface at an Eulerian outflow boundary. +The mesh constraint normal to the Eulerian outflow boundary is applied by moving node N along the free +surface of the material, so that the outflow boundary “expands” with the material arriving from upstream. +Although not shown in the figure, mesh smoothing causes all other nodes on the outflow boundary, with +the exception of the node on the symmetry plane, to move up toward node N as the boundary expands. +No special material boundary conditions are required at outflow Eulerian boundaries. Boundary +conditions tangential to the outflow boundary are recommended only if they are the same as those defined +upstream (e.g., a symmetry plane running along the length of an Eulerian domain). However, to improve +convergence to the steady-state solution in steady-state process simulations, it is often useful to constrain +the material velocity to be uniform normal to the outflow boundary using multi-point constraints or linear +constraint equations. +Defining Eulerian boundary regions that act as both inflow and outflow boundaries +Although it is rarely appropriate, an Eulerian boundary region can act as both an inflow and an outflow +boundary at different times during the same analysis step. Adaptive mesh constraints and material +boundary conditions at such a boundary should be chosen to be physically meaningful for both inflow +and outflow situations. +For each node on the edges and corners of an Eulerian boundary region that does not have mesh +constraints tangential to the boundary surface, Abaqus/Explicit will determine in each adaptive mesh +increment whether the boundary at the node is acting as an inflow or an outflow boundary. If an inflow +condition is detected, the node will move with the material in the tangential direction but with the mesh +constraints in the normal direction. If an outflow condition is detected, the movement of the node will +both follow the adjacent Lagrangian boundary region and satisfy the mesh constraint normal to the +Eulerian boundary region. +Lagrangian versus sliding boundary regions on Eulerian domains +Many applications using Eulerian adaptive mesh domains, including the simulation of steady-state +processes, have a primary direction of material flow and use a control volume approach to model the +process zone. These problems usually include two Eulerian boundary regions, representing an inflow +boundary and outflow boundary. The remaining surfaces between the Eulerian boundaries can be either +Lagrangian or sliding boundary regions. Determining which type of boundary region to use between +the two Eulerian boundary regions depends on the type of load or boundary condition that is required: +• Use a sliding boundary region to define boundary conditions or loads that act at a spatial location on +a portion of the surface along the length of the control volume. Apply adaptive mesh constraints to +fix the mesh spatially in the flow direction (and possibly in the direction transverse to the flow). For +example, a distributed pressure can be applied around the circumference of the control volume, as +shown in Figure 12.2.4–5. The distributed pressure load is defined using a sliding boundary region. +Mesh constraints are applied to fix the boundary region spatially in the flow direction. Similarly, a +concentrated load could be applied to a specific spatial location to model the effect of a very sharp +body pressing into the workpiece at a known location with a known force. +• Use a sliding boundary region to define boundary conditions or loads that act along the entire length +of the Eulerian control volume between the inflow and outflow boundaries and act in a spatial +manner transversely to the flow. If the load acts on only a portion of the surface in the transverse +direction, it may be necessary to apply mesh constraints in the direction transverse to the flow. For +example, a boundary condition that acts as a knife edge along the length of the domain is shown +in Figure 12.2.4–6. Mesh constraints are applied in the transverse direction (and, if the line of +application is curved, along the line) to keep the boundary condition fixed spatially. +• Use a Lagrangian boundary region (default) to define boundary conditions or loads that act +along the entire length of the surface of the Eulerian control volume between the inflow and +sliding edge +Lagrangian edge +geometric edge +node set +BACK +node set +BOTTOM +flo +element set LOAD +zero-displacement adaptive mesh constraint +applied to node set LOADEDGE in direction 3 +sliding boundary region defined by a pressure load +applied to element set LOAD in direction 1 +Lagrangian boundary region defined by symmetry +boundary conditions applied to node set BACK +about the x-direction and node set BOTTOM about +the y-direction +Figure 12.2.4–5 Applying a spatial pressure load to a portion of +the surface along the length of an Eulerian control volume. +sliding edge +sliding boundary region defined +by a boundary condition +adaptive mesh constraint +flow +Figure 12.2.4–6 Applying a boundary condition along the +entire length of the Eulerian control volume. +outflow boundary and act in a Lagrangian manner transversely to the flow. In three dimensions, +symmetry conditions should typically act in a Lagrangian manner transverse to the flow direction. +In many cases geometric edges will prevent material from flowing off the symmetry plane and +onto the free surface. However, since geometric edges can be deactivated as surfaces flatten, +Lagrangian boundary regions should be used to define the symmetry planes for these types of +problems. In Figure 12.2.4–5 quarter-symmetry is assumed, and the symmetry planes are defined +using Lagrangian boundary regions. The resulting Lagrangian edges that run from one Eulerian +boundary to the other separate the symmetry planes from the free surface. +• Boundary conditions or loads that act on only a specific portion of the material between the +inflow and outflow boundaries cannot usually be modeled for problems utilizing Eulerian control +volumes. Since the mesh underneath the load or boundary condition must follow the material, +it will eventually be restricted by the Eulerian boundary. This treatment of loads and boundary +conditions is not usually consistent with a steady-state model and should not arise in practical +simulations using Eulerian adaptive mesh domains. +12.2.5 +OUTPUT AND DIAGNOSTICS FOR ALE ADAPTIVE MESHING IN Abaqus/Explicit +Products: Abaqus/Explicit Abaqus/CAE +References +• “Output to the output database,” Section 4.1.3 +• “ALE adaptive meshing: overview,” Section 12.2.1 +• “Defining ALE adaptive mesh domains in Abaqus/Explicit,” Section 12.2.2 +• *ADAPTIVE MESH +• *ADAPTIVE MESH CONTROLS +• *DIAGNOSTICS +• *TRACER PARTICLE +• Chapter 78, “Using display groups to display subsets of your model,” of the Abaqus/CAE User’s +Manual +Overview +Output for ALE adaptive meshing: +• can be used to verify the automatic splitting of user-defined domains, the formation of Lagrangian +the formation of geometric edges and corners, and the determination of +edges and corners, +nonadaptive nodes; +• must be interpreted carefully, since the values of output variables at specific locations in the mesh +are no longer linked to values at particular material points; +• can include the definition of tracer particles, which follow material points and allow you to examine +the trajectory of those points and plot material time histories of all element and nodal variables at +those points; and +• can include diagnostic information on the efficiency of adaptive meshing and the accuracy of +advection. +Verifying the model +Output that can be used to verify adaptive meshing models is available in the data (.dat) file and in the +output database (.odb) . +Element sets +When user-defined adaptive mesh domains are split by Abaqus/Explicit, the elements that compose the +new subdivided domains are printed to the data (.dat) file. +New element sets are created and written to the output database (.odb) for all adaptive mesh +domains. The name of the element set created for each domain is the user-defined name, plus the +number of the subdivision (1 if no subdivisions were created), plus the step number. For example, if the +user-defined adaptive mesh domain specified for the element set domain_name spanned three disjoint +parts, Abaqus/Explicit would subdivide the user-defined domain into three domains and create three +element sets in the output database (.odb) for the first step: domain_name-1-1, domain_name-2-1, +and domain_name-3-1. +Abaqus/CAE can be used to verify the creation of the subdivided domains. +Edges and nonadaptive nodes +Abaqus/Explicit automatically forms Lagrangian edges and corners and identifies nonadaptive nodes +based on the topology of the adaptive mesh domains, connections to nonadaptive domains, and +user-specified boundary regions. Furthermore, geometric edges and corners are formed automatically +based on the initial geometry and the value of the initial feature angle. See “Defining ALE adaptive +mesh domains in Abaqus/Explicit,” Section 12.2.2. Lagrangian edges, geometric edges and corners, and +nonadaptive nodes (including Lagrangian corners) are output to the data (.dat) file for each adaptive +mesh domain. This information can be obtained by requesting a history definition summary printout to +the data file or by monitoring +the progress of the adaptive meshing . +In addition, up to three node sets are created in the output database (.odb) for each adaptive mesh +domain in each step. The names of the node sets are created by concatenating the following information: +• the domain element set name; +• the number of the subdivision (1 if no subdivisions were created); +• the letters LE for Lagrangian edge, GE for geometric edge or corner, or NA for nonadaptive nodes +(including Lagrangian corners); and +• the step number. +For example, if a user-defined three-dimensional adaptive mesh domain specified for element set +domain_name is subdivided automatically into two adaptive mesh domains, Abaqus/Explicit will +generate up to six node sets in the output database for the first step: domain_name-1-LE-1, +domain_name-1-GE-1, domain_name-1-NA-1, domain_name-2-LE-1, domain_name-2-GE-1, +and domain_name-2-NA-1. +Since boundary regions are separated by corners, not edges, in two dimensions, node sets will not +be created for Lagrangian edges in two-dimensional adaptive mesh domains. The Lagrangian corners +are included in the nonadaptive (NA) node set, as for three-dimensional domains. +Abaqus/CAE can be used to verify the creation of Lagrangian edges and corners, geometric edges +and corners, and nonadaptive nodes. +Interpreting results +When adaptive meshing is not performed, the finite element mesh follows the material, which enables +a straightforward interpretation of analysis results. You can visualize deformation and material motion +by studying the motion of the mesh. Each nodal and element output variable corresponds to a specific +material location, because the mesh is fixed to the same material point throughout time. +Once adaptive meshing takes place, the locations of mesh and material points deviate, and analysis +results must be interpreted accordingly. The motion of the mesh on the interior of an adaptive mesh +domain represents the composite effects of the material motion and adaptive meshing. The motion of +the mesh and the motion of the material on Lagrangian and sliding boundary regions is identical in the +direction normal to the boundary but not in the direction tangential to it. +Nodal variables +When adaptive meshing is performed, a material point that is coincident with a node at the beginning +of the step may not remain coincident with that node throughout the step. Values of displacement and +current coordinates represent the motion of the node, not necessarily the motion of the material. All +other nodal variables—including velocity, acceleration, and reaction forces—represent the value of the +variable for the material particle at the current location of the node. Contour or vector plots of these +variables will show their correct spatial distribution and are, therefore, meaningful. However, time +histories of nodal variables for nodes that undergo adaptive meshing are generally not meaningful. In +steady-state problems, though, a velocity or acceleration time history based at a fixed spatial location +rather than at a specific material point may be useful. +Element variables +Similarly, when adaptive meshing is performed, a material particle that is coincident with an element +integration point at the beginning of a step may not remain so throughout the step. Therefore, element +integration point variables do not necessarily represent values at the same material point throughout the +step. Contour or vector plots of element integration point variables are meaningful for the same reasons +described for nodal variables. However, time histories are based at the spatial location of the element +integration point and not at a specific material point. +Whole element variables have a similar interpretation. +Tracking nodal or element variables at material points +Tracer particles can be defined to track material points in an adaptive mesh domain. These particles can +also be used to obtain time histories of nodal or element integration point variables that correspond to the +time variation of the variable at a specific material point. Tracer particles are defined as described below +. Node and element variable +output can be requested for tracer particle sets to examine the trajectory of material particles or to obtain +material time histories. Output for tracer particles can be written only to the output database (.odb). +Using tracer particles in Lagrangian domains +In most adaptive meshing simulations using Lagrangian domains, the nodes and elements in the domain +correspond neither to a specific spatial location nor to a specific material point or volume. Thus, time +histories of variables at nodes and at element integration points are often physically meaningless in a +Lagrangian adaptive mesh domain. Tracer particles should be defined to view time history information. +Tracer particles can also be used to visualize the motion of the material. +The initial location of a tracer particle is defined to be coincident with a node, termed the parent +node. Tracer particles are defined in sets by defining multiple parent nodes or node sets. You indicate the +nodes whose current locations correspond to the initial location of the tracer particles and assign a name +to the tracer particle set to identify it for use in output requests. Tracer particles are released from their +parent nodes repeatedly at specified intervals during the step in which they are defined. The particles +follow material points for the remainder of that step and in all subsequent steps. +Tracer particles are typically defined only on adaptive mesh domains, although they can be defined +on nodes connected to any low-order solid element in the model. For analyses in which adaptive +meshing is not performed until later steps, tracer particles can be defined on nonadaptive domains at the +beginning of an analysis and will be tracked continuously as the domain becomes adaptive. Similarly, +tracer particles will be tracked from domain to domain if adaptive mesh domain topologies change from +step to step. +Input File Usage: +Use the following option to define a tracer particle set: +*TRACER PARTICLE, TRACER SET=tracer_set_name +list of tracer particle parent nodes +Abaqus/CAE Usage: +Tracer particles are not supported in Abaqus/CAE. +Using tracer particles in Eulerian domains +Time histories at nodes and element integration points in an Eulerian domain may have physical +meaning at points where spatial adaptive mesh constraints are applied. For example, the time variation +of equivalent plastic strain in elements along an outflow Eulerian boundary acts as a spatial time history +of that variable and can be used to evaluate whether the process has reached a steady-state solution. +Tracer particles can be defined to evaluate the material time history of variables at a material point +as it flows through the Eulerian domain. Tracer particles can also be used to evaluate the trajectory and +path of material points as they pass through the domain. +Tracer particles can be assigned to any parent node in an Eulerian adaptive mesh domain. If a +tracer particle reaches an outflow boundary and material continues to flow out, the tracer particle will +no longer be tracked and all output history variables associated with the tracer particle will be zero after +deactivation. +When material flow through the mesh domain is significant, sets of tracer particles can be released +from the current locations of the parent nodes at multiple times during the step. Each release of tracer +particles is referred to as particle birth. After particle birth the tracer particles follow the motion of the +material regardless of the motion of the mesh. You can indicate the number of particle birth stages in a +step. These stages will be evenly spaced throughout the time period of the step. +For example, a tracer particle set can be defined such that all nodes along an inflow Eulerian +boundary are parent nodes. Multiple birth stages can be specified so that a set of tracer particles is +released from the mesh at the inflow boundary periodically during the step. If enough birth stages are +defined, the domain will eventually be spanned with tracer particles as material flows from the inflow +boundary to the outflow boundary. +Input File Usage: +Use the following option to define a tracer particle set with multiple birth stages: +*TRACER PARTICLE, TRACER SET=tracer_set_name, +PARTICLE BIRTH STAGES=n +list of tracer particle parent nodes +Abaqus/CAE Usage: +Tracer particles are not supported in Abaqus/CAE. +Monitoring the progress of ALE adaptive meshing +Diagnostic information can be written to the message (.msg) file to track the efficiency and accuracy of +adaptive meshing. You can select the level of diagnostic output that is written. +Obtaining a summary at the end of a step +By default, a summary of adaptive meshing information for each adaptive mesh domain will be written +to the message (.msg) file at the end of each step. This summary information includes: +• the average percentage of nodes moved, +• the maximum percentage of nodes moved, +• the minimum percentage of nodes moved, and +• the average number of advection sweeps. +Each value is calculated for a single adaptive mesh domain over all adaptive mesh increments. The cost +of advection is approximately proportional to the percentage of nodes moved, since variables are not +advected for elements that have not been relocated during adaptive meshing. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to request a summary for each adaptive mesh domain +at the end of each step: +*DIAGNOSTICS, ADAPTIVE MESH=STEP SUMMARY +Adaptive mesh diagnostics are not supported in Abaqus/CAE. +Obtaining a summary for every ALE adaptive mesh increment +In addition to the step summary information, the following diagnostics can be obtained for each adaptive +mesh domain at every adaptive mesh increment: +• the percentage of nodes moved, and +• the number of advection sweeps. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to obtain summary information at the end of the step +and at every adaptive mesh increment: +*DIAGNOSTICS, ADAPTIVE MESH=SUMMARY +Adaptive mesh diagnostics are not supported in Abaqus/CAE. +Obtaining details of advection accuracy for every ALE adaptive mesh increment +The following detailed diagnostic information can also be written to the message (.msg) file to track the +accuracy of the advection: +• mass and momentum before and after advection, and +• percentage volume change. +Input File Usage: +Use the following option to request the most detailed diagnostics, which include +advection accuracy measures and summary information for each adaptive mesh +domain, reported at every adaptive mesh increment: +Abaqus/CAE Usage: +*DIAGNOSTICS, ADAPTIVE MESH=DETAIL +Adaptive mesh diagnostics are not supported in Abaqus/CAE. +Suppressing ALE adaptive mesh diagnostics +You can suppress output of all adaptive mesh diagnostic information. +Input File Usage: +Abaqus/CAE Usage: +*DIAGNOSTICS, ADAPTIVE MESH=OFF +Adaptive mesh diagnostics are not supported in Abaqus/CAE. +12.2.6 +DEFINING ALE ADAPTIVE MESH DOMAINS IN Abaqus/Standard +Products: Abaqus/Standard Abaqus/CAE +References +• “ALE adaptive meshing: overview,” Section 12.2.1 +• “ALE adaptive meshing and remapping in Abaqus/Standard,” Section 12.2.7 +• *ADAPTIVE MESH +• *ADAPTIVE MESH CONSTRAINT +• *ADAPTIVE MESH CONTROLS +• “Customizing ALE adaptive meshing,” Section 14.14 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +ALE adaptive meshing in Abaqus/Standard: +• maintains a topologically similar mesh; +• can be used to solve Lagrangian problems (in which no material leaves the mesh) and to model +effects of ablation, or wear (in which material is eroded at the boundary); +• can be used in static stress/displacement analysis, steady-state transport analysis, coupled pore fluid +flow and stress analysis, and coupled temperature-displacement analysis; +• can be used only in geometrically nonlinear general analysis steps; and +• is available only for acoustic elements and a subset of the solid elements. +Defining an ALE adaptive mesh domain +You can apply ALE adaptive mesh smoothing to an entire model or to individual parts of the model as +a step-dependent feature. Adaptive meshing for solid elements in Abaqus/Standard uses a subset of the +adaptive meshing functionality available in Abaqus/Explicit. +You must specify the portion of the original mesh that will be subject to adaptive meshing. +Input File Usage: +Abaqus/CAE Usage: +*ADAPTIVE MESH, ELSET=name +Multiple adaptive mesh domains can be defined in a step by reusing the +*ADAPTIVE MESH option, but each element set must refer to a unique set +of elements. +Step module: Other→ALE Adaptive Mesh Domain→Edit: toggle on Use +the ALE adaptive mesh domain below, and click Edit to select the region +Only one adaptive mesh domain can be defined in Abaqus/CAE for any +particular step. +Modifying an ALE adaptive mesh domain +By default, all adaptive mesh domains defined in the previous analysis step remain unchanged in +the subsequent step. You define the adaptive mesh domains in effect for a given step relative to the +preexisting adaptive mesh domains. At each new step the existing adaptive mesh domains can be +modified and additional adaptive mesh domains can be specified (except in Abaqus/CAE, where only +one adaptive mesh domain can be in effect for a given step). +Input File Usage: +Abaqus/CAE Usage: +Use either of the following options to modify an existing adaptive mesh domain +or to specify an additional adaptive mesh domain: +*ADAPTIVE MESH, ELSET=name +*ADAPTIVE MESH, ELSET=name, OP=MOD +Step module: Other→ALE Adaptive Mesh Domain→Edit +Removing an ALE adaptive mesh domain +If you choose to remove any adaptive mesh domain in a step, no adaptive mesh domains will be +propagated from the previous step. Therefore, all adaptive mesh domains that are in effect during this +step must be respecified. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to remove all previously defined adaptive mesh +domains and to specify new adaptive mesh domains: +*ADAPTIVE MESH, ELSET=name, OP=NEW +If the OP=NEW parameter is used on any *ADAPTIVE MESH option within +a step, it must be used on all *ADAPTIVE MESH options in the step. +Step module: Other→ALE Adaptive Mesh Domain→Edit: toggle +on No ALE adaptive mesh domain for this step +Splitting ALE adaptive mesh domains +Abaqus/Standard may subdivide each adaptive mesh domain that you specify such that +• all elements in an adaptive domain refer to one element property definition; and +• all elements in an adaptive domain are of similar type (such as hybrid elements with linear pressure). +If Abaqus/Standard subdivides the adaptive mesh domains that you specified, each of the adaptive +mesh domain subdivisions will have a new name, which will be used for output and diagnostic purposes. +The new names will be formed by concatenating the name of the user-specified element set, a number +identifying the subdivision, and the step number. Each of the subdivisions will be further examined to +ensure that all the elements in a subdivision are subjected to the same body forces. You may be asked to +modify the definition of the adaptive mesh domain to satisfy this requirement. +ALE adaptive mesh regions +Each adaptive mesh domain has an interior region and a boundary region. The boundary region may +include distinct kinks that take the form of geometric edges or corners. The nodes on the boundary region +are, therefore, further separated into free surface nodes, edge nodes, and constrained nodes. Different +updating rules are applied to nodes in these different regions. These regions are created automatically by +Abaqus/Standard. You can control the detection of the geometric features. In addition, mesh constraints +can be applied to any node in the adaptive mesh domain. +Since acoustic elements do not have displacement degrees of freedom, their treatment for adaptive +meshing includes some additional considerations. The acoustic adaptive domain must be connected to +the structural domain using a surface-based tie constraint with the slave surface defined on the acoustic +domain. Thus, an acoustic adaptive domain has an additional boundary region that is connected to +the structural domain. These slave surface nodes are updated based on the displaced configuration +of the master surface nodes on the structural domain, without permitting relative sliding between the +surfaces. The displacements of the master surface defined on the structural domain, together with nonzero +adaptive mesh constraints, serve as the forcing function that drives adaptive mesh smoothing of an +acoustic adaptive domain. The mesh smoothing algorithm will produce no changes in the acoustic +adaptive domain if these displacements are zero. +Options for controlling the mesh smoothing algorithm are described in “ALE adaptive meshing +and remapping in Abaqus/Standard,” Section 12.2.7. +ALE adaptive mesh interior regions +Nodes in the interior region are defined as nodes that are surrounded entirely by elements in the adaptive +mesh domain. By default, the new position of an interior node is computed from the positions of the +adjacent nodes that are connected through element edges to the node in question. These nodes can move +in any direction. +To control the displacement of these nodes, you can apply an adaptive mesh constraint in any +direction. +ALE adaptive mesh boundary regions +The boundary region is that part of the surface of the adaptive mesh domain that is not constrained to +other elements in the mesh. The nodes on the boundary region are further separated into surface nodes, +edge nodes, corner nodes, and constrained nodes. +Surface, edge, and corner nodes +Surface nodes are defined as nodes at which the surrounding surface facets have the same normal vector +within a user-defined angle. These nodes are constrained against movement in the normal direction, but +sliding in any tangential direction is permitted. The new position of a surface node is computed from the +positions of the adjacent nodes that are connected through the edges of the surface facets to the node in +question. +Edge nodes are nodes in a three-dimensional model at which the surrounding surface facets have +two different normals and where the vectors along two of the surface edges are colinear. Nodes on an +edge can slide only along the edge. The new position of an edge node is computed from the positions of +the two adjacent nodes along the edge. +Corner nodes are nodes at which all the surrounding surface facet normals are different. These +nodes are constrained against all mesh smoothing movement. +You can control the displacement of these node types on the boundary region by applying an adaptive +mesh constraint in any direction. +Constrained nodes in an acoustic adaptive domain +A surface-based tie constraint can be used to connect two acoustic surfaces together. When both the +master and slave nodes of the tie constraint belong to the same adaptive mesh domain, the master surface +nodes are updated according to the rules for surface, edge, and corner nodes. An adaptive mesh constraint +can be applied at master surface nodes. Slave nodes are updated by applying a tie constraint. Adaptive +mesh constraints cannot be applied at slave surface nodes. +Mesh smoothing is not applied to these nodes when the master and slave nodes belong to different +acoustic adaptive mesh domains. +Constrained nodes in a solid adaptive domain +Mesh smoothing is not applied to nodes that are involved in multi-point constraints , equations , or +kinematic coupling constraints ( “Coupling constraints,” Section 34.3.2). +Geometric features +The classification of boundary region nodes as surface, edge, and corner nodes is performed based on +the identification of geometric features in the mesh’s configuration at the start of a step where adaptive +mesh domains are defined and is updated as the analysis proceeds and the configuration changes. You +can define the criteria that Abaqus/Standard uses in classifying geometric features through adaptive mesh +controls. +Controlling the detection of geometric edges and corners +Geometric features are identified initially as edges on boundary regions where the angle between the +normals on adjacent element faces is greater than the initial geometric feature angle, +( +), as shown in Figure 12.2.6–1. The default value for the initial geometric feature angle is +. +Setting +will ensure that no geometric edges or corners are formed on the boundary of the +adaptive mesh domain. You can define adaptive mesh controls to change the value of the angle that will +be used to recognize geometric features. +Input File Usage: +*ADAPTIVE MESH CONTROLS, NAME=name, +INITIAL FEATURE ANGLE= +Abaqus/CAE Usage: +Step module: Other→ALE Adaptive Mesh Controls→Create: +Name: name, Initial feature angle: +Controlling the activation and deactivation of geometric edges and corners +Abaqus/Standard allows geometric features, and consequently the updating rules applied at a node, to +change during the analysis. For example, nodes are constrained to lie along a discrete geometric edge +unless the angle forming the geometric edge becomes less than the transition geometric feature angle, +θ > θ +θ ≤ θ +Initial mesh with a geometric +feature: no mesh flow is +permitted past the corner. +The geometric feature +is deactivated during +simulation. +Figure 12.2.6–1 Detection and deactivation of geometric features. +). The default value for the transition feature angle is +( +. If the angle across the +geometric edge becomes less than +, the boundary surface is considered to be flattened sufficiently for +the feature to be deactivated, and the mesh is allowed to slide freely on the surface. Geometric corners +are allowed to flatten in a similar fashion. In addition, surfaces that are initially flat may develop edges +or corners during the simulation. This logic allows great flexibility in mesh adaptation while preserving +geometric features in the model. +Setting +will ensure that no geometric edges or corners are ever deactivated. You can +change the transition feature angle using adaptive mesh controls. +Abaqus/Standard will issue a warning message when geometric features are activated or deactivated. +Input File Usage: +*ADAPTIVE MESH CONTROLS, NAME=name, +TRANSITION FEATURE ANGLE= +Abaqus/CAE Usage: +Step module: Other→ALE Adaptive Mesh Controls→Create: +Name: name, Transition feature angle: +Mesh constraints +In most adaptive mesh problems the motion of nodes in the mesh is determined by the mesh smoothing +algorithm, with constraints imposed by the domain boundary and the boundary region edges. However, +there may be cases when you will want to define the motion of the nodes explicitly. You may also wish +to keep certain nodes fixed, to move nodes in a particular direction, or to force certain nodes to move +with the material. +Adaptive mesh constraints give you the flexibility to define the motion of the node explicitly. +Input File Usage: +Abaqus/CAE Usage: +*ADAPTIVE MESH CONSTRAINT +Step module: Other→ALE Adaptive Mesh Constraint→Create +Applying spatial mesh constraints +Spatial mesh constraints are applied to define the motion of the nodes explicitly. Spatial mesh constraints +allow full control over the mesh movement and can be applied to any node except those that have +Lagrangian mesh constraints applied to them. +You can also prescribe the spatial mesh constraints via user subroutine UMESHMOTION. The user +subroutine allows you to let the spatial mesh constraints depend on available nodal or material point +information. +Input File Usage: +Use the following option to define the mesh constraints explicitly: +*ADAPTIVE MESH CONSTRAINT, CONSTRAINT TYPE=SPATIAL, +TYPE=DISPLACEMENT or VELOCITY +Use the following option to define the mesh constraints in user subroutine +UMESHMOTION: +*ADAPTIVE MESH CONSTRAINT, CONSTRAINT TYPE=SPATIAL, +TYPE=DISPLACEMENT or VELOCITY, USER +Abaqus/CAE Usage: +To define the mesh constraints explicitly: +Step module: Other→ALE Adaptive Mesh Constraint→Create: Types +for selected step: Displacement/Rotation or Velocity/Angular velocity: +select region: Motion: Independent of underlying material +To define the mesh motion in user subroutine UMESHMOTION: +Step module: Other→ALE Adaptive Mesh Constraint→Create: Types +for selected step: Displacement/Rotation or Velocity/Angular +velocity: select region: Motion: User-defined +Defining mesh constraints that vary with time +The prescribed magnitude of a nonzero mesh constraint can vary with time during a step according to an +amplitude definition . +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*AMPLITUDE, NAME=name +*ADAPTIVE MESH CONSTRAINT, AMPLITUDE=name +Step module: Other→ALE Adaptive Mesh Constraint→Create: Types +for selected step: Displacement/Rotation or Velocity/Angular +velocity: select region: Motion: Independent of underlying +material: Amplitude: amplitude +Applying spatial mesh constraints in local directions +Mesh constraints are applied in local directions if a transformed coordinate system is used at a node +(“Transformed coordinate systems,” Section 2.1.5); otherwise, they are applied in global directions. +Applying Lagrangian mesh constraints +Lagrangian mesh constraints on a node are used to indicate that mesh smoothing should not be applied; +i.e., the node must follow the material. +Input File Usage: +*ADAPTIVE MESH CONSTRAINT, +CONSTRAINT TYPE=LAGRANGIAN +Abaqus/CAE Usage: +Step module: Other→ALE Adaptive Mesh Constraint→Create: Types +for selected step: Displacement/Rotation or Velocity/Angular velocity: +select region: Motion: Follow underlying material +Spatial mesh constraint considerations +When you decide on the type of spatial adaptive mesh constraint, (displacement, velocity, or specified +with a user subroutine), you should consider the guidelines below. +Choosing between displacement and velocity adaptive mesh constraints +Displacement and velocity mesh constraints differ in their application. Displacement constraints define a +node’s displacement relative to its original coordinates, while velocity constraints define a node’s velocity +relative to the motion of the material. You will use a displacement constraint to control a node’s motion to +a specific coordinate location, while you will use a velocity constraint to control a node’s motion relative +to the Lagrangian motion. Therefore, a constant velocity adaptive mesh constraint does not in general +lead to a constant velocity of the node relative to it’s original coordinates. +Applying spatial adaptive mesh constraints to model material ablation +Your spatial mesh constraint is applied without regard to the current material displacement at the node. +This behavior allows you to prescribe mesh motion that differs from the current material displacement +at the free surface of the adaptive mesh domain, effectively eroding, or adding, material at the boundary. +Using adaptive mesh constraints this way is an effective technique for modeling wear or ablation +processes. As described above, in common ablation modeling cases you will use the velocity form +of the constraint. In addition, for general boundary shapes the most effective interface for ablation is +user subroutine UMESHMOTION, where you can apply spatial mesh constraints to the nodes on the +free surface in general ways according to solution-dependent variables, if needed. The user subroutine +interface provides a local coordinate system that is normal to the free surface at the surface node, +enabling you to describe mesh motions in this local system. +Modifying ALE adaptive mesh constraints +By default, all adaptive mesh constraints defined in the previous analysis step remain unchanged in +the subsequent step. You define the adaptive mesh constraints in effect for a given step relative to the +preexisting adaptive mesh constraints. At each new step the existing adaptive mesh constraints can be +modified and additional adaptive mesh constraints can be specified. +Input File Usage: +Use either of the following options to modify an existing adaptive mesh +constraint or to specify an additional adaptive mesh constraint: +Abaqus/CAE Usage: +*ADAPTIVE MESH CONSTRAINT, +*ADAPTIVE MESH CONSTRAINT, OP=MOD +Step module: Other→ALE Adaptive Mesh Constraint→Manager: +select the desired step and mesh constraint: Edit +Removing ALE adaptive mesh constraints +If you choose to remove any adaptive mesh constraint in a step, no adaptive mesh constraints will be +propagated from the previous step. Therefore, all adaptive mesh constraints that are in effect during this +step must be respecified. +Input File Usage: +Use the following option to remove all previously defined adaptive mesh +constraints and to specify new adaptive mesh constraints: +*ADAPTIVE MESH CONSTRAINT, OP=NEW +If the OP=NEW parameter is used on any *ADAPTIVE MESH CONSTRAINT +option within a step, +it must be used on all *ADAPTIVE MESH +CONSTRAINT options in the step. +Abaqus/CAE Usage: +Step module: Other→ALE Adaptive Mesh Constraint→Manager: +select the desired step and mesh constraint: Deactivate +Contact +When surfaces are defined for large-sliding contact, adaptive meshing may relocate the nodes on the +surfaces. If the bodies in contact are sliding or deforming considerably, you may want to use Lagrangian +mesh constraints on the boundary of the surfaces to prevent the surfaces from sliding from their intended +place. +For small-sliding contact Abaqus/Standard assumes that the reference configuration does not +change significantly. If the reference configuration does not change significantly, the amount of adaptive +meshing on these surfaces should be small and the contact quantities computed based on the reference +configuration should continue to remain valid (Abaqus/Standard updates the tangent planes if nodes +change positions). Hence, Abaqus/Standard will allow the nodes on the contact surface to move as +needed by the mesh smoothing. You should apply Lagrangian mesh constraints in cases where nodes +are intended to remain nonadaptive. +Initial conditions +Initial temperatures and field variables can be defined on any region subjected to adaptive mesh +smoothing. However, +to the updated +configuration. +these variables will not be remapped from the original +Loads +For elements with displacement degrees of freedom, no restrictions are made to loads applied to adaptive +In cases where loads are intended to follow the material motion, Lagrangian mesh +mesh domains. +constraints must be applied to the nodes on the boundary of the surface on which distributed loads are +applied to prevent the surface from sliding. This will allow adaptive meshing to occur inside the surface +while maintaining the location of the distributed load. +All the nodes on which concentrated loads are applied become nonadaptive. +The loads that can be applied to an acoustic domain are described in “Acoustic, shock, and coupled +acoustic-structural analysis,” Section 6.10.1. These loads cannot be applied in procedures in which mesh +smoothing can be performed. +Boundary conditions +Special consideration is given to nodes on which boundary conditions are applied. No adaptive meshing +is done in the direction in which the boundary condition is applied, but adaptive meshing is carried out in +other directions. When a boundary condition is removed in a step, the same restriction applies since Abaqus/Standard will +ramp off the contribution of the boundary condition over the duration of the step. +The boundary conditions that can be applied to an acoustic domain are described in “Acoustic, +shock, and coupled acoustic-structural analysis,” Section 6.10.1. These boundary conditions cannot be +applied in any analysis procedure in which mesh smoothing can be performed. +Predefined fields +There are no restrictions on applying prescribed temperatures or field variables in an adaptive mesh +domain, but these nodal values are not remapped when adaptive meshing is performed. Therefore, +predefined fields that are not constant may not be meaningful in an adaptive mesh domain. +Material options +For elements with displacement degrees of freedom all material models that are isotropic and +homogeneous can be used in an adaptive domain. Material options that have anisotropic behavior +such as anisotropic materials , jointed material models , and concrete +material models cannot be used in an adaptive mesh +domain. +For acoustic elements the relevant material models are described in “Acoustic, shock, and coupled +acoustic-structural analysis,” Section 6.10.1. Mesh smoothing assumes that the geometric changes in the +acoustic domain do not lead to changes in material properties, such as fluid density. +Elements +Adaptive mesh domains can be defined for all acoustic first-order and second-order planar, +axisymmetric, and three-dimensional elements in Abaqus/Standard and for a limited number of other +elements. Table 12.2.6–1 provides a list of supported elements. +Table 12.2.6–1 Elements supported for adaptive meshing. +AC1D2, AC1D3, AC2D3, AC2D4, AC2D6, AC2D8, AC3D4, AC3D6, +AC3D8, AC3D10, AC3D15, AC3D20, ACAX3, ACAX4, ACAX6, ACAX8 +CPS4, CPS4T, CPS3 +CPE4, CPE4H, CPE4T, CPE4HT, CPE4P, CPE4PH, CPE3, CPE3H +CAX4, CAX4H, CAX4T, CAX4HT, CAX4P, CAX4PH, CAX3, CAX3H +C3D8, C3D8R, C3D8H, C3D8RH, C3D8T, C3D8HT, C3D8RT, C3D8RHT, +C3D8P, C3D8PH, C3D8RP, C3D8RPH +Procedures +Adaptive meshing can be used only in geometrically nonlinear general steps that invoke one of the +following procedures: +• Static stress/displacement analysis (“Static stress analysis procedures: overview,” Section 6.2.1) +• Steady-state transport analysis (“Steady-state transport analysis,” Section 6.4.1) +• Coupled temperature-displacement analysis (“Fully coupled thermal-stress analysis,” Section 6.5.3) +• Coupled pore fluid flow and stress analysis (“Coupled pore fluid diffusion and stress analysis,” +Section 6.8.1) +Acoustic elements will typically undergo adaptive meshing during static procedures and then +participate in subsequent acoustic procedures in their updated configuration. +Limitations +• Elements within the adaptive domain cannot be removed or added (“Element and contact pair +removal and reactivation,” Section 11.2.1). +• Deformable elements that are declared rigid cannot be part of adaptive mesh domains. +• Elements in the adaptive domain cannot contain embedded elements or rebars. +• Symmetric results transfer cannot be done from an axisymmetric model that had solid elements in +an adaptive domain. +• Import cannot be done from a model that had solid elements in the adaptive domain. +• It is not meaningful to drive a submodel using the nodes from a global model that were part of an +adaptive mesh domain. +• Only enhanced hourglass control can be used with reduced-integration elements. +• When used with acoustic elements, adaptive mesh smoothing must be applied in steps prior to +a coupled structural-acoustic analysis. It cannot be applied during a large-displacement dynamic +analysis. +• Mesh smoothing assumes that the geometric changes in the acoustic domain do not lead to changes +in material properties, such as fluid density. +• The coupling between the fluid and structure must be defined using a surface-based tie constraint +with the slave surface defined on the acoustic domain. +• Nodes in the adaptive domain that are involved in constraints such as multi-point constraints +(“General multi-point constraints,” Section 34.2.2) and equations (“Linear constraint equations,” +Section 34.2.1) should be made non-adaptive by applying Lagrangian constraints. +Input file template +Applying ALE adaptive meshing for acoustic analysis +*HEADING +… +*ELEMENT, TYPE=…, ELSET=ACOUSTIC +Data lines to define acoustic elements +*ELEMENT, TYPE=…, ELSET=SOLID +Data lines to define structural elements +*SURFACE, NAME=TIE_ACOUSTIC +Data lines to define the acoustic surface interface with the structural mesh +*SURFACE, NAME=TIE_SOLID +Data lines to define the solid surface interface with the acoustic mesh +*TIE, NAME=COUPLING +TIE_ACOUSTIC, TIE_SOLID +… +*STEP +*STATIC +*ADAPTIVE MESH, ELSET=ACOUSTIC, MESH SWEEPS=10 +… +*END STEP +** +*STEP +*STEADY STATE DYNAMICS, DIRECT +… +*END STEP +Applying ALE adaptive meshing in other uses +*HEADING +… +*ELEMENT, TYPE=C3D8, ELSET=.. +Data lines to define solid elements +*NSET, NSET=LAG +Data lines to define nodes that should be nonadaptive +*NSET, NSET=SPATIAL +Data lines to define nodes that will have spatial adaptive mesh constraints applied +*ELEMENT, TYPE=…, ELSET=SOLID +Data lines to define structural elements +*STEP, NLGEOM=YES +*STATIC +*ADAPTIVE MESH, ELSET=SOLID, MESH SWEEPS=10 +*ADAPTIVE MESH CONSTRAINT, CONSTRAINT TYPE=LAGRANGIAN +LAG +*ADAPTIVE MESH CONSTRAINT, CONSTRAINT TYPE=SPATIAL, USER +SPATIAL +*END STEP +12.2.7 +ALE ADAPTIVE MESHING AND REMAPPING IN Abaqus/Standard +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining ALE adaptive mesh domains in Abaqus/Standard,” Section 12.2.6 +• *ADAPTIVE MESH +• *ADAPTIVE MESH CONSTRAINT +• *ADAPTIVE MESH CONTROLS +�� “Customizing ALE adaptive meshing,” Section 14.14 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +ALE adaptive meshing consists of two fundamental tasks: +• creating a new mesh through a process called sweeping, and +• remapping solution variables from the old mesh to the new mesh with a process called advection. +You can control the process of mesh sweeping after which, +if necessary, Abaqus/Standard will +automatically perform advection. The default methods for creating a new mesh have been chosen +carefully to work for acoustic analysis and for modeling the effects of ablation, or wear, of material. +However, you may need to override the default choices to balance the robustness and efficiency of +adaptive meshing or to extend the use of adaptive meshing for other types of applications. +Adaptive mesh smoothing is defined as part of a step definition. The adaptive meshing in +Abaqus/Standard uses an operator split method wherein each analysis increment consists of a +Lagrangian phase followed by an Eulerian phase. The Lagrangian phase is the typical Abaqus/Standard +solution increment where neither mesh sweeps nor advection occur. Once the equilibrium equations +have converged, mesh smoothing is applied. Following the adjustment of nodes through the mesh +sweeping process, material point quantities are advected in an Eulerian phase to account for the +revised meshing of the model in its current configuration. This operator split method is chosen to +avoid unsymmetric Jacobian terms that would result when the advection and material straining occur +simultaneously. Advection is not required for, and is not applied to, acoustic elements. +The ALE adaptive mesh sweeping algorithm +Adaptive mesh smoothing is performed after the structural equilibrium equations have converged. The +mesh smoothing equations are solved explicitly by sweeping iteratively over the adaptive mesh domain. +During each mesh sweep, nodes in the domain are relocated—based on the positions of neighboring +nodes obtained during the previous mesh sweep—to reduce element distortion. The new position, +, +of a node is obtained as +is the original position of the node, +are the neighboring +where +nodal positions obtained during the previous mesh sweep, and +are weight functions obtained from +one or a weighted mixture of the following methods. The displacements applied during sweeps are not +associated with mechanical behavior. +is the nodal displacement, +Original configuration projection +Original configuration projection is the default in Abaqus/Standard and determines the weight function +from a least squares minimization procedure that minimizes node displacement in a projection of the +mesh back to the original configuration. This method of smoothing affects only deformations of the +mesh and not the original mesh. +Volume smoothing +Volume smoothing determines the weight function by computing a volume-weighted average of the +element centers in the elements surrounding the node. +In Figure 12.2.7–1 the new position of node +M is determined by a volume-weighted average of the positions of the element centers, C, of the four +surrounding elements. The volume weighting will tend to push the node away from element center C1 +and toward element center C3, thus reducing element distortion. +L3 +C4 +C3 +L4 +C1 +C2 +L1 +L2 +Figure 12.2.7–1 Relocation of a node during a mesh sweep. +Volume smoothing is supported in structured domains, where every node is surrounded by four +elements in two dimensions or eight elements in three dimensions. +Combining smoothing methods +The default smoothing method in Abaqus/Standard is original configuration projection. To choose an +alternate smoothing method or to combine the smoothing methods, you specify the weighting factor +for each method. When more than one smoothing method is used, a node is relocated by computing +a weighted average of the locations predicted by each chosen method. All weights must be zero or +positive, and their sum must be nonzero. The weights are significant only in a relative sense; their values +are normalized so that their sum is 1.0. +Input File Usage: +*ADAPTIVE MESH CONTROLS, NAME=name +original configuration projection weight, volume smoothing weight +Abaqus/CAE Usage: +For example, the following option could be used to define an equal blend of +original configuration projection and volume smoothing: +*ADAPTIVE MESH CONTROLS, NAME=name +0.5, 0.5 +Step module: Other→ALE Adaptive Mesh Controls→Create: Name: +name, Original configuration projection: original configuration +projection weight, Volumetric: volume smoothing weight +Geometric enhancements to the basic smoothing methods +The conventional forms of the basic smoothing methods may not perform well in highly distorted +domains. You can use geometrically enhanced forms of the basic smoothing algorithms as a technique +to mitigate distortion. These forms are heuristic and based on nodal locations only. Due to their heuristic +nature, geometric enhancements may not always improve the mesh smoothing. +Input File Usage: +Use the following option to apply geometric enhancements to the smoothing +algorithm: +*ADAPTIVE MESH CONTROLS, NAME=name, +GEOMETRIC ENHANCEMENT=YES +Abaqus/CAE Usage: +Step module: Other→ALE Adaptive Mesh Controls→Create: +Name: name, toggle on Use enhanced algorithm based on +evolving element geometry +Application of the sweeping algorithm +The mesh smoothing process begins with the mesh in its current displaced equilibrium configuration. +Nodes that have no displacement degrees of freedom, such as those connected to acoustic elements, are +maintained at their most recent configuration. Mesh smoothing is then driven by distortions in the current +configuration and by boundary constraints. These boundary constraints can be described directly through +adaptive mesh constraints. In the case of structural-acoustic boundaries the structural mesh boundary +provides a constraint that controls the smoothing of adjacent acoustic element regions. +When these boundary constraints are much larger than the characteristic element length in the +adaptive mesh domain, significant geometric changes, such as the development of corners, can occur. +To prevent such changes, the constraints are applied gradually over a series of “sub-increments” onto +the domain boundary. The number of sub-increments used is determined on the basis of the magnitude +of the maximum surface displacement and the characteristic element dimension. +The remaining nodes (nodes not driven by constraints) are identified as interior nodes, free surface +nodes, edge nodes, or corner nodes. These nodes are treated as described in “Defining ALE adaptive +mesh domains in Abaqus/Standard,” Section 12.2.6. +At the end of mesh sweeping the new geometry is checked to ensure that elements did not become +severely distorted during mesh smoothing. Abaqus/Standard responds to severe distortion in different +ways, depending on the elements and procedures used. When adaptive meshing is used with acoustic +elements, the current analysis increment is repeated with a reduced time increment, followed by another +adaptive mesh smoothing attempt. When adaptive meshing is used with other elements, severe distortion +results in abandonment of mesh smoothing for that increment. In cases where adaptive mesh constraints +are also defined, Abaqus/Standard aborts since the constraints cannot be satisfied. +Controlling the frequency of ALE adaptive mesh smoothing +In most cases the frequency of adaptive meshing is the parameter that most affects the mesh quality. By +default, mesh smoothing will be performed after each converged structural analysis increment. You can +change the frequency of adaptive meshing, except when adaptive mesh constraints are defined. +Input File Usage: +Abaqus/CAE Usage: +*ADAPTIVE MESH, FREQUENCY=number of increments +Step module: Other→ALE Adaptive Mesh Domain→Edit: toggle on Use +the adaptive mesh domain below, Frequency: number of increments +Controlling convergence of ALE adaptive mesh smoothing +The adaptive mesh smoothing equations are solved explicitly by sweeping iteratively over the adaptive +mesh domain. During each mesh sweep, nodes in the domain are relocated based on the current positions +of neighboring nodes to reduce element distortion. +Mesh smoothing is performed following the end of a converged increment. You can control +the intensity of the mesh smoothing by defining the number of mesh sweeps required. When the +displacements are large, more iterations are usually required. When used in acoustic analyses, more +iterations are usually required when the volume of the elements in the acoustic domain decreases +compared to the case when the volume increases during structural loading. +You can specify the number of mesh sweeps to be performed in each adaptive mesh increment. The +default number of mesh sweeps is one. +By applying the mesh sweeping algorithm repeatedly, the mesh will converge; in other words, +nodal positions are obtained that do not change with further mesh sweeping. However, it is usually +not necessary to apply mesh smoothing until a converged mesh is obtained; the main objective is to +reduce element distortion. +Input File Usage: +Abaqus/CAE Usage: +*ADAPTIVE MESH, MESH SWEEPS=number of sweeps +Step module: Other→ALE Adaptive Mesh Domain→Edit: +toggle on Use the adaptive mesh domain below, Remeshing +sweeps per increment: number of sweeps +The ALE adaptive mesh advection algorithm +Abaqus/Standard applies an explicit method, based on the Lax-Wendroff method, to integrate the +advection equation. The key principle of the Lax-Wendroff method is replacement of the time +derivatives of the material point quantities with the spatial derivatives using the classical relationship +between the material time derivative, the referential derivative, and the spatial derivative. The update +scheme is second-order accurate and provides some upwinding. Nodal quantities are advected by first +converting them to the material point quantities. +Advection of the material quantities will generally result in loss of equilibrium, for two main +reasons. The first reason is the errors in the advection process itself. To minimize the errors in advection, +Abaqus/Standard imposes restrictions on the magnitude of the advection velocity by requiring that the +Courant number for every element in the adaptive domain be less than one. In cases where the Courant +number is greater than one you will be informed and Abaqus/Standard will generate multiple advection +passes per increment. The second reason for the loss of equilibrium is changes in the representation of +the underlying material quantities by the changed mesh. For example, consider a region of the structure +having some stress gradients spanned initially by two elements. After mesh smoothing, the same +region might have more than two elements. This will lead to slightly different volume integration while +computing the internal force even when there are no errors in advection. +These sources of error in equilibrium are significant only when the mesh is too coarse to provide +a good solution and mesh smoothing is carried out with such small frequency that the mesh motion is +larger than the average element size. In practical applications these errors are typically insignificant, the +resulting loss of equilibrium is generally small, and the residuals generated by the loss of the equilibrium +fall within the limits of the Abaqus/Standard convergence criterion. Any loss of equilibrium is not +propagated since equilibrium will again be satisfied at the end of the Lagrangian phase of the next +increment. +Impact of advection on subsequent steps +To ensure that the results are output only for the configuration that satisfies equilibrium, Abaqus/Standard +always outputs the results at the end of the Lagrangian phase. The Eulerian phase that follows the +Lagrangian phase will leave the structure out of equilibrium for the next increment. This sequence has a +consequence that after the last Eulerian phase is carried out at the end of the step, equilibrium will not be +satisfied exactly at the beginning of the next step and the solution at the end of the step will differ slightly +from the solution at the zero increment of the following step. Equilibrium can again be established by +following the step that had adaptive meshing by a step that removes all the adaptive mesh domains +and allows the structure to equilibrate. A one-increment step will usually suffice. This is particularly +important when the following step is a perturbation procedure that uses the solution from the previous +step as the base state. +Frequency steps that follow adaptive mesh steps will also be impacted, because element mass is not +advected during mesh smoothing. This impact on the element mass can be significant, depending on the +extent of adaptive mesh motion and change in element size due to mesh smoothing. Abaqus will provide +a warning message in cases where adaptive meshing precedes a frequency step; you should evaluate +the impact of your updated mesh configuration when interpreting results from a frequency step in these +cases. +Output +In adaptive meshing the integration point of an element will generally not refer to the same material +point throughout the analysis. Contour plots of material variables will show correct spatial distribution, +but history plots are not meaningful. The displacement of the nodes contains the material displacement +as well as the displacement due to mesh motion. You can obtain measures of the volume lost due to +adaptive mesh constraints with the partial model variable VOLC, which is useful when using adaptive +mesh constraints to model ablation. +A summary of the adaptive meshing in each adaptive mesh domain is written to the message +(.msg) file. This summary includes the total number of load increments over which the structural +displacement is transferred to the fluid, the total number of mesh sweeps performed, the magnitude of +the maximum displacement increment, and the node and degree of freedom at which the maximum +displacement increment is measured. Warning messages are issued when geometric features change +during mesh smoothing. +More detailed diagnostic output for adaptive mesh smoothing can be requested; see “The +Abaqus/Standard message file” in “Output,” Section 4.1.1. This output provides the magnitude of +the maximum displacement and the node and degree of freedom where the maximum displacement +increment occurs during each mesh sweep. In addition, the nodes experiencing changes in geometric +features are listed. +Additional references +• Lax, P. D., and B. Wendroff, “Difference Schemes for Hyperbolic Equations with High-Order +Accuracy,” Communications on Pure and Applied Mathematics, vol. 17, p. 381, 1964. +• Lax, P. D., and B. Wendroff, “Systems of Conservations Laws,” Communications on Pure and +Applied Mathematics, vol. 13, pp. 217–237, 1960. +12.3 +Adaptive remeshing +• “Adaptive remeshing: overview,” Section 12.3.1 +• “Selection of error indicators influencing adaptive remeshing,” Section 12.3.2 +• “Solution-based mesh sizing,” Section 12.3.3 +12.3.1 +ADAPTIVE REMESHING: OVERVIEW +Abaqus/CAE provides an automated process to remesh your model adaptively. The goal of the adaptive +remeshing process is to approach or reach targets on selected error indicators for a specified model and its +accompanying load history. See “Adaptivity techniques,” Section 12.1.1, for a comparison of this process to +other Abaqus adaptivity methods. +Overview +The following steps are required to incorporate adaptive remeshing into your Abaqus/CAE model: +• You identify regions of the model where you wish to apply one or more adaptive remeshing rules. A +remeshing rule defines the step during which it will be applied, the error indicator output variables +and targets for those error indicators, the sizing method, and any constraints on element size. See +“What are remeshing rules?,” Section 17.13.1 of the Abaqus/CAE User’s Manual. +• You define a succession of analysis jobs, an “adaptivity process,” that will be run as Abaqus/CAE +attempts to meet your remeshing rule targets. See “What is an adaptivity process?,” Section 19.3.1 +of the Abaqus/CAE User’s Manual. +Based on these remeshing rules and your adaptivity process definition, Abaqus/CAE iteratively: +• executes an Abaqus/Standard analysis, which will write selected error indicator output variables +based on your remeshing rule settings , +• uses the error indicator variables in a sizing function to compute element sizes for a new +mesh, respecting any size constraints you might specify , and +• generates a new mesh in the regions specified, based on the computed element sizes. The +neighboring regions will also be remeshed. +These iterations continue until either: +• all remeshing rule targets are satisfied, or +• a maximum number of remesh iterations is reached. +See “When will my mesh adaptivity stop iterating?,” Section 19.3.2 of the Abaqus/CAE User’s Manual, +for more details. Figure 12.3.1–1 shows the interaction of Abaqus products and files in this process. +Typical applications +Adaptive remeshing can improve the quality of your simulation results. Adaptive remeshing can be +helpful when: +• you are unsure how refined a mesh needs to be to reach a particular level of accuracy or how coarse +the mesh can be without unacceptably impacting solution accuracy; +• it is difficult to design an adequately refined mesh near a region of interest, such as near a stress +riser; or +Automated Abaqus/CAE Actions +Figure 12.3.1–1 User actions and automated Abaqus/CAE +actions in the adaptive remeshing process. +• you do not know a location of interest, such as with formation of a plastic zone, a priori. +An example of using adaptive remeshing to study the thermal and stress behavior of a bolted vessel +is provided in “Thermal-stress analysis of a reactor pressure vessel bolted closure,” Section 5.1.6 of +the Abaqus Example Problems Manual. The example includes a Python script that you can run from +Abaqus/CAE to create the model and the remeshing rules. A second script allows you to submit the +adaptivity process and to view the changing mesh as Abaqus/CAE computes new element sizes. +Example: stress riser +Figure 12.3.1–2 shows how adaptive remeshing generates a high-quality mesh for a typical notched +specimen subjected to axial loading. +Figure 12.3.1–2 Stress riser mesh before and after refinement. +Figure 12.3.1–3 shows the effect of these mesh changes on solution accuracy in comparison to the effect +of uniform mesh refinement on solution accuracy. Adaptive mesh refinement is much more efficient than +uniform mesh refinement at reducing solution error. +Example: plastic hinge +This example, a doubly-notched specimen axially strained until a plastic hinge or band forms, is used +to demonstrate how adaptive remeshing will focus a mesh on a plastic hinge. It illustrates the value of +adaptive remeshing in cases where the region of interest may not be known a priori. Figure 12.3.1–4 +shows the specimen and the region of active yielding. Figure 12.3.1–5 shows the original mesh and the +adapted mesh after three adaptive remeshing iterations. +Figure 12.3.1–3 Comparison of adaptive remeshing to uniform mesh +refinement based on boundary seeding. +Figure 12.3.1–4 Region of active yielding in a doubly-notched specimen. +Figure 12.3.1–5 Mesh of doubly-notched specimen before and after adaptive remeshing. +Preparing your model for adaptive remeshing +You use Abaqus/CAE to do the following when performing adaptive remeshing: +• create the model and specify the boundary conditions and loading history, +• create remeshing rules, +• create an adaptivity process, and +• start and monitor the progress of the adaptivity process. +Creating the model +You do not have to consider adaptive remeshing when you create the model and specify the boundary +conditions and loading history; however, before using adaptive remeshing you must do the following: +• create the geometry of the model—you cannot use an orphan mesh part—and +• provide an initial, nominal, mesh. This mesh can be fairly coarse. Providing an extremely coarse +mesh, however, can result in more adaptive remesh iterations due to the poor quality of early remesh +iteration error indicator calculations. You can, in typical cases, define a reasonable initial mesh by +using the default part instance mesh seeding in Abaqus/CAE. +Creating a remeshing rule +You create and configure a remeshing rule using the Mesh module in Abaqus/CAE. See “Creating a +remeshing rule,” Section 17.21.1 of the Abaqus/CAE User’s Manual, for details on defining remesh rules. +Refer to “Selection of error indicators influencing adaptive remeshing,” Section 12.3.2, and “Solution- +based mesh sizing,” Section 12.3.3, for details on the methods used to determine revised mesh size +distributions. +Abaqus/CAE Usage: Mesh module: Adaptivity→Remeshing Rule→Create +Creating an adaptivity process +You create and configure an adaptivity process using the Job module in Abaqus/CAE. When you create +an adaptivity process, you can specify the maximum number of remesh iterations to be performed and +set various system resource parameters. See “Creating, editing, and manipulating jobs,” Section 19.7 of +the Abaqus/CAE User’s Manual, for details. +Abaqus/CAE Usage: +Job module: Adaptivity→Create +Performing adaptive remeshing with a provisional analysis +In some cases you will want to determine an adequate mesh for your model prior to conducting a fully +detailed analysis, which might include many steps and complex behavior. A “provisional” analysis can +often be used, along with adaptive remeshing, to efficiently determine a good mesh for a model. The +provisional analysis may include various simplifications of your fully detailed analyis, such as +• replacing your steps with a single linear perturbation step with loading that adequately reflects your +more general loading cases, +• removing plasticity and other material nonlinearities, and +• disabling geometric nonlinearity. +The provisional analysis approach may result in a mesh that is not ideally suited to your ultimate choice +of loading. However, the cost for obtaining a mesh from a provisional model may be significantly lower +than the case where your adaptivity process considers all of the complexity in the fully detailed analysis, +and you may find the refined mesh adequate for use in a variety of analysis situations. +Special considerations +In general, the Abaqus adaptive remeshing process iterates automatically toward a better quality mesh; +however, you should be aware of certain considerations. +Singularities +Stress singularities frequently result from geometric abstractions, such as reentrant corners and contact +of a sharp edge in elastic materials, and from point loads or abruptly ended distributed load regions. In +these situations the stress field near the singularity is unbounded, and no amount of mesh refinement will +enable resolution of the correct solution. If you apply the adaptive remeshing process to regions of your +model that include singularities, the process will drive elements near the singularity to very small sizes. +The end result may be unacceptably expensive analyses. +You can prevent excessively expensive analyses of models with singularities using the following +techniques: +• Exclude the region of the singularity from consideration in the remeshing process. You exclude +a region by partitioning the model and assigning remeshing rules only to regions away from the +singularity. +• Apply a minimum element size constraint in the remeshing rule. Abaqus/CAE does assign a +minimum element size by default, which is a fraction of the default part instance mesh seed. +You can modify this constraint to achieve a quality solution near the singularity while avoiding +an excessively refined mesh. You can also use the remeshing rule to control the rate at which +Abaqus/CAE refines the size of the elements. Element size constraints may prevent an adaptivity +process from achieving specified error indicator targets. +• Specify a maximum number of elements for a remeshing rule region. Abaqus/CAE adjusts the mesh +sizing such that the generated total number of elements approximately satisfies this constraint. +Convergence issues +Figure 12.3.1–6 shows a typical history of an error indicator and the computational cost, +Abaqus/Standard, versus remesh iteration. +in +Error Indicator +Computational Cost +50% +25% +3x +2x +1x +Remesh Iteration +Figure 12.3.1–6 Error indicator and computational cost versus iteration for a +model with a 25% error indicator target. +The example in Figure 12.3.1–6 shows a desirable convergence profile. The solution error indicator +decreases monotonically and quickly to the desired 25% error indicator target. Accompanying this error +indicator decrease is a moderate increase in computational cost, measured either in model degrees of +freedom or time in Abaqus/Standard. Certain situations can interfere with this desirable convergence +profile, as follows: +• If your initial mesh is too coarse, the error indicator variables may be of insufficient quality to +result in a mesh that is sufficiently improved in the next iteration. The adaptive remeshing process +typically creates a high-quality mesh eventually even if the initial mesh is quite coarse. However, +some mesh iterations can be avoided with a reasonably refined initial mesh. +• Minimum element size constraints and constraints on the maximum number of elements that you +specify when creating the remeshing rule can prevent the mesh from achieving sufficient refinement +(in the extreme case of singularities this will always be the case) to satisfy your error indicator +targets. You may be able to satisfy your targets by relaxing these constraints; for example, by +decreasing the minimum element size. For more information, see “What are remeshing rules?,” +Section 17.13.1 of the Abaqus/CAE User’s Manual. +• In addition to producing small mesh sizes resulting in a large number of elements, singularities +can cause an adaptivity process to fail in achieving the error target or to require more remeshing +iterations. As described in “Singularities,” above, you can control the computational cost by +specifying a minimum element size constraint or the maximum number of elements. In any case +where a singularity exists within a remeshing rule region, you may see poor convergence in the +error indicator results. +• Linear elements (C3D4, CPS4, etc.) and modified elements (C3D10M, CPS6M, etc.) converge +slowly compared to quadratic elements (C3D10, CPS6, etc.) requiring a relatively large number +of elements to achieve a given error target. Hence, you should use quadratic elements whenever +possible. +Continuing a stopped adaptive remeshing process +The adaptive remeshing process is designed to be automatic—Abaqus/CAE performs a sequence of +analyses as it continues to refine your mesh. However, there are occasions where the process will stop +and you will want to continue adaptive remeshing from your most recent mesh: +• when you want to change remeshing rules for later remesh iterations, or +• when the adaptive remesh process fails to complete due to machine resource problems. +You can continue the adaptive remeshing process by resubmitting an existing adaptivity process, creating +and submitting a new adaptivity process, or performing manual remeshing. See “Manually resizing and +remeshing,” Section 17.21.6 of the Abaqus/CAE User’s Manual. +Limitations +Adaptive remeshing requires the use of Abaqus/CAE, and only Abaqus/Standard procedures are +supported. Other specific limitations also apply. +Element types +Abaqus/CAE can perform adaptive remeshing only with elements of the following shapes : +• Planar continuum triangles and quadrilaterals +• Shell triangles and quadrilaterals +• Tetrahedrals +Procedures +Abaqus/CAE can perform remeshing with the following Abaqus/Standard procedures: +• “Static stress analysis,” Section 6.2.2 (general and linear perturbation). +• “Quasi-static analysis,” Section 6.2.5. +• “Uncoupled heat transfer analysis,” Section 6.5.2. +• “Fully coupled thermal-stress analysis,” Section 6.5.3. +• “Coupled thermal-electrical analysis,” Section 6.7.3. +• “Coupled pore fluid diffusion and stress analysis,” Section 6.8.1. +12.3.2 +SELECTION OF ERROR INDICATORS INFLUENCING ADAPTIVE REMESHING +Products: Abaqus/Standard Abaqus/CAE +References +• “Error indicator output,” Section 4.1.4 +• “Adaptive remeshing: overview,” Section 12.3.1 +• “Abaqus/Standard output variable identifiers,” Section 4.2.1 +• *CONTACT OUTPUT +• *ELEMENT OUTPUT +• “Understanding adaptive remeshing,” Section 17.13 of the Abaqus/CAE User’s Manual +• “Controlling adaptive remeshing,” Section 17.21 of the Abaqus/CAE User’s Manual +Overview +Your selection of which error indicator variables to use in adaptive remeshing rules for a particular +analysis should take into consideration: +• characteristics of the error indicator variables; +• which fields exist and are of interest; and +• the nature of the loading. +Error indicator characteristics +Error indicator output variables provide estimates of solution accuracy . In the context of adaptive remeshing, error indicators help determine where the mesh +should be refined or coarsened to achieve the specified accuracy targets . This Section discusses +additional characteristics of error indicators in the context of how well-suited they are for influencing +adaptive remeshing in various analysis types. +Which fields exist and are of interest +Certain variables apply naturally to certain types of analyses. For example, the heat flux indicator +(HFLERI) is used in analyses with temperature degrees of freedom. When selecting error indicator +variables in the Remeshing Rule editor in Abaqus/CAE , your choices will be restricted to variables +available for the selected procedure type. +The nature of the loading +Some error indicator variables only indicate discretization error at the current analysis time—the +particular increment in a step. Other error indicator variables provide a record of the solution history +up to the current analysis time. For example, if your simulation involves non-proportional loading or +a significantly nonlinear response, you will typically see better adaptive remeshing results when using +error indicator variables that record the solution history. Table 12.3.2–1 lists the error indicator variables +applicable to adaptive remeshing and indicates whether they record the solution history. +Table 12.3.2–1 Error indicator variables applicable to adaptive +remeshing that record the solution history. +Solution Quantity +Error indicator +Element energy density +Mises stress +Equivalent plastic strain +Plastic strain +Creep strain +Heat flux +Electric flux +Electric potential gradient +variable ( +) +ENDENERI +MISESERI +PEEQERI +PEERI +CEERI +HFLERI +EFLERI +EPGERI +Records the +solution history? +Yes +No +Yes +No +No +No +No +No +By default, when you create a remeshing rule, error indicators are specified for the final increment +of the final step of your analysis and adaptive remeshing is based on error indicators in this final +increment. When you select an error indicator that records the solution history, this default error +indicator specification is appropriate for almost all analyses. However, for other error indicator +variables that do not record the solution history, you may find it appropriate (for multistep cases with +non-proportional loading, for example) to define mutiple remeshing rules for the same region, with +each rule applied to a different step. +The examples that follow provide simple illustrations of typical cases and show appropriate choices +of error indicator output variables. +Linear response example +Figure 12.3.2–1 illustrates the simplest load case, where the load is proportional to the step time and the +model’s response is linear. In this case the solution at the final increment would be proportional to any +other increment. Therefore, it is appropriate to base the remeshing on the value of the error indicator in +the last increment for any choice of error indicator variable. +Monotonic response example +Figure 12.3.2–2 illustrates a more general case, where the model has a nonlinear response—in this case +resulting from a geometric nonlinearity—and the loading is monotonic but not generally proportional +to the step time. The response of the model is slightly more general because the solution at a particular +increment is not proportional to the solution at the final increment. However, the value of the error +indicator output in the final increment still reflects the extreme of the model’s response to the load history. +Figure 12.3.2–1 Proportional-loading, linear-response example: small deflection of a cantilever. +Figure 12.3.2–2 Monotonic response example: large deflection of a cantilever. +Therefore, it is appropriate to base the remeshing on the value of the error indicator in the last increment +for any choice of error indicator variable. +General response example +Figure 12.3.2–3 illustrates a case where the loading characteristics change dramatically during the +analysis. +Your choice of error indicator in this case will depend on the material model. The element energy +density error indicator, ENDENERI, will account for the complexity of load history (and lead to an +adapted mesh that provides an accurate solution through the analysis) regardless of the material type. +If plastic deformation occurs, you also have the option to use the equivalent plastic strain, PEEQERI, +or plastic strain, PEERI, error indicators. Plastic strain and the plastic strain error indicator generally +do not capture history effects; for example, they do not account for peak straining in models undergoing +symmetric strain reversals. This example, however, involves no strain reversals; therefore, PEERI would +be a valid error indicator choice. +Figure 12.3.2–3 General response example: block subjected to a rigid indenter. +General multistep response example: die forming and springback +Figure 12.3.2–4 illustrates a further generalization of a general response. Here, a forming operation is +simulated, and different steps are used for different stages of the operation. +Figure 12.3.2–4 General multistep response example. +In this case the response of the model varies from step to step. You will typically want the error +indicator to capture the extreme of the model’s response to the load history adequately. However, you +do not know if any particular increment captures this extreme. Therefore, you should select an error +indicator variable that records the solution history. +12.3.3 +SOLUTION-BASED MESH SIZING +Products: Abaqus/Standard Abaqus/CAE +References +• “Adaptive remeshing: overview,” Section 12.3.1 +• “Selection of error indicators influencing adaptive remeshing,” Section 12.3.2 +• “Understanding ALE adaptive meshing,” Section 14.6 of the Abaqus/CAE User’s Manual +• “Advanced meshing techniques,” Section 17.14 of the Abaqus/CAE User’s Manual +Overview +Solution-based mesh sizing: +• is performed in Abaqus/CAE; and +• operates on error indicator output variables and your remeshing rule parameters to determine an improved +element size distribution for your mesh. +Basic operation of the sizing method +The sizing method calculates new element sizes during the adaptive remeshing process. Abaqus/CAE +applies the sizing method to a field of error indicator variables and their corresponding base solution +variables over the region defined by the remeshing rule. The output of a sizing method is a set of scalar +sizes located at the nodes in the region defined by the remeshing rule. Figure 12.3.3–1 illustrates the +sizing operation. Figure 12.3.3–1 shows the base solution and error indicator distributions after the first +remesh iteration. The sizing method determines that the element size should be reduced in the region +of greatest error indicator and increased in the region of the lowest error indicator. The mesh that is +generated from these target element sizes is illustrated. +Characteristics of error indicators +The sizing method and parameter settings that you select have a significant impact on how adaptive +remeshing changes the error indicator distribution in your model. You may, for example, choose a sizing +method that aggressively reduces error indicators only near a stress riser. In other cases, where the global +response of your structure is more important than local effects, you may choose a sizing method that +attempts to reduce the error indicators to a uniform level throughout the region. To understand how the +sizing methods affect the error indicators, you should first understand typical characteristics of the error +indicator variables. +Figure 12.3.3–2 provides an illustration of an error indicator and corresponding base solution +distribution on a generalized slice through a model. +Lowest +base +solution +Figure 12.3.3–1 Sizing method operation and interaction with meshing. +Figure 12.3.3–2 illustrates the following error indicator characteristics: +• In regions where the value of the base solution is high, such as for element “i” in Figure 12.3.3–2, +error indicator values can be low relative to local values of the base solution. In many cases you +may want to use mesh refinement to drive these error indicators even lower. +error indicator +solution +cb +ce +SOLUTION-BASED MESH SIZING +maximum base solution +ce +cb +minimum base solution +position +element i +element j +Figure 12.3.3–2 Error indicator and base solution distribution. +• In regions where the base solution is low, such as for element “j” in Figure 12.3.3–2, error indicator +values can be high relative to the local values of the base solution. In many cases you may not be +interested in obtaining an accurate solution in these regions. +These characteristics can affect your decision on which sizing method to use and what parameters to set +in the sizing method. +Sizing methods +Sizing methods employ the concept of an error target, +form and which defines a general goal +, which is expressed in a normalized percentage +is a measure of the error indicator and +where +is a measure of the base solution. Based on +your definition of the error targets when you created the remeshing rule, Abaqus/CAE creates a size +distribution that attempts to meet your error target in the subsequent analysis job using the remeshed +model. The specific meaning of an error target depends on your choice of the sizing method. +Abaqus/CAE provides two fundamental sizing methods: Minimum/maximum control and +Uniform error distribution. You can also choose a third method, Default method and parameters, +which results in Abaqus/CAE choosing one of the fundamental sizing methods for you, based on your +choice of error indicator variable. +Abaqus/CAE Usage: Mesh module: Create Remeshing Rule: Sizing Method +Minimum/maximum control +The minimum/maximum control method provides the most flexibility in the remeshing of your model. +This method has the following characteristics: +• Two error indicator targets for controlling the sizing. +the base solution (such as stress) is highest, and +solution is lowest. +controls the sizing in regions where +controls the sizing in regions where the base +• A continuous variation in error targets between regions of high and low base solution values, with +a bias factor parameter provided to control the variation. +• To avoid excessive refinement at elements with a small base solution, a global averaged element +base is chosen when the element base solution is smaller than the global averaged element base. +• If singularities are present in the remeshing rule region, this method will fail to satisfy the error target +because the maximum base solution, which occurs at the location of the singularity, is unbounded. +You can either allow Abaqus to choose the targets automatically, or you can specify the error targets. +Similarly, you can accept the default bias factor displayed by Abaqus/CAE, or you can specify a +qualitative bias factor. +Abaqus/CAE Usage: Mesh module: Create Remeshing Rule: Sizing Method: Method: +choose Minimum/Maximum control +Allowing Abaqus/CAE to choose the error targets +If you specify the minimum/maximum error control method without setting error targets, Abaqus/CAE +automatically chooses the error targets, +. Both targets are computed as a fraction of the +error indicator result in the previous remesh iteration analysis. Automatic error target reduction is a +good choice for mesh refinement studies, where you have no specific error target goal but want to see +the impact of mesh refinement on your results. +and +Abaqus/CAE Usage: Mesh module: Create Remeshing Rule: Sizing Method: Error +Targets; choose Automatic error target reduction +Specifying the error targets +As an alternative to automatic error target reduction, you can specify the two error targets, +. Figure 12.3.3–2 illustrates these two locations. +is applied to element +, and +and +is applied +to element +. +Using the value of the two error targets, Abaqus/CAE applies a sizing method that attempts to meet +both +and +at their respective locations. +Abaqus/CAE Usage: Mesh module: Create Remeshing Rule: Sizing Method: Error Targets; +choose Fixed error targets; enter the maximum base solution error indicator +target, +, and the minimum base solution error indicator target, +. +Bias factor +You can use the bias factor definition in the remeshing rule to further tune the distribution of sizing +between maximum and minimum base solution locations. The bias factor defines the gradient of the size +distribution between these two extremes in your remesh region, as shown in Figure 12.3.3–3. +Figure 12.3.3–3 The impact of the bias factor on the element size distribution. +You can set this factor between two qualitative extremes, “weak” and “strong.” At the weak extreme, +element sizes will increase most quickly at locations moving away from the maximum base solution. +At the strong extreme, element sizes will increase most slowly. The default setting is a bias toward the +strong extreme. +Abaqus/CAE Usage: Mesh module: Create Remeshing Rule: Sizing Method: Mesh Bias; +drag the slider to a setting between Weak and Strong +Uniform error distribution +The uniform error distribution method provides a single error indicator target, +, for controlling the sizing. +Abaqus/CAE applies a sizing method such that the total error in the remeshing rule region is distributed +uniformly across all the elements and satisfies the given error indicator target. This method attempts to +satisfy the error indicator target collectively for the whole remeshing rule region but not at every element. +Therefore, the presence of singularities will not prevent the adaptivity process from achieving the error +target. +Abaqus/CAE Usage: Mesh module: Create Remeshing Rule: Sizing Method: Method: +choose Uniform error distribution +Allowing Abaqus/CAE to choose the error target +If you specify the uniform error distribution method without setting an error target, Abaqus/CAE +automatically chooses the error target, +. The target is computed as a fraction of the error indicator +result in the previous remesh iteration analysis. Automatic error target reduction is a good choice for +mesh refinement studies, where you have no specific error target goal but want to see the impact of +mesh refinement on your results. +Abaqus/CAE Usage: Mesh module: Create Remeshing Rule: Sizing Method: Error +Targets; choose Automatic error target reduction +Specifying the error target +As an alternative to the automatic error target reduction, you can specify the single error target, +. When +you use the uniform error distribution method, Abaqus/CAE compares the error target to a global norm +of a normalized form of the error indicator. Such an approach ensures a globally converging mesh within +the region. +Abaqus/CAE Usage: Mesh module: Create Remeshing Rule: Sizing Method: Error Targets: +choose Fixed error target; enter the error indicator target, +Default sizing methods and parameters +This method results in application of the Automatic error target reduction form of either the +Minimum/maximum control or Uniform error distribution method, with the method applied based +on the error indicator variable according to Table 12.3.3–1. +Table 12.3.3–1 Default sizing method for each error indicator. +Solution Quantity +Error +indicator +variable +Default sizing method +Element energy density +ENDENERI +Uniform error distribution +Mises stress +MISESERI +Minimum/maximum control +Equivalent plastic strain +PEEQERI +Minimum/maximum control +Plastic strain +Creep strain +Heat flux +Electric flux +Electric potential gradient +PEERI +CEERI +HFLERI +EFLERI +EPGERI +Minimum/maximum control +Minimum/maximum control +Uniform error distribution +Minimum/maximum control +Minimum/maximum control +When your remeshing rule refers to multiple error indicators, sizing methods will be applied +independently to each error indicator variable with the resulting local size based on the smallest size +calculated from each sizing method. +Abaqus/CAE Usage: Mesh module: Create Remeshing Rule: Sizing Method: Method: +choose Default methods and parameters +Example: Plate with a circular stress riser +The difference between the basic behavior of the minimum/maximum control and the uniform error +distribution methods is illustrated by a simple example. Figure 12.3.3–4 shows the stress result for a +simple loading of a plate with a hole. +Figure 12.3.3–4 Initial mesh and Mises stress distribution for a plane stress plate with +a hole, subjected to a uniform horizontal boundary traction. +Minimum/maximum control +Figure 12.3.3–5 illustrates the adaptive mesh that was generated by Abaqus/CAE when the user selected +the minimum/maximum control method and specified the two error targets ( +). In this +example +=1%, and the mesh bias is set to the default setting. These settings result in +a mesh that focuses tightly around the hole, the stress riser, while transitioning smoothly to a relatively +coarse mesh away from the hole. +=5% and +and +Uniform error distribution +Figure 12.3.3–6 illustrates the adaptive mesh that was generated by Abaqus/CAE when the user selected +the uniform error distribution method and specified the single uniform error indicator target ( ). In this +example =1%. This setting results in a mesh that focuses around the hole, the stress riser, while also +refining the mesh in less stressed regions. +Impact of additional remeshing rule settings +You specify the sizing method when you create a remeshing rule, and the sizing method calculates new +element sizes during the adaptive remeshing process. However, the following additional settings in the +remeshing rule can affect the mesh generated by Abaqus/CAE, regardless of the sizing method that you +selected: +• region selection, +• step and frame selection, +Figure 12.3.3–5 Adaptive remesh resulting from the minimum/maximum control sizing method. +Figure 12.3.3–6 Adaptive remesh resulting from the uniform error distribution sizing method. +• size constraints, +• approximate maximum number of elements, and +• refinement and coarsening rate factors. +Region selection +Sizing methods are defined across sets of elements, corresponding to the regions over which the +remeshing rules were applied in Abaqus/CAE. Within each set of elements, Abaqus/CAE applies the +sizing operation to the error indicator variables specified in the remeshing rule. The results of the sizing +operation are based on the extrapolation of whole element calculations to the nearest nodes, and the +results are node based. +Abaqus/CAE Usage: Mesh module: Create Remeshing Rule: Edit Region +Step and frame selection +Abaqus applies sizing operations to error indicator variables from only the last available frame in a +specified step. See “Error indicator characteristics” in “Selection of error indicators influencing adaptive +remeshing,” Section 12.3.2, for a discussion of how your selection of the step, frame, and error indicator +can affect your ability to capture the response in transient analyses. +Abaqus/CAE Usage: Mesh module: Create Remeshing Rule: Step and Indicator: +Step; select the step to which the rule is applied +and +Mesh module: Create Remeshing Rule: Step and Indicator: +Output Frequency; choose either Last increment of step +or All increments of step +Size constraints +When you create the remeshing rule, you can constrain the sizing operation from specifying elements +greater than or less than size constraints that you define for the remesh rule region. Abaqus/CAE provides +default settings for these constraints. +• The default minimum element size constraint is 1% of the default boundary seed size for the part +instance to which the remeshing rule is applied. +• The default maximum element size constraint is 10 times the default boundary seed size for the part +instance to which the remeshing rule is applied. +Abaqus/CAE Usage: Mesh module: Create Remeshing Rule: Constraints: Element Size +Approximate maximum number of elements +For a remeshing rule you can specify an approximate limit for the maximum number of elements. By +using this constraint, you can control the cost of your analysis and ensure that unreasonably large meshes +are not created. If the target error requires more elements than the specified limit when this constraint is +defined, Abaqus/CAE will reduce the target error internally so that the generated elements approximately +satisfy the specified element count. The use of this constraint may prevent an adaptivity process from +achieving the error targets. By default, this constraint is not active. +Abaqus/CAE Usage: Mesh module: Create Remeshing Rule: Constraints: Approximate +maximum number of elements +Refinement and coarsening rate factors +The refinement and coarsening factors that you specify define a constraint on the mesh size in terms of +iteration to iteration changes to the mesh. These factors modulate the aggressivity of the sizing methods. +The refinement factor controls the refinement of the mesh or the introduction of smaller elements. The +coarsening factor controls the coarsening of the mesh or the introduction of larger elements. Abaqus/CAE +provides default settings for these rate factors, which are designed to prevent excessive coarsening or +prohibitively expensive refinement in a single remesh iteration. +The refinement factor can have a significant effect on the convergence of the adaptive meshing +procedure. Once you have settled on sizing method parameters that work well for your application, you +may be able to achieve faster and more efficient mesh convergence by increasing the refinement factor. +In cases where your adaptivity process is not converging well, however, an increased refinement factor +could result in an excessive increase in elements in a remesh iteration. +Abaqus/CAE Usage: Mesh module: Create Remeshing Rule: Constraints: Rate Limits +Reconciling overlapping remeshing rules +Abaqus/CAE imposes no restrictions on the region or the steps associated with your remeshing rules. +You can apply multiple remeshing rules and, hence, sizing functions to the same region at the same time. +Similarly, you can specify remeshing rules that overlap one another. When Abaqus/CAE generates the +new mesh, it considers all of the remeshing rules at all of the locations and uses the smallest calculated +element size to drive the meshing algorithm. +12.3 +Adaptive remeshing +This Abaqus functionality is not applicable to V6. +12.4 +Analysis continuation after mesh replacement +• “Mesh-to-mesh solution mapping,” Section 12.4.1 +12.4.1 +MESH-TO-MESH SOLUTION MAPPING +Product: Abaqus/Standard +Reference +• *MAP SOLUTION +Overview +Mapping a solution from one mesh to another is a step in a remeshing analysis technique, where a mesh +that has deformed significantly from its original configuration is replaced by a mesh of better quality and +the analysis continues. The solution mapping technique: +• is used when elements become so severely distorted during an analysis that they no longer provide +a good discretization of the problem; +• maps the solution from an old, deformed mesh to a new mesh so that the analysis can continue; and +• can be used only with continuum elements. +Refer to “Adaptivity techniques,” Section 12.1.1 for a high-level discussion comparing this and other +Abaqus adaptivity methods. +When to remesh +Abaqus/Standard uses a Lagrangian formulation: the mesh is attached to the material and, thus, deforms +with the material. When the strains become large in geometrically nonlinear analyses, the elements may +become so severely distorted that they no longer provide a good discretization of the problem. Severe +distortion may occur in rubber elasticity problems or in plastic or viscoplastic calculations, especially +when modeling manufacturing processes. When severe distortion occurs, it is necessary to remesh: to +create a new mesh better designed to continue the analysis and to map the old-model solution onto this +mesh. +You must decide when remeshing is needed. This decision can be assisted by looking at the +magnitude of strains that have occurred during the phase of the analysis using a particular mesh, as +discussed later. When remeshing is required, a new mesh for the deformed object must be generated +using the mesh generation capability in Abaqus or an external mesh generator. The analysis is then +In most cases it will be desirable to transfer the +continued as a new problem using the new mesh. +solution from the old mesh to the new mesh. +Discontinuity in the solution +Whenever the solution is mapped from another mesh, you can expect that there will be some discontinuity +in the solution because of the change in the mesh and as a consequence of the solution mapping algorithm. +If the discontinuity is significant, it is an indication that the meshes are too coarse or that the remeshing +should have been done at an earlier stage before too much distortion occurred. +The remeshing technique works well, provided that the meshes are sufficiently fine for the problem +and that the remeshing is done before the elements become too distorted. +Remeshing criterion +The first requirement for remeshing is some indication that the mesh is becoming distorted in regions +where this distortion could cause the solution to be inaccurate. One possible criterion for remeshing +would be extreme element distortion in areas where high strain gradients need to be resolved accurately. +Inaccuracy is less of a concern if the distorted elements have moved into an area where further changes +in the strain field are uniform; the elements can represent states of constant strain accurately no matter +how distorted they are. Ultimately, however, the decision to remesh is a matter of judgment. +Generating a new mesh +Once you have decided that the current mesh is inadequate, a new mesh that is more suitable to the current +state of the problem must be generated by using the mesh generation capabilities in Abaqus or an external +mesh generator. Deformed configuration plots may be useful to provide data about the current shape of +the object being modeled. Usually the external surface can be defined for use in a mesh generator from the +results file output at the sets of nodes that form the surfaces of the body. See “Erosion of material (sand +production) in an oil wellbore,” Section 1.1.22 of the Abaqus Example Problems Manual and “Upsetting +of a cylindrical billet: quasi-static analysis with mesh-to-mesh solution mapping (Abaqus/Standard) and +adaptive meshing (Abaqus/Explicit),” Section 1.3.1 of the Abaqus Example Problems Manual. +Remeshing a contact problem +In a region of contact the new mesh must conform closely to the shape of the surface from the old analysis. +This requirement is especially important for problems involving contact between two deformable bodies; +if the surfaces defined by the new mesh are even slightly different from the surfaces in the old analysis, +the contact algorithms may fail to converge. +Specifying the solution to be interpolated onto the new mesh +The simulation is continued by interpolating the solution onto the new mesh from the output databases +generated with the old mesh. +Specifying the time at which the solution must be read +Solution transfer will occur, by default, from the latest step and increment for which solution variables +are available. Alternatively, you can specify the step and increment at which the old solution will be +read. +Input File Usage: +*MAP SOLUTION, STEP=step, INC=increment +Obtaining equilibrium +An initial step should be included to allow Abaqus/Standard to check for equilibrium after this +interpolation has been done. By default, Abaqus/Standard resolves the stress unbalance linearly over +the step . You can choose to have the +stress unbalance resolved in the first increment instead. +Input File Usage: +Use the following option to have Abaqus/Standard resolve the stress unbalance +linearly over the step: +*MAP SOLUTION, UNBALANCED STRESS=RAMP +Use the following option to have Abaqus/Standard resolve the stress unbalance +in the first increment of the step: +*MAP SOLUTION, UNBALANCED STRESS=STEP +Translating and rotating the old-job mesh +The mesh from the old job can be repositioned prior to performing the mapping by giving a translation +and/or rotation relative to the global origin. Specify a translation by giving a translation vector. Specify +a rotation by giving two points to define a rotation axis plus a right-handed angular rotation around that +axis. +Input File Usage: +*MAP SOLUTION, STEP=step, INC=increment +translation vector data +rotation axis and angular rotation data +Required output from the old job +The files required for restart and the output database must be requested for the old job. Nodal +displacement results are not output automatically from the old job; you must explicitly request output +of the displacement variable U for all nodes, as described in “Node output” in “Output to the output +database,” Section 4.1.3. Alternatively, you can request preselected field output and obtain node +displacement output sufficient for solution mapping. +In fully coupled procedures you must request nodal output of the coupled field variable to the output +database . +Table 12.4.1–1 Output database nodal output requirements for fully coupled procedures. +Procedure +Nodal output variable +“Fully coupled thermal-stress analysis,” Section 6.5.3 +“Coupled pore fluid diffusion and stress analysis,” Section 6.8.1 +“Geostatic stress state,” Section 6.8.2 +NT11 +POR +POR +Identifying the old job +Specify the name of the old job from which restart and results data will be obtained by using the oldjob +parameter in the command for running Abaqus or by answering a request made by the command +procedure . The +files required from the old job include: the restart file (.res), the output database (.odb), the model +database (.mdl), the state database (.stt), and the part (.prt) file. +Solution mapping algorithm +Solution mapping operates by interpolating results from nodes in the old mesh to points (either nodes +or integration points) in the new mesh. The first step, therefore, involves associating solution variables +with nodes in the old mesh. For nodal solution variables, such as nodal temperature or pore pressure, the +association is already made. For integration point variables Abaqus obtains the solution variables at the +nodes of the old mesh by extrapolating values from the integration points to the nodes of each element +and then averaging these values over all similar elements abutting each node. +Next, the location of each point in the new mesh is obtained with respect to the old mesh. The +new mesh points include integration points in all cases and nodes in procedures that record nodal state +in addition to displacements (for example, nodal temperatures in coupled temperature-displacement +procedures). +1. The element (in the old mesh) in which the point lies is found, and the point’s location in that element +is obtained. (This procedure assumes that all points in the new mesh lie within the bounds of the old +mesh: warning messages are issued if this is not so, and the values of the variables are set to zero.) +2. The variables are then interpolated from the nodes of the old element to the points in the new model. +All necessary variables are interpolated automatically in this way so that the solution can proceed with +the new mesh. +Solution diffusion +This algorithm introduces some diffusion in the mapped solution. The effect of the diffusion scales with +the solution gradient in the old mesh; hence, even for regions of the model where the mesh does not +change from the old to the new model, diffusion due to the mapping can result in significantly different +mapped quantities when the old-mesh solution gradient is high. You can moderate this effect by refining +the old mesh in regions where solution gradients are high or by remeshing earlier. +Procedures +The solution mapping capability is supported for the following procedures: +• “Static stress analysis,” Section 6.2.2 +• “Quasi-static analysis,” Section 6.2.5 +• “Fully coupled thermal-stress analysis,” Section 6.5.3 +• “Coupled pore fluid diffusion and stress analysis,” Section 6.8.1 +• “Geostatic stress state,” Section 6.8.2 +Initial conditions +The solution mapped from the initial analysis forms the initial conditions for the remeshed analysis. +Initial conditions such as temperature for a pure stress/displacement analysis can be specified. Any other +specified initial conditions will be ignored. +Boundary conditions +Boundary conditions are not carried over from the old mesh to the new mesh. The boundary conditions +applied at the beginning of the remeshed analysis should normally be the same as those in effect at the +step and increment selected from the initial analysis. Although boundary conditions can be changed, the +problem may fail to converge if the structure is far from an equilibrium state. +There are no restrictions on applying boundary conditions in a mapped solution analysis. +Boundary conditions can be applied to all available degrees of freedom in the same way as they are +applied in an analysis without a mapped solution . +Loads +There are no restrictions on applying loads in a mapped solution analysis. Loads can be applied in the +same way as they are applied in an analysis without a mapped solution. +The loads applied at the beginning of the remeshed analysis should normally be the same as those +in effect at the end of the initial analysis. Although the loads can be changed, the problem may fail to +converge if the structure is far from an equilibrium state. +Predefined fields +Temperature and field variables are mapped from the old mesh to the new mesh. If the number of field +variables is changed in the remeshed analysis, the number common to both analyses will be transferred. +Predefined fields can be modified in the same way as they are modified in an analysis without solution +mapping . +Material options +Any of the mechanical constitutive models available in Abaqus can be used in a mapped solution analysis +. There is no restriction on agreement between material models in the old and +new analyses. The solution mapping algorithm will transfer those variables common to both models. +You must ensure that the material models are compatible. +Elements +The solution mapping capability can be used only with continuum elements +elements,” Section 28.1.1). +Output +There is no output specific to a mapped solution analysis. Output can be requested in the same way +as in an analysis without a mapped solution. The output variables available in Abaqus are listed in +“Abaqus/Standard output variable identifiers,” Section 4.2.1. +Input file template +*HEADING +*NODE +Data lines to define the new-model nodes occupying the space of the old model +in its deformed configuration +*ELEMENT +Data lines to define the new-model elements occupying the space of the old model +in its deformed configuration +… +*MAP SOLUTION, STEP=step, INC=inc +translation and rotation data +*STEP +*STATIC (or *COUPLED TEMPERATURE-DISPLACEMENT or *GEOSTATIC +or *SOILS or *VISCO) +… +*END STEP +13. +Optimization Techniques +Structural optimization: overview +Optimization models +13.1 +13.1 +Structural optimization: overview +• “Structural optimization: overview,” Section 13.1.1 +13.1.1 +STRUCTURAL OPTIMIZATION: OVERVIEW +Structural optimization using Abaqus is an iterative process that helps you refine your designs. The result +of a well-designed structural optimization is a component that is lightweight, rigid, and durable. Abaqus +provides two approaches to structural optimization—topology optimization and shape optimization. Topology +optimization starts with an initial model and determines an optimum design by modifying the properties of the +material in selected elements, effectively removing elements from the analysis. Shape optimization further +refines the model by modifying the surface of the component by moving the surface nodes to reduce local stress +concentrations. Both topology and shape optimization are governed by a set of objectives and constraints. +Optimization is a tool for shortening the development process by adding value to a designer’s experience +and intuition with an automated procedure. To optimize your model, you need to know what to optimize. It +is not sufficient to say that you want to minimize stresses or maximize eigenvalues, your statements must be +more specific. For example, you might want to minimize the maximal nodal stresses experienced during +two load cases. Similarly, you might want to maximize the sum of the first five eigenvalues. The goal +of an optimization is called the objective function. In addition, you can enforce certain values during the +optimization. For example, you can specify that the displacement of a given node must not exceed a certain +value. An enforced value is called a constraint. +You use Abaqus/CAE to create the model to be optimized and to define, configure, and execute +the structural optimization. For more information, see Chapter 18, “The Optimization module,” of the +Abaqus/CAE User’s Manual. +Terminology +Structural optimization introduces its own terminology. The following terms are used throughout the +Abaqus documentation and the Abaqus/CAE user interface: +• Design area: The design area is the region of your model that the structural optimization +modifies. The design area can be the whole model, or it can be a subset of the model containing +only selected regions. Given the prescribed conditions (such as boundary conditions, loads, and +manufacturing constraints), +• a topology optimization process removes and adds material from elements in the design area +while it attempts to reach an optimal design, and +• a shape optimization modifies the surface of the design area by moving surface nodes. +• Design variables: For an optimization problem, the design variables represent the parameters to +be changed during the optimization. +For a topology optimization, the densities of the elements in the design area are the design +variables. The Abaqus Topology Optimization Module changes the density during each iteration +In effect, the +of the optimization and couples the stiffness of each element with the density. +optimization removes elements from your model by giving them a mass and stiffness that is small +enough to ensure they no longer participate in the overall response of the structure. The model +with the revised material properties is then analyzed by Abaqus. +For a shape optimization, the displacements of the surface nodes in the design area are the +design variables. During the optimization, the Abaqus Topology Optimization Module either +moves a node outward (growth) or inward (shrinkage) or leaves the position unchanged (neutral). +Restrictions influence the amount a surface node can move and the direction in which it can +move. The optimization directly modifies only the position of the corner nodes of elements; the +Abaqus Topology Optimization Module interpolates the displacement of midside nodes from the +movement of the corner nodes. +• Design cycle: Optimization is an iterative design process that updates the design variables, +executes an Abaqus analysis of the modified model, and reviews the results to determine if an +optimized solution has been reached. Each optimization iteration is called a design cycle. +• Optimization task: An optimization task contains the definition of your optimization, such as +the design responses, objectives, constraints, and geometric restrictions. To run an optimization, +you execute an optimization process. An optimization process refers to an optimization task. +• Design responses: The inputs to the optimization are called the design responses. +Design responses can be read directly from the Abaqus output database (.odb) file; +for example, +the +Abaqus Topology Optimization Module can read data from the output database file and +calculate the design responses from your model; for example, its weight, center of mass, or relative +displacements. +stress, eigenfrequencies, and displacements. +Alternatively, +stiffness, +A design response is associated with a region of your model; however, it consists of a single +In +scalar value, such as the maximum stress within a region or the total volume of the model. +addition, a design response can be associated with a particular step or load case. +• Objective functions: Objective functions define the objective of the optimization. An +objective function is a single scalar value extracted from a design response, such as the maximum +displacement or the maximum stress. An objective function can be formulated from multiple +If you specify that the objective functions minimize or maximize the design +design responses. +responses, the Abaqus Topology Optimization Module calculates the objective function by adding +each of the values determined from the design responses. +In addition, if you have multiple +objective functions, you can use a weighting factor to scale their influence on the optimization. +• Constraints: Constraints are also a single scalar value extracted from a design response; +however, a constraint cannot be derived from a combination of design responses. Constraints +restrict the value of a design response; for example, you can specify that the volume must be +reduced by 45% or the absolute displacement in a region must not exceed 1 mm. You can also apply +manufacturing and geometric constraints that are independent of the optimization; for example, a +structure must be able to be cast or stamped or the diameter of a bearing surface cannot be changed. +• Stop conditions: A global stop condition defines the maximum number of iterations an +optimization can perform. A local stop condition specifies that the optimization should end when a +local minimum (or maximum) has been reached. +Structural optimization with Abaqus/CAE +The following steps are required to incorporate structural optimization into your Abaqus/CAE model: +• You create an Abaqus model that can be optimized. For example, the design area must include only +supported elements and materials. See “Creating Abaqus optimization models,” Section 13.2.3. +• You create an optimization task. See “Creating and configuring an optimization task,” Section 18.6 +of the Abaqus/CAE User’s Manual. +• You create design responses. See “Design responses,” Section 13.2.1. +• You use the design responses to create objective functions and constraints. See “Objectives and +constraints,” Section 13.2.2. +• You create an optimization process and submit it for analysis. See “What is an optimization +process?,” Section 19.5.1 of the Abaqus/CAE User’s Manual. +Based on the definition of +the optimization task and the optimization process, +the +Abaqus Topology Optimization Module iteratively: +• prepares the design variables (element densities or surface node positions) and updates the Abaqus +finite element model, and +• executes an Abaqus/Standard analysis. +These iterations or design cycles continue until either: +• the maximum number of design cycles is reached, or +• the specified stop conditions are reached. +Figure 13.1.1–1 shows the interaction of Abaqus and the optimization process. +Topology optimization +Topology optimization starts with an initial design (the original design area), which also contains any +prescribed conditions (such as boundary conditions and loads). The optimization process determines a +new material distribution by changing the density and the stiffness of the elements in the initial design +while continuing to satisfy the optimization constraints, such as the minimum volume or the maximum +displacement of a region. +Figure 13.1.1–2 show the progression of a topology optimization of an automotive control arm +during 17 design cycles. The objective function in the optimization is trying to minimize the maximum +strain energy calculated from all the elements in the arm, in effect maximizing the structural stiffness +of the arm. The constraint is forcing the optimization to reduce the volume by 57% from the initial +value. During the optimization the density and the stiffness of the elements in the center of the arm +are reduced so that the elements are, in effect, “removed” from the analysis. However, the elements +are still present, and they could play a role in the analysis if their density and stiffness increase as the +optimization continues. A geometry restriction forces the optimization to create a model that could be +cast and removed from a mold—the Abaqus Topology Optimization Module cannot create voids and +undercuts. +Abaqus can apply the following objectives to a topology optimization process: +• strain energy (a measure of structural stiffness), +• eigenfrequencies, +• internal and reaction forces, +Create model +Create optimization task +User actions +Automated +optimization +actions +Setup +optimization +Create design responses +Create objective functions +Create constraints +Create optimization process +Submit optimization process +Perform +optimization +Prepare design +variables and update +finite element model +Monitor optimization +progress +Design +cycle +iteration +Abaqus analysis +Monitor job progress +No +Optimization +complete? +Yes +Optimization +process is +finished +Review results +Figure 13.1.1–1 User actions and automated Abaqus/CAE actions in the optimization process. +Start +100% volume +After 5 cycles +85% volume +After 10 cycles +77% volume +After 15 cycles +61% volume +After 17 cycles +57% volume +Figure 13.1.1–2 The progression of a topology optimization. +• weight and volume, +• center of gravity, and +• moment of inertia. +You can apply the same variables as constraints to a topology optimization process. In addition, you +can apply a number of manufacturing constraints that ensure the proposed design can be created using +standard production processes, such as casting and stamping. You can also freeze selected regions and +apply member size, symmetry, and coupling constraints. +An example of using topology optimization is provided in “Topology optimization of an automotive +control arm,” Section 11.1.1 of the Abaqus Example Problems Manual. The example includes a Python +script that you can run from Abaqus/CAE to create the model and configure the optimization. +General versus condition-based topology optimization +Topology optimization supports two algorithms—the general algorithm, which is more flexible and +can be applied to most problems, and the condition-based algorithm, which is more efficient but has +limited capabilities. By default, the Abaqus Topology Optimization Module uses the general algorithm; +however, you can choose which algorithm to use when you create the optimization task. Each algorithm +has a different approach for determining the optimized solution. +Algorithms +General topology optimization uses an algorithm that adjusts the density and stiffness of the design +variables while trying to satisfy the objective function and the constraints. The general algorithm is +partly described in Bendsøe and Sigmund (2003). In contrast, condition-based topology optimization +uses a more efficient algorithm that uses the strain energy and the stresses at the nodes as input data and +does not need to calculate the local stiffness of the design variables. The condition-based algorithm was +developed at the University of Karlsruhe, Germany and is described in Bakhtiary (1996). +Elements with intermediate densities +The general algorithm generates intermediate elements in the final design (their relative density is +between zero and one). In contrast, the condition-based optimization algorithm generates elements in +the final design that are either void (their relative density is very close to zero) or solid (their relative +density is equal to one). +Number of optimization design cycles +The number of design cycles used by the general optimization algorithm is unknown before +the optimization starts, but normally the number of design cycles is between 30 and 45. The +condition-based optimization algorithm is more efficient and searches for a solution until it reaches the +maximum number of optimization design cycles (15 by default). +Analysis types +The general algorithm supports the responses of linear and nonlinear static and linear eigenfrequency +finite element analyses. Both algorithms support geometrical nonlinearities and contact, and many +nonlinear materials are also supported. +Furthermore, prescribed displacements are allowed in the Abaqus model for static topology +optimization. However, prescribed displacements are not allowed for modal analysis. You can use +topology optimization on a structure that uses a composite material; however, the individual laminates +of a composite material cannot be modified using topology optimization. For example, you cannot +change the orientation of the fibers. +Objective functions and constraints +The general topology optimization algorithm can use one objective function and several constraints, +where the constraints are all inequality constraints. A variety of design responses can be used to define +the objective and the constraints, such as strain energy, displacements and rotations, reaction and internal +forces, eigenfrequencies, and material volume and weight. The condition-based topology optimization +algorithm is more efficient; however, it is less flexible and supports only strain energy (a measure of +stiffness) as the objective function and the material volume as an equality constraint. +Shape optimization +Shape optimization uses an algorithm that is similar to the algorithm used by condition-based topology +optimization. You use shape optimization at the end of the design process when the general layout of +a component is fixed, and only minor changes are allowed by repositioning surface nodes in selected +regions. A shape optimization starts with a finite element model that needs minor improvement or with +the finite element model generated by a topology optimization. +Typically, the objective of a shape optimization is to minimize stress concentrations using the results +of a stress analysis to modify the surface geometry of a component until the required stress level is +reached. Shape optimization tries to position the surface nodes of the selected region until the stress +across the region is constant (stress homogenization). Figure 13.1.1–3 shows a region at the base of a +connecting rod where the surface nodes have been moved by shape optimization to reduce the effect of +a stress concentration. +Original model +After shape +optimization +Figure 13.1.1–3 The effect of shape optimization. +You can apply the following objectives to a shape optimization process: +• stresses and contact stresses, +• selected natural frequencies, and +• elastic, plastic, and total strain and strain energy density. +You can apply only a volume constraint to a shape optimization. In addition, you can apply a number of +manufacturing geometric restrictions that ensure the proposed design can continue to be produced using +casting or stamping processes. You can also freeze selected regions and apply member size, symmetry, +and coupling restrictions. +An example of using shape optimization is provided in “Shape optimization of a connecting rod,” +Section 11.2.1 of the Abaqus Example Problems Manual. The example includes a Python script that you +can run from Abaqus/CAE to create the model and configure the optimization. +Applying mesh smoothing to a shape optimization +During a shape optimization, the Abaqus Topology Optimization Module modifies the surface of your +model. If the Abaqus Topology Optimization Module modifies only the surface nodes without adjusting +the inner nodes, the layer of surface elements becomes distorted. Therefore, the results of the Abaqus +analysis are no longer reliable, and the quality of the optimization suffers. To maintain the quality of +the surface elements, the Abaqus Topology Optimization Module can apply mesh smoothing to selected +regions, which adjusts the position of the inner nodes in relation to the movement of the surface nodes. +You must have a good quality finite element mesh before you start the shape optimization, especially in +areas where you expect the shape to change. +The Abaqus Topology Optimization Module can apply mesh smoothing to the standard continuum +elements, such as triangular, quadrilateral, and tetrahedral elements. Other element types are ignored +during the mesh smoothing. You can specify the relative quality of the smoothed mesh, and you can +specify the range of angles (quadrilateral and triangular elements) or the range of aspect ratios (tetrahedral +elements) that define an element that is considered good quality. Elements that are considered poor are +given a quality rating. The poorer an element is rated, the greater the consideration it will be given in +improving the element quality. +Mesh smoothing can be computationally expensive. The mesh smoothing algorithm is element- +based; and computing time increases in regions with many elements with limited degrees of freedom, +such as regions with small tetrahedral elements. You should apply mesh smoothing only to regions where +you expect the surface nodes to move—regions that will benefit from mesh smoothing. The nodes in the +regions to which you apply mesh smoothing must be free to move. For example, you should not apply +mesh smoothing to fixed nodes or to frozen regions. +You can apply limits to the result of mesh smoothing by applying minimum and maximum growth +restrictions to the selected region. See “Creating a growth restriction” in “Creating a geometric restriction +in a shape optimization,” Section 18.10.3 of the Abaqus/CAE User’s Manual, for more information. +Mesh smoothing can be applied to regions that are included in the design region and to regions +that are outside the design region. In particular, you can prevent element distortion by applying mesh +smoothing to the region of transition between the design region and the rest of your model. However, +the design region must be contained within the region to which you apply mesh smoothing. +Free surface nodes are defined as the nodes that lie outside the design area and are not included +in a geometric restriction. By default, the Abaqus Topology Optimization Module fixes all degrees of +freedom of all of the free surface nodes, and they are not modified during the mesh smoothing operation. +Alternatively, you can choose to allow the free surface nodes to move along with a specified number of +layers of nodes adjacent to the nodes in the design area. (A “layer” of nodes is created from only corner +nodes; midside nodes are not taken into consideration.) +You should allow free surface nodes to move in regions that are adjacent to the design area to create +a smooth transition between optimized and non-optimized regions. However, in some cases you will +want free surface nodes to remain fixed; for example, on a planar face that does not play a role in your +optimized model and must remain planar. +By default, a constrained Laplacian mesh smoothing algorithm is used. Alternatively, if you have +a relatively small model (less than 1000 nodes in the mesh smooth area), you can select a local gradient +mesh smoothing algorithm. In each iteration the local gradient mesh smoothing algorithm identifies the +elements with the worst element quality and improves them by displacing the nodes. Local gradient mesh +smoothing usually generates elements having the optimal shape, where the optimal is defined as the ratio +of the element volume (area for shell elements) to the corresponding power of its diameter. For larger +models the local gradient mesh smoothing algorithm tends to stop before the optimal mesh quality is +reached because the computation time becomes excessive. When the mesh smoothing ends prematurely, +only the elements with the worst element quality will be smoothed. +13.2 +Optimization models +• “Design responses,” Section 13.2.1 +• “Objectives and constraints,” Section 13.2.2 +�� “Creating Abaqus optimization models,” Section 13.2.3 +13.2.1 +DESIGN RESPONSES +Product: Abaqus/CAE +References +• “Structural optimization: overview,” Section 13.1.1 +• “Configuring design responses,” Section 18.7 of the Abaqus/CAE User’s Manual +Overview +A design response: +• is a single scalar value, such as the volume of your structure; +• is calculated by the Abaqus Topology Optimization Module by reading results and model data from +the output database file; +• can be referred to from objective functions and constraints (for example, you can create an objective +function that tries to minimize the displacement at a node or a constraint that forces the weight of +the structure to be reduced by at least 50%); and +• is available only for certain analysis procedures (for example, you must perform an +tries to maximize the +eigenvalue extraction analysis if you select a design response that +lowest eigenfrequencies). +Design response operators +You must specify the operation that the Abaqus Topology Optimization Module will use to arrive at a +single scalar value for the design response, although some restrictions apply. For example, a volume +design response can only use the sum of the volume within the design area. A design response that +calculates the von Mises stress must use the maximum value of the stress within a region of the model. +(None of the operators are relevant when the Abaqus Topology Optimization Module calculates a +dynamic frequency design response.) The following design response operators are provided by the +Abaqus Topology Optimization Module: +• Minimum or maximum: The minimum or maximum value within the selected region. The +Abaqus Topology Optimization Module allows only the maximum operator for stress, contact +stress, and strain design responses. +• Sum: The sum of all the values within the selected area. The Abaqus Topology Optimization +Module allows only the sum operator for volume, weight, moment of inertia, and gravity design +responses. +Design responses for condition-based topology optimization +The Abaqus Topology Optimization Module provides strain energy and volume design responses for +condition-based topology optimization. +Strain energy +for linear models, where +The compliance of a structure is a measure of its overall flexibility or stiffness and is defined as the sum of +the strain energy of all the elements, +is the global stiffness matrix. Compliance is the reciprocal of stiffness, and minimizing the compliance is +equivalent to maximizing the global stiffness. If a load case is driven by forces or pressures, you should +choose to minimize the strain energy to maximize the global stiffness. However, if a load case is driven +by a thermal field, strain energy decreases when the optimization modifies the structure to make it softer. +As a result, you should always choose to maximize the strain energy because attempting to minimize the +strain energy can result in a stiff structure. In addition, you should always choose to maximize the strain +energy if prescribed displacements are applied to your model. +is the displacement vector and +Topology optimization considers the total strain energy for all of the elements; therefore, if you +choose strain energy as an objective function, you must apply the objective to the entire model. You +cannot use strain energy as a constraint in your optimization. +Abaqus/CAE Usage: +Optimization module: Task→condition-based topology task, Design +Response→Create: Single-term, Variable Strain energy +Volume +The volume is defined as the sum of the volume of the elements in the design area, +is the +element volume. During a topology optimization, the elements are scaled with the current relative density +defined in your Abaqus model. For most optimization problems, you must apply a volume constraint. +For example, if you are trying to minimize the strain energy (maximize the stiffness) and do not apply +a volume constraint, the Abaqus Topology Optimization Module simply fills the entire design area with +material. +, where +Abaqus/CAE Usage: +Optimization module: Task→condition-based topology task, Design +Response→Create: Single-term, Variable: Volume +Design responses for general topology optimization +The Abaqus Topology Optimization Module provides center of gravity, displacement, rotation, +eigenfrequency, moment of inertia, internal and reaction forces and moments, strain energy, volume, +and weight design responses for general topology optimization. +Center of gravity +You can use the center of gravity of a selected region as a design response in an optimization. You can +choose the center of gravity in the three principal directions: +When the Abaqus Topology Optimization Module calculates the center of gravity, the elements are scaled +with the current relative density defined in your Abaqus model. +For example, you might want to constrain the center of gravity in the Y-direction so that it remains +within a minimum and maximum range during the optimization. The design response can consider the +center of gravity of the whole model or a region of the model. +If you select a local coordinate system, the Abaqus Topology Optimization Module uses both +the direction of the axes and the position of the origin to recalculate the center of gravity. The +Abaqus Topology Optimization Module applies the global coordinate system if you do not select a local +coordinate system. +When the Abaqus Topology Optimization Module calculates the center of gravity, it treats shell +and membrane regions as three-dimensional regions by applying the thickness of the region. The +Abaqus Topology Optimization Module calculates the center of gravity using only the element types +that are supported by topology optimization. As a result, the center of gravity calculated by the +Abaqus Topology Optimization Module might not be the same as the center of gravity calculated by +Abaqus/Standard or Abaqus/Explicit; for example, if your model contains wire regions. +Abaqus/CAE Usage: +Optimization module: Task→general topology task, Design +Response→Create: Single-term, Variable: Center of gravity +Displacement and rotation +In most optimization problems you will use displacement and/or rotation to define your objective +function or constraints. For example, the maximum displacement of a vertex could be either an +objective or a constraint of an optimization. The performance of the optimization is improved if you +apply displacements and rotations to only vertices or to small regions. +In addition, performance is +improved if you assign regions that are used to define displacements or reactions as frozen regions +(the Abaqus Topology Optimization Module will not remove elements from frozen regions during the +optimization). +Table 13.2.1–1 lists the available displacement and rotation variables. +Abaqus/CAE Usage: +Optimization module: Task→general topology task, Design +Response→Create: Single-term, Variable: Displacement +Modal eigenfrequency analysis +Modal eigenvalues are the simplest dynamic responses in structural analysis. Typical uses of data from +an eigenfrequency analysis during a topology optimization include the following: +Table 13.2.1–1 Displacement and rotation variables for a general topology optimization. +Displacement +Rotation +i-direction +Absolute +Absolute in i-direction +• maximize the lowest eigenfrequencies, +• maximize a selected eigenfrequency, +• constrain an eigenfrequency to be higher or lower than a given value, +• maximize or minimize an eigenfrequency at a certain mode, and +• perform a bandgap optimization that force modes away from a certain frequency. +The Abaqus Topology Optimization Module supports two approaches for evaluating the +eigenfrequencies: +• single eigenfrequencies from modal analysis and +• the Kreisselmaier-Steinhauser formulation. +The Kreisselmaier-Steinhauser formulation is the more efficient of the two approaches and should +be used whenever possible. The only advantage of evaluating single eigenfrequencies is that you can use +the sum of the eigenfrequencies as a constraint in a general topology optimization. You cannot use the +sum of the eigenfrequencies from the Kreisselmaier-Steinhauser formulation as a constraint in a general +topology optimization. +When you are trying to maximize the lowest eigenfrequency, it is recommended that you consider +not only the first eigenfrequency but also at least the next two highest natural frequencies. During the +optimization, the various natural frequencies are weighted by their distance from the lowest natural +frequency—the closer a natural frequency approaches the first natural frequency during the optimization, +the more it is weighted. You should use the Kreisselmaier-Steinhauser eigenvalue formulation if you +are trying to maximize the lowest eigenfrequency or, in particular, if you are trying to maximize more +than one of the lowest eigenfrequencies. You do not need to use mode tracking if you are using the +Kreisselmaier-Steinhauser formulation to maximize the lowest eigenfrequency, but you should use mode +tracking for the higher modes because the modes might switch. For example, while the model is being +optimized, the frequency of the first mode is maximized and the second eigenmode can become the mode +with the lowest frequency. +Abaqus/CAE Usage: +Optimization module: Task→general topology task, Design +Response→Create: Single-term, Variable: Eigenfrequency +from modal analysis or Eigenfrequency calculated with +Kreisselmaier-Steinhauser formula +Moment of inertia +You can use a moment of inertia design response in an optimization to minimize the rotational inertia +about a selected axis. You can use the sum of the moment of inertia of the whole model or a region of +the model as an objective function or a constraint in a general topology optimization. +You can choose the moment of inertia in the three principal directions or the three principal planes: +If you select a local coordinate system, the Abaqus Topology Optimization Module uses the +direction of the axes to recalculate the center of gravity. The Abaqus Topology Optimization Module +applies the global coordinate system if you do not select a local coordinate system. +When the Abaqus Topology Optimization Module calculates the moment of inertia, it treats +shell and membrane regions as three-dimensional regions by applying the thickness of the region. +The Abaqus Topology Optimization Module calculates the moment of inertia using only the element +types that are supported by topology optimization. As a result, the moment of inertia calculated by the +Abaqus Topology Optimization Module might not be the same as the moment of inertia calculated by +Abaqus/Standard or Abaqus/Explicit; for example, if your model contains wire regions. +The moment of inertia with respect to any two orthogonal axes is zero if you have selected either +of the axes to be an axis of symmetry. +Abaqus/CAE Usage: +Optimization module: Task→general topology task, Design +Response→Create: Single-term, Variable: Moment of inertia +Internal forces and moments +You can use nodal internal forces and moments of the whole model or a region of the model as an +objective function or a constraint in a general topology optimization. +Table 13.2.1–2 lists the available nodal internal force and moment variables. +Table 13.2.1–2 Nodal internal force and moment variables for a general topology optimization. +Nodal internal +force +Nodal internal +moment +i-direction +Absolute +Absolute in i-direction +You cannot use a reference coordinate system with absolute internal force or with absolute internal +moment. Your structure must have stiffness in the direction of the force used in the optimization; +otherwise, the internal force will be zero in this direction. +Abaqus/CAE Usage: +Optimization module: Task→general topology task, Design +Response→Create: Single-term, Variable: Internal force +or Internal moment +Reaction forces and moments +Nodal reaction forces and moments can be used as a design response only in general topology +optimization. As with displacements, the performance of the optimization is improved if you apply +reaction forces or moments to only vertices or to small regions and assign those regions as frozen +regions (the Abaqus Topology Optimization Module will not remove elements during the optimization). +Table 13.2.1–3 lists the available nodal reaction force and moment variables. +Table 13.2.1–3 Nodal reaction force and moment variables for a general topology optimization. +Nodal reaction +force +Nodal reaction +moment +i-direction +Absolute +Absolute in i-direction +You cannot use a reference coordinate system with an absolute reaction force or with an absolute +reaction moment. Your structure must have stiffness in the direction of the force used in the optimization; +otherwise, the reaction force will be zero in this direction. +Abaqus/CAE Usage: +Optimization module: Task→general topology task, Design +Response→Create: Single-term, Variable: Reaction force +or Reaction moment +Strain energy +The compliance of a structure is a measure of its overall stiffness and is defined as the sum of the strain +energy of all the elements, +is the +global stiffness matrix. Compliance is the reciprocal of stiffness, and minimizing the compliance is +equivalent to maximizing the global stiffness. If a load case is driven by a thermal field, strain energy +decreases when the structure is made softer. As a result, attempting to minimize strain energy can result +in a stiff structure. In addition, you should always choose to maximize the strain energy if prescribed +displacements are applied to your model. +is the displacement vector and +for linear models, where +Topology optimization considers the total strain energy for all of the elements; therefore, if you +choose strain energy as an objective function, you must apply the objective to the entire model. +Abaqus/CAE Usage: +Optimization module: Task→general topology task, Design +Response→Create: Single-term, Variable: Strain energy +Volume +The volume is defined as the sum of the volume of all the elements in the design area, +, where +is the element volume. For most optimization problems, you must apply a volume constraint. For +example, if you are trying to minimize the strain energy (maximize the stiffness) and do not apply a +volume constraint, the Abaqus Topology Optimization Module simply fills the design area with material. +Abaqus/CAE Usage: +Optimization module: Task→general topology task, Design +Response→Create: Single-term, Variable: Volume +Weight +The weight is defined as the sum of the weight of all the elements in the design area, +is the element weight. The Abaqus Topology Optimization Module scales elements using the current +relative density. For most optimization problems, you must apply either a volume or a weight constraint. +Using weight instead of volume allows you to constrain the optimized model to a specified physical +weight. The Abaqus Topology Optimization Module uses only supported element types when calculating +the weight. +, where +Abaqus/CAE Usage: +Optimization module: Task→general topology task, Design +Response→Create: Single-term, Variable: Weight +Design responses for shape optimization +The Abaqus Topology Optimization Module provides eigenfrequency, stress, contact stress, strain, +nodal strain energy density, and volume design responses for shape optimization. Only a volume design +response can be used to define a constraint; all other design responses are used to define objective +functions. +Eigenfrequency from the Kreisselmaier-Steinhauser formulation +You should use the Kreisselmaier-Steinhauser formulation of the eigenvalues as an objective function in +a shape optimization if you are trying to maximize the first eigenfrequency or, in particular, if you are +trying to maximize more than one of the first eigenfrequencies. You do not need to use mode tracking if +you are using the Kreisselmaier-Steinhauser formulation of the eigenvalues. +Abaqus/CAE Usage: +Optimization module: Task→shape task, Design Response→Create: +Single-term, Variable: Eigenfrequency calculated with +Kreisselmaier-Steinhauser formula +Stress and contact stress +Equivalent stresses are the most commonly used objective function of a shape optimization. All of +the stress values that are calculated by the Abaqus Topology Optimization Module, whether nodal or +from Gauss points or elements, are interpolated to the nodes. For example, you can try to optimize +your model with an objective function that tries to minimize the maximum von Mises stresses in a +region with stress concentrations or tries to minimize contact pressure in a region with contact. The +Abaqus Topology Optimization Module considers only the maximum value of an equivalent stress +within a region. The Abaqus Topology Optimization Module issues warnings for nodes that do not have +the appropriate stress values. For example, if you select an objective response of contact stress, the +Abaqus Topology Optimization Module issues warnings about nodes of elements that are not in contact. +If your Abaqus model contains multiple load cases, the design response is evaluated by summing the +stress values from each load case. +You can choose from the following equivalent stresses: +• von Mises +• Maximum principal and absolute maximum principal +• Minimum principal and absolute minimum principal +• Second principal +• Beltrami +• Drucker Prager +• Galilei +• Kuhn +• Mariotte +• Sandel +• Sauter +• Tresca +You can choose from the following equivalent contact stresses: +• Contact stress pressure +• Total shear contact stress +• Shear contact stress in the 1-direction +• Shear contact stress in the 2-direction +• Total contact stress +You can create a design response that uses stress or contact stress only in shape optimization, and it can +be used only as an objective function. +Abaqus/CAE Usage: +Optimization module: Task→shape task, Design Response→Create: +Single-term, Variable: Stress or Contact stress +Strain +If your model is undergoing large deformations, a measure of the stress is not always a good indicator of +the model’s response. For example, a structure undergoing plastic deformation will, for an ideal plastic +material, experience a large constant stress over the plastic area. In these circumstances a measure of the +strain is a more reliable indicator of the model’s response. You can choose from the following equivalent +strains: +• Elastic +• Plastic +• Total (the sum of the elastic and plastic) +You can create a design response that uses strain only in shape optimization, and it can be used only as +an objective function. +Abaqus/CAE Usage: +Optimization module: Task→shape task, Design Response→Create: +Single-term, Variable: Strain +Nodal strain energy density +The nodal strain energy density, +representation of failure than stresses in nonlinear materials. +, is a local point-wise strain energy that can provide a better +Abaqus/CAE Usage: +Optimization module: Task→shape task, Design Response→Create: +Single-term, Variable: Strain energy density +Volume +Volume is the only constraint allowed for a shape optimization. The volume is defined as the sum of the +volume of all the elements in the design area, +is the element volume. +, where +For most optimization problems, you must apply a volume constraint to a region of your model. +For example, if you are trying to minimize the strain energy (maximize the stiffness) and do not apply a +volume constraint, Abaqus simply fills the design area with material. +Abaqus/CAE Usage: +Optimization module: Task→shape task, Design Response→Create: +Single-term, Variable: Volume +Operating on design responses +You can define a design response that is a combination of the single values generated by multiple design +responses; for example, you can add values or find the maximum of several values. You can also define a +design response that is the result of an operation on another design response; for example, the difference +between the value of the design response at different nodes. +For example, you can create two design responses that correspond to the displacement in the 1- +direction of two selected vertices. Alternatively, you can create a design response that is the difference +between the displacement in the 1-direction of two selected vertices. You can then define a constraint that +forces the design response to be close to zero. In effect, the constraint forces the two selected vertices to +move together in the 1-direction. +Abaqus/CAE Usage: +Optimization module: Design Response→Create: Combined-term +Additional references +• Bakhtiary, N., P. Allinger, M. Friedrich, F. Mulfinger, J. Sauter, O. Müller, and J. Puchinger, “A +New Approach for Size, Shape and Topology Optimization,” SAE International Congress and +Exposition, Detroit, Michigan, USA, February 26–29, 1996. +• Bendsøe, M. P., E. Lund, N. Ohloff, and O. Sigmund, “Topology Optimization - Broadening the +Areas of Application,” Control and Cybernetics, vol. 34, pp. 7–35, 2005. +• Bendsøe, M. P., and O. Sigmund, Topology Optimization: Theory, Methods and Applications, +Springer-Verlag, Berlin Heidelberg New York, 2003. +• Bendsøe, M. P., and O. Sigmund, “Material Interpolations in Topology Optimization,” Archive of +Applied Mechanics, vol. 69, pp. 635–654, 1999. +• Clausen, P. M., and C. B. W. Pedersen, Non-Parametric Large Scale Structural Optimization, +ECCM 2006 III European Conference on Computational Mechanics, Lisbon, Portugal, June 5–9, +2006. +• Cook, R. D., D. S. Malkus, and M. E. Plesha, Concepts and Applications of Finite Element +Analysis, John Wiley & Sons Inc., 1989. +• Hansen, L. V., “Topology Optimization of Free Vibrations of Fiber Laser Packages,” Structural and +Multidisciplinary Optimization, vol. 29(5), pp. 341–348, 2005. +• Olhoff, N., and J. Du, Topology Optimization of Vibrating Bi-Material Plate Structures with +Respect to Sound Radiation, IUTUAM Symposium on Topological Design Optimization of +Structures, Machines and Materials: Status and Perspectives, M. P. Bendsøe, N. Olhoff, and O. +Sigmund, eds., pp. 147–156, Springer, 2006. +• Pedersen, C. B. W., and P. Allinger, Industrial Implementation and Applications of Topology +Optimization and Future Needs, IUTUAM Symposium on Topological Design Optimization of +Structures, Machines and Materials: Status and Perspectives, M. P. Bendsøe, N. Olhoff, and O. +Sigmund, eds., pp. 147–156, Springer, 2006. +• Sigmund, O., and J. S. Jensen, “Systematic Design of Phononic Band Gap Materials and Structures +by Topology Optimization,” Philosophical Transactions of the Royal Society: Mathematical, +Physical and Engineering Sciences, vol. 361, pp. 1001–1019, 2003. +• Stolpe, M., and K. Svanberg, “An Alternative Interpolation Scheme for Minimum Compliance +Optimization,” Structural and Multidisciplinary Optimization, vol. 22, pp. 116–124, 2001. +• Svanberg, K., “The Method of Moving Asymptotes—A New Method for Structural Optimization,” +International Journal for Numerical Methods in Engineering, vol. 24, pp. 359–373, 1987. +13.2.2 +OBJECTIVES AND CONSTRAINTS +Product: Abaqus/CAE +References +• “Structural optimization: overview,” Section 13.1.1 +• “Creating objective functions,” Section 18.8 of the Abaqus/CAE User’s Manual +• “Creating constraints,” Section 18.9 of the Abaqus/CAE User’s Manual +• “Configuring geometric restrictions,” Section 18.10 of the Abaqus/CAE User’s Manual +• “Creating local stop conditions,” Section 18.11 of the Abaqus/CAE User’s Manual +Overview +For an optimization problem: +• an objective function defines the objective of the optimization; +• a constraint imposes limitations on the optimization and defines a feasible design; +• geometric restrictions impose limitations on the topology or shape of the structure that can be +generated by the optimization; and +• stop conditions define when an optimization task is considered complete. +Objective functions +Objective functions define the objective of the optimization. An objective function is a single scalar +value that is formulated from a set of design responses. For example, if the design responses are defined +from the strain energy of the nodes in a region, the objective function could minimize the sum of the +design responses; i.e., minimize the sum of the strain energy, in effect maximizing the stiffness of the +region. +An optimization problem can be stated as: +where +is the objective function that depends on the state variables, +, and the design variables, +. +The formula for the objective function that tries to minimize +design responses can be stated as: +where each design response, +objective function that tries to maximize +, is given a weight, +, and a reference value, +. The formula for the +design responses can be stated as: +For a topology optimization the default +is 1.0. +for a shape optimization the default +reference +The default weighting factor +reference value is calculated by the +value is 0.0; +Abaqus Topology Optimization Module. For the most common optimization problems you do not +need to change the default values of the weighting factor and the reference value. However, in some +cases you may have to change the weighting factor to balance the effect of an objective function that +is dominating the optimization. You should be aware that changing the weighting factor can have a +significant impact on the final design. In addition, a design response that is dominant at the start of the +optimization may have less effect as the Abaqus Topology Optimization Module modifies your model. +An objective function that tries to minimize the maximum design response is an important +optimization formulation. During each design cycle the Abaqus Topology Optimization Module first +determines which of the set of weighted design responses has the maximum value and then tries to +minimize that design response. In many problems, minimizing the maximum design response provides +a satisfactory solution because it reduces the maximum of a number of design responses. For example, +if your design responses are defined from the stress in multiple regions of your model, minimizing the +maximum design response attempts to minimize the stress in the region that is exhibiting the maximum +stress. The formula can be stated as: +The design responses provided with the Abaqus Topology Optimization Module are listed in +“Design responses,” Section 13.2.1. +Defining the target of an objective function +The target of an objective function can be minimized or maximized. Alternatively, the target of an +objective function can be set to minimize the maximum, such that the design response targets the +maximum value, and the objective attempts to minimize that maximum value. In all cases, the weighting +and reference values of the design responses are accounted for. +Abaqus/CAE Usage: +Optimization module: Objective Function→Create: Target +Constraints +As outlined in the previous section, an optimization problem can be stated as: +where +Constraints, +design variables: +is the objective function that depends on the state variables, +, can be applied to the optimization problem, and constraints, +, and the design variables, +. +, can be applied to the +where +, where +and +. In addition, +is an expression for the layout of the design variables, such as manufacturability, +is the design response that is constrained by the value +and +is the constraint on the design variables. +The Abaqus Topology Optimization Module can arrive at a solution that optimizes the objective +function; however, if the constraints are not satisfied, the result of the optimization may not be a feasible +design. A constraint is based on a design response and, similar to a design response, is formulated +from a single scalar value. Most optimizations have constraints that prevent the optimization from +arriving at a trivial solution. For example, if you are trying to maximize the stiffness of a structure, +the Abaqus Topology Optimization Module will simply fill the entire design area if you do not apply any +constraints. However, if you apply a weight constraint that limits the weight to 50% of its initial value, +the Abaqus Topology Optimization Module is forced to seek an optimum solution that both optimizes +the stiffness objective and satisfies the weight constraint. You can apply only volume constraints to both +topology optimization and to shape optimization; you cannot use volume as an objective function. You +cannot apply multiple constraints of the same type, such as volume, to the whole model or to a single +region. +Abaqus/CAE Usage: +Optimization module: Constraint→Create +Applying constraints to regions +You can apply different constraints to different regions of your model. +In addition, those regions +can have different material properties or a material property can vary within a region. When the +Abaqus Topology Optimization Module calculates the design response, it considers varying material +properties within the region. You cannot apply multiple volume constraints to the whole model or to a +single region. +Geometric restrictions +Geometric restrictions are constraints that are applied directly to the design variables. Geometric +restrictions allow you to model design limitations and manufacturing limitations. +Defining a frozen area +You can specify that a region within the optimization region is excluded from the optimization by freezing +the region. For example, you could exclude a circular shaft that forms a bearing surface or a boss that is +used to attach the structure to a rigid surface. You must freeze regions that are used to apply prescribed +conditions. To simplify this operation, you can request that the Abaqus Topology Optimization Module +automatically freeze regions that are used to apply prescribed conditions and loads when you create an +optimization process. +Abaqus/CAE Usage: +Optimization module: Geometric Restriction→Create: Frozen area +Specifying minimum and maximum member size +In most cases you should try to avoid the generation of thin trusses in the structure by defining a +minimum member size. However, the Abaqus Topology Optimization Module cannot ensure that the +optimized structure will not contain regions with a diameter that is smaller than the minimum member +size. The minimum member size must be larger than the average element edge length. The maximum +member size must be larger than twice the element length; otherwise, the optimization algorithm may +experience issues with element connectivity. A coarse mesh and a fine mesh lead to an optimization +with the topological equivalent result if you specify the same minimum member size for both cases. +The Abaqus Topology Optimization Module will not generate a thin region where prescribed conditions +have been applied to the structure. Removing material from these regions may result in the structure +collapsing. +If your structure will be cast, you may want to avoid the generation of overly thick parts by +specifying a region with a maximum member size. The optimization process will avoid creating a +thick region by generating several thinner regions. You do not need to specify both a maximum and a +minimum member size. The Abaqus Topology Optimization Module assumes the value that you enter +for the maximum member size also applies to the minimum member size and will generate trusses of +the specified size. The combination of a maximum member size constraint with a restraint that imposes +a pull direction, such as a moldable or stampable manufacturing constraint, is allowed only for a general +topology optimization. (The “pull direction” is the direction in which the two halves of a mold separate +or the direction in which a stamping tool moves.) +Computational time increases significantly when you specify regions with a minimum or maximum +member size. Therefore, you should apply the member size restrictions only to regions where thin or +thick members must be avoided. You should run an optimization without member size restrictions to +identify such regions. +Abaqus/CAE Usage: +Optimization module: Geometric Restriction→Create: Member size +Applying manufacturing restrictions +The topology optimization process always creates a structural layout that satisfies the objective function +and the constraints; however, the design may be impossible to create using standard manufacturing +techniques, such as casting and forging. You can apply geometric restrictions that force the topology +optimization process to consider only designs that can be manufactured. For example, when you are using +topology optimization you can force the Abaqus Topology Optimization Module to create a castable +shape that can be extracted from a mold or a stampable shape that can be created with a tool and die. +Maintaining a moldable structure +In cases where bending and torsion loads are applied, topology optimization is likely to generate a +model with hollow areas or with undercuts that cannot be manufactured. You can prevent the topology +optimization from generating cavities and undercuts by specifying the following: +• A forgeable structure that can be removed from the forging die, as shown in Figure 13.2.2–1. +Pull +direction +Back +plane +Figure 13.2.2–1 A forgable part. +• A moldable structure that can be removed from two halves of a mold, as shown in Figure 13.2.2–2. +Pull +directions +Center +plane +Pull direction +(normal to every surface) +Figure 13.2.2–2 A moldable part. +In contrast, Figure 13.2.2–3 illustrates parts with a cavity and an undercut that are not moldable. +Pull +directions +Pull +directions +Center +plane +Center +plane +Figure 13.2.2–3 Cavities and undercuts prevent a part from being moldable. +Abaqus/CAE Usage: +Optimization module: Geometric Restriction→Create: Demold control; +Demold technique, Demolding with a central plane +Optimization module: Geometric Restriction→Create: Demold control; +Demold technique, Demolding at the region surface +Optimization module: Geometric Restriction→Create: Demold +control; Demold technique, Forging +Maintaining a stampable structure +You can specify that the structure is to be manufactured by a stamping process. +If the optimization +process removes one element from the structure, it also removes all elements positioned either behind or +in front of the element (with respect to the pull direction), as shown in Figure 13.2.2–4. +Elements removed +during optimization +Pull +directions +Center +plane +Figure 13.2.2–4 A stampable structure. +The rate at which the Abaqus Topology Optimization Module modifies the element properties should +not be set too high if the stamping restriction is activated in a condition-based topology optimization; +otherwise, supports or trusses generated by the optimization may become unattached from the rest of the +structure. +Abaqus/CAE Usage: +Use the following option to create a stamping geometric restriction in a +topology optimization: +Optimization module: Geometric Restriction→Create: Demold +control; Demold technique, Stamping +Use the following option to create a stamping geometric restriction in a shape +optimization: +Optimization module: Geometric Restriction→Create: Stamp control +the +Use +at which +to +Abaqus Topology Optimization Module modifies the element properties: +following +specify +option +rate +the +the +Optimization module: Task→Create: Advanced , Size of +increment for volume modification +Specifying a symmetric structure +Introducing symmetry constraints into your model can significantly increase the speed at which +the Abaqus Topology Optimization Module calculates the optimized structure. You can use the +Abaqus Topology Optimization Module to apply the following symmetry constraints: +• Symmetry about an axis or plane (reflection symmetry) +• Symmetry about a point +• Rotational symmetry +• Cyclic symmetry (replication of an area with a given distance) +You can apply a symmetry restriction to unstructured meshes or to tetrahedron meshes +in a topology optimization. The elements should be approximately the same size because the +resulting symmetry is based on the resolution of the coarsest part of the mesh. +In addition, the +Abaqus Topology Optimization Module may fail to create the symmetric conditions if the difference in +the element size is too large. +To define symmetry for a shape optimization, the Abaqus Topology Optimization Module assembles +nodes that are approximately symmetric into a symmetry group (normally there are two symmetric nodes +in each symmetry group). The Abaqus Topology Optimization Module then determines the master node +of the symmetry group and calculates the design displacements of the client nodes in such a way that +they move symmetrically to the plane of the master node. +If you are performing a topology optimization, your meshed Abaqus model does not have to be +symmetric before the optimization starts. Conversely, if you are performing a shape optimization, +your meshed Abaqus model should be symmetric before the optimization starts to allow the +Abaqus Topology Optimization Module to identify symmetric nodes and maintain their symmetry when +the surface nodes are moved. +Abaqus/CAE Usage: +Optimization module: Geometric Restriction→Create: Planar +symmetry, Point symmetry, Rotational symmetry, or Cyclic symmetry +Applying additional restrictions during a shape optimization +the displacement of +Shape optimization determines +to +homogenize the stress on the surface and satisfy the objective function and any constraints. The +Abaqus Topology Optimization Module does not couple the displacement of neighboring nodes; +each of the design nodes can move independently of the other design nodes. For example, during the +optimization a planar surface can develop into a nonplanar free-form surface. By coupling the design +nodes you can force the optimization to maintain the regularity of a plane. +each surface node +in an effort +Coupling conditions restrict the range of solutions for the system and reduce the optimization +potential. In addition, defining the appropriate coupling conditions can be very time consuming. To +simplify your optimization, you should start with an optimization with as few restrictions as possible and +only a few coupling conditions and introduce additional coupling conditions only if they are required. +You can apply additional restrictions while the Abaqus Topology Optimization Module is moving +surface nodes during a shape optimization: +• The optimized shape can be manufactured by a tool on a lathe cutting into the model along a specified +direction. +• The optimized shape can be manufactured by a tool drilling into the model along a specified +direction. The hole created by the tool is symmetric about the axis of the tool. In addition, the tool +can be withdrawn from the hole. +• Selected faces in the optimized shape can slide along each other and/or cannot penetrate each other. +• Nodes are restricted to move: +– along a specified vector, +– a specified distance either inward or outward (shrinkage or growth), +– along a specified direction, +– only along selected degrees of freedom, and +– only in the direction of applied loads. +Abaqus/CAE Usage: +Optimization module: Geometric Restriction→Create: Turn control, +Drill control, Penetration check, Slide region control, or Vector +Combining geometric constraints +Each geometric constraint that you apply reduces the possibility of Abaqus arriving at an optimized +solution. In addition, if you apply too many geometric restrictions, the solution that Abaqus generates +may not be the most optimal solution available. Therefore, you should start by allowing Abaqus to +perform an optimization with no geometric restrictions applied or with only a limited number. After you +have studied the results of the unrestricted, or less-restricted, optimization, you should apply only the +restrictions that are required to solve the problem. +You can combine geometric constraints; however, only certain combinations are permissible. +Abaqus processes geometrical constraints in the following order: +• Minimum member size +• Symmetry constraints +• Manufacturing constraints +• Maximum member size +Applying one constraint may weaken the effect of another constraint. For example, you cannot define +symmetry about a plane in conjunction with a demold pull direction that is not parallel with the axis or +plane of symmetry. +The following manufacturing restriction combinations are permissible: +• You can combine symmetry about a plane with a pull direction provided the pull direction is +perpendicular or parallel to the plane of symmetry. +• You can combine rotational symmetry with a pull direction provided the pull direction is parallel to +the axis of rotation. +• You can combine two symmetries about a plane provided the planes are perpendicular. +• When you first run a condition-based topology optimization, you should not use a combination +of a maximum member size and a pull direction because the optimization may not converge, +depending on the finite element mesh. When you are confident the optimization will converge, you +can introduce this combination of geometric constraints. +• You can specify a minimum member size that is greater than the maximum member size. Abaqus +first processes the minimum member size requirement and creates relatively thick supports. The +thick supports are subsequently divided into smaller parallel members when Abaqus processes the +maximum size requirement. +Stop conditions +Stop conditions are examined after each design cycle and determine whether an optimization should +end because the maximum number of design cycles has been reached or because the optimization has +converged on an optimal solution. The Abaqus Topology Optimization Module provides both global and +local stop conditions; however, local stop conditions are rarely required. +Global stop conditions +The global convergence stop condition defines the maximum number of design cycles that should be +performed. To limit the number of design cycles, you must define a global stop condition for each +optimization task. The default value for the maximum number of design cycles depends on the type of +optimization, as shown in Table 13.2.2–1. +Abaqus/CAE Usage: +Job module: Optimization→Create: Maximum cycles +Local stop conditions +Local stop conditions indicate if a general topology optimization has converged on an optimal solution. +Local stop conditions apply to the displacements or stresses in a region of your model and define when +the goals of an optimization have been reached. A local stop condition compares a single scalar value of +displacement or equivalent stress to a reference value. The single scalar value can be either the maximum +Table 13.2.2–1 Default maximum number of design cycles. +Optimization Type +Default maximum number +of design cycles +Condition-based topology optimization +General topology optimization +Shape optimization +15 +50 +10 +or minimum value over a region or the sum of all the values. The reference value can be taken from the +value of the single scalar value after the previous iteration or after the first iteration. In addition, you can +modify the reference value by a fixed amount or by a percentage. For example, you can specify a local +stop condition that ends the optimization if the sum of the displacements within a region is smaller than +1% of the sum of the displacements after the first optimization cycle. You can define one or two local +stop conditions, and you can specify if either or both (default) of the local stop conditions must be met +for the Abaqus Topology Optimization Module to end the optimization. +Examples of local stop conditions include the following: +• If you have specified that the displacement or stress should be minimized (or maximized), a local +stop condition can end the optimization if the value of the displacement or stress increases (or +decreases) after an optimization cycle. +• When the optimization approaches the optimum solution, you can expect only small changes in the +value of the displacement or stress. A local stop condition can end the optimization if the relative +change in the displacement or stress falls below a tolerance limit after an optimization cycle. +• When the optimization approaches the optimum solution, you can expect only small changes in +the sum of the displacements and, therefore, only minor modifications to the model. A local stop +condition can end the optimization if the change in the sum of the displacements falls below a +tolerance limit after an optimization cycle. You can use the sum of the displacements as a stop +condition for optimizations with and without constraints. In addition, this stop condition is suitable +for a variety of objective functions, such as stress or frequency. +Abaqus/CAE Usage: +Optimization module: Stop Condition→Create +13.2.3 +CREATING Abaqus OPTIMIZATION MODELS +Product: Abaqus/CAE +References +• “Structural optimization: overview,” Section 13.1.1 +• “Understanding optimization,” Section 18.3 of the Abaqus/CAE User’s Manual +Overview +For each design cycle the optimization process: +• generates new material and element properties during topology optimization; +• modi��es nodal coordinates during shape optimization; +• sends the modified model to an Abaqus analysis; and +• reads the results of the analysis. +Preparing the Abaqus model +You should take care to ensure that your Abaqus model is supported by structural optimization. Any +restrictions imposed by the use of structural optimization, such as the supported element types, apply +only to the design area; regions outside the design area do not play a role in the optimization. +• You must ensure that your Abaqus model can be analyzed and produces the expected mechanical +results before you attempt to optimize your model. +• You should account for nonlinearities only if your model is truly nonlinear; the optimization will +be significantly less expensive computationally if your Abaqus model is linear. You may want to +ensure that an optimization of a linear version of your model produces reasonable results before you +introduce geometric or material nonlinearities. +• An optimization takes multiple design cycles to complete, and the time required to reach an +optimized solution can be significant. As a result, you must configure your Abaqus model to +minimize computational time; for example, by removing small details that are not important to the +optimization. +• The Abaqus Topology Optimization Module does not support the use of parts and assemblies in the +Abaqus input file. When you run an optimization task, the Abaqus Topology Optimization Module +generates a flattened input file that does not use parts and assemblies. +• The Abaqus Topology Optimization Module reads data from the output database (.odb) file. The +Abaqus Topology Optimization Module requests data only from the end of each step. To minimize +the size of the output database file, you should also request data only from the end of each step. +Support for analysis types +The following Abaqus analysis types are supported by both topology and shape optimization: +• Static stress/displacement, general analysis +• Static stress/displacement, linear perturbation analysis +• Extract natural frequencies and modal vectors +Support for geometric nonlinearities +You can specify that geometric nonlinearity should be accounted for only during static +stress/displacement analyses. +Elements that have limited stiffness, such as elements with hyperelastic material properties, can +deform excessively during topology optimization in a nonlinear analysis. This deformation can lead to +an adverse effect on the convergence and result in the termination of the analysis. You should be aware +of this potential issue when applying topology optimization using hyperelastic materials. +Support for multiple load cases +If your model is undergoing a sequence of loads, you can significantly reduce the computational cost by +defining a multiple load case analysis within a single step. +Support for acceleration loading +General topology optimization supports prescribed acceleration loading from +• gravity, +• rotational body forces, and +• centrifugal forces. +Coriolis forces are not supported. +Support for contact during the optimization +You can avoid contact in optimized regions of your model by defining geometric restrictions, such as +casting or minimum member size restrictions. In some cases, you cannot specify the exact boundary +conditions early in the design phase. +In addition, nonlinear boundary conditions, such as contact +definitions, can change if the Abaqus Topology Optimization Module changes the topology of the +model. +The optimization process is more efficient if you create an Abaqus model with the appropriate +contact definitions and allow Abaqus to calculate the contact. The contact conditions are included in +the optimization through the forces at the nodes and the stresses in the elements, and both topology and +shape optimization permit contact conditions in the Abaqus model. +You can define a contact surface directly on the edge of the design space in topology optimization. +However, if the design edge belongs to a contact surface in shape optimization, you must invert the shape +optimization algorithm by entering a negative growth scale factor. You may encounter convergence +difficulties in your Abaqus model if you have a complex contact problem or if the optimization results +in large changes in the model. +Restrictions on an Abaqus model used for topology optimization +Topology optimization determines +the optimal material distribution in the design space, +given the prescribed conditions applied to the model along with the objective function and +constraints. Your optimization must apply appropriate constraints and restrictions; otherwise, the +Abaqus Topology Optimization Module can extensively alter the topology of the component. The +resolution of the structure that has been optimized with topology optimization is very dependent on the +discretization. A fine mesh produces a structure with a higher resolution than a coarse mesh; however, +it will also substantially increase the processing time required. You must determine the appropriate +compromise between structural resolution and processing time. +During topology optimization the Abaqus Topology Optimization Module modifies the material +definition of the elements in the design area. As a result, you must provide the initial density of the +materials in the design area, even if it is not required by the Abaqus analysis. +Restrictions on an Abaqus model used for shape optimization +Abaqus performs a shape optimization by modifying the boundaries or surfaces of a component. The +optimization uses the stress condition to calculate new coordinates for nodes on the surface of the +component and then adjusts the underlying mesh accordingly. The mesh quality must be sufficient to +ensure that the analysis results are mostly unchanged by the movement of the surface nodes. High stress +gradients must not be present within an element. +When the Abaqus Topology Optimization Module is performing a shape optimization on a shell +structure, it optimizes the form of the shell structure and not its thickness. The nodal position along shell +edges can be modified; however, Abaqus does not modify the shell definition. +Supported materials in the design area +The material models supported by structural optimization in the elements in the design area depend on the +type of optimization—condition-based topology optimization, general topology optimization, or shape +optimization. +Materials supported by condition-based topology optimization +Condition-based topology optimization in Abaqus supports linear elastic, plastic, and hyperelastic +material models. +Support for linear elastic material models +The following linear elastic material models are supported by condition-based topology optimization: +• Linear elastic materials with isotropic behavior. +• Linear elastic materials with fully anisotropic behavior. +• Linear elastic materials with orthotropic behavior. All of the behavior models are supported, except +for orthotropic shear behavior for warping elements and coupled and uncoupled traction behavior +for cohesive elements. +Support for plastic material models +Metal plasticity material properties—the plastic part of the material model for elastic-plastic materials +that use the Mises or Hill yield surface—are supported by condition-based topology optimization. +Isotropic hardening is supported; however, cyclic loading is not supported—each material point can be +unloaded only once and should not become elastoplastic again. +Support for hyperelastic material models +All of the hyperelastic material models are supported by condition-based topology optimization, except +for the Marlow material model and the hyperelastic material models with test data. +Support for temperature and field variable dependency +Condition-based topology optimization supports materials that have temperature and field variable +dependency. +Materials supported by general topology optimization +General topology optimization in Abaqus supports linear elastic, plastic, and hyperelastic material +models. +Support for linear elastic material models +The following linear elastic material models are supported by general topology optimization: +• Linear elastic materials with isotropic behavior. +• Linear elastic materials with fully anisotropic behavior. +• Linear elastic materials with orthotropic behavior. All of the behavior models are supported, except +for orthotropic shear behavior for warping elements and coupled and uncoupled traction behavior +for cohesive elements. +Support for plastic material models +Metal plasticity material properties—the plastic part of the material model for elastic-plastic materials +that use the Mises or Hill yield surface—are supported by general topology optimization. +Isotropic +hardening is supported; however, cyclic loading is not supported—each material point can be unloaded +only once and should not become elastoplastic again. +Support for hyperelastic material models +All of the hyperelastic material models are supported by general topology optimization, except for the +Marlow material model and the hyperelastic material models with test data. +Support for temperature and field variable dependency +General topology optimization supports materials that have temperature and field variable dependency. +Material support in shape optimization +Shape optimization in Abaqus supports all of the Abaqus material models. +Support for coordinate systems +In most cases, you will use the same coordinate system to define your model and the optimization task. +However, the Abaqus Topology Optimization Module allows you refer to a different coordinate system +when you are defining a design response. +Supported element types +The Abaqus elements that are supported as design elements by topology and shape optimization are +listed in Table 13.2.3–1 through Table 13.2.3–4. The tables also list the Abaqus elements that support +the reaction and internal force design responses. Unsupported elements are ignored during optimization +and remain unchanged. Structural optimization does not place any restrictions on the type of elements +that you use outside the design area. +Supported two-dimensional solid elements +Topology optimization (both condition-based and general) and shape optimization support +two-dimensional solid elements listed in Table 13.2.3–1. +the +Table 13.2.3–1 Supported two-dimensional solid elements. +CPE31, CPE3H, CPE41 , CPE4H, CPE4I, CPE4IH, CPE4R1 , +CPE4RH, +CPE6H, CPE6M, CPE6MH +CPE81, CPE8H, CPE8R1 , CPE8RH +CPS31 , CPS41 , CPS4I, CPS4R1, CPS61 , CPS6M, CPS6MT, CPS81. +CPS8R1 +CPEG3, CPEG3H, CPEG4, CPEG4H, CPEG4I, CPEG4IH, CPEG4R, +CPEG4RH, CPEG6, CPEG6H, CPEG6M, CPEG6MH, CPEG8, +CPEG8H, CPEG8R, CPEG8RH +CPE3T, CPE4T, CPE4HT, CPE4RT, CPE4RHT, CPE6MT, +CPE6MHT, CPE8T, CPE8HT, CPE8RT, CPE8RHT +CPS3T, CPS4T, CPS4RT, CPS8T, CPS8RT +CPEG3T, CPEG3HT, CPEG4T, CPEG4RT, CPEG4RHT, CPEG6MT, +CPEG6MHT, CPEG8T, CPEG8HT, CPEG8RHT +1 Can include reaction and internal force design responses. +Supported three-dimensional solid elements +Topology optimization (both condition-based and general) and shape optimization support the three- +dimensional solid elements listed in Table 13.2.3–2. +Table 13.2.3–2 Supported three-dimensional solid elements. +C3D41, C3D4H, C3D81 +C3D61, C3D6H +C3D8H, C3D8I, C3D8IH, C3D8R1 , C3D8RH +C3D101 , C3D10H, C3D10M, C3D10MH +C3D151 , C3D15H +C3D201 , C3D20H, C3D20R1 , C3D20RH +C3D4T, C3D6T, C3D8T, C3D8HT, C3DHRT, C3D8RHT, C3D10MT, +C3D10MHT, C3D20T, C3D20HT, C3D20RT, C3D20RHT +1 Can include reaction and internal force design responses. +Supported axisymmetric solid elements +Topology optimization (both condition-based and general) and shape optimization support +axisymmetric solid elements listed in Table 13.2.3–3. +the +Table 13.2.3–3 Supported axisymmetric solid elements. +CAX31, CAX3H, CAX41 , CAX4H, CAX4I, CAX4IH, CAX4R1, +CAX4RH +CAX81, CAX8H, CAX8R1 , CAX8RH +CGAX3, CGAX3H, CGAX4, CGAX4H, CGAX4R, CGAX4RH, +CGAX8, CGAX8H, CGAX8R, CGAX8RH +CAX3T, CAX4T, CAX4HT, CAX4RT, CAX4RHT, CAX8T, +CAX8HT, CAX8RT, CAX8RHT +CGAX3T, CGAX3HT, CGAX4T, CGAX4HT, CGAX4RT, +CGAX4RHT, CGAX8T, CGAX8HT, CGAX8RT, CGAX8RHT +1 Can include reaction and internal force design responses. +Additional supported elements +Table 13.2.3–4 lists the general membrane, three-dimensional conventional shell, and beam elements +that are supported by optimization. +Table 13.2.3–4 Additional supported elements +General membrane elements (topology +and shape optimization) +M3D31, M3D41, M3D4R1, +M3D61, M3D81 , M3D8R1 +Three-dimensional conventional shell +elements (topology optimization only) +STRI3, S3, S3R, STRI65, S4, +S4R, S4R5, S8R, S8R5, S8RT +Three-dimensional conventional shell +elements (shape optimization only) +STRI31 , S31, S3R1 , S41, S4R1 , +S8R1 +Beam elements (shape optimization only) +B212 , B21H2, B312 , B31H2 +1 Can include reaction and internal force design responses. +2 You can include beam elements in shape optimization only to define a +neighboring component that is used to restrict the movement of nodes in the +optimized region. +13. +Optimization Techniques +14. +Eulerian Analysis +Eulerian analysis +14.1 +Eulerian analysis +• “Eulerian analysis,” Section 14.1.1 +• “Defining Eulerian boundaries,” Section 14.1.2 +• “Eulerian mesh motion,” Section 14.1.3 +• “Defining adaptive mesh refinement in the Eulerian domain,” Section 14.1.4 +14.1.1 +EULERIAN ANALYSIS +Products: Abaqus/Explicit Abaqus/CAE +References +• “Eulerian surface definition,” Section 2.3.5 +• “Eulerian elements,” Section 32.14.1 +• *EULERIAN SECTION +• *INITIAL CONDITIONS +• *SURFACE +• “Creating Eulerian sections,” Section 12.13.3 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Defining a material assignment field,” Section 16.11.10 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• Chapter 28, “Eulerian analyses,” of the Abaqus/CAE User’s Manual +Overview +In a traditional Lagrangian analysis nodes are fixed within the material, and elements deform as the +material deforms. Lagrangian elements are always 100% full of a single material, so the material +boundary coincides with an element boundary. +By contrast, in an Eulerian analysis nodes are fixed in space, and material flows through elements +that do not deform. Eulerian elements may not always be 100% full of material—many may be partially +or completely void. The Eulerian material boundary must, therefore, be computed during each time +increment and generally does not correspond to an element boundary. The Eulerian mesh is typically a +simple rectangular grid of elements constructed to extend well beyond the Eulerian material boundaries, +giving the material space in which to move and deform. If any Eulerian material moves outside the +Eulerian mesh, it is lost from the simulation. +Eulerian material can interact with Lagrangian elements through Eulerian-Lagrangian contact; +simulations that include this type of contact are often referred to as coupled Eulerian-Lagrangian (CEL) +analyses. This powerful, easy-to-use feature of Abaqus/Explicit general contact enables fully coupled +multi-physics simulation such as fluid-structure interaction. +Applications +Eulerian analyses are effective for applications involving extreme deformation, up to and including +In these applications, traditional Lagrangian elements become highly distorted and lose +fluid flow. +accuracy. Liquid sloshing, gas flow, and penetration problems can all be handled effectively using +Eulerian analysis. Eulerian-Lagrangian contact allows the Eulerian materials to be combined with +traditional nonlinear Lagrangian analyses. +An example of using Eulerian analysis for a severe deformation analysis is discussed in “Rivet +forming,” Section 2.3.1 of the Abaqus Example Problems Manual; using coupled Eulerian-Lagrangian +contact for a fluid-structure interaction application is illustrated in “Impact of a water-filled bottle,” +Section 2.3.2 of the Abaqus Example Problems Manual. +Eulerian volume fraction +The Eulerian implementation in Abaqus/Explicit is based on the volume-of-fluid method. In this method, +material is tracked as it flows through the mesh by computing its Eulerian volume fraction (EVF) within +each element. By definition, if a material completely fills an element, its volume fraction is one; if no +material is present in an element, its volume fraction is zero. +Eulerian elements may simultaneously contain more than one material. If the sum of all material +volume fractions in an element is less than one, the remainder of the element is automatically filled with +“void” material. Void material has neither mass nor strength. +Material interfaces +Volume fraction data are computed for each Eulerian material in an element. Within each time +increment, the boundaries of each Eulerian material are reconstructed using these data. The interface +reconstruction algorithm approximates the material boundaries within an element as simple planar +facets (the Eulerian method is implemented only for three-dimensional elements). This assumption +produces a simple, approximate material surface that may be discontinuous between neighboring +elements. Therefore, accurate determination of a material’s location within an element is possible only +for simple geometries, and fine grid resolution is required in most Eulerian analyses. +The discontinuities in an Eulerian material surface can lead to physically unrealistic configurations +when visualizing the results of an Eulerian analysis. Abaqus/CAE can apply a nodal averaging algorithm +to estimate a more realistic, continuous surface during visualization. For more information on visualizing +the material interfaces in an Eulerian model, see “Viewing output from Eulerian analyses,” Section 28.7 +of the Abaqus/CAE User’s Manual. +Eulerian section definition +An Eulerian section definition lists all of the materials that may appear within an Eulerian element. Void +material is automatically included in this list. +The material list supports an optional material instance name. Material instance names are required +to uniquely identify materials that you use more than once. Repeated materials are useful, for example, +in mixing simulations where the motion of a material interface is to be computed: the water in a tank +could be divided by creating water material instances named “water_left” and “water_right,” and the +evolution of the interface between these materials could be simulated. +By default, all Eulerian elements are initially filled with void material, regardless of the section +assignment. You must introduce nonvoid material into your Eulerian mesh using an initial condition +. +Eulerian mesh deformation +The Eulerian time incrementation algorithm is based on an operator split of the governing equations, +resulting in a traditional Lagrangian phase followed by an Eulerian, or transport, phase. This formulation +is known as “Lagrange-plus-remap.” During the Lagrangian phase of the time increment nodes are +assumed to be temporarily fixed within the material, and elements deform with the material. During the +Eulerian phase of the time increment deformation is suspended, elements with significant deformation +are automatically remeshed, and the corresponding material flow between neighboring elements is +computed. +At the end of the Lagrangian phase of each time increment, a tolerance is used to determine which +elements are significantly deformed. This test improves performance by allowing those elements with +little or no deformation to remain inactive during the Eulerian phase. The inactive elements typically +have no impact on the visualization of an Eulerian analysis; however, plotting an Eulerian mesh using a +very large deformation scale factor may reveal slight deformations for elements within the deformation +tolerance. +Eulerian material advection +As material flows through an Eulerian mesh, state variables are transferred between elements by +advection. The variables are assumed to be linear or constant in each old element, then these values are +integrated over the new elements after remeshing. The new value of the variable is found by dividing +the value of each integral by the material volume or mass in the new element. +Second-order advection +Second-order advection assumes a linear distribution of the variable in each old element. To construct +the linear distribution, a quadratic interpolation is constructed from the constant values at the integration +points of the middle element and its adjacent elements. A trial linear distribution is found by +differentiating the quadratic function to find the slope at the integration point of the middle element. +The trial linear distribution in the middle element is limited by reducing its slope until its minimum and +maximum values are within the range of the original constant values in the adjacent elements. This +process is referred to as flux limiting and is essential to ensure that the advection is monotonic. +Second-order advection is used by default, and it is recommended for all problems, ranging from +quasi-static to transient dynamic shock. +Input File Usage: +Abaqus/CAE Usage: +*EULERIAN SECTION, ADVECTION=SECOND ORDER +The second-order advection method is used by default in Abaqus/CAE. +First-order advection +First-order advection assumes a constant value of the variable in each old element. This method is simple +and computationally efficient; however, it tends to diffuse sharp gradients over time. Therefore, this +technique should be used only as a computationally efficient alternative for quasi-static simulations. +Input File Usage: +*EULERIAN SECTION, ADVECTION=FIRST ORDER +Abaqus/CAE Usage: +The first-order advection method cannot be specified in Abaqus/CAE. +Reducing the stable time increment based on the advection speed +The stable time increment size is adjusted automatically to prevent material from flowing across more +than one element in each increment. When the material velocity approaches the speed of sound (for +example, in simulations involving blast and shocks), further restrictions on the time increment size may +be needed to maintain accuracy and stability. You can specify a flux limit ratio to restrict the stable time +increment size such that material can flow across only a fraction of an element in each increment. The +default flux limit ratio is 1.0, and recommended values range from 0.1 to 1.0. +Input File Usage: +Abaqus/CAE Usage: +*EULERIAN SECTION, FLUX LIMIT RATIO=maximum ratio +The flux limit ratio cannot be modified in Abaqus/CAE. +Initial conditions +You can apply initial conditions to Eulerian nodes and elements in the same way that they are used +for Lagrangian nodes and elements. Initial stress, temperature, and velocity are common examples. In +addition, most Eulerian analyses require the initialization of Eulerian material. +By default, all Eulerian elements are initially void. You can use initial conditions to fill Eulerian +elements with one or more of the materials listed in the Eulerian section definition. By selectively filling +elements, you can create the initial shape of each Eulerian material. +To fill an Eulerian element, you must define an initial volume fraction for each available material +instance. Material is filled until a volume fraction of 1.0 is reached; any excess material is ignored. The +initial conditions apply only at the beginning of an analysis; during the analysis the materials deform +according to the applied loads, and the volume fractions are recalculated accordingly. +*INITIAL CONDITIONS, TYPE=VOLUME FRACTION +Load module: Create Predefined Field: Step: Initial: choose Other for the +Category and Material Assignment for the Types for Selected Step +Abaqus/CAE Usage: +Input File Usage: +Boundary conditions +By default, Eulerian material can flow freely into and out of the Eulerian domain through mesh +boundaries. You can constrain degrees of freedom at Eulerian nodes to restrict material flow. For +example, you can define typical fluid “stick” or “sliding” walls using constraints normal and/or +tangential to the boundary. Since Eulerian nodes are automatically repositioned during the Eulerian +transport phase, you cannot apply prescribed displacement boundary conditions to them. +You can use prescribed velocity or acceleration conditions on Eulerian nodes to control material +flow. Prescribed velocity or acceleration is implemented in an Eulerian frame, so material velocity +will reach the prescribed value as the material passes the Eulerian node. If velocity is directed outward +at an Eulerian mesh boundary, either by prescribed condition or naturally as a result of dynamic +equilibrium, material may flow out of the Eulerian domain. This material is lost from the simulation, +and corresponding decreases in total mass and energy will occur. +Similarly, if velocity is directed inward at a boundary, inflow of material into the Eulerian domain +will occur. When materials flow into an element through a boundary face, the material content and the +state of each inflowing material are equal to that which presently exists within the element. For example, +if a boundary element contains 60% hot water and 40% cold air and the interface normal is parallel to +the boundary face, inflow velocity will introduce a mixture of 60% hot water and 40% cold air. In this +case corresponding increases in total mass and energy will occur. +You can also define inflow and outflow conditions at an Eulerian domain boundary, as described in +“Defining Eulerian boundaries,” Section 14.1.2. +Loads +You can apply loads to Eulerian nodes, elements, and faces in the same way as to their Lagrangian +counterparts. Eulerian loads act in an Eulerian frame: they affect Eulerian material as it passes the point +of load application. +Material options +You can define material properties for Eulerian analysis in the same way as for Lagrangian analysis. +Liquids and gases can be modeled using equation of state materials . Anisotropic materials are not supported because of inaccuracies introduced to +orientation data during material transport. Brittle cracking is not supported because the failure mode +is anisotropic. Hyperelastic materials can be used in an Eulerian analysis, but due to inaccuracies +introduced to the deformation gradient during material transport, these materials might not fully recover +their original configuration after loads are removed; the same inaccuracies also affect user-defined +materials. The low-density foam material model (“Low-density foams,” Section 22.9.1) is not +supported. +Eulerian analysis allows materials to undergo extreme strain without the mesh distortion limitations +of Lagrangian analysis. Therefore, it is especially important to define your material behavior through +the entire strain range, which often requires definition of a failure behavior. +Isotropic material failure is supported using a damage variable to characterize the failure level. +Element deletion is suppressed for Eulerian sections because undamaged material may flow into “failed” +elements. Shear failure models are not supported. +Rayleigh mass proportional damping is not supported. +Elements +The Eulerian method is implemented in the multi-material element type EC3D8R and the multi-material +thermally coupled element type EC3D8RT. The underlying mechanical response formulation of these +elements is based on the Lagrangian C3D8R element with extensions to allow multiple materials and +to support the Eulerian transport phase. The formulation applies the same strain to each material in the +element, then allows the stress and other state data to evolve independently within each material. These +stresses are combined using volume fraction data to create element averaged values, which are integrated +to obtain nodal forces. Similarly, the thermal response formulation for the thermally coupled element is +based on the Lagrangian element C3D8RT with the extension to allow multiple materials with different +thermal properties and to support temperature advection. All the materials have the same temperature, +and the thermal properties (such as thermal conductivity and thermal capacitance) are volume averaged +before being used in solving one single heat transfer equation for the multi-material model. +Element averaged values of other state data are computed similarly for output purposes. +The Eulerian EC3D8R and EC3D8RT elements require eight nodes. Degenerate elements are not +supported. The Eulerian method is not implemented for two-dimensional elements. Axisymmetry can +be simulated using a wedge-shaped mesh and symmetry boundary conditions. +By default, the Eulerian elements use viscous hourglass control. Hourglass control is disabled by +default for incompressible liquids modeled using equation of state material types. These choices can be +modified using section controls . +Constraints +Since Eulerian nodes are automatically repositioned during the Eulerian transport phase, you cannot use +Eulerian nodes in Lagrangian modeling features such as elements, connectors, and constraints. However, +constraints between Eulerian materials and Lagrangian parts can be modeled using tied contact interfaces. +Interactions +Eulerian material instances interact with each other with a sticky behavior. This sticking occurs because +of the kinematic assumption that a single strain field is applied to all materials within an element. Tensile +stress can be transmitted across an interface between two Eulerian materials, and no slip occurs at these +interfaces. This Eulerian-to-Eulerian contact behavior can be reasonable in some situations, such as in +a simulation of a lead bullet penetrating a steel plate. Ablation of the bullet surface against the steel is +captured by the sticky behavior within the Eulerian elements at the bullet-steel interface. Relative motion +along this interface will occur only due to shearing of the lead material. +Eulerian-to-Eulerian contact occurs by default in an Eulerian analysis; you do not need to define +contact interactions between Eulerian materials. +More complex contact interactions can be simulated when one of the contacting bodies is modeled +using Lagrangian elements. This powerful capability supports applications such as fluid-structure +interaction, where an Eulerian fluid contacts a Lagrangian structure. +is an extension of general contact +The implementation of Eulerian-Lagrangian contact +in +Abaqus/Explicit. The general contact property models and defaults apply to Eulerian-Lagrangian +contact . For example, by default, +tensile stresses are not transmitted across an Eulerian-Lagrangian contact interface, and the interface +friction coefficient is zero. Specifying automatic contact for an entire Eulerian-Lagrangian model allows +for interactions between all Lagrangian structures and all Eulerian materials in the model. You can +also use Eulerian surfaces to create material-specific +interactions or to exclude contact between particular Lagrangian surfaces and Eulerian materials. +Input File Usage: +Use both of the following options to define contact between all Lagrangian +bodies and all Eulerian materials: +*CONTACT +*CONTACT INCLUSIONS, ALL EXTERIOR +Use the following options to include or exclude contact between particular +Lagrangian surfaces and Eulerian materials: +*CONTACT +*CONTACT INCLUSIONS +Lagrangian_surface, Eulerian_surface +*CONTACT EXCLUSIONS +Lagrangian_surface, Eulerian_surface +Abaqus/CAE Usage: +Use the following option to define contact between all Lagrangian bodies and +all Eulerian materials: +Interaction module: Create Interaction: General contact (Explicit): +Included surface pairs: All* with self +Use the following options to include contact between particular Lagrangian +surfaces and Eulerian materials: +Interaction module: Create Interaction: General contact (Explicit): +Included surface pairs: Selected surface pairs: Edit, select the +Lagrangian surface in the left column and the Eulerian material instance in the +right column, then click the arrows to transfer them to the list of included pairs +Use the following options to exclude contact between particular Lagrangian +surfaces and Eulerian materials: +Interaction module: Create Interaction: General contact (Explicit): +Excluded surface pairs: Edit, select the Lagrangian surface in the left +column and the Eulerian material instance in the right column, then click +the arrows to transfer them to the list of excluded pairs +Formulation of Eulerian-Lagrangian contact +The Eulerian-Lagrangian contact formulation is based on an enhanced immersed boundary method. +In this method the Lagrangian structure occupies void regions inside the Eulerian mesh. The contact +algorithm automatically computes and tracks the interface between the Lagrangian structure and the +Eulerian materials. A great benefit of this method is that there is no need to generate a conforming mesh +for the Eulerian domain. In fact, a simple regular grid of Eulerian elements often yields the best accuracy. +If the Lagrangian body is initially positioned inside the Eulerian mesh, you must make sure that +the underlying Eulerian elements contain void after material initialization. During the analysis the +Lagrangian body pushes material out of the Eulerian elements that it passes through, and they become +filled with void. Similarly, Eulerian material flowing toward the Lagrangian body is prevented from +entering the underlying Eulerian elements. This formulation ensures that two materials never occupy +the same physical space. +If the Lagrangian body is initially positioned outside the Eulerian mesh, at least one layer of void +Eulerian elements must be present at the Eulerian mesh boundary. This creates a free surface on the +Eulerian material inside the Eulerian mesh boundary and provides a source for void material to replace +Eulerian material that is driven out of interior elements. Several layers of void elements are typically +used above free surfaces to allow simulation of crater formation and backsplashing before this material +leaves the Eulerian domain. +Eulerian-Lagrangian contact also supports failure and erosion in the Lagrangian body. Lagrangian +element failure can open holes in a surface through which Eulerian material may flow. When modeling +erosion of a solid Lagrangian body, the interior faces of the solid body must be included in the +contact surface definition . +Eulerian-Lagrangian contact constraints are enforced using a penalty method, where the default +penalty stiffness parameter is automatically maximized subject to stability limits. +Eulerian-Lagrangian contact supports thermal +interactions when using coupled temperature- +displacement Eulerian element EC3D8RT in a dynamic coupled thermal-stress analysis. However, gap +radiation and gap conductance as a function of clearance are not supported. +Output +The set of element output variables EVF gives the Eulerian volume fraction for each material in the +Eulerian section definition, including void. It is important to request output for EVF in all Eulerian +analyses because visualization of Eulerian material boundaries is based on the material volume fractions. +Material-specific Eulerian field output variables are distinguished by appending material names to +the base field name. For example, if you request output variable S (stress components) in an Eulerian +analysis involving material instances named “steel” and “tin,” you will see results for individual material +stresses named “S_steel” and “S_tin.” +Several volume fraction averaged field data are also available for output. For example, output +variable SVAVG gives a single value of stress for each element computed as a volume fraction average +of stress over all materials present in the element. Use of these volume fraction averaged output data has +the advantage of substantially reducing the size of the output database for the case where several materials +are defined in the Eulerian section. See “Abaqus/Explicit output variable identifiers,” Section 4.2.2, for +a complete list of Eulerian-specific output variables. +Output variables EVF and SVAVG are included in the PRESELECT variable list when Eulerian +elements appear in the model. +You can also request integrated volume (VOLEUL) and integrated mass (MASSEUL) over a +particular Eulerian element set. These output variables are material specific and are distingushed by +having the material names appended to the variable name. +Limitations +Eulerian analyses are subject to the following limitations: +• Boundary conditions: You cannot apply prescribed nonzero displacement boundary conditions to +Eulerian nodes. +• Lagrangian attachments: You cannot attach Lagrangian elements to Eulerian nodes. Use tied contact +interfaces instead. +• Constraints: You cannot apply Lagrangian constraints (MPCs, etc.) to Eulerian nodes. Use tied +contact interfaces instead. +• Materials: Materials with orientation (anisotropic, etc.) are not supported for Eulerian elements. +Brittle cracking and shear failure models are also not supported. Rayleigh mass proportional +damping is not supported. +• Elements: The Eulerian formulation is implemented only for EC3D8R and EC3D8RT elements. +• Element import: Eulerian elements are not available for import. +• Double-sided contact: Penetration of Eulerian material through the contact interface can occur in +some cases involving Eulerian material contacting Lagrangian shell or membrane elements. This +type of contact introduces complexity because the sign of the outward normal direction must be +determined on the fly as material approaches the Lagrangian element; contact with either side of +the element is potentially allowable. You should simplify the contact problem wherever possible by +using Lagrangian solid elements instead of shell or membrane elements, since the outward normal +direction at solid element faces is unique. For example, if a model involves Eulerian material +flowing around a rigid Lagrangian obstacle, mesh the obstacle with solid elements rather than shell +elements. +• Contact penetration: In some cases Eulerian material may penetrate through the Lagrangian contact +surface near corners. This penetration should be limited to an area equal to the local Eulerian +element size. Penetration can be minimized by refining the Eulerian mesh or adding a fillet to +the Lagrangian mesh with radius equal to the local Eulerian element size. +• Contact +types: Eulerian-Lagrangian contact does not support Lagrangian beam elements, +Lagrangian pipe elements, Lagrangian truss elements, or analytical rigid surfaces. Thermal contact +is also not supported. +• Contact import: Import of the Eulerian-Lagrangian contact states is not supported. +• Thermal contact: Gap radiation and gap conductance as a function of clearance are not supported. +• Contact output: Contact variables are output only for the Lagrangian side of Eulerian-Lagrangian +interfaces. +• Surface loads: You cannot use the Eulerian material surface type for general surface loading. +However, distributed loads such as pressure can be applied to surfaces defined on Eulerian element +faces. +• Mass scaling: You cannot apply mass scaling to Eulerian elements. +• Heat transfer: Use coupled temperature-displacement EC3D8RT Eulerian elements to model a +fully coupled thermal-stress analysis. Adiabatic conditions are assumed in Eulerian materials when +EC3D8R elements are used. +• Output: Total strain (LE) is not available for Eulerian elements in field or history output, but it can +be accessed via the utility routine VGETVRM. +• Subcycling: You cannot include Eulerian elements in subcycling zones. +Input file template +The following example illustrates a coupled Eulerian-Lagrangian analysis of a Lagrangian boat floating +on Eulerian water. A conforming mesh is assumed, so Eulerian material initialization is achieved by +whole element filling. Material-specific interactions between the Lagragian body and the Eulerian +materials are implemented: a contact interaction is defined between the boat and water, but contact +between the boat and air is ignored. Output is requested for Eulerian volume fractions, Eulerian +element-averaged stress, and material stress. +*HEADING +… +*ELEMENT, TYPE=C3D8R, ELSET=BOAT_ELSET +element definitions for Lagrangian boat +*ELEMENT, TYPE=EC3D8R, ELSET=ALL_EULERIAN +element definitions for whole Eulerian mesh +*ELSET, NAME=AIR_ELSET +data lines giving Eulerian elements that are initially filled with air +*ELSET, NAME=WATER_ELSET +data lines giving Eulerian elements that are initially filled with water +** +*MATERIAL, NAME=AIR +material definition for air +*MATERIAL, NAME=WATER +material definition for water +** +*EULERIAN SECTION, ELSET=ALL_EULERIAN +AIR +WATER +** +*INITIAL CONDITIONS, TYPE=VOLUME FRACTION +AIR_ELSET, AIR, 1.0 +WATER_ELSET, WATER, 1.0 +*INITIAL CONDITIONS, TYPE=STRESS, GEOSTATIC +data lines to define water pressure due to gravity +** +*SURFACE, NAME=WATER_SURFACE, TYPE=EULERIAN MATERIAL +WATER +*SURFACE, NAME=BOAT_SURFACE +BOAT_ELSET +** +*STEP +*DYNAMIC, EXPLICIT +*DLOAD +data lines to define gravity load +** +*CONTACT +*CONTACT INCLUSIONS +BOAT_SURFACE, WATER_SURFACE +** +*OUTPUT, FIELD +*ELEMENT OUTPUT +EVF, SVAVG, PEEQVAVG +*END STEP +Additional references +• Benson, D. J., “Computational Methods in Lagrangian and Eulerian Hydrocodes,” Computer +Methods in Applied Mechanics and Engineering, vol. 99, pp. 235–394, 1992. +• Benson, D. J., “Contact in a Multi-Material Eulerian Finite Element Formulation,” Computer +Methods in Applied Mechanics and Engineering, vol. 193, pp. 4277–4298, 2004. +• Peery, J. S., and D. E. Carroll, “Multi-Material ALE methods in Unstructured Grids,” Computer +Methods in Applied Mechanics and Engineering, vol. 187, pp. 591–619, 2000. +14.1.2 +DEFINING EULERIAN BOUNDARIES +Products: Abaqus/Explicit Abaqus/CAE +References +• “Eulerian analysis,” Section 14.1.1 +• “Eulerian elements,” Section 32.14.1 +• *EULERIAN BOUNDARY +• “Defining an Eulerian boundary condition,” Section 16.10.21 of the Abaqus/CAE User’s Manual +Overview +In an Eulerian analysis you can define independent inflow and outflow conditions at an Eulerian boundary. +An Eulerian boundary condition: +• can be used to control the flow of material into the Eulerian domain; +• can be used to define a pressure field at the boundary of an Eulerian domain; +• can be used to apply a nonreflecting boundary condition at the truncated artificial boundary to +simulate an infinite domain; and +• is associated with a surface defined on the Eulerian mesh boundary where inflow or outflow occurs. +Defining the Eulerian boundary +Eulerian boundaries must be defined at surfaces on the Eulerian mesh boundary. You cannot define +multiple Eulerian boundaries at the same surface. +Input File Usage: +*EULERIAN BOUNDARY +surface name +Abaqus/CAE Usage: +Load module: Create Boundary Condition: Category: Other, +Types for Selected Step: Eulerian boundary: select region +Defining the inflow condition +You can use the inflow condition to control the flow of material into the Eulerian domain. +Free inflow +If no Eulerian boundary is defined, material can flow into the Eulerian domain freely; and the material +content and the state of each inflow material are equal to that which presently exists within the element. +If an Eulerian boundary is defined, free inflow is the default inflow condition. +Input File Usage: +Abaqus/CAE Usage: +*EULERIAN BOUNDARY, INFLOW=FREE +Eulerian boundary condition editor: Flow type: Inflow, Inflow: Free +No inflow +You can specify an Eulerian boundary where no inflow can occur—no material or void can flow into the +Eulerian domain through the specified boundary. The normal component of the velocity is set to zero if +the velocity is directed inward at the boundary, while the tangential component of the velocity remains +unchanged. +Input File Usage: +Abaqus/CAE Usage: +*EULERIAN BOUNDARY, INFLOW=NONE +Eulerian boundary condition editor: Flow type: Inflow, Inflow: None +Void inflow +You can also specify a boundary through which inflow can occur but the influx volume contains only +void. Due to the inflow of void, an Eulerian domain that is initially completely full of material might +become partially full during the analysis. +Input File Usage: +Abaqus/CAE Usage: +*EULERIAN BOUNDARY, INFLOW=VOID +Eulerian boundary condition editor: Flow type: Inflow, Inflow: Void +Defining the outflow condition +The outflow condition can be used to simulate an unbounded domain by reducing reflection at the outflow +boundary or to prescribe a pressure field at the boundary. +Free outflow +If no Eulerian boundary condition is specified, material can flow out of the Eulerian domain freely; and +the material content and the state of each outflow material are equal to that which presently exists within +the element. If an Eulerian boundary condition is defined, free outflow is the default behavior if the void +inflow condition is specified at the same surface. +Input File Usage: +Abaqus/CAE Usage: +*EULERIAN BOUNDARY, OUTFLOW=FREE +Eulerian boundary condition editor: Flow type: Outflow, Outflow: Free +Nonreflecting outflow +A nonreflecting outflow condition can be used in boundary value problems defined in unbounded +domains or problems in which the region of interest is small in size compared to the surrounding +medium. Like the infinite element formulation described in “Using solid medium infinite elements in +dynamic analyses” in “Infinite elements,” Section 28.3.1, the nonreflecting outflow condition introduces +additional normal and shear tractions on the domain boundary that are proportional to the normal and +shear components of the velocity of the boundary. These boundary damping constants are chosen to +minimize the reflection of dilatational and shear wave energy back into the finite element mesh. This +condition does not provide perfect transmission of energy out of the mesh except in the case of plane +body waves impinging orthogonally on the boundary in an isotropic medium. However, it usually +provides acceptable modeling for most practical cases. An exception is the case when significant +material transport occurs through the boundary, in which case this condition is not suitable to be used. +Input File Usage: +Abaqus/CAE Usage: +*EULERIAN BOUNDARY, OUTFLOW=NONREFLECTING +Eulerian boundary condition editor: Flow type: Outflow, +Outflow: Nonreflecting +Equilibrium outflow +Equilibrium outflow is another outflow condition that can effectively reduce spurious reflection +at artificial outflow boundaries in unbounded domains. +It is assumed that the stress is zero-order +continuous across the element faces on the boundary. Traction is applied to these element faces to +balance the nodal forces created by the stress in the boundary elements. This condition is usually +applied at the outflow boundary where the pressure distribution is unknown. +Input File Usage: +Abaqus/CAE Usage: +*EULERIAN BOUNDARY, OUTFLOW=NONUNIFORM PRESSURE +Eulerian boundary condition editor: Flow type: Outflow, +Outflow: Equilibrium +Zero-pressure outflow +It is common in flow problems to specify a zero pressure at the outlet of the flow. Since the normal +traction on the boundary contains the contribution from both the pressure and the shear stress, the +natural boundary condition, also known as the “do-nothing condition,” is not sufficient to provide such +a condition if the shear behavior of the flow is also considered. The zero pressure outflow condition +applies a traction that counteracts the shear contribution and, thus, generates a uniformly distributed +pressure field on the boundary. You can apply a distributed surface load on the same boundary to specify a nonzero +pressure. This is the default outflow condition if the inflow condition is not specified. +Input File Usage: +Abaqus/CAE Usage: +*EULERIAN BOUNDARY, OUTFLOW=ZERO PRESSURE +Eulerian boundary condition editor: Flow type: Outflow, +Outflow: Zero pressure +Using Eulerian boundaries in restart analyses +You can define a new Eulerian boundary in a restart analysis, but you cannot specify a void inflow +condition at this boundary. In addition, you cannot change the inflow condition at an existing Eulerian +boundary to the void inflow condition in a restart analysis. +14.1.3 +EULERIAN MESH MOTION +Products: Abaqus/Explicit Abaqus/CAE +References +• “Eulerian surface definition,” Section 2.3.5 +• “Eulerian analysis,” Section 14.1.1 +• *EULERIAN MESH MOTION +• *EULERIAN SECTION +• *SURFACE +• “Defining an Eulerian mesh motion boundary condition,” Section 16.10.22 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +In a traditional Eulerian analysis, material flows through an Eulerian mesh that is fixed in space. Since it +is stationary, the Eulerian mesh must be large enough to enclose the entire trajectory of interest. In some +simulations, such as a tumbling liquid-filled bottle, this trajectory can be long, requiring a large Eulerian +mesh whose elements are mostly empty. The Eulerian mesh motion feature allows the Eulerian mesh to +move in space, following, expanding, and contracting to enclose a target object. This can greatly reduce +mesh size and, hence, simulation cost. Mesh motion can also simplify modeling by ensuring that the +entire trajectory of interest, which may be unpredictable, is indeed covered by the Eulerian mesh. +Activating mesh motion +You can independently activate mesh motion for each Eulerian section in a model. The motion applies +to all of the elements in the section. +Input File Usage: +Abaqus/CAE Usage: +*EULERIAN MESH MOTION, ELSET=name +Load module: BC→Create, Category: Other, Types for Selected Step: +Eulerian mesh motion: select an Eulerian part instance +Computing mesh motion +The motion of the Eulerian mesh is computed using an internally constructed bounding box that encloses +the entire Eulerian section. The bounding box has six degrees of freedom: translation of the box center +and scaling of each of the three box dimensions. +The bounding box is constructed in a local coordinate system. Its six degrees of freedom are also +defined in this local system. The local coordinate directions remain fixed in space during the simulation. +If no local coordinate system is specified, the local system coincides with the global system. +Input File Usage: +*EULERIAN MESH MOTION, ORIENTATION= name +Abaqus/CAE Usage: +Load module: Eulerian mesh motion editor: Bounding Box +Csys: Edit or Create +Defining the target object +You use a surface to define the target object that the Eulerian mesh will follow. By default, the Eulerian +mesh bounding box (and, hence, the Eulerian mesh) moves to enclose the surface at all times, subject +to any constraints specified on the mesh motion. If the surface type is Lagrangian, the Eulerian mesh +bounding box moves to enclose the surface nodes . If the surface type is Eulerian, +the Eulerian mesh bounding box moves to enclose the Eulerian material named in the surface definition +. +Figure 14.1.3–1 Mesh motion, where the target object is the Lagrangian bottle. +Figure 14.1.3–2 Mesh motion, where the target object is the Eulerian liquid. +The Eulerian mesh may not fully enclose the target object due to: +• constraints on the bounding box motion; +• a misalignment of the bounding box local orientation; +• a mismatch between the shape of the mesh boundary and the bounding box (i.e., the Eulerian mesh +is not a rectangular box); or +• an inadequately sized or positioned initial Eulerian mesh. +Input File Usage: +Abaqus/CAE Usage: +*EULERIAN MESH MOTION, SURFACE=name +Load module: Eulerian mesh motion editor: Object to Follow: name +Constraining Eulerian mesh motion +Once the motion of the bounding box is computed, the translations and scaling factors are applied directly +to the Eulerian mesh. Several types of constraints are available to restrict these motions. Conflicts +between competing constraints are resolved in the following order of precedence: +1. constraining the center and faces of the mesh bounding box, +2. limiting the rate of mesh motion, +3. turning off mesh contraction, +4. centering the mesh bounding box on the target’s center of mass or bounding box center, +5. preventing mesh expansion or contraction outside the scale factor limits, +6. limiting aspect ratio changes, and +7. maintaining a buffer between the mesh and target. +Constraining mesh expansion and contraction +By default, the Eulerian mesh may expand or contract by an unlimited amount in each direction, as +necessary to contain the target object. This can be undesirable: expansion creates large Eulerian elements +that crudely approximate the shape of Eulerian objects, while contraction leads to decreased stable time +increment sizes. +You can apply constraints to limit the expansion and contraction independently in each local +direction by specifying lower and/or upper limits on the bounding box size scale factors. For example, +a maximum scale factor of 1.0 constrains the box dimension to be no larger than 1.0 times the initial +box dimension, effectively prohibiting any expansion, while a minimum scale factor of 0.5 limits the +box dimension to be no smaller than half its initial dimension. +Input File Usage: +*EULERIAN MESH MOTION +scaling factor limits +Abaqus/CAE Usage: +Load module: Eulerian mesh motion editor: Axis n: +Expansion ratio, Contraction ratio +Preventing mesh contraction +An additional control is available to prevent incremental contraction. If specified, the box dimensions +may increase, but at no point during the simulation may they decrease below their current values. This +option prevents oscillations in mesh size during simulations where the mesh is nominally expanding. +Input File Usage: +Abaqus/CAE Usage: +*EULERIAN MESH MOTION, CONTRACT=NO +Load module: Eulerian mesh motion editor: Controls: +toggle off Allow mesh contraction +Constraining mesh translation +You can specify the motion of the center of the bounding box to be either free (default) or fixed in each +of the local directions. You can also independently specify free (default) or fixed normal motion of the +positive and negative box faces in the local coordinate directions. +Input File Usage: +Abaqus/CAE Usage: +*EULERIAN MESH MOTION +, +face constraints +center constraints +Load module: Eulerian mesh motion editor: Axis n: Center position, +Positive plane position, Negative plane position +Centering the mesh bounding box +If the motion of the mesh bounding box is unconstrained, the center of the bounding box is aligned +with the center of a box enclosing the target surface. If the target surface fragments or “emits” low +density material, aligning the center of the bounding box with the center of mass of the target may be +advantageous. +Input File Usage: +Use the following option to center the mesh bounding box on the center of mass +of the target object: +*EULERIAN MESH MOTION, CENTER=MASS +Use the following option to center the mesh bounding box on the center of the +target object’s bounding box: +*EULERIAN MESH MOTION, CENTER=BOUNDING BOX +The center of the mesh bounding box cannot be changed in Abaqus/CAE; the +center of the mesh bounding box corresponds to the center of the target object’s +bounding box. +Abaqus/CAE Usage: +Controlling the mesh buffer around the target object +The mesh moves to maintain a buffer of Eulerian elements between the target object and the bounding +box. By default, this buffer is equal to twice the maximum Eulerian element size in the mesh. You can +specify the buffer size as a multiple of the maximum Eulerian element size. You can also specify that +the initial spacing between the target object and the mesh (set to zero where the target initially extends +outside of the mesh) is used to compute the buffer size. +Input File Usage: +Use the following option to use a buffer equal to the initial spacing between the +target object and the mesh: +*EULERIAN MESH MOTION, BUFFER=INITIAL +Use the following option to specify a buffer as a multiple of the maximum +Eulerian element size: +Abaqus/CAE Usage: +*EULERIAN MESH MOTION, BUFFER= value +Load module: Eulerian mesh motion editor: Controls: Buffer +size: Initial or Specify +Limiting aspect ratio changes +Excessive mesh motion in a single direction can produce badly shaped Eulerian elements. An optional +parameter is available to limit the change in maximum aspect ratio of the bounding box. By default, this +limit is 10. When the aspect ratio limit is reached, motion in one local direction will induce motion in +the other directions to preserve the box aspect ratio. This aspect ratio limit applies to the bounding box +dimensions, not the underlying Eulerian element dimensions. +Input File Usage: +Abaqus/CAE Usage: +*EULERIAN MESH MOTION, ASPECT RATIO MAX= value +Load module: Eulerian mesh motion editor: Controls: Aspect +ratio limit: value +Limiting the rate of mesh motion +The Eulerian mesh must not be allowed to move abruptly. A hard limit on its motion is given by the +advective Courant condition, which prohibits mesh velocity larger than the material wave speed. In +addition you can limit the mesh velocity to a multiple of the maximum velocity in the target object. By +default, this limit is set to 1.01. +Input File Usage: +Abaqus/CAE Usage: +*EULERIAN MESH MOTION, VMAX FACTOR= value +Load module: Eulerian mesh motion editor: Controls: Mesh +velocity factor: value +Ignoring fragments of Eulerian material +When the target object is an Eulerian material, tiny fragments can drive excessive mesh motion. You can +specify a minimum Eulerian volume fraction below which Eulerian material is ignored during the mesh +motion calculation. This can be particularly useful for impact calculations, where tiny fragments of an +impacting, splattering projectile may be allowed to leave the Eulerian domain. The default minimum +volume fraction is 0.5. +Input File Usage: +Abaqus/CAE Usage: +*EULERIAN MESH MOTION, VOLFRAC MIN= value +Load module: Eulerian mesh motion editor: Controls: Volume +fraction threshold: value +Limitations +An Eulerian mesh can move only according to the available Eulerian mesh motion options. You cannot +apply prescribed displacement boundary conditions to Eulerian nodes. +DEFINING ADAPTIVE MESH REFINEMENT IN THE EULERIAN DOMAIN +EULERIAN ADAPTIVE MESH REFINEMENT +Product: Abaqus/Explicit +References +• “Eulerian analysis,” Section 14.1.1 +• *ADAPTIVE MESH REFINEMENT +• *EULERIAN SECTION +• *EULERIAN MESH MOTION +Overview +The adaptive mesh refinement feature: +• can refine elements locally inside an Eulerian mesh; +• allows the user to define various criteria for refinement; +• can remove the refinement automatically once the refinement criteria are no longer met; and +• is available for Eulerian elements only. +Adaptive mesh refinement +In a traditional Eulerian analysis the topology of the Eulerian mesh does not change during the analysis. +Although the Eulerian mesh motion feature allows the Eulerian mesh to move in space to cover areas of +interest, its ability to create a nonuniformly refined mesh that changes with time is limited. The adaptive +mesh refinement feature can locally refine the mesh by subdividing elements identified by user-defined +criteria. This refinement can be removed automatically during the analysis once the criteria are no longer +satisfied. This feature offers great savings in computational cost over an equivalent uniformly refined +mesh. +Activating adaptive mesh refinement +You can independently activate adaptive mesh refinement for each Eulerian section in a model. The +feature applies to all of the elements in the section, and these elements are equally divided into eight +subelements when refined. +Input File Usage: +*ADAPTIVE MESH REFINEMENT, ELSET=name +Setting the refinement limit +When adaptive mesh refinement occurs, more elements are added to the Eulerian mesh. You can set a +limit on the maximum increase in the number of elements. The default ratio of the increment is 8.0. +Input File Usage: +*ADAPTIVE MESH REFINEMENT, RATIO=maximum increase in +number of elements/original number of elements +Defining refinement criteria +You must specify at least one refinement criterion. An element will be selected for refinement if any of the +criteria are met. To reduce the numerical artifacts at the mesh transition boundaries (where a fine mesh +meets a coarse mesh), the elements adjacent to the selected elements are also refined. The elements are +coarsened once the refinement criteria are no longer met. Table 14.1.4–1 lists all the refinement criteria +available in Abaqus/Explicit. +Table 14.1.4–1 Refinement criteria. +Refinement criteria description +Refinement +criteria label +User-specified values +Refine elements containing material interfaces +VF +Refine elements that are in contact with +Lagrangian bodies +Refine elements in which plastic deformation +occurs. Not supported for the critical state (clay) +plasticity model. +CONT +PEEQ +Refine elements near a sharp density gradient +DENSITY +N/A +N/A +Critical value of the equivalent plastic +strain +Critical value of the density gradient, +computed as the ratio between the change +of density across element faces and the +density of the material inside the element +Input File Usage: +*ADAPTIVE MESH REFINEMENT, +refinement criteria label, value of the criteria +15. +Particle Methods +Smoothed particle hydrodynamic analyses +15.1 +Smoothed particle hydrodynamic analyses +• “Smoothed particle hydrodynamic analysis,” Section 15.1.1 +• “Finite element conversion to SPH particles,” Section 15.1.2 +SMOOTHED PARTICLE HYDRODYNAMIC ANALYSIS +SPH ANALYSIS +Product: Abaqus/Explicit +References +• “Particle elements,” Section 28.5.1 +• *SOLID SECTION +• *SECTION CONTROLS +• *INITIAL CONDITIONS +Overview +Smoothed particle hydrodynamics (SPH) is a numerical method that is part of the larger family of +meshless (or mesh-free) methods. For these methods you do not define nodes and elements as you +would normally define in a finite element analysis; instead, only a collection of points are necessary +to represent a given body. In smoothed particle hydrodynamics these nodes are commonly referred to +as particles or pseudo-particles. +Smoothed particle hydrodynamics is a fully Lagrangian modeling scheme permitting the +discretization of a prescribed set of continuum equations by interpolating the properties directly at a +discrete set of points distributed over the solution domain without the need to define a spatial mesh. +The method’s Lagrangian nature, associated with the absence of a fixed mesh, is its main strength. +Difficulties associated with fluid flow and structural problems involving large deformations and free +surfaces are resolved in a relatively natural way. The method has received substantial theoretical +support since its inception (Gingold and Monaghan, 1977), and the number of publications related to +the method is now very large. A number of references are listed below. +At its core, the method is not based on discrete particles (spheres) colliding with each other in +compression or exhibiting cohesive-like behavior in tension as the word particle might suggest. Rather, +it is simply a clever discretization method of continuum partial differential equations. In that respect, +smoothed particle hydrodynamics is quite similar to the finite element method. +The method can use any of the materials available in Abaqus/Explicit (including user materials). +You can specify initial conditions and boundary conditions as for any other Lagrangian model. Contact +interactions with other Lagrangian bodies are also allowed, thus expanding the range of applications for +which this method can be used. +The method is less accurate in general than Lagrangian finite element analyses when the deformation +is not too severe and than coupled Eulerian-Lagrangian analyses in higher deformation regimes. If a large +percentage of all nodes in the model are associated with smoothed particle hydrodynamics, the analysis +may not scale well if multiple CPUs are used. +Applications +Smoothed particle hydrodynamic analyses are effective for applications involving extreme deformation. +Fluid sloshing, wave engineering, ballistics, spraying (as in paint spraying), gas flow, and obliteration and +fragmentation followed by secondary impacts are a few examples. There are many applications for which +both the coupled Eulerian-Lagrangian and the smoothed particle hydrodynamic methods can be used. In +many coupled Eulerian-Lagrangian analyses the material to void ratio is small and, consequently, the +computational effort may be prohibitively high. In these cases, the smoothed particle hydrodynamic +method is preferred. For example, tracking fragments from primary impacts through a large volume until +secondary impact occurs can be very expensive in a coupled Eulerian-Lagrangian analysis but comes at +no additional cost in a smoothed particle hydrodynamic analysis. +“Impact of a water-filled bottle,” Section 2.3.2 of the Abaqus Example Problems Manual, includes +an example of using the smoothed particle hydrodynamic method to model the violent sloshing associated +with the impact. +Artificial viscosity +Artificial viscosity in smoothed particle hydrodynamics has the same meaning as bulk viscosity for +finite elements. Similar to other Lagrangian elements, particle elements use linear and quadratic viscous +contributions to dampen high frequency noise from the computed response. In rare cases when the default +values are not appropriate, you can control the amount of artificial viscosity included in a smoothed +particle hydrodynamic analysis. +Input File Usage: +Use the following options to specify scale factors for the linear and quadratic +artificial viscosities: +*SECTION CONTROLS +, , , scale factor for linear artificial viscosity, scale factor +for quadratic artificial viscosity +Initial conditions +“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1, describes all of the initial +conditions that are available for an explicit dynamic analysis. Initial conditions pertinent to mechanical +analyses can be used in a smoothed particle hydrodynamic analysis. +Boundary conditions +Boundary conditions are defined as described in “Boundary conditions in Abaqus/Standard and +Abaqus/Explicit,” Section 33.3.1. +Loads +The loading types available for an explicit dynamic analysis are explained in “Applying loads: overview,” +Section 33.4.1. Concentrated nodal loads can be applied as usual. Gravity loads are the only distributed +loads allowed in a smoothed particle hydrodynamic analysis. +Material options +Any of the material models in Abaqus/Explicit can be used in a smoothed particle hydrodynamic analysis. +Elements +The smoothed particle hydrodynamic method is implemented via the formulation associated with PC3D +elements. These 1-node elements are simply a means of defining particles in space that model a particular +body or bodies. These particle elements utilize existing functionality in Abaqus to reference element- +related features such as materials, initial conditions, distributed loads, and visualization. +You define these elements in a similar fashion as you would define point masses. The coordinates +of these points lie either on the surface or in the interior of the body being modeled, similar to the nodes +of a body meshed with brick elements. For more accurate results, you should strive to space the nodal +coordinates of these particles as uniformly as possible in all directions. +An alternative to directly defining PC3D elements is to define conventional continuum finite element +types C3D8R, C3D6, or C3D4 and automatically convert them to particle elements at the beginning +of the analysis or during the analysis, as discussed in “Finite element conversion to SPH particles,” +Section 15.1.2. +The smoothed particle hydrodynamic method implemented in Abaqus/Explicit uses a cubic spline +as the interpolation polynomial and is based on the classical smoothed particle hydrodynamic theory as +outlined in the references below. +The smoothed particle hydrodynamic method is not implemented for two-dimensional elements. +Axisymmetry can be simulated using a wedge-shaped sector and symmetry boundary conditions. There +are no hourglass or distortion control forces associated with PC3D elements. These elements do not have +faces or edges associated with them. +SPH kernel interpolator +By default, the smoothed particle hydrodynamic method implemented in Abaqus/Explicit uses a cubic +spline as the interpolation polynomial. Alternatively, you can choose a quadratic (Johnson et al, 1996) +or quintic (Wendland, 1995) interpolator. +The implementation is based on the classical smoothed particle hydrodynamic theory as outlined +in the references below. You also have the option of using a mean flow correction configuration update, +commonly referred to in the literature as the XSPH method , as well as the corrected +kernel of Randles and Libersky, 1997, also referred to as the normalized SPH (NSPH) method. +You can control these settings as discussed in “Using section controls for smoothed particle +hydrodynamics (SPH)” in “Section controls,” Section 27.1.4. +Computing the particle volume +There is currently no capability to automatically compute the volume associated with these particles. +Hence, you need to supply a characteristic length that will be used to compute the particle volume, +which in turn is used to compute the mass associated with the particle. It is assumed that the nodes +are distributed uniformly in space and that each particle is associated with a small cube centered at the +particle. When stacked together, these cubes will fill the overall volume of the body with some minor +approximation at the free surface of the body. The characteristic length is half the length of the cube side. +From a practical perspective, once you have created the nodes, you can use the half-distance between +two nodes as the characteristic length. Alternatively, if you know the mass and density of the part, you +can compute the volume of the part and divide it by the total number of particles in the part to obtain +the volume of the small cube associated with each particle. Half of the cubic root of this small volume +is a reasonable characteristic length for this particle set. You can check the mass of individual sets in +the model if you request that model definition data be printed to the data (.dat) file . +Input File Usage: +Use the following options to define a smoothed particle hydrodynamic body: +*ELEMENT, TYPE=PC3D, ELSET=particle_body +element number, node number +Repeat the data line as often as necessary. +*SOLID SECTION, ELSET=particle_body, MATERIAL=material_name +characteristic length associated with particle volume +Smoothing length calculation +Even though particle elements are defined in the model using one node per element, the smoothed particle +hydrodynamic method computes contributions for each element based on neighboring particles that are +within a sphere of influence. The radius of this sphere of influence is referred to in the literature as the +smoothing length. The smoothing length is independent of the characteristic length discussed above +and governs the interpolation properties of the method. By default, the smoothing length is computed +automatically. As the deformation progresses, particles move with respect to each other and, hence, the +neighbors of a given particle can (and typically do) change. Every increment Abaqus/Explicit recomputes +this local connectivity internally and computes kinematic quantities (such as normal and shear strains, +deformation gradients, etc.) based on contributions from this cloud of particles centered at the particle of +interest. Stresses are then computed in a similar fashion as for reduced-integration brick elements, which +are in turn used to compute element nodal forces for the particles in the cloud based on the smoothed +particle hydrodynamic formulation. +By default, Abaqus/Explicit computes a smoothing length at the beginning of the analysis such that +the average number of particles associated with an element is roughly between 30 and 50. The smoothing +length is kept constant during the analysis. Therefore, the average number of particles per element can +either decrease or increase during the analysis depending on whether the average behavior in the model is +expansive or compressive, respectively. If the analysis is mostly compressive in nature, the total number +of particles associated with a given element might exceed the maximum allowed and the analysis will +be stopped. By default, the maximum number of allowed particles associated with one element is 140. +You can control most of these settings as discussed in “Using section controls for smoothed particle +hydrodynamics (SPH)” in “Section controls,” Section 27.1.4. +Smoothed particle hydrodynamic domain +A rectangular region is computed at the beginning of the analysis as the bounding box within which the +particles will be tracked. This fixed rectangular box is 10% larger than the overall dimensions of the +whole model, and it is centered at the geometric center of the model. As the analysis progresses, if a +particle is outside this box, it behaves like a free-flying point mass and does not contribute to smoothed +particle hydrodynamic calculations. +If the particle reenters the box at a later stage, it is once again +included in the calculations. +You can modify the size of the bounding box as discussed in “Using section controls for smoothed +particle hydrodynamics (SPH)” in “Section controls,” Section 27.1.4. +Constraints +Since the PC3D elements are Lagrangian elements, their nodes can be involved in other features, such as +other elements, connectors, or constraints. Since these elements do not have faces or edges, an element- +based surface cannot be defined using PC3D elements. Consequently, constraints that require element- +based surfaces (such as fasteners) cannot be defined for particles. +Interactions +Bodies modeled with particles can interact with other finite element meshed bodies via contact. The +contact interaction is the same as any contact interaction between a node-based surface (associated with +the particles) and an element-based or analytical surface. Both general contact and contact pairs can be +used. All interaction types and formulations available for contact involving a node-based surface are +allowed, including cohesive behavior. Different contact properties can be assigned via the usual options. +By default, the particles are not part of the general contact domain similar to other 1-node elements +(such as point masses). The default contact thickness for particles is the same value specified as the +characteristic length on the section definition; thus, for contact purposes, particles behave as spheres +with radii equal to the radius of a sphere inscribed in the small cube associated with the particle volume +as described above. +You should not specify a contact thickness of zero for the nodes associated with PC3D elements +or contact may not be resolved robustly. The recommended approach is to use the default or specify a +reasonable contact thickness. +Interaction between different bodies all modeled with PC3D elements is allowed. However, this +interaction is meaningful only in cases when the colliding smoothed particle hydrodynamic bodies are +made of the same fluid-like material, such as a water drop falling in a bucket partially filled with water. +In solids-related applications, such as modeling a bullet perforating an armor plate, one of the bodies +must be modeled using regular finite elements. +Contact interactions cannot be defined between particles and Eulerian regions. +Input File Usage: +Output +Use the following options to define contact between a meshed or analytical +surface with a particle-based surface: +*CONTACT +*CONTACT INCLUSIONS +node-based particle surface, element-based/analytical_surface +The element output available for PC3D elements includes all mechanics-related output for continuum +elements: stress; strain; energies; and the values of state, field, and user-defined variables. The nodal +output includes all output variables generally available in Abaqus/Explicit analyses. +Particles can be visualized in Abaqus/CAE via circular discs. In contour plots the values of field +output variables are shown as circular patches of color. Symbol plots are also available. +Limitations +Smoothed particle hydrodynamic analyses are subject to the following limitations: +• They are less accurate in general than Lagrangian finite element analyses when the deformation is +not too severe and the elements are not distorted. In higher deformation regimes coupled Eulerian- +Lagrangian analyses are also generally more accurate. The smoothed particle dynamic method +should be used primarily in cases when the conventional finite element method or the coupled +Eulerian-Lagrangian method have reached their inherent limitations or are prohibitively expensive +to perform. +• When the material is in a state of tensile stress, the particle motion may become unstable leading +to the so-called tensile instability. This instability, which is strictly related to the interpolation +technique of the standard smoothed particle dynamic method, +is especially noticeable when +simulating the stretched state of a solid. As a consequence, particles tend to clump together and +show fracture-like behavior. +• Mass distribution in a body defined with particle elements is somewhat different when compared to +the mass distribution of the same body defined with continuum elements, such as C3D8R elements. +When particle elements are used, the volume of all particles in that body are the same. Consequently, +the nodal mass associated with all particles in that body is the same. If the nodes are not placed in a +regular cubic arrangement, the mass distribution is somewhat inexact, particularly at the free surface +of the body being modeled. +• Surface loads cannot be specified on PC3D elements. However, distributed loads, such as pressure, +can be applied to other finite element surfaces that can apply a pressure onto the particle elements +via contact interactions. +• Bodies modeled with particles that were not defined using the same section definition do not interact +with each other. Hence, you cannot use smoothed particle hydrodynamics to model the mixing of +bodies with dissimilar materials. +• The functionality is not supported in Abaqus/CAE. You can use the existing functionality in +Abaqus/CAE to generate mass elements, write an input file, and then manually edit the input file +to convert the mass elements to particles. Alternatively, you can create a mesh using C3D8R +elements, write an input file, and then use a script to convert these elements to particles as described +in “Generating particle elements from a solid mesh” in the Dassault Systèmes Knowledge Base +at www.3ds.com/support/knowledge-base or the SIMULIA Online Support System, which is +accessible through the My Support page at www.simulia.com. +• If a large percentage of all nodes in the model are associated with smoothed particle hydrodynamics, +the analysis may not scale well if multiple CPUs are used. +• Within a given body (part) defined via one solid section definition, gravity loads and mass scaling +cannot be specified selectively on a subset of elements referenced by this definition. Instead, the +two features must be applied to all the elements in the element set associated with the solid section +definition. +Input file template +The following example illustrates a smoothed particle hydrodynamic analysis of a bottle filled with fluid +being dropped on the floor. The plastic bottle and the floor are modeled with conventional shell elements. +The fluid is modeled via smoothed particle hydrodynamics using PC3D elements. The nodal coordinates +of the particles are defined such they are all located inside the bottle. Material property definitions are +defined as usual for both the fluid and the bottle. Contact interaction is defined between the smoothed +particle hydrodynamic particles representing the water (node-based surface) and the interior walls of +the bottle and also between the bottle exterior and the floor using element-based surfaces (not shown). +Output is requested for stresses (pressure) and density in the fluid. +*HEADING +… +*ELEMENT, TYPE=PC3D, ELSET=Fluid_Inside_The_Bottle +Element number, node number +… +*SOLID SECTION, ELSET=Fluid_Inside_The_Bottle, MATERIAL=Water +Element characteristic length associated with particle volume +*MATERIAL, NAME=Water +Material definition for water, such as an EOS material +*ELEMENT, TYPE=S4R, ELSET=Plastic_Bottle +Element definitions for the shells +** +*INITIAL CONDITIONS, TYPE=VELOCITY +Data lines to define velocity initial conditions +*NSET, NSET=Water_Nodes, ELSET=Fluid_Inside_The_Bottle +*SURFACE, NAME=Water_Surface, TYPE=NODE +Water_Nodes, +*SURFACE, NAME=Bottle_Interior +Plastic_Bottle, SNEG +** +*STEP +*DYNAMIC, EXPLICIT +*DLOAD +Data lines to define gravity load +** +*CONTACT +*CONTACT INCLUSIONS +Water_Surface, Bottle_Interior +** +*OUTPUT, FIELD +*ELEMENT OUTPUT, ELSET=Fluid_Inside_The_Bottle +S, DENSITY +*END STEP +Additional references +• Gingold, R. A., and J. J. Monaghan, “Smoothed Particle Hydrodynamics: Theory and Application +to Non-Spherical Stars,” Royal Astronomical Society, Monthly Notices, vol. 181, pp. 375–389, +1977. +• Johnson, J., R. Stryk, and S. Beissel, “SPH for High Velocity Impact Calculations,” Computer +Methods in Applied Mechanics and Engineering, 1996. +• Libersky, L. D., and A. G. Petschek, “High Strain Lagrangian Hydrodynamics,” Journal of +Computational Physics, vol. 109, pp. 67–75, 1993. +• Monaghan, +Astrophysics, 1992. +J., “Smoothed Particle Hydrodynamics,” Annual Review of Astronomy and +• Munjiza, A., and K. R. F. Andrews, “NBS Contact Detection Algorithm for Bodies of Similar +Size,” International Journal for Numerical Methods in Engineering, vol. 43, pp. 131–149, 1998. +• Randles, P. W., and L. D. Libersky, “Recent Improvements in SPH Modeling of Hypervelocity +Impact,” International Journal of Impact Engineering, 1997. +• Swegle, J. W., and S. W. Attaway, “An Analysis of Smoothed Particle Hydrodynamics,” Sandia +National Lab Report SAND93–2513, 1994. +• Wendland, H., “Piecewise Polynomial, Positive Definite and Compactly Supported Radial +Functions of Minimal Degree,” Advances in Computational Mathematics, 1995. +15.1.2 +FINITE ELEMENT CONVERSION TO SPH PARTICLES +Products: Abaqus/Explicit Abaqus/CAE +References +• “Particle elements,” Section 28.5.1 +• *CONTACT +• *INITIAL CONDITIONS +• *OUTPUT +• *SECTION CONTROLS +• *SOLID SECTION +Overview +You can take advantage of the intrinsic strengths of both Lagrangian finite element and SPH methods +when modeling a body. You can define the model with Lagrangian finite elements and convert them to +SPH particles either at the beginning of an analysis or after the deformation becomes significant. It is +sometimes easier to create the mesh with Lagrangian finite elements, and Lagrangian finite elements are +often more accurate for small deformations. SPH methods are well suited for large deformation. +You start by defining a part as usual. You mesh the part with C3D8R, C3D6, or C3D4 reduced- +integration elements or a combination of these elements. You then specify that these “parent” elements +are to convert to internally generated SPH particles when a user-specified criterion is met. Gravity +loads, contact interactions, initial conditions, mass scaling, and output requests associated with the parent +elements or nodes of the parent elements will be transferred appropriately to the generated particles upon +conversion in an intuitive way as explained below. A special formulation is used to ensure the smoothest +possible transition between the two modeling methods. The technique can use any of the materials +available in Abaqus/Explicit (including user materials). +Activating the conversion to SPH particles functionality +The element conversion to particles functionality is not active by default. The conversion functionality +is intended to be used when the deformations in the original finite element mesh are significant and +elements may distort. Traditionally, in such cases deletion of the soon-to-be distorted Lagrangian +elements would be the only choice to allow the analysis to continue. Converting to SPH particles offers +an improvement over the element deletion option because the generated particles are able to provide +resistance to deformation beyond finite element distortion levels. Consequently, element deletion +cannot be used together with element conversion. +You can control the number of particles generated per parent element and choose between one of +four criteria to specify when the conversion is to be triggered. +Input File Usage: +*SECTION CONTROLS, ELEMENT CONVERSION=YES +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Conversion to particles: Yes +Specifying the number of particles to be generated +By default, one particle is generated per parent element. You can control the number of particles +generated per element by specifying the number of particles to be generated per parent element +isoparametric direction. The total number of particles generated per element depends on the element +type that is being converted. For example, if you specify 3 particles to be generated per isoparametric +direction, upon conversion 27 particles would be generated from a C3D8R element, 18 from a C3D6 +element, and 10 from a C3D4 element, as illustrated in Figure 15.1.2–1. A maximum value of seven +particles per direction can be specified. The particles are evenly spaced inside the parent element such +that they fill the volume as uniformly as possible. For example, if cubic parent elements are stacked in +the user-defined mesh, the particles would be evenly spaced throughout the part. +You can control the number of particles generated per isoparametric direction as discussed in “Using +section controls to convert continuum elements to particles” in “Section controls,” Section 27.1.4. +Figure 15.1.2–1 Internally generated particles per parent element +illustrated for three particles per isoparametric direction. +Time-based criterion +You can specify the time when the conversion of all the elements in the affected element set is to take place +regardless of the deformation levels. This option is intended for applications where the SPH functionality +is the preferred modeling method, such as fluid sloshing in a tank or a synthetic bird strike on an aircraft. +If the conversion time is specified as zero, the conversion takes place at the beginning of the analysis. +For example, fluid sloshing is a good candidate for using a time-based criterion if sloshing is expected +to start at the beginning of the analysis. You can specify a later time at which the conversion takes place +if extreme deformations do not occur until later in the analysis. A bird strike analysis is a potential +candidate as the bird might travel for some time without any deformation prior to hitting the intended +target. +You can control the time when the conversion is to occur as discussed in “Using section controls to +convert continuum elements to particles” in “Section controls,” Section 27.1.4. +Strain-based criterion +You can specify the absolute value of the maximum principal strain when the conversion of a given +element is to take place. As elements deform, if the absolute value of the maximum principal strain is +greater than the specified threshold, the parent elements will convert progressively to SPH particles. This +option is intended for applications where the finite element method is the preferred modeling method but +severe deformations could occur in certain regions. Examples include blast applications and crushing. +You can control the strain-based threshold upon which conversion is to occur as discussed in “Using +section controls to convert continuum elements to particles” in “Section controls,” Section 27.1.4. +Stress-based criterion +You can specify the absolute value of the maximum principal stress value at which the conversion of a +given element takes place. As elements deform, if the absolute value of the maximum principal stress is +greater than the specified threshold, the parent elements will convert progressively to SPH particles. This +option is intended for the same candidate applications as those discussed for the strain-based criterion. +You can control the stress-based threshold upon which conversion is to occur as discussed in “Using +section controls to convert continuum elements to particles” in “Section controls,” Section 27.1.4. +User subroutine–based criterion +The user subroutine–based criterion provides the flexibility of a user subroutine implementation that +allows you to implement your own conversion criterion. Element conversion can be controlled during the +course of an Abaqus/Explicit analysis through any of the user subroutines that can actively modify state +variables associated with a material point, such as VUSDFLD and VUMAT. You specify the state variable +number controlling the element conversion flag. For example, specifying a state variable number of two +indicates that the second state variable is the conversion flag in the user subroutine. The conversion state +variable should be set to a value of one or zero. A value of one indicates that the element is active, +while a value of zero indicates that Abaqus/Explicit should convert the element to particles. Since user +subroutines have access via arguments (or in the case of the VUSDFLD subroutine via utility routines) +to material point state data, the functionality provides a comprehensive means to define the conversion +state variable. +Input File Usage: +Use the following options to define a user subroutine–based conversion +criterion: +*SECTION CONTROLS, ELEMENT CONVERSION=YES, +CONVERSION CRITERION=USER +... +*MATERIAL +*DEPVAR, CONVERT=variable number +Abaqus/CAE Usage: +Specifying a user subroutine–based criterion for element conversion is not +supported in Abaqus/CAE. +Conversion to particles formulation +When using the conversion technique, particles are generated internally at the beginning of the +preprocessing phase of the analysis, and they are placed in an inactive or dormant state. The particles +are attached to the parent elements in a similar fashion as the nodes of embedded elements are attached +, and they follow the motion of the parent element nodes in +an average sense. The inertial properties of the particles in this inactive state (while the parent finite +elements are active) are automatically disregarded to avoid doubling the momentum at a given location. +Similar to SPH particles defined directly as PC3D elements, particles generated from parent element +sets associated with different section definitions will not interact with each other. +Upon conversion a number of internally generated particles per parent element are activated, as +illustrated for various element types in Figure 15.1.2–1. The computational cost of the analysis can +increase significantly after conversion takes place if a large number of particles are generated per element +since a larger number of active elements needs to be processed. In addition, the computational cost +increases because the stable time increment associated with the internally generated particles decreases +as the particle density increases. +Upon conversion the state information (such as stress or equivalent plastic strain) associated with +the element being converted is transferred to the generated particles to ensure the smoothest possible +transition. The activated particles will interact via the SPH formalism with both the previously activated +particles and the neighboring inactive particles that are still embedded in active parent elements. +Automatically generated sets and surfaces +Since the particles are generated internally, you do not have the ability to define element sets, node sets, +or surfaces associated with these particles. Consequently, a number of sets and surfaces are created +internally for convenience. You can visualize these internal sets and surfaces via the usual techniques. +Table 15.1.2–1, Table 15.1.2–2, and Table 15.1.2–3 describe the internally generated sets and surfaces. +Table 15.1.2–1 Internally generated element sets. +Internally generated element set +Description +ALL_GENERATED_ELEMENTS_SPH +All generated SPH particles in the entire +model +ALL_PARENT_ELEMENTS_SPH +All parent elements in the entire model +Internally generated element set +Description +UserDefinedElsetName_SECT_SPH +UserDefined_AElsetName_SPH +All generated particles associated with the +UserDefinedElsetName element set used +in the section definition +All generated particles associated with the +element set UserDefined_AElsetName +Table 15.1.2–2 Internally generated node sets. +Internally generated node set +Description +ALL_PARENT_ELEMENT_NODES_E_SPH +ALL_GENERATED_NODES_SPH +UserDefinedElsetName_SECT_E_SPH +UserDefined_ANsetName_SPH +All nodes of all parent elements in the +entire model +All nodes of all generated particles in the +entire model +All nodes of generated particles associated +with the UserDefinedElsetName element +set used in the section definition +Nodes of generated particles from +parent elements touching nodes of the +UserDefined_ANsetName node set +Table 15.1.2–3 Internally generated surfaces. +Internally generated surfaces +Description +UserDefinedElsetName_PARENT_EE_SPH +UserDefinedElsetName_SECT_NE_SPH +UserDefinedSurfaceName_NS_SPH +Element-based surface containing all +facets of all elements associated with the +UserDefinedElsetName element set used +in the section definition +Node-based surface with all nodes of all +generated particles associated with the +UserDefinedElsetName element set used +in the section definition +Node-based surface containing all nodes +of generated particles associated with +the elements used in the definition of the +UserDefinedSurfaceName element-based +surface +These sets and surfaces are used by features that are automatically generated internally, such +as loads, initial conditions, mass scaling, contact definitions, and output requests. These internally +generated features extend the features that you have defined for the associated parent sets and surfaces +to internally generated particles. In all cases the internally generated features preserve the attributes +that you have defined. +Initial conditions +Initial conditions +cannot be specified directly for the generated particles. However, a subset of the possible initial +conditions (stresses, velocity and rotating velocity) is applied to the generated particles automatically. +You specify these initial conditions on the original element or node set you have defined in the model, +and they are applied appropriately to the associated generated particles. The initial conditions are +applied via the internally created sets described above; hence, you must use an element or node set +rather than element or node numbers when applying initial conditions. +Initial stresses specified on parent elements are applied to the generated particles. This feature is +leveraged in cases where parent elements convert to particles at the very beginning of the analysis (time +zero). All other initial conditions associated with elements are taken into account for the generated +particles as long as the parent elements convert to particles after the first increment in the analysis. The +state transfer mechanism described above appropriately transfers the information to particles and, hence, +initial conditions are accounted for correctly in the particles. +Boundary conditions + cannot be applied directly to the generated particles. Boundary conditions applied to +nodes of the parent elements are not transferred to the generated particles. However, you can use contact +interactions to enforce boundary conditions as explained in “Interactions.” +Temperature and field variables specified on node sets that include parent element nodes are +extended to the generated particles. Abaqus/Explicit generates corresponding temperature and field +variables definitions internally via the internal node sets described in “Automatically generated sets and +surfaces.” If all of the nodes of a particular parent element have the same value at a given time, the +generated particles would have that same value as well. If different values are specified, no interpolation +occurs. Instead, the value of the last definition is used. +Loads +The loading types available for an explicit dynamic analysis are explained in “Applying loads: +overview,” Section 33.4.1. Concentrated nodal loads cannot be applied to generated particles. Gravity +loads specified on the parent elements are the only distributed loads that are transferred upon conversion +to the generated particles. +Material options +Any of the material models in Abaqus/Explicit can be used with the conversion technique. +Elements +When using the conversion technique and C3D8R, C3D6, and/or C3D4 reduced-integration parent +elements to define the part, PC3D elements are generated internally at the beginning of the analysis; +the parent elements are active, and the PC3D elements are inactive. Upon conversion the active status +switches. At no time are a parent element and the associated generated particles both active. By default, +the Visualization module automatically displays only the elements that are active at any given time. +Particle mass (and volume) is computed automatically from the mass (volume) of the parent element. +All particles associated with a specific parent element will have the same mass (volume). The SPH +smoothing length and domain required for the SPH formalism are computed in the same fashion as +in the case when you define PC3D elements directly . +If mass scaling is defined on element sets containing parent elements, Abaqus/Explicit internally +generates mass scaling definitions associated with the corresponding internal element sets described in +“Automatically generated sets and surfaces.” +Constraints +Constraints such as couplings or ties cannot be applied directly to the generated particles. However, +constraints can be defined on nodes and surfaces associated with the parent element nodes and faces. If +such constraints are used to attach parent elements to other Lagrangian bodies or they are used to drive +the motion of a part, care must be exercised when the parent element faces involved in such constraints +convert to particles. The constraint may be nullified upon parent element conversion and, consequently, +the connection to other parts (in the case of tie constraints) or to the driving feature (in the case of coupling +constraints) would no longer be realized. Hence, in certain cases you may need to place these constraints +far enough from the parent elements that can convert for the constraints to be active throughout the +analysis. +Element sets that are marked for possible conversion to particles but that are also part of the rigid +body definition will never convert because the rigid body constraint is always enforced on the parent +elements. +Interactions +Bodies modeled with elements that may convert to particles can interact with other finite element–meshed +or analytical bodies via contact. Upon conversion the internally generated particles may also interact via +contact with these bodies but only via the general contact functionality. +By default, if general contact interactions are included in your model, contact inclusions and +exclusions involving internal node-based surfaces associated with the internal particles are generated. +inclusions and exclusions referencing element-based surfaces that include +User-specified contact +convertible elements will also be reflected in internally generated requests. Table 15.1.2–4 and +Table 15.1.2–5 show all correspondences. The naming convention used for the internally generated +surfaces is explained in “Automatically generated sets and surfaces” above. +Table 15.1.2–4 Internally generated contact inclusions. +User-defined contact inclusion +Internally generated contact inclusions +*CONTACT INCLUSIONS, ALL +EXTERIOR +blank, AllUserElsets_SECT_NE_SPH +blank, UserElemBased +blank, UserElemBased_NS_SPH +UserElemBased, +None +UserElemBased1, UserElemBased2 +UserElemBased1, UserElemBased2_NS_SPH and +UserElemBased2, UserElemBased1_NS_SPH +Table 15.1.2–5 Internally generated contact exclusions. +User-defined contact exclusion +Internally generated contact exclusions +Always, regardless of user definitions +UserElemBased_PARENT_EE_SPH, +UserElemBased_SECT_NE_SPH +blank, UserElemBased +blank, UserElemBased_NS_SPH +UserElemBased, +None +UserElemBased1, UserElemBased2 +UserElemBased1, UserElemBased2_NS_SPH and +UserElemBased2, UserElemBased1_NS_SPH +As shown in the second row of Table 15.1.2–5, contact between the generated particles and the faces +of the associated parent elements is always excluded from the general contact domain. The activated +internal particles will interact with the neighboring yet inactive particles still attached to parent elements +with exposed faces via the SPH formalism. +The contact interaction for the generated particles is the same as any contact interaction between +a node-based surface (associated with the internal particles) and an element-based or analytical surface. +All interaction types and formulations available for contact involving a node-based surface are allowed, +including cohesive behavior. Different contact properties can be assigned via the usual options. The +contact control and property assignment options used for pairs of surfaces that involve parent elements +that can convert to particles will be reflected in internally generated assignments for the internal particle- +based surfaces. Table 15.1.2–6 shows the internally generated assignments associated with user-defined +requests. +Table 15.1.2–6 Internally generated contact control and property assignments. +User-defined contact inclusion +Internally generated contact inclusions +blank, blank +blank, AllUserElsets_SECT_NE_SPH +blank, UserElemBased +blank, UserElemBased_NS_SPH +UserElemBased, +UserElemBased, UserElemBased_NS_SPH +UserElemBased1, UserElemBased2 +UserElemBased1, UserElemBased2_NS_SPH and +UserElemBased2, UserElemBased1_NS_SPH +The generated particles may have different contact +thicknesses since they are computed +automatically at the beginning of the analysis. If one or two particles per isoparametric direction are +requested to be generated upon conversion, all generated particles will have a contact thickness such +that they are barely touching the closest face of the parent element. +If three or more particles per +direction are requested, some of the particles will not be touching the faces of the parent element. +For these particles, the contact thickness will be the minimum thickness of all of the particles that are +touching the parent element faces on that parent element. +You can specify the contact thickness of the generated particles by using the surface property +assignment option for an element-based surface that includes the faces of the parent elements. This +modeling choice affects contact interactions on parent elements before they convert. +Output +Output requests associated with parent elements, nodes of parent elements, or contact involving faces +of parent elements trigger the creation of output requests associated with the corresponding internally +generated particles. For example, if you request element output for an element set that contains +parent elements, Abaqus/Explicit automatically creates an additional element output request using +the corresponding internal element set containing generated particles, as described in “Automatically +generated sets and surfaces.” +A field output request for the STATUS output variable is created automatically for all parent +elements and generated particles. The value of the STATUS output variable is toggled automatically +between a value of zero and one upon conversion for both parent and generated particles. By default, +only the active elements are displayed in the Visualization module. In addition, contour and vector plots +are displayed appropriately on the elements that are currently active. +History output requests are also replicated for the generated particles. Since the actual element or +node numbers of generated particles are defined internally, you can query the actual number of a particle +in the Visualization module before identifying which output curve to display. For example, assume that +you requested equivalent plastic strain history output for a small element set containing three C3D8R +parent elements and that you requested that two particles per isoparametric direction (eight particles per +parent element) are to be generated upon conversion. Before conversion you would have 3 curves to +analyze; but after the three elements are converted, there are 24 curves from which to choose. You can +query the element number of a particle and then select that curve from the 24 available history curves. +Before conversion the curves associated with the particles have a value of zero. Upon conversion there +will be a jump to the equivalent plastic strain value at the current time. +Limitations +Analyses involving finite element conversion to SPH particles are subject to the following limitations: +• Only reduced-integration continuum elements C3D8R, C3D6, and C3D4 are available for +conversion. +• Surface loads specified on the faces of parent elements that convert during the analysis are not +applied after conversion to particles. However, distributed loads, such as pressure, can be applied +to other finite element surfaces that do not convert (e.g., on a piston surface) that can apply a pressure +onto the particle elements (e.g., the fluid pushed by the piston) via contact interactions. +• Bodies modeled with elements that may convert to particles that were not defined using the same +section definition will not interact with each other between the converted portions of the bodies. +For example, body A and body B allow elements to convert to particles, but these elements are +associated with different section definitions. After conversion, the particles will not interact. +• Within a given body (part) defined via one solid section definition, gravity loads and mass scaling +cannot be specified selectively on a subset of elements referenced by this definition. Instead, the +two features must be applied to all the elements in the element set associated with the solid section +definition. +Input file template +The following example illustrates a smoothed particle hydrodynamic analysis of a bottle filled with fluid +being dropped on the floor using the conversion technique. The plastic bottle and the floor are modeled +with conventional shell elements. The fluid is modeled with C3D4 elements that will convert to two +particles per isoparametric direction (four particles per element) at the beginning of the analysis based +on a time-based criterion. Material property definitions are defined as usual for both the fluid and the +bottle. Contact interaction is defined using the default options. Output is requested for stresses (pressure) +and density in the fluid. +*HEADING +… +*ELEMENT, TYPE=C3D4, ELSET=Fluid_Inside_The_Bottle +… +*SOLID SECTION, ELSET=Fluid_Inside_The_Bottle, MATERIAL=Water, +CONTROLS=Time_Based_Conversion +*SECTION CONTROLS, ELEMENT CONVERSION=YES, +CONVERSION CRITERION=TIME, NAME=Time_Based_Conversion +First data line +Second data line +Third data line +2, 0.0 +*MATERIAL, NAME=Water +Material definition for water, such as an EOS material +*ELEMENT, TYPE=S4R, ELSET=Plastic_Bottle +Element definitions for the shells +** +*INITIAL CONDITIONS, TYPE=VELOCITY +Data lines to define velocity initial conditions +** +*STEP +*DYNAMIC, EXPLICIT +*DLOAD +Data lines to define gravity load +** +*CONTACT +*OUTPUT, FIELD +*ELEMENT OUTPUT, ELSET=Fluid_Inside_The_Bottle +S, DENSITY +*END STEP +16. +Sequentially Coupled Multiphysics Analyses +Sequentially coupled multiphysics analyses +16.1 +Sequentially coupled multiphysics analyses +• “Predefined fields for sequential coupling,” Section 16.1.1 +• “Sequentially coupled thermal-stress analysis,” Section 16.1.2 +• “Predefined loads for sequential coupling,” Section 16.1.3 +16.1.1 +PREDEFINED FIELDS FOR SEQUENTIAL COUPLING +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “Sequentially coupled thermal-stress analysis,” Section 16.1.2 +• “Predefined fields,” Section 33.6.1 +• “Creating and modifying output requests,” Section 14.4.5 of the Abaqus/CAE User’s Manual +• “Defining a temperature field,” Section 16.11.9 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +The time history of the following nodal output quantities, generated in an Abaqus/Standard analysis, +can be read into subsequent Abaqus/Standard analyses as predefined fields for sequentially coupled +multiphysics workflows: +• Temperature +• Normalized concentration +• Electric potential +A sequentially coupled multiphysics analysis can be used when the coupling between one or more +of the physical fields in a model is only important in one direction—a special common case is a +sequential thermal-stress analysis (“Sequentially coupled thermal-stress analysis,” Section 16.1.2). +While the uncoupled thermal-stress analysis is the most common sequential multiphysics workflow, +the predefined field capability in Abaqus/Standard directly supports similar sequential workflows +involving normalized concentrations (“Mass diffusion analysis,” Section 6.9.1) and electric potentials +(“Coupled thermal-electrical analysis,” Section 6.7.3). As with temperatures, normalized concentrations +and electric potentials can be read from the output database (.odb) file into subsequent analyses as +predefined fields. +When defined by results from a previous analysis, predefined fields typically vary with position +and are time dependent—they are predefined because they are not changed by the current analysis. +When predefined fields are read from a previous analysis, they are read in at the nodes. They are +then interpolated within elements as needed . Any number of predefined fields can be read in, and material properties can +be defined to depend on them. In addition, volumetric strain will arise in a stress analysis if thermal +expansion (“Thermal expansion,” Section 26.1.2) or field expansion (“Field expansion,” Section 26.1.3) +are included in the material property definition. +Predefined fields may affect the system response through: +• the constitutive behavior, such as the yield stress defined as a function of temperature or field +variables; or +• volumetric strains when thermal or field expansion behaviors +(“Thermal expansion,” +Section 26.1.2, and “Field expansion,” Section 26.1.3) are included in the material definition in +a stress/displacement analysis. +Saving temperatures, normalized concentrations, and electric potentials for predefined fields in +subsequent analyses +Nodal temperatures, normalized concentrations, and electrical potentials can be stored as functions of +time for use in subsequent analyses. Temperatures can be stored in either the results (.fil) file or the +output database (.odb) file, but normalized concentrations and electrical potentials can be used only if +they are stored in the output database file. Saved values must be read into the new analyses as predefined +fields. See “Node output” in “Output to the data and results files,” Section 4.1.2, and “Node output” in +“Output to the output database,” Section 4.1.3. +Saving temperatures for predefined fields in subsequent analyses +To be read as a predefined field, nodal temperatures must be stored as functions of time in the results +(.fil) file or output database (.odb) file. You can request nodal temperature output (NT) in an +uncoupled heat transfer analysis or in a coupled thermal-electrical analysis. +Saving normalized concentrations for predefined fields in subsequent analyses +To be read as predefined fields, normalized concentrations must be stored as functions of time in the +output database (.odb) file—unlike nodal temperatures they cannot be read directly from a results file. +You can request nodal normalized concentrations output (NNC) in a mass diffusion analysis. +Saving electric potentials for predefined fields in subsequent analyses +To be read as predefined fields, electrical potentials must be stored as functions of time in the output +database (.odb) file—unlike nodal temperatures they cannot be read directly from a results file. You can +request nodal electric potential output (EPOT) in a coupled thermal-electrical analysis or a piezoelectric +analysis. +Transferring temperatures as temperature fields +To define the temperature field at different times in the current analysis, you read the nodal temperatures +stored as a function of time in the heat transfer results or output database file. Nodes can be removed +for the current problem; for example, in a sequential thermal-stress analysis elements that represent +nonstructural parts of the heat transfer mesh (such as insulation or cooling fluid) can be omitted in the +stress analysis. When the heat transfer results file or output database file is read, temperatures at nodes +that are not present in the mesh for the current analysis are ignored. +You must specify the name of the thermal analysis results file or output database file that contains +the required nodal temperatures. The file extension is optional. If the heat transfer model and the current +analysis model share the same mesh, the default is the results file. If the heat transfer model and the +current analysis model have dissimilar meshes, the output database file must be used. See “Reading the +values of a field from a user-specified file” in “Predefined fields,” Section 33.6.1, for more information. +If both models contain part and assembly definitions, the part (.prt) files from both analyses are +required to transfer temperatures from the thermal analysis to the current analysis. If the thermal model is +defined in terms of an assembly of part instances, the current analysis must be as well. The part instance +names and local node numbers must be the same in both analyses for the nodes at which temperatures +are transferred. +Transferring temperatures, normalized concentrations, and electric potentials from the output +database to predefined fields +To define predefined fields at different times in the current analysis, you can read nodal temperatures, +normalized concentrations, or electric potentials stored as a function of time in the output database file. +Nodes can be removed for the current problem. When the nodal output variables on the output database +file are on nodes that are not present in the mesh for the current analysis, they are ignored. +You must specify the name of the output database file that contains the required nodal output +variables as well as the nodal output label (NT, NNC, or EPOT) to identify the field that is being read. +See “Defining fields using nodal scalar output values from a user-specified output database file” in +“Predefined fields,” Section 33.6.1. +If both models contain part and assembly definitions, the part (.prt) files from both analyses are +required to transfer nodal results from the original analysis to the current analysis. If the original model is +defined in terms of an assembly of part instances, the current analysis must be as well. The part instance +names and local node numbers must be the same in both analyses for the nodes at which nodal results +are transferred. +Initial conditions +Appropriate initial conditions for Abaqus/Standard procedures are discussed in Chapter 6, “Analysis +Procedures.” You can read the nodal temperatures, normalized concentrations, or electric potentials +from previous analyses to initialize predefined fields. See “Initial conditions in Abaqus/Standard and +Abaqus/Explicit,” Section 33.2.1, for details. +Boundary conditions +Appropriate boundary conditions for Abaqus/Standard procedures are discussed in Chapter 6, “Analysis +Procedures.” See also “Boundary conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1. +Loads +Appropriate loadings for Abaqus/Standard procedures are discussed in Chapter 6, “Analysis Procedures.” +See also “Applying loads: overview,” Section 33.4.1. +Predefined fields +See “Predefined fields,” Section 33.6.1, for additional details on predefined temperatures and fields. +Material options +See Part V, “Materials,” for details on the material models available in Abaqus/Standard. +Volumetric strain will arise in a stress analysis if thermal expansion (“Thermal expansion,” +Section 26.1.2) or field expansion (“Field expansion,” Section 26.1.3) is included in the material +property definition. +Elements +Continuum and structural elements available in Abaqus/Standard are discussed in Chapter 28, +“Continuum Elements,” and Chapter 29, “Structural Elements.” Details on how results from a previous +analysis can be transferred to a current analysis are discussed in “Predefined fields,” Section 33.6.1. +Output +Appropriate output variables for Abaqus/Standard are described in Part V, “Materials.” All of the output +variables are outlined in “Abaqus/Standard output variable identifiers,” Section 4.2.1. +Input file template +A moisture-stress analysis is an example of a sequentially coupled multiphysics analysis. A typical +sequentially coupled moisture-stress analysis consists of two Abaqus/Standard runs: a mass diffusion +analysis and a subsequent stress analysis. Normalized concentrations are stored in the output database +file for the mass diffusion analysis and read into the subsequent stress analysis as a predefined field. +The following template shows the input for the mass diffusion analysis massdiffusion.inp: +*HEADING +… +*ELEMENT, TYPE=DC2D4 +(Choose the mass diffusion element type) +… +*STEP +*MASS DIFFUSION +… +Apply loads and boundary conditions +… +** Write all normalized concentrations to the output +** database file, massdiffusion.odb +*OUTPUT, FIELD +*NODE OUTPUT, NSET=NALL +NNC +*END STEP +The following template shows the input for the subsequent static structural analysis: +*HEADING +… +*ELEMENT, TYPE=CPE4R +(Choose the continuum element type compatible with the mass diffusion element type used) +*MATERIAL +*EXPANSION, FIELD=1 +(Define field expansion for field 1 so that the normalized concentration causes volumetric +strain in the stress analysis) +… +*STEP +*STATIC +… +Apply structural loads and boundary conditions +… +*FIELD, FILE=massdiffusion.odb, OUTPUT VARIABLE=NNC, FIELD=1 +Read in all normalized concentrations from the output database file into field variable 1 +… +*END STEP +16.1.2 +SEQUENTIALLY COUPLED THERMAL-STRESS ANALYSIS +Products: Abaqus/Standard Abaqus/CAE +References +• “Defining an analysis,” Section 6.1.2 +• “Heat transfer analysis procedures: overview,” Section 6.5.1 +• “Predefined fields for sequential coupling,” Section 16.1.1 +• “Creating and modifying output requests,” Section 14.4.5 of the Abaqus/CAE User’s Manual +• “Defining a temperature field,” Section 16.11.9 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +A sequentially coupled heat transfer analysis: +• is used when the stress/deformation field in a structure depends on the temperature field in that +structure, but the temperature field can be found without knowledge of the stress/deformation +response; and +• is usually performed by first conducting an uncoupled heat +stress/deformation analysis. +transfer analysis and then a +A thermal-stress analysis in which the temperature field does not depend on the stress field is a common +example of a sequential multiphysics workflow and is one case of the more general workflow described in +“Predefined fields for sequential coupling,” Section 16.1.1. In such thermal-stress analyses, temperature +is calculated in an uncoupled heat transfer analysis (“Uncoupled heat transfer analysis,” Section 6.5.2) +or in a coupled thermal-electrical analysis (“Coupled thermal-electrical analysis,” Section 6.7.3). +Saving the nodal temperatures +Nodal temperatures are stored as a function of time in the heat transfer results (.fil) file or output +database (.odb) file by requesting output variable NT as nodal output to the results or output database +file. See “Node output” in “Output to the data and results files,” Section 4.1.2, and “Node output” in +“Output to the output database,” Section 4.1.3. +Transferring the heat transfer results to the stress analysis +The temperatures are read into the stress analysis as a predefined field; the temperature varies with +position and is usually time dependent. It is predefined because it is not changed by the stress analysis +solution. Such predefined fields are always read into Abaqus/Standard at the nodes. They are then +interpolated to the calculation points within elements as needed . The temperature interpolation in the stress elements is usually +approximate and one order lower than the displacement interpolation to obtain a compatible variation of +thermal and mechanical strain. Any number of predefined fields can be read in, and material properties +can be defined to depend on them. +For more information, see “Transferring temperatures as temperature fields” in “Predefined fields +for sequential coupling,” Section 16.1.1. +Initial conditions +Appropriate initial conditions for the thermal and stress analysis problems are described in the heat +transfer and stress analysis sections—for example, see “Heat transfer analysis procedures: overview,” +Section 6.5.1; “Coupled thermal-electrical analysis,” Section 6.7.3; “Static stress analysis procedures: +overview,” Section 6.2.1; and “Dynamic analysis procedures: overview,” Section 6.3.1. See also “Initial +conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1. +Boundary conditions +Appropriate boundary conditions for the thermal and stress analysis problems are described in the heat +transfer and stress analysis sections—for example, see “Heat transfer analysis procedures: overview,” +Section 6.5.1; “Coupled thermal-electrical analysis,” Section 6.7.3; “Static stress analysis procedures: +overview,” Section 6.2.1; and “Dynamic analysis procedures: overview,” Section 6.3.1. See also +“Boundary conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1. +Loads +Appropriate loading for the thermal and stress analysis problems is described in the heat transfer and +stress analysis sections—for example, see “Heat transfer analysis procedures: overview,” Section 6.5.1; +“Coupled thermal-electrical analysis,” Section 6.7.3; “Static stress analysis procedures: overview,” +Section 6.2.1; and “Dynamic analysis procedures: overview,” Section 6.3.1. See also “Applying loads: +overview,” Section 33.4.1. +Predefined fields +In addition to the temperatures read in from the heat transfer analysis, user-defined field variables can be +specified; these values only affect field-variable-dependent material properties, if any. See “Predefined +fields,” Section 33.6.1. +Material options +The materials in the thermal analysis must have thermal properties such as conductivity defined . Any mechanical properties such as elasticity will be +ignored in the thermal analysis, but they must be defined for the stress analysis procedure. See Part V, +“Materials,” for details on the material models available in Abaqus/Standard. +Thermal strain will arise in the stress analysis if thermal expansion (“Thermal expansion,” +Section 26.1.2) is included in the material property definition. +Elements +Any of the heat transfer elements in Abaqus/Standard can be used in the thermal analysis. In the stress +analysis the corresponding continuum or structural elements must be chosen. For example, if heat +transfer shell element type DS4 is defined by nodes 100, 101, 102, and 103 in the heat transfer analysis, +three-dimensional shell element type S4R or S4R5 must be defined by these nodes in the stress analysis +procedure. For continuum elements heat transfer results from a mesh using first-order elements can +be transferred to a stress analysis with a mesh using second-order elements ” in “Predefined +fields,” Section 33.6.1). +Output +The nodal temperatures must be written to the heat transfer analysis results or output database file by +requesting the output variable NT . These +temperatures will be read into the stress analysis procedure. +Appropriate output variables are described in the heat transfer and stress analysis sections. All of +the output variables are outlined in “Abaqus/Standard output variable identifiers,” Section 4.2.1. +Input file template +A typical sequentially coupled thermal-stress analysis consists of two Abaqus/Standard runs: a heat +transfer analysis and a subsequent stress analysis. +The following template shows the input for the heat transfer analysis heat.inp: +*HEADING +… +*ELEMENT, TYPE=DC2D4 +(Choose the heat transfer element type) +… +*STEP +*HEAT TRANSFER +… +Apply thermal loads and boundary conditions +… +** Write all nodal temperatures to the results or +** output database file, heat.fil/heat.odb +*NODE FILE, NSET=NALL +NT +*OUTPUT, FIELD +*NODE OUTPUT, NSET=NALL +NT +*END STEP +The following template shows the input for the subsequent static structural analysis: +*HEADING +… +*ELEMENT, TYPE=CPE4R +(Choose the continuum element type compatible with the heat transfer element type used) +… +*STEP +*STATIC +… +Apply structural loads and boundary conditions +… +*TEMPERATURE, FILE=heat +Read in all nodal temperatures from the results or output database file, heat.fil/heat.odb +… +*END STEP +16.1.3 +PREDEFINED LOADS FOR SEQUENTIAL COUPLING +Product: Abaqus/Standard +References +• “Mapping thermal and magnetic loads,” Section 3.2.22 +• “Defining an analysis,” Section 6.1.2 +• “Eddy current analysis,” Section 6.7.5 +• “Concentrated loads,” Section 33.4.2 +Overview +The values of the following whole element output quantities, generated in an Abaqus/Standard time- +harmonic eddy current analysis, can be read into subsequent Abaqus/Standard analyses as point loads +for sequentially coupled multiphysics workflows: +• Rate of Joule heat dissipation +• Magnetic body force intensity +A sequentially coupled multiphysics analysis can be used to apply electromagnetically generated loads +(from a time-harmonic eddy current analysis) in a heat transfer, coupled temperature-displacement, or +stress/displacement analysis. In many cases coupling is important only from the time-harmonic eddy +current analysis; the impact of loading on the structure’s mechanical or thermal response is not great +enough to affect the validity of the original time-harmonic eddy current analysis. +Saving Joule heat dissipation or magnetic body force intensity for use in subsequent analyses +You can request Joule heat dissipation output (EMJH) or magnetic body force intensity output (EMBF) +in a time-harmonic eddy current analysis. Only values stored in the output database (.odb) file are +available for use with sequential coupling. +Converting results for subsequent use +The whole element quantities are converted to nodal load quantities using the abaqus emloads utility. +The utility converts Joule heat dissipation output to concentrated heat flux and magnetic body force +intensity output to point loads. This utility also enables conversion of results between dissimilar meshes. +For more information, see “Mapping thermal and magnetic loads,” Section 3.2.22. +Conversion limitations +When converting results values between dissimilar meshes, global conservation of the net flux is +ensured provided that the model domain in the heat transfer, coupled temperature-displacement, or +stress/displacement analysis matches the model domain in the time-harmonic eddy current analysis. +The conservative mapping algorithm used in the abaqus emloads utility also provides a locally smooth +distribution of point flux values (either body force or concentrated heat flux) in cases where the mesh +in the time-harmonic eddy current analysis is finer than the “target” representative mesh. In situations +where this is not the case and the “target” representative mesh is finer or of similar size to the mesh in +the time-harmonic eddy current analysis, you may observe nodal locations with zero converted flux +values. In these cases you will still observe global conservation of the flux, but your solution may be +adversely affected locally. You can correct for these situations by always performing the time-harmonic +eddy current analysis with a finer mesh. +Transferring nodal loads from the output database to concentrated loads +To define loads in a heat transfer, coupled temperature-displacement, or stress/displacement analysis, +you can read nodal concentrated heat fluxes and point loads from the output database (.odb) file created +by the abaqus emloads utility. +Input file template +In this example heat flux values are stored in the output database from a time-harmonic eddy current +analysis. These values, after conversion to point heat fluxes, are read into a subsequent analysis as a +concentrated flux. +The following template shows +the input +for +the time-harmonic eddy current analysis +electromagnetic.inp: +*HEADING +… +*ELEMENT, TYPE=EMC3D8 +(Choose the electromagnetic element type) +… +*STEP +*ELECTROMAGNETIC, LOW FREQUENCY, TIME HARMONIC +… +Apply loads and boundary conditions +… +** Write element Joule heat dissipation results to the output +** database file, electromagnetic.odb +*OUTPUT, FIELD +*ELEMENT OUTPUT, ELSET=CONDUCTOR +EMJH +*END STEP +The following template shows the input for the heat transfer analysis, heattransfer.inp, +which refers to an output database, pointflux.odb, created using the abaqus emloads utility, and +which has mapped quantities from the results of the time-harmonic eddy current analysis, stored in +electromagnetic.odb: +*HEADING +… +*ELEMENT, TYPE=DC3D8 +(Choose the heat transfer continuum element type) +… +*STEP +*HEAT TRANSFER, STEADY STATE +… +Apply heat transfer loads and boundary conditions +… +*CFLUX, FILE=pointflux.odb +Read in all nodal heat flux values from the output database and apply as concentrated nodal fluxes +… +*END STEP +Co-simulation +Co-simulation +Preparing an Abaqus analysis for co-simulation +Co-simulation between Abaqus solvers +CO-SIMULATION +17.1 +17.2 +17.1 +Co-simulation +• “Co-simulation: overview,” Section 17.1.1 +17.1.1 +CO-SIMULATION: OVERVIEW +The co-simulation technique is a capability for run-time coupling of Abaqus and another analysis program. +An Abaqus analysis can be coupled to another Abaqus analysis or to a third-party analysis program to perform +multiphysics simulations and multidomain (multimodel) coupling. +Abaqus provides built-in procedures to solve multiphysics simulations as described in “Multiphysics +analyses” in “Solving analysis problems: overview,” Section 6.1.1. For multiphysics problems for which +Abaqus does not provide a built-in solution procedure or where the solution procedure is limited in +functionality, you can use the co-simulation technique to couple Abaqus with a third-party analysis program; +for example, fluid-structure interaction (FSI) simulation in conjunction with computational fluid dynamics +(CFD) analysis programs. +Co-simulation between Abaqus/Standard and Abaqus/Explicit illustrates a multiple domain analysis +approach, where each Abaqus analysis operates on a complementary section of the model domain where it +is expected to provide the more computationally efficient solution. For example, Abaqus/Standard provides +a more efficient solution for light and stiff components, while Abaqus/Explicit is more efficient for solving +complex contact interactions. +Another application area is solving complex problems where the model is divided into multiple domains +and different analysis programs are used to obtain solutions for each domain; for example, crash safety +simulation performed in conjunction with the occupant simulation program MADYMO. +Features of the Abaqus co-simulation technique +The Abaqus co-simulation technique: +• can be used to solve complex fluid-structure interactions by coupling Abaqus with CFD analysis +programs, including Abaqus/CFD analyses; +• can be used to solve conjugate heat transfer problems by coupling Abaqus/Standard with CFD +analysis programs, including Abaqus/CFD analyses; +• can be used to solve complex analyses more effectively by coupling Abaqus/Standard to +Abaqus/Explicit; +• can be used for multiphysics simulations by coupling Abaqus with third-party analysis programs; +• can be used to couple Abaqus with in-house codes using the SIMULIA Co-Simulation Engine or +the multiphysics code coupling interface, MpCCI; +• can be used for crash safety simulations by coupling Abaqus/Explicit with the occupant simulation +program MADYMO; +• is intended for advanced users with in-depth knowledge of Abaqus and the third-party analysis +program; +• allows for both unidirectional and bidirectional transfer of data; +• can be used with Abaqus models having linear or nonlinear structural response; and +• supports both steady-state and transient simulations. +Interaction between domains modeled with different analysis programs +In a co-simulation the interaction between the domains is through a common physical interface region +over which data are exchanged in a synchronized manner between Abaqus and the coupled analysis +program. +One domain may affect the response of another domain through one or more of the following: +• the constitutive behavior, such as the yield stress defined as a function of temperature or stress +defined as a function of other solution fields, such as thermal strains or the piezoelectric effect; +• surface tractions/fluxes, such as a fluid exerting pressure on a structure; +• body forces/fluxes, such as heat generation due to flow of current in a coupled thermal-electrical +simulation; +• contact forces, such as the forces due to contact between a vehicle and an occupant/pedestrian +modeled as separate domains; and +• kinematics, such as fluid in contact with a compliant structure where the interface motion affects +the fluid flow. +Abaqus offers two approaches to couple Abaqus with another analysis program: +• Direct coupling using SIMULIA Co-Simulation methods. +• Coupling using MpCCI, a third-party connectivity middleware. +Coupling Abaqus using SIMULIA Co-Simulation methods +SIMULIA Co-Simulation methods provide direct coupling between two Abaqus analyses or between +Abaqus and third-party analysis programs, without any third-party communication tool. +These +methods are used for fluid-structure simulations, conjugate heat transfer, coupling Abaqus/Standard to +Abaqus/Explicit for interaction between implicit dynamic and explicit dynamic domains, and coupling +Abaqus to MADYMO for vehicle-occupant/pedestrian interaction. +Fluid-structure interaction +You can perform complex fluid-structure interaction (FSI) problems by coupling Abaqus/Standard or +Abaqus/Explicit to a computational fluid dynamics (CFD) analysis program. Abaqus/Standard and +Abaqus/Explicit solve the structural domain, and the CFD analysis program solves the fluid domain. +Abaqus/Standard and Abaqus/Explicit can be coupled with Abaqus/CFD as well as with several +third-party CFD analysis programs. +For detailed information on coupling Abaqus/CFD to Abaqus/Standard or to Abaqus/Explicit, see +“Preparing an Abaqus analysis for co-simulation,” Section 17.2.1, and “Abaqus/CFD to Abaqus/Standard +or to Abaqus/Explicit co-simulation,” Section 17.3.2. For a complete list of qualified partner products, +see www.simulia.com. +Conjugate heat transfer +You can perform conjugate heat +transfer problems involving fluids and structures by coupling +Abaqus/Standard to a computational fluid dynamics (CFD) analysis program. Abaqus/Standard +models heat transfer within the structure , and the CFD analysis program solves the +energy equation for the fluid flow surrounding the structure. Abaqus/Standard can be coupled with +Abaqus/CFD as well as with several third-party CFD analysis programs. +For an example of Abaqus/CFD to Abaqus/Standard co-simulation, refer to “Conjugate heat +transfer analysis of a component-mounted electronic circuit board,” Section 6.1.1 of the Abaqus +Example Problems Manual. For detailed information on coupling Abaqus/CFD to Abaqus/Standard, +see “Preparing an Abaqus analysis for co-simulation,” Section 17.2.1, and “Abaqus/CFD to +Abaqus/Standard or to Abaqus/Explicit co-simulation,” Section 17.3.2. For a complete list of qualified +partner products, see www.simulia.com. +Interaction between an implicit transient analysis and an explicit dynamics analysis +In certain cases you can realize significant computational cost savings by partitioning a model and +combining the Abaqus/Standard and Abaqus/Explicit solutions, such as +• when the simulation is principally a candidate for Abaqus/Explicit, but where certain parts of the +model can be idealized using substructures in Abaqus/Standard, or +• when the simulation is principally a candidate for Abaqus/Standard, but where complex contact +conditions would be handled more effectively by Abaqus/Explicit. +For an example of Abaqus/Standard to Abaqus/Explicit co-simulation, refer to “Dynamic impact +of a scooter with a bump,” Section 2.4.1 of the Abaqus Example Problems Manual. For detailed +information on coupling Abaqus/Standard and Abaqus/Explicit, see “Preparing an Abaqus analysis +for co-simulation,” Section 17.2.1, and “Abaqus/Standard to Abaqus/Explicit co-simulation,” +Section 17.3.1. +Vehicle-occupant/pedestrian interaction +Crash safety simulation generally includes interaction between a vehicle and its occupant or a vehicle +and a pedestrian. Abaqus/Explicit is used to model the vehicle, and MADYMO is used to model the +occupant or the pedestrian. +In some cases the influence of the human response on the structural response of the vehicle is so +small as to be negligible. In these cases only a part of the vehicle surrounding the human is used in a +coupled analysis. The vehicle analysis is performed without the human, and the motion from a portion of +the vehicle immediately surrounding the human is extracted as a submodel of the full vehicle response. +The co-simulation technique is used to perform a coupled analysis with the human model and the vehicle +submodel. +For an example of co-simulation with MADYMO, +refer to “Rigid body dynamics with +Abaqus/Explicit,” Section 1.3.7 of the Abaqus Benchmarks Manual. +The coupling between +Abaqus/Explicit and MADYMO is actively supported and tested by both SIMULIA and TNO +MADYMO BV. For detailed information, refer to “Using coupling between Abaqus/Explicit and +MADYMO in Abaqus” in the Dassault Systèmes Knowledge Base at www.3ds.com/support/knowledge- +base or the SIMULIA Online Support System, which is accessible through the My Support page at +www.simulia.com. +Coupling using MpCCI +MpCCI, the multiphysics code coupling interface developed and distributed by the Fraunhofer-Institute +for Algorithms and Scientific Computing (SCAI), provides an open system approach for general +multidisciplinary simulations between Abaqus and any third-party analysis program that supports +MpCCI. MpCCI provides a scalable communication infrastructure and mapping algorithms for multiple +physics domains. In a co-simulation using MpCCI, Abaqus communicates in real time with the MpCCI +coupling server to exchange fields with the third-party analysis program while each analysis advances +its simulation time. +Coupling through MpCCI may occur between Abaqus and any third-party analysis program that +supports the MpCCI interface. This includes in-house codes that have the MpCCI adapter embedded. +SIMULIA actively supports and qualifies a link between Abaqus and FLUENT for fluid-structure +interaction. For more information, refer to “Abaqus User’s Guide for Fluid-Structure Interaction (FSI)” +in the Dassault Systèmes Knowledge Base at www.3ds.com/support/knowledge-base or the SIMULIA +Online Support System, which is accessible through the My Support page at www.simulia.com. +Strength of physics coupling +You will typically apply co-simulation techniques to problems where the most complex physics occurs +within domains that are handled exclusively within an analysis program (e.g., Abaqus or a CFD analysis +program). Due to the comparative numerical simplicity of the numerical techniques applied at the +co-simulation interface, the physics controlling the interaction at the interface of the separate analysis +domains (the strength of the physics coupling) must be relatively weak for the co-simulation technique +to be applied effectively. +Coupling to third-party analysis programs +In a fluid-structure interaction (FSI) co-simulation the analysis domains are coupled in a staggered +approach in a globally explicit manner; that is, the equations for each domain are solved separately, and +loads and boundary conditions are exchanged at the common interface. +Similarly, in a crash safety simulation with the vehicle modeled in Abaqus/Explicit and the dummy +modeled in MADYMO, the interaction of the domains is resolved by application of the forces resulting +from the contact condition between the interface of the two domains. +The staggered approach is applicable to many problems that exhibit weak to moderate physics +coupling. In cases where the coupling is sufficiently weak, the coupling may be required only in one +direction (such as when a temperature field contributes to the structural response, but a reverse coupling +provides no significant impact on the simulation results). The staggered approach may not be effective +for problems that exhibit strong physics coupling. +Figure 17.1.1–1 illustrates the coupling strength with an analogy in the frequency domain. +Consider a lumped parameter dynamic system with a coupling impedance directly related to a response +frequency +In a staggered solution approach each domain is solved by temporarily ignoring the +coupling terms represented by the gray spring and dashpot in Figure 17.1.1–1. When the response +frequency and coupling impedance are low, a staggered approach will likely provide adequate solution +. +ks +Fs +ms +Ff +mf +cf +structure +coupling +fluid +Figure 17.1.1–1 Mechanical impedance analogy. +accuracy and performance. However, when the response frequency is high, such that the coupling +impedance is relatively large compared to the structure or fluid, you may encounter solution stability +issues with the staggered approach. +Coupling in Abaqus/Standard to Abaqus/Explicit co-simulation +The strength of the physics coupling can generally be greater in the coupling of Abaqus/Standard to +Abaqus/Explicit using the co-simulation technique. Through communication of “right-hand-side” +and “left-hand-side” terms, Abaqus/Standard to Abaqus/Explicit co-simulation provides a robust +interface solution across a wide range of problem parameters. In many cases you can choose to have +Abaqus/Standard and Abaqus/Explicit each advance their solutions according to their own automatic +time incrementation scheme without adversely affecting the interface solution stability. +References +For the latest support information and tips on running FSI simulations and crash safety simulations, +see the Dassault Systèmes Knowledge Base at www.3ds.com/support/knowledge-base or the SIMULIA +Online Support System, which is accessible through the My Support page at www.simulia.com. +17.2 +Preparing an Abaqus analysis for co-simulation +• “Preparing an Abaqus analysis for co-simulation,” Section 17.2.1 +17.2.1 +PREPARING AN Abaqus ANALYSIS FOR CO-SIMULATION +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD +References +• “Co-simulation: overview,” Section 17.1.1 +• “Abaqus/Standard to Abaqus/Explicit co-simulation,” Section 17.3.1 +• “Abaqus/CFD to Abaqus/Standard or to Abaqus/Explicit co-simulation,” Section 17.3.2 +• *CO-SIMULATION +• *CO-SIMULATION REGION +• *CO-SIMULATION CONTROLS +Overview +This section provides an overview of preparing an Abaqus analysis for a co-simulation. The discussion +in this section is general and may not apply to every product pairing. “Co-simulation between Abaqus +solvers,” Section 17.3, provides setup, execution, and limitation details for co-simulation between +Abaqus solvers. For co-simulation between Abaqus and third-party analysis programs, consult the +appropriate User’s Guide. +Preparing an Abaqus analysis for co-simulation involves the following: +• identifying the Abaqus analysis step for a co-simulation analysis; +• identifying the analysis program, which may be another Abaqus analysis, that is communicating +with Abaqus during the co-simulation analysis; +• identifying the co-simulation interface regions in the Abaqus model; +• identifying the fields exchanged during the co-simulation; and +• defining the coupling and rendezvousing schemes. +Each of these steps is described in detail below. +Identifying the Abaqus step for the co-simulation analysis +The co-simulation event need not begin at the start of the first step in an Abaqus analysis. However, +it does need to start with the beginning of an analysis step and end within that analysis step. Hence, +you need to define the step durations in Abaqus such that the start of the co-simulation event falls at the +beginning of an Abaqus analysis step and to define that particular step so that the co-simulation event +ends by the end of that step. Regular loads and boundary conditions for the Abaqus model, particularly +away from the interface regions, are specified as usual. +Communication with the coupled analysis is initiated as the co-simulation event begins and is +terminated when the co-simulation event is ended by either program. Abaqus may terminate the +co-simulation event when the end of the analysis step is reached or when the analysis cannot proceed +any further; for example, due to convergence problems. +Co-simulation is supported by the following Abaqus procedures: +• “Static stress analysis,” Section 6.2.2 +• “Quasi-static analysis,” Section 6.2.5 +• “Implicit dynamic analysis using direct integration,” Section 6.3.2 +• “Explicit dynamic analysis,” Section 6.3.3 +• “Uncoupled heat transfer analysis,” Section 6.5.2 +• “Fully coupled thermal-stress analysis,” Section 6.5.3 +• “Incompressible fluid dynamic analysis,” Section 6.6.2 +• “Piezoelectric analysis,” Section 6.7.2 +• “Coupled thermal-electrical analysis,” Section 6.7.3 +• “Coupled pore fluid diffusion and stress analysis,” Section 6.8.1 +Input File Usage: +Use the following option within a step definition to indicate the beginning of a +co-simulation event: +*CO-SIMULATION, NAME=name +Identifying the analysis program communicating with Abaqus during the co-simulation +The Abaqus co-simulation technique provides several interfaces, such as the SIMULIA Co-Simulation +Engine for coupling Abaqus-to-Abaqus and Abaqus to third-party analysis programs; an interface for +coupling Abaqus/Standard to Abaqus/Explicit; a general open interface through the multiphysics code +coupling interface, MpCCI; and an interface coupling Abaqus to MADYMO. +Coupling using the SIMULIA Co-Simulation Engine +You can couple Abaqus with another Abaqus analysis or Abaqus with certain third-party analysis +programs using the SIMULIA Co-Simulation Engine. For details on coupling with third-party analysis +programs, see the respective User’s Guides. +Input File Usage: +*CO-SIMULATION, NAME=name, PROGRAM=MULTIPHYSICS +Coupling Abaqus/Standard and Abaqus/Explicit +You can couple an Abaqus/Standard analysis to an Abaqus/Explicit analysis. +Input File Usage: +*CO-SIMULATION, NAME=name, PROGRAM=ABAQUS +Coupling using MpCCI +You can use MpCCI to communicate with any third-party analysis program that is MpCCI compliant. +MpCCI is a third-party connectivity program for general multidisciplinary simulation and is distributed +by the Fraunhofer-Institute for Algorithms and Scientific Computing. In this case Abaqus communicates +with the MpCCI server, which in turn communicates with the third-party analysis program. +For more information on coupling using MpCCI, refer to “Abaqus User’s Guide for Fluid-Structure +Interaction (FSI)” in the Dassault Systèmes Knowledge Base at www.3ds.com/support/knowledge-base +or the SIMULIA Online Support System, which is accessible through the My Support page at +www.simulia.com. +Input File Usage: +*CO-SIMULATION, NAME=name, PROGRAM=MPCCI +Coupling Abaqus/Explicit and MADYMO +For information on coupling using MADYMO, refer to “Using coupling between Abaqus/Explicit and +MADYMO in Abaqus” in the Dassault Systèmes Knowledge Base at www.3ds.com/support/knowledge- +base or the SIMULIA Online Support System, which is accessible through the My Support page at +www.simulia.com. +Identifying the co-simulation interface region +Interaction between two Abaqus models or between an Abaqus model and a third-party analysis model +takes place through a common interface region referred to as the co-simulation interface region. The +co-simulation interface region may be a set of discrete points, a surface region, or a volume region. You +must be consistent in your interface region definition; if you define a surface co-simulation region in one +analysis, then you must define a surface co-simulation region in the other analysis. Furthermore, these +co-simulation regions need to be co-located and have the same region boundaries. +Interacting through discrete points +Interaction can occur through a set of discrete points where only nodal position information without +element topology information (e.g., tributary area) defines the co-simulation interface region. In this case +the spatial mapping is limited to point-to-point mapping, and you must ensure that there are matching +nodes between the models. +In Abaqus you can use a node set or a node-based surface to define a co-simulation interface region +consisting of discrete points. +Input File Usage: +Use the following option to define a node set as a co-simulation region in an +Abaqus model: +*CO-SIMULATION REGION, TYPE=NODE +nodeset_A +Use the following options to define a node-based surface as a co-simulation +region in an Abaqus model: +*SURFACE, TYPE=NODE +nodeset_A +*CO-SIMULATION REGION, TYPE=SURFACE +node-based surface name +Interacting through a surface +Interaction between distinct domains occurs through a common interface surface. For example, when a +fluid interacts with a solid without penetrating it, the fluid-solid interface is defined through a surface. +In this case both nodal position and element topology information define the co-simulation interface, +and appropriate spatial mapping between dissimilar surface meshes is performed to conservatively map +fields. +Input File Usage: +Use the following option to define an element-based surface as a co-simulation +region in an Abaqus model: +*CO-SIMULATION REGION, TYPE=SURFACE (default) +element-based surface name +Interacting through a volume +Interaction between overlapping domains occurs through a volume. In this case both nodal position and +element topology information define the co-simulation region, and appropriate spatial mapping between +dissimilar volume meshes is performed to conservatively map fields. +The interface region is defined by an element set. +Input File Usage: +Use the following option to define a volume as a co-simulation region in an +Abaqus model: +*CO-SIMULATION REGION, TYPE=VOLUME +elset_A +Identifying the fields exchanged across a co-simulation interface +The coupling of the domain models can be through loads and/or boundary conditions prescribed at the co- +simulation interface. In addition, mass, rotary inertia, and heat capacitance terms can also be exchanged. +Based on the physics and the interaction type and its enforcement, you must specify the fields that are +imported and/or exported in an Abaqus analysis during the co-simulation. +The co-simulation interface can consist of a group of discrete points (nodes), a surface region, or a +volume region. Not all fields can be exchanged across all region types. +This section provides a general overview of all fields available in Abaqus. For detailed information +on the fields exchanged between two Abaqus solvers, see “Abaqus/Standard to Abaqus/Explicit +co-simulation,” Section 17.3.1, and “Abaqus/CFD to Abaqus/Standard or +to Abaqus/Explicit +co-simulation,” Section 17.3.2. +For detailed information on fields exchanged by Abaqus and a +third-party analysis program, see the respective User’s Guides. +Input File Usage: +Use the following option to import field data over a region into Abaqus: +*CO-SIMULATION REGION, IMPORT +region_A, import_field_1 +region_A, import_field_2 +Use the following option to export data from Abaqus: +*CO-SIMULATION REGION, EXPORT +region_A, export_field_1 +region_A, export_field_2 +When using the SIMULIA Co-Simulation Engine, only a single region can be +specified. If multiple regions are involved, you must combine these regions +into a single region. For example, you can use the *SURFACE, COMBINE +option to create a combined surface region. +Procedures involving mechanical degrees of freedom +Table 17.2.1–1 lists the fields that can be exchanged for procedures supporting mechanical degrees of +freedom (degrees of freedom 1–6), their associated field identifiers, the supported co-simulation interface +region types, and which Abaqus solvers support import and export of the field values. +Table 17.2.1–1 +Exchanging fields for procedures supporting mechanical degrees of freedom. +Field ID +Fields +Interface +Type1 +Abaqus Solver2 +Import Export +Units +UT or U +Displacement +P, S, V +S, E, C +S, E +VT or V +AT or A +UR +VR +AR +Velocity (transient +procedures) +Acceleration (transient +procedures) +Rotations +Angular velocity +(transient procedures) +Angular acceleration +(transient procedures) +COORD +Current coordinates +CF +CM +Concentrated forces +Concentrated moments +TRSHR +Traction vector +PRESS +Pressure normal to +element surface +P, S, V +P, S, V +P, S +P, S +P, S +P, S, V +P, S, V +P, S +S, E +S, E +S, E +radians +S, E +radians +S, E +radians +S, E +S, E +S, E +S, E +1 P (points), S (surface region), V (volume region) +2 S (Abaqus/Standard), E (Abaqus/Explicit), C (Abaqus/CFD) +The following procedures support co-simulation using mechanical degrees of freedom: +• “Static stress analysis,” Section 6.2.2 +• “Quasi-static analysis,” Section 6.2.5 +• “Implicit dynamic analysis using direct integration,” Section 6.3.2 +• “Explicit dynamic analysis,” Section 6.3.3 +• “Fully coupled thermal-stress analysis,” Section 6.5.3 +• “Incompressible fluid dynamic analysis,” Section 6.6.2 +• “Piezoelectric analysis,” Section 6.7.2 +• “Coupled pore fluid diffusion and stress analysis,” Section 6.8.1 +Displacements +Displacements (field ID UT or U) for the translational degrees of freedom can be exported by +Abaqus/Standard and Abaqus/Explicit. +Displacements can be imported by Abaqus/Standard, +Abaqus/Explicit, and Abaqus/CFD. When imported, displacements are ramped from the values of the +previous exchange time point to those of the next target time point. The displacements are exported +in the global coordinate system. +Displacements are available for points, surface regions, and volume regions in Abaqus/Standard +and for surface regions in Abaqus/Explicit and Abaqus/CFD. +Displacements can be viewed in the Visualization module of Abaqus/CAE. +Velocity and acceleration +Velocity (field ID VT or V) and acceleration (field ID AT or A) for the translational degrees of freedom +can be exported by Abaqus/Standard for transient procedures and by Abaqus/Explicit. Velocity can be +imported by Abaqus/CFD. Velocity and acceleration are in the global coordinate system. +Velocity is available for points and surface regions in Abaqus/Standard and Abaqus/Explicit and +for surface regions in Abaqus/CFD. +Rotations +Rotations (field ID UR) can be exported by Abaqus/Standard and Abaqus/Explicit and imported by +Abaqus/Explicit. Rotations are in the global coordinate system. +Rotations are available for points and surface regions. +Rotations can be viewed in the Visualization module of Abaqus/CAE. +Rotational velocity and rotational acceleration +Rotational velocity (field ID VR) and rotational acceleration (field ID AR) can be exported by +Abaqus/Standard for transient procedures and by Abaqus/Explicit. Rotational velocity and rotational +acceleration are in the global coordinate system. +Rotational velocity and rotational acceleration are available for points and surface regions. +Current coordinates +Current nodal coordinates (field ID COORD) can be exported by Abaqus/Standard and Abaqus/Explicit. +The coordinates are the current coordinates of +small- or +is preferred to export displacements +large-displacement analysis is performed. +(field ID UT or U) rather than current coordinates when results are mapped between dissimilar interface +regions. In cases where the partner client does not retain the original coordinates, it may be necessary +to send current coordinate values rather than displacements. +Current coordinates are available for points, +Abaqus/Standard and for surface regions in Abaqus/Explicit. +the deformed structure whether +and volume regions +surface regions, +In general, +in +it +Concentrated forces +Concentrated forces (field ID CF), if imported, are ramped from the values of the previous exchange time +point to those of the next target time point in Abaqus/Standard and are kept constant over the exchange +interval in Abaqus/Explicit. The concentrated forces are in the global coordinate system. +When exporting concentrated forces, Abaqus/Standard transfers reaction forces at interface nodes +that have prescribed displacements. The reaction forces are exported in the global coordinate system. +Concentrated forces are available for points, surface regions, and, in Abaqus/Standard only, volume +regions. +Concentrated normal forces can be viewed in the Visualization module of Abaqus/CAE for an +Abaqus/Standard simulation by requesting output variable CF. +Concentrated moments +Concentrated moments (field ID CM), if imported, are ramped from the values of the previous exchange +time point to those of the next target time point in Abaqus/Standard and are kept constant over the +exchange interval in Abaqus/Explicit. The concentrated moments are in the global coordinate system. +Concentrated moments are available for points, surface regions, and, in Abaqus/Standard only, +volume regions. +Concentrated normal moments can be viewed in the Visualization module of Abaqus/CAE for an +Abaqus/Standard simulation by requesting output variable CM. +Traction vector +The traction vector (field ID TRSHR), supported by Abaqus/CFD, exports the fluid total traction (normal +and shear components) on the interface surface. Usually, the exported traction vector is integrated to +concentrated forces (field ID CF) when imported into Abaqus/Standard or Abaqus/Explicit in a fluid- +structure simulation. +The traction vector is a force vector in the global Cartesian coordinate system. +The traction vector is available for surface regions in Abaqus/CFD. +Normal pressure +Normal pressure (field ID PRESS), supported for import by Abaqus/Standard, is the traction normal +component to the surface. Pressure values are ramped from the values of the previous exchange time +point to those of the next target time point when imported into Abaqus/Standard. In most cases it is +preferred to import concentrated forces (field ID CF) since these contain both the normal and shear +traction components. For membrane-like structures it might be preferable to import pressures. +Normal pressure can be viewed in the Visualization module of Abaqus/CAE for an Abaqus/Standard +simulation by requesting output variable P. +Procedures involving thermal degrees of freedom +Table 17.2.1–2 lists the thermal fields available for co-simulation exchange, their associated field +identifiers, the supported co-simulation interface region types, and which Abaqus solvers support import +and export of the field values. +Table 17.2.1–2 +Exchanging fields for procedures supporting thermal degrees of freedom. +Interface +Type1 +Abaqus Solver2 +Import +Export +Units +P, S, V +S, E +P, S, V +S, E +Fields +Temperature +as a nodal +degree of +freedom +Concentrated +heat flux at a +node +Heat flux +normal to +element +surface +Film +properties +Film +properties +(MpCCI +only) +17.2.1–8 +Field ID +NT +CFL +HFL +CFILM +Field ID +TEMP +LUMPEDHEATCAPACITANCE +Fields +Temperature +as a nodal +degree of +freedom +Lumped heat +capacitance +Interface +Type1 +Abaqus Solver2 +Import +Export +Units +P, S, V +P, S, V +S, E +1 P (points), S (surface region), V (volume region) +2 S (Abaqus/Standard), E (Abaqus/Explicit), C (Abaqus/CFD) +The following procedures support co-simulation using thermal degrees of freedom: +• “Uncoupled heat transfer analysis,” Section 6.5.2 +• “Fully coupled thermal-stress analysis,” Section 6.5.3 +• “Incompressible fluid dynamic analysis,” Section 6.6.2 +• “Coupled thermal-electrical analysis,” Section 6.7.3 +Nodal temperature +Nodal temperature (field ID NT) can be exported by Abaqus/Standard and Abaqus/Explicit and imported +by Abaqus/CFD (as field ID TEMP). Temperature values are ramped from the values of the previous +exchange time point to those of the next target time point when imported into Abaqus/Standard and +Abaqus/CFD. +Temperature values can be imported either on the top surface (SPOS) or the bottom surface (SNEG) +of structural elements. Temperatures cannot be exchanged on double-sided surfaces where both the +SPOS and the SNEG facets have the same underlying shell element. For volume regions, only degree of +freedom NT11 is exported, and it should not be used for exchanging temperature values over volumes +discretized with structural elements. +Nodal temperature values can be viewed in the Visualization module of Abaqus/CAE for an +Abaqus/Standard simulation by requesting output variable NT. +Heat flux +Use concentrated heat flux (field ID CFL) for heat entering at a node in Abaqus/Standard and +Abaqus/Explicit. Concentrated heat flux is available for points, surface regions, and, in Abaqus/Standard +only, volume regions. +Concentrated heat flux values can be viewed in the Visualization module of Abaqus/CAE for an +Abaqus/Standard simulation by requesting output variable CFL. +Use surface heat flux (field ID HFL) for a distributed heat flux entering the surface in +Abaqus/Standard or distributed heat flux leaving a surface in Abaqus/CFD. Distributed heat flux is +available only for surface regions. +Film properties +Use surface film properties (field ID FILM) or concentrated (nodal) film properties (field ID CFILM) to +model convection governed by +where q is the heat flux entering the surface, h is a film coefficient, +is the wall temperature, and +is the fluid or ambient temperature. The film coefficient is computed from the heat flux and fluid +temperature obtained from the computational fluid dynamics analysis and the wall temperature from the +Abaqus analysis computed during the previous exchange interval, according to +Both the film coefficient and fluid temperature are passed into Abaqus/Standard and are kept constant +over the subsequent exchange interval. When the fluid and wall temperatures coincide, an arbitrary small +value for the heat transfer coefficient is passed into Abaqus. To obtain reasonable film properties for the +first exchange interval, you should ensure that the wall temperatures are initialized properly in Abaqus +and that you provide a good estimate for the initial fluid temperature. +Film properties are available only for surface regions in Abaqus/Standard. +Heat capacitance +Nodal (lumped) heat capacitance (field ID LUMPEDHEATCAPACITANCE) can be exported by +Abaqus/CFD in models in which heat capacitance is defined. Nodal heat capacitance can be imported +into Abaqus/Standard and Abaqus/Explicit. +Procedures involving pore fluid pressure +Table 17.2.1–3 lists additional fields that can be exchanged for a coupled pore fluid diffusion/stress +analysis, their associated field identifiers, the supported co-simulation interface region types, and which +Abaqus solvers support import and export of the field values. +Table 17.2.1–3 +Exchanging fields for a coupled pore fluid diffusion/stress analysis. +Field ID +Fields +POR +CFF +Pore fluid pressure +at a node +Concentrated fluid +flow at a node +Interface +Type1 +Abaqus Solver2 +Import Export +Units +P, S, V +P, S, V +Field ID +Fields +RVF +Reaction fluid +volume flux due to +prescribed pressure +Interface +Type1 +Abaqus Solver2 +Import Export +Units +P, S, V +1 P (points), S (surface region), V (volume region) +2 S (Abaqus/Standard), E (Abaqus/Explicit), C (Abaqus/CFD) +The following procedure involving pore fluid pressure supports co-simulation: +• “Coupled pore fluid diffusion and stress analysis,” Section 6.8.1 +Pore pressure +Nodal pore pressure (field ID POR) can be imported and exported by Abaqus/Standard for points, surface +regions, and volume regions. +Nodal pore pressure values can be viewed in the Visualization module of Abaqus/CAE for an +Abaqus/Standard simulation by requesting output variable POR. +Concentrated fluid flow +Fluid flow (field ID CFF) defines the seepage flow at a node. Concentrated fluid flow can be imported +by Abaqus/Standard for points, surface regions, and volume regions. +Concentrated fluid flow values can be viewed in the Visualization module of Abaqus/CAE for an +Abaqus/Standard simulation by requesting output variable CFF. +Reaction fluid volume flow +Reaction fluid volume flux (field ID RVF) defines the rate at which fluid volume is entering or leaving +the model through the node to maintain the prescribed pore pressure. Reaction fluid volume flux can be +exported by Abaqus/Standard for points, surface regions, and volume regions. +Temperature and independent field variables +Field variables are time-dependent, predefined fields that exist over the spatial domain of the model . Field variables in conjunction with the co-simulation technique +extend the possibilities of multiphysics by allowing material point dependencies on an external field +defined by another application. +Field variables must be numbered consecutively starting with one. Field variables can be defined: +• by entering the data directly, +• by reading an Abaqus results file or output database file, +• in an Abaqus/Standard user subroutine, and +• through the co-simulation interface. +If field variables are defined by multiple methods, Abaqus processes them in the order defined +above. Care needs be taken when field variables are used with structural elements, such as membranes +and shells. In this case only the top or bottom face forming the interface region receives a value. +Table 17.2.1–4 lists the temperature and independent field variables available for co-simulation +exchange, their associated field identifiers, the supported co-simulation interface region types, and which +Abaqus solvers support import and export of the field values. +Table 17.2.1–4 +Exchanging temperature and independent field variables. +Field ID +Fields +Interface +Type1 +Abaqus Solver2 +Import Export +Units +TEMP +FV1 +FV2 +FV3 +Temperature as field +variable +Field variable 1 +Field variable 2 +Field variable 3 +1 P (points), S (surface region), V (volume region) +2 S (Abaqus/Standard), E (Abaqus/Explicit), C (Abaqus/CFD) +The following Abaqus/Standard procedures support import of temperature and independent field +variables: +• “Static stress analysis,” Section 6.2.2 +• “Quasi-static analysis,” Section 6.2.5 +• “Implicit dynamic analysis using direct integration,” Section 6.3.2 +• “Fully coupled thermal-stress analysis,” Section 6.5.3 +• “Piezoelectric analysis,” Section 6.7.2 +• “Coupled pore fluid diffusion and stress analysis,” Section 6.8.1 +Temperature +Temperature (field ID TEMP) can be imported by Abaqus/Standard for procedures that allow material +properties to be defined as a function of an external temperature field. When imported, temperature +values are ramped from the values of the previous exchange time point to those of the next target time +point. Use field ID NT instead of field ID TEMP to import temperature values for thermal procedures +(procedures using degrees of freedom 11, 12, etc.). +Temperature can be viewed in the Visualization module of Abaqus/CAE for an Abaqus/Standard +simulation by requesting element output variable TEMP. +Independent field variables +Independent field variables (field IDs FV1, FV2, and FV3) can be imported by Abaqus/Standard, +allowing material properties to be defined as a function of the external fields. When imported, +independent field variable values are ramped from the values of the previous exchange time point to +those of the next target time point. +Field variables can be viewed in the Visualization module of Abaqus/CAE for an Abaqus/Standard +simulation by requesting output variables FV1, FV2, and/or FV3. +Miscellaneous fields +Table 17.2.1–5 lists miscellaneous fields available for co-simulation exchange, their associated field +identifiers, the supported co-simulation interface region types, and which Abaqus solvers support import +and export of the field values. +Table 17.2.1–5 +Exchanging miscellaneous fields. +Field ID +Fields +MASS or +LUMPEDMASS +Mass +RI +Rotary inertia +Interface +Type1 +Abaqus Solver2 +Import Export +Units +P, S +P, S +S, E +S, E, C +1 P (points), S (surface region), V (volume region) +2 S (Abaqus/Standard), E (Abaqus/Explicit), C (Abaqus/CFD) +Lumped mass +Lumped mass values (field ID MASS or LUMPEDMASS) at nodes can be exported by Abaqus/Standard, +Abaqus/Explicit, and Abaqus/CFD and can be imported by Abaqus/Standard and Abaqus/Explicit. +Lumped mass is available for points and surface regions. +Rotary inertia +Nodal (lumped) rotary inertia (field ID RI) can be imported by Abaqus/Standard and exported by +Abaqus/Explicit over points or surface regions for models using structural elements. +Defining the rendezvousing scheme +Different types of analyses have different time integration requirements that will influence or dictate +the frequency of interaction between the analyses in a co-simulation to obtain an accurate and robust +solution. For example, consider the difference in time integration between an implicit and an explicit +dynamic analysis. Furthermore, Abaqus/Standard can adjust the increment sizes automatically to obtain +an economical and accurate solution for transient problems (see “Incrementation” in “Defining an +analysis,” Section 6.1.2). For example, consider a transient heat transfer analysis modeling a diffusive +process; here the analysis may use small time increments at the beginning of the analysis where there +is a high gradient in the solution and large time increments toward the end of the analysis when steady +state is reached. +Co-simulation controls are used to control the frequency of exchange between the analyses in a +co-simulation and to control the time incrementation process in Abaqus. +Input File Usage: +Use both of the following options to specify co-simulation controls using the +SIMULIA Co-Simulation Engine: +*CO-SIMULATION, CONTROLS=name +*CO-SIMULATION CONTROLS, NAME=name +Defining the coupling scheme +The coupling scheme defines the sequence of exchanges between analysis programs and also defines +whether a coupled simulation can be run in a serial, parallel, or iterative manner. When deciding on the +coupling scheme, you should consider solution stability issues as well as the utilization impact on your +computing resources. +When coupling through the SIMULIA Co-Simulation Engine, you have the choice between a +parallel explicit coupling scheme (referred to as the Jacobi coupling algorithm), a sequential explicit +coupling scheme (referred to as the Gauss-Seidel coupling algorithm), or an iterative scheme. +Parallel explicit coupling scheme (Jacobi) +In a parallel explicit coupling scheme, both simulations are executed concurrently, exchanging fields to +update the respective solutions at the next target time. The parallel coupling scheme may make more +efficient use of computing resources; however, it is considered less stable than the sequential scheme and +should be employed only for weakly coupled physics simulations. The co-simulation partner analysis +must also specify a Jacobi coupling algorithm. +Input File Usage: +*CO-SIMULATION CONTROLS, COUPLING SCHEME=JACOBI +Sequential explicit coupling scheme (Gauss-Seidel) +In a sequential explicit coupling scheme, the simulations are executed in sequential order. One analysis +leads while the other analysis lags the co-simulation. The co-simulation partner analysis must also +specify a Gauss-Seidel coupling algorithm. +Input File Usage: +Use the following option to specify that Abaqus leads the co-simulation: +*CO-SIMULATION CONTROLS, COUPLING SCHEME=GAUSS- +SEIDEL, SCHEME MODIFIER=LEAD +The partner analysis must lag the co-simulation. +Use the following option to specify that Abaqus lag the co-simulation: +*CO-SIMULATION CONTROLS, COUPLING SCHEME=GAUSS- +SEIDEL, SCHEME MODIFIER=LAG +The partner analysis must lead the co-simulation. +Iterative coupling scheme +In an iterative coupling scheme, the simulations are executed in sequential order. One analysis leads +while the other analysis lags the co-simulation. Multiple exchanges per coupling step are performed until +termination criteria are met. The co-simulation partner analysis must also specify an iterative coupling +algorithm. +The termination criteria depend on the analyses in the co-simulation; for co-simulation between +Abaqus and third-party analysis products, consult the appropriate User’s Guide. +Input File Usage: +Use the following option to specify that Abaqus leads the co-simulation: +*CO-SIMULATION CONTROLS, COUPLING SCHEME=ITERATIVE, +SCHEME MODIFIER=LEAD +The partner analysis must lag the co-simulation. +Use the following option to specify that Abaqus lag the co-simulation: +*CO-SIMULATION CONTROLS, COUPLING SCHEME=ITERATIVE, +SCHEME MODIFIER=LAG +The partner analysis must lead the co-simulation. +Coupling step size +The coupling step is the period between two consecutive exchanges and consequently defines the +frequency of exchange between the analyses in a co-simulation. The coupling step size is established +at the beginning of each coupling step and is used to compute the target time (the time when the next +synchronized exchange occurs). +When you use the SIMULIA Co-Simulation Engine, several methods are available for computing +the coupling step size. The methods available in Abaqus are described in the sections below. To +determine the methods available for a co-simulation partner analysis, consult the appropriate third-party +program documentation. +Using a constant coupling step size +A constant user-defined coupling step size is the most basic method of defining a coupling step size. +Both analyses advance while exchanging data at target points according to +where +is a value that defines the coupling step size to be used throughout the coupled simulation, +is the time at the start of the coupling step. For this method both Abaqus +is the target time, and +and the co-simulation partner analysis need to specify the same value for the coupling step size. +Input File Usage: +*CO-SIMULATION CONTROLS, STEP SIZE= +Selecting the minimum coupling step size +This method selects the minimum of the coupling step sizes suggested by each analysis. Abaqus always +uses the next increment suggested by its automatic incrementation as its suggested coupling step size. For +this method both Abaqus and the co-simulation partner analysis need to specify the minimum coupling +step size method. +Input File Usage: +*CO-SIMULATION CONTROLS, STEP SIZE=MIN +Selecting the maximum coupling step size +This method selects the maximum of the coupling step sizes suggested by each analysis. Abaqus always +uses the next increment suggested by its automatic incrementation as its suggested coupling step size. For +this method both Abaqus and the co-simulation partner analysis need to specify the maximum coupling +step size method. +Input File Usage: +*CO-SIMULATION CONTROLS, STEP SIZE=MAX +Importing the coupling step size +Abaqus can import a coupling step size suggested by the co-simulation partner analysis. For this method +the co-simulation partner analysis needs to export a coupling step size. +Input File Usage: +*CO-SIMULATION CONTROLS, STEP SIZE=IMPORT +Exporting the coupling step size +Abaqus can export a suggested coupling step size to the co-simulation partner analysis. For this method +the co-simulation partner analysis needs to import a coupling step size determined by Abaqus. Abaqus +exports the next increment suggested by its automatic incrementation scheme. +Input File Usage: +*CO-SIMULATION CONTROLS, STEP SIZE=EXPORT +Time incrementation scheme +Abaqus may take multiple increments per coupling step, or you can force Abaqus to use a single +increment per coupling step. +Allowing Abaqus to subcycle +By default, Abaqus may perform several increments (referred to as “subcycling”) during the coupling +step. During subcycling, Abaqus/Standard ramps the loads and boundary conditions (with the exception +of film properties) from the values at the end of the previous coupling step to the values at the target time, +while in Abaqus/Explicit the loads are applied at the start of the coupling step and kept constant over the +coupling step. +Subcycling allows Abaqus to use its own time incrementation to reach the target coupling time; +specifically, it allows Abaqus to cut back the increment size if there are nonlinear events that require the +increment size to be reduced. +Input File Usage: +*CO-SIMULATION CONTROLS, +TIME INCREMENTATION=SUBCYCLE +Forcing Abaqus to use a single increment per coupling step +In certain cases you may force Abaqus to use a time increment size dictated by the coupling step size (i.e., +no subcycling). This allows both solvers to use the same time incrementation and avoid interpolation of +quantities during the coupling step. When proceeding in this manner, Abaqus will not be able to reduce +the time increment to resolve nonlinear events and, consequently, will terminate the simulation in cases +where the nonlinear events require that the increment size be reduced. +Input File Usage: +*CO-SIMULATION CONTROLS, +TIME INCREMENTATION=LOCKSTEP +Reaching target times +The Abaqus target times can be reached in an exact or loose manner. +Reaching target times in an exact manner +By default, Abaqus exchanges the data in an exact manner; that is, Abaqus temporarily reduces the time +increment so that the solution exchange occurs exactly at the target time. +Input File Usage: +*CO-SIMULATION CONTROLS, TIME MARKS=YES +Reaching target times in a loose manner +When subcycling Abaqus may reach the target time in a loose manner; that is, when the current simulation +time, t, is within half of an Abaqus increment size away from the target time, +In this case performance is selected over solution accuracy. Loose coupling should be employed +only for cases where Abaqus uses more increments than the third-party analysis program; for example, +when coupling an explicit solver with an implicit solver. +Input File Usage: +*CO-SIMULATION CONTROLS, TIME MARKS=NO +Model dimension and coordinate systems +Three-dimensional Abaqus models are fully supported. Two-dimensional and axisymmetric Abaqus +models are supported only for Abaqus/Standard to Abaqus/Explicit co-simulation and coupling using +MpCCI. For co-simulations that do not support two-dimensional and axisymmetric models, you can +represent these models as a three-dimensional slice of unit thickness (or wedge element) with the +appropriate boundary conditions applied. +Vector quantities are defined according to Abaqus conventions; the first component represents the +quantity along the x-axis, the second quantity represents the quantity along the y-axis, and the third +quantity represents the quantity along the +-axis (for three-dimensional models). For axisymmetric +models in Abaqus the axis of revolution is about the y-axis. These conventions apply to both the exported +and the imported vector quantities. +All exported vector quantities are expressed in the global coordinate system of the Abaqus +model, ignoring any transformation definitions. Similarly, the third-party program must provide vector +quantities that are imported into Abaqus in the global coordinate system of the Abaqus model. +The third-party analysis program may use different conventions, please refer to the appropriate +third-party program documentation for further modeling details and/or limitations. +Unit system +Abaqus does not require that the analysis be run with a particular unit system. In general, the unit system +used in creating the Abaqus model may not be the same as that used with the third-party program model. +When the two unit systems differ, the fields exchanged between the two programs must go through a +transformation of units. Refer to the appropriate third-party program documentation for further modeling +details. +For the coupling with MADYMO you can specify a set of conversion factors for the basic units of +mass, length, and time. If a field with the units of length is exported, Abaqus multiplies this quantity by +the length unit conversion factor prior to exporting the value to the third-party program. Similarly, if a +field with the units of length is imported, Abaqus divides this quantity from the third-party program by +the length unit conversion factor prior to using the field in the Abaqus model. The conversion factors are +constructed for the various fields that are exchanged based on the conversion factors for the basic units. +Input File Usage: +Use the following option to specify unit conversion factors when there is +a mismatch in unit systems between the Abaqus/Explicit model and the +MADYMO model: +*CO-SIMULATION, PROGRAM=MADYMO +mass unit conversion factor, length unit conversion factor, +time unit conversion factor +Restarting a co-simulation +Interface loads imported into Abaqus/Standard, Abaqus/Explicit, or Abaqus/CFD are not saved to the +Abaqus restart database. Thus, to restart a co-simulation, the coupled analysis must send the loads +at the start of the restart analysis. These loads must balance the current deformation of the Abaqus +analysis such that the structure is in equilibrium. You must synchronize the restart information written +between the analyses to ensure that the simulation is restarted at the same solution (step) time. For +more information, see “Synchronizing restart information written in a co-simulation” in “Restarting an +analysis,” Section 9.1.1. For example, to restart an FSI co-simulation, the solution time for the particular +step/increment number from which Abaqus is restarted must correspond to the coupled analysis solution. +Limitations +The following limitations apply: +• The steps in the Abaqus model must be defined such that the co-simulation fits entirely within a +single Abaqus step. Further, there can be only one co-simulation in the Abaqus job. You can use the +restart capability to perform multiple co-simulations for an analysis . +• A co-simulation surface or volume defined over beam, pipe, and truss elements or defined over the +edges of three-dimensional elements cannot be used as an interface region. You should use discrete +points to transfer loads and boundary conditions. +• A co-simulation surface or volume defined over modified triangular elements or modified tetrahedral +elements cannot be used as an interface region. +There may be further limitations depending on the third-party analysis program being used. For more +information, refer to the appropriate third-party program documentation. +17.3 +Co-simulation between Abaqus solvers +• “Abaqus/Standard to Abaqus/Explicit co-simulation,” Section 17.3.1 +• “Abaqus/CFD to Abaqus/Standard or to Abaqus/Explicit co-simulation,” Section 17.3.2 +17.3.1 +Abaqus/Standard TO Abaqus/Explicit CO-SIMULATION +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD co-simulation execution,” Section 3.2.4 +• “Co-simulation: overview,” Section 17.1.1 +• “Preparing an Abaqus analysis for co-simulation,” Section 17.2.1 +• *CO-SIMULATION +• *CO-SIMULATION CONTROLS +• “Defining a Standard-Explicit co-simulation interaction,” Section 15.13.14 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +• Chapter 26, “Co-simulation,” of the Abaqus/CAE User’s Manual +Overview +This section discusses analysis setup, execution, and limitation details specific to Abaqus/Standard to +Abaqus/Explicit co-simulation. +Refer to “Dynamic impact of a scooter with a bump,” Section 2.4.1 of the Abaqus Example Problems +Manual, for an example of Abaqus/Standard to Abaqus/Explicit co-simulation. +Identifying the Abaqus step for the co-simulation analysis +The following Abaqus/Standard analysis procedures can be used for an Abaqus/Standard to +Abaqus/Explicit co-simulation: +• “Static stress analysis,” Section 6.2.2 +• “Implicit dynamic analysis using direct integration,” Section 6.3.2 +The following Abaqus/Explicit analysis procedure can be used for an Abaqus/Standard to +Abaqus/Explicit co-simulation: +• “Explicit dynamic analysis,” Section 6.3.3 +Input File Usage: +Use the following option within a step definition for an Abaqus/Standard to +Abaqus/Explicit co-simulation: +Abaqus/CAE Usage: +*CO-SIMULATION, PROGRAM=ABAQUS +Use the following option for an Abaqus/Standard to Abaqus/Explicit +co-simulation: +Interaction module: Create Interaction: Standard-Explicit co-simulation +Identifying the co-simulation interface region +Interaction between the Abaqus/Standard and Abaqus/Explicit models takes place through a common +interface region. +You can specify an interface region using either node sets or surfaces when coupling +Abaqus/Standard to Abaqus/Explicit. You must, however, be consistent in your region definition +in Abaqus/Standard and Abaqus/Explicit; if you define a co-simulation region with a node set or +node-based surface in one analysis, you must use the same type of co-simulation region definition in +the other analysis. Likewise, if you define a co-simulation region with an element-based surface in one +analysis, you must define your co-simulation region with an element-based surface in the other analysis. +You may have dissimilar meshes in regions shared in the Abaqus/Standard and Abaqus/Explicit +model definitions. In some cases, however, you can improve solution stability and accuracy by ensuring +that you have matching nodes at the interface . In these cases +you can use the modeling practice described in “Ensuring matching nodes at the interface regions,” +Section 26.4 of the Abaqus/CAE User’s Manual, to ensure these matching nodes. +Input File Usage: +Use the following option to define an element-based or node-based surface as +a co-simulation region in an Abaqus model: +*CO-SIMULATION REGION, TYPE=SURFACE (default) +surface_A +Use the following option to define a node set as a co-simulation region in an +Abaqus model: +*CO-SIMULATION REGION, TYPE=NODE +nodeset_A +Only one *CO-SIMULATION REGION option can be defined in each Abaqus +analysis. In addition, only one node set or surface can be defined. +Abaqus/CAE Usage: +Interaction module: Create Interaction: Standard-Explicit co-simulation: +Surface or Node Region: select region +Identifying the fields exchanged across a co-simulation interface +For Abaqus/Standard to Abaqus/Explicit co-simulation, you do not define the fields exchanged; they are +determined automatically according to the procedures and co-simulation parameters used. +Defining the rendezvousing scheme +Co-simulation controls are used to control the time incrementation process and the frequency of exchange +between the two Abaqus analyses. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options to specify co-simulation controls: +*CO-SIMULATION, PROGRAM=ABAQUS, CONTROLS=name +*CO-SIMULATION CONTROLS, NAME=name +Interaction module: Create Interaction: Standard-Explicit co-simulation +Time incrementation scheme +You can force Abaqus/Standard to use the same increment size as Abaqus/Explicit, or you can allow +the increment sizes in Abaqus/Standard to differ from those in Abaqus/Explicit (subcycling). The time +incrementation scheme that you choose for coupling affects the solution computational cost and accuracy +but not the solution stability. +The subcycling scheme is frequently the most cost effective since Abaqus/Standard time +increments, free of any forced co-simulation time incrementation constraints, are commonly much +longer than Abaqus/Explicit time increments. The subcycling scheme, however, may be less cost +effective when a large portion of the nodes in the model are at the co-simulation interface. This is +because Abaqus/Standard performs a set of stabilization operations at the interface (a “free solve”) for +each increment in the Abaqus/Explicit analysis. These free-solve operations require an implicit solution +of a dense system of equations that scale with the number of interface nodes. In cases of a large number +of interface nodes the computational cost of this interface solve can exceed any cost savings seen due to +subcycling. Hence, for a model where a significant share of the nodes are at the co-simulation interface +performance may be poorer with the subcycling scheme. +Forcing Abaqus to use a single increment per coupling step +You can force Abaqus/Standard to match the increment size of Abaqus/Explicit, and fields will be +exchanged at each of the shared increments. +Input File Usage: +Use the following option in the Abaqus/Standard analysis and in the +Abaqus/Explicit analysis: +Abaqus/CAE Usage: +*CO-SIMULATION CONTROLS, TIME INCREMENTATION=LOCKSTEP +Use the following input +in the Abaqus/Standard analysis and in the +Abaqus/Explicit analysis: +Interaction module: Create Interaction: Standard-Explicit co-simulation: +Incrementation control: Lock time steps +Allowing Abaqus to subcycle +You can allow the Abaqus/Standard increment size to differ from those in Abaqus/Explicit. In this case +fields will be exchanged as needed. +Input File Usage: +Use the following option in the Abaqus/Standard analysis and in the +Abaqus/Explicit analysis: +*CO-SIMULATION CONTROLS, +TIME INCREMENTATION=SUBCYCLE +Abaqus/CAE Usage: +Use the following input +Abaqus/Explicit analysis: +in the Abaqus/Standard analysis and in the +Interaction module: Create Interaction: Standard-Explicit co-simulation: +Incrementation control: Allow subcycling +Controlling interface matrix factorization frequency +For the subcycling time incrementation scheme an interface solve is performed, by default, +in +Abaqus/Standard for every Abaqus/Explicit increment. This solve can be significantly costly for two +reasons. First, the interface matrix used for the interface solve is dense and its size scales with the +number of interface nodes. Second, the interface matrix changes every Abaqus/Explicit increment, +requiring factorization in Abaqus/Standard for every Abaqus/Explicit increment. You can reduce the +impact of this cost by approximating the interface matrix and factorizing it typically once for the +duration of an Abaqus/Standard increment, rather than for each Abaqus/Explicit increment. However, +if the Abaqus/Explicit stable time increment changes significantly, the interface matrix is refactored for +stability reasons. +Allowing Abaqus/Standard to factorize the interface matrix every Abaqus/Explicit increment +Factorizing the interface matrix every Abaqus/Explicit increment is the default approach. +Input File Usage: +Use the following option in the Abaqus/Standard analysis: +*CO-SIMULATION CONTROLS, +FACTORIZATION FREQUENCY=EXPLICIT INCREMENT +Abaqus/CAE Usage: +Factorizing the interface matrix every Abaqus/Explicit increment is used by +default in Abaqus/CAE. +Forcing Abaqus/Standard to factorize the interface matrix once per Abaqus/Standard increment +When the number of interface nodes is large, the cost of the interface factorization can be significantly +reduced by using this approach. Only the interface matrix factorization is performed once per +Abaqus/Standard increment; the interface solve is performed every Abaqus/Explicit increment using +this factorized interface matrix. Since this approach approximates the interface matrix, it may slightly +increase the drift in the displacement solution at the co-simulation interface. The performance gain with +this method depends on the number of interface nodes, the subcycling ratio (which is the ratio between +Abaqus/Standard and Abaqus/Explicit increments), and the size of the models. For models with greater +than 100 interface nodes and a subcycling ratio greater than 50, this method typically reduces the +analysis time by a factor between 1.2 and 3.0. The performance gain increases for larger subcycling +ratios and decreases for larger models. +Input File Usage: +Use the following option in the Abaqus/Standard analysis: +*CO-SIMULATION CONTROLS, +FACTORIZATION FREQUENCY=STANDARD INCREMENT +Abaqus/CAE Usage: +Factorizing the interface matrix once per Abaqus/Standard increment is not +supported in Abaqus/CAE. +Coupling step size +The coupling step size is the period between two consecutive co-simulation data exchanges between +Abaqus/Standard and Abaqus/Explicit and always equals the current Abaqus/Explicit increment size. +When using the subcycling method, +this data exchange does not represent a constraint on +Abaqus/Standard incrementation; the Abaqus/Standard analysis advances in time using its normal time +incrementation logic, but performs data exchanges as needed at the coupling step size intervals. +Variable coupling step size +If you do not specify a constant coupling step size, Abaqus/Standard and Abaqus/Explicit use the next +Abaqus/Explicit increment size as the coupling step size. +Input File Usage: +Abaqus/CAE Usage: +Use the following option in either or both of the Abaqus/Standard and +Abaqus/Explicit analyses: +*CO-SIMULATION CONTROLS (omit the STEP SIZE parameter) +Use the following input in the Abaqus/Standard and Abaqus/Explicit analyses: +Interaction module: Create Interaction: Standard-Explicit co-simulation: +Coupling step period: Determined by analysis +Constant user-defined coupling step size +A constant user-defined coupling step size can be specified. Since data exchange occurs at every +Abaqus/Explicit increment, the Abaqus/Explicit increment will be set equal to the user-defined coupling +step size. This is functionally equivalent to specifying direct user control on the increment size +in Abaqus/Explicit. +In Abaqus/Standard the step size parameter is ignored for Abaqus/Standard to +Abaqus/Explicit co-simulation. +Input File Usage: +Abaqus/CAE Usage: +In the Abaqus/Explicit analysis you may optionally specify a step size: +*CO-SIMULATION CONTROLS, STEP SIZE=coupling_step_size +Use the following input in the Abaqus/Explicit analysis: +Interaction module: Create Interaction: Standard-Explicit co-simulation: +Coupling step period: Specified: coupling_step_size +Executing the coupled analysis +jobs as described in “Abaqus/Standard, +You execute the Abaqus/Standard and Abaqus/Explicit +Abaqus/Explicit, and Abaqus/CFD co-simulation execution,” Section 3.2.4. +the +Abaqus/Explicit packager and analysis are both run in double precision to avoid numerical instabilities. +You can execute the coupled analysis interactively in Abaqus/CAE as described in “Understanding +By default, +co-executions,” Section 19.4 of the Abaqus/CAE User’s Manual. +Input File Usage: +Enter the following input on the command line: +Abaqus/CAE Usage: +abaqus cosimulation cosimjob=cosim-job-name +job=job-name-A,job-name-B +Job module: +Co-execution→Create: select the Abaqus/Standard model and the +Abaqus/Explicit model; Communication time out: timeout-value +Co-execution→Manager: Submit +Considerations for using the timeout parameter +The timeout execution parameter specifies the amount of time in seconds that each analysis waits to +receive the co-simulation message expected from the other analysis that is running. The default timeout +value is 60 minutes when submitting jobs using the command line options and 10 minutes when executing +the jobs in Abaqus/CAE. When the timeout period is large compared to typical analysis increment +wallclock times, you have greater flexibility in starting jobs and performing operations that precede +the co-simulation analysis step. Examples where this flexibility is needed include: job submission using +queues, analyses where steps that precede the co-simulation step have long run times, and cases where one +job is resubmitted because of an input error. However, a large timeout period can cause problems when +one of the co-simulation jobs fails (for reasons such as convergence issues or availability of computer +resources) before the initial co-simulation communication is established. In these cases you may prefer +to kill the job left running rather than have it wait the entire timeout period. +Command usage example +Use the following command to submit a co-simulation between an Abaqus/Standard analysis called “std” +and an Abaqus/Explicit analysis called “xpl”: +abaqus cosimulation cosimjob=beam job=std,xpl +Diagnostics information +The Abaqus/Standard job provides detailed descriptions of co-simulation operations in the message +(.msg) file. For the subcycling scheme the status (.sta) file provides summary information indicating +when the interface calculations followed by re-solve of the increment are made, as shown in the +following example status file. The E suffix in the attempt-count entry (column 3) indicates an increment +performing interface calculations. An increment without the E suffix indicates re-solve of the increment. +SUMMARY OF JOB INFORMATION: +STEP +INC ATT SEVERE EQUIL TOTAL +DISCON ITERS ITERS +ITERS +1E +1E +1E +1E +TOTAL +TIME/ +FREQ +0.000 +0.00100 +0.00100 +0.00200 +0.00200 +0.00300 +0.00300 +0.00400 +STEP +TIME/LPF +INC OF +TIME/LPF +DOF +IF +MONITOR RIKS +0.000 +0.00100 +0.00100 +0.00200 +0.00200 +0.00300 +0.00300 +0.00400 +0.001000 +0.001000 +0.001000 +0.001000 +0.001000 +0.001000 +0.001000 +0.001000 +The Abaqus/Explicit job provides summary descriptions of co-simulation operations in the status +(.sta) file. +Limitations +The following limitations apply to Abaqus/Standard to Abaqus/Explicit co-simulation in addition to the +limitations discussed in “Preparing an Abaqus analysis for co-simulation,” Section 17.2.1. +General limitations +• Displacement compatibility at the co-simulation interface is not maintained when you allow the +Abaqus/Standard increment size to differ from that in Abaqus/Explicit (i.e., when you specify +subcycling as a co-simulation time incrementation control). In this case velocity compatibility is +maintained, but you may see small amounts of displacement mismatch between Abaqus/Standard +and Abaqus/Explicit as the simulation advances in time. This “drift” is more pronounced if +severe nonlinearity such as plastic deformation occurs at the co-simulation interface. You can +control this drift by adjusting Abaqus/Standard solution parameters so that the Abaqus/Standard +increment size is reduced (e.g., by limiting the maximum time increment size or specifying a +smaller half-increment residual tolerance for implicit dynamic analyses). +• Nodal transformations are not permitted on the co-simulation region nodes. +• The ALE technique may not be used in elements attached to co-simulation region nodes. +• Fully coupled temperature-displacement elements can be used, but no temperature quantities are +exchanged. +• An Abaqus/Standard static stress analysis cannot be used with the lockstep time incrementation +scheme in Abaqus/Standard to Abaqus/Explicit co-simulation. +Dissimilar mesh-related limitations +When your Abaqus/Standard and Abaqus/Explicit co-simulation region meshes differ, the following +limitations apply: +• Solution accuracy may be affected when your co-simulation region meshes are not uniform in the +presence or absence of rotational degrees of freedom; for example, if a continuum element mesh is +locally reinforced with beam or shell elements at the co-simulation region interface. +• In cases where the stress state near the co-simulation interface is significant (approaching 1% or +more) relative to the material stiffness, you may observe appreciable irregular mesh distortion if +the mesh density adjacent to the co-simulation region differs greatly between the Abaqus/Explicit +and Abaqus/Standard models. For example, this effect is common with large deformation of +hyperelastic materials. You can minimize this effect by choosing a similar or finer mesh at the +Abaqus/Standard co-simulation region when using the subcycling time integration scheme or +by choosing a similar or finer mesh at the Abaqus/Explicit co-simulation region when using the +lockstep time integration scheme. +Abaqus/Standard analysis limitations +Abaqus/Standard elements that have no equivalent degree-of-freedom counterpart in Abaqus/Explicit +cannot be connected to co-simulation region nodes. These elements include +• Axisymmetric elements with twist degrees of freedom (the CGAX element family) +• Axisymmetric solid elements with asymmetric deformation (the CAXA element family) +• Generalized plane strain elements (the CPEG element family) +• Coupled pore pressure-displacement elements +• Heat transfer and thermal-electrical elements +• Acoustic elements +• Piezoelectric elements +The following specific limitations also apply: +• A co-simulation region node cannot be a slave node in a tie constraint, an MPC constraint, or a +kinematic coupling constraint. +Abaqus/Explicit analysis limitations +Stability and accuracy of the co-simulation solution may be adversely affected when the following model +features are defined at or near the co-simulation region: +• Connector elements connected to co-simulation region nodes. +• Co-simulation region nodes that participate in a tie constraint, an MPC constraint, or a kinematic +coupling constraint. +When using these features, you should compare the Abaqus/Standard and Abaqus/Explicit solutions +(e.g., compatibility of the displacement history) at the co-simulation interface as an indicator of solution +accuracy. +17.3.2 +Abaqus/CFD TO Abaqus/Standard OR TO Abaqus/Explicit CO-SIMULATION +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD Abaqus/CAE +References +• “Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD co-simulation execution,” Section 3.2.4 +• “Co-simulation: overview,” Section 17.1.1 +• “Preparing an Abaqus analysis for co-simulation,” Section 17.2.1 +• *CO-SIMULATION +• *CO-SIMULATION CONTROLS +• “Defining a fluid-structure co-simulation interaction,” Section 15.13.15 of the Abaqus/CAE User’s +Manual, in the online HTML version of this manual +• Chapter 26, “Co-simulation,” of the Abaqus/CAE User’s Manual +Overview +This section discusses analysis setup, execution, and limitation details specific to Abaqus/CFD to +Abaqus/Standard or to Abaqus/Explicit co-simulation for fluid-structure interaction and conjugate heat +transfer. +Refer to “Conjugate heat transfer analysis of a component-mounted electronic circuit board,” +for an example of Abaqus/CFD to +Section 6.1.1 of the Abaqus Example Problems Manual, +Abaqus/Standard co-simulation. +Identifying the Abaqus step for the co-simulation analysis +The following Abaqus/CFD analysis procedure can be used for co-simulation with Abaqus/Standard or +Abaqus/Explicit: +• “Incompressible fluid dynamic analysis,” Section 6.6.2 +The following Abaqus/Standard analysis procedures can be used for co-simulation with Abaqus/CFD: +• “Implicit dynamic analysis using direct integration,” Section 6.3.2 +• “Uncoupled heat transfer analysis,” Section 6.5.2 +The following Abaqus/Explicit analysis procedures can be used for co-simulation with Abaqus/CFD: +• “Explicit dynamic analysis,” Section 6.3.3 +• “Fully coupled thermal-stress analysis in Abaqus/Explicit” in “Fully coupled thermal-stress +analysis,” Section 6.5.3 +Input File Usage: +Use the following option within a step definition for an Abaqus/CFD to +Abaqus/Standard or to Abaqus/Explicit co-simulation: +*CO-SIMULATION, PROGRAM=MULTIPHYSICS +Abaqus/CAE Usage: +Use the following option for an Abaqus/CFD to Abaqus/Standard or to +Abaqus/Explicit co-simulation: +Interaction module: Create Interaction: Fluid-Structure +Co-simulation boundary +Identifying the co-simulation interface region +You specify an interface region using surfaces when coupling Abaqus/CFD to Abaqus/Standard or to +Abaqus/Explicit. You must define an element-based surface, and you can specify only one surface to be +used as the interface region in the analysis. You may have dissimilar meshes in regions shared in the +model definitions. +Input File Usage: +Use the following option to define an element-based surface as a co-simulation +region: +*CO-SIMULATION REGION, TYPE=SURFACE +surface_A +Abaqus/CAE Usage: +Interaction module: Create Interaction: Fluid-Structure Co-simulation +boundary: select surface region +Identifying the fields exchanged across a co-simulation interface +For Abaqus/CFD to Abaqus/Standard or to Abaqus/Explicit co-simulation, see the tables in “Identifying +the fields exchanged across a co-simulation interface” in “Preparing an Abaqus analysis for +co-simulation,” Section 17.2.1, for lists of fields that are available for co-simulation exchange. When +using Abaqus/CAE, the fields exchanged are determined automatically by Abaqus/CAE. +Defining the rendezvousing scheme +Co-simulation controls are used to control the time incrementation process and the frequency of exchange +between the two Abaqus analyses. These controls are specified automatically in Abaqus/CAE. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options to specify co-simulation controls: +*CO-SIMULATION, PROGRAM=MULTIPHYSICS, CONTROLS=name +*CO-SIMULATION CONTROLS, NAME=name +Interaction module: Create Interaction: Fluid-Structure +Co-simulation boundary +Defining the coupling scheme +The sequential explicit coupling scheme (also referred to as the Gauss-Seidel coupling algorithm) +is the only coupling scheme available for Abaqus/CFD to Abaqus/Standard or to Abaqus/Explicit +co-simulation. By default, the Abaqus/CFD analysis lags the co-simulation and the Abaqus/Standard or +Abaqus/Explicit analysis leads the co-simulation. For conjugate heat transfer, the Abaqus/CFD analysis +can either lag or lead the co-simulation. For fluid-structure interaction, the Abaqus/CFD analysis must +lag the co-simulation and the Abaqus/Standard or Abaqus/Explicit analysis must lead the co-simulation. +Input File Usage: +Use the following option to specify that the analysis leads the co-simulation: +*CO-SIMULATION CONTROLS, SCHEME MODIFIER=LEAD +Use the following option to specify that the analysis lags the co-simulation: +*CO-SIMULATION CONTROLS, SCHEME MODIFIER=LAG +The coupling scheme is specified automatically in Abaqus/CAE when you +define a fluid-structure co-simulation interaction. +Abaqus/CAE Usage: +Coupling step size +The coupling step size is the period between two consecutive co-simulation data exchanges. The +coupling step size is determined automatically based on the type of analysis and is used to obtain +time-accurate solutions for the coupled physics problem. For fluid-structure interaction (FSI) and +conjugate heat transfer (CHT) analyses that couple Abaqus/CFD and Abaqus/Standard, the coupling +step size is the minimum of the time step sizes determined by the automatic time incrementation +schemes of the individual analyses. For FSI problems that couple Abaqus/CFD and Abaqus/Explicit, +Abaqus/Explicit imports the coupling step size from Abaqus/CFD; consequently, Abaqus/CFD exports +the coupling step size to Abaqus/Explicit. +Time incrementation scheme +Depending on the type of analysis, Abaqus may either perform one increment (referred to as “lockstep”) +or several increments (referred to as “subcycling”) per coupling step. By default, for FSI and CHT +analyses that couple Abaqus/CFD and Abaqus/Standard, there is no subcycling involved because the +coupling step size is based on the minimum of the individual analyses. For FSI analyses that couple +Abaqus/CFD and Abaqus/Explicit, Abaqus/Explicit typically uses subcycling while Abaqus/CFD uses +lockstep behavior. +Input File Usage: +Use the following option to allow the analysis to subcycle: +*CO-SIMULATION CONTROLS, TIME +INCREMENTATION=SUBCYCLE +Use the following option to force the analysis to use a single increment per +coupling step: +*CO-SIMULATION CONTROLS, TIME INCREMENTATION=LOCKSTEP +The time incrementation scheme is specified automatically in Abaqus/CAE +when you define a fluid-structure co-simulation interaction. +Abaqus/CAE Usage: +Reaching target times +The Abaqus target times can be reached in an exact or loose manner. By default, Abaqus exchanges +the data in an exact manner; that is, Abaqus temporarily reduces the time increment so that the solution +exchange occurs exactly at the target time. When subcycling Abaqus may reach the target time in a loose +manner; that is, when the current simulation time, t, is within half of an Abaqus increment size away +from the target time, +Input File Usage: +Use the following option to reach target times in an exact manner: +*CO-SIMULATION CONTROLS, TIME MARKS=YES (default) +Use the following option to reach target times in a loose manner: +Abaqus/CAE Usage: +*CO-SIMULATION CONTROLS, TIME MARKS=NO +The manner is which target times are reached is specified automatically in +Abaqus/CAE when you define a fluid-structure co-simulation interaction. +Executing the coupled analysis +You execute the Abaqus/CFD and Abaqus/Standard or Abaqus/Explicit +jobs as described in +“Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD co-simulation execution,” Section 3.2.4. By +default, when coupling Abaqus/CFD to Abaqus/Explicit, the Abaqus/Explicit packager and analysis are +both run in single precision. +You can execute the coupled analysis interactively in Abaqus/CAE as described in “Understanding +co-executions,��� Section 19.4 of the Abaqus/CAE User’s Manual. +Input File Usage: +Enter the following input on the command line: +Abaqus/CAE Usage: +abaqus cosimulation cosimjob=cosim-job-name +job=job-name-A,job-name-B +Job module: +Co-execution→Create: select the models and define initial +job parameter settings +Co-execution→Manager: Submit +Considerations for using the timeout parameter +The timeout execution parameter specifies the amount of time in seconds that each analysis waits to +receive the co-simulation message expected from the other analysis that is running. The default timeout +value is 60 minutes when submitting jobs using the command line options and 10 minutes when executing +the jobs in Abaqus/CAE. When the timeout period is large compared to typical analysis increment +wallclock times, you have greater flexibility in starting jobs and performing operations that precede +the co-simulation analysis step. Examples where this flexibility is needed include: job submission using +queues, analyses where steps that precede the co-simulation step have long run times, and cases where one +job is resubmitted because of an input error. However, a large timeout period can cause problems when +one of the co-simulation jobs fails (for reasons such as convergence issues or availability of computer +resources) before the initial co-simulation communication is established. In these cases you may prefer +to kill the job left running rather than have it wait the entire timeout period. +Command usage example +Use the following command to run a co-simulation between a heat transfer analysis called “solid_heat” +and a fluids analysis called “fluid”, interactively: +abaqus cosimulation cosimjob=cosim_cht +job=solid_heat,fluid interactive +Limitations +The following limitations apply to Abaqus/CFD to Abaqus/Standard or to Abaqus/Explicit co-simulation +in addition to the limitations discussed in “Preparing an Abaqus analysis for co-simulation,” +Section 17.2.1. +General limitation +An interface region can be used for fluid-structure interaction or conjugate heat transfer but not both. +Abaqus/Standard analysis limitations +Abaqus/Standard elements that have no equivalent degree-of-freedom counterpart in Abaqus/CFD +cannot be connected to co-simulation region nodes. These elements include the following: +• Axisymmetric elements with twist degrees of freedom (the CGAX element family) +• Axisymmetric solid elements with asymmetric deformation (the CAXA element family) +• Generalized plane strain elements (the CPEG element family) +• Coupled pore pressure-displacement elements +• Acoustic elements +• Piezoelectric elements +18. +Extending Abaqus Analysis Functionality +User subroutines and utilities +18.1 +User subroutines and utilities +• “User subroutines: overview,” Section 18.1.1 +• “Available user subroutines,” Section 18.1.2 +• “Available utility routines,” Section 18.1.3 +18.1.1 +USER SUBROUTINES: OVERVIEW +References +• “Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD execution,” Section 3.2.2 +• Abaqus User Subroutines Reference Manual +Overview +User subroutines: +• are provided to increase the functionality of several Abaqus capabilities for which the usual data +input methods alone may be too restrictive; +• provide an extremely powerful and flexible tool for analysis; +• are typically written as FORTRAN code and must be included in a model when you execute the +analysis, as discussed below; +• must be included and, if desired, can be revised in a restarted run, since they are not saved to the +restart files ; +• cannot be called one from another; and +• can in some cases call utility routines that are also available in Abaqus . +Including user subroutines in a model +You can include one or more user subroutines in a model by specifying the name of a FORTRAN source +or object file that contains the subroutines. Details are provided in “Abaqus/Standard, Abaqus/Explicit, +and Abaqus/CFD execution,” Section 3.2.2. +Input File Usage: +Enter the following input on the command line: +Abaqus/CAE Usage: +Job module: job editor: General: User subroutine file +abaqus job=job-name user={source-file | object-file} +Managing external databases in Abaqus/Standard and exchanging information with other +software +In Abaqus/Standard it is sometimes desirable to set up the FORTRAN environment and manage +interactions with external data files that are used in conjunction with user subroutines. For example, +there may be history-dependent quantities to be computed externally, once per increment, for use during +the analysis; or output quantities that are accumulated over multiple elements in COMMON block +variables within user subroutines may need to be written to external files at the end of a converged +increment for postprocessing. Such operations can be performed with user subroutine UEXTERNALDB. +This user interface can potentially be used to exchange data with another code, allowing for “stagger” +between Abaqus/Standard and another code. +Writing a user subroutine +User subroutines should be written with great care. To ensure their successful implementation, the +rules and guidelines below should be followed. For a detailed discussion of the individual subroutines, +including coding interfaces and requirements, refer to the Abaqus User Subroutines Reference Manual. +Required INCLUDE statement +Every Abaqus/Standard user subroutine must include the statement +include 'aba_param.inc' +as the first statement after the argument list. +Every Abaqus/Explicit user subroutine must include the statement +include 'vaba_param.inc' +as the first statement after the argument list. +If variables are exchanged between the main user subroutine and subsequent subroutines, the user +should specify the above include statement in all the subroutines to preserve precision. +The files aba_param.inc and vaba_param.inc are installed on the system by the Abaqus +installation procedure and contain important installation parameters. These statements tell the Abaqus +execution procedure, which compiles and links the user subroutine with the rest of Abaqus, to include +the aba_param.inc or vaba_param.inc file automatically. It is not necessary to find the file and +copy it to any particular directory; Abaqus will know where to find it. +Naming convention +If user subroutines call other subroutines or use COMMON blocks to pass information, such subroutines +or COMMON blocks should begin with the letter K since this letter is never used to start the name of +any subroutine or COMMON block in Abaqus. +Redefining variables +User subroutines must perform their intended function without overwriting other parts of Abaqus. In +particular, you should redefine only those variables identified in this chapter as “variables to be defined.” +Redefining “variables passed in for information” will have unpredictable effects. +Compilation and linking problems +If problems are encountered during compilation or linking of the subroutine, make sure that the Abaqus +environment file (the default location for this file is the site subdirectory of the Abaqus installation) +contains the correct compile and link commands as specified in the Abaqus Installation and Licensing +Guide. These commands should have been set up by the Abaqus site manager during installation. The +number and type of arguments must correspond to what is specified in the documentation. Mismatches +in type or number of arguments may lead to platform-dependent linking or runtime errors. +Memory allocation considerations +Your user subroutine will share memory resources with Abaqus. When you need to use large arrays or +other large data structures, you should allocate their memory dynamically, so that memory is allocated +from the heap and not the stack. Failure to dynamically allocate large arrays may result in stack overflow +errors and an abort of your Abaqus analysis. For an example of dynamic allocation of an array in a +FORTRAN program, refer to “Creation of a data file to facilitate the postprocessing of elbow element +results: FELBOW,” Section 14.1.6 of the Abaqus Example Problems Manual. +Testing and debugging +When developing user subroutines, test them thoroughly on smaller examples in which the user +subroutine is the only complicated aspect of the model before attempting to use them in production +analysis work. +If needed, debug output can be written to the Abaqus/Standard message (.msg) file using +FORTRAN unit 7 or to the Abaqus/Standard data (.dat) file or the Abaqus/Explicit status (.sta) +file using FORTRAN unit 6; these units should not be opened by your routines since they are already +opened by Abaqus. +FORTRAN units 15 through 18 or units greater than 100 can be used to read or write other user- +specified information. The use of other FORTRAN units may interfere with Abaqus file operations; +see “FORTRAN unit numbers used by Abaqus,” Section 3.7.1. You must open these FORTRAN units; +and because of the use of scratch directories, the full pathname for the file must be used in the OPEN +statement. +Terminating an analysis +Utility routine XIT (Abaqus/Standard) or XPLB_EXIT (Abaqus/Explicit) should be used instead +of STOP when terminating an analysis from within a user subroutine. This will ensure that all files +associated with the analysis are closed properly (“Terminating an analysis,” Section 2.1.15 of the +Abaqus User Subroutines Reference Manual). +Models defined in terms of an assembly of part instances +An Abaqus model can be defined in terms of an assembly of part instances . +Reference coordinate system +Although a local coordinate system can be defined for each part instance, all variables (such as current +coordinates) are passed to a user subroutine in the global coordinate system, not in a part-local coordinate +system. The only exception to this rule is when the user subroutine interface specifically indicates that a +variable is in a user-defined local coordinate system (“Orientations,” Section 2.2.5, or “Transformed +coordinate systems,” Section 2.1.5). The local coordinate system originally may have been defined +relative to a part coordinate system, but it was transformed according to the positioning data given for +the part instance. As a result, a new local coordinate system was created relative to the assembly (global) +coordinate system. This new coordinate system definition is the one used for local orientations in user +subroutines. +Node and element numbers +The node and element numbers passed to a user subroutine are internal numbers generated by +Abaqus. These numbers are global in nature; all internal node and element numbers are unique. If the +original number and the part instance name are required, call the utility subroutine GETPARTINFO +(Abaqus/Standard) or VGETPARTINFO (Abaqus/Explicit) from within your user subroutine . The +expense of calling these routines is not trivial, so minimal use of them is recommended. +utility +Another +or VGETINTERNAL +(Abaqus/Explicit), can be used to retrieve the internal node or element number corresponding to +a given part instance name and local number. +GETINTERNAL (Abaqus/Standard) +subroutine, +Set and surface names +Set and surface names passed to user subroutines are always prefixed by the assembly and part instance +names, separated by underscores. For example, a surface named surf1 belonging to part instance +Part1-1 in assembly Assembly1 will be passed to a user subroutine as +Assembly1_Part1-1_surf1 +Solution-dependent state variables +Solution-dependent state variables are values that can be defined to evolve with the solution of an +analysis. +Defining and updating +Any number of solution-dependent state variables can be used in the following user subroutines: +• CREEP +• FRIC +• HETVAL +• UANISOHYPER_INV +• UANISOHYPER_STRAIN +• UEL +• UEXPAN +• UGENS +• UHARD +• UHYPER +• UINTER +• UMAT +• UMATHT +• UMULLINS +• USDFLD +• UTRS +• VFABRIC +• VFRIC +• VFRICTION +• VUANISOHYPER_INV +• VUANISOHYPER_STRAIN +• VUFLUIDEXCH +• VUHARD +• VUINTER +• VUINTERACTION +• VUMAT +• VUMULLINS +• VUSDFLD +• VUTRS +• VUVISCOSITY +• VWAVE +The state variables can be defined as a function of any other variables appearing in these subroutines +and can be updated accordingly. Solution-dependent state variables should not be confused with field +variables, which may also be needed in the constitutive routines and can vary with time; field variables +are discussed in detail in “Predefined fields,” Section 33.6.1. +state +and +VUINTERACTION are defined as state variables at slave nodes and are updated with other contact +variables. +in VFRIC, VUINTER, VFRICTION, +Solution-dependent +variables +used +Allocating space +You must allocate space for each of the solution-dependent state variables at every applicable integration +point or contact slave node. +Separate user subroutine groups have been identified that differ in the way the number of +solution-dependent state variables is defined. These groups are described below. Solution-dependent +state variables can be shared by subroutines within the same group; they cannot be shared between +subroutines belonging to different groups. +Input File Usage: +For most subroutines the number of such variables required at the points or +nodes is entered as the only value on the data line of the *DEPVAR option, +Abaqus/CAE Usage: +which should be included as part of the material definition for every material +in which solution-dependent state variables are to be considered: +*DEPVAR +For subroutines that do not use the material behavior defined with the +*MATERIAL option, the *DEPVAR option is not used. +For subroutine UEL: +*USER ELEMENT, VARIABLES=number of variables +For subroutine UGENS: +*SHELL GENERAL SECTION, USER, VARIABLES=number of variables +For subroutines FRIC and VFRIC: +*FRICTION, USER, DEPVAR=number of variables +For subroutines UINTER and VUINTER: +*SURFACE INTERACTION, USER, DEPVAR=number of variables +For subroutine VFRICTION: +*FRICTION, USER=FRICTION, DEPVAR=number of variables +For subroutine VUFLUIDEXCH: +*FLUID EXCHANGE PROPERTY, TYPE=USER, +DEPVAR=number of variables +For subroutine VUINTERACTION: +*SURFACE INTERACTION, USER=INTERACTION, +DEPVAR=number of variables +For subroutine VWAVE: +*WAVE, TYPE=USER, DEPVAR=number of variables +For most subroutines the number of such variables required at the points or +nodes is entered as part of the material definition for every material in which +solution-dependent state variables are to be considered: +Property module: material editor: General→Depvar: Number of +solution-dependent state variables +Defining initial values +You can define the initial values of solution-dependent state variable fields directly or in Abaqus/Standard +through a user subroutine. The initial values of solution-dependent state variables for contact or for user +subroutine VWAVE in Abaqus/Explicit are assigned as zero internally. +Defining initial values directly +You can define the initial values in a tabular format for elements and/or element sets. See “Initial +conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1, for additional details. +Input File Usage: +*INITIAL CONDITIONS, TYPE=SOLUTION +Defining initial values in a user subroutine in Abaqus/Standard +For complicated cases in Abaqus/Standard you can call user subroutine SDVINI so that dependencies +on coordinates, element numbers, etc. can be used in the definition of the variable field. +Input File Usage: +*INITIAL CONDITIONS, TYPE=SOLUTION, USER +Output +User-defined, solution-dependent state variables can be written to the data (.dat) file, the output +database (.odb) file, and the results (.fil) file; the output identifiers SDV and SDVn are available +as element integration variables . Output of these variables is not available +for user subroutines VFRIC, VUINTER, VFRICTION, VUINTERACTION, and VWAVE. +Alphanumeric data +Alphanumeric data, such as labels (names) of surfaces or materials, are always passed into user +subroutines in the upper case. As a result, direct comparison of these labels with corresponding +lower-case characters will fail. Upper case must be used for all such comparisons. An example of such +a comparison can be found in “UMAT,” Section 1.1.40 of the Abaqus User Subroutines Reference +It illustrates the code setup inside user subroutine UMAT when more than one user-defined +Manual. +material model needs to be defined. The variable CMNAME is compared against MAT1 and MAT2 (even +in situations where the material names may have been defined as mat1 and mat2, respectively.) +Precision in Abaqus/Explicit +Abaqus/Explicit is installed with both single precision and double precision executables. To use +the double precision executable, you must specify double precision when you run the analysis . All variables in the +user subroutines that start with the letters a to h and o to z will automatically be defined in the precision +of the executable that you run. The precision of the executable is defined in the vaba_param.inc +file, and it is not necessary to define the precision of the variables explicitly. +Vectorization in Abaqus/Explicit +Abaqus/Explicit user subroutines are written with a vector interface, which means that blocks of data +are passed to the user subroutines. For example, the vectorized user material routines (VFABRIC +and VUMAT) are passed stresses, strains, state variables, etc. for nblock material points. One of the +parameters defined by vaba_param.inc is maxblk, the maximum block size. If the user subroutine +requires the dimensioning of temporary arrays, they can be dimensioned by maxblk. +Parallelization +User subroutines can be used when running jobs in parallel. However, the use of common block +statements in the user subroutines or in subroutines called by the user subroutines must be avoided since +it will result in unpredictable behavior of the executable. +User subroutine calls +Most of the user subroutines available in Abaqus are called at least once for each increment during an +analysis step. However, as discussed below, many subroutines are called more or less often. +Subroutines that define material, element, or interface behavior +Most user subroutines that are used to define material, element, or interface behavior are called twice per +material point, element, or slave surface node in the first iteration of every increment such that the model’s +initial stiffness matrix can be formulated appropriately for the step procedure chosen. The subroutines +are called only once per material point, element, or slave surface node in each succeeding iteration within +the increment. +By default, +in transient implicit dynamic analyses (“Implicit dynamic analysis using direct +integration,” Section 6.3.2) Abaqus/Standard calculates accelerations at the beginning of each dynamic +step. Abaqus/Standard must call user subroutines that are used to define material, element, or interface +behavior two extra times for each material point, element, or slave surface node prior to the zero +increment. The extra calls to the user subroutines are not made if the initial acceleration calculations +If the half-increment residual tolerances are being checked in a transient implicit +are suppressed. +dynamic step, Abaqus/Standard must call these user subroutines (except UVARM) one extra time for +each material point, element, or slave surface node at the end of each increment. If the calculation of +the half-increment residual is suppressed, the extra call to the user subroutines is not made. +User subroutines UHARD, UHYPEL, UHYPER, and UMULLINS, when used in plane stress analyses, +are called more often. +Subroutines that define initial conditions or orientations +User subroutines that are used to define initial conditions or orientations are called before the first iteration +of the first step’s initial increment within an analysis. +Subroutines that define predefined fields +User subroutines that are used to define predefined fields are called prior to the first iteration of the +relevant step’s first increment for all iterations of all increments whenever the current field variable is +needed. +Verification of subroutine calls +If there is any doubt as to how often a user subroutine is called, this information can be obtained +upon testing the subroutine on a small example, as suggested earlier. The current step and increment +numbers are commonly passed into these subroutines, and they can be printed out as debug output +(also discussed earlier). The iteration number for which the subroutine is called may not be passed +into the user subroutine; however, if printed output is sent from the subroutine to the message (.msg) +file (“Output,” Section 4.1.1), the location of the output within this file will give the iteration number, +provided that the output to the message file is written at every increment. +Utility routines +A variety of utility routines are available to assist in the coding of user subroutines. You include the utility +routine inside a user subroutine. When called, the utility routine will perform a predefined function or +action whose output or results can be integrated into the user subroutine. Some utility routines are only +applicable to particular user subroutines. Each utility routine is discussed in detail in “Utility routines,” +Section 2.1 of the Abaqus User Subroutines Reference Manual. +Variables provided for use in utility routines +The following utility routines require the use of Abaqus-provided variables passed into the user +subroutines from which they are called: +• GETNODETOELEMCONN +• GETVRM +• GETVRMAVGATNODE +• GETVRN +• IGETSENSORID +• IVGETSENSORID +• MATERIAL_LIB_MECH +• MATERIAL_LIB_HT +These variables will be defined properly when passed into your user subroutine; you cannot modify the +variables or create alternative variables for use in the utility routines. +For example, the GETVRM utility routine requires the variable JMAC, which is passed from +Abaqus/Standard into user subroutine UVARM and other user subroutines for which GETVRM is a +supported utility. The variable JMAC represents an Abaqus data structure that requires no further +manipulation on your part. If you use the GETVRM utility routine from within user subroutine UVARM, +you will pass the JMAC variable from UVARM into GETVRM. +18.1.2 +AVAILABLE USER SUBROUTINES +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD Abaqus/Aqua +References +• “User subroutines: overview,” Section 18.1.1 +• Abaqus User Subroutines Reference Manual +Overview +User subroutines allow advanced users to customize a wide variety of Abaqus capabilities. Information +on writing user subroutines and detailed descriptions of each subroutine appear online in the Abaqus User +Subroutines Reference Manual. A listing and explanations of associated utility routines also appear in +that manual. +Available user subroutines for Abaqus/Standard +The available user subroutines for Abaqus/Standard are as follows: +• CREEP: Define time-dependent, viscoplastic behavior (creep and swelling). +• DFLOW: Define nonuniform pore fluid velocity in a consolidation analysis. +• DFLUX: Define nonuniform distributed flux in a heat transfer or mass diffusion analysis. +• DISP: Specify prescribed boundary conditions. +• DLOAD: Specify nonuniform distributed loads. +• FILM: Define nonuniform film coefficient and associated sink temperatures for heat transfer +analysis. +• FLOW: Define nonuniform seepage coefficient and associated sink pore pressure for consolidation +analysis. +• FRIC: Define frictional behavior for contact surfaces. +• FRIC_COEF: Define frictional coefficient for contact surfaces. +• GAPCON: Define conductance between contact surfaces or nodes in a fully coupled temperature- +displacement analysis, a fully coupled thermal-electrical-structural analysis, or a pure heat transfer +analysis. +• GAPELECTR: Define electrical conductance between surfaces in a coupled thermal-electric analysis +or a fully coupled thermal-electrical-structural analysis. +• HARDINI: Define initial equivalent plastic strain and initial backstress tensor. +• HETVAL: Provide internal heat generation in heat transfer analysis. +• MPC: Define multi-point constraints. +• ORIENT: Provide an orientation for defining local material directions or local directions for +kinematic coupling constraints or local rigid body directions for inertia relief. +• RSURFU: Define a rigid surface. +• SDVINI: Define initial solution-dependent state variable fields. +• SIGINI: Define an initial stress field. +• UAMP: Specify amplitudes. +• UANISOHYPER_INV: Define anisotropic hyperelastic material behavior using the invariant +formulation. +• UANISOHYPER_STRAIN: Define anisotropic hyperelastic material behavior based on Green +strain. +• UCORR: Define cross-correlation properties for random response loading. +• UDECURRENT: Define nonuniform volume current density in an eddy current or magnetostatic +analysis. +• UDEMPOTENTIAL: Define nonuniform magnetic vector potential on a surface in an eddy current +or magnetostatic analysis. +• UDMGINI: Define the damage initiation criterion. +• UDSECURRENT: Define nonuniform surface current density in an eddy current or magnetostatic +analysis. +• UEL: Define an element. +• UELMAT: Define an element with access to Abaqus materials +• UEXPAN: Define incremental thermal strains. +• UEXTERNALDB: Manage user-defined external databases and calculate model-independent history +information. +• UFIELD: Specify predefined field variables. +• UFLUID: Define fluid density and fluid compliance for hydrostatic fluid elements. +• UFLUIDLEAKOFF: Define the fluid leak-off coefficients for pore pressure cohesive elements. +• UGENS: Define the mechanical behavior of a shell section. +• UHARD: Define the yield surface size and hardening parameters for isotropic plasticity or combined +hardening models. +• UHYPEL: Define a hypoelastic stress-strain relation. +• UHYPER: Define a hyperelastic material. +• UINTER: Define surface interaction behavior for contact surfaces. +• UMASFL: Specify prescribed mass flow rate conditions for a convection/diffusion heat transfer +analysis. +• UMAT: Define a material’s mechanical behavior. +• UMATHT: Define a material’s thermal behavior. +• UMESHMOTION: Specify mesh motion constraints during adaptive meshing. +• UMOTION: Specify motions during cavity radiation heat transfer analysis or steady-state transport +analysis. +• UMULLINS: Define damage variable for the Mullins effect material model. +• UPOREP: Define initial fluid pore pressure. +• UPRESS: Specify prescribed equivalent pressure stress conditions. +• UPSD: Define the frequency dependence for random response loading. +• URDFIL: Read the results file. +• USDFLD: Redefine field variables at a material point. +• UTEMP: Specify prescribed temperatures. +• UTRACLOAD: Specify nonuniform traction loads. +• UTRS: Define a reduced time shift function for a viscoelastic material. +• UVARM: Generate element output. +• UWAVE: Define wave kinematics for an Abaqus/Aqua analysis. +• VOIDRI: Define initial void ratios. +Available user subroutines for Abaqus/Explicit +The available user subroutines for Abaqus/Explicit are as follows: +• VDISP: Specify prescribed boundary conditions. +• VDLOAD: Specify nonuniform distributed loads. +• VFABRIC: Define fabric material behavior. +• VFRIC: Define contact frictional behavior between surfaces defined with the contact pair algorithm. +• VFRIC_COEF: Define contact frictional coefficient between surfaces defined with the general +contact algorithm. +• VFRICTION: Define contact frictional behavior between surfaces defined with the general contact +algorithm. +• VUAMP: Specify amplitudes. +• VUANISOHYPER_INV: Define anisotropic hyperelastic material behavior using the invariant +formulation. +• VUANISOHYPER_STRAIN: Define anisotropic hyperelastic material behavior based on Green +strain. +• VUEL: Define an element. +• VUFIELD: Specify predefined field variables. +• VUFLUIDEXCH: Define mass/heat energy flow rates for fluid exchange. +• VUFLUIDEXCHEFFAREA: Define effective area for fluid exchange. +• VUHARD: Define the yield surface size and hardening parameters for isotropic plasticity or combined +hardening models. +• VUINTER: Define the contact interaction between surfaces defined with the contact pair algorithm. +• VUINTERACTION: Define the contact interaction between surfaces defined with the general contact +algorithm. +• VUMAT: Define material behavior. +• VUMULLINS: Define damage variable for the Mullins effect material model. +• VUSDFLD: Redefine field variables at a material point. +• VUTRS: Define a reduced time shift function for a viscoelastic material. +• VUVISCOSITY: Define the shear viscosity for equation of state models. +• VWAVE: Define wave kinematics for an Abaqus/Aqua analysis. +Available user subroutines for Abaqus/CFD +The available user subroutines for Abaqus/CFD are as follows: +• SMACfdUserPressureBC: Specify prescribed pressure boundary conditions. +• SMACfdUserVelocityBC: Specify prescribed velocity boundary conditions. +18.1.3 +AVAILABLE UTILITY ROUTINES +Products: Abaqus/Standard Abaqus/Explicit Abaqus/Aqua +References +• “User subroutines: overview,” Section 18.1.1 +• “Utility routines,” Section 2.1 of the Abaqus User Subroutines Reference Manual +Overview +A variety of utility routines are available to assist in the coding of user subroutines. When called, the +utility routine will perform a predefined function or action whose output or results can be integrated into +the user subroutine. +Available utility routines +The following utility routines are available for use in coding user subroutines in Abaqus: +• GETENVVAR or VGETENVVAR can be called from any Abaqus/Standard or Abaqus/Explicit +user subroutine, respectively, to obtain the value of an environment variable (“Obtaining Abaqus +environment variables,” Section 2.1.1 of the Abaqus User Subroutines Reference Manual). +• GETJOBNAME or VGETJOBNAME can be called from any Abaqus/Standard or Abaqus/Explicit user +subroutine, respectively, to obtain the name of the current analysis job (“Obtaining the Abaqus job +name,” Section 2.1.2 of the Abaqus User Subroutines Reference Manual). +• GETOUTDIR or VGETOUTDIR can be called from any Abaqus/Standard or Abaqus/Explicit user +subroutine, respectively, to obtain the name of the directory where analysis job output is being placed +(“Obtaining the Abaqus output directory name,” Section 2.1.3 of the Abaqus User Subroutines +Reference Manual). +• GETNUMCPUS can be called from any Abaqus/Standard user subroutine to obtain the number +of MPI processes; VGETNUMCPUS can be called from any Abaqus/Explicit user subroutine in a +domain-parallel run to obtain the number of processes used for the parallel run (“Obtaining parallel +processes information,” Section 2.1.4 of the Abaqus User Subroutines Reference Manual). +• GETRANK can be called from any Abaqus/Standard user subroutine to obtain the rank of the MPI +process from which the function is called; VGETRANK can be called from any Abaqus/Explicit +user subroutine in a domain-parallel run to obtain the individual process rank (“Obtaining parallel +processes information,” Section 2.1.4 of the Abaqus User Subroutines Reference Manual). +• GETPARTINFO or VGETPARTINFO can be called from any Abaqus/Standard or Abaqus/Explicit +user subroutine, respectively, to retrieve the part instance name and local node or element number +corresponding to an internal node or element number. GETINTERNAL or VGETINTERNAL can +be called from any Abaqus/Standard or Abaqus/Explicit user subroutine, respectively, to retrieve +the internal node or element number corresponding to a given part instance name and local number +(“Obtaining part information,” Section 2.1.5 of the Abaqus User Subroutines Reference Manual.) +• GETVRM provides access to material point information for Abaqus/Standard user subroutines +UVARM and/or USDFLD (“Obtaining material point information in an Abaqus/Standard analysis,” +Section 2.1.6 of the Abaqus User Subroutines Reference Manual). +• VGETVRM provides access to selected output variables at material points for Abaqus/Explicit user +subroutine VUSDFLD (“Obtaining material point information in an Abaqus/Explicit analysis,” +Section 2.1.7 of the Abaqus User Subroutines Reference Manual). +• GETVRMAVGATNODE provides access to material point information, extrapolated to and averaged +at a node, for Abaqus/Standard user subroutine UMESHMOTION (“Obtaining material point +information averaged at a node,” Section 2.1.8 of the Abaqus User Subroutines Reference Manual). +information for Abaqus/Standard user subroutine +the Abaqus User +information,” Section 2.1.9 of +• GETVRN provides access to node point +UMESHMOTION (“Obtaining node point +Subroutines Reference Manual). +• GETNODETOELEMCONN can be called from user subroutine UMESHMOTION to retrieve a list of +elements connected to a specific node. This element list can then be used with utility routine +GETVRMAVGATNODE (“Obtaining node to element connectivity,” Section 2.1.10 of the Abaqus +User Subroutines Reference Manual). +• SINV determines +the first and second stress +in +Abaqus/Standard (“Obtaining stress invariants, principal stress/strain values and directions, and +rotating tensors in an Abaqus/Standard analysis,” Section 2.1.11 of the Abaqus User Subroutines +Reference Manual). +for a given stress +invariants +tensor +• SPRINC or VSPRINC determines the principal values for a given stress or strain tensor in +Abaqus/Standard or Abaqus/Explicit, +respectively (“Obtaining stress invariants, principal +stress/strain values and directions, and rotating tensors in an Abaqus/Standard analysis,” +Section 2.1.11 of the Abaqus User Subroutines Reference Manual, and “Obtaining principal +stress/strain values and directions in an Abaqus/Explicit analysis,” Section 2.1.12 of the Abaqus +User Subroutines Reference Manual). +• SPRIND or VSPRIND determines both the principal values and principal directions for a given +stress or strain tensor in Abaqus/Standard or Abaqus/Explicit, respectively (“Obtaining stress +invariants, principal stress/strain values and directions, and rotating tensors in an Abaqus/Standard +analysis,” Section 2.1.11 of the Abaqus User Subroutines Reference Manual, and “Obtaining +principal stress/strain values and directions in an Abaqus/Explicit analysis,” Section 2.1.12 of the +Abaqus User Subroutines Reference Manual). +• ROTSIG can be called from Abaqus/Standard user subroutine UMAT to perform the rotation +of tensors when large-strain calculations are performed (“Obtaining stress invariants, principal +stress/strain values and directions, and rotating tensors in an Abaqus/Standard analysis,” +Section 2.1.11 of the Abaqus User Subroutines Reference Manual). +• GETWAVE determines wave kinematic data associated with the applied wave theory in +an Abaqus/Aqua analysis (“Obtaining wave kinematic data in an Abaqus/Aqua analysis,” +Section 2.1.13 of the Abaqus User Subroutines Reference Manual). +• GETWAVEVEL, GETWINDVEL, and GETCURRVEL are used to obtain the wave, wind, and steady +current velocity components, respectively, for a given point in an Abaqus/Aqua analysis (“Obtaining +wave kinematic data in an Abaqus/Aqua analysis,” Section 2.1.13 of the Abaqus User Subroutines +Reference Manual). +• STDB_ABQERR or XPLB_ABQERR can be called from any Abaqus/Standard or Abaqus/Explicit +user subroutine, respectively, to print an informational, warning, or error message to the message +file in Abaqus/Standard or the status file in Abaqus/Explicit (“Printing messages to the message or +status file,” Section 2.1.14 of the Abaqus User Subroutines Reference Manual). +• XIT or XPLB_EXIT can be called from any Abaqus/Standard or Abaqus/Explicit user subroutine, +respectively, to terminate an analysis (“Terminating an analysis,” Section 2.1.15 of the Abaqus User +Subroutines Reference Manual). +• IGETSENSORID or IVGETSENSORID can be called from Abaqus/Standard user subroutine UAMP +or Abaqus/Explicit user subroutine VUAMP, respectively, to obtain the ID of a user-defined sensor. +GETSENSORVALUE or VGETSENSORVALUE can be called from Abaqus/Standard user subroutine +UAMP or Abaqus/Explicit user subroutine VUAMP, respectively, to obtain the value of a user-defined +sensor (“Obtaining sensor information,” Section 2.1.16 of the Abaqus User Subroutines Reference +Manual). +• MATERIAL_LIB_MECH can be called from Abaqus/Standard user subroutine UELMAT to access +the Abaqus material library (“Accessing Abaqus materials,” Section 2.1.17 of the Abaqus User +Subroutines Reference Manual). +• MATERIAL_LIB_HT can be called from Abaqus/Standard user subroutine UELMAT to access +the Abaqus thermal material library (“Accessing Abaqus thermal materials,” Section 2.1.18 of the +Abaqus User Subroutines Reference Manual). +• SMACfdUserSubroutineGetScalar can be called from any Abaqus/CFD user subroutine to +access selected output variables for elements or surface facets that are part of a boundary condition +definition (“Obtaining scalar state information in an Abaqus/CFD analysis,” Section 2.1.19 of the +Abaqus User Subroutines Reference Manual). +• SMACfdUserSubroutineGetVector can be called from any Abaqus/CFD user subroutine to +access selected output variables for elements and surface facets that are part of a boundary condition +definition (“Obtaining vector state information in an Abaqus/CFD analysis,” Section 2.1.20 of the +Abaqus User Subroutines Reference Manual). +• SMACfdUserSubroutineGetMpiComm can be called from within any Abaqus/CFD user +subroutine to obtain the MPI communicator used in a parallel analysis job (“Obtaining the MPI +communicator in an Abaqus/CFD analysis,” Section 2.1.21 of the Abaqus User Subroutines +Reference Manual). +19. +Design Sensitivity Analysis +Design sensitivity analysis +19.1 +Design sensitivity analysis +• “Design sensitivity analysis,” Section 19.1.1 +19.1.1 +DESIGN SENSITIVITY ANALYSIS +Product: Abaqus/Design +References +• “Parametric input,” Section 1.4.1 +• “Parametric shape variation,” Section 2.1.2 +• *STEP +• *DESIGN PARAMETER +• *DESIGN RESPONSE +Overview +Design sensitivity analysis (DSA): +• is performed with Abaqus/Design, an add-on option for Abaqus/Standard; +• provides the sensitivities of responses with respect to specified design parameters; +• is available for static stress and frequency analysis using models that have only stress/displacement +elements; and +• can include design parameters affecting: material properties (elastic, hyperelastic, and hyperfoam +models); section properties; concentrated forces and moments; and nodal coordinates (and beam +and shell normals if applicable). +Design sensitivity analysis +The design sensitivity analysis (DSA) capability provides the derivatives of certain output variables +with respect to specified design parameters. These derivatives are commonly referred to as sensitivities, +because they provide a first-order measure of how sensitive the output variable is to a change in the +design parameter. The output variables for which sensitivities are computed are called design responses +or simply responses. Design parameters are chosen from a set of existing analysis parameters. As an +example, you can choose to obtain the derivatives of stresses with respect to Young’s modulus; stress is +the response, and Young’s modulus is the design parameter. The sensitivities are computed based on the +direct differentiation method used in conjunction with the semi-analytical computational technique. In +the semi-analytical technique some derivatives are computed using numerical (finite) differencing, thus +requiring perturbations of the design parameters. For these derivatives by default Abaqus/Design will +use a central differencing scheme and automatically determine appropriate perturbation sizes based on a +heuristic algorithm. You can override these defaults by specifying the numerical differencing method and +the perturbation sizes directly. A full discussion of DSA theory is given in “Design sensitivity analysis,” +Section 2.18.1 of the Abaqus Theory Manual. +Activating DSA +You activate DSA on a step-by-step basis. +Input File Usage: +Use the following option to activate DSA in a particular step: +*STEP, DSA=YES +Activating DSA in multiple steps +Once DSA is activated in a general step, it remains active in all subsequent general steps until it is +deactivated in a subsequent general step. Once DSA is activated in a perturbation step, it remains +active in all subsequent consecutive perturbation steps until it is deactivated in a subsequent consecutive +perturbation step. However, if DSA is activated in a step whose procedure is not supported for DSA, +DSA will be deactivated until it is activated again. +Input File Usage: +Use the following option to deactivate DSA in a particular step: +*STEP, DSA=NO +Specifying design parameters +You can define multiple parameters to be used in place of Abaqus input quantities for an analysis. You +must indicate which of these parameters are to be considered as design parameters. +Input File Usage: +Use the following option to define analysis parameters: +*PARAMETER +par1=x +par2=y +Use the following option to specify the design parameters: +*DESIGN PARAMETER +par1, par2, +Restrictions on design parameters +The following are restrictions on design parameters: +• Design parameters can be associated only with floating point data. The following analysis +components can include design-dependent data: +– Beam sections integrated during analysis (“Using a beam section integrated during the analysis +to define the section behavior,” Section 29.3.6) +– Concentrated loads (“Concentrated loads,” Section 33.4.2) +– Elastic materials (“Linear elastic behavior,” Section 22.2.1) +– Friction (“Frictional behavior,” Section 36.1.5) +– Gasket sections (“Gasket elements: overview,” Section 32.6.1) +– Hyperelastic materials (“Hyperelastic behavior of rubberlike materials,” Section 22.5.1) +– Hyperfoam materials (“Hyperelastic behavior in elastomeric foams,” Section 22.5.2) +– Membrane sections (“Membrane elements,” Section 29.1.1) +– Local orientations (“Orientations,” Section 2.2.5) +– Shell sections integrated during analysis (“Using a shell section integrated during the analysis +to define the section behavior,” Section 29.6.5) +– Solid sections (“Solid (continuum) elements,” Section 28.1.1) +– Transverse shear stiffnesses (“Choosing a beam element,” Section 29.3.3, or “Shell section +behavior,” Section 29.6.4) +• Shape design parameters (i.e., design parameters that affect nodal coordinates and beam and/or shell +normals) can be used only in conjunction with parametric shape variations . +• Design parameters must be mutually independent. +• Design parameters cannot be tabularly dependent . +Specifying responses +Response requests are specified using a syntax analogous to that for specifying output requests to the +output database. Except for eigenvalues and eigenfrequencies, there are no default responses—if no +responses are requested, no response sensitivities will be output. If DSA is active in a frequency step, +eigenvalue and eigenfrequency sensitivities will be output automatically. Specifying a response will +cause output of both the response and the response sensitivities. +Input File Usage: +Use the following options to request design responses: +*DESIGN RESPONSE, FREQUENCY=interval, MODE LIST +*CONTACT RESPONSE, MASTER=master name, NSET=nset name, +SLAVE=slave name +*ELEMENT RESPONSE, ELSET=elset name +*NODE RESPONSE, NSET=nset name +Requesting responses in multiple steps +Unless respecified, response requests defined in a step propagate to subsequent steps according to the +following rules: +1. Requests in general steps propagate to subsequent general steps. +2. Requests in linear perturbation steps propagate to subsequent consecutive linear perturbation steps. +3. When a non-DSA step appears between DSA steps, the responses must be respecified in the DSA +step following the non-DSA step. +Restrictions on responses +The available responses are a subset of the existing output variables. The valid responses based on +procedure type are described below. +• For static steps the valid responses are: +– Node responses: U and RF +– Element responses: S, SF, SINV, SP, E, SE, EP, EE, EEP, LE, LEP, NE, NEP, ENER, ELEN, +EVOL, and MASS +– Contact responses: CSTRESS and CDISP +• For frequency steps the valid responses are: +– Node responses: None +– Element responses: MASS +– Contact responses: None +– Eigenvalue (EIGVAL) and eigenfrequency (EIGFREQ) sensitivities are output automatically. +Specifying design gradients of design-dependent input data +The DSA calculations require the gradients of the design-dependent input data with respect to the design +parameters. For example, if Poisson’s ratio, +, is made dependent on a design parameter, say h, the +gradient +is required. Design gradients with respect to shape design parameters are specified +differently than those with respect to other design parameters. +Specifying design gradients with respect to shape design parameters +Gradients with respect to shape design parameters must be specified using a parametric shape variation +definition . For the purposes of DSA if the parameter +to which the shape variation data refer is a design parameter, the shape variation data are interpreted as +the gradients of the nodal coordinates with respect to the design parameter. If a nonzero value is given +for the shape parameter, Abaqus/Design will also perturb the base coordinates. +Input File Usage: +Use the following option to specify the design gradients for shape design +parameters: +*PARAMETER SHAPE VARIATION, PARAMETER=design parameter +Specifying gradients for non-shape design parameters +For non-shape design parameters, by default Abaqus/Design will use numerical differentiation to +calculate design gradients based on the information you provide. However, you can override this +default behavior by specifying the gradients directly using Python expressions . You specify a design parameter as the independent parameter and a list of the parameters +that depend on that design parameter. Only one independent (design) parameter can be given for each +design gradient definition. +Input File Usage: +Use the following option to specify the design gradients for non-shape design +parameters: +*DESIGN GRADIENT, INDEPENDENT=design parameter, +DEPENDENT=(list of dependent parameters) +History dependence and formulation type in a multi-increment analysis +Both total and incremental formulations are implemented for DSA. The choice of formulation depends +on whether or not an analysis is history dependent. Below is a brief description of these formulation +types. A more detailed discussion can be found in “Design sensitivity analysis,” Section 2.18.1 of the +Abaqus Theory Manual. By default, the incremental DSA formulation is used. You can specify the DSA +formulation only for the entire model; this specification is ignored if given as part of a step definition. +Incremental DSA formulation +In the incremental formulation the problem is assumed to be history dependent. Abaqus/Design solves +for the incremental displacement sensitivities, and the total displacement sensitivity is updated at the +end of the increment. Due to the history dependence, the incremental displacement sensitivities for the +current increment depend on the sensitivities of the state variables at the beginning of the increment, +in the same sense that incremental displacements depend on the state variables at the beginning of the +increment for equilibrium analyses. Thus, Abaqus/Design must also compute and update state variable +sensitivities in each increment. Consequently, DSA must be activated for all steps up to the last step in +which DSA is active, and the DSA calculations will be done at all increments in these steps, regardless +of whether or not a design response is requested for a given step. If a response is requested for a step, +the specified response frequency is ignored for the purposes of the DSA calculations (the frequency at +which the output is written will still be governed by the specified response frequency). +The disadvantage of the incremental DSA formulation is its cost, due to the necessity of computing +both state variable and incremental displacement sensitivities at each increment prior to the last DSA +increment. This increased cost is unavoidable if the problem is history dependent but is unnecessary if +the problem is history independent. Thus, the total DSA formulation should be chosen for problems that +are not history dependent. +Input File Usage: +*DSA CONTROLS, FORMULATION=INCREMENTAL +Total DSA formulation +In the total displacement formulation the total displacement sensitivities are calculated directly based on +the assumption that the problem is not history dependent. In other words, the displacement sensitivities +do not depend on sensitivity results calculated in previous increments. Thus, the advantage of the total +formulation is that the sensitivity calculations need only be done at increments of interest. You can +control when DSA calculations are done by activating DSA for only the desired steps and specifying the +desired frequency for each design response request. +You may choose to use the total DSA formulation in problems that are known to be history +dependent. However, in this case the DSA solution is approximate, with the degree of approximation +increasing as the problem becomes more strongly history dependent. To assess the validity of using the +total DSA formulation, it is recommended that you run both an incremental and total sensitivity analysis +for a typical problem and compare the results. +Input File Usage: +*DSA CONTROLS, FORMULATION=TOTAL +DSA in linear perturbation steps +The sensitivity of the perturbation response can be calculated in a linear perturbation step . The perturbation response will include the effects +of stress and load stiffening in the base state if geometric nonlinearity is considered. Since we need to +calculate the sensitivity of an incremental (perturbation) response, the sensitivity of the stress and load +stiffening effects must be known at the end of the base step. Thus, if geometric nonlinearity is considered +in the base step, DSA must also be active in the base step, irrespective of the type of formulation (total +or incremental). +Determination of design parameter perturbation sizes +The basis of the semi-analytic technique is the use of numerical differencing to obtain derivatives of +certain element vectors and matrices . Abaqus/Design will automatically determine appropriate perturbation sizes to be +used in the semi-analytic technique unless you specify them directly. Abaqus/Design determines the +perturbation sizes using a heuristic perturbation sizing algorithm based on the behavior of a scalar s +associated with an element. By default, the perturbation sizing algorithm is applied only for the first +increment (static procedure) or first mode (frequency procedure) in each step for which DSA is active. +The perturbation sizes are then reused for the remaining increments or modes in the step for which DSA +calculations are done. +The goal of the algorithm is to find perturbation sizes that are optimal for numerical differencing. +Differencing formulas are based on Taylor series expansions, and the order of approximation of the +derivative to be computed is reflected in the terms that are neglected in the series. The accuracy of +the approximated derivatives often depends strongly on the perturbation size used in the differencing +formula. Choosing a perturbation size that is too large will cause a truncation error, which occurs when +the order of approximation is no longer valid (i.e., as a result of truncating higher-order terms in the Taylor +series). A perturbation size that is too small will lead to inaccuracies in the differencing operations due +to round-off, typically referred to as a cancellation error. +The algorithm attempts to find perturbation sizes giving the best compromise between cancellation +and truncation errors by observing the behavior of s. For each design parameter s is computed for +perturbation sizes spanning several orders of magnitude. The error in s between consecutive perturbation +sizes is calculated as +, is chosen +as the best perturbation size. +. The perturbation size yielding an acceptable error, +This scalar s is selected as follows: +• Static procedure. For static steps s is chosen as the norm of the element pseudoload (the partial +derivative of the element residual with respect to the design parameters). +• Frequency procedure. For frequency steps s is computed from the element contribution to a matrix +, where +involving the derivatives of the mass and stiffness matrices (namely +is the stiffness, +is the mass, h is the design parameter, and +scalar s is taken as the projection of this matrix onto an eigenvector +algorithm is applied to a mode with a distinct eigenvalue, +is an eigenvalue). The +. If the perturbation sizing +is taken as the eigenvector associated +with this mode. However, if a mode happens to be associated with a repeated eigenvalue, +is +taken as the sum of all the eigenvectors associated with the repeated eigenvalue. Thus, the entire set +of modes associated with a repeated eigenvalue will be treated simultaneously by the perturbation +sizing algorithm (the eigenvalue sensitivities of a repeated eigenvalue are obtained simultaneously +from the same reduced eigenvalue system). +See “Design sensitivity analysis,” Section 2.18.1 of the Abaqus Theory Manual, for further details on +the selection of s. +Controlling the numerical differencing behavior +You can control various aspects of the numerical differencing operations. These aspects are described in +detail in the following sections. You can specify DSA controls for the entire model and/or for individual +steps. Specifying these controls for the entire model has the effect of creating new default values for the +various settings. When you specify these controls for individual steps, the following propagation rules +are enforced: +• Once DSA controls are specified in a non-perturbation step, they remain in effect for all subsequent +non-perturbation steps, unless they are respecified or reset. +• Once DSA controls are specified in a perturbation step, they remain in effect for all subsequent +consecutive perturbation steps, unless they are respecified or reset. +Resetting DSA controls +You can reset DSA controls only for individual steps. If DSA controls are specified for the entire model, +resetting them in a particular step will reset the numerical differencing behavior to the behavior specified +for the entire model; otherwise, the behavior will be reset to the original default values. Any additional +changes specified will be applied after the behavior is reset. +Input File Usage: +Use the following option to reset the DSA controls for a particular step: +*DSA CONTROLS, RESET +Changing the defaults for the heuristic perturbation sizing algorithm +The following two sections describe how certain parameters associated with the perturbation sizing +algorithm can be changed from their default values for purposes of computational efficiency and +accuracy. +Changing the default tolerance +is set to 1.0 × 10−4. Warning messages are written to the message file for +By default, the tolerance +elements for which this tolerance is not achieved. These elements are collected in element sets and can +be viewed in the Visualization module of Abaqus/CAE. It is important to understand that this tolerance +controls the effort expended in obtaining an optimum perturbation size; it is not a direct measure of the +accuracy of the numerical differentiation. +Input File Usage: +Use the following option to override the default tolerance: +*DSA CONTROLS, TOLERANCE=tolerance +Changing the frequency at which the perturbation sizing algorithm is used +Determining perturbation sizes using the heuristic algorithm is computationally intensive. You can +specify the frequency at which the perturbation sizes are recalculated. For example, specifying a sizing +frequency of n will cause Abaqus/Design to determine new perturbation sizes at every n increments or +eigenmodes. The perturbation size will always be recalculated at the first increment or eigenmode in +each step for which DSA is active, which is equivalent to specifiying a sizing frequency of 0. Since +the perturbation sizing algorithm is computationally intensive, care should be exercised to ensure that +the sizing frequency is as large as possible (or zero). +As discussed above, the perturbation sizing algorithm is applied simultaneously to all modes +associated with a repeated eigenvalue. Thus, the actual number of modes associated with a repeated +eigenvalue that are “hit” based on the sizing frequency is irrelevant, so long as it is at least one. +Input File Usage: +Use the following option to specify the frequency at which the perturbation +sizes are recalculated: +*DSA CONTROLS, SIZING FREQUENCY=frequency +Overriding the default heuristic perturbation sizing algorithm +If an appropriate perturbation size is already known for a particular design parameter (from previous +analyses of similar problems, for example), economy can be gained by applying this perturbation size +directly rather than having Abaqus/Design automatically find the perturbation size. You can specify +either forward differencing or central differencing directly together with an absolute perturbation size +for each design parameter. If you override the default algorithm, it is up to you to choose perturbation +sizes that will lead to accurate sensitivities. +Input File Usage: +Use the following option to override the default heuristic perturbation sizing +algorithm for a given design parameter: +*DSA CONTROLS +design parameter, FD (forward differencing) or CD (central +differencing), absolute perturbation size +For example, to specify an absolute perturbation size of 0.001 and forward +differencing for design parameter despar use the following input: +*DSA CONTROLS +despar, FD, 0.001 +This data line is specified for each design parameter for which the default +scheme is to be overridden. +Accuracy of the DSA solution +As can be seen in “Design sensitivity analysis,” Section 2.18.1 of the Abaqus Theory Manual, the +accuracy of the DSA solution is dictated by both the accuracy of the numerically computed derivatives +and, for nonlinear static analysis, the accuracy of the tangent stiffness matrix. The accuracy of the +numerically computed derivatives is governed by the semi-analytic DSA algorithm; you can control it +by specifying DSA controls. In nonlinear static analysis DSA uses the tangent stiffness matrix formed +It is possible that the accuracy of the tangent stiffness matrix +during the last equilibrium iteration. +needed to achieve an accurate equilibrium solution may be insufficient to achieve an accurate DSA +solution. In such cases you can tighten the convergence tolerances during the equilibrium analysis so +that a more accurate tangent stiffness matrix is obtained . Furthermore, an accurate equilibrium solution often can be obtained when unsymmetric +terms in the tangent stiffness are ignored (i.e., the unsymmetric matrix storage and solution scheme is not +used; see “Defining an analysis,” Section 6.1.2). However, even if mildly unsymmetric stiffness terms +are neglected, the DSA solution may be inaccurate. Therefore, it is recommended that the unsymmetric +solution scheme be used for DSA when the tangent stiffness matrix is known to be unsymmetric. +In some cases a response at a certain instant in time may be discontinuous with respect to a design +parameter. For example, at this point of discontinuity a variation in the design parameter may cause a +node to come into contact, frictional behavior to change from sticking to sliding, or a material point +to transition from elastic to inelastic behavior. Since the DSA calculations make use of numerical +differencing, it is possible that the perturbation of the design parameter used in the differencing scheme +may result in values of the response to be differenced that lie on opposite sides of the discontinuity. If +this occurs, the accuracy of the computed derivative cannot be guaranteed. Mathematically speaking, +the derivative (sensitivity) of the response with respect to the design parameter does not exist at the +point of discontinuity. Practically speaking, it is unlikely that the response at any given instant will +lie precisely on the discontinuity. In cases where the response is near a discontinuity, if you choose to +use the default perturbation sizing algorithm, the algorithm will attempt to choose design parameter +perturbation sizes such that the values of the perturbed responses remain on the same side of the +discontinuity. In addition, for contact elements DSA calculations are not performed in increments in +which the associated contact node is open. Typically, the global results in any increment are not affected +by a few discontinuous points in the model. +Design dependence and supported features +Responses depend on design parameters explicitly and implicitly. +Implicit design dependence is the +dependence on the design parameter through the solution variables; therefore, this type of dependence +can be quantified only after the DSA solution is obtained (recall that the DSA solution is the total +displacement sensitivity for the total formulation and the incremental displacement sensitivity for the +incremental formulation). All other design dependencies are explicit, meaning that they can be resolved +without knowing the DSA solution. The types of dependencies can be identified by looking at the form +of the sensitivity of a response, say r, with respect to a design parameter, say h. This sensitivity is +expressed as +for the total formulation and +for the incremental formulation, where +represents +state variables at the beginning of the increment . The state variables include the displacements at the +beginning of the increment. In both cases the last term on the right-hand side represents the implicit +design dependence through the solution variables. +is a displacement degree of freedom and +It is observed from the incremental equation above that the explicit design dependence consists of +two terms. The first of these, +, represents a direct design dependence, because this term arises from the +direct dependence of the response on the design parameter. The second explicit term, +, represents +the dependence on the design parameter through the state variables at the beginning of the increment. +For the total formulation, it is seen that the explicit term involves only direct design dependence. +Any feature for which direct design dependence calculations are implemented in Abaqus will be +referred to as supported for DSA. Supported and unsupported features can be mixed in an analysis, unless +the supported features cause unsupported features to become directly design dependent (an example of +this would be making the Young’s modulus for a frame element design dependent, since frames are not +supported for DSA). +To make a clearer distinction between the types of design dependencies, consider the more concrete +example of a linear elastic truss element, fixed at one end and pulled with a concentrated load at the other +end. Let +represent the displacement at the free end, E represent Young’s modulus, and L +represent the length of the truss. Consider the axial stress +as the response. Although it is clear in this +simple example that the stress can be computed easily as the load divided by the cross-sectional area, the +finite element analysis computes the stress equivalently as +. Choosing Young’s modulus, +E, as the design parameter, the stress sensitivity is given by +for the total formulation and +for the incremental formulation. This example is a valid analysis since elastic materials and truss +elements are supported for DSA. Suppose now that a frame element is added, extending the length of +the structure. If the frame element shares the same Young’s modulus, the analysis becomes invalid since +the dependency on the design parameter E causes the frame element, which is unsupported, to become +directly design dependent (i.e., the term +would need to be computed). On the other hand, if the +frame uses a different modulus, say +that is not a design parameter, the analysis again becomes valid, +since the frame no longer depends directly on the design parameter E. +Contact interactions +Surface-based contact between deformable and rigid surfaces with small- or finite-sliding relative surface +motion including friction is supported in a design sensitivity analysis. In all the friction models only the +friction coefficients (no test data input) can be made design dependent. Shape design parameters are not +valid for rigid surfaces. Contact between deformable surfaces is not supported. +Restarting a design sensitivity analysis +A design sensitivity analysis can be restarted . However, +DSA must have been active in the base analysis, and no design parameter or gradient data can be modified +in the restart run. The restarted analysis will follow all the DSA propagation rules that are applicable +to a regular analysis. For total formulation DSA, you may choose to activate or deactivate DSA in any +new step that is added to the restart run. However, for the incremental formulation DSA must have been +active in the step at which restart is attempted for you to continue doing DSA in the restarted analysis. +Procedures +DSA is available in the following analysis procedures: +• Frequency analysis +• Static stress analysis (including nonlinear geometric effects and contact) +The following analysis procedures and techniques are not supported: +• Static stress analysis with the Riks method +• Substructuring +• Mesh modification or replacement +• Importing and transferring results +• Symmetric model generation and results transfer +• Contour integrals +• Cyclic symmetry in frequency procedures +Submodeling limitations +Design sensitivity analysis can be performed in both the global model and submodel, with the limitation +that the DSA solution will not be interpolated from the global model to the submodel. This means that +DSA is valid in the submodel only if the global solution that is interpolated onto the boundary of the +submodel can be considered independent of the design parameters chosen for the submodel sensitivity +analysis. +Material options +The following material models are supported: +• Isotropic, orthotropic, and anisotropic elasticity +• Hyperelasticity +• Hyperfoam +In these models only directly input material coefficients (not test data) can be made design dependent. +If test data are specified, that material definition can be replaced by specifying the material coefficients +calculated by Abaqus/Design directly. Supported and unsupported material models can be mixed in the +same analysis. +Elements +Solid, truss, shell, beam, gasket, and membrane stress/displacement elements are supported. Shell +elements with five degrees of freedom per node cannot be used in a total DSA formulation. Supported +and unsupported elements can be mixed in the same analysis. +Output +The responses and response sensitivities are output only to the output +database (sensitivity output to the data file and results file is not supported). The names of the sensitivities +are related to the names of the responses as follows: +d response name +design parameter name +For example, if the name of the response is S and the name of the design parameter is Young, the name +of the sensitivity is d_S_Young. +Input file template +*HEADING +… +*PARAMETER +Python expressions defining parameters. +*DESIGN PARAMETER +List of independent parameters to be considered as design parameters. +… +*NODE, NSET=nset +Data lines to define the nodes. +*PARAMETER SHAPE VARIATION, PARAMETER=parameter +Data lines to define the gradients of coordinates with respect to the parameter. +… +*ELEMENT, TYPE=solid element type, ELSET=elset_elastic +Data lines to define the elements. +*ELEMENT, TYPE=solid element type, ELSET=elset_hyper +Data lines to define the elements. +*SOLID SECTION, ELSET=elset_elastic, MATERIAL=elastic +*SOLID SECTION, ELSET=elset_hyper, MATERIAL=hyper +*MATERIAL, NAME=elastic +*ELASTIC +Data lines to define the elastic properties. +*MATERIAL, NAME=hyper +*HYPERELASTIC +Data lines to define the hyperelastic properties. +… +*STEP,DSA +*STATIC +… +*DESIGN RESPONSE, FREQUENCY=interval +*ELEMENT RESPONSE, ELSET=elset +Data lines to specify the element response identifier keys. +*NODE RESPONSE, NSET=nset +Data lines to specify the nodal response identifier keys. +*END STEP +Parametric Studies +Scripting parametric studies +Parametric studies: commands +PARAMETRIC STUDIES +20.1 +20.1 +Scripting parametric studies +• “Scripting parametric studies,” Section 20.1.1 +20.1.1 +SCRIPTING PARAMETRIC STUDIES +Products: Abaqus/Standard Abaqus/Explicit +References +• “Parametric input,” Section 1.4.1 +• “Parametric shape variation,” Section 2.1.2 +• “Parametric studies,” Section 3.2.8 +Overview +Parametric studies allow you to generate, execute, and gather the results of multiple analyses that differ +only in the values of some of the parameters used in place of input quantities. +Parametric studies can be performed by: +• Creating a “template” parametrized input file from which the different parametric variations are +generated. +• Preparing a script (a file with the .psf extension) that contains Python (Lutz, 1996) instructions to +generate, execute, and gather output for the parametric variations of the parametrized input file. +The Python commands for scripting parametric studies are discussed in this section. +Introduction +Parametric studies require that multiple analyses be performed to provide information about the behavior +of a structure or component at different design points in a design space. The inputs for these analyses +differ only in the values assigned to the parameters of a parametrized keyword input file (identified with +the .inp extension). +Parametric studies in Abaqus require a user-developed Python script in a file (identified with the +.psf extension) that contains Python commands to define the parametric study. For example, consider +a case where you wish to perform a parametric study in which the thickness of a shell is varied. You need +to create a parametrized input file (in this example, a file named shell.inp) containing the parameter +definition +*PARAMETER +thick1 = 5. +and the parameter usage: +*SHELL SECTION,ELSET=name, MATERIAL=name + +You create the parametric study by developing a .psf file that contains a script of Python instructions +specifying the different designs that are to be analyzed, as follows: +thick = ParStudy(par='thick1', name='shell') +thick.define(CONTINUOUS, par='thick1', domain=(10., 20.)) +thick.sample(NUMBER, par='thick1', number=5) +thick.combine(MESH) +These scripting commands create five designs with corresponding section thicknesses of 10., 12.5, 15., +17.5, and 20.0. Each of these thicknesses will, in turn, replace the value of 5. specified in the parameter +definition in shell.inp. You may then provide additional Python scripting commands in the .psf +file instructing Abaqus to do the following: +• Generate a number of shell_id.inp files and corresponding Abaqus jobs using the shell.inp +file as a template. (The identifier id that is appended to the input file name is unique to each design +in the parametric study.) An example of the Python command for this is +thick.generate(template='shell') +In this example the shell_id.inp files will differ only in the value to be used for the shell +thickness. +• Execute all the Abaqus jobs representing the different variations of the parametric study. The Python +command for this is +thick.execute(ALL) +You generally want to review certain key results from the large amount of data that is generated by +a parametric study. Abaqus provides the following capabilities for this purpose: +• A command specifying the source from which the results of a parametric study will be gathered. +For example: +thick.output(file=ODB, step=1, inc=LAST) +The command above sets the output location to the last frame of the first step in the output database +(.odb) file. The default behavior is to gather results from the last frame of a given step in the results +(.fil) file. +• Commands to gather the required results from the multiple analyses generated by the parametric +study and report them in a file or table. For example, the sequence of Python scripting commands +used to gather and report the value of a displacement at a key node for each of the designs is: +thick.gather(results='n33_u', variable='U', node=33, step=1) +thick.report(PRINT, par='thick1', results=('n33_u.2')) +The commands above gather the results record ’n33_u’ (the displacement vector of node 33 at +the end of Step 1 of the analysis) for each of the designs and then print a table of the U2 component +(the second component of the results record) of displacement for all designs. +• The ability to visualize X–Y plot data gathered across multiple analyses using the Visualization +module of Abaqus/CAE. A typical example is to obtain an X–Y plot of the value of the displacement +at a key node versus the value of the shell thickness. This is done by gathering the appropriate +parametric study results in an ASCII file that can be read into the Visualization module to display +the plot. +Organization of parametric studies +A parametric study in Abaqus is associated with a particular set of parameters that define the design +space. Only the values of the parameters can change in a parametric study. A new parametric study +must be created if you wish to consider a different set of parameters. Having selected the parameters to +be considered in a parametric study, you must specify how each parameter is defined. Parameters are +distinguished as either continuous or discrete in nature and may have a domain and reference value. +The design points in the design space that are to be analyzed are created by specifying sample values +for each parameter (sampling) and by combining the parameter samples to create sets of design points. +A few simple commands are provided for parameter value sampling and for combining the sampled +parameter values; these commands are described in detail later. +An initial definition and sampling of the parameters in the parametric study must be given before +any combinations of parameter samples can be specified. After the first combination the initial definition +and/or sampling of any individual parameter can be changed before the next combination is specified, +thus providing a great deal of flexibility within one parametric study. +The domain of possible values and the reference value for a parameter given in the parameter +definition can be temporarily redefined in any sampling of that parameter by specifying them differently +during the sampling. You need not specify the parameter domain and reference value in the parameter +definition so long as these are specified during sampling. +Design constraints can be imposed on all of the designs. A design that violates any of the constraints +will be eliminated. +Finally, after all parametric study variations have been analyzed, you can gather and report results +across all or some of the designs of the parametric study. +In summary, parametric studies in Abaqus are organized as follows: +• Create parametric study. +• Define parameters: define parameter type (continuous or discrete valued) and possibly the parameter +domain and reference value. +• Sample parameters: +parameter domain and reference value. +specify sampling option and data and possibly temporarily redefine the +• Combine parameter samples to create sets of designs. +• Constrain designs (optional). +• Generate designs and analysis job data. +• Execute the analysis jobs for selected designs of the study. +• Gather key results for selected designs of the study. +• Report gathered results. +Note: The sequence of steps—define, sample, and combine—can be repeated as often as is necessary to +create all the required design sets. Multiple parametric studies can be performed on a model contained +in one input file. In general, more parameters will be defined and used in place of input quantities in the +input file than those involved in any particular parametric study. In these cases parameters not involved +in a particular parametric study will retain their values defined in the input file for the purposes of that +parametric study. Therefore, we can think of the parameter values defined in the input file as representing +a nominal design; parametric studies create modified designs by overwriting the values of some (or all) +parameters. +Defining the design space +The design space is defined by the selection of the parameters to be varied in the study as well as the +specification of the parameter types and possible values they can have. +Parametric study creation +Use the aStudy=ParStudy scripting command to create +a parametric study and select the independent parameters to be considered for variation. aStudy is the +Python variable name assigned by you to the parametric study object created by the command. The +methods of the parametric study object are used to carry out all the actions of the parametric study. +Input File Usage: +aStudy=ParStudy (par=, name=, verbose=, directory=) +Parameter definition +Use the aStudy.define command to +specify the parameter type (choose the CONTINUOUS or the DISCRETE token; a token is a symbolic +constant used to select an option within a specific command) and, optionally, to specify the domain of +possible parameter values and a reference value for the parameter. If the domain and/or reference value +are not specified in this command, they can be specified in the parameter sampling. +Redefinitions of a parameter are treated as complete redefinitions; that is, no information is retained +from the previous definition of that parameter. +Input File Usage: +aStudy.define (token, par=, domain=, reference=) +CONTINUOUS parameter type +In this case the parameter can take any value in a continuous domain specified by minimum and maximum +values; for example, domain=(3., 10.). +DISCRETE parameter type +In this case the parameter can take only the values specified in a list that defines the discrete domain; for +example, domain=(1, 4, 9, 16). +Sampling and combining parameter values to create sets of design points +Each parameter in the parametric study must be sampled before the combination operation is used to +create the first set of design points. Any parameter in the parametric study can be redefined or resampled +before a subsequent combination operation is performed. +Parameter sampling +Use the aStudy.sample command +and choose one of the available tokens (INTERVAL, NUMBER, REFERENCE, or VALUES) to select +how the sampling is done. The sampling data that must be given depend on how the sampling is done, +as described next. +Sampling by INTERVAL +This sampling command assumes that you specify a domain of possible parameter values and wish +to sample parameter values at fixed intervals in the domain. Sampling of the extreme values of the +parameter is always done. The number of parameter values sampled depends on the interval and the +domain. Because the extreme values are sampled, the last sampling interval will generally be smaller +than the interval you specify. +The domain specification in this sampling command is optional: +• If a domain is specified in this command, it temporarily redefines a domain specified in the define +command. +• If a domain is not specified in this command, the domain specification from the define command is +used for sampling. +• An error is flagged when a domain is not specified in this command or in the define command. +The sampling interval is interpreted differently for continuous and discrete parameters: +• For continuously valued parameters the interval at which the samples are spaced is based on +For example, specifying interval=10. for a continuous parameter with +a numerical value. +domain=(10., 35.) will sample values of 10., 20., 30., and 35. for this parameter. +• For discrete valued parameters the interval at which the samples are spaced is based on the index +of the list of values. The index means the position of the entry in the list, starting at position 0 and +continuing with positions 1, 2, 3, etc. In this case interval must be an integer number. For example, +specifying interval=−2 for a discrete parameter with domain=(1., 2., 3., 5., 7., 10.) will create +sample values of 10., 5., 2., and 1. for this parameter. +The interval can have a positive or negative value (zero is not permitted). A positive interval indicates +that sampling starts at the minimum value for a continuous parameter or at the first value in the list of +values for a discrete parameter (forward sampling). A negative interval indicates that sampling starts +at the maximum value for a continuous parameter or at the last value in the list of values for a discrete +parameter (reverse sampling). Reverse sampling is useful when the TUPLE combination operation is +used . +Two special cases of the INTERVAL option are noteworthy: +• A positive interval value larger than the range of continuous parameter values or the number +of discrete parameter values will sample the minimum and maximum values of the continuous +parameter or the first and last values in the discrete parameter list. +• A negative interval value larger (in absolute terms) than the range of continuous parameter values +or the number of discrete parameter values will sample the maximum and minimum values of the +continuous parameter or the last and first values in the discrete parameter list. +Input File Usage: +aStudy.sample (INTERVAL, par=, interval=, domain=) +Sampling by NUMBER +This sampling option assumes that you specify a domain of possible parameter values and wish to sample +a fixed number of parameter values in the domain. Except for a special case documented below, sampling +of the extreme values of the parameter is always done. The parameter is sampled at equally spaced +intervals (with some exceptions for discrete parameters, as discussed below) and the size of the interval +depends on the number of values sampled as well as the domain. +The domain specification in this sampling command is optional: +• If a domain is specified in this command, it temporarily redefines the domain specified in the define +command. +• If a domain is not specified in this command, the domain specification from the define command is +used for sampling. +• An error is flagged when a domain is not specified in this command or in the define command. +The sampling interval is calculated and interpreted differently for continuous and discrete parameters: +• For continuous valued parameters the interval at which the samples are spaced is based on +For example, specifying number=4 for a continuous parameter with +a numerical value. +domain=(10., 25.) will sample values of 10., 15., 20., and 25. for this parameter. +• For discrete valued parameters the interval at which the samples are spaced is based on the index +of the list of values (indexing starts at zero). For example, specifying number=3 for a discrete +parameter with domain=(1., 2., 3., 5., 7., 10., 12.) will create sample values of 1., 5., and 12. for +this parameter. The number of discrete parameter samples specified by you may not allow equally +spaced sampling; for example, specifying number=5 or number=6 for the discrete parameter above +does not allow equally spaced sampling. This is resolved by sampling the parameter values that are +closest to being equally spaced by rounding the sampling index to the closest index in the list of +values. For example, specifying number=5 for the discrete parameter above will create sample +values of 1., 3., 5., 10., and 12. The values 1. and 12. are sampled because they are the extreme +values. The explanation for the second sampled value being the third value in the list (the value 3.) +is as follows: the sampling interval is (highest index − lowest index)/(number − 1) = (6 − 0)/(5 − 1) += 1.5; the second sampled value should then be the one with index = 0 + 1.5 = 1.5 in the list; since +the index has to be an integer number, we round off to index = 2 and, thus, sample the third value in +the list. The other sampled values can be explained similarly. The same rule is used for character +string type discrete parameters. For example, specifying number=3 for a discrete parameter with +domain=(’C3D8’, ’C3D8R’, ’C3D8I’, ’C3D8H’) will create sample values of ’C3D8’, ’C3D8I’, +and ’C3D8H’. +Three special cases of the NUMBER option are noteworthy: +• Specifying number=1 will sample the central value of a parameter, which is useful when the center +of the design space is of interest. It is the only case in which the use of the NUMBER option does +not sample the extreme values of the parameter. +• Specifying number=2 will sample the extreme values of a parameter, which is useful when the +boundaries of the design space are of interest. +• Specifying number=3 will sample the central and the extreme values of a parameter, which is useful +when the center and the boundaries of the design space are of interest. +Specification of number=0 is not permitted. A negative value for number is permitted; this indicates +that the sampling is to be in reverse order. For continuous parameters reverse order means that the first +sampled value is the largest and the last sampled value is the smallest. For discrete parameters reverse +order means that the first sampled value is the last in the list of values and the last sampled value is the +first in the list of values. Sampling in reverse order is useful when the TUPLE combination operation is +used . +Input File Usage: +aStudy.sample (NUMBER, par=, number=, domain=) +Sampling by REFERENCE +This sampling option allows you to specify a reference value for the parameter and to sample parameter +values with respect to this reference value. It is useful for studying alternate designs with respect to an +existing (reference) design. +This sampling command creates sample values symmetrically about the reference value at multiples +of a given interval; in addition, the reference value is also sampled. The number of parameter values in +the sample depends on the number of symmetrical pairs of values you specify. +The reference value specification in this sampling option is optional: +• If a reference value is specified in this command, it temporarily redefines the reference specified in +the define command. +• If a reference value is not specified in this command, the reference specification from the define +command is used for sampling. +• An error is flagged when a reference value is not specified in this command or in the define +command. +The reference value is interpreted differently for continuous and discrete parameters: +• For continuous valued parameters reference is the parameter’s numerical value about which a +symmetrical sample will be created. +• For discrete valued parameters reference is the index of the list of values about which a symmetrical +sample will be created. +A reference value that falls outside the domain definition for the parameter is flagged as an error. +The sampling interval is interpreted differently for continuous and discrete parameters: +• For continuous valued parameters the interval at which the samples are taken is based on a +numerical value. For example, specifying reference=50., interval=10., and numSymPairs=2 for +a continuous parameter will create sample values of 30., 40., 50., 60., and 70. for this parameter. +• For discrete valued parameters the interval at which the samples are spaced is based on the index +of the list of values (indexing starts at zero); in this case interval must be an integer value. For +example, specifying reference=5, interval=−2 and numSymPairs=2 for a discrete parameter with +domain=[1, 2, 3, 5, 7, 10, 12, 15, 20, 25] will create sample values of 25, 15, 10, 5, and 2 for this +parameter. +The specified interval can have a positive or negative value, but a value of zero is not permitted. A +positive interval indicates that the list of sampled values starts with the smallest sampled value for a +continuous parameter or with the sampled value closest to the beginning of the list of values for a discrete +parameter (forward sampling). A negative interval indicates that the list of sampled values starts with +the largest sampled value for a continuous parameter or with the sampled value closest to the end of the +list of values for a discrete parameter (reverse sampling). Reverse sampling is useful when the TUPLE +combination operation is used . +The number of symmetrical pairs you specify must be zero or a positive integer; setting the number +of symmetrical pairs equal to zero indicates that only the reference value is sampled. +The domain specification in this command is optional: +• If a domain is specified in this command, it temporarily redefines the domain specified in the define +command. +• If a domain is not specified in this command, the domain specification from the define command is +used for sampling. +• An error is flagged in the case of discrete valued parameters when a domain is not specified in this +command or in the define command. +A domain specification (either in this command or in the define command) is required for discrete valued +parameters because the possible discrete values that can be sampled must be known. Although a domain +specification is not required for continuous valued parameters, it may be given. In either the case of +discrete parameters or the case of continuous parameters, a domain specification can be used to limit the +number of values sampled using the REFERENCE option since the domain is treated as a bound on the +possible sampling values. For example, specifying reference=50., interval=10., and numSymPairs=3 +for a continuous parameter with domain=(35., 100.) will sample values of 40., 50., 60., 70., and 80. for +this parameter. The minimum value of the domain acts as a bound in this sampling. +Input File Usage: +aStudy.sample (REFERENCE, par=, reference=, interval=, +numSymPairs=, domain=) +Sampling by VALUES +This sampling option assumes that you wish to create the parameter sample values directly. You must +specify the actual parameter values, irrespective of whether the parameter is continuous or discrete. +A parameter domain specified in the define command does not affect the values sampled for the +parameter when this option is used. +Input File Usage: +aStudy.sample (VALUES, par=, values=) +Combination of parameter samples +Use the aStudy.combine command to create sets of design points from the parameter samples. Choose how the combining +is done using one of the following tokens: MESH, TUPLE, or CROSS. The use of each combination +command results in the creation of a number of design points, which are grouped into design sets. If +a combine operation creates a design that duplicates a design in an existing design set, the duplicate +design is deleted immediately. The total number of designs in a parametric study (before the application +of any design constraints) is the sum of the number of designs in each design set. +You can name a design set; if you do not, it is named by default. The default naming convention +is p1 for the first non-user-named design set in the parametric study, p2 for the second non-user-named +design set, and so on. The design set name is used to help identify individual designs. A design set named +by you with a name identical to a previously specified design set name indicates that it is a respecification +of the design set and, thus, overwrites the previously existing one. +Input File Usage: +aStudy.combine (token, name=) +MESH combination +This combine option indicates that every sampled value for a parameter is to be combined with every +sampled value of every other parameter in the parametric study. +The following examples illustrate the use of the MESH combine option. In a two-parameter study +with the parameters defined and sampled as +study=ParStudy(par=('par1', 'par2')) +study.define(DISCRETE, par='par1', +domain=(1, 3, 5, 7, 9, 11, 13)) +study.sample(REFERENCE, par='par1', reference=0, +interval=2, numSymPairs=2) +study.define(CONTINUOUS, par='par2', domain=(10., 60.)) +study.sample(INTERVAL, par='par2', interval=20.) +the combine command +study.combine(MESH, name='dSet1') +creates the following 12 design points (par1, par2): (1, 10.), (5, 10.), (9, 10.), (1, 30.), (5, 30.), (9, 30.), +(1, 50.), (5, 50.), (9, 50.), (1, 60.), (5, 60.), and (9, 60.) . +A second use of the combine command preceded by a respecification of the parameter sampling +study.sample(NUMBER, par='par1', number=3) +study.sample(NUMBER, par='par2', number=3) +study.combine(MESH, name='dSet2') +par2 +60. +50. +40. +30. +20. +10. +9 11 13 +par1 +Figure 20.1.1–1 Design points in design set dSet1 created +with the MESH option of the combine command. +creates designs at the following nine points: (1, 10.), (7, 10.), (13, 10.), (1, 35.), (7, 35.), (13, 35.), +(1, 60.), (7, 60.), and (13, 60.) . The extreme and center values of both parameters +are combined. +par2 +60. +50. +40. +30. +20. +10. +9 11 13 +par1 +Figure 20.1.1–2 Design points in design set dSet2 created with the MESH option of +the combine command after the parameter sampling is redefined. +TUPLE combination +This combine option creates design sets consisting of n-tuples of the sampled parameter values, where +n is the number of parameters in the parametric study. Each n-tuple consists of one sampled value for +each parameter. For example, in a three-parameter study the first sampled value of each of the three +parameters makes up the first 3-tuple, the second sampled value of each of the three parameters makes +up the second 3-tuple, and so on. The creation of tuples ceases when any of the parameter samples runs +out of sampled values. +The following examples illustrate the use of the TUPLE combination operation. +For a +two-parameter study with the parameters defined and sampled as +study=ParStudy(par=('par1', 'par2')) +study.define(DISCRETE, par='par1', +domain=(1, 3, 5, 7, 9, 11, 13)) +study.define(CONTINUOUS, par='par2', domain=(10., 60.)) +study.sample(INTERVAL, par='par1', interval=1) +study.sample(INTERVAL, par='par2', interval=10.) +the combination operation +study.combine(TUPLE, name='dSet3') +creates designs at the following 6 points: (1, 10.), (3, 20.), (5, 30.), (7, 40.), (9, 50.), and (11, 60.) . This represents a diagonal pattern in the two-parameter space. We see that all par2 +values are used in the tuple combination but the last par1 value is not used because there are no more +par2 sample values to form additional tuples. +par2 +60. +50. +40. +30. +20. +10. +9 11 13 +par1 +Figure 20.1.1–3 Design points in design set dSet3 created +with the TUPLE option of the combine command. +A second invocation of the above combine command after respecifying the par2 sampling as +study.sample(INTERVAL, par='par2', interval=-10.) +study.combine(TUPLE, name='dSet4') +creates designs at the following 6 points: (1, 60.), (3, 50.), (5, 40.), (7, 30.), (9, 20.), and (11, 10.) . This represents the other diagonal in the two-parameter space. +par2 +60. +50. +40. +30. +20. +10. +9 11 13 +par1 +Figure 20.1.1–4 Design points in design set dSet4 created with the TUPLE option of +the combine command after the parameter sampling is redefined. +CROSS combination +This combine option creates designs in the form of “cross-shaped” patterns as follows: each value +sampled for an individual parameter is combined with the reference value, as specified in the define +command, of all the other parameters used in the parametric study. To use the CROSS combine option, +it is necessary to specify a reference value in the define command for all parameters in the parametric +study. +The reference value specified for a parameter in the define command does not have to coincide with +a value sampled by that parameter’s sampling rule. However, if the reference value does not coincide +with a sampled value, the reference parameter value is not added to the list of sampled values for that +parameter; it is used only to form the CROSS combination. +The following examples illustrate the use of the CROSS combine option. For a two-parameter study +with the parameters defined and sampled as +study=ParStudy(par=('par1', 'par2')) +study.define(DISCRETE, par='par1', +domain=(1, 3, 5, 7, 9, 11, 13), reference=3) +study.define(CONTINUOUS, par='par2', +domain=(10., 60.), reference=40.) +study.sample(REFERENCE, par='par1', interval=1, +numSymPairs=3) +study.sample(INTERVAL, par='par2', interval=10.) +the combine cross option +study.combine(CROSS, name='dSet5') +creates designs at the following 12 points: (1, 40.), (3, 40.), (5, 40.), (7, 40.), (9, 40.), (11, 40.), (13, 40.), +(7, 10.), (7, 20.), (7, 30.), (7, 50.), and (7, 60.) . This combination is a cross-shaped +pattern where the cross intersection is at (7, 40.) as specified [7 is the fourth value (reference=3) of the +discrete parameter par1]. +par2 +60. +50. +40. +30. +20. +10. +9 11 13 +par1 +Figure 20.1.1–5 Design points in design set dSet5 created +with the CROSS option of the combine command. +A second invocation of the above combine command after respecifying par2 as +study.define(CONTINUOUS, par='par2', domain=(10., 60.), +reference=45.) +study.combine(CROSS, name='dSet6') +creates designs at the following 13 design points: (1, 45.), (3, 45.), (5, 45.), (7, 45.), (9, 45.), (11, 45.), +(13, 45.), (7, 10.), (7, 20.), (7, 30.), (7, 40.), (7, 50.), and (7, 60.) . +Constraining designs +A constraint that determines the allowable design points in the parametric study can be specified using +the aStudy.constrain scripting command . When such a constraint is specified, existing designs that violate the constraint +are eliminated immediately. +For example, the constrain command +aStudy.constrain('height*width < 12.') +where height and width are parameters in the parametric study, can be used to enforce that the cross- +sectional area of a rectangular beam must be less than 12.0 in all designs. +Input File Usage: +aStudy.constrain ('constraint expression') +par2 +60. +50. +40. +30. +20. +10. +9 11 13 +par1 +Figure 20.1.1–6 Design points in design set dSet6 created with the CROSS option of +the combine command when the parameter par2 is redefined. +Generation and execution of the designs of a parametric study +Once the required design points have been specified, it is necessary to generate the corresponding analysis +job data and execute the analyses. +Generation of analysis job data +Use the aStudy.generate scripting command to generate an input file for each design. +The name of the parametrized template input file from which the input files of each design are +generated must be specified. +The naming convention for the input files generated by the parametric study is as follows: +• The name of each analysis job will start with the template input file name; for example, shell. +• The name of the parametric study (specified by you in the ParStudy command using the name= +option) is appended, preceded by an underscore (_); for example, shell_thickness for a +parametric study defined with the study = ParStudy(name=’thickness’) command. +(If no parametric study name has been given, the parametric study name defaults to the name of +the Python script file in which the study is defined.) If the template input file name and parametric +study name are the same, the name is not repeated. +• The name of the design set (specified or created by default in the combine command) is appended, +preceded by an underscore (_); for example, shell_thickness_p1 for the first design set +(named by default) of the above parametric study. +• The design name (created automatically in the combine command) is appended, preceded by an +underscore (_); for example, shell_thickness_p1_c1 for the first design in the first design +set of the above parametric study. +As usual, the input files each have the extension .inp. You can examine and/or edit these input files +before execution. +The generate command creates a file with the .var extension that contains a description of the +parametric study. This file is given the parametric study name—for example, studyName.var—and +contains a list of all the designs generated, together with the parameter values associated with each design. +You can examine and/or edit this file; however, editing this file will affect the gathering of results across +the designs of the parametric study . +Each time the generate command is used, new versions of the studyName.var files are created +reflecting the designs specified by all previous combine commands. +The define, sample, and combine steps are performed before the generate command is executed. It +is, thus, possible for you to refer to parameters that do not exist or are not independent parameters in the +template input file. These errors are detected and flagged by the generate command. +Input File Usage: +aStudy.generate (template) +Execution of the analysis of the designs of a parametric study +Use the aStudy.execute command to execute the analysis of the designs of the study. +The command will submit a number of analysis jobs for execution under the control of a Python +process. All designs can be evaluated without further user interaction by specifying the ALL or +DISTRIBUTED options of this command, or you can control the execution of the analyses interactively +by specifying the INTERACTIVE option. In the interactive case you are prompted for further execution +instructions. The prompt allows you to: +• Specify a number of analyses to be executed before the process pauses and prompts you again. +• Execute the remaining analyses without further user interaction. +• Specify a number of analyses whose execution is to be skipped before the process pauses and +prompts you again. +• Stop execution. +The interactive option is useful because it provides the opportunity to: +• Study the results of the analyses already executed. +• Delete unnecessary files generated by the analyses to conserve disk space when many designs are +being analyzed. +• Analyze only certain designs of the parametric study. +The ALL and INTERACTIVE tokens are used for sequential execution of the Abaqus analyses on +your machine. The DISTRIBUTED token can be used to schedule analysis jobs on multiple machines +or multiple CPUs of one machine. +The DISTRIBUTED option is available only on variants of the UNIX operating system. +In +particular the implementation depends on the operating system for support of the rsh, rcp, and +xhost UNIX commands. Because of the use of these commands, it is necessary that for distributed +execution of parametric studies the parametric study must itself be executed on your local computer. +If binary results are output during the analyses, both the local and remote computers must be binary +compatible. Before the distributed execution capability can be used, it is necessary to configure the +appropriate queue interfaces in the Abaqus environment file. +Each analysis of a design of the parametric study that is executed when you issue the execute +command is, by default, executed by Abaqus in background mode, irrespective of the command option +used. Files created by the Abaqus analysis of each design will overwrite any existing files of the same +name without you being prompted. +You can add any necessary Abaqus execution options (refer to “Abaqus/Standard, Abaqus/Explicit, +and Abaqus/CFD execution,” Section 3.2.2) to the execution command for each of the analyses by +specifying them with the execOptions option. +Input File Usage: +aStudy.execute (token, files= , queues= , execOptions= ) +Parametric study results +Once the analyses associated with a parametric study have been executed, the variation of key results +across the different designs can be examined. First, results must be gathered from the results file or +output database of each of the analyses; then, these results must be reported. +the specification of the file, +The aStudy.output command +can be used to specify the source of the results to be gathered. All arguments to the aStudy.output +the analysis step, and the increment (for +command are optional: +non-frequency steps) or the mode (for frequency steps) from which the results are to be gathered. If +the file is not specified, the results (.fil) file will be used. +If the step is not specified, it must be +specified in the gather command . The defaults of the increment (for +non-frequency steps) or the mode (for frequency steps) are the last increment of the step and the first +mode calculated in the step unless specified in the gather command. Some arguments are applicable +only to the output (.odb) database: the instance name, the request type (field or history), the frame +value where the results are to be gathered, and whether the memory used to access an output database +should be overlayed when a different output database is accessed. +The specification of the source of the gathered results remains in effect for all subsequent gather +commands until the source is respecified. Respecification of the gathering source is treated as a complete +respecification; that is, nothing is retained from the previous specification of the gathering source. +Input File Usage: +aStudy.output (file=, instance=, overlay=, request=, step=, +frameValue= | inc= | mode=) +Gathering results +Use the aStudy.gather command to +gather results from the results file or output database of each of the analyses. +In each use of the gather command you must specify a name that is associated with the gathered +result record. This label is used to refer to the results record in the report commands. +When gathering results from the results (.fil) file, each result record to be gathered must be +chosen by specifying one of the available output variable identifier keys appearing under the .fil +column heading in “Abaqus/Standard output variable identifiers,” Section 4.2.1, or “Abaqus/Explicit +output variable identifiers,” Section 4.2.2. For example, the U or S variable identifier keys can be +specified, but the U1 or S11 variable identifier keys cannot be specified. +In addition, the MODAL +variable identifier key can be specified to gather eigenvalue results records (those written to the results +file with the record key 1980); in this case, no variable location data are required. +When gathering results from the output (.odb) database, each result record to be gathered is +chosen by specifying one of the available output variable identifier keys appearing under the .odb +column heading in “Abaqus/Standard output variable identifiers,” Section 4.2.1, or “Abaqus/Explicit +output variable identifiers,” Section 4.2.2. For field output the component must not be specified, while +for history output the component number is required; for example, the U or S variable identifier keys +can be specified for field output, while the U1 or S11 variable identifier keys can be specified for history +output. Unless the output is at the assembly level, an instance name must be provided as an argument +to the gather command. An exception to this instance-name requirement is the case where the output +(.odb) database is generated from a model not defined as an assembly of part instances, which is +inferred from the presence in the output database of a single assembly named Assembly-1 and a single +part instance named PART–1–1. In this case you need not explicitly refer to the instance PART–1–1. +The names of components of the result records are created automatically. For example, the +command +myStudy.gather(results='e52_stress', variable='S', element=52) +creates a result record e52_stress whose six components (in the case of a three-dimensional +solid element) are named: e52_stress.1 (the S11 stress component), e52_stress.2 (the S22 +stress component), e52_stress.3 (the S33 stress component), e52_stress.4 (the S12 stress +component), e52_stress.5 (the S13 stress component), and e52_stress.6 (the S23 stress +component). +The variable location data that must be given depend on the output variable identifier key specified. +(Refer to “Gather the results of a parametric study.,” Section 20.2.5, for a description of the location +data.) Enough variable location data must be given to define a unique result record. +Input File Usage: +aStudy.gather (request=, results=, step=, frameValue= | inc= | mode=, +variable=, additional location data) +Reporting results +Use the aStudy.report scripting command to +report results gathered from the results files of the parametric study. Use the PRINT, FILE, or XYPLOT +options to specify the kind of report to be produced: +• PRINT indicates that a table of results (with headings) is to be printed to the default output device +(the screen). You may wish to limit the number of columns in a table so as to make the table readable. +• FILE indicates that a table of results (with headings) is to be written to an ASCII file. +• XYPLOT indicates that a table of results (without headings) is to be written to an ASCII file that +can later be read into the Visualization module in Abaqus/CAE to display X–Y plots. +Each row in a table represents a design in the parametric study. A column in a table can represent values +of a parameter, values of a gathered result, or design names. +One or more parameters can be specified in the report command. If no parameters are specified, the +default is that all parameters in the parametric study are included in the table. The column corresponding +to each parameter shows the value of that parameter in each of the designs included in the table. +A design set name can be specified to restrict the rows in the table to designs that are part of the set +(refer to the combine command described earlier). If a design set is not specified, the default is that all +designs are included in the table. +Use variations=ON to specify that the first column in a table must show the design names. +If +variations=ON is not specified or variations=OFF is included, the column of design names is not +included in the table. +The names of the results to be reported must be specified as a sequence; for example, the Mises +stress of element 33, the S22 stress of element 52, and the U3 displacement of node 10 are gathered in +the following three separate commands: +myStudy.gather(results='e33_sinv', variable='SINV', element=33) +myStudy.gather(results='e52_s', variable='S', element=52) +myStudy.gather(results='n10_u', variable='U', node=10) +These results can be printed in a single table using the following report command: +myStudy.report(PRINT, +results=('e33_sinv.1', 'e52_s.2', 'n10_u.3')) +This example shows not only how gathered results of different types (element, nodal, etc.) can be +collected in a single table but also how to refer to components of results records (the Mises stress is the +first component of SINV, S22 is the second component of S, and U3 is the third component of U—refer +to “Results file output format,” Section 5.1.2, or the Abaqus Scripting User’s Manual for a description +of how the results are stored in the results file and the output database, respectively). +When either the FILE token or the XYPLOT token is used, a file name must be given to specify +the file to which the results are to be written. A subsequent report command issued in the same session +using the same file name will append the new results to the file. However, a subsequent report command +issued in a different session using the same file name overwrites the existing file. +Input File Usage: +aStudy.report (token, results=, par=, designSet=, variations=, file=) +Execution of parametric studies +To carry out a parametric study, you must prepare a parametrized input file (inputFile.inp). This input +file is the template used for the generation of the parametric variations of the study and must contain the +parameter definitions necessary to use parameters in place of input quantities. The parameters must be +defined in the template file; they cannot be defined in any include files that are referred to by the template +file. +In addition, you must prepare a Python scripting file, scriptFile.psf, containing instructions that +script the actions of the parametric study. +Typically, you prepare the Python scripting file using an editor and then invoke execution of this +file using the Abaqus execution command abaqus script=scriptFile. This command starts the Python +interpreter and executes the instructions in the scripting file. Alternatively, you simply start the Python +interpreter, without giving a scripting file, with the Abaqus execution command abaqus script. In this +case the Python interpreter remains active, and you can execute additional commands interactively or +execute additional commands contained in a file (for example, fileName) using the Python command +execfile(’fileName’). The Python interpreter can be terminated using [Ctrl]+d on a UNIX machine or +[Ctrl]+z on a Windows machine. +It is normally preferable to execute a previously prepared scripting file because it is likely that you +will want to develop the script iteratively; in this case you simply have to go back and edit the scripting +file and re-execute it until satisfied with the result. +You can monitor the progress of the parametric variation analyses using normal operating system +commands. +Execution in more than one session +You may want to gather and report results multiple times, after the parametric variations of the study +have been executed. It is possible to define, generate, and execute a parametric study in one session and +gather and report results in a separate session. Only the command used to create the parametric study +needs to be reissued when you start a new session. +Visualization of parametric study results +The results of the analysis of a particular parametric study variation can be visualized like any other +results of a single analysis. +Visualization of results gathered across designs of a parametric study requires gathering of results. +For visualization the results must be reported in ASCII files (using the XYPLOT option in the gather +command), which can be read by the Visualization module in Abaqus/CAE to produce X–Y plots of +results versus parameter values or design names. +Scripting commands +Parametric studies are scripted in files with the .psf extension using the Python language (Lutz, 1996). +A parametric study object, constructed from the ParStudy class, is provided whose methods make +scripting of parametric studies straightforward; these methods are described in this chapter. +Syntax of scripting commands +Scripting commands generally have the following form: +aStudy.method (token, data) +aStudy is the parametric study object to which the method applies; this object is constructed using the +parametric study constructor command. method is the method to be used; for example, define, sample, +or execute. +Most (but not all) commands have a token that selects an option of the command; for example, +aStudy.define (CONTINUOUS, par= ) indicates that one or more continuous parameters are being +defined in a parametric study. Tokens are always given in capital letters and are mutually exclusive. +For most (but not all) commands additional data must be specified. +Python language rules +The parametric study scripts contained in scripting files must follow the syntax and semantics of the +Python language. Some important aspects of this language are described here (more general Python +language rules are discussed in “Parametric input,” Section 1.4.1). +Comments +Comments must be preceded by the # symbol. The comment is understood to continue to the end of the +line. For example, +# +# This parametric study ... +# +studyTempEffects.generate(template='shell') #use shell input file +Case sensitivity +All variable and method names, tokens, and character string literals are case sensitive across all operating +systems. For example, +study.execute( ) # is valid +study.Execute( ) # is not valid because of the capital E +study.sample(NUMBER, ...) # uses the valid token NUMBER +study.sample(number, ...) # lower case token is not valid +study.generate(template='aFile') # 'aFile' is different +study.generate(template='afile') # from 'afile' +Character strings +Character strings are indicated by using paired single (’ ’) or double (” ”) quotation marks. Backward +single quotation marks (‘ ‘) cannot be used for this purpose. For example, +"double quoted string" +'single quoted string' +Printing +The Python print command can be used to obtain a printed representation of any Python object. For +example, +print 'MY TEXT' +will print MY TEXT on the standard output device. +Lists and tuples +The scripting methods for parametric studies accept integer, real, and character string types. These +primitive types can, in many cases, optionally be contained within tuple or list structures. Although +there are some differences between lists and tuples in Python, they can be used interchangeably in the +parametric study scripting commands; they simply represent ordered sequences of items. Items in lists +or tuples must be separated by commas and enclosed in parentheses or brackets. For example, +aStudy.define(CONTINUOUS, par=('xCoord',))# tuple contains a +# single string item +aStudy.define(CONTINUOUS, par=['xCoord']) # list contains a +# single string item +aStudy.define(CONTINUOUS, par=('xCoord', 'yCoord')) # tuple +aStudy.define(CONTINUOUS, par=['xCoord', 'yCoord']) # list +Indentation +Python uses indentation to group blocks of statements. Therefore, a Python statement should begin in +the same column as the preceding statement except where grouping of statements is required by Python. +Accessing the data of a parametric study +In some cases it is desirable to have direct programmatic access to the data of a parametric study. +Therefore, all of the important data of the study are stored in repositories that can be accessed as data +members of the parametric study object. The repositories have a similar interface and similar behavior +to that of Python dictionaries. Repository data are stored as key, value pairs; and methods are provided +for accessing the repository keys and values. The syntax aValue = aRepository[aKey] is used +to retrieve the value associated with a repository key. A list of the keys of the repository is obtained +using the keys() method of the repository; for example, allKeys = aRepository.keys(). +Similarly, a list of the values of the repository is obtained using the values() method of the repository; +for example, allValues = aRepository.values(). The following parametric study script +shows an example of how the parameter repository of a parametric study can be accessed and how a list +of the parameter names and a list of the sample values for the parameter t1 can be obtained: +studyTempEffect = ParStudy(par=('t1', 't2')) +studyTempEffect.define(CONTINUOUS, par=('t1', 't2')) +studyTempEffect.sample(VALUES, par='t1', values=(200.,300.,400.)) +studyTempEffect.sample(VALUES, par='t2', values=(250.,350.,450.)) +parRepository = studyTempEffect.parameter +listOfParameters = parRepository.keys() +t1Sample = parRepository['t1'].sample +The script results in the following assignments: listOfParameters = [’t1’, ’t2’] and +t1Sample = [200.0, 300.0, 400.0]. The Python print command can be used to obtain +information on the contents of a repository. +Parametric study repositories +A parametric study has the following repositories and objects as data members: +• aStudy.parameter: A repository for parameter objects keyed by parameter name. Each parameter +object has a name, type, domain, reference, and sample data member. +• aStudy.designSet: A repository for design sets keyed by design set name. Each design set is +represented as a list of design points. +• aStudy.job: A repository for analysis job objects keyed by the name of the corresponding analysis +input file name (without the .inp extension). Each job object has a design, status, root, designSet, +and designName data member. +• aStudy.resultData: A repository for result records keyed by a name constructed by successively +appending the result name, the underscore character (_), and the design name. For results retrieved +from the result (.fil) file, each result record is in the format of the result (.fil) file record for +the corresponding output variable. For field results retrieved from the output (.odb) database, each +result record will be a tuple containing the components of the results. The result record for history +results from the output (.odb) database, which can only be retrieved for a single component, will +be a tuple containing a single value. +• aStudy.table: A table object containing a representation of the table formatted by the last use of the +report command. The table object has title, variation, designs, and results data members. +Additional reference +• Lutz, M., Programming Python, O’Reilly & Associates, Inc., 1996. +20.2 +Parametric studies: commands +• “Combine parameter samples for parametric studies.,” Section 20.2.1 +• “Constrain parameter value combinations in parametric studies.,” Section 20.2.2 +• “Define parameters for parametric studies.,” Section 20.2.3 +• “Execute the analysis of parametric study designs.,” Section 20.2.4 +• “Gather the results of a parametric study.,” Section 20.2.5 +• “Generate the analysis job data for a parametric study.,” Section 20.2.6 +• “Specify the source of parametric study results.,” Section 20.2.7 +• “Create a parametric study.,” Section 20.2.8 +• “Report parametric study results.,” Section 20.2.9 +• “Sample parameters for parametric studies.,” Section 20.2.10 +20.2.1 +aStudy.combine(): Combine parameter samples for parametric studies. +Products: Abaqus/Standard Abaqus/Explicit +This command is used to combine the sampled parameter values in a parametric study. +Reference: +• “Scripting parametric studies,” Section 20.1.1 +Command: +aStudy.combine (token, additional data) +Tokens: +CROSS +Use this token to create designs in a “cross-shaped” pattern from the sampled values of the parameters +in the parametric study. +MESH +Use this token to create designs in a “mesh” pattern in which every sampled value of a parameter is +combined with every sampled value of every other parameter in the parametric study. +PRINT +Use this token to print the design points created for the parametric study. +TUPLE +Use this token to create designs in a “tuple” pattern consisting of tuples of sampled values of the +parameters in the parametric study. +Additional data for CROSS, MESH, and TUPLE: +Optional data: +name +Set name equal to the name of the design set being defined; this name must be enclosed by quotation +marks. A default design set name is created if a name is not specified. +Additional data for PRINT: +Optional data: +name +Set name equal to the name of the design set for which information is being printed; this name must +be enclosed by quotation marks. If a design set name is not specified, information is printed for all the +design sets in the parametric study. +20.2.2 +aStudy.constrain(): Constrain parameter value combinations in parametric studies. +Products: Abaqus/Standard Abaqus/Explicit +This command is used to define constraints on parameter value combinations; combinations that violate any +of the constraints are eliminated from the parametric study. +Reference: +• “Scripting parametric studies,” Section 20.1.1 +Command: +aStudy.constrain (constraint expression) +Required data: +constraint expression +Provide a constraint expression enclosed by matching quotation marks. This expression may involve +operations among parameters, numbers, and previously defined Python variables; +for example, +’height*width < maxArea-2.0’. The constraint can be an equality or an inequality. +20.2.3 +aStudy.define(): Define parameters for parametric studies. +Products: Abaqus/Standard Abaqus/Explicit +This command is used to define the parameters specified for a parametric study. +Reference: +• “Scripting parametric studies,” Section 20.1.1 +Command: +aStudy.define (token, additional data) +Tokens: +CONTINUOUS +Use this token to indicate that the parameter is continuous valued. +DISCRETE +Use this token to indicate that the parameter is discrete valued. +PRINT +Use this token to print parameter definitions. +Additional data for CONTINUOUS: +Required data: +par +Set par equal to the name of the parameter or the sequence of parameters being defined. If a single +parameter is specified, it must be enclosed by matching quotation marks; for example, ’par1’. If a list +of parameters is specified, it must be given inside parentheses or brackets and must contain parameter +names enclosed by matching quotation marks and separated by commas; for example, (’par1’, +’par2’, ’par3’) or [’par1’, ’par2’, ’par3’]. +Optional data: +domain +Set domain equal to the minimum and maximum values of the parameter separated by a comma and +enclosed by parentheses or brackets; for example, (10., 20.) or [10., 20.]. +If domain is omitted from this command and the parameter is later sampled using a method that +requires a domain definition, the domain must be specified in the sample command. +reference +Set reference equal to the reference value of the parameter. +If reference is omitted from this command and the parameter is later sampled using a method that +requires a reference definition, the reference must be specified in the sample command. +Additional data for DISCRETE: +Required data: +par +Set par equal to the name of the parameter or the list of parameters being defined. If a single parameter +is specified, it must be enclosed by matching quotation marks; for example, ’par1’. +If a list of +parameters is specified, it must be given inside parentheses or brackets and must contain parameter +names enclosed by matching quotation marks and separated by commas; for example, (’par1’, +’par2’, ’par3’) or [’par1’, ’par2’, ’par3’]. +Optional data: +domain +Set domain equal to the sequence of values that the parameter may have. The values must be separated +by commas and enclosed by parentheses or brackets; for example, (1., 2., 5., 3.) or [1., +2., 5., 3.]. +If domain is omitted from this command and the parameter is later sampled using a method that +requires a domain definition, the domain must be specified in the sample command. +reference +Set reference equal to the index in the sequence of parameter values. Indexing starts at zero, so that the +first value of the sequence corresponds to index zero and the last value of the sequence corresponds to +an index equal to the number of values in the sequence minus one. +If reference is omitted from this command and the parameter is later sampled using a method that +requires a reference definition, the reference must be specified in the sample command. +Additional data for PRINT: +Optional data: +par +Set par equal to the name of the parameter or the sequence of parameters whose definition is to be +printed. If a single parameter is specified, it must be enclosed by matching quotation marks; for example, +’par1’. If a sequence of parameters is specified, it must be given inside parentheses or brackets and +must contain parameter names enclosed by matching quotation marks and separated by commas; for +example, (’par1’, ’par2’, ’par3’) or [’par1’, ’par2’, ’par3’]. +If par is omitted, parameter definitions are printed for all parameters in the parametric study. +20.2.4 +aStudy.execute(): Execute the analysis of parametric study designs. +Products: Abaqus/Standard Abaqus/Explicit +This command is used to execute the analyses of the designs generated by a parametric study. +Reference: +• “Scripting parametric studies,” Section 20.1.1 +Command: +aStudy.execute (token, execOptions= , additional data) +Tokens: +ALL +Use this token to sequentially execute the analyses of all the designs of the parametric study. This option +is the default. +DISTRIBUTED +Use this token to execute the analyses of all designs using the specified queue interfaces of the local and/or +remote computers. A similar number of analyses will be distributed to each of the specified queues. +INTERACTIVE +Use this token to sequentially execute the analyses of all the designs of the parametric study in interactive +mode. In this case the process pauses to prompt you for further execution instructions. The prompt allows +you to specify the number of analyses to be executed, to execute the remaining analyses, to specify the +number of analyses whose execution is to be skipped, or to skip all the remaining analyses. +Optional data: +execOptions +Set execOptions equal to a character string of Abaqus execution options (refer to “Abaqus/Standard, +Abaqus/Explicit, and Abaqus/CFD execution,” Section 3.2.2) that are to be added to the Abaqus +execution command when executing the analyses of the designs of the parametric study; this string must +be enclosed in matching quotation marks. +Additional data for DISTRIBUTED: +Required data: +queues +Set queues equal to the queue interface name or a sequence of queue interface names. If a single name +is given, it must be enclosed in matching quotation marks. If a sequence of names is given, it must be +enclosed in parentheses or brackets and contain queue interface names enclosed in matching quotation +marks and separated by commas. +Optional data: +files +Set files equal to the symbolic constant or a sequence of symbolic constants that identifies the file or +files that must be returned to the local computer after remote execution. The sequence items must be +separated by commas, and the sequence must be enclosed in parentheses or brackets. +The allowed symbolic constants are: DAT, LOG, FIL, SEL, MSG, STA, ODB, IPM, RES, ABQ, and +PAC. The default value is files = (DAT, FIL, LOG, ODB, SEL). +Defining queues and queue interfaces: +Before being used for a distributed parametric study, queue interfaces must be defined within the +design_startup portion of the Abaqus environment file. For example, to define a queue interface for an +existing queue short on the remote computer server, the following entry in the environment file is +required: +def onDesignStartup(): +from session import Queue +import os +# convenience assignment +SCRATCH = '/scratch/' + os.environ['USER'] +# create remote queue interface +Queue(name='short_interface', hostName='server', +driver='abaqus', queueName='short', directory=SCRATCH) +If, in addition, a local queue is required, the entry must be expanded to: +def onDesignStartup(): +from session import Queue +import os +# convenience assignment +SCRATCH = '/scratch/' + os.environ['USER'] +# create remote queue interface +Queue(name='short_interface', hostName='server', +driver='abaqus', queueName='short', directory=SCRATCH) +# create local queue interface +Queue(name='local_interface', driver='abaqus', +queue_name="local" +local="echo "./%S 1>%L 2>&1" | batch" +aStudy.execute() +20.2.5 +aStudy.gather(): Gather the results of a parametric study. +Products: Abaqus/Standard Abaqus/Explicit +This command is used to gather analysis results across the designs of a parametric study. +Reference: +• “Scripting parametric studies,” Section 20.1.1 +Command: +aStudy.gather (request= , results= , step= , frameValue= | inc= | mode= , variable= , additional data) +Required data: +results +Set results equal to a name that will be used to identify the results record gathered by this command. +This name must be enclosed in matching quotation marks. +variable +Set variable equal to an output variable identifier key; this key must be enclosed in matching quotation +marks. +For gathering results from the results (.fil) file only those output variable identifier keys +appearing under the .fil column heading in “Abaqus/Standard output variable identifiers,” Section 4.2.1, +or “Abaqus/Explicit output variable identifiers,” Section 4.2.2, are available. For example, the U or S +variable identifier keys can be specified, but the U1 or S11 variable identifier keys cannot be specified. +In addition, the MODAL variable identifier key can be specified to gather frequency results (those +written to the results file with the record key 1980); in this case no additional data are required in this +command. +When gathering results from the output database (.odb) file, each result record to be gathered +is chosen by specifying one of the available output variable identifier keys appearing under the .odb +column heading in “Abaqus/Standard output variable identifiers,” Section 4.2.1, or “Abaqus/Explicit +output variable identifiers,” Section 4.2.2. For field output the component must not be specified, while +for history output the component number is required; for example, the U or S variable identifier keys +can be specified for field output, while the U1 or S11 variable identifier keys can be specified for history +output. +Optional data: +request +This option is applicable only if the results are to be gathered from the output database file. +Set request equal to FIELD or HISTORY to specify whether the results must be gathered from the +field data or the history data in the output database file. +If request is omitted from this command, the results will be gathered from the field data. +step +Set step equal to the analysis step number from which the results are to be gathered. +If step is specified in this command as well as in the output command, the step specification in this +command is used. +If step is omitted from this command, it must have been specified in the output command. +Optional and mutually exclusive data: +frameValue +This option is applicable only if the results are to be gathered from the output database file. +Set frameValue equal to the step time or frequency value of the analysis increment in the analysis +step specified from which the results are to be gathered. frameValue can also be set equal to the symbolic +constant LAST to specify that results are to be gathered from the last increment of the step. If no results +are available at the frameValue specified, a warning will be issued and the results will be gathered from +the closest increment. +If frameValue is specified in this command as well as in the output command, the frameValue +specification in this command is used for gathering. +If frameValue is omitted from this command, the results are gathered for the frameValue specified +in the output command or are gathered from the last increment in the step. +inc +Set inc equal to the number of the analysis increment of the non-frequency analysis step specified from +which the results are to be gathered across the parametric study variations. inc can also be set equal to +the symbolic constant LAST to specify that results are to be gathered from the last increment of the step. +If inc is specified in this command as well as in the output command, the inc specification in this +command is used for gathering. +If inc is omitted from this command, the results are gathered from the increment specified in the +output command or are gathered from the last increment in the step. +This option is not valid for gathering history results from the output database file. +mode +Set mode equal to the number of the mode of the frequency analysis step specified from which the results +are to be gathered across the parametric study variations. +If mode is specified in this command as well as in the output command, the mode specification in +this command is used. +If mode is omitted from this command, the results are gathered from the mode specified in the +output command or are gathered from the first mode in the step. +Additional data for element integration point variables: +Required data: +element +Set element equal to the number of the element for which results are to be gathered. +instance +This option is required only if results are gathered for an element on a part instance in an output database +file generated from a model described as an assembly of part instances. +Set instance equal to the name of the part instance for which results are to be gathered. This name +must be enclosed in matching quotation marks. +If instance is specified in this command as well as in the output command, +the instance +specification in this command is used. +Optional data: +centroid +Set centroid equal to the symbolic constant ON to indicate that the results are to be gathered at the +centroid of the element. This option is valid only when the results have been written to the results file at +the centroid of the element. +centroid, int, and node are mutually exclusive. +If centroid, int, and node are omitted, the default is int=1. +int +Set int equal to the number of the integration point of the element for which results are to be gathered. +This option is valid only when the results have been written to the results file at the integration points of +the element. +centroid, int, and node are mutually exclusive. +If int is omitted, the default is int=1. If centroid, int, and node are omitted, the default is int=1. +node +Set node equal to the number of the node in the element for which results are to be gathered. This option +is valid only when the results have been written to the results file at the nodes of the element. +centroid, int, and node are mutually exclusive. +If centroid, int, and node are omitted, the default is int=1. +rbnum +Set rbnum equal to the number of the rebar for which results are to be gathered. The rebar number is +consistent with the order, per element, in which you define the rebar . +If rbnum is omitted, the default is rbnum=1. +Rebar information cannot be gathered from the output database file. +rebar +Set rebar equal to the name of the rebar for which results are to be gathered (defined as described in +“Defining rebar as an element property,” Section 2.2.4). Rebar results can be obtained for continuum +and beam elements only at integration points; for shell and membrane elements rebar results can be +obtained at integration points and at the centroid of the element. +Rebar information cannot be gathered from the output database file. +section +Set section equal to the number of the section point of the element for which results are to be gathered. +This applies to beam, shell, or layered solid elements. section is not relevant for rebar results. +If section is omitted, the default is section=1. +Additional data for element section variables: +Required data: +element +Set element equal to the number of the element for which results are to be gathered. +instance +This option is required only if results are gathered for an element on a part instance in an output database +file generated from a model described as an assembly of part instances. +Set instance equal to the name of the part instance for which results are to be gathered. This name +must be enclosed in matching quotation marks. +If instance is specified in this command as well as in the output command, +the instance +specification in this command is used. +Optional data: +centroid +Set centroid equal to the symbolic token ON to indicate that the results are to be gathered at the centroid +of the element. This option is valid only when the results have been written to the results file or output +database at the centroid of the element. +centroid, int, and node are mutually exclusive. +If centroid, int, and node are omitted, the default is int=1. +int +Set int equal to the number of the integration point of the element for which results are to be gathered. +This option is valid only when the results have been written to the results file or output database at the +integration points of the element. +centroid, int, and node are mutually exclusive. +If int is omitted, the default is int=1. If centroid, int, and node are omitted, the default is int=1. +node +Set node equal to the number of the node in the element for which results are to be gathered. This option +is valid only when the results have been written to the results file or output database at the nodes of the +element. +centroid, int, and node are mutually exclusive. +If centroid, int, and node are omitted, the default is int=1. +Additional data for whole element variables: +Required data: +element +Set element equal to the number of the element for which results are to be gathered. +int +Set int = –1. +instance +This option is required only if results are gathered for an element on a part instance in an output database +file generated from a model described as an assembly of part instances. +Set instance equal to the name of the part instance for which results are to be gathered. This name +must be enclosed in matching quotation marks. +If instance is specified in this command as well as in the output command, +the instance +specification in this command is used. +Additional data for partial model (element set) or whole model variables: +Optional data: +elset +Set elset equal to the element set name for which results are to be gathered. If elset is omitted, results +will be gathered for the whole model. This name must be enclosed in matching quotation marks. +instance +This option is required only if results are gathered from an output database file and if the element set is +defined on an instance. +Set instance equal to the name of the instance on which the element set is defined. This name must +be enclosed in matching quotation marks. +If the element set is defined on the assembly, instance must not be specified in both this command +and the output command. +If instance is specified in this command as well as in the output command, +the instance +specification in this command is used. +Additional data for nodal variables: +Required data: +node +Set node equal to the number of the node for which results are to be gathered. +instance +This option is required only if results are gathered for a node on a part instance in an output database file +generated from a model described as an assembly of part instances. +Set instance equal to the name of the instance for which results are to be gathered. This name must +be enclosed in matching quotation marks. +If instance is specified in this command as well as in the output command, +the instance +specification in this command is used. +Additional data for modal variables: +There are no additional data. +Additional data for contact surface variables: +Required data: +master +Set master equal to the name of the master surface of the contact pair for which results are to be gathered. +This name must be enclosed in matching quotation marks. +slave +Set slave equal to the name of the slave surface of the contact pair for which results are to be gathered. +This name must be enclosed in matching quotation marks. +Optional data: +masterInstance +This option is required only if results are gathered from an output database file and if the master surface +is defined on an instance. +Set masterInstance equal to the name of the instance on which the master surface is defined. This +name must be enclosed in matching quotation marks. +slaveInstance +This option is required only if results are gathered from an output database file and if the slave surface +is defined on an instance. +Set slaveInstance equal to the name of the instance on which the slave surface is defined. This +name must be enclosed in matching quotation marks. +Required data when slave surface node variable results are requested: +node +If slave surface node variable results are to be gathered, set node equal to the number of the node for +which results are to be gathered. +nset and node are mutually exclusive. +instance +This option is required only if results are gathered for a node on a part instance in an output database file +generated from a model described as an assembly of part instances. +Set instance equal to the name of the part instance for which results are to be gathered. This name +must be enclosed in matching quotation marks. +If instance is specified in this command as well as in the output command, +the instance +specification in this command is used. +Optional data when whole surface variable results are requested: +nset +Set nset equal to the name of the node set for which whole surface variable results are to be gathered. +This name must be enclosed in matching quotation marks. +If nset is omitted, the default is the whole surface. +If the results are collected from the output database file and the node set is defined on an instance, the +node set name must be prefixed with the instance name and a period (for example: “PART–1–1.TOP”). +nset and node are mutually exclusive. +instance +This option is required only if results are gathered from an output database file and if the node set is +defined on an instance. +Set instance equal to the name of the instance on which the node set is defined. This name must be +enclosed in matching quotation marks. +If the node set is defined on the assembly, instance must not be specified in both this command and +the output command. +If instance is specified in this command as well as in the output command, +the instance +specification in this command is used. +Additional data for cavity radiation surface variables: +Required data: +element +Set element equal to the number of the element underlying the cavity facet for which results are to be +gathered. +elface +Set elface equal to the face identifier of the face of the element underlying the cavity facet for which +results are to be gathered. +instance +This option is required only if results are gathered from an output database file generated from a model +described as an assembly of part instances. +Set instance equal to the name of the part instance for which results are to be gathered. This name +must be enclosed in matching quotation marks. +If instance is specified in this command as well as in the output command, +the instance +specification in this command is used. +Additional data for section file output: +Required data: +sectionName +Set sectionName equal to the name of the section for which results are to be gathered. This name must +be enclosed in matching quotation marks . +20.2.6 +aStudy.generate(): Generate the analysis job data for a parametric study. +Products: Abaqus/Standard Abaqus/Explicit +This command is used to generate the analysis input files for a parametric study. +Reference: +• “Scripting parametric studies,” Section 20.1.1 +Command: +aStudy.generate (template= ) +Required data: +template +Set template equal to the name of the template input file from which the input files of each of the +parametric study variations are to be generated; this name must be enclosed in matching quotation marks. +20.2.7 +aStudy.output(): Specify the source of parametric study results. +Products: Abaqus/Standard Abaqus/Explicit +This command should precede any results gather commands. It is used to specify from where the results of a +parametric study will be gathered. +Reference: +• “Scripting parametric studies,” Section 20.1.1 +Command: +aStudy.output (file=, instance=, overlay=, request=, step= , frameValue= | inc= | mode= ) +Optional data: +file +Set file equal to FIL or ODB to specify that results must be read from the results (.fil) file or output +database (.odb) file. +If file is omitted from this command, the results will be read from the results (.fil) file. +instance +This option is applicable only if results are gathered from an output (.odb) database containing multiple +instances. +Set instance equal to the name of the part instance for which results are to be gathered. This name +must be enclosed in matching quotation marks. +If results are gathered for a set defined on the assembly, instance must not be specified in both this +command and the gather command. +If instance is omitted from this command and an instance name is required to gather the results, it +must be specified in the gather command. +overlay +This option is applicable only if results are gathered from an output (.odb) database. +This option is used to control the trade-off between memory usage and execution speed. Set overlay +equal to OFF (the default) or ON to specify whether the memory used for an output database should be +overwritten. If memory usage is a problem, set overlay equal to ON to specify that the memory used for +an output database must be overwritten after a gather is performed for the specific output database. If +execution speed is more important than memory usage, set overlay equal to OFF to specify that memory +must be allocated for each output database. +The overlay option affects your ability to separately manipulate the output database (.odb) file. +When you set overlay equal to OFF, the file will remain open after accessing the results from the gather +command, which may affect your ability to separately access or manipulate the file (to delete the file, for +example). Set overlay equal to ON to separately access the .odb file after accessing the gather based +results. +request +This option is applicable only if the results are to be gathered from the output (.odb) database. +Set request equal to FIELD or HISTORY to specify whether the results must be gathered from the +field data or the history data in the output database. +If request is omitted from this command, the results will be gathered from the field data. +step +Set step equal to the analysis step number from which the results are to be gathered. +If step is omitted from this command, it must be specified in the gather command. +Optional and mutually exclusive data: +frameValue +This option is applicable only if the results are to be gathered from the output (.odb) database. +Set frameValue equal to the step time or frequency value of the analysis increment in the analysis +step specified from which the results are to be gathered. frameValue can also be set equal to the symbolic +constant LAST to specify that results are to be gathered from the last increment of the step. If no results +are available at the frameValue specified, a warning will be issued and the results will be gathered from +the closest increment. +If frameValue is omitted from this command, the results are gathered from the last increment in +the step or are gathered from the increment specified in the gather command. +inc +Set inc equal to the number of the analysis increment of the non-frequency analysis step specified from +which the results are to be gathered. inc can also be set equal to the symbolic constant LAST to specify +that results are to be gathered from the last increment of the step specified. +If inc is omitted from this command, the results are gathered from the last increment in the step or +are gathered from the increment specified in the gather command. +This option is not valid for gathering history results from the output (.odb) database. +mode +Set mode equal to the mode number of the frequency analysis step specified from which the results are +to be gathered across the parametric study variations. +If mode is omitted, the results are gathered from the mode specified in the gather command or are +gathered from the first mode in the step. +20.2.8 +aStudy=ParStudy(): Create a parametric study. +Products: Abaqus/Standard Abaqus/Explicit +This command is used to create a parametric study. It must precede any other scripting commands that refer +to the parametric study. +Reference: +• “Scripting parametric studies,” Section 20.1.1 +Command: +aStudy=ParStudy (par= , name= , verbose= , directory= ) +Required data: +par +Set par equal to the sequence of independent input parameters selected for the parametric study. This +sequence must be given inside parentheses or brackets and must contain independent parameter names +enclosed by matching quotation marks and separated by commas; for example, (’par1’, ’par2’, +’par3’) or [’par1’, ’par2’, ’par3’]. If only one parameter is to be listed, its name can be +given enclosed by matching quotation marks; for example, ’par1’. +Optional data: +name +Set name equal to the name of the parametric study; the name must be enclosed in matching quotation +marks. If a name is not specified, its value defaults to the name of the Python script file that contains the +parametric study commands. +verbose +Set verbose equal to the symbolic token OFF to suppress the printing of comment and warning messages. +The default is verbose=ON. +directory +Set directory equal to the symbolic token ON to select that subdirectories of the current directory are +used to organize the files of the parametric study. A subdirectory will be created for each design that is +analyzed. The default is directory=OFF. +aStudy.report(): Report parametric study results. +aStudy.report() +Products: Abaqus/Standard Abaqus/Explicit +This command is used to report results gathered across the designs of a parametric study. +Reference: +• “Scripting parametric studies,” Section 20.1.1 +Command: +aStudy.report (token, results= , par= , designSet= , variations=, truncation= , additional data) +Tokens: +FILE +Use this token to specify that results are to be written to an ASCII file as a table with the relevant headings. +PRINT +Use this token to specify that results are to be printed as a table with the relevant headings. Since the +results are printed to the default output device (the screen), you may wish to limit the number of columns +in a table so as to make the table readable. +XYPLOT +Use this token to specify that results are to be written to an ASCII file as a table without headings. This +table can subsequently be read by the Visualization module in Abaqus/CAE to display X–Y plots of result +and parameter values. +Required data: +results +Set results equal to the sequence of result names to be reported; this sequence must be enclosed +For example, results=(’e33_sinv.1’, ’e52_strain’, +by parentheses or brackets. +’n25_u.3’), where ’e33_sinv.1’ is the Mises stress of element 33 (Mises is the first component +of the SINV record), ’e52_strain’ are all the strain components of element 52, and ’n25_u.3’ +is the third component of displacement of node 25. This example assumes that the three results above +were gathered in previous gather commands by requesting the SINV, E, and U variable identifier keys, +respectively. +Optional data: +par +Set par equal to the name of the parameter or the sequence of parameters to be included in the report +table. If a single parameter is specified, it must be enclosed by matching quotation marks; for example, +’par1’. If a sequence of parameters is specified, it must be given inside parentheses or brackets and +must contain parameter names enclosed by matching quotation marks and separated by commas; for +example, (’par1’, ’par2’, ’par3’) or [’par1’, ’par2’, ’par3’]. +If par is omitted, all parameters in the parametric study are included in the report table. +designSet +Set designSet equal to the name of the design set whose results are to be included in the report table; this +name must be enclosed by matching quotation marks. +If designSet is omitted, results for all design sets in the parametric study are included in the report +table. +variations +Set variations equal to ON to indicate that the first column of the report table must show the names of +the designs being reported. Set variations equal to OFF to indicate that the names of the designs being +reported are not to be given in the first column of the report table. +If variations is omitted, the column of design names is not included in the report table. +truncation +Set truncation equal to ON to indicate that the data of the report table must be reported with limited +precision. Set truncation equal to OFF to indicate that the data of the report table must be reported with +full precision. +If truncation is omitted, the data of the report table are reported with limited precision. +Additional data for FILE and XYPLOT: +Required data: +file +Set file equal to the name of the file to which the report table is to be written. The file name must be +enclosed by matching quotation marks. +20.2.10 +aStudy.sample(): Sample parameters for parametric studies. +Products: Abaqus/Standard Abaqus/Explicit +This command is used to create samples of the values of the parameters of the study. +Reference: +• “Scripting parametric studies,” Section 20.1.1 +Command: +aStudy.sample (token, additional data) +Tokens: +INTERVAL +Use this token to sample a parameter at equal intervals. +NUMBER +Use this token to sample a given number of values of a parameter. +PRINT +Use this token to print parameter samples. +REFERENCE +Use this token to sample parameter values specified with respect to a reference parameter value. +VALUES +Use this token to sample particular values of a parameter. +Additional data for INTERVAL: +Required data: +interval +Set interval equal to the sampling interval. For a continuous valued parameter, values are sampled at +equally spaced intervals based on the numerical value of the parameter. For a discrete valued parameter, +values are sampled at equally spaced intervals based on the indexing of the sequence of parameter values. +par +Set par equal to the name of the parameter or the sequence of parameters whose samples are to be +printed. If a single parameter is specified, it must be enclosed by matching quotation marks; for example, +’par1’. If a sequence of parameters is specified, it must be given inside parentheses or brackets and +must contain parameter names enclosed by matching quotation marks and separated by commas; for +example, (’par1’, ’par2’, ’par3’) or [’par1’, ’par2’, ’par3’]. +Optional data: +domain +For a continuous valued parameter, set domain equal to the minimum and maximum values of the +parameter separated by a comma and enclosed by parentheses or brackets; for example, (10., 20.) +or [10., 20.]. For a discrete valued parameter, set domain equal to the sequence of values that the +parameter may have separated by commas and enclosed by parentheses or brackets; for example, (1., +2., 5., 3.) or [1., 2., 5., 3.]. +If domain is specified in this command as well as in the define command for this parameter, the +domain specification in this command is used for sampling. +If domain is omitted from this command, it must have been specified in the define command. +Additional data for NUMBER: +Required data: +number +Set number equal to the number of equally spaced values to be sampled for the parameter. +par +Set par equal to the name of the parameter or the sequence of parameters whose samples are to be +printed. If a single parameter is specified, it must be enclosed by matching quotation marks; for example, +’par1’. If a sequence of parameters is specified, it must be given inside parentheses or brackets and +must contain parameter names enclosed by matching quotation marks and separated by commas; for +example, (’par1’, ’par2’, ’par3’) or [’par1’, ’par2’, ’par3’]. +Optional data: +domain +For a continuous valued parameter, set domain equal to the minimum and maximum values of the +parameter separated by a comma and enclosed by parentheses or brackets; for example, (10., 20.) +or [10., 20.]. For a discrete valued parameter, set domain equal to the sequence of values that the +parameter may have separated by commas and enclosed by parentheses or brackets; for example, (1., +2., 5., 3.) or [1., 2., 5., 3.]. +If domain is specified in this command as well as in the define command for this parameter, the +domain specification in this command is used for sampling. +If domain is omitted from this command, it must have been specified in the define command. +Additional data for PRINT: +Optional data: +par +Set par equal to the name of the parameter or the sequence of parameters whose samples are to be +printed. If a single parameter is specified, it must be enclosed by matching quotation marks; for example, +’par1’. If a sequence of parameters is specified, it must be given inside parentheses or brackets and +must contain parameter names enclosed by matching quotation marks and separated by commas; for +example, (’par1’, ’par2’, ’par3’) or [’par1’, ’par2’, ’par3’]. +If par is omitted, parameter samplings are printed for all parameters in the parametric study. +Additional data for REFERENCE: +Required data: +interval +Set interval equal to the sampling interval. For a continuous valued parameter, values are sampled at +equally spaced intervals about the reference value based on the numerical value of the parameter. For a +discrete valued parameter, values are sampled at equally spaced intervals about the reference value based +on the indexing of the sequence of parameter values. +numSymPairs +Set numSymPairs equal to the number of pairs of parameter values to be sampled symmetrically about +the reference value of the parameter. +par +Set par equal to the name of the parameter being sampled. This name must be enclosed by matching +quotation marks; for example, ’par1’. +Optional data: +domain +For a continuous valued parameter, set domain equal to the minimum and maximum values of the +parameter separated by a comma and enclosed by parentheses or brackets; for example, (10., 20.) +or [10., 20.]. For a discrete valued parameter, set domain equal to the sequence of values that the +parameter may have separated by commas and enclosed by parentheses or brackets; for example, (1., +2., 5., 3.) or [1., 2., 5., 3.]. +If domain is specified in this command as well as in the define command for this parameter, the +domain specification in this command is used for sampling. +In the case of a discrete valued parameter if domain is omitted from this command, it must have +been specified in the define command. +reference +For a continuous valued parameter, set reference equal to the reference value of the parameter. For +discrete valued parameters, set reference equal to the index in the sequence of parameter values; indexing +starts at zero, so that the first value of the sequence corresponds to index zero and the last value of the +sequence corresponds to an index equal to the number of values in the sequence minus one. +If reference is specified in this command as well as in the define command for this parameter, the +reference specification in this command is used for sampling. +If reference is omitted from this command, it must have been specified in the define command. +Additional data for VALUES: +Required data: +par +Set par equal to the name of the parameter or the sequence of parameters whose samples are to be +printed. If a single parameter is specified, it must be enclosed by matching quotation marks; for example, +’par1’. If a sequence of parameters is specified, it must be given inside parentheses or brackets and +must contain parameter names enclosed by matching quotation marks and separated by commas; for +example, (’par1’, ’par2’, ’par3’) or [’par1’, ’par2’, ’par3’]. +values +Set values equal to the sequence of parameter values that constitute the sample. This sequence must +be given inside parentheses or brackets and must contain values separated by commas; for example, +(’CAX4’, ’CAX4R’, ’CAX4H’) or [10., 20., 40.]. +SIMULIA is the Dassault Systèmes brand that delivers a scalable portfolio of +Realistic Simulation solutions including the Abaqus product suite for Unified Finite +Element Analysis; multiphysics solutions for insight into challenging engineering +problems; and lifecycle management solutions for managing simulation data, +processes, and intellectual property. 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If you contact +us by means outside the system to discuss an existing support problem and you know the incident or support +request number, please mention it so that we can query the database to see what the latest action has been. +Many questions about Abaqus can also be answered by visiting the Products page and the Support +page at www.simulia.com. +Anonymous ftp site +To facilitate data transfer with SIMULIA, an anonymous ftp account is available at ftp.simulia.com. +Login as user anonymous, and type your e-mail address as your password. Contact support before placing +files on the site. +Training +All offices and representatives offer regularly scheduled public training classes. The courses are offered in +a traditional classroom form and via the Web. We also provide training seminars at customer sites. All +training classes and seminars include workshops to provide as much practical experience with Abaqus as +possible. For a schedule and descriptions of available classes, see www.simulia.com or call your local office +or representative. +Feedback +We welcome any suggestions for improvements to Abaqus software, the support program, or documentation. +We will ensure that any enhancement requests you make are considered for future releases. If you wish to +make a suggestion about the service or products, refer to www.simulia.com. Complaints should be made by +contacting your local office or through www.simulia.com by visiting the Quality Assurance section of the +1.1.1 +1.2.1 +1.2.2 +1.3.1 +1.4.1 +2.1.1 +2.1.2 +2.1.3 +2.1.4 +2.1.5 +2.1.6 +2.2.1 +2.2.2 +2.2.3 +2.2.4 +2.2.5 +2.3.1 +2.3.2 +2.3.3 +2.3.4 +Contents +Volume I +PART I +INTRODUCTION, SPATIAL MODELING, AND EXECUTION +1. +Introduction +Introduction: general +Abaqus syntax and conventions +Input syntax rules +Conventions +Abaqus model definition +Defining a model in Abaqus +Parametric modeling +Parametric input +2. Spatial Modeling +Node definition +Node definition +Parametric shape variation +Nodal thicknesses +Normal definitions at nodes +Transformed coordinate systems +Adjusting nodal coordinates +Element definition +Element definition +Element foundations +Defining reinforcement +Defining rebar as an element property +Orientations +Surface definition +Surfaces: overview +Element-based surface definition +Node-based surface definition +Analytical rigid surface definition +Eulerian surface definition +Operating on surfaces +Rigid body definition +Rigid body definition +Integrated output section definition +Integrated output section definition +Mass adjustment +Adjust and/or redistribute mass of an element set +Nonstructural mass definition +Nonstructural mass definition +Distribution definition +Distribution definition +Display body definition +Display body definition +Assembly definition +Defining an assembly +Matrix definition +Defining matrices +3. Job Execution +Execution procedures: overview +Execution procedure for Abaqus: overview +Execution procedures +Obtaining information +Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD execution +SIMULIA Co-Simulation Engine controller execution +Abaqus/Standard, Abaqus/Explicit, and Abaqus/CFD co-simulation execution +Abaqus/CAE execution +Abaqus/Viewer execution +Python execution +Parametric studies +Abaqus documentation +Licensing utilities +ASCII translation of results (.fil) files +Joining results (.fil) files +Querying the keyword/problem database +ii +Abaqus ID:usb-toc +Printed on: Fri February 3 -- 18:01:12 2012 +2.3.5 +2.3.6 +2.4.1 +2.5.1 +2.6.1 +2.7.1 +2.8.1 +2.9.1 +2.10.1 +2.11.1 +3.1.1 +3.2.1 +3.2.2 +3.2.3 +3.2.4 +3.2.5 +3.2.6 +3.2.7 +3.2.8 +3.2.9 +3.2.10 +Making user-defined executables and subroutines +Input file and output database upgrade utility +Generating output database reports +Joining output database (.odb) files from restarted analyses +Combining output from substructures +Combining data from multiple output databases +Network output database file connector +Mapping thermal and magnetic loads +Fixed format conversion utility +Translating Nastran bulk data ���les to Abaqus input files +Translating Abaqus files to Nastran bulk data files +Translating ANSYS input files to Abaqus input files +Translating PAM-CRASH input files to partial Abaqus input files +Translating RADIOSS input files to partial Abaqus input files +Translating Abaqus output database files to Nastran Output2 results files +Translating LS-DYNA data files to Abaqus input files +Exchanging Abaqus data with ZAERO +Encrypting and decrypting Abaqus input data +Job execution control +Environment file settings +Using the Abaqus environment settings +Managing memory and disk resources +Managing memory and disk use in Abaqus +Parallel execution +Parallel execution: overview +Parallel execution in Abaqus/Standard +Parallel execution in Abaqus/Explicit +Parallel execution in Abaqus/CFD +File extension definitions +File extensions used by Abaqus +FORTRAN unit numbers +FORTRAN unit numbers used by Abaqus +CONTENTS +3.2.14 +3.2.15 +3.2.16 +3.2.17 +3.2.18 +3.2.19 +3.2.20 +3.2.21 +3.2.22 +3.2.23 +3.2.24 +3.2.25 +3.2.26 +3.2.27 +3.2.28 +3.2.29 +3.2.30 +3.2.31 +3.2.32 +3.2.33 +3.3.1 +3.4.1 +3.5.1 +3.5.2 +3.5.3 +3.5.4 +3.6.1 +3.7.1 +4.1.2 +4.1.3 +4.1.4 +4.2.1 +4.2.2 +4.2.3 +4.3.1 +5.1.1 +5.1.2 +5.1.3 +5.1.4 +CONTENTS +4. Output +PART II +OUTPUT +Output +Output to the data and results files +Output to the output database +Error indicator output +Output variables +Abaqus/Standard output variable identifiers +Abaqus/Explicit output variable identifiers +Abaqus/CFD output variable identifiers +The postprocessing calculator +The postprocessing calculator +5. File Output Format +Accessing the results file +Accessing the results file: overview +Results file output format +Accessing the results file information +Utility routines for accessing the results file +OI.1 Abaqus/Standard Output Variable Index +OI.2 Abaqus/Explicit Output Variable Index +OI.3 Abaqus/CFD Output Variable Index +6.1.1 +6.1.2 +6.1.3 +6.1.4 +6.1.5 +6.1.6 +6.2.1 +6.2.2 +6.2.3 +6.2.4 +6.2.5 +6.2.6 +6.2.7 +6.3.1 +6.3.2 +6.3.3 +6.3.4 +6.3.5 +6.3.6 +6.3.7 +6.3.8 +6.3.9 +6.3.10 +6.3.11 +6.4.1 +6.5.1 +6.5.2 +Volume II +PART III +ANALYSIS PROCEDURES, SOLUTION, AND CONTROL +6. Analysis Procedures +Introduction +Solving analysis problems: overview +Defining an analysis +General and linear perturbation procedures +Multiple load case analysis +Direct linear equation solver +Iterative linear equation solver +Static stress/displacement analysis +Static stress analysis procedures: overview +Static stress analysis +Eigenvalue buckling prediction +Unstable collapse and postbuckling analysis +Quasi-static analysis +Direct cyclic analysis +Low-cycle fatigue analysis using the direct cyclic approach +Dynamic stress/displacement analysis +Dynamic analysis procedures: overview +Implicit dynamic analysis using direct integration +Explicit dynamic analysis +Direct-solution steady-state dynamic analysis +Natural frequency extraction +Complex eigenvalue extraction +Transient modal dynamic analysis +Mode-based steady-state dynamic analysis +Subspace-based steady-state dynamic analysis +Response spectrum analysis +Random response analysis +Steady-state transport analysis +Steady-state transport analysis +Heat transfer and thermal-stress analysis +Heat transfer analysis procedures: overview +Uncoupled heat transfer analysis +6.5.4 +6.6.1 +6.6.2 +6.7.1 +6.7.2 +6.7.3 +6.7.4 +6.7.5 +6.7.6 +6.8.1 +6.8.2 +6.9.1 +6.10.1 +6.11.1 +6.12.1 +7.1.1 +7.2.1 +7.2.2 +7.2.3 +7.2.4 +CONTENTS +Fully coupled thermal-stress analysis +Adiabatic analysis +Fluid dynamic analysis +Fluid dynamic analysis procedures: overview +Incompressible fluid dynamic analysis +Electromagnetic analysis +Electromagnetic analysis procedures +Piezoelectric analysis +Coupled thermal-electrical analysis +Fully coupled thermal-electrical-structural analysis +Eddy current analysis +Magnetostatic analysis +Coupled pore fluid flow and stress analysis +Coupled pore fluid diffusion and stress analysis +Geostatic stress state +Mass diffusion analysis +Mass diffusion analysis +Acoustic and shock analysis +Acoustic, shock, and coupled acoustic-structural analysis +Abaqus/Aqua analysis +Abaqus/Aqua analysis +Annealing +Annealing procedure +7. Analysis Solution and Control +Solving nonlinear problems +Solving nonlinear problems +Analysis convergence controls +Convergence and time integration criteria: overview +Commonly used control parameters +Convergence criteria for nonlinear problems +Time integration accuracy in transient problems +ANALYSIS TECHNIQUES +8. Analysis Techniques: Introduction +Analysis techniques: overview +9. Analysis Continuation Techniques +Restarting an analysis +Restarting an analysis +Importing and transferring results +Transferring results between Abaqus analyses: overview +Transferring results between Abaqus/Explicit and Abaqus/Standard +Transferring results from one Abaqus/Standard analysis to another +Transferring results from one Abaqus/Explicit analysis to another +10. Modeling Abstractions +Substructuring +Using substructures +Defining substructures +Submodeling +Submodeling: overview +Node-based submodeling +Surface-based submodeling +Generating global matrices +Generating matrices +CONTENTS +8.1.1 +9.1.1 +9.2.1 +9.2.2 +9.2.3 +9.2.4 +10.1.1 +10.1.2 +10.2.1 +10.2.2 +10.2.3 +10.3.1 +Symmetric model generation, results transfer, and analysis of cyclic symmetry models +Symmetric model generation +Transferring results from a symmetric mesh or a partial three-dimensional mesh to +a full three-dimensional mesh +Analysis of models that exhibit cyclic symmetry +Periodic media analysis +Periodic media analysis +Meshed beam cross-sections +Meshed beam cross-sections +vii +10.4.1 +10.4.2 +10.4.3 +10.5.1 +Modeling discontinuities as an enriched feature using the extended finite element method +Modeling discontinuities as an enriched feature using the extended finite element +10.7.1 +11.1.1 +11.2.1 +11.3.1 +11.4.1 +11.4.2 +11.4.3 +11.5.1 +11.5.2 +11.5.3 +11.5.4 +11.6.1 +11.7.1 +11.8.1 +12.1.1 +12.2.1 +12.2.2 +12.2.3 +12.2.4 +method +11. Special-Purpose Techniques +Inertia relief +Inertia relief +Mesh modification or replacement +Element and contact pair removal and reactivation +Geometric imperfections +Introducing a geometric imperfection into a model +Fracture mechanics +Fracture mechanics: overview +Contour integral evaluation +Crack propagation analysis +Surface-based fluid modeling +Surface-based fluid cavities: overview +Fluid cavity definition +Fluid exchange definition +Inflator definition +Mass scaling +Mass scaling +Selective subcycling +Selective subcycling +Steady-state detection +Steady-state detection +12. Adaptivity Techniques +Adaptivity techniques: overview +Adaptivity techniques +ALE adaptive meshing +ALE adaptive meshing: overview +Defining ALE adaptive mesh domains in Abaqus/Explicit +ALE adaptive meshing and remapping in Abaqus/Explicit +Modeling techniques for Eulerian adaptive mesh domains in Abaqus/Explicit +12.2.5 +12.2.6 +12.2.7 +12.3.1 +12.3.2 +12.3.3 +12.4.1 +13.1.1 +13.2.1 +13.2.2 +13.2.3 +14.1.1 +14.1.2 +14.1.3 +14.1.4 +15.1.1 +15.1.2 +16.1.1 +16.1.2 +16.1.3 +17.1.1 +17.2.1 +Output and diagnostics for ALE adaptive meshing in Abaqus/Explicit +Defining ALE adaptive mesh domains in Abaqus/Standard +ALE adaptive meshing and remapping in Abaqus/Standard +Adaptive remeshing +Adaptive remeshing: overview +Selection of error indicators influencing adaptive remeshing +Solution-based mesh sizing +Analysis continuation after mesh replacement +Mesh-to-mesh solution mapping +13. Optimization Techniques +Structural optimization: overview +Structural optimization: overview +Optimization models +Design responses +Objectives and constraints +Creating Abaqus optimization models +14. Eulerian Analysis +Eulerian analysis +Defining Eulerian boundaries +Eulerian mesh motion +Defining adaptive mesh refinement in the Eulerian domain +15. Particle Methods +Smoothed particle hydrodynamic analyses +Smoothed particle hydrodynamic analysis +Finite element conversion to SPH particles +16. Sequentially Coupled Multiphysics Analyses +Predefined fields for sequential coupling +Sequentially coupled thermal-stress analysis +Predefined loads for sequential coupling +17. Co-simulation +Co-simulation: overview +Preparing an Abaqus analysis for co-simulation +Preparing an Abaqus analysis for co-simulation +Co-simulation between Abaqus solvers +Abaqus/Standard to Abaqus/Explicit co-simulation +Abaqus/CFD to Abaqus/Standard or to Abaqus/Explicit co-simulation +18. Extending Abaqus Analysis Functionality +User subroutines and utilities +User subroutines: overview +Available user subroutines +Available utility routines +19. Design Sensitivity Analysis +Design sensitivity analysis +20. Parametric Studies +Scripting parametric studies +Scripting parametric studies +Parametric studies: commands +aStudy.combine(): Combine parameter samples for parametric studies. +aStudy.constrain(): Constrain parameter value combinations in parametric studies. +aStudy.define(): Define parameters for parametric studies. +aStudy.execute(): Execute the analysis of parametric study designs. +aStudy.gather(): Gather the results of a parametric study. +aStudy.generate(): Generate the analysis job data for a parametric study. +aStudy.output(): Specify the source of parametric study results. +aStudy=ParStudy(): Create a parametric study. +aStudy.report(): Report parametric study results. +aStudy.sample(): Sample parameters for parametric studies. +17.3.1 +17.3.2 +18.1.1 +18.1.2 +18.1.3 +19.1.1 +20.1.1 +20.2.1 +20.2.2 +20.2.3 +20.2.4 +20.2.5 +20.2.6 +20.2.7 +20.2.8 +20.2.9 +20.2.10 +21.1.1 +21.1.2 +21.1.3 +21.2.1 +22.1.1 +22.2.1 +22.2.2 +22.2.3 +22.3.1 +22.4.1 +22.5.1 +22.5.2 +22.5.3 +22.6.1 +22.6.2 +22.7.1 +22.7.2 +Volume III +PART V MATERIALS +21. Materials: Introduction +Introduction +Material library: overview +Material data definition +Combining material behaviors +General properties +Density +22. Elastic Mechanical Properties +Overview +Elastic behavior: overview +Linear elasticity +Linear elastic behavior +No compression or no tension +Plane stress orthotropic failure measures +Porous elasticity +Elastic behavior of porous materials +Hypoelasticity +Hypoelastic behavior +Hyperelasticity +Hyperelastic behavior of rubberlike materials +Hyperelastic behavior in elastomeric foams +Anisotropic hyperelastic behavior +Stress softening in elastomers +Mullins effect +Energy dissipation in elastomeric foams +Viscoelasticity +Time domain viscoelasticity +Frequency domain viscoelasticity +Nonlinear viscoelasticity +Hysteresis in elastomers +Parallel network viscoelastic model +Rate sensitive elastomeric foams +Low-density foams +23. +Inelastic Mechanical Properties +Overview +Inelastic behavior +Metal plasticity +Classical metal plasticity +Models for metals subjected to cyclic loading +Rate-dependent yield +Rate-dependent plasticity: creep and swelling +Annealing or melting +Anisotropic yield/creep +Johnson-Cook plasticity +Dynamic failure models +Porous metal plasticity +Cast iron plasticity +Two-layer viscoplasticity +ORNL – Oak Ridge National Laboratory constitutive model +Deformation plasticity +Other plasticity models +Extended Drucker-Prager models +Modified Drucker-Prager/Cap model +Mohr-Coulomb plasticity +Critical state (clay) plasticity model +Crushable foam plasticity models +Fabric materials +Fabric material behavior +Jointed materials +Jointed material model +Concrete +Concrete smeared cracking +Cracking model for concrete +Concrete damaged plasticity +xii +Abaqus ID:usb-toc +Printed on: Fri February 3 -- 18:01:12 2012 +22.8.1 +22.8.2 +22.9.1 +23.1.1 +23.2.1 +23.2.2 +23.2.3 +23.2.4 +23.2.5 +23.2.6 +23.2.7 +23.2.8 +23.2.9 +23.2.10 +23.2.11 +23.2.12 +23.2.13 +23.3.1 +23.3.2 +23.3.3 +23.3.4 +23.3.5 +23.4.1 +23.5.1 +23.7.1 +24.1.1 +24.2.1 +24.2.2 +24.2.3 +24.3.1 +24.3.2 +24.3.3 +24.4.1 +24.4.2 +24.4.3 +25.1.1 +25.2.1 +26.1.1 +26.1.2 +26.1.3 +26.1.4 +26.2.1 +26.2.2 +26.2.3 +26.2.4 +Permanent set in rubberlike materials +Permanent set in rubberlike materials +24. Progressive Damage and Failure +Progressive damage and failure: overview +Progressive damage and failure +Damage and failure for ductile metals +Damage and failure for ductile metals: overview +Damage initiation for ductile metals +Damage evolution and element removal for ductile metals +Damage and failure for fiber-reinforced composites +Damage and failure for fiber-reinforced composites: overview +Damage initiation for fiber-reinforced composites +Damage evolution and element removal for fiber-reinforced composites +Damage and failure for ductile materials in low-cycle fatigue analysis +Damage and failure for ductile materials in low-cycle fatigue analysis: overview +Damage initiation for ductile materials in low-cycle fatigue +Damage evolution for ductile materials in low-cycle fatigue +25. Hydrodynamic Properties +Overview +Hydrodynamic behavior: overview +Equations of state +Equation of state +26. Other Material Properties +Mechanical properties +Material damping +Thermal expansion +Field expansion +Viscosity +Heat transfer properties +Thermal properties: overview +Conductivity +Specific heat +Latent heat +Acoustic properties +Acoustic medium +Mass diffusion properties +Diffusivity +Solubility +Electromagnetic properties +Electrical conductivity +Piezoelectric behavior +Magnetic permeability +Pore fluid flow properties +Pore fluid flow properties +Permeability +Porous bulk moduli +Sorption +Swelling gel +Moisture swelling +User materials +User-defined mechanical material behavior +User-defined thermal material behavior +26.3.1 +26.4.1 +26.4.2 +26.5.1 +26.5.2 +26.5.3 +26.6.1 +26.6.2 +26.6.3 +26.6.4 +26.6.5 +26.6.6 +26.7.1 +26.7.2 +27.1.1 +27.1.2 +27.1.3 +27.1.4 +28.1.1 +28.1.2 +28.1.3 +28.1.4 +28.1.5 +28.1.6 +28.1.7 +28.2.1 +28.2.2 +28.3.1 +28.3.2 +28.4.1 +28.4.2 +28.5.1 +28.5.2 +29.1.1 +29.1.2 +29.1.3 +Volume IV +PART VI +ELEMENTS +27. Elements: Introduction +Element library: overview +Choosing the element’s dimensionality +Choosing the appropriate element for an analysis type +Section controls +28. Continuum Elements +General-purpose continuum elements +Solid (continuum) elements +One-dimensional solid (link) element library +Two-dimensional solid element library +Three-dimensional solid element library +Cylindrical solid element library +Axisymmetric solid element library +Axisymmetric solid elements with nonlinear, asymmetric deformation +Fluid continuum elements +Fluid (continuum) elements +Fluid element library +Infinite elements +Infinite elements +Infinite element library +Warping elements +Warping elements +Warping element library +Particle elements +Particle elements +Particle element library +29. Structural Elements +Membrane elements +Membrane elements +General membrane element library +Cylindrical membrane element library +Axisymmetric membrane element library +Truss elements +Truss elements +Truss element library +Beam elements +Beam modeling: overview +Choosing a beam cross-section +Choosing a beam element +Beam element cross-section orientation +Beam section behavior +Using a beam section integrated during the analysis to define the section behavior +Using a general beam section to define the section behavior +Beam element library +Beam cross-section library +Frame elements +Frame elements +Frame section behavior +Frame element library +Elbow elements +Pipes and pipebends with deforming cross-sections: elbow elements +Elbow element library +Shell elements +Shell elements: overview +Choosing a shell element +Defining the initial geometry of conventional shell elements +Shell section behavior +Using a shell section integrated during the analysis to define the section behavior +Using a general shell section to define the section behavior +Three-dimensional conventional shell element library +Continuum shell element library +Axisymmetric shell element library +Axisymmetric shell elements with nonlinear, asymmetric deformation +29.1.4 +29.2.1 +29.2.2 +29.3.1 +29.3.2 +29.3.3 +29.3.4 +29.3.5 +29.3.6 +29.3.7 +29.3.8 +29.3.9 +29.4.1 +29.4.2 +29.4.3 +29.5.1 +29.5.2 +29.6.1 +29.6.2 +29.6.3 +29.6.4 +29.6.5 +29.6.6 +29.6.7 +29.6.8 +29.6.9 +29.6.10 +30.1.1 +30.1.2 +30.2.1 +30.2.2 +30.3.1 +30.3.2 +30.4.1 +30.4.2 +31.1.1 +31.1.2 +31.1.3 +31.1.4 +31.1.5 +31.2.1 +31.2.2 +31.2.3 +31.2.4 +31.2.5 +31.2.6 +31.2.7 +31.2.8 +31.2.9 +31.2.10 +32.1.1 +32.1.2 +30. +Inertial, Rigid, and Capacitance Elements +Point mass elements +Point masses +Mass element library +Rotary inertia elements +Rotary inertia +Rotary inertia element library +Rigid elements +Rigid elements +Rigid element library +Capacitance elements +Point capacitance +Capacitance element library +31. Connector Elements +Connector elements +Connectors: overview +Connector elements +Connector actuation +Connector element library +Connection-type library +Connector element behavior +Connector behavior +Connector elastic behavior +Connector damping behavior +Connector functions for coupled behavior +Connector friction behavior +Connector plastic behavior +Connector damage behavior +Connector stops and locks +Connector failure behavior +Connector uniaxial behavior +32. Special-Purpose Elements +Spring elements +Springs +Spring element library +Dashpot elements +Dashpots +Dashpot element library +Flexible joint elements +Flexible joint element +Flexible joint element library +Distributing coupling elements +Distributing coupling elements +Distributing coupling element library +Cohesive elements +Cohesive elements: overview +Choosing a cohesive element +Modeling with cohesive elements +Defining the cohesive element’s initial geometry +Defining the constitutive response of cohesive elements using a continuum approach +Defining the constitutive response of cohesive elements using a traction-separation +description +Defining the constitutive response of fluid within the cohesive element gap +Two-dimensional cohesive element library +Three-dimensional cohesive element library +Axisymmetric cohesive element library +Gasket elements +Gasket elements: overview +Choosing a gasket element +Including gasket elements in a model +Defining the gasket element’s initial geometry +Defining the gasket behavior using a material model +Defining the gasket behavior directly using a gasket behavior model +Two-dimensional gasket element library +Three-dimensional gasket element library +Axisymmetric gasket element library +Surface elements +Surface elements +General surface element library +Cylindrical surface element library +Axisymmetric surface element library +32.2.1 +32.2.2 +32.3.1 +32.3.2 +32.4.1 +32.4.2 +32.5.1 +32.5.2 +32.5.3 +32.5.4 +32.5.5 +32.5.6 +32.5.7 +32.5.8 +32.5.9 +32.5.10 +32.6.1 +32.6.2 +32.6.3 +32.6.4 +32.6.5 +32.6.6 +32.6.7 +32.6.8 +32.6.9 +32.7.1 +32.7.2 +32.7.3 +32.7.4 +32.8.1 +32.8.2 +32.9.1 +32.9.2 +32.10.1 +32.10.2 +32.11.1 +32.11.2 +32.12.1 +32.12.2 +32.13.1 +32.13.2 +32.14.1 +32.14.2 +32.15.1 +32.15.2 +Tube support elements +Tube support elements +Tube support element library +Line spring elements +Line spring elements for modeling part-through cracks in shells +Line spring element library +Elastic-plastic joints +Elastic-plastic joints +Elastic-plastic joint element library +Drag chain elements +Drag chains +Drag chain element library +Pipe-soil elements +Pipe-soil interaction elements +Pipe-soil interaction element library +Acoustic interface elements +Acoustic interface elements +Acoustic interface element library +Eulerian elements +Eulerian elements +Eulerian element library +User-defined elements +User-defined elements +User-defined element library +EI.1 Abaqus/Standard Element Index +EI.2 Abaqus/Explicit Element Index +EI.3 Abaqus/CFD Element Index +Volume V +PART VII +PRESCRIBED CONDITIONS +33. Prescribed Conditions +Overview +Prescribed conditions: overview +Amplitude curves +Initial conditions +Initial conditions in Abaqus/Standard and Abaqus/Explicit +Initial conditions in Abaqus/CFD +Boundary conditions +Boundary conditions in Abaqus/Standard and Abaqus/Explicit +Boundary conditions in Abaqus/CFD +Loads +Applying loads: overview +Concentrated loads +Distributed loads +Thermal loads +Electromagnetic loads +Acoustic and shock loads +Pore fluid flow +Prescribed assembly loads +Prescribed assembly loads +Predefined fields +Predefined fields +PART VIII +CONSTRAINTS +34. Constraints +Overview +Kinematic constraints: overview +Multi-point constraints +Linear constraint equations +xx +Abaqus ID:usb-toc +Printed on: Fri February 3 -- 18:01:12 2012 +33.1.1 +33.1.2 +33.2.1 +33.2.2 +33.3.1 +33.3.2 +33.4.1 +33.4.2 +33.4.3 +33.4.4 +33.4.5 +33.4.6 +33.4.7 +33.5.1 +34.2.2 +34.2.3 +34.3.1 +34.3.2 +34.3.3 +34.3.4 +34.4.1 +34.5.1 +34.6.1 +35.1.1 +35.2.1 +35.2.2 +35.2.3 +35.2.4 +35.2.5 +35.2.6 +35.3.1 +35.3.2 +35.3.3 +35.3.4 +35.3.5 +35.3.6 +35.3.7 +35.3.8 +General multi-point constraints +Kinematic coupling constraints +Surface-based constraints +Mesh tie constraints +Coupling constraints +Shell-to-solid coupling +Mesh-independent fasteners +Embedded elements +Embedded elements +Element end release +Element end release +Overconstraint checks +Overconstraint checks +PART IX +INTERACTIONS +35. Defining Contact Interactions +Overview +Contact interaction analysis: overview +Defining general contact in Abaqus/Standard +Defining general contact interactions in Abaqus/Standard +Surface properties for general contact in Abaqus/Standard +Contact properties for general contact in Abaqus/Standard +Controlling initial contact status in Abaqus/Standard +Stabilization for general contact in Abaqus/Standard +Numerical controls for general contact in Abaqus/Standard +Defining contact pairs in Abaqus/Standard +Defining contact pairs in Abaqus/Standard +Assigning surface properties for contact pairs in Abaqus/Standard +Assigning contact properties for contact pairs in Abaqus/Standard +Modeling contact interference fits in Abaqus/Standard +Adjusting initial surface positions and specifying initial clearances in Abaqus/Standard +contact pairs +Adjusting contact controls in Abaqus/Standard +Defining tied contact in Abaqus/Standard +Extending master surfaces and slide lines +Contact modeling if substructures are present +Contact modeling if asymmetric-axisymmetric elements are present +Defining general contact in Abaqus/Explicit +Defining general contact interactions in Abaqus/Explicit +Assigning surface properties for general contact in Abaqus/Explicit +Assigning contact properties for general contact in Abaqus/Explicit +Controlling initial contact status for general contact in Abaqus/Explicit +Contact controls for general contact in Abaqus/Explicit +Defining contact pairs in Abaqus/Explicit +Defining contact pairs in Abaqus/Explicit +Assigning surface properties for contact pairs in Abaqus/Explicit +Assigning contact properties for contact pairs in Abaqus/Explicit +Adjusting initial surface positions and specifying initial clearances for contact pairs +in Abaqus/Explicit +Contact controls for contact pairs in Abaqus/Explicit +36. Contact Property Models +Mechanical contact properties +Mechanical contact properties: overview +Contact pressure-overclosure relationships +Contact damping +Contact blockage +Frictional behavior +User-defined interfacial constitutive behavior +Pressure penetration loading +Interaction of debonded surfaces +Breakable bonds +Surface-based cohesive behavior +Thermal contact properties +Thermal contact properties +Electrical contact properties +Electrical contact properties +Pore fluid contact properties +Pore fluid contact properties +37. Contact Formulations and Numerical Methods +Contact formulations and numerical methods in Abaqus/Standard +Contact formulations in Abaqus/Standard +xxii +Abaqus ID:usb-toc +Printed on: Fri February 3 -- 18:01:12 2012 +35.3.9 +35.3.10 +35.4.1 +35.4.2 +35.4.3 +35.4.4 +35.4.5 +35.5.1 +35.5.2 +35.5.3 +35.5.4 +35.5.5 +36.1.1 +36.1.2 +36.1.3 +36.1.4 +36.1.5 +36.1.6 +36.1.7 +36.1.8 +36.1.9 +36.1.10 +36.2.1 +37.1.2 +37.1.3 +37.2.1 +37.2.2 +37.2.3 +38.1.1 +38.1.2 +38.2.1 +38.2.2 +39.1.1 +39.2.1 +39.2.2 +39.3.1 +39.3.2 +39.4.1 +39.4.2 +39.5.1 +39.5.2 +40.1.1 +Contact constraint enforcement methods in Abaqus/Standard +Smoothing contact surfaces in Abaqus/Standard +Contact formulations and numerical methods in Abaqus/Explicit +Contact formulation for general contact in Abaqus/Explicit +Contact formulations for contact pairs in Abaqus/Explicit +Contact constraint enforcement methods in Abaqus/Explicit +38. Contact Difficulties and Diagnostics +Resolving contact difficulties in Abaqus/Standard +Contact diagnostics in an Abaqus/Standard analysis +Common difficulties associated with contact modeling in Abaqus/Standard +Resolving contact difficulties in Abaqus/Explicit +Contact diagnostics in an Abaqus/Explicit analysis +Common difficulties associated with contact modeling using contact pairs in +Abaqus/Explicit +39. Contact Elements in Abaqus/Standard +Contact modeling with elements +Contact modeling with elements +Gap contact elements +Gap contact elements +Gap element library +Tube-to-tube contact elements +Tube-to-tube contact elements +Tube-to-tube contact element library +Slide line contact elements +Slide line contact elements +Axisymmetric slide line element library +Rigid surface contact elements +Rigid surface contact elements +Axisymmetric rigid surface contact element library +40. Defining Cavity Radiation in Abaqus/Standard +Cavity radiation +Printed on: +• Chapter 27, “Elements: Introduction” +• Chapter 28, “Continuum Elements” +• Chapter 29, “Structural Elements” +• Chapter 30, “Inertial, Rigid, and Capacitance Elements” +• Chapter 31, “Connector Elements” +27. +Elements: Introduction +Introduction +27.1 +Introduction +• “Element library: overview,” Section 27.1.1 +• “Choosing the element’s dimensionality,” Section 27.1.2 +• “Choosing the appropriate element for an analysis type,” Section 27.1.3 +• “Section controls,” Section 27.1.4 +27.1.1 +ELEMENT LIBRARY: OVERVIEW +Abaqus has an extensive element library to provide a powerful set of tools for solving many different problems. +Characterizing elements +Five aspects of an element characterize its behavior: +• Family +• Degrees of freedom (directly related to the element family) +• Number of nodes +• Formulation +• Integration +Each element in Abaqus has a unique name, such as T2D2, S4R, C3D8I, or C3D8R. The element +name identifies each of the five aspects of an element. For details on defining elements, see “Element +definition,” Section 2.2.1. +Family +Figure 27.1.1–1 shows the element families that are used most commonly in a stress analysis; in addition, +continuum (fluid) elements are used in a fluid analysis. One of the major distinctions between different +element families is the geometry type that each family assumes. +Continuum +(solid and fluid) +elements +Shell +elements +Beam +elements +Rigid +elements +Membrane +elements +Infinite +elements +Connector elements +such as springs +and dashpots +Truss +elements +Figure 27.1.1–1 Commonly used element families. +The first letter or letters of an element’s name indicate to which family the element belongs. For +example, S4R is a shell element, CINPE4 is an infinite element, and C3D8I is a continuum element. +Degrees of freedom +The degrees of freedom are the fundamental variables calculated during the analysis. +For a +stress/displacement simulation the degrees of freedom are the translations and, for shell, pipe, and +beam elements, the rotations at each node. For a heat transfer simulation the degrees of freedom are +the temperatures at each node; for a coupled thermal-stress analysis temperature degrees of freedom +exist in addition to displacement degrees of freedom at each node. Heat transfer analyses and coupled +thermal-stress analyses therefore require the use of different elements than does a stress analysis since +the degrees of freedom are not the same. See “Conventions,” Section 1.2.2, for a summary of the +degrees of freedom available in Abaqus for various element and analysis types. +Number of nodes and order of interpolation +Displacements or other degrees of freedom are calculated at the nodes of the element. At any other point +in the element, the displacements are obtained by interpolating from the nodal displacements. Usually +the interpolation order is determined by the number of nodes used in the element. +• Elements that have nodes only at their corners, such as the 8-node brick shown in Figure 27.1.1–2(a), +use linear interpolation in each direction and are often called linear elements or first-order elements. +• In Abaqus/Standard elements with midside nodes, such as the 20-node brick shown in +Figure 27.1.1–2(b), use quadratic interpolation and are often called quadratic elements or +second-order elements. +• Modified triangular or tetrahedral elements with midside nodes, such as the 10-node tetrahedron +shown in Figure 27.1.1–2(c), use a modified second-order interpolation and are often called +modified or modified second-order elements. +(a) Linear element +(8-node brick, C3D8) +(b) Quadratic element +(20-node brick, C3D20) +(c) Modified second-order element +(10-node tetrahedron, C3D10M) +Figure 27.1.1–2 Linear brick, quadratic brick, and modified tetrahedral elements. +Typically, the number of nodes in an element is clearly identified in its name. The 8-node brick +element is called C3D8, and the 4-node shell element is called S4R. +The beam element family uses a slightly different convention: the order of interpolation is identified +in the name. Thus, a first-order, three-dimensional beam element is called B31, whereas a second-order, +three-dimensional beam element is called B32. A similar convention is used for axisymmetric shell and +membrane elements. +Formulation +An element’s formulation refers to the mathematical theory used to define the element’s behavior. In the +Lagrangian, or material, description of behavior the element deforms with the material. In the alternative +Eulerian, or spatial, description elements are fixed in space as the material flows through them. Eulerian +methods are used commonly in fluid mechanics simulations. Abaqus/Standard uses Eulerian elements +to model convective heat transfer. Abaqus/Explicit also offers multimaterial Eulerian elements for use +in stress/displacement analyses. Adaptive meshing in Abaqus/Explicit combines the features of pure +Lagrangian and Eulerian analyses and allows the motion of the element to be independent of the material +. All other stress/displacement elements in +Abaqus are based on the Lagrangian formulation. In Abaqus/Explicit the Eulerian elements can interact +with Lagrangian elements through general contact . +To accommodate different types of behavior, some element families in Abaqus include elements +with several different formulations. For example, the conventional shell element family has three +classes: one suitable for general-purpose shell analysis, another for thin shells, and yet another for thick +shells. In addition, Abaqus also offers continuum shell elements, which have nodal connectivities like +continuum elements but are formulated to model shell behavior with as few as one element through the +shell thickness. +Some Abaqus/Standard element families have a standard formulation as well as some alternative +formulations. Elements with alternative formulations are identified by an additional character at the end +of the element name. For example, the continuum, beam, and truss element families include members +with a hybrid formulation (to deal with incompressible or inextensible behavior); these elements are +identified by the letter H at the end of the name (C3D8H or B31H). +Abaqus/Standard uses the lumped mass formulation for low-order elements; Abaqus/Explicit uses +the lumped mass formulation for all elements. As a consequence, the second mass moments of inertia +can deviate from the theoretical values, especially for coarse meshes. +Abaqus/CFD uses hybrid elements to circumvent well known div-stability issues for incompressible +flow. Abaqus/CFD also permits the addition of degrees of freedom based on procedure settings such as +the optional energy equation and turbulence models. +Integration +Abaqus uses numerical techniques to integrate various quantities over the volume of each element, +thus allowing complete generality in material behavior. Using Gaussian quadrature for most elements, +Abaqus evaluates the material response at each integration point in each element. Some continuum +elements in Abaqus can use full or reduced integration, a choice that can have a significant effect on the +accuracy of the element for a given problem. +Abaqus uses the letter R at the end of the element name to label reduced-integration elements. For +example, CAX4R is the 4-node, reduced-integration, axisymmetric, solid element. +Shell, pipe, and beam element properties can be defined as general section behaviors; or each cross- +section of the element can be integrated numerically, so that nonlinear response associated with nonlinear +material behavior can be tracked accurately when needed. In addition, a composite layered section can +be specified for shells and, in Abaqus/Standard, three-dimensional bricks, with different materials for +each layer through the section. +Combining elements +The element library is intended to provide a complete modeling capability for all geometries. Thus, any +combination of elements can be used to make up the model; multi-point constraints (“General multi-point +constraints,” Section 34.2.2) are sometimes helpful in applying the necessary kinematic relations to form +the model (for example, to model part of a shell surface with solid elements and part with shell elements +or to use a beam element as a shell stiffener). +Heat transfer and thermal-stress analysis +In cases where heat transfer analysis is to be followed by thermal-stress analysis, corresponding heat +transfer and stress elements are provided in Abaqus/Standard. See “Sequentially coupled thermal-stress +analysis,” Section 16.1.2, for additional details. +Information available for element libraries +The complete element library in Abaqus is subdivided into a number of smaller libraries. Each library +is presented as a separate section in this manual. In each of these sections, information regarding the +following topics is provided where applicable: +• conventions; +• element types; +• degrees of freedom; +• nodal coordinates required; +• element property definition; +• element faces; +• element output; +• loading (general loading, distributed loads, foundations, distributed heat fluxes, film conditions, +radiation types, distributed flows, distributed impedances, electrical fluxes, distributed electric +current densities, and distributed concentration fluxes); +• nodes associated with the element; +• node ordering and face ordering on elements; and +• numbering of integration points for output. +For element libraries that are available in both Abaqus/Standard and Abaqus/Explicit, individual +element or load types that are available only in Abaqus/Standard are designated with an (S) ; similarly, +individual element or load types that are available only in Abaqus/Explicit are designated with an (E) . +Element or load types that are available in Abaqus/Aqua are designated with an (A) . +Most of the element output variables available for an element are discussed. Additional variables +may be available depending on the material model or the analysis procedure that is used. Some elements +have solution variables that do not pertain to other elements of the same type; these variables are specified +explicitly. +27.1.2 +CHOOSING THE ELEMENT’S DIMENSIONALITY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD Abaqus/CAE +References +• “Element library: overview,” Section 27.1.1 +• “Part modeling space,” Section 11.4.1 of the Abaqus/CAE User’s Manual +• “Assigning Abaqus element types,” Section 17.5 of the Abaqus/CAE User’s Manual +Overview +The Abaqus element library contains the following for modeling a wide range of spatial dimensionality: +• one-dimensional elements; +• two-dimensional elements; +• three-dimensional elements; +• cylindrical elements; +• axisymmetric elements; and +• axisymmetric elements with nonlinear, asymmetric deformation. +One-dimensional (link) elements +One-dimensional heat transfer, coupled thermal/electrical, and acoustic elements are available only in +Abaqus/Standard. In addition, structural link (truss) elements are available in both Abaqus/Standard and +Abaqus/Explicit. These elements can be used in two- or three-dimensional space to transmit loads or +fluxes along the length of the element. +Two-dimensional elements +Abaqus provides several different types of two-dimensional elements. For structural applications these +include plane stress elements and plane strain elements. Abaqus/Standard also provides generalized +plane strain elements for structural applications. +Plane stress elements +Plane stress elements can be used when the thickness of a body or domain is small relative to its lateral +(in-plane) dimensions. The stresses are functions of planar coordinates alone, and the out-of-plane +normal and shear stresses are equal to zero. +Plane stress elements must be defined in the X–Y plane, and all loading and deformation are also +restricted to this plane. This modeling method generally applies to thin, flat bodies. For anisotropic +materials the Z-axis must be a principal material direction. +Plane strain elements +Plane strain elements can be used when it can be assumed that the strains in a loaded body or domain are +functions of planar coordinates alone and the out-of-plane normal and shear strains are equal to zero. +Plane strain elements must be defined in the X–Y plane, and all loading and deformation are also +restricted to this plane. This modeling method is generally used for bodies that are very thick relative to +their lateral dimensions, such as shafts, concrete dams, or walls. Plane strain theory might also apply to +a typical slice of an underground tunnel that lies along the Z-axis. For anisotropic materials the Z-axis +must be a principal material direction. +Since plane strain theory assumes zero strain in the thickness direction, isotropic thermal expansion +may cause large stresses in the thickness direction. +Generalized plane strain elements +Generalized plane strain elements provide for the modeling of cases in Abaqus/Standard where the +structure has constant curvature (and, hence, no gradients of solution variables) with respect to one +material direction—the “axial” direction of the model. The formulation, thus, involves a model that +lies between two planes that can move with respect to each other and, hence, cause strain in the axial +direction of the model that varies linearly with respect to position in the planes, the variation being due to +the change in curvature. In the initial configuration the bounding planes can be parallel or at an angle to +each other, the latter case allowing the modeling of initial curvature of the model in the axial direction. +The concept is illustrated in Figure 27.1.2–1. Generalized plane strain elements are typically used to +model a section of a long structure that is free to expand axially or is subjected to axial loading. +Each generalized plane strain element has three, four, six, or eight conventional nodes, at each +of which x- and y-coordinates, displacements, etc. are stored. These nodes determine the position and +motion of the element in the two bounding planes. Each element also has a reference node, which is +usually the same node for all of the generalized plane strain elements in the model. The reference node of +a generalized plane strain element should not be used as a conventional node in any element in the model. +The reference node has three degrees of freedom 3, 4, and 5: ( +). The first degree +of freedom ( +) is the change in length of the axial material fiber connecting this node and its image +in the other bounding plane. This displacement is positive as the planes move apart; therefore, there is a +tensile strain in the axial fiber. The second and third degrees of freedom ( +) are the components +of the relative rotation of one bounding plane with respect to the other. The values stored are the two +components of rotation about the X- and Y-axes in the bounding planes (that is, in the cross-section of the +model). Positive rotation about the X-axis causes increasing axial strain with respect to the y-coordinate +in the cross-section; positive rotation about the Y-axis causes decreasing axial strain with respect to +the x-coordinate in the cross-section. The x- and y-coordinates of a generalized plane strain element +reference node ( +discussed below) remain fixed throughout all steps of an analysis. From the +degrees of freedom of the reference node, the length of the axial material fiber passing through the point +with current coordinates (x, y) in a bounding plane is defined as +, and +and +, +, +Bounding planes +(x,y) +(X ,Y ) +0 0 +Reference node +Conventional element node +Length of line through the thickness at (x,y) is + t0 + Δuz + Δφ +x (y - Y0) - Δφ +y (x - X0) +where quantities are defined in the text. +Figure 27.1.2–1 Generalized plane strain model. +where +and +is the current length of the fiber, +is the initial length of the fiber passing through the reference node (given as part +of the element section definition), +is the displacement at the reference node (stored as degree of freedom 3 at the +reference node), +are the total values of the components of the angle between the bounding +planes (the original values of +are given as part of the element +section definition—see “Defining the element’s section properties” in “Solid +, +(continuum) elements,” Section 28.1.1: +degrees of freedom 4 and 5 of the reference node), and +are the coordinates of the reference node in a bounding plane. +the changes in these values are the +and +The strain in the axial direction is defined immediately from this axial fiber length. The strain +components in the cross-section of the model are computed from the displacements of the regular nodes +of the elements in the usual way. Since the solution is assumed to be independent of the axial position, +there are no transverse shear strains. +Three-dimensional elements +Three-dimensional elements are defined in the global X, Y, Z space. These elements are used when +the geometry and/or the applied loading are too complex for any other element type with fewer spatial +dimensions. +Cylindrical elements +Cylindrical elements are three-dimensional elements defined in the global X, Y, Z space. These elements +are used to model bodies with circular or axisymmetric geometry subjected to general, nonaxisymmetric +loading. Cylindrical elements are available only in Abaqus/Standard. +Cylindrical elements are useful in situations where the expected solution over a relatively large +angle is nearly axisymmetric. In this case a very coarse mesh of cylindrical elements is often sufficient. +Footprint and steady-state rolling analyses of tires are good examples of where cylindrical elements +have distinct advantages over conventional continuum elements . If, however, the expected solution has +significant non-axisymmetric components, a finer mesh of cylindrical elements will be needed and it may +be more economical to use conventional continuum elements. +Axisymmetric elements +Axisymmetric elements provide for the modeling of bodies of revolution under axially symmetric loading +conditions. A body of revolution is generated by revolving a plane cross-section about an axis (the +symmetry axis) and is readily described in cylindrical polar coordinates r, z, and . Figure 27.1.2–2 +shows a typical reference cross-section at +. The radial and axial coordinates of a point on this +cross-section are denoted by r and z, respectively. At +, the radial and axial coordinates coincide +with the global Cartesian X- and Y-coordinates. +Abaqus does not apply boundary conditions automatically to nodes that are located on the symmetry +axis in axisymmetric models. If required, you should apply them directly. Radial boundary conditions at +nodes located on the z-axis are appropriate for most problems because without them nodes may displace +across the symmetry axis, violating the principle of compatibility. However, there are some analyses, +such as penetration calculations, where nodes along the symmetry axis should be free to move; boundary +conditions should be omitted in these cases. +If the loading and material properties are independent of +, the solution in any r–z plane completely +defines the solution in the body. Consequently, axisymmetric elements can be used to analyze the +z (Y) +cross-section +at θ = 0 +i +r (X) +Figure 27.1.2–2 Reference cross-section and element in an axisymmetric solid. +problem by discretizing the reference cross-section at +. Figure 27.1.2–2 shows an element of an +axisymmetric body. The nodes i, j, k, and l are actually nodal “circles,” and the volume of material +associated with the element is that of a body of revolution, as shown in the figure. The value of a +prescribed nodal load or reaction force is the total value on the ring; that is, the value integrated around +the circumference. +Regular axisymmetric elements +Regular axisymmetric elements for structural applications allow for only radial and axial loading +and have isotropic or orthotropic material properties, with +being a principal direction. Any radial +displacement in such an element will induce a strain in the circumferential direction (“hoop” strain); +and since the displacement must also be purely axisymmetric, there are only four possible nonzero +components of strain ( +, and +). +, +, +Generalized axisymmetric stress/displacement elements with twist +Axisymmetric solid elements with twist are available only in Abaqus/Standard for the analysis of +structures that are axially symmetric but can twist about their symmetry axis. This element family is +similar to the axisymmetric elements discussed above, except that it allows for a circumferential loading +component (which is independent of +) and for general material anisotropy. Under these conditions, +there may be displacements in the -direction that vary with r and z but not with . The problem remains +axisymmetric because the solution does not vary as a function of +so that the deformation of any r–z +plane characterizes the deformation in the entire body. Initially the elements define an axisymmetric +reference geometry with respect to the r–z plane at +, where the r-direction corresponds to the +global X-direction and the z-direction corresponds to the global Y-direction. Figure 27.1.2–3 shows an +axisymmetric model consisting of two elements. The figure also shows the local cylindrical coordinate +system at node 100. +Y (z at θ = 0) +e z +e θ +100 +e r +φ100 +e z +e θ +100 +e r +X (r at θ = 0) +(a) +(b) +Figure 27.1.2–3 Reference and deformed cross-section +in an axisymmetric solid with twist. +, the axial displacement +The motion at a node of an axisymmetric element with twist is described by the radial displacement +(in radians) about the z-axis, each of which is constant in +the circumferential direction, so that the deformed geometry remains axisymmetric. Figure 27.1.2–3(b) +shows the deformed geometry of the reference model shown in Figure 27.1.2–3(a) and the local +cylindrical coordinate system at the displaced location of node 100, for a twist +, and the twist +. +The formulation of these elements is discussed in “Axisymmetric elements,” Section 3.2.8 of the +Abaqus Theory Manual. +Generalized axisymmetric elements with twist cannot be used in contour integral calculations and +in dynamic analysis. Elastic foundations are applied only to degrees of freedom and +. +These elements should not be mixed with three-dimensional elements. +Axisymmetric elements with twist and the nodes of these elements should be used with caution +within rigid bodies. If the rigid body undergoes large rotations, incorrect results may be obtained. It +is recommended that rigid constraints on axisymmetric elements with twist be modeled with kinematic +coupling . +Stabilization should not be used with these elements if the deformation is dominated by twist, since +stabilization is applied only to the in-plane deformation. +Axisymmetric elements with nonlinear, asymmetric deformation +These elements are intended for the linear or nonlinear analysis of structures that are initially +axisymmetric but undergo nonlinear, nonaxisymmetric deformation. They are available only in +Abaqus/Standard. +The elements use standard isoparametric interpolation in the r–z plane, combined with Fourier +interpolation with respect to . The deformation is assumed to be symmetric with respect to the r–z +plane at +. +Up to four Fourier modes are allowed. For more general cases, full three-dimensional modeling or +cylindrical element modeling is probably more economical because of the complete coupling between +all deformation modes. +These elements use a set of nodes in each of several r–z planes: the number of such planes depends +on the order N of Fourier interpolation used with respect to , as follows: +Number of +Fourier modes N +Number +of nodal +planes +Nodal plane locations +with respect to +Each element type is defined by a name such as CAXA8RN (continuum elements) or SAXA1N +(shell elements). The number N should be given as the number of Fourier modes to be used with the +element (N=1, 2, 3, or 4). For example, element type CAXA8R2 is a quadrilateral in the r–z plane with +biquadratic interpolation in this plane and two Fourier modes for interpolation with respect to . The +nodal planes associated with various Fourier modes are illustrated in Figure 27.1.2–4. +Y (z at θ = 0) +e z +e θ +e r +(a) +2π +(b) +3π +X (r at θ = 0) +(c) +(d) +Figure 27.1.2–4 Nodal planes of a second-order axisymmetric element with nonlinear, +asymmetric deformation and (a) 1, (b) 2, (c) 3, or (d) 4 Fourier modes. +27.1.3 +CHOOSING THE APPROPRIATE ELEMENT FOR AN ANALYSIS TYPE +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CFD Abaqus/CAE +References +• “Element library: overview,” Section 27.1.1 +• “Element type assignment,” Section 17.5.3 of the Abaqus/CAE User’s Manual +Overview +The Abaqus element library contains the following: +• stress/displacement elements, including contact elements, connector elements such as springs, and +special-purpose elements such as Eulerian elements and surface elements; +• pore pressure elements; +• coupled temperature-displacement elements; +• coupled thermal-electrical-structural elements; +• coupled temperature–pore pressure displacement elements; +• heat transfer or mass diffusion elements; +• forced convection heat transfer elements; +• incompressible flow elements; +• coupled thermal-electrical elements; +• piezoelectric elements; +• electromagnetic elements; +• acoustic elements; and +• user-defined elements. +Each of these element types is described below. +Within Abaqus/Standard or Abaqus/Explicit, a model can contain elements that are not appropriate +for the particular analysis type chosen; such elements will be ignored. However, an Abaqus/Standard +model cannot contain elements that are not available in Abaqus/Standard; likewise, an Abaqus/Explicit +model cannot contain elements that are not available in Abaqus/Explicit. The same rule applies to +Abaqus/CFD. +Stress/displacement elements +Stress/displacement elements are used in the modeling of linear or complex nonlinear mechanical +analyses that possibly involve contact, plasticity, and/or large deformations. Stress/displacement +elements can also be used for thermal-stress analysis, where the temperature history can be obtained +from a heat transfer analysis carried out with diffusive elements. +Analysis types +Stress/displacement elements can be used in the following analysis types: +• static and quasi-static analysis (“Static stress analysis procedures: overview,” Section 6.2.1); +• implicit transient dynamic, explicit transient dynamic, modal dynamic, and steady-state dynamic +analysis (“Dynamic analysis procedures: overview,” Section 6.3.1); +• “Acoustic, shock, and coupled acoustic-structural analysis,” Section 6.10.1; and +• “Fracture mechanics: overview,” Section 11.4.1. +Active degrees of freedom +Stress/displacement elements have only displacement degrees of freedom. +Section 1.2.2, for a discussion of the degrees of freedom in Abaqus. +See “Conventions,” +Choosing a stress/displacement element +Stress/displacement elements are available in several different element families. +Continuum elements +• “Solid (continuum) elements,” Section 28.1.1; and +• “Infinite elements,” Section 28.3.1. +Structural elements +• “Membrane elements,” Section 29.1.1; +• “Truss elements,” Section 29.2.1; +• “Beam modeling: overview,” Section 29.3.1; +• “Frame elements,” Section 29.4.1; +• “Pipes and pipebends with deforming cross-sections: elbow elements,” Section 29.5.1; and +• “Shell elements: overview,” Section 29.6.1. +Rigid elements +• “Point masses,” Section 30.1.1; +• “Rotary inertia,” Section 30.2.1; and +• “Rigid elements,” Section 30.3.1. +Connector elements +• “Connector elements,” Section 31.1.2; +• “Springs,” Section 32.1.1; +• “Dashpots,” Section 32.2.1; +• “Flexible joint element,” Section 32.3.1; +• “Tube support elements,” Section 32.8.1; and +• “Drag chains,” Section 32.11.1. +Special-purpose elements +• “Cohesive elements: overview,” Section 32.5.1; +• “Gasket elements: overview,” Section 32.6.1; +• “Surface elements,” Section 32.7.1; +• “Line spring elements for modeling part-through cracks in shells,” Section 32.9.1; +• “Elastic-plastic joints,” Section 32.10.1; and +• “Eulerian elements,” Section 32.14.1. +Contact elements +• “Gap contact elements,” Section 39.2.1; +• “Tube-to-tube contact elements,” Section 39.3.1; +• “Slide line contact elements,” Section 39.4.1; and +• “Rigid surface contact elements,” Section 39.5.1. +Pore pressure elements +Pore pressure elements are provided in Abaqus/Standard for modeling fully or partially saturated fluid +flow through a deforming porous medium. The names of all pore pressure elements include the letter P +(pore pressure). These elements cannot be used with hydrostatic fluid elements. +Analysis types +Pore pressure elements can be used in the following analysis types: +• soils analysis (“Coupled pore fluid diffusion and stress analysis,” Section 6.8.1); and +• geostatic analysis (“Geostatic stress state,” Section 6.8.2). +Active degrees of freedom +Pore pressure elements have both displacement and pore pressure degrees of freedom. In second-order +elements the pore pressure degrees of freedom are active only at the corner nodes. See “Conventions,” +Section 1.2.2, for a discussion of the degrees of freedom in Abaqus. +Interpolation +These elements use either linear- or second-order (quadratic) interpolation for the geometry and +displacements in two or three directions. The pore pressure is interpolated linearly from the corner +nodes. Curved element edges should be avoided; exact linear spatial pore pressure variations cannot be +obtained with curved edges. +For output purposes the pore pressure at the midside nodes of second-order elements is determined +by linear interpolation from the corner nodes. +Choosing a pore pressure element +Pore pressure elements are available only in the following element family: +• “Solid (continuum) elements,” Section 28.1.1. +Coupled temperature-displacement elements +Coupled temperature-displacement elements are used in problems for which the stress analysis depends +on the temperature solution and the thermal analysis depends on the displacement solution. An example +is the heating of a deforming body whose properties are temperature dependent by plastic dissipation or +friction. The names of all coupled temperature-displacement elements include the letter T. +Analysis types +Coupled temperature-displacement elements are for use in fully coupled temperature-displacement +analysis (“Fully coupled thermal-stress analysis,” Section 6.5.3). +Active degrees of freedom +Coupled temperature-displacement elements have both displacement and temperature degrees of +freedom. In second-order elements the temperature degrees of freedom are active at the corner nodes. +In modified triangle and tetrahedron elements the temperature degrees of freedom are active at every +node. See “Conventions,” Section 1.2.2, for a discussion of the degrees of freedom in Abaqus. +Interpolation +Coupled temperature-displacement elements use either linear or parabolic interpolation for the geometry +and displacements. The temperature is always interpolated linearly. In second-order elements curved +edges should be avoided; exact linear spatial temperature variations for these elements cannot be obtained +with curved edges. +For output purposes the temperature at the midside nodes of second-order elements is determined +by linear interpolation from the corner nodes. +Choosing a coupled temperature-displacement element +Coupled temperature-displacement elements are available in the following element families: +• “Solid (continuum) elements,” Section 28.1.1; +• “Truss elements,” Section 29.2.1; +• “Shell elements: overview,” Section 29.6.1; +• “Gap contact elements,” Section 39.2.1; and +• “Slide line contact elements,” Section 39.4.1. +Coupled thermal-electrical-structural elements +Coupled thermal-electrical-structural elements are used when a solution for the displacement, electrical +potential, and temperature degrees of freedom must be obtained simultaneously. +In these types +of problems, coupling between the temperature and displacement degrees of freedom arises from +temperature-dependent material properties, thermal expansion, and internal heat generation, which +is a function of inelastic deformation of the material. The coupling between the temperature and +electrical degrees of freedom arises from temperature-dependent electrical conductivity and internal +heat generation (Joule heating), which is a function of the electrical current density. The names of the +coupled thermal-electrical-structural elements begin with the letter Q. +Analysis types +Coupled thermal-electrical-structural elements are for use in a fully coupled thermal-electrical-structural +analysis (“Fully coupled thermal-electrical-structural analysis,” Section 6.7.4). +Active degrees of freedom +Coupled thermal-electrical-structural elements have displacement, electrical potential, and temperature +degrees of freedom. In second-order elements the electrical potential and temperature degrees of freedom +are active at the corner nodes. In modified tetrahedron elements the electrical potential and temperature +degrees of freedom are active at every node. See “Conventions,” Section 1.2.2, for a discussion of the +degrees of freedom in Abaqus. +Interpolation +Coupled thermal-electrical-structural elements use either linear or parabolic interpolation for the +geometry and displacements. The electrical potential and temperature are always interpolated linearly. +In second-order elements curved edges should be avoided; exact linear spatial electrical potential and +temperature variations for these elements cannot be obtained with curved edges. +For output purposes the electrical potential and temperature at the midside nodes of second-order +elements are determined by linear interpolation from the corner nodes. +Choosing a coupled thermal-electrical-structural element +Coupled thermal-electrical-structural elements are available only in the following element family: +• “Solid (continuum) elements,” Section 28.1.1; +Coupled temperature–pore pressure elements +Coupled temperature–pore pressure elements are used in Abaqus/Standard for modeling fully or partially +saturated fluid flow through a deforming porous medium in which the stress, fluid pore pressure, and +temperature fields are fully coupled to one another. The names of all coupled temperature–pore pressure +elements include the letters T and P. These elements cannot be used with hydrostatic fluid elements. +Analysis types +Coupled temperature–pore pressure elements are for use in fully coupled temperature–pore pressure +analysis (“Coupled pore fluid diffusion and stress analysis,” Section 6.8.1). +Active degrees of freedom +Coupled temperature–pore pressure elements have displacement, pore pressure, and temperature degrees +of freedom. See “Conventions,” Section 1.2.2, for a discussion of the degrees of freedom in Abaqus. +Interpolation +These elements use either linear- or second-order (quadratic) interpolation for the geometry and +displacements. The temperature and pore pressure are always interpolated linearly. +Choosing a coupled temperature–pore pressure element +Coupled temperature–pore pressure elements are available in the following element family: +• “Solid (continuum) elements,” Section 28.1.1; +Diffusive (heat transfer) elements +Diffusive elements are provided in Abaqus/Standard for use in heat transfer analysis (“Uncoupled heat +transfer analysis,” Section 6.5.2), where they allow for heat storage (specific heat and latent heat effects) +and heat conduction. They provide temperature output that can be used directly as input to the equivalent +stress elements. The names of all diffusive heat transfer elements begin with the letter D. +Analysis types +The diffusive elements can be used in mass diffusion analysis (“Mass diffusion analysis,” Section 6.9.1) +as well as in heat transfer analysis. +Active degrees of freedom +When used for heat transfer analysis, the diffusive elements have only temperature degrees of freedom. +When they are used in a mass diffusion analysis, they have normalized concentration, instead of +temperature, degrees of freedom. See “Conventions,” Section 1.2.2, for a discussion of the degrees of +freedom in Abaqus. +Interpolation +The diffusive elements use either first-order +interpolation in one, two, or three dimensions. +(linear) +interpolation or second-order +(quadratic) +Choosing a diffusive element +Diffusive elements are available in the following element families: +• “Solid (continuum) elements,” Section 28.1.1; +• “Shell elements: overview,” Section 29.6.1 (these elements cannot be used in a mass diffusion +analysis); and +• “Gap contact elements,” Section 39.2.1. +Forced convection heat transfer elements +Forced convection heat transfer elements are provided in Abaqus/Standard to allow for heat storage +(specific heat) and heat conduction, as well as the convection of heat by a fluid flowing through the mesh +(forced convection). All forced convection heat transfer elements provide temperature output, which +can be used directly as input to the equivalent stress elements. The names of all forced convection heat +transfer elements begin with the letters DCC. +Analysis types +transfer analysis,” Section 6.5.2), +The forced convection heat transfer elements can be used in heat transfer analyses (“Uncoupled +heat +including cavity radiation modeling (“Cavity radiation,” +Section 40.1.1). The forced convection heat transfer elements can be used together with the diffusive +elements. +Active degrees of freedom +The forced convection heat transfer elements have temperature degrees of freedom. See “Conventions,” +Section 1.2.2, for a discussion of the degrees of freedom in Abaqus. +Interpolation +The forced convection heat transfer elements use only first-order (linear) interpolation in one, two, or +three dimensions. +Choosing a forced convection heat transfer element +Forced convection heat transfer elements are available only in the following element family: +• “Solid (continuum) elements,” Section 28.1.1. +Incompressible flow elements +Hybrid elements suitable for incompressible flow are available in Abaqus/CFD. These elements permit +the automatic addition of degrees of freedom for the optional energy equation and turbulence models. +The names of all fluid elements begin with the letters FC. +Analysis types +The incompressible flow elements can be used in a variety of flow analyses (“Incompressible fluid +dynamic analysis,” Section 6.6.2), including laminar or turbulent flows, heat transfer, and fluid-solid +interaction. +Active degrees of freedom +The incompressible flow elements provide primarily pressure and velocity degrees of freedom. See +“Fluid element library,” Section 28.2.2, for more information on the degrees of freedom in Abaqus/CFD. +Interpolation +The incompressible flow elements use only first-order (linear) interpolation in one, two, or three +dimensions. +Choosing an incompressible flow element +The incompressible flow elements are available only in the following element family: +• “Fluid (continuum) elements,” Section 28.2.1. +Coupled thermal-electrical elements +Coupled thermal-electrical elements are provided in Abaqus/Standard for use in modeling heating that +arises when an electrical current flows through a conductor (Joule heating). +Analysis types +the thermal and electrical problems . +temperature-dependent electrical conductivity and the heat generated in the thermal problem by electric +conduction. +These elements can also be used to perform uncoupled electric conduction analysis in all or part of +the model. In such analysis only the electric potential degree of freedom is activated, and all heat transfer +effects are ignored. This capability is available by omitting the thermal conductivity from the material +definition. +The coupled thermal-electrical elements can also be used in heat transfer analysis (“Uncoupled heat +transfer analysis,” Section 6.5.2), in which case all electric conduction effects are ignored. This feature is +quite useful if a coupled thermal-electrical analysis is followed by a pure heat conduction analysis (such +as a welding simulation followed by cool down). +The elements cannot be used in any of the stress/displacement analysis procedures. +Active degrees of freedom +Coupled thermal-electrical elements have both temperature and electrical potential degrees of freedom. +See “Conventions,” Section 1.2.2, for a discussion of the degrees of freedom in Abaqus. +Interpolation +Coupled thermal-electrical elements are provided with first- or second-order interpolation of the +temperature and electrical potential. +Choosing a coupled thermal-electrical element +Coupled thermal-electrical elements are available only in the following element family: +• “Solid (continuum) elements,” Section 28.1.1. +Piezoelectric elements +Piezoelectric elements are provided in Abaqus/Standard for problems in which a coupling between the +stress and electrical potential (the piezoelectric effect) must be modeled. +Analysis types +Piezoelectric elements are for use in piezoelectric analysis (“Piezoelectric analysis,” Section 6.7.2). +Active degrees of freedom +The piezoelectric elements have both displacement and electric potential degrees of freedom. See +“Conventions,” Section 1.2.2, for a discussion of the degrees of freedom in Abaqus. The piezoelectric +effect is discussed further in “Piezoelectric analysis,” Section 6.7.2. +Interpolation +Piezoelectric elements are available with first- or second-order interpolation of displacement and +electrical potential. +Choosing a piezoelectric element +Piezoelectric elements are available in the following element families: +• “Solid (continuum) elements,” Section 28.1.1; and +• “Truss elements,” Section 29.2.1. +Electromagnetic elements +Electromagnetic elements are provided in Abaqus/Standard for problems that require the computation +of the magnetic fields (such as a magnetostatic analysis) or for problems in which a coupling between +electric and magnetic fields must be modeled (such as an eddy current analysis). +Analysis types +Electromagnetic elements are for use in magnetostatic and eddy current analyses (“Magnetostatic +analysis,” Section 6.7.6, and “Eddy current analysis,” Section 6.7.5). +Active degrees of freedom +Electromagnetic elements have magnetic vector potential as the degree of freedom. See “Conventions,” +Section 1.2.2, for a discussion of the degrees of freedom in Abaqus. Magnetostatic analysis is discussed +further in “Magnetostatic analysis,” Section 6.7.6, while the electromagnetic coupling that occurs in an +eddy current analysis is discussed further in “Eddy current analysis,” Section 6.7.5. +Interpolation +Electromagnetic elements are available with zero-order element edge–based interpolation of the +magnetic vector potential. +Choosing an electromagnetic element +Electromagnetic elements are available in the following element family: +• “Solid (continuum) elements,” Section 28.1.1. +Acoustic elements +Acoustic elements are used for modeling an acoustic medium undergoing small pressure changes. The +solution in the acoustic medium is defined by a single pressure variable. Impedance boundary conditions +representing absorbing surfaces or radiation to an infinite exterior are available on the surfaces of these +acoustic elements. +Acoustic infinite elements, which improve the accuracy of analyses involving exterior domains, and +acoustic-structural interface elements, which couple an acoustic medium to a structural model, are also +provided. +Analysis types +Acoustic elements are for use in acoustic and coupled acoustic-structural analysis (“Acoustic, shock, and +coupled acoustic-structural analysis,” Section 6.10.1). +Active degrees of freedom +Acoustic elements have acoustic pressure as a degree of freedom. Coupled acoustic-structural elements +also have displacement degrees of freedom. See “Conventions,” Section 1.2.2, for a discussion of the +degrees of freedom in Abaqus. +Choosing an acoustic element +Acoustic elements are available in the following element families: +• “Solid (continuum) elements,” Section 28.1.1; +• “Infinite elements,” Section 28.3.1; and +• “Acoustic interface elements,” Section 32.13.1. +The acoustic elements can be used alone but are often used with a structural model in a coupled +analysis. “Acoustic interface elements,” Section 32.13.1, describes interface elements that allow this +acoustic pressure field to be coupled to the displacements of the surface of the structure. Acoustic +elements can also interact with solid elements through the use of surface-based tie constraints; see +“Acoustic, shock, and coupled acoustic-structural analysis,” Section 6.10.1. +Using the same mesh with different analysis or element types +You may want to use the same mesh with different analysis or element types. This may occur, for +example, if both stress and heat transfer analyses are intended for a particular geometry or if the effect +of using either reduced- or full-integration elements is being investigated. Care should be taken when +doing this since unexpected error messages may result for one of the two element types if the mesh is +distorted. For example, a stress analysis with C3D10 elements may run successfully, but a heat transfer +analysis using the same mesh with DC3D10 elements may terminate during the datacheck portion of +the analysis with an error message stating that the elements are excessively distorted or have negative +volumes. This apparent inconsistency is caused by the different integration locations for the different +element types. Such problems can be avoided by ensuring that the mesh is not distorted excessively. +27.1.4 +SECTION CONTROLS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• *SECTION CONTROLS +• *HOURGLASS STIFFNESS +• “Element type assignment,” Section 17.5.3 of the Abaqus/CAE User’s Manual +Overview +Section controls in Abaqus/Standard: +• choose the hourglass control formulation for most first-order elements with reduced integration; +• define the distortion control for C3D10I elements; +• select the hourglass control scale factors for all elements with reduced integration; and +• select the choice of element deletion and the value of maximum degradation for cohesive elements, +connector elements, elements with plane stress formulations (plane stress, shell, continuum shell, +and membrane elements) with constitutive behavior that includes damage evolution, any element +that can be used with damage evolution models for ductile metals, and any element that can be used +with the damage evolution law in a low-cycle fatigue analysis. +Section controls in Abaqus/Explicit: +• choose the hourglass control formulation or scale factors for all elements with reduced integration; +• define the distortion control for solid elements; +• select the scale factors for the drill stiffness of shell elements or deactivate the drill stiffness for +small-strain shell elements S3RS and S4RS; +• select an amplitude for ramping of any initial stresses in membrane elements; +• select the kinematic formulation for hexahedron solid elements; +• select the accuracy order of the formulation for solid and shell elements; +• select the scale factors for linear and quadratic bulk viscosity parameters; +• select the choice of element deletion and the value of maximum degradation for elements with +constitutive behavior that includes damage evolution; and +• control many aspects related to a smoothed particle hydrodynamic (SPH) analysis. +In Abaqus/CAE section controls are specified when you assign an element type to particular mesh regions +and are referred to as element controls. +Using section controls +In Abaqus/Standard section controls are used to select the enhanced hourglass control formulation for +solid, shell, and membrane elements. This formulation provides improved coarse mesh accuracy with +slightly higher computational cost and performs better for nonlinear material response at high strain +levels when compared with the default total stiffness formulation. Section controls can also be used to +select some element formulations that may be relevant for a subsequent Abaqus/Explicit analysis. +In Abaqus/Explicit the default formulations for solid, shell, and membrane elements have been +chosen to perform satisfactorily on a wide class of quasi-static and explicit dynamic simulations. +However, certain formulations give rise to some trade-off between accuracy and performance. +Abaqus/Explicit provides section controls to modify these element formulations so that you can +optimize these objectives for a specific application. Section controls can also be used in Abaqus/Explicit +to specify scale factors for linear and quadratic bulk viscosity parameters. You can also control the +initial stresses in membrane elements for applications such as airbags in crash simulations and introduce +the initial stresses gradually based on an amplitude definition. +In addition, section controls are used to specify the maximum stiffness degradation and to choose +the behavior upon complete failure of an element, once the material stiffness is fully degraded, +including the removal of failed elements from the mesh. This functionality applies only to elements +with a material definition that includes progressive damage . In Abaqus/Standard this +functionality is limited to +• cohesive elements with a traction-separation constitutive response that includes damage evolution, +• any element with a plane stress formulation that can be used with the damage evolution model for +fiber-reinforced composites, +• any element that can be used with the damage evolution models for ductile metals, +• any element that can be used with the damage evolution law in a low-cycle fatigue analysis, and +• connector elements with a constitutive response that includes damage evolution. +Input File Usage: +Use the following option to specify a section controls definition: +*SECTION CONTROLS, NAME=name +This option is used in conjunction with one or more of the following options to +associate the section control definition with an element section definition: +*COHESIVE SECTION, CONTROLS=name +*CONNECTOR SECTION, CONTROLS=name +*EULERIAN SECTION, CONTROLS=name +*MEMBRANE SECTION, CONTROLS=name +*SHELL GENERAL SECTION, CONTROLS=name +*SHELL SECTION, CONTROLS=name +*SOLID SECTION, CONTROLS=name +You can apply a single section control definition to several element section +definitions. +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Element Controls +Methods for suppressing hourglass modes +The formulation for reduced-integration elements considers only the linearly varying part of the +incremental displacement field in the element for the calculation of the increment of physical strain. The +remaining part of the nodal incremental displacement field is the hourglass field and can be expressed +in terms of hourglass modes. +Excitation of these modes may lead to severe mesh distortion, with no stresses resisting the +deformation. Similarly, the formulation for element type C3D4H considers in the constraint equations +only the constant part of the incremental pressure Lagrange multiplier field. The remaining part of the +nodal incremental pressure Lagrange multiplier interpolation is comprised of hourglass modes. +Hourglass control attempts to minimize these problems without introducing excessive constraints +on the element’s physical response. +Several methods are available in Abaqus for suppressing the hourglass modes, as described below. +Integral viscoelastic approach in Abaqus/Explicit +The integral viscoelastic approach available in Abaqus/Explicit generates more resistance to hourglass +forces early in the analysis step where sudden dynamic loading is more probable. +Let q be an hourglass mode magnitude and Q be the force (or moment) conjugate to q. The integral +viscoelastic approach is defined as +, +, and +that you can define (by default, +where K is the hourglass stiffness selected by Abaqus/Explicit, and s is one of up to three scaling factors +). The scale factors are dimensionless +scales +scales the hourglass stiffnesses related to the in-plane +scales the hourglass stiffnesses related to the rotational degrees +scales the hourglass stiffness related to the transverse displacement for small- +and relate to specific displacement degrees of freedom. For solid and membrane elements +all hourglass stiffnesses. For shell elements +displacement degrees of freedom, and +of freedom. In addition, +strain shell elements. +The integral viscoelastic form of hourglass control is available for all reduced-integration elements +and is the default form in Abaqus/Explicit, except for elements modeled with hyperelastic, hyperfoam, +and low-density foam materials. It is the most computationally intensive hourglass control method. It is +not supported for Eulerian EC3D8R elements. +Input File Usage: +*SECTION CONTROLS, NAME=name, +HOURGLASS=RELAX STIFFNESS +, +, +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Hourglass control: +Relax stiffness, Displacement hourglass scaling factor: +, Out-of-plane +, Rotational hourglass scaling factor: +displacement hourglass scaling factor: +Kelvin viscoelastic approach in Abaqus/Explicit +The Kelvin-type viscoelastic approach available in Abaqus/Explicit is defined as +where K is the linear stiffness and C is the linear viscous coefficient. This general form has pure stiffness +and pure viscous hourglass control as limiting cases. When the combination is used, the stiffness term +acts to maintain a nominal resistance to hourglassing throughout the simulation and the viscous term +generates additional resistance to hourglassing under dynamic loading conditions. +Three approaches are provided in Abaqus/Explicit for specifying Kelvin viscoelastic hourglass +control. +Specifying the pure stiffness approach +The pure stiffness form of hourglass control is available for all reduced-integration elements and is +recommended for both quasi-static and transient dynamic simulations. +Input File Usage: +*SECTION CONTROLS, NAME=name, HOURGLASS=STIFFNESS +, +, +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Hourglass control: +Stiffness, Displacement hourglass scaling factor: +hourglass scaling factor: +hourglass scaling factor: +, Out-of-plane displacement +, Rotational +Specifying the pure viscous approach +The pure viscous form of hourglass control is available only for solid and membrane elements with +reduced integration and is the default form in Abaqus/Explicit for Eulerian EC3D8R elements. It is the +most computationally efficient form of hourglass control and has been shown to be effective for high-rate +dynamic simulations. However, the pure viscous method is not recommended for low frequency dynamic +or quasi-static problems since continuous (static) loading in hourglass modes will result in excessive +hourglass deformation due to the lack of any nominal stiffness. +Input File Usage: +*SECTION CONTROLS, NAME=name, HOURGLASS=VISCOUS +, +, +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Hourglass control: +Viscous, Displacement hourglass scaling factor: +hourglass scaling factor: +hourglass scaling factor: +, Out-of-plane displacement +, Rotational +Specifying a combination of stiffness and viscous hourglass control +A linear combination of stiffness and viscous hourglass control is available only for solid and membrane +elements with reduced integration. You can specify the blending weight factor +) to scale the +stiffness and viscous contributions. Specifying a weight factor equal to 0.0 or 1.0 results in the limiting +cases of pure stiffness and pure viscous hourglass control, respectively. The default weight factor is 0.5. +( +Input File Usage: +*SECTION CONTROLS, NAME=name, HOURGLASS=COMBINED, +WEIGHT FACTOR= +, +, +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Hourglass control: Combined, +Stiffness-viscous weight factor: +factor: +displacement hourglass scaling factor: +, Rotational hourglass scaling factor: +, Displacement hourglass scaling +, Out-of-plane +Total stiffness approach in Abaqus/Standard +The total stiffness approach available in Abaqus/Standard is the default hourglass control approach for +all first-order, reduced-integration elements in Abaqus/Standard, except for elements modeled with +hyperelastic, hyperfoam, or hysteresis materials. +It is the only hourglass control approach available +in Abaqus/Standard for S8R5, S9R5, and M3D9R elements and the only hourglass control approach +available for the pressure Lagrange multiplier interpolation for C3D4H elements. Hourglass stiffness +factors for first-order, reduced-integration elements depend on the shear modulus, while factors for +C3D4H elements depend on the bulk modulus. A scale factor can be applied to these stiffness factors to +increase or decrease the hourglass stiffness. +Let q be an hourglass mode magnitude and Q be the force (moment, pressure, or volumetric flux) +conjugate to q. The total stiffness approach for hourglass control in membrane or solid elements or +membrane hourglass control in shell elements is defined as +is a dimensionless scale factor (by default, +where +with units of stress; +( +direction, and +for the pressure Lagrange multiplier interpolation for C3D4H elements is defined as +is an hourglass stiffness factor +); +is the gradient interpolator used to define constant gradients in the element +refers to a +is a material coordinate); and V is the element volume. Similarly, the hourglass control +where the superscript P refers to an element node, the subscript +is a volumetric gradient operator; +is a dimensionless scale factor (by default, +where +and +is an hourglass stiffness factor with units of stress for compressible hyperelastic and hyperfoam +materials and units of stress compliance for all other materials. The total stiffness approach for bending +hourglass control in shell elements is defined as +); +where +of the shell element, and A is the area of the shell element. +is the scale factor (by default, +), +is the hourglass stiffness factor, t is the thickness +Input File Usage: +*SECTION CONTROLS, NAME=name, HOURGLASS=STIFFNESS +, +, , , , +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Hourglass control: +Stiffness, Displacement hourglass scaling factor: +hourglass scaling factor: +, Rotational +Default hourglass stiffness values +Normally the hourglass control stiffness is defined from the elasticity associated with the material. In +most cases, the control stiffness of first-order, reduced-integration elements is based on a typical value +of the initial shear modulus of the material, which may, for example, be given as part of the elastic +material definition (“Linear elastic behavior,” Section 22.2.1). Similarly, hourglass control stiffness of +the reduced-integration pressure and volumetric Lagrange multiplier interpolations of C3D4H elements +is based on a typical value of the initial bulk modulus. For an isotropic elastic or hyperelastic material +G is the shear modulus. For a nonisotropic elastic material average moduli are used to calculate the +hourglass stiffness: for orthotropic elasticity defined by specifying the terms in the elastic stiffness matrix +or for anisotropic elasticity +and for orthotropic elasticity defined by specifying the engineering constants or for orthotropic elasticity +in plane stress +If the elastic moduli are dependent on temperature or field variables, the first value in the table is +used. The default values for the stiffness factors are defined below. +For membrane or solid elements +For membrane hourglass control in a shell +For control of bending hourglass modes in a shell +For a general shell section defined by specifying the equivalent section properties directly, t is defined as +and an effective shear modulus for the section is used to calculate the hourglass stiffness: +where +is the section stiffness matrix. +User-defined hourglass stiffness +When the initial shear modulus is not defined, you must define the hourglass stiffness parameters; an +example is when user subroutine UMAT is used to describe the material behavior of elements with +hourglassing modes. In some cases the default value provided for the hourglass control stiffness may +not be suitable and you should define the value. +In some coupled pore fluid diffusion and stress analyses the prevailing pore pressure in the medium +may approach the magnitude of the stiffness of the material skeleton, as measured by constitutive +parameters such as the elastic modulus. These cases are expected in some partial saturation evaluations +of the wetting of relatively compliant materials such as tissues or cloth. When reduced-integration or +modified tetrahedral or triangular elements are used in such analyses, the default choice of the hourglass +control stiffness parameter, which is based on a scaling of skeleton material constitutive parameters, +may not be adequate to control hourglassing in the presence of large pore pressure fields. An appropriate +hourglass control stiffness in these cases should scale with the expected magnitude of pore pressure +changes over an element. +Input File Usage: +Use the following option to specify nondefault values for the hourglass stiffness +factors: +*HOURGLASS STIFFNESS +, +, +, drilling hourglass scaling factor for shells +This option must immediately follow one of the following options: +*MEMBRANE SECTION +*SHELL GENERAL SECTION +*SHELL SECTION +*SOLID SECTION +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Hourglass stiffness: Specify +or for shells Membrane hourglass stiffness: Specify +, Bending +hourglass stiffness: Specify +factor: Specify drilling hourglass scaling factor for shells +, and Drilling hourglass scaling +Enhanced hourglass control approach in Abaqus/Standard and Abaqus/Explicit +The enhanced hourglass control approach available in both Abaqus/Standard and Abaqus/Explicit +represents a refinement of the pure stiffness method in which the stiffness coefficients are based on +It is the default hourglass control +the enhanced assumed strain method; no scale factor is required. +approach for hyperelastic, hyperfoam, and low-density foam materials in Abaqus/Explicit and for +hyperelastic, hyperfoam, and hysteresis materials in Abaqus/Standard. This method gives more accurate +displacement solutions for coarse meshes with linear elastic materials as compared to other hourglass +control methods. It also provides increased resistance to hourglassing for nonlinear materials. Although +generally beneficial, this may give overly stiff response in problems displaying plastic yielding under +bending. In Abaqus/Explicit the enhanced hourglass method will generally predict a much better return +to the original configuration for hyperelastic or hyperfoam materials when loading is removed. +The enhanced hourglass control approach is compatible between Abaqus/Standard and +Abaqus/Explicit. It is recommended that enhanced hourglass control be used for both Abaqus/Standard +and Abaqus/Explicit for all import analyses. See “Transferring results between Abaqus/Explicit and +Abaqus/Standard,” Section 9.2.2. +The enhanced hourglass method is not supported for enriched elements . +Specifying the enhanced hourglass control approach +The enhanced hourglass control method is available for first-order solid, membrane, and finite-strain shell +elements with reduced integration. In Abaqus/Explicit it cannot be used for a hyperelastic or hyperfoam +material when adaptive meshing is used on that domain . +Input File Usage: +*SECTION CONTROLS, NAME=name, HOURGLASS=ENHANCED +Any scaling factors specified on the data line following this option will be +ignored. +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Hourglass control: Enhanced +Special considerations for hyperelastic and hyperfoam materials in an adaptive mesh domain in +Abaqus/Explicit +The enhanced hourglass method cannot be used with elements modeled with hyperelastic or hyperfoam +materials that are included in an adaptive mesh domain. Thus, if you decide to use hyperelastic or +hyperfoam materials in an adaptive mesh domain, you must specify section controls to choose a +different hourglass control approach. The use of adaptive meshing in domains modeled with finite-strain +elastic materials is not recommended since better results are generally predicted using the enhanced +hourglass method and, for solid elements, element distortion control (discussed below). Therefore, for +these materials it is recommended that the analysis be run without adaptive meshing but with enhanced +hourglass control. +Use in coupled pore pressure analysis +When first-order, reduced-integration, or modified tetrahedral or triangular elements are used in coupled +pore fluid diffusion and stress analyses or coupled temperature–pore pressure analyses with enhanced +hourglass control, the hourglass control stiffness, which is based on skeleton material constitutive +parameters, may not be adequate to control hourglassing in the presence of large pore pressure fields. +Since enhanced hourglass control does not allow you to change the hourglass control stiffness, it is +recommended that total stiffness hourglass control be used in these cases with an appropriate hourglass +control stiffness scaled with the expected magnitude of pore pressure changes over an element. +Controlling element distortion for crushable materials in Abaqus/Explicit +Many analyses with volumetrically compacting materials such as crushable foams see large compressive +and shear deformations, especially when the crushable materials are used as energy absorbers between +stiff or heavy components. The material behavior for crushable materials usually stiffens significantly +under high compression. When a finer mesh is used, the stiffening behavior of the material model is +enough to prevent excessive negative element volumes or other excessive distortion from occurring under +high compressive loads. However, analyses may fail prematurely when the mesh is coarse relative to +strain gradients and the amount of compression. +Abaqus/Explicit offers distortion control to prevent solid elements from inverting or distorting +excessively for these cases. The constraint method used in Abaqus/Explicit prevents each node on an +element from punching inward toward the center of the element past a point where the element would +become non-convex. Constraints are enforced by using a penalty approach, and you can control the +associated distortion length ratio. +Distortion control is available only for solid elements and cannot be used when the elements are +included in an adaptive mesh domain. Distortion control is activated by default for elements modeled +with hyperelastic, hyperfoam, or low-density foam materials. Using adaptive meshing in a domain +modeled with hyperelastic or hyperfoam materials is not recommended since better results are generally +predicted using the enhanced hourglass method in combination with element distortion control. However, +if you decide to use hyperelastic or hyperfoam materials in an adaptive mesh domain, you must specify +section controls to deactivate distortion control. +If distortion control is used, the energy dissipated by distortion control can be output upon request +. Although developed for +analyses of energy absorbing, volumetrically compacting materials, distortion control can be used with +any material model. However, care must be used in interpreting results since the distortion control +constraints may inhibit legitimate deformation modes and lock up the mesh. Distortion control cannot +prevent elements from being distorted due to temporal instabilities, hourglass instabilities, or physically +unrealistic deformation. +Input File Usage: +Use the following option to activate distortion control: +*SECTION CONTROLS, NAME=name, DISTORTION CONTROL=YES +Use the following option to deactivate distortion control: +*SECTION CONTROLS, NAME=name, DISTORTION CONTROL=NO +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Distortion control: Yes or No +Controlling the distortion length ratio +By default, the constraint penalty forces are applied when the node moves to a point a small offset +distance away from the actual plane of constraint. This appears to improve the robustness of the method +and limits the reduction of time increment due to severe shortening of the element characteristic length. +This offset distance is determined by the distortion length ratio times the initial element characteristic +length. The default value of the distortion length ratio, r, is 0.1. You can change the distortion length +ratio by specifying a value for r, +. +Input File Usage: +*SECTION CONTROLS, NAME=name, DISTORTION CONTROL=YES, +LENGTH RATIO=r +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Distortion control: +Yes, Length ratio: r +Selecting a scale factor for the drill stiffness in Abaqus/Explicit +A drill constraint acts to keep the element nodal rotations in the direction of the shell normal consistent +with the average in-plane rotation of the element. Lack of such a constraint can lead to large rotations at +these element nodes. Section controls can be used to select a scale factor for the default drill stiffness of +an individual element set. +Input File Usage: +Use the following options to specify a scale factor for the drill stiffness: +*SECTION CONTROLS, NAME=name +, , , , , , , scale factor for drill stiffness +Drill constraint in small strain shell elements S3RS and S4RS in Abaqus/Explicit +The formulation of small strain shell elements S3RS and S4RS includes a drill constraint and does so by +default. Alternatively, you can deactivate the drill constraint for these elements. The drill constraint is +always active for the finite strain conventional shell elements such as S4R, but the default value of the +drill stiffness can be scaled as mentioned above. +Input File Usage: +Use the following option to activate the drill constraint (default): +*SECTION CONTROLS, DRILL STIFFNESS=ON +Use the following option to deactivate the drill constraint: +*SECTION CONTROLS, DRILL STIFFNESS=OFF +Ramping of initial stresses in membrane elements in Abaqus/Explicit +For applications such as airbags in crash simulations the initial strains (hence, the initial stresses) are +introduced into the model through a reference configuration that is different from the initial configuration. +Often the components that confine the airbag in the initial configuration are excluded from the numerical +model causing motion of the airbag under initial stresses at the beginning of the analysis. Abaqus/Explicit +provides a technique to introduce the initial stresses in the membrane elements gradually based on an +amplitude definition. This amplitude must be defined with its value starting from zero and reaching a +final value of one. The initial stresses will not be applied for the duration that the amplitude stays at zero. +Input File Usage: +Use both of the following options: +*AMPLITUDE, NAME=name +*SECTION CONTROLS, RAMP INITIAL STRESS=name +Defining the kinematic formulation for hexahedron solid elements +The default kinematic formulation for reduced-integration solid elements in Abaqus (and the only +kinematic formulation available in Abaqus/Standard) is based on the uniform strain operator and the +hourglass shape vectors. Details can be found in “Solid isoparametric quadrilaterals and hexahedra,” +Section 3.2.4 of the Abaqus Theory Manual. These kinematic assumptions result in elements that pass +the constant strain patch test for a general configuration and give zero strain under large rigid body +rotation. However, the formulation is relatively expensive, especially in three dimensions. +Abaqus/Explicit offers two alternative kinematic formulations for the C3D8R solid element that +can reduce the computational cost. The performance for each kinematic formulation on the patch test +and under large rigid body rotation for various element configurations is summarized in Table 27.1.4–1. +Suitable applications for each kinematic formulation are summarized in Table 27.1.4–2. +Table 27.1.4–1 Element performance for patch test and large rigid +body rotations for various element configurations. +Element +configuration +Satisfaction of the +three-dimensional +patch test +Parallelepiped +General +Zero straining under +rigid body rotation +Parallelepiped +General +Kinematic formulation type +Average +strain +Yes +Yes +Yes +Yes +Orthogonal +Centroid +Yes +No +Yes +Yes +Yes +No +Yes +No +You can specify the kinematic formulation for 8-node brick elements. +Default formulation +The default average strain formulation of uniform strain and hourglass shape vectors is the only +formulation available in Abaqus/Standard. This formulation is recommended for all problems and is +Table 27.1.4–2 Different element formulations and their suitable +applications. The default formulation is highlighted below. +Kinematic +formulation +Order of +accuracy +Average strain +Second-order +Average strain +First-order +Orthogonal +Centroid +— +— +Suitable applications +All; recommended for problems involving +a large number of revolutions (>5). +All; except those involving a large number +of revolutions (>5). +All; except those involving high +confinement, very coarse meshes, or +highly distorted elements. +Problems with little rigid body rotation +and reasonable mesh refinement. +particularly well suited for applications exhibiting high confinement, such as closed-die forming and +bushing analyses. +Input File Usage: +*SECTION CONTROLS, KINEMATIC SPLIT=AVERAGE STRAIN +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Kinematic split: Average strain +Orthogonal formulation in Abaqus/Explicit +A noticeable reduction in computational cost can be obtained by using the orthogonal formulation +available in Abaqus/Explicit. This formulation is based on the centroidal strain operator and a slight +modification to the hourglass shape vectors. The centroidal strain operator requires three times fewer +floating point operations than the uniform strain operator. Elements formulated with an orthogonal +kinematic split pass the patch test only for rectangular or parallelepiped element configurations. +However, numerical experience has shown that the element converges on the exact solution for general +element configurations as the mesh is refined. It also performs well for large rigid body motions. +This formulation provides a good balance between computational speed and accuracy. +It is +recommended for all analyses except those involving highly distorted elements, very coarse meshes, or +high confinement. Suitable applications for this formulation include elastic drop testing. +Input File Usage: +*SECTION CONTROLS, NAME=name, +KINEMATIC SPLIT=ORTHOGONAL +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Kinematic split: Orthogonal +Centroid formulation in Abaqus/Explicit +The fastest formulation available in Abaqus/Explicit is specified by selecting the centroid formulation. +The centroid formulation is based on the centroidal strain operator and the hourglass base vectors. Using +the hourglass base vectors instead of the hourglass shape vectors reduces hourglass mode computations +by a factor of three. However, the hourglass base vectors are not orthogonal to rigid body rotation for +general element configurations, so that hourglass strain may be generated with large rigid body rotations +with this formulation. +This formulation should be used only to improve computational performance on problems that have +reasonable mesh refinement and no significant amount of rigid body rotation (e.g., transient flat rolling +simulation). +Input File Usage: +*SECTION CONTROLS, NAME=name, KINEMATIC SPLIT=CENTROID +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Kinematic split: Centroid +Choosing the order of accuracy in solid and shell element formulations +Abaqus/Standard offers only a second-order accurate formulation for all elements. +Abaqus/Explicit offers both first- and second-order accurate formulations for solid and shell +elements. First-order accuracy is the default and yields sufficient accuracy for nearly all Abaqus/Explicit +problems because of the inherently small time increment size. Second-order accuracy is usually required +for analyses with components undergoing a large number of revolutions (>5). For three-dimensional +solids the second-order accuracy formulation is available only with the default average strain kinematic +formulation. +First-order accuracy +In Abaqus/Explicit the first-order accurate formulation for solid and shell elements is the default. This +formulation is not available in Abaqus/Standard. +Input File Usage: +*SECTION CONTROLS, NAME=name, +SECOND ORDER ACCURACY=NO +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Second-order accuracy: No +Second-order accuracy +The second-order accurate element formulation is appropriate for problems with a large number of +revolutions (>5). This is the only formulation available in Abaqus/Standard. “Simulation of propeller +rotation,” Section 2.3.15 of the Abaqus Benchmarks Manual, illustrates the performance of second-order +accurate shell and solid elements in Abaqus/Explicit as they undergo about 100 revolutions. +*SECTION CONTROLS, NAME=name, +SECOND ORDER ACCURACY=YES +Input File Usage: +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Second-order accuracy: Yes +Selecting scale factors for bulk viscosity in Abaqus/Explicit +Bulk viscosity introduces damping associated with volumetric straining. Its purpose is to improve the +modeling of high-speed dynamic events. Abaqus/Explicit contains two forms of bulk viscosity, linear +and quadratic, which can be defined for the whole model at each step of the analysis, as discussed in +“Bulk viscosity” in “Explicit dynamic analysis,” Section 6.3.3. Section controls can be used to select +scale factors for the linear and quadratic bulk viscosities of an individual element set. +The pressure term generated by bulk viscosity may introduce unexpected results in the volumetric +response of highly compressible materials; therefore, it is recommended to suppress bulk viscosity for +these materials by specifying scale factors equal to zero. +Input File Usage: +Use the following options to specify scale factors for the linear and quadratic +bulk viscosities: +*SECTION CONTROLS, NAME=name +, , , scale factor for linear bulk viscosity, scale factor for quadratic bulk viscosity +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Linear bulk viscosity scaling +factor or Quadratic bulk viscosity scaling factor +Controlling element deletion and maximum degradation for materials with damage evolution +Abaqus offers a general capability for modeling progressive damage and failure of materials +In Abaqus/Standard this capability is available +(“Progressive damage and failure,” Section 24.1.1). +only for cohesive elements, connector elements, elements with plane stress formulations (plane stress, +shell, continuum shell, and membrane elements), any element that can be used with the damage +evolution models for ductile metals, and any element that can be used with the damage evolution law +In Abaqus/Explicit this capability is available for all elements with +in a low-cycle fatigue analysis. +progressive damage behavior except connector elements. Section controls are provided to specify +the value of the maximum stiffness degradation, +, and whether element deletion occurs when +the degradation reaches this level. By default, an element is deleted when it is fully damaged (i.e., +). The choice of element deletion also affects how the damage is applied; details can be +found in the following sections: +• “Maximum degradation and choice of element removal” in “Damage evolution and element removal +for ductile metals,” Section 24.2.3; +• “Maximum degradation and choice of element removal in Abaqus/Standard” in “Connector damage +behavior,” Section 31.2.7; +• “Maximum degradation and choice of element removal” in “Defining the constitutive response of +cohesive elements using a traction-separation description,” Section 32.5.6; +• “Maximum degradation and choice of element removal” in “Damage evolution and element removal +for fiber-reinforced composites,” Section 24.3.3; and +• “Damage evolution for ductile materials in low-cycle fatigue,” Section 24.4.3. +Input File Usage: +Use the following option to delete the element from the mesh: +*SECTION CONTROLS, ELEMENT DELETION=YES +Use the following option to keep the element in the computation: +*SECTION CONTROLS, ELEMENT DELETION=NO +Use the following option to specify +: +*SECTION CONTROLS, MAX DEGRADATION= +. +Abaqus/CAE Usage: +Use the following option to control whether completely damaged elements +remain in the computation: +Mesh module: Mesh→Element Type: Element deletion +Use the following option to determine when an element +completely damaged: +is considered +Mesh module: Mesh→Element Type: Max degradation +Using viscous regularization with cohesive elements, connector elements, and elements +that can be used with the damage evolution models for ductile metals and fiber-reinforced +composites in Abaqus/Standard +Material models exhibiting softening behavior and stiffness degradation often lead to severe convergence +difficulties in implicit analysis programs, such as Abaqus/Standard. A common technique to overcome +some of these convergence difficulties is the use of viscous regularization of the constitutive equations, +which causes the tangent stiffness matrix of the softening material to be positive for sufficiently small +time increments. +The traction-separation laws used to describe the constitutive behavior of cohesive elements can be +regularized in Abaqus/Standard using viscosity, by permitting stresses to be outside the limits defined +by the traction-separation law. The details of the regularization procedure are discussed in “Viscous +regularization in Abaqus/Standard” in “Defining the constitutive response of cohesive elements using +a traction-separation description,” Section 32.5.6. The same technique is also used to regularize the +following: +• damaged (softening) connector response , +• damaged response of elements with plane stress formulations when they are used with the damage +model for fiber-reinforced materials , and +• damage response of elements used with the damage model for ductile metals . +You specify the amount of viscosity to be used for the regularization procedure. By default, no viscosity +is included so that no viscous regularization is performed. +Input File Usage: +*SECTION CONTROLS, VISCOSITY= +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Viscosity +Using viscous damping with connector elements in Abaqus/Standard +Material failure in connector elements often causes convergence problems in Abaqus/Standard. To +avoid such convergence problems, you can introduce viscous damping into the connector components +by specifying the value of the damping coefficient as discussed in “Connector failure behavior,” +Section 31.2.9. By default, no damping is included. +Input File Usage: +*SECTION CONTROLS, VISCOSITY= +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Viscosity +Using section controls in an import analysis +The recommended procedure for doing import analysis is to specify the enhanced hourglass control +formulation in the original analysis. Once the section controls have been specified in the original analysis, +they cannot be modified in subsequent import analyses. This ensures that the enhanced hourglass control +formulation is used in the original as well as import analyses. The default values for other section controls +are usually appropriate and should not be changed. For further details on using section controls in an +import analysis, see “Transferring results between Abaqus/Explicit and Abaqus/Standard,” Section 9.2.2. +Using section controls for flexion-torsion type connector +When the third axes of the two local coordinate systems for a flexion-torsion type connector are exactly +aligned, a numerical singularity occurs that may lead to convergence difficulties. To avoid this, a small +perturbation can be applied to the local coordinate system defined at the second connector node. +Input File Usage: +Abaqus/CAE Usage: +*SECTION CONTROLS, PERTURBATION=small angle +You cannot specify a perturbation for flexion-torsion type connectors in +Abaqus/CAE. +Using section controls for smoothed particle hydrodynamics (SPH) +You can control many aspects of the smoothed particle hydrodynamic (SPH) formulation implemented +in Abaqus/Explicit. +Using section controls for specifying the SPH kernel +For a smoothed particle hydrodynamic analysis, you can choose the order of the kernel used for +interpolation. For a list of references that discuss the various kernels that can be used, see “Smoothed +particle hydrodynamic analysis,” Section 15.1.1. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options: +*SECTION CONTROLS, KERNEL=CUBIC +*SECTION CONTROLS, KERNEL=QUADRATIC +*SECTION CONTROLS, KERNEL=QUINTIC +In Abaqus/CAE you can choose the order of the kernel used for interpolation +only in Abaqus/Explicit analyses involving the conversion of continuum +elements to SPH particles. +Mesh module: Mesh→Element Type: Conversion to particles: +Kernel: Cubic, Quadratic, or Quintic +Using section controls for specifying other SPH formulation parameters +You can control the way the smoothing length is computed . You can specify the smoothing length (units of length) for precise control +of the radius of influence associated with a given particle. Alternatively, you can scale the default +smoothing length by specifying a dimensionless smoothing length factor. By default, the smoothing +length is kept constant throughout the analysis. You can specify a variable smoothing length that will +increase or decrease during the analysis depending on the divergence of the velocity field, which is a +measure of compressive or expansive behavior. +By default, the maximum number of particles associated internally with a PC3D element cannot +exceed 140. You can modify this number; however, a large value leads to larger memory requirements +and, in most cases, to a significant degradation in performance. +You can specify a mean velocity filtering coefficient that is used for the modified coordinate updates +for particles. A zero value for this coefficient (default) leads to the classical SPH method. As discussed +in “Smoothed particle hydrodynamic analysis,” Section 15.1.1, a nonzero value for this coefficient leads +to the XSPH method. +By default, +the SPH kernels satisfy the zero-order completeness requirement. A first-order +complete corrected (normalized) kernel is also available, which is sometimes referred in the literature +as the normalized SPH (NSPH) method. In high-deformation solid mechanics analyses the use of this +kernel may lead to more accurate results. +Input File Usage: +Abaqus/CAE Usage: +*SECTION CONTROLS +first data line +smoothing length, smoothing length factor, flag for variable smoothing length, +maximum number of neighboring particles, mean velocity filtering coefficient, +flag for corrected kernel +In Abaqus/CAE you can only specify section controls for SPH parameters in +Abaqus/Explicit analyses involving the conversion of continuum elements to +SPH particles. +Using section controls for specifying the control box used for SPH particles +You can also control the rectangular region within which the particle search (finding all neighbors for +all particles) is performed. By default, a region that is 10% larger in all directions than the overall +model initial dimensions and is centered at the geometric center of the model is used. When a particle is +outside this box, it behaves like a free-flying point mass and does not contribute to the SPH calculations. +If necessary, you can enlarge (or shrink) this rectangular region by specifying the coordinates of two +opposite corners (lower left and upper right) of this box. +Input File Usage: +*SECTION CONTROLS +first data line +second data line +X, Y, and Z-coordinates (lower box corner) and X, Y, and Z-coordinates +(upper box corner) +Abaqus/CAE Usage: +In Abaqus/CAE you can only specify section controls for SPH parameters in +Abaqus/Explicit analyses involving the conversion of continuum elements to +SPH particles. +Using section controls to convert continuum elements to particles +Reduced-integration continuum elements can convert to particles if a certain criterion is met, as discussed +in “Finite element conversion to SPH particles,” Section 15.1.2. You can specify the number of particles +per parent element to be generated. Several criteria to trigger the conversion are available. +Input File Usage: +Use the following option to prevent finite elements from converting to particles: +*SECTION CONTROLS, ELEMENT CONVERSION=NO (default) +Use the following option to trigger the conversion of finite elements to particles: +*SECTION CONTROLS, ELEMENT CONVERSION=YES +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Conversion to particles: No or Yes +Specifying the number of particles generated +You specify the number of particles to be generated per isoparametric direction. The number of particles +can range from 1 to 7. +Input File Usage: +*SECTION CONTROLS, ELEMENT CONVERSION=YES +first data line +second data line +third data line +number of particles to be generated per isoparametric direction +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Conversion to particles: Yes, +PPD: number of particles to be generated per isoparametric direction +Specifying a time-based criterion +The time-based criterion is primarily intended as a modeling tool to allow all particles to convert from +the defined finite element mesh at the same time. +Input File Usage: +*SECTION CONTROLS, ELEMENT CONVERSION=YES, +CONVERSION CRITERION=TIME (default) +first data line +second data line +third data line +, time of conversion +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Conversion to particles: +Yes, Criterion: Time +Specifying a strain-based criterion +The strain-based criterion is primarily intended for cases in which you want to use a progressive +conversion approach. You specify the maximum principle strain (absolute value) when continuum +elements are to convert to SPH particles. +Input File Usage: +*SECTION CONTROLS, ELEMENT CONVERSION=YES, +CONVERSION CRITERION=STRAIN +first data line +second data line +third data line +, maximum principle strain (absolute value) +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Conversion to particles: +Yes, Criterion: Strain +Specifying a stress-based criterion +Similar to the strain-based criterion, the stress-based criterion is primarily intended for cases in which +you want to use a progressive conversion approach. You specify the maximum principle stress (absolute +value) when continuum elements are to convert to SPH particles. +Input File Usage: +*SECTION CONTROLS, ELEMENT CONVERSION=YES, +CONVERSION CRITERION=STRESS +first data line +second data line +third data line +, maximum principle stress (absolute value) +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Conversion to particles: +Yes, Criterion: Stress +Specifying a user subroutine–based criterion +The user subroutine–based criterion allows you to implement a user-defined conversion criterion. You +can control element conversion during the course of an Abaqus/Explicit analysis through any of the user +subroutines that can actively modify state variables associated with a material point, such as VUSDFLD +and VUMAT. +Input File Usage: +Use the following option to trigger a user subroutine–based conversion +criterion: +*SECTION CONTROLS, ELEMENT CONVERSION=YES, +CONVERSION CRITERION=USER +(no data lines) +Abaqus/CAE Usage: +Specifying a user subroutine–based criterion for element conversion is not +supported in Abaqus/CAE. +Continuum Elements +General-purpose continuum elements +Fluid continuum elements +Infinite elements +Warping elements +Particle elements +CONTINUUM ELEMENTS +28.1 +28.2 +28.3 +28.4 +28.1 +General-purpose continuum elements +• “Solid (continuum) elements,” Section 28.1.1 +• “One-dimensional solid (link) element library,” Section 28.1.2 +• “Two-dimensional solid element library,” Section 28.1.3 +• “Three-dimensional solid element library,” Section 28.1.4 +• “Cylindrical solid element library,” Section 28.1.5 +• “Axisymmetric solid element library,” Section 28.1.6 +• “Axisymmetric solid elements with nonlinear, asymmetric deformation,” Section 28.1.7 +28.1.1 +SOLID (CONTINUUM) ELEMENTS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Choosing the element’s dimensionality,” Section 27.1.2 +• “One-dimensional solid (link) element library,” Section 28.1.2 +• “Two-dimensional solid element library,” Section 28.1.3 +• “Three-dimensional solid element library,” Section 28.1.4 +• “Cylindrical solid element library,” Section 28.1.5 +• “Axisymmetric solid element library,” Section 28.1.6 +• “Axisymmetric solid elements with nonlinear, asymmetric deformation,” Section 28.1.7 +• *SOLID SECTION +• *HOURGLASS STIFFNESS +• “Creating homogeneous solid sections,” Section 12.13.1 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Creating composite solid sections,” Section 12.13.4 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Creating electromagnetic solid sections,” Section 12.13.5 of the Abaqus/CAE User’s Manual, in +the online HTML version of this manual +• “Assigning a material orientation” in “Assigning a material orientation or rebar reference +orientation,” Section 12.15.4 of the Abaqus/CAE User’s Manual, in the online HTML version of +this manual +• Chapter 23, “Composite layups,” of the Abaqus/CAE User’s Manual +Overview +Solid (continuum) elements: +• are the standard volume elements of Abaqus; +• do not include structural elements such as beams, shells, membranes, and trusses; special-purpose +elements such as gap elements; or connector elements such as connectors, springs, and dashpots; +• can be composed of a single homogeneous material or, in Abaqus/Standard, can include several +layers of different materials for the analysis of laminated composite solids; and +• are more accurate if not distorted, particularly for quadrilaterals and hexahedra. The triangular and +tetrahedral elements are less sensitive to distortion. +Typical applications +The solid (or continuum) elements in Abaqus can be used for linear analysis and for complex nonlinear +analyses involving contact, plasticity, and large deformations. They are available for stress, heat transfer, +acoustic, coupled thermal-stress, coupled pore fluid-stress, piezoelectric, magnetostatic, electromagnetic, +and coupled thermal-electrical analyses . +Choosing an appropriate element +There are some differences in the solid element +Abaqus/Explicit. +Abaqus/Standard solid element library +libraries available in Abaqus/Standard and +The Abaqus/Standard solid element library includes first-order (linear) interpolation elements and +second-order (quadratic) interpolation elements in one, two, or three dimensions. Triangles and +quadrilaterals are available in two dimensions; and tetrahedra, triangular prisms, and hexahedra +(“bricks”) are provided in three dimensions. Modified second-order triangular and tetrahedral +elements are also provided. +Curved (parabolic) edges can be used on the quadratic elements but are not recommended for +pore pressure or coupled temperature-displacement elements. Cylindrical elements are provided +for structures with edges that are initially circular. +In addition, reduced-integration, hybrid, and incompatible mode elements are available in +Abaqus/Standard. +Electromagnetic elements, based on an edge-based interpolation of the magnetic vector +potential, are provided both in two and three dimensions. +Abaqus/Explicit solid element library +The Abaqus/Explicit solid element library includes first-order (linear) interpolation elements +and modified second-order interpolation elements in two or three dimensions. Triangular and +quadrilateral first-order elements are available in two dimensions; and tetrahedral, triangular +prism, and hexahedral (“brick”) first-order elements are available in three dimensions. The +modified second-order elements are limited to triangles and tetrahedra. The acoustic elements in +Abaqus/Explicit are limited to first-order (linear) interpolations. For incompatible mode elements +only three-dimensional elements are available. +Various two-dimensional models (plane stress, plane strain, axisymmetric) are available in both +Abaqus/Standard and Abaqus/Explicit. See “Choosing the element’s dimensionality,” Section 27.1.2, +for details. +Given the wide variety of element types available, it is important to select the correct element +for a particular application. Choosing an element for a particular analysis can be simplified by +full or reduced integration; +considering specific element characteristics: first- or second-order; +hexahedra/quadrilaterals or tetrahedra/triangles; or normal, hybrid, or incompatible mode formulation. +By considering each of these aspects carefully, the best element for a given analysis can be selected. +Choosing between first- and second-order elements +In first-order plane strain, generalized plane strain, axisymmetric quadrilateral, hexahedral solid +elements, and cylindrical elements, the strain operator provides constant volumetric strain throughout +the element. This constant strain prevents mesh “locking” when the material response is approximately +incompressible . +Second-order elements provide higher accuracy in Abaqus/Standard than first-order elements for +“smooth” problems that do not involve severe element distortions. They capture stress concentrations +more effectively and are better for modeling geometric features: they can model a curved surface with +fewer elements. Finally, second-order elements are very effective in bending-dominated problems. +First-order triangular and tetrahedral elements should be avoided as much as possible in stress +analysis problems; the elements are overly stiff and exhibit slow convergence with mesh refinement, +which is especially a problem with first-order tetrahedral elements. If they are required, an extremely +fine mesh may be needed to obtain results of sufficient accuracy. +Choosing between full- and reduced-integration elements +Reduced integration uses a lower-order integration to form the element stiffness. The mass matrix and +distributed loadings use full integration. Reduced integration reduces running time, especially in three +dimensions. For example, element type C3D20 has 27 integration points, while C3D20R has only 8; +therefore, element assembly is roughly 3.5 times more costly for C3D20 than for C3D20R. +In Abaqus/Standard you can choose between full or reduced integration for quadrilateral and +hexahedral (brick) elements. In Abaqus/Explicit you can choose between full or reduced integration +for hexahedral (brick) elements. Only reduced-integration first-order elements are available for +quadrilateral elements in Abaqus/Explicit; the elements with reduced integration are also referred to as +uniform strain or centroid strain elements with hourglass control. +Second-order reduced-integration elements in Abaqus/Standard generally yield more accurate +results than the corresponding fully integrated elements. However, for first-order elements the accuracy +achieved with full versus reduced integration is largely dependent on the nature of the problem. +Hourglassing +Hourglassing can be a problem with first-order, reduced-integration elements (CPS4R, CAX4R, C3D8R, +etc.) in stress/displacement analyses. Since the elements have only one integration point, it is possible +for them to distort in such a way that the strains calculated at the integration point are all zero, which, in +turn, leads to uncontrolled distortion of the mesh. First-order, reduced-integration elements in Abaqus +include hourglass control, but they should be used with reasonably fine meshes. Hourglassing can also +be minimized by distributing point loads and boundary conditions over a number of adjacent nodes. +In Abaqus/Standard the second-order reduced-integration elements, with the exception of the +27-node C3D27R and C3D27RH elements, do not have the same difficulty and are recommended in all +cases when the solution is expected to be smooth. The C3D27R and C3D27RH elements have three +unconstrained, propagating hourglass modes when all 27 nodes are present. These elements should +not be used with all 27 nodes, unless they are sufficiently constrained through boundary conditions. +First-order elements are recommended when large strains or very high strain gradients are expected. +Shear and volumetric locking +Fully integrated elements in Abaqus/Standard and Abaqus/Explicit do not hourglass but may suffer +from “locking” behavior: both shear and volumetric locking. Shear locking occurs in first-order, fully +integrated elements (CPS4, CPE4, C3D8, etc.) that are subjected to bending. The numerical formulation +of the elements gives rise to shear strains that do not really exist—the so-called parasitic shear. Therefore, +these elements are too stiff in bending, in particular if the element length is of the same order of magnitude +as or greater than the wall thickness. See “Performance of continuum and shell elements for linear +analysis of bending problems,” Section 2.3.5 of the Abaqus Benchmarks Manual, for further discussion +of the bending behavior of solid elements. +Volumetric locking occurs in fully integrated elements when the material behavior is (almost) +incompressible. Spurious pressure stresses develop at the integration points, causing an element to +behave too stiffly for deformations that should cause no volume changes. +If materials are almost +incompressible (elastic-plastic materials for which the plastic strains are incompressible), second-order, +fully integrated elements start to develop volumetric locking when the plastic strains are on the order of +the elastic strains. However, the first-order, fully integrated quadrilaterals and hexahedra use selectively +reduced integration (reduced integration on the volumetric terms). Therefore, these elements do not +lock with almost incompressible materials. Reduced-integration, second-order elements develop +volumetric locking for almost incompressible materials only after significant straining occurs. In this +case, volumetric locking is often accompanied by a mode that looks like hourglassing. Frequently, this +problem can be avoided by refining the mesh in regions of large plastic strain. +If volumetric locking is suspected, check the pressure stress at the integration points (printed output). +If the pressure values show a checkerboard pattern, changing significantly from one integration point to +the next, volumetric locking is occurring. Choosing a quilt-style contour plot in the Visualization module +of Abaqus/CAE will show the effect. +Specifying nondefault section controls +You can specify a nondefault hourglass control formulation or scale factor for reduced-integration +first-order elements (4-node quadrilaterals and 8-node bricks with one integration point). See “Section +controls,” Section 27.1.4, for more information about section controls. +In Abaqus/Explicit section controls can also be used to specify a nondefault kinematic formulation +for 8-node brick elements, the accuracy order of the element formulation, and distortion control for either +4-node quadrilateral or 8-node brick elements. Section controls are also used with coupled temperature- +displacement elements in Abaqus/Explicit to change the default values for the mechanical response +analysis. +In Abaqus/Standard you can specify nondefault hourglass stiffness factors based on the default total +stiffness approach for reduced-integration first-order elements (4-node quadrilaterals and 8-node bricks +with one integration point) and modified tetrahedral and triangular elements. +There are no hourglass stiffness factors or scale factors for the nondefault enhanced hourglass +control formulation. See “Section controls,” Section 27.1.4, for more information about hourglass +control. +Input File Usage: +Use both of the following options to associate a section control definition with +the element section definition: +*SECTION CONTROLS, NAME=name +*SOLID SECTION, CONTROLS=name +Use both of the following options in Abaqus/Standard to specify nondefault +hourglass stiffness factors for the total stiffness approach: +*SOLID SECTION +*HOURGLASS STIFFNESS +Abaqus/CAE Usage: Mesh module: +Element Type: Element Controls +Element Type: Hourglass stiffness: Specify +Choosing between bricks/quadrilaterals and tetrahedra/triangles +Triangular and tetrahedral elements are geometrically versatile and are used in many automatic meshing +algorithms. +It is very convenient to mesh a complex shape with triangles or tetrahedra, and the +second-order and modified triangular and tetrahedral elements (CPE6, CPE6M, C3D10, C3D10M, +etc.) in Abaqus are suitable for general usage. However, a good mesh of hexahedral elements usually +provides a solution of equivalent accuracy at less cost. Quadrilaterals and hexahedra have a better +convergence rate than triangles and tetrahedra, and sensitivity to mesh orientation in regular meshes +is not an issue. However, triangles and tetrahedra are less sensitive to initial element shape, whereas +first-order quadrilaterals and hexahedra perform better if their shape is approximately rectangular. The +elements become much less accurate when they are initially distorted . +First-order triangles and tetrahedra are usually overly stiff, and extremely fine meshes are required +to obtain accurate results. As mentioned earlier, fully integrated first-order triangles and tetrahedra in +Abaqus/Standard also exhibit volumetric locking in incompressible problems. As a rule, these elements +should not be used except as filler elements in noncritical areas. Therefore, try to use well-shaped +elements in regions of interest. +Tetrahedral and wedge elements +For stress/displacement analyses the first-order tetrahedral element C3D4 is a constant stress tetrahedron, +which should be avoided as much as possible; the element exhibits slow convergence with mesh +refinement. This element provides accurate results only in general cases with very fine meshing. +Therefore, C3D4 is recommended only for filling in regions of low stress gradient in meshes of C3D8 +or C3D8R elements, when the geometry precludes the use of C3D8 or C3D8R elements throughout the +model. For tetrahedral element meshes the second-order or the modified tetrahedral elements, C3D10 +or C3D10M, should be used. +Similarly, the linear version of the wedge element C3D6 should generally be used only when +necessary to complete a mesh, and, even then, the element should be far from any areas where accurate +results are needed. This element provides accurate results only with very fine meshing. +Modified triangular and tetrahedral elements +to regular second-order +triangular and tetrahedral elements. +A family of modified 6-node triangular and 10-node tetrahedral elements is available that provides +improved performance over the first-order triangular and tetrahedral elements and that occasionally +provides improved behavior +In +Abaqus/Explicit these modified triangular and tetrahedral elements are the only 6-node triangular and +10-node tetrahedral elements available. Regular second-order triangular and tetrahedral elements are +typically preferable in Abaqus/Standard; however, regular second-order triangular and tetrahedral +elements may exhibit “volumetric locking” when incompressibility is approached, such as in problems +with a large amount of plastic deformation. As discussed in “Three-dimensional surfaces with +second-order faces and a node-to-surface formulation” in “Common difficulties associated with contact +modeling in Abaqus/Standard,” Section 38.1.2, regular second-order tetrahedral elements cannot +underly a slave surface for the node-to-surface contact formulation with strict enforcement of a “hard” +contact relationship. This limitation is typically not significant because the surface-to-surface contact +formulation and penalty contact enforcement are generally recommended. +Modified triangular and tetrahedral elements work well in contact, exhibit minimal shear and +volumetric locking, and are robust during finite deformation . These elements use a lumped matrix formulation for dynamic analysis. Modified triangular +elements are provided for planar and axisymmetric analysis, and modified tetrahedra are provided +for three-dimensional analysis. +In addition, hybrid versions of these elements are provided in +Abaqus/Standard for use with incompressible and nearly incompressible constitutive models. +When the total stiffness approach is chosen, modified tetrahedral and triangular elements (C3D10M, +CPS6M, CAX6M, etc.) use hourglass control associated with their internal degrees of freedom. The +hourglass modes in these elements do not usually propagate; hence, the hourglass stiffness is usually not +as significant as for first-order elements. +For most Abaqus/Standard analysis models the same mesh density appropriate for the regular +second-order triangular and tetrahedral elements can be used with the modified elements to achieve +similar accuracy. For comparative results, see the following: +• “Geometrically nonlinear analysis of a cantilever beam,” Section 2.1.2 of the Abaqus Benchmarks +Manual +• “Performance of continuum and shell elements for linear analysis of bending problems,” +Section 2.3.5 of the Abaqus Benchmarks Manual +• “LE1: Plane stress elements—elliptic membrane,” Section 4.2.1 of the Abaqus Benchmarks Manual +• “LE10: Thick plate under pressure,” Section 4.2.10 of the Abaqus Benchmarks Manual +• “FV32: Cantilevered tapered membrane,” Section 4.4.7 of the Abaqus Benchmarks Manual +• “FV52: Simply supported “solid” square plate,” Section 4.4.10 of the Abaqus Benchmarks Manual +However, in analyses involving thin bending situations with finite deformations and in frequency analyses where high bending +modes need to be captured accurately , the mesh has to be more refined for the modified triangular and +tetrahedral elements (by at least one and a half times) to attain accuracy comparable to the regular second- +order elements. +The modified triangular and tetrahedral elements might not be adequate to be used in the coupled +pore fluid diffusion and stress analysis in the presence of large pore pressure fields if enhanced hourglass +control is used. +The modified elements are more expensive computationally than lower-order quadrilaterals and +hexahedron and sometimes require a more refined mesh for the same level of accuracy. However, in +Abaqus/Explicit they are provided as an attractive alternative to the lower-order triangles and tetrahedron +to take advantage of automatic triangular and tetrahedral mesh generators. +Compatibility with other elements +The modified triangular and tetrahedral elements are incompatible with the regular second-order solid +elements in Abaqus/Standard. Thus, they should not be connected with these elements in a mesh. +Surface stress output +In areas of high stress gradients, stresses extrapolated from the integration points to the nodes are +not as accurate for the modified elements as for similar second-order triangles and tetrahedra in +Abaqus/Standard. In cases where more accurate surface stresses are needed, the surface can be coated +with membrane elements that have a significantly lower stiffness than the underlying material. The +stresses in these membrane elements will then reflect more accurately the surface stress and can be used +for output purposes. +Fully constrained displacements +In Abaqus/Standard if all the displacement degrees of freedom on all the nodes of a modified element +are constrained with boundary conditions, a similar boundary condition is applied to an internal node in +the element. If a distributed load is subsequently applied to this element, the reported reaction forces at +the nodes you defined will not sum up to the applied load since some of the applied load is taken by the +internal node whose reaction force is not reported. +Choosing between regular and hybrid elements +Hybrid elements are intended primarily for use with incompressible and almost incompressible material +these elements are available only in Abaqus/Standard. When the material response is +behavior; +incompressible, the solution to a problem cannot be obtained in terms of the displacement history only, +since a purely hydrostatic pressure can be added without changing the displacements. +Almost incompressible material behavior +Near-incompressible behavior occurs when the bulk modulus is very much larger than the shear +modulus (for example, in linear elastic materials where the Poisson’s ratio is greater than .48) and +exhibits behavior approaching the incompressible limit: a very small change in displacement produces +extremely large changes in pressure. Therefore, a purely displacement-based solution is too sensitive to +be useful numerically (for example, computer round-off may cause the method to fail). +This singular behavior is removed from the system by treating the pressure stress as an +independently interpolated basic solution variable, coupled to the displacement solution through the +constitutive theory and the compatibility condition. This independent interpolation of pressure stress is +the basis of the hybrid elements. Hybrid elements have more internal variables than their nonhybrid +counterparts and are slightly more expensive. See “Hybrid incompressible solid element formulation,” +Section 3.2.3 of the Abaqus Theory Manual, for further details. +Fully incompressible material behavior +Hybrid elements must be used if the material is fully incompressible (except in the case of plane stress +since the incompressibility constraint can be satisfied by adjusting the thickness). If the material is almost +incompressible and hyperelastic, hybrid elements are still recommended. For almost incompressible, +elastic-plastic materials and for compressible materials, hybrid elements offer insufficient advantage and, +hence, should not be used. +For Mises and Hill plasticity the plastic deformation is fully incompressible; therefore, the rate of +total deformation becomes incompressible as the plastic deformation starts to dominate the response. +All of the quadrilateral and brick elements in Abaqus/Standard can handle this rate-incompressibility +condition except for the fully integrated quadrilateral and brick elements without the hybrid formulation: +CPE8, CPEG8, CAX8, CGAX8, and C3D20. These elements will “lock” (become overconstrained) as +the material becomes more incompressible. +Elastic strains in hybrid elements +Hybrid elements use an independent interpolation for the hydrostatic pressure, and the elastic volumetric +strain is calculated from the pressure. Hence, the elastic strains agree exactly with the stress, but they +agree with the total strain only in an element average sense and not pointwise, even if no inelastic strains +are present. For isotropic materials this behavior is noticeable only in second-order, fully integrated +hybrid elements. +In these elements the hydrostatic pressure (and, thus, the volumetric strain) varies +linearly over the element, whereas the total strain may exhibit a quadratic variation. +For anisotropic materials this behavior also occurs in first-order, fully integrated hybrid elements. +In such materials there is typically a strong coupling between volumetric and deviatoric behavior: +volumetric strain will give rise to deviatoric stresses and, conversely, deviatoric strains will give rise +to hydrostatic pressure. Hence, the constant hydrostatic pressure enforced in the fully integrated, +first-order hybrid elements does not generally yield a constant elastic strain; whereas the total volume +strain is always constant for these elements, as discussed earlier in this section. Therefore, hybrid +elements are not recommended for use with anisotropic materials unless the material is approximately +incompressible, which usually implies that the coupling between deviatoric and volume behavior is +relatively weak. +Using hybrid elements with material models that exhibit volumetric plasticity +If the material model exhibits volumetric plasticity, such as the (capped) Drucker-Prager model, slow +convergence or convergence problems may occur if second-order hybrid elements are used. In that case +good results can usually be obtained with regular (nonhybrid) second-order elements. +Determining the need for hybrid elements +For nearly incompressible materials a displaced shape plot that shows a more or less homogeneous +but nonphysical pattern of deformation is an indication of mesh locking. As previously discussed, +fully integrated elements should be changed to reduced-integration elements in this case. +If +reduced-integration elements are already being used, the mesh density should be increased. Finally, +hybrid elements can be used if problems persist. +Hybrid triangular and tetrahedral elements +The following hybrid, triangular, two-dimensional and axisymmetric elements should be used only for +mesh refinement or to fill in regions of meshes of quadrilateral elements: CPE3H, CPEG3H, CAX3H, and +CGAX3H. Hybrid, three-dimensional tetrahedral elements C3D4H and prism elements C3D6H should +be used only for mesh refinement or to fill in regions of meshes of brick-type elements. Since each +C3D6H element introduces a constraint equation in a fully incompressible problem, a mesh containing +only these elements will be overconstrained. Abutting regions of C3D4H elements with different material +properties should be tied rather than sharing nodes to allow discontinuity jumps in the pressure and +volumetric fields. +In addition, the second-order three-dimensional hybrid elements C3D10H, C3D10MH, C3D15H, +and C3D15VH are significantly more expensive than their nonhybrid counterparts. +Multi-purpose, improved surface stress visualization tetrahedra +The C3D10I tetrahedron has been developed for improved bending results in coarse meshes while +avoiding pressure locking in metal plasticity and quasi-incompressible and incompressible rubber +elasticity. These elements are available only in Abaqus/Standard. Internal pressure degrees of freedom +are activated automatically for a given element once the material exhibits behavior approaching the +incompressible limit (i.e., an effective Poisson’s ratio above .45). This unique feature of C3D10I +elements make it especially suitable for modeling metal plasticity, since it activates the pressure degrees +of freedom only in the regions of the model where the material is incompressible. Once the internal +degrees of freedom are activated, C3D10I elements have more internal variables than either hybrid or +nonhybrid elements and, thus, are more expensive. This element also uses a unique 11-point integration +scheme, providing a superior stress visualization scheme in coarse meshes as it avoids errors due to the +extrapolation of stress components from the integration points to the nodes. +Incompatible mode elements +Incompatible mode elements (CPS4I, CPE4I, CAX4I, CPEG4I, and C3D8I and the corresponding hybrid +elements) are first-order elements that are enhanced by incompatible modes to improve their bending +behavior; all of these elements are available in Abaqus/Standard and only element C3D8I is available in +Abaqus/Explicit. +In addition to the standard displacement degrees of freedom, incompatible deformation modes are +added internally to the elements. The primary effect of these modes is to eliminate the parasitic shear +stresses that cause the response of the regular first-order displacement elements to be too stiff in bending. +In addition, these modes eliminate the artificial stiffening due to Poisson’s effect in bending (which +is manifested in regular displacement elements by a linear variation of the stress perpendicular to the +bending direction). In the nonhybrid elements—except for the plane stress element, CPS4I—additional +incompatible modes are added to prevent locking of the elements with approximately incompressible +material behavior. For fully incompressible material behavior the corresponding hybrid elements must +be used. +Because of the added internal degrees of freedom due to the incompatible modes (4 for CPS4I; 5 for +CPE4I, CAX4I, and CPEG4I; and 13 for C3D8I), these elements are somewhat more expensive than the +regular first-order displacement elements; however, they are significantly more economical than second- +order elements. The incompatible mode elements use full integration and, thus, have no hourglass modes. +in “Continuum elements with +Incompatible mode elements are discussed in more detail +incompatible modes,” Section 3.2.5 of the Abaqus Theory Manual. +Shape considerations +The incompatible mode elements perform almost as well as second-order elements in many situations +if the elements have an approximately rectangular shape. The performance is reduced considerably if +the elements have a parallelogram shape. The performance of trapezoidal-shaped incompatible mode +elements is not much better than the performance of the regular, fully integrated, first-order interpolation +elements; see “Performance of continuum and shell elements for linear analysis of bending problems,” +Section 2.3.5 of the Abaqus Benchmarks Manual, which illustrates the loss of accuracy associated with +distorted elements. +Using incompatible mode elements in large-strain applications +Incompatible mode elements should be used with caution in applications involving large compressive +strains. Convergence may be slow at times, and inaccuracies may accumulate in hyperelastic +applications. Hence, erroneous residual stresses may sometimes appear in hyperelastic elements that +are unloaded after having been subjected to a complex deformation history. +Using incompatible mode elements with regular elements +Incompatible mode elements can be used in the same mesh with regular solid elements. Generally +the incompatible mode elements should be used in regions where bending response must be modeled +accurately, and they should be of rectangular shape to provide the most accuracy. While these elements +often provide accurate response in such cases, it is generally preferable to use structural elements (shells +or beams) to model structural components. +Variable node elements +Variable node elements (such as C3D27 and C3D15V) allow midface nodes to be introduced on any +element face (on any rectangular face only for the triangular prism C3D15V). The choice is made by the +nodes specified in the element definition. These elements are available only in Abaqus/Standard and can +be used quite generally in any three-dimensional model. The C3D27 family of elements is frequently +used as the ring of elements around a crack line. +Cylindrical elements +Cylindrical elements (CCL9, CCL9H, CCL12, CCL12H, CCL18, CCL18H, CCL24, CCL24H, and +CCL24RH) are available only in Abaqus/Standard for precise modeling of regions in a structure with +circular geometry, such as a tire. The elements make use of trigonometric functions to interpolate +displacements along the circumferential direction and use regular isoparametric interpolation in the +radial or cross-sectional plane of the element. All the elements use three nodes along the circumferential +direction and can span angles between 0 and 180°. Elements with both first-order and second-order +interpolation in the cross-sectional plane are available. +The geometry of the element is defined by specifying nodal coordinates in a global Cartesian system. +The default nodal output is also provided in a global Cartesian system. Output of stress, strain, and other +material point output quantities are done, by default, in a fixed local cylindrical system where direction 1 +is the radial direction, direction 2 is the axial direction, and direction 3 is the circumferential direction. +This default system is computed from the reference configuration of the element. An alternative local +system can be defined . In this case the output of stress, strain, and +other material point quantities is done in the oriented system. +The cylindrical elements can be used in the same mesh with regular elements. In particular, regular +solid elements can be connected directly to the nodes on the cross-sectional plane of cylindrical elements. +For example, any face of a C3D8 element can share nodes with the cross-sectional faces (faces 1 and 2; +see “Cylindrical solid element library,” Section 28.1.5, for a description of the element faces) of a CCL12 +element. Regular elements can also be connected along the circular edges of cylindrical elements by +using a surface-based tie constraint (“Mesh tie constraints,” Section 34.3.1) provided that the cylindrical +elements do not span a large segment. However, such usage may result in spurious oscillations in the +solution near the tied surfaces and should be avoided when an accurate solution in this region is required. +Compatible membrane elements (“Membrane elements,” Section 29.1.1) and surface elements with +rebar (“Surface elements,” Section 32.7.1) are available for use with cylindrical solid elements. +All elements with first-order interpolation in the cross-sectional plane use full integration for the +deviatoric terms and reduced integration for the volumetric terms and, thus, have no hourglass modes and +do not lock with almost incompressible materials. The hybrid elements with first-order and second-order +interpolation in the cross-sectional plane use an independent interpolation for hydrostatic pressure. +Summary of recommendations for element usage +The following recommendations apply to both Abaqus/Standard and Abaqus/Explicit: +• Make all elements as “well shaped” as possible to improve convergence and accuracy. +• If an automatic tetrahedral mesh generator is used, use the second-order elements C3D10 (in +Abaqus/Standard) or C3D10M (in Abaqus/Explicit). Use the modified tetrahedral element +C3D10M in Abaqus/Standard in analyses with large amounts of plastic deformation. +• If possible, use hexahedral elements in three-dimensional analyses since they give the best results +for the minimum cost. +Abaqus/Standard users should also consider the following recommendations: +• For linear and “smooth” nonlinear problems use reduced-integration, second-order elements if +possible. +• Use second-order, fully integrated elements close to stress concentrations to capture the severe +gradients in these regions. However, avoid these elements in regions of finite strain if the material +response is nearly incompressible. +• Use first-order quadrilateral or hexahedral elements or the modified triangular and tetrahedral +If the mesh distortion is severe, use +elements for problems involving large distortions. +reduced-integration, first-order elements. +• If +the problem involves bending and large distortions, use a fine mesh of first-order, +reduced-integration elements. +• Hybrid elements must be used if the material is fully incompressible (except when using plane stress +elements). Hybrid elements should also be used in some cases with nearly incompressible materials. +• Incompatible mode elements can give very accurate results in problems dominated by bending. +Naming convention +The naming conventions for solid elements depend on the element dimensionality. +One-dimensional, two-dimensional, three-dimensional, and axisymmetric elements +One-dimensional, two-dimensional, three-dimensional, and axisymmetric solid elements in Abaqus are +named as follows: +3D 20 +R H T +Optional: +heat transfer convection/diffusion with +dispersion control (D), +coupled temperature-displacement (T), +piezoelectric (E), or pore pressure (P) +hybrid (optional) +Optional: +reduced integration (R), +incompatible mode quad/bricks or +improved surface stress formulation tets (I), or modified (M) +number of nodes +link (1D), plane strain (PE), plane stress (PS), +generalized plane strain (PEG), two-dimensional (2D), +three-dimensional (3D), axisymmetric (AX), or +axisymmetric with twist (GAX) +continuum stress/displacement (C), heat transfer or mass diffusion (DC), +heat transfer convection/diffusion (DCC), acoustic (AC), electromagnetic (EMC), +or coupled thermal-electrical-structural (Q) +For example, CAX4R is an axisymmetric continuum stress/displacement, 4-node, reduced-integration +element; and CPS8RE is an 8-node, reduced-integration, plane stress piezoelectric element. The +exception for this naming convention is C3D6 and C3D6T in Abaqus/Explicit, which are 6-node linear +triangular prism, reduced integration elements. +The pore pressure elements violate this naming convention slightly: the hybrid elements have the +letter H after the letter P. For example, CPE8PH is an 8-node, hybrid, plane strain, pore pressure element. +Axisymmetric elements with nonlinear asymmetric deformation +The axisymmetric solid elements with nonlinear asymmetric deformation in Abaqus/Standard are named +as follows: +AXA 8 R H P +number of Fourier modes +pore pressure (optional) +hybrid (optional) +reduced integration (optional) +number of nodes (in the reference plane) +axisymmetric with nonlinear, asymmetric deformation +continuum stress/displacement +For example, CAXA4RH1 is a 4-node, reduced-integration, hybrid, axisymmetric element with +nonlinear asymmetric deformation and one Fourier mode . +Cylindrical elements +The cylindrical elements in Abaqus/Standard are named as follows: +CL +24 +R H +hybrid (optional) +reduced integration (optional) +number of nodes +cylindrical +continuum stress/displacement +For example, CCL24RH is a 24-node, hybrid, reduced-integration cylindrical element. +Defining the element’s section properties +A solid section definition is used to define the section properties of solid elements. +In Abaqus/Standard solid elements can be composed of a single homogeneous material or +In +can include several layers of different materials for the analysis of laminated composite solids. +Abaqus/Explicit solid elements can be composed only of a single homogeneous material. +Defining homogeneous solid elements +You must associate a material definition (“Material data definition,” Section 21.1.2) with the solid section +definition. In an Abaqus/Standard analysis spatially varying material behavior defined with one or more +distributions (“Distribution definition,” Section 2.8.1) can be assigned to the solid section definition. In +addition, you must associate the section definition with a region of your model. +In Abaqus/Standard if any of the material behaviors assigned to the solid section definition (through +the material definition) are defined with distributions, spatially varying material properties are applied to +all elements associated with the solid section. Default material behaviors (as defined by the distributions) +are applied to any element that is not specifically included in the associated distribution. +Input File Usage: +*SOLID SECTION, MATERIAL=name, ELSET=name +where the ELSET parameter refers to a set of solid elements. +Abaqus/CAE Usage: +Property module: +Create Section: select Solid as the section Category and Homogeneous +or Electromagnetic, Solid as the section Type: Material: name +Assign→Section: select regions +Assigning an orientation definition +You can associate a material orientation definition with solid elements . +A spatially varying local coordinate system defined with a distribution (“Distribution definition,” +Section 2.8.1) can be assigned to the solid section definition. +If the orientation definition assigned to the solid section definition is defined with distributions, +spatially varying local coordinate systems are applied to all elements associated with the solid section. +A default local coordinate system (as defined by the distributions) is applied to any element that is not +specifically included in the associated distribution. +Input File Usage: +Abaqus/CAE Usage: +*SOLID SECTION, ORIENTATION=name +Property module: Assign→Material Orientation +Defining the geometric attributes, if required +For some element types additional geometric attributes are required, such as the cross-sectional area for +one-dimensional elements or the thickness for two-dimensional plane elements. The attributes required +for a particular element type are defined in the solid element libraries. These attributes are given as part +of the solid section definition. +Defining composite solid elements in Abaqus/Standard +The use of composite solids is limited to three-dimensional brick elements that have only displacement +degrees of freedom (they are not available for coupled temperature-displacement elements, piezoelectric +elements, pore pressure elements, and continuum cylindrical elements). Composite solid elements are +primarily intended for modeling convenience. They usually do not provide a more accurate solution than +composite shell elements. +The thickness, the number of section points required for numerical integration through each layer +(discussed below), and the material name and orientation associated with each layer are specified as part +of the composite solid section definition. In Abaqus/Standard spatially varying orientation angles can be +specified on a layer using distributions (“Distribution definition,” Section 2.8.1). +The material layers can be stacked in any of the three isoparametric coordinates, parallel to opposite +faces of the isoparametric master element as shown in Figure 28.1.1–1. The number of integration +points within a layer at any given section point depends on the element type. Figure 28.1.1–1 shows +the integration points for a fully integrated element. +stack direction = 1 +from face 6 to face 4 +stack direction = 2 +from face 3 to face 5 +stack direction = 3 +from face 1 to face 2 +face 6 +face 1 +face 3 +Figure 28.1.1–1 Stacking direction and associated element faces and positions of element +integration point output variables in the layer plane. +The element faces are defined by the order in which the nodes are specified when the element is defined. +The element matrices are obtained by numerical integration. Gauss quadrature is used in the plane +of the lamina, and Simpson’s rule is used in the stacking direction. If one section point through the layer +is used, it will be located in the middle of the layer thickness. The location of the section points in the +plane of the lamina coincides with the location of the integration points. The number of section points +required for the integration through the thickness of each layer is specified as part of the solid section +definition; this number must be an odd number. The integration points for a fully integrated second-order +composite element are shown in Figure 28.1.1–1, and the numbering of section points that are associated +with an arbitrary integration point in a composite solid element is illustrated in Figure 28.1.1–2. +15 +stack +direction +11 +10 +layer 3 +layer 2 +layer 1 +(5 section points per layer) +Figure 28.1.1–2 Numbering of section points in a three-layered composite element. +The thickness of each layer may not be constant from integration point to integration point within an +element since the element dimensions in the stack direction may vary. Therefore, it is defined indirectly +by specifying the ratio between the thickness and the element length along the stack direction in the +solid section definition, as shown in Figure 28.1.1–3. Using the ratios that are defined for all layers, +actual thicknesses will be determined at each integration point such that their sum equals the element +length in the stack direction. The thickness ratios for the layers need not reflect actual element or model +dimensions. +0.05 +0.10 +0.05 +(a) +composite solid section with the material +layers stacked in direction 3 +0.10 +0.20 +0.10 +layer 3 +layer 2 +layer 1 +stack +direction +0.25 +0.50 +0.25 +(b) +thickness ratios +Figure 28.1.1–3 Lamina in (a) real space and (b) isoparametric space. +Unless your model is relatively simple, you will find it increasingly difficult to define your model +using composite solid sections as you increase the number of layers and as you assign different sections to +different regions. It can also be cumbersome to redefine the sections after you add new layers or remove +or reposition existing layers. To manage a large number of layers in a typical composite model, you may +want to use the composite layup functionality in Abaqus/CAE. For more information, see Chapter 23, +“Composite layups,” of the Abaqus/CAE User’s Manual. +Input File Usage: +*SOLID SECTION, COMPOSITE, STACK DIRECTION=1, 2, or 3, +ELSET=name +thickness, number of integration points, material name, orientation name +Abaqus/CAE Usage: +Abaqus/CAE uses a composite layup or a composite solid section to define the +layers of a composite solid. +Use the following option for a composite layup: +Property module: Create Composite Layup: select Solid as the +Element Type: specify stacking direction, regions, thicknesses, number +of integration points, materials, and orientations +Use the following options for a composite solid section: +Property module: +Create Section: select Solid as the section Category and Composite +as the section Type +Assign→Material Orientation: select regions: Use Default Orientation +or Other Method: Stacking Direction: Element direction 1, Element +direction 2, Element direction 3, or From orientation +Assign→Section: select regions +Output locations for composite solid elements +You specify the location of the output variables in the plane of the lamina (layers) when you request output +of element variables. For example, you can request values at the centroid of each layer. In addition, you +specify the number of output points through the thickness of the layers by providing a list of the “section +points.” The default section points for the output are the first and the last section point corresponding +to the bottom and the top face, respectively . See “Element output” in “Output +to the data and results files,” Section 4.1.2, and “Element output” in “Output to the output database,” +Section 4.1.3, for more information. +Modeling thick composites with solid elements in Abaqus/Standard +While laminated composite solids are typically modeled using shell elements, the following cases require +three-dimensional brick elements with one or multiple brick elements per layer: when transverse shear +effects are predominant; when the normal stress cannot be ignored; and when accurate interlaminar +stresses are required, such as near localized regions of complex loading or geometry. +One case in which shell elements perform somewhat better than solid elements is in modeling the +transverse shear stress through the thickness. The transverse shear stresses in solid elements usually do +not vanish at the free surfaces of the structure and are usually discontinuous at layer interfaces. This +deficiency may be present even if several elements are used in the discretization through the section +thickness. Since the transverse shear stresses in thick shell elements are calculated by Abaqus on the +basis of linear elasticity theory, such stresses are often better estimated by thick shell elements than by +solid elements . +Defining pressure loads on continuum elements +The convention used for pressure loading on a continuum element is that positive pressure is directed into +the element; that is, it pushes on the element. In large-strain analyses special consideration is necessary +for plane stress elements that are pressure loaded on their edges; this issue is discussed in “Distributed +loads,” Section 33.4.3. +Using solid elements in a rigid body +All solid elements can be included in a rigid body definition. When solid elements are assigned to a +rigid body, they are no longer deformable and their motion is governed by the motion of the rigid body +reference node . +Section properties for solid elements that are part of a rigid body must be defined to properly account +for rigid body mass and rotary inertia. All associated material properties will be ignored except for the +density. Element output is not available for solid elements assigned to a rigid body. +Automatic conversion of certain element types in Abaqus/Standard +Element +types C3D20 and C3D15 are converted automatically to the corresponding variable +node element types C3D27 and C3D15V, respectively, if they are adjacent to a slave surface in a +node-to-surface contact pair with strict enforcement of “hard” contact conditions. +Special considerations for various element types in Abaqus/Standard +The following considerations should be acknowledged in the context of the stress/displacement, coupled +temperature-displacement, and heat transfer elements in Abaqus/Standard. +Interpolation of temperature and field variables in stress/displacement elements +The value of temperatures at the integration points used to compute the thermal stresses depends on +whether first-order or second-order elements are used. An average temperature is used at the integration +points in (compatible) linear elements so that the thermal strain is constant throughout the element; in the +case of elements with incompatible modes the temperatures are interpolated linearly. An approximate +linearly varying temperature distribution is used in higher-order elements with full integration. Higher- +order reduced-integration elements pose no special problems since the temperatures are interpolated +linearly. Field variables in a given stress/displacement element are interpolated using the same scheme +used to interpolate temperatures. +Interpolation in coupled temperature-displacement elements +Coupled temperature-displacement elements use either linear or parabolic interpolation for the geometry +and displacements. Temperature is interpolated linearly, but certain rules can apply to the temperature +and field variable evaluation at the Gauss points, as discussed below. +The elements that use linear interpolation for displacements and temperatures have temperatures +at all nodes. The thermal strain is taken as constant throughout the element because it is desirable to +have the same interpolation for thermal strains as for total strains so as to avoid spurious hydrostatic +stresses. Separate integration schemes are used for the internal energy storage, heat conduction, and +plastic dissipation (coupling contribution) terms for the first-order elements. The internal energy storage +term is integrated at the nodes, which yields a lumped internal energy matrix and, thereby, improves +the accuracy for problems with latent heat effects. In fully integrated elements both the heat conduction +and plastic dissipation terms are integrated at the Gauss points. While the plastic dissipation term is +integrated at each Gauss point, the heat generated by the mechanical deformation at a Gauss point is +applied at the nearest node. The temperature at a Gauss point is assumed to be the temperature of its +nearest node to be consistent with the temperature treatment throughout the formulation. In reduced- +integration elements the plastic dissipation term is obtained at the centroid and the heat generated by the +mechanical deformation is applied as a weighted average at each node. The temperature at the centroid +of reduced-integration elements is a weighted average of the nodal temperatures to be consistent with +the temperature treatment throughout the formulation. +The elements that use parabolic interpolation for displacements and linear interpolation for +temperatures have displacement degrees of freedom at all of the nodes, but temperature degrees of +freedom exist only at the corner nodes. The temperatures are interpolated linearly so that the thermal +strains have the same interpolation as the total strains. Temperatures at the midside nodes are calculated +by linear interpolation from the corner nodes for output purposes only. In contrast to the linear coupled +elements, all terms in the governing equations are integrated using a conventional Gauss scheme. For +these elements the stiffness matrix can be generated using either full integration (3 Gauss points in +each parametric direction) or reduced integration (2 Gauss points in each parametric direction). The +same integration scheme is always used for the specific heat and conductivity matrices as for the +stiffness matrix; however, because of the lower-order interpolation for temperature, this implies that we +always use a full integration scheme for the heat transfer matrices, even when the stiffness integration +is reduced. Reduced integration uses a lower-order integration to form the element stiffness: +the +mass matrix and distributed loadings are still integrated exactly. Reduced integration usually provides +more accurate results (providing that the elements are not distorted) and significantly reduces running +time, especially in three dimensions. Reduced integration for the quadratic displacement elements is +recommended in all cases except when very sharp strain gradients are expected (such as in finite-strain +metal forming applications); these elements are considered to be the most cost-effective elements of +this class. +The value of field variables at the integration points depends on whether first-order or second-order +coupled temperature-displacement elements are used. An average field variable is used at the integration +points in linear elements. An approximate linearly varying field variable distribution is used in higher- +order elements with full integration. Higher-order reduced-integration elements pose no special problems +since the field variables are interpolated linearly. +Modified triangle and tetrahedron elements use a special consistent interpolation scheme for +displacement and temperature. Displacement and temperature degrees of freedom are active at all +user-defined nodes. +Integration in diffusive heat transfer elements +In all of the first-order elements (2-node links, 3-node triangles, 4-node quadrilaterals, 4-node tetrahedra, +6-node triangular prisms, and 8-node bricks) the internal energy storage term (associated with specific +heat and latent heat storage) is integrated at the nodes. This integration scheme gives a diagonal +internal energy matrix and improves the accuracy for problems with latent heat effects. Conduction +contributions in these elements and all contributions in second-order elements use conventional Gauss +schemes. Second-order elements are preferable for smooth problems without latent heat effects. +The one-dimensional element cannot be used in a mass diffusion analysis. +Forced convection heat transfer elements +These elements are available with linear interpolation only. They use an “upwinding” (Petrov-Galerkin) +method to provide accurate solutions for convection-dominated problems . Consequently, the internal energy (associated with +specific heat storage) is not integrated at the nodes, which yields a consistent internal energy matrix +and may cause oscillatory temperatures if strong temperature gradients occur along boundaries that are +parallel to the flow direction. +Electromagnetic elements +These elements are available with linear edge-based interpolation only. The user-defined nodes define +the geometry of the element but do not directly participate in the interpolation of the electromagnetic or, +in the case of a magnetostatic analysis, the magnetic fields. However, temperature and predefined field +variables are defined at the user-defined nodes and are interpolated to the integration points for evaluating +material properties that are temperature and predefined field variable dependent. +28.1.2 +ONE-DIMENSIONAL SOLID (LINK) ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/CAE +References +• “Solid (continuum) elements,” Section 28.1.1 +• *SOLID SECTION +Overview +This section provides a reference to the one-dimensional solid (link) elements available in +Abaqus/Standard. For structural link (truss) elements, refer to “Truss elements,” Section 29.2.1. +Element types +Diffusive heat transfer elements +DC1D2 +DC1D3 +2-node link +3-node link +Active degree of freedom +11 +Additional solution variables +None. +Forced convection heat transfer elements +DCC1D2 +2-node link +DCC1D2D +2-node link with dispersion control +Active degree of freedom +11 +Additional solution variables +None. +Coupled thermal-electrical elements +DC1D2E +DC1D3E +2-node link +3-node link +Active degrees of freedom +9, 11 +Additional solution variables +None. +Acoustic elements +AC1D2 +AC1D3 +2-node link +3-node link +Active degree of freedom +Additional solution variables +None. +Nodal coordinates required +X, Y, Z +Element property definition +You must provide the cross-sectional area of the element; by default, unit area is assumed. +Input File Usage: +Abaqus/CAE Usage: +*SOLID SECTION +Property module: Create Section: select Solid as the section Category +and Homogeneous as the section Type +Element-based loading +Distributed heat fluxes +Distributed heat fluxes are available for elements with temperature degrees of freedom. They are +specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*DFLUX) +BF +BFNU +Abaqus/CAE +Load/Interaction +Units +Description +Body heat flux +Body heat flux +JL−3 T−1 +JL−3 T−1 +Heat body flux per unit volume. +Nonuniform heat body flux per unit +volume with magnitude supplied via +user subroutine DFLUX. +Heat surface flux per unit area into the +first end of the link (node 1). +S1 +Surface heat flux +JL−2 T−1 +Abaqus/CAE +Load/Interaction +Units +Description +Surface heat flux +JL−2 T−1 +Load ID +(*DFLUX) +S2 +S1NU +Not supported +JL−2 T−1 +S2NU +Not supported +JL−2 T−1 +Heat surface flux per unit area into +the second end of the link (node 2 or +node 3). +Nonuniform heat surface flux per +unit area into the first end of the link +(node 1) with magnitude supplied via +user subroutine DFLUX. +Nonuniform heat surface flux per unit +area into the second end of the link +(node 2 or node 3) with magnitude +supplied via user subroutine DFLUX. +Film conditions +Film conditions are available for elements with temperature degrees of freedom. They are specified as +described in “Thermal loads,” Section 33.4.4. +Load ID +(*FILM) +Abaqus/CAE +Load/Interaction +Units +Description +F1 +F2 +Not supported +JL−2 T−1 −1 +Not supported +JL−2 T−1 −1 +F1NU +Not supported +JL−2 T−1 −1 +F2NU +Not supported +JL−2 T−1 −1 +Film coefficient and sink temperature +(units of +) at the first end of the link +(node 1). +Film coefficient and sink temperature +(units of +) at the second end of the +link (node 2 or node 3). +Nonuniform film coefficient and sink +temperature (units of +) at the first end +of the link (node 1) with magnitude +supplied via user subroutine FILM. +Nonuniform film coefficient and sink +temperature (units of +) at the second +end of the link (node 2 or node 3) +with magnitude supplied via user +subroutine FILM. +Radiation types +Radiation conditions are available for elements with temperature degrees of freedom. They are specified +as described in “Thermal loads,” Section 33.4.4. +Load ID +(*RADIATE) +Abaqus/CAE +Load/Interaction +Units +Description +R1 +R2 +Surface radiation Dimensionless +Surface radiation Dimensionless +Emissivity and sink temperature +(units of +) at the first end of the +link (node 1). +Emissivity and sink temperature +(units of +) at the second end of the +link (node 2 or node 3). +Distributed impedances +Distributed impedances are available for elements with acoustic pressure degrees of freedom. They are +specified as described in “Acoustic and shock loads,” Section 33.4.6. +Load ID +(*IMPEDANCE) +Abaqus/CAE +Load/Interaction +Units +Description +I1 +I2 +Not supported +None +Not supported +None +Name of the impedance property that +defines the impedance at the first end +of the link (node 1). +Name of the impedance property that +defines the impedance at the second +end of the link (node 2 or node 3). +Distributed electric current densities +Distributed electric current densities are available for coupled thermal-electrical elements. They are +specified as described in “Coupled thermal-electrical analysis,” Section 6.7.3. +Load ID +(*DECURRENT) Load/Interaction +Abaqus/CAE +Units +Description +CBF +CS1 +CS2 +Body current +Surface current +CL−3T−1 +CL−2T−1 +Surface current +CL−2T−1 +Volumetric current source density. +Current density at the first end of the +link (node 1). +Current density at the second end of +the link (node 2 or node 3). +Element output +Heat flux components +Available for elements with temperature degrees of freedom. +HFL1 +Heat flux along the element axis. +Electrical potential gradient +Available for coupled thermal-electrical elements. +EPG1 +Electrical potential gradient along the element axis. +Electrical current density components +Available for coupled thermal-electrical elements. +ECD1 +Electrical current density along the element axis. +Node ordering and face numbering on elements +end 2 +end 1 +end 1 +2 - node element +3 - node element +end 2 +Numbering of integration points for output +2 - node element +3 - node element +28.1.3 +TWO-DIMENSIONAL SOLID ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Solid (continuum) elements,” Section 28.1.1 +• *SOLID SECTION +Overview +This section provides a reference to the two-dimensional solid elements available in Abaqus/Standard +and Abaqus/Explicit. +Element types +Plane strain elements +CPE3 +CPE3H(S) +CPE4(S) +CPE4H(S) +CPE4I(S) +3-node linear +3-node linear, hybrid with constant pressure +4-node bilinear +4-node bilinear, hybrid with constant pressure +4-node bilinear, incompatible modes +CPE4IH(S) +4-node bilinear, incompatible modes, hybrid with linear pressure +CPE4R +4-node bilinear, reduced integration with hourglass control +CPE4RH(S) +CPE6(S) +CPE6H(S) +CPE6M +4-node bilinear, reduced integration with hourglass control, hybrid with constant +pressure +6-node quadratic +6-node quadratic, hybrid with linear pressure +6-node modified, with hourglass control +CPE6MH(S) +6-node modified, with hourglass control, hybrid with linear pressure +CPE8(S) +CPE8H(S) +CPE8R(S) +8-node biquadratic +8-node biquadratic, hybrid with linear pressure +8-node biquadratic, reduced integration +CPE8RH(S) +8-node biquadratic, reduced integration, hybrid with linear pressure +Active degrees of freedom +1, 2 +Additional solution variables +The constant pressure hybrid elements have one additional variable relating to pressure, and the linear +pressure hybrid elements have three additional variables relating to pressure. +Element types CPE4I and CPE4IH have five additional variables relating to the incompatible modes. +Element types CPE6M and CPE6MH have two additional displacement variables. +Plane stress elements +CPS3 +CPS4(S) +CPS4I(S) +CPS4R +CPS6(S) +CPS6M +CPS8(S) +3-node linear +4-node bilinear +4-node bilinear, incompatible modes +4-node bilinear, reduced integration with hourglass control +6-node quadratic +6-node modified, with hourglass control +8-node biquadratic +CPS8R(S) +8-node biquadratic, reduced integration +Active degrees of freedom +1, 2 +Additional solution variables +Element type CPS4I has four additional variables relating to the incompatible modes. +Element type CPS6M has two additional displacement variables. +Generalized plane strain elements +CPEG3(S) +CPEG3H(S) +CPEG4(S) +CPEG4H(S) +CPEG4I(S) +CPEG4IH(S) +CPEG4R(S) +CPEG4RH(S) +3-node linear triangle +3-node linear triangle, hybrid with constant pressure +4-node bilinear quadrilateral +4-node bilinear quadrilateral, hybrid with constant pressure +4-node bilinear quadrilateral, incompatible modes +4-node bilinear quadrilateral, incompatible modes, hybrid with linear pressure +4-node bilinear quadrilateral, reduced integration with hourglass control +4-node bilinear quadrilateral, reduced integration with hourglass control, hybrid with +constant pressure +CPEG6(S) +CPEG6H(S) +CPEG6M(S) +6-node quadratic triangle +6-node quadratic triangle, hybrid with linear pressure +6-node modified, with hourglass control +CPEG6MH(S) +6-node modified, with hourglass control, hybrid with linear pressure +CPEG8(S) +CPEG8H(S) +CPEG8R(S) +8-node biquadratic quadrilateral +8-node biquadratic quadrilateral, hybrid with linear pressure +8-node biquadratic quadrilateral, reduced integration +CPEG8RH(S) +8-node biquadratic quadrilateral, reduced integration, hybrid with linear pressure +Active degrees of freedom +1, 2 at all but the reference node +3, 4, 5 at the reference node +Additional solution variables +The constant pressure hybrid elements have one additional variable relating to pressure, and the linear +pressure hybrid elements have three additional variables relating to pressure. +Element types CPEG4I and CPEG4IH have five additional variables relating to the incompatible modes. +Element types CPEG6M and CPEG6MH have two additional displacement variables. +Coupled temperature-displacement plane strain elements +CPE3T +CPE4T(S) +CPE4HT(S) +CPE4RT +CPE4RHT(S) +3-node linear displacement and temperature +4-node bilinear displacement and temperature +4-node bilinear displacement and temperature, hybrid with constant pressure +4-node bilinear displacement and temperature, reduced integration with hourglass +control +4-node bilinear displacement and temperature, reduced integration with hourglass +control, hybrid with constant pressure +CPE6MT +6-node modified displacement and temperature, with hourglass control +CPE6MHT(S) +CPE8T(S) +CPE8HT(S) +CPE8RT(S) +CPE8RHT(S) +6-node modified displacement and temperature, with hourglass control, hybrid with +constant pressure +8-node biquadratic displacement, bilinear temperature +8-node biquadratic displacement, bilinear temperature, hybrid with linear pressure +8-node biquadratic displacement, bilinear temperature, reduced integration +8-node biquadratic displacement, bilinear temperature, reduced integration, hybrid +with linear pressure +Active degrees of freedom +1, 2, 11 at corner nodes +1, 2 at midside nodes of second-order elements in Abaqus/Standard +1, 2, 11 at midside nodes of modified displacement and temperature elements in Abaqus/Standard +Additional solution variables +The constant pressure hybrid elements have one additional variable relating to pressure, and the linear +pressure hybrid elements have three additional variables relating to pressure. +Element types CPE6MT and CPE6MHT have two additional displacement variables and one additional +temperature variable. +Coupled temperature-displacement plane stress elements +CPS3T +CPS4T(S) +CPS4RT +CPS6MT +CPS8T(S) +CPS8RT(S) +3-node linear displacement and temperature +4-node bilinear displacement and temperature +4-node bilinear displacement and temperature, reduced integration with hourglass +control +6-node modified displacement and temperature, with hourglass control +8-node biquadratic displacement, bilinear temperature +8-node biquadratic displacement, bilinear temperature, reduced integration +Active degrees of freedom +1, 2, 11 at corner nodes +1, 2 at midside nodes of second-order elements in Abaqus/Standard +1, 2, 11 at midside nodes of modified displacement and temperature elements in Abaqus/Standard +Additional solution variables +Element type CPS6MT has two additional displacement variables and one additional temperature +variable. +Coupled temperature-displacement generalized plane strain elements +CPEG3T(S) +CPEG3HT(S) +CPEG4T(S) +CPEG4HT(S) +CPEG4RT(S) +3-node linear displacement and temperature +3-node linear displacement and temperature, hybrid with constant pressure +4-node bilinear displacement and temperature +4-node bilinear displacement and temperature, hybrid with constant pressure +4-node bilinear displacement and temperature, reduced integration with hourglass +control +CPEG4RHT(S) +4-node bilinear displacement and temperature, reduced integration with hourglass +control, hybrid with constant pressure +CPEG6MT(S) +6-node modified displacement and temperature, with hourglass control +CPEG6MHT(S) +CPEG8T(S) +CPEG8HT(S) +CPEG8RHT(S) +6-node modified displacement and temperature, with hourglass control, hybrid with +constant pressure +8-node biquadratic displacement, bilinear temperature +8-node biquadratic displacement, bilinear temperature, hybrid with linear pressure +8-node biquadratic displacement, bilinear temperature, reduced integration, hybrid +with linear pressure +Active degrees of freedom +1, 2, 11 at corner nodes +1, 2 at midside nodes of second-order elements +1, 2, 11 at midside nodes of modified displacement and temperature elements +3, 4, 5 at the reference node +Additional solution variables +The constant pressure hybrid elements have one additional variable relating to pressure, and the linear +pressure hybrid elements have three additional variables relating to pressure. +Element types CPEG6MT and CPEG6MHT have two additional displacement variables and one +additional temperature variable. +Diffusive heat transfer or mass diffusion elements +DC2D3(S) +DC2D4(S) +DC2D6(S) +DC2D8(S) +3-node linear +4-node linear +6-node quadratic +8-node biquadratic +Active degree of freedom +11 +Additional solution variables +None. +Forced convection/diffusion elements +DCC2D4(S) +4-node +DCC2D4D(S) +4-node with dispersion control +Active degree of freedom +11 +Additional solution variables +None. +Coupled thermal-electrical elements +DC2D3E(S) +DC2D4E(S) +DC2D6E(S) +DC2D8E(S) +3-node linear +4-node linear +6-node quadratic +8-node biquadratic +Active degrees of freedom +9, 11 +Additional solution variables +None. +Pore pressure plane strain elements +CPE4P(S) +CPE4PH(S) +CPE4RP(S) +CPE4RPH(S) +CPE6MP(S) +CPE6MPH(S) +CPE8P(S) +CPE8PH(S) +CPE8RP(S) +CPE8RPH(S) +4-node bilinear displacement and pore pressure +4-node bilinear displacement and pore pressure, hybrid with constant pressure stress +4-node bilinear displacement and pore pressure, reduced integration with hourglass +control +4-node bilinear displacement and pore pressure, reduced integration with hourglass +control, hybrid with constant pressure +6-node modified displacement and pore pressure, with hourglass control +6-node modified displacement and pore pressure, with hourglass control, hybrid with +linear pressure +8-node biquadratic displacement, bilinear pore pressure +8-node biquadratic displacement, bilinear pore pressure, hybrid with linear pressure +stress +8-node biquadratic displacement, bilinear pore pressure, reduced integration +8-node biquadratic displacement, bilinear pore pressure, reduced integration, hybrid +with linear pressure stress +Active degrees of freedom +1, 2, 8 at corner nodes +1, 2 at midside nodes for all elements except CPE6MP and CPE6MPH, which also have degree of +freedom 8 active at midside nodes +Additional solution variables +The constant pressure hybrid elements have one additional variable relating to the effective pressure +stress, and the linear pressure hybrid elements have three additional variables relating to the effective +pressure stress to permit fully incompressible material modeling. +Element types CPE6MP and CPE6MPH have two additional displacement variables and one additional +pore pressure variable. +Acoustic elements +AC2D3 +AC2D4(S) +AC2D4R(E) +AC2D6(S) +AC2D8(S) +3-node linear +4-node bilinear +4-node bilinear, reduced integration with hourglass control +6-node quadratic +8-node biquadratic +Active degree of freedom +Additional solution variables +None. +Piezoelectric plane strain elements +CPE3E(S) +CPE4E(S) +CPE6E(S) +CPE8E(S) +3-node linear +4-node bilinear +6-node quadratic +8-node biquadratic +CPE8RE(S) +8-node biquadratic, reduced integration +Active degrees of freedom +1, 2, 9 +Additional solution variables +None. +Piezoelectric plane stress elements +CPS3E(S) +CPS4E(S) +CPS6E(S) +3-node linear +4-node bilinear +6-node quadratic +CPS8E(S) +CPS8RE(S) +8-node biquadratic +8-node biquadratic, reduced integration +Active degrees of freedom +1, 2, 9 +Additional solution variables +None. +Electromagnetic elements +EMC2D3(S) +EMC2D4(S) +3-node zero-order +4-node zero-order +Active degree of freedom +Magnetic vector potential (for more information, see “Boundary conditions” in “Eddy current analysis,” +Section 6.7.5, and “Boundary conditions” in “Magnetostatic analysis,” Section 6.7.6). +Additional solution variables +None. +Nodal coordinates required +X, Y +Element property definition +For all elements except generalized plane strain elements, you must provide the element thickness; by +default, unit thickness is assumed. +For generalized plane strain elements, you must provide three values: +material fiber through the reference node, the initial value of +the initial length of the axial +(in radians), and the initial value of +(in radians). If you do not provide these values, Abaqus assumes the default values of one unit +. In addition, you must define the reference point for +and +as the initial length and zero for +generalized plane strain elements. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to define the element properties for all elements except +generalized plane strain elements: +*SOLID SECTION +Use the following option to define the element properties for generalized plane +strain elements: +*SOLID SECTION, REF NODE=node number or node set name +Property module: Create Section: select Solid as the section +Category and Homogeneous, Generalized plane strain, or +Electromagnetic, Solid as the section Type +Generalized plane strain sections must be assigned to regions of parts that have +a reference point associated with them. To define the reference point: +Part module: Tools→Reference Point: select reference point +Element-based loading +Distributed loads +Distributed loads are available for all elements with displacement degrees of freedom. They are specified +as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +BX +BY +BXNU +Body force +Body force +Body force +FL−3 +FL−3 +FL−3 +BYNU +Body force +FL−3 +Body force in global X-direction. +Body force in global Y-direction. +Nonuniform body force in global +X-direction with magnitude supplied +subroutine DLOAD in +via +Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +user +Nonuniform body force in global +Y-direction with magnitude supplied +subroutine DLOAD in +via +user +and VDLOAD in +Abaqus/Standard +Abaqus/Explicit. +CENT(S) +Not supported +FL−4 (ML−3T−2) Centrifugal load (magnitude is input +as +is the mass density +, where +per unit volume, +is the angular +velocity). Not available for pore +pressure elements. +Centrifugal load (magnitude is input +as +the angular +velocity). +, where +is +Coriolis force (magnitude is input +as +is the mass density +, where +per unit volume, +is the angular +velocity). Not available for pore +pressure elements. +CENTRIF(S) +Rotational body +force +T−2 +CORIO(S) +Coriolis force +FL−4 T +(ML−3 T−1 ) +Load ID +(*DLOAD) +GRAV +Abaqus/CAE +Load/Interaction +Gravity +HPn(S) +Pn +PnNU +Not supported +Pressure +Not supported +Units +Description +LT−2 +FL−2 +FL−2 +FL−2 +Gravity +loading +direction (magnitude is +acceleration). +in +specified +input as +Hydrostatic pressure on face n, linear +in global Y. +Pressure on face n. +on +with +user +face +Nonuniform pressure +supplied +magnitude +subroutine DLOAD in +via +Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +ROTA(S) +Rotational body +force +T−2 +SBF(E) +Not supported +FL−5 T2 +Rotary acceleration load (magnitude +is input as +is the rotary +acceleration). +, where +Stagnation body force in global X- +and Y-directions. +Not supported +FL−4 T2 +Stagnation pressure on face n. +Shear traction on face n. +Nonuniform shear traction on face +and direction +n with magnitude +supplied +subroutine +via +UTRACLOAD. +user +General traction on face n. +Nonuniform general traction on face +and direction +n with magnitude +supplied +subroutine +via +UTRACLOAD. +user +Viscous body force in global X- and +Y-directions. +Viscous pressure on face n, applying +a pressure proportional to the velocity +normal to the face and opposing the +motion. +SPn(E) +TRSHRn +Surface traction +TRSHRnNU(S) +Not supported +TRVECn +Surface traction +TRVECnNU(S) +Not supported +FL−2 +FL−2 +FL−2 +FL−2 +VBF(E) +VPn(E) +Not supported +FL−4 T +Not supported +FL−3 T +Foundations +Foundations are available for Abaqus/Standard elements with displacement degrees of freedom. They +are specified as described in “Element foundations,” Section 2.2.2. +Load ID +(*FOUNDATION) Load/Interaction +Abaqus/CAE +Fn(S) +Elastic +foundation +Distributed heat fluxes +Units +Description +FL−3 +Elastic foundation on face n. +Distributed heat fluxes are available for all elements with temperature degrees of freedom. They are +specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*DFLUX) +BF +BFNU(S) +Abaqus/CAE +Load/Interaction +Units +Description +Body heat flux +Body heat flux +JL−3 T−1 +JL−3 T−1 +Heat body flux per unit volume. +Nonuniform heat body flux per unit +volume with magnitude supplied via +user subroutine DFLUX. +Heat surface flux per unit area into +face n. +Nonuniform heat surface flux per +unit area into face n with magnitude +supplied via user subroutine DFLUX. +Film coefficient and sink temperature +(units of +) provided on face n. +Nonuniform film coefficient and sink +temperature (units of +) provided on +face n with magnitude supplied via +user subroutine FILM. +Film conditions +Film conditions are available for all elements with temperature degrees of freedom. They are specified +as described in “Thermal loads,” Section 33.4.4. +Abaqus/CAE +Load/Interaction +Units +Description +Sn +Surface heat flux +JL−2 T−1 +SnNU(S) +Not supported +JL−2 T−1 +Load ID +(*FILM) +Fn +Surface film +condition +JL−2 T−1 −1 +FnNU(S) +Not supported +JL−2 T−1 −1 +Radiation types +Radiation conditions are available for all elements with temperature degrees of freedom. They are +specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*RADIATE) +Abaqus/CAE +Load/Interaction +Units +Description +Rn +Surface radiation Dimensionless +Emissivity and sink temperature +(units of +) provided on face n. +Distributed flows +Distributed flows are available for all elements with pore pressure degrees of freedom. They are specified +as described in “Pore fluid flow,” Section 33.4.7. +Load ID +(*FLOW) +Qn(S) +Abaqus/CAE +Load/Interaction +Units +Description +Not supported +F−1 L3T−1 +QnD(S) +Not supported +F−1 L3T−1 +QnNU(S) +Not supported +F−1 L3T−1 +Seepage coefficient and reference +sink pore pressure (units of FL−2 ) +provided on face n. +Drainage-only seepage +provided on face n. +coefficient +coefficient +Nonuniform seepage +and reference sink pore pressure +(units of FL−2 ) provided on face n +with magnitude supplied via user +subroutine FLOW. +Load ID +(*DFLOW) +Sn(S) +Abaqus/CAE +Load/Interaction +Units +Description +Surface pore +fluid +LT−1 +pore +Prescribed +effective +velocity (outward from the face) on +face n. +fluid +SnNU(S) +Not supported +LT−1 +Nonuniform prescribed pore fluid +effective velocity (outward from +the face) on face n with magnitude +supplied via user subroutine DFLOW. +Distributed impedances +Distributed impedances are available for all elements with acoustic pressure degrees of freedom. They +are specified as described in “Acoustic and shock loads,” Section 33.4.6. +Load ID +(*IMPEDANCE) +Abaqus/CAE +Load/Interaction +Units +Description +In +Not supported +None +Name of the impedance property that +defines the impedance on face n. +Electric fluxes +Electric fluxes are available for piezoelectric elements. They are specified as described in “Piezoelectric +analysis,” Section 6.7.2. +Load ID +(*DECHARGE) +Abaqus/CAE +Load/Interaction +Units +Description +EBF(S) +ESn(S) +Body charge +Surface charge +CL−3 +CL−2 +Body flux per unit volume. +Prescribed surface charge on face n. +Distributed electric current densities +Distributed electric current densities are available for coupled thermal-electrical elements, coupled +thermal-electrical-structural elements, and electromagnetic elements. They are specified as described +in “Coupled thermal-electrical analysis,” Section 6.7.3; “Fully coupled thermal-electrical-structural +analysis,” Section 6.7.4; and “Eddy current analysis,” Section 6.7.5. +Load ID +(*DECURRENT) Load/Interaction +Abaqus/CAE +Units +Description +CBF(S) +CSn(S) +CJ(S) +Body current +Surface current +CL−3T−1 +CL−2T−1 +Volumetric current source density. +Current density on face n. +Body +density +current +CL−2T−1 +Volume current density vector in an +eddy current analysis. +Distributed concentration fluxes +Distributed concentration fluxes are available for mass diffusion elements. They are specified as +described in “Mass diffusion analysis,” Section 6.9.1. +Load ID +(*DFLUX) +BF(S) +BFNU(S) +Sn(S) +SnNU(S) +Surface-based loading +Distributed loads +Abaqus/CAE +Load/Interaction +Units +Description +Body +concentration +flux +Body +concentration +flux +Surface +concentration +flux +Surface +concentration +flux +PT−1 +PT−1 +PLT−1 +PLT−1 +Concentration body flux per unit +volume. +Nonuniform concentration body flux +per unit volume with magnitude +supplied via user subroutine DFLUX. +Concentration surface flux per unit +area into face n. +Nonuniform concentration surface +flux per unit area into face n +with magnitude supplied via user +subroutine DFLUX. +Surface-based distributed loads are available for all elements with displacement degrees of freedom. +They are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +HP(S) +PNU +Pressure +Pressure +Pressure +FL−2 +FL−2 +FL−2 +SP(E) +Pressure +FL−4 T2 +TRSHR +Surface traction +TRSHRNU(S) +Surface traction +FL−2 +FL−2 +Hydrostatic pressure on the element +surface, linear in global Y. +Pressure on the element surface. +Nonuniform pressure on the element +surface with magnitude +supplied +subroutine DLOAD in +via +Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +user +Stagnation pressure on the element +surface. +Shear traction on the element surface. +Nonuniform shear +traction on the +element surface with magnitude and +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +2-D SOLIDS +TRVEC +Surface traction +FL−2 +TRVECNU(S) +Surface traction +FL−2 +VP(E) +Pressure +FL−3 T +direction supplied via user subroutine +UTRACLOAD. +General +surface. +traction on the element +Nonuniform general traction on the +element surface with magnitude and +direction supplied via user subroutine +UTRACLOAD. +Viscous pressure on the element +The viscous pressure is +surface. +proportional to the velocity normal to +the element surface and opposing the +motion. +Distributed heat fluxes +Surface-based heat fluxes are available for all elements with temperature degrees of freedom. They are +specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*DSFLUX) +Abaqus/CAE +Load/Interaction +Units +Description +Surface heat flux +JL−2 T−1 +SNU(S) +Surface heat flux +JL−2 T−1 +Heat surface flux per unit area into the +element surface. +Nonuniform heat surface flux per unit +area applied on the element surface +with magnitude supplied via user +subroutine DFLUX. +Film conditions +Surface-based film conditions are available for all elements with temperature degrees of freedom. They +are specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*SFILM) +Abaqus/CAE +Load/Interaction +Units +Description +Surface film +condition +JL−2 T−1 −1 +Film coefficient and sink temperature +(units of +) provided on the element +surface. +Load ID +(*SFILM) +FNU(S) +Radiation types +Abaqus/CAE +Load/Interaction +Surface film +condition +Units +Description +JL−2 T−1 −1 +Nonuniform film coefficient and sink +temperature (units of +) provided on +the element surface with magnitude +supplied via user subroutine FILM. +Surface-based radiation conditions are available for all elements with temperature degrees of freedom. +They are specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*SRADIATE) +Abaqus/CAE +Load/Interaction +Units +Description +Surface radiation Dimensionless +Emissivity and sink temperature +(units of +) provided on the element +surface. +Distributed flows +Surface-based flows are available for all elements with pore pressure degrees of freedom. They are +specified as described in “Pore fluid flow,” Section 33.4.7. +Load ID +(*SFLOW) +Q(S) +Abaqus/CAE +Load/Interaction +Units +Description +Not supported +F−1 L3T−1 +QD(S) +Not supported +F−1 L3T−1 +QNU(S) +Not supported +F−1 L3T−1 +Seepage coefficient and reference +sink pore pressure (units of FL−2 ) +provided on the element surface. +Drainage-only seepage +provided on the element surface. +coefficient +Nonuniform seepage coefficient and +reference sink pore pressure (units +of FL−2 ) provided on the element +surface with magnitude supplied via +user subroutine FLOW. +Abaqus/CAE +Load/Interaction +Units +Description +Surface pore +fluid +LT−1 +28.1.3–16 +pore +Prescribed +effective +velocity outward from the element +surface. +fluid +Load ID +(*DSFLOW) +Load ID +(*DSFLOW) +SNU(S) +Abaqus/CAE +Load/Interaction +Units +Description +Surface pore +fluid +LT−1 +Nonuniform prescribed pore fluid +effective velocity outward from the +surface with magnitude +element +supplied via user subroutine DFLOW. +Distributed impedances +Surface-based impedances are available for all elements with acoustic pressure degrees of freedom. They +are specified as described in “Acoustic and shock loads,” Section 33.4.6. +Incident wave loading +Surface-based incident wave loads are available for all elements with displacement degrees of freedom +or acoustic pressure degrees of freedom. They are specified as described in “Acoustic and shock loads,” +Section 33.4.6. If the incident wave field includes a reflection off a plane outside the boundaries of the +mesh, this effect can be included. +Electric fluxes +Surface-based electric fluxes are available for piezoelectric elements. They are specified as described in +“Piezoelectric analysis,” Section 6.7.2. +Load ID +(*DSECHARGE) Load/Interaction +Abaqus/CAE +Units +Description +ES(S) +Surface charge +CL−2 +Prescribed surface charge on the +element surface. +Distributed electric current densities +Surface-based electric current densities are available for coupled thermal-electrical elements, coupled +thermal-electrical-structural elements, and electromagnetic elements. They are specified as described +in “Coupled thermal-electrical analysis,” Section 6.7.3; “Fully coupled thermal-electrical-structural +analysis,” Section 6.7.4; and “Eddy current analysis,” Section 6.7.5. +Load ID +(*DSECURRENT) Load/Interaction +Abaqus/CAE +Units +Description +CS(S) +CK(S) +Surface current +CL−2T−1 +Current density applied on the +element surface. +Surface +density +current +CL−1T−1 +Surface current density vector in an +eddy current analysis. +Element output +For most elements output is in global directions unless a local coordinate system is assigned to the +element through the section definition (“Orientations,” Section 2.2.5) in which case output is in the local +coordinate system (which rotates with the motion in large-displacement analysis). See “State storage,” +Section 1.5.4 of the Abaqus Theory Manual, for details. +Stress, strain, and other tensor components +Stress and other tensors (including strain tensors) are available for elements with displacement degrees +of freedom. All tensors have the same components. For example, the stress components are as follows: +S11 +S22 +S33 +S12 +, direct stress. +, direct stress. +, direct stress (not available for plane stress elements). +, shear stress. +Heat flux components +Available for elements with temperature degrees of freedom. +HFL1 +HFL2 +Heat flux in the X-direction. +Heat flux in the Y-direction. +Pore fluid velocity components +Available for elements with pore pressure degrees of freedom. +FLVEL1 +FLVEL2 +Pore fluid effective velocity in the X-direction. +Pore fluid effective velocity in the Y-direction. +Mass concentration flux components +Available for elements with normalized concentration degrees of freedom. +MFL1 +MFL2 +Concentration flux in the X-direction. +Concentration flux in the Y-direction. +Electrical potential gradient +Available for elements with electrical potential degrees of freedom. +EPG1 +EPG2 +Electrical potential gradient in the X-direction. +Electrical potential gradient in the Y-direction. +Electrical flux components +Available for piezoelectric elements. +EFLX1 +EFLX2 +Electrical flux in the X-direction. +Electrical flux in the Y-direction. +Electrical current density components +Available for coupled thermal-electrical elements. +ECD1 +ECD2 +Electrical current density in the X-direction. +Electrical current density in the Y-direction. +Electrical field components +Available for electromagnetic elements in an eddy current analysis. +EME1 +EME2 +Electric field in the X-direction. +Electric field in the Y-direction. +Magnetic flux density components +Available for electromagnetic elements. +EMB3 +Magnetic flux density in the Z-direction. +Magnetic field components +Available for electromagnetic elements. +EMH3 +Magnetic field in the Z-direction. +Electrical current density components in an eddy current analysis +Available for electromagnetic elements in an eddy current analysis. +EMCD1 +EMCD2 +Electrical current density in the X-direction. +Electrical current density in the Y-direction. +Node ordering and face numbering on elements +face 3 +face 3 +face 2 +face 4 +face 2 +1 2 +face 1 +3 - node element +face 1 +4 - node element +face 3 +4 7 3 +face 3 +6 5 +face 2 +face 4 +face 2 +1 +face 1 +6 - node element + 2 +face 1 +8 - node element +For generalized plane strain elements, the reference node associated with each element (where the +generalized plane strain degrees of freedom are stored) is not shown. The reference node should be +the same for all elements in any given connected region so that the bounding planes are the same for +that region. Different regions may have different reference nodes. The number of the reference node is +not incremented when the elements are generated incrementally . +Triangular element faces +Face 1 +Face 2 +Face 3 +1 – 2 face +2 – 3 face +3 – 1 face +Quadrilateral element faces +Face 1 +Face 2 +Face 3 +Face 4 +1 – 2 face +2 – 3 face +3 – 4 face +4 – 1 face +2-D SOLIDS +6 5 +1 2 +1 + 2 +3 - node element +6 - node element +4 - node element +4-node reduced +integration element +4 7 3 +4 7 3 +8 - node element +8-node reduced +integration element +For heat transfer applications a different integration scheme is used for triangular elements, as described +in “Triangular, tetrahedral, and wedge elements,” Section 3.2.6 of the Abaqus Theory Manual. +28.1.4 +THREE-DIMENSIONAL SOLID ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Solid (continuum) elements,” Section 28.1.1 +• *SOLID SECTION +Overview +This section provides a reference to the three-dimensional solid elements available in Abaqus/Standard +and Abaqus/Explicit. +Element types +Stress/displacement elements +C3D4 +C3D4H(S) +C3D6(S) +C3D6(E) +C3D6H(S) +C3D8 +C3D8H(S) +C3D8I +4-node linear tetrahedron +4-node linear tetrahedron, hybrid with linear pressure +6-node linear triangular prism +6-node linear triangular prism, reduced integration with hourglass control +6-node linear triangular prism, hybrid with constant pressure +8-node linear brick +8-node linear brick, hybrid with constant pressure +8-node linear brick, incompatible modes +C3D8IH(S) +8-node linear brick, incompatible modes, hybrid with linear pressure +C3D8R +8-node linear brick, reduced integration with hourglass control +C3D8RH(S) +C3D10(S) +C3D10H(S) +C3D10I(S) +C3D10M +8-node linear brick, reduced integration with hourglass control, hybrid with constant +pressure +10-node quadratic tetrahedron +10-node quadratic tetrahedron, hybrid with constant pressure +10-node general-purpose quadratic tetrahedron, improved surface stress visualization +10-node modified tetrahedron, with hourglass control +C3D10MH(S) +10-node modified tetrahedron, with hourglass control, hybrid with linear pressure +C3D15(S) +15-node quadratic triangular prism +C3D15H(S) +C3D20(S) +C3D20H(S) +C3D20R(S) +15-node quadratic triangular prism, hybrid with linear pressure +20-node quadratic brick +20-node quadratic brick, hybrid with linear pressure +20-node quadratic brick, reduced integration +C3D20RH(S) +20-node quadratic brick, reduced integration, hybrid with linear pressure +Active degrees of freedom +1, 2, 3 +Additional solution variables +The constant pressure hybrid elements have one additional variable relating to pressure, and the linear +pressure hybrid elements have four additional variables relating to pressure. +Element types C3D8I and C3D8IH have thirteen additional variables relating to the incompatible modes. +Element types C3D10M and C3D10MH have three additional displacement variables. +Stress/displacement variable node elements +C3D15V(S) +C3D15VH(S) +C3D27(S) +C3D27H(S) +C3D27R(S) +15 to 18-node triangular prism +15 to 18-node triangular prism, hybrid with linear pressure +21 to 27-node brick +21 to 27-node brick, hybrid with linear pressure +21 to 27-node brick, reduced integration +C3D27RH(S) +21 to 27-node brick, reduced integration, hybrid with linear pressure +Active degrees of freedom +1, 2, 3 +Additional solution variables +The hybrid elements have four additional variables relating to pressure. +Coupled temperature-displacement elements +C3D4T +C3D6T(S) +C3D6T(E) +C3D8T +C3D8HT(S) +C3D8RT +4-node linear displacement and temperature +6-node linear displacement and temperature +6-node linear displacement and temperature, reduced integration with hourglass control +8-node trilinear displacement and temperature +8-node trilinear displacement and temperature, hybrid with constant pressure +8-node trilinear displacement and temperature, reduced integration with hourglass +control +C3D8RHT(S) +8-node trilinear displacement and temperature, reduced integration with hourglass +control, hybrid with constant pressure +C3D10MT +10-node modified displacement and temperature tetrahedron, with hourglass control +C3D10MHT(S) +C3D20T(S) +C3D20HT(S) +C3D20RT(S) +C3D20RHT(S) +10-node modified displacement and temperature tetrahedron, with hourglass control, +hybrid with linear pressure +20-node triquadratic displacement, trilinear temperature +20-node triquadratic displacement, trilinear temperature, hybrid with linear pressure +20-node triquadratic displacement, trilinear temperature, reduced integration +20-node triquadratic displacement, trilinear temperature, reduced integration, hybrid +with linear pressure +Active degrees of freedom +1, 2, 3, 11 at corner nodes +1, 2, 3 at midside nodes of second-order elements in Abaqus/Standard +1, 2, 3, 11 at midside nodes of modified displacement and temperature elements in Abaqus/Standard +Additional solution variables +The constant pressure hybrid element has one additional variable relating to pressure, and the linear +pressure hybrid elements have four additional variables relating to pressure. +Element types C3D10MT and C3D10MHT have three additional displacement variables and one +additional temperature variable. +Coupled thermal-electrical-structural elements +Q3D4(S) +Q3D6(S) +Q3D8(S) +Q3D8H(S) +Q3D8R(S) +Q3D8RH(S) +Q3D10M(S) +Q3D10MH(S) +4-node linear displacement, electric potential and temperature +6-node linear displacement, electric potential and temperature +8-node trilinear displacement, electric potential and temperature +8-node trilinear displacement, electric potential and temperature, hybrid with constant +pressure +8-node trilinear displacement, electric potential and temperature, reduced integration +with hourglass control +8-node trilinear displacement, electric potential and temperature, reduced integration +with hourglass control, hybrid with constant pressure +10-node modified displacement, electric potential and temperature tetrahedron, with +hourglass control +10-node modified displacement, electric potential and temperature tetrahedron, with +hourglass control, hybrid with linear pressure +Q3D20(S) +Q3D20H(S) +Q3D20R(S) +Q3D20RH(S) +20-node triquadratic displacement, trilinear electric potential and trilinear temperature +20-node triquadratic displacement, trilinear electric potential, trilinear temperature, +hybrid with linear pressure +20-node triquadratic displacement, trilinear electric potential, trilinear temperature, +reduced integration +20-node triquadratic displacement, trilinear electric potential, trilinear temperature, +reduced integration, hybrid with linear pressure +Active degrees of freedom +1, 2, 3, 9, 11 at corner nodes +1, 2, 3 at midside nodes of second-order elements in Abaqus/Standard +1, 2, 3, 9, 11 at midside nodes of modified displacement and temperature elements in Abaqus/Standard +Additional solution variables +The constant pressure hybrid element has one additional variable relating to pressure, and the linear +pressure hybrid elements have four additional variables relating to pressure. +Element types Q3D10M and Q3D10MH have three additional displacement variables, one additional +electric potential variable, and one additional temperature variable. +Diffusive heat transfer or mass diffusion elements +DC3D4(S) +DC3D6(S) +DC3D8(S) +DC3D10(S) +DC3D15(S) +DC3D20(S) +4-node linear tetrahedron +6-node linear triangular prism +8-node linear brick +10-node quadratic tetrahedron +15-node quadratic triangular prism +20-node quadratic brick +Active degree of freedom +11 +Additional solution variables +None. +Forced convection/diffusion elements +DCC3D8(S) +8-node +DCC3D8D(S) +8-node with dispersion control +Active degree of freedom +11 +Additional solution variables +None. +Coupled thermal-electrical elements +DC3D4E(S) +DC3D6E(S) +DC3D8E(S) +4-node linear tetrahedron +6-node linear triangular prism +8-node linear brick +DC3D10E(S) +10-node quadratic tetrahedron +DC3D15E(S) +15-node quadratic triangular prism +DC3D20E(S) +20-node quadratic brick +Active degrees of freedom +9, 11 +Additional solution variables +None. +Pore pressure elements +C3D4P(S) +C3D6P(S) +C3D8P(S) +C3D8PH(S) +C3D8RP(S) +C3D8RPH(S) +C3D10MP(S) +C3D10MPH(S) +C3D20P(S) +C3D20PH(S) +C3D20RP(S) +C3D20RPH(S) +4-node linear displacement and pore pressure +6-node linear displacement and pore pressure +8-node trilinear displacement and pore pressure +8-node trilinear displacement and pore pressure, hybrid with constant pressure +8-node trilinear displacement and pore pressure, reduced integration +8-node trilinear displacement and pore pressure, reduced integration, hybrid with +constant pressure +10-node modified displacement and pore pressure tetrahedron, with hourglass control +10-node modified displacement and pore pressure tetrahedron, with hourglass control, +hybrid with linear pressure +20-node triquadratic displacement, trilinear pore pressure +20-node triquadratic displacement, trilinear pore pressure, hybrid with linear pressure +20-node triquadratic displacement, trilinear pore pressure, reduced integration +20-node triquadratic displacement, trilinear pore pressure, reduced integration, hybrid +with linear pressure +Active degrees of freedom +1, 2, 3 at midside nodes for all elements except C3D10MP and C3D10MPH, which also have degree of +freedom 8 active at midside nodes +1, 2, 3, 8 at corner nodes +Additional solution variables +The constant pressure hybrid elements have one additional variable relating to the effective pressure +stress, and the linear pressure hybrid elements have four additional variables relating to the effective +pressure stress to permit fully incompressible material modeling. +Element types C3D10MP and C3D10MPH have three additional displacement variables and one +additional pore pressure variable. +Coupled temperature–pore pressure elements +C3D8PT(S) +C3D8PHT(S) +C3D8RPT(S) +C3D8RPHT(S) +C3D10MPT(S) +8-node trilinear displacement, pore pressure, and temperature. +8-node trilinear displacement, pore pressure, and temperature; hybrid with constant +pressure +8-node trilinear displacement, pore pressure, and temperature; reduced integration +8-node trilinear displacement, pore pressure, and temperature; reduced integration, +hybrid with constant pressure +10-node modified displacement, pore pressure, and temperature tetrahedron, with +hourglass control +Active degrees of freedom +1, 2, 3, 8, 11 +Additional solution variables +The constant pressure hybrid elements have one additional variable relating to the effective pressure +stress to permit fully incompressible material modeling. +Element type C3D10MPT has three additional displacement variables, one additional pore pressure +variable, and one additional temperature variable. +Acoustic elements +AC3D4 +AC3D6 +AC3D8(S) +AC3D8R(E) +AC3D10(S) +4-node linear tetrahedron +6-node linear triangular prism +8-node linear brick +8-node linear brick, reduced integration with hourglass control +10-node quadratic tetrahedron +AC3D15(S) +AC3D20(S) +15-node quadratic triangular prism +20-node quadratic brick +Active degree of freedom +Additional solution variables +None. +Piezoelectric elements +C3D4E(S) +C3D6E(S) +C3D8E(S) +C3D10E(S) +C3D15E(S) +C3D20E(S) +4-node linear tetrahedron +6-node linear triangular prism +8-node linear brick +10-node quadratic tetrahedron +15-node quadratic triangular prism +20-node quadratic brick +C3D20RE(S) +20-node quadratic brick, reduced integration +Active degrees of freedom +1, 2, 3, 9 +Additional solution variables +None. +Electromagnetic elements +EMC3D4(S) +EMC3D8(S) +4-node zero-order +8-node zero-order +Active degree of freedom +Magnetic vector potential (for more information, see “Boundary conditions” in “Eddy current analysis,” +Section 6.7.5, and “Boundary conditions” in “Magnetostatic analysis,” Section 6.7.6). +Additional solution variables +None. +Nodal coordinates required +X, Y, Z +Element property definition +Input File Usage: +*SOLID SECTION +Abaqus/CAE Usage: +Property module: Create Section: select Solid as the section Category and +Homogeneous or Electromagnetic, Solid as the section Type +Element-based loading +Distributed loads +Distributed loads are available for all elements with displacement degrees of freedom. They are specified +as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +BX +BY +BZ +BXNU +Body force +Body force +Body force +Body force +FL−3 +FL−3 +FL−3 +FL−3 +BYNU +Body force +FL−3 +Body force in global X-direction. +Body force in global Y-direction. +Body force in global Z-direction. +Nonuniform body force in global +X-direction with magnitude supplied +subroutine DLOAD in +via +Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +user +Nonuniform body force in global +Y-direction with magnitude supplied +subroutine DLOAD in +via +user +and VDLOAD in +Abaqus/Standard +Abaqus/Explicit. +BZNU +Body force +CENT(S) +Not supported +FL−3 +Nonuniform body force in global +Z-direction with magnitude supplied +subroutine DLOAD in +via +user +and VDLOAD in +Abaqus/Standard +Abaqus/Explicit. +FL−4 (ML−3T−2) Centrifugal load (magnitude is input +as +is the mass density +, where +per unit volume, +is the angular +velocity). Not available for pore +pressure elements. +CENTRIF(S) +Rotational body +force +T−2 +Centrifugal load (magnitude is input +as +the angular +velocity). +, where +is +CORIO(S) +Coriolis force +FL−4 T +(ML−3 T−1 ) +Coriolis force (magnitude is input +is the mass density +as +, where +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +3-D SOLIDS +GRAV +Gravity +HPn(S) +Pn +PnNU +Not supported +Pressure +Not supported +LT−2 +FL−2 +FL−2 +FL−2 +is the angular +per unit volume, +velocity). Not available for pore +pressure elements. +Gravity +loading +direction (magnitude is +acceleration). +in +specified +input as +Hydrostatic pressure on face n, linear +in global Z. +Pressure on face n. +on +with +user +face +Nonuniform pressure +supplied +magnitude +subroutine DLOAD in +via +Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +ROTA(S) +Rotational body +force +T−2 +ROTDYNF(S) +Not supported +T−1 +SBF(E) +Not supported +FL−5 T2 +Rotary acceleration load (magnitude +is input as +is the rotary +acceleration). +, where +Rotordynamic load (magnitude is +input as +is the angular +velocity). +, where +Stagnation body force in global X-, +Y-, and Z-directions. +Not supported +FL−4 T2 +Stagnation pressure on face n. +Shear traction on face n. +Nonuniform shear traction on face +and direction +n with magnitude +subroutine +via +supplied +UTRACLOAD. +user +General traction on face n. +Nonuniform general traction on face +and direction +n with magnitude +supplied +subroutine +via +UTRACLOAD. +user +FL−2 +FL−2 +FL−2 +FL−2 +28.1.4–9 +SPn(E) +TRSHRn +Surface traction +TRSHRnNU(S) +Not supported +TRVECn +Surface traction +TRVECnNU(S) +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +VBF(E) +VPn(E) +Not supported +FL−4 T +Not supported +FL−3 T +Viscous body force in global X-, Y-, +and Z-directions. +Viscous pressure on face n, applying +a pressure proportional to the velocity +normal to the face and opposing the +motion. +Foundations +Foundations are available for Abaqus/Standard elements with displacement degrees of freedom. They +are specified as described in “Element foundations,” Section 2.2.2. +Load ID +(*FOUNDATION) Load/Interaction +Abaqus/CAE +Fn(S) +Elastic +foundation +Distributed heat fluxes +Units +Description +FL−3 +Elastic foundation on face n. +Distributed heat fluxes are available for all elements with temperature degrees of freedom. They are +specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*DFLUX) +BF +BFNU(S) +Abaqus/CAE +Load/Interaction +Units +Description +Body heat flux +Body heat flux +JL−3 T−1 +JL−3 T−1 +Sn +Surface heat flux +JL−2 T−1 +SnNU(S) +Not supported +JL−2 T−1 +Heat body flux per unit volume. +Nonuniform heat body flux per unit +volume with magnitude supplied via +user subroutine DFLUX. +Heat surface flux per unit area into +face n. +Nonuniform heat surface flux per +unit area into face n with magnitude +supplied via user subroutine DFLUX. +Film conditions +Film conditions are available for all elements with temperature degrees of freedom. They are specified +as described in “Thermal loads,” Section 33.4.4. +Load ID +(*FILM) +Fn +Abaqus/CAE +Load/Interaction +Units +Description +Surface film +condition +JL−2 T−1 −1 +Film coefficient and sink temperature +(units of +) provided on face n. +FnNU(S) +Not supported +JL−2 T−1 −1 +Nonuniform film coefficient and sink +temperature (units of +) provided on +face n with magnitude supplied via +user subroutine FILM. +Radiation types +Radiation conditions are available for all elements with temperature degrees of freedom. They are +specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*RADIATE) +Abaqus/CAE +Load/Interaction +Units +Description +Rn +Surface radiation Dimensionless +Emissivity and sink temperature +(units of +) provided on face n. +Distributed flows +Distributed flows are available for all elements with pore pressure degrees of freedom. They are specified +as described in “Pore fluid flow,” Section 33.4.7. +Load ID +(*FLOW) +Qn(S) +Abaqus/CAE +Load/Interaction +Units +Description +Not supported +F−1 L3T−1 +Seepage coefficient and reference +sink pore pressure (units of FL−2 ) +provided on face n. +Drainage-only seepage +provided on face n. +coefficient +Nonuniform seepage +coefficient +and reference sink pore pressure +(units of FL−2 ) provided on face n +with magnitude supplied via user +subroutine FLOW. +QnD(S) +Not supported +F−1 L3T−1 +QnNU(S) +Not supported +F−1 L3T−1 +Load ID +(*DFLOW) +Sn(S) +Abaqus/CAE +Load/Interaction +Units +Description +Surface pore +fluid +LT−1 +pore +Prescribed +effective +velocity (outward from the face) on +face n. +fluid +SnNU(S) +Not supported +LT−1 +Nonuniform prescribed pore fluid +effective velocity (outward from +the face) on face n with magnitude +supplied via user subroutine DFLOW. +Distributed impedances +Distributed impedances are available for all elements with acoustic pressure degrees of freedom. They +are specified as described in “Acoustic and shock loads,” Section 33.4.6. +Load ID +(*IMPEDANCE) +Abaqus/CAE +Load/Interaction +Units +Description +In +Not supported +None +Name of the impedance property that +defines the impedance on face n. +Electric fluxes +Electric fluxes are available for piezoelectric elements. They are specified as described in “Piezoelectric +analysis,” Section 6.7.2. +Load ID +(*DECHARGE) +Abaqus/CAE +Load/Interaction +Units +Description +EBF(S) +ESn(S) +Body charge +Surface charge +CL−3 +CL−2 +Body flux per unit volume. +Prescribed surface charge on face n. +Distributed electric current densities +Distributed electric current densities are available for coupled thermal-electrical, +coupled +thermal-electrical-structural elements, and electromagnetic elements. They are specified as described +in “Coupled thermal-electrical analysis,” Section 6.7.3; “Fully coupled thermal-electrical-structural +analysis,” Section 6.7.4; and “Eddy current analysis,” Section 6.7.5. +Load ID +(*DECURRENT) Load/Interaction +Abaqus/CAE +Units +Description +CBF(S) +CSn(S) +Body current +Surface current +CL−3T−1 +CL−2T−1 +Volumetric current source density. +Current density on face n. +Load ID +(*DECURRENT) Load/Interaction +CJ(S) +current +Body +density +3-D SOLIDS +Units +Description +CL−2T−1 +Volume current density vector in an +eddy current analysis. +Distributed concentration fluxes +Distributed concentration fluxes are available for mass diffusion elements. They are specified as +described in “Mass diffusion analysis,” Section 6.9.1. +Load ID +(*DFLUX) +BF(S) +BFNU(S) +Sn(S) +SnNU(S) +Abaqus/CAE +Load/Interaction +Units +Description +Body +concentration +flux +Body +concentration +flux +Surface +concentration +flux +Surface +concentration +flux +PT−1 +PT−1 +PLT−1 +PLT−1 +Concentration body flux per unit +volume. +Nonuniform concentration body flux +per unit volume with magnitude +supplied via user subroutine DFLUX. +Concentration surface flux per unit +area into face n. +Nonuniform concentration surface +flux per unit area into face n +with magnitude supplied via user +subroutine DFLUX. +Surface-based loading +Distributed loads +Surface-based distributed loads are available for all elements with displacement degrees of freedom. +They are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +HP(S) +PNU +Pressure +Pressure +Pressure +FL−2 +FL−2 +FL−2 +Hydrostatic pressure on the element +surface, linear in global Z. +Pressure on the element surface. +Nonuniform pressure on the element +supplied +surface with magnitude +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +SP(E) +Pressure +FL−4 T2 +TRSHR +Surface traction +TRSHRNU(S) +Surface traction +FL−2 +FL−2 +TRVEC +Surface traction +FL−2 +TRVECNU(S) +Surface traction +FL−2 +VP(E) +Pressure +FL−3 T +user +subroutine DLOAD in +via +Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +Stagnation pressure on the element +surface. +Shear traction on the element surface. +Nonuniform shear +traction on the +element surface with magnitude and +direction supplied via user subroutine +UTRACLOAD. +General +surface. +traction on the element +Nonuniform general traction on the +element surface with magnitude and +direction supplied via user subroutine +UTRACLOAD. +Viscous pressure applied on the +element surface. The viscous pressure +is proportional to the velocity normal +to the element face and opposing the +motion. +Distributed heat fluxes +Surface-based heat fluxes are available for all elements with temperature degrees of freedom. They are +specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*DSFLUX) +Abaqus/CAE +Load/Interaction +Units +Description +Surface heat flux +JL−2 T−1 +SNU(S) +Surface heat flux +JL−2 T−1 +Heat surface flux per unit area into the +element surface. +Nonuniform heat surface flux per +unit area into the element surface +with magnitude supplied via user +subroutine DFLUX. +Film conditions +Surface-based film conditions are available for all elements with temperature degrees of freedom. They +are specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*SFILM) +FNU(S) +Radiation types +Abaqus/CAE +Load/Interaction +Units +Description +Surface film +condition +Surface film +condition +JL−2 T−1 −1 +JL−2 T−1 −1 +Film coefficient and sink temperature +(units of +) provided on the element +surface. +Nonuniform film coefficient and sink +temperature (units of +) provided on +the element surface with magnitude +supplied via user subroutine FILM. +Surface-based radiation conditions are available for all elements with temperature degrees of freedom. +They are specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*SRADIATE) +Abaqus/CAE +Load/Interaction +Units +Description +Surface radiation Dimensionless +Emissivity and sink temperature +(units of +) provided on the element +surface. +Distributed flows +Surface-based flows are available for all elements with pore pressure degrees of freedom. They are +specified as described in “Pore fluid flow,” Section 33.4.7. +Load ID +(*SFLOW) +Q(S) +Abaqus/CAE +Load/Interaction +Units +Description +Not supported +F−1 L3T−1 +Seepage coefficient and reference +sink pore pressure (units of FL−2 ) +provided on the element surface. +Drainage-only seepage +provided on the element surface. +coefficient +Nonuniform seepage coefficient and +reference sink pore pressure (units +of FL−2 ) provided on the element +QD(S) +Not supported +F−1 L3T−1 +QNU(S) +Not supported +F−1 L3T−1 +Load ID +(*SFLOW) +Abaqus/CAE +Load/Interaction +Units +Description +Load ID +(*DSFLOW) +S(S) +SNU(S) +surface with magnitude supplied via +user subroutine FLOW. +Abaqus/CAE +Load/Interaction +Units +Description +Surface pore +fluid +Surface pore +fluid +LT−1 +LT−1 +pore +Prescribed +effective +velocity outward from the element +surface. +fluid +Nonuniform prescribed pore fluid +effective velocity outward from the +surface with magnitude +element +supplied via user subroutine DFLOW. +Distributed impedances +Surface-based impedances are available for all elements with acoustic pressure degrees of freedom. They +are specified as described in “Acoustic and shock loads,” Section 33.4.6. +Incident wave loading +Surface-based incident wave loads are available for all elements with displacement degrees of freedom +or acoustic pressure degrees of freedom. They are specified as described in “Acoustic and shock loads,” +Section 33.4.6. If the incident wave field includes a reflection off a plane outside the boundaries of the +mesh, this effect can be included. +Electric fluxes +Surface-based electric fluxes are available for piezoelectric elements. They are specified as described in +“Piezoelectric analysis,” Section 6.7.2. +Load ID +(*DSECHARGE) Load/Interaction +Abaqus/CAE +Units +Description +ES(S) +Surface charge +CL−2 +Prescribed surface charge on the +element surface. +Distributed electric current densities +Surface-based electric current densities are available for coupled thermal-electrical, coupled thermal- +electrical-structural, and electromagnetic elements. They are specified as described in “Coupled thermal- +electrical analysis,” Section 6.7.3, “Fully coupled thermal-electrical-structural analysis,” Section 6.7.4, +and “Eddy current analysis,” Section 6.7.5. +Load ID +(*DSECURRENT) Load/Interaction +Abaqus/CAE +Units +Description +CS(S) +CK(S) +Surface current +CL−2T−1 +Surface +density +current +CL−1T−1 +Current density on the +surface. +element +Surface current density vector in an +eddy current analysis. +Element output +For most elements output is in global directions unless a local coordinate system is assigned to the +element through the section definition (“Orientations,” Section 2.2.5) in which case output is in the local +coordinate system (which rotates with the motion in large-displacement analysis). See “State storage,” +Section 1.5.4 of the Abaqus Theory Manual, for details. +Stress, strain, and other tensor components +Stress and other tensors (including strain tensors) are available for elements with displacement degrees +of freedom. All tensors have the same components. For example, the stress components are as follows: +S11 +S22 +S33 +S12 +S13 +S23 +, direct stress. +, direct stress. +, direct stress. +, shear stress. +, shear stress. +, shear stress. +Note: the order shown above is not the same as that used in user subroutine VUMAT. +Heat flux components +Available for elements with temperature degrees of freedom. +HFL1 +HFL2 +HFL3 +Heat flux in the X-direction. +Heat flux in the Y-direction. +Heat flux in the Z-direction. +Pore fluid velocity components +Available for elements with pore pressure degrees of freedom. +FLVEL1 +FLVEL2 +FLVEL3 +Pore fluid effective velocity in the X-direction. +Pore fluid effective velocity in the Y-direction. +Pore fluid effective velocity in the Z-direction. +Mass concentration flux components +Available for elements with normalized concentration degrees of freedom. +MFL1 +MFL2 +MFL3 +Concentration flux in the X-direction. +Concentration flux in the Y-direction. +Concentration flux in the Z-direction. +Electrical potential gradient +Available for elements with electrical potential degrees of freedom. +EPG1 +EPG2 +EPG3 +Electrical potential gradient in the X-direction. +Electrical potential gradient in the Y-direction. +Electrical potential gradient in the Z-direction. +Electrical flux components +Available for piezoelectric elements. +EFLX1 +EFLX2 +EFLX3 +Electrical flux in the X-direction. +Electrical flux in the Y-direction. +Electrical flux in the Z-direction. +Electrical current density components +Available for coupled thermal-electrical and coupled thermal-electrical-structural elements. +ECD1 +ECD2 +ECD3 +Electrical current density in the X-direction. +-direction. +Electrical current density in the +Electrical current density in the Z-direction. +Electrical field components +Available for electromagnetic elements in an eddy current analysis. +EME1 +EME2 +EME3 +Electric field in the X-direction. +Electric field in the Y-direction. +Electric field in the Z-direction. +Magnetic flux density components +Available for electromagnetic elements. +EMB1 +EMB2 +EMB3 +Magnetic flux density in the X-direction. +Magnetic flux density in the Y-direction. +Magnetic flux density in the Z-direction. +Magnetic field components +Available for electromagnetic elements. +EMH1 +EMH2 +EMH3 +Magnetic field in the X-direction. +Magnetic field in the Y-direction. +Magnetic field in the Z-direction. +Electrical current density components in an eddy current analysis +Available for electromagnetic elements in an eddy current analysis. +EMCD1 +EMCD2 +EMCD3 +Electrical current density in the X-direction. +Electrical current density in the Y-direction. +Electrical current density in the Z-direction. +Node ordering and face numbering on elements +All elements except variable node elements +face 4 +face 4 +face 3 +face 2 +face 2 +face 3 +face 1 +4 - node element +face 2 +face 5 +face 4 +face 1 +6 - node element +face 2 +face 5 +face 6 +face 4 +10 +face 3 +face 1 +face 3 +13 +10 - node element +face 2 +12 +face 5 +10 +11 +14 +15 - node element +15 +face 4 +face 1 +face 6 +17 +face 2 +16 +13 +20 +12 +18 +face 5 +15 +19 +face 4 +14 +11 +10 +face 1 +face 3 +face 3 +face 1 +8 - node element +20 - node element +Tetrahedral element faces +Face 1 +Face 2 +Face 3 +Face 4 +1 – 2 – 3 face +1 – 4 – 2 face +2 – 4 – 3 face +3 – 4 – 1 face +Wedge (triangular prism) element faces +Face 1 +Face 2 +Face 3 +Face 4 +Face 5 +1 – 2 – 3 face +4 – 6 – 5 face +1 – 4 – 5 – 2 face +2 – 5 – 6 – 3 face +3 – 6 – 4 – 1 face +Hexahedron (brick) element faces +Face 1 +Face 2 +Face 3 +Face 4 +Face 5 +Face 6 +1 – 2 – 3 – 4 face +5 – 8 – 7 – 6 face +1 – 5 – 6 – 2 face +2 – 6 – 7 – 3 face +3 – 7 – 8 – 4 face +4 – 8 – 5 – 1 face +Variable node elements +13 +15 +11 +17 +12 +10 +18 +16 +14 +15 to 18 - node element +16–18 are midface nodes on the three rectangular faces . These +nodes +can be omitted from an element by entering a zero or blank in the corresponding position when giving +the nodes on the element. Only nodes 16–18 can be omitted. +Face location of nodes 16 to 18 +Face node number +Corner nodes on face +16 +17 +18 +1 – 4 – 5 – 2 +2 – 5 – 6 – 3 +3 – 6 – 4 – 1 +15 +14 +26 +25 +10 +23 +20 +18 +11 +21 +22 +19 +16 +13 +27 +17 +24 +12 +21 to 27 - node element +Node 21 is located at the centroid of the element. +(nodes 22–27) are midface nodes on the six faces . These +nodes can be +deleted from an element by entering a zero or blank in the corresponding position when giving the nodes +on the element. Only nodes 22–27 can be omitted. +Face location of nodes 22 to 27 +Face node number +Corner nodes on face +1 – 2 – 3 – 4 +5 – 8 – 7 – 6 +1 – 5 – 6 – 2 +2 – 6 – 7 – 3 +3 – 7 – 8 – 4 +4 – 8 – 5 – 1 +28.1.4–23 +22 +23 +24 +25 +26 +Numbering of integration points for output +All elements except variable node elements +4 - node element +10 - node element +10 +1 2 +6 - node element +8 - node element +15 - node element +8 - node reduced +integration element +4 11 3 +4 11 3 +12 +10 +2 0 - node element +12 +2 0 - node reduced +integration element +10 +This shows the scheme in the layer closest to the 1–2–3 and 1–2–3–4 faces. The integration points in +the second and third layers are numbered consecutively. Multiple layers are used for composite solid +elements. +For heat transfer applications a different integration scheme is used for tetrahedral and wedge elements, as +described in “Triangular, tetrahedral, and wedge elements,” Section 3.2.6 of the Abaqus Theory Manual. +For linear triangular prisms in Abaqus/Explicit reduced integration is used; therefore, a C3D6 element +and a C3D6T element have only one integration point. +For the general-purpose C3D10I 10-node tetrahedra in Abaqus/Standard improved stress visualization is +obtained through an 11-point integration rule, consisting of 10 integration points at the elements’ nodes +and one integration point at their centroid. +For acoustic tetrahedra and wedges in Abaqus/Standard full integration is used; therefore, an AC3D4 +element has 4 integration points, an AC3D6 element has 6 integration points, an AC3D10 element has +10 integration points, and an AC3D15 element has 18 integration points. +Variable node elements +4 11 3 +10 +12 +15 to 18 - node element +21 to 27 - node element +This shows the scheme in the layer closest to the 1–2–3 and 1–2–3–4 faces. The integration points in +the second and third layers are numbered consecutively. Multiple layers are used for composite solid +elements. The face nodes do not appear. +14 +11 +10 +12 +13 +21 to 27 - node reduced +integration element +Node 21 is located at the centroid of the element. +28.1.5 +CYLINDRICAL SOLID ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/CAE +References +• “Solid (continuum) elements,” Section 28.1.1 +• *SOLID SECTION +Overview +This section provides a reference to the cylindrical solid elements available in Abaqus/Standard. +Element types +CCL9 +CCL9H +CCL12 +CCL12H +CCL18 +CCL18H +CCL24 +CCL24H +9-node cylindrical prism, linear interpolation in the radial plane and trigonometric +interpolation along the circumferential direction +9-node cylindrical prism, linear interpolation in the radial plane and trigonometric +interpolation along the circumferential direction, hybrid with constant pressure in +plane and linear pressure in the circumferential direction +12-node cylindrical brick, linear interpolation in the radial plane and trigonometric +interpolation along the circumferential direction +12-node cylindrical brick, linear interpolation in the radial plane and trigonometric +interpolation along the circumferential direction, hybrid with constant pressure in plane +and linear pressure in circumferential direction +18-node cylindrical prism, quadratic interpolation in the radial plane and trigonometric +interpolation along the circumferential direction +18-node cylindrical prism, quadratic interpolation in the radial plane and trigonometric +interpolation along the circumferential direction, hybrid with linear pressure in plane +and linear pressure in the circumferential direction +24-node cylindrical brick, quadratic interpolation in the radial plane and trigonometric +interpolation along the circumferential direction +24-node cylindrical brick, quadratic interpolation in the radial plane and trigonometric +interpolation along the circumferential direction, hybrid with linear pressure in plane +and linear pressure in circumferential direction +CCL24R +24-node cylindrical brick, reduced integration, quadratic interpolation in the radial +plane and trigonometric interpolation along the circumferential direction +CCL24RH +24-node cylindrical brick, reduced integration, quadratic interpolation in the radial +plane and trigonometric interpolation along the circumferential direction, hybrid with +linear pressure in plane and linear pressure in circumferential direction +Active degrees of freedom +1, 2, 3 +Additional solution variables +The hybrid elements with constant pressure in plane have two additional variables relating to pressure, +and the linear pressure hybrid elements have six additional variables relating to pressure. +Nodal coordinates required +X, Y, Z +Element property definition +Input File Usage: +Abaqus/CAE Usage: +*SOLID SECTION +Property module: Create Section: select Solid as the section Category +and Homogeneous as the section Type +Element-based loading +Distributed loads +Distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Units +Description +FL−3 +FL−3 +FL−3 +FL−3 +FL−3 +FL−3 +Body force in global X-direction. +Body force in global Y-direction. +Body force in global Z-direction. +Nonuniform body force in global X- +direction with magnitude supplied via user +subroutine DLOAD. +Nonuniform body force in global Y- +direction with magnitude supplied via user +subroutine DLOAD. +Nonuniform body force in global Z- +direction with magnitude supplied via user +subroutine DLOAD. +28.1.5–2 +Load ID +(*DLOAD) +BX +BY +BZ +BXNU +BYNU +Units +Description +Load ID +(*DLOAD) +CENT +FL−4 (ML−3T−2) +CENTRIF +FL−4 (ML−3T−1) +CORIO +FL−4 T (ML−3 T−1 ) +GRAV +HPn +Pn +ROTA +LT−2 +FL−2 +FL−2 +T−2 +ROTDYNF(S) +T−1 +TRSHRn +TRSHRnNU(S) +TRVECn +TRVECnNU(S) +FL−2 +FL−2 +FL−2 +FL−2 +Centrifugal load (magnitude is input as +where +, +is the mass density per unit volume, +is the angular velocity). +Centrifugal load (magnitude is input as +where +is the angular velocity). +, +Coriolis force (magnitude is input as +where +, +is the mass density per unit volume, +is the angular velocity). +Gravity loading in a specified direction +(magnitude is input as acceleration). +Hydrostatic pressure on face n, linear in +global Z. +Pressure on face n. +Rotary acceleration load (magnitude is input +as +is the rotary acceleration). +, where +Rotordynamic load (magnitude is input as +, where +is the angular velocity). +Shear traction on face n. +Nonuniform shear traction on face n with +magnitude and direction supplied via user +subroutine UTRACLOAD. +General traction on face n. +Nonuniform general traction on face n with +magnitude and direction supplied via user +subroutine UTRACLOAD. +Foundations +Foundations are available for all cylindrical elements. They are specified as described in “Element +foundations,” Section 2.2.2. +Load ID +(*FOUNDATION) +Units +Description +Fn +FL−3 +Elastic foundation on face n. +Surface-based loading +Distributed loads +Surface-based distributed loads are available for elements with displacement degrees of freedom. They +are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DSLOAD) +HP +Pn +PnNU +TRSHR +TRSHRNU(S) +TRVEC +TRVECNU(S) +Element output +Units +Description +FL−2 +FL−2 +FL−2 +FL−2 +FL−2 +FL−2 +FL−2 +Hydrostatic pressure on the element surface, +linear in global Z. +Pressure on the element surface. +Nonuniform pressure on the element surface +with magnitude supplied via user subroutine +DLOAD. +Shear traction on the element surface. +Nonuniform shear traction on the element +surface with magnitude +and direction +supplied via user subroutine UTRACLOAD. +General traction on the element surface. +Nonuniform general traction on the element +surface with magnitude +and direction +supplied via user subroutine UTRACLOAD. +Output is in a fixed cylindrical system (1=radial, 2=axial, 3=circumferential) unless a local coordinate +system is assigned to the element through the section definition (“Orientations,” Section 2.2.5) in which +case output is in the local coordinate system (which rotates with the motion in large-displacement +analysis). See “State storage,” Section 1.5.4 of the Abaqus Theory Manual, for details. +Stress, strain, and other tensor components +Stress and other tensors (including strain tensors) are available for elements with displacement degrees +of freedom. All tensors have the same components. For example, the stress components are as follows: +S11 +S22 +S33 +S12 +Local 11 direct stress. +Local 22 direct stress. +Local 33 direct stress. +Local 12 shear stress. +S23 +Local 13 shear stress. +Local 23 shear stress. +Node ordering and face numbering on elements +face 1 +14 +23 +15 +12 +13 +16 +12 +face 1 +face 6 +face 5 +11 +10 +face 4 +face 3 +face 6 +24 +21 +20 +face 2 +face 3 +face 2 +CYLINDRICAL SOLIDS +11 +face 5 +22 +10 +19 +17 +face 4 +18 +12-node element +12-node element +24-node element +face 1 +face 3 +face 1 +12 +face 4 +face 5 +10 +face 2 +face 3 +face 5 +11 +18 +16 +face 4 +17 +15 +14 +13 +face 2 +9-node element +18-node element +12-node and 24-node cylindrical element faces +Face 1 +Face 2 +1 – 2 – 3 – 4 face +5 – 8 – 7 – 6 face +Face 3 +Face 4 +Face 5 +Face 6 +1 – 5 – 6 – 2 face +2 – 6 – 7 – 3 face +3 – 7 – 8 – 4 face +4 – 8 – 5 – 1 face +9-node and 18-node cylindrical element faces +Face 1 +Face 2 +Face 3 +Face 4 +Face 5 +1 – 2 – 3 face +4 – 6 – 5 face +1 – 4 – 5 – 2 face +2 – 5 – 6 – 3 face +3 – 6 – 4 – 1 face +Numbering of integration points for output +15 + 7 8 9 +16 + 4 5 6 +14 + 1 2 3 +13 +24-node full +integration element +16 +12-node element +15 +14 +13 +24-node reduced +integration element +This shows the scheme in the layer closest to the 1–2–3–4 face. The integration points in the second and +third layers are numbered consecutively. +28.1.6 +AXISYMMETRIC SOLID ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Solid (continuum) elements,” Section 28.1.1 +• *SOLID SECTION +Overview +This section provides a reference to the axisymmetric solid elements available in Abaqus/Standard and +Abaqus/Explicit. +Conventions +Coordinate 1 is , coordinate 2 is +the r-direction corresponds to the global x-direction and +the z-direction corresponds to the global y-direction. This is important when data must be given in global +directions. Coordinate 1 must be greater than or equal to zero. +. At +Degree of freedom 1 is +have an additional degree of freedom, 5, corresponding to the twist angle +, degree of freedom 2 is +. Generalized axisymmetric elements with twist +(in radians). +Abaqus does not automatically apply any boundary conditions to nodes located along the symmetry axis. +You must apply radial or symmetry boundary conditions on these nodes if desired. +In certain situations in Abaqus/Standard it may become necessary to apply radial boundary conditions on +nodes that are located on the symmetry axis to obtain convergence in nonlinear problems. Therefore, the +application of radial boundary conditions on nodes on the symmetry axis is recommended for nonlinear +problems. +Point loads and moments, concentrated (nodal) fluxes, electrical currents, and seepage should be given +as the value integrated around the circumference (that is, the total value on the ring). +Element types +Stress/displacement elements without twist +CAX3 +CAX3H(S) +CAX4(S) +CAX4H(S) +CAX4I(S) +3-node linear +3-node linear, hybrid with constant pressure +4-node bilinear +4-node bilinear, hybrid with constant pressure +4-node bilinear, incompatible modes +CAX4IH(S) +4-node bilinear, incompatible modes, hybrid with linear pressure +CAX4R +4-node bilinear, reduced integration with hourglass control +CAX4RH(S) +CAX6(S) +CAX6H(S) +4-node bilinear, reduced integration with hourglass control, hybrid with constant +pressure +6-node quadratic +6-node quadratic, hybrid with linear pressure +CAX6M +6-node modified, with hourglass control +CAX6MH(S) +6-node modified, with hourglass control, hybrid with linear pressure +CAX8(S) +CAX8H(S) +CAX8R(S) +8-node biquadratic +8-node biquadratic, hybrid with linear pressure +8-node biquadratic, reduced integration +CAX8RH(S) +8-node biquadratic, reduced integration, hybrid with linear pressure +Active degrees of freedom +1, 2 +Additional solution variables +The constant pressure hybrid elements have one additional variable and the linear pressure elements have +three additional variables relating to pressure. +Element types CAX4I and CAX4IH have five additional variables relating to the incompatible modes. +Element types CAX6M and CAX6MH have two additional displacement variables. +Stress/displacement elements with twist +CGAX3(S) +3-node linear +CGAX3H(S) +3-node linear, hybrid with constant pressure +CGAX4(S) +4-node bilinear +CGAX4H(S) +CGAX4R(S) +CGAX4RH(S) +4-node bilinear, hybrid with constant pressure +4-node bilinear, reduced integration with hourglass control +4-node bilinear, reduced integration with hourglass control, hybrid with constant +pressure +CGAX6(S) +6-node quadratic +CGAX6H(S) +CGAX6M(S) +6-node quadratic, hybrid with linear pressure +6-node modified, with hourglass control +CGAX6MH(S) +6-node modified, with hourglass control, hybrid with linear pressure +CGAX8(S) +8-node biquadratic +CGAX8H(S) +CGAX8R(S) +8-node biquadratic, hybrid with linear pressure +8-node biquadratic, reduced integration +CGAX8RH(S) +8-node biquadratic, reduced integration, hybrid with linear pressure +Active degrees of freedom +1, 2, 5 +Additional solution variables +The constant pressure hybrid elements have one additional variable and the linear pressure elements have +three additional variables relating to pressure. +Element types CGAX6M and CGAX6MH have three additional displacement variables. +Diffusive heat transfer or mass diffusion elements +DCAX3(S) +DCAX4(S) +DCAX6(S) +DCAX8(S) +3-node linear +4-node linear +6-node quadratic +8-node quadratic +Active degree of freedom +11 +Additional solution variables +None. +Forced convection/diffusion elements +DCCAX2(S) +2-node +DCCAX2D(S) +2-node with dispersion control +DCCAX4(S) +4-node +DCCAX4D(S) +4-node with dispersion control +Active degree of freedom +11 +Additional solution variables +None. +Coupled thermal-electrical elements +DCAX3E(S) +DCAX4E(S) +DCAX6E(S) +3-node linear +4-node linear +6-node quadratic +DCAX8E(S) +8-node quadratic +Active degrees of freedom +9, 11 +Additional solution variables +None. +Coupled temperature-displacement elements without twist +CAX3T +CAX4T(S) +CAX4HT(S) +CAX4RT +3-node linear displacement and temperature +4-node bilinear displacement and temperature +4-node bilinear displacement and temperature, hybrid with constant pressure +4-node bilinear displacement and temperature, reduced integration with hourglass +control +CAX4RHT(S) +4-node bilinear displacement and temperature, reduced integration with hourglass +control, hybrid with constant pressure +CAX6MT +6-node modified displacement and temperature, with hourglass control +CAX6MHT(S) +CAX8T(S) +CAX8HT(S) +CAX8RT(S) +CAX8RHT(S) +6-node modified displacement and temperature, with hourglass control, hybrid with +linear pressure +8-node biquadratic displacement, bilinear temperature +8-node biquadratic displacement, bilinear temperature, hybrid with linear pressure +8-node biquadratic displacement, bilinear temperature, reduced integration +8-node biquadratic displacement, bilinear temperature, reduced integration, hybrid +with linear pressure +Active degrees of freedom +1, 2, 11 at corner nodes +1, 2 at midside nodes of second-order elements in Abaqus/Standard +1, 2, 11 at midside nodes of the modified displacement and temperature elements in Abaqus/Standard +Additional solution variables +The constant pressure hybrid elements have one additional variable and the linear pressure elements have +three additional variables relating to pressure. +Element types CAX6MT and CAX6MHT have two additional displacement variables and one additional +temperature variable. +Coupled temperature-displacement elements with twist +CGAX3T(S) +3-node linear displacement and temperature +CGAX3HT(S) +3-node linear displacement and temperature, hybrid with constant pressure +CGAX4T(S) +4-node bilinear displacement and temperature +CGAX4HT(S) +CGAX4RT(S) +4-node bilinear displacement and temperature, hybrid with constant pressure +4-node bilinear displacement and temperature, reduced integration with hourglass +control +CGAX4RHT(S) 4-node bilinear displacement and temperature, reduced integration with hourglass +control, hybrid with constant pressure +CGAX6MT(S) +6-node modified displacement and temperature, with hourglass control +CGAX6MHT(S) 6-node modified displacement and temperature, with hourglass control, hybrid with +constant pressure +CGAX8T(S) +8-node biquadratic displacement, bilinear temperature +CGAX8HT(S) +CGAX8RT(S) +8-node biquadratic displacement, bilinear temperature, hybrid with linear pressure +8-node biquadratic displacement, bilinear temperature, reduced integration +CGAX8RHT(S) 8-node biquadratic displacement, bilinear temperature, reduced integration, hybrid +with linear pressure +Active degrees of freedom +1, 2, 5, 11 at corner nodes +1, 2, 5 at midside nodes of second-order elements +1, 2, 5, 11 at midside nodes of the modified displacement and temperature elements +Additional solution variables +The constant pressure hybrid elements have one additional variable and the linear pressure elements have +three additional variables relating to pressure. +Element types CGAX6MT and CGAX6MHT have two additional displacement variables and one +additional temperature variable. +Pore pressure elements +CAX4P(S) +CAX4PH(S) +CAX4RP(S) +CAX4RPH(S) +4-node bilinear displacement and pore pressure +4-node bilinear displacement and pore pressure, hybrid with constant pressure +4-node bilinear displacement and pore pressure, reduced integration with hourglass +control +4-node bilinear displacement and pore pressure, reduced integration with hourglass +control, hybrid with constant pressure +CAX6MP(S) +6-node modified displacement and pore pressure, with hourglass control +CAX6MPH(S) +CAX8P(S) +CAX8PH(S) +CAX8RP(S) +CAX8RPH(S) +6-node modified displacement and pore pressure, with hourglass control, hybrid with +linear pressure +8-node biquadratic displacement, bilinear pore pressure +8-node biquadratic displacement, bilinear pore pressure, hybrid with linear pressure +8-node biquadratic displacement, bilinear pore pressure, reduced integration +8-node biquadratic displacement, bilinear pore pressure, reduced integration, hybrid +with linear pressure +Active degrees of freedom +1, 2, 8 at corner nodes +1, 2 at midside nodes +Additional solution variables +The constant pressure hybrid elements have one additional variable relating to the effective pressure +stress, and the linear pressure hybrid elements have three additional variables relating to the effective +pressure stress to permit fully incompressible material modeling. +Element types CAX6MP and CAX6MPH have two additional displacement variables and one additional +pore pressure variable. +Coupled temperature–pore pressure elements +CAX4PT(S) +CAX4RPT(S) +4-node bilinear displacement, pore pressure, and temperature +4-node bilinear displacement, pore pressure, and temperature; reduced integration with +hourglass control +CAX4RPHT(S) +4-node bilinear displacement, pore pressure, and temperature; reduced integration with +hourglass control, hybrid with constant pressure +Active degrees of freedom +1, 2, 8, 11 +Additional solution variables +The constant pressure hybrid elements have one additional variable relating to the effective pressure +stress to permit fully incompressible material modeling. +Acoustic elements +ACAX3 +3-node linear +ACAX4R(E) +4-node linear, reduced integration with hourglass control +ACAX4(S) +ACAX6(S) +ACAX8(S) +4-node linear +6-node quadratic +8-node quadratic +Active degree of freedom +Additional solution variables +None. +Piezoelectric elements +CAX3E(S) +CAX4E(S) +CAX6E(S) +CAX8E(S) +3-node linear +4-node bilinear +6-node quadratic +8-node biquadratic +CAX8RE(S) +8-node biquadratic, reduced integration +Active degrees of freedom +1, 2, 9 +Additional solution variables +None. +Nodal coordinates required +r, z at +Element property definition +For element types DCCAX2 and DCCAX2D, you must specify the channel thickness of the element in +the (r–z) plane. The default is unit thickness if no thickness is given. +For all other elements, you do not need to specify the thickness. +Input File Usage: +Abaqus/CAE Usage: +*SOLID SECTION +Property module: Create Section: select Solid as the section Category +and Homogeneous as the section Type +Element-based loading +Distributed loads +Distributed loads are available for all elements with displacement degrees of freedom. They are specified +as described in “Distributed loads,” Section 33.4.3. Distributed load magnitudes are per unit area or per +unit volume. They do not need to be multiplied by +. +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +BR +BZ +BRNU +Body force +Body force +Body force +FL−3 +FL−3 +FL−3 +BZNU +Body force +FL−3 +CENT(S) +Not supported +FL−4 M−3 T−2 +CENTRIF(S) +Rotational body +force +T−2 +Body force in radial direction. +Body force in axial direction. +Nonuniform body force in radial +direction with magnitude supplied +subroutine DLOAD in +via +Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +user +Nonuniform body force in axial +direction with magnitude supplied +subroutine DLOAD in +via +Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +user +, where +load (magnitude input +Centrifugal +as +is the mass density +per unit volume, +is the angular +velocity). Not available for pore +pressure elements. +Centrifugal load (magnitude is input +as +the angular +velocity). +, where +is +GRAV +Gravity +Not supported +Pressure +Not supported +LT−2 +FL−2 +FL−2 +FL−2 +loading +Gravity +direction (magnitude is +acceleration). +in +specified +input as +Hydrostatic pressure on face n, linear +in global Y. +Pressure on face n. +on +with +user +face +Nonuniform pressure +supplied +magnitude +subroutine DLOAD in +via +Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +Not supported +FL−5 T2 +Stagnation body force in radial and +axial directions. +Not supported +FL−4 T2 +Stagnation pressure on face n. +28.1.6–8 +HPn(S) +Pn +PnNU +SBF(E) +Units +Description +Load ID +(*DLOAD) +TRSHRn +Abaqus/CAE +Load/Interaction +Surface traction +TRSHRnNU(S) +Not supported +TRVECn +Surface traction +TRVECnNU(S) +Not supported +FL−2 +FL−2 +FL−2 +FL−2 +VBF(E) +VPn(E) +Not supported +FL−4 T +Not supported +FL−3 T +Shear traction on face n. +Nonuniform shear traction on face +and direction +n with magnitude +supplied +subroutine +via +UTRACLOAD. +user +General traction on face n. +Nonuniform general traction on face +and direction +n with magnitude +supplied +subroutine +via +UTRACLOAD. +user +Viscous body force in radial and axial +directions. +Viscous pressure on face n, applying +a pressure proportional to the velocity +normal to the face and opposing the +motion. +Foundations +Foundations are available for Abaqus/Standard elements with displacement degrees of freedom. They +are specified as described in “Element foundations,” Section 2.2.2. +Load ID +(*FOUNDATION) Load/Interaction +Abaqus/CAE +Units +Description +Fn(S) +Elastic +foundation +FL−3 +on +foundation +face +n. +Elastic +the elastic +For CGAX elements +foundations are applied to degrees +of freedom +only. +and +Distributed heat fluxes +Distributed heat fluxes are available for all elements with temperature degrees of freedom. They are +specified as described in “Thermal loads,” Section 33.4.4. Distributed heat flux magnitudes are per unit +area or per unit volume. They do not need to be multiplied by +. +Load ID +(*DFLUX) +BF +Abaqus/CAE +Load/Interaction +Units +Description +Body heat flux +JL−3 T−1 +Heat body flux per unit volume. +Load ID +(*DFLUX) +BFNU(S) +Abaqus/CAE +Load/Interaction +Units +Description +Body heat flux +JL−3 T−1 +Sn +Surface heat flux +JL−2 T−1 +SnNU(S) +Not supported +JL−2 T−1 +Nonuniform heat body flux per unit +volume with magnitude supplied via +user subroutine DFLUX. +Heat surface flux per unit area into +face n. +Nonuniform heat surface flux per +unit area into face n with magnitude +supplied via user subroutine DFLUX. +Film conditions +Film conditions are available for all elements with temperature degrees of freedom. They are specified +as described in “Thermal loads,” Section 33.4.4. +Abaqus/CAE +Load/Interaction +Units +Description +Load ID +(*FILM) +Fn +Surface film +condition +JL−2 T−1 −1 +FnNU(S) +Not supported +JL−2 T−1 −1 +Film coefficient and sink temperature +(units of +) provided on face n. +Nonuniform film coefficient and sink +temperature (units of +) provided on +face n with magnitude supplied via +user subroutine FILM. +Radiation types +Radiation conditions are available for all elements with temperature degrees of freedom. They are +specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*RADIATE) +Abaqus/CAE +Load/Interaction +Units +Description +Rn +Surface radiation Dimensionless +Emissivity and sink temperature +provided for face n. +Distributed flows +Distributed flows are available for all elements with pore pressure degrees of freedom. They are specified +as described in “Pore fluid flow,” Section 33.4.7. Distributed flow magnitudes are per unit area or per +unit volume. They do not need to be multiplied by +. +Abaqus/CAE +Load/Interaction +Units +Description +Not supported +F−1 L3T−1 +Load ID +(*FLOW) +Qn(S) +QnD(S) +Not supported +F−1 L3T−1 +QnNU(S) +Not supported +F−1 L3T−1 +Seepage coefficient and reference +sink pore pressure (units of FL−2 ) +provided on face n. +Drainage-only seepage +provided on face n. +coefficient +Nonuniform seepage +coefficient +and reference sink pore pressure +(units of FL−2 ) provided on face n +with magnitude supplied via user +subroutine FLOW. +Load ID +(*DFLOW) +Sn(S) +Abaqus/CAE +Load/Interaction +Units +Description +Surface pore +fluid +LT−1 +pore +Prescribed +effective +velocity (outward from the face) on +face n. +fluid +SnNU(S) +Not supported +LT−1 +Nonuniform prescribed pore fluid +effective velocity (outward from +the face) on face n with magnitude +supplied via user subroutine DFLOW. +Distributed impedances +Distributed impedances are available for all elements with acoustic pressure degrees of freedom. They +are specified as described in “Acoustic and shock loads,” Section 33.4.6. +Load ID +(*IMPEDANCE) +Abaqus/CAE +Load/Interaction +Units +Description +In +Not supported +None +Name of the impedance property that +defines the impedance on face n. +Electric fluxes +Electric fluxes are available for piezoelectric elements. They are specified as described in “Piezoelectric +analysis,” Section 6.7.2. +Load ID +(*DECHARGE) +Abaqus/CAE +Load/Interaction +Units +Description +EBF(S) +ESn(S) +Body charge +Surface charge +CL−3 +CL−2 +Body flux per unit volume. +Prescribed surface charge on face n. +Distributed electric current densities +Distributed electric current densities are available for coupled thermal-electrical elements. They are +specified as described in “Coupled thermal-electrical analysis,” Section 6.7.3. +Load ID +(*DECURRENT) Load/Interaction +Abaqus/CAE +Units +Description +CBF(S) +CSn(S) +Body current +CL−3T−1 +Volumetric current source density. +Surface current +CL−2T−1 +Current density on face n. +Distributed concentration fluxes +Distributed concentration fluxes are available for mass diffusion elements. They are specified as +described in “Mass diffusion analysis,” Section 6.9.1. +Load ID +(*DFLUX) +BF(S) +BFNU(S) +Sn(S) +SnNU(S) +Abaqus/CAE +Load/Interaction +Units +Description +Body +concentration +flux +Body +concentration +flux +Surface +concentration +flux +Surface +concentration +flux +PT−1 +PT−1 +PLT−1 +PLT−1 +28.1.6–12 +Concentration body flux per unit +volume. +Nonuniform concentration body flux +per unit volume with magnitude +supplied via user subroutine DFLUX. +Concentration surface flux per unit +area into face n. +Nonuniform concentration surface +flux per unit area into face n +with magnitude supplied via user +Surface-based loading +Distributed loads +Surface-based distributed loads are available for all elements with displacement degrees of freedom. +They are specified as described in “Distributed loads,” Section 33.4.3. Distributed load magnitudes are +per unit area or per unit volume. They do not need to be multiplied by +. +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +HP(S) +PNU +Pressure +Pressure +Pressure +FL−2 +FL−2 +FL−2 +SP(E) +Pressure +FL−4 T2 +TRSHR +Surface traction +TRSHRNU(S) +Surface traction +FL−2 +FL−2 +TRVEC +Surface traction +FL−2 +TRVECNU(S) +Surface traction +FL−2 +VP(E) +Pressure +FL−3 T +28.1.6–13 +Hydrostatic pressure on the element +surface, linear in global Y. +Pressure on the element surface. +Nonuniform pressure on the element +supplied +surface with magnitude +subroutine DLOAD in +via +Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +user +Stagnation pressure on the element +surface. +Shear traction on the element surface. +Nonuniform shear +traction on the +element surface with magnitude and +direction supplied via user subroutine +UTRACLOAD. +General +surface. +traction on the element +Nonuniform general traction on the +element surface with magnitude and +direction supplied via user subroutine +UTRACLOAD. +Viscous pressure applied on the +element surface. The viscous pressure +is proportional to the velocity normal +Distributed heat fluxes +Surface-based heat fluxes are available for all elements with temperature degrees of freedom. They are +specified as described in “Thermal loads,” Section 33.4.4. Distributed heat flux magnitudes are per unit +area or per unit volume. They do not need to be multiplied by +. +Load ID +(*DSFLUX) +Abaqus/CAE +Load/Interaction +Units +Description +Surface heat flux +JL−2 T−1 +SNU(S) +Surface heat flux +JL−2 T−1 +Heat surface flux per unit area into the +element surface. +Nonuniform heat surface flux per +unit area into the element surface +with magnitude supplied via user +subroutine DFLUX. +Film conditions +Surface-based film conditions are available for all elements with temperature degrees of freedom. They +are specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*SFILM) +FNU(S) +Radiation types +Abaqus/CAE +Load/Interaction +Units +Description +Surface film +condition +Surface film +condition +JL−2 T−1 −1 +JL−2 T−1 −1 +Film coefficient and sink temperature +(units of +) provided on the element +surface. +Nonuniform film coefficient and sink +temperature (units of +) provided on +the element surface with magnitude +supplied via user subroutine FILM. +Surface-based radiation conditions are available for all elements with temperature degrees of freedom. +They are specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*SRADIATE) +Abaqus/CAE +Load/Interaction +Units +Description +Surface radiation Dimensionless +Emissivity and sink temperature +provided for the element surface. +Distributed flows +Surface-based distributed flows are available for all elements with pore pressure degrees of freedom. +They are specified as described in “Pore fluid flow,” Section 33.4.7. Distributed flow magnitudes are per +unit area or per unit volume. They do not need to be multiplied by +. +Load ID +(*SFLOW) +Abaqus/CAE +Load/Interaction +Units +Description +Q(S) +Not supported +F−1 L3T−1 +QD(S) +Not supported +F−1 L3T−1 +QNU(S) +Not supported +F−1 L3T−1 +Seepage coefficient and reference +sink pore pressure (units of FL−2 ) +provided on the element surface. +Drainage-only seepage +provided on the element surface. +coefficient +Nonuniform seepage coefficient and +reference sink pore pressure (units +of FL−2 ) provided on the element +surface with magnitude supplied via +user subroutine FLOW. +Load ID +(*DSFLOW) +S(S) +SNU(S) +Abaqus/CAE +Load/Interaction +Units +Description +Surface pore +fluid +Surface pore +fluid +LT−1 +LT−1 +pore +Prescribed +effective +velocity outward from the element +surface. +fluid +Nonuniform prescribed pore fluid +effective velocity outward from the +element +surface with magnitude +supplied via user subroutine DFLOW. +Distributed impedances +Surface-based impedances are available for all elements with acoustic pressure degrees of freedom. They +are specified as described in “Acoustic and shock loads,” Section 33.4.6. +Incident wave loading +Surface-based incident wave loads are available for all elements with displacement degrees of freedom +or acoustic pressure degrees of freedom. They are specified as described in “Acoustic and shock loads,” +Section 33.4.6. If the incident wave field includes a reflection off a plane outside the boundaries of the +mesh, this effect can be included. +Electric fluxes +Surface-based electric fluxes are available for piezoelectric elements. They are specified as described in +“Piezoelectric analysis,” Section 6.7.2. +Load ID +(*DSECHARGE) Load/Interaction +Abaqus/CAE +Units +Description +ES(S) +Surface charge +CL−2 +Prescribed surface charge on the +element surface. +Distributed electric current densities +Surface-based electric current densities are available for coupled thermal-electrical elements. They are +specified as described in “Coupled thermal-electrical analysis,” Section 6.7.3. +Load ID +(*DSECURRENT) Load/Interaction +Abaqus/CAE +Units +Description +CS(S) +Surface current +CL−2T−1 +Current density on the +surface. +element +Element output +Output is in global directions unless a local coordinate system is assigned to the element through the +section definition (“Orientations,” Section 2.2.5) in which case output is in the local coordinate system +(which rotates with the motion in large-displacement analysis). See “State storage,” Section 1.5.4 of the +Abaqus Theory Manual, for details. For regular axisymmetric elements, the local orientation must be in +the –z plane with +being a principal direction. For generalized axisymmetric elements with twist, the +local orientation can be arbitrary. +Stress, strain, and other tensor components +Stress and other tensors (including strain tensors) are available for elements with displacement degrees +of freedom. All tensors have the same components. For example, the stress components are as follows: +For elements with displacement degrees of freedom without twist: +S11 +S22 +S33 +S12 +Stress in the radial direction or in the local 1-direction. +Stress in the axial direction or in the local 2-direction. +Hoop direct stress. +Shear stress. +For elements with displacement degrees of freedom with twist: +S11 +S22 +Stress in the radial direction or in the local 1-direction. +Stress in the axial direction or in the local 2-direction. +S33 +S12 +S13 +S23 +Stress in the circumferential direction or in the local 3-direction. +Shear stress. +Shear stress. +Shear stress. +Heat flux components +Available for elements with temperature degrees of freedom. +HFL1 +HFL2 +Heat flux in the radial direction or in the local 1-direction. +Heat flux in the axial direction or in the local 2-direction. +Pore fluid velocity components +Available for elements with pore pressure degrees of freedom, except for acoustic elements. +FLVEL1 +FLVEL2 +Pore fluid effective velocity in the radial direction or in the local 1-direction. +Pore fluid effective velocity in the axial direction or in the local 2-direction. +Mass concentration flux components +Available for elements with normalized concentration degrees of freedom. +MFL1 +MFL2 +Concentration flux in the radial direction or in the local 1-direction. +Concentration flux in the axial direction or in the local 2-direction. +Electrical potential gradient +Available for elements with electrical potential degrees of freedom. +EPG1 +EPG2 +Electrical potential gradient in the 1-direction. +Electrical potential gradient in the 2-direction. +Electrical flux components +Available for piezoelectric elements. +EFLX1 +EFLX2 +Electrical flux in the 1-direction. +Electrical flux in the 2-direction. +Electrical current density components +Available for coupled thermal-electrical elements. +ECD1 +ECD2 +Electrical current density in the 1-direction. +Electrical current density in the 2-direction. +Node ordering and face numbering on elements +face 2 +face 1 +2 - node element +face 3 +face 3 +face 2 +face 4 +face 2 +1 2 +face 1 +face 1 +3 - node element +4 - node element +face 3 +4 7 3 +face 3 +6 5 +face 2 +face 4 +face 2 +1 +face 1 + 2 +face 1 +6 - node element +8 - node element +2-node element faces +Face 1 +Face 2 +Section at node 1 +Section at node 2 +Triangular element faces +Face 1 +Face 2 +Face 3 +1 – 2 face +2 – 3 face +3 – 1 face +Quadrilateral element faces +Face 1 +Face 2 +Face 3 +Face 4 +1 – 2 face +2 – 3 face +3 – 4 face +4 – 1 face +Numbering of integration points for output +2 - node element +4 - node element +1 2 +3 - node element +4 - node reduced +integration element +6 5 +1 + 2 +6 - node element +4 7 3 +4 7 3 +8 - node element +8 - node reduced +integration element +For heat transfer applications a different integration scheme is used for triangular elements, as described +in “Triangular, tetrahedral, and wedge elements,” Section 3.2.6 of the Abaqus Theory Manual. +28.1.7 +AXISYMMETRIC SOLID ELEMENTS WITH NONLINEAR, ASYMMETRIC +DEFORMATION +Product: Abaqus/Standard +References +• “Choosing the element’s dimensionality,” Section 27.1.2 +• “Solid (continuum) elements,” Section 28.1.1 +• *SOLID SECTION +Overview +This section provides a reference to the axisymmetric solid elements available in Abaqus/Standard. +These elements are intended for analysis of hollow bodies, such as pipes and pressure vessels. They +can also be used to model solid bodies, but spurious stresses may occur at zero radius, particularly if +transverse shear loads are applied. +Conventions +Coordinate 1 is r, coordinate 2 is z. Referring to the figures shown in “Choosing the element’s +dimensionality,” Section 27.1.2, the r-direction corresponds to the global X-direction in the +plane and the negative global Z-direction in the +global Y-direction. Coordinate 1 must be greater than or equal to zero. +plane, and the z-direction corresponds to the +Degree of freedom 1 is +you cannot control it. +Element types +, degree of freedom 2 is +. The +degree of freedom is an internal variable: +Stress/displacement elements +CAXA4N +Bilinear, Fourier quadrilateral with 4 nodes per r–z plane +CAXA4HN +CAXA4RN +Bilinear, Fourier quadrilateral with 4 nodes per r–z plane, hybrid with constant Fourier +pressure +Bilinear, Fourier quadrilateral with 4 nodes per r–z plane, reduced integration in r–z +planes with hourglass control +CAXA4RHN +Bilinear, Fourier quadrilateral with 4 nodes per r–z plane, reduced integration in r–z +planes, hybrid with constant Fourier pressure +CAXA8N +Biquadratic, Fourier quadrilateral with 8 nodes per r–z plane +CAXA8HN +Biquadratic, Fourier quadrilateral with 8 nodes per –z plane, hybrid with linear Fourier +pressure +CAXA8RN +Biquadratic, Fourier quadrilateral with 8 nodes per r–z plane, reduced integration in +r–z planes +CAXA8RHN +Biquadratic, Fourier quadrilateral with 8 nodes per r–z plane, reduced integration in +r–z planes, hybrid with linear Fourier pressure +Active degrees of freedom +1, 2 +Additional solution variables +The bilinear elements have 4N and the biquadratic elements 8N additional variables relating to +. +Element types CAXA4HN and CAXA4RHN have +stress. +Element types CAXA8HN and CAXA8RHN have +stress. +additional variables relating to the pressure +additional variables relating to the pressure +Pore pressure elements +CAXA8PN +Biquadratic, Fourier quadrilateral with 8 nodes per r–z plane, bilinear Fourier pore +pressure +CAXA8RPN +Biquadratic, Fourier quadrilateral with 8 nodes per r–z plane, bilinear Fourier pore +pressure, reduced integration in r–z planes +Active degrees of freedom +1, 2, 8 at corner nodes +1, 2 at midside nodes +Additional solution variables +8N additional variables relating to +. +Nodal coordinates required +r, z +Element property definition +Input File Usage: +*SOLID SECTION +Element-based loading +Even though the symmetry in the r–z plane at +allows the modeling of half of the initially +axisymmetric structure, the loading must be specified as the total load on the full axisymmetric body. +Consider, for example, a cylindrical shell loaded by a unit uniform axial force. To produce a unit load +on a CAXA element with 4 modes, the nodal forces are 1/8, 1/4, 1/4, 1/4, and 1/8 at +, +, +, +, and , respectively. +Distributed loads +Distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DLOAD) +Units +Description +BX +BZ +BXNU +BZNU +Pn +PnNU +HPn +FL−3 +FL−3 +FL−3 +FL−3 +FL−2 +FL−2 +FL−2 +Body force per unit volume in the global X- +direction. +Body force per unit volume +z-direction. +in the +Nonuniform body force in the global +X-direction with magnitude supplied via +user subroutine DLOAD. +Nonuniform body force in the z-direction +with magnitude supplied via user subroutine +DLOAD. +Pressure on face n. +Nonuniform pressure on face n with +magnitude supplied via user subroutine +DLOAD. +Hydrostatic pressure on face n, linear in the +global Y-direction. +Foundations +Foundations are specified as described in “Element foundations,” Section 2.2.2. +Load ID +(*FOUNDATION) +Units +Description +Fn +FL−3 +Elastic foundation on face n. +Distributed flows +Distributed flows are available for elements with pore pressure degrees of freedom. They are specified +as described in “Coupled pore fluid diffusion and stress analysis,” Section 6.8.1. +Load ID +(*FLOW/ +*DFLOW) +Units +Description +Qn +F−1 L3T−1 +QnD +F−1 L3T−1 +QnNU +F−1 L3T−1 +Sn +SnNU +LT−1 +LT−1 +Element output +(outward +flow) +normal +Seepage +proportional +to the difference between +surface pore pressure and a reference sink +pore pressure on face n (units of FL−2 ). +Drainage-only seepage (outward normal +flow) proportional +to the surface pore +pressure on face n only when that pressure +is positive. +Nonuniform seepage (outward normal flow) +proportional +to the difference between +surface pore pressure and a reference sink +pore pressure on face n (units of FL−2 ) with +magnitude supplied via user subroutine +FLOW. +Prescribed pore fluid velocity (outward +from the face) on face n. +Nonuniform prescribed pore fluid velocity +(outward from the face) on face n with +magnitude supplied via user subroutine +DFLOW. +equally +The numerical integration with respect to +spaced integration planes in the element, including the +planes, with N being the +number of Fourier modes. Consequently, the radial nodal forces corresponding to pressure loads applied +in the circumferential direction are distributed in this direction in the ratio of +in the 1 Fourier mode +element, +in the 4 Fourier mode element. The +sum of these consistent nodal forces is equal to the integral of the applied pressure over +employs the trapezoidal rule. There are +and +in the 2 Fourier mode element, and +. +Output is as defined below unless a local coordinate system in the r–z plane is assigned to the element +through the section definition (“Orientations,” Section 2.2.5) in which case the components are in the +local directions. These local directions rotate with the motion in large-displacement analysis. See “State +storage,” Section 1.5.4 of the Abaqus Theory Manual, for details. +Stress, strain, and other tensor components +Stress and other tensors (including strain tensors) are available for elements with displacement degrees +of freedom. All tensors have the same components. For example, the stress components are as follows: +S11 +S22 +S33 +S12 +S13 +S23 +Stress in the radial direction or in the local 1-direction. +Stress in the axial direction or in the local 2-direction. +Hoop direct stress. +Shear stress. +Shear stress. +Shear stress. +Node ordering and face numbering on elements +The node ordering in the first r–z plane of each element, at +, is shown below. Each element must +have N more planes of nodes defined, where N is the number of Fourier modes. The node ordering is the +same in each plane. You can specify the nodes in each plane. Alternatively, you can specify the node +ordering in the first r–z plane of an element, and Abaqus/Standard will generate all other nodes for the +element by adding successively a constant offset to each node for each of the N planes of the element. +By default, Abaqus/Standard uses an offset of 100000 . +face 3 +face 4 +face 2 +face 1 +face 3 +4 3 +face 4 +face 1 +face 2 +4 - node element +8 - node element +Element faces +Face 1 +Face 2 +Face 3 +Face 4 +1 – 2 face +2 – 3 face +3 – 4 face +4 – 1 face +Numbering of integration points for output +The integration points in the first r–z plane of integration, at +points follow in sequence at the r–z integration planes in ascending order of +, are shown below. The integration +location. +4 - node element +4 - node reduced +integration element +4 7 3 +4 7 3 +8 - node element +8 - node reduced +integration element +28.2 +Fluid continuum elements +• “Fluid (continuum) elements,” Section 28.2.1 +• “Fluid element library,” Section 28.2.2 +28.2.1 +FLUID (CONTINUUM) ELEMENTS +Products: Abaqus/CFD Abaqus/CAE +References +• “Fluid element library,” Section 28.2.2 +• “Creating homogeneous fluid sections,” Section 12.13.13 of the Abaqus/CAE User’s Manual, in +the online HTML version of this manual +Overview +Fluid elements are provided to discretize the fluid domain. +Choosing an appropriate element +Three-dimensional fluid elements are available. +Naming convention +Fluid elements in Abaqus are named as follows: +FC +3D 4 +number of nodes +three-dimensional +fluid continuum +For example, FC3D8 is a three-dimensional, 8-node brick fluid element. +Active fields for fluid elements +The fields active in a fluid flow analysis are not determined by the element type but by the analysis +procedure and its options. The sole purpose of the element type is to define the shape of the element +used to discretize the continuum. +28.2.2 +FLUID ELEMENT LIBRARY +Products: Abaqus/CFD Abaqus/CAE +Reference +• “Fluid (continuum) elements,” Section 28.2.1 +Overview +This section provides a reference to the fluid elements available in Abaqus/CFD. +Element types +Fluid elements +FC3D4 +FC3D6 +FC3D8 +4-node tetrahedron +6-node prism +8-node brick +Active degrees of freedom +The active degrees of freedom depend on the analysis procedure and options, such as the energy equation +and turbulence model. For more information, see “Active degrees of freedom” in “Boundary conditions +in Abaqus/CFD,” Section 33.3.2. +Additional solution variables +None. +Nodal coordinates required +X, Y, Z +Element property definition +Input File Usage: +Use either of the following options: +Abaqus/CAE Usage: +*FLUID SECTION +*SOLID SECTION +Property module: Create Section: select Fluid as the section +Element-based loading +Distributed loads +Distributed loads are available for all fluid element types. They are specified as described in “Distributed +loads,” Section 33.4.3. +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +BX +BY +BZ +Body force +Body force +Body force +GRAV +Gravity +FL−3 +FL−3 +FL−3 +LT−2 +Body force in global X-direction. +Body force in global Y-direction. +Body force in global Z-direction. +Gravity +loading +direction (magnitude is +acceleration). +in +specified +input as +PDBF +Porous +body force +drag +None +Porous drag body force load (specify +porosity as the input). +Distributed heat fluxes +Distributed heat fluxes are available when the temperature equation is activated on the analysis procedure. +They are specified as described in “Thermal loads,” Section 33.4.4. +Abaqus/CAE +Load/Interaction +Units +Description +Body heat flux +JL−3 T−1 +Heat body flux per unit volume. +Load ID +(*DFLUX) +BF +Surface-based loading +Distributed heat fluxes +Surface-based heat fluxes are available for all elements when the temperature equation is activated on +the analysis procedure. They are specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*DSFLUX) +Abaqus/CAE +Load/Interaction +Units +Description +Surface heat flux +JL−2 T−1 +Heat surface flux per unit area into the +element surface. +face 2 +face 5 +6 - node element +face 4 +face 1 +Element output +Element output is always in the global directions. +Node ordering and face numbering on elements +All elements +face 4 +face 2 +face 3 +face 3 +face 1 +4 - node element +face 2 +face 5 +face 6 +face 4 +face 1 +face 3 +8 - node element +28.2.2–3 +Tetrahedral element faces +Face 1 +Face 2 +Face 3 +Face 4 +1 – 3 – 2 face +1 – 2 – 4 face +2 – 3 – 4 face +Wedge (triangular prism) element faces +Face 1 +Face 2 +Face 3 +Face 4 +Face 5 +1 – 3 – 2 face +4 – 5 – 6 face +1 – 2 – 5 – 4 face +2 – 3 – 6 – 5 face +1 – 4 – 6 – 3 face +Hexahedron (brick) element faces +Face 1 +Face 2 +Face 3 +Face 4 +Face 5 +Face 6 +1 – 4 – 3 – 2 face +5 – 6 – 7 – 8 face +1 – 2 – 6 – 5 face +2 – 3 – 7 – 6 face +3 – 4 – 8 – 7 face +1 – 5 – 8 – 4 face +28.3 +Infinite elements +• “Infinite elements,” Section 28.3.1 +• “Infinite element library,” Section 28.3.2 +28.3.1 +INFINITE ELEMENTS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Infinite element library,” Section 28.3.2 +• *SOLID SECTION +• “Creating acoustic infinite sections,” Section 12.13.17 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +Infinite elements: +• are used in boundary value problems defined in unbounded domains or problems in which the region +of interest is small in size compared to the surrounding medium; +• are usually used in conjunction with finite elements; +• can have linear behavior only; +• provide stiffness in static solid continuum analyses; and +• provide “quiet” boundaries to the finite element model in dynamic analyses. +A solid section definition is used to define the section properties of infinite elements. +Typical applications +The analyst is sometimes faced with boundary value problems defined in unbounded domains or +problems in which the region of interest is small in size compared to the surrounding medium. Infinite +elements are intended to be used for such cases in conjunction with first- and second-order planar, +axisymmetric, and three-dimensional finite elements. Standard finite elements should be used to model +the region of interest, with the infinite elements modeling the far-field region. +Choosing an appropriate element +Plane stress, plane strain, three-dimensional, and axisymmetric infinite elements are available. Reduced- +integration elements are also available in Abaqus/Standard. +Element type CIN3D18R is intended for use with the three-dimensional variable-number-of-node +solids C3D15V, C3D27, and C3D27R in Abaqus/Standard. +Acoustic infinite elements are also available in Abaqus. +Naming convention +Infinite elements in Abaqus are named as follows: +CIN +PS 5 R +reduced integration (optional) +number of user nodes +plane strain (PE), plane stress (PS), two-dimensional (2D) +three-dimensional (3D), or axisymmetric (AX) +continuum infinite element +acoustic (optional) +For example, CINAX4 is a 4-node, axisymmetric, infinite element. +Defining the element’s section properties +You use a solid section definition to define the section properties. You must associate these properties +with a region of your model. +Input File Usage: +*SOLID SECTION, ELSET=name +where the ELSET parameter refers to a set of infinite elements. +Abaqus/CAE Usage: +Only acoustic infinite sections are supported in Abaqus/CAE. +Property module: +Create Section: select Other as the section Category and +Acoustic infinite as the section Type +Assign→Section: select regions +Defining the thickness for plane strain and plane stress elements +You define the thickness for plane strain and plane stress elements as part of the section definition. If +you do not specify a thickness, unit thickness is assumed. +Input File Usage: +*SOLID SECTION +thickness +Abaqus/CAE Usage: +Structural infinite sections are not supported in Abaqus/CAE. +Defining the reference point and thickness for acoustic infinite elements +For acoustic infinite elements you specify the thickness and the reference point. The thickness is ignored +in three-dimensional and axisymmetric elements. You can prescribe the reference point either as a +reference node on the section definition or directly by giving its coordinates on the data +line following the thickness value. If both methods are used, the former takes precedence. If you do not +define the reference point at all, an error message is issued. +acoustic infinite elements, as shown in Figure 28.3.1–1. +INFINITE ELEMENTS +reference +point (X ) +radius (R ) +node +(X ) +node +ray (n ) +Figure 28.3.1–1 Reference point and node rays for acoustic infinite elements. +Each node ray is a unit vector in the direction of the line between the reference point and the node. These +radii and rays are used in the formulation of acoustic infinite elements. The placement of the reference +point is not extremely critical as long as it is near the center of the finite region enclosed by the infinite +elements. If acoustic infinite elements are placed on the surface of a sphere, the optimal location for the +reference point is the center of the sphere. +Acoustic infinite elements whose section properties are defined using a particular solid section +definition should not have any nodes in common with acoustic infinite elements associated with a +different solid section definition. This is to ensure a unique reference point (and, therefore, a unique +“radius” and “node ray”) for each acoustic infinite element node. +The node rays are used to compute “cosine” values at each node of the infinite element interface. +The “cosine” is equal to the smallest dot product of the unit node ray and the unit normals of all acoustic +infinite element faces surrounding the node . An error message is issued for negative +values of “cosine.” Both the “radius” and “cosine” for all nodes of acoustic infinite elements are printed to +the data (.dat) file as nodal (model) data. For details of how these quantities are used in the formulation, +see “Acoustic infinite elements,” Section 3.3.2 of the Abaqus Theory Manual. +Input File Usage: +*SOLID SECTION, REF NODE=node number or node set name +thickness +nj +n2 +n3 +n1 +X R +nj +n2 +n3 +n1 +cosine +Figure 28.3.1–2 Defining the cosine for acoustic infinite elements. +Abaqus/CAE Usage: +Property module: Create Section: select Other as the section +Category and Acoustic infinite as the section Type: Plane +stress/strain thickness: thickness +Acoustic infinite sections must be assigned to regions of parts that have a +reference point associated with them. To define the reference point: +Part module or Property module: Tools→Reference Point: +select reference point +Defining the order of interpolation for acoustic infinite elements +For acoustic infinite elements the variation of the acoustic field in the infinite direction is given by +functions that are members of a set of 10 ninth-order polynomials (for further details, see “Acoustic +infinite elements,” Section 3.3.2 of the Abaqus Theory Manual). The members of this set are constructed +to correspond to the Legendre modes of a sphere; that is, if infinite elements are placed on a sphere and +if tangential refinement is adequate, an ith order acoustic infinite element will absorb waves associated +with the ( +)th Legendre mode. The computational cost involved in using all 10 members in this set +of polynomials to resolve the variation of the acoustic field in the infinite direction may be significant +in certain applications in Abaqus/Explicit. In such cases you may wish to include only the first few +members of the set, although you should be aware of the possibility of degraded accuracy (i.e., increased +reflection at acoustic infinite elements) due to using a reduced set of polynomials. In Abaqus/Explicit +you can specify the number, N, of ninth-order polynomials to be used. By default, all 10 members of the +set will be used; all 10 are always used in Abaqus/Standard. Specifying a value less than 10 would result +in the first N members of the set being used to model the variation of the acoustic field in the infinite +direction. +Input File Usage: +Abaqus/CAE Usage: +*SOLID SECTION, ORDER=N +Property module: Create Section: select Other as the section Category +and Acoustic infinite as the section Type: Order: N +Assigning a material definition to a set of infinite elements +You must associate a material definition with each infinite element section definition. Optionally, you +can associate a material orientation definition with the section . +The solution in the far field is assumed to be linear, so that only linear behavior can be associated with +infinite elements (“Linear elastic behavior,” Section 22.2.1). In dynamic analysis the material response +in the infinite elements is also assumed to be isotropic. +In Abaqus/Explicit the material properties assigned to the infinite elements must match the material +properties of the adjacent finite elements in the linear domain. +Only an acoustic medium material (“Acoustic medium,” Section 26.3.1) is valid for acoustic infinite +elements. +Input File Usage: +Abaqus/CAE Usage: +*SOLID SECTION, MATERIAL=name, ORIENTATION=name +Only acoustic infinite sections are supported in Abaqus/CAE. +Property module: +Create Section: select Other as the section Category and Acoustic +infinite as the section Type: Material: name +Assign→Material Orientation: select regions +Assign→Section: select regions +Defining nodes for solid medium infinite elements +The node numbering for infinite elements must be defined such that the first face is the face that is +connected to the finite element part of the mesh. +The infinite element nodes that are not part of the first face are treated differently in explicit dynamic +analysis than in other procedures. These nodes are located away from the finite element mesh in the +infinite direction. The location of these nodes is not meaningful for explicit analysis, and loads and +boundary conditions must not be specified using these nodes in explicit dynamic procedures. In other +procedures these outer nodes are important in the element definition and can be used in load and boundary +condition definitions. +Except for explicit procedures, the basis of the formulation of the solid medium elements is that +the far-field solution along each element edge that stretches to infinity is centered about an origin, called +the “pole.” For example, the solution for a point load applied to the boundary of a half-space has its +pole at the point of application of the load. It is important to choose the position of the nodes in the +infinite direction appropriately with respect to the pole. The second node along each edge pointing in +the infinite direction must be positioned so that it is twice as far from the pole as the node on the same +edge at the boundary between the finite and the infinite elements. Three examples of this are shown in +Figure 28.3.1–3, Figure 28.3.1–4, and Figure 28.3.1–5. In addition to this length consideration, you must +specify the second nodes in the infinite direction such that the element edges in the infinite direction do +not cross over, which would give nonunique mappings . Abaqus will stop with an +error message if such problems occur. A convenient way of defining these second nodes in the infinite +direction is to project the original nodes from a pole node; see “Projecting the nodes in the old set from +a pole node” in “Node definition,” Section 2.1.1. The positions of the pole and of the nodes on the +boundary between the finite and the infinite elements are used. +CAX8R +CINAX5R +CL +Figure 28.3.1–3 Point load on elastic half-space. +CPE4R +CINPE4 +CL +Figure 28.3.1–4 Strip footing on infinitely extending layer of soil. +CPS4 +CINPS4 +Figure 28.3.1–5 Quarter plate with square hole. +Figure 28.3.1–6 Examples of an acceptable and an unacceptable +two-dimensional infinite element. +Defining nodes for acoustic infinite elements +The nodes of acoustic infinite elements need to be defined only for the face that is connected to the finite +element part of the mesh. Additional nodes are generated internally by Abaqus in the direction of the +“node ray” . The node rays, which are discussed earlier in this section in the context +of defining the reference point, define the sides of the acoustic infinite elements. +Using solid medium infinite elements in plane stress and plane strain analyses +the far-field +In plane stress and plane strain analyses when the loading is not self-equilibrating, +displacements typically have the form +, where r is distance from the origin. This form +implies that the displacement approaches infinity as +. Infinite elements will not provide a unique +displacement solution for such cases. Experience shows, however, that they can still be used, provided +that the displacement results are treated as having an arbitrary reference value. Thus, strain, stress, and +relative displacements within the finite element part of the model will converge to unique values as +the model is refined; the total displacements will depend on the size of the region modeled with finite +If the loading is self-equilibrating, the total displacements will also converge to a unique +elements. +solution. +Using solid medium infinite elements in dynamic analyses +In direct-integration implicit dynamic response analysis (“Implicit dynamic analysis using direct +integration,” Section 6.3.2), +steady-state dynamic frequency domain analysis (“Direct-solution +steady-state dynamic +analysis,” Section 6.3.4), matrix generation (“Generating matrices,” +Section 10.3.1), superelement generation (“Using substructures,” Section 10.1.1), and explicit +infinite elements provide “quiet” +dynamic analysis (“Explicit dynamic analysis,” Section 6.3.3), +boundaries to the finite element model through the effect of a damping matrix; the stiffness matrix of the +element is suppressed. The elements do not provide any contribution to the eigenmodes of the system. +The elements maintain the static force that was present at the start of the dynamic response analysis on +this boundary; as a consequence, the far-field nodes in the infinite elements will not displace during the +dynamic response. +During dynamic steps the infinite elements introduce additional normal and shear tractions on the +finite element boundary that are proportional to the normal and shear components of the velocity of +the boundary. These boundary damping constants are chosen to minimize the reflection of dilatational +and shear wave energy back into the finite element mesh. This formulation does not provide perfect +transmission of energy out of the mesh except in the case of plane body waves impinging orthogonally +on the boundary in an isotropic medium. However, it usually provides acceptable modeling for most +practical cases. +During dynamic response analysis the infinite elements hold the static stress on the boundary +constant but do not provide any stiffness. Therefore, some rigid body motion of the region modeled +will generally occur. This effect is usually small. +Optimizing the transmission of energy out of the finite element mesh +For dynamic cases the ability of the infinite elements to transmit energy out of the finite element mesh, +without trapping or reflecting it, is optimized by making the boundary between the finite and infinite +elements as close as possible to being orthogonal to the direction from which the waves will impinge on +this boundary. Close to a free surface, where Rayleigh waves may be important, or close to a material +interface, where Love waves may be important, the infinite elements are most effective if they are +orthogonal to the surface. (Rayleigh and Love waves are surface waves that decay with distance from +the surface.) +For acoustic medium infinite elements, these general guidelines apply as well. +Defining an initial stress field and corresponding body force field +In many applications, especially geotechnical problems, an initial stress field and a corresponding +body force field must be defined. For standard elements you define the initial stress field as an initial +condition (“Defining initial stresses” in “Initial conditions in Abaqus/Standard and Abaqus/Explicit,” +Section 33.2.1) and the corresponding body force field as a distributed load (“Distributed loads,” +Section 33.4.3). The body force cannot be defined for infinite elements since the elements are of +infinite extent. Therefore, Abaqus automatically inserts forces at the nodes of the infinite elements that +cause those nodes to be in static equilibrium at the start of the analysis. These forces remain constant +throughout the analysis. This capability allows the initial geostatic stress field to be defined in the +infinite elements, but it does not check whether or not the geostatic stress field is reasonable. If the +initial stress field is due to a body force loading (such as gravity loading), this loading must be held +constant during the step. In multistep analyses it must be maintained constant over all steps. +You must remember that when infinite elements are used in conjunction with an initial stress +condition, it is essential that the initial stress field be in equilibrium. In Abaqus/Standard any procedure +that determines the initial static (steady-state) equilibrium conditions is suitable as the first step of the +analysis; for example, static (“Static stress analysis,” Section 6.2.2); geostatic stress field (“Geostatic +stress state,” Section 6.8.2); coupled pore fluid diffusion/stress (“Coupled pore fluid diffusion and stress +analysis,” Section 6.8.1); and steady-state fully coupled thermal-stress (“Fully coupled thermal-stress +analysis,” Section 6.5.3) steps can be used. To check for equilibrium in Abaqus/Explicit, perform an +initial step with no loading (except for the body forces that created the initial stress field) and verify +that the accelerations are small. +28.3.2 +INFINITE ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Infinite elements,” Section 28.3.1 +• *SOLID SECTION +Overview +This section provides a reference to the infinite elements available in Abaqus/Standard and +Abaqus/Explicit. +Element types +Plane strain solid continuum infinite elements +CINPE4 +4-node linear, one-way infinite +CINPE5R(S) +5-node quadratic, one-way infinite +Active degrees of freedom +1, 2 +Additional solution variables +None. +Plane stress solid continuum infinite elements +CINPS4 +4-node linear, one-way infinite +CINPS5R(S) +5-node quadratic, one-way infinite +Active degrees of freedom +1, 2 +Additional solution variables +None. +3-D solid continuum infinite elements +CIN3D8 +8-node linear, one-way infinite +CIN3D12R(S) +12-node quadratic, one-way infinite +CIN3D18R(S) +18-node quadratic, one-way infinite +Active degrees of freedom +1, 2, 3 +Additional solution variables +None. +Axisymmetric solid continuum infinite elements +CINAX4 +4-node linear, one-way infinite +CINAX5R(S) +5-node quadratic, one-way infinite +Active degrees of freedom +1, 2 +Additional solution variables +None. +2-D acoustic infinite elements +ACIN2D2 +2-node linear, acoustic infinite +ACIN2D3(S) +3-node quadratic, acoustic infinite +Active degree of freedom +3-D acoustic infinite elements +ACIN3D3 +3-node linear, acoustic infinite triangular element +ACIN3D4 +4-node linear, acoustic infinite quadrilateral element +ACIN3D6(S) +ACIN3D8(S) +6-node quadratic, acoustic infinite triangular element +8-node quadratic, acoustic infinite quadrilateral element +Active degree of freedom +Axisymmetric acoustic infinite elements +ACINAX2 +2-node linear, acoustic infinite +ACINAX3(S) +3-node quadratic, acoustic infinite +Active degree of freedom +Nodal coordinates required +Plane stress and plane strain solid continuum elements: X, Y +2-D acoustic elements: X, Y +3-D solid continuum and acoustic elements: X, Y, Z +Axisymmetric solid continuum and acoustic elements: r, z +Normal directions are not specified at nodes used in acoustic infinite elements; they will be computed +automatically. See “Infinite elements,” Section 28.3.1, for details. +Element property definition +For two-dimensional, plane strain, and plane stress elements, you must provide the thickness of the +elements; by default, unit thickness is assumed. +For three-dimensional and axisymmetric solid elements, you do not need to specify a thickness. +For acoustic elements, you must specify the reference point in addition to the thickness. +Input File Usage: +Abaqus/CAE Usage: +*SOLID SECTION +Only acoustic infinite sections are supported in Abaqus/CAE. +Property module: Create Section: select Other as the section Category +and Acoustic infinite as the section Type +Element-based loading +None. +Element output +Stress, strain, and other tensor components +No output is available from Abaqus/Explicit for infinite elements. Stress and other tensors (including +strain tensors) are available from Abaqus/Standard for infinite elements with displacement degrees of +freedom. All tensors have the same components. For example, the stress components are as follows: +S11 +S22 +S33 +S12 +S13 +S23 +direct stress or radial stress for axisymmetric elements. +direct stress or axial stress for axisymmetric elements. +direct stress (not available for plane stress elements) or hoop stress for +axisymmetric elements. +shear stress or shear stress for axisymmetric elements. +shear stress (not available for plane stress, plane strain, and axisymmetric +elements). +shear stress (not available for plane stress, plane strain, and axisymmetric +elements). +Node ordering and face numbering on elements +Plane stress and plane strain solid continuum elements +CINPS4 +CINPE4 +CINPS5R +CINPE5R +Axisymmetric solid continuum elements +CINAX4 +CINAX5R +INFINITE ELEMENTS +CIN3D8 +12 +11 +10 +CIN3D12R +16 +13 +12 +15 +18 +17 +11 +14 +10 +CIN3D18R +Two-dimensional and axisymmetric acoustic infinite elements +E1 +E2 +SPOS +E1 +SPOS +E2 +ACIN2D2 +ACIN2D3 +E1 +E1 +E2 +SPOS +ACINAX2 +SPOS +ACINAX3 +E2 +INFINITE ELEMENTS +E3 +SPOS +E2 +E1 +ACIN3D3 +E3 +SPOS +E2 +E1 +ACIN3D6 +E3 +E4 +SPOS +E2 +E1 +ACIN3D4 +E3 +E2 +E4 +SPOS +E1 +ACIN3D8 +Numbering of integration points for output +Plane stress and plane strain solid continuum elements +CINPS4 +CINPE4 +CINPS5R +CINPE5R +Axisymmetric solid continuum elements +CINAX4 +CINAX5R +Three-dimensional solid continuum elements +4 7 3 +CIN3D8 +CIN3D12R +4 7 3 +CIN3D18R +This shows the scheme in the layer closest to the 1–2–3–4 face. The integration points in the second +layer are numbered consecutively. +28.4 +Warping elements +• “Warping elements,” Section 28.4.1 +• “Warping element library,” Section 28.4.2 +28.4.1 +WARPING ELEMENTS +Product: Abaqus/Standard +References +• “Meshed beam cross-sections,” Section 10.6.1 +• *SOLID SECTION +Overview +Warping elements: +• are used to model an arbitrarily shaped beam cross-section profile for use with Timoshenko beams; +• are used in conjunction with the beam section generation procedure described in “Meshed beam +cross-sections,” Section 10.6.1; and +• model linear elastic behavior only. +Typical applications +Warping elements are special-purpose elements that are used to discretize a two-dimensional model of a +beam cross-section. This two-dimensional cross-section model is used in Abaqus/Standard to calculate +the out-of-plane component of the warping function, as well as relevant sectional stiffness and mass +properties that are required in a subsequent beam analysis in either Abaqus/Standard or Abaqus/Explicit. +Applications include any structure whose overall behavior is beam-like, yet the cross-section is non- +standard or includes multiple materials. Examples include the cross-section of a ship for performing +whipping analysis, a beam model of an airfoil-shaped rotor blade or wing, a laminated I-beam, etc. +Choosing an appropriate element +To mesh an arbitrarily shaped solid beam cross-section Abaqus/Standard offers two elements: a 3-node +linear triangle, WARP2D3, and a 4-node bilinear quadrilateral, WARP2D4. Adjacent elements in the +cross-sectional mesh must share common nodes; mesh refinement using multi-point constraints is not +allowed. +Naming convention +Warping elements are named as follows: +WARP +2D 3 +number of nodes +two-dimensional +warping elements +For example, WARP2D4 is 4-node warping element in two dimensions. +Defining the element’s section properties +You use a solid section definition to define the section properties. You must associate these properties +with a region of your model. No additional data are necessary. +Input File Usage: +*SOLID SECTION, ELSET=name +where the ELSET parameter refers to a set of warping elements. +Assigning a material definition to a set of warping elements +You must associate a linear elastic material definition with each warping element section definition. +Optionally, you can associate a material orientation definition with the section . +Only isotropic linear elasticity (“Defining isotropic elasticity” in “Linear elastic behavior,” +Section 22.2.1) or orthotropic linear elasticity for warping elements (“Defining orthotropic elasticity for +warping elements” in “Linear elastic behavior,” Section 22.2.1) are valid material models for warping +elements. +Input File Usage: +*SOLID SECTION, ELSET=name, MATERIAL=name, +ORIENTATION=name +28.4.2 +WARPING ELEMENT LIBRARY +Product: Abaqus/Standard +References +• “Meshed beam cross-sections,” Section 10.6.1 +• *SOLID SECTION +Overview +This section provides a reference to the warping elements available in Abaqus/Standard. +Element types +WARP2D3 +3-node linear two-dimensional warping element +WARP2D4 +4-node bilinear two-dimensional warping element +Active degree of freedom +3, representing the out-of-plane warping function +Additional solution variables +None. +Nodal coordinates required +X, Y +Element property definition +Input File Usage: +*SOLID SECTION +Element-based loading +There is no loading for these element types. +Element output +No output is available for these element types. The two-dimensional warping elements are used to +calculate the out-of-plane warping function for beams using a meshed cross-section. This warping +function can be viewed in the Visualization module of Abaqus/CAE. The derivatives of the warping +function are used to calculate the shear strain and stress at the integration points of the elements due +to torsion. +Node ordering on elements +1 2 +3 - node element +4 - node element +Numbering of integration points for output +1 2 +3 - node element +4 - node element +28.5 +Particle elements +• “Particle elements,” Section 28.5.1 +• “Particle element library,” Section 28.5.2 +28.5.1 +PARTICLE ELEMENTS +Product: Abaqus/Explicit +References +• “Smoothed particle hydrodynamic analysis,” Section 15.1.1 +• “Particle element library,” Section 28.5.2 +• *SOLID SECTION +Overview +Continuum particle elements: +• can be used only in explicit dynamic analyses; +• must have one node only; +• have one integration point; +• can be initialized similarly to continuum elements; and +• are fully filled with material. +Typical applications +Continuum particle elements (PC3D) are useful for simulations involving material that undergoes +extreme deformation such as open-surface fluid flow or obliteration/fragmentation of solid structures. +They are defined using only one node; however, the element centered at a given node (particle) receives +contributions from all particles within a sphere of influence whose radius is commonly referred to as +the smoothing length. The smoothed particle hydrodynamic (SPH) formulation determines at every +increment of the analysis the connectivity associated with a given particle. Since nodal connectivity is +not fixed, severe element distortion is avoided and, hence, the formulation allows for very high strain +gradients. +The 1-node PC3D element is used to define points both on the surface and in the interior of the body +to be modeled. You define these nodes similarly to mass elements, and the nodes can be placed in space +the same as the nodes of a regular brick mesh. A smoothed particle hydrodynamic mesh is typically a +uniformly spaced grid of elements that conforms to the shape of the body being modeled. +For more information, see “Smoothed particle hydrodynamic analysis,” Section 15.1.1. +Defining the element’s section properties +You must associate a solid section definition with a set of continuum particle elements. The section +definition provides the material associated with the PC3D elements. +As part of the solid section definition, you can define a characteristic length. This characteristic +length, not to be confused with the smoothing length, is used to compute the particle volume. The volume +is assumed to be a cube whose sides are equal to twice the specified characteristic length. +Input File Usage: +*SOLID SECTION, ELSET=element_set_name +characteristic length associated with the particle volume +where the ELSET parameter refers to a set of particle elements. +28.5.2 +PARTICLE ELEMENT LIBRARY +Product: Abaqus/Explicit +References +• “Smoothed particle hydrodynamic analysis,” Section 15.1.1 +• “Particle elements,” Section 28.5.1 +• *SOLID SECTION +Overview +This section provides a reference to the particle elements available in Abaqus/Explicit. +Element type +Stress/displacement element +PC3D +1-node continuum particle +Active degrees of freedom +1, 2, 3 +Nodal coordinates required +X, Y, Z +Element property definition +Input File Usage: +*SOLID SECTION +Element-based loading +Distributed loads +Gravity loads as described in “Distributed loads,” Section 33.4.3, are the only distributed loads that are +available for particle elements. You define gravity loading in a specified direction, and the magnitude is +input as acceleration. +Element output +Output is in global directions unless a local coordinate system is assigned to the element through the +section definition (“Orientations,” Section 2.2.5), in which case output is in the local coordinate system +(which rotates with the motion in large-displacement analysis). See “State storage,” Section 1.5.4 of the +Abaqus Theory Manual, for details. +Stress, strain, and other tensor components +Stress, strain, and other tensors are available. All tensors have the same components. For example, the +stress components are as follows: +S11 +S22 +S33 +S12 +S13 +S23 +, direct stress. +, direct stress. +, direct stress. +, shear stress. +, shear stress. +, shear stress. +Note: the order shown above is not the same as that used in user subroutine VUMAT. +Nodes associated with the element +1 node. +Structural Elements +Membrane elements +Truss elements +Beam elements +Frame elements +Elbow elements +Shell elements +STRUCTURAL ELEMENTS +29.1 +29.2 +29.3 +29.4 +29.5 +29.1 +Membrane elements +• “Membrane elements,” Section 29.1.1 +• “General membrane element library,” Section 29.1.2 +• “Cylindrical membrane element library,” Section 29.1.3 +• “Axisymmetric membrane element library,” Section 29.1.4 +29.1.1 +MEMBRANE ELEMENTS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “General membrane element library,” Section 29.1.2 +• “Cylindrical membrane element library,” Section 29.1.3 +• “Axisymmetric membrane element library,” Section 29.1.4 +• *MEMBRANE SECTION +• *NODAL THICKNESS +• *DISTRIBUTION +• *HOURGLASS STIFFNESS +• “Creating membrane sections,” Section 12.13.8 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +Membrane elements: +• are surface elements that transmit in-plane forces only (no moments); and +• have no bending stiffness. +Typical applications +Membrane elements are used to represent thin surfaces in space that offer strength in the plane of the +element but have no bending stiffness; for example, the thin rubber sheet that forms a balloon. In addition, +they are often used to represent thin stiffening components in solid structures, such as a reinforcing layer +in a continuum. (If the reinforcing layer is made up of chords, rebar should be used. See “Defining rebar +as an element property,” Section 2.2.4.) +Choosing an appropriate element +In addition to the general membrane elements available in both Abaqus/Standard and Abaqus/Explicit, +cylindrical membrane elements and axisymmetric membrane elements are available in Abaqus/Standard +only. +General membrane elements +General membrane elements should be used in three-dimensional models in which the deformation of +the structure can evolve in three dimensions. +Cylindrical membrane elements +Cylindrical membrane elements are available in Abaqus/Standard for precise modeling of regions in a +structure with circular geometry, such as a tire. The elements make use of trigonometric functions to +interpolate displacements along the circumferential direction and use regular isoparametric interpolation +in the radial or cross-sectional plane. They use three nodes along the circumferential direction and can +span a 0 to 180° segment. Elements with both first-order and second-order interpolation in the cross- +sectional plane are available. +The geometry of the element is defined by specifying nodal coordinates in a global Cartesian system. +The default nodal output is also provided in a global Cartesian system. Output of stress, strain, and other +material point quantities is done in a corotational system that rotates with the average material rotation. +The cylindrical elements can be used in the same mesh with regular elements. In particular, regular +membrane elements can be connected directly to the nodes on the cross-sectional edge of cylindrical +elements. For example, any edge of an M3D4 element can share nodes with the cross-sectional edges of +an MCL6 element. +Compatible cylindrical solid elements (“Cylindrical solid element library,” Section 28.1.5) and +surface elements with rebar (“Surface elements,” Section 32.7.1) are available for use with cylindrical +membrane elements. +Axisymmetric membrane elements +The axisymmetric membrane elements available in Abaqus/Standard are divided into two categories: +those that do not allow twist about the symmetry axis and those that do. These elements are referred to +as the regular and generalized axisymmetric membrane elements, respectively. +The generalized axisymmetric membrane elements (axisymmetric membrane elements with twist) +allow a circumferential component of loading or material anisotropy, which may cause twist about the +symmetry axis. Both the circumferential load component and material anisotropy are independent of +the circumferential coordinate . Since there is no dependence of the loading or the material on the +circumferential coordinate, the deformation is axisymmetric. +The generalized axisymmetric membrane elements cannot be used in dynamic or eigenfrequency +extraction procedures. +Naming convention +The naming convention for membrane elements depends on the element dimensionality. +General membrane elements +General membrane elements in Abaqus are named as follows: +3D 4 R +reduced integration (optional) +number of nodes +three-dimensional +membrane +For example, M3D4R is a three-dimensional, 4-node membrane element with reduced integration. +Cylindrical membrane elements +Cylindrical membrane elements in Abaqus/Standard are named as follows: +M CL 6 +number of nodes +cylindrical +membrane +For example, MCL6 is a 6-node cylindrical membrane element with circumferential interpolation. +Axisymmetric membrane elements +Axisymmetric membrane elements in Abaqus/Standard are named as follows: +G AX 2 +order of interpolation +axisymmetric +generalized (optional) +membrane +For example, MAX2 is a regular axisymmetric, quadratic-interpolation membrane element. +Element normal definition +The “top” surface of a membrane is the surface in the positive normal direction (defined below) and is +called the SPOS face for contact definition. The “bottom” surface is in the negative direction along the +normal and is called the SNEG face for contact definition. +General membrane elements +For general membrane elements the positive normal direction is defined by the right-hand rule going +around the nodes of the element in the order that they are specified in the element definition. See +Figure 29.1.1–1. +face SPOS +face SNEG +Figure 29.1.1–1 Positive normals for general membranes. +Cylindrical membrane elements +For cylindrical membrane elements the positive normal direction is defined by the right-hand rule going +around the nodes of the element in the order that they are specified in the element definition. See +Figure 29.1.1–2. +Axisymmetric membrane elements +For axisymmetric membrane elements the positive normal is defined by a 90° counterclockwise rotation +from the direction going from node 1 to node 2. See Figure 29.1.1–3. +Defining the element’s section properties +You use a membrane section definition to define the section properties. You must associate these +properties with a region of your model. +Input File Usage: +*MEMBRANE SECTION, ELSET=name +where the ELSET parameter refers to a set of membrane elements. +Abaqus/CAE Usage: +Property module: +Create Section: select Shell as the section Category and Membrane as the +section Type +Assign→Section: select regions +face SNEG +face SPOS +Figure 29.1.1–2 Positive normals for cylindrical membranes. +face SPOS +face SNEG +Figure 29.1.1–3 Positive normals for axisymmetric membranes. +Defining a constant section thickness +You can define a constant section thickness as part of the section definition. +Input File Usage: +*MEMBRANE SECTION, ELSET=name +thickness +Abaqus/CAE Usage: +Property module: Create Section: select Shell as the section Category and +Membrane as the section Type: Membrane thickness: thickness +Defining a variable thickness using distributions +In Abaqus/Standard you can define a spatially varying thickness for membranes using a distribution +(“Distribution definition,” Section 2.8.1). +The distribution used to define membrane thickness must have a default value. The default thickness +is used by any membrane element assigned to the membrane section that is not specifically assigned a +value in the distribution. +If the membrane thickness is defined for a membrane section with a distribution, nodal thicknesses +cannot be used for that section definition. +Input File Usage: +Use the following option to define a spatially varying thickness: +*MEMBRANE SECTION, MEMBRANE THICKNESS=distribution name +Defining a continuously varying thickness +Alternatively, you can define a continuously varying thickness over the element. In this case any constant +section thickness you specify will be ignored, and the section thickness will be interpolated from the +specified nodal values . The thickness must be defined at all +nodes connected to the element. +If the membrane thickness is defined for a membrane section with a distribution, nodal thicknesses +cannot be used for that section definition. +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*MEMBRANE SECTION, NODAL THICKNESS +*NODAL THICKNESS +Continuously varying membrane +Abaqus/CAE. +thicknesses +are not +supported in +Assigning a material definition to a set of membrane elements +You must associate a material definition with each membrane section definition. Optionally, you can +associate a material orientation definition with the section . An +arbitrary material orientation is valid only for general membrane elements and axisymmetric membrane +elements with twist. You can define other directions by defining a local orientation, except for MAX1 +and MAX2 elements (“Axisymmetric membrane element library,” Section 29.1.4), which do not support +orientations. +In Abaqus/Standard if the orientation assigned to a membrane section is defined with distributions, +spatially varying local coordinate systems are applied to all membrane elements associated with the +membrane section. A default local coordinate system (as defined by the distributions) is applied to any +membrane element that is not specifically included in the associated distribution. +Input File Usage: +Abaqus/CAE Usage: +*MEMBRANE SECTION, MATERIAL=name, ORIENTATION=name +Property module: +Create Section: select Shell as the section Category and Membrane as the +section Type: Material: name +Assign→Material Orientation +Specifying how the membrane thickness changes with deformation +You can define how the membrane thickness will change with deformation by specifying a nonzero value +for the section Poisson’s ratio that will allow for a change in the thickness of the membrane as a function +of the in-plane strains in geometrically nonlinear analysis . +Alternatively in Abaqus/Explicit, you can choose to have the thickness change computed through +integration of the thickness-direction strain that is based on the element material definition and the plane +stress condition. +The value of the effective Poisson’s ratio for the section must be between −1.0 and 0.5. By default, +the section Poisson’s ratio is 0.5 in Abaqus/Standard to enforce incompressibility of the element; in +Abaqus/Explicit the default thickness change is based on the element material definition. +A section Poisson’s ratio of 0.0 means that the thickness will not change. Values between 0.0 +and 0.5 mean that the thickness changes proportionally between the limits of no thickness change and +incompressibility, respectively. A negative value of the section Poisson’s ratio will result in an increase +of the section thickness in response to tensile strains. +Input File Usage: +Use one of the following options: +*MEMBRANE SECTION, POISSON= +*MEMBRANE SECTION, POISSON=MATERIAL (available +in Abaqus/Explicit only) +Abaqus/CAE Usage: +Property module: Create Section: select Shell as the section Category +and Membrane as the section Type: Section Poisson's ratio: +Use analysis default or Specify value: +Specifying nondefault hourglass control parameters for reduced-integration membrane elements +See “Methods for suppressing hourglass modes” in “Section controls,” Section 27.1.4, for more +information about hourglass control. +Specifying a nondefault hourglass control formulation or scale factors +You can specify a nondefault hourglass control formulation or scale factors for reduced-integration +membrane elements. The nondefault enhanced hourglass control formulation is available only for +M3D4R elements. +Input File Usage: +Use the following option to specify a nondefault hourglass control formulation +in a section control definition: +*SECTION CONTROLS, NAME=name, +HOURGLASS=hourglass_control_formulation +Use the following option to associate the section control definition with the +membrane section: +*MEMBRANE SECTION, CONTROLS=name +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Hourglass control: +hourglass_control_formulation +Specifying nondefault hourglass stiffness factors +In Abaqus/Standard you can specify nondefault hourglass stiffness factors based on the default total +stiffness approach for reduced-integration general membrane elements. These stiffness factors are +ignored for axisymmetric membrane elements. There are no hourglass stiffness factors or scale factors +for the nondefault enhanced hourglass control formulation. +Input File Usage: +Use both of the following options: +*MEMBRANE SECTION +*HOURGLASS STIFFNESS +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Hourglass stiffness: Specify +Using membrane elements in large-displacement implicit analyses +Buckling can occur in Abaqus/Standard if a membrane structure is subject to compressive loading in +a large-displacement analysis, causing out-of-plane deformation. Since a stress-free flat membrane +has no stiffness perpendicular to its plane, out-of-plane loading will cause numerical singularities and +convergence difficulties. Once some out-of-plane deformation has developed, the membrane will be +able to resist out-of-plane loading. +In some cases loading the membrane elements in tension or adding initial tensile stress can overcome +the numerical singularities and convergence difficulties associated with out-of-plane loading. However, +you must choose the magnitude of the loading or initial stress such that the final solution is unaffected. +Using membrane elements in Abaqus/Standard contact analyses +Element types M3D8 and M3D8R are converted automatically to element types M3D9 and M3D9R, +respectively, if a slave surface on a contact pair is attached to the element. +29.1.2 +GENERAL MEMBRANE ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Membrane elements,” Section 29.1.1 +• *NODAL THICKNESS +• *MEMBRANE SECTION +Overview +This section provides a reference to the general membrane elements available in Abaqus/Standard and +Abaqus/Explicit. +Element types +M3D3 +M3D4 +M3D4R +M3D6(S) +M3D8(S) +M3D8R(S) +M3D9(S) +M3D9R(S) +3-node triangle +4-node quadrilateral +4-node quadrilateral, reduced integration, hourglass control +6-node triangle +8-node quadrilateral +8-node quadrilateral, reduced integration +9-node quadrilateral +9-node quadrilateral, reduced integration, hourglass control +Active degrees of freedom +1, 2, 3 +Additional solution variables +None. +Nodal coordinates required +X, Y, Z +Element property definition +Input File Usage: +*MEMBRANE SECTION +In addition, use the following option for variable thickness membranes: +Abaqus/CAE Usage: +*NODAL THICKNESS +Property module: Create Section: select Shell as the section Category and +Membrane as the section Type +You cannot define variable thickness membranes in Abaqus/CAE. +Element-based loading +Distributed loads +Distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +BX +BY +BZ +BXNU +Body force +Body force +Body force +Body force +FL−3 +FL−3 +FL−3 +FL−3 +BYNU +Body force +FL−3 +BZNU +Body force +FL−3 +Body force in the global X-direction. +Body force in the global Y-direction. +Body force in the global Z-direction. +in +force +Nonuniform body +the +global X-direction with magnitude +supplied via user subroutine DLOAD +in Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +in +force +Nonuniform body +the +global Y-direction with magnitude +supplied via user subroutine DLOAD +in Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +in +force +the +Nonuniform body +global Z-direction with magnitude +supplied via user subroutine DLOAD +in Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +CENT(S) +Not supported +FL−4 +(ML−3 T−2 ) +, where +Centrifugal load (magnitude is input +is the mass density +as +per unit volume, +is the angular +velocity). +Centrifugal load (magnitude is input +as +the angular +velocity). +, where +is +CENTRIF(S) +Rotational body +force +T−2 +Units +Description +Load ID +(*DLOAD) +CORIO(S) +Abaqus/CAE +Load/Interaction +Coriolis force +FL−4 T +(ML−3 T−1 ) +GRAV +Gravity +LT−2 +HP(S) +Not supported +FL−2 +Pressure +FL−2 +PNU +Not supported +FL−2 +Coriolis force (magnitude is input +is the mass density +as +, where +per unit volume, +is the angular +velocity). The load stiffness due to +Coriolis loading is not accounted +for in direct steady-state dynamic +analysis. +Gravity +loading +direction (magnitude is +acceleration). +in +specified +input as +Hydrostatic pressure applied to the +element reference surface and linear +in global Z. The pressure is positive in +the direction of the positive element +normal. +Pressure +applied to the element +reference surface. The pressure is +positive in the direction of the positive +element normal. +applied +reference +to +Nonuniform pressure +surface +element +the +supplied +via +with magnitude +DLOAD +in +user +subroutine +and VDLOAD +Abaqus/Standard +The pressure +in Abaqus/Explicit. +is positive in the direction of the +positive element normal. +ROTA(S) +Rotational body +force +T−2 +ROTDYNF(S) +Not supported +T−1 +SBF(E) +Not supported +FL−5 T2 +Rotary acceleration load (magnitude +is input as +is the rotary +acceleration). +, where +Rotordynamic load (magnitude is +input as +is the angular +velocity). +, where +Stagnation body force in global X-, +Y-, and Z-directions. +Load ID +(*DLOAD) +SP(E) +Abaqus/CAE +Load/Interaction +Units +Description +Not supported +FL−4 T2 +TRSHR +Surface traction +FL−2 +TRSHRNU(S) +Not supported +FL−2 +TRVEC +Surface traction +FL−2 +TRVECNU(S) +Not supported +FL−2 +VBF(E) +VP(E) +Not supported +FL−4 T +Not supported +FL−3 T +Stagnation pressure applied to the +element reference surface. +traction +Shear +reference surface. +on +the +element +traction on the +Nonuniform shear +surface with +reference +element +magnitude and direction supplied +via user subroutine UTRACLOAD. +General +reference surface. +traction on the element +traction +Nonuniform general +on +the element reference surface with +magnitude and direction supplied via +user subroutine UTRACLOAD. +Viscous body force in global X-, Y-, +and Z-directions. +surface pressure +applied +Viscous +to the element +reference surface. +The pressure is proportional to the +velocity normal to the element face +and opposing the motion. +Foundations +Foundations are available only in Abaqus/Standard and are specified as described in “Element +foundations,” Section 2.2.2. +Load ID +(*FOUNDATION) Load/Interaction +Abaqus/CAE +F(S) +Elastic +foundation +Units +Description +FL−3 +Elastic foundation. +Surface-based loading +Distributed loads +Surface-based distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +HP(S) +Pressure +FL−2 +Pressure +FL−2 +PNU +Pressure +FL−2 +SP(E) +Pressure +FL−4 T2 +TRSHR +Surface traction +FL−2 +TRSHRNU(S) +Surface traction +FL−2 +TRVEC +Surface traction +FL−2 +TRVECNU(S) +Surface traction +FL−2 +VP(E) +Pressure +FL−3 T +29.1.2–5 +Hydrostatic pressure on the element +reference surface and linear in global +Z. The pressure is positive in the +direction opposite to the surface +normal. +Pressure on the element reference +surface. The pressure is positive in +the direction opposite to the surface +normal. +Nonuniform pressure on the element +reference surface with magnitude +supplied via user subroutine DLOAD +and VDLOAD +in Abaqus/Standard +in Abaqus/Explicit. The pressure is +positive in the direction opposite to +the surface normal. +Stagnation pressure applied to the +element reference surface. +traction +Shear +reference surface. +on +the +element +traction on the +Nonuniform shear +element +surface with +reference +magnitude and direction supplied +via user subroutine UTRACLOAD. +General +reference surface. +traction on the element +traction +Nonuniform general +on +the element reference surface with +magnitude and direction supplied via +user subroutine UTRACLOAD. +Viscous surface pressure applied to +the element reference surface. The +pressure is proportional to the velocity +normal to the element surface and +Incident wave loading +Surface-based incident wave loads are available. They are specified as described in “Acoustic and shock +loads,” Section 33.4.6. If the incident wave field includes a reflection off a plane outside the boundaries +of the mesh, this effect can be included. +Element output +If a local orientation (“Orientations,” Section 2.2.5) is not used with the element, the stress/strain +components are in the default directions on the surface defined by the convention given in “Conventions,” +Section 1.2.2. If a local orientation is used with the element, the stress/strain components are in the +surface directions defined by the orientation. +In large-displacement problems the local directions +defined in the reference configuration are rotated into the current configuration by the average material +rotation. See “State storage,” Section 1.5.4 of the Abaqus Theory Manual, for details. +Stress, strain, and other tensor components +Stress and other tensors (including strain tensors) are available for elements with displacement degrees +of freedom. All tensors have the same components. For example, the stress components are as follows: +S11 +S22 +S12 +Local 11 direct stress. +Local 22 direct stress. +Local 12 shear stress. +Section thickness +STH +Current thickness. +Node ordering on elements +1 2 +3 - node element +4 - node element +6 5 +1 + 2 +4 7 3 +6 - node element +8 - node element +4 7 3 +9 - node element +Numbering of integration points for output +6 5 +1 2 +1 + 2 +3 - node element +6 - node element +4 - node element +4 - node reduced +integration element +4 7 3 +4 7 3 +8 - node element +8 - node reduced +integration element +4 7 3 +4 7 3 +9 - node element +9 - node reduced +integration element +29.1.3 +CYLINDRICAL MEMBRANE ELEMENT LIBRARY +Product: Abaqus/Standard +References +• “Membrane elements,” Section 29.1.1 +• *MEMBRANE SECTION +Overview +This section provides a reference to the cylindrical membrane elements available in Abaqus/Standard. +Element types +MCL6 +MCL9 +6-node cylindrical membrane +9-node cylindrical membrane +Active degrees of freedom +1, 2, 3 +Additional solution variables +None. +Nodal coordinates required +X, Y, Z +Element property definition +Input File Usage: +*MEMBRANE SECTION +Element-based loading +Distributed loads +Distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DLOAD) +BX +BY +BZ +Units +Description +FL−3 +FL−3 +FL−3 +Body force in the global X-direction. +Body force in the global Y-direction. +Body force in the global Z-direction. +Description +CYLINDRICAL MEMBRANES +Load ID +(*DLOAD) +BXNU +BYNU +BZNU +FL−3 +FL−3 +FL−3 +CENT +FL−4 (ML−3 T−2 ) +CENTRIF +T−2 +CORIO +FL−4 T (ML−3 T−1 ) +GRAV +HP +PNU +ROTA +ROTDYNF(S) +LT−2 +FL−2 +FL−2 +FL−2 +T−2 +T−1 +Abaqus ID: +Printed on: +Nonuniform body force in the global +X-direction with magnitude supplied via +user subroutine DLOAD. +Nonuniform body force in the global +Y-direction with magnitude supplied via +user subroutine DLOAD. +Nonuniform body force in the global +Z-direction with magnitude supplied via +user subroutine DLOAD. +Centrifugal load (magnitude is input as +where +, +is the mass density per unit volume, +is the angular velocity). +Centrifugal load (magnitude is input as +where +is the angular velocity). +, +Coriolis force (magnitude is input as +where +, +is the mass density per unit volume, +is the angular velocity). +Gravity loading in a specified direction +(magnitude is input as acceleration). +Hydrostatic pressure applied to the element +reference surface and linear in global Z. The +pressure is positive in the direction of the +positive element normal. +Pressure applied to the element reference +surface. The pressure is positive in the +direction of the positive element normal. +Nonuniform pressure applied to the element +reference surface with magnitude supplied +via user subroutine DLOAD. The pressure +is positive in the direction of the positive +element normal. +Rotary acceleration load (magnitude is input +as +is the rotary acceleration. +, where +Rotordynamic load (magnitude is input as +Load ID +(*DLOAD) +TRSHR +Units +FL−2 +TRSHRNU(S) +FL−2 +TRVEC +FL−2 +TRVECNU(S) +FL−2 +Description +Shear traction on the element reference +surface. +Nonuniform shear traction on the element +reference surface with magnitude and +direction supplied via user +subroutine +UTRACLOAD. +General traction on the element reference +surface. +Nonuniform general traction on the element +reference surface with magnitude and +direction supplied via user +subroutine +UTRACLOAD. +Foundations +Foundations are specified as described in “Element foundations,” Section 2.2.2. +Load ID +(*FOUNDATION) +Units +Description +FL−3 +Elastic foundation. +Surface-based loading +Distributed loads +Surface-based distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DSLOAD) +Units +Description +on +pressure +Hydrostatic +element +reference surface and linear in global Z. +The pressure is positive in the direction +opposite to the surface normal. +the +Pressure on the element reference surface. +The pressure is positive in the direction +opposite to the surface normal. +Nonuniform pressure on the +element +reference surface with magnitude supplied +29.1.3–3 +HP +PNU +FL−2 +FL−2 +Load ID +(*DSLOAD) +Units +Description +TRSHR +FL−2 +TRSHRNU(S) +FL−2 +TRVEC +FL−2 +TRVECNU(S) +FL−2 +via user subroutine DLOAD. The pressure +is positive in the direction opposite to the +surface normal. +Shear traction on the element reference +surface. +Nonuniform shear traction on the element +reference surface with magnitude and +direction supplied via user +subroutine +UTRACLOAD. +General traction on the element reference +surface. +Nonuniform general traction on the element +reference surface with magnitude and +subroutine +direction supplied via user +UTRACLOAD. +Element output +If a local orientation (“Orientations,” Section 2.2.5) is not used with the element, the stress/strain +components are expressed in the default directions on the surface defined by the convention given +in “Conventions,” Section 1.2.2. +If a local orientation is used with the element, the stress/strain +components are in the surface directions defined by the orientation. In large-displacement problems the +local directions defined in the reference configuration are rotated into the current configuration by the +average material rotation. See “State storage,” Section 1.5.4 of the Abaqus Theory Manual, for details. +Stress, strain, and other tensor components +Stress and other tensors (including strain tensors) are available for elements with displacement degrees +of freedom. All tensors have the same components. For example, the stress components are as follows: +S11 +S22 +S12 +Local +Local +Local +direct stress. +direct stress. +shear stress. +Section thickness +STH +Current thickness. +Node ordering and face numbering on elements +6-node element + 9-node element +Numbering of integration points for output +6-node element +9-node element +AXISYMMETRIC MEMBRANE ELEMENT LIBRARY +AXISYMMETRIC MEMBRANE LIBRARY +Products: Abaqus/Standard Abaqus/CAE +References +• “Membrane elements,” Section 29.1.1 +• *MEMBRANE SECTION +• *NODAL THICKNESS +Overview +This section provides a reference to the axisymmetric membrane elements available in Abaqus/Standard. +Conventions +Coordinate 1 is r, coordinate 2 is z. At +, the r-direction corresponds to the global X-direction and +the z-direction corresponds to the global Y-direction. This is important when data are required in global +directions. Coordinate 1 should be greater than or equal to zero. +Degree of freedom 1 is +have an additional degree of freedom, 5, corresponding to the twist angle +, degree of freedom 2 is +. Generalized axisymmetric elements with twist +(in radians). +Abaqus/Standard does not automatically apply any boundary conditions to nodes located along the +symmetry axis. You must apply radial or symmetry boundary conditions on these nodes if desired. +Point loads and moments should be given as the value integrated around the circumference; that is, the +total value on the ring. +Element types +Regular axisymmetric membranes +MAX1 +MAX2 +2-node linear, without twist +3-node quadratic, without twist +Active degrees of freedom +1, 2 +Additional solution variables +None. +Generalized axisymmetric membranes +MGAX1 +MGAX2 +2-node linear, with twist +3-node quadratic, with twist +Active degrees of freedom +1, 2, 5 +Additional solution variables +None. +Nodal coordinates required +R, Z +Element property definition +Input File Usage: +*MEMBRANE SECTION +In addition, use the following option for variable thickness membranes: +Abaqus/CAE Usage: +*NODAL THICKNESS +Property module: Create Section: select Shell as the section +Category and Membrane as the section Type +You cannot define variable thickness membranes in Abaqus/CAE. +Element-based loading +Distributed loads +Distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +BR +BZ +Body force +Body force +BRNU +Body force +FL−3 +FL−3 +FL−3 +BZNU +Body force +FL−3 +CENT +Not supported +FL−4 +(ML−3 T−2 ) +29.1.4–2 +Body force in the radial (1 or r) +direction. +Body force in the axial (2 or z) +direction. +Nonuniform body force in the radial +direction with magnitude supplied via +user subroutine DLOAD. +Nonuniform body force in the axial +direction with magnitude supplied via +user subroutine DLOAD. +Centrifugal load (magnitude is input +is the mass density +as +per unit volume, +is the angular +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +velocity). Since only axisymmetric +deformation is allowed, the spin axis +must be the z-axis. +CENTRIF +Rotational body +force +T−2 +GRAV +Gravity +LT−2 +HP +Not supported +FL−2 +Pressure +FL−2 +PNU +Not supported +FL−2 +, where +Centrifugal load (magnitude is input +as +the angular +velocity). Since only axisymmetric +deformation is allowed, the spin axis +must be the z-axis. +is +Gravity +direction +acceleration). +loading +in +(magnitude +specified +as +input +Hydrostatic pressure applied to the +element reference surface and linear +in global Z. The pressure is positive in +the direction of the positive element +normal. +Pressure +applied to the element +reference surface. The pressure is +positive in the direction of the positive +element normal. +applied +reference +to +Nonuniform pressure +surface +element +the +with magnitude supplied via user +subroutine DLOAD. The pressure is +positive in the direction of the positive +element normal. +TRSHR +Surface traction +FL−2 +TRSHRNU(S) +Not supported +FL−2 +TRVEC +Surface traction +FL−2 +TRVECNU(S) +Not supported +FL−2 +traction +Shear +reference surface. +on +the +element +Nonuniform shear +traction on the +surface with +reference +element +magnitude and direction supplied +via user subroutine UTRACLOAD. +General +reference surface. +traction on the element +Nonuniform general +on +the element reference surface with +traction +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +magnitude and direction supplied via +user subroutine UTRACLOAD. +Foundations +Foundations are specified as described in “Element foundations,” Section 2.2.2. +Load ID +(*FOUNDATION) Load/Interaction +Abaqus/CAE +Units +Description +Elastic +foundation +FL−3 +Elastic foundation. +For MGAX +elements the elastic foundations are +applied to degrees of freedom +and +only. +Surface-based loading +Distributed loads +Surface-based distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +HP +Pressure +FL−2 +Pressure +FL−2 +PNU +Pressure +FL−2 +TRSHR +Surface traction +FL−2 +29.1.4–4 +Hydrostatic pressure on the element +reference surface and linear in global +Z. The pressure is positive in the +direction opposite to the surface +normal. +Pressure on the element reference +surface. The pressure is positive in +the direction opposite to the surface +normal. +Nonuniform pressure on the element +reference surface with magnitude +supplied via user subroutine DLOAD. +The pressure is positive in the +the surface +direction opposite of +normal. +traction +Shear +reference surface. +on +the +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +TRSHRNU(S) +Surface traction +FL−2 +TRVEC +Surface traction +FL−2 +TRVECNU(S) +Surface traction +FL−2 +traction on the +Nonuniform shear +element +surface with +reference +magnitude and direction supplied +via user subroutine UTRACLOAD. +General +reference surface. +traction on the element +traction +Nonuniform general +on +the element reference surface with +magnitude and direction supplied via +user subroutine UTRACLOAD. +Incident wave loading +Surface-based incident wave loads are available. They are specified as described in “Acoustic and shock +loads,” Section 33.4.6. If the incident wave field includes a reflection off a plane outside the boundaries +of the mesh, this effect can be included. +Element output +The default local material directions are such that local material direction 1 lies along the line of the +element and local material direction 2 is the hoop direction. +Stress, strain, and other tensor components +Stress and other tensors (including strain tensors) are available for elements with displacement degrees +of freedom. All tensors have the same components. For example, the stress components are as follows: +S11 +S22 +S12 +Local +direct stress. +Local +direct stress. +Local +elements. +shear stress. Only available for generalized axisymmetric membrane +Section thickness +STH +Current thickness. +Node ordering on elements +2 - node element +3 - node element +Numbering of integration points for output +2 - node element +3 - node element +29.2 +Truss elements +• “Truss elements,” Section 29.2.1 +• “Truss element library,” Section 29.2.2 +29.2.1 +TRUSS ELEMENTS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Truss element library,” Section 29.2.2 +• *SOLID SECTION +• “Creating truss sections,” Section 12.13.12 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +Truss elements: +• are long, slender structural members that can transmit only axial force (nonstructural link elements +are presented in “One-dimensional solid (link) element library,” Section 28.1.2); and +• do not transmit moments. +Typical applications +Truss elements are used in two and three dimensions to model slender, line-like structures that support +loading only along the axis or the centerline of the element. No moments or forces perpendicular to the +centerline are supported. +The two-dimensional truss elements can be used in axisymmetric models to represent components, +such as bolts or connectors, where the strain is computed from the change in length in the r–z plane +only. Two-dimensional trusses can also be used to define master surfaces for contact applications in +Abaqus/Standard . In this case the direction +of the master surface’s outward normal is critical for proper detection of contact. +The 3-node truss element available in Abaqus/Standard is often useful for modeling curved +reinforcing cables in structures, such as prestressed tendons in reinforced concrete or long slender +pipelines used in the off-shore industry. +Choosing an appropriate element +A 2-node straight truss element, which uses linear interpolation for position and displacement and has a +constant stress, is available in both Abaqus/Standard and Abaqus/Explicit. In addition, a 3-node curved +truss element, which uses quadratic interpolation for position and displacement so that the strain varies +linearly along the element, is available in Abaqus/Standard. +Hybrid versions of the stress/displacement trusses, coupled temperature-displacement trusses, and +piezoelectric trusses are available in Abaqus/Standard. +Hybrid stress/displacement truss elements +Hybrid (mixed) versions of the stress/displacement trusses, in which the axial force is treated as an +additional unknown, are available in two and three dimensions in Abaqus/Standard. These elements +are useful (to offset the effects of numerical ill-conditioning on governing equations) when a truss +represents a very rigid link whose stiffness is much larger than that of the overall structural model. +In such a case a hybrid truss provides an alternative to a truly rigid link, modeled with multi-point +constraints or rigid elements . +Coupled temperature-displacement truss elements +truss elements are available in two and three dimensions in +Coupled temperature-displacement +Abaqus/Standard. +These elements have temperature as an additional degree of freedom (11). +See “Fully coupled thermal-stress analysis,” Section 6.5.3, for information about fully coupled +temperature-displacement analysis in Abaqus/Standard. +Piezoelectric truss elements +Piezoelectric truss elements are available in two and three dimensions in Abaqus/Standard. These +elements have electric potential as an additional degree of freedom (9). See “Piezoelectric analysis,” +Section 6.7.2, for information about piezoelectric analysis. +Naming convention +Truss elements in Abaqus are named as follows: +3D 2 H +Optional: hybrid (H), +coupled temperature-displacement (T), +or piezoelectric (E) +number of nodes +two-dimensional (2D) or three-dimensional (3D) +truss +For example, T2D3E is a two-dimensional, 3-node piezoelectric truss element. +Element normal definition +For two-dimensional trusses the positive outward normal, +rotation from the direction going from node 1 to node 2 or node 3 of the element, as shown. +, is defined by a 90° counterclockwise +Defining the element’s section properties +You use a solid section definition to define the section properties. You must associate these properties +with a region of your model. +Input File Usage: +*SOLID SECTION, ELSET=name +where the ELSET parameter refers to a set of truss elements. +Abaqus/CAE Usage: +Property module: +Create Section: select Beam as the section Category and Truss as the +section Type +Assign→Section: select regions +Defining the cross-sectional area of a truss element +You can define the cross-sectional area associated with the truss element as part of the section definition. +If you do not specify a value for the cross-sectional area, unit area is assumed. +When truss elements are used in large-displacement analysis, the updated cross-sectional area is +calculated by assuming that the truss is made of an incompressible material, regardless of the actual +material definition. This assumption affects cases only where the strains are large. It is adopted because +the most common applications of trusses at large strains involve yielding metal behavior or rubber +elasticity, in which cases the material is effectively incompressible. Therefore, a linear elastic truss +element does not provide the same force-displacement response as a linear SPRINGA spring element +when the axial strain is not infinitesimal. +Input File Usage: +*SOLID SECTION, ELSET=name +cross-sectional area +Abaqus/CAE Usage: +Property module: Create Section: select Beam as the section Category and +Truss as the section Type: Cross-sectional area: cross-sectional area +Assigning a material definition to a set of truss elements +You must associate a material definition with each solid section definition. No material orientation is +permitted with truss elements. +Input File Usage: +*SOLID SECTION, MATERIAL=name +Any value given to the ORIENTATION parameter on the *SOLID SECTION +option will be ignored by truss elements. +Abaqus/CAE Usage: +Property module: Create Section: select Beam as the section Category +and Truss as the section Type: Material: name +Using truss elements in large-displacement implicit analysis +Truss elements have no initial stiffness to resist loading perpendicular to their axis. +If a stress-free +line of trusses is loaded perpendicular to its axis in Abaqus/Standard, numerical singularities and lack +of convergence can result. After the first iteration in a large-displacement implicit analysis, stiffness +perpendicular to the initial line of the elements develops, sometimes allowing an analysis to overcome +numerical problems. +In some cases loading the truss elements along their axis first or including initial tensile stress can +overcome these numerical singularities. However, you must choose the magnitude of the loading or +initial stress such that the final solution is unaffected. +29.2.2 +TRUSS ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Truss elements,” Section 29.2.1 +• *SOLID SECTION +Overview +This section provides a reference to the truss elements available in Abaqus/Standard and Abaqus/Explicit. +Element types +2-D stress/displacement truss elements +T2D2 +T2D2H(S) +T2D3(S) +T2D3H(S) +2-node linear displacement +2-node linear displacement, hybrid +3-node quadratic displacement +3-node quadratic displacement, hybrid +Active degrees of freedom +1, 2 +Additional solution variables +Element type T2D2H has one additional variable and element type T2D3H has two additional variables +relating to axial force. +3-D stress/displacement truss elements +T3D2 +T3D2H(S) +T3D3(S) +T3D3H(S) +2-node linear displacement +2-node linear displacement, hybrid +3-node quadratic displacement +3-node quadratic displacement, hybrid +Active degrees of freedom +1, 2, 3 +Additional solution variables +Element type T3D2H has one additional variable and element type T3D3H has two additional variables +relating to axial force. +2-D coupled temperature-displacement truss elements +T2D2T(S) +T2D3T(S) +2-node, linear displacement, linear temperature +3-node, quadratic displacement, linear temperature +Active degrees of freedom +1, 2 at middle node for T2D3T +1, 2, 11 at all other nodes +Additional solution variables +None. +3-D coupled temperature-displacement truss elements +T3D2T(S) +T3D3T(S) +2-node, linear displacement, linear temperature +3-node, quadratic displacement, linear temperature +Active degrees of freedom +1, 2, 3 at middle node for T3D3T +1, 2, 3, 11 at all other nodes +Additional solution variables +None. +2-D piezoelectric truss elements +T2D2E(S) +T2D3E(S) +2-node, linear displacement, linear electric potential +3-node, quadratic displacement, quadratic electric potential +Active degrees of freedom +1, 2, 9 +Additional solution variables +None. +3-D piezoelectric truss elements +T3D2E(S) +T3D3E(S) +2-node, linear displacement, linear electric potential +3-node, quadratic displacement, quadratic electric potential +Active degrees of freedom +1, 2, 3, 9 +Additional solution variables +None. +Nodal coordinates required +2-D: X, Y +3-D: X, Y, Z +Element property definition +You must provide the cross-sectional area of the element. If no area is given, Abaqus assumes unit area. +Input File Usage: +Abaqus/CAE Usage: +*SOLID SECTION +Property module: Create Section: select Beam as the section +Category and Truss as the section Type +Element-based loading +Distributed loads +Distributed loads are available for elements with displacement degrees of freedom. They are specified +as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +BX +BY +BZ +Body force +Body force +Body force +BXNU +Body force +FL−3 +FL−3 +FL−3 +FL−3 +BYNU +Body force +FL−3 +BZNU +Body force +FL−3 +Body force in global X-direction. +Body force in global Y-direction. +Body force in global Z-direction. +(Only for 3-D trusses.) +Nonuniform body force in global +X-direction with magnitude supplied +subroutine DLOAD in +user +via +and VDLOAD in +Abaqus/Standard +Abaqus/Explicit. +Nonuniform body force in global +Y-direction with magnitude supplied +subroutine DLOAD in +via +user +and VDLOAD in +Abaqus/Standard +Abaqus/Explicit. +Nonuniform body force in global +Z-direction with magnitude supplied +subroutine DLOAD in +via +user +and VDLOAD in +Abaqus/Standard +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +CENT(S) +Not supported +FL−4 +(ML−3 T−2 ) +CENTRIF(S) +Rotational body +force +T−2 +CORIO(S) +Coriolis force +FL−4 T +(ML−3 T−1 ) +GRAV +Gravity +LT−2 +ROTA(S) +Rotational body +force +T−2 +Abaqus/Explicit. +trusses.) +(Only for 3-D +, where +Centrifugal load (magnitude is input +is the mass density +as +per unit volume, +is the angular +velocity). +Centrifugal load (magnitude is input +as +the angular +velocity). +, where +is +Coriolis force (magnitude is input +is the mass density +as +, where +per unit volume, +is the angular +velocity). +loading +Gravity +direction (magnitude is +acceleration). +in +specified +input as +Rotary acceleration load (magnitude +is input as +is the rotary +acceleration). +, where +Abaqus/Aqua loads +Abaqus/Aqua loads are specified as described in “Abaqus/Aqua analysis,” Section 6.11.1. They are +available only for stress/displacement trusses. +Load ID +(*CLOAD/ +*DLOAD) +FDD(A) +FD1(A) +FD2(A) +FDT(A) +FI(A) +Abaqus/CAE +Load/Interaction +Units +Description +Not supported +FL−1 +Transverse fluid drag load. +Not supported +Not supported +Not supported +Not supported +FL−1 +FL−1 +Fluid drag force on the first end of the +truss (node 1). +Fluid drag force on the second end of +the truss (node 2 or node 3). +Tangential fluid drag load. +Fluid inertia load. +Load ID +(*CLOAD/ +*DLOAD) +FI1(A) +FI2(A) +PB(A) +WDD(A) +WD1(A) +WD2(A) +Abaqus/CAE +Load/Interaction +Units +Description +Not supported +Not supported +Not supported +Not supported +Not supported +Not supported +FL−1 +FL−1 +Fluid inertia force on the first end of +the truss (node 1). +Fluid inertia force on the second end +of the truss (node 2 or node 3). +Buoyancy load (with closed end +condition). +Transverse wind drag load. +Wind drag force on the first end of the +truss (node 1). +Wind drag force on the second end of +the truss (node 2 or node 3). +Distributed heat fluxes +Distributed heat fluxes are available for coupled temperature-displacement trusses. They are specified +as described in “Thermal loads,” Section 33.4.4. +Abaqus/CAE +Load/Interaction +Units +Description +Load ID +(*DFLUX) +BF(S) +BFNU(S) +S1(S) +S2(S) +Body heat flux +Body heat flux +JL−3 T−1 +JL−3 T−1 +Surface heat flux +JL−2 T−1 +Surface heat flux +JL−2 T−1 +Heat body flux per unit volume. +Nonuniform heat body flux per unit +volume with magnitude supplied via +user subroutine DFLUX. +Heat surface flux per unit area into the +first end of the truss (node 1). +Heat surface flux per unit area into +the second end of the truss (node 2 or +node 3). +Nonuniform heat surface flux per unit +area into the first end of the truss (node +1) with magnitude supplied via user +subroutine DFLUX. +Nonuniform heat surface flux per unit +area into the second end of the truss +S1NU(S) +Not supported +JL−2 T−1 +S2NU(S) +Not supported +JL−2 T−1 +Load ID +(*DFLUX) +Abaqus/CAE +Load/Interaction +Units +Description +(node 2 or node 3) with magnitude +supplied via user subroutine DFLUX. +Film conditions +Film conditions are available for coupled temperature-displacement trusses. They are specified as +described in “Thermal loads,” Section 33.4.4. +Load ID +(*FILM) +F1(S) +F2(S) +Abaqus/CAE +Load/Interaction +Units +Description +Not supported +JL−2 T−1 −1 +Not supported +JL−2 T−1 −1 +F1NU(S) +Not supported +JL−2 T−1 −1 +F2NU(S) +Not supported +JL−2 T−1 −1 +Film coefficient and sink temperature +at the first end of the truss (node 1). +Film coefficient and sink temperature +at the second end of the truss (node 2 +or node 3). +Nonuniform film coefficient and sink +temperature at the first end of the truss +(node 1) with magnitude supplied via +user subroutine FILM. +Nonuniform film coefficient +and +sink temperature at the second end +of +the truss (node 2 or node 3) +with magnitude supplied via user +subroutine FILM. +Radiation types +Radiation conditions are available for coupled temperature-displacement trusses. They are specified as +described in “Thermal loads,” Section 33.4.4. +Load ID +(*RADIATE) +Abaqus/CAE +Load/Interaction +Units +Description +R1(S) +R2(S) +Surface radiation Dimensionless +Surface radiation Dimensionless +Emissivity and sink temperature at the +first end of the truss (node 1). +Emissivity and sink temperature at the +second end of the truss (node 2 or +node 3). +Electric fluxes +Electric fluxes are available for piezoelectric trusses. They are specified as described in “Piezoelectric +analysis,” Section 6.7.2. +Load ID +(*DECHARGE) +Abaqus/CAE +Load/Interaction +Units +Description +EBF(S) +Body charge +CL−3 +Body flux per unit volume. +Element output +Stress, strain, and other tensor components +Stress and other tensors (including strain tensors) are available for elements with displacement degrees +of freedom. All tensors have the same components. For example, the stress components are as follows: +S11 +Axial stress. +Heat flux components +Available for coupled temperature-displacement trusses. +HFL1 +Heat flux along the element axis. +Node ordering on elements +end 2 +end 1 +end 1 +2 - node element +3 - node element +end 2 +Numbering of integration points for output +2 - node element +3 - node element +29.3 +Beam elements +• “Beam modeling: overview,” Section 29.3.1 +• “Choosing a beam cross-section,” Section 29.3.2 +• “Choosing a beam element,” Section 29.3.3 +• “Beam element cross-section orientation,” Section 29.3.4 +• “Beam section behavior,” Section 29.3.5 +• “Using a beam section integrated during the analysis to define the section behavior,” Section 29.3.6 +• “Using a general beam section to define the section behavior,” Section 29.3.7 +• “Beam element library,” Section 29.3.8 +• “Beam cross-section library,” Section 29.3.9 +29.3.1 +BEAM MODELING: OVERVIEW +Abaqus offers a wide range of beam modeling options. +Overview +Beam modeling consists of: +• choosing a beam cross-section (“Choosing a beam cross-section,” Section 29.3.2, and “Beam cross- +section library,” Section 29.3.9); +• choosing the appropriate beam element type (“Choosing a beam element,” Section 29.3.3, and +“Beam element library,” Section 29.3.8); +• defining the beam cross-section orientation (“Beam element cross-section orientation,” +Section 29.3.4); +• determining whether or not numerical integration is needed to define the beam section behavior +(“Beam section behavior,” Section 29.3.5); and +• defining the beam section behavior (“Using a beam section integrated during the analysis to define +the section behavior,” Section 29.3.6, or “Using a general beam section to define the section +behavior,” Section 29.3.7). +Determining whether beam modeling is appropriate +Beam theory is the one-dimensional approximation of a three-dimensional continuum. The reduction in +dimensionality is a direct result of slenderness assumptions; that is, the dimensions of the cross-section +are small compared to typical dimensions along the axis of the beam. The axial dimension must be +interpreted as a global dimension (not the element length), such as +• distance between supports, +• distance between gross changes in cross-section, or +• wavelength of the highest vibration mode of interest. +In Abaqus a beam element is a one-dimensional line element in three-dimensional space or +in the X–Y plane that has stiffness associated with deformation of the line (the beam’s “axis”). +These deformations consist of axial stretch; curvature change (bending); and, +torsion. +(“Truss elements,” Section 29.2.1, are one-dimensional line elements that have only axial stiffness.) +Beam elements offer additional flexibility associated with transverse shear deformation between the +beam’s axis and its cross-section directions. Some beam elements in Abaqus/Standard also include +warping—nonuniform out-of-plane deformation of the beam’s cross-section—as a nodal variable. +The main advantage of beam elements is that they are geometrically simple and have few degrees of +freedom. This simplicity is achieved by assuming that the member’s deformation can be estimated +entirely from variables that are functions of position along the beam axis only. Thus, a key issue in +using beam elements is to judge whether such one-dimensional modeling is appropriate. +in space, +The fundamental assumption used is that the beam section (the intersection of the beam with a +plane that is perpendicular to the beam axis; see the discussion in “Choosing a beam cross-section,” +Section 29.3.2) cannot deform in its own plane (except for a constant change in cross-sectional area, +which may be introduced in geometrically nonlinear analysis and causes a strain that is the same in +all directions in the plane of the section). The implications of this assumption should be considered +carefully in any use of beam elements, especially for cases involving large amounts of bending or axial +tension/compression of non-solid cross-sections such as pipes, I-beams, and U-beams. Section collapse +may occur and result in very weak behavior that is not predicted by beam theory. Similarly, thin-walled, +curved pipes exhibit much softer bending behavior than would be predicted by beam theory because +the pipe wall readily bends in its own section—another effect precluded by this basic assumption of +beam theory. This effect, which must generally be considered when designing piping elbows, can be +modeled by using shell elements to model the pipe as a three-dimensional shell or, in Abaqus/Standard, by using elbow elements . +In addition to beam elements, frame elements are provided in Abaqus/Standard. These elements +provide efficient modeling for design calculations of frame-like structures composed of initially straight, +slender members. They operate directly in terms of axial force, bending moments, and torque at the +element’s end nodes. They are implemented for small or large displacements (large rotations with small +strains) and permit the formation of plastic hinges at their ends through a “lumped” plasticity model that +includes kinematic hardening. See “Frame elements,” Section 29.4.1, for details. +In addition to the various beam elements, Abaqus also provides pipe elements to model beams with +pipe cross-sections that are subject to internal stress due to internal and/or external pressure loading. +Abaqus provides a choice of two formulations for pipe elements: +• the thin-walled formulation, where the hoop stress is assumed to be constant and the radial stress is +neglected, is available in Abaqus/Explicit and Abaqus/Standard; and +• the thick-walled formulation, where the hoop and radial stress vary through the cross-section, is +available only in Abaqus/Standard. +The pipe elements are a specialized form of the corresponding beam elements that allow for internal +and/or external pressure load specification and take the resulting hoop stress (as well as radial stress for +thick-walled pipes) into account for the material constitutive calculations. Usage of the pipe elements +is identical to that of the corresponding beam elements with respect to the section definition, boundary +conditions at the element nodes, surface definitions, interactions such as tie constraints, etc. +Using beam elements in dynamic and eigenfrequency analysis +The rotary inertia of a beam cross-section is usually insignificant for slender beam structures, except for +twist around the beam axis. Therefore, Abaqus/Standard ignores rotary inertia of the cross-section for +Euler-Bernoulli beam elements in bending. For thicker beams the rotary inertia plays a role in dynamic +analysis, but to a lesser extent than shear deformation effects. +For Timoshenko beams the inertia properties are calculated from the cross-section geometry. The +rotary inertia associated with torsional modes is different from that of flexural modes. For unsymmetric +cross-sections the rotary inertia is different in each direction of bending. Abaqus allows you to choose +the rotary inertia formulation for Timoshenko beams. When an approximate isotropic formulation is +requested, the rotary inertia associated with the torsional mode is used for all rotational degrees of +freedom in Abaqus/Standard, and a scaled flexural inertia with a scaling factor chosen to maximize the +stable time increment is used for all rotational degrees of freedom in Abaqus/Explicit. The center of mass +of the cross-section is taken to be located at the beam node. When the exact (anisotropic) formulation +is requested, the rotary inertia associated with bending and torsion differ and the coupling between the +translational and rotational degrees of freedom is included for beam cross-section definitions where the +beam node is not located at the center of mass of the cross-section. For Timoshenko beams with the exact +(default) rotary inertia formulation, you can define an additional mass and rotary inertia contribution to +the beam’s inertia response that does not add to its structural stiffness; see “Adding inertia to the beam +section behavior for Timoshenko beams” in “Beam section behavior,” Section 29.3.5. +29.3.2 +CHOOSING A BEAM CROSS-SECTION +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Beam modeling: overview,” Section 29.3.1 +• “Beam cross-section library,” Section 29.3.9 +• “Meshed beam cross-sections,” Section 10.6.1 +• “Defining profiles,” Section 12.2.2 of the Abaqus/CAE User’s Manual +Overview +The choice of cross-section is determined by the geometry of the cross-section and its behavior. A beam’s +cross-section: +• can be solid or thin-walled; +• if thin-walled, can be open or closed; and +• can be defined by choosing from the Abaqus cross-section library; by specifying geometric +quantities such as area, moments of inertia, and torsional constant; or by using a mesh of special +two-dimensional elements, for which geometric quantities are calculated numerically. +You must consider whether the section should be treated as a solid cross-section or as a thin-walled +cross-section. This choice determines the basis upon which Abaqus computes the axial and shear strains +at each point in the section. +Solid cross-sections +For solid sections under bending, plane (beam) sections remain plane. Under torsional loading any +noncircular beam section will warp: the beam section will not remain planar. However, for solid sections +the warping of the section is small enough so that the axial strain due to warping of the section can be +neglected and St. Venant warping theory can be used to construct a single component of shear strain +at each integration point in the section. This is done automatically for the rectangular and trapezoidal +sections in the beam section library. The St. Venant warping functions are used to define the shear +strain even when the response in the section is no longer purely elastic. This limits the accuracy of the +modeling for cases involving noncircular solid beam sections subjected to torsional loadings that cause +large amounts of inelastic deformation. When using a meshed beam profile, two shear strain components +are available for output in the user-specified material system. The thick pipe section is treated as a solid +cross-section. +Nonsolid (“thin-walled”) cross-sections +In Abaqus nonsolid sections are treated as “thin-walled” sections; that is, in the plane of the section, the +thickness of a branch of the section is assumed to be small compared to its length. Thin-walled beam +theory determines the shear in the wall of the section depending on whether the section is closed or open. +Closed sections +A closed section is a nonsolid section whose branches form closed loops. Closed sections offer significant +resistance to torsion and do not warp significantly. Abaqus ignores warping effects for closed sections. +In Abaqus predefined beam sections can model only one closed loop. Sections with multiple loops +must be modeled with a meshed beam section or with shells. +For sufficiently small thickness of the section walls, the variation of shear stress across the thickness +is negligible; the formulation of the closed sections available in Abaqus is based on this assumption. +Open sections +An open section is a nonsolid section with branches that do not form closed loops, such as an I-section +or a U-section. In such sections the shear stress is assumed to vary linearly over the wall thickness +and to vanish at the center of the wall. Open sections can warp significantly and generally require the +use of open-section warping theory (available with beam element types BxxOS in Abaqus/Standard) +with suitable warping constraints (applied to degree of freedom 7) at supports or joints. Such warping +constraints may significantly increase the torsional stiffness of the beam. Open, thin-walled sections +whose branches are straight lines that meet at a single point (such as the L-section in the Abaqus beam +element section library, T-sections, or X-sections) do not warp; therefore, warping constraints have no +effect. Such sections always have very little torsional stiffness. +If an open section is used with a regular beam element type (not BxxOS), the open section is assumed +to be free to warp and the axial strain due to warping is neglected. Consequently, the section will have +very little torsional stiffness. +Section property calculations +Thin-walled assumptions are used when calculating nonsolid section properties. Properties for sections +comprised of intersecting straight segments (arbitrary, box, hexagonal, I-, and L-sections) also include +an approximation of the intersection geometry. +Available beam cross-sections +You can specify any of the following types of beam cross-sections: an Abaqus library cross-section, +a generalized cross-section for which you specify the geometric quantities directly, or a meshed cross- +section. +The Abaqus beam cross-section library +The Abaqus beam cross-section library contains solid sections (circular, rectangular, and trapezoidal), +closed thin-walled sections (box, hexagonal, and pipe), open thin-walled sections (I-shaped, T-shaped, +or L-shaped), and a thick-walled pipe section. Abaqus also provides an arbitrary thin-walled section +definition; Abaqus will treat this section type as a closed or open section, depending on how the section +is defined. +Trapezoidal, I, and arbitrary library sections allow you to define the location of the origin of the local +coordinate system. Other section types—such as rectangular, circular, L, or pipe—have preset origins. +Input File Usage: +Use the following option to define a beam section integrated during the analysis: +*BEAM SECTION, SECTION=name +where name can be ARBITRARY, BOX, CIRC, HEX, I, L, PIPE, RECT, +THICK PIPE, or TRAPEZOID. A T-section is defined by specifying geometric +data for only one flange of an I-section. +Use the following option to define a general beam section: +*BEAM GENERAL SECTION, SECTION=name +where name can be ARBITRARY, BOX, CIRC, HEX, I, L, PIPE, RECT, or +TRAPEZOID. A T-section is defined by specifying geometric data for only +one flange of an I-section. +Abaqus/CAE Usage: +Property module: Create Profile: choose Box, Pipe, Circular, Rectangular, +Hexagonal, Trapezoidal, I, L, T, or Arbitrary +Generalized cross-sections +Abaqus also allows you to specify “generalized” cross-sections by specifying the geometric quantities +necessary to define the section. Such generalized sections can be used only with linear material behavior +although the section response can be linear or nonlinear. +Input File Usage: +Use the following option to define a linear generalized cross-section: +*BEAM GENERAL SECTION, SECTION=GENERAL +Use the following option to define a nonlinear generalized cross-section: +Abaqus/CAE Usage: +*BEAM GENERAL SECTION, SECTION=NONLINEAR GENERAL +Property module: Create Profile: choose Generalized +Nonlinear generalized cross-sections are not supported in Abaqus/CAE. +Meshed cross-sections +Abaqus allows you to mesh an arbitrarily shaped solid cross-section by using warping elements in a two-dimensional analysis to generate beam cross-section +properties that can be used in a subsequent two- or three-dimensional beam analysis. Such sections +permit only linear, elastic material behavior. Therefore, a meshed cross-section can be used only with a +general beam section definition; for details, see “Meshed beam cross-sections,” Section 10.6.1. +Input File Usage: +*BEAM GENERAL SECTION, SECTION=MESHED +Abaqus/CAE Usage: Meshed cross-sections are not supported in Abaqus/CAE. +CHOOSING A BEAM ELEMENT +BEAM ELEMENTS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Beam modeling: overview,” Section 29.3.1 +• “Beam element library,” Section 29.3.8 +• *TRANSVERSE SHEAR STIFFNESS +• “Creating beam sections,” Section 12.13.11 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +Abaqus offers a wide range of beam elements, +“Timoshenko”-type beams with solid, thin-walled closed and thin-walled open sections. +including “Euler-Bernoulli”-type beams and +The Abaqus/Standard beam element library includes: +• Euler-Bernoulli (slender) beams in a plane and in space; +• Timoshenko (shear flexible) beams in a plane and in space; +• linear, quadratic, and cubic interpolation formulations; +• warping (open section) beams; +• pipe elements; and +• hybrid formulation beams, typically used for very stiff beams that rotate significantly (applications +in robotics or in very flexible structures such as offshore pipelines). +The Abaqus/Explicit beam element library includes: +• Timoshenko (shear flexible) beams in a plane and in space; +• linear and quadratic interpolation formulations; and +• linear pipe elements. +Naming convention +Beam elements in Abaqus are named as follows: +1 OS H +hybrid (optional) +open section (optional) +linear (1), quadratic (2), cubic (3), +or initially straight cubic (4) +beam or pipe in plane (2) or beam or pipe in space (3) +beam (B) or pipe (PIPE) element +For example, B21H is a planar beam that uses linear interpolation and a hybrid formulation. +Euler-Bernoulli (slender) beams +Euler-Bernoulli beams (B23, B23H, B33, and B33H) are available only in Abaqus/Standard. These +elements do not allow for transverse shear deformation; plane sections initially normal to the beam’s axis +remain plane (if there is no warping) and normal to the beam axis. They should be used only to model +slender beams: the beam’s cross-sectional dimensions should be small compared to typical distances +along its axis (such as the distance between support points or the wavelength of the highest mode that +participates in a dynamic response). For beams made of uniform material, typical dimensions in the +cross-section should be less than about 1/15 of typical axial distances for transverse shear flexibility to +be negligible. (The ratio of cross-section dimension to typical axial distance is called the slenderness +ratio.) +Load stiffness for pressure loads is not included for these elements. +Interpolation +The Euler-Bernoulli beam elements use cubic interpolation functions, which makes them reasonably +accurate for cases involving distributed loading along the beam. Therefore, they are well suited for +dynamic vibration studies, where the d’Alembert (inertia) forces provide such distributed loading. +The cubic beam elements are written for small-strain, large-rotation analysis. They may not be +appropriate for torsional stability problems due to the approximations in the underlying formulation and +cannot be used in analyses involving very large rotations (of the order 180°); quadratic or linear beam +elements should be used instead. +Mass formulation +The Euler-Bernoulli beam elements use a consistent mass formulation. Rotary inertia for twist around +the beam axis is the same as for Timoshenko beams. For details, see “Mass and inertia for Timoshenko +beams,” Section 3.5.5 of the Abaqus Theory Manual. Any additional inertia defined for these elements + is ignored. +Timoshenko (shear flexible) beams +Timoshenko beams (B21, B22, B31, B31OS, B32, B32OS, PIPE21, PIPE22, PIPE31, PIPE32, and their +“hybrid” equivalents) allow for transverse shear deformation. They can be used for thick (“stout”) as +well as slender beams. For beams made from uniform material, shear flexible beam theory can provide +useful results for cross-sectional dimensions up to 1/8 of typical axial distances or the wavelength of the +highest natural mode that contributes significantly to the response. Beyond this ratio the approximations +that allow the member’s behavior to be described solely as a function of axial position no longer provide +adequate accuracy. +Abaqus assumes that the transverse shear behavior of Timoshenko beams is linear elastic with a +fixed modulus and, thus, independent of the response of the beam section to axial stretch and bending. +For most beam sections Abaqus will calculate the transverse shear stiffness values required in +the element formulation. You can override these default values as described below in “Defining the +transverse shear stiffness and the slenderness compensation factor.” The default shear stiffness values +are not calculated in some cases if estimates of shear moduli are unavailable during the preprocessing +stage of input; for example, when the material behavior is defined by user subroutine UMAT, UHYPEL, +UHYPER, or VUMAT. In such cases you must define the transverse shear stiffnesses as described below. +The Timoshenko beams can be subjected to large axial strains. The axial strains due to torsion are +assumed to be small. In combined axial-torsion loading, torsional shear strains are calculated accurately +only when the axial strain is not large. +Transverse shear stiffness definition +The effective transverse shear stiffness of the section of a shear flexible beam is defined in Abaqus as +is the section shear stiffness in the +where +the shear stiffness from becoming too large in slender beam elements; +of the section; and +are the local directions of the cross-section. The +-direction; +is a dimensionless factor used to prevent +is the actual shear stiffness +have units of force. +The dimensionless factors +are always included in the calculation of transverse shear stiffness +and are defined as +is the inertia in the +-direction, +is a constant of value +where l is the length of the element, A is the cross-sectional area, +is the slenderness compensation factor (with a default value of 0.25), and +1.0 for first-order elements and 10−4 for second-order elements. +For meshed cross-sections the above expressions change to +You can define the +or +as described below. If you do not specify them, they are defined by +or +where G is the elastic shear modulus or moduli and A is the cross-sectional area of the beam section. +Temperature and field variable dependencies of G are not taken into account when calculating +and +. The shear factor k (Cowper, 1966) is defined as: +Section type +Shear factor, k +Arbitrary +Box +Circular +Elbow +Generalized +Hexagonal +I (and T) +Meshed +Nonlinear generalized +Pipe +Rectangular +Thick pipe +Trapezoidal +1.0 +0.44 +0.89 +0.85 +1.0 +0.53 +0.44 +1.0 +1.0 +1.0 +0.53 +0.85 +0.53–0.89 +0.822 +When a beam section definition integrated during the analysis is used , G is calculated from the +elastic material definition used with the section. When a general beam section definition is used (see +“Using a general beam section to define the section behavior,” Section 29.3.7), you provide G as part of +the beam section data. +Defining the transverse shear stiffness and the slenderness compensation factor +You can define the transverse shear stiffness for beam sections integrated during the analysis and general +beam sections. In the case of two-dimensional beams, you can input a single value of transverse shear +stiffness, namely +is omitted or given as zero, the nonzero value will be used +for both. +. If either value of +You can also define the slenderness compensation factor. The default value for the slenderness +If a slenderness compensation factor value is provided, you must also +compensation factor is 0.25. +provide the values of the shear stiffness +. +In the case of first-order elements, you may define the slenderness compensation factor by including +, and any values +values are calculated from the elastic material +the label SCF. Abaqus will then use a slenderness compensation factor of +of +definition. +that you specify are ignored. Instead, the +The transverse shear stiffness is not relevant to Euler-Bernoulli beam elements for which the +transverse shear constraints are satisfied exactly. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options to define the transverse shear stiffness for +beam sections integrated during the analysis: +*BEAM SECTION +*TRANSVERSE SHEAR STIFFNESS +Use both of the following options to define the transverse shear stiffness for +general beam sections: +*BEAM GENERAL SECTION +*TRANSVERSE SHEAR STIFFNESS +To define transverse shear stiffness for beam sections integrated during the +analysis: +Property module: beam section editor: Section integration: During +analysis: Stiffness: toggle on Specify transverse shear +To define transverse shear stiffness for general beam sections: +Property module: beam section editor: Section integration: Before +analysis: Stiffness, toggle on Specify transverse shear +Interpolation +Abaqus provides finite axial strain, shear flexible beams with linear and quadratic interpolations. Their +formulation is described in “Beam element formulation,” Section 3.5.2 of the Abaqus Theory Manual. +Element types B21, B31, B31OS, PIPE21, PIPE31, and their hybrid equivalents use linear +interpolation. These elements are well suited for cases involving contact, such as the laying of a pipeline +in a trench or on the seabed or the contact between a drill string and a well hole, and for dynamic +versions of similar problems (impact). +Element types B22, B32, B32OS, PIPE22, PIPE32, and their hybrid equivalents use quadratic +interpolation. +Mass formulation +The linear Timoshenko beam elements use a lumped mass formulation by default. The quadratic +Timoshenko beam elements in Abaqus/Standard use a consistent mass formulation, except in dynamic +procedures in which a lumped mass formulation with a 1/6, 2/3, 1/6 distribution is used. For details, see +“Mass and inertia for Timoshenko beams,” Section 3.5.5 of the Abaqus Theory Manual. The quadratic +Timoshenko beam elements in Abaqus/Explicit use a lumped mass formulation with a 1/6, 2/3, 1/6 +distribution. +Using a consistent mass matrix in Abaqus/Standard +Alternatively, in Abaqus/Standard you can use the McCalley-Archer consistent mass matrix based on +the cubic interpolation of deflections and quadratic interpolation of rotations. +Input File Usage: +Abaqus/CAE Usage: +Use the following option for linear Timoshenko beam elements with beam +sections integrated during the analysis: +*BEAM SECTION, LUMPED=NO +Use the following option for linear Timoshenko beam elements with general +beam sections: +*BEAM GENERAL SECTION, LUMPED=NO +Use the following option for linear Timoshenko beam elements with beam +sections integrated during the analysis: +Property module: beam section editor: Section integration: +During analysis: Stiffness tabbed page: toggle on Use +consistent mass matrix formulation +Use the following option for linear Timoshenko beam elements with general +beam sections: +Property module: beam section editor: Section integration: +Before analysis: Stiffness tabbed page: toggle on Use +consistent mass matrix formulation +Rotary inertia treatment and additional beam inertia +the exact (anisotropic with displacement-rotation coupling) rotary inertia is used for +By default, +Timoshenko beams. Optionally, an uncoupled isotropic approximation to the rotary inertia can be used. +See “Rotary inertia for Timoshenko beams” in “Beam section behavior,” Section 29.3.5, for further +details. +The exception to this rule is the static procedure with automatic stabilization , where the mass matrix for Timoshenko beams is always calculated assuming +isotropic rotary inertia, regardless of the type of rotary inertia specified for the beam section definition +. +In some structural applications the beam element may be a one-dimensional approximation of a +structure with complex cross-sectional geometry and mass distribution. In such a cross-section there may +be inertia contributions that represent heavy machinery, cargo loaded in a ship compartment, fluid-filled +ballast tanks, or any other mass distributed along the length of the beam that is not part of the beam’s +structural stiffness. In such cases you can define additional mass and rotary inertia associated with the +beam section properties. Multiple masses per unit length (with location other than the origin of the beam +cross-section) and rotary inertias per unit length can be specified. Mass proportional damping (alpha or +composite damping) associated with this additional inertia can also be specified. Abaqus will use the +mass weighted average (based on the material damping and the added inertial damping) for the element +mass proportional damping. See “Material damping,” Section 26.1.1, for details. +Additional inertia due to immersion in fluid +When a beam is fully or partially submerged, the effect of the surrounding fluid can be modeled as an +additional distributed inertia on the beam. See “Additional inertia due to immersion in fluid” in “Beam +section behavior,” Section 29.3.5, for details. +Warping (open-section) beams +When modeling beams in space, a further consideration arises from the possible warping of the beam’s +cross-section under torsional loading. For all but circular sections the beam’s cross-section will deform +out of its original plane when subject to torsion. This warping deformation will modify the shear strain +distribution throughout the section. +Open sections will typically twist very easily if warping is not prevented, especially if the walls that +form the beam section are thin. Constraint of this warping at certain points along the beam (such as where +the beam is built into some other member, Figure 29.3.3–1, or into a wall) is then a major determinant +of the beam’s overall torsional response. +Figure 29.3.3–1 Intersection of open section beams. +Element types B31OS, B32OS (and their “hybrid” equivalents) have the warping magnitude, w, +as a degree of freedom at each node; they are available only in Abaqus/Standard. In these elements +Abaqus/Standard assumes that the warping of the cross-section follows a certain pattern as a function of +position in the cross-section (Abaqus will calculate this warping pattern if you have specified a standard +library section or an “arbitrary” section): only the warping magnitude varies with position along the +beam’s axis. These elements are meant for the analysis of thin-walled open sections in which warping +constraints play a role and the axial strains due to warping cannot be neglected. Examples of such open +sections that may warp in this fashion are the I-section and any open arbitrary section. In the other beam +element types warping is considered unconstrained and any axial stress due to warping is neglected; +torsional behavior will not be represented adequately when these element types are used with thin-walled, +open sections. +In general, the warping magnitude can be continuous only when the beam axis is continuous +through a node and the beam cross-section is the same on both sides of the node. Thus, if open-section +members intersect at a node (such as the cross-member of a vehicle chassis abutting a longitudinal +member, Figure 29.3.3–1), separate nodes may have to be used for the intersecting members with +different axial directions and appropriate constraints must be chosen for the warping amplitudes in each +member at this point. The choice of these constraints is a matter of detail of the local construction. For +example, if the joint is reinforced, warping may be prevented; therefore, degree of freedom 7 should be +fully constrained with a boundary condition on the appropriate members at the joint. +“Pipe” elements +The pipe elements in Abaqus assume a hollow circular section. The internal stress caused by internal or +external pressure loading in the pipe is included in these elements so that on the pipe cross-section a point +under tension will have different yield than a point under compression (Figure 29.3.3–2), thus causing +an asymmetry in the section’s response to inelastic bending. Two formulations are available for pipe +elements in Abaqus. The thin-walled pipe formulation assumes constant hoop stress across the cross- +section and neglects the radial stress, whereas thick-walled pipes (available only in Abaqus/Standard) +allow the hoop and radial stress components to vary across the cross-section. +The hoop stress in thin-walled pipe elements is computed as the average stress in equilibrium +with the internal and external pressure loading on the pipe section. For the thin-walled formulation, an +integration rule with one point through the thickness suffices to obtain an accurate solution. +For thick-walled pipes, the hoop stress and radial stress variation under applied internal and/or +external pressure are calculated using Lamé’s equations. The constitutive calculations at each material +point take into account the imposed hoop and radial stress values to determine the structural response. +A two-dimensional integration rule is used for thick-walled pipes to capture the effect of stress variation +across the section accurately. +“Hybrid” beams +Hybrid beam element types (B21H, B33H, etc.) are provided in Abaqus/Standard for use in cases where +it is numerically difficult to compute the axial and shear forces in the beam by the usual finite element +displacement method. This problem arises most commonly in geometrically nonlinear analysis when the +beam undergoes large rotations and is very rigid in axial and transverse shear deformation, such as a link +in a vehicle’s suspension system or a flexing long pipe or cable. The problem in such cases is that slight +differences in nodal positions can cause very large forces, which, in turn, cause large motions in other +directions. The hybrid elements overcome this difficulty by using a more general formulation in which +the axial and transverse shear forces in the elements are included, along with the nodal displacements and +rotations, as primary variables. Although this formulation makes these elements more expensive, they +generally converge much faster when the beam’s rotations are large and, therefore, are more efficient +overall in such cases. +Additional references +• Archer, J. S., “Consistent Matrix Formulations for Structural Analysis using Finite-Element +Techniques,” American Institute of Aeronautics and Astronautics Journal, vol. 3, pp. 1910–1918, +1965. +• Cowper, R. G., “The Shear Coefficient in Timoshenko’s Beam Theory,” Journal of Applied +Mechanics, vol. 33, pp. 335–340, 1966. +σ hoop +hoop stress caused by +pressurization +σ axial +asymmetric stress +limits in tension +and compression +Mises +yield surface +Figure 29.3.3–2 Yield behavior in thin-walled PIPE elements. +29.3.4 +BEAM ELEMENT CROSS-SECTION ORIENTATION +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Beam modeling: overview,” Section 29.3.1 +• “Beam cross-section library,” Section 29.3.9 +• “Beam section behavior,” Section 29.3.5 +• “Assigning a beam orientation,” Section 12.15.3 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +The orientation of a beam cross-section: +• is defined in terms of a local, right-handed axis system; and +• can be user-defined or calculated by Abaqus. +Beam cross-sectional axis system +The orientation of a beam cross-section is defined in Abaqus in terms of a local, right-handed ( , +axis system, where +the second node of the element, and +of the cross-section. +to the beam. This beam cross-sectional axis system is illustrated in Figure 29.3.4–1. +) +is the tangent to the axis of the element, positive in the direction from the first to +are basis vectors that define the local 1- and 2-directions +is referred to as the normal +is referred to as the first beam section axis, and +and +, +Defining the n1 -direction +For beams in a plane the +motion occurs. Therefore, planar beams can bend only about the first beam-section axis. +-direction is always (0.0, 0.0, −1.0); that is, normal to the plane in which the +For beams in space the approximate direction of +must be defined directly as part of the beam +section definition or by specifying an additional node off the beam axis as part of the element definition +. This additional node is included in the element’s connectivity +list. +• If an additional node is specified, the approximate direction of +from the first node of the element to the additional node. +is defined by the vector extending +• If +is defined directly for the section and an additional node is specified, the direction calculated +by using the additional node will take precedence. +• If the approximate direction is not defined by either of the above methods, the default value is (0.0, +0.0, −1.0). +n2 +n1 +Figure 29.3.4–1 Local axis definition for beam-type elements. +This approximate +-direction may be used to determine the +-direction has been defined or calculated, the actual +-direction (discussed below). Once the +, possibly +-direction will be calculated as +resulting in a direction that is different from the specified direction. +Input File Usage: +Use the following option to specify the +integrated during the analysis: +*BEAM SECTION +-direction directly for a beam section +-direction (the data line number depends on the value +of the SECTION parameter) +Use the following option to specify the +section: +*BEAM GENERAL SECTION +-direction directly for a general beam +-direction (the data line number depends on the value +of the SECTION parameter) +-direction: +Use the following option to specify an additional node off the beam axis to +define the +*ELEMENT +Property module: Assign→Beam Section Orientation: select +region and enter the +-direction +Specifying an additional node off +Abaqus/CAE. +the beam axis is not supported in +29.3.4–2 +Defining nodal normals +For beams in space you can define the nodal normal ( +-direction) by giving its direction cosines as the +fourth, fifth, and sixth coordinates of each node definition or by giving them in a user-specified normal +definition; see “Normal definitions at nodes,” Section 2.1.4, for details. Otherwise, the nodal normal will +be calculated by Abaqus, as described below. +If the nodal normal is defined as part of the node definition, this normal is used for all of the structural +elements attached to the node except those for which a user-specified normal is defined. If a user-specified +normal is defined at a node for a particular element, this normal definition takes precedence over the +normal defined as part of the node definition. If the specified normal subtends an angle that is greater +than 20° with the plane perpendicular to the element axis, a warning message is issued in the data (.dat) +file. If the angle between the normal defined as part of the node definition or the user-specified normal +and +is greater than 90°, the reverse of the specified normal is used. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to specify the +definition: +*NODE +node number, nodal coordinates, nodal normal coordinates +-direction as part of the node +Use the following option to define a user-specified normal: +*NORMAL +Defining the nodal normal is not supported in Abaqus/CAE; the nodal normal +calculated by Abaqus is always used. +Calculation of the average nodal normals by Abaqus +If the nodal normal is not defined as part of the node definition, element normal directions at the node +are calculated for all shell and beam elements for which a user-specified normal is not defined (the +“remaining” elements). For shell elements the normal direction is orthogonal to the shell midsurface, as +described in “Shell elements: overview,” Section 29.6.1. For beam elements the normal direction is the +second cross-section direction, as described in “Beam element cross-section orientation,” Section 29.3.4. +The following algorithm is then used to obtain an average normal (or multiple averaged normals) for the +remaining elements that need a normal defined: +1. If a node is connected to more than 30 remaining elements, no averaging occurs and each element +is assigned its own normal at the node. The first nodal normal is stored as the normal defined as +part of the node definition. Each subsequent normal is stored as a user-specified normal. +2. If a node is shared by 30 or fewer remaining elements, the normals for all the elements connected +to the node are computed. Abaqus takes one of these elements and puts it in a set with all the other +elements that have normals within 20° of it. Then: +a. Each element whose normal is within 20° of the added elements is also added to this set (if it +is not yet included). +b. This process is repeated until the set contains for each element in the set all the other elements +whose normals are within 20°. +c. If all the normals in the final set are within 20° of each other, an average normal is computed +for all the elements in the set. If any of the normals in the set are more than 20° out of line +from even a single other normal in the set, no averaging occurs for elements in the set and a +separate normal is stored for each element. +d. This process is repeated until all the elements connected to the node have had normals +computed for them. +e. The first nodal normal is stored as the normal defined as part of the node definition. Each +subsequently generated nodal normal is stored as a user-specified normal. +This algorithm ensures that the nodal averaging scheme has no element order dependence. A simple +example illustrating this process is included below. +Example: beam normal averaging +Consider the three beam element model in Figure 29.3.4–2. Elements 1, 2, and 3 share a common node +10, with no user-specified normal defined. + 10 + 20 + 40 + 30 +Figure 29.3.4–2 Three-element example for nodal averaging algorithm. +In the first scenario, suppose that at node 10 the normal for element 2 is within 20° of both elements +1 and 3, but the normals for elements 1 and 3 are not within 20° of each other. In this case, each element is +assigned its own normal: one is stored as part of the node definition and two are stored as user-specified +normals. +In the second scenario, suppose that at node 10 the normal for element 2 is within 20° of both +elements 1 and 3 and the normals for elements 1 and 3 are within 20° of each other. In this case, a single +average normal for elements 1, 2, and 3 would be computed and stored as part of the node definition. +In the last scenario, suppose that at node 10 the normal for element 2 is within 20° of element 1 but +the normal of element 3 is not within 20° of either element 1 or 2. In this case, an average normal is +computed and stored for elements 1, and 2 and the normal for element 3 is stored by itself: one is stored +as part of the node definition and the other is stored as a user-specified normal. +Appropriate beam normals +To ensure proper application of loads that act normal to the beam cross-section, it is important to have +beam normals that correctly define the plane of the cross-section. When linear beams are used to model +a curved geometry, appropriate beam normals are the normals that are averaged at the nodes. For such +cases it is preferable to define the cross-sectional axis system such that beam normals lie in the plane of +curvature and are properly averaged at the nodes. +Initial curvature and initial twist +In Abaqus/Standard normal direction definitions can result in a beam element having an initial curvature +or an initial twist, which will affect the behavior of some elements. +• When the normal to an element is not perpendicular to the beam axis (obtained by interpolation +using the nodes of the element), the beam element is curved. Initial curvature can result when you +define the normal directly (as part of the node definition or as a user-specified normal) or can result +when beams intersect at a node and the normals to the beams are averaged as described above. +The effect of this initial curvature is considered in cubic beam elements. Initial curvature resulting +from normal definitions is not considered in quadratic beam elements; however, these elements do +properly account for any initial curvature represented by the node positions. +• Similarly, nodal-normal directions that are in different orientations about the beam axis at different +nodes imply a twist. The effect of an initial twist, which could result from normal averaging or +user-defined normal definitions, is considered in quadratic beam elements. +Since the behavior of initially curved or initially twisted beams is quite different from straight beams, +the changes caused by averaging the normals may result in changes in the deformation of some beam +elements. You should always check the model to ensure that the changes caused by averaging the normals +are intended. If the normal directions at successive nodes subtend an angle that is greater than 20°, a +warning message is issued in the data (.dat) file. In addition, a warning message will be issued during +input file preprocessing if the average curvature computed for a beam differs by more than 0.1 degrees per +unit length or if the approximate integrated curvature for the entire beam differs by more than 5 degrees +as compared to the curvature computed without nodal averaging and without user-defined normals. +In Abaqus/Explicit initial curvature of the beam is not taken into account: all beam elements are +assumed to be initially straight. The element’s cross-section orientation is calculated by averaging the +-directions associated with its nodes. These two vectors are then projected onto the plane that +are made orthogonal +is perpendicular to the beam element’s axis. These projected directions +to each other by rotating in this plane by an equal and opposite angle. +- and +and +29.3.5 +BEAM SECTION BEHAVIOR +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Beam modeling: overview,” Section 29.3.1 +• *BEAM GENERAL SECTION +• *BEAM SECTION +• “Creating beam sections,” Section 12.13.11 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +The beam section behavior: +• is defined in terms of the response of the beam section to stretching, bending, shear, and torsion; +• may or may not require numerical integration over the section; and +• can be linear or nonlinear (as a result of nonlinear material response). +Beam section behavior +Defining a beam section’s response to stretching, bending, shear, and torsion of the beam’s axis requires +a suitable definition of the axial force, N; bending moments, +; and torque, T, as functions +and +of the axial strain, +. Here the subscripts 1 and 2 refer to +; curvature changes, +local, orthogonal axes in the beam section. +; and twist, +and +If open-section beam types are used, the section behavior must also define the warping bimoment, +W, and the generalized strain measures include the warping amplitude, w, and the bicurvature of the +beam, +, which is the gradient of the warping amplitude with respect to position along the beam: +. +The type of section definition you choose determines whether the beam section properties are +recomputed during the progression of the analysis or established in the preprocessor for the duration +If a general beam section definition is used , the cross-section properties are computed once, during +preprocessing. Alternatively, a beam section definition that is integrated during the analysis can +be used , in which case Abaqus will use numerical integration of the stress over the cross-section +to define the beam’s response as the analysis proceeds. +Since planar beams deform only in the X–Y plane, only N and +, +, and w are assumed to be zero. +the response in these elements: +, and +and +, contribute to +In Abaqus bending moments in beam sections are always measured about the centroid of the beam +section, while torque is measured with respect to the shear center. The beam axis (defined as the line +joining the nodes that define the beam element) need not pass through the centroid of the beam section. +coordinate system +defined in the cross-section of the beam; that is, the line of the element connecting the element’s nodes +passes through the origin of the cross-section’s local coordinate system. +The degrees of freedom of the beam element are at the origin of the local +Determining whether to use a beam section integrated during the analysis or a general beam +section +When a beam section integrated during the analysis is used , Abaqus integrates numerically over the +section as the beam deforms, evaluating the material behavior independently at each point on the section. +This type of beam section should be used when the section nonlinearity is caused only by nonlinear +material response. +When a general beam section is used , Abaqus precomputes the beam cross-section quantities and performs all +section computations during the analysis in terms of the precomputed values. This method combines +the functions of beam section and material descriptions (a material definition is not needed). The +precomputed section properties may be specified in a variety of ways, +including quite complex +geometries defined with a two-dimensional finite element mesh . A general beam section should be used when the beam section response is linear or +when it is nonlinear and the nonlinearity arises from more than just material nonlinearity, such as in +cases when section collapse occurs. +Input File Usage: +Use the following option to define a beam section integrated during the analysis: +*BEAM SECTION +Use the following option to define a general beam section: +*BEAM GENERAL SECTION +To define a beam section integrated during the analysis: +Abaqus/CAE Usage: +Property module: Create Section: select Beam as the section Category and +Beam as the section Type: Section integration: During analysis +To define a general beam section: +Property module: Create Section: select Beam as the section Category and +Beam as the section Type: Section integration: Before analysis +Geometric section quantities +The section quantities described below are needed to define the behavior of a general beam section. +Moments of inertia +The moments of inertia with respect to the centroid are defined as +and +where ( +position of the centroid of the cross-sectional area. +) is the position of the point in the local +beam section axis system and ( +) is the +Bending stiffness and rotary inertia contributions for a meshed section profile are calculated using the two-dimensional +cross-section model. The following integrated properties are defined for the entire cross-section model +meshed with warping elements: +and +where ( +) is the center of mass of the cross section. +Torsional constant +The torsional constant, J, depends on the shape of the cross section. The torsional constant of a circular +section is the polar moment of inertia, +. +The torsional constant for the rectangular and trapezoidal library sections is calculated numerically +by Abaqus using the Prandtl stress function approach. A local finite element model of the cross-section +is created internally for this purpose. The number of integration points selected for the cross-section +determines the accuracy of this finite element model. For increased accuracy specify a higher-order rule +by selecting nondefault integration. +The above rule is also applied to both the thin-walled box section and the arbitrary section to +increase the accuracy of the model. +If the thickness for each segment making up the section varies +significantly, more integration points for the box section or smaller segments for the arbitrary section +should be specified in the area where the thickness varies. +The torsional stiffness for a meshed section is calculated over the two-dimensional region meshed +with warping elements. The accuracy of the integration depends on the number of elements in the model: +where +denotes the derivative of the warping function with respect to the cross-section (1, 2) axis and +is the position of the shear center of the cross-sectional area. All indices take values 1, 2. For more +details, see “Meshed beam cross-sections,” Section 3.5.6 of the Abaqus Theory Manual. +For closed thin-walled sections the torsional constant is calculated from +where t is the thickness of the section, +is the area enclosed by the median line of the section, and s +is the length of the median line, measured along the circumference of the section in a counterclockwise +direction. +For open, built-up, thin-walled sections, +Abaqus will check if a built-up section is closed or not and will use the appropriate torsional constant. +Sectorial moment and warping constant +For open, thin-walled sections the sectorial moment is defined as +and the warping constant is defined as +where +is the sectorial area at a point in the section with the shear center as its pole. +Rotary inertia for Timoshenko beams +In general, the rotary inertia associated with torsional modes is different from that of flexural modes. For +unsymmetric cross-sections the rotary inertia is different in each direction of bending. For cross-sections +where the beam node is not located at the center of mass, coupling exists between the translational and +rotational degrees of freedom. +By default, the exact (anisotropic and coupled) rotary inertia is used for Timoshenko beams. In +Abaqus/Standard the anisotropic rotary inertia introduces unsymmetric terms in the Jacobian operator +during geometrically nonlinear, transient, direct-integration dynamic simulations. If the rotary inertia +effects are significant in the geometrically nonlinear dynamic response and the exact rotary inertia is +used, the unsymmetric solver should be used for better convergence. +Optionally, an approximate isotropic and uncoupled rotary inertia can be selected. +In +Abaqus/Standard this means that the rotary inertia associated with the torsional mode only is used for all +rotational degrees of freedom; potentially destabilizing rotary inertia effects in impact problems due to +the anisotropy or displacement-rotation coupling will not be introduced. In Abaqus/Explicit this means +a scaled flexural inertia with a scaling factor chosen to maximize the stable element time increment is +used for all rotational degrees of freedom; i.e., the stable time increment will not be determined by the +flexural response of the beam. In some slender beam analyses an isotropic approximation to the rotary +inertia may be accurate enough. +If beam elements are used to model plate-type structures in Abaqus/Explicit (i.e., if the moment +of inertia about one section axis of the beam is more than a thousand times greater than the moment +of inertia about the other axis), the exact rotary inertia formulation may lead to a sharp cut-back in the +stable time increment. In this case it is recommended that you either use the isotropic approximation or +alternatively consider modeling the structure with shell elements, which might be better suited to this +type of analysis. +For a definition of rotary inertia for the beam’s cross-section, see “Mass and inertia for Timoshenko +beams,” Section 3.5.5 of the Abaqus Theory Manual. +Input File Usage: +Use the following option to specify isotropic rotary inertia for a beam section +integrated during the analysis: +*BEAM SECTION, ROTARY INERTIA=ISOTROPIC +Use the following option to specify isotropic rotary inertia for a general beam +section: +Abaqus/CAE Usage: +*BEAM GENERAL SECTION, ROTARY INERTIA=ISOTROPIC +Isotropic rotary inertia for beam sections is not supported in Abaqus/CAE. The +default exact rotary inertia is always used. +Adding inertia to the beam section behavior for Timoshenko beams +Additional mass and rotary inertia properties for Timoshenko beams (including PIPE elements) can be +defined. This added inertia defined within the cross-section per unit length along the beam contributes to +the inertia response of the beam without contributing to the structural stiffness. Additional beam inertia +cannot be defined for a section if isotropic rotary inertia is used. +To specify additional beam inertia, you define the mass (per unit length) with the mass center +in the local (1, 2) beam cross-section axis system. To include rotary inertia +(in degrees) within the cross-section local (1, 2) system +relative to the local 1-direction +positioned at point +(per unit length), you can also define the angle +that positions the first axis of the rotary inertia coordinate system +in the beam cross-section axis system. See Figure 29.3.5–1 for an illustration. +x 2 +x 1 +Figure 29.3.5–1 Beam element with added inertia. +The rotary inertia components relative to the rotary inertia coordinate system +are defined as +and +where A is the area, +measured from +is the mass density, and X and Y are the local rotary inertia system coordinates +, the center of the added mass contribution. +As many point masses and rotary inertia contributions as are needed to define the added inertia can +be specified. Mass proportional damping associated with the added inertia can be specified by assigning a +value to the mass proportional Rayleigh damping coefficient, +, or the composite damping coefficient, +. Abaqus will use the mass weighted average (based on the material damping and the added inertia +damping) for the element mass proportional damping. +Input File Usage: +Use the following option in conjunction with the beam section definition to +specify additional inertia properties: +*BEAM ADDED INERTIA, ALPHA= +mass per unit length, +, +, +, +, +, COMPOSITE= +, +Abaqus/CAE Usage: +Additional inertia properties are not supported in Abaqus/CAE. +Additional inertia due to immersion in fluid +When a beam is fully or partially submerged, the effect of the surrounding fluid can be modeled as +an additional distributed inertia on the beam . By default, the beam is assumed to be fully submerged. +Alternatively, you can specify that the added inertia per unit length should be reduced by a factor of +one-half to model a partially submerged beam. +You specify the fluid mass density, +(per unit volume); beam local x and y coordinates of the +wetted cross-section centroid; wetted section effective radius, r; and empirical drag or flow coefficients, +and +. The inertia added per unit length to a fully immersed beam cross-section is given by +Because the beam cross-section origin may not be coincident with the centroid of the wetted +cross-section, the additional fluid inertia may include rotary effects. Nonzero values for the x- and +y-offsets of the wetted cross-section centroid will produce rotation-displacement coupling in the inertia +formulation. The default model for the added inertia derives from inviscid flow around a cylindrical +cross-section ( +, that models flow around a different +cross-section geometry. +); you can specify a coefficient, +An immersed beam also experiences an additional added mass effect at its free ends. If a beam +element’s end node is not attached to any other element and additional fluid inertia is defined for this +element, an additional mass may be added in the form: +For +this added mass corresponds to that of a hemispherical cap; the default value is +can be changed to model other geometries. If the beam is partially +submerged, the end inertia is automatically reduced by one-half. However, the added mass at the free +ends is always isotropic: axial and transverse motions experience the same additional inertia. +. The coefficient +The “virtual mass” added to a submerged or partially submerged beam is not included in the total +mass, center of mass, moments, or products of inertia reported in the data (.dat) file. +Input File Usage: +Use the following option in conjunction with the beam section definition to +define a fully immersed beam: +*BEAM FLUID INERTIA, FULL +, x, y, r, +, +Use the following option in conjunction with the beam section definition to +define a partially immersed beam: +*BEAM FLUID INERTIA, HALF +, x, y, r, +, +Abaqus/CAE Usage: +To define a fully immersed beam: +Property module: beam section editor: Fluid Inertia: toggle on +Specify fluid inertia effects: Fully submerged +To define a partially immersed beam: +Property module: beam section editor: Fluid Inertia: toggle on +Specify fluid inertia effects: Half submerged +Additional reference +• Blevins, R. D., Formulas for Natural Frequency and Mode Shape, R. E. Krieger Publishing Co., +Inc., 1987. +29.3.6 +USING A BEAM SECTION INTEGRATED DURING THE ANALYSIS TO DEFINE THE +SECTION BEHAVIOR +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Beam modeling: overview,” Section 29.3.1 +• “Beam section behavior,” Section 29.3.5 +• *BEAM SECTION +• “Specifying properties for beam sections integrated during analysis” in “Creating beam sections,” +Section 12.13.11 of the Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +A beam section integrated during the analysis: +• is used when section properties must be recomputed as the beam deforms over the course of the +analysis; and +• can be associated with linear or nonlinear material behavior. +Defining the behavior of a beam section integrated during the analysis +Use a beam section integrated during the analysis to define the section behavior when numerical +integration over the section is required as the beam deforms. You can choose a section shape from +the library of beam section shapes provided and +define the section’s dimensions. +In addition, you can specify the number of section points to use +for integration. The default number of section points is adequate for monotonic loading that causes +plasticity. If reversed plasticity will occur, more section points are required. +Use a material definition (“Material data definition,” Section 21.1.2) to define the material properties +of the section, and associate these properties with the section definition. Linear or nonlinear material +behavior can be associated with the section definition. However, if the material response is linear, the +more economic approach is to use a general beam section . +You must associate the section properties with a region of your model. +Input File Usage: +*BEAM SECTION, ELSET=name, SECTION=library_section, +MATERIAL=name +The ELSET parameter is used to associate the section properties with a set of +beam elements. +Abaqus/CAE Usage: +Property module: +Create Profile: Name: library_section +Create Section: select Beam as the section Category and Beam as +the section Type: Section integration: During analysis, Profile +name: library_section, Material name: name +Assign→Section: select regions +Defining a change in cross-sectional area due to straining +In the shear flexible elements Abaqus provides for a possible uniform cross-sectional area change by +allowing you to specify an effective Poisson’s ratio for the section. This effect is considered only in +geometrically nonlinear analysis and is provided to model the +reduction or increase in the cross-sectional area for a beam subjected to large axial stretch. +The value of the effective Poisson’s ratio must be between −1.0 and 0.5. By default, this effective +Poisson’s ratio for the section is set to 0.0 so that this effect is ignored. Setting the effective Poisson’s ratio +to 0.5 implies that the overall response of the section is incompressible. This behavior is appropriate if the +beam is made of a typical metal whose overall response at large deformation is essentially incompressible +(because it is dominated by plasticity). Values between 0.0 and 0.5 mean that the cross-sectional area +changes proportionally between no change and incompressibility, respectively. A negative value of the +effective Poisson’s ratio will result in an increase in the cross-sectional area in response to tensile axial +strains. +This effective Poisson’s ratio is not available for use with Euler-Bernoulli beam elements. +Input File Usage: +Abaqus/CAE Usage: +*BEAM SECTION, POISSON= +Property module: Create Section: select Beam as the section +Category and Beam as the section Type: Section integration: +During analysis, Section Poisson's ratio: +Defining material damping +When a beam section integrated during the analysis is used, damping can be introduced through the +material behavior definition. See “Material damping,” Section 26.1.1, for more information about the +material damping types available in Abaqus. +Specifying temperature and field variables +Temperature and field variables can be specified at specific points through the section or by defining +the value at the origin of the cross-section and specifying the gradients in the local 1- and 2-directions. +The actual values of the temperature and field variables are specified as either predefined fields or +initial conditions . +In any element it is assumed that the temperature definitions at all the nodes of the element are +compatible with the temperature definition method chosen for the element. For cases in which the +temperature definition method changes from one element to the next, separate nodes must be used on the +interface between elements with different temperature definition methods and MPCs must be applied to +make the displacements and rotations the same at the nodes. +By defining the value at the origin and the gradients in the 1- and 2-directions +Temperatures and field variables can be defined by giving the value at the origin of the cross-section and +the gradients in the 2- and 1-directions of the cross-section (that is, give +in the +predefined field or initial condition definition). For beams in a plane only and +need be given; +gradients in the 1-direction are ignored in this case. +and +Input File Usage: +Abaqus/CAE Usage: +*BEAM SECTION, TEMPERATURE=GRADIENTS +Property module: Create Section: select Beam as the section +Category and Beam as the section Type: Section integration: +During analysis, Linear by gradients +By defining the values at points through the section +Temperatures and field variables can be defined at a set of points on the section, as indicated for each +cross-section in “Beam cross-section library,” Section 29.3.9. +This technique cannot be used for any beam element that is adjacent to a general beam section +element, as it can lead to incorrect temperature distributions at the shared cross-section. If you cannot +avoid this modeling scenario, you must define the adjacent elements using separate nodes connected by +MPCs, as discussed above. +Input File Usage: +Abaqus/CAE Usage: +*BEAM SECTION, TEMPERATURE=VALUES +Property module: Create Section: select Beam as the section Category +and Beam as the section Type: Section integration: During analysis, +Interpolated from temperature points +Output +Beam section properties such as cross-sectional area, moments of inertia, etc. are printed in the model +data output. When a beam section integrated during the analysis is used, section forces, moments, and +transverse shear forces and section strains, curvatures, and transverse shear strains can be output for +the section . In addition, stress and strain can be output at +each section point. “Beam element library,” Section 29.3.8, lists some of the element output quantities +that are available for beam elements. +Axial strains due to warping are included in the stress/strain output from Abaqus/Standard if a beam +section integrated during the analysis is used. +Temperature output at the section points can be obtained using the element variable TEMP. If the +temperatures are given at specific points through the section, output at the temperature points can be +obtained using the nodal variable NTxx. The nodal variable NTxx should not be used for output at the +temperature points if the temperatures are specified by defining the value at the origin of the cross-section +and specifying the gradients in the local 1- and 2-directions. In this case output variable NT should be +requested; NT11 (the reference temperature value) and NT12 and NT13 (the temperature gradients in +the local 1- and 2-directions, respectively) will be output automatically. +Beam normals are written to the output database automatically for all frames that include field +output of nodal displacements. The normal directions can be visualized in the Visualization module of +Abaqus/CAE. +29.3.7 +USING A GENERAL BEAM SECTION TO DEFINE THE SECTION BEHAVIOR +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Beam modeling: overview,” Section 29.3.1 +• “Beam section behavior,” Section 29.3.5 +• *BEAM GENERAL SECTION +• “Specifying properties for general beam sections” in “Creating beam sections,” Section 12.13.11 of +the Abaqus/CAE User’s Manual, in the online HTML version of this manual +Overview +A general beam section: +• is used to define beam section properties that are computed once and held constant for the entire +analysis; +• can be used to define linear or nonlinear section behavior; +• for linear section behavior can be associated only with linear material behavior +• enables the use of meshed cross-sections (“Meshed beam cross-sections,” Section 10.6.1); and +• enables the use of tapered cross-sections (Abaqus/Standard only). +Linear section behavior +Linear section response is calculated as follows. At each point in the cross-section the axial stress, +and the shear stress, +, are given by +, +where +and +is Young’s modulus (which may depend on the temperature, +beam axis); +is the shear modulus (which may also depend on the temperature and field variables at the +beam axis); +is the axial strain; +is the shear caused by twist; and +is the thermal expansion strain. +, and field variables, +, at the +The thermal expansion strain is given by +where +is the thermal expansion coefficient, +is the current temperature at a point in the beam section, +are field variables, +is the reference temperature for +is the initial temperature at this point , and +are the initial values of the field variables at this point . +, +If the thermal expansion coefficient is temperature or field-variable dependent, it is evaluated at the +temperature and field variables at the beam axis. Therefore, since we assume that +varies linearly over +the section, +also varies linearly over the section. +The temperature is defined from the temperature of the beam axis and the gradients of temperature +with respect to the local +- and +-axes: +The axial force, N; bending moments, +and +T; and bimoment, W, are defined in terms of the axial stress +formulation,” Section 3.5.2 of the Abaqus Theory Manual). These terms are +about the 1 and 2 beam section local axes; torque, +(see “Beam element +and the shear stress +is the area of the section, +is the moment of inertia for bending about the 1-axis of the section, +is the moment of inertia for cross-bending, +is the moment of inertia for bending about the 2-axis of the section, +is the torsional constant, +is the sectorial moment of the section, +is the warping constant of the section, +is the axial strain measured at the centroid of the section, +29.3.7–2 +where +is the thermal axial strain, +is the curvature change about the first beam section local axis, +is the curvature change about the second beam section local axis, +is the twist, +is the bicurvature defining the axial strain in the section due to the twist of the +beam, and +is the difference between the unconstrained warping amplitude, +warping amplitude, w. +, and the actual +, +, +, and +are nonzero only for open-section beam elements. +Defining linear section behavior for library cross-sections or linear generalized cross-sections +Linear beam section response is defined geometrically by A, +, +, +, J, and—if necessary— and +. +You can input these geometric quantities directly or specify a standard library section and Abaqus +will calculate these quantities. +In either case define the orientation of the beam section ; give Young’s modulus, the torsional shear modulus, +and the coefficient of thermal expansion, as functions of temperature; and associate the section properties +with a region of your model. +If the thermal expansion coefficient is temperature dependent, the reference temperature for thermal +expansion must also be defined as described later in this section. +Specifying the geometric quantities directly +, J, and—if +You can define “generalized” linear section behavior by specifying A, +necessary— and +directly. In this case you can specify the location of the centroid, thus allowing +the bending axis of the beam to be offset from the line of its nodes. In addition, you can specify the +location of the shear center. +, +, +, +, +, +, J, +Use the following option to define generalized linear beam section properties: +*BEAM GENERAL SECTION, SECTION=GENERAL, ELSET=name +A, +If necessary, use the following option to specify the location of the centroid: +*CENTROID +If necessary, use the following option to specify the location of the shear center: +*SHEAR CENTER +Property module: +Create Profile: Name: generalized_section, Generalized +Create Section: select Beam as the section Category and Beam +as the section Type: Section integration: Before analysis, Profile +name: generalized_section: Centroid and Shear Center +Assign→Section: select regions +29.3.7–3 +Input File Usage: +Specifying a standard library section and allowing Abaqus to calculate the geometric quantities +You can select one of the standard library sections +and specify the geometric input data needed to define the shape of the cross-section. Abaqus will then +calculate the geometric quantities needed to define the section behavior automatically. +Input File Usage: +Abaqus/CAE Usage: +*BEAM GENERAL SECTION, SECTION=library_section, ELSET=name +Property module: +Create Profile: Name: library_section +Create Section: select Beam as the section Category and Beam +as the section Type: Section integration: Before analysis, +Profile name: library_section +Assign→Section: select regions +Defining linear section behavior for meshed cross-sections +Linear beam section response for a meshed section profile is obtained by numerical integration from the +two-dimensional model. The numerical integration is performed once, determining the beam stiffness +and inertia quantities, as well as the coordinates of the centroid and shear center, for the duration of +the analysis. These beam section properties are calculated during the beam section generation and are +written to the text file jobname.bsp. This text file can be included in the beam model. See “Meshed +beam cross-sections,” Section 10.6.1, for a detailed description of the properties defining the linear beam +section response for a meshed section, as well as for how a typical meshed section is analyzed. +Input File Usage: +Use the following options: +*BEAM GENERAL SECTION, SECTION=MESHED, ELSET=name +*INCLUDE, INPUT=jobname.bsp +Abaqus/CAE Usage: Meshed cross-sections are not supported in Abaqus/CAE. +Defining linear section behavior for tapered cross-sections in Abaqus/Standard +In Abaqus/Standard you can define Timoshenko beams with linearly tapered cross-sections. General +beam sections with linear response and standard library sections are supported, with the exception of +arbitrary sections. The section parameters are defined at the two end nodes of each beam element. The +effective beam area and moment of inertia for bending about the 1- and 2-axis of the section used in the +calculation of the beam stiffness matrix, section forces, and stresses are +eff +eff +eff +and +where the superscripts +refer to the two end nodes of the beam. The remaining effective geometric +quantities are calculated as the average between the values at the two end nodes. This approximation +suffices for mild tapering along each element, but it can lead to large errors if the tapering is not gradual. +Abaqus/Standard issues a warning message during input file preprocessing if the area or inertia ratio is +larger than 2.0 and an error message if the ratio is larger than 10.0. +The effective area and inertia are not used in the computation of the mass matrix. Instead, terms +on the diagonal quadrants use the properties from the respective nodes, while off-diagonal quadrants use +averaged quantities. For example, the axial inertia a linear element would have the diagonal term coming +from node +, while node +and the two off-diagonal contributions +equal +. Mild tapering is assumed in this formulation, since the total mass of the element +totals +contributes with +of +. +Note: When you apply a tapered beam section to geometry in Abaqus/CAE, the full tapering is applied +to each element along the beam’s length. For beams that include multiple elements, this modeling style +can create a “sawtooth” pattern along the length of the beam. If you want to model gradual tapering +along the entire length of the beam in Abaqus/CAE, you must calculate the size and shape of the beam +profiles at the intermediate nodes, then apply different tapered beam sections to each beam element along +the length. +Input File Usage: +Use the following option to define linear section behavior of tapered cross- +sections: +Abaqus/CAE Usage: +*BEAM GENERAL SECTION, TAPER, ELSET=name +Property module: +Create Profile: Name: library_section +Create Section: select Beam as the section Category and Beam +as the section Type: Section integration: Before analysis, +Beam shape along length: Tapered: Beam start and Beam +end options: Profile name: library_section +Assign→Section: select regions +Nonlinear section behavior +Typically nonlinear section behavior is used to include the experimentally measured nonlinear response +of a beam-like component whose section distorts in its plane. When the section behaves according to +beam theory (that is, the section does not distort in its plane) but the material has nonlinear response, it is +usually better to use a beam section integrated during the analysis to define the section geometrically , in +association with a material definition. +Nonlinear section behavior can also be used to model beam section collapse in an approximate sense: +“Nonlinear dynamic analysis of a structure with local inelastic collapse,” Section 2.1.1 of the Abaqus +Example Problems Manual, illustrates this for the case of a pipe section that may suffer inelastic collapse +due to the application of a large bending moment. In following this approach you should recognize +that such unstable section collapse, like any unstable behavior, typically involves localization of the +deformation: results will, therefore, be strongly mesh sensitive. +Calculation of nonlinear section response +Nonlinear section response is assumed to be defined by +means a functional dependence on the conjugate variables: +, +where +etc. For example, +, the temperature of the +beam axis; and of +, any predefined field variables at the beam axis. When the section behavior is +defined in this way, only the temperature and field variables of the beam axis are used: any temperature +or field-variable gradients given across the beam section are ignored. +means that N is a function of: +; +, +These nonlinear responses may be purely elastic (that is, fully reversible—the loading and unloading +responses are the same, even though the behavior is nonlinear) or may be elastic-plastic and, therefore, +irreversible. +The assumption that these nonlinear responses are uncoupled is restrictive; in general, there is some +interaction between these four behaviors, and the responses are coupled. You must determine if this +approximation is reasonable for a particular case. The approach works well if the response is dominated +by one behavior, such as bending about one axis. However, it may introduce additional errors if the +response involves combined loadings. +Defining nonlinear section behavior +You can define “generalized” nonlinear section behavior by specifying the area, A; moments of inertia, +for bending about the 1-axis of the section, +for bending about the 2-axis of the section, and +for cross-bending; and torsional constant, J. These values are used only to calculate the transverse shear +stiffness; and, if needed, A is used to compute the mass density of the element. In addition, you can define +the orientation and the axial, bending, and torsional behavior of the beam section (N, +, T), as +well as the thermal expansion coefficient. If the thermal expansion coefficient is temperature dependent, +the reference temperature for thermal expansion must also be defined as described below. +, +Nonlinear generalized beam section behavior cannot be used with beam elements with warping +degrees of freedom. +The axial, bending, and torsional behavior of the beam section and the thermal expansion coefficient +are defined by tables. See “Material data definition,” Section 21.1.2, for a detailed discussion of the +tabular input conventions. In particular, you must ensure that the range of values given for the variables +is sufficient for the application since Abaqus assumes a constant value of the dependent variable outside +this range. +Input File Usage: +Abaqus/CAE Usage: +, +, J +Use the following options to define generalized nonlinear beam section +properties: +*BEAM GENERAL SECTION, SECTION=NONLINEAR GENERAL, +ELSET=name +A, +, +*AXIAL for N +*M1 for +*M2 for +*TORQUE for T +*THERMAL EXPANSION for the thermal expansion coefficient +Nonlinear generalized cross-sections are not supported in Abaqus/CAE. +Defining linear response for N, M1 , M2 , and T +If the particular behavior is linear, N, +and predefined field variables, if appropriate. +As an example of axial behavior, if +, +, and T should be specified as functions of the temperature +where +as a function of temperature and field variables. +is constant for a given temperature, the value of +is entered. +can still be varied +Input File Usage: +Abaqus/CAE Usage: +Use the following options to define linear axial, bending, and torsional +behavior: +*AXIAL, LINEAR +*M1, LINEAR +*M2, LINEAR +*TORQUE, LINEAR +Nonlinear generalized cross-sections are not supported in Abaqus/CAE. +Defining nonlinear elastic response for N, M1 , M2 , and T +If the particular behavior is nonlinear but elastic, the data should be given from the most negative value of +the kinematic variable to the most positive value, always giving a point at the origin. See Figure 29.3.7–1 +for an example. +Input File Usage: +Abaqus/CAE Usage: +Use the following options to define nonlinear elastic axial, bending, and +torsional behavior: +*AXIAL, ELASTIC +*M1, ELASTIC +*M2, ELASTIC +*TORQUE, ELASTIC +Nonlinear generalized cross-sections are not supported in Abaqus/CAE. +Bending moment, M +M 5 +M 4 +The origin should be included +in the data +M=M6 for K K6 +K 2 +K 3 +K4 +K5 +K6 +Curvature, K +M 3 +M 2 +M 1 +M=M1 for K K1 +Figure 29.3.7–1 Example of elastic nonlinear beam section behavior definition. +Defining elastic-plastic response for N, M1 , M2 , and T +By default, elastic-plastic response is assumed for N, +, +, and T. +The inelastic model is based on assuming linear elasticity and isotropic hardening (or softening) +plasticity. The data in this case must begin with the +point and proceed to give positive values of +the kinematic variable at increasing positive values of the conjugate force or moment. Strain softening is +allowed. The elastic modulus is defined by the slope of the initial line segment, so that straining beyond +the point that terminates that initial line segment will be partially inelastic. If strain reversal occurs in +that part of the response, it will be elastic initially. See Figure 29.3.7–2 for an example. +Input File Usage: +Use the following options to define elastic-plastic axial, bending, and torsional +behavior: +*AXIAL +*M1 +*M2 +*TORQUE +Nonlinear generalized cross-sections are not supported in Abaqus/CAE. +Abaqus/CAE Usage: +Bending moment, M +Elastic-plastic response for +continued straining beyond +here +Elastic modulus defined by +first line segment +The origin must be the first +data point +Curvature, K +Elastic unloading +behavior +Response to opposite curvature +of the response given +Figure 29.3.7–2 Example of inelastic nonlinear beam section behavior definition. +Defining the reference temperature for thermal expansion +The thermal expansion coefficient may be temperature dependent. In this case the reference temperature +for thermal expansion, +, must be defined. +*BEAM GENERAL SECTION, ZERO= +Property module: Create Section: select Beam as the section Category +and Beam as the section Type: Section integration: Before analysis: +Basic: Specify reference temperature: +Input File Usage: +Abaqus/CAE Usage: +Defining the initial section forces and moments +You can define initial stresses for general beam sections that will be applied as initial section +forces and moments. Initial conditions can be specified only for the axial force, the bending moments, +and the twisting moment. Initial conditions cannot be prescribed for the transverse shear forces. +Defining a change in cross-sectional area due to straining +In the shear flexible elements Abaqus provides for a possible uniform cross-sectional area change by +allowing you to specify an effective Poisson’s ratio for the section. This effect is considered only in +geometrically nonlinear analysis and is provided to model the +reduction or increase in the cross-sectional area for a beam subjected to large axial stretch. +The value of the effective Poisson’s ratio must be between −1.0 and 0.5. By default, this effective +Poisson’s ratio for the section is set to 0.0 so that this effect is ignored. Setting the effective Poisson’s ratio +to 0.5 implies that the overall response of the section is incompressible. This behavior is appropriate if the +beam is made of rubber or if it is made of a typical metal whose overall response at large deformation is +essentially incompressible (because it is dominated by plasticity). Values between 0.0 and 0.5 mean that +the cross-sectional area changes proportionally between no change and incompressibility, respectively. +A negative value of the effective Poisson’s ratio will result in an increase in the cross-sectional area in +response to tensile axial strains. +This effective Poisson’s ratio is not available for use with Euler-Bernoulli beam elements. +Input File Usage: +Abaqus/CAE Usage: +*BEAM GENERAL SECTION, POISSON= +Property module: Create Section: select Beam as the section +Category and Beam as the section Type: Section integration: Before +analysis: Basic: Section Poisson's ratio: +Defining damping +When the beam section and material behavior are defined by a general beam section, you can include mass +and viscous stiffness proportional damping in the dynamic response (calculated in Abaqus/Standard with +the direct time integration procedure, “Implicit dynamic analysis using direct integration,” Section 6.3.2). +See “Material damping,” Section 26.1.1, for more information about the material damping types +available in Abaqus. +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*BEAM GENERAL SECTION +*DAMPING +Property module: Create Section: select Beam as the section Category +and Beam as the section Type: Section integration: Before analysis: +Damping: Alpha, Beta, Structural, and Composite +Specifying temperature and field variables +Define temperatures and field variables by giving the values at the origin of the cross-section as either +predefined fields or initial conditions . Temperature gradients can be specified in the +local 1- and 2-directions; other field-variable gradients defined through the cross-section will be ignored +in the response of beam elements that use a general beam section definition. +Output +Only the section forces, moments, and transverse shear forces and section strains, curvatures, and +transverse shear strains can be output . +You can output stress and strain at particular points in the section. For linear section behavior +defined using a standard library section or a generalized section, only axial stress and axial strain values +are available. For linear section behavior defined using a meshed section, axial and shear stress and strain +are available. For nonlinear generalized section behavior, axial strain output only is provided. +Specifying the output section points for standard library sections and generalized sections +To locate points in the section at which output of axial strain (and, for linear section behavior, axial stress) +is required, specify the local +coordinates of the point in the cross-section: Abaqus numbers the +points 1, 2, … in the order that they are given. +The variation of +over the section is given by +where +changes of curvature for the section. +are the local coordinates of the centroid of the beam section and +and +are the +For open-section beam element types, the variation of +over the section has an additional term of +the form +is the warping function. The warping function itself is undefined +in the general beam section definition. Therefore, Abaqus will not take into account the axial strain +due to warping when calculating section points output. Axial strains due to warping are included in the +stress/strain output if a beam section integrated during the analysis is used. +, where +Abaqus uses St. Venant torsion theory for noncircular solid sections. The torsion function and its +derivatives are necessary to calculate shear stresses in the plane of the cross-section. The function and +its derivatives are not stored for a general beam section. Therefore, you can request output of axial +components of stress/strain only. A beam section integrated during the analysis must be used to obtain +output of shear stresses. +Input File Usage: +Use both of the following options to specify the output section points for general +beam sections: +*BEAM GENERAL SECTION +*SECTION POINTS +, +, ... +Abaqus/CAE Usage: +Property module: Create Section: select Beam as the section +Category and Beam as the section Type: Section integration: +Before analysis: Output Points: x1, x2, ... +Requesting output of maximum axial stress/strain in Abaqus/Standard +If you specify the output section points to obtain the maximum axial stress/strain (MAXSS) for a linear +generalized section, the output value will be the maximum of the values at the user-specified section +points. You must select enough section points to ensure that this is the true maximum. MAXSS output +is not available for nonlinear generalized sections or for an Abaqus/Explicit analysis. +Specifying the output section points for meshed cross-sections +For meshed cross-sections you can indicate in the two-dimensional cross-section analysis the elements +and integration points where the stress and strain will be calculated during the subsequent beam analysis. +Abaqus will then add the section points specification to the resulting jobname.bsp text file. This text +file is then included as the data for the general beam section definition in the subsequent beam analysis. +See “Meshed beam cross-sections,” Section 10.6.1, for details. +The variation of the axial strain +over the meshed section is given by +where +changes of curvature for the section. +are the local coordinates of the centroid of the beam section and +and +are the +The variations of shear components +and +over the meshed section are given by +where +beam axis, +shear forces. +are the local coordinates of the shear center of the beam section, +is the twist of the +are shear strains due to the transverse +is the warping function, and +and +For the case of an orthotropic composite beam material, the axial stress +and the two shear +components +and +are calculated in the beam section (1, 2) axis as follows: +where +determines the material orientation. +Input File Usage: +Use both of the following options in the two-dimensional meshed cross-section +analysis to specify the output section points for the subsequent beam analysis: +*BEAM SECTION GENERATE +*SECTION POINTS +section_point_label, element_number, integration_point_number +Abaqus/CAE Usage: Meshed cross-sections are not supported in Abaqus/CAE. +29.3.8 +BEAM ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Beam modeling: overview,” Section 29.3.1 +• “Choosing a beam element,” Section 29.3.3 +• *BEAM GENERAL SECTION +• *BEAM SECTION +Overview +This section provides a reference to the beam elements available in Abaqus/Standard and +Abaqus/Explicit. +Element types +Beams in a plane +B21 +B21H(S) +B22 +B22H(S) +B23(S) +B23H(S) +PIPE21 +2-node linear beam +2-node linear beam, hybrid formulation +3-node quadratic beam +3-node quadratic beam, hybrid formulation +2-node cubic beam +2-node cubic beam, hybrid formulation +2-node linear pipe +PIPE21H(S) +PIPE22(S) +PIPE22H(S) +2-node linear pipe, hybrid formulation +3-node quadratic pipe +3-node quadratic pipe, hybrid formulation +Active degrees of freedom +1, 2, 6 +Additional solution variables +All of the cubic beam elements have two additional variables relating to axial strain. +The linear thin-walled pipe elements have one additional variable, and the quadratic thin-walled pipe +elements have two additional variables relating to the hoop strain. The linear thick-walled pipe elements +have two additional variables, and the quadratic thick-walled pipe elements have four additional variables +relating to the hoop and radial strain components. +The hybrid beam and pipe elements have additional variables relating to the axial force and transverse +shear force. The linear elements have two, the quadratic elements have four, and the cubic elements have +three additional variables. +Beams in space +B31 +B31H(S) +B32 +B32H(S) +B33(S) +B33H(S) +PIPE31 +2-node linear beam +2-node linear beam, hybrid formulation +3-node quadratic beam +3-node quadratic beam, hybrid formulation +2-node cubic beam +2-node cubic beam, hybrid formulation +2-node linear pipe +PIPE31H(S) +PIPE32(S) +PIPE32H(S) +2-node linear pipe, hybrid formulation +3-node quadratic pipe +3-node quadratic pipe, hybrid formulation +Active degrees of freedom +1, 2, 3, 4, 5, 6 +Additional solution variables +All of the cubic beam elements have two additional variables relating to axial strain. +The linear thin-walled pipe elements have one additional variable, and the quadratic thin-walled pipe +elements have two additional variables relating to the hoop strain. The linear thick-walled pipe elements +have two additional variables, and the quadratic thick-walled pipe elements have four additional variables +relating to the hoop and radial strain components. +The hybrid beam and pipe elements have additional variables relating to the axial force and transverse +shear force in the linear and quadratic elements and to the axial force only in the cubic elements. The +linear and cubic elements have three and the quadratic elements have six additional variables. +Open-section beams in space +B31OS(S) +B31OSH(S) +B32OS(S) +B32OSH(S) +2-node linear beam +2-node linear beam, hybrid formulation +3-node quadratic beam +3-node quadratic beam, hybrid formulation +Active degrees of freedom +1, 2, 3, 4, 5, 6, 7 +Additional solution variables +Element type B31OSH has three additional variables and element type B32OSH has six additional +variables relating to the axial force and transverse shear force. +Nodal coordinates required +Beams in a plane: X, Y, also (optional) +, +, the direction cosines of the normal. +Beams in space: X, Y, Z, also (optional) +section axis. +, +, +, the direction cosines of the second local cross- +Element property definition +For PIPE elements use the pipe section type to specify the thin-walled pipe formulation or the thick pipe +section type to specify the thick-walled pipe formulation. No other section types can be used with PIPE +elements. +For open-section elements use only the arbitrary, I, L, and linear generalized section types. +Local orientations defined as described in “Orientations,” Section 2.2.5, cannot be used with beam +elements to define local material directions. The orientation of the local beam section axes in space is +discussed in “Beam element cross-section orientation,” Section 29.3.4. +Input File Usage: +Use either of the following options: +*BEAM SECTION +*BEAM GENERAL SECTION +Property module: Create Section: select Beam as the section +Category and Beam as the section Type +Abaqus/CAE Usage: +Element-based loading +Distributed loads +Distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DLOAD) +CENT(S) +Abaqus/CAE +Load/Interaction +Not supported +Units +Description +FL−2 +(ML−1 T−2 ) +Centrifugal force (magnitude is input +, where m is the mass per unit +as +length and +is the angular velocity). +Load ID +(*DLOAD) +CENTRIF(S) +Abaqus/CAE +Load/Interaction +Units +Description +Rotational body +force +T−2 +Centrifugal load (magnitude is input +as +the angular +velocity). +, where +is +CORIO(S) +Coriolis force +FL−2 T +(ML−1 T−1 ) +GRAV +Gravity +PX +PY +PZ +Line load +Line load +Line load +PXNU +Line load +LT−2 +FL−1 +FL−1 +FL−1 +FL−1 +PYNU +Line load +FL−1 +PZNU +Line load +FL−1 +P1 +Line load +FL−1 +29.3.8–4 +Coriolis force (magnitude is input as +, where m is the mass per unit +length and +is the angular velocity). +The load stiffness due to Coriolis +loading is not accounted for in direct +steady-state dynamics analysis. +Gravity +loading +direction (magnitude is +acceleration). +in +specified +input as +Force per unit length in global X- +direction. +Force per unit length in global Y- +direction. +Force per unit +length in global +Z-direction (only for beams in space). +Nonuniform force per unit length in +global X-direction with magnitude +supplied via user subroutine DLOAD +in Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +Nonuniform force per unit length in +global Y-direction with magnitude +supplied via user subroutine DLOAD +in Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +Nonuniform force per unit length in +global Z-direction with magnitude +supplied via user subroutine DLOAD +in Abaqus/Standard and VDLOAD in +Abaqus/Explicit. (Only for beams in +space.) +Force per unit length in beam local +(*DLOAD) +P2 +Abaqus/CAE +Load/Interaction +Line load +P1NU +Line load +BEAM ELEMENT LIBRARY +Units +Description +FL−1 +FL−1 +Force per unit length in beam local +2-direction. +per +unit +force +Nonuniform +length in beam local 1-direction +via +with magnitude +user +in +subroutine +VDLOAD +Abaqus/Standard +in Abaqus/Explicit. (Only for beams +in space.) +supplied +DLOAD +and +P2NU +Line load +FL−1 +ROTA(S) +Rotational body +force +T−2 +ROTDYNF(S) +Not supported +T−1 +per +Nonuniform +unit +force +length in beam local 2-direction +supplied +via +with magnitude +DLOAD +user +in +subroutine +and VDLOAD +Abaqus/Standard +in Abaqus/Explicit. +Rotary acceleration load (magnitude +is input as +is the rotary +acceleration). +, where +Rotordynamic load (magnitude is +input as +is the angular +velocity). +, where +The following load types are available only for PIPE elements: +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +HPI +HPE +PI +PE +Pipe pressure +FL−2 +Pipe pressure +FL−2 +Pipe pressure +Pipe pressure +FL−2 +FL−2 +Hydrostatic internal pressure (closed- +end condition), varying linearly with +the global Z-coordinate. +Hydrostatic external pressure (closed- +end condition), varying linearly with +the global Z-coordinate. +Uniform internal pressure (closed-end +condition). +Uniform external pressure (closed- +end condition). +Load ID +(*DLOAD) +PENU +Abaqus/CAE +Load/Interaction +Units +Description +Pipe pressure +FL−2 +Nonuniform +(closed-end +magnitude +subroutine DLOAD. +external +condition) +supplied +via +pressure +with +user +PINU +Pipe pressure +FL−2 +Nonuniform +(closed-end +magnitude +subroutine DLOAD. +internal +condition) +supplied +via +pressure +with +user +Abaqus/Aqua loads +Abaqus/Aqua loads are specified as described in “Abaqus/Aqua analysis,” Section 6.11.1. They are not +available for open-section beams and do not apply to beams that are defined to have additional inertia +due to immersion in fluid . +Abaqus/CAE +Load/Interaction +Units +Description +Not supported +FL−1 +Transverse fluid drag load. +Not supported +Not supported +Not supported +Not supported +Not supported +Not supported +Not supported +Not supported +Not supported +FL−1 +FL−1 +FL−1 +FL−1 +29.3.8–6 +Fluid drag force on the first end of the +beam (node 1). +Fluid drag force on the second end of +the beam (node 2 or node 3). +Tangential fluid drag load. +Transverse fluid inertia load. +Fluid inertia force on the first end of +the beam (node 1). +Fluid inertia force on the second end +of the beam (node 2 or node 3). +Buoyancy load (closed-end +condition). +Transverse wind drag load. +Wind drag force on the first end of the +beam (node 1). +Load ID +(*CLOAD/ +*DLOAD) +FDD(A) +FD1(A) +FD2(A) +FDT(A) +FI(A) +FI1(A) +FI2(A) +PB(A) +WDD(A) +Load ID +(*CLOAD/ +*DLOAD) +WD2(A) +Foundations +Abaqus/CAE +Load/Interaction +Units +Description +Not supported +Wind drag force on the second end of +the beam (node 2 or node 3). +Foundations are available only in Abaqus/Standard and are specified as described in “Element +foundations,” Section 2.2.2. +Load ID +(*FOUNDATION) Load/Interaction +Abaqus/CAE +Units +Description +FX(S) +FY(S) +FZ(S) +F1(S) +F2(S) +Not supported +Not supported +Not supported +Not supported +Not supported +FL−2 +FL−2 +FL−2 +FL−2 +FL−2 +Stiffness per unit length in global X- +direction. +Stiffness per unit length in global Y- +direction. +Stiffness per unit length in global Z- +direction (only for beams in space). +Stiffness per unit length in beam local +1-direction (only for beams in space). +Stiffness per unit length in beam local +2-direction. +Surface-based loading +Distributed loads +Surface-based distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +Force per unit length in beam local +2-direction. The distributed surface +force is positive in the direction +opposite to the surface normal. +per +unit +force +Nonuniform +length in beam local 2-direction +via +with magnitude +in +subroutine +user +supplied +DLOAD +Pressure +FL−1 +PNU +Pressure +FL−1 +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +and VDLOAD +Abaqus/Standard +in Abaqus/Explicit. The distributed +surface force is positive in the +direction opposite to the surface +normal. +Incident wave loading +Incident wave loading is also available for these elements, with some restrictions. See “Acoustic and +shock loads,” Section 33.4.6. +Element output +See “Beam cross-section library,” Section 29.3.9, for a description of the beam element output locations. +Stress, strain, and other tensor components +Stress and other tensors (including strain tensors) are available for elements with displacement degrees +of freedom. All tensors, except for meshed sections, have the same components. For example, the stress +components are as follows: +S11 +S22 +S33 +S12 +Axial stress. +Hoop stress (available only for pipe elements). +Radial stress (available only for thick-walled pipe elements). +Shear stress caused by torsion (available only for beam-type elements in space). This +component is not available when thin-walled, open sections are employed (I-section, +L-section, and arbitrary open section). +Stress and strain for section points for meshed sections +S11 +S12 +S13 +Axial stress. +Shear stress along the second cross-section axis caused by shear force and, for beam +elements in space, torsion. +Shear stress along the first cross-section axis caused by shear force and torsion +(available only for beams in space). +Section forces, moments, and transverse shear forces +SF1 +SF2 +SF3 +Axial force. +Transverse shear force in the local 2-direction (not available for B23, B23H, B33, +B33H). +Transverse shear force in the local 1-direction (available only for beams in space, +not available for B33, B33H). +SM1 +SM2 +SM3 +BIMOM +ESF1 +Bending moment about the local 1-axis. +Bending moment about the local 2-axis (available only for beams in space). +Twisting moment about the beam axis (available only for beams in space). +Bimoment due to warping (available only for open-section beams in space). +Effective axial force for beams subjected to pressure loading (available for all +Abaqus/Standard stress/displacement analysis types except response spectrum and +random response). +See “Beam element formulation,” Section 3.5.2 of the Abaqus Theory Manual, for the definitions of the +section forces and moments. +The effective axial section force for beams subjected to pressure loading is defined as +and +are the external and the internal pressures, respectively, and +where +are the external +and the internal pipe areas as defined in the load definition. The pressure loadings (with a closed- +end condition) that are relevant to the effective axial force are external/internal pressure (load types +PE, PI, PENU, and PINU); external/internal hydrostatic pressure (load types HPE and HPI); and, in +an Abaqus/Aqua environment, buoyancy pressure, PB, which includes dynamic pressure if waves are +present. +and +For beams that are not subjected to pressure loading, the effective axial force ESF1 is equal to the usual +axial force SF1. +Section strains, curvatures, and transverse shear strains +SE1 +SE2 +SE3 +SK1 +SK2 +SK3 +Axial strain. +Transverse shear strain in the local 2-direction (not available for B23, B23H, B33, +and B33H). +Transverse shear strain in the local 1-direction (available only for beams in space, +not available for B33 and B33H). +Curvature change about the local 1-axis. +Curvature change about the local 2-axis (available only for beams in space). +Twist of the beam (available only for beams in space). +BICURV +Bicurvature due to warping (available only for open-section beams in space). +Node ordering on elements +2 - node element +3 - node element +For beams in space an additional node may be given after a beam element’s connectivity (in the element +definition—see “Element definition,” Section 2.2.1) to define the approximate direction of the first cross- +section axis, +. See “Beam element cross-section orientation,” Section 29.3.4, for details. +Numbering of integration points for output +2 - node element +3 - node quadratic element +2 - node cubic element +29.3.9 +BEAM CROSS-SECTION LIBRARY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Beam modeling: overview,” Section 29.3.1 +• “Choosing a beam cross-section,” Section 29.3.2 +• “Frame elements,” Section 29.4.1 +• “Defining profiles,” Section 12.2.2 of the Abaqus/CAE User’s Manual +Overview +This section describes the standard beam sections that are available in Abaqus/Standard and +Abaqus/Explicit for use with beam elements. A subset of the standard beam sections are available +for use with frame elements in Abaqus/Standard. General (nonstandard) beam cross-sections can be +defined as described in “Choosing a beam cross-section,” Section 29.3.2. +Arbitrary, thin-walled, open and closed sections +t AB +t BC +t CD +Example of arbitrary section +The arbitrary section type is provided to permit modeling of simple, arbitrary, thin-walled, open and +closed sections. You specify the section by defining a series of points in the thin-walled cross-section of +the beam; these points are then linked by straight line segments, each of which is integrated numerically +along the axis of the section so that the section can be used together with nonlinear material behavior. +An independent thickness is associated with each of the segments making up the arbitrary section. +Warping effects are included when an arbitrary section is used with open-section beam elements +(available only in Abaqus/Standard). +Input File Usage: +Use either of the following options: +*BEAM SECTION, SECTION=ARBITRARY +*BEAM GENERAL SECTION, SECTION=ARBITRARY +Property module: Create Profile: Arbitrary +Abaqus/CAE Usage: +Restrictions +• An arbitrary section can be used only with beams in space (three-dimensional models). +• An arbitrary section should not be used to define closed sections with branches, multiply connected +closed sections, or open sections with disconnected regions. +• For each individual segment of an arbitrary section there is no bending stiffness about the line joining +the end points of the segment. Thus, an arbitrary section cannot be made up of only one segment. +Geometric input data +First, give the number of segments, the local coordinates of points A and B, and the thickness of the +segment connecting these two vertices. Then, proceed by giving the local coordinates of point C and the +thickness of the segment between points B and C, followed by the local coordinates of point D and the +thickness of the segment between points C and D, and so on. An arbitrary section can contain as many +segments as needed. All coordinates of section definition points are given in the local 1–2 axis system +of the section. +The origin of the local 1–2 axis system is the beam node, and the position of this node used to define the +section is arbitrary: it does not have to be the centroid. +Defining a closed section +A closed section is defined by making the starting and end points coincident. Only single-cell closed +sections can be modeled accurately. Closed sections with fins (single branches attached to the cell) cannot +be modeled with the capability in Abaqus. +Defining an arbitrary section with discontinuous branches +If the arbitrary section contains discontinuous sections (branches), a section with zero thickness should +be used to return from the ending point of the branch to the starting point of the subsequent section. +This zero thickness section should always coincide with a nonzero thickness section. For an example of +an I-section defined using this method, see “Buckling analysis of beams,” Section 1.2.1 of the Abaqus +Benchmarks Manual. +Default integration +A three-point Simpson integration scheme is used for each segment making up the section. For more +detailed integration, specify several segments along each straight portion of the section. +Default stress output points if a beam section integrated during the analysis is used +The vertices of the section. +Temperature and field variable input at specific points through beam sections integrated +during the analysis +Give the value at each vertex of the section (points A, B, C, D in the figure). +Box section +Input File Usage: +Use one of the following options: +*BEAM SECTION, SECTION=BOX +*BEAM GENERAL SECTION, SECTION=BOX +*FRAME SECTION, SECTION=BOX +Property module: Create Profile: Box +Abaqus/CAE Usage: +t 2 +t 4 +t 3 +14 +15 +t 1 +16 +Default integration, +beam in space +t 2 +t 4 +t 3 +t 1 +10 +11 +12 +13 +Default integration, +beam in a plane +Geometric input data +a, b, +, +, +, +Default integration (Simpson) +Beam in a plane: 5 points +Beam in space: 5 points in each wall (16 total) +Nondefault integration input for a beam section integrated during the analysis +Beam in a plane: Give the number of points in each wall that is parallel to the 2-axis. This number must +be odd and greater than or equal to three. +Beam in space: Give the number of points in each wall that is parallel to the 2-axis, then the number of +points in each wall that is parallel to the 1-axis. Both numbers must be odd and greater than or equal to +three. +Default stress output points if a beam section integrated during the analysis is used +Beam in a plane: Bottom and top (points 1 and 5 above for default integration). +Beam in space: 4 corners (points 1, 5, 9, and 13 above for default integration). +Temperature and field variable input at specific points for beam sections integrated during +the analysis +Give the value at each of the points shown below. +Beam in a plane +Beam in space +Temperature input for a frame section +Constant temperature throughout the element cross-section is assumed; therefore, only one temperature +value per node is required. +Circular section +Input File Usage: +Use one of the following options: +*BEAM SECTION, SECTION=CIRC +*BEAM GENERAL SECTION, SECTION=CIRC +*FRAME SECTION, SECTION=CIRC +Property module: Create Profile: Circular +Abaqus/CAE Usage: +11 +10 +8 9 +15 +13 +12 +14 +16 +17 +Default integration, +beam in a plane +Default integration, +beam in space +Geometric input data +Radius +Default integration +Beam in a plane: 5 points +Beam in space: 3 points radially, 8 circumferentially (17 total; trapezoidal rule). Integration point 1 is +situated at the center of the beam and is used for output purposes only. It makes no contribution to the +stiffness of the element; therefore, the integration point volume (IVOL) associated with this point is zero. +Nondefault integration input for a beam section integrated during the analysis +Beam in a plane: A maximum of 9 points are permitted. +Beam in space: Give an odd number of points in the radial direction, then an even number of points in +the circumferential direction. +Default stress output points if a beam section integrated during the analysis is used +Beam in a plane: Bottom and top (points 1 and 5 above for default integration). +Beam in space: On the intersection of the surface with the 1- and 2-axes (points 3, 7, 11, and 15 above +for default integration). +Temperature and field variable input at specific points for beam sections integrated during +the analysis +Give the value at each of the points shown below. +Beam in a plane +Beam in space +Temperature input for a frame section +Constant temperature throughout the element cross-section is assumed; therefore, only one temperature +value per node is required. +Hexagonal section +Input File Usage: +Abaqus/CAE Usage: +Use either of the following options: +*BEAM SECTION, SECTION=HEX +*BEAM GENERAL SECTION, SECTION=HEX +Property module: Create Profile: Hexagonal +12 +10 +11 +Default integration, +beam in a plane +Default integration, +beam in space +Geometric input data +d (circumscribing radius), t (wall thickness) +Default integration (Simpson) +Beam in a plane: 5 points +Beam in space: 3 points in each wall segment (12 total) +Nondefault integration input for a beam section integrated during the analysis +Beam in a plane: Give the number of points along the section wall, moving in the second beam section +axis direction. This number must be odd and greater than or equal to three. +Beam in space: Give the number of points in each wall segment. This number must be odd and greater +than or equal to three. +Default stress output points if a beam section integrated during the analysis is used +Beam in a plane: Bottom and top (points 1 and 5 above for default integration). +Beam in space: Vertices (points 1, 3, 5, 7, 9, and 11 above for default integration). +Temperature and field variable input at specific points for beam sections integrated during +the analysis +Give the value at each of the points shown below. +Beam in a plane +Beam in space +I-section +Input File Usage: +Use one of the following options: +*BEAM SECTION, SECTION=I +*BEAM GENERAL SECTION, SECTION=I +*FRAME SECTION, SECTION=I +Property module: Create Profile: I +Abaqus/CAE Usage: +t 3 +t 2 +t 1 +b 1 +Default integration, +beam in a plane +Geometric input data +l, h, +, +, +, +, +10 +11 +12 13 +t 2 +t 1 +t 3 +b1 +Default integration, +beam in space +By allowing you to specify l, the origin of the local cross-section axis can be placed anywhere on the +symmetry line (the local 2-axis). In the above figures a negative value of l implies that the origin of +the local cross-section axis is below the lower edge of the bottom flange, which may be needed when +constraining a beam stiffener to a shell. +Defining a T-section +Input File Usage: +Set +and +or +and +to zero to model a T-section. +Abaqus/CAE Usage: +Property module: Create Profile: T +Default integration (Simpson) +Beam in a plane: 5 points (one in each flange plus 3 in web) +Beam in space: 5 points in web, 5 in each flange (13 total) +Nondefault integration input for a beam section integrated during the analysis +Beam in a plane: Give the number of points in the second beam section axis direction. This number must +be odd and greater than or equal to three. +Beam in space: Give the number of points in the lower flange first, then in the web, and then in the upper +flange. These numbers must be odd and greater than or equal to three in each nonvanishing section. +Default stress output points if a beam section integrated during the analysis is used +Beam in a plane: Flanges (points 1 and 5 above for default integration). +Beam in space: Ends of flanges (points 1, 5, 9, and 13 above for default integration). +Temperature and field variable input at specific points for beam sections integrated during +the analysis +Give the value at each of the points shown below. +Beam in a plane +Beam in space +For a beam in space the temperature is first interpolated linearly through the flanges based on the +temperature at points 1 and 2, and then 4 and 5, respectively. +It is then interpolated parabolically +through the web. +Temperature input for a frame section +Constant temperature throughout the element cross-section is assumed; therefore, only one temperature +value per node is required. +L-section +Input File Usage: +Use either of the following options: +Abaqus/CAE Usage: +*BEAM SECTION, SECTION=L +*BEAM GENERAL SECTION, SECTION=L +Property module: Create Profile: L +t 2 +t 2 +t 1 +t 1 +Default integration, +beam in a plane +Default integration, +beam in space +Geometric input data +a, b, +, +Default integration (Simpson) +Beam in a plane: 5 points +Beam in space: 5 points in each flange (9 total) +Nondefault integration input for a beam section integrated during the analysis +Beam in a plane: Give the number of points in the second beam section axis direction. This number must +be odd and greater than or equal to three. +Beam in space: Give the number of points in the first beam section axis direction, then the number of +points in the second beam section axis direction. These numbers must be odd and greater than or equal +to three. +Default stress output points if a beam section integrated during the analysis is used +Beam in a plane: Bottom and top (points 1 and 5 above for default integration). +Beam in space: End of flange along positive local 1-axis; section corner; end of flange along positive +local 2-axis (points 1, 5, and 9 above for default integration). +Temperature and field variable input at specific points for beam sections integrated during +the analysis +Give the value at each of the points shown below. +Beam in a plane +Beam in space +Pipe section (thin-walled) +Pipe cross-sections can be associated with beam, pipe, or frame elements. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options: +*BEAM SECTION, SECTION=PIPE +*BEAM GENERAL SECTION, SECTION=PIPE +*FRAME SECTION, SECTION=PIPE +Property module: Create Profile: Pipe: Thin walled +Default integration, +beam in a plane +Default integration, +beam in space +Geometric input data +r (outside radius), t (wall thickness) +Default integration +Beam in a plane: 5 points (Simpson’s rule) +Beam in space: 8 points (trapezoidal rule) +Nondefault integration input for a beam section integrated during the analysis +Beam in a plane: Give an odd number of points. This number must be greater than or equal to five. +Beam in space: Give an even number of points. This number must be greater than or equal to eight. +Default stress output points if a beam section integrated during the analysis is used +Beam in a plane: Bottom and top (points 1 and 5 above for default integration). +Beam in space: On the intersection of the surface with the 1- and 2-axes (points 1, 3, 5, and 7 above for +default integration). +Temperature and field variable input at specific points for beam sections integrated during +the analysis +Give the value at each of the points shown below. +Beam in a plane +Beam in space +Temperature input for a frame section +Constant temperature throughout the element cross-section is assumed; therefore, only one temperature +value per node is required. +Pipe section (thick-walled) +Thick-walled pipe cross-sections can be associated with beam or pipe elements. +Input File Usage: +Use the following option: +Abaqus/CAE Usage: +*BEAM SECTION, SECTION=THICK PIPE +Property module: Create Profile: Pipe: Thick walled +12 +11 +10 +9 8 +15 +14 +13 +12 +11 +10 +18 +17 +16 +98 +21 +20 +19 +22 +23 +24 +15 +14 +13 +12 +11 +10 +98 +Default integration, +beam in a plane +Default integration, +beam in space +Geometric input data +r (outside radius), t (wall thickness) +Default integration +Beam in a plane: 3 points radially (Simpson’s rule), 5 circumferentially (trapezoidal rule) +Beam in space: 3 points radially (Simpson’s rule), 8 circumferentially (trapezoidal rule) +Nondefault integration input for a beam section integrated during the analysis +Beam in a plane: Give an odd number of points in the radial direction, then an odd number of points +(greater than or equal to 5) in the circumferential direction. +Beam in space: Give an odd number of points in the radial direction, then an even number of points +(greater than or equal to 8) in the circumferential direction. +Default stress output points if a beam section integrated during the analysis is used +Beam in a plane: Bottom and top on the pipe midsurface (points 2 and 14 above for default integration). +Beam in space: On the intersection of the pipe midsurface with the 1- and 2-axes (points 2, 8, 14, and +20 above for default integration). +Temperature and field variable input at specific points for beam sections integrated during +the analysis +Give the value at each of the points shown below. +Beam in a plane +Beam in space +Rectangular section +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options: +*BEAM SECTION, SECTION=RECT +*BEAM GENERAL SECTION, SECTION=RECT +*FRAME SECTION, SECTION=RECT +Property module: Create Profile: Rectangular +21 +16 +11 +23 +18 +13 +22 +17 +12 +24 +19 +14 +25 +20 +15 +10 +Default integration, +beam in a plane +Default integration, +beam in space +Geometric input data +a, b +Default integration (Simpson) +Beam in a plane: 5 points +Beam in space: 5 × 5 (25 total) +Nondefault integration input for a beam section integrated during the analysis +Beam in a plane: Give the number of points in the second beam section axis direction. This number must +be odd and greater than or equal to five. +Beam in space: Give the number of points in the first beam section axis direction, then the number of +points in the second beam section axis direction. These numbers must be odd and greater than or equal +to five. +Default stress output points if a beam section integrated during the analysis is used +Beam in a plane: Bottom and top (points 1 and 5 above for default integration). +Beam in space: Corners (points 1, 5, 21, and 25 above for default integration). +Temperature and field variable input at specific points for beam sections integrated during +the analysis +Give the value at each of the points shown below. +Beam in a plane +Beam in space +Temperature input for a frame section +Constant temperature throughout the element cross-section is assumed; therefore, only one temperature +value per node is required. +Trapezoidal section +Input File Usage: +Use either of the following options: +Abaqus/CAE Usage: +*BEAM SECTION, SECTION=TRAPEZOID +*BEAM GENERAL SECTION, SECTION=TRAPEZOID +Property module: Create Profile: Trapezoidal +21 +22 +16 +17 +11 +12 +23 +18 +13 +24 +25 +19 +20 +14 +15 +10 +Default integration, +beam in a plane +Default integration, +beam in space +Geometric input data +a, b, c, d +By allowing you to specify d, the origin of the local cross-section axes can be placed anywhere on the +symmetry line (the local 2-axis). In the above figures a negative value of d implies that the origin of the +local cross-section axis is below the lower edge of the section. This may be needed when constraining a +beam stiffener to a shell. +Default integration (Simpson) +Beam in a plane: 5 points +Beam in space: 5 × 5 (25 total) +Nondefault integration input for a beam section integrated during the analysis +Beam in a plane: Give the number of points in the second beam section axis direction. This number must +be odd and greater than or equal to five. +Beam in space: Give the number of points in the first beam section axis direction, then the number of +points in the second beam section axis direction. These numbers must be odd and greater than or equal +to five. +Default stress output points if a beam section integrated during the analysis is used +Beam in a plane: Bottom and top (points 1 and 5 above for default integration). +Beam in space: Corners (points 1, 5, 21, and 25 above for default integration). +Temperature and field variable input at specific points for beam sections integrated during +the analysis +Give the value at each of the points shown below. +b/2 +b/2 +Beam in a plane +Beam in space +29.4 +Frame elements +• “Frame elements,” Section 29.4.1 +• “Frame section behavior,” Section 29.4.2 +• “Frame element library,” Section 29.4.3 +29.4.1 +FRAME ELEMENTS +Product: Abaqus/Standard +References +• “Beam modeling: overview,” Section 29.3.1 +• “Frame section behavior,” Section 29.4.2 +• “Frame element library,” Section 29.4.3 +• *FRAME SECTION +Overview +Frame elements: +• are 2-node, initially straight, slender beam elements intended for use in the elastic or elastic-plastic +analysis of frame-like structures; +• are available in two or three dimensions; +• have elastic response that follows Euler-Bernoulli beam theory with fourth-order interpolation for +the transverse displacements; +• have plastic response that is concentrated at the element ends (plastic hinges) and is modeled with +a lumped plasticity model that includes nonlinear kinematic hardening; +• are implemented for small or large displacements (large rotations with small strains); +• output forces and moments at the element ends and midpoint; +• output elastic axial strain and curvatures at the element ends and midpoint and plastic displacements +and rotations at the element ends only; +• admit, optionally, a uniaxial “buckling strut” response where the axial response of the element is +governed by a damaged elasticity model in compression and an isotropic hardening plasticity model +in tension and where all transverse forces and moments are zero; +• can switch to buckling strut response during the analysis (for pipe sections only); and +• can be used in static, implicit dynamic, and eigenfrequency extraction analyses only. +Typical applications +Frame elements are designed to be used for small-strain elastic or elastic-plastic analysis of frame-like +structures composed of slender, initially straight beams. Typically, a single frame element will represent +the entire structural member connecting two joints. A frame element’s elastic response is governed +by Euler-Bernoulli beam theory with fourth-order interpolations for the transverse displacement field; +hence, the element’s kinematics include the exact (Euler-Bernoulli) solution to concentrated end forces +and moments and constant distributed loads. The elements can be used to solve a wide variety of +civil engineering design applications, such as truss structures, bridges, internal frame structures of +buildings, off-shore platforms, and jackets, etc. A frame element’s plastic response is modeled with a +lumped plasticity model at the element ends that simulates the formation of plastic hinges. The lumped +plasticity model includes nonlinear kinematic hardening. The elements can, thus, be used for collapse +load prediction based on the formation of plastic hinges. +Slender, frame-like members loaded in compression often buckle in such a way that only axial force +is supported by the member; all other forces and moments are negligibly small. Frame elements offer +optional buckling strut response whereby the element only carries axial force, which is calculated based +on a damaged elasticity model in compression and an isotropic hardening plasticity model in tension. +This model provides a simple phenomenological approximation to the highly nonlinear geometric and +material response that takes place during buckling and postbuckling deformation of slender members +loaded in compression. +For pipe sections only, frame elements allow switching to optional uniaxial buckling strut response +during the analysis. The criterion for switching is the “ISO” equation together with the “strength” +equation . +When the ISO and strength equations are satisfied, the elastic or elastic-plastic frame element undergoes +a one-time-only switch in behavior to buckling strut response. +Element cross-sectional axis system +, +) axis system, where +The orientation of the frame element’s cross-section is defined in Abaqus/Standard in terms of a local, +right-handed ( , +is the tangent to the axis of the element, positive in the +direction from the first to the second node of the element, and +are basis vectors that define +the local 1- and 2-directions of the cross-section. +is +referred to as the normal to the element. Since these elements are initially straight and assume small +strains, the cross-section directions are constant along each element and possibly discontinuous between +elements. +is referred to as the first axis direction, and +and +Defining the n1 -direction at the nodes +For frame elements in a plane the +-direction is always (0.0, 0.0, −1.0); that is, normal to the plane in +which the motion occurs. Therefore, planar frame elements can bend only about the first axis direction. +must be defined directly as part of the +element section definition or by specifying an additional node off the element’s axis. This additional +node is included in the element’s connectivity list . +For frame elements in space the approximate direction of +• If an additional node is specified, the approximate direction of +from the first node of the element to the additional node. +is defined by the vector extending +• If both input methods are used, the direction calculated by using the additional node will take +precedence. +• If the approximate direction is not defined by either of the above methods, the default value is (0.0, +0.0, −1.0). +-direction is then the normal to the element’s axis that lies in the plane defined by the element’s +The +axis and this approximate +-direction. The +-direction is defined as +. +Large-displacement assumptions +The frame element’s formulation includes the effect of large rigid body motions (displacements and +rotations) when geometrically nonlinear analysis is selected . Strains in these elements are assumed to remain small. +Material response (section properties) of frame elements +For frame elements the geometric and material properties are specified together as part of the frame +section definition. No separate material definition is required. You can choose one of the section shapes +that is valid for frame elements from the beam cross-section library . The valid section shapes depend upon whether elastic or elastic-plastic material response +is specified or whether buckling strut response is included. See “Frame section behavior,” Section 29.4.2, +for a complete discussion of specifying the geometric and material section properties. +Input File Usage: +*FRAME SECTION, SECTION=section_type +Mechanical response and mass formulation +The mechanical response of a frame element includes elastic and plastic behavior. Optionally, uniaxial +buckling strut response is available. +Elastic response +The elastic response of a frame element is governed by Euler-Bernoulli beam theory. The displacement +interpolations for the deflections transverse to the frame element’s axis (the local 1- and 2-directions +in three dimensions; the local 2-direction in two dimensions) are fourth-order polynomials, allowing +quadratic variation of the curvature along the element’s axis. Thus, each single frame element exactly +models the static, elastic solution to force and moment loading at its ends and constant distributed loading +along its axis (such as gravity loading). The displacement interpolation along an element’s axis is a +second-order polynomial, allowing linear variation of the axial strain. In three dimensions the twist +rotation interpolation along an element’s axis is linear, allowing constant twist strain. The elastic stiffness +matrix is integrated numerically and used to calculate 15 nodal forces and moments in three dimensions: +an axial force, two shear forces, two bending moments, and a twist moment at each end node, and an +axial force and two shear forces at the midpoint node. In two dimensions 8 nodal forces and moments +exist: an axial force, a shear force, and a moment at each end, and an axial force and a shear force at the +midpoint. The forces and moments are illustrated in Figure 29.4.1–1. +Elastic-plastic response +The plastic response of the element is treated with a “lumped” plasticity model such that plastic +deformations can develop only at the element’s ends through plastic rotations (hinges) and plastic axial +displacement. The growth of the plastic zone through the element’s cross-section from initial yield to a +fully yielded plastic hinge is modeled with nonlinear kinematic hardening. It is assumed that the plastic +deformation at an end node is influenced by the moments and axial force at that node only. Hence, the +N2 +N1 +N2 +N1 +N2 +N1 +n2 +n1 +M1 +M2 +M1 +M2 +Figure 29.4.1–1 Forces and moments on a frame element in space. +yield function at each node, also called the plastic interaction surface, is assumed to be a function of that +node’s axial force and three moment components only. No length is associated with the plastic hinge. +In reality, the plastic hinge will have a finite size determined by the element’s length and the specific +loading that causes yielding; the hinge size will influence the hardening rate but not the ultimate load. +Hence, if the rate of hardening and, thus, the plastic deformation for a given load are important, the +lumped plasticity model should be calibrated with the element’s length and the loading situation taken +into account. For details on the elastic-plastic element formulation, see “Frame elements with lumped +plasticity,” Section 3.9.2 of the Abaqus Theory Manual. +Uniaxial linear elastic and buckling strut response with tensile yield +You can obtain a frame element’s response to uniaxial force only, based on linear elasticity, buckling +strut response, and tensile yield. +In that case all transverse forces and moments in the element are +zero. For linear elastic response the element behaves like an axial spring with constant stiffness. For +buckling strut response if the tensile axial force in the element does not exceed the yield force, the axial +force in the element is constrained to remain inside a buckling envelope. See “Frame section behavior,” +Section 29.4.2, for a description of this envelope. Inside the envelope the force is related to strain by +a damaged elastic modulus. The cyclic, hysteretic response of this model is phenomenological and +approximates the response of thin-walled, pipe-like members. When the element is loaded in tension +beyond the yield force, the force response is governed by isotropic hardening plasticity. In reverse loading +the response is governed by the buckling envelope translated along the strain axis by an amount equal +to the axial plastic strain. For details of the buckling strut formulation, see “Buckling strut response for +frame elements,” Section 3.9.3 of the Abaqus Theory Manual. +Mass formulation +The frame element uses a lumped mass formulation for both dynamic analysis and gravity loading. The +mass matrix for the translational degrees of freedom is derived from a quadratic interpolation of the axial +and transverse displacement components. The rotary inertia for the element is isotropic and concentrated +at the two ends. +For buckling strut response a lumped mass scheme is used, where the element’s mass is concentrated +at the two ends; no rotary inertia is included. +Using frame elements in contact problems +When contact conditions play a role in a structure’s behavior, frame elements have to be used with +caution. A frame element has one additional internal node, located in the middle of the element. No +contact constraint is imposed on this node, so this internal node may penetrate the surface in contact, +resulting in a sagging effect. +Output +The forces and moments, elastic strains, and plastic displacements and rotations in a frame element +are reported relative to a corotational coordinate system. The local coordinate directions are the axial +direction and the two cross-sectional directions. Output of section forces and moments as well as elastic +strains and curvatures is available at the element ends and midpoint. Output of plastic displacement and +rotations is available only at the element ends. You can request output to the output database (at the +integration points only), to the data file, or to the results file . Since frame elements are formulated +in terms of section properties, stress output is not available. +29.4.2 +FRAME SECTION BEHAVIOR +Product: Abaqus/Standard +References +• “Frame elements,” Section 29.4.1 +• *FRAME SECTION +Overview +The frame section behavior: +• requires definition of the section’s shape and its material response; +• uses linear elastic behavior in the interior of the frame element; +• can include “lumped” plasticity at the element ends to model the formation of plastic hinges; +• can be uniaxial only, with response governed by a phenomenological buckling strut model, together +with linear elasticity and tensile plastic yielding; and +• for pipe sections only, can switch to buckling strut response during the analysis. +Defining elastic section behavior +The elastic response of the frame elements is formulated in terms of Young’s modulus, E; the torsional +shear modulus, G; coefficient of thermal expansion, +; and cross-section shape. Geometric properties +such as the cross-sectional area, A, or bending moments of inertia are constant along the element and +during the analysis. +If present, thermal strains are constant over the cross-section, which is equivalent to assuming that +the temperature does not vary in the cross-section. As a result of this assumption only the axial force, N, +depends on the thermal strain +where defines the total axial strain, including any initial elastic strain caused by a user-defined nonzero +initial axial force, and +defines the thermal expansion strain given by +where +is the thermal expansion coefficient, +is the current temperature at the section, +is the reference temperature for +, +is the user-defined initial temperature at this point (“Initial conditions in Abaqus/Standard +and Abaqus/Explicit,” Section 33.2.1), +are field variables, and +are the user-defined initial values of field variables at this point (“Initial conditions in +Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1). +The bending moment and twist torque responses are defined by the constitutive relations +where +is the moment of inertia for bending about the 1-axis of the section, +is the moment of inertia for bending about the 2-axis of the section, +is the moment of inertia for cross-bending, +is the torsional constant, +is the curvature change about the first beam section local axis, including any elastic curvature +change associated with a user-defined nonzero initial moment +(“Initial conditions in +Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1), +is the curvature change about the second beam section local axis, including any elastic +curvature change associated with a user-defined nonzero initial moment +(“Initial +conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1), and +is the twist, including any elastic twist associated with a user-defined nonzero initial +twisting moment (torque) T (“Initial conditions in Abaqus/Standard and Abaqus/Explicit,” +Section 33.2.1). +Defining temperature and field-variable-dependent section properties +The temperature and predefined field variables may vary linearly over the element’s length. Material +constants such as Young’s modulus, +, and the coefficient +of thermal expansion, +. You must +associate the section definition with an element set. +, can also depend on the temperature, +, the torsional shear modulus, +, and field variables +Input File Usage: +*FRAME SECTION, ELSET=name +Specifying a standard library section and allowing Abaqus/Standard to calculate the +cross-section’s parameters +Select one of the following section profiles from the standard library of cross-sections : box, circular, I, pipe, or rectangular. Specify the geometric input data +needed to define the shape of the cross-section. Abaqus/Standard will then calculate the geometric +quantities needed to define the section behavior automatically. +Input File Usage: +*FRAME SECTION, SECTION=library_section, ELSET=name +Specifying the geometric quantities directly +Specify a general cross-section to define the area of the cross-section, moments of inertia, and torsional +constant directly. These data are sufficient for defining the elastic section behavior since the axial +stretching, bending response, and torsional behavior are assumed to be uncoupled. +Input File Usage: +*FRAME SECTION, SECTION=GENERAL, ELSET=name +Specifying the elastic behavior +Specify the elastic modulus, the torsional shear modulus, and the coefficient of thermal expansion as +functions of temperature and field variables. +Input File Usage: +*FRAME SECTION, SECTION=section_type, ELSET=name +first_data_line +second_data_line +elastic_modulus, torsional_shear_modulus, +coefficient_of_thermal_expansion, temperature, fv_1, fv_2, etc. +Defining elastic-plastic section behavior +, +, +, and T directly as functions of their conjugate +To include elastic-plastic response, specify N, +plastic deformation variables or use the default plastic response for N, +, and T based on the +material yield stress. Abaqus/Standard uses the specified or default values to define a nonlinear kinematic +hardening model that is “lumped” into plastic hinges at the element ends. Since the plasticity is lumped +at the element ends, no length dimension is associated with the hinge. Generalized forces are related +to generalized plastic displacements, not strains. +In reality, the plastic hinge will have a finite size +determined by the structural member’s length and the loading, which will affect the hardening rate but +not the ultimate load. For example, yielding under pure bending (a constant moment over the member) +will produce a hinge length equal to the member length, whereas yielding of a cantilever with transverse +tip load (a linearly varying moment over the member) will produce a much more localized hinge. Hence, +if the rate of hardening and, thus, the plastic deformation at a given load are of importance, you should +calibrate the plastic response appropriately for different lengths and different loading situations. +In the plastic range the only plastic surface available is an ellipsoid. This yield surface is only +reasonably accurate for the pipe cross-section. Box, circular, I, and rectangular cross-sections can be +used at your discretion with the understanding that the elliptic yield surface may not approximate the +elastic-plastic response accurately. The general cross-section type cannot be used with plasticity. +Defining N, M1 , M2 , and T directly +, +You can define N, +, and T directly. Abaqus/Standard will fit an exponential curve to +the user-supplied data as discussed below (see “Elastic-plastic data curve fit and calculation of default +values” below). The plastic data describe the response to axial force, moment about the cross-sectional +1- and 2-directions, and torque. +You must specify pairs of data relating the generalized force component to the appropriate plastic +variable. Since the plasticity is concentrated at the element ends, the overall plastic response is dependent +on the length of the element; hence, members with different lengths might require different hardening +data. The plasticity model for frame elements is intended for frame-like structures: each member between +structural joints is modeled with a single frame element where plastic hinges are allowed to develop at +the end connections. +At least three data pairs for each plastic variable are required to describe the elastic-plastic section +hardening behavior. If fewer than three data pairs are given, Abaqus/Standard will issue an error message. +Input File Usage: +Use the following options: +*FRAME SECTION, SECTION=PIPE, ELSET=name +*PLASTIC AXIAL for N +*PLASTIC M1 for +*PLASTIC M2 for +*PLASTIC TORQUE for T +Allowing Abaqus/Standard to calculate default values for N, M1 , M2 , and T +You can use the default elastic-plastic material response for the plastic variables based on the yield stress +for the material. The default elastic-plastic material response differs for each of the plastic variables: the +plastic axial force, first plastic bending moment, second plastic bending moment, and plastic torsional +moment. Specific default values are given below. +If you define the plastic variables directly and specify that the default response should be used, the +data defined by you will take precedence over the default values. +Input File Usage: +Use the following options: +*FRAME SECTION, SECTION=PIPE, ELSET=name, +PLASTIC DEFAULTS, YIELD STRESS= +plastic options if user-defined values are necessary for a +particular generalized force +Elastic-plastic data curve fit and calculation of default values +The elastic-plastic response is a nonlinear kinematic hardening plasticity model. See “Models for metals +subjected to cyclic loading,” Section 23.2.2, for a discussion of the nonlinear kinematic hardening +formulation. +Nonlinear kinematic hardening with N, M1 , M2 , and T defined directly +For each of the four plastic material variables Abaqus/Standard uses an exponential curve fit of the +user-supplied generalized force versus generalized plastic displacement to define the limits on the elastic +range. The curve-fit procedure generates a hardening curve from the user-supplied data. It requires at +least three data pairs. +The nonlinear kinematic hardening model describes the translation of the yield surface in +generalized force space through a generalized backstress, +. The kinematic hardening is defined to be +an additive combination of a purely kinematic linear hardening term and a relaxation (recall) term such +that the backstress evolution is defined by +sign +where F is a component of generalized force, and C and +based on the user-defined or default hardening data. C is the initial hardening modulus, and +determines the rate at which the kinematic hardening modulus decreases with increasing backstress, +are material parameters that are calibrated +. The saturation value of +( +), called +, is +See Figure 29.4.2–1 for an illustration of the elastic range for the nonlinear kinematic hardening +model. +F0 +F0 +F = F0+ +qpl +Figure 29.4.2–1 Nonlinear kinematic hardening model: yield +. +surface for positive loading and the center of the yield surface, +Allowing Abaqus/Standard to generate the default nonlinear kinematic hardening model +To define the default plastic response, three data points are generated from the yield stress value and the +cross-section shape. These three data points relate generalized force to generalized plastic displacement +per unit length of the element. Since the model is calibrated per unit element length, the generated +default plastic response is different for different element lengths. The generalized force levels for these +, +and +, and +three points are +is the generalized force at zero plastic generalized displacement. +are generalized force magnitudes that characterize the ultimate load-carrying capacity. The +) characterize the hardening +slopes between the data points (i.e., the generalized plastic moduli +response. See Figure 29.4.2–2 for an illustration of the default nonlinear kinematic hardening model. +and +. +F2 +F1 +F0 +D1 +D2 +qpl +Figure 29.4.2–2 Data points generated for the default nonlinear kinematic hardening model. +For the plastic axial force, +is the axial force that causes initial yielding. For the plastic bending +moments about the first and second axes, +is the moment about the first and second cross-sectional +directions, respectively, that produces first fiber yielding. For the plastic torsional moment, +is the +torque about the axis that produces first fiber yielding. The generalized force levels +and +, along +with the connecting slopes +, are chosen to approximate the response of a pipe cross-section +made of a typical structural steel, with mild work hardening, from initial yielding to the development +of a fully plastic hinge. The work hardening of the material corresponds to the default hardening of the +section during axial loading. For different loading situations the size of the plastic hinge will vary; hence, +the default model should be checked for validity against all anticipated loading situations. Default values +for +corresponding to each plastic variable are listed in Table 29.4.2–1. These default +values are available for pipe, box, and I cross-section types with the values for the coefficients +, +and +as shown in Table 29.4.2–2. +, and +and +, +, +, +Table 29.4.2–1 Default values for generalized forces and +connecting slopes for corresponding plastic variables. +Plastic axial force +First plastic bending moment +Second plastic bending moment +Plastic torsional moment (for box +and pipe sections) +Plastic torsional moment (for +I-sections) +Table 29.4.2–2 Coefficients +, +, and +. +Cross-section type +Pipe +Box +I (strong) +I (weak) +0.30 +0.17 +0.10 +0.43 +0.07 +0.02 +0.02 +0.10 +1.35 +1.20 +1.12 +1.50 +Defining optional uniaxial strut behavior +Frame elements optionally allow only uniaxial response (strut behavior). In this case neither end of +the element supports moments or forces transverse to the axis; hence, only a force along the axis of +the element exists. Furthermore, this axial force is constant along the length of the element, even if a +distributed load is applied tangentially to the element axis. The uniaxial response of the element is linear +elastic or nonlinear, in which case it includes buckling and postbuckling in compression and isotropic +hardening plasticity in tension. +Defining linear elastic uniaxial behavior +, where +A linear elastic uniaxial frame element behaves like an axial spring with constant stiffness +E is Young’s modulus, A is the cross-sectional area, and L is the original element length. The strain +measure is the change in length of the element divided by the element’s original length. +Input File Usage: +*FRAME SECTION, SECTION=library_section, ELSET=name, PINNED +Defining buckling, postbuckling, and plastic uniaxial behavior: buckling strut response +If uniaxial buckling and postbuckling in compression and isotropic hardening plasticity in tension are +modeled (buckling strut response), the buckling envelope must be defined. The buckling envelope +defines the force versus axial strain (change in length divided by the original length) response of the +element. It is illustrated in Figure 29.4.2–3. +force +Py +ζPy + EA +κPcr +Pcr +γEA +strain +βEA +αEA +Figure 29.4.2–3 Buckling envelope for uniaxial buckling response. +The buckling envelope derives from Marshall Strut theory, which is developed for pipe cross-section +profiles only. No other cross-section types are permitted with buckling strut response. +Seven coefficients determine the buckling envelope as follows (the default values are listed, where +D is the pipe outer diameter and t is the pipe wall thickness): +). +is the yield stress. +Elastic limit force ( +Isotropic hardening slope ( +Critical compressive buckling force predicted by the ISO equation, defined in +“Buckling strut response for frame elements,” Section 3.9.3 of the Abaqus Theory +Manual. +Slope of a segment on the buckling envelope, +and +). +( +). +Corner on the buckling envelope ( +). +Slope of a segment on the buckling envelope ( +Corner on the buckling envelope ( +). +). +The axial force in the element is required to stay inside or on the buckling envelope. When tension +yielding occurs, the enclosed part of the envelope translates along the strain axis by an amount equal to +the plastic strain. When reverse loading occurs for points on the boundary of the enclosed part of the +envelope, the strut exhibits “damaged elastic” behavior. This damaged elastic response is determined by +drawing a line from the point on the envelope to the tension yield point (force value +). As long as the +force and axial strain remain inside the enclosed part of the envelope, the force response is linear elastic +with a modulus equal to the damaged elastic modulus. At any time that the compressive strain is greater +in magnitude than the negative extreme strain point of the envelope, the force is constant with a value +of zero. +The value of +yield stress value. +is a function of an element’s geometrical and material properties, including the +Buckling strut response cannot be used with elastic-plastic frame section behavior; the strut’s plastic +behavior is defined by +and the isotropic hardening slope +. +Defining the buckling envelope +You can specify that the default buckling envelope should be used, or you can define the buckling +envelope. +If you define the buckling envelope directly and specify that the default envelope should +be used, the values defined by you will take precedence. +In either case you must provide the yield stress value, which will be used to determine the yield +force in tension and the critical compressive buckling load (through the ISO equation described later in +this section). +Input File Usage: +To specify the default buckling envelope, use the following option: +*FRAME SECTION, SECTION=PIPE, ELSET=name, BUCKLING, +PINNED, YIELD STRESS= +To specify a user-defined buckling envelope, use both of the following options: +*FRAME SECTION, SECTION=PIPE, ELSET=name, PINNED, +YIELD STRESS= +*BUCKLING ENVELOPE +Defining the critical buckling load +The critical buckling load, +, is determined by the ISO equation, which is an empirical relationship +determined by the International Organization for Standardization based on experimental results for pipe- +like or tubular structural members. Within the ISO equation, four variables can be changed from their +default values: the effective length factors, +, in the first and second sectional directions (the +default values are 1.0) and the added length, +, in the first and second sectional directions +and +(the default values are 0). These variables account for the buckling member’s end connectivity. The +effective element length in the transverse direction i ( +. For details on +the ISO equation, see “Buckling strut response for frame elements,” Section 3.9.3 of the Abaqus Theory +Manual. +and +) is +Input File Usage: +To define nondefault coefficients for the ISO equation with the default buckling +envelope, use both of the following options: +*FRAME SECTION, SECTION=PIPE, ELSET=name, BUCKLING, +PINNED, YIELD STRESS= +*BUCKLING LENGTH +To define nondefault coefficients for the ISO equation with a user-defined +buckling envelope, use all of the following options: +*FRAME SECTION, SECTION=PIPE, ELSET=name, PINNED, +YIELD STRESS= +*BUCKLING ENVELOPE +*BUCKLING LENGTH +Switching to optional uniaxial strut behavior during an analysis +Frame elements allow switching to uniaxial buckling strut response during the analysis. The criterion for +switching is the “ISO” equation together with the “strength” equation . When the ISO equation is satisfied, the +elastic or elastic-plastic frame element undergoes a one-time-only switch in behavior to buckling strut +response. The strength equation is introduced to prevent switching in the absence of significant axial +forces. +When the frame element switches to buckling strut response, a dramatic loss of structural stiffness +If the global +occurs. The switched element no longer supports bending, torsion, or shear loading. +structure is unstable as a result of the switch (that is, the structure would collapse under the applied +loading), the analysis may fail to converge. +To permit switching of the element response, use the default buckling envelope or define a buckling +envelope and provide a yield stress, but do not activate linear elastic uniaxial behavior for the frame +element. +The ISO equation is an empirical relationship based on experiments with slender, pipe-like (tubular) +members. Since the equation is written explicitly in terms of the pipe outer diameter and thickness, only +pipe sections are permitted with buckling strut response. The ISO equation incorporates several factors +that you can define. Effective and added length factors account for element end fixity, and buckling +reduction factors account for bending moment influence on buckling. You can define nondefault values +for these factors in each local cross-section direction. +Input File Usage: +To allow switching to buckling strut response with default coefficients for the +ISO equation and the default buckling envelope, use the following option: +*FRAME SECTION, SECTION=PIPE, ELSET=name, BUCKLING, +YIELD STRESS= +To allow switching to buckling strut response with nondefault coefficients for +the ISO equation and the default buckling envelope, use all of the following +options: +*FRAME SECTION, SECTION=PIPE, ELSET=name, BUCKLING, +YIELD STRESS= +*BUCKLING LENGTH +*BUCKLING REDUCTION FACTORS +To allow switching to buckling strut response with nondefault coefficients for +the ISO equation and a user-defined buckling envelope, use all of the following +options: +*FRAME SECTION, SECTION=PIPE, ELSET=name, YIELD STRESS= +*BUCKLING ENVELOPE +*BUCKLING LENGTH +*BUCKLING REDUCTION FACTORS +Defining the reference temperature for thermal expansion +You can define a thermal expansion coefficient for the frame section. The thermal expansion coefficient +may be temperature dependent. +In this case you must define the reference temperature for thermal +expansion, +. +Input File Usage: +Use both of the following options: +*FRAME SECTION, ZERO= +*THERMAL EXPANSION +Specifying temperature and field variables +Define temperatures and field variables by giving the value at the origin of the cross-section (i.e., only +one temperature or field-variable value is given). +Input File Usage: +Use one or more of the following options: +*TEMPERATURE +*FIELD +*INITIAL CONDITIONS, TYPE=TEMPERATURE +*INITIAL CONDITIONS, TYPE=FIELD +29.4.3 +FRAME ELEMENT LIBRARY +Product: Abaqus/Standard +References +• “Frame elements,” Section 29.4.1 +• *FRAME SECTION +Overview +This section provides a reference to the frame elements available in Abaqus/Standard. +Element types +Frame in a plane +FRAME2D +2-node straight frame element +Active degrees of freedom +1, 2, 6 +Additional solution variables +Two additional variables relating to the axial and lateral displacements. +Frame in space +FRAME3D +2-node straight frame element +Active degrees of freedom +1, 2, 3, 4, 5, 6 +Additional solution variables +Three additional variables relating to the axial and lateral displacements. +Nodal coordinates required +Frame in a plane: X, Y (Direction cosines of the normal are not used; any values given are ignored.) +Frame in space: X, Y, Z (Direction cosines of the normal are not used; any values given are ignored.) +Element property definition +Local orientations defined as described in “Orientations,” Section 2.2.5, cannot be used with frame +elements to define local material directions. The orientation of the local section axes in space is discussed +in “Frame elements,” Section 29.4.1. +Input File Usage: +*FRAME SECTION +Element-based loading +Distributed loads +Distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DLOAD) +GRAV +PX +PY +PZ +P1 +P2 +Units +Description +LT−2 +FL−1 +FL−1 +FL−1 +FL−1 +FL−1 +Gravity loading in a specified direction +(magnitude is input as acceleration). +Force per unit length in global X-direction. +Force per unit length in global Y-direction. +Force per unit length in global Z-direction +(only for frames in space). +Force per unit +1-direction (only for frames in space). +length in frame local +Force per unit +2-direction. +length in frame local +Abaqus/Aqua loads +Abaqus/Aqua loads are specified as described in “Abaqus/Aqua analysis,” Section 6.11.1. +Units +Description +FL−1 +FL−1 +FL−1 +Transverse fluid drag load. +Fluid drag force on the first end of the frame +(node 1). +Fluid drag force on the second end of the +frame (node 2). +Tangential fluid drag load. +Transverse fluid inertia load. +Fluid inertia force on the first end of the +frame (node 1). +Fluid inertia force on the second end of the +frame (node 2). +29.4.3–2 +Load ID +(*CLOAD/ +*DLOAD) +FDD(A) +FD1(A) +FD2(A) +FDT(A) +FI(A) +FI1(A) +Load ID +(*CLOAD/ +*DLOAD) +PB(A) +WDD(A) +WD1(A) +WD2(A) +Foundations +Units +Description +FL−1 +FL−1 +Buoyancy load (closed-end condition). +Transverse wind drag load. +Wind drag force on the first end of the frame +(node 1). +Wind drag force on the second end of the +frame (node 2). +Foundations are specified as described in “Element foundations,” Section 2.2.2. +Load ID +(*FOUNDATION) +Units +Description +FX +FY +FZ +F1 +F2 +FL−2 +FL−2 +FL−2 +FL−2 +FL−2 +Stiffness per unit +direction. +Stiffness per unit +direction. +length in global X- +length in global Y- +Stiffness per unit +direction (only for frames in space). +length in global Z- +Stiffness per unit length in frame local 1- +direction (only for frames in space). +Stiffness per unit +2-direction. +length in frame local +Element output +All element output variables are given at the element ends (nodes 1 and 2) and midpoint (node 3). +Section forces and moments +SF1 +SF2 +SF3 +SM1 +SM2 +SM3 +Axial force. +Transverse shear force in the local 2-direction. +Transverse shear force in the local 1-direction (only available for frames in space). +Bending moment about the local 1-axis. +Bending moment about the local 2-axis (only available for frames in space). +Twisting moment about the frame axis (only available for frames in space). +See “Frame elements with lumped plasticity,” Section 3.9.2 of the Abaqus Theory Manual, for a +discussion of the section forces and moments. +Section elastic strains and curvatures +SEE1 +SKE1 +SKE2 +SKE3 +Elastic axial strain. +Elastic curvature change about the local 1-axis. +Elastic curvature change about the local 2-axis (only available for frames in space). +Elastic twist of the beam (only available for frames in space). +Plastic displacements and rotations in the element coordinate system +SEP1 +SKP1 +SKP2 +SKP3 +Plastic axial displacement. +Plastic rotation about the local 1-axis. +Plastic rotation about the local 2-axis (only available for frames in space). +Plastic rotation about the beam axis (only available for frames in space). +Section force and moment backstresses +SALPHA1 +SALPHA2 +SALPHA3 +SALPHA4 +Axial force backstress. +Bending moment backstress about the local 1-axis. +Bending moment backstress about the local 2-axis (only available for frames in +space). +Twisting moment backstress about the beam axis (only available for frames in space). +Node ordering on elements +end 2 +end 1 +2 - node element +For frames in space an additional node may be given after a frame element’s connectivity (in the element +definition—see “Element definition,” Section 2.2.1) to define the approximate direction of the first cross- +section axis, +. See “Frame elements,” Section 29.4.1, for details. +29.5 +Elbow elements +• “Pipes and pipebends with deforming cross-sections: elbow elements,” Section 29.5.1 +• “Elbow element library,” Section 29.5.2 +PIPES AND PIPEBENDS WITH DEFORMING CROSS-SECTIONS: ELBOW +ELEMENTS +ELBOW ELEMENTS +Product: Abaqus/Standard +References +• “Elbow element library,” Section 29.5.2 +• *BEAM SECTION +Overview +Elbow elements: +• are intended to provide accurate modeling of the nonlinear response of initially circular pipes and +pipebends when distortion of the cross-section by ovalization and warping dominates the behavior; +• appear as beams but are shells with quite complex deformation patterns allowed; +• use plane stress theory to model the deformation through the pipe wall; and +• cannot provide nodal values of stress, strain, and other constitutive results. +Typical applications +In the usual approach to linear analysis of elbows, the response prediction is based on semianalytical +results, used as “flexibility factors” to correct results obtained with simple beam theory. Such factors do +not apply in nonlinear cases, and the pipeline must be modeled as a shell to predict the response accurately +(for example, see “Parametric study of a linear elastic pipeline under in-plane bending,” Section 1.1.3 of +the Abaqus Example Problems Manual). Although the elbow elements appear as beams, they are, in fact, +shells, with quite complex deformation patterns allowed. In thin-walled elbows the interaction of elbows +and adjacent straight segments is an important aspect of elbow modeling, as are the large rotations that +readily occur in the cross-sectional deformation, even at small relative rotations of the pipe axis itself. All +of these effects (including the stiffening effect of internal pressure) can be modeled with these elements. +Elbow elements are intended to provide accurate modeling of the nonlinear response of initially +circular pipes and pipebends when distortion of the cross-section by ovalization and warping dominates +the behavior. Such behavior arises in two circumstances: in pipebends, where the initial curvature of +the pipe, together with the thinness of the wall of the pipe, causes ovalization to dominate the response, +and in straight pipe sections, where excessive bending can lead to a buckling collapse of the thin-walled +circular section (“Brazier buckling”). +Because the elbow elements use a full shell formulation around the circumference, the number of +degrees of freedom per element is high. Elbow elements that use all Fourier modes (discussed below) to +model ovalization and warping are considerably more expensive computationally than beam elements, +but their cost is comparable to that of coarse shell models, which can be used to model the section. +If an analysis requires connecting pipe elements to a pipebend, it is easier to connect elbow elements +to pipe elements than it is to connect shell elements to pipe elements. +Choosing an appropriate element +Elbow elements use polynomial interpolation along their length (linear or quadratic depending on the +element type), together with Fourier interpolation around the pipe to model the ovalization and warping +of the section. Shell theory is then used to model the behavior. +Two types of elbow elements are provided. +ELBOW31 and ELBOW32 +Element types ELBOW31 and ELBOW32 are the most complete elbow elements. In these elements the +ovalization of the pipe wall is made continuous from one element to the next, thus modeling such effects +as the interaction between pipe bends (elbows) and adjacent straight segments of the pipeline. +ELBOW31 and ELBOW32 should not be used for the analysis of unconnected straight pipes unless +the warping and ovalization are restrained at some point in the pipe. +ELBOW31B and ELBOW31C +Element types ELBOW31B and ELBOW31C use a simplified version of the formulation, in which +ovalization only is considered (no warping) and axial gradients of the ovalization are neglected. These +approximations are often satisfactory, and indeed they form the basis of the standard flexibility factor +approach used in linear analysis of piping systems. They provide a considerably less expensive capability. +ELBOW31C includes the further approximation that the odd numbered terms in the Fourier interpolation +around the pipe, except the first term, are neglected. This formulation provides a slightly less expensive +model for cases where the radius of the pipe is small compared to the radius of curvature of the pipe axis. +Defining the element’s section properties +You use a beam section definition integrated during the analysis to define the section properties of elbow +elements. Give the outside radius of the pipe, r; pipe wall thickness, t; and elbow torus radius, measured +to the pipe axis, R. For a straight pipe, set R to zero. +You must associate these properties with a set of elbow elements. +Input File Usage: +*BEAM SECTION, SECTION=ELBOW, ELSET=name +r, t, R +Defining the section orientation +For all elbow elements the section must be oriented in space by specifying a point that, together with +the nodes of the element, defines the plane of the +-axis in Figure 29.5.1–1. For bent pipes this point +should lie outside the bend (the side of the pipe on the outside of the bend is referred to as the extrados). +For pipebends of less than 180° this point can be set to be the point of intersection of the tangents to +the adjacent straight pipe runs. If a pipebend subtends an angle greater than or equal to 180°, the bend +should be partitioned into sections of less than 180° and a separate beam section should be defined for +each partition so that the point used to define the plane of the +When the elements are used to model straight pipes, the point can be any point off the pipe axis. +-axis can lie outside of the extrados. +Second cross-sectional direction +a = a x a +a - positive from +1st to 2nd node +torus radius +Figure 29.5.1–1 Elbow element geometry. +When ovalization modeling is extended onto straight runs adjacent to a pipebend by using +ELBOW31 or ELBOW32 elements for the pipebend and for the straight pipe, you must ensure that the +-axis is defined so that its orientation about the axis of the pipe is the same between the pipebend and +each of the straight segments. When possible, the +-axis should also be the same between adjacent +pipebends. In some cases, such as adjacent pipebends in different planes, the +-axes are necessarily +discontinuous. In such cases separate nodes must be introduced at the point where the +-axis changes +orientation, and MPC type ELBOW must be invoked to impose the appropriate constraints to ensure +continuity of displacements. See Figure 29.5.1–2. +Use two coincident nodes with MPC type ELBOW + to allow for change in direction of a2 +a2 +a2 + x + x +xx +a2 +a2 +a2 +a2 +a2 +a2 +Figure 29.5.1–2 Use of MPC type ELBOW with ELBOW31 or ELBOW32. +Input File Usage: +*BEAM SECTION, SECTION=ELBOW +first data line +coordinates of orientation point +Defining the number of integration points and Fourier modes +You can specify the number of integration points and Fourier modes for an elbow section. Experience +suggests that for relatively thick-walled cases 4 Fourier modes with 12 integration points around the +pipe are sufficient. For thin-walled elbows 6 Fourier modes and 18 integration points around the pipe +are needed. As a general rule, the number of integration points around the pipe should not be less than +three times the number of Fourier modes used; otherwise, singularities may arise in the stiffness matrix. +When used with zero Fourier modes, the elements become simple pipe elements with hoop strain and +stress included: when Poisson’s ratio is set to zero, they show similar behavior to the PIPE elements in +Abaqus . +Input File Usage: +*BEAM SECTION, SECTION=ELBOW +first data line +second data line +number of int. pts. through thickness, number of int. pts. around +pipe, number of Fourier modes +Assigning a material definition to a set of elbow elements +You must associate a material definition with each elbow section definition. +Input File Usage: +*BEAM SECTION, SECTION=ELBOW, MATERIAL=name +Specifying temperature and field variables +Temperature and field variables can be specified by defining the values at specific points through the +section or by defining the value at the middle of the pipe wall and specifying the gradient through the +pipe thickness. +By defining the values at points through the section +You can define temperatures and field variables by giving the values at each of the three points shown +below. +outside +inside +3 points through thickness +No matter how many section points there are through the thickness of the elbow, specify the values at +only these three points. These three values are applied to all integration points around the circumference +so that the only admissible variation is in the radial direction. +Input File Usage: +*BEAM SECTION, SECTION=ELBOW, TEMPERATURE=VALUES +By defining the value at the middle of the pipe wall and the gradient through the thickness +Alternatively, you can define temperatures and field variables by giving the value on the middle surface +of the pipe wall and the gradient of temperature with respect to position through the pipe wall thickness, +positive when the outside surface is hotter than the inside surface. +Input File Usage: +*BEAM SECTION, SECTION=ELBOW, TEMPERATURE=GRADIENTS +Using elbow elements in large-displacement analysis +When elbow elements are subjected to pipe pressure loads (load types PI, PE, HPI, or HPE) in large- +displacement analysis (“General and linear perturbation procedures,” Section 6.1.3), the most significant +contributions to the load stiffness are taken into account. +Defining kinematic boundary conditions on elbow elements +Kinematic boundary conditions on the standard degrees of freedom at the nodes of elbow elements (that +is, degrees of freedom 1–6) should be treated in the usual way. +In addition, the elements have ovalization and warping terms stored internally. For ELBOW31B and +ELBOW31C elements this requires no additional consideration. For ELBOW31 or ELBOW32 elements +you may often need to provide kinematic boundary conditions on these additional degrees of freedom. +For example, it is common to model a pipeline with ovalization and warping allowed in the elbows +and adjacent straight pipe segments but no ovalization in the middle segments of long, straight pipe +runs . (The latter is usually accomplished by specifying ELBOW31 elements with +zero modes or PIPE31 elements so that the usual bending terms and the uniform radial expansion term, +associated with pressure in the pipe, are included; if internal pressure is not important, a simple beam +element, B31, can be used instead.) Where the segments with ovalization and warping end, the warping +must be restrained; and if a stiff flange or vessel exists at that point, the ovalization should also be +restrained. To do so, specify NOWARP and/or NOOVAL or NODEFORM boundary conditions for that +node (“Boundary conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.3.1). +NOWARP means that no warping is allowed at the node, but ovalization and uniform radial +expansion are allowed; NOOVAL means that there can be no ovalization at the node, but warping +and uniform radial expansion are allowed; NODEFORM means that there can be no cross-section +deformation at all—no warping, ovalization, or uniform radial expansion. +Typically, NOWARP will be specified at the end of a pipebend segment modeled with ELBOW31 +adjacent to a straight pipe run, while NOWARP and NOOVAL would be specified at a stiff flange or +vessel attachment point. NODEFORM restrains all cross-sectional deformation, including the uniform +radial expansion term: this will result in large stresses if thermal expansion occurs. NODEFORM should +be used, for example, at a built-in end. +Visualizing the cross-section deformation +The current release of Abaqus/Standard does not provide a direct way of visualizing the cross-section +the utility routine felbow.f (“Creation of a data file to facilitate the +ovalization. However, +postprocessing of elbow element results: FELBOW,” Section 14.1.6 of the Abaqus Example Problems +Manual) creates a data file that can be used in Abaqus/CAE to plot the current coordinates of the +integration points around the circumference of the elbow section of interest. The routine uses output +variable COORD (“Abaqus/Standard output variable identifiers,” Section 4.2.1) to obtain the current +coordinates of the integration points. These values are available only if geometric nonlinearity is +considered in the step. You will have to ensure that the variable COORD is written to the results (.fil) +file for this purpose. +The routine is suitable for elbow elements oriented arbitrarily in space: the integration points of +the elbow section are projected appropriately to a coordinate system suitable for plotting the cross- +section. The input data for plotting are written to a file that can be read into Abaqus/CAE. An X–Y +plot of the elbow element’s deformed cross-section can be displayed using the XY Data Manager in the +Visualization module. +a. Typical pipeline +b. Sections modeled with continuous ovalization +Figure 29.5.1–3 Pipeline schematic. +In addition to facilitating the visualization of the cross-section ovalization, the program also allows +you to create data files to plot the variation of a variable along a line of elbow elements and around the +circumference of a given elbow element. +Similar C++ and Python utility routines, felbow.C (“A C++ version of FELBOW,” +Section 10.15.6 of the Abaqus Scripting User’s Manual) and felbow.py (“An Abaqus Scripting +Interface version of FELBOW,” Section 9.10.12 of the Abaqus Scripting User’s Manual), are provided +to process the pertinent elbow element results output written to the output database (.odb) file. When +these programs are executed, they write data to an ASCII format file and/or an output database file +that can be used in Abaqus/CAE to plot the current coordinates of the integration points around the +circumference of the elbow section. Both these routines can also be used to visualize the variation of +an output variable around the circumference of the elbow section. +29.5.2 +ELBOW ELEMENT LIBRARY +Product: Abaqus/Standard +References +• “Pipes and pipebends with deforming cross-sections: elbow elements,” Section 29.5.1 +• *BEAM SECTION +Overview +This section provides a reference to the elbow elements available in Abaqus/Standard. +Element types +ELBOW31 +2-node pipe in space with deforming section, linear interpolation along the pipe +ELBOW32 +3-node pipe in space with deforming section, quadratic interpolation along the pipe +ELBOW31B +2-node pipe in space with ovalization only, axial gradients of ovalization neglected +ELBOW31C +2-node pipe in space with ovalization only, axial gradients of ovalization neglected. +This formulation is the same as that for element type ELBOW31B, with the exception +that all odd numbered terms in the Fourier interpolation around the pipe but the first +term are neglected. +Active degrees of freedom +1, 2, 3, 4, 5, 6 +Additional solution variables +Elbow elements have numerous variables to model cross-sectional ovalization and warping. The number +of variables depends on the type of elbow element, the number of nodes, and the number of Fourier modes +chosen. In the following table p is the number of Fourier modes: +Element type +Number of variables +ELBOW31 +ELBOW32 +ELBOW31B +16, if p=0 +(16p+8), if p +24, if p=0 +(24p+12), if +13+2p, if p=0,1 +11+4p, if +Element type +Number of variables +ELBOW31C +13+2p, if p=0,1,3,5 +15+2p, if p=2,4,6 +Nodal coordinates required +Element property definition +Input File Usage: +*BEAM SECTION, SECTION=ELBOW +Element-based loading +Distributed loads +Distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DLOAD) +Units +Description +BX +BY +BZ +BXNU +BYNU +BZNU +FL−3 +FL−3 +FL−3 +FL−3 +FL−3 +FL−3 +CENT +FL−4 (ML−3T−2) +Body force per unit volume in global X- +direction. +Body force per unit volume in global Y- +direction. +Body force per unit volume in global Z- +direction. +Nonuniform body force in global X- +direction with magnitude supplied via user +subroutine DLOAD. +Nonuniform body force in global Y- +direction with magnitude supplied via user +subroutine DLOAD. +Nonuniform body force in global Z- +direction with magnitude supplied via user +subroutine DLOAD. +, +is the mass density per unit volume +Centrifugal load (magnitude is input as +where +and +is the angular velocity). +Units +Description +T−2 +LT−2 +FL−2 +FL−2 +FL−2 +FL−2 +FL−2 +FL−2 +T−2 +Centrifugal load (magnitude is input as +where +is the angular velocity). +, +Gravity loading in a specified direction +(magnitude is input as acceleration). +Hydrostatic external pressure, with linear +variation in global Z (closed-end condition). +Hydrostatic internal pressure, with linear +variation in global Z (closed-end condition). +Uniform external pressure +condition). +(closed-end +Uniform internal pressure +condition). +(closed-end +pressure with +Nonuniform external +magnitude supplied via user subroutine +DLOAD (closed-end condition). +Nonuniform internal +with +magnitude supplied via user subroutine +DLOAD (closed-end condition). +pressure +Rotary acceleration load (magnitude is input +as +is the rotary acceleration). +, where +Load ID +(*DLOAD) +CENTRIF +GRAV +HPE +HPI +PE +PI +PENU +PINU +ROTA +Abaqus/Aqua loads +Abaqus/Aqua loads are specified as described in “Abaqus/Aqua analysis,” Section 6.11.1. +Units +Description +FL−1 +FL−1 +FL−1 +Transverse fluid drag load. +Fluid drag force on the first end of the elbow +(node 1). +Fluid drag force on the second end of the +elbow (node 2 or node 3). +Tangential fluid drag load. +Transverse fluid inertia load. +29.5.2–3 +Load ID +(*CLOAD/ +*DLOAD) +FDD(A) +FD1(A) +FD2(A) +FDT(A) +Load ID +(*CLOAD/ +*DLOAD) +FI1(A) +FI2(A) +PB(A) +WDD(A) +WD1(A) +WD2(A) +Element output +Units +Description +FL−1 +FL−1 +Fluid inertia force on the first end of the +elbow (node 1). +Fluid inertia force on the second end of the +elbow (node 2 or node 3). +Buoyancy force (closed-end condition). +Transverse wind drag load. +Wind drag force on the first end of the elbow +(node 1). +Wind drag force on the second end of the +elbow (node 2 or node 3). +The default stress output points are on the inside surface and the outside surface at all integration stations +around the pipe. +Stress, strain, and other tensor components +Stress and other tensors (including strain tensors) are available for elements with displacement degrees +of freedom. All tensors have the same components. For example, the stress components are as follows: +S11 +S22 +S12 +Direct stress along the pipe. +Direct stress around the pipe section. +Shear stress in the pipe wall. +Section forces and moments +SF1 +SM1 +SM2 +SM3 +Axial force. +Bending moment about the local 1-axis. +Bending moment about the local 2-axis. +Twisting moment about the elbow axis. +Node ordering on elements +2-node element +3-node element +Numbering of integration points for output +13 +14 +15 +16 +17 +18 +19 +12 +11 +10 +extrados +20 +intrados +outside +inside + x + x +x +The extrados is the side of the pipebend that is furthest away from the center of the torus defining the +pipebend; that is, the side of the pipebend to which the +-axis points. The intrados is the side of the +pipebend closest to the center of the torus. +The middle surface integration points around a section are shown above. There is a default of five +thickness direction integration points at each such point, with point 1 on the inside surface of the pipe +and point 5 on the outside surface. +For ELBOW31 and ELBOW31B only one integration station is used along the axis of the element. For +ELBOW32 two integration stations are used along the axis of the elbow and the point numbers on the +second section are a continuation of those on the first section (e.g., 21, 22, …, 40 in the default case), +located around the pipe as shown above. +29.6 +Shell elements +• “Shell elements: overview,” Section 29.6.1 +• “Choosing a shell element,” Section 29.6.2 +• “Defining the initial geometry of conventional shell elements,” Section 29.6.3 +• “Shell section behavior,” Section 29.6.4 +• “Using a shell section integrated during the analysis to define the section behavior,” Section 29.6.5 +• “Using a general shell section to define the section behavior,” Section 29.6.6 +• “Three-dimensional conventional shell element library,” Section 29.6.7 +• “Continuum shell element library,” Section 29.6.8 +• “Axisymmetric shell element library,” Section 29.6.9 +• “Axisymmetric shell elements with nonlinear, asymmetric deformation,” Section 29.6.10 +29.6.1 +SHELL ELEMENTS: OVERVIEW +Abaqus offers a wide variety of shell modeling options. +Overview +Shell modeling consists of: +• choosing the appropriate shell element type (“Choosing a shell element,” Section 29.6.2); +• defining the initial geometry of the surface (“Defining the initial geometry of conventional shell +elements,” Section 29.6.3); +• determining whether or not numerical integration is needed to define the shell section behavior +(“Shell section behavior,” Section 29.6.4); and +• defining the shell section behavior (“Using a shell section integrated during the analysis to define the +section behavior,” Section 29.6.5, or “Using a general shell section to define the section behavior,” +Section 29.6.6). +Conventional shell versus continuum shell +Shell elements are used to model structures in which one dimension, the thickness, is significantly smaller +than the other dimensions. Conventional shell elements use this condition to discretize a body by defining +the geometry at a reference surface. In this case the thickness is defined through the section property +definition. Conventional shell elements have displacement and rotational degrees of freedom. +In contrast, continuum shell elements discretize an entire three-dimensional body. The thickness is +determined from the element nodal geometry. Continuum shell elements have only displacement degrees +of freedom. From a modeling point of view continuum shell elements look like three-dimensional +continuum solids, but their kinematic and constitutive behavior is similar to conventional shell elements. +Figure 29.6.1–1 illustrates the differences between a conventional shell and a continuum shell +element. +Conventions +The conventions that are used for shell elements are defined below. +Definition of local directions on the surface of a shell in space +The default local directions used on the surface of a shell for definition of anisotropic material properties +and for reporting stress and strain components are defined in “Conventions,” Section 1.2.2. You can +define other directions by defining a local orientation , except for +SAX1, SAX2, and SAX2T elements (“Axisymmetric shell element library,” Section 29.6.9), which +do not support orientations. A spatially varying local coordinate system defined with a distribution +(“Distribution definition,” Section 2.8.1) can be assigned to shell elements. For SAXA elements +structural body +being modeled +Conventional shell model - +geometry is specified at the reference surface; +thickness is defined by section property. +displacement and rotation +degrees of freedom +Finite Element Model +Element +displacement +degrees of freedom only +Continuum shell model - +full 3-D geometry is specified; +element thickness is defined by nodal geometry. +Figure 29.6.1–1 Conventional versus continuum shell element. +(“Axisymmetric shell elements with nonlinear, asymmetric deformation,” Section 29.6.10) any +anisotropic material definition must be symmetric with respect to the r–z plane at +and . +In large-deformation (geometrically nonlinear) analysis these local directions rotate with the +average rotation of the surface at that point. They are output as directions in the current configuration +except in the shell elements in Abaqus/Standard that provide only large rotation but small strain +(element types STRI3, STRI65, S4R5, S8R, S8RT, S8R5, S9R5—see “Choosing a shell element,” +Section 29.6.2), where they are output as directions in the reference configuration. Therefore, in +geometrically nonlinear analysis, when displaying these directions or when displaying principal values +of stress, strain, or section forces or moments in Abaqus/CAE, the current (deformed) configuration +should be used except for the small-strain elements in Abaqus/Standard, for which the reference +configuration should be used. +Positive normal definition for conventional shell elements +The “top” surface of a conventional shell element is the surface in the positive normal direction and is +referred to as the positive (SPOS) face for contact definition. The “bottom” surface is in the negative +direction along the normal and is referred to as the negative (SNEG) face for contact definition. Positive +and negative are also used to designate top and bottom surfaces when specifying offsets of the reference +surface from the shell’s midsurface. +The positive normal direction defines the convention for pressure load application and output of +quantities that vary through the thickness of the shell. A positive pressure load applied to a shell element +produces a load that acts in the direction of the positive normal. +Three-dimensional conventional shells +For shells in space the positive normal is given by the right-hand rule going around the nodes of the +element in the order that they are specified in the element definition. See Figure 29.6.1–2. +face SPOS +face SNEG +Figure 29.6.1–2 Positive normals for three-dimensional conventional shells. +Axisymmetric conventional shells +For axisymmetric conventional shells (including the SAXA1n and SAXA2n elements that allow for +nonsymmetric deformation) the positive normal direction is defined by a 90° counterclockwise rotation +from the direction going from node 1 to node 2. See Figure 29.6.1–3. +face SPOS +face SNEG +Figure 29.6.1–3 Positive normal for conventional axisymmetric shells. +Normal definition for continuum shell elements +Figure 29.6.1–4 illustrates the key geometrical features of continuum shells. +It is important that the +continuum shells are oriented properly, since the behavior in the thickness direction is different from that +in the in-plane directions. By default, the element top and bottom faces and, hence, the element normal, +stacking direction, and thickness direction are defined by the nodal connectivity. For the triangular in- +plane continuum shell element (SC6R) the face with corner nodes 1, 2, and 3 is the bottom face; and the +face with corner nodes 4, 5, and 6 is the top face. For the quadrilateral continuum shell element (SC8R) +thickness +direction +top face +bottom face +thickness +direction +Figure 29.6.1–4 Default normals and thickness direction for continuum shell elements. +the face with corner nodes 1, 2, 3, and 4 is the bottom face; and the face with corner nodes 5, 6, 7, and 8 is +the top face. The stacking direction and thickness direction are both defined to be the direction from the +bottom face to the top face. Additional options for defining the element thickness direction, including +one option that is independent of nodal connectivity, are presented below. +Surfaces on continuum shells can be defined by specifying the face identifiers S1–S6 identifying the +individual faces as defined in “Continuum shell element library,” Section 29.6.8. Free surface generation +can also be used. +Pressure loads applied to faces P1–P6 are defined similar to continuum elements, with a positive +pressure directed into the element. +Defining the stacking and thickness direction +By default, the continuum shell stacking direction and thickness direction are defined by the nodal +connectivity as illustrated in Figure 29.6.1–4. Alternatively, you can define the element stacking +direction and thickness direction by either selecting one of the element’s isoparametric directions or by +using an orientation definition. +Defining the stacking and thickness direction based on the element isoparametric direction +You can define the element stacking direction to be along one of the element’s isoparametric directions +. The 8-node hexahedron continuum shell has three +possible stacking directions; the 6-node in-plane triangular continuum shell has only one stack direction, +which is in the element 3-isoparametric direction. The default stacking direction is 3, providing the same +thickness and stacking direction as outlined in the previous section. +To obtain a desired thickness direction, the choice of the isoparametric direction depends on +the element connectivity. For a mesh-independent specification, use an orientation-based method as +described below. +Input File Usage: +Use one of the following options to define the element stacking direction based +on the element’s isoparametric directions: +F6 +F2 +F5 +F4 +F3 +F1 +Stack direction +F2 +F5 +F3 +F1 +F4 +Stack direction +Stack direction = 1 +from face 6 to face 4 +Stack direction = 2 +from face 3 to face 5 +Stack direction = 3 +from face 1 to face 2 +Stack direction = 3 +from face 1 to face 2 +Figure 29.6.1–5 Stack directions for SC6R and SC8R elements. +Abaqus/CAE Usage: +*SHELL SECTION, STACK DIRECTION=n +*SHELL GENERAL SECTION, STACK DIRECTION=n +where n = 1, 2, or 3. +Use the following option to define the stacking direction based on the element’s +isoparametric directions if the continuum shell is defined using a composite +layup: +Property module: Create Composite Layup: select Continuum Shell +as the Element Type: Stacking Direction: Element direction 1, +Element direction 2, or Element direction 3 +Use the following option to define the stacking direction based on the element’s +isoparametric directions if the continuum shell is defined using a composite +shell section: +Assign→Material Orientation: select regions: Use Default +Orientation or Other Method: Stacking Direction: Element +isoparametric direction 1, Element isoparametric direction 2, +or Element isoparametric direction 3 +Defining the stacking and thickness direction based on an orientation definition +Alternatively, you can define the element stacking direction based on a local orientation definition. +For shell elements the orientation definition defines an axis about which the local 1 and 2 material +directions may be rotated. This axis also defines an approximate normal direction. The element stacking +and thickness directions are defined to be the element isoparametric direction that is closest to this +approximate normal . +“The pinched cylinder problem,” Section 2.3.2 of the Abaqus Benchmarks Manual, and “LE3: +Hemispherical shell with point loads,” Section 4.2.3 of the Abaqus Benchmarks Manual, illustrate the use +Cohesive section, stack direction +based on cylor1 +' +(10, 0, 0) +Local cylindrical orientation cylor1: +a = 0, 0, 0 +b = 10, 0, 0 +' +2 +Global +(0, 0, 0) +Abaqus selects the isoparametric direction  that is +closest to the 1st (i.e., x , or radial) axis, at the center. +Figure 29.6.1–6 Example illustrating the use of a cylindrical system to define the stacking direction. +of a cylindrical and spherical orientation system, respectively, to define the stack and thickness direction +independent of nodal connectivity. +Input File Usage: +Use one of the following options to define the element stacking direction based +on a user-defined orientation: +*SHELL SECTION, STACK DIRECTION=ORIENTATION, +ORIENTATION=name +*SHELL GENERAL SECTION, STACK DIRECTION=ORIENTATION, +ORIENTATION=name +Abaqus/CAE Usage: +Use the following option to define the stacking direction based on a user-defined +orientation if the continuum shell is defined using a composite layup: +Property module: Create Composite Layup: select Continuum Shell as +the Element Type: Stacking Direction: Layup orientation +Use the following option to define the stacking direction based on a user-defined +orientation if the continuum shell is defined using a composite shell section: +Assign→Material Orientation: select regions: Use Default +Orientation or Other Method: Stacking Direction: Normal +direction of material orientation +Verifying the element stack and thickness direction +You can verify the element stack and thickness direction visually in Abaqus/CAE by either contouring +the element section thickness or plotting the material axis. Generally, the in-plane dimensions are +significantly larger than the element thickness. By contouring the shell section thickness, output variable +STH, you can easily verify that all elements are oriented appropriately and have the correct thickness. +If the element is oriented improperly, one of the in-plane dimensions will become the element section +thickness, resulting in a discontinuous contour plot. +Alternatively, you can plot the material axis to verify that the 3-axis points in the desired normal +direction. If the element is oriented improperly, one of the in-plane axes (either the 1- or 2-axis) would +point in the normal direction. +Numbering of section points through the shell thickness +The section points through the thickness of the shell are numbered consecutively, starting with point 1. +For shell sections integrated during the analysis, section point 1 is exactly on the bottom surface of the +shell if Simpson’s rule is used, and it is the point that is closest to the bottom surface if Gauss quadrature +is used. For general shell sections, section point 1 is always on the bottom surface of the shell. +For a homogeneous section the total number of section points is defined by the number of integration +points through the thickness. For shell sections integrated during the analysis, you can define the number +of integration points through the thickness. The default is five for Simpson’s rule and three for Gauss +quadrature. For general shell sections, output can be obtained at three section points. +For a composite section the total number of section points is defined by adding the number of +integration points per layer for all of the layers. For shell sections integrated during the analysis, you +can define the number of integration points per layer. The default is three for Simpson’s rule and two for +Gauss quadrature. For general shell sections, the number of section points for output per layer is three. +Default output points +In Abaqus/Standard the default output points through the thickness of a shell section are the points that +are on the bottom and top surfaces of the shell section (for integration with Simpson’s rule) or the points +that are closest to the bottom and top surfaces (for Gauss quadrature). For example, if five integration +points are used through a single layer shell, output will be provided for section points 1 (bottom) and 5 +(top). +In Abaqus/Explicit all section points through the thickness of a shell section are written to the results +file for element output requests. +29.6.2 +CHOOSING A SHELL ELEMENT +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Shell elements: overview,” Section 29.6.1 +• “Three-dimensional conventional shell element library,” Section 29.6.7 +• “Continuum shell element library,” Section 29.6.8 +• “Axisymmetric shell element library,” Section 29.6.9 +• “Axisymmetric shell elements with nonlinear, asymmetric deformation,” Section 29.6.10 +• “Creating homogeneous shell sections,” Section 12.13.6 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Creating composite shell sections,” Section 12.13.7 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +The Abaqus/Standard shell element library includes: +• elements for three-dimensional shell geometries; +• elements for axisymmetric geometries with axisymmetric deformation; +• elements for axisymmetric geometries with general deformation that is symmetric about one plane; +• elements for stress/displacement, heat +transfer, and fully coupled temperature-displacement +analysis; +• general-purpose elements, as well as elements specifically suitable for the analysis of “thick” or +“thin” shells; +• general-purpose, three-dimensional, first-order elements that use reduced or full integration; +• elements that account for finite membrane strain; +• elements that use five degrees of freedom per node where possible, as well as elements that always +use six degrees of freedom per node; and +• continuum shell elements. +The Abaqus/Explicit shell element library includes: +• general-purpose three-dimensional elements to model “thick” or “thin” shells that account for finite +membrane strains; +• small-strain elements; +• fully coupled temperature-displacement analysis elements; +• an element for axisymmetric geometries with axisymmetric deformation; and +• continuum shell elements. +Naming convention +The naming convention for shell elements depends on the element dimensionality. +Three-dimensional shell elements +Three-dimensional shell elements in Abaqus are named as follows: +8 R 5 W +warping considered in small-strain formulation +in ABAQUS/Explicit (optional) +optional: 5 dof (5); +coupled temperature-displacement (T); +small-strain formulation in ABAQUS/Explicit (S) +reduced integration (optional) +number of nodes +conventional stress/displacement shell (S); +continuum stress/displacement shell (SC); +triangular stress/displacement thin shell (STRI); +heat transfer shell (DS) +For example, S4R is a 4-node, quadrilateral, stress/displacement shell element with reduced integration +and a large-strain formulation; and SC8R is an 8-node, quadrilateral, first-order interpolation, +stress/displacement continuum shell element with reduced integration. +Axisymmetric shell elements +Axisymmetric shell elements in Abaqus are named as follows: +AX 2 +Optional: +coupled temperature-displacement (T); +number of Fourier modes (1, 2, 3, or 4) +order of interpolation +axisymmetric (AX); axisymmetric with +nonlinear, asymmetric deformation (AXA) +stress/displacement shell (S); +heat transfer shell (DS) +For example, DSAX1 is an axisymmetric, heat transfer shell element with first-order interpolation. +Conventional stress/displacement shell elements +The conventional stress/displacement shell elements in Abaqus can be used in three-dimensional +or axisymmetric analysis. +In Abaqus/Standard they use linear or quadratic interpolation and allow +mechanical and/or thermal (uncoupled) loading; in Abaqus/Explicit they use linear interpolation and +allow mechanical loading. These elements can be used in static or dynamic procedures. Some elements +include the effect of transverse shear deformation and thickness change, while others do not. Some +elements allow large rotations and finite membrane deformation, while others allow large rotations but +small strains. +Interpolation of temperature and field variables in stress/displacement shell elements +The value of temperatures at the integration locations in the surface of the shell used to compute +the thermal stresses depends on whether first-order or second-order elements are used. An average +temperature is used at the integration location in linear elements so that the thermal strain is constant +throughout the shell surface. A linearly varying temperature distribution is used in higher-order shell +elements. Field variables in stress/displacement shell elements are interpolated the same way as +temperatures. +Stress/displacement continuum shell elements +The stress/displacement continuum shell elements in Abaqus can be used in three-dimensional analysis. +Continuum shells discretize an entire three-dimensional body, unlike conventional shells which discretize +a reference surface . These elements have displacement +degrees of freedom only, use linear interpolation, and allow mechanical and/or thermal (uncoupled) +loading for static and dynamic procedures. The continuum shell elements are general-purpose shells that +allow finite membrane deformation and large rotations and, thus, are suitable for nonlinear geometric +analysis. These elements include the effects of transverse shear deformation and thickness change. +Continuum shell elements employ first-order layer-wise composite theory, and estimate through- +thickness section forces from the initial elastic moduli. Unlike conventional shells, continuum shell +elements can be stacked to provide more refined through-thickness response. Stacking continuum shell +elements allows for a richer transverse shear stress and force prediction. +Although continuum shell elements discretize a three-dimensional body, care should be taken to +verify whether the overall deformation sustained by these elements is consistent with their layer-wise +plane stress assumption; that is, the response is bending dominated and no significant thickness change +is observed (i.e., approximately less than 10% thickness change). Otherwise, regular three-dimensional +solid elements (“Three-dimensional solid element library,” Section 28.1.4) should be used. Furthermore, +the thickness strain mode may yield a small stable time increment for thin continuum shell elements in +Abaqus/Explicit . +Coupled temperature-displacement continuum shell elements +The coupled temperature-displacement continuum shell elements in Abaqus have continuum shell +geometry and use linear interpolation for the geometry and displacements. The temperature is +interpolated linearly as well. The thermal formulation is similar to that used for three-dimensional +coupled temperature-displacement solid elements with reduced integration, for which the temperature +variation is trilinear elements,” Section 28.1.1). The temperatures at the section +points through the thickness are interpolated linearly from the temperatures at the nodes. +Heat transfer shell elements +These elements, available only in Abaqus/Standard and only with conventional shell element geometry, +are intended to model heat transfer in shell-type structures. They provide the values of temperature at +a number of points through the thickness at each shell node. This output can be input directly to the +equivalent stress analysis shell element for sequentially coupled thermal-stress analysis (“Sequentially +coupled thermal-stress analysis,” Section 16.1.2). +Temperature variation through the shell thickness +The temperature variation is assumed to be piecewise quadratic through the thickness, while the +interpolation on the reference surface of the shell is the same as that of the corresponding stress +elements. For shell sections integrated during the analysis (“Using a shell section integrated during the +analysis to define the section behavior,” Section 29.6.5) you can specify the number of section points +used for cross-section integration and thickness-direction temperature interpolation at each node. Only +Simpson’s rule can be used for integration through the shell thickness. +The temperature on the bottom surface of the shell (the surface in the negative direction along +the shell normal—see “Defining the initial geometry of conventional shell elements,” Section 29.6.3) is +degree of freedom 11. The temperature on the top surface is degree of freedom +. A maximum +of 20 temperature degrees of freedom can exist at a node. For a single-layer shell +is the total number +of integration points used through the shell section. If a single section point is used for the cross-section +integration, there is no temperature variation through the thickness of the shell and the temperature of +the entire shell cross-section is degree of freedom 11. For a multi-layered shell the temperature at the +top of each layer is the same as the temperature at the bottom of the next layer. Therefore, +( +> 1) is the number of integration points used in layer l. If +where +is equal to the number +of composite layers. In this case, there is no temperature variation through the thickness of the shell, and +the temperature of the entire composite is degree of freedom 11. The internal energy storage and heat +conduction terms for shells are integrated in the same way as in the corresponding continuum elements + elements,” Section 28.1.1). +=1, +Using shells in a thermal-stress analysis +To use the temperatures that are saved in the Abaqus/Standard results file directly as input to a thermal- +stress analysis, the mesh and the specification of the number of temperature points in the shell sections +must be the same in the heat transfer and the stress analysis models. In addition, multi-layered heat +transfer shell elements must have the same number of integration points in each layer. +Coupled temperature-displacement shell elements +The coupled temperature-displacement shell elements available in Abaqus have conventional shell +element geometry and use linear or quadratic interpolation for the geometry and displacements. +The temperature is interpolated linearly from the corner or end nodes; the lower-order temperature +interpolation in quadratic shells is chosen to give the same interpolation order for thermal strain, which +is proportional to temperature, as for total strain. All terms in the governing equations are integrated in +the reference surface of the shell using a conventional Gauss scheme; Simpson’s rule is used to integrate +through the shell thickness. +Temperature variation through the shell thickness +The temperature variation through the shell thickness is assumed to be piecewise quadratic and is +interpolated from temperatures at a series of points through the thickness of the shell at each node. The +number of temperature values to be used at each node is determined by the number of integration points +that you specify in the shell section definition . Up to a +maximum of 20 temperature values are stored as degrees of freedom 11, 12, 13, etc. (up to degree of +freedom 30) in a manner that is identical to that used for heat transfer shell elements . +“Thick” versus “thin” conventional shell elements +Abaqus includes general-purpose, conventional shell elements as well as conventional shell elements that +are valid for thick and thin shell problems. See below for a discussion of what constitutes a “thick” or +“thin” shell problem. This concept is relevant only for elements with displacement degrees of freedom. +The general-purpose, conventional shell elements provide robust and accurate solutions to most +applications and will be used for most applications. However, in certain cases, for specific applications +in Abaqus/Standard, enhanced performance may be obtained with the thin or thick conventional shell +elements; for example, if only small strains occur and five degrees of freedom per node are desired. +The continuum shell elements can be used for any thickness; however, thin continuum shell +elements may result in a small stable time increment in Abaqus/Explicit. +General-purpose conventional shell elements +These elements allow transverse shear deformation. They use thick shell theory as the shell thickness +increases and become discrete Kirchhoff thin shell elements as the thickness decreases; the transverse +shear deformation becomes very small as the shell thickness decreases. +Element types S3/S3R, S3RS, S4, S4R, S4RS, S4RSW, SAX1, SAX2, SAX2T, SC6R, and SC8R +are general-purpose shells. +Thick conventional shell elements +In Abaqus/Standard thick shells are needed in cases where transverse shear flexibility is important and +second-order interpolation is desired. When a shell is made of the same material throughout its thickness, +this occurs when the thickness is more than about 1/15 of a characteristic length on the surface of the +shell, such as the distance between supports for a static case or the wavelength of a significant natural +mode in dynamic analysis. +Abaqus/Standard provides element types S8R and S8RT for use only in thick shell problems. +Thin conventional shell elements +In Abaqus/Standard thin shells are needed in cases where transverse shear flexibility is negligible and the +Kirchhoff constraint must be satisfied accurately (i.e., the shell normal remains orthogonal to the shell +reference surface). For homogeneous shells this occurs when the thickness is less than about 1/15 of a +characteristic length on the surface of the shell, such as the distance between supports or the wave length +of a significant eigenmode. However, the thickness may be larger than 1/15 of the element length. +Abaqus/Standard has two types of thin shell elements: +those that solve thin shell theory (the +Kirchhoff constraint is satisfied analytically) and those that converge to thin shell theory as the thickness +decreases (the Kirchhoff constraint is satisfied numerically). +• The element that solves thin shell theory is STRI3. STRI3 has six degrees of freedom at the nodes +and is a flat, faceted element (initial curvature is ignored). If STRI3 is used to model a thick shell +problem, the element will always predict a thin shell solution. +• The elements that impose the Kirchhoff constraint numerically are S4R5, STRI65, S8R5, S9R5, +SAXA1n, and SAXA2n. These elements should not be used for applications in which transverse +shear deformation is important. +If these elements are used to model a thick shell problem, the +elements may predict inaccurate results. +Finite-strain versus small-strain shell elements +Abaqus has both finite-strain and small-strain shell elements. This concept is relevant only for elements +with displacement degrees of freedom. +Finite-strain shell elements +Element types S3/S3R, S4, S4R, SAX1, SAX2, SAX2T, SAXA1n, and SAXA2n account for finite +membrane strains and arbitrarily large rotations; therefore, they are suitable for large-strain analysis. +The underlying formulation is described in “Axisymmetric shell elements,” Section 3.6.2 of the Abaqus +Theory Manual; “Finite-strain shell element formulation,” Section 3.6.5 of the Abaqus Theory Manual; +and “Axisymmetric shell element allowing asymmetric loading,” Section 3.6.7 of the Abaqus Theory +Manual. +Continuum shell elements SC6R and SC8R account for finite membrane strains, arbitrary large +rotation, and allow for changes in thickness, making them suitable for large-strain analysis. Computation +of the change in thickness is based on the element nodal displacements, which in turn are computed from +an effective elastic modulus defined at the beginning of an analysis. +Small-strain shell elements +In Abaqus/Standard the three-dimensional “thick” and “thin” element types STRI3, S4R5, STRI65, S8R, +S8RT, S8R5, and S9R5 provide for arbitrarily large rotations but only small strains. The change in +thickness with deformation is ignored in these elements. +In Abaqus/Explicit element types S3RS, S4RS, and S4RSW are provided for shell problems +with small membrane strains and arbitrarily large rotations. Many impact dynamics analyses fall +within this class of problems, including those of shell structures undergoing large-scale buckling +behavior but relatively small amounts of membrane stretching and compression. Although solution +the small-strain shell elements in +accuracy may degrade as membrane strains become large, +Abaqus/Explicit provide a computationally efficient alternative to the finite-membrane-strain elements +for appropriate applications. The underlying formulation is described in “Small-strain shell elements in +Abaqus/Explicit,” Section 3.6.6 of the Abaqus Theory Manual. +Change of shell thickness +Thickness change is considered only in geometrically nonlinear analyses. For conventional shells, stress +in the thickness direction is zero and the strain results only from the Poisson’s effect. For continuum +shells, the stress in the thickness direction may not be zero and may cause additional strain beyond that +due to Poisson’s effect. The thickness strain due to Poisson’s effect is referred as the “Poisson strain,” +and any additional strain beyond the “Poisson strain” is referred to as the “effective thickness strain.” +For shell elements in Abaqus/Explicit defined by integrating the section during the analysis, the +Poisson strain is calculated by enforcing the plane stress condition either at the individual material points +in the section and then integrating the Poisson strain from these material points, or at the integration +station for the whole section using a “section Poisson’s ratio.” For shell elements in Abaqus/Standard +only the section Poisson’s ratio method is available. For shell elements defined by general shell sections, +only the section Poisson’s ratio method is applicable. +See “Defining the Poisson strain in shell elements in the thickness direction” in “Using a shell +section integrated during the analysis to define the section behavior,” Section 29.6.5, and “Defining the +Poisson strain in shell elements in the thickness direction” in “Using a general shell section to define the +section behavior,” Section 29.6.6, for details. +Thickness direction stress in continuum shell elements +The thickness direction stress is computed by penalizing the effective thickness strain with a constant +“thickness modulus.” The thickness modulus used for a single layer shell element with an elastic or +elastic-plastic material is twice the in-plane elastic shear modulus. In the case of a composite shell with +each layer either an elastic or elastic-plastic material, the thickness modulus is computed as the thickness- +weighted harmonic mean of the contributions from the individual layers: +where +thickness of layer +the material definition for layer +is the thickness modulus, +, and +in the initial configuration. +is the layer index, +is the relative +is the number of layers, +is twice the initial in-plane elastic shear modulus based on +See “Defining the thickness modulus in continuum shell elements” in “Using a shell section +integrated during the analysis to define the section behavior,” Section 29.6.5, and “Defining the +thickness modulus in continuum shell elements” in “Using a general shell section to define the section +behavior,” Section 29.6.6, for details. +Five degree of freedom shells versus six degree of freedom shells +Two types of three-dimensional conventional shell elements are provided in Abaqus/Standard: ones that +use five degrees of freedom (three displacement components and two in-surface rotation components) +where possible and ones that use six degrees of freedom (three displacement components and three +rotation components) at all nodes. +The elements that use five degrees of freedom (S4R5, STRI65, S8R5, S9R5) can be more +economical. However, they are available only as “thin” shells (they cannot be used as “thick” shells) +and cannot be used for finite-strain applications (although they model large rotations with small strains +accurately). In addition, output for the five degree of freedom shell elements is restricted as follows: +• At nodes that use the two in-surface rotation components, the values of these in-surface rotations +are not available for output. +• When output variable NFORC is requested, moments corresponding to the in-surface rotations are +not available for output. +When five degree of freedom shell elements are used, Abaqus/Standard will automatically switch to +using three global rotation components at any node that: +• has kinematic boundary conditions applied to rotational degrees of freedom, +• is used in a multi-point constraint (“General multi-point constraints,” Section 34.2.2) that involves +rotational degrees of freedom, +• is shared with a beam element or a shell element that uses the three global rotation components at +all nodes, +• is on a fold line in the shell (that is, on a line where shells with different surface normals come +together), or +• is loaded with moments. +In all elements that use three global rotation components at all nodes (whether activated as described +above or always present), a singularity exists at any node where the surface is assumed to be continuously +curved: three rotation components are used, but only two are actively associated with stiffness. A small +stiffness is associated with the rotation about the normal to avoid this difficulty. The default stiffness +values used are sufficiently small such that the artificial energy content is negligible. In some rare cases +this stiffness may need to be altered. You can define a scaling factor for this stiffness, as described in +“Using a shell section integrated during the analysis to define the section behavior,” Section 29.6.5, and +“Using a general shell section to define the section behavior,” Section 29.6.6. +Reduced integration +Many shell element types in Abaqus use reduced (lower-order) integration to form the element stiffness. +The mass matrix and distributed loadings are still integrated exactly. Reduced integration usually +provides more accurate results (provided the elements are not distorted or loaded in in-plane bending) +and significantly reduces running time, especially in three dimensions. +When reduced integration is used with first-order (linear) elements, hourglass control is required. +Therefore, when using first-order reduced-integration elements, you must check if hourglassing is +occurring; if it is, a finer mesh may be required or concentrated loads must be distributed over multiple +nodes. The second-order reduced-integration elements available in Abaqus/Standard generally do not +have the same difficulty and are recommended in cases when the solution is expected to be smooth. +First-order elements are recommended when large strains or very high strain gradients are expected. +Specifying section controls for shell elements +In Abaqus/Standard you can specify nondefault hourglass control parameters for shell elements. +In +Abaqus/Explicit you can specify second-order accuracy in the element formulation, nondefault hourglass +control parameters for S4R, S4RS, and S4RSW elements, or deactivate the drill constraint for S3RS and +S4RS elements. See “Section controls,” Section 27.1.4, for more information. +Input File Usage: +Use the following options in Abaqus/Standard: +*SHELL SECTION or *SHELL GENERAL SECTION +*HOURGLASS STIFFNESS +Use one of the following options in Abaqus/Explicit: +*SHELL SECTION, CONTROLS=name +*SHELL GENERAL SECTION, CONTROLS=name +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Element Controls +Modeling issues +A number of modeling issues must be considered when using shell elements. +Using S3/S3R and S3RS elements +Both S3 and S3R refer to the same 3-node triangular shell element. This element is a degenerated version +of S4R that is fully compatible with S4R and, in Abaqus/Standard, S4. +Element S3RS, available in Abaqus/Explicit, is a degenerated version of S4RS that is fully +compatible with S4RS. +S3/S3R and S3RS provide accurate results in most loading situations. However, because of their +constant bending and membrane strain approximations, high mesh refinement may be required to capture +pure bending deformations or solutions to problems involving high strain gradients. A consequence of +the degenerated element formulation is that the solution changes slightly when the element connectivity +is permuted. +Degenerating elements +Element types S4, S4R, S4R5, S4RS, S8R5, and S9R5 can be degenerated to triangles. However, +for elements S4 (element S4 degenerated to a triangle may exhibit overly stiff response in membrane +deformation), S4R, and S4RS it is recommended that S3R and S3RS be used instead. +The quarter-point technique (moving the midside nodes to the quarter points to give a +singularity for elastic fracture mechanics applications) can be used with the quadratic element types +S8R5 and S9R5 . The accuracy of the element is very +significantly reduced when it is degenerated to a triangle; therefore, this is not recommended except +for special applications, such as fracture. +Element types S8R and S8RT cannot be degenerated to triangles. Element types DS4 and DS8 can +be degenerated to triangles, but it is recommended that DS3 and DS6 elements be used instead. +Modeling with continuum shell elements +Continuum shell elements are similar to continuum solids from a modeling point of view. The element +geometries for the SC6R and SC8R elements are a triangular prism and hexahedron, respectively, with +displacement degrees of freedom only. +Continuum shell elements must be oriented correctly, since these elements have a thickness direction +associated with them. See “Shell elements: overview,” Section 29.6.1, for further details on element +connectivity and orientation. +When classical shell structures (structures in which only the midsurface geometry and kinematic +constraints are provided) are analyzed, care must be taken that appropriate moments and rotations are +specified. For example, a moment may be applied as a force-couple system at the corresponding nodes on +the top and bottom faces. A rotation boundary condition may be specified through a kinematic constraint +to yield the appropriate displacement boundary conditions on the edge of the continuum shell. +Continuum shell elements can be connected directly to first-order continuum solids without any +kinematic transition. An appropriate kinematic transition needs to be provided when conventional shell +elements are connected to continuum shell elements to correctly transfer the moment/rotation at the +reference surface of a conventional shell. Such a transition can be defined with a shell-to-solid coupling +constraint or any other kinematic constraint, such as a surface-based coupling constraint, a multi-point +constraint, or a linear constraint equation. +Using the SC6R element +The SC6R element is a degenerated version of the SC8R element. The SC6R element provides +accurate results in most loading situations. However, because of its constant bending and membrane +strain approximations, high mesh refinement may be required to capture pure bending deformations or +solutions to problems involving high strain gradients. +Modeling contact with continuum shell elements +Continuum shell elements, SC6R and SC8R, allow two-sided contact with changes in the thickness and +are thus suitable for modeling contact. +Stable time increment in Abaqus/Explicit +In Abaqus/Explicit the element stable time increment can be controlled by the continuum shell +element thickness, particularly for thin shell applications. This may increase significantly the number +of increments taken to complete the analysis when compared to the same problem modeled with +conventional shell elements. The small stable time increment size may be mitigated by specifying a +lower stiffness in the thickness direction when appropriate. +Limitations with continuum shell elements +Continuum shell elements cannot be used with the hyperfoam material definitions, nor can they be used +with general shell sections where the section stiffness is provided directly. +Modeling a “sandwich” shell +For a “sandwich” shell, in which parts of the cross-section are made of a softer material (especially when +the layers are nonisotropic so that some layers are weak in particular directions), the transverse shear +flexibility can be important even when the shell is rather thin. Use of general-purpose shell elements +or stacking continuum shell elements is recommended in such cases. See “Shell section behavior,” +Section 29.6.4, for a discussion of transverse shear stiffness in shell elements. +Modeling bending of a thin curved shell in Abaqus/Standard +In Abaqus/Standard curved elements (STRI65, S8R5, S9R5) are preferable for modeling bending of a +thin curved shell. +Element type STRI3 is a flat facet element. If this element is used to model bending of a curved +shell, a dense mesh may be required to obtain accurate results. +Modeling buckling of doubly curved shells in Abaqus/Standard +Element type S8R5 may give inaccurate results for buckling problems of doubly curved shells due to the +fact that the internally defined center node may not be positioned on the actual shell surface. Element +type S9R5 should be used instead. +Using S8R5 in contact analyses +Element type S8R5 is converted automatically to element type S9R5 if a slave surface in a contact pair +is attached to the element. +Applying moments to S9R5 elements +Moments should not be applied to the center node of S9R5 elements. +Using S4 elements +Element type S4 is a fully integrated, general-purpose, finite-membrane-strain shell element. The +element’s membrane response is treated with an assumed strain formulation that gives accurate solutions +to in-plane bending problems, is not sensitive to element distortion, and avoids parasitic locking. +Element type S4 does not have hourglass modes in either the membrane or bending response of +the element; hence, the element does not require hourglass control. The element has four integration +locations per element compared with one integration location for S4R, which makes the element +computationally more expensive. S4 is compatible with both S4R and S3R. S4 can be used for +problems prone to membrane- or bending-mode hourglassing, in areas where greater solution accuracy +In all of these situations S4 will +is required, or for problems where in-plane bending is expected. +outperform element type S4R. S4 cannot be used with the hyperelastic or hyperfoam material definitions +in Abaqus/Standard. +29.6.3 +DEFINING THE INITIAL GEOMETRY OF CONVENTIONAL SHELL ELEMENTS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Shell elements: overview,” Section 29.6.1 +• “Assigning a section,” Section 12.15.1 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +• “Assigning shell/membrane normal directions,��� Section 12.15.5 of the Abaqus/CAE User’s Manual, +in the online HTML version of this manual +Overview +The initial shell geometry: +• must be defined accurately since most shell elements are true curved shell elements; +• is defined by initial normal directions, which can be user-defined or calculated by Abaqus; +• requires that sufficient mesh refinement be used so that the discretized surface accurately represents +the actual surface; and +• can include an offset of the reference surface from the shell’s midsurface. +Defining nodal normals +This discussion applies to conventional shell elements only. The normals of a continuum shell element +are defined by the position of the top and bottom nodes along the shell corner edge . +Conventional shell elements in Abaqus (with the exception of element types S3/S3R, S3RS, S4R, +S4RS, S4RSW, and STRI3) are true curved shell elements; true curved shell elements require special +attention to accurate calculation of the initial curvature of the surface. Shell normals can be defined by +giving the direction cosines of the normal to the surface at all nodes attached to shell elements. These +direction cosines can be entered as the fourth, fifth, and sixth coordinates of each node definition or in +a user-specified normal definition, as described below; see “Normal definitions at nodes,” Section 2.1.4, +for more information. If the user-defined normal differs from the midsurface normal by more than 20°, a +warning message is issued to the data (.dat) file. However, if the angle is more than 160°, the direction +of the midsurface normal is reversed and no warning message is issued. An additional warning message +is issued if the nodal normal deviates more than 10° from the average element normal. +Specifying the same normal at a node for all shell elements attached to the node creates a smooth +shell surface at the node. Define a user-specified normal to introduce a fold line. +If the normals are not defined as part of the node definition or by a user-specified normal, Abaqus +will calculate the normal using the algorithm given below. Since the only information available for +this calculation is the nodal coordinates, it may not define the normal directions accurately. Accurate +definition can be important on edges of the model, especially if they are also symmetry planes, or on +lines where the curvature of the shell changes discontinuously. It is also important when relatively coarse +meshing is used on highly curved shells, since Abaqus may estimate that the change in direction from +one element to its neighbor is so large that it represents a fold line, not a smoothly curving surface. You +are, therefore, advised to enter the direction cosines whenever the shell normal is defined ambiguously +by the nodal coordinates. Failure to do so may lead to inaccurate results. +The normal direction at a node is needed for temperature input and nodal stress output. The direction +is taken from the definitions below for the elements adjacent to the nodes. If this leads to a conflict at +a node, the positive normal direction used at that node will be the one defined by the lowest numbered +element at the node. +Calculation of average nodal normals by Abaqus +If the nodal normal is not defined as part of the node definition, element normal directions at the node +are calculated for all shell and beam elements for which a user-specified normal is not defined (the +“remaining” elements). For shell elements the normal direction is orthogonal to the shell midsurface, as +described in “Shell elements: overview,” Section 29.6.1. For beam elements the normal direction is the +second cross-section direction, as described in “Beam element cross-section orientation,” Section 29.3.4. +The following algorithm is then used to obtain an average normal (or multiple averaged normals) +for the remaining elements that need a normal defined: +1. If a node is connected to more than 30 remaining elements, no averaging occurs and each element +is assigned its own normal at the node. The first nodal normal is stored as the normal defined as +part of the node definition. Each subsequent normal is stored as a user-specified normal. +2. If a node is shared by 30 or fewer remaining elements, the normals for all the elements connected +to the node are computed. Abaqus takes one of these elements and puts it in a set with all the other +elements that have normals within 20° of it. Then: +a. Each element whose normal is within 20° of the added elements is also added to this set (if it +is not yet included). +b. This process is repeated until the set contains for each element in the set all the other elements +whose normals are within 20°. +c. If all the normals in the final set are within 20° of each other, an average normal is computed +for all the elements in the set. If any of the normals in the set are more than 20° out of line +from even a single other normal in the set, no averaging occurs for elements in the set and a +separate normal is stored for each element. +d. This process is repeated until all the elements connected to the node have had normals +computed for them. +e. The first nodal normal is stored as the normal defined as part of the node definition. Each +subsequently generated nodal normal is stored as a user-specified normal. +This algorithm ensures that the nodal averaging scheme has no element order dependence. A simple +example illustrating this process is included below. +Example: shell normal averaging +Consider the three element model in Figure 29.6.3–1. Elements 1, 2, and 3 share a common node, +node 10, with no user-specified normal defined. + 10 + 20 + 50 + 30 + 40 +Figure 29.6.3–1 Three element example for nodal averaging algorithm. +In the first scenario, suppose that at node 10 the normal for element 2 is within 20° of both elements +1 and 3, but the normals for elements 1 and 3 are not within 20° of each other. In this case, each element is +assigned its own normal: one is stored as part of the node definition and two are stored as user-specified +normals. +In the second scenario, suppose that at node 10 the normal for element 2 is within 20° of both +elements 1 and 3 and the normals for elements 1 and 3 are within 20° of each other. In this case, a single +average normal for elements 1, 2, and 3 would be computed and stored as part of the node definition. +In the last scenario, suppose that at node 10 the normal for element 2 is within 20° of element 1 but +the normal of element 3 is not within 20° of either element 1 or 2. In this case, an average normal is +computed and stored for elements 1, and 2 and the normal for element 3 is stored by itself: one is stored +as part of the node definition and the other is stored as a user-specified normal. +Meshing concerns +In a coarse mesh this algorithm may introduce fold lines where the shell is smooth, or it may create a +smooth shell where there should be a fold if the angle of the fold line is less than 20°. Difficulties in large- +displacement shell analysis are sometimes caused by false fold lines introduced by coarse meshing. To +model a smooth shell, the mesh should be refined enough to create unique nodal normals or the normals +must be defined as part of the node definition or by a user-specified normal. To model plates or shells +with fold lines, you should define user-specified normals. +Verifying the normal definitions +Normal definitions can be checked by examining the analysis input file processor output. The direction +cosines of the reference normal associated with a node are listed under the NODE DEFINITIONS output +in the data (.dat) file. User-specified normals are listed under the NORMAL DEFINITIONS output in +the data file. +Offset: reference surface versus midsurface +This discussion applies to conventional shell elements only. Continuum shell elements define a top and +bottom surface around the structural body being modeled. The notion of a shell reference surface is not +applicable for these types of elements. +The reference surface for conventional shell elements is defined by the shell’s nodes and normal +definitions. When modeling with shell elements, the reference surface is typically coincident with the +shell’s midsurface. However, many situations arise in which it is more convenient to define the reference +surface as offset from the shell’s midsurface. For example, CAD surfaces usually represent either the top +or bottom surface of the shell. In this case it may be easier to define the reference surface to be coincident +with the CAD surface and, therefore, offset from the shell’s midsurface. +Shell offsets can also be used to define a more precise surface geometry for contact problems where +shell thickness is important. Another situation where the offset from the midsurface may be important +is when a shell with continuously varying thickness is modeled. In this case if one surface of the shell +is smooth while the other surface is rough, as in some aircraft structures, using the smooth surface as +the reference surface, with an offset of half the shell’s thickness from the midsurface, will represent the +physical geometry more accurately. The use of the midsurface as the reference surface for this case is +much more complicated and may result in an inaccurate model. +You can introduce offsets in the section definitions for both shell sections integrated during the +analysis and general shell sections. The offset value is defined as a fraction of the shell thickness +measured from the shell’s midsurface to the shell’s reference surface. See “Using a shell section +integrated during the analysis to define the section behavior,” Section 29.6.5, and “Using a general shell +section to define the section behavior,” Section 29.6.6, for details. +The degrees of freedom for the shell are associated with the reference surface. All kinematic +quantities, including the element’s area, are calculated there. Any loading in the plane of the reference +surface will, therefore, cause both membrane forces and bending moments when a nonzero offset value +is used. Large offset values for curved shells may also lead to a surface integration error, affecting +the stiffness, mass, and rotary inertia for the shell section. For stability purposes Abaqus/Explicit also +automatically scales the rotary inertia used for shell elements by a factor proportional to the offset +squared, which may result in errors for large offsets. When a large offset from the shell’s midsurface is +necessary, use multi-point constraints instead . +29.6.4 +SHELL SECTION BEHAVIOR +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Shell elements: overview,” Section 29.6.1 +• “Using a shell section integrated during the analysis to define the section behavior,” Section 29.6.5 +• “Using a general shell section to define the section behavior,” Section 29.6.6 +• *SHELL GENERAL SECTION +• *SHELL SECTION +• “Creating homogeneous shell sections,” Section 12.13.6 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Creating composite shell sections,” Section 12.13.7 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +The shell section behavior: +• may or may not require numerical integration over the section; +• can be linear or nonlinear; and +• can be homogeneous or composed of layers of different material. +Methods for defining the shell section behavior +Two methods are provided to define the cross-sectional behavior of a shell. +• Linear moment-bending and force-membrane strain relationships can be defined by using a general +shell section . In +this case all calculations are done in terms of section forces and moments. +In Abaqus/Standard when section properties are given directly (i.e., the section is not associated +with one or more material definitions), strains and stresses are not available for output. However, +when section properties are specified by one or more elastic material layers, strains and stresses are +available when requested for output. In Abaqus/Explicit stresses and strains are not available for +output at the section points whenever a general shell section is used; only section forces, section +moments, and section strains are available for output. +In Abaqus/Standard nonlinear behavior of the shell section, formulated in terms of forces +and moments, can be defined by using a general shell section in conjunction with user subroutine +UGENS. +• Alternatively, a shell section integrated during the analysis allows the cross-sectional +behavior to be calculated by numerical integration through the shell thickness, thus providing +complete generality in material modeling. With this type of section any number of material points +can be defined through the thickness and the material response can vary from point to point. +Both general shell sections and shell sections integrated during the analysis allow layers of different +materials, in different orientations, to be used through the cross-section. +In these cases the section +definition provides the shell thickness, material, and orientation per layer. +For conventional shell elements you can specify an offset of the reference surface from the shell’s +midsurface when the section properties are specified by one or more material layers. When the section +properties are given directly, you cannot directly specify an offset; however, an offset can be included +implicitly in the section properties. A nonzero offset cannot be specified for continuum shell elements. +If a nonzero offset is specified for a continuum shell element, an error message is issued during input file +preprocessing. +Determining whether to use a shell section integrated during the analysis or a general shell +section +When a shell section integrated during the analysis is used, Abaqus uses numerical integration +through the thickness of the shell to calculate the section properties. This type of shell section is generally +used with nonlinear material behavior in the section. It must be used with shells that provide for heat +transfer, since general shell sections do not allow the definition of heat transfer properties. +Use a general shell section if the response of the shell is linear elastic and its behavior is not dependent on changes in +temperature or predefined field variables or, in Abaqus/Standard, if nonlinear behavior in terms of forces +and moments is to be defined in user subroutine UGENS. +Transverse shear stiffness +For all shell elements in Abaqus/Standard that use transverse shear stiffness and for the finite-strain shell +elements in Abaqus/Explicit, the transverse shear stiffness is computed by matching the shear response +for the shell to that of a three-dimensional solid for the case of bending about one axis. For the small- +strain shell elements in Abaqus/Explicit the transverse shear stiffness is based on the effective shear +modulus. +Transverse shear stiffness for shell elements in Abaqus/Standard and finite-strain shell +elements in Abaqus/Explicit +In all shell elements in Abaqus/Standard that are valid for thick shell problems or that enforce the +Kirchhoff constraint numerically (i.e., all shell elements except STRI3) and in the finite-strain shell +elements in Abaqus/Explicit (S3R, S4, S4R, SAX1, SC6R, and SC8R), Abaqus computes the transverse +shear stiffness by matching the shear response for the case of the shell bending about one axis, using a +parabolic variation of transverse shear stress in each layer. The approach is described in “Transverse +shear stiffness in composite shells and offsets from the midsurface,” Section 3.6.8 of the Abaqus +Theory Manual, and generally provides a reasonable estimate of the shear flexibility of the shell. It +also provides estimates of interlaminar shear stresses in composite shells. In calculating the transverse +shear stiffness, Abaqus assumes that the shell section directions are the principal bending directions +(bending about one principal direction does not require a restraining moment about the other direction). +For composite shells with orthotropic layers that are not symmetric about the shell midsurface, the +shell section directions may not be the principal bending directions. In such cases the transverse shear +stiffness is a less accurate approximation and will change if different shell section directions are used. +Abaqus computes the transverse shear stiffness only once at the begining of the analysis based on initial +elastic properties given in the model data. Any changes to the transverse shear stiffness that occur due +to changes in the material stiffness during the analysis are ignored. +Axisymmetric shell elements SAX1 and SAX2; three-dimensional shell elements S3/S3R, S4, +S4R, S8R, and S8RT; and continuum shell elements SC6R and SC8R are based on a first-order shear +deformation theory. Other shell elements—such as S4R5, S8R5, S9R5, STRI65, and SAXAmn—use +the transverse shear stiffness to enforce the Kirchhoff constraints numerically in the thin shell limit. The +transverse shear stiffness is not relevant for shells without displacement degrees of freedom nor is it +relevant for element type STRI3. Although element type S4 has four integration points, the transverse +shear calculation is assumed constant over the element. Higher resolution of the transverse shear may +be obtained by stacking continuum shell elements. +For most shell sections, including layered composite or sandwich shell sections, Abaqus will +calculate the transverse shear stiffness values required in the element formulation. You can override +these default values. The default shear stiffness values are not calculated in some cases if estimates of +shear moduli are unavailable during the preprocessing stage of input; for example, when the material +behavior is defined by user subroutine UMAT, UHYPEL, UHYPER, or VUMAT or, in Abaqus/Standard, +when the section behavior is defined in UGENS. You must define the transverse shear stiffnesses in such +cases. +Transverse shear stiffness definition +The transverse shear stiffness of the section of a shear flexible shell element is defined in Abaqus as +where +are the components of the section shear stiffness ( +refer to the default surface +directions on the shell, as defined in “Conventions,” Section 1.2.2, or to the local directions +associated with the shell section definition); +is a dimensionless factor that is used to prevent the shear stiffness from becoming too large +in thin shells; and +is the actual shear stiffness of the section (calculated by Abaqus or user-defined). +You can specify all three shear stiffness terms ( +the default values defined below. The dimensionless factor +transverse shear stiffness, regardless of the way +); otherwise, they will take +is always included in the calculation of +is obtained. For shell elements of type S4R5, S8R5, +, and +, +S9R5, STRI65, or SAXAn the average of +of force per length. +The dimensionless factor +is defined as +and +is used and +is ignored. The +have units +where A is the area of the element and t is the thickness of the shell. When a general shell section +definition not associated with one or more material definitions is used to define the shell section stiffness, +the thickness of the shell, t, is estimated as +If you do not specify the +, they are calculated as follows. For laminated plates and sandwich +constructions the +are estimated by matching the elastic strain energy associated with shear +deformation of the shell section with that based on piecewise quadratic variation of the transverse shear +stress across the section, under conditions of bending about one axis. For unsymmetric lay-ups the +coupling term +can be nonzero. +When a general shell section is used and the section stiffness is given directly, the +are defined +as +where +is the section stiffness matrix and Y is the initial scaling modulus. +When a user subroutine (for example, UMAT, UHYPEL, UHYPER, or VUMAT) is used to define a +shell element’s material response, you must define the transverse shear stiffness. The definition of an +appropriate stiffness depends on the shell’s material composition and its lay-up; that is, how material is +distributed through the thickness of the cross-section. +The transverse shear stiffness should be specified as the initial, linear elastic stiffness of the shell in +response to pure transverse shear strains. For a homogeneous shell made of a linear, orthotropic elastic +material, where the strong material direction aligns with the element’s local 1-direction, the transverse +shear stiffness should be +and +and +are the material’s shear moduli in the out-of-plane direction. The number 5/6 is the +shear correction coefficient that results from matching the transverse shear energy to that for a +three-dimensional structure in pure bending. For composite shells the shear correction coefficient will +be different from the value for homogeneous ones; see “Transverse shear stiffness in composite shells +and offsets from the midsurface,” Section 3.6.8 of the Abaqus Theory Manual, for a discussion of how +the effective shear stiffness for elastic materials is obtained in Abaqus. +Checking the validity of using shell theory +For linear elastic materials the slenderness ratio, +, where =1 or 2 (no sum on ) and +l is a characteristic length on the surface of the shell, can be used as a guideline to decide if the assumption +that plane sections must remain plane is satisfied and, hence, shell theory is adequate. Generally, if +shell theory will be adequate; for smaller values the membrane strains will not vary linearly through the +section, and shell theory will probably not give sufficiently accurate results. The characteristic length, l, +is independent of the element length and should not be confused with the element’s characteristic length, +. +To obtain the +, you must run a data check analysis using a composite general +and +shell section definition. The +will be printed under the title “TRANSVERSE SHEAR STIFFNESS +FOR THE SECTION” in the data (.dat) file if you request model definition data . +The +will be printed out under the title “SECTION STIFFNESS MATRIX.” +Transverse shear stiffness for small-strain shell elements in Abaqus/Explicit +When a shell section integrated during the analysis is used, the transverse shear stresses for the small- +strain shells in Abaqus/Explicit are assumed to have a piecewise constant distribution in each layer. The +transverse shear force will converge to the correct solution for single or multilayer isotropic sections and +single-layer orthotropic sections. The transverse shear stiffness is approximate for multilayer orthotropic +sections where convergence to the proper transverse shear behavior may not be obtained as shells become +thick and principal material directions deviate from the principal section directions. The finite-strain S4R +element should be used with a shell section integrated during the analysis if accurate through-thickness +transverse shear stress distributions are required for the analysis of composite shells. +The same transverse shear stiffness described for the finite-strain shells is used to calculate the +transverse shear force for the small-strain shells in Abaqus/Explicit when a general shell section is used. +Thus, for this case the transverse shear force for multilayer composite shells will converge to the correct +value for both thin and thick sections. +Bending strain measures +All three-dimensional shell elements in Abaqus use bending strain measures that are approximations to +those of Koiter-Sanders shell theory . As per the Koiter-Sanders theory the displacement field normal to the shell surface does not +produce any bending moments. For example, a purely radial expansion of a cylinder will result in only +membrane stress and strains—there are no variations through the thickness and, hence, no bending. This +applies to both the incremental strain measures for linear elastic materials and the deformation gradient +for hyperelastic materials. +Nodal mass and rotary inertia for composite sections +For composite shell sections Abaqus computes the nodal masses based on an average density through +the section, weighted with respect to the layer thicknesses. This average density is used to compute an +average rotary inertia as if the section were homogeneous. As a consequence, Abaqus does not account +for an unsymmetric distribution of mass: the center of mass is assumed to be at the reference surface of +the shell. For continuum shells the mass is equally distributed to the top and bottom surface nodes. +29.6.5 +USING A SHELL SECTION INTEGRATED DURING THE ANALYSIS TO DEFINE +THE SECTION BEHAVIOR +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Shell elements: overview,” Section 29.6.1 +• “Shell section behavior,” Section 29.6.4 +• *DISTRIBUTION +• *HOURGLASS STIFFNESS +• *SHELL SECTION +• *TRANSVERSE SHEAR STIFFNESS +• “Creating homogeneous shell sections,” Section 12.13.6 of the Abaqus/CAE User’s Manual +• “Creating composite shell sections,” Section 12.13.7 of the Abaqus/CAE User’s Manual +• Chapter 23, “Composite layups,” of the Abaqus/CAE User’s Manual +Overview +A shell section integrated during the analysis: +• is used when numerical integration through the thickness of the shell is required; and +• can be associated with linear or nonlinear material behavior. +Defining a homogeneous shell section +To define a shell made of a single material, use a material definition (“Material data definition,” +Section 21.1.2) to define the material properties of the section and associate these properties with the +section definition. Optionally, you can refer to an orientation (“Orientations,” Section 2.2.5) to be +associated with this material definition. A spatially varying local coordinate system defined with a +distribution (“Distribution definition,” Section 2.8.1) can be assigned to the shell section definition. +Linear or nonlinear material behavior can be associated with the section definition. However, if the +material response is linear, the more economic approach is to use a general shell section . +You specify the shell thickness and the number of integration points to be used through the shell +section . For continuum shell elements the specified shell thickness is used to estimate +certain section properties, such as hourglass stiffness, which are later computed using the actual thickness +computed from the element geometry. +You must associate the section properties with a region of your model. +If the orientation definition assigned to a shell section definition is defined with distributions, +spatially varying local coordinate systems are applied to all shell elements associated with the shell +section. A default local coordinate system (as defined by the distributions) is applied to any shell +element that is not specifically included in the associated distribution. +Input File Usage: +*SHELL SECTION, ELSET=name, MATERIAL=name, +ORIENTATION=name +Abaqus/CAE Usage: +where the ELSET parameter refers to a set of shell elements. +Property module: +Create Section: select Shell as the section Category and +Homogeneous as the section Type: Section integration: During +analysis; Basic: Material: name +Assign→Material Orientation: select regions +Assign→Section: select regions +Defining a composite shell section +You can define a laminated (layered) shell made of one or more materials. You specify the thickness, +the number of integration points , the material, and the orientation (either as a reference to +an orientation definition or as an angle measured relative to the overall orientation definition) for each +layer of the shell. The order of the laminated shell layers with respect to the positive direction of the +shell normal is defined by the order in which the layers are specified. +Optionally, you can specify an overall orientation definition for the layers of a composite shell. +A spatially varying local coordinate system defined with a distribution (“Distribution definition,” +Section 2.8.1) can be used to specify the overall orientation definition for the layers of a composite shell. +For continuum shell elements the thickness is determined from the element geometry and may +vary through the model for a given section definition. Hence, the specified thicknesses are only relative +thicknesses for each layer. The actual thickness of a layer is the element thickness times the fraction of +the total thickness that is accounted for by each layer. The thickness ratios for the layers need not be +given in physical units, nor do the sum of the layer relative thicknesses need to add to one. The specified +shell thickness is used to estimate certain section properties, such as hourglass stiffness, which are later +computed using the actual thickness computed from the element geometry. +Spatially varying thicknesses can be specified on the layers of conventional shell elements using +distributions (“Distribution definition,” Section 2.8.1). A distribution that is used to define layer thickness +must have a default value. The default layer thickness is used by any shell element assigned to the shell +section that is not specifically assigned a value in the distribution. +An example of a section with three layers and three section points per layer is shown in +Figure 29.6.5–1. +The material name specified for each layer refers to a material definition (“Material data definition,” +Section 21.1.2). The material behavior can be linear or nonlinear. +The orientation for each layer is specified by either the name of the orientation (“Orientations,” +Section 2.2.5) associated with the layer or the orientation angle in degrees for the layer. Spatially varying +orientation angles can be specified on a layer using distributions (“Distribution definition,” Section 2.8.1). +Orientation angles, +, are measured positive counterclockwise around the normal and relative to the +overall section orientation. If either of the two local directions from the overall section orientation is +t3 +t2 +t1 +Layer 3 (material 1, orientation 3) +Layer 2 (material 2, orientation 2) +Layer 1 (material 1, orientation 1) +Layers 1 & 3 use the same material in different orientations +n, shell + normal +Specify 3 temperature values read +per layer for stress analysis +Use default of 3 section points +per layer (also define temperature +degrees of freedom for heat +transfer) +Figure 29.6.5–1 Example of composite shell section definition. +not in the surface of the shell, +surface. If you do not specify an overall section orientation, +shell directions . +is applied after the section orientation has been projected onto the shell +is measured relative to the default local +You must associate the section properties with a region of your model. +If the orientation definition assigned to a shell section definition is defined with distributions, +spatially varying local coordinate systems are applied to all shell elements associated with the shell +section. A default local coordinate system (as defined by the distributions) is applied to any shell +element that is not specifically included in the associated distribution. +Unless your model is relatively simple, you will find it increasingly difficult to define your model +using composite shell sections as you increase the number of layers and as you assign different sections to +different regions. It can also be cumbersome to redefine the sections after you add new layers or remove +or reposition existing layers. To manage a large number of layers in a typical composite model, you may +want to use the composite layup functionality in Abaqus/CAE. For more information, see Chapter 23, +“Composite layups,” of the Abaqus/CAE User’s Manual. +Input File Usage: +*SHELL SECTION, ELSET=name, COMPOSITE, ORIENTATION=name +where the ELSET parameter refers to a set of shell elements. +Abaqus/CAE Usage: +Abaqus/CAE uses a composite layup or a composite shell section to define the +layers of a composite shell. +Use the following option for a composite layup: +Property module: Create Composite Layup: select Conventional Shell +or Continuum Shell as the Element Type: Section integration: During +analysis: specify orientations, regions, and materials +Use the following options for a composite shell section: +Property module: +Create Section: select Shell as the section Category and Composite +as the section Type: Section integration: During analysis +Assign→Material Orientation: select regions +Assign→Section: select regions +Defining the shell section integration +Simpson’s rule and Gauss quadrature are provided to calculate the cross-sectional behavior of a shell. +You can specify the number of section points through the thickness of each layer and the integration +method as described below. The default integration method is Simpson’s rule with five points for a +homogeneous section and Simpson’s rule with three points in each layer for a composite section. +The three-point Simpson’s rule and the two-point Gauss quadrature are exact for linear problems. +The default number of section points should be sufficient for routine thermal-stress calculations and +nonlinear applications (such as predicting the response of an elastic-plastic shell up to limit load). For +more severe thermal shock cases or for more complex nonlinear calculations involving strain reversals, +more section points may be required; normally no more than nine section points (using Simpson’s rule) +are required. Gaussian integration normally requires no more than five section points. +Gauss quadrature provides greater accuracy than Simpson’s rule when the same number of section +points are used. Therefore, to obtain comparable levels of accuracy, Gauss quadrature requires fewer +section points than Simpson’s rule does and, thus, requires less computational time and storage space. +Using Simpson’s rule +By default, Simpson’s rule will be used for the shell section integration. The default number of section +points is five for a homogeneous section and three in each layer for a composite section. +Simpson’s integration rule should be used if results output on the shell surfaces or transverse shear +stress at the interface between two layers of a composite shell is required and must be used for heat +transfer and coupled temperature-displacement shell elements. +Input File Usage: +Abaqus/CAE Usage: +*SHELL SECTION, SECTION INTEGRATION=SIMPSON +Use the following option for a composite layup: +Property module: composite layup editor: Section integration: During +analysis, Thickness integration rule: Simpson +Use the following option for a homogeneous or composite shell section: +Property module: shell section editor: Section integration: During +analysis; Basic: Thickness integration rule: Simpson +Using Gauss quadrature +If you use Gauss quadrature for the shell section integration, the default number of section points is three +for a homogeneous section and two in each layer for a composite section. +In Gauss quadrature there are no section points on the shell surfaces; therefore, Gauss quadrature +should be used only in cases where results on the shell surfaces are not required. +Gauss quadrature cannot be used for heat transfer and coupled temperature-displacement shell +elements. +Input File Usage: +Abaqus/CAE Usage: +*SHELL SECTION, SECTION INTEGRATION=GAUSS +Use the following option for a composite layup: +Property module: composite layup editor: Section integration: During +analysis, Thickness integration rule: Gauss +Use the following option for a homogeneous or composite shell section: +Property module: shell section editor: Section integration: During +analysis; Basic: Thickness integration rule: Gauss +Defining a shell offset value for conventional shells +You can define the distance (measured as a fraction of the shell’s thickness) from the shell’s midsurface to +the reference surface containing the element’s nodes . Positive values of the offset are in the positive normal direction . When the offset is set equal to 0.5, the top surface of the +shell is the reference surface. When the offset is set equal to −0.5, the bottom surface is the reference +surface. The default offset is 0, which indicates that the middle surface of the shell is the reference +surface. +You can specify an offset value that is greater in magnitude than 0.5. However, this technique should +be used with caution in regions of high curvature. All kinematic quantities, including the element’s +area, are calculated relative to the reference surface, which may lead to a surface area integration error, +affecting the stiffness and mass of the shell. +In an Abaqus/Standard analysis a spatially varying offset can be defined for conventional shells +using a distribution (“Distribution definition,” Section 2.8.1). The distribution used to define the shell +offset must have a default value. The default offset is used by any shell element assigned to the shell +section that is not specifically assigned a value in the distribution. +An offset to the shell’s top surface is illustrated in Figure 29.6.5–2. The shell offset value is ignored +for continuum shell elements. +Input File Usage: +Use the following option to specify a value for the shell offset: +*SHELL SECTION, OFFSET=offset +The OFFSET parameter accepts a value, a label (SPOS or SNEG), or in an +Abaqus/Standard analysis the name of a distribution that is used to define a +spatially varying offset. Specifying SPOS is equivalent to specifying a value +of 0.5; specifying SNEG is equivalent to specifying a value of −0.5. +SPOS +SPOS +SPOS +SNEG +SNEG +SNEG +Mid surface +a) OFFSET= 0 +Reference surface and +midsurface are coincident +b) OFFSET= −0.5 (SNEG) +Reference surface is +the bottom surface +c) OFFSET= +0.5 (SPOS) +Reference surface is +the top surface +Figure 29.6.5–2 Schematic of shell offset for an offset value of 0.5. +Abaqus/CAE Usage: +Use the following option for a composite layup: +Property module: composite layup editor: Section integration: +During analysis; Offset: choose a reference surface, specify an +offset, or select a scalar discrete field +Use the following option for a shell section assignment: +Property module: Assign→Section: select regions: Section: select a +homogeneous or composite shell section: Definition: select a reference +surface, specify an offset, or select a scalar discrete field +Defining a variable thickness for conventional shells using distributions +You can define a spatially varying thickness for conventional shells using a distribution (“Distribution +definition,” Section 2.8.1). The thickness of continuum shell elements is defined by the element +geometry. +For composite shells the total thickness is defined by the distribution, and the layer thicknesses you +specify are scaled proportionally such that the sum of the layer thicknesses is equal to the total thickness +(including spatially varying layer thicknesses defined with a distribution). +The distribution used to define shell thickness must have a default value. The default thickness is +used by any shell element assigned to the shell section that is not specifically assigned a value in the +distribution. +If the shell thickness is defined for a shell section with a distribution, nodal thicknesses cannot be +used for that section definition. +Input File Usage: +Use the following option to define a spatially varying thickness: +*SHELL SECTION, SHELL THICKNESS=distribution name +Abaqus/CAE Usage: +Use the following option for a conventional shell composite layup: +Property module: composite layup editor: Section integration: During +analysis; Shell Parameters: Shell thickness: Element distribution: +select an analytical field or an element-based discrete field +Use the following option for a homogeneous shell section: +Property module: shell section editor: Section integration: During +analysis; Basic: Shell thickness: Element distribution: select an +analytical field or an element-based discrete field +Use the following option for a composite shell section: +Property module: shell section editor: Section integration: During +analysis; Advanced: Shell thickness: Element distribution: select +an analytical field or an element-based discrete field +Defining a variable nodal thickness for conventional shells +You can define a conventional shell with continuously varying thickness by specifying the thickness of +the shell at the nodes. The thickness of continuum shell elements is defined by the element geometry. +If you indicate that the nodal thicknesses will be specified, for homogeneous shells any constant +shell thickness you specify will be ignored, and the shell thickness will be interpolated from the nodes. +The thickness must be defined at all nodes connected to the element. +For composite shells the total thickness is interpolated from the nodes, and the layer thicknesses you +specify are scaled proportionally such that the sum of the layer thicknesses is equal to the total thickness +(including spatially varying layer thicknesses defined with a distribution). +If the shell thickness is defined for a shell section with a distribution, nodal thicknesses cannot be +used for that section definition. However, if nodal thicknesses are used, you can still use distributions to +define spatially varying thicknesses on the layers of conventional shell elements. +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*NODAL THICKNESS +*SHELL SECTION, NODAL THICKNESS +Use the following option for a conventional shell composite layup: +Property module: composite layup editor: Section integration: +During analysis; Shell Parameters: Nodal distribution: select +an analytical field or a node-based discrete field +Use the following option for a homogeneous shell section: +Property module: shell section editor: Section integration: +During analysis; Basic: Nodal distribution: select an analytical +field or a node-based discrete field +Use the following option for a composite shell section: +Property module: shell section editor: Section integration: During +analysis; Advanced: Nodal distribution: select an analytical +field or a node-based discrete field +Defining the Poisson strain in shell elements in the thickness direction +Abaqus allows for a possible uniform change in the shell thickness in a geometrically nonlinear analysis +. The Poisson’s strain +can be based on a fixed section Poisson’s ratio, either user specified or computed by Abaqus based on +the elastic portion of the material definition. Alternatively, in Abaqus/Explicit the Poisson strain can +be integrated through the section based on the material response at the individual material points in the +section. +By default, Abaqus/Standard computes the Poisson’s strain using a fixed section Poisson’s ratio of +0.5; Abaqus/Explicit uses the material response to compute the Poisson’s strain. See “Finite-strain shell +element formulation,” Section 3.6.5 of the Abaqus Theory Manual, for details regarding the underlying +formulation. +Input File Usage: +Use the following option to specify a value for the effective Poisson’s ratio: +*SHELL SECTION, POISSON= +Use the following option to cause the shell thickness to change based on the +element initial elastic material definition: +*SHELL SECTION, POISSON=ELASTIC +Use the following option (available only in Abaqus/Explicit) to cause the +thickness direction strain under plane stress conditions to be a function of the +membrane strains and the in-plane material properties: +Abaqus/CAE Usage: +*SHELL SECTION, POISSON=MATERIAL +Use the following option for a composite layup: +Property module: composite layup editor: Section integration: +During analysis; Shell Parameters: Section Poisson's ratio: +Use analysis default or Specify value: +Use the following option for a homogeneous or composite shell section: +Property module: shell section editor: Section integration: +During analysis; Advanced: Section Poisson's ratio: Use +analysis default or Specify value: +You cannot specify a shell thickness direction behavior based on the initial +elastic material definition in Abaqus/CAE. +Defining the thickness modulus in continuum shell elements +The thickness modulus is used in computing the stress in the thickness direction . Abaqus computes a +thickness modulus value by default based on the elastic portion of the material definitions in the initial +configuration. Alternatively, you can provide a value. +If the material properties are unavailable during the preprocessing stage of input; for example, when +the material behavior is defined by the fabric material model or user subroutine UMAT or VUMAT, you +must specify the effective thickness modulus directly. +Input File Usage: +Use the following option to define an effective thickness modulus directly: +Abaqus/CAE Usage: +*SHELL SECTION, THICKNESS MODULUS= +Use the following option for a composite layup: +Property module: composite layup editor: Section integration: +During analysis; Shell Parameters: Thickness modulus +specify the thickness properties directly +to +Use the following option for a homogeneous or composite shell section: +Property module: shell section editor: Section integration: +During analysis; Advanced: Thickness modulus +to +specify the thickness properties directly +You cannot specify a shell thickness direction behavior based on the initial +elastic material definition in Abaqus/CAE. +Defining the transverse shear stiffness +You can provide nondefault values of the transverse shear stiffness. You must specify the transverse shear +stiffness in Abaqus/Standard if the section is used with shear flexible shells and the material definitions +used in the shell section do not include linear elasticity (“Linear elastic behavior,” Section 22.2.1). See +“Shell section behavior,” Section 29.6.4, for more information about transverse shear stiffness. +If you do not specify the transverse shear stiffness values, Abaqus will integrate through the section +to determine them. The transverse shear stiffness is precalculated based on the initial elastic material +properties, as defined by the initial temperature and predefined field variables evaluated at the midpoint +of each material layer. This stiffness is not recalculated during the analysis. +For most shell sections, including layered composite or sandwich shell sections, Abaqus will +calculate the transverse shear stiffness values required in the element formulation. You can override +these default values. The default shear stiffness values are not calculated in some cases if estimates of +shear moduli are unavailable during the preprocessing stage of input; for example, when the material +behavior is defined by the fabric material model or by user subroutine UMAT, UHYPEL, UHYPER, or +VUMAT. You must define the transverse shear stiffnesses in such cases except for STRI3 elements. +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*SHELL SECTION +*TRANSVERSE SHEAR STIFFNESS +Use the following option for a composite layup: +Property module: composite layup editor: Section integration: During +analysis; Shell Parameters: toggle on Specify transverse shear +Use the following option for a homogeneous or composite shell section: +Property module: shell section editor: Section integration: During +analysis; Advanced: toggle on Specify transverse shear +Specifying the order of accuracy in the Abaqus/Explicit shell element formulation +In Abaqus/Explicit you can specify second-order accuracy in the shell element formulation. See “Section +controls,” Section 27.1.4, for more information. +Input File Usage: +*SHELL SECTION, CONTROLS=name +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Element Controls +Defining density for conventional shells +You can define additional mass per unit area for conventional shell elements directly in the section +definition. This functionality is similar to the more general functionality of defining a nonstructural +mass contribution The only difference between the +two definitions is that the nonstructural mass contributes to the rotary inertia terms about the midsurface +while the additional mass defined in the section definition does not. +Input File Usage: +Use the following option to define the density directly: +Abaqus/CAE Usage: +*SHELL SECTION, ELSET=name, DENSITY= +Use the following option for a composite layup: +Property module: composite layup editor: Section integration: During +analysis; Shell Parameters: toggle on Density, and enter +Use the following option for a homogeneous or composite shell section: +Property module: shell section editor: Section integration: During +analysis; Advanced: toggle on Density, and enter +Specifying nondefault hourglass control parameters for reduced-integration shell elements +You can specify a nondefault hourglass control formulation or scale factors for elements that use reduced +integration. See “Section controls,” Section 27.1.4, for more information. +In Abaqus/Standard the nondefault enhanced hourglass control formulation is available only for +S4R and SC8R elements. When the enhanced hourglass control formulation is used with composite +shells, the average value of the bulk material properties and the minimum value of the shear material +properties over all the layers are used for computing the hourglass forces and moments. +In Abaqus/Standard you can modify the default values for hourglass control stiffness based on the +default total stiffness approach for elements that use reduced integration and define a scaling factor for +the stiffness associated with the drill degree of freedom (rotation about the surface normal) for elements +that use six degrees of freedom at a node. +The stiffness associated with the drill degree of freedom is the average of the direct components +of the transverse shear stiffness multiplied by a scaling factor. In most cases the default scaling factor +is appropriate for constraining the drill rotation to follow the in-plane rotation of the element. If an +additional scaling factor is defined, the additional scaling factor should not increase or decrease the drill +stiffness by more than a factor of 100.0 for most typical applications. Usually, a scaling factor between +0.1 and 10.0 is appropriate. Continuum shell elements do not use a drill stiffness; hence, the scale factor +is ignored. +There are no hourglass stiffness factors or scale factors for hourglass stiffness for the nondefault +enhanced hourglass control formulation. You can define the scale factor for the drill stiffness for the +nondefault enhanced hourglass control formulation. +Input File Usage: +Use both of the following options to specify a nondefault hourglass control +formulation or scale factors for reduced-integration elements: +*SECTION CONTROLS, NAME=name +*SHELL SECTION, CONTROLS=name +Use both of the following options in Abaqus/Standard to modify the default +values for hourglass control stiffness based on the default total stiffness +approach for reduced-integration elements and to define a scaling factor for +the stiffness associated with the drill degree of freedom (rotation about the +surface normal) for six degree of freedom elements: +*SHELL SECTION +*HOURGLASS STIFFNESS +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Element Controls +Specifying temperature and field variables +You can specify temperatures and field variables for conventional shell elements by defining the value at +the reference surface of the shell and the gradient through the shell thickness or by defining the values at +equally spaced points through each layer of the shell’s thickness. You can specify a temperature gradient +only for elements without temperature degrees of freedom. The temperatures and field variables for +continuum shell elements are defined at the nodes and then interpolated to the section points. +The actual values of the temperatures and field variables are specified as either predefined fields or +initial conditions . +If temperature is to be read as a predefined field from the results file or the output database file of +a previous analysis, the temperature must be defined at equally spaced points through each layer of the +thickness. In addition, the results file must be modified so that the field variable data are stored in record +201. See “Predefined fields,” Section 33.6.1, for additional details. +Defining the value at the reference surface and the gradient through the thickness +You can define the temperature or predefined field by its magnitude on the reference surface of the shell +and the gradient through the thickness. If only one value is given, the magnitude will be constant through +the thickness. +Input File Usage: +Use the following option to specify that the temperatures or predefined fields +are defined by a gradient: +*SHELL SECTION +Use any of the following options to specify the actual values of the temperatures +or predefined fields: +*TEMPERATURE +*FIELD +*INITIAL CONDITIONS, TYPE=TEMPERATURE +*INITIAL CONDITIONS, TYPE=FIELD +Abaqus/CAE Usage: +Use the following option for a composite layup: +Property module: composite layup editor: Section integration: +During analysis; Shell Parameters; Temperature variation: +Linear through thickness +Use the following option for a homogeneous or composite shell section: +Property module: shell section editor: Section integration: During +analysis: Advanced; Temperature variation: Linear through thickness +Only initial temperatures and predefined temperature fields are supported in +Abaqus/CAE. +Load module: Create Predefined Field: Step: initial_step or +analysis_step: choose Other for the Category and Temperature +for the Types for Selected Step +Defining the values at equally spaced points through the thickness +Alternatively, you can define the temperature and field variable values at equally spaced points through +the thickness of a shell or of each layer of a composite shell. +For a sequentially coupled thermal-stress analysis in Abaqus/Standard, the number (n) of equally +spaced points through the thickness of a layer is an odd number when temperature values are obtained +from the results file or the output database file generated by a previous Abaqus/Standard heat transfer +analysis (since only Simpson’s rule can be used for integration through the section in heat transfer +analysis). n may be even or odd if the values are supplied from some other source. +In either case +Abaqus/Standard interpolates linearly between the two closest defined temperature points to find the +temperature values at the section points. +The number of predefined field points through each layer, n, must be the same as the number of +integration points used through the same layer in the analysis from which the temperatures are obtained. +This requirement implies that in the previous analysis each of the layers must have the same number of +integration points. +You specify +in the shell section and +variable value for a given node or node set. +( +temperature or field variable values, where +=1, you specify +> 1) is the value of n. For +is the number of layers +one temperature or field +Input File Usage: +Use the following option to specify that the temperatures or predefined fields +are defined at equally spaced points: +*SHELL SECTION, TEMPERATURE=n +Use any of the following options to specify the actual values of the temperatures +or predefined fields: +*TEMPERATURE +*FIELD +*INITIAL CONDITIONS, TYPE=TEMPERATURE +*INITIAL CONDITIONS, TYPE=FIELD +Use the following option for a composite layup: +Abaqus/CAE Usage: +Property module: composite layup editor: Section integration: +During analysis; Shell Parameters; Temperature variation: +Piecewise linear over n values +Use the following option for a homogeneous or composite shell section: +Property module: shell section editor: Section integration: During analysis: +Advanced; Temperature variation: Piecewise linear over n values +Only initial temperatures and predefined temperature fields are supported in +Abaqus/CAE. +Load module: Create Predefined Field: Step: initial_step or +analysis_step: choose Other for the Category and Temperature +for the Types for Selected Step +Example +An example of this scheme is illustrated in Figure 29.6.5–3 and Figure 29.6.5–4. The following +Abaqus/Standard heat transfer shell section definition corresponds to this example: +*SHELL SECTION, COMPOSITE +, 3, MAT1, ORI1 +, 3, MAT2, ORI2 +, 3, MAT3, ORI3 +Composite shell section + 9 +layer 3 +t3 + 7 +layer 2 +t2 +layer 1 +t1 +⎫⎫⎬⎬⎭⎭ +Use default of 3 section +points per layer +⎫⎫⎬⎬⎭⎭ +Specify 3 temperature points +per layer, shared at layer intersections, +7 total +nT = 3 +nl = 3 +1 + nl (nT -1) = 7 +Figure 29.6.5–3 Defining temperature values at n equally spaced points using Simpson’s rule. +This creates degrees of freedom 11–17 in the heat transfer analysis. Temperatures corresponding to these +degrees of freedom are then read into the stress analysis at the temperature points shown and interpolated +to the section points shown. +Defining a continuous temperature field +In Abaqus/Standard if an element with temperature degrees of freedom other than a shell abuts the bottom +surface of a shell element with temperature degrees of freedom, the temperature field is made continuous +when the elements share nodes. If another element with temperature degrees of freedom abuts the top +surface, separate nodes must be used and a linear constraint equation (“Linear constraint equations,” +Section 34.2.1) must be used to constrain the temperatures to be the same (that is, to give the same value +to the top surface degree of freedom on the shell and degree of freedom 11 on the other element). +For the same reason you must be careful if a different number of temperature points is used in +adjacent shell elements. For compatibility MPCs (“General multi-point constraints,” Section 34.2.2) or +equation constraints are also needed in this case. +composite shell section +layer 3 +t3 +layer 2 +t2 +layer 1 +t1 +⎫⎫⎬⎬⎭⎭ +Use default of 2 section +points per layer +⎫⎫⎬⎬⎭⎭ +Specify 3 temperature points per layer, +shared at layer intersections, +7 total +nT = 3 +nl = 3 +1 + nl (nT -1) = 7 +Figure 29.6.5–4 Defining temperature values at n equally spaced points using Gauss integration. +In Abaqus/Explicit since no thermal MPCs and no thermal equation constraints are available for +degrees of freedom greater than 11, care must be taken when using a different number of temperature +points in adjacent shell elements. This should usually have a localized effect on the temperature +distribution, but it may affect the overall solution for the cases in which the temperature gradient +through the thickness is significant. +In both Abaqus/Standard and Abaqus/Explicit be careful in the models in which the shell’s normals +are reversed. In this case the temperature at the bottom of the shell becomes the temperature at the top +of the adjacent shell. This may have a small impact on the overall solution for the cases in which the +thermal gradient through the thickness is negligible and the temperature variation is mainly in plane. +However, if the temperature gradient through the thickness is significant, it may lead to incorrect results. +Output +In an Abaqus/Standard stress analysis temperature output at the section points can be obtained using the +element variable TEMP. +If the temperature values were specified at equally spaced points through the thickness, output at the +temperature points can be obtained in an Abaqus/Standard stress analysis, as in a heat transfer analysis, +by using the nodal variable NTxx. This nodal output variable is also available in Abaqus/Explicit for +coupled temperature-displacement analyses. The nodal variable NTxx should not be used for output +at the temperature points with the default gradient method. In this case output variable NT should be +requested; NT11 (the reference temperature value) and NT12 (the temperature gradient) will be output +automatically. For continuum shell elements, there is only NT11; all other NTxx are irrelevant. +Other output variables that are relevant for shells are listed in each of the library sections describing +the specific shell elements. For example, stresses, strains, section forces and moments, average section +stresses, section strains, etc. can be output. The section moments are calculated relative to the reference +surface. +29.6.6 +USING A GENERAL SHELL SECTION TO DEFINE THE SECTION BEHAVIOR +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Shell elements: overview,” Section 29.6.1 +• “Shell section behavior,” Section 29.6.4 +• “UGENS,” Section 1.1.34 of the Abaqus User Subroutines Reference Manual +• *DISTRIBUTION +• *HOURGLASS STIFFNESS +• *SHELL GENERAL SECTION +• *TRANSVERSE SHEAR STIFFNESS +• “Creating homogeneous shell sections,” Section 12.13.6 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Creating composite shell sections,” Section 12.13.7 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +• “Creating general shell stiffness sections,” Section 12.13.10 of the Abaqus/CAE User’s Manual, in +the online HTML version of this manual +• Chapter 23, “Composite layups,” of the Abaqus/CAE User’s Manual +Overview +A general shell section: +• is used when numerical integration through the thickness of the shell is not required; +• can be associated with linear elastic material behavior or, in Abaqus/Standard, can invoke user +subroutine UGENS to define nonlinear section properties in terms of forces and moments; +• can be used to model an equivalent shell section for some more complex geometry (for example, +replacing a corrugated shell with an equivalent smooth plate for global analysis); and +• cannot be used with heat transfer and coupled temperature-displacement shells. +Defining the shell section behavior +A general shell section can be defined as follows: +• The section response can be specified by associating the section with a material definition or, in the +case of a composite shell, with several different material definitions. +• The section properties can be specified directly. +• In Abaqus/Standard the section response can be programmed in user subroutine UGENS. +Specifying the equivalent section properties by defining the layers (thickness, material, and +orientation) +You can define the shell section’s mechanical response by specifying the thickness; +the material +reference; and the orientation of the section or, for a composite shell, the orientation of each of its layers. +Abaqus will determine the equivalent section properties. You must associate the section behavior with +a region of your model. +The linear elastic material behavior is defined with a material definition (“Material data definition,” +Section 21.1.2), which may contain linear elastic behavior (“Linear elastic behavior,” Section 22.2.1) +and thermal expansion behavior (“Thermal expansion,” Section 26.1.2). The density (“Density,” +Section 21.2.1) and damping (“Material damping,” Section 26.1.1) behavior can also be specified as +described below; in Abaqus/Explicit the density of the material must be defined. However, no nonlinear +material properties, such as plastic behavior, can be included since Abaqus will precompute the section +response and will not update that response during the analysis. Dependence of the linear elastic material +behavior on temperature or predefined field variables is not allowed. +The shell section response is defined by +No temperature-dependent scaling of the modulus is included. The section forces and moments caused +by thermal strains, +, vary linearly with temperature and are defined by +are the generalized stresses caused by a fully constrained unit temperature rise that result from +where +the user-defined thermal expansion, +is the initial (stress-free) temperature at +this point in the shell (defined by the initial nodal temperatures given as initial conditions; see “Defining +initial temperatures” in “Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1). +is the temperature, and +Defining a shell made of a single linear elastic material +To define a shell made of a single linear elastic material, you refer to the name of a material definition +(“Material data definition,” Section 21.1.2) as described above. Optionally, you can define an orientation +definition to be used with the section (“Orientations,” Section 2.2.5). A spatially varying local coordinate +system defined with a distribution (“Distribution definition,” Section 2.8.1) can be assigned to the shell +In addition, you specify the shell thickness as part of the section definition. For +section definition. +continuum shell elements the specified thickness is used to estimate certain section properties, such as +hourglass stiffness, that are later computed from the element geometry. +You must associate this section behavior with a region of your model. +You can redefine the thickness, offset, section stiffness, and material orientation specified in the +section definition on an element-by-element basis. See “Distribution definition,” Section 2.8.1. +If the orientation definition assigned to a shell section definition is defined with distributions, +spatially varying local coordinate systems are applied to all shell elements associated with the shell +section. A default local coordinate system (as defined by the distributions) is applied to any shell +element that is not specifically included in the associated distribution. +Input File Usage: +*SHELL GENERAL SECTION, ELSET=name, MATERIAL=name, +ORIENTATION=name +Abaqus/CAE Usage: +where the ELSET parameter refers to a set of shell elements. +Property module: +Create Section: select Shell as the section Category and Homogeneous as +the section Type: Section integration: Before analysis; +Basic: Material: name +Assign→Material Orientation: select regions +Assign→Section: select regions +Defining a shell made of layers with different linear elastic material behaviors +You can define a shell made of layers with different linear elastic material behaviors. Optionally, you can +define an orientation definition to be used with the section (“Orientations,” Section 2.2.5). A spatially +varying local coordinate system defined with a distribution (“Distribution definition,” Section 2.8.1) can +be assigned to the shell section definition. +You specify the layer thickness; the name of the material forming this layer (as described above); and +the orientation angle, +, (in degrees) measured positive counterclockwise relative to the specified section +orientation definition. Spatially varying orientation angles can be specified on a layer using distributions +(“Distribution definition,” Section 2.8.1). If either of the two local directions from the specified section +orientation is not in the surface of the shell, +is applied after the section orientation has been projected +onto the shell surface. If you do not specify a section orientation, +is measured relative to the default shell +local directions . The order of the laminated shell layers with respect +to the positive direction of the shell normal is defined by the order in which the layers are specified. +For continuum shell elements the thickness is determined from the element geometry and may +vary through the model for a given section definition. Hence, the specified thicknesses are only relative +thicknesses for each layer. The actual thickness of a layer is the element thickness times the fraction of +the total thickness that is accounted for by each layer. The thickness ratios for the layers need not be +given in physical units, nor do the sum of the layer relative thicknesses need to add to one. The specified +shell thickness is used to estimate certain section properties, such as hourglass stiffness, that are later +computed from the element geometry. +Spatially varying thicknesses can be specified on the layers of conventional shell elements (not +continuum shell elements) using distributions (“Distribution definition,” Section 2.8.1). A distribution +that is used to define layer thickness must have a default value. The default layer thickness is used by +any shell element assigned to the shell section that is not specifically assigned a value in the distribution. +You must associate this section behavior with a region of your model. +If the orientation definition assigned to a shell section definition is defined with distributions, +spatially varying local coordinate systems are applied to all shell elements associated with the shell +section. A default local coordinate system (as defined by the distributions) is applied to any shell +element that is not specifically included in the associated distribution. +Unless your model is relatively simple, you will find it increasingly difficult to define your model +using composite shell sections as you increase the number of layers and as you assign different sections to +different regions. It can also be cumbersome to redefine the sections after you add new layers or remove +or reposition existing layers. To manage a large number of layers in a typical composite model, you may +want to use the composite layup functionality in Abaqus/CAE. For more information, see Chapter 23, +“Composite layups,” of the Abaqus/CAE User’s Manual. +Input File Usage: +*SHELL GENERAL SECTION, ELSET=name, COMPOSITE, +ORIENTATION=name +where the ELSET parameter refers to a set of shell elements. +Abaqus/CAE Usage: +Abaqus/CAE uses a composite layup or a composite shell section to define a +shell made of layers with different linear elastic material behaviors. +Use the following option for a composite layup: +Property module: Create Composite Layup: select Conventional Shell +or Continuum Shell as the Element Type: Section integration: Before +analysis: specify orientations, regions, and materials +Use the following options for a composite shell section: +Property module: +Create Section: select Shell as the section Category and Composite +as the section Type: Section integration: Before analysis +Assign→Material Orientation: select regions +Assign→Section: select regions +Specifying the equivalent section properties directly for conventional shells +You can define the section’s mechanical response by specifying the general section stiffness and thermal +expansion response— , +, as defined below—directly. Since this method +then provides the complete specification of the section’s mechanical response, no material reference is +needed. Optionally, you can define +, the reference temperature for thermal expansion. +and +, +You must associate this section behavior with a region of your model. +In this case the shell section response is defined by +are the forces and moments on the shell section (membrane forces per unit length, bending +moments per unit length); +are the generalized section strains in the shell (reference surface strains and curvatures); +is the section stiffness matrix; +is a scaling modulus, which can be used to introduce temperature +dependence of the cross-section stiffness; and +and field-variable +29.6.6–4 +are the section forces and moments (per unit length) caused by thermal strains. +These thermal forces and moments in the shell are generated according to the formula +where +is a scaling factor (the “thermal expansion coefficient”); +is the initial (stress-free) temperature at this point in the shell, defined by the initial +nodal temperatures given as initial conditions (“Defining initial temperatures” in “Initial +conditions in Abaqus/Standard and Abaqus/Explicit,” Section 33.2.1); and +are the user-specified generalized section forces and moments (per unit length) caused by a +fully constrained unit temperature rise. +If the coefficient of thermal expansion, +needed. Note the distinction between +temperature, +. +is not +, is not a function of temperature, the value of +, the reference value used in defining , and the stress-free initial +In these equations the order of the terms is +that is, the direct membrane terms come first, then the shear membrane term, then the direct and shear +bending terms, with six terms in all. Engineering measures of shear membrane strain ( +) and twist +( +) are used in Abaqus. +This method of defining the shell section properties cannot be used with variable thickness shells +or continuum shell elements. +See “Laminated composite shells: buckling of a cylindrical panel with a circular hole,” Section 1.2.2 +of the Abaqus Example Problems Manual, for more information. +The stiffness matrix, +, can be defined as a constant stiffness for the section or as a spatially +varying stiffness by referring to a distribution (“Distribution definition,” Section 2.8.1). If a spatially +varying stiffness is used, the distribution must have a default stiffness defined. The default stiffness is +used by any shell element assigned to the shell section that is not specifically assigned a value in the +distribution. +Input File Usage: +*SHELL GENERAL SECTION, ELSET=name, ZERO= +where the ELSET parameter refers to a set of shell elements. +Abaqus/CAE Usage: +Property module: +Create Section: select Shell as the section Category and General +shell stiffness as the section Type +Assign→Section: select regions +Specifying the section properties in user subroutine UGENS +In Abaqus/Standard you can define the section response in user subroutine UGENS for the more general +case where the section response may be nonlinear. User subroutine UGENS is particularly useful if the +nonlinear behavior of the section involves geometric as well as material nonlinearity, such as may occur +due to section collapse. If only nonlinear material behavior is present, it is simpler to use a shell section +integrated during the analysis with the appropriate nonlinear material model. +You must specify a constant section thickness as part of the section definition or a continuously +varying thickness by defining the thickness at the nodes as described below. Even though the section’s +mechanical behavior is defined in user subroutine UGENS, the thickness of the shell section is required +for calculation of the hourglass control stiffness. You must associate this section behavior with a region +of your model. +Abaqus/Standard calls user subroutine UGENS for each integration point at each iteration of every +increment. The subroutine provides the section state at the start of the increment (section forces and +moments, +; solution-dependent state variables; temperature; and any +predefined field variables); the increments in temperature and predefined field variables; the generalized +section strain increments, +; generalized section strains, +; and the time increment. +The subroutine must perform two functions: +it must update the forces, the moments, and the +solution-dependent state variables to their values at the end of the increment; and it must provide the +section stiffness matrix, +. The complete section response, including the thermal expansion +effects, must be programmed in the user subroutine. +You should ensure that the strain increment is not used or changed in user subroutine UGENS for +linear perturbation analyses. For this case the quantity is undefined. +This method of defining the shell section properties cannot be used with continuum shell elements. +*SHELL GENERAL SECTION, ELSET=name, USER +Input File Usage: +Abaqus/CAE Usage: +where the ELSET parameter refers to a set of shell elements. +User subroutine UGENS is not supported in Abaqus/CAE. +Defining whether or not the section stiffness matrices are symmetric +If the section stiffness matrices are not symmetric, you can specify that Abaqus/Standard should use its +unsymmetric equation solution capability . +Input File Usage: +Abaqus/CAE Usage: +*SHELL GENERAL SECTION, ELSET=name, USER, UNSYMM +User subroutine UGENS is not supported in Abaqus/CAE. +Defining the section properties +Any number of constants can be defined to be used in determining the section behavior. You can specify +the number of integer property values required, m, and the number of real (floating point) property values +required, n; the total number of values required is the sum of these two numbers. The default number of +integer property values required is 0, and the default number of real property values required is 0. +Integer property values can be used inside user subroutine UGENS as flags, indices, counters, etc. +Examples of real (floating point) property values are material properties, geometric data, and any other +information required to calculate the section response in UGENS. +The property values are passed into user subroutine UGENS each time the subroutine is called. +Input File Usage: +*SHELL GENERAL SECTION, ELSET=name, USER, I PROPERTIES=m, +PROPERTIES=n +To define the property values, enter all floating point values on the data lines +first, followed immediately by the integer values. Eight values can be entered +per line. +User subroutine UGENS is not supported in Abaqus/CAE. +Abaqus/CAE Usage: +Defining the number of solution-dependent variables that must be stored for the section +You can define the number of solution-dependent state variables that must be stored at each integration +point within the section. There is no restriction on the number of variables associated with a user-defined +section. The default number of variables is 1. Examples of such variables are plastic strains, damage +variables, failure indices, user-defined output quantities, etc. +These solution-dependent state variables can be calculated and updated in user subroutine UGENS. +Input File Usage: +Abaqus/CAE Usage: +*SHELL GENERAL SECTION, ELSET=name, USER, VARIABLES=n +User subroutine UGENS is not supported in Abaqus/CAE. +Idealizing the section response +Idealizations allow you to modify the stiffness coefficients in a shell section based on assumptions about +the shell’s makeup or expected behavior. The following idealizations are available for general shell +sections: +• Retain only the membrane stiffness for shells whose predominant response will be in-plane +stretching. +• Retain only the bending stiffness for shells whose predominant response will be pure bending. +• Ignore the effects of the material layer stacking sequence for composite shells. +The membrane stiffness and bending stiffness idealizations can be applied to homogeneous shell +sections, composite shell sections, or shell sections with the stiffness coefficients specified directly. The +idealization to ignore stacking effects can be applied only to composite shell sections. +Idealizations modify the shell general stiffness coefficients after they have been computed normally, +including the effects of offset. +• If you use any idealization, all membrane-bending coupling terms are set to zero. +• If you retain only the membrane stiffness, off-diagonal terms of the bending submatrix are set to +zero, and diagonal bending terms are set to 1 × 10−6 times the largest diagonal membrane coefficient. +• If you retain only the bending stiffness, off-diagonal terms of the membrane submatrix are set to +zero, and diagonal membrane terms are set to 1 × 10−6 times the largest diagonal bending coefficient. +• If you ignore the material layer stacking sequence in a composite shell, each term of the bending +submatrix is set equal to T 2 /12 times the corresponding membrane submatrix term, where T is the +total thickness of the shell. +Input File Usage: +Use the following option to retain only the membrane stiffness: +*SHELL GENERAL SECTION, MEMBRANE ONLY +Use the following option to retain only the bending stiffness: +*SHELL GENERAL SECTION, BENDING ONLY +Use the following option to ignore the effects of the layer stacking sequence: +*SHELL GENERAL SECTION, COMPOSITE, SMEAR ALL LAYERS +Multiple idealization options can be used on the same general shell section. +Abaqus/CAE Usage: +Use any of the following options to apply an idealization to a shell section: +Property module: Homogeneous shell section editor: Section integration: +Before analysis; Basic: Idealization: Membrane only or Bending only +Property module: Composite shell section editor: Section integration: +Before analysis; Basic: Idealization: Membrane only, Bending only, +or Smear all layers +Property module: Shell (conventional or continuum) composite layup editor: +Section integration: Before analysis; Basic: Idealization: Membrane +only, Bending only, or Smear all layers +You cannot apply multiple idealizations to the same shell section in +Abaqus/CAE, and you cannot apply idealizations to a general shell stiffness +section. +Defining a shell offset value for conventional shells +You can define the distance (measured as a fraction of the shell’s thickness) from the shell’s midsurface to +the reference surface containing the element’s nodes . Positive values of the offset are in the positive normal direction . When the offset is set equal to 0.5, the top surface of the +shell is the reference surface. When the offset is set equal to −0.5, the bottom surface is the reference +surface. The default offset is 0, which indicates that the middle surface of the shell is the reference +surface. +You can specify an offset value that is greater in magnitude than 0.5. However, this technique should +be used with caution in regions of high curvature. All kinematic quantities, including the element’s +area, are calculated relative to the reference surface, which may lead to a surface area integration error, +affecting the stiffness and mass of the shell. +In an Abaqus/Standard analysis a spatially varying offset can be defined for conventional shells +using a distribution (“Distribution definition,” Section 2.8.1). The distribution used to define the shell +offset must have a default value. The default offset is used by any shell element assigned to the shell +section that is not specifically assigned a value in the distribution. +An offset to the shell’s top surface is illustrated in Figure 29.6.6–1. +SPOS +SPOS +SPOS +SNEG +SNEG +SNEG +Mid surface +a) OFFSET= 0 +Reference surface and +midsurface are coincident +b) OFFSET= −0.5 (SNEG) +Reference surface is +the bottom surface +c) OFFSET= +0.5 (SPOS) +Reference surface is +the top surface +Figure 29.6.6–1 Schematic of shell offset for an offset value of 0.5. +A shell offset value can be specified only if a material definition is referenced or a composite shell +section is defined. The shell offset value is ignored when the section definition is applied to continuum +shell elements. +Input File Usage: +Use the following option to specify a value for the shell offset: +*SHELL GENERAL SECTION, OFFSET=offset +The OFFSET parameter accepts a value, a label (SPOS or SNEG), or in an +Abaqus/Standard analysis the name of a distribution that is used to define a +spatially varying offset. Specifying SPOS is equivalent to specifying a value +of 0.5; specifying SNEG is equivalent to specifying a value of −0.5. +Abaqus/CAE Usage: +Use the following option for a composite layup: +Property module: composite layup editor: Section integration: +Before analysis; Offset: choose a reference surface, specify an +offset, or select a scalar discrete field +Use the following option for a shell section assignment: +Property module: Assign→Section: select regions: Section: select a +homogeneous or composite shell section: Definition: select a reference +surface, specify an offset, or select a scalar discrete field +Defining a variable thickness for conventional shells using distributions +You can define a spatially varying thickness for conventional shells using a distribution (“Distribution +definition,” Section 2.8.1). The thickness of continuum shell elements is defined by the element +geometry. +For composite shells the total thickness is defined by the distribution, and the layer thicknesses you +specify are scaled proportionally such that the sum of the layer thicknesses is equal to the total thickness +(including spatially varying layer thicknesses defined with a distribution). +The distribution used to define shell thickness must have a default value. The default thickness is +used by any shell element assigned to the shell section that is not specifically assigned a value in the +distribution. +If the shell thickness is defined for a shell section with a distribution, nodal thicknesses cannot be +used for that section definition. +Input File Usage: +Use the following option to define a spatially varying thickness: +Abaqus/CAE Usage: +*SHELL SECTION, SHELL THICKNESS=distribution name +Use the following option for a conventional shell composite layup: +Property module: composite layup editor: Section integration: Before +analysis; Shell Parameters: Shell thickness: Element distribution: +select an analytical field or an element-based discrete field +Use the following option for a homogeneous shell section: +Property module: shell section editor: Section integration: Before +analysis; Basic: Shell thickness: Element distribution: select an +analytical field or an element-based discrete field +Use the following option for a composite shell section: +Property module: shell section editor: Section integration: Before +analysis; Advanced: Shell thickness: Element distribution: select +an analytical field or an element-based discrete field +Defining a variable nodal thickness for conventional shells +You can define a conventional shell with continuously varying thickness by specifying the thickness of the +shell at the nodes. This method can be used only if the section is defined in terms of material properties; it +cannot be used if the section behavior is defined by specifying the equivalent section properties directly. +For continuum shell elements a continuously varying thickness can be defined through the element nodal +geometry; hence, the nodal thickness is not meaningful. +If you indicate that the nodal thicknesses will be specified, for homogeneous shells any constant +shell thickness you specify will be ignored, and the shell thickness will be interpolated from the nodes. +The thickness must be defined at all nodes connected to the element. +For composite shells the total thickness is interpolated from the nodes, and the layer thicknesses you +specify are scaled proportionally such that the sum of the layer thicknesses is equal to the total thickness +(including spatially varying layer thicknesses defined with a distribution). +If the shell thickness is defined for a shell section with a distribution, nodal thicknesses cannot be +used for that section definition. However, if nodal thicknesses are used, you can still use distributions to +define spatially varying thicknesses on the layers of conventional shell elements. +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*NODAL THICKNESS +*SHELL GENERAL SECTION, NODAL THICKNESS +Use the following option for a conventional shell composite layup: +Property module: composite layup editor: Section integration: +Before analysis; Shell Parameters: Nodal distribution: select +an analytical field or a node-based discrete field +Use the following option for a homogeneous shell section: +Property module: shell section editor: Section integration: +Before analysis; Basic: Nodal distribution: select an analytical +field or a node-based discrete field +Use the following option for a composite shell section: +Property module: shell section editor: Section integration: Before +analysis; Advanced: Nodal distribution: select an analytical +field or a node-based discrete field +Defining the Poisson strain in shell elements in the thickness direction +Abaqus allows for a possible uniform change in the shell thickness in a geometrically nonlinear analysis +. The Poisson’s strain is +based on a fixed section Poisson’s ratio, either user specified or computed by Abaqus based on the elastic +portion of the material definition. +By default, Abaqus computes the Poisson’s strain using a fixed section Poisson’s ratio of 0.5. +Input File Usage: +Use the following option to specify a value for the effective Poisson’s ratio: +*SHELL GENERAL SECTION, POISSON= +Use the following option to cause the shell thickness to change based on the +initial elastic properties of the material: +*SHELL GENERAL SECTION, POISSON=ELASTIC +Abaqus/CAE Usage: +Use the following option for a composite layup: +Property module: composite layup editor: Section integration: +Before analysis; Shell Parameters: Section Poisson's ratio: +Use analysis default or Specify value: +Use the following option for a homogeneous or composite shell section: +Property module: shell section editor: Section integration: +Before analysis; Advanced: Section Poisson's ratio: Use +analysis default or Specify value: +You cannot specify a shell thickness direction behavior based on the initial +elastic material definition in Abaqus/CAE. +Defining the thickness modulus in continuum shell elements +The thickness modulus is used in computing the stress in the thickness direction . Abaqus computes a +thickness modulus value by default based on the elastic portion of the material definitions in the initial +configuration. Alternatively, you can provide a value. +If the material properties are unavailable during the preprocessing stage of input; for example, when +the material behavior is defined by the fabric material model or user subroutine UMAT or VUMAT, you +must specify the effective thickness modulus directly. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to define an effective thickness modulus directly: +*SHELL GENERAL SECTION, THICKNESS MODULUS= +Use the following option for a composite layup: +Property module: composite layup editor: Section integration: +Before analysis; Shell Parameters: Thickness modulus +specify the thickness properties directly +to +Use the following option for a homogeneous or composite shell section: +Property module: shell section editor: Section integration: +Before analysis; Advanced: Thickness modulus +specify the thickness properties directly +to +Defining the transverse shear stiffness +You can provide nondefault values of the transverse shear stiffness. You must specify the transverse +shear stiffness for shear flexible shells in Abaqus/Standard if the section properties are specified in user +subroutine UGENS. If you do not specify the transverse shear stiffness, it will be calculated as described +in “Shell section behavior,” Section 29.6.4. +Input File Usage: +Use both of the following options: +*SHELL GENERAL SECTION +*TRANSVERSE SHEAR STIFFNESS +Abaqus/CAE Usage: +Use the following option for a composite layup: +Property module: composite layup editor: Section integration: Before +analysis; Shell Parameters: toggle on Specify transverse shear +Use the following option for a homogeneous or composite shell section: +Property module: shell section editor: Section integration: Before +analysis; Advanced: toggle on Specify transverse shear +Defining the initial section forces and moments +You can define initial stresses for general shell sections that will be applied as initial section +Initial conditions can be specified only for the membrane forces, the bending +forces and moments. +Initial conditions cannot be prescribed for the transverse shear +moments, and the twisting moment. +forces. +Specifying the order of accuracy in the Abaqus/Explicit shell element formulation +In Abaqus/Explicit you can specify second-order accuracy in the shell element formulation. See “Section +controls,” Section 27.1.4, for more information. +Input File Usage: +*SHELL GENERAL SECTION, CONTROLS=name +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Element Controls +Specifying nondefault hourglass control parameters for reduced-integration shell elements +You can specify a nondefault hourglass control formulation or scale factors for elements that use reduced +integration. See “Section controls,” Section 27.1.4, for more information. +In Abaqus/Standard the nondefault enhanced hourglass control formulation is available only for +S4R and SC8R elements. +In Abaqus/Standard you can modify the default values for hourglass control stiffness based on the +default total stiffness approach for elements that use hourglass control and define a scaling factor for the +stiffness associated with the drill degree of freedom (rotation about the surface normal) for elements that +use six degrees of freedom at a node. +No default values are available for hourglass control stiffness if the section properties are specified +in user subroutine UGENS. Therefore, you must specify the hourglass control stiffness when UGENS is +used to specify the section properties for reduced-integration elements. +The stiffness associated with the drill degree of freedom is the average of the direct components +of the transverse shear stiffness multiplied by a scaling factor. In most cases the default scaling factor +is appropriate for constraining the drill rotation to follow the in-plane rotation of the element. If an +additional scaling factor is defined, the additional scaling factor should not increase or decrease the drill +stiffness by more than a factor of 100.0 for most typical applications. Usually, a scaling factor between +0.1 and 10.0 is appropriate. +There are no hourglass stiffness factors or scale factors for hourglass stiffness for the nondefault +enhanced hourglass control formulation. You can define the scale factor for the drill stiffness for the +nondefault enhanced hourglass control formulation. +Input File Usage: +Use both of the following options to specify a nondefault hourglass control +formulation or scale factors for reduced-integration elements: +*SECTION CONTROLS, NAME=name +*SHELL GENERAL SECTION, CONTROLS=name +Use both of the following options in Abaqus/Standard to modify the default +values for hourglass control stiffness based on the default total stiffness +approach for reduced-integration elements and to define a scaling factor for +the stiffness associated with the drill degree of freedom (rotation about the +surface normal) for six degree of freedom elements: +*SHELL GENERAL SECTION +*HOURGLASS STIFFNESS +Abaqus/CAE Usage: Mesh module: Mesh→Element Type: Element Controls +Defining density for conventional shells +You can define the mass per unit area for conventional shell elements whose section properties +are specified directly in terms of the section stiffness (either directly in the section definition or, in +Abaqus/Standard, in user subroutine UGENS). The density is required, for example, in a dynamic +analysis or for gravity loading. See “Density,” Section 21.2.1, for details. +The density is defined as part of the material definition for shells whose section properties include +a material definition. +This functionality is similar to the more general functionality of defining a nonstructural mass +contribution The only difference between the two +definitions is that the nonstructural mass contributes to the rotary inertia terms about the midsurface while +the additional mass defined in the section definition does not. +Input File Usage: +Use the following option to define the density directly: +*SHELL GENERAL SECTION, ELSET=name, DENSITY= +Use the following option in Abaqus/Standard to define the density in user +subroutine UGENS: +*SHELL GENERAL SECTION, ELSET=name, USER, +DENSITY= +Abaqus/CAE Usage: +Use the following option for a composite layup: +Property module: composite layup editor: Section integration: Before +analysis; Shell Parameters: toggle on Density, and enter +Use the following option for a homogeneous or composite shell section: +Property module: shell section editor: Section integration: Before +analysis; Advanced: toggle on Density, and enter +You cannot define the shell section properties in user subroutine UGENS in +Abaqus/CAE. +Defining damping +You can include mass and stiffness proportional damping in a shell section definition. See “Material +damping,” Section 26.1.1, for more information about material damping in Abaqus. +Specifying temperature and field variables +Temperatures and field variables can be specified by defining the value at the reference surface of the shell +or by defining the values at the nodes of a continuum shell element. The actual values of the temperatures +and field variables are specified as either predefined fields or initial conditions . +Output +The following output variables are available from Abaqus/Explicit as element output: section forces and +moments, section strains, element energies, element stable time increment, and element mass scaling +factor. +The output that is available from Abaqus/Standard depends on how the section behavior is defined. +Output if the section is defined in terms of material properties +For shells whose section properties include a material definition (homogeneous or composite), +section forces and moments and section strains are available as element output. The section +moments are calculated relative to the reference surface. +In addition, stress (in-plane and, for +certain elements, transverse shear), strain, and orthotropic failure measures can be output. Since +the behavior of the material is linear, three section points per layer (the bottom, middle, and top, +respectively) are available for output. Stress invariants and principal stresses are not available as +output but can be visualized in Abaqus/CAE. +Output if the equivalent section properties are specified directly or in UGENS +matrix is used to specify the equivalent section properties directly or if user subroutine +If the +UGENS is used, section point stresses and strains and section strains are not available for output +or visualization inAbaqus/CAE; only section forces and moments can be requested for outputor +visualized inAbaqus/CAE. +THREE-DIMENSIONAL CONVENTIONAL SHELL ELEMENT LIBRARY +3-D CONVENTIONAL SHELL ELEMENTS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Shell elements: overview,” Section 29.6.1 +• “Choosing a shell element,” Section 29.6.2 +• *NODAL THICKNESS +• *SHELL GENERAL SECTION +• *SHELL SECTION +Overview +This section provides a reference to the three-dimensional shell elements available in Abaqus/Standard +and Abaqus/Explicit. +Element types +Stress/displacement elements +STRI3(S) +3-node triangular facet thin shell +S3 +S3R +S3RS(E) +STRI65(S) +S4 +S4R +S4RS(E) +S4RSW(E) +S4R5(S) +S8R(S) +3-node triangular general-purpose shell, finite membrane strains (identical to element +S3R) +3-node triangular general-purpose shell, finite membrane strains (identical to element +S3) +3-node triangular shell, small membrane strains +6-node triangular thin shell, using five degrees of freedom per node +4-node general-purpose shell, finite membrane strains +4-node general-purpose shell, +membrane strains +reduced integration with hourglass control, finite +4-node, reduced integration, shell with hourglass control, small membrane strains +4-node, reduced integration, shell with hourglass control, small membrane strains, +warping considered in small-strain formulation +4-node thin shell, reduced integration with hourglass control, using five degrees of +freedom per node +8-node doubly curved thick shell, reduced integration +S8R5(S) +S9R5(S) +8-node doubly curved thin shell, reduced integration, using five degrees of freedom per +node +9-node doubly curved thin shell, reduced integration, using five degrees of freedom per +node +Active degrees of freedom +1, 2, 3, 4, 5, 6 for STRI3, S3R, S3RS, S4, S4R, S4RS, S4RSW, S8R +1, 2, 3 and two in-surface rotations for STRI65, S4R5, S8R5, S9R5 at most nodes +1, 2, 3, 4, 5, 6 for STRI65, S4R5, S8R5, S9R5 at any node that +• has a boundary condition on a rotational degree of freedom; +• is involved in a multi-point constraint that uses rotational degrees of freedom; +• is attached to a beam or to a shell element that uses six degrees of freedom at all nodes (such as +S4R, S8R, STRI3, etc.); +• is a point where different elements have different surface normals (user-specified normal definitions +or normal definitions created by Abaqus because the surface is folded); or +• is loaded with moments. +Additional solution variables +Element type S8R5 has three displacement and two rotation variables at an internally generated midbody +node. +Heat transfer elements +DS3(S) +DS4(S) +DS6(S) +DS8(S) +3-node triangular shell +4-node quadrilateral shell +6-node triangular shell +8-node quadrilateral shell +Active degrees of freedom +11, 12, etc. (temperatures through the thickness as described in “Choosing a shell element,” +Section 29.6.2) +Additional solution variables +None. +Coupled temperature-displacement elements +S3T(S) +S3RT +3-node triangular general-purpose shell, finite membrane strains, bilinear temperature +in the shell surface (identical to element S3RT) +3-node triangular general-purpose shell, finite membrane strains, bilinear temperature +in the shell surface (for Abaqus/Standard it is identical to element S3T ) +S4T(S) +S4RT +4-node general-purpose shell, finite membrane strains, bilinear temperature in the shell +surface +4-node general-purpose shell, +membrane strains, bilinear temperature in the shell surface +reduced integration with hourglass control, finite +S8RT(S) +8-node thick shell, biquadratic displacement, bilinear temperature in the shell surface +Active degrees of freedom +1, 2, 3, 4, 5, 6 at all nodes +11, 12, 13, etc. (temperatures through the thickness as described in “Choosing a shell element,” +Section 29.6.2) at all nodes for S3T, S3RT, S4T, and S4RT; and at the corner nodes only for S8RT +Additional solution variables +None. +Nodal coordinates required +and, optionally for shells with displacement degrees of freedom in Abaqus/Standard, +, the direction cosines of the shell normal at the node. +Element property definition +Input File Usage: +Use either of the following options for stress/displacement elements: +*SHELL SECTION +*SHELL GENERAL SECTION +Use the following option for heat transfer or coupled temperature-displacement +elements: +*SHELL SECTION +In addition, use the following option for variable thickness shells: +*NODAL THICKNESS +Property module: Create Section: select Shell as the section Category +and Homogeneous or Composite as the section Type +Abaqus/CAE Usage: +Element-based loading +Distributed loads +Distributed loads are available for all elements with displacement degrees of freedom. They are specified +as described in “Distributed loads,” Section 33.4.3. +Body forces, centrifugal loads, and Coriolis forces must be given as force per unit area if the equivalent +section properties are specified directly as part of the general shell section definition. +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +BX +BY +BZ +Body force +FL−3 +Body force +FL−3 +Body force +FL−3 +BXNU +Body force +FL−3 +BYNU +Body force +FL−3 +BZNU +Body force +FL−3 +(give magnitude +Body force +as +force per unit volume) in the global +X-direction. +(give magnitude +Body force +as +force per unit volume) in the global +Y-direction. +(give magnitude +Body force +as +force per unit volume) in the global +Z-direction. +as +per +force +force +(give +Nonuniform body +magnitude +unit +volume) in the global X-direction, +via +with magnitude +user +in +subroutine +VDLOAD +Abaqus/Standard +in Abaqus/Explicit. +supplied +DLOAD +and +as +per +force +force +(give +Nonuniform body +magnitude +unit +volume) in the global Y-direction, +via +with magnitude +in +subroutine +user +VDLOAD +Abaqus/Standard +in Abaqus/Explicit. +supplied +DLOAD +and +as +per +force +force +Nonuniform body +(give +unit +magnitude +volume) in the global Z-direction, +supplied +via +with magnitude +DLOAD +user +in +subroutine +and VDLOAD +Abaqus/Standard +in Abaqus/Explicit. +CENT(S) +Not supported +FL−4 +(ML−3 T−2 ) +CENTRIF(S) +Rotational body +force +T−2 +Centrifugal load (magnitude defined +is the mass density +as +and +, where +is the angular speed). +Centrifugal load (magnitude is input +as +is the angular speed). +, where +Units +Description +Coriolis force (magnitude input +where +, +is the mass density and +is the angular speed). The load +stiffness due to Coriolis loading is not +accounted for in direct steady-state +dynamics analysis. +General traction on edge n. +Nonuniform general traction on edge +and direction +n with magnitude +subroutine +via +supplied +UTRACLOAD. +user +Moment on edge n. +Nonuniform moment on edge n +with magnitude supplied via user +subroutine UTRACLOAD. +Normal traction on edge n. +Nonuniform normal traction on edge +n with magnitude supplied via user +subroutine UTRACLOAD. +Shear traction on edge n. +Nonuniform shear traction on edge +n with magnitude supplied via user +subroutine UTRACLOAD. +Transverse traction on edge n. +Nonuniform transverse traction on +edge n with magnitude supplied via +user subroutine UTRACLOAD. +Gravity +loading +direction (magnitude is +acceleration). +in +specified +input as +Hydrostatic pressure applied to the +element reference surface and linear +in global Z. The pressure is positive in +Load ID +(*DLOAD) +CORIO(S) +Abaqus/CAE +Load/Interaction +Coriolis force +FL−4 T +(ML−3 T−1 ) +EDLDn +Shell edge load +EDLDnNU(S) +Not supported +EDMOMn +Shell edge load +EDMOMnNU(S) +Not supported +EDNORn +Shell edge load +EDNORnNU(S) +Not supported +EDSHRn +Shell edge load +EDSHRnNU(S) +Not supported +EDTRAn +Shell edge load +EDTRAnNU(S) +Not supported +GRAV +Gravity +FL−1 +FL−1 +FL−1 +FL−1 +FL−1 +FL−1 +FL−1 +FL−1 +LT−2 +HP(S) +Not supported +FL−2 +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +Pressure +FL−2 +PNU +Not supported +FL−2 +the direction of the positive element +normal. +applied to the element +Pressure +reference surface. The pressure is +positive in the direction of the positive +element normal. +applied +reference +to +Nonuniform pressure +surface +the +element +via +with magnitude +in +user +subroutine +VDLOAD +Abaqus/Standard +in Abaqus/Explicit. +The pressure +is positive in the direction of the +positive element normal. +supplied +DLOAD +and +ROTA(S) +Rotational body +force +T−2 +ROTDYNF(S) +Not supported +T−1 +SBF(E) +SP(E) +Not supported +FL−5 T +Not supported +FL−4 T2 +TRSHR +Surface traction +FL−2 +TRSHRNU(S) +Not supported +FL−2 +TRVEC +Surface traction +FL−2 +TRVECNU(S) +Not supported +FL−2 +29.6.7–6 +Rotary acceleration load (magnitude +is input as +is the rotary +acceleration). +, where +Rotordynamic load (magnitude is +input as +is the angular +velocity). +, where +Stagnation body force in global X-, +Y-, and Z-directions. +Stagnation pressure applied to the +element reference surface. +traction +Shear +reference surface. +on +the +element +Nonuniform shear +traction on the +surface with +reference +element +magnitude and direction supplied +via user subroutine UTRACLOAD. +General +reference surface. +traction on the element +Nonuniform general +on +the element reference surface with +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +VBF(E) +VP(E) +Not supported +FL−4 T +Not supported +FL−3 T +magnitude and direction supplied via +user subroutine UTRACLOAD. +Viscous body force in global X-, Y-, +and Z-directions. +Viscous surface pressure. The viscous +pressure is proportional to the velocity +face and +normal +opposing the motion. +to the element +Foundations +Foundations are available for Abaqus/Standard elements with displacement degrees of freedom. They +are specified as described in “Element foundations,” Section 2.2.2. +Load ID +(*FOUNDATION) Load/Interaction +Abaqus/CAE +Units +Description +F(S) +Elastic +foundation +FL−3 +Elastic foundation in the direction of +the shell normal. +Distributed heat fluxes +Distributed heat fluxes are available for elements with temperature degrees of freedom. They are +specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*DFLUX) +BF(S) +BFNU(S) +Abaqus/CAE +Load/Interaction +Units +Description +Body heat flux +Body heat flux +JL−3 T−1 +JL−3 T−1 +Body heat flux per unit volume. +Nonuniform body heat flux per unit +volume with magnitude supplied via +user subroutine DFLUX. +Surface heat flux per unit area into the +bottom face of the element. +Surface heat flux per unit area into the +top face of the element. +Nonuniform surface heat flux per +unit area into the bottom face of the +element with magnitude supplied via +user subroutine DFLUX. +SNEG(S) +Surface heat flux +JL−2 T−1 +SPOS(S) +Surface heat flux +JL−2 T−1 +SNEGNU(S) +Not supported +JL−2 T−1 +Load ID +(*DFLUX) +Abaqus/CAE +Load/Interaction +Units +Description +SPOSNU(S) +Not supported +JL−2 T−1 +Nonuniform surface heat flux per unit +area into the top face of the element +with magnitude supplied via user +subroutine DFLUX. +Film conditions +Film conditions are available for elements with temperature degrees of freedom. They are specified as +described in “Thermal loads,” Section 33.4.4. +Load ID +(*FILM) +FNEG(S) +FPOS(S) +Abaqus/CAE +Load/Interaction +Units +Description +Surface film +condition +Surface film +condition +JL−2 T−1 −1 +JL−2 T−1 −1 +FNEGNU(S) +Not supported +JL−2 T−1 −1 +FPOSNU(S) +Not supported +JL−2 T−1 −1 +Film coefficient and sink temperature +(units of +) provided on the bottom +face of the element. +Film coefficient and sink temperature +(units of +) provided on the top face +of the element. +Nonuniform film coefficient and sink +temperature (units of +) provided +on the bottom face of the element +with magnitude supplied via user +subroutine FILM. +Nonuniform film coefficient and sink +temperature (units of +) provided +on the top face of +the element +with magnitude supplied via user +subroutine FILM. +Radiation types +Radiation conditions are available for elements with temperature degrees of freedom. They are specified +as described in “Thermal loads,” Section 33.4.4. +Load ID +(*RADIATE) +RNEG(S) +Abaqus/CAE +Load/Interaction +Units +Description +Surface radiation Dimensionless +Emissivity and sink temperature +(units of +) provided for the bottom +face of the shell. +Load ID +(*RADIATE) +RPOS(S) +Abaqus/CAE +Load/Interaction +Units +Description +Surface radiation Dimensionless +Emissivity and sink temperature +(units of +) provided for the top face +of the shell. +Surface-based loading +Distributed loads +Surface-based distributed loads are available for all elements with displacement degrees of freedom. +They are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +EDLD +Shell edge load +FL−1 +EDLDNU(S) +Shell edge load +FL−1 +EDMOM +Shell edge load +EDMOMNU(S) +Shell edge load +EDNOR +Shell edge load +FL−1 +EDNORNU(S) +Shell edge load +FL−1 +EDSHR +Shell edge load +EDSHRNU(S) +Shell edge load +FL−1 +FL−1 +General +surface. +traction +on +edge-based +traction +Nonuniform general +on +edge-based surface with magnitude +and direction supplied via user +subroutine UTRACLOAD. +Moment on edge-based surface. +Nonuniform moment on edge-based +surface with magnitude supplied via +user subroutine UTRACLOAD. +Normal +surface. +traction +on +edge-based +traction +on +Nonuniform normal +edge-based surface with magnitude +supplied +subroutine +via +UTRACLOAD. +user +Shear traction on edge-based surface. +traction +Nonuniform shear +on +edge-based surface with magnitude +subroutine +via +supplied +UTRACLOAD. +user +EDTRA +Shell edge load +FL−1 +Transverse traction on edge-based +surface. +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +EDTRANU(S) +Shell edge load +FL−1 +HP(S) +Pressure +FL−2 +Pressure +FL−2 +PNU +Pressure +FL−2 +SP(E) +Pressure +FL−4 T2 +TRSHR +Surface traction +FL−2 +TRSHRNU(S) +Surface traction +FL−2 +TRVEC +Surface traction +FL−2 +TRVECNU(S) +Surface traction +FL−2 +29.6.7–10 +Nonuniform transverse traction on +edge-based surface with magnitude +subroutine +via +supplied +UTRACLOAD. +user +Hydrostatic pressure on the element +reference surface and linear in global +Z. The pressure is positive in the +direction opposite to the surface +normal. +Pressure on the element reference +surface. The pressure is positive in +the direction opposite to the surface +normal. +Nonuniform pressure on the element +reference surface with magnitude +supplied via user subroutine DLOAD +in Abaqus/Standard and VDLOAD +in Abaqus/Explicit. The pressure is +positive in the direction opposite to +the surface normal. +Stagnation pressure applied to the +element reference surface. +traction +Shear +reference surface. +on +the +element +traction on the +Nonuniform shear +element +surface with +reference +magnitude and direction supplied +via user subroutine UTRACLOAD. +General +reference surface. +traction on the element +traction +on +Nonuniform general +the element reference surface with +magnitude and direction supplied via +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +VP(E) +Pressure +FL−3 T +Viscous surface pressure. The viscous +pressure is proportional to the velocity +face and +normal +opposing the motion. +to the element +Distributed heat fluxes +Surface-based distributed heat fluxes are available for elements with temperature degrees of freedom. +They are specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*DSFLUX) +Abaqus/CAE +Load/Interaction +Units +Description +S(S) +Surface heat flux +JL−2 T−1 +SNU(S) +Surface heat flux +JL−2 T−1 +Surface heat flux per unit area into the +element surface. +Nonuniform surface heat flux per +unit area into the element surface +with magnitude supplied via user +subroutine DFLUX. +Film conditions +Surface-based film conditions are available for elements with temperature degrees of freedom. They are +specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*SFILM) +F(S) +FNU(S) +Radiation types +Abaqus/CAE +Load/Interaction +Units +Description +Surface film +condition +Surface film +condition +JL−2 T−1 −1 +JL−2 T−1 −1 +Film coefficient and sink temperature +(units of +) provided on the element +surface. +Nonuniform film coefficient and sink +temperature (units of +) provided on +the element surface with magnitude +supplied via user subroutine FILM. +Surface-based radiation conditions are available for elements with temperature degrees of freedom. They +are specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*SRADIATE) +Abaqus/CAE +Load/Interaction +Units +Description +R(S) +Surface radiation Dimensionless +Emissivity and sink temperature +(units of +) provided for the element +surface. +Incident wave loading +Surface-based incident wave loads are available. They are specified as described in “Acoustic, shock, +and coupled acoustic-structural analysis,” Section 6.10.1. If the incident wave field includes a reflection +off a plane outside the boundaries of the mesh, this effect can be included. +Element output +If a local coordinate system is not assigned to the element, the stress/strain components, as well as the +section forces/strains, are in the default directions on the surface defined by the convention given in +“Conventions,” Section 1.2.2. If a local coordinate system is assigned to the element through the section +definition (“Orientations,” Section 2.2.5), the stress/strain components and the section forces/strains are +in the surface directions defined by the local coordinate system. +In large-displacement problems with elements that allow finite membrane strains in Abaqus/Standard +and in all problems in Abaqus/Explicit, the local directions defined in the reference configuration are +rotated into the current configuration by the average material rotation. +Stress, strain, and other tensor components +Stress and other tensors (including strain tensors) are available for elements with displacement degrees +of freedom. All tensors have the same components. For example, the stress components are as follows: +S11 +S22 +S12 +Local +Local +Local +direct stress. +direct stress. +shear stress. +Section forces, moments, and transverse shear forces +Available for elements with displacement degrees of freedom. +SF1 +SF2 +SF3 +SF4 +SF5 +Direct membrane force per unit width in local 1-direction. +Direct membrane force per unit width in local 2-direction. +Shear membrane force per unit width in local 1–2 plane. +Transverse shear force per unit width in local 1-direction (available only for S3/S3R, +S3RS, S4, S4R, S4RS, S4RSW, S8R, and S8RT). +Transverse shear force per unit width in local 2-direction (available only for S3/S3R, +S3RS, S4, S4R, S4RS, S4RSW, S8R, and S8RT). +SM1 +SM2 +SM3 +Bending moment force per unit width about local 2-axis. +Bending moment force per unit width about local 1-axis. +Twisting moment force per unit width in local 1–2 plane. +The section force and moment resultants per unit length in the normal basis directions in a given shell +section of thickness h can be defined on this basis as +where +is the offset of the reference surface from the midsurface. +The section force SF6, which is the integral of +through the shell thickness, is reported only for finite- +strain shell elements and is zero because of the plane stress constitutive assumption. The total number +of attributes written to the results file for finite-strain shell elements is 9; SF6 is the sixth attribute. +Average section stresses +Available for elements with displacement degrees of freedom. +SSAVG1 +SSAVG2 +SSAVG3 +SSAVG4 +SSAVG5 +Average membrane stress in local 1-direction. +Average membrane stress in local 2-direction. +Average membrane stress in local 1–2 plane. +Average transverse shear stress in local 1-direction. +Average transverse shear stress in local 2-direction. +The average section stresses are defined as +where h is the current section thickness. +Section strains, curvatures, and transverse shear strains +Available for elements with displacement degrees of freedom. +SE1 +SE2 +SE3 +SE4 +Direct membrane strain in local 1-direction. +Direct membrane strain in local 2-direction. +Shear membrane strain in local 1–2 plane. +Transverse shear strain in the local 1-direction (available only for S3/S3R, S3RS, +S4, S4R, S4RS, S4RSW, S8R, and S8RT). +SE5 +SE6 +SK1 +SK2 +SK3 +Transverse shear strain in the local 2-direction (available only for S3/S3R, S3RS, +S4, S4R, S4RS, S4RSW, S8R, and S8RT). +Strain in the thickness direction (available only for S3/S3R, S3RS, S4, S4R, S4RS, +and S4RSW). +Curvature change about local 2-axis. +Curvature change about local 1-axis. +Surface twist in local 1–2 plane. +The local directions are defined in “Shell elements: overview,” Section 29.6.1. +Shell thickness +STH +Shell thickness, which is the current section thickness for S3/S3R, S3RS, S4, S4R, +S4RS, and S4RSW elements. +Transverse shear stress estimates +Available for S3/S3R, S3RS, S4, S4R, S4RS, S4RSW, S8R, and S8RT elements. +TSHR13 +TSHR23 +13-component of transverse shear stress. +23-component of transverse shear stress. +Estimates of the transverse shear stresses are available at section integration points as output variables +TSHR13 or TSHR23 for both Simpson’s rule and Gauss quadrature. For Simpson’s rule output of +variables TSHR13 or TSHR23 should be requested at nondefault section points, since the default output +is at section point 1 of the shell section where the transverse shear stresses vanish. For the small- +strain elements in Abaqus/Explicit, transverse shear stress distributions are assumed constant for non- +composite sections and piecewise constant for composite sections; therefore, transverse shear stresses at +integration points should be interpreted accordingly. +For element type S4 the transverse shear calculation is performed at the center of the element and assumed +constant over the element. Hence, transverse shear strain, force, and stress will not vary over the area of +the element. +For numerically integrated shell sections (with the exception of small-strain shells in Abaqus/Explicit), +estimates of the interlaminar shear stresses in composite sections—i.e., the transverse shear stresses at +the interface between two composite layers—can be obtained only by using Simpson’s rule. With Gauss +quadrature no section integration point exists at the interface between composite layers. +Unlike the S11, S22, and S12 in-plane stress components, transverse shear stress components TSHR13 +and TSHR23 are not calculated from the constitutive behavior at points through the shell section. They +are estimated by matching the elastic strain energy associated with shear deformation of the shell section +with that based on piecewise quadratic variation of the transverse shear stress across the section, under +conditions of bending about one axis . Therefore, interlaminar shear stress +calculation is supported only when the elastic material model is used for each layer of the shell section. +If you specify the transverse shear stiffness values, interlaminar shear stress output is not available. +Heat flux components +Available for elements with temperature degrees of freedom. +HFL1 +HFL2 +HFL3 +Heat flux in local 1-direction. +Heat flux in local 2-direction. +Heat flux in local 3-direction. +Node ordering on elements +face 3 +face 2 +face 4 +face 3 +face 2 +1 2 +face 1 +face 1 +3-node element +4-node element +face 3 +4 7 3 +face 3 +face 2 +face 4 +6 5 +1 +face 1 + 2 +face 2 +face 1 +6-node element +8-node element +face 3 +4 7 3 +face 4 +face 2 +face 1 +9-node element +Numbering of integration points for output +Stress/displacement analysis +9-node reduced +integration element +S3R element +4-node reduced +integration element +STRI3 element +6 +6-node element +4-node full +integration element +4 +8-node reduced +integration element +Heat transfer analysis +DS3 +DS4 +DS6 +DS8 +29.6.8 +CONTINUUM SHELL ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Shell elements: overview,” Section 29.6.1 +• “Choosing a shell element,” Section 29.6.2 +• *SHELL GENERAL SECTION +• *SHELL SECTION +Overview +This section provides a reference to the continuum shell elements available in Abaqus/Standard and +Abaqus/Explicit. +Element types +Stress/displacement elements +SC6R +6-node triangular in-plane continuum shell wedge, general-purpose, finite membrane +strains +SC8R +8-node hexahedron, general-purpose, finite membrane strains +Active degrees of freedom +1, 2, 3 +Additional solution variables +None. +Coupled temperature-displacement elements +SC6RT +SC8RT +6-node linear displacement and temperature, +wedge, general-purpose, finite membrane strains +triangular in-plane continuum shell +8-node linear displacement and temperature, hexahedron, general-purpose, finite +membrane strains +Active degrees of freedom +1, 2, 3, 11 +Additional solution variables +None. +Nodal coordinates required +Element property definition +Input File Usage: +Abaqus/CAE Usage: +Use either of the following options: +*SHELL SECTION +*SHELL GENERAL SECTION +Property module: Create Section: select Shell as the section Category +and Homogeneous or Composite as the section Type +Element-based loading +Distributed loads +Distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +(give magnitude +Body force +as +force per unit volume) in the global +X-direction. +(give magnitude +Body force +as +force per unit volume) in the global +Y-direction. +(give magnitude +Body force +as +force per unit volume) in the global +Z-direction. +as +per +force +force +(give +Nonuniform body +magnitude +unit +volume) in the global X-direction, +via +with magnitude +user +in +subroutine +VDLOAD +Abaqus/Standard +in Abaqus/Explicit. +supplied +DLOAD +and +force +(give +Nonuniform body +magnitude +unit +volume) in the global Y-direction, +via +with magnitude +supplied +force +per +as +BX +BY +BZ +Body force +FL−3 +Body force +FL−3 +Body force +FL−3 +BXNU +Body force +FL−3 +BYNU +Body force +FL−3 +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +subroutine +user +Abaqus/Standard +in Abaqus/Explicit. +DLOAD +in +and VDLOAD +as +per +force +force +(give +Nonuniform body +magnitude +unit +volume) in the global Z-direction, +via +with magnitude +user +in +subroutine +VDLOAD +Abaqus/Standard +in Abaqus/Explicit. +supplied +DLOAD +and +Centrifugal load (magnitude defined +as +is the mass density +and +, where +is the angular speed). +Centrifugal load (magnitude is input +as +is the angular speed). +, where +Coriolis force (magnitude input +where +, +is the mass density and +is the angular speed). The load +stiffness due to Coriolis loading is not +accounted for in direct steady-state +dynamics analysis. +Gravity +loading +direction (magnitude is +acceleration). +in +specified +input as +Hydrostatic pressure on face n, linear +in global Z. A positive pressure is +directed into the element. +A positive +Pressure on face n. +pressure is directed into the element. +on +with +user +Nonuniform pressure +face +magnitude +supplied +subroutine DLOAD in +via +Abaqus/Standard and VDLOAD in +Abaqus/Explicit. A positive pressure +is directed into the element. +BZNU +Body force +FL−3 +CENT(S) +Not supported +FL−4 +(ML−3 T−2 ) +CENTRIF(S) +Rotational body +force +T−2 +CORIO(S) +Coriolis force +FL−4 T +(ML−3 T−1 ) +GRAV +Gravity +LT−2 +HPn(S) +Not supported +FL−2 +Pn +Pressure +PnNU +Not supported +FL−2 +FL−2 +Load ID +(*DLOAD) +ROTA(S) +Abaqus/CAE +Load/Interaction +Units +Description +Rotational body +force +T−2 +Not supported +FL−4 T2 +Stagnation pressure on face n. +ROTDYNF(S) +Not supported +T−1 +SBF(E) +Not supported +FL−5 T2 +SPn(E) +TRSHRn +Surface traction +TRSHRnNU(S) +Not supported +TRVECn +Surface traction +TRVECnNU(S) +Not supported +FL−2 +FL−2 +FL−2 +FL−2 +VBF(E) +VPn(E) +Not supported +FL−4 T +Not supported +FL3T +Rotary acceleration load (magnitude +is input as +is the rotary +acceleration). +, where +Rotordynamic load (magnitude is +input as +is the angular +velocity). +, where +Stagnation body force in global X-, +Y-, and Z-directions. +Shear traction on face n. +Nonuniform shear traction on face +and direction +n with magnitude +subroutine +via +supplied +UTRACLOAD. +user +General traction on face n. +Nonuniform general traction on face +and direction +n with magnitude +supplied +subroutine +via +UTRACLOAD. +user +Viscous body force in global X-, Y-, +and Z-directions. +Viscous pressure on face n, applying +a pressure proportional to the velocity +normal to the face and opposing the +motion. +Foundations +Foundations are specified as described in “Element foundations,” Section 2.2.2. +Load ID +(*FOUNDATION) Load/Interaction +Abaqus/CAE +Units +Description +Fn(S) +Elastic +foundation +FL−3 +Elastic foundation on face n. A +positive pressure is directed into the +element. +Distributed heat fluxes +Distributed heat fluxes are available for all elements with temperature degrees of freedom. They are +specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*DFLUX) +BF +BFNU(S) +Abaqus/CAE +Load/Interaction +Units +Description +Body heat flux +Body heat flux +JL−3 T−1 +JL−3 T−1 +Sn +Surface heat flux +JL−2 T−1 +SnNU(S) +Not supported +JL−2 T−1 +Heat body flux per unit volume. +Nonuniform heat body flux per unit +volume with magnitude supplied via +user subroutine DFLUX. +Heat surface flux per unit area into +face n. +Nonuniform heat surface flux per +unit area into face n with magnitude +supplied via user subroutine DFLUX. +Film conditions +Film conditions are available for all elements with temperature degrees of freedom. They are specified +as described in “Thermal loads,” Section 33.4.4. +Abaqus/CAE +Load/Interaction +Units +Description +Load ID +(*FILM) +Fn +Surface film +condition +JL−2 T−1 −1 +FnNU(S) +Not supported +JL−2 T−1 −1 +Film coefficient and sink temperature +(units of +) provided on face n. +Nonuniform film coefficient and sink +temperature (units of +) provided on +face n with magnitude supplied via +user subroutine FILM. +Radiation types +Radiation conditions are available for all elements with temperature degrees of freedom. They are +specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*RADIATE) +Abaqus/CAE +Load/Interaction +Units +Description +Rn +Surface radiation Dimensionless +Emissivity and sink temperature +(units of +) provided on face n. +Surface-based loading +Distributed loads +Surface-based distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +HP(S) +Pressure +FL−2 +Pressure +FL−2 +PNU +Pressure +FL−2 +SP(E) +Pressure +FL−4 T2 +TRSHR +Surface traction +FL−2 +TRSHRNU(S) +Surface traction +FL−2 +TRVEC +Surface traction +FL−2 +TRVECNU(S) +Surface traction +FL−2 +29.6.8–6 +Hydrostatic pressure applied to the +element surface, +in global +Z. The pressure is positive in the +direction opposite to the surface +normal. +linear +Pressure +applied to the element +surface. The pressure is positive in +the direction opposite to the surface +normal. +Nonuniform pressure applied to the +element +surface with magnitude +supplied via user subroutine DLOAD +and VDLOAD +in Abaqus/Standard +in Abaqus/Explicit. The pressure is +positive in the direction opposite to +the surface normal. +Stagnation pressure applied to the +element reference surface. +traction +Shear +reference surface. +on +the +element +traction on the +Nonuniform shear +element +surface with +reference +magnitude and direction supplied +via user subroutine UTRACLOAD. +General +reference surface. +traction on the element +traction +on +Nonuniform general +the element reference surface with +magnitude and direction supplied via +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +VP(E) +Pressure +FL3T +Viscous surface pressure. The viscous +pressure is proportional to the velocity +face and +normal +opposing the motion. +to the element +Distributed heat fluxes +Surface-based heat fluxes are available for all elements with temperature degrees of freedom. They are +specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*DSFLUX) +Abaqus/CAE +Load/Interaction +Units +Description +Surface heat flux +JL−2 T−1 +SNU(S) +Surface heat flux +JL−2 T−1 +Heat surface flux per unit area into the +element surface. +Nonuniform heat surface flux per +unit area into the element surface +with magnitude supplied via user +subroutine DFLUX. +Film conditions +Surface-based film conditions are available for all elements with temperature degrees of freedom. They +are specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*SFILM) +FNU(S) +Radiation types +Abaqus/CAE +Load/Interaction +Units +Description +Surface film +condition +Surface film +condition +JL−2 T−1 −1 +JL−2 T−1 −1 +Film coefficient and sink temperature +(units of +) provided on the element +surface. +Nonuniform film coefficient and sink +temperature (units of +) provided on +the element surface with magnitude +supplied via user subroutine FILM. +Surface-based radiation conditions are available for all elements with temperature degrees of freedom. +They are specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*SRADIATE) +Abaqus/CAE +Load/Interaction +Units +Description +Surface radiation Dimensionless +Emissivity and sink temperature +(units of +) provided on the element +surface. +Element output +If a local coordinate system is not assigned to the element, the stress/strain components, as well as the +section forces/strains, are in the default directions on the surface defined by the convention given in +“Conventions,” Section 1.2.2. If a local coordinate system is assigned to the element through the section +definition (“Orientations,” Section 2.2.5), the stress/strain components and the section forces/strains are +in the surface directions defined by the local coordinate system. +The local directions defined in the reference configuration are rotated into the current configuration by +the average material rotation. +In the case of composite shells the components of section forces, section strains, and transverse +shear stress estimates for stacked continuum shells (CTSHR13 and CTSHR23) are reported in the +local orientation defined for the entire section (or the default shell coordinate directions if no section +orientation is used). Components of stress, strain, and transverse shear stress (TSHR13 and TSHR23) +are given with respect to the individual layer orientations. +Stress, strain, and other tensor components +Stress and other tensors (including strain tensors) are available. All tensors have the same components. +For example, the stress components are as follows: +S11 +S22 +S12 +Local +Local +Local +direct stress. +direct stress. +shear stress. +The stress in the thickness direction, +, is reported as zero to the output database as discussed in +“Abaqus/Standard output variable identifiers,” Section 4.2.1. +may be obtained through the average +section stress variable SSAVG6. Output of in-plane stress components of continuum shell elements does +not include Poisson effects due to changes in the thickness direction. +Heat flux components +Available for elements with temperature degrees of freedom. +HFL1 +HFL2 +HFL3 +Heat flux in the X-direction. +Heat flux in the Y-direction. +Heat flux in the Z-direction. +Section forces, moments, and transverse shear forces +SF1 +SF2 +SF3 +SF4 +SF5 +SF6 +SM1 +SM2 +SM3 +Direct membrane force per unit width in local 1-direction. +Direct membrane force per unit width in local 2-direction. +Shear membrane force per unit width in local 1–2 plane. +Transverse shear force per unit width in local 1-direction. +Transverse shear force per unit width in local 2-direction. +Thickness stress integrated over the element thickness. +Bending moment force per unit width about local 2-axis. +Bending moment force per unit width about local 1-axis. +Twisting moment force per unit width in local 1–2 plane. +The section force and moment resultants per unit length in the normal basis directions in a given shell +section of thickness h can be defined on this basis as +where stress in the thickness direction +is constant through the thickness. Outputs of in-plane section +forces of continuum shell elements do not include Poisson effects due to changes in the thickness +direction. +Average section stresses +SSAVG1 +SSAVG2 +SSAVG3 +SSAVG4 +SSAVG5 +SSAVG6 +Average membrane stress in local 1-direction. +Average membrane stress in local 2-direction. +Average membrane stress in local 1–2 plane. +Average transverse shear stress in local 1-direction. +Average transverse shear stress in local 2-direction. +Average thickness stress in the local 3-direction. +The average section stresses are defined as +where +and h is the current section thickness. +is constant through the thickness. +Section strains, curvatures, and transverse shear strains +SE1 +SE2 +SE3 +SE4 +SE5 +SE6 +SK1 +SK2 +SK3 +Direct membrane strain in local 1-direction. +Direct membrane strain in local 2-direction. +Shear membrane strain in local 1–2 plane. +Transverse shear strain in the local 1-direction. +Transverse shear strain in the local 2-direction. +Total strain in the thickness direction. +Curvature change about local 1-axis. +Curvature change about local 2-axis. +Surface twist in local 1–2 plane. +The local directions are defined in “Shell elements: overview,” Section 29.6.1. +Shell thickness +STH +Section thickness, which is the current section thickness if geometric nonlinearity is +considered; otherwise, it is the initial section thickness. +Transverse shear stress estimates +TSHR13 +TSHR23 +13-component of transverse shear stress. +23-component of transverse shear stress. +Estimates of the transverse shear stresses are available at section integration points as output variables +TSHR13 or TSHR23 for both Simpson’s rule and Gauss quadrature. For Simpson’s rule output of +variables TSHR13 or TSHR23 should be requested at nondefault section points, since the default output +is at section point 1 of the shell section where the transverse shear stresses vanish. +For numerically integrated sections, estimates of the interlaminar shear stresses in composite +sections—i.e., the transverse shear stresses at the interface between two composite layers—can be +obtained only by using Simpson’s rule. With Gauss quadrature no section integration point exists at +the interface between composite layers. +Unlike the S11, S22, and S12 in-surface stress components, TSHR13 and TSHR23 are not calculated +from the constitutive behavior at points through the shell section. They are estimated by matching the +elastic strain energy associated with shear deformation of the shell section with that based on piecewise +quadratic variation of the transverse shear stress across the section, under conditions of bending about one +axis . Therefore, interlaminar shear stress calculation is supported only when +If you specify the transverse +the elastic material model is used for each layer of the shell section. +shear stiffness values, interlaminar shear stress output is not available. TSHR13 and TSHR23 are valid +only for sections that have one element through the thickness direction. For sections with two or more +continuum shell elements stacked in the thickness direction, output variables SSAVG4 and SSAVG5 or +CTSHR13 and CTSHR23 should be used instead. An example using SSAVG4 and SSAVG5 to estimate +the transverse shear stress distribution in stacked continuum shells can be found in “Composite shells in +cylindrical bending,” Section 1.1.3 of the Abaqus Benchmarks Manual. +Transverse shear stress estimates for stacked continuum shells +13-component of transverse shear stress for stacked continuum shells. +23-component of transverse shear stress for stacked continuum shells. +CTSHR13 +CTSHR23 +Estimates of the transverse shear stresses that take into account the continuity of interlaminar transverse +shear stress for stacked continuum shells are available at section integration points as output variables +CTSHR13 or CTSHR23 for both Simpson’s rule and Gauss quadrature. CTSHR13 or CTSHR23 are +available only in Abaqus/Standard. +CTSHR13 and CTSHR23 are not calculated from the constitutive behavior at points through the shell +section. They are estimated by assuming a quadratic variation of shear stress across the element section +and by enforcing the continuity of interface transverse shear between adjoining continuum elements in +a stack. It is also assumed that the transverse shear is zero at the free boundaries of a stack. +The intended use case for CTSHR13 and CTSHR23 is to estimate the through-the-thickness transverse +shear stress for flat or nearly flat composite plates that are modeled with stacked continuum shell elements +where each continuum element in the stack models a single material layer. Central to CTSHR13 and +CTSHR23 is the concept of a “stack” of continuum shell elements. +During input file preprocessing Abaqus partitions all the continuum shells in a model into stacks. A +“stack” is defined as a contiguous set of continuum shells whose first and last elements lie on a free +boundary and who are connected through shared nodes on the top and bottom element surfaces (as +determined by the elements’ stack directions). +In this context a “free boundary” is a top or bottom +surface of a continuum shell element that is not connected through its nodes to another continuum shell +element. For example, assuming that the stack direction of all the elements in Figure 29.6.8–1 is in the +z-direction, elements 1–6 would form a stack. +z +A stack of continuum shell elements +x +Figure 29.6.8–1 Composite plate meshed with six stacked continuum shells through the thickness. +It is important to emphasize that stacks of continuum shells are connected through shared nodes, not +through constraints or other elements. Suppose, for example, that in Figure 29.6.8–1 element pairs 1–2, +2–3, 4–5, and 5–6 are connected to each other through shared nodes, but elements 3 and 4 are connected +through a constraint (such as a tied constraint). In that case Abaqus would interpret the bottom surface +of element 3 and the top surface of element 4 as free boundaries; therefore, elements 1–3 would form +one stack, and elements 4–6 would form a second independent stack. For another example, suppose +that element 4 is not a continuum shell element. In this case elements 1–3 would form one stack, and +elements 5–6 would form another stack. In a final example, suppose the stack directions of elements +1–5 are in the global z-direction and the stack direction of element 6 is in the global x-direction. In this +case elements 1–5 would form a stack separate from element 6. In the three cases just discussed the +computed values of CTSHR13 and CTSHR23 would probably not be what you wanted. It is more likely +that you want elements 1–6 to be in the same stack. It may be necessary to make changes in your model +to achieve this. You can review the partitioning of the continuum shell elements into stacks in the data +file by making a model definition data request. +The continuum shell elements in a stack must satisfy certain criteria; otherwise, Abaqus marks the stack +as invalid with respect to computing CTSHR13 or CTSHR23. If a stack is marked as invalid, CTSHR13 +or CTSHR23, if requested, are not computed and are set to zero for all continuum shell elements in that +stack. If a continuum shell element does not have an elastic material model, if you specify the transverse +shear for any element in the stack, or if the element is specified as rigid, that stack is marked as invalid. +A stack is also marked as invalid if the normal of any element in a stack is not within 10° of the average +normal for the stack. In addition, if a continuum shell element is removed during the analysis, the stack +to which the element belongs is marked as invalid until the element is reactivated. +There are several other certain restrictions on CTSHR13 and CTSHR23. CTSHR13 and CTSHR23 are +not available in any continuum shell element with a multi-layer composite material definition. However, +having a multi-layer composite element in the stack does not invalidate the stack. For the purposes +of computing CTSHR13 and CTSHR23, a maximum of 500 continuum shell elements can be put in +any individual stack. +If more than 500 continuum shell elements are stacked on top of each other, +Abaqus issues a warning message during input file preprocessing, and CTSHR13 and CTSHR23 are not +computed and are set to zero for all continuum shell elements in the model. CTSHR13 and CTSHR23 +are not available if element operations are run in parallel . CTSHR13 or CTSHR23 are currently available only for static and direct-integration +dynamic analyses. +An example using CTSHR13 and CTSHR23 to estimate the transverse shear stress distribution in stacked +continuum shells can be found in “Composite shells in cylindrical bending,” Section 1.1.3 of the Abaqus +Benchmarks Manual. +Node ordering on elements +face 5 +face 1 +face 3 +face 2 +face 4 +face 2 +face 3 +face 6 +face 1 +face 5 +face 4 +6-node continuum shell +8-node continuum shell +Numbering of integration points for output +Stress/displacement analysis +6-node continuum shell +8-node continuum shell +29.6.9 +AXISYMMETRIC SHELL ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Shell elements: overview,” Section 29.6.1 +• “Choosing a shell element,” Section 29.6.2 +• *NODAL THICKNESS +• *SHELL GENERAL SECTION +• *SHELL SECTION +Overview +This section provides a reference to the axisymmetric shell elements available in Abaqus/Standard and +Abaqus/Explicit. For axisymmetric shell geometries in which nonaxisymmetric behavior is expected, +use the SAXA elements available in Abaqus/Standard . +Conventions +Coordinate 1 is r, coordinate 2 is z. The r-direction corresponds to the global X-direction, and the z- +direction corresponds to the global Y-direction. Coordinate 1 should be greater than or equal to zero. +Degree of freedom 1 is +plane. +, degree of freedom 2 is +, and degree of freedom 6 is rotation in the r–z +Abaqus does not automatically apply any boundary conditions to nodes located along the symmetry axis. +You should apply radial or symmetry boundary conditions on these nodes if desired. +Point loads and concentrated fluxes should be given as the value integrated around the circumference +(that is, the load on the complete ring). +The meridional direction is the direction that is tangent to the element in the r–z plane; that is, the +meridional direction is along the line that is rotated about the axis of symmetry to generate the full +three-dimensional body. +The circumferential or hoop direction is the direction normal to the r–z plane. +Element types +Stress/displacement elements +SAX1 +SAX2(S) +2-node thin or thick linear shell +3-node thin or thick quadratic shell +Active degrees of freedom +1, 2, 6 +Additional solution variables +None. +Heat transfer elements +DSAX1(S) +DSAX2(S) +2-node shell +3-node shell +Active degrees of freedom +11, 12, 13, etc. (temperatures through the thickness as described in “Choosing a shell element,” +Section 29.6.2) +Additional solution variables +None. +Coupled temperature-displacement element +SAX2T(S) +3-node thin or thick shell, quadratic displacement, linear temperature in the shell +surface +Active degrees of freedom +1, 2, 6 at all three nodes +11, 12, 13, etc. (temperatures through the thickness as described in “Choosing a shell element,” +Section 29.6.2) at the end nodes +Additional solution variables +None. +Nodal coordinates required +r, z, and optionally for shells with displacement degrees of freedom, +shell normal at the node. +, +, the direction cosines of the +Element property definition +Input File Usage: +Use either of the following options for stress/displacement elements: +*SHELL SECTION +*SHELL GENERAL SECTION +Use the following option for heat transfer or coupled temperature-displacement +elements: +*SHELL SECTION +In addition, use the following option for variable thickness shells: +*NODAL THICKNESS +Property module: Create Section: select Shell as the section Category +and Homogeneous or Composite as the section Type +Abaqus/CAE Usage: +Element-based loading +Distributed loads +Distributed loads are available for elements with displacement degrees of freedom. They are specified +as described in “Distributed loads,” Section 33.4.3. +Distributed load magnitudes are per unit area or per unit volume. They do not need to be multiplied by +. +Body forces and centrifugal loads must be given as force per unit area if a general shell section is used. +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +BR +BZ +Body force +Body force +BRNU +Body force +FL−3 +FL−3 +FL−3 +BZNU +Body force +FL−3 +Body force per unit volume in the +radial direction. +Body force per unit volume in the +axial direction. +in the +the magnitude +Nonuniform body force per unit +radial direction, +volume +with +supplied +subroutine DLOAD in +via +Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +user +the magnitude +Nonuniform body force per unit +volume in the global z-direction, +with +supplied +subroutine DLOAD in +via +Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +user +CENT(S) +Not supported +FL−4 +(ML−3 T−2 ) +Centrifugal load (magnitude given as +is the mass density and +is the angular velocity). Since only +, where +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +axisymmetric deformation is allowed, +the spin axis must be the z-axis. +CENTRIF(S) +Rotational body +force +T−2 +GRAV +Gravity +LT−2 +HP(S) +Not supported +FL−2 +Pressure +FL−2 +PNU +Not supported +FL−2 +, where +Centrifugal load (magnitude is input +as +the angular +velocity). Since only axisymmetric +deformation is allowed, the spin axis +must be the z-axis. +is +Gravity +direction +acceleration). +loading +in +(magnitude +specified +as +input +Hydrostatic pressure applied to the +element reference surface and linear +in global Z. The pressure is positive in +the direction of the positive element +normal. +Pressure +applied to the element +reference surface. The pressure is +positive in the direction of the positive +element normal. +applied +reference +to +Nonuniform pressure +surface +the +element +via +with magnitude +in +user +subroutine +VDLOAD +Abaqus/Standard +in Abaqus/Explicit. +The pressure +is positive in the direction of the +positive element normal. +supplied +DLOAD +and +SBF(E) +SP(E) +Not supported +FL−5 T2 +Not supported +FL−4 T2 +TRSHR +Surface traction +FL−2 +TRSHRNU(S) +Not supported +FL−2 +Stagnation body force in radial and +axial directions. +Stagnation pressure applied to the +element reference surface. +traction +Shear +reference surface. +on +the +element +Nonuniform shear +reference +element +traction on the +surface with +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +AXISYMMETRIC SHELLS +TRVEC +Surface traction +FL−2 +TRVECNU(S) +Not supported +FL−2 +VBF(E) +VP(E) +Not supported +FL−4 T +Not supported +FL−3 T +magnitude and direction supplied +via user subroutine UTRACLOAD. +General +reference surface. +traction on the element +traction +Nonuniform general +on +the element reference surface with +magnitude and direction supplied via +user subroutine UTRACLOAD. +Viscous body force in radial and axial +directions. +Viscous surface pressure. The viscous +pressure is proportional to the velocity +normal +face and +opposing the motion. +to the element +Foundations +Foundations are available for Abaqus/Standard elements with displacement degrees of freedom. They +are specified as described in “Element foundations,” Section 2.2.2. +Load ID +(*FOUNDATION) Load/Interaction +Abaqus/CAE +Units +Description +F(S) +Elastic +foundation +FL−3 +Elastic foundation in the direction of +the shell normal. +Distributed heat fluxes +Distributed heat fluxes are available for elements with temperature degrees of freedom. They are +specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*DFLUX) +BF(S) +BFNU(S) +Abaqus/CAE +Load/Interaction +Units +Description +Body heat flux +Body heat flux +JL−3 T−1 +JL−3 T−1 +Body heat flux per unit volume. +Nonuniform body heat flux per unit +volume with magnitude supplied via +user subroutine DFLUX. +Surface heat flux per unit area into the +bottom face of the element. +SNEG(S) +Surface heat flux +JL−2 T−1 +Load ID +(*DFLUX) +Abaqus/CAE +Load/Interaction +Units +Description +SPOS(S) +Surface heat flux +JL−2 T−1 +SNEGNU(S) +Not supported +JL−2 T−1 +SPOSNU(S) +Not supported +JL−2 T−1 +Surface heat flux per unit area into the +top face of the element. +Nonuniform surface heat flux per +unit area into the bottom face of the +element with magnitude supplied via +user subroutine DFLUX. +Nonuniform surface heat flux per unit +area into the top face of the element +with magnitude supplied via user +subroutine DFLUX. +Film conditions +Film conditions are available for elements with temperature degrees of freedom. They are specified as +described in “Thermal loads,” Section 33.4.4. +Load ID +(*FILM) +FNEG(S) +FPOS(S) +Abaqus/CAE +Load/Interaction +Units +Description +Surface film +condition +Surface film +condition +JL−2 T −1 −1 +JL−2 T−1 −1 +Film coefficient and sink temperature +(units of +) provided on the bottom +face of the element. +Film coefficient and sink temperature +(units of +) provided on the top face +of the element. +Nonuniform film coefficient and sink +temperature (units of +) provided +on the bottom face of the element +with magnitude supplied via user +subroutine FILM. +Nonuniform film coefficient and sink +temperature (units of +) provided +on the top face of +the element +with magnitude supplied via user +subroutine FILM. +FNEGNU(S) +Not supported +JL−2 T−1 −1 +FPOSNU(S) +Not supported +JL−2 T−1 −1 +Radiation types +Radiation conditions are available for elements with temperature degrees of freedom. They are specified +as described in “Thermal loads,” Section 33.4.4. +Load ID +(*RADIATE) +RNEG(S) +Abaqus/CAE +Load/Interaction +Units +Description +Surface radiation Dimensionless +Emissivity and sink temperature +(units of +) provided for the bottom +face of the shell. +Emissivity and sink temperature +(units of +) provided for the top face +of the shell. +RPOS(S) +Surface radiation Dimensionless +Surface-based loading +Distributed loads +Surface-based distributed loads are available for elements with displacement degrees of freedom. They +are specified as described in “Distributed loads,” Section 33.4.3. +Distributed load magnitudes are per unit area or per unit volume. They do not need to be multiplied by +. +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +HP(S) +Pressure +FL−2 +Pressure +FL−2 +PNU +Pressure +FL−2 +Hydrostatic pressure on the element +reference surface and linear in global +Z. The pressure is positive in the +direction opposite the surface normal. +Pressure on the element reference +surface. The pressure is positive in +the direction opposite to the surface +normal. +Nonuniform pressure on the element +reference surface with magnitude +supplied via user subroutine DLOAD +in Abaqus/Standard and VDLOAD +in Abaqus/Explicit. The pressure is +positive in the direction opposite to +the surface normal. +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +SP(E) +Pressure +FL−4 T2 +TRSHR +Surface traction +FL−2 +TRSHRNU(S) +Surface traction +FL−2 +TRVEC +Surface traction +FL−2 +TRVECNU(S) +Surface traction +FL−2 +VP(E) +Pressure +FL−3 T +Stagnation pressure applied to the +element reference surface. +traction +Shear +reference surface. +on +the +element +traction on the +Nonuniform shear +surface with +reference +element +magnitude and direction supplied +via user subroutine UTRACLOAD. +General +reference surface. +traction on the element +traction +Nonuniform general +on +the element reference surface with +magnitude and direction supplied via +user subroutine UTRACLOAD. +Viscous surface pressure. The viscous +pressure is proportional to the velocity +normal to the element surface and +opposing the motion. +Distributed heat fluxes +Surface-based heat fluxes are available for elements with temperature degrees of freedom. They are +specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*DSFLUX) +Abaqus/CAE +Load/Interaction +Units +Description +S(S) +Surface heat flux +JL−2 T−1 +SNU(S) +Surface heat flux +JL−2 T−1 +Surface heat flux per unit area into the +element surface. +Nonuniform surface heat flux per +unit area into the element surface +with magnitude supplied via user +subroutine DFLUX. +Film conditions +Surface-based film conditions are available for elements with temperature degrees of freedom. They are +specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*SFILM) +F(S) +FNU(S) +Radiation types +Abaqus/CAE +Load/Interaction +Units +Description +Surface film +condition +Surface film +condition +JL−2 T−1 −1 +JL−2 T−1 −1 +Film coefficient and sink temperature +(units of +) provided on the element +surface. +Nonuniform film coefficient and sink +temperature (units of +) provided on +the element surface with magnitude +supplied via user subroutine FILM. +Surface-based radiation conditions are available for elements with temperature degrees of freedom. They +are specified as described in “Thermal loads,” Section 33.4.4. +Load ID +(*SRADIATE) +Abaqus/CAE +Load/Interaction +Units +Description +R(S) +Surface radiation Dimensionless +Emissivity and sink temperature +(units of +) provided for the element +surface. +Incident wave loading +Surface-based incident wave loads are available. They are specified as described in “Acoustic, shock, +and coupled acoustic-structural analysis,” Section 6.10.1. If the incident wave field includes a reflection +off a plane outside the boundaries of the mesh, this effect can be included. +Element output +Stress, strain, and other tensor components +Stress and other tensors (including strain tensors) are available for elements with displacement degrees +of freedom. All tensors have the same components. For example, the stress components are as follows: +S11 +S22 +Meridional stress. +Hoop (circumferential) stress. +Section forces, moments, and transverse shear forces +Available for elements with displacement degrees of freedom. +SF1 +SF2 +Membrane force per unit width in the meridional direction. +Membrane force per unit width in the hoop direction. +SF3 +SF4 +SM1 +SM2 +Transverse shear force per unit width in the meridional direction (available only from +Abaqus/Standard). +Integrated stress in the thickness direction; always zero (available only from +Abaqus/Standard). +Bending moment per unit width about the hoop direction. +Bending moment per unit width about the meridional direction. +Section strains, curvature changes, and transverse shear strains +Available for elements with displacement degrees of freedom. +SE1 +SE2 +SE3 +SE4 +SK1 +SK2 +Membrane strain in the meridional direction. +Membrane strain in the hoop direction. +Transverse shear +Abaqus/Standard). +Strain in the thickness direction (available only from Abaqus/Standard). +Curvature change about the hoop direction. +Curvature change about the meridional direction. +strain in the meridional direction (available only from +Shell thickness +STH +Shell thickness, which is the current thickness for SAX1, SAX2, and SAX2T +elements. +Heat flux components +Available for elements with temperature degrees of freedom. +HFL1 +HFL2 +Heat flux in the meridional direction. +Heat flux in the thickness direction. +Node ordering on elements +2 - node element +3 - node element +Numbering of integration points for output +2 - node element +3 - node element +29.6.10 +AXISYMMETRIC SHELL ELEMENTS WITH NONLINEAR, ASYMMETRIC +DEFORMATION +Product: Abaqus/Standard +References +• “Shell elements: overview,” Section 29.6.1 +• “Choosing a shell element,” Section 29.6.2 +• *NODAL THICKNESS +• *SHELL GENERAL SECTION +• *SHELL SECTION +Overview +This section provides a reference to the axisymmetric shell elements with nonlinear, asymmetric +deformation available in Abaqus/Standard. +For an axisymmetric reference geometry where +axisymmetric deformation is expected, use regular axisymmetric elements . For an axisymmetric reference geometry where nonaxisymmetric +deformation is expected and the thickness to characteristic radius is high or through the thickness detail +is required, use CAXA-type elements . +Conventions +Coordinate 1 is r, coordinate 2 is z. The r-direction corresponds to the global X-direction in the +plane and the global Y-direction in the +Z-direction. Coordinate 1 should be greater than or equal to zero. +plane, and the z-direction corresponds to the global +Degree of freedom 1 is +, degree of freedom 2 is +, degree of freedom 6 is rotation in the r–z plane. +allows the modeling of half of the initially +Even though the symmetry in the r–z plane at +axisymmetric structure, the loading must be specified as the total load on the full axisymmetric body. +Consider, for example, a cylindrical shell loaded by a unit uniform axial force. To produce a unit load +on a SAXA element with four modes, the nodal forces are 1/8, 1/4, 1/4, 1/4, and 1/8 at +, +, +, +, and , respectively. +The meridional direction is the direction tangent to the element in the r–z plane; that is, the meridional +direction is along the line that is rotated about the axis of symmetry to generate the full three-dimensional +body. +The circumferential or hoop direction is the direction normal to the r–z plane. +Element types +SAXA1N +SAXA2N +Linear interpolation, Fourier shell element with 2 nodes in the meridional direction and +N Fourier modes +Quadratic interpolation, Fourier shell element with 3 nodes in the meridional direction +and N Fourier modes +Active degrees of freedom +1, 2, 6 +See Figure 29.6.10–1 for the positive nodal displacement and rotation directions. The nodal rotation, +is consistent with the SAX elements; however, a positive nodal rotation is in the negative -direction. +, +uz +ur +φθ +uz +φθ +ur +uz +ur +φθ +Figure 29.6.10–1 Element coordinate system and positive +displacement/rotation directions. SAXA22 element shown. +Additional solution variables +elements have +SAXA +variables relating to ( +SAXA +elements have +variables relating to ( +, +, +, +, +). +). +Nodal coordinates required +r, z (given in the r–z plane for +) +The two direction cosines, +or by a user-specified normal definition . +, of the nodal normal field can be specified either in the nodal data +and +Element property definition +If a general shell section is used and the section stiffness matrix is given directly, a full 6 × 6 section +stiffness should be specified (i.e., 21 constants as for a three-dimensional shell). +Input File Usage: +Use either of the following options: +*SHELL SECTION +*SHELL GENERAL SECTION +In addition, use the following option for variable thickness shells: +*NODAL THICKNESS +Element-based loading +Distributed loads +Distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Distributed load magnitudes are per unit area or per unit volume. They do not need to be multiplied by +times the radius. +Load ID +(*DLOAD) +Units +Description +FL−3 +FL−3 +FL−3 +FL−3 +FL−2 +FL−2 +FL−2 +Body force per unit volume in the global X- +direction. +Body force per unit volume in the global Z- +direction. +Nonuniform body force in the global +X-direction with magnitude supplied via +user subroutine DLOAD. +Nonuniform body force in the global +Z-direction with magnitude supplied via +user subroutine DLOAD. +Hydrostatic pressure on the shell surface, +linear in the global Z-direction. +Pressure on the shell surface. +Nonuniform pressure on the shell surface +with magnitude supplied via user subroutine +DLOAD. +29.6.10–3 +BX +BZ +BXNU +BZNU +HP +Element output +employs the trapezoidal rule. There are +and +equally +The numerical integration with respect to +spaced integration planes in the element, including the +planes, with N being the +number of Fourier modes. Consequently, the radial nodal forces corresponding to pressure loads applied +in the circumferential direction are distributed in this direction in the ratio of +in the 1 Fourier mode +element, +in the 4 Fourier mode element. +The sum of these consistent nodal forces is equal to the integral of the applied pressure over the full +circumference ( +in the 2 Fourier mode element, and +). +Stress, strain, and other tensor components +Stress and other tensors (including strain tensors) are available for elements with displacement degrees +of freedom. All tensors have the same components. For example, the stress components are as follows: +S11 +S22 +S12 +Meridional stress. +Hoop (circumferential) stress. +Local 12 shear stress (zero at +and +). +Section forces +SF1 +SF2 +SF3 +SF4 +SM1 +SM2 +SM3 +Section strains +SE1 +SE2 +SE3 +SE4 +SK1 +SK2 +SK3 +Direct membrane force per unit width in local 1-direction. +Direct membrane force per unit width in local 2-direction. +Shear membrane force per unit width in local 1–2 plane. +Integrated stress in the thickness direction; always zero. +Bending moment per unit width about local 2-axis. +Bending moment per unit width about local 1-axis. +Twisting moment per unit width in local 1–2 plane. +Direct membrane strain in local 1-direction. +Direct membrane strain in local 2-direction. +Shear membrane strain in local 1–2 plane. +Strain in the thickness direction. +Bending strain in local 1-direction. +Bending strain in local 2-direction. +Twisting strain in local 1–2 plane. +The section force and moment resultants per unit length in the normal basis directions for a given layer +of thickness h can be defined, in components relative to this basis, as: +where +is the offset of the reference surface from the midsurface. +The local directions are defined in “Defining the initial geometry of conventional shell elements,” +Section 29.6.3. +Current shell thickness +STH +Current shell thickness. +Node ordering on elements +The node ordering in the first generator plane ( +) of each element is shown below. You specify +the line or curve of nodes in the generator plane just as with the SAX1 and SAX2 elements. Each +element must have N more planes of nodes defined, where N is the number of Fourier modes used. +Abaqus/Standard will generate these additional circumferential nodes and number them by adding a +constant offset value to the nodes specified in the first plane . +30. +Inertial, Rigid, and Capacitance Elements +Point mass elements +Rotary inertia elements +Rigid elements +Capacitance elements +30.1 +30.2 +30.3 +30.1 +Point mass elements +• “Point masses,” Section 30.1.1 +• “Mass element library,” Section 30.1.2 +30.1.1 +POINT MASSES +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Mass element library,” Section 30.1.2 +• *MASS +• “Defining point mass and rotary inertia,” Section 33.3 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +Mass elements: +• allow the introduction of concentrated mass that is either isotropic or anisotropic at a point; +• are associated with the three translational degrees of freedom at a node. +If rotary inertia is also required (for example, to represent a rigid body), use element type ROTARYI +(“Rotary inertia,” Section 30.2.1). +In addition to point masses, Abaqus provides a convenient nonstructural mass definition that can be +used to smear mass from features that have negligible structural stiffness over a region that is typically +adjacent to the nonstructural feature. The nonstructural mass can be specified in the form of a total mass +value, a mass per unit volume, a mass per unit area, or a mass per unit length . +Defining the isotropic mass value +You specify a mass magnitude, which is associated with the three translational degrees of freedom at +the node of the element. Specify mass, not weight. You must associate this mass with a region of your +model. +Input File Usage: +*MASS, ELSET=name +mass magnitude +where the ELSET parameter refers to a set of MASS elements. +Abaqus/CAE Usage: +Property or Interaction module: Special→Inertia→Create: Point +mass/inertia: select point: Magnitude: Isotropic: mass magnitude +Defining the mass matrix explicitly in Abaqus/Standard +You can define a general mass matrix explicitly in Abaqus/Standard if the introduction of individual terms +on and off the diagonal of the mass matrix is desired. See “User-defined elements,” Section 32.15.1, for +details. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options: +*USER ELEMENT +*MATRIX +Defining the mass matrix explicitly is not supported in Abaqus/CAE. +Defining the anisotropic mass tensor +You can specify the mass as anisotropic by giving the three principal values and the principal directions. +When the orientation of the principal directions is not specified, they are assumed to coincide with the +In a large-displacement analysis the local axes of the anisotropic mass rotate with the +global axes. +rotation, if active, of the node to which the anisotropic mass is attached. The rotation degree of freedom +is active at a node if that node is connected to a beam, a conventional shell, a rotary inertia element, +or a rigid body. You can specify mass proportional loads such as gravitation on an anisotropic mass. +Damping and mass scaling can also be used with an anisotropic mass. +Specify mass, not weight. You must associate this mass with a region of your model. +Input File Usage: +*MASS, ELSET=name, TYPE=ANISOTROPIC, +ORIENTATION=orientation_name +, +, +where the ELSET parameter refers to a set of MASS elements. +Abaqus/CAE Usage: +Property or Interaction module: Special→Inertia→Create: Point +mass/inertia: select point: Magnitude: Anisotropic: +, +, and +Defining damping for MASS elements +In Abaqus/Standard you can define mass proportional damping for direct-integration dynamic analysis or +composite damping for modal dynamic analysis. Although both damping definitions can be specified for +a set of MASS elements, only the damping that is relevant to the particular dynamic analysis procedure +will be used. +In Abaqus/Explicit mass proportional damping can be defined for MASS elements. +Dynamics +You can define inertia proportional damping for MASS elements in direct-integration dynamic analysis +or explicit dynamic analysis. See “Material damping,” Section 26.1.1, for details. +Input File Usage: +Abaqus/CAE Usage: +*MASS, ALPHA= +Property or Interaction module: Special→Inertia→Create: Point +mass/inertia: select point: Damping: Alpha: +Modal dynamics +You can define the fraction of critical damping to be used with the MASS elements when calculating +composite damping factors for the modes when used in modal dynamic analysis. See “Material +damping,” Section 26.1.1, for details. +Abaqus/CAE Usage: +*MASS, COMPOSITE= +Property or Interaction module: Special→Inertia→Create: Point +mass/inertia: select point: Damping: Composite: +POINT MASSES +30.1.2 +MASS ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Point masses,” Section 30.1.1 +• *MASS +Overview +This section provides a reference to the mass elements available in Abaqus/Standard and +Abaqus/Explicit. +Element type +MASS +Point mass +Active degrees of freedom +1, 2, 3 +Additional solution variables +None. +Nodal coordinates required +X, Y, Z +Element property definition +Input File Usage: +Abaqus/CAE Usage: +*MASS +Not supported +Element-based loading +Distributed loads +Distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +Centrifugal load (magnitude is input +as +the angular +velocity). +, where +is +CENTRIF(S) +Not supported +T−2 +Load ID +(*DLOAD) +GRAV +Abaqus/CAE +Load/Interaction +Units +Description +Not supported +LT−2 +ROTA(S) +Not supported +T−2 +Gravity +direction. +loading +in +specified +Rotary acceleration load (magnitude +is input as +is the rotary +acceleration). +, where +Element output +ELKE +Element kinetic energy (available only from Abaqus/Standard). +Nodes associated with the element +1 node. +30.2 +Rotary inertia elements +• “Rotary inertia,” Section 30.2.1 +• “Rotary inertia element library,” Section 30.2.2 +30.2.1 +ROTARY INERTIA +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Rotary inertia element library,” Section 30.2.2 +• *ROTARY INERTIA +• “Defining point mass and rotary inertia,” Section 33.3 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +Rotary inertia elements: +• allow rotary inertia to be included at a node; +• are associated with the three rotational degrees of freedom at a node; and +• can be paired with a MASS element (“Point masses,” Section 30.1.1) to define the mass and inertia +properties of a rigid body directly (“Rigid body definition,” Section 2.4.1). +Defining the rotary inertia +The ROTARYI element allows rotary inertia to be included at a node. The node is assumed to be the +center of mass of the body so that only second moments of inertia are required. If the node is part of +a rigid body, the offset between the node and the center of mass of the rigid body is accounted for. All +six components of the rotary inertia tensor— , +, and —about the global coordinate +, +system are defined as follows: +, +, +The rotary inertia tensor must be positive semi-definite. +You specify the moments of inertia, which should be given in units of ML2 . You must associate +these moments of inertia with a region of your model. +Optionally, you can refer to a local orientation (“Orientations,” Section 2.2.5) that defines the +directions of the local axes for which the rotary inertia values are being given. If you do not specify a +local orientation and the rotary inertia element is defined within a part or a part instance , the components of the inertia tensor must be given with respect to the +local part axes. If you do not specify a local orientation and the rotary inertia element is not defined +within a part or a part instance, the components of the inertia tensor must be given with respect to the +global axes. +Input File Usage: +*ROTARY INERTIA, ELSET=name, ORIENTATION=name +, +, +, +, +, +where the ELSET parameter refers to a set of ROTARYI elements. +Abaqus/CAE Usage: +Property or Interaction module: Special→Inertia→Create: Point +mass/inertia: select point: Magnitude: I11: +, I33: +; if necessary, toggle on Specify off-diagonal terms: I12: +, I13: +; CSYS: Edit +, I23: +, I22: +Defining damping for ROTARYI elements +In Abaqus/Standard you can define mass proportional damping for direct-integration dynamic analysis +or composite damping for modal dynamic analysis. Although both damping definitions can be specified +for a set of ROTARYI elements, only the damping that is relevant to the particular dynamic analysis +procedure will be used. +In Abaqus/Explicit mass proportional damping can be defined for ROTARYI elements. +Dynamics +You can define inertia proportional damping for ROTARYI elements in direct-integration dynamic +analysis or explicit dynamic analysis. See “Material damping,” Section 26.1.1, for details. +Input File Usage: +Abaqus/CAE Usage: +*ROTARY INERTIA, ALPHA= +Property or Interaction module: Special→Inertia→Create: Point +mass/inertia: select point: Damping: Alpha: +Modal dynamics +You can define the fraction of critical damping to be used with the ROTARYI elements when calculating +composite damping factors for the modes when used in modal dynamic analysis. See “Material +damping,” Section 26.1.1, for details. +Input File Usage: +Abaqus/CAE Usage: +*ROTARY INERTIA, COMPOSITE= +Property or Interaction module: Special→Inertia→Create: Point +mass/inertia: select point: Damping: Composite: +Speeding up convergence in three-dimensional implicit analyses +In geometrically nonlinear analysis in Abaqus/Standard, rigid body rotary inertia contributes some +unsymmetric terms to the system matrix when the motion is in three dimensions and the rotary inertia +is not the same about all three axes. Therefore, in cases when the rotary inertia effects are significant, +the solution may converge faster if you use the unsymmetric matrix storage and solution scheme for the +step (“Defining an analysis,” Section 6.1.2). +30.2.2 +ROTARY INERTIA ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Rotary inertia,” Section 30.2.1 +• *ROTARY INERTIA +Overview +This section provides a reference to the rotary inertia elements available in Abaqus/Standard and +Abaqus/Explicit. +Element type +ROTARYI +Rotary inertia at a point +Active degrees of freedom +4, 5, 6 +Additional solution variables +None. +Nodal coordinates required +X, Y, Z +Element property definition +Input File Usage: +Abaqus/CAE Usage: +*ROTARY INERTIA +Property or Interaction module: Special→Inertia→Create: Point +mass/inertia: select point: Magnitude: Rotary Inertia +Element-based loading +Distributed loads +Distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +ROTA(S) +Not supported +T−2 +ROTDYNF(S) +Not supported +T−1 +Rotary acceleration load (magnitude +is input as +is the rotary +acceleration). +, where +Rotordynamic load (magnitude is +input as +is the angular +velocity). +, where +Element output +ELKE +Element kinetic energy (available only from Abaqus/Standard). +Nodes associated with the element +1 node. +30.3 +Rigid elements +• “Rigid elements,” Section 30.3.1 +• “Rigid element library,” Section 30.3.2 +30.3.1 +RIGID ELEMENTS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Rigid body definition,” Section 2.4.1 +• “Rigid element library,” Section 30.3.2 +• *RIGID BODY +• “Defining rigid body constraints,” Section 15.15.2 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +Rigid elements: +• can be used to define the surfaces of rigid bodies for contact; +• can be used to define rigid bodies for multibody dynamic simulations; +• can be attached to deformable elements; +• can be used to constrain parts of a model; +• are used to apply Abaqus/Aqua loads to rigid structures; and +• are associated with a given rigid body and share a common node known as the rigid body reference +node. +Choosing an appropriate element +Use R2D2 elements in plane strain or plane stress analysis, RAX2 elements in axisymmetric planar +geometries, and R3D3 and R3D4 elements in three-dimensional analysis. +RB2D2 and RB3D2 elements are often used in Abaqus/Standard to model offshore structures that +will transmit Abaqus/Aqua loads but will not deform. They can also be used as rigid links between nodes +on deformable bodies. +Naming convention +Rigid elements in Abaqus are named as follows: +3D 2 +number of nodes +two-dimensional (2D), +three-dimensional (3D), +or axisymmetric (AX) +beam (optional) +rigid element +For example, R2D2 is a two-dimensional, 2-node, rigid element. +Element normal definition +For all rigid elements the face on the side of the element with the positive outward normal is referred to +as SPOS. The face on the opposite side is referred to as SNEG. The positive normal direction for each +element is defined below. +R2D2, RAX2, RB2D2, R3D3, and R3D4 rigid elements can be used in Abaqus/Standard to define +master surfaces for contact applications. The direction of the master surface’s outward normal is critical +for proper detection of contact. See “Defining contact pairs in Abaqus/Standard,” Section 35.3.1, for a +more detailed discussion of contact surface definitions. +Two-dimensional rigid elements +The positive outward normal direction, +going from node 1 to node 2 of the element. See Figure 30.3.1–1. +, is defined by a 90° counterclockwise rotation from the direction +face SPOS +face SNEG +Y or z +X or r +Figure 30.3.1–1 Positive normal for two-dimensional rigid elements. +Three-dimensional rigid elements +The positive normal for R3D3 and R3D4 elements is given by the right-hand rule going around the nodes +of the element in the order that they are given in the element’s connectivity. See Figure 30.3.1–2. +RB3D2 elements do not have a unique normal definition. +face SPOS +face SNEG +Figure 30.3.1–2 Positive normals for R3D3 and R3D4 elements. +Defining rigid elements +Rigid elements must always be part of a rigid body. See “Rigid body definition,” Section 2.4.1, for +complete details on the definition of a rigid body. +Input File Usage: +*RIGID BODY, ELSET=name +where the ELSET parameter refers to a set of rigid elements. +Abaqus/CAE Usage: +Interaction module: Create Constraint: Rigid body: Body (elements) +Mass distribution +In Abaqus/Standard rigid elements do not contribute mass to the rigid body to which they are assigned. +The mass distribution on the rigid surface can be accounted for by using point mass (“Point masses,” +Section 30.1.1) and rotary inertia elements (“Rotary inertia,” Section 30.2.1) on the nodes connected to +the rigid elements. +By default in Abaqus/Explicit, rigid elements do not contribute mass to the rigid body to which they +are assigned. To define the mass distribution, you can specify the density of all rigid elements in a rigid +body. When a nonzero density and thickness are specified, mass and rotary inertia contributions to the +rigid body from rigid elements will be computed in an analogous manner to structural elements. +Input File Usage: +Abaqus/CAE Usage: +Use the following option in Abaqus/Explicit to specify the density of rigid +elements: +*RIGID BODY, DENSITY=density +You cannot specify the density of rigid elements in Abaqus/CAE. +Geometry in Abaqus/Explicit +In Abaqus/Explicit you can specify the cross-sectional area or thickness for all of the rigid elements that +are part of a rigid body. Abaqus/Explicit assumes a default zero cross-sectional area or thickness if you +do not specify one. +To account for a continuously varying thickness of a surface formed by rigid elements in +Abaqus/Explicit, you can specify the thickness of the rigid elements at the nodes. +Specifying a nonzero thickness for rigid elements that form a rigid surface in a contact pair definition +can be used to account for the effect of surface thickness in the contact constraint. It also enables the use +of the double-sided surface contact feature with rigid surfaces formed by rigid elements. +Input File Usage: +Use the following option in Abaqus/Explicit to specify the cross-sectional area +or thickness for all rigid elements in a rigid body: +*RIGID BODY +cross-sectional area or thickness +Use both of the following options to specify a continuously varying thickness +for a surface formed by rigid elements: +*NODAL THICKNESS +*RIGID BODY, NODAL THICKNESS +You cannot specify the cross-sectional area or thickness of rigid elements in +Abaqus/CAE. +Abaqus/CAE Usage: +Offset in Abaqus/Explicit +In Abaqus/Explicit you can define the distance (measured as a fraction of the rigid element’s thickness) +from the rigid element’s midsurface to the reference surface containing the element’s nodes. The positive +values of the offset are in the direction of the element normal. When the offset distance is 0.5, the top +surface is the reference surface. When the offset distance is −0.5, the bottom surface is the reference +surface. The default offset distance is 0, which indicates that the middle surface of the rigid element is +the reference surface. You can specify a value for the offset distance that is greater in magnitude than +half the rigid element’s thickness. +Since no element-level calculations are performed for rigid elements, a specified offset affects only +the handling of contact pairs with rigid surfaces formed by rigid elements . Mass and rotary inertia contributions to the rigid body from rigid elements +defined with an offset are computed as if the offset is zero. +Input File Usage: +Use the following option in Abaqus/Explicit to specify a surface offset for a +rigid element: +*RIGID BODY, OFFSET=offset +The OFFSET parameter accepts a value or a label (SPOS or SNEG). Specifying +SPOS is equivalent to specifying a value of 0.5; specifying SNEG is equivalent +to specifying a value of −0.5. +Abaqus/CAE Usage: +You cannot specify an offset for rigid elements in Abaqus/CAE. +30.3.2 +RIGID ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Rigid elements,” Section 30.3.1 +• *RIGID BODY +Overview +This section provides a reference to the rigid elements available in Abaqus/Standard and Abaqus/Explicit. +Element types +2-D rigid elements +R2D2 +RAX2 +2-node, linear link (for use in plane strain or plane stress) +2-node, linear link (for use in axisymmetric planar geometries) +RB2D2(S) +2-node, rigid beam +Slave kinematic variables +R2D2 and RAX2: 1, 2 +RB2D2: 1, 2, 6 +Master degrees of freedom +R2D2, RAX2, and RB2D2: 1, 2, 6 at the rigid body reference node +Additional solution variables +None. +3-D rigid elements +R3D3 +R3D4 +3-node, triangular facet +4-node, bilinear quadrilateral +RB3D2(S) +2-node, rigid beam +Slave kinematic variables +R3D3 and R3D4: 1, 2, 3 +RB3D2: 1, 2, 3, 4, 5, 6 +Master degrees of freedom +1, 2, 3, 4, 5, 6 at the rigid body reference node +Additional solution variables +None. +Nodal coordinates required +R2D2 and RB2D2: X, Y +RAX2: r, z +R3D3, R3D4, and RB3D2: X, Y, Z +Element property definition +For R2D2, RB2D2, and RB3D2 elements you can specify the cross-sectional area of the element. In +Abaqus/Standard if no area is given, unit area is assumed; the area is required in Abaqus/Explicit. +For RAX2, R3D3, and R3D4 elements you can specify the thickness of the element. In Abaqus/Standard +if no thickness is given, unit thickness is assumed; the thickness is required in Abaqus/Explicit. +The cross-sectional area or element thickness is used for the purpose of defining body forces, which are +given in units of force per unit volume, and, in Abaqus/Explicit, determining the total mass. +Input File Usage: +Abaqus/CAE Usage: +*RIGID BODY +Interaction module: Create Constraint: Rigid body: Body (elements) +Element-based loading +Distributed loads +Distributed loads are available for elements with displacement degrees of freedom. They are specified +as described in “Distributed loads,” Section 33.4.3. +Available for R2D2 elements only: +Load ID +(*DLOAD) +BX(S) +BY(S) +BXNU(S) +Abaqus/CAE +Load/Interaction +Units +Description +Body force +Body force +Body force +FL−3 +FL−3 +FL−3 +Body force in global X-direction. +Body force in global Y-direction. +Nonuniform body force in global X- +direction with magnitude supplied via +user subroutine DLOAD. +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +BYNU(S) +Body force +FL−3 +CENT(S) +Not supported +CORIO(S) +Coriolis force +FL−4 +(ML−3 T−2 ) +FL−4 T +(ML−3 T−1 ) +P(E) +Pressure +FL−2 +PNU(E) +Not supported +FL−2 +Nonuniform body force in global Y- +direction with magnitude supplied via +user subroutine DLOAD. +Centrifugal load (magnitude is input +is the mass density +as +, where +per unit volume and +is the angular +velocity). +Coriolis force (magnitude is input +is the mass density +as +, where +per unit volume and +is the angular +velocity). The load stiffness due to +Coriolis loading is not accounted +for in direct steady-state dynamics +analysis. +Pressure on the element surface. The +pressure is positive in the direction of +the positive element normal. +Nonuniform pressure on the element +surface with magnitude +supplied +via user subroutine VDLOAD. The +pressure is positive in the direction of +the positive element normal. +Available for RAX2 elements only: +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +BR(S) +BZ(S) +Body force +Body force +BRNU(S) +Body force +FL−3 +FL−3 +FL−3 +Body force per unit volume in the +radial direction. +Body force per unit volume in the +axial direction. +Nonuniform body force per unit +volume in the radial direction, with +the magnitude supplied via user +subroutine DLOAD. +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +BZNU(S) +Body force +FL−3 +CENT(S) +Not supported +FL−4 +3 T−2 ) +(ML− +HP(S) +Not supported +FL−2 +Pressure +FL−2 +PNU +Not supported +FL−2 +TRSHR +Surface traction +TRSHRNU(S) +Not supported +FL−2 +FL−2 +TRVEC +Surface traction +FL−2 +TRVECNU(S) +Not supported +FL−2 +30.3.2–4 +Nonuniform body force per unit +volume +z-direction, with +the magnitude supplied via user +subroutine DLOAD. +in the +, where +Centrifugal load (magnitude given as +is the mass density and +is the angular speed). Since only +axisymmetric deformation is allowed, +the spin axis must be the z-axis. +Hydrostatic pressure on the element +surface and linear in global Z. The +pressure is positive in the direction of +the positive element normal. +Pressure on the element surface. The +pressure is positive in the direction of +the positive element normal. +Nonuniform pressure on the element +surface with the magnitude supplied +subroutine DLOAD in +via +user +and VDLOAD in +Abaqus/Standard +The pressure is +Abaqus/Explicit. +positive in the direction of the positive +element normal. +Shear traction on the element surface. +Nonuniform shear +traction on the +element surface with magnitude and +direction supplied via user subroutine +UTRACLOAD. +General +surface. +traction on the element +Nonuniform general traction on the +element surface with magnitude and +direction supplied via user subroutine +RIGID ELEMENT LIBRARY +Abaqus/CAE +Load/Interaction +Units +Description +Load ID +(*DLOAD) +BX(S) +BY(S) +BZ(S) +BXNU(S) +Body force +Body force +Body force +Body force +FL−3 +FL−3 +FL−3 +FL−3 +Body force in the global X-direction. +Body force in the global Y-direction. +Body force in the global Z-direction. +Nonuniform body force in the global +X-direction with magnitude supplied +via user subroutine DLOAD. +Nonuniform body force in the global +Y-direction with magnitude supplied +via user subroutine DLOAD. +Nonuniform body force in the global +Z-direction with magnitude supplied +via user subroutine DLOAD. +Centrifugal load (magnitude is input +is the mass density +as +, where +per unit volume and +is the angular +velocity). +Coriolis force (magnitude is input +as +is the mass density +, where +per unit volume and +is the angular +velocity). The load stiffness due to +Coriolis loading is not accounted +for in direct steady-state dynamics +analysis. +Hydrostatic pressure on the element +surface and linear in global Z. The +pressure is positive in the direction of +the positive element normal. +Pressure on the element surface. The +pressure is positive in the direction of +the positive element normal. +Nonuniform pressure on the element +surface with magnitude +supplied +subroutine DLOAD in +via +user +BYNU(S) +Body force +FL−3 +BZNU(S) +Body force +FL−3 +CENT(S) +Not supported +CORIO(S) +Coriolis force +FL−4 +(ML−3 T−2 ) +FL−4 T +(ML−3 T−1 ) +HP(S) +Not supported +FL−2 +Pressure +FL−2 +PNU +Not supported +FL−2 +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +TRSHR +Surface traction +TRSHRNU(S) +Not supported +FL−2 +FL−2 +TRVEC +Surface traction +FL−2 +TRVECNU(S) +Not supported +FL−2 +Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +The pressure is +positive in the direction of the positive +element normal. +Shear traction on the element surface. +Nonuniform shear +traction on the +element surface with magnitude and +direction supplied via user subroutine +UTRACLOAD. +General +surface. +traction on the element +Nonuniform general traction on the +element surface with magnitude and +direction supplied via user subroutine +UTRACLOAD. +Abaqus/Aqua loads +Abaqus/Aqua loads are specified as described in “Abaqus/Aqua analysis,” Section 6.11.1. +Available for R3D3 and R3D4 elements only: +Load ID +(*CLOAD/ +*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +PB(A) +Not supported +FL−2 +Buoyancy force. +Available for RB2D2 and RB3D2 elements only: +Load ID +(*CLOAD/ +*DLOAD) +FDD(A) +FD1(A) +FD2(A) +Abaqus/CAE +Load/Interaction +Units +Description +Not supported +FL−1 +Transverse fluid drag force. +Not supported +Not supported +Fluid drag force on the first end of the +rigid link (node 1). +Fluid drag force on the second end of +the rigid link (node 2). +Load ID +(*CLOAD/ +*DLOAD) +FDT(A) +FI(A) +FI1(A) +FI2(A) +PB(A) +WDD(A) +WD1(A) +WD2(A) +Abaqus/CAE +Load/Interaction +Units +Description +Not supported +Not supported +Not supported +Not supported +Not supported +Not supported +Not supported +Not supported +FL−1 +FL−1 +FL��1 +FL−1 +Tangential fluid drag load. +Transverse fluid inertia load. +Fluid inertia load on the first end of +the rigid link (node 1). +Fluid inertia load on the second end of +the rigid link (node 2). +Buoyancy force (with closed-end +condition). +Transverse wind drag force. +Wind drag force on the first end of the +rigid link (node 1). +Wind drag force on the second end of +the rigid link (node 2). +Surface-based loading +Distributed loads +Surface-based distributed loads are available for elements with displacement degrees of freedom. They +are specified as described in “Distributed loads,” Section 33.4.3. +Available for RAX2, R3D3, and R3D4 elements only: +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +HP(S) +Pressure +FL−2 +Pressure +PNU +Pressure +FL−2 +FL−2 +30.3.2–7 +Hydrostatic pressure on the element +surface and linear in global Z. The +pressure is positive in the direction +opposite to the surface normal. +Pressure on the element surface. The +pressure is positive in the direction +opposite to the surface normal. +Nonuniform pressure on the element +surface with the magnitude supplied +subroutine DLOAD in +via +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +The pressure is +positive in the direction opposite to +the surface normal. +Shear traction on the element surface. +Nonuniform shear +traction on the +element surface with magnitude and +direction supplied via user subroutine +UTRACLOAD. +General +surface. +traction on the element +Nonuniform general traction on the +element surface with magnitude and +direction supplied via user subroutine +UTRACLOAD. +TRSHR +Surface traction +TRSHRNU(S) +Surface traction +FL−2 +FL−2 +TRVEC +Surface traction +FL−2 +TRVECNU(S) +Surface traction +FL−2 +Element output +None. +RIGID ELEMENT LIBRARY +R2D2, RAX2 +RB2D2, RB3D2 +R3D3 +R3D4 +30.4 +Capacitance elements +• “Point capacitance,” Section 30.4.1 +• “Capacitance element library,” Section 30.4.2 +30.4.1 +POINT CAPACITANCE +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Capacitance element library,” Section 30.4.2 +• *HEATCAP +• “Defining heat capacitance,” Section 33.5 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +Capacitance elements: +• allow the introduction of concentrated heat capacitance at a point; +• are associated with the temperature degree of freedom at a node; and +• have a capacitance that can be specified as a function of temperature and/or field variables. +Defining the capacitance value +The heat capacitance is associated with the temperature degree of freedom at the node of the element. +You specify the capacitance magnitude, +(density × specific heat × volume). Specify capacitance, +not specific heat. You must associate this capacitance with a region of your model. +Input File Usage: +*HEATCAP, ELSET=name +Abaqus/CAE Usage: +where the ELSET parameter refers to a set of HEATCAP elements. +Property or Interaction module: Special→Inertia→Create: Heat +capacitance: select points: Capacitance +30.4.2 +CAPACITANCE ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Point capacitance,” Section 30.4.1 +• *HEATCAP +Overview +This section provides a reference to the capacitance elements available in Abaqus/Standard and +Abaqus/Explicit. +Element type +HEATCAP +Point heat capacitance +Active degree of freedom +11 +Nodal coordinates required +X, Y, Z +Element property definition +Input File Usage: +Abaqus/CAE Usage: +*HEATCAP +Property or Interaction module: Special→Inertia→Create: +Heat capacitance +Element-based loading +None. +Element output +None. +Nodes associated with the element +1 node. +Connector Elements +Connector elements +Connector element behavior +CONNECTOR ELEMENTS +31.1 +31.1 +Connector elements +• “Connectors: overview,” Section 31.1.1 +• “Connector elements,” Section 31.1.2 +• “Connector actuation,” Section 31.1.3 +• “Connector element library,” Section 31.1.4 +• “Connection-type library,” Section 31.1.5 +31.1.1 +CONNECTORS: OVERVIEW +Abaqus offers a library of connector types and connector elements to model the behavior of connectors. +Overview +Connector modeling consists of: +• choosing and defining the appropriate connector elements (“Connector elements,” Section 31.1.2); +• defining the connector behavior (“Connector behavior,” Section 31.2.1); +• defining any connector actuations (“Connector actuation,” Section 31.1.3); and +• monitoring connector output (“Connector elements,” Section 31.1.2, and “Connector element +library,” Section 31.1.4). +Typical applications +The analyst is often faced with modeling problems in which two different parts are connected in some +way. Sometimes connections are simple, such as two panels of sheet metal spot welded together or a +door connected to a frame with a hinge. In other cases the connection may impose more complicated +kinematic constraints, such as constant velocity joints, which transmit constant spinning velocity +In addition to imposing kinematic constraints, connections +between misaligned and moving shafts. +may include (nonlinear) force versus displacement (or velocity) behavior in their unconstrained relative +motion components, such as a muscle force resisting the rotation of a knee joint in a crash-test occupant +model. More complex connections may include the following: +• stopping mechanisms, which restrict the range of motion of an otherwise unconstrained relative +motion; +• internal friction, such as the lateral force or moments on a bolt generating friction in the translation +of the bolt along a slot; +• failure conditions, where excess force or displacement inside the connection causes the entire +connection or a single component of relative motion to break free; and +• locking mechanisms that engage after some force or displacement criteria is met, such as a snap-fit +connector or a falling-pin locking mechanism on a satellite deployment arm. +In many situations the connection can be actuated either through displacement or force control, such as +a hydraulic piston or a gear-driven robot arm. +In Abaqus/Standard if the two parts being connected are rigid bodies, multi-point constraints cannot +be used to connect the bodies at nodes other than the reference nodes, since multi-point constraints use +degree-of-freedom elimination and the other nodes on a rigid body do not have independent degrees +of freedom. In Abaqus/Explicit this restriction does not apply. See “General multi-point constraints,” +Section 34.2.2. +Connector elements in Abaqus provide an easy and versatile way to model these and many other +types of physical mechanisms whose geometry is discrete (i.e., node-to-node), yet the kinematic and +kinetic relationships describing the connection are complex. +Connector elements versus multi-point constraints +In many instances connector elements perform functions similar to multi-point constraints (“General +multi-point constraints,” Section 34.2.2). However, in most cases multi-point constraints eliminate +degrees of freedom at one of the nodes involved in the connection. This elimination has the advantage +that the problem size is reduced; it has the disadvantage that output and other functionality provided +with connector elements is not available. +In addition, in Abaqus/Standard the degree of freedom +elimination prevents the use of multi-point constraints between nodes without independent degrees of +freedom (such as nodes on a rigid body whose degrees of freedom are dependent on the degrees of +freedom at the reference node). +In contrast, connector elements do not eliminate degrees of freedom; kinematic constraints are +enforced with Lagrange multipliers. These Lagrange multipliers are additional solution variables +in Abaqus/Standard. The Lagrange multipliers provide constraint force and moment output. Since +connector elements do not eliminate degrees of freedom, they can be used in many situations where +multi-point constraints cannot be used or do not exist for the function required; for example, to connect +two rigid bodies at nodes other than the reference node in Abaqus/Standard. +Multi-point constraints are more efficient than connector elements; and if the requirements of the +analysis can be satisfied with multi-point constraints, they should be used in place of connector elements. +Input file template +The following template shows the options used to define and activate the connector elements shown in +Figure 31.1.1–1 and Figure 31.1.1–2. In the respective figures on the left is a schematic representation +of a connection to be modeled; on the right is a representation of the equivalent finite element model. +All options are discussed in detail in the following sections. +extensible +range +7.5 +node 12 +1 (local orientation) +node 11 +Figure 31.1.1–1 Simplified connector model of a shock absorber. +2.0 +15.0 +body 2 +node 120 +⇒ +node 110 +node 120 +1 (local orientation) +node 110 +45° +body 1 +global directions +Figure 31.1.1–2 A pin-in-slot connection modeled with SLOT and CARDAN connection types. +*HEADING +... +*ELEMENT, TYPE=CONN3D2, ELSET=shock +101, 11, 12 +*ELEMENT, TYPE=CONN3D2, ELSET=pininslot +1010, 110, 120 +... +*ORIENTATION, NAME=ori60 +0.5, 0.866025, 0.0, -0.866025, 0.5, 0.0 +*ORIENTATION, NAME=ori45 +0.707, 0.707, 0.0, -0.707, 0.707, 0.0 +*CONNECTOR SECTION, ELSET=shock, BEHAVIOR=sbehavior +revolute, slot +ori60, +... +*CONNECTOR BEHAVIOR, NAME=sbehavior +*CONNECTOR DAMPING, COMPONENT=1 +1500.0 +*CONNECTOR LOCK, COMPONENT=3, LOCK=4 +, , -500.0, 500.0 +*CONNECTOR ELASTICITY, COMPONENT=4, NONLINEAR +-900., -0.7 +0.0 +0.7 +0., +1250., +*CONNECTOR CONSTITUTIVE REFERENCE +, , , 22.5, +0.0 +0.45 +*CONNECTOR STOP, COMPONENT=1 +7.5, 15.0 +... +*CONNECTOR FRICTION +0.34, 0.55, +0.34, 0.10, +*FRICTION +.15 +... +*CONNECTOR SECTION, ELSET=pininslot +cardan, slot +ori45, +*CONNECTOR MOTION +pininslot, 4 +pininslot, 5 +... +*STEP +... +*CONNECTOR MOTION, TYPE=VELOCITY +pininslot, 6, 0.7854 +... +*CONNECTOR LOAD +pininslot, 1, 1000.0 +... +*END STEP +31.1.2 +CONNECTOR ELEMENTS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Connectors: overview,” Section 31.1.1 +• “Connector element library,” Section 31.1.4 +• “Connection-type library,” Section 31.1.5 +• *CONNECTOR SECTION +• “Creating connector sections,” Section 15.12.11 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Creating and modifying connector section assignments,” Section 15.12.12 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +Overview +Connector elements: +• are available for two-dimensional, axisymmetric, and three-dimensional analyses; +• can define a connection between two nodes (each node can be connected to a rigid part, a deformable +part, or not connected to any part); +• can define a connection between a node and ground; +• have relative displacements and rotations that are local to the element, which are referred to as +components of relative motion; +• are functionally defined by specifying the connector attributes; +• have comprehensive kinematic and kinetic output; and +• can be used to monitor kinematics in local coordinate systems. +Choosing an appropriate element +Two connector elements are provided. The element type to be chosen depends on the dimensionality +of the analysis: CONN2D2 for two-dimensional and axisymmetric analyses and CONN3D2 for three- +dimensional analyses. Both connector elements have at most two nodes. The position and motion of the +second node on the connector element are measured relative to the first node. +Naming convention +Connector elements in Abaqus are named as follows: +CONN +3D 2 +number of nodes +two-dimensional (2D) or three-dimensional (3D) +connector +For example, CONN2D2 is a two-dimensional, 2-node connector element. +Defining a connection between points +A connector element can be used to connect two points. +Input File Usage: +*ELEMENT, TYPE=name +connector element number, node_1, node_2 +Abaqus/CAE Usage: +Interaction module: Connector→Assignment→Create: select wires +Defining a connection between a point and ground +A connector element can be connected to ground, and the ground “node” can be the first or second point +on the connector element. The initial position of the ground node used for calculating relative position +and displacement is the initial position of the other point on the element. All displacements and rotations +at the ground node, if they exist, are fixed. +Input File Usage: +Use one of the following options: +*ELEMENT, TYPE=name +connector element number, node number on the body +*ELEMENT, TYPE=name +connector element number, , node number on the body +Abaqus/CAE Usage: +Interaction module: Connector→Assignment→Create: +select wires connected to ground +Components of relative motion +Connector elements have relative displacements and rotations that are local to the element. These relative +displacements and rotations are referred to as components of relative motion. In the three-dimensional +case connector elements use 12 nodal degrees of freedom to define six relative motion components: three +displacements and three rotations in element local directions. In two dimensions six nodal degrees of +freedom define three relative motion components: two displacements and one rotation. The components +of relative motion are either constrained or unconstrained (“available”), depending upon the definition +of the connector element. +Constrained components of relative motion +Constrained components of relative motion are displacements and rotations that are fixed by the +connector element. +In connector elements with constrained components of relative motion, Abaqus/Standard uses +Lagrange multipliers to enforce the kinematic constraints. Accordingly, +in Abaqus/Standard the +constraint forces and moments carried by the element appear as additional solution variables. The +number of additional solution variables is equal to the number of constrained components of relative +motion. In Abaqus/Explicit the constraints are enforced using an augmented Lagrangian technique for +which no additional solution variables are needed. +Available components of relative motion +Available components of relative motion are displacements and rotations that are not constrained +kinematically and, hence, +specifying +time-dependent motion, applying loading, or assigning complex interactions, such as contact or +friction. Many connection types have available components of relative motion, and their meaning is +described in “Connection-type library,” Section 31.1.5, for each individual connection type. +remain available for defining material-like behavior, +Defining the connection attributes +The connection attributes define the connector element’s function. In the most general case you specify +the following attributes: +• the connection type or types, +• the local directions associated with the connector’s nodes, +• additional data for certain connection types, and +• the connector behavior. +The connector definition that is defined with these attributes is associated with a set of connector elements. +Input File Usage: +Abaqus/CAE Usage: +*CONNECTOR SECTION, ELSET=name +Interaction module: +Connector→Geometry→Create Wire Feature +Connector→Section→Create: Name: connector section name +Connector→Assignment→Create: select wires: Section: +connector section name +Defining the connection type +Abaqus provides a comprehensive library of connection types. +See “Connection-type library,” +Section 31.1.5, for the available connection types. The connection types are divided into three +categories: basic connection components, assembled connections, and complex connections. The basic +connection components affect either translations or rotations on the second node. A connector element +may include one translational basic connection component and/or one rotational basic connection +component. The assembled connections are constructed from the basic connection components. +They are provided for convenience and cannot be combined in the same connector element definition +with a basic connection component or other assembled connections. Complex connections affect a +combination of degrees of freedom at the nodes in the connection and cannot be combined with other +connection components. +The connection type is specified as: +• a single basic connection type (translational or rotational), +• one translational and one rotational basic connection type, +• one assembled connection type, or +• one complex connection type. +Input File Usage: +Use one of the following options: +Abaqus/CAE Usage: +*CONNECTOR SECTION, ELSET=name +basic connection type, basic connection type +*CONNECTOR SECTION, ELSET=name +assembled connection or complex connection +Interaction module: +Connector→Section→Create: Connection Category: Basic, +Translational type: translational basic connection type and/or +Rotational type: rotational basic connection type +or +Connector→Section→Create: Connection Category: +Assembled/Complex, Assembled/Complex type: assembled +connection or complex connection +Defining the local connector directions +Local directions at the nodes are often required to define the connection types used to define the +connector element. The local directions and how they are used to define the connection are described in +“Connection-type library,” Section 31.1.5. In the most general case the connection type uses two sets of +local directions, which are defined as described in “Orientations,” Section 2.2.5. The names associated +with the two orientation definitions must be referred to from the connector section definition. +Input File Usage: +Use the following options for the most general case: +*ORIENTATION, NAME=orientation_1 +*ORIENTATION, NAME=orientation_2 +*CONNECTOR SECTION, ELSET=name +basic connection type(s) or assembled connection +orientation_1 for first node (or ground), orientation_2 for +second node (or ground) +Abaqus/CAE Usage: +Interaction module: Connector→Assignment→Create: select wires: +Orientation 1, Orientation 2: Edit: select the orientations for the first +and second points, respectively, of the selected wires +Degree of freedom activation and co-rotation of connection directions +Many connection types either require connection directions at the nodes on the element or allow optional +directions to be defined. In cases where an orientation definition is permitted for defining connection +directions (required or optional), connector elements activate the rotational degrees of freedom at the +nodes to which they are attached, if they do not exist already. The only exception is connection type +JOIN, for which connection directions are optional at the first node of the element, but rotation degrees +of freedom are not activated. +The connector element’s orientation directions co-rotate with the rotational degrees of freedom at +the corresponding node on the element. If there is no element with rotational degrees of freedom or +rotation constraint (such as an equation or a multi-point constraint) attached to the node, you must ensure +that sufficient rotational boundary conditions are provided to avoid numerical singularities associated +with unconstrained rotational degrees of freedom. Connection type JOIN uses fixed directions when +rotational degrees of freedom are not active at the nodes on the connector element. +Example +Figure 31.1.2–1 illustrates the use of the CONN3D2 element to connect two bodies with a cylindrical- +like connector oriented at 60° from the global 1-axis. On the left is a schematic representation of the +connection to be modeled; on the right is a representation of the equivalent finite element model. See +“Connection-type library,” Section 31.1.5, for a list of connector type names. +extensible +range +7.5 +node 12 +1 (local orientation) +node 11 +Figure 31.1.2–1 Simplified connector model of a shock absorber. +The connection requires node b to remain on the line of the shock absorber, which is determined +by the position and orientation directions of node a. Furthermore, the two rotation components +perpendicular to the line of the shock absorber at node b must be the same as those at node a. Hence, +the only relative motion components permitted in the connection are the displacement of node b relative +to node a along the line of the shock absorber and the rotation of node b relative to node a about the +line of the shock absorber. This displacement and this rotation are the available components of relative +motion. The connector is defined using the following lines in the input file: +*ELEMENT, TYPE=CONN3D2, ELSET=shock +101, 11, 12 +*CONNECTOR SECTION, ELSET=shock +slot, revolute +ori60, +*ORIENTATION, NAME=ori60 +**Defines the local 1-direction along the slot (required) +**Also defines the rotation axis for the revolute (required) +0.5, 0.866025, 0.0, -0.866025, 0.5, 0.0 +Alternatively, you could use the assembled connection type CYLINDRICAL instead of the two basic +connection types SLOT and REVOLUTE. +Defining additional connection type data +Some connection types allow additional data to define the kinematic behavior of the connector. For +example, the connection type FLOW-CONVERTER allows you to specify a scaling factor for material +flow at node b. See “Connection-type library,” Section 31.1.5, for more information. +Defining the connector behavior +Abaqus provides comprehensive kinetic behavior modeling in the available components of relative +motion. Defining connector behavior is optional and can be used to incorporate spring, dashpot, +locking, friction, plasticity-like effects, and failure. The kinetic modeling +node-to-node contact, +capabilities in connectors are described in detail in “Connector behavior,” Section 31.2.1. +Using connector elements in two-dimensional and axisymmetric analysis +Not all connection types can be used with element type CONN2D2. The connection-type library contains +many connection types whose mechanics are valid for three-dimensional analyses only. In other cases +the local directions required in the definition of the connection type conflict with the two-dimensional +coordinate system. See “Connection-type library,” Section 31.1.5, for more information. +Using multiple connector elements in parallel +Connector elements in Abaqus allow most physical connections to be modeled with a single connector +element. However, in certain circumstances more complex connections or output considerations may +require multiple connector elements to be used in parallel. This is accomplished by defining two or more +connector elements between the same nodes. In this case you must ensure that a constrained component +of relative motion in one connector element is not constrained (either by a kinematic constraint or through +motion specified as described in “Connector actuation,” Section 31.1.3) by one of the other connector +elements. +Multiple connector elements are sometimes used in parallel to obtain output in different coordinate +systems. For a connector element between two bodies, the local directions at the nodes can be determined +by the requirements of the connection type. However, output may be needed in a different, possibly +co-rotating, coordinate system. For example, the angular acceleration history could be reported in a local, +body-fixed coordinate system (other than the one used to define the connector element) by using a second +connector element (such as connection type CARDAN) that does not impose kinematic constraints or +use connector behavior but aligns with the desired local output directions. +Defining connectors in a model that contains parts and an assembly +An Abaqus model can be defined in terms of an assembly of part instances . Connector elements can be defined at either the part level or the assembly level in such +a model. +Using connector elements with nodal transformations +Nodal transformations can be defined for either +node connected to the connector element. Since these transformations affect only the nodal degrees of +freedom, their use does not affect the behavior of the connector element. Connector elements operate on +components of motion local to the connection. +Using nonlinear connections in geometrically linear analyses +If a connector element with a nonlinear kinematic constraint is used in a geometrically linear analysis, +the kinematic constraint is linearized. For example, if connection type LINK is used in a geometrically +linear analysis, the distance between the two nodes is held constant after projection onto the direction +of the line between the original positions of the nodes. The difference should be noticeable only if the +magnitudes of the rotations and displacements are not small. +Mismatched masses at connector nodes in Abaqus/Explicit +If the nodes of a connector element in Abaqus/Explicit have masses that are highly mismatched, the +implicit solver may encounter convergence problems due to the resulting ill-conditioned coef���cient +matrix. To prevent this from happening, if the nodal masses or rotary inertias of a connector element +differ by more than three orders of magnitude, Abaqus/Explicit adds mass/rotary inertia to the connector +element node that has the smaller mass/rotary inertia. The mass/rotary inertia added is negligibly +small (less than three orders of magnitude smaller) compared to the larger of the connector element’s +nodal inertias. This additional mass almost never affects the solution significantly. However, in certain +situations (for example, for a strongly dynamic analysis that has connector elements with highly +mismatched nodal masses) this adjustment may have a noticeable effect. +Connector output +The connector element force, moment, and kinematic output is defined in “Connector element library,” +Section 31.1.4. These output quantities include total, elastic, viscous, and friction forces and moments. +In addition, reaction forces and moments caused by connector stops and locks are available as well as +connector contact forces used for friction calculation. +To obtain accurate reaction force and moment output for connectors from Abaqus/Explicit, it may +sometimes be necessary to run the analysis in double precision. In such situations a double precision run +will also yield a better estimate of the work done by the reaction forces and moments, thereby providing +a more accurate value of the energy due to the external work reported by Abaqus/Explicit. +Kinematic output includes relative position, relative displacement, relative velocity, relative +acceleration, frictional slip, and constitutive displacements (the displacement used in the elastic force +and hysteretic friction calculations defined as the difference between the current relative positions +and the reference positions; see “Defining reference lengths and angles for constitutive response” +in “Connector behavior,” Section 31.2.1). For relative rotations the Abaqus convention of reporting +angles between +radians is not used with connector elements. Connector element output +of angles and rotational components or relative motion includes accumulated multiple rotations whose +magnitudes can be arbitrarily large. Energy output is available, as are output flags to identify whether a +connector has failed (in Abaqus/Explicit only), locked, or reached a connector stop. +and +In a geometrically linear step in Abaqus/Standard the relative position output variable does not +change (in the same fashion that the nodal coordinates are output). Therefore, care must be exercised in +interpreting output for connector stops and locks since they use updated coordinates. +Using connector elements for output only +Connector elements defined without kinematic constraints or constitutive behavior can be used +to monitor kinematic output in local coordinate systems. Quantities of interest include relative +position, displacement, velocity, and acceleration in local coordinate parametrization. Finite rotation +parametrizations include Euler and Cardan angles, rotation vector, and flexion-torsion-sweep. For +an example that uses a connector element to monitor Euler angles, see “Motion of a rigid body in +Abaqus/Standard,” Section 1.3.6 of the Abaqus Benchmarks Manual. +In Abaqus/Explicit all such connectors are solved without invoking the implicit solver, which leads +to better performance in domain parallel mode (particularly when such connectors nodes overlap with +other constraints such as slave nodes of tie constraints). +31.1.3 +CONNECTOR ACTUATION +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Connectors: overview,” Section 31.1.1 +• *CONNECTOR LOAD +• *CONNECTOR MOTION +• “Defining a connector force,” Section 16.9.13 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Defining a connector moment,” Section 16.9.14 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Defining a connector displacement boundary condition,” Section 16.10.5 of the Abaqus/CAE +User’s Manual, in the online HTML version of this manual +• “Defining a connector velocity boundary condition,” Section 16.10.6 of the Abaqus/CAE User’s +Manual, in the online HTML version of this manual +• “Defining a connector acceleration boundary condition,” Section 16.10.7 of the Abaqus/CAE User’s +Manual, in the online HTML version of this manual +Overview +Connector actuation: +• is meant to model situations, such as deployment maneuvers, where a motor attached to the body +loads the connection with an internal force or moment history or a hydraulic system imposes a +known motion; +• can be used to fix available components of relative motion; and +• consists of driving an available component of relative motion by a prescribed displacement +(rotation) or by a specified force (moment). +The prescribed relative motions and loads are in the local directions associated with the available +components of relative motion for the connector. +Prescribing displacements/rotations for available components of relative motion that also include +connector stop or connector lock behaviors may lead to overconstraints. Abaqus will issue a warning +message if an overconstraint occurs. +Fixing available components of relative motion +A common practice is to fix available components of motion. Such fixed motion conditions can be used +to customize connection types for specific applications. As an example, the REVOLUTE connection +type uses the local 1-direction as the shared revolute axis and, hence, the available component of relative +motion. If, for convenience, a revolute connection about the local 3-direction were needed, you could +fix the relative rotations about the local 1- and 2-directions in a CARDAN connection type. In doing so, +a connection type identical to the REVOLUTE connection type would be created; however, the shared +axis would be the local 3-direction instead of the local 1-direction. +An example is provided later in this section in which the pin part of a pin-in-slot connection is +modeled with a CARDAN connection type with fixed rotations. +Input File Usage: +Use the following option in the model portion of the input file to fix available +connector components of relative motion: +Abaqus/CAE Usage: +*CONNECTOR MOTION +Load module: Create Boundary Condition: Step: Initial: +Mechanical: Connector displacement +Displacement-controlled actuation +You can specify a relative displacement, velocity, or acceleration between two parts in the connector’s +local directions in a manner similar to defining a boundary condition . You specify the connector element set name +or connector element number; the component number identifying the available component of relative +motion being actuated; and the value of the relative displacement, velocity, or acceleration. +You cannot specify the motion of connectors in a subspace dynamic analysis. +Input File Usage: +Use the following option in the history portion of the input file to specify a +relative displacement for a connector: +*CONNECTOR MOTION, AMPLITUDE=name, OP=MOD or NEW, +TYPE=DISPLACEMENT +Use the following option in the history portion of the input file to specify a +relative velocity for a connector: +*CONNECTOR MOTION, AMPLITUDE=name, OP=MOD or NEW, +TYPE=VELOCITY +Use the following option in the history portion of the input file to specify a +relative acceleration for a connector: +*CONNECTOR MOTION, AMPLITUDE=name, OP=MOD or NEW, +TYPE=ACCELERATION +Abaqus/CAE Usage: +Load module: Create Boundary Condition: Mechanical: Connector +displacement, Connector velocity, or Connector acceleration +Example +Figure 31.1.3–1 illustrates a pin-in-slot connection oriented at 45° from the global 1-axis modeled with +element type CONN3D2. +2.0 +15.0 +body 2 +node 120 +⇒ +node 110 +node 120 +1 (local orientation) +node 110 +45° +body 1 +global directions +Figure 31.1.3–1 A pin-in-slot connection modeled with SLOT and CARDAN connection types. +The figure on the left is a schematic representation of the connection to be modeled, while the figure +on the right is the finite element mesh. Displacements in the slot are allowed only along the line of +the slot, and connection type SLOT is appropriate for enforcing these kinematics. Assume the pin and +slot are constructed in such a way that the only rotation of the pin relative to the slot is along the local +3-direction. This is a revolute constraint; however, basic rotation connection type REVOLUTE uses the +local 1-direction as the revolute axis. In this case connection type CARDAN combined with a specified +constraint can be used to define a revolute-type connection with the appropriate revolute axis. +For illustrative purposes assume the connection is actuated by a rotational velocity of +radians +per second around the pin’s axis. Using input parametrization for convenience, the following lines are +used: +*PARAMETER +PI = 3.141592 +rotangvel = PI/4 +... +*ELEMENT, TYPE=CONN3D2, ELSET=pininslot +101, 110, 120 +*CONNECTOR SECTION, ELSET=pininslot +cardan, slot +ori45, +*CONNECTOR MOTION +pininslot, 4 +pininslot, 5 +*ORIENTATION, NAME=ori45 +0.707, 0.707, 0.0, -0.707, 0.707, 0.0 +... +*STEP +... +*CONNECTOR MOTION, TYPE=VELOCITY +pininslot, 6, +... +*END STEP +Force-controlled actuation +You can specify concentrated loads applied to the available components of relative motion in a +manner similar to defining concentrated loads for other elements in Abaqus . However, connector loads are always follower loads that rotate with the rotation of the +available components of relative motion as the connector element moves. You specify the connector +element set name or connector element number, the component number identifying the available +component of relative motion being loaded, and the value of the actuation force or moment. +Input File Usage: +Abaqus/CAE Usage: +Use the following option in the history portion of the input file to specify a +concentrated load for a connector: +*CONNECTOR LOAD, AMPLITUDE=name, OP=MOD +Load module: Create Load: Mechanical: Connector force +or Connector moment +Example +Returning to the example in Figure 31.1.3–1, assume that the pin is pushed along the slot by a constant +force of 1000.0 units (for example, through a hydraulic system). The following lines should be added to +the input file: +*STEP +... +*CONNECTOR LOAD +pininslot, 1, 1000.0 +... +*END STEP +Connector actuation in linear perturbation procedures +Nonzero magnitude connector motions are allowed only in the eigenvalue buckling, direct-solution +steady-state dynamic, and linear static perturbation procedures. Any nonzero magnitude specified +during an eigenfrequency extraction procedure is ignored, and the specified available component of +relative motion is held fixed. Connector motions cannot be used in any modal-based procedure. +In direct-solution steady-state dynamic analyses the real and imaginary parts of any available +connector component of relative motion are either restrained or unrestrained simultaneously; +it is +physically impossible to have one part restrained and the other part unrestrained. Abaqus/Standard +will automatically restrain both the real and the imaginary parts of a component of relative motion +even when only one part is prescribed specifically. The unspecified part will be assumed to have a +perturbation magnitude of zero. +A nonzero prescribed connector motion in an eigenvalue buckling step will contribute to the +incremental stress and, thus, will contribute to the differential initial stress stiffness. When prescribing +nonzero connector motions, you must interpret the resulting eigenproblem carefully. See the discussion +for boundary conditions in “Eigenvalue buckling prediction,” Section 6.2.3, for more details. +In steady-state dynamic analyses both real and imaginary connector loads can be applied in a +manner similar to concentrated loads . Multiple connector load cases can be defined in random response +analyses in the same manner as concentrated loads. +Connector loads are ignored during an eigenfrequency extraction analysis. +31.1.4 +CONNECTOR ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Connector elements,” Section 31.1.2 +• “Connection-type library,” Section 31.1.5 +• *CONNECTOR BEHAVIOR +• *CONNECTOR LOAD +• *CONNECTOR SECTION +Overview +This section provides a reference to the connector elements available in Abaqus/Standard and +Abaqus/Explicit. +Element types +Connector in a plane +CONN2D2 +Connector element between two nodes or ground and a node. +Active degrees of freedom +1, 2, 6 for the most general connection types. +Additional solution variables +In Abaqus/Standard there can be up to three additional constraint variables related to forces and a moment +associated with the connector. The number of additional constraint variables depends on the connection +type. +Connector in space +CONN3D2 +Connector element between two nodes or ground and a node. +Active degrees of freedom +1, 2, 3, 4, 5, 6 for the most general connection types. +Additional solution variables +In Abaqus/Standard there can be up to six additional constraint variables related to forces and moments +associated with the connector. The number of additional constraint variables depends on the connection +type. +Nodal coordinates required +CONN2D2: X, Y +CONN3D2: X, Y, Z +Element property definition +Input File Usage: +Abaqus/CAE Usage: +*CONNECTOR SECTION +Interaction module: Connector→Section→Create +Element-based loading +Use connector loads to apply loading to the available components of relative motion. Prescribe connector +motion to specify relative kinematics (zero or nonzero values) for the available components of relative +motion. See “Connector actuation,” Section 31.1.3, for details. +Element output +Total force components +CTF1 +CTF2 +CTF3 +CTM1 +CTM2 +CTM3 +Total force in the 1-direction. +Total force in the 2-direction. +Total force in the 3-direction. +Total moment about the 1-direction. +Total moment about the 2-direction. +Total moment about the 3-direction. +The total force is obtained as CTF = CEF + CVF + CUF + CSF + CRF – CCF. +Elastic force components +CEF1 +CEF2 +CEF3 +CEM1 +CEM2 +CEM3 +Elastic force in the 1-direction. +Elastic force in the 2-direction. +Elastic force in the 3-direction. +Elastic moment about the 1-direction. +Elastic moment about the 2-direction. +Elastic moment about the 3-direction. +Elastic displacement components +CUE1 +CUE2 +Elastic displacement in the 1-direction. +Elastic displacement in the 2-direction. +CUE3 +CURE1 +CURE2 +CURE3 +Elastic displacement in the 3-direction. +Elastic rotation about the 1-direction. +Elastic rotation about the 2-direction. +Elastic rotation about the 3-direction. +Plastic relative displacement components +CUP1 +CUP2 +CUP3 +CURP1 +CURP2 +CURP3 +Plastic relative displacement in the 1-direction. +Plastic relative displacement in the 2-direction. +Plastic relative displacement in the 3-direction. +Plastic relative rotation about the 1-direction. +Plastic relative rotation about the 2-direction. +Plastic relative rotation about the 3-direction. +Equivalent plastic relative displacement components +CUPEQ1 +CUPEQ2 +CUPEQ3 +CURPEQ1 +CURPEQ2 +CURPEQ3 +CUPEQC +Equivalent plastic relative displacement in the 1-direction. +Equivalent plastic relative displacement in the 2-direction. +Equivalent plastic relative displacement in the 3-direction. +Equivalent plastic relative rotation about the 1-direction. +Equivalent plastic relative rotation about the 2-direction. +Equivalent plastic relative rotation about the 3-direction. +Equivalent plastic relative motion for a coupled plasticity definition. +Kinematic hardening shift force components +CALPHAF1 +CALPHAF2 +CALPHAF3 +CALPHAM1 +CALPHAM2 +CALPHAM3 +Kinematic hardening shift force in the 1-direction. +Kinematic hardening shift force in the 2-direction. +Kinematic hardening shift force in the 3-direction. +Kinematic hardening shift moment about the 1-direction. +Kinematic hardening shift moment about the 2-direction. +Kinematic hardening shift moment about the 3-direction. +Viscous force components +CVF1 +CVF2 +CVF3 +CVM1 +Viscous force in the 1-direction. +Viscous force in the 2-direction. +Viscous force in the 3-direction. +Viscous moment about the 1-direction. +CVM2 +CVM3 +Viscous moment about the 2-direction. +Viscous moment about the 3-direction. +Uniaxial force components +Connector uniaxial behavior can be defined only in Abaqus/Explicit; therefore, there is no uniaxial force +output available in Abaqus/Standard. +CUF1 +CUF2 +CUF3 +CUM1 +CUM2 +CUM3 +Uniaxial force in the 1-direction. +Uniaxial force in the 2-direction. +Uniaxial force in the 3-direction. +Uniaxial moment in the 1-direction. +Uniaxial moment in the 2-direction. +Uniaxial moment in the 3-direction. +Friction force components +CSF1 +CSF2 +CSF3 +CSM1 +CSM2 +CSM3 +CSFC +Force due to frictional stress in the 1-direction. +Force due to frictional stress in the 2-direction. +Force due to frictional stress in the 3-direction. +Frictional moment about the 1-direction. +Frictional moment about the 2-direction. +Frictional moment about the 3-direction. +Force due to frictional stress in the instantaneous slip direction. Available only for +predefined or user-defined coupled friction interactions. +Contact force components generating friction +CNF1 +CNF2 +CNF3 +CNM1 +CNM2 +CNM3 +CNFC +Contact force generating friction in the 1-direction. +Contact force generating friction in the 2-direction. +Contact force generating friction in the 3-direction. +Contact moment generating friction about the 1-direction. +Contact moment generating friction about the 2-direction. +Contact moment generating friction about the 3-direction. +Contact force generating friction in the instantaneous slip direction. +Total overall damage components +CDMG1 +CDMG2 +CDMG3 +CDMGR1 +Overall damage variable in the 1-direction. +Overall damage variable in the 2-direction. +Overall damage variable in the 3-direction. +Overall damage variable along the 1-direction. +CDMGR2 +CDMGR3 +Overall damage variable along the 2-direction. +Overall damage variable along the 3-direction. +Connector force-based damage initiation criteria +CDIF1 +CDIF2 +CDIF3 +CDIFR1 +CDIFR2 +CDIFR3 +CDIFC +Connector force-based damage initiation criterion in the 1-direction. +Connector force-based damage initiation criterion in the 2-direction. +Connector force-based damage initiation criterion in the 3-direction. +Connector force-based damage initiation criterion along the 1-direction. +Connector force-based damage initiation criterion along the 2-direction. +Connector force-based damage initiation criterion along the 3-direction. +Connector force-based damage initiation criterion in the instantaneous slip direction. +Connector motion-based damage initiation criteria +CDIM1 +CDIM2 +CDIM3 +CDIMR1 +CDIMR2 +CDIMR3 +CDIMC +Connector motion-based damage initiation criterion in the 1-direction. +Connector motion-based damage initiation criterion in the 2-direction. +Connector motion-based damage initiation criterion in the 3-direction. +Connector motion-based damage initiation criterion along the 1-direction. +Connector motion-based damage initiation criterion along the 2-direction. +Connector motion-based damage initiation criterion along the 3-direction. +Connector motion-based damage initiation criterion in the instantaneous slip +direction. +Connector plastic motion-based damage initiation criteria +CDIP1 +CDIP2 +CDIP3 +CDIPR1 +CDIPR2 +CDIPR3 +CDIPC +Connector plastic motion-based damage initiation criterion in the 1-direction. +Connector plastic motion-based damage initiation criterion in the 2-direction. +Connector plastic motion-based damage initiation criterion in the 3-direction. +Connector plastic motion-based damage initiation criterion along the 1-direction. +Connector plastic motion-based damage initiation criterion along the 2-direction. +Connector plastic motion-based damage initiation criterion along the 3-direction. +Connector plastic motion-based damage initiation criterion in the instantaneous slip +direction. +Connector lock or stop status +CSLSTi +Flags for connector stop and connector lock status +. +Friction-related accumulated slip +CASU1 +Accumulated frictional slip in the 1-direction. +CASU2 +CASU3 +CASUR1 +CASUR2 +CASUR3 +CASUC +Accumulated frictional slip in the 2-direction. +Accumulated frictional slip in the 3-direction. +Accumulated frictional rotation about the 1-direction. +Accumulated frictional rotation about the 2-direction. +Accumulated frictional rotation about the 3-direction. +Accumulated frictional slip in the instantaneous slip direction. +Frictional instantaneous velocity in the slip direction (available only if friction is defined in the +slip direction) +CIVC +Friction-related instantaneous velocity in the slip direction. +Reaction force components due to kinematic constraints, connector locks, connector stops, +and prescribed connector motion +CRF1 +CRF2 +CRF3 +CRM1 +CRM2 +CRM3 +Connector reaction force in the 1-direction. +Connector reaction force in the 2-direction. +Connector reaction force in the 3-direction. +Connector reaction moment about the 1-direction. +Connector reaction moment about the 2-direction. +Connector reaction moment about the 3-direction. +Connector concentrated force components due to connector loads +CCF1 +CCF2 +CCF3 +CCM1 +CCM2 +CCM3 +Connector concentrated force in the 1-direction. +Connector concentrated force in the 2-direction. +Connector concentrated force in the 3-direction. +Connector concentrated moment about the 1-direction. +Connector concentrated moment about the 2-direction. +Connector concentrated moment about the 3-direction. +Relative position components +CP1 +CP2 +CP3 +CPR1 +CPR2 +CPR3 +Relative position in the 1-direction. +Relative position in the 2-direction. +Relative position in the 3-direction. +Relative angular position in the 1-direction. +Relative angular position in the 2-direction. +Relative angular position in the 3-direction. +Relative displacement components +CU1 +CU2 +CU3 +CUR1 +CUR2 +CUR3 +Relative displacement in the 1-direction. +Relative displacement in the 2-direction. +Relative displacement in the 3-direction. +Relative rotation in the 1-direction. +Relative rotation in the 2-direction. +Relative rotation in the 3-direction. +Constitutive displacement components +CCU1 +CCU2 +CCU3 +CCUR1 +CCUR2 +CCUR3 +Constitutive displacement in the 1-direction. +Constitutive displacement in the 2-direction. +Constitutive displacement in the 3-direction. +Constitutive rotation in the 1-direction. +Constitutive rotation in the 2-direction. +Constitutive rotation in the 3-direction. +Relative velocity components +CV1 +CV2 +CV3 +CVR1 +CVR2 +CVR3 +Relative velocity in the 1-direction. +Relative velocity in the 2-direction. +Relative velocity in the 3-direction. +Relative angular velocity in the 1-direction. +Relative angular velocity in the 2-direction. +Relative angular velocity in the 3-direction. +Relative acceleration components +CA1 +CA2 +CA3 +CAR1 +CAR2 +CAR3 +Relative acceleration in the 1-direction. +Relative acceleration in the 2-direction. +Relative acceleration in the 3-direction. +Relative angular acceleration in the 1-direction. +Relative angular acceleration in the 2-direction. +Relative angular acceleration in the 3-direction. +Connector failure status +CFAILSTi +Flags for connector failure status +. +Node ordering on elements +or +or +31.1.5 +CONNECTION-TYPE LIBRARY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Connector elements,” Section 31.1.2 +• “Connector element library,” Section 31.1.4 +• *CONNECTOR BEHAVIOR +• *CONNECTOR SECTION +Overview +The connection-type library contains: +• translational basic connection components, which affect translational degrees of freedom at both +nodes and may affect rotational degrees of freedom at the first node or at both nodes on the connector +element; +• rotational basic connection components, which affect only rotational degrees of freedom at both +nodes on the connector element; +• specialized rotational basic connection components, which in addition to rotational degrees of +freedom affect other degrees of freedom at the nodes on the connector element; +• assembled connections, which are predefined combinations of translational and rotational or +translational and specialized rotational basic connection components; and +• complex connections, which affect a combination of degrees of freedom at the nodes on the +connector element and cannot be combined with any other connection component. +Using the connection-type library +Each connection type is described in the connection-type library. Each library entry includes a figure, +which relates the physical behavior to the idealized model and defines the local coordinate directions. +Following the figure, each library entry defines kinematic constraints; constraint forces and moments +internal to the connection; components of relative motion available for defining the connector behavior, +connector motion, or connector loads (called available components); and kinetic forces and moments +conjugate to the available components of relative motion. If appropriate, a discussion of the predicted +Coulomb-like friction in the connection is included. Finally, the connection type is summarized in a +table. +Connection figures +A schematic drawing of each connection type is included along with the Abaqus idealization of +the connection. The idealization indicates in what sense available components of relative motion +are measured and how the nodes’ positions and orientation directions define the connection. When +orientation directions are used to define the connection, the idealization shows these local directions +at the appropriate nodes. If available components of relative motion exist in the connection, they are +indicated in the figure as free relative motions. Figure 31.1.5–1 shows the connection figure for the +REVOLUTE connection type, which affects only rotations. It has one available component (the rotation +about the shared axis), requires an orientation at node a, and allows an optional orientation at node b. +eb +eb +eb +ea +ea +ea +ea +eb +Figure 31.1.5–1 Example connection type: REVOLUTE. +Orientation directions +, where +The orientation directions at node a (the first node on the connector element) are indicated as unit base +vectors +. +When orientation directions are required at a node, you must define them as described in “Orientations,” +Section 2.2.5. If orientation directions are optional but not provided at node a, the global directions are +used by default. If orientation directions are optional but not provided at node b, the orientation directions +from node a are used by default. +. Similarly, the orientation directions at node b are indicated as +Connector elements activate rotational degrees of freedom at the nodes to which they are attached +if they do not exist already and an orientation is permitted at that node. The only exception is connection +type JOIN, where an orientation is optional at node a but rotation degrees of freedom are not activated. +The orientation directions co-rotate with the rotation of the node to which they are attached (with +the exception of connection type JOIN, which uses fixed directions when rotation degrees of freedom are +not active at node a). If there are no elements with rotational degrees of freedom attached to the node, +rotational multi-point constraints, or rotational equations, you must ensure that sufficient rotational +boundary conditions are provided to avoid numerical singularities associated with unconstrained +rotational degrees of freedom. +Components of relative motion and connector forces and moments +The six components of relative motion, denoted +, are defined in the description +and +for each connection, where needed. These components include constrained and available components of +relative motion. Forces and moments are denoted and +. These quantities are either constraint forces +and moments, which enforce the kinematic constraints on the constrained components of relative motion, +or kinetic forces and moments, which are the work conjugate variables to the available components of +for +relative motion. For example, the REVOLUTE connection type has one available component of relative +motion, +and +the local +, and two kinematic rotation constraints (equivalent to setting two rotation components, +, to zero). Conjugate to the available rotation component is the kinetic moment +acting about +-direction. +In general, kinetic forces and moments include the effects of connector behaviors, such as elastic +springs, viscous damping, friction, and reaction forces and moments due to connector stops and locks. +For constitutive response defined as a function of displacement or rotation, the initial position may +not correspond with the reference position where constitutive forces and moments are zero. You can +define reference lengths and angles (given in degrees) for connector behavior as described in “Defining +reference lengths and angles for constitutive response” in “Connector behavior,” Section 31.2.1. These +reference quantities define +, the connector constitutive displacements and rotations. +These constitutive displacements and rotations are used only to define constitutive response and differ +from the relative displacements and rotations measured in the connector elements only when you define +the reference lengths or angles. +and +As an example, if the REVOLUTE connection included linear spring and dashpot behavior +combined with a connector stop, +is the spring stiffness, +where +by the connector stop. In the REVOLUTE connection there are two constraint moment components, +about +is the dashpot coefficient, and +is the reaction moment caused +about +and +. +Interpreting connector forces and moments +-direction aligned with the global X-direction and the local +The kinematic constraint and kinetic forces and moments are always computed as work conjugates of +the kinematics in the connector (components of relative motion). In most connection types one direct +consequence is that the constraint forces (and moments) in connectors are reported as the forces (and +moments) applied at the second node but in the local system associated with the first node. Since the +kinematics are complex in many of the connection types, the connector forces and moments can be +somewhat surprising upon first inspection. For example, consider the case of a HINGE connection +defined with the local +-direction aligned +with the global Y-direction. Assume that the second connector node is grounded and that the first node +is subjected to a concentrated load along the global Y-direction. If the only available relative rotation +in the HINGE is constrained with a zero-valued connector motion, the second node does not rotate with +respect to the first node and the connector reaction force along the local +-direction matches the applied +load while the other two connector reaction forces are zero. However, if a nonzero connector motion is +specified, the first connector reaction force is still zero while both the second and third connector reaction +forces are nonzero and only the vector-norm of these two forces matches the applied load. In both cases +the only nonzero nodal reaction force at the second connector node is the one in the global Y-direction, +as dictated by the equilibrium in a free body diagram. Hence, the connector reaction forces and nodal +reaction forces are not equivalent in most cases. +Coulomb-like friction behavior +Coulomb-like friction behavior is possible for any connection type that has available components +of relative motion; see “Connector friction behavior,” Section 31.2.5, for details. Friction behavior +requires a “tangent” direction (the direction in which slipping may occur) and a “normal” direction (the +direction perpendicular to the contacting surfaces). In the most general case you define the normal force +causing friction in the connector. However, Abaqus predefines friction behavior for a limited number of +connection types, as discussed in the connection-type library in this section. In these predefined friction +cases you do not have to define the contact normal force. +Summary table +Each connection library entry includes a table summarizing the connection type. This summary +table indicates whether the connection type is basic, assembled, or complex. +It gives the kinematic +constraints; constraint force or moment components; available components of relative motion; “kinetic” +force or moment components following from the constitutive behavior in the available components of +relative motion; which orientation directions are required, optional, or ignored; how connector stops +limit the available components of relative motion; what reference lengths and angles are used to define +the constitutive behavior; what parameters are used for predefined Coulomb-like friction; and how the +contact normal forces are defined by Abaqus in association with predefined Coulomb-like friction. +Basic connection components +Basic connection components are divided into three categories: +• Translational basic connection components, which affect translational degrees of freedom at both +nodes and may affect rotational degrees of freedom at the first node or at both nodes +• Rotational basic connection components, which affect only rotational degrees of freedom at both +nodes +• Specialized rotational basic connection components, which in addition to rotational degrees of +freedom affect other degrees of freedom at the nodes +Only one translational basic connection component and one rotational or specialized rotational basic +connection component can be used in the definition of a connector element. +If a more complicated +connection requires more basic connection components than this, use multiple connector elements +attached to the same nodes. +Translational basic connection components +The following basic connection components affect translational degrees of freedom at both node a and +node b. Some of these connector components affect rotational degrees of freedom at node a or at both +node a and node b. Any basic connection component from this list can be used to define the translational +behavior of a connector element. +AXIAL +CARTESIAN +JOIN +LINK +PROJECTION CARTESIAN +RADIAL-THRUST +SLIDE-PLANE +SLOT +CONNECTION-TYPE LIBRARY +Provide a connection between two nodes to measure the relative +acceleration, velocity, and position of a body in a local coordinate +system. This connection type is available only in Abaqus/Explicit. +If it is defined in an Abaqus/Standard model, it will be converted +internally to a CARTESIAN connector type. +Provide a connection between two nodes that acts along the line +connecting the nodes. +Provide a connection between two nodes that allows independent +behavior in three local Cartesian directions that follow the system +at node a. +Join the position of two nodes. +Provide a pinned rigid link between two nodes to keep the distance +between the two nodes constant. +Provide a connection between two nodes that allows independent +behavior in three local Cartesian directions that follow the system +at both nodes a and b. +Provide a connection between two nodes that allows different +behavior for radial and thrust displacements. +Provide a slide-plane connection to make the position of the second +node remain on a plane defined by the orientation of the first node +and the initial position of the second node. +Provide a slot connection to make the position of the second node +remain on a line defined by the orientation of the first node and the +initial position of the second node. +Rotational basic connection components +The following basic connection components affect only rotational degrees of freedom at the nodes in the +connection. Any basic connection component from this list can be used to define the rotational behavior +of a connector element. +ALIGN +CARDAN +CONSTANT VELOCITY +EULER +FLEXION-TORSION +Provide a connection between two nodes that aligns their local +directions. +Provide a rotational connection between two nodes parameterized +by Cardan (or Bryant) angles. +Provide a constant velocity connection between two nodes. +Provide a rotational connection between two nodes parameterized +by Euler angles. +Provide a connection between two nodes that allows different +behavior for flexural and torsional rotations. +PROJECTION FLEXION- +TORSION +REVOLUTE +ROTATION +Provide a connection between two nodes that allows different +behavior for two flexural rotations and one torsional rotation. +Provide a revolute connection between two nodes. +Provide a rotational connection between two nodes parameterized +by the rotation vector. +ROTATION-ACCELEROMETER Provide a connection between two nodes to measure the relative +angular acceleration, velocity, and position of a body in a local +coordinate system. This connection type is available only in +Abaqus/Explicit. If it is defined in an Abaqus/Standard model, it +will be converted internally to a CARDAN connector type. +Provide a universal connection between two nodes. +UNIVERSAL +Specialized rotational basic connection components +The following basic connection component affects rotational and other non-translational degrees of +freedom at the nodes in the connection. The specialized rotational basic connection component can be +combined with translational basic connection components. +FLOW-CONVERTER +Provide a means of converting the material flow (degree of +freedom 10) at a connector node into a rotation. +Assembled connections +Assembled connections are included for convenience. Each assembled connection is created by +combinations of basic connection components. The equivalent basic connection components used for +each assembled connection are listed in parentheses. +(JOIN + +Provide a rigid beam connection between two nodes. +ALIGN) +Provide a connection between two nodes that allows independent +behavior in three local Cartesian directions that follow the system +at both nodes a and b and that allows different behavior in two +flexural rotations and one torsional rotation. +(PROJECTION +CARTESIAN + PROJECTION FLEXION-TORSION) +Join the position of two nodes, and provide a constant velocity +connection between their rotational degrees of freedom. (JOIN + +CONSTANT VELOCITY) +Provide a slot connection between two nodes, and constrain the +rotations by a revolute connection. (SLOT + REVOLUTE) +Join the position of +and provide a revolute +connection between their rotational degrees of freedom. (JOIN + +REVOLUTE) +two nodes, +31.1.5–6 +BEAM +BUSHING +CVJOINT +CYLINDRICAL +Provide a slide-plane connection between two nodes with a +revolute connection about the normal direction to the plane. The +PLANAR connection creates a local two-dimensional system in +three-dimensional analyses. (SLIDE-PLANE + REVOLUTE) +Join the position of two nodes, and convert material flow into +rotation. (JOIN + FLOW-CONVERTER) +Provide a slot connection between two nodes, and align their three +local axis directions. (SLOT + ALIGN) +Join the position of two nodes, and provide a universal connection +between their rotational degrees of freedom at the nodes. (JOIN + +UNIVERSAL) +Join the position of two nodes, and align their three local axis +directions. (JOIN + ALIGN) +PLANAR +RETRACTOR +TRANSLATOR +UJOINT +WELD +Complex connections +Complex connections affect a combination of degrees of freedom at the nodes in the connection and +cannot be combined with other connection components. They typically model highly coupled physical +connections. +SLIPRING +Model material flow and stretching between two points of a belt +system (such as an automotive seat belt). +Connection-type library +The following descriptions list all the basic connection components and assembled connections in +alphabetical order. +ACCELEROMETER +Connection type ACCELEROMETER provides a convenient way to measure the relative position, +velocity, and acceleration of a body in a local coordinate system. These kinematic quantities are +measured relative to the motion of node a and are reported in the coordinate system of node b. Each +node of the connector can translate and rotate independently, although fixing the first of the two nodes +to ground is more common. With the first node fixed, connection type ACCELEROMETER provides a +convenient way to measure the local components of the velocity and acceleration in a coordinate system +fixed to a moving body (for example, an accelerometer). +Connection type ACCELEROMETER is available only in Abaqus/Explicit. It is the translation +counterpart +relative +to connection type ROTATION-ACCELEROMETER, which measures +angular position, velocity, and acceleration. ACCELEROMETER connections cannot be used in +two-dimensional and axisymmetric analyses in Abaqus/Explicit. +ea +ea +ea +Figure 31.1.5–2 Connection type ACCELEROMETER. +Description +The ACCELEROMETER connection does not impose kinematic constraints. +It defines three local +directions at node a and three local directions at node b. The ACCELEROMETER connection’s +formulation is similar to that for the CARTESIAN connection. The ACCELEROMETER connection +measures the position of node b relative to node a +and +There are no available components of relative motion for the ACCELEROMETER connection. The +connector displacement components are +where +, +, and +are the initial coordinates of node b relative to node a. +The ACCELEROMETER connection measures velocity and acceleration in the local directions +In contrast to the CARTESIAN connection, the +at node a as if node a were an inertial frame. +and +ACCELEROMETER connection reports the computed velocity and acceleration in the local directions +at node b. Let +. Then the ACCELEROMETER connection +measures velocity and acceleration as +be the transformation from +to +and +where the derivatives above are time derivatives in a system moving with +. +In two-dimensional and axisymmetric analyses +. +Summary +ACCELEROMETER +Basic, assembled, or complex: +Kinematic constraints: +Constraint force output: +Available components: +Kinetic force output: +Orientation at a: +Orientation at b: +Connector stops: +Constitutive reference lengths: +Predefined friction parameters: +Contact force for predefined friction: +Basic +None +None +None +None +Optional +Optional +None +None +None +None +ALIGN +Connection type ALIGN provides a connection between two nodes where all three local directions are +aligned. If both local axes are given and do not align initially, their initial relative angular position is +held constant. +ea +eb +eb +ea +eb +ea +Figure 31.1.5–3 Connection type ALIGN. +Description +The ALIGN connection imposes kinematic constraints only. The local directions at node b are set equal +to those at node a. If the local directions do not align initially, the ALIGN connection holds fixed the +Cardan angles between the local orientation directions at node b, +, and those at node a, +. These fixed angular positions are the connector position output quantities. See connection +type CARDAN for a definition of Cardan angles. +The constraint moment enforcing the alignment of the local directions is +In two-dimensional analysis +. +Summary +ALIGN +Basic, assembled, or complex: +Basic +Kinematic constraints: +Constraint moment output: +Available components: +Kinetic moment output: +Orientation at a: +None +None +Optional +ALIGN +Orientation at b: +Connector stops: +Constitutive reference angles: +Predefined friction parameters: +Contact force for predefined friction: +Optional +None +None +None +None +AXIAL +Connection type AXIAL provides a connection between two nodes where the relative displacement is +along the line separating the two nodes. It models discrete physical connections such as axial springs, +axial dashpots, or node-to-node (gap-like) contact. +u1 +Figure 31.1.5–4 Connection type AXIAL. +Description +The AXIAL connection does not constrain any component of relative motion. The distance between +nodes a and b is +The available component of relative motion, +the change in distance separating the two nodes, and is defined as +, acts along the line connecting the two nodes, measures +where +is the initial distance from node a to b. The connector constitutive displacement is +The kinetic force is +where +In Abaqus/Standard an optional orientation can be provided at one of the nodes in an AXIAL +connection to provide direction for the force if the nodes are coincident or when one of the nodes is +a “ground node.” If the orientation is provided at both of the coincident nodes, the orientation at the +first node in the connectivity will be used. The orientation definitions remain fixed during the analysis +and will be ignored when the two nodes separate. Rotational degrees of freedom are not activated for +connection type AXIAL. +Symbol plots in the Visualization module of Abaqus/CAE display vector field output for the AXIAL +connector along the 1-direction of the orientation at the first node instead of along the line joining the two +nodes. If an orientation is not defined for the first node of the connector, the vector is displayed along +the 1-direction of the global coordinate system. +Summary +AXIAL +Basic, assembled, or complex: +Kinematic constraints: +Constraint force output: +Available components: +Kinetic force output: +Orientation at a: +Orientation at b: +Connector stops: +Basic +None +None +Optional +Optional +Constitutive reference lengths: +Predefined friction parameters: +Contact force for predefined friction: +None +None +BEAM +Connection type BEAM provides a rigid beam connection between two nodes. +eb +eb +ea +eb +ea +ea +Figure 31.1.5–5 Connection type BEAM. +Description +Connection type BEAM imposes kinematic constraints and uses local orientation definitions equivalent +to combining connection types JOIN and ALIGN. +Summary +BEAM +Basic, assembled, or complex: +Assembled +Kinematic constraints: +JOIN + ALIGN +Constraint force and moment output: +Available components: +Kinetic force and moment output: +Orientation at a: +Orientation at b: +Connector stops: +Constitutive reference lengths and angles: +Predefined friction parameters: +Contact force for predefined friction: +None +None +Optional +Optional +None +None +None +None +BUSHING +Connection type BUSHING provides a bushing-like connection between two nodes. It cannot be used +in two-dimensional or axisymmetric analyses. +attached to Part A +deformable +material +attached to Part B +deformable material +(e.g. rubber) +attached to +Part A +attached to +Part B +Figure 31.1.5–6 Connection type BUSHING. +Description +Connection type BUSHING does not constrain any components of relative motion and uses local +orientation definitions equivalent to combining connection types PROJECTION CARTESIAN and +PROJECTION FLEXION-TORSION. +Summary +BUSHING +Basic, assembled, or complex: +Assembled +Kinematic constraints: +Constraint force and moment output: +Available components: +None +None +BUSHING +Kinetic force and moment output: +Orientation at a: +Orientation at b: +Connector stops: +Required +Optional +Constitutive reference lengths and angles: +Predefined friction parameters: +Contact force for predefined friction: +None +None +CARDAN +Connection type CARDAN provides a rotational connection between two nodes where the relative +rotation between the nodes is parameterized by Cardan (or Bryant) angles. A Cardan-angle +parameterization of finite rotations is also called a 1–2–3 or yaw-pitch-roll parameterization. +Connection type CARDAN cannot be used in two-dimensional or axisymmetric analysis. +When connection type CARDAN is used with connector behavior, the relative rotation axis with the +highest resistance to rotational motion should be assigned to the second component of relative rotation +(component number 5) to avoid “gimbal lock,” a singularity in the rotation parameterization for relative +rotation angles +. +α rotation +ea +β rotation +ea +eb +ea +ea +γ rotation +ea +eb +ea +e2 +eb +ea +ea +eb +Figure 31.1.5–7 Connection type CARDAN. +ea +Description +The CARDAN connection does not impose kinematic constraints. A CARDAN connection is a finite +rotation connection where the local directions at node b are parameterized in terms of Cardan (or Bryant) +angles relative to the local directions at node a. Local directions +are positioned relative to +by three successive finite rotations +, +, and +as follows: +1. Rotate by +2. Rotate by +3. Rotate by +radians about axis +radians about the intermediate 2-axis, +radians about axis +; +. +Rotation angle +large (i.e., magnitude greater than +should be moderate (magnitude less than +). The Cardan angles are determined by the local directions as +; and +), whereas +and may be arbitrarily +Here, m and n are integers that account for rotations with a magnitude greater than . +The three available components of relative motion in the CARDAN connection are the changes in +the Cardan angles positioning the local directions at node b relative to the local directions at node a. +Therefore, +where +, +, and +are the initial Cardan angles. The connector constitutive rotations are +and +The kinetic moment +in a CARDAN connection is determined from the three component +relationships: +and +Summary +CARDAN +Basic, assembled, or complex: +Kinematic constraints: +Constraint moment output: +Available components: +Kinetic moment output: +Orientation at a: +Orientation at b: +Connector stops: +and +Basic +None +None +Required +Optional +Constitutive reference angles: +Predefined friction parameters: +Contact force for predefined friction: +None +None +CARTESIAN +Connection type CARTESIAN provides a connection between two nodes where the change in position +is measured in three local connection directions for node a, shown in Figure 31.1.5–8. +ea +ea +ea +Figure 31.1.5–8 Connection type CARTESIAN. +Description +The CARTESIAN connection does not impose kinematic constraints. It defines three local directions +at node a and measures the change in position of node b along these local coordinate +directions. The local directions at node a follow the rotation of node a. +The position of node b relative to node a is +The available components of relative motion are +and +and +where +The connector constitutive displacements are +, and +, +are the initial coordinates of node b relative to the local coordinate system at node a. +The kinetic force is +and +In two-dimensional analysis +, +, +, and +. +Summary +CARTESIAN +Basic, assembled, or complex: +Kinematic constraints: +Constraint force output: +Available components: +Kinetic force output: +Orientation at a: +Orientation at b: +Connector stops: +Basic +None +None +Optional +Ignored +Constitutive reference lengths: +Predefined friction parameters: +Contact force for predefined friction: +None +None +CONSTANT VELOCITY +Connection type CONSTANT VELOCITY provides the rotational part of connection type CVJOINT. +It cannot be used in two-dimensional or axisymmetric analysis. Furthermore, the connection type does +not have available components of relative motion. To include connector behavior in flexural motion, use +connection type FLEXION-TORSION with the torsion angle set to zero. +This connection type models physical connectors that under certain conditions transmit a constant +spinning velocity about misaligned shafts. +ea +ea +eb +eb +eb +ea +Figure 31.1.5–9 Connection type CONSTANT VELOCITY. +Description +The shaft direction at node a is +is stated as follows. In any configuration there are two unit length orthogonal vectors +plane perpendicular to the shaft at node b. These vectors can be written +, and the shaft direction at node b is +. The constant velocity constraint +in the +and +The angle +is chosen such that +and +The constant velocity constraint requires that the angle +is constant at all times. The constant velocity +constraint is equivalent to constraining the torsion angle to be constant in a FLEXION-TORSION +connection. +The name “constant velocity” for this connection type derives from the following property. If the +, have components only along each shaft, respectively, and +direction), +angular velocities of the two shafts, +in the direction of the normal to the plane containing the two shafts (that is, along the +the components of angular velocity along the respective shaft directions are equal: +and +Hence, the “spinning” angular velocity component is the same about each shaft. +The constraint moment imposing the constant velocity constraint has a single component about the +average shaft direction +and is written +Summary +CONSTANT VELOCITY +Basic, assembled, or complex: +Basic +Kinematic constraints: +Constraint moment output: +Available components: +Kinetic moment output: +Orientation at a: +Orientation at b: +Connector stops: +Constitutive reference angles: +Predefined friction parameters: +Contact force for predefined friction: +None +None +Required +Optional +None +None +None +None +CVJOINT +Connection type CVJOINT joins the position of two nodes and provides a constant velocity +constraint between their rotational degrees of freedom. Connection type CVJOINT cannot be used in +two-dimensional or axisymmetric analysis. +ea +a, b +eb +ea +eb +1eb +ea +Figure 31.1.5–10 Connection type CVJOINT. +Description +Connection type CVJOINT imposes kinematic constraints and uses local orientation definitions +equivalent to combining connection types JOIN and CONSTANT VELOCITY. +Summary +CVJOINT +Basic, assembled, or complex: +Assembled +Kinematic constraints: +JOIN + CONSTANT VELOCITY +Constraint force and moment output: +Available components: +Kinetic force and moment output: +Orientation at a: +Orientation at b: +Connector stops: +Constitutive reference lengths and angles: +Predefined friction parameters: +Contact force for predefined friction: +None +None +Required +Optional +None +None +None +None +CYLINDRICAL +Connection type CYLINDRICAL provides a slot connection between two nodes and a revolute constraint +where the free rotation is about the line of the slot. It cannot be used in two-dimensional or axisymmetric +analysis. +ea +eb +ea +ea +eb +ur1 +eb +u1 +Figure 31.1.5–11 Connection type CYLINDRICAL. +Description +Connection type CYLINDRICAL imposes kinematic constraints and uses local orientation definitions +equivalent to combining connection types SLOT and REVOLUTE. +The connector constraint forces and moments reported as connector output depend strongly on +the order and the location of the nodes in the connector . +Since the kinematic constraints are enforced at node b (the second node of the connector element), the +reported forces and moments are the constraint forces and moments applied at node b to enforce the +CYLINDRICAL constraint. Thus, in most cases the connector output associated with a CYLINDRICAL +connection is best interpreted when node b is located at the center of the device enforcing the constraint. +This choice is essential when moment-based friction is modeled in the connector since the contact +forces are derived on the connector forces and moments, as illustrated below. Proper enforcement of the +kinematic constraints is independent of the order or location of the nodes. +Friction +Predefined Coulomb-like friction in the CYLINDRICAL connection defines the friction force (CSFC) +along the instantaneous slip direction on the two contacting cylindrical surfaces (the pin and the sleeve) +illustrated above. The table below summarizes the parameters that are used to specify predefined friction +in this connection type as discussed in detail next. +The frictional effect is formally written as +where the potential +in a direction tangent to the cylindrical surface on which contact occurs, +normal force on the same cylindrical surface, and +represents the magnitude of the frictional tangential tractions in the connector +is the friction-producing +is the friction coefficient. Frictional stick occurs if +; and sliding occurs if +, in which case the friction force is +. +The normal force +is the sum of a magnitude measure of friction-producing connector forces, +, and a self-equilibrated internal contact force (such as from a press-fit assembly), +: +The magnitude measure of friction-producing connector contact force, +, is defined by summing +the following two contributions: +• a radial force contribution, +constraint): +(the magnitude of the constraint forces enforcing the SLOT +• a force contribution from “bending,” +(the +magnitude of the constraint moments enforcing the REVOLUTE constraint), by a length factor, as +follows: +, obtained by scaling the bending moment, +where L represents a characteristic overlapping length between the shaft and the outer sleeve in the +1-direction. If L is 0.0, +is ignored. +Thus, +where +. +The magnitude of the frictional tangential moment, +is computed using +where R is an effective radius of the shaft cross-section in the local 2–3 plane. The potential +represents the magnitude of connector tangential tractions on the cylindrical contact surface due to +simultaneous translation and rotation. The instantaneous slip direction is a result of combined motion +in these directions. +Summary +CYLINDRICAL +Basic, assembled, or complex: +Assembled +Kinematic constraints: +SLOT + REVOLUTE +Constraint force and moment output: +Available components: +Kinetic force and moment output: +Orientation at a: +Orientation at b: +Connector stops: +, +, +Required +Optional +Constitutive reference lengths and angles: +, +Predefined friction parameters: +Required: R; optional: L, +Contact force for predefined friction: +EULER +Connection type EULER provides a rotational connection between two nodes where the total relative +rotation between the nodes is parameterized by Euler angles. An Euler-angle parameterization of finite +rotations is also called a 3–1–3 or precession-nutation-spin parameterization. Connection type EULER +cannot be used in two-dimensional or axisymmetric analysis. +α rotation +ea +β rotation +γ rotation +ea +eb +ea +eb +ea +ea +ea +ea +e1 +ea +Figure 31.1.5–12 Connection type EULER. +Description +eb +ea +eb +The EULER connection does not impose kinematic constraints. An EULER connection is a finite rotation +connection where the local directions at node b are parameterized in terms of Euler angles relative to the +local directions at node a. Local directions +by three +successive finite rotations +are positioned relative to +as follows: +, and +, +; +1. Rotate by +2. Rotate by +3. Rotate by +; +radians about axis +radians about the intermediate 1-axis, +radians about axis +. +The Euler angles are determined by the local directions as +Here i, j, and k are integers that account for rotations with magnitudes greater than . Initially, the +intermediate rotation angle +is chosen in the interval +If the intermediate rotation is an even multiple of +, +. +, where +, the other +two Euler angles become non-unique. In this case +Similarly, if the intermediate rotation is an odd multiple of +the other two Euler angles become nonunique as well. In this case +, +, where +0, +, +In both of these cases a singularity results in the rotation parameterization when the +axes +align. The EULER connection should be used in such a way that these axes do not align throughout +the computation. For a singularity-free condition Abaqus will choose +such that a smooth +parameterization results for the above values of the intermediate angle +. +and +and +The available components of relative motion in the EULER connection are the changes in the Euler +angles that position the local directions at node b relative to the local directions at node a. Therefore, +where +, +, and +are the initial Euler angles. The connector constitutive rotations are +and +The kinetic moment in a EULER connection is determined from the three component relationships: +and +and +EULER +Basic, assembled, or complex: +Kinematic constraints: +Constraint moment output: +Available components: +Basic +None +None +31.1.5–28 +EULER +Kinetic moment output: +Orientation at a: +Orientation at b: +Connector stops: +Required +Optional +Constitutive reference angles: +Predefined friction parameters: +Contact force for predefined friction: +None +None +FLEXION-TORSION +Connection type FLEXION-TORSION provides a rotational connection between two nodes. It models +the bending and twisting of a cylindrical coupling between two shafts. +In this case the response to +twist rotations about the shafts may differ from the response to bending of the shafts. Connection type +FLEXION-TORSION cannot be used in two-dimensional or axisymmetric analysis. +The flexural part of the connection resists angular misalignment of the two shafts, whereas the +torsional part of the connection resists relative rotations about the shafts. Connection type FLEXION- +TORSION can be used in conjunction with connection type RADIAL-THRUST when resistance to +relative radial and thrust displacements is modeled. +ea +eb +ea +ea +Figure 31.1.5–13 Connection type FLEXION-TORSION. +Description +The FLEXION-TORSION connection does not +TORSION connection describes a finite rotation by three angles: flexion, torsion, and sweep ( , +The FLEXION- +, and +). However, the flexion, torsion, and sweep angles do not represent three successive rotations. The +flexion angle between two shafts measures the angle of misalignment of the two shafts and is always +reported as a positive angle. The torsion angle measures the twist of one shaft relative to the other. +impose kinematic constraints. +– +The sweep angle orients the rotation vector, in the +plane, for the flexion motion. See +Figure 31.1.5–13. Since the flexion angle is never negative, the sweep angle may undergo discontinuous +jumps by up to +radians when the flexion angle passes through zero. An analysis may give inaccurate +results or may not converge if any jump occurs in the sweep angle. In general, the sweep angle is not +used as an available component of relative motion for which connector behavior is defined. Rather, it +is used to define angular dependence for the elastic constitutive response in flexion deformations (as an +independent component in the connector elastic behavior definition). Since the sweep angle is restricted +to the interval +radians, any dependence on the sweep angle should be periodic, such that the +to +. Since +is the same as +behavior for +is a singular point for which the sweep angle +is not uniquely defined, it is strongly recommended that any connector behavior that defines flexural +moment versus flexion angle gives zero moment at zero flexion angle. If connector behavior is defined +in the sweep available component, the sweep moment must be zero at flexion angles +. +The FLEXION-TORSION connection is similar to a finite successive rotation parameterization +3–2–3. However, in terms of the 3–2–3 parameterization, the sweep angle is the first rotation angle, the +flexion angle is the second rotation angle, and the torsion angle is the sum of the first and third rotation +angles. +and +The first shaft direction at node a is +, and the second shaft direction at node b is +. Let the two +shafts form an angle +, called the flexion angle. Then, +The flexion angle is a rotation by +about the (unit) rotation vector +where +The torsion angle +between the two shafts is defined as +where +where positive torsion angles are rotations about the positive +The sweep angle measures the angle from to the projection of +-direction, and m is an integer. +onto the +– +plane. With +this definition +It follows that the flexion rotation vector, +, can be written +where +A singularity in the definition of the sweep angles occurs when the flexion angle +vanishes. In this +; that is, the torsion and sweep angle axes are coincident, and the two angles are no longer +case +independent. When +, the sweep angle is assumed zero, +. +The available components of relative motion +, +, and +are the changes in the flexion, +torsion, and sweep angles and are defined as +where +angle +and +are the initial flexion and torsion angles, respectively. The initial value of the sweep +is chosen to be zero if the shafts align initially. The connector constitutive rotations are +and +The kinetic moment in a FLEXION-TORSION connection is determined from the three component +relationships: +and +Summary +FLEXION-TORSION +Basic, assembled, or complex: +Kinematic constraints: +Constraint moment output: +Available components: +Kinetic moment output: +Orientation at a: +Orientation at b: +Connector stops: +and +Basic +None +None +Required +Optional +Constitutive reference angles: +Predefined friction parameters: +Contact force for predefined friction: +None +None +FLOW-CONVERTER +Connection type FLOW-CONVERTER converts the relative rotation about a user-specified axis between +the two nodes of the connector into material flow degree of freedom (10) at the second node of a connector +element. This connection type can be used to model retractor and pretensioner devices in automotive +seat belts or cable drums in winch-like devices. Belt or cable material is considered to be +wrapped around an axle or a drum, and material can be spooled either into or out of the connector element. +In certain cases, material flow needs to be converted into a displacement rather than a rotation. +Examples include pretensioner devices for which experimental force vs. displacement data need to +be specified. Although this connection type always converts the material flow into a rotation, the two +modeling cases are equivalent. The experimentally available force vs. displacement data can be input +directly as moment vs. rotation data for the same end result. +This connection type activates degree of freedom 10 at the second node of a connector. As with +any other nodal degree of freedom, you must be careful in constraining it. This is typically done by +attaching the connector to a SLIPRING connector that is part of the belt system or by applying a boundary +condition. FLOW-CONVERTER connections cannot be used in two-dimensional and axisymmetric +analyses in Abaqus/Explicit. +L W +Figure 31.1.5–14 Connection type FLOW-CONVERTER. +Description +The FLOW-CONVERTER connection constrains the relative rotation between the two nodes about the +third local direction, +. The constraint can be written as +, to the material flow at node b, +is the relative nodal rotation between node a andb and +where +part of the associated connector section definition. By default, +with the nodal rotation at node a. +is a scaling factor specified as +rotates +. The local direction +There are no available components of relative motion for this connection type; hence, kinetic +behavior cannot be specified. However, the following kinematic quantities are available for output: +which will be output as CPR1 and CPR2, respectively. +The constraint moment is +and +Limitation +At most two FLOW-CONVERTER connectors can share their second node where degree of freedom 10 +is active. +Summary +FLOW-CONVERTER +Basic, assembled, or complex: +Specialized basic rotational +Kinematic constraints: +Constraint moment output: +Available components: +Kinetic force output: +Orientation at a: +Orientation at b: +Connector stops: +Constitutive reference lengths: +Predefined friction parameters: +Contact force for predefined friction: +None +None +Required +Ignored +None +None +None +None +HINGE +Connection type HINGE joins the position of two nodes and provides a revolute constraint between +their rotational degrees of freedom. Connection type HINGE cannot be used in two-dimensional or +axisymmetric analysis. +ea +, eb +ea +a, b +ea +eb +eb +Figure 31.1.5–15 Connection type HINGE. +Description +Connection type HINGE imposes kinematic constraints and uses local orientation definitions equivalent +to combining connection types JOIN and REVOLUTE. +The connector constraint forces and moments reported as connector output depend strongly on the +order and the location of the nodes in the connector element . +Since the kinematic constraints are enforced at node b (the second node of the connector element), the +reported forces and moments are the constraint forces and moments applied at node b to enforce the +HINGE constraint. Thus, in most cases the connector output associated with a HINGE connection is +best interpreted when node b is located at the center of the device enforcing the constraint. This choice +is essential when moment-based friction is modeled in the connector since the contact forces are derived +from the connector forces and moments, as illustrated below. Proper enforcement of the kinematic +constraints is independent of the order or location of the nodes. +Friction +Predefined Coulomb-like friction in the HINGE connection relates the kinematic constraint forces and +moments in the connector to a friction moment (CSM1) in the rotation about the hinge axis. The table +below summarizes the parameters that are used to specify predefined friction in this connection type +as discussed in detail next. A typical interpretation of the geometric scaling constants is illustrated in +Figure 31.1.5–16. +Since the rotation about the 1-direction is the only possible relative motion in the connection, the +frictional effect is formally written in terms of moments generated by tangential tractions and moments +generated by contact forces, as follows: +L s +Part B +Pin +2Ra +Part A +2R +Contact on this face +between Part A and Part B +Figure 31.1.5–16 Illustration of the geometric scaling constants for a HINGE connection. +where the potential +connector in a direction tangent to the cylindrical surface on which contact occurs, +producing normal moment on the same cylindrical surface, and +stick occurs if +; and sliding occurs if +represents the moment magnitude of the frictional tangential tractions in the +is the friction- +is the friction coefficient. Frictional +, in which case the friction moment is +is the sum of a magnitude measure of friction-producing connector +, and a self-equilibrated internal contact moment (such as from a press-fit +The normal moment +. +moments, +assembly), +: +The magnitude measure of friction-producing connector contact moments, +, is defined by +summing the following contributions: +• a moment from an axial force, +is an effective friction arm associated +with the constraint force in the axial direction (the +radius could be interpreted as an average +radius of the outer sleeve cylindrical sections as found in a typical door hinge or as an effective +radius associated with the hinge end caps, if they exist; if +is ignored); and +, where +is 0.0, +and +• a moment from normal forces to the cylindrical face, +section in the local 2–3 plane and +, where +is itself a sum of the following two contributions: +is the radius of the pin cross- +– a radial force contribution, +(the magnitude of the constraint forces enforcing the translation +constraints in the local 2–3 plane): +– a force contribution from “bending,” +, obtained by scaling the bending moment, +(the magnitude of the constraint moments enforcing the REVOLUTE constraint), by a length +factor, as follows: +represents a characteristic overlapping length between the pin and the sleeve. If +is ignored. +where +is 0.0, +Thus, +where +. +The moment magnitude of the frictional tangential tractions, +. +Summary +HINGE +Basic, assembled, or complex: +Assembled +Kinematic constraints: +JOIN + REVOLUTE +Constraint force and moment output: +Available components: +Kinetic force and moment output: +Orientation at a: +Orientation at b: +Required +Optional +HINGE +Connector stops: +Constitutive reference lengths: +Predefined friction parameters: +Required: +; optional: +, +, +Contact moment for predefined friction: +JOIN +Connection type JOIN makes the position of two nodes the same. If the two nodes are not co-located +initially, the position of node b is fixed relative to that of node a in a Cartesian coordinate system attached +to node a. +Even though an orientation is optional at node a, connection type JOIN does not activate rotational +degrees of freedom at node a. +ea +a, b +ea +ea +Figure 31.1.5–17 Connection type JOIN. +Description +The JOIN connection makes the position of node b equal to that of node a. If the two nodes are not +coincident initially, the Cartesian coordinates of node b relative to node a are fixed. See connection type +CARTESIAN for a definition of the Cartesian coordinates of node b relative to node a. If rotational +degrees of freedom exist at node a, the local directions co-rotate with the node. +The constraint force in the JOIN connection acts in the three local directions at node a and is +where +in two-dimensional analysis. +Friction +When used by itself, there is no predefined Coulomb-like friction in the JOIN connection, since there are +no available components of relative motion for which friction can be defined. However, when the JOIN +and REVOLUTE connection types are used together, the predefined friction is the same as the HINGE +connection. When the JOIN and UNIVERSAL connection types are used together, the predefined friction +is the same as the UJOINT connection. +Summary +JOIN +Basic, assembled, or complex: +Basic +Kinematic constraints: +JOIN +Constraint force output: +Available components: +Kinetic force output: +Orientation at a: +Orientation at b: +Connector stops: +Constitutive reference lengths: +Predefined friction parameters: +Contact force for predefined friction: +None +None +Optional +Ignored +None +None +None +None +LINK +Connection type LINK maintains a constant distance between two nodes. Rotational degrees of freedom, +if they exist, are not affected at either node. +Figure 31.1.5–18 Connection type LINK. +Description +The LINK connection constrains the position of node b, +distance between the two nodes is +, to a constant distance from node a. The +and is constant. The constraint force in the LINK connection acts along the line connecting the two nodes +and is +where +Symbol plots in the Visualization module of Abaqus/CAE display vector field output for the LINK +connector along the 1-direction of the orientation at the first node instead of along the line joining the two +nodes. If an orientation is not defined for the first node of the connector, the vector is displayed along +the 1-direction of the global coordinate system. +Summary +LINK +Basic, assembled, or complex: +Basic +Kinematic constraints: +Constraint force output: +Available components: +Kinetic force output: +Orientation at a: +Orientation at b: +Connector stops: +None +None +Ignored +Ignored +None +LINK +Constitutive reference lengths: +Predefined friction parameters: +Contact force for predefined friction: +None +None +None +PLANAR +Connection type PLANAR provides a local two-dimensional system in a three-dimensional analysis. +Connection type PLANAR cannot be used in two-dimensional or axisymmetric analysis. +ea +ea +eb +ea +u2 +ur1 +u3 +eb +eb +Figure 31.1.5–19 Connection type PLANAR. +Description +Connection type PLANAR imposes kinematic constraints and uses local orientation definitions +equivalent to combining connection types SLIDE-PLANE and REVOLUTE. +Friction +Predefined Coulomb-like friction in the PLANAR connection relates the kinematic constraint forces and +moments in the connector to the friction forces in the translations in the local 2–3 plane and the frictional +moment in the rotation about the local 1-direction. These two frictional effects are discussed separately +below. +A. The frictional effect due to sliding in the 2–3 plane is formally written as +where the potential +connector in a direction tangent to the local 2–3 plane on which contact occurs, +producing normal force on the same plane, and +if +represents the magnitude of the frictional tangential tractions in the +is the friction- +is the friction coefficient. Frictional stick occurs +; and sliding occurs if +, in which case the friction force (CSFC) is +is the sum of a magnitude measure of force-producing connector forces, +: +, and a self-equilibrated internal contact force, +The normal force +. +The contact force magnitude +is defined by summing the following two contributions: +• a force contribution, +and +(the constraint force enforcing the SLIDE-PLANE constraint); +• a force contribution from “bending,” +, obtained by scaling the bending moment, +(the magnitude of the constraint moments enforcing the REVOLUTE constraint), by a length +factor, as follows: +where R represents a characteristic radius of the “puck” (as illustrated in Figure 31.1.5–20) in +the local 2–3 plane. If R is 0.0, +is ignored. +bend +F1 + bend +2R + bend +2R +Figure 31.1.5–20 Illustration of the effective internal friction contact forces. +Thus, +where +. +The magnitude of the frictional tangential moment, +is computed using +B. Since the frictional effects due to rotation about the 1-direction are quantified, the frictional effect +is formally written in terms of moments generated by tangential tractions and moments generated +by contact forces as +where the potential +connector about the 1-direction, +axis, and +occurs if +represents the magnitude of the frictional tangential moment in the +is the friction-producing normal moment about the same +; and sliding +is the friction coefficient. Frictional stick in rotation occurs if +. +, in which case the friction moment (CSM1) is +The normal moment +is the sum of a magnitude measure of friction-producing connector +moments, +, and a self-equilibrated internal contact moment, +: +The contact moment magnitude +is defined by summing the following two contributions: +• a moment from a contact force in the 2–3 plane, +SLIDE-PLANE constraint): +(the constraint moment enforcing the +where +Figure 31.1.5–20) in the local 2–3 plane (if R is 0.0, +from integrating moment contributions from a uniform pressure ( +contact patch; and +, R represents a characteristic radius of the “puck” (as illustrated in +is ignored), and the 2/3 factor comes +) over the circular +• a moment contribution from “bending,” +enforcing the REVOLUTE constraint): +(the magnitude of the constraint moments +Thus, +The magnitude of the frictional tangential tractions, +is computed using +Summary +PLANAR +Basic, assembled, or complex: +Assembled +Kinematic constraints: +SLIDE-PLANE + REVOLUTE +Constraint force and moment output: +Available components: +Kinetic force and moment output: +Orientation at a: +Orientation at b: +Connector stops: +Required +Optional +Constitutive reference lengths and angles: +Predefined friction parameters: +Optional: R, +, +Contact forces and moments for predefined +friction: +, +PROJECTION CARTESIAN +Connection type PROJECTION CARTESIAN provides a connection between two nodes where the +response in three local connection directions (that is, the axes of the local Cartesian coordinate system) +is measured. Unlike the CARTESIAN connection, which uses an orthonormal coordinate system that +follows node a, the PROJECTION CARTESIAN connection uses an orthonormal system that follows +the systems at both nodes a and b. +The connector local directions used in the PROJECTION CARTESIAN connection are identical +to those used in the PROJECTION FLEXION-TORSION connection. Connection type PROJECTION +CARTESIAN is compatible with connection type PROJECTION FLEXION-TORSION and is +appropriate for modeling the displacement response of bushing-like or spot-weld-like components. +ea +e3 +eb +e1 +a, b +e2 +Figure 31.1.5–21 Connection type PROJECTION CARTESIAN. +Description +The PROJECTION CARTESIAN connection does not impose kinematic constraints. It defines three +local directions +as a function of the directions at both nodes a and b. These directions +are the projection directions defined by the PROJECTION FLEXION-TORSION connection. The +PROJECTION CARTESIAN connection measures the change in position of node b relative to node a +along the (projection) coordinate directions +. +The position of node b relative to node a is +The available components of relative motion are +and +and +where +directions. The connector constitutive displacements are +, and +, +are the initial coordinates of node b relative to node a along the initial +and +The local directions in a PROJECTION CARTESIAN connection are “centered” between the +systems at the two connector nodes. PROJECTION CARTESIAN connections are appropriate where +isotropic or anisotropic material response is modeled and the local material directions evolve as a +function of the rotations at both ends of the connection. The kinetic force is +In two-dimensional analysis +, +, +, and +. +Summary +PROJECTION CARTESIAN +Basic, assembled, or complex: +Kinematic constraints: +Constraint force output: +Available components: +Kinetic force output: +Orientation at a: +Orientation at b: +Connector stops: +Basic +None +None +Optional +Optional +Constitutive reference lengths: +Predefined friction parameters: +Contact force for predefined friction: +None +None +PROJECTION FLEXION-TORSION +It models the bending and twisting of a cylindrical coupling between two shafts. +Connection type PROJECTION FLEXION-TORSION provides a rotational connection between +two nodes. +In +this case the response to twist rotations about the shafts may differ from the response to bending +of the shafts. Connection type PROJECTION FLEXION-TORSION is similar to connection type +FLEXION-TORSION. Whereas the FLEXION-TORSION connection has rotation parameterization +angles consisting of total flexion, +the PROJECTION FLEXION-TORSION +connection has rotation parameterization angles consisting of two component flexion angles and +a torsion angle. The flexion angle of the FLEXION-TORSION connection is the resultant flexion +angle resulting from the two component flexion angles of the PROJECTION FLEXION-TORSION +connection. Connection type PROJECTION FLEXION-TORSION cannot be used in two-dimensional +or axisymmetric analysis. +torsion, and sweep, +The flexural part of the connection resists angular misalignment of the two shafts, whereas the +torsional part of the connection resists relative rotations about the shafts. Connection type PROJECTION +FLEXION-TORSION can be used in conjunction with connection type PROJECTION CARTESIAN +when modeling the response of bushing-like or spot-weld-like components. +ea +e3 +eb +e1 +a, b +e2 +Figure 31.1.5–22 Connection type PROJECTION FLEXION-TORSION. +Description +The PROJECTION FLEXION-TORSION connection does not impose kinematic constraints. The +PROJECTION FLEXION-TORSION connection describes a finite rotation by three angles: flexion 1, +flexion 2, and torsion ( +, and ). However, the flexion 1, flexion 2, and torsion angles do not +represent three successive rotations. The two component flexion angles ( +) make up the total +flexion angle between two shafts and measure the angle of misalignment of the two shafts. The torsion +angle measures the twist of one shaft relative to the other. +and +, +The first shaft direction at node a is +, and the second shaft direction at node b is +. Let the two +shafts form an angle +, called the total flexion angle. Then, +where +The flexion angle is a rotation by +about the (unit) rotation vector, +where +The PROJECTION FLEXION-TORSION connection is formulated in terms of the unit vector +. See Figure 31.1.5–22. The +is referred to as the flexion-torsion plane. The component flexion angles +, and two unit vectors spanning this plane, +normal to a plane, +plane with normal vector +and +and +are determined from and +by projection onto the two in-plane directions: +and +The torsion angle in a PROJECTION FLEXION-TORSION connection can be understood from +a finite successive rotation parameterization 3–2–3. In terms of the 3–2–3 parameterization the total +flexion angle is the second successive rotation angle, and the torsion angle is the sum of the first and +third successive rotation angles. The torsion angle +between the two shafts is defined as +where positive torsion angles are rotations about the positive +-direction and m is an integer. +The PROJECTION FLEXION-TORSION connection avoids the singularity that occurs in the +sweep angle of the FLEXION-TORSION connection when the total flexion angle +vanishes. As a +result, the PROJECTION FLEXION-TORSION connection is better suited for defining bushing-like +behavior for flexion response that varies with the direction of +in the flexion-torsion plane. +The available components of relative motion +, +, and +are the changes in the two flexion +angles and the torsion angle and are defined as +and +where +, and +connector constitutive rotations are +, +are the initial flexion component angles and torsion angle, respectively. The +The kinetic moment in a PROJECTION FLEXION-TORSION connection is +and +Summary +PROJECTION FLEXION-TORSION +Basic, assembled, or complex: +Kinematic constraints: +Constraint moment output: +Available components: +Kinetic moment output: +Orientation at a: +Orientation at b: +Connector stops: +Basic +None +None +Required +Optional +Constitutive reference angles: +Predefined friction parameters: +Contact force for predefined friction: +None +None +RADIAL-THRUST +Connection type RADIAL-THRUST provides a connection between two nodes where the response +differs in the radial and cylindrical axis directions. Connection type RADIAL-THRUST models +situations such as a point inside a cylindrical bearing where the response to radial displacements +differs from the response to thrusting motions. Connection type RADIAL-THRUST cannot be used in +two-dimensional or axisymmetric analysis. +If the rotational degrees of freedom at the two nodes are connected through flexural and torsional +resistance, connection type FLEXION-TORSION can be used in conjunction with connection type +RADIAL-THRUST. +ea +Figure 31.1.5–23 Connection type RADIAL-THRUST. +Description +The RADIAL-THRUST connection does not impose kinematic constraints. An orientation at node a is +required to define the axis of the rectangular coordinate system, +. The position of node b relative to +node a is given by the radial and axial-direction distances +and +The RADIAL-THRUST connection has two available components of relative motion, +radial displacement +coordinate system and is defined as +. The +measures the change in distance from node b to the axis of the cylindrical +and +where +change in distance from node a to node b along the cylindrical axis and is defined as +is the initial radial distance from node b to the axis. The thrust displacement +measures the +where +displacements are +is the initial distance along the axis from node b to node a. The connector constitutive +The kinetic force is +and +where the radial unit vector is +– +The radial resistance of the RADIAL-THRUST connector is analogous to a single spring in the +plane. Loads applied in this plane and perpendicular to the current radial unit vector will initially +encounter no resistance and may lead to numerical singularity and/or zero pivot warnings from the solver +during static analyses. If the numerical singularities cause convergence difficulties, one modeling option +is to overlay the RADIAL-THRUST connector with a CARTESIAN connector with a very small elastic +stiffness. +Summary +RADIAL-THRUST +Basic, assembled, or complex: +Kinematic constraints: +Constraint force output: +Available components: +Kinetic force output: +Orientation at a: +Orientation at b: +Connector stops: +Basic +None +None +Required +Ignored +Constitutive reference lengths: +Predefined friction parameters: +Contact force for predefined friction: +None +None +RETRACTOR +Connection type RETRACTOR joins the position of two nodes and provides a FLOW-CONVERTER +constraint between the material flow degree of freedom (10) at the second node and the rotational degrees +of freedom at the first node of the connector. This connection type can be used to model retractor and +pretensioner devices in automotive seat belts or cable drums in winch-like devices. +RETRACTOR connections cannot be used in two-dimensional and axisymmetric analyses in +Abaqus/Explicit. +L W +Figure 31.1.5–24 Connection type RETRACTOR. +Description +Connection type RETRACTOR imposes kinematic constraints and uses local orientation definitions +equivalent to combining connection types JOIN and FLOW-CONVERTER. +Summary +RETRACTOR +Basic, assembled, or complex: +Assembled +Kinematic constraints: +JOIN + FLOW-CONVERTER +Constraint force output: +Available components: +Kinetic force output: +Orientation at a: +Orientation at b: +None +None +Required +Ignored +RETRACTOR +Connector stops: +Constitutive reference lengths: +Predefined friction parameters: +None +None +None +Contact force for predefined friction: None +REVOLUTE +Connection type REVOLUTE provides a connection between two nodes where the rotations are +constrained about two local directions and free about a shared axis. The shared axis of rotation is +the connector local 1-direction. Connection type REVOLUTE cannot be used in two-dimensional or +axisymmetric analysis. +Connection type REVOLUTE models the rotational part of a HINGE or CYLINDRICAL joint. +eb +eb +eb +ea +ea +ea +ea +eb +Figure 31.1.5–25 Connection type REVOLUTE. +Description +A REVOLUTE connection constrains two rotational components of relative motion between two nodes +and allows one free rotational component. The two kinematic constraints imposed by the REVOLUTE +connection are +and +which are equivalent to the requirement that +. Alternatively, the REVOLUTE constraint is +equivalent to setting the second and third Cardan angles to zero in a CARDAN connection. If the shared +axes +do not align initially, the REVOLUTE constraint will hold the second and third Cardan +angles fixed at their initial values. The constraint moment in the REVOLUTE connection is +and +Node b can rotate about the shared local direction +. The relative angular position of the +local directions at node b relative to a is +is the first Cardan angle measuring a counterclockwise rotation about the +-direction of +to +where +. +, measures the change in angular position and is +defined as +CONNECTION-TYPE LIBRARY +where +shared axis. The connector constitutive rotation is +is the initial angular position and n is an integer accounting for multiple rotations about the +The kinetic moment in the REVOLUTE connection is +Friction +When used by itself, there is no predefined Coulomb-like friction in the REVOLUTE connection. +However, when the REVOLUTE connection is used in combination with a JOIN, SLIDE-PLANE, or +SLOT connection, the predefined friction is the same as the HINGE, PLANAR, and CYLINDRICAL +connections, respectively. +Summary +REVOLUTE +Basic, assembled, or complex: +Basic +Kinematic constraints: +Constraint moment output: +Available components: +Kinetic moment output: +Orientation at a: +Orientation at b: +Connector stops: +Constitutive reference angles: +Required +Optional +Predefined friction parameters: +None +Contact moment for predefined friction: None +ROTATION +Connection type ROTATION provides a rotational connection between two nodes where the relative +rotation between the nodes is parameterized by the rotation vector. In two-dimensional and axisymmetric +analyses, the ROTATION connection type involves a single (scalar) relative rotation component. +Although available components of relative motion exist for the ROTATION connection type in +three-dimensional analysis, the finite rotation parameterization of the connection is not necessarily +well-suited for defining connector behavior. +If a finite, three-dimensional ROTATION connection +with connector behavior is desired, either the CARDAN or EULER connection type typically is more +appropriate. +When connection type ROTATION is used in a connector element connected to ground at the +element’s first node, the rotational components relative to the orientation at ground are identical to the +Abaqus convention for nodal rotation degrees of freedom. Hence, connection type ROTATION can be +used in conjunction with prescribed connector motion to +specify finite rotation boundary conditions in local coordinate directions using the Abaqus convention +for finite rotation boundary conditions. +eb +eb +eb +ea +ea +ea +Figure 31.1.5–26 Connection type ROTATION. +Description +The rotation connection does not impose kinematic constraints. The rotation connection is a finite +rotation connection where the local directions at node b are parameterized relative to the local directions +at node a by the rotation vector. Let +relative to +be the rotation vector that positions local directions +; that is, +for all +Section 1.3.1 of the Abaqus Theory Manual, for a discussion of finite rotations. +is the skew-symmetric matrix with axial vector +, where +. See “Rotation variables,” +The available components of relative motion in the ROTATION connection are the change in the +rotation vector components positioning the local directions at node b relative to the local directions at +node a. Therefore, +, all vector components are components relative to the local directions +is an integer accounting for rotations with magnitude greater +. The +, and +is the initial rotation vector, +where +than +connector constitutive rotations are +The kinetic moment in a rotation connection is +In two-dimensional and axisymmetric analyses +and +. +Summary +ROTATION +Basic, assembled, or complex: +Kinematic constraints: +Constraint moment output: +Available components: +Kinetic moment output: +Orientation at a: +Orientation at b: +Connector stops: +Basic +None +None +Optional +Optional +Constitutive reference angles: +Predefined friction parameters: +Contact force for predefined friction: +None +None +ROTATION-ACCELEROMETER +Connection type ROTATION-ACCELEROMETER provides a convenient way to measure the relative +angular position, velocity, and acceleration of a body in a local coordinate system. These kinematic +quantities are measured relative to the motion of node a and are reported in the coordinate system of +node b. Each node of the connector can translate and rotate independently, although fixing the first +of the two nodes to ground is more common. With the first node fixed, connection type ROTATION- +ACCELEROMETER provides a convenient way to measure the local components of the angular velocity +and angular acceleration in a coordinate system fixed to a moving body (for example, an accelerometer). +Connection type ROTATION-ACCELEROMETER is available only in Abaqus/Explicit. It is the +rotation counterpart to connection type ACCELEROMETER, which measures relative translational +position, velocity, and acceleration. +ROTATION-ACCELEROMETER connectors +cannot be used in two-dimensional +and +axisymmetric analysis in Abaqus/Explicit. +eb +eb +eb +ea +ea +ea +Figure 31.1.5–27 Connection type ROTATION-ACCELEROMETER. +Description +The ROTATION-ACCELEROMETER connection does not +It +defines three local directions at node a and three local directions at node b. The ROTATION- +ACCELEROMETER connection’s formulation is similar to that for the ROTATION connection. The +ROTATION-ACCELEROMETER connection measures the finite rotation that takes the local directions +at node a into the local directions at node b and parameterizes that finite rotation by the rotation vector. +Let +be the rotation vector that positions local directions +impose kinematic constraints. +relative to +; that is, +, where +. See “Rotation variables,” +is the skew-symmetric matrix with axial vector +for all +Section 1.3.1 of the Abaqus Theory Manual, for a discussion of finite rotations. The connection measures +the change in the rotation vector components in the local directions rotating with the body at node b. The +rotation vector components are calculated as +There are no available components of relative motion for the ROTATION-ACCELEROMETER +connection. The connector rotation is +where +greater than +. +is the initial rotation vector and +is an integer accounting for rotations with magnitude +The ROTATION-ACCELEROMETER connection differs from the ROTATION connection in the +way angular velocity and acceleration are calculated. The ROTATION-ACCELEROMETER connection +measures velocity and acceleration from the nodes as +where +, +, +, and +are the nodal angular velocities and accelerations at nodes a and b, respectively. +In two-dimensional and axisymmetric analyses +. +and +Summary +ROTATION-ACCELEROMETER +Basic, assembled, or complex: +Kinematic constraints: +Constraint force output: +Available components: +Kinetic force output: +Orientation at a: +Orientation at b: +Connector stops: +Constitutive reference lengths: +Predefined friction parameters: +Contact force for predefined friction: +Basic +None +None +None +None +Optional +Optional +None +None +None +None +SLIDE-PLANE +Connection type SLIDE-PLANE keeps node b on a plane defined by the orientation of node a and +the initial position of node b. Connection type SLIDE-PLANE cannot be used in two-dimensional or +axisymmetric analysis. The normal direction defining the plane at node a is +. +Connection type SLIDE-PLANE models a point confined between parallel plates or a pin-in-slot +connection where the pin is free to move normal to the plane of the slot. +ea +ea +x0 +ea +u2 +u3 +Figure 31.1.5–28 Connection type SLIDE-PLANE. +Description +The SLIDE-PLANE connection constrains the position of node b, +the local normal direction +. The normal direction distance from node a to the plane is constant: +, to remain on a plane defined by +where +connection is +is the initial distance from node a to the plane. The constraint force in the SLIDE-PLANE +Node b can move in the plane defined by the normal of node a. The position of node b in the plane +relative to node a is +The two available components of relative motion, +and +, are +and +and +where +displacements are +and +are the coordinates of the initial position of node b. The connector constitutive +The kinetic force in the plane is +and +Friction +Predefined Coulomb-like friction in the SLIDE-PLANE connection relates the kinematic constraint +forces in the connector to the friction forces (CSFC) in the translations along the two local directions +in the 2–3 plane. +The frictional effect is formally written as +where the potential +in a direction tangent to the 2–3 plane on which contact occurs, +on the same plane, and +if +represents the magnitude of the frictional tangential tractions in the connector +is the friction-producing normal force +; and sliding occurs +is the friction coefficient. Frictional stick occurs if +, in which case the friction force is +. +The normal force +is the sum of a magnitude measure of friction-producing connector forces, +, and a self-equilibrated internal contact force, +: +The force magnitude +The magnitude of the frictional tangential tractions, +. +is computed using +The predefined Coulomb-like friction is computed differently when the SLIDE-PLANE connection +is used in combination with a REVOLUTE connection. See the description of the PLANAR connection +for the predefined friction definition in this case. +Summary +SLIDE-PLANE +Basic, assembled, or complex: +Basic +Kinematic constraints: +Constraint force output: +Available components: +Kinetic force output: +Orientation at a: +Orientation at b: +Connector stops: +Required +Ignored +Constitutive reference lengths: +Predefined friction parameters: +Optional: +Contact force for predefined friction: +SLIPRING +Connection type SLIPRING provides a connection between two nodes that models material flow and +stretching between two points of a belt system. It can be used to model seat belts , pulley systems, and +taut cable systems. The angle between two adjacent belt segments is used only for friction calculations. +By default, the angle, +and . Alternatively, you can specify the angle between two adjacent belt segments (in radians) as part +of the connector section definition. You can use this option to specify wrapping angles larger than . +, is computed automatically from the nodal coordinates as an angle between +This connection type activates the material flow degree of freedom (10) at both nodes of the +connector. As with any other nodal degree of freedom, you must be careful in constraining it. This is +typically done by attaching the connector to other SLIPRING connectors that are part of the belt system, +attaching it to a RETRACTOR (FLOW-CONVERTER) connector, or applying a boundary condition. +SLIPRING connections cannot be used in two-dimensional and axisymmetric analyses in +Abaqus/Explicit. + +radius +ignored + +Figure 31.1.5–29 Connection type SLIPRING. +Description +The SLIPRING connection does not constrain any component of relative motion. Hence, there is no +restriction on the position of the connector nodes. +The distance between nodes is +The belt material can flow and stretch between nodes a and b. Flow can occur with no stretching (such +as in a rigid belt), stretching can occur with no flow (such as when the flow is constrained at both nodes +of the connector), or both flow and stretching can occur simultaneously (such as in compliant belts). By +convention, the material flow at node a is positive if it enters segment +and is positive at node b if it +exits the segment. A reference length can be defined in incremental fashion as +is the reference length at the end of the current increment, +where +beginning of the current increment, +flow at node b. The stretch in the belt can then be defined as +is the incremental flow at node a, and +is the reference length at the +is the incremental +and the “strain” in the belt can be computed as +At the beginning of the analysis, the reference length at +is +is the initial stretch of the belt. By default, the initial stretch is +where +no initial strains in the belt. You can specify initial strains in the belt, +constitutive reference. The initial stretch is then computed using +meaning that there are +, by specifying a connector +The second available component of relative motion is simply the material flow past node b, +The third component of relative motion is the material flow into node a and is used only for output: +The kinetic force is +where +Symbol plots in the Visualization module of Abaqus/CAE display vector field output for the +SLIPRING connector along the 1-direction of the orientation at the first node instead of along the line +joining the two nodes. If an orientation is not defined for the first node of the connector, the vector is +displayed along the 1-direction of the global coordinate system. +Limitations +At most two SLIPRING connectors can share a common node. The following limitations apply with +respect to the kinetic behavior that can be defined in the SLIPRING connection type: +• Only predefined friction can be defined in the second component of relative motion as outlined +below. +• In Abaqus/Explicit plasticity, damage and lock connector behavior cannot be specified. +• The connectivities of the two adjacent SLIPRING connector elements sharing a common node +b (Figure 31.1.5–29) should be in the typical order a–b and b–c. In addition, any two adjacent +SLIPRING connector elements must refer to the same connector behavior except for the friction +data. +Friction +in component 1) to the tension in the adjacent belt segment +Predefined Coulomb-like friction in the SLIPRING connection relates the tension in the belt segment +. In the simpler case of +(kinetic force +frictionless sliding, the two tensions are equal (apart from inertial effects due to the motion of the belt in +dynamic analyses). If frictional effects are included as material flows past node b, the two tensions differ +by the total friction force (CSF2) over the contact arch between the belt and the ring (angle +). +The Coulomb-like frictional effect is a well-known analytical result. In the case when frictional +sliding occurs in the direction illustrated in Figure 31.1.5–29, the tensions in the two segments, +and +, are related as follows: +where +is the friction coefficient. The friction force is simply the difference +More formally, the frictional relationship is modeled by considering the potential function +Frictional stick occurs if +; and sliding occurs if +. Friction forces do not develop if the kinetic force += +, in which case the tension force +is compressive. When sliding occurs in +the opposite direction, the sign of the exponent in the potential equation changes. +The friction force is reported as +in this connection type. The friction-generating “contact force” +is reported as CNF2= . +In Abaqus/Explicit, by default, the distance between the two nodes of the SLIPRING is not +allowed to become less then one hundredth of the original distance between the nodes, which prevents +the SLIPRING from collapsing to zero length during the analysis. The two nodes of the SLIPRING can +move apart after coming to the minimum distance configuration during the analysis. In addition, the belt +can continue to slip over the nodes while they are stopped at the minimum distance configuration. This +default value of the minimum distance can be overridden by specifying a lower limit of the connector +stop in component 1 of the SLIPRING. +Output +Some of the connector output variables have a somewhat different meaning for this connection type than +usual, as follows: +• CP1 is the current distance between the nodes; +• CP2 is the material flow at node b; +• CP3 is the material flow at node a; and +• CU1 is the strain (dimensionless) in the segment +. +Summary +SLIPRING +Basic, assembled, or complex: +Complex +Kinematic constraints: +Constraint force output: +Available components: +Kinetic force output: +Orientation at a: +Orientation at b: +Connector stops: +None +None +Ignored +Ignored +None +Constitutive reference lengths: +Predefined friction parameters: +None +Contact force for predefined friction: +SLOT +Connection type SLOT provides a connection where node b stays on the line defined by the orientation +of node a and the initial position of node b. The line of action of the slot is the +-direction. +In three-dimensional analysis node b cannot move in the direction normal to the slot; i.e., the +direction. If node b is free to move in the normal direction, connection type SLIDE-PLANE should be +used. +ea +ea +y0 +u1 +Figure 31.1.5–30 Connection type SLOT. +Description +The line of the slot is defined by the first local direction at node a, +The SLOT connection constrains the position of node b, +the relative position of node b is fixed in the directions perpendicular to the slot: +, and the initial position of node b. +, to remain on the line of the slot. Therefore, +where +is the initial distance from node a to the slot in the local 2-direction. In three dimensions +where +the slot is +is the initial distance from node a to the slot in the local 3-direction. The constraint force in +where +in two-dimensional analysis. +Node b can move along the line of the slot. The relative position in the slot is the distance between +node b and node a along the +-direction and is defined as +The available component of relative motion is the displacement +relative position in length along the slot and is defined as +, which measures the change of the +where +displacement is +is the initial distance between node b and node a along the slot. The connector constitutive +The kinetic force in the slot is +Friction +Predefined Coulomb-like friction in the SLOT connection relates the kinematic constraint forces in the +connector to the friction force (CSF1) in the translation along the slot. +The frictional effect is formally written as +where the potential +in a direction tangent to the slot axis along which contact occurs, +(contact) force in the direction normal to the slot, and +if +represents the magnitude of the frictional tangential tractions in the connector +is the friction-producing normal +is the friction coefficient. Frictional stick occurs +. +, in which case the friction force is +; and sliding occurs if +The normal force +is the sum of a magnitude measure of the friction-producing connector force, +, and a self-equilibrated internal contact force, +: +The force magnitude +is computed using +The magnitude of the frictional tangential tractions +The predefined Coulomb-like friction is computed differently when the SLOT connection is used in +combination with a REVOLUTE or an ALIGN connection. See CYLINDRICAL and TRANSLATOR, +respectively, for the predefined friction definition in these cases. +. +Summary +SLOT +Basic, assembled, or complex: +Basic +Kinematic constraints: +Constraint force output: +Available components: +Kinetic force output: +Orientation at a: +Orientation at b: +Connector stops: +Required +Ignored +Constitutive reference lengths: +Predefined friction parameters: +Optional: +Contact force for predefined friction: +TRANSLATOR +Connection type TRANSLATOR provides a slot constraint between two nodes and aligns their local +directions. +ea +ea +eb +ea +eb +eb +u1 +Figure 31.1.5–31 Connection type TRANSLATOR. +Description +Connection type TRANSLATOR imposes kinematic constraints and uses local orientation definitions +equivalent to combining connection types SLOT and ALIGN. +The connector constraint forces and moments reported as connector output depend strongly on +the order and location of the nodes in the connector . Since +the kinematic constraints are enforced at node b (the second node of the connector element), the +reported forces and moments are the constraint forces and moments applied at node b to enforce the +TRANSLATOR constraint. Thus, in most cases the connector output associated with a TRANSLATOR +connection is best interpreted when node b is located at the center of the device enforcing the constraint. +This choice is essential when moment-based friction is modeled in the connector since the contact +forces are derived from the connector forces and moments, as illustrated below. Proper enforcement of +the kinematic constraints is independent of the order or location of the nodes. +Friction +Predefined Coulomb-like friction in the TRANSLATOR connection relates the kinematic constraint +forces and moments in the connector to the friction force (CSF1) in the translation along the slot. +The frictional effect is formally written as +where the potential +the local 1-direction, +slot, and +which case the friction force is +is the friction coefficient. Frictional stick occurs if +. +represents the magnitude of the frictional tangential traction in the connector in +is the friction-producing normal (contact) force in the direction normal to the +, in +; and sliding occurs if +is the sum of a magnitude measure of contact friction-producing connector +forces, +, and a self-equilibrated internal contact force, +: +CONNECTION-TYPE LIBRARY +The contact force magnitude +• a force contribution from torque, +is defined by summing the following three contributions: +, obtained by scaling the torque constraint moment about the +1-direction, +, by a length factor, as follows: +where +0.0, +represents the effective radius of the shaft cross-section in the local 2–3 plane (if +is ignored); +is +• a radial force contribution, +constraint): +(the magnitude of the constraint forces enforcing the SLOT +and +• a force contribution from “bending,” +, by a length factor, as follows: +, obtained by scaling the bending constraint moment, +where L represents a characteristic overlapping length in the slot direction. If L is 0.0, +ignored. +is +Thus, +where +. +The magnitude of the frictional tangential tractions, +is +. +Summary +TRANSLATOR +Basic, assembled, or complex: +Assembled +Kinematic constraints: +SLOT + ALIGN +Constraint force and moment output: +Available components: +Kinetic force and moment output: +Orientation at a: +Orientation at b: +Connector stops: +Constitutive reference lengths: +Required +Optional +Predefined friction parameters: +Optional: +, L, +Contact force for predefined friction: +UJOINT +Connection type UJOINT joins the position of two nodes and provides a universal constraint between +their rotational degrees of freedom. Connection type UJOINT cannot be used in two-dimensional or +axisymmetric analysis. +ea +eb +ea +eb +Figure 31.1.5–32 Connection type UJOINT. +Description +Connection type UJOINT imposes kinematic constraints and uses local orientation definitions equivalent +to combining connection types JOIN and UNIVERSAL. +The connector constraint forces and moments reported as connector output depend strongly on the +order of the nodes and location of the nodes in the connector . +Since the kinematic constraints are enforced at node b (the second node of the connector element), the +reported forces and moments are the constraint forces and moments applied at node b to enforce the +UJOINT constraint. Thus, in most cases the connector output associated with a UJOINT connection +is best interpreted when node b is located at the center of the device enforcing the constraint. This +choice is essential when moment-based friction is modeled in the connector since the contact forces +are derived from the connector forces and moments, as illustrated below. Proper enforcement of the +kinematic constraints is independent of the order or location of the nodes. +Friction +Predefined Coulomb-like friction in the UJOINT connection relates the kinematic constraint forces and +moments in the connector to friction moments about the unconstrained rotations (about the two directions +of the connection cross). The UJOINT connection type consists of four hinge-like connections placed +at the four ends of the connection cross that generate frictional moments about +the cross axes. The frictional moments in each of these hinges are computed in a fashion similar to the +HINGE connection. +The constraint forces and moments are used first to compute a reaction force, +of the constraint forces enforcing the JOIN constraint), and a “twisting” constraint moment, +magnitude of the constraint moment enforcing the UNIVERSAL connection), as follows: +(the magnitude +(the +and +The two cross directions are given by +perpendicular to the connection cross given by +to be applied at the center of the connection cross. The constraint moment, +the four hinges a bending-like moment about +. The constraint moment, +. Both +: +and +, acts about an axis +are considered +, produces in each of +and a transverse force in the cross plane +, where +where +represents a characteristic length of the cross arm between the center of the cross and the ends +of the cross. The scaling factors +and +are nonlinear functions of the slenderness of the cross +axes (the aspect ratio +is the average radius of the four pins at the ends of the connection +cross): they can be approximated by assuming the cross arm with rigid bodies for infinitely small aspect +ratios, with Timoshenko beams for small aspect ratios (less than 20), and with Euler-Bernoulli beams +for slender axes (large aspect ratios). Abaqus chooses the appropriate values automatically based on the +user-specified geometric constants +. Figure 31.1.5–33 illustrates the evolution of the scaling +factors as a function of the aspect ratio: as the aspect ratio approaches 0.0, +approaches 0.0 and +approaches 0.375. +, can be decomposed into axial forces along the two axes of the connection cross +approaches 0.25; for large aspect ratios, +The constraint force, +and a “bending” force perpendicular to the connection cross plane: +approaches 0.125 and +and +where +axial +twist +twist +axial +Figure 31.1.5–33 Scaling factors in the UJOINT connection. +Friction in the UJOINT connection is the superposition of four HINGE-like frictional effects due +to rotations about the two cross axes. Since the rotations about the local 1- and 3-directions are the only +possible relative motions in the connection, the frictional effects (CSM1 and CSM3) are formally written +in terms of moments generated by tangential tractions and moments generated by contact forces. In the +following equations subscript 1 refers to frictional effects about the local 1-direction, and subscript 3 +refers to frictional effects about the local 3-direction. The frictional effects are written as follows: +and +where the potentials +tractions in the connector in directions tangent to the cylindrical surface on which contact occurs, +and +friction coefficient. Frictional stick occurs in a particular direction if +occurs if +are the friction-producing normal moments on the same cylindrical surface, and +, in which case the friction moments are +represent the moment magnitudes of the frictional tangential +is the +; and sliding +and +or +or +. +The normal moments +and +connector moments, +(such as from a press-fit assembly), +and +are the sums of magnitude measures of force-producing +, and self-equilibrated internal contact moments +and +, respectively: +The factor of two in the above equations comes from the fact that there are two hinges on each cross +direction. +The moment magnitudes +and +are defined by summing the following contributions: +• moment from axial forces, +, and +constraint force in the axial direction in each of the pins (if +ignored); and +and +, +is an average effective friction arm associated with the +are +is 0.0, +, where +and +• moment from normal forces, +following contributions: +and +, where +and +are themselves sums of the +– transverse force contributions, +hinges along the +two hinges along the +-direction) and +-direction): +(the magnitude of the total transverse force in the two +(the magnitude of the total transverse force in the +where +, +is defined above, +, and +; and +– force contributions from “bending,” +, obtained by scaling the total bending moment, +(the magnitude of the total bending moment on each of the four hinges), by a length +factor, as follows: +where +overlapping length between the pins and their sleeves. If +is defined above, and +, +is 0.0, +represents a characteristic +is ignored. +Thus, +The moment magnitudes of the frictional tangential tractions are +and +. +Summary +UJOINT +Basic, assembled, or complex: +Assembled +Kinematic constraints: +JOIN + UNIVERSAL +Constraint force and moment output: +Available components: +Kinetic force and moment output: +Orientation at a: +Orientation at b: +Connector stops: +Constitutive reference lengths: +Predefined friction parameters: +Required +Optional +Required: +, +, +, +; optional: +, +Contact moments for predefined friction: +, +UNIVERSAL +Connection type UNIVERSAL provides a connection between two nodes where the rotations are +fixed about one local direction and free about two others. Connection type UNIVERSAL provides +the rotational part of a UJOINT connection. Connection type UNIVERSAL cannot be used in +two-dimensional or axisymmetric analysis. +ea +ea +ea +eb +eb +eb +Figure 31.1.5–34 Connection type UNIVERSAL. +Description +A UNIVERSAL connection constrains the rotation about the shaft directions at two nodes. The shaft +directions at nodes a and b are +, respectively. A UNIVERSAL connection requires that local +direction +and +. This single constraint is written +be perpendicular to +This constraint is equivalent to constraining the second Cardan angle to be zero in a Cardan angle +parameterization of the local directions at node b relative to those at node a. If the initial orientation +directions at node b do not satisfy the above constraint condition, the universal constraint will hold the +second Cardan angle fixed at its initial value. +The constraint moment imposed by the UNIVERSAL connection is +A UNIVERSAL connection allows two free rotational components of relative motion between two +nodes. The first and third Cardan angles that position local directions at node b relative to those at node +a are +and +The two available components of relative motion for the UNIVERSAL connection, +changes in the two unconstrained Cardan angles when the second Cardan angle is fixed. Therefore, +and +, are the +where +and +are the initial Cardan angles. The connector constitutive rotations are +and +The kinetic moment in the UNIVERSAL connection is +and +Friction +When used by itself, there is no predefined Coulomb-like friction in the UNIVERSAL connection. +However, when the UNIVERSAL connection is used in combination with the JOIN connection type, +the predefined friction is the same as the UJOINT connection. +Summary +UNIVERSAL +Basic, assembled, or complex: +Basic +Kinematic constraints: +Constraint moment output: +Available components: +Kinetic moment output: +Orientation at a: +Orientation at b: +Connector stops: +Required +Optional +Constitutive reference angles: +Predefined friction parameters: +Contact force for predefined friction: +None +None +WELD +Connection type WELD provides a fully bonded connection between two nodes. +ea +2, eb +ea +1, eb +a, b +ea +3, eb +Figure 31.1.5–35 Connection type WELD. +Description +Connection type WELD imposes kinematic constraints and uses local orientation definitions equivalent +to combining connection types JOIN and ALIGN. +Summary +WELD +Basic, assembled, or complex: +Kinematic constraints: +Constraint force and moment output: +Available components: +Kinetic force and moment output: +Orientation at a: +Orientation at b: +Connector stops: +Constitutive reference lengths and angles: +Predefined friction parameters: +Contact force for predefined friction: +Assembled +JOIN + ALIGN +None +None +Optional +Optional +None +None +None +None +31.2 +Connector element behavior +• “Connector behavior,” Section 31.2.1 +• “Connector elastic behavior,” Section 31.2.2 +• “Connector damping behavior,” Section 31.2.3 +• “Connector functions for coupled behavior,” Section 31.2.4 +• “Connector friction behavior,” Section 31.2.5 +• “Connector plastic behavior,” Section 31.2.6 +• “Connector damage behavior,” Section 31.2.7 +• “Connector stops and locks,” Section 31.2.8 +• “Connector failure behavior,” Section 31.2.9 +• “Connector uniaxial behavior,” Section 31.2.10 +31.2.1 +CONNECTOR BEHAVIOR +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Connectors: overview,” Section 31.1.1 +• “Connector elastic behavior,” Section 31.2.2 +• “Connector damping behavior,” Section 31.2.3 +• “Connector functions for coupled behavior,” Section 31.2.4 +• “Connector friction behavior,” Section 31.2.5 +• “Connector plastic behavior,” Section 31.2.6 +• “Connector damage behavior,” Section 31.2.7 +• “Connector stops and locks,” Section 31.2.8 +• “Connector failure behavior,” Section 31.2.9 +• “Connector uniaxial behavior,” Section 31.2.10 +• *CONNECTOR BEHAVIOR +• *CONNECTOR CONSTITUTIVE REFERENCE +• *CONNECTOR SECTION +• “Creating connector sections,” Section 15.12.11 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Defining a reference length,” Section 15.17.12 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +• “Defining time integration,” Section 15.17.13 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +Connector behavior: +• can be defined for connection types with available components of relative motion; +• can incorporate simple spring, dashpot, and node-to-node contact as particular applications; +• may include linear or nonlinear force versus displacement and force versus velocity behavior for +the unconstrained relative motion components; +• can include uncoupled or coupled behavior specifications; +• can allow frictional force in an unconstrained component of relative motion to be generated by any +force or moment in the connection; +• can allow for plasticity definitions for individual components or coupled plasticity definitions using +user-defined yield functions; +• can be used to specify sophisticated damage mechanisms with various damage evolution laws; +• can provide user-defined locking criteria to lock in the current position all relative motion in the +connector element or a single unconstrained component of relative motion; +• can be used to specify failure of the connector element; and +• can be used to specify complex uniaxial models by specifying the loading and unloading behavior +in an available component of relative motion. +Assigning a connector behavior to a connector element +You can assign the name of a connector behavior to particular connector elements. +Input File Usage: +Abaqus/CAE Usage: +Use the following options to define the connector behavior: +*CONNECTOR SECTION, ELSET=name, BEHAVIOR=behavior name +*CONNECTOR BEHAVIOR, NAME=behavior name +Interaction module: +Connector→Section→Create: Name: connector section name: +Behavior Options, Add +Connector→Assignment→Create: select wires: Section: +connector section name +Connector behavior models +Connector behaviors allow for modeling of the following types of effects: +• spring-like elastic behavior; +• rigid-like elastic behavior; +• dashpot-like (damping) behavior; +• friction; +• plasticity; +• damage; +• stops; +• locks; +• failure; and +• uniaxial behavior. +Kinetic behavior can be specified only in available components of relative motion. The list of +available components of relative motion for each connector type is given in “Connection-type library,” +Section 31.1.5. A connector behavior can be specified in any of the following ways: +• uncoupled: +motion; +the behavior is specified separately in individual available components of relative +• coupled: all or several of the available components of relative motion are used simultaneously in a +coupled manner to define the behavior; or +• combined: a combination of both uncoupled and coupled definitions are used simultaneously. +A conceptual model illustrating how connector behaviors interact with each other is shown +locks, friction) act in parallel. +in Figure 31.2.1–1. Most behaviors (elasticity, damping, stops, +Plasticity models are always defined in conjunction with spring-like or rigid-like elasticity definitions. +Degradation due to damage can be specified either for the elastic-plastic or rigid-plastic response alone +or for the entire kinetic response in the connector. The failure behavior will apply to the entire connector +response. +elastic/rigid + plastic +damage +elastic/rigid plastic +first +connector +node +DMG +ERP +damping +stop/lock +friction +damage failure +DMG +ALL +FAIL +second +connector +node +Figure 31.2.1–1 Conceptual illustration of connector behaviors. +Multiple definitions for the same behavior type are permitted. For example, if connector elasticity +(or damping) is defined several times in an uncoupled fashion for the same available component of +relative motion, in a coupled fashion, or in both fashions, the spring-like (or dashpot-like) responses are +added together. Multiple definitions of friction, plasticity, and damage behaviors are permitted as long +as the rules outlined in the corresponding behavior sections are followed. Multiple uncoupled stop and +lock definitions for the same component are permitted, but only one will be enforced at a time. +Defining coupled and uncoupled connector behavior +In many cases connector behavior is specified in an uncoupled manner in individual available components +of relative motion. Coupled behavior can be defined for all or some of the available components of +relative motion in a connector. +For coupled plasticity, damage, and, in certain situations, friction behavior, additional functions +describing the nature of the coupling effects must be defined . These functions do not define a behavior by themselves but are used as tools +for building a desired behavior. For example, these functions may be used to define: +• sophisticated yield functions in the connector force space for coupled plasticity behavior; +• friction-generating contact forces for friction behavior; or +• force or relative motion magnitude measures needed for damage behavior specifications. +Input File Usage: +Use the following input to define uncoupled behavior: +*CONNECTOR BEHAVIOR OPTION, COMPONENT=n +Use the following input to define coupled behavior: +*CONNECTOR BEHAVIOR OPTION +Abaqus/CAE Usage: +Interaction module: connector section editor: Add→connector +behavior: Coupling: Uncoupled or Coupled +Defining nonlinear connector behavior properties to depend on relative positions or constitutive +displacements/rotations +In all nonlinear uncoupled connector kinetic behaviors the independent variable is the connector available +component in the direction for which the response is defined. When modeling the following connector +behaviors, the properties can also depend on relative positions or constitutive displacements/rotations in +several component directions: +• connector elasticity, +• connector damping, +• connector derived components, and +• connector friction. +When modeling connector uniaxial behavior, +displacements/rotations +Section 31.2.10, for more information. +in several component directions; +the properties can also depend on constitutive +see “Connector uniaxial behavior,” +Input File Usage: +Use the following option to specify that the connector behavior properties +are dependent on components of relative position included in the behavior +definition: +*CONNECTOR BEHAVIOR OPTION, +INDEPENDENT COMPONENTS=POSITION (default) +Use the following option to specify that the connector behavior properties are +dependent on components of constitutive relative displacements or rotations +included in the behavior definition: +*CONNECTOR BEHAVIOR OPTION, +INDEPENDENT COMPONENTS=CONSTITUTIVE MOTION +In either case the first data line identifies the independent component numbers +to be used in determining the dependencies, and the additional data for the +connector behavior definition begin on the second data line. +Abaqus/CAE Usage: +For elasticity or damping behavior, use the following input to specify that +connector behavior properties are dependent on relative position or constitutive +relative displacements/rotations: +Interaction module: connector section editor: Add→Elasticity +or Damping: Coupling: Coupled on position or Coupled on +motion, select components and enter data +For connector derived components, use the following input to specify that +connector behavior properties are dependent on relative position or constitutive +relative displacements/rotations: +Interaction module: connector section editor: +Add→Friction, Plasticity, or Damage: Force Potential, Initiation +Potential, or Evolution Potential +Specify derived component, Use local directions: Independent +position components or Independent constitutive motion +components, select components and enter data +For friction behavior specifying internal contact forces, use the following input +to specify that connector behavior properties are dependent on relative position +or constitutive relative displacements/rotations: +Interaction module: connector section editor: Add→Friction: Friction +model: User-defined, Contact Force, Use independent components: +Position or Motion, select components and enter data +Defining reference lengths and angles for constitutive response +In many connector behavior definitions, material-like behavior has a reference position where the force +or moment is zero, which is different from the initial position. This is the case, for example, in a spring +that has nonzero force or moment in the initial configuration. In these situations the most convenient +way to define the connector behavior is relative to the nominal or reference geometry where the forces +or moments vanish. +You can define the translational or angular positions at which constitutive forces and moments are +zero by specifying up to six reference values (one per component of relative motion): +three lengths +and three angles (in degrees). The reference lengths and angles affect only spring-like elastic connector +behavior and, if the friction-generating contact force (moment) is a function of the relative displacement +(rotation), connector friction behavior. By default, the reference lengths and angles are the length and +angle values determined from the initial geometry. See “Connection-type library,” Section 31.1.5, for +the meaning of the reference lengths and angles for each connection type. +Input File Usage: +*CONNECTOR CONSTITUTIVE REFERENCE +length 1, length 2, length 3, angle 1, angle 2, angle 3 +Abaqus/CAE Usage: +Interaction module: connector section editor: Add→Reference +Length: Length associated with CORM +Defining precompressed or preextended linear elastic behavior +In many cases connectors are precompressed or preextended when installed in assemblies. In such cases +the connector force is nonzero in the initial configuration. While nonlinear elasticity could be used to +define nonzero force in the initial configuration, it is often more convenient to specify a (linear) spring +stiffness plus a reference length or angle at which the force or moment is zero. For example, linear +uncoupled elastic behavior defined with the connection type AXIAL would have force given by the +equation +where +constitutive reference length. The connector constitutive displacement quantities, +different connection types as described in “Connection-type library,” Section 31.1.5. +. l is the current length of the AXIAL connection, and +is the user-defined +, are defined for +Example +An input file template for a connector model of the shock absorber in Figure 31.2.1–2 is presented in +“Connectors: overview,” Section 31.1.1. A reference angle of 22.5° is defined for the nonlinear torsional +spring as the fourth data item (corresponding to the connector’s fourth component of relative motion) in +the connector constitutive reference: +*CONNECTOR BEHAVIOR, NAME=sbehavior +... +*CONNECTOR CONSTITUTIVE REFERENCE +, , , 22.5 +The effect of this reference angle is that the nonlinear torsional spring has a zero moment at an angle of +22.5°. +extensible +range +7.5 +node 12 +1 (local orientation) +node 11 +Figure 31.2.1–2 Simplified connector model of a shock absorber. +Defining the time integration method for constitutive response in Abaqus/Explicit +In Abaqus/Explicit kinematic constraints, stops, locks, and actuated motion in connector elements +are treated with implicit time integration. By default, connector constitutive behavior (for example, +elasticity, damping, and friction) is also integrated implicitly. The advantage of implicit time integration +is that elements with these behaviors do not affect the stability or time incrementation of the analysis +in any way. +When “soft” springs are modeled with connectors, a more traditional explicit time integration for +the constitutive response can be used. This explicit time integration may lead to a small improvement +in computational performance. However, explicit integration of relatively stiff springs will reduce the +global time increment size, since such connector elements are included in the stable time increment size +calculation. +Input File Usage: +Use the following option to specify implicit integration of the constitutive +response: +*CONNECTOR BEHAVIOR, INTEGRATION=IMPLICIT +Use the following option to specify explicit integration of the constitutive +response: +Abaqus/CAE Usage: +*CONNECTOR BEHAVIOR, INTEGRATION=EXPLICIT +Interaction module: connector section editor: Add→Integration: +Integration: Implicit or Explicit +Defining connector behavior in linear perturbation procedures +In linear perturbation procedures the +connector element kinematics are linearized about the base state. Hence, linearized versions of kinematic +constraints are applied, and the connector behavior is linearized about the state at the end of the previous +general analysis step. +Using several connectors in series or in parallel +Connector element behaviors allow for proper modeling of most physical connection behaviors within +a single connector element. However, in rare circumstances more complex connection behaviors may +require multiple connector elements to be used in parallel or in series. You place connector elements in +parallel by defining two or more connector elements between the same nodes. You place connectors in +series by specifying additional nodes (most often in the same location as the nodes of interest) and then +stringing connector elements between these nodes. +For example, assume that you would like to define a connector stop that exhibits elastic-plastic +behavior upon contact. Since this is not permitted within the context of one connector behavior definition, +you can circumvent the limitation by using two connector elements in series. This concept is illustrated in +Figure 31.2.1–3. The first connector defines the stop, and the second defines the elastic-plastic behavior. +Since both elements are subject to the same load (because they are in series), the desired behavior is +obtained. +first connector element +second connector element +node on the +first body +stop +elastic-plastic +additional +node +node on the +second body +Figure 31.2.1–3 Conceptual illustration of two connector elements/behaviors in series. +Connectors in parallel can be used as well to model complex kinetic behavior. For example, +assume that you need to define an elastic-viscous connector with spring-like and dashpot-like behaviors +in parallel (for example, the strut in an automotive suspension). Assume that damage can occur only +in the dashpot once it is stretched/compressed beyond specified limits. Since this is not permitted +within the context of one connector behavior definition, you can circumvent the limitation by using two +connector elements in parallel. This concept is illustrated in Figure 31.2.1–4. +first connector +element +elastic +node on the +first body +DMG +ALL +node on the +second body +damping +second connector +element +Figure 31.2.1–4 Conceptual illustration of two connector elements/behaviors in parallel. +The first connector defines the elastic behavior, and the second defines the dashpot behavior. Since +the two connector elements are in parallel, they undergo the same motion (stretching/compression). +A motion-based damage behavior can be used to +degrade the entire behavior in the second element. Thus, only the dashpot behavior will eventually +degrade. +Defining connector behavior using tabular data +Tabular data are often used to define connector behaviors, such as nonlinear elasticity, +isotropic +hardening, etc. As shown in Figure 31.2.1–5, the data points make up a nonlinear curve in the +constitutive space. +Force, F +F(0) +F1 +Linear extrapolation +Constant extrapolation +Displacement, u +Constant extrapolation +Linear extrapolation +Figure 31.2.1–5 Nonlinear connector behaviors defined as tabular data. +The options to define table lookups are described below. +Extrapolation options +By default, the dependent variables are extrapolated as a constant (with a value corresponding to the +endpoints of the curve) outside the specified range of the independent variables. This choice may cause +a zero stiffness response, which may lead to convergence problems. You can specify linear extrapolation +to extrapolate the dependent variables outside the specified range of the independent variables assuming +that the slope given by the end points of the curve remains constant. The extrapolation behavior is +illustrated in Figure 31.2.1–5. +You define the extrapolation choice globally for all connector behaviors but can redefine the +extrapolation choice for the following connector behaviors individually: +• connector elasticity; +• connector plasticity (connector hardening); +• connector damping; +• derived components for connector elements; +• connector friction; +• connector damage (connector damage initiation and evolution); +• connector locks; and +• connector uniaxial behavior. +Tabular data for connector stop and lock behavior options are not supported in Abaqus/CAE. +Specifying constant extrapolation for all connector behaviors +You can specify constant extrapolation for tabular data for all connector behaviors. +Input File Usage: +Abaqus/CAE Usage: +*CONNECTOR BEHAVIOR, EXTRAPOLATION=CONSTANT (default) +Interaction module: connector section editor: Table Options +tabbed page: Extrapolation: Constant +Specifying linear extrapolation for all connector behaviors +You can specify linear extrapolation for tabular data for all connector behaviors. +Input File Usage: +Abaqus/CAE Usage: +*CONNECTOR BEHAVIOR, EXTRAPOLATION=LINEAR +Interaction module: connector section editor: Table Options +tabbed page: Extrapolation: Linear +Redefining the extrapolation choice for individual connector behaviors +You can redefine the extrapolation choice for individual connector behaviors. +Input File Usage: +Use either of the following options: +Abaqus/CAE Usage: +*CONNECTOR BEHAVIOR OPTION, EXTRAPOLATION=CONSTANT +*CONNECTOR BEHAVIOR OPTION, EXTRAPOLATION=LINEAR +For example, use the following options to use constant extrapolation for all +connector behaviors except for connector elasticity: +*CONNECTOR BEHAVIOR, EXTRAPOLATION=CONSTANT +*CONNECTOR ELASTICITY, EXTRAPOLATION=LINEAR +Use the following input for elasticity, damping, friction, plasticity, and damage +behaviors: +Interaction module: connector section editor: Behavior Options +tabbed page: Table Options button: Extrapolation: toggle off Use +behavior settings and choose Constant or Linear +Use the following input for connector derived components: +Interaction module: derived component editor: Add: Table +Options button: Extrapolation: toggle off Use behavior settings +and choose Constant or Linear +Regularization options for Abaqus/Explicit +By default, Abaqus/Explicit regularizes the data into tables that are defined in terms of even intervals +of the independent variables since table lookups are most economical if the interpolation is from even +intervals of the independent variables. In some cases, where it is necessary to capture sharp changes in +connector behavior accurately, you can use the user-defined tabular connector behavior data directly by +turning regularization off. However, the table lookups will be more computationally expensive compared +to using regular intervals. Therefore, the use of regularization is almost always recommended. +Abaqus/Explicit uses an error tolerance to regularize the input data. The number of intervals in the +range of each independent variable is chosen such that the error between the piecewise linear regularized +data and each of your defined points is less than the tolerance times the range of the dependent variable. +The default tolerance is 0.03. +In some cases where the dependent quantities are defined at uneven +intervals of the independent variables and the range of the independent variable is large compared to +the smallest interval, Abaqus/Explicit may fail to obtain an accurate regularization of your data in a +reasonable number of intervals. In this case Abaqus/Explicit stops after all data are processed and issues +an error message that you must redefine the behavior data. See “Material data definition,” Section 21.1.2, +for a more detailed discussion of data regularization. +You define the choice of regularization and regularization tolerance globally for all connector +behaviors but can redefine the choice of regularization and regularization tolerance for the following +connector behaviors individually: +• connector elasticity; +• connector plasticity (connector hardening) +• connector damping; +• derived components for connector elements; +• connector friction; +• connector damage (connector damage initiation and evolution); +• connector locks; and +• connector uniaxial behavior. +Tabular data for connector stop and lock behavior options are not supported in Abaqus/CAE. +Specifying the regularization of user-defined tabular data for all connector behaviors +You can specify regularization of tabular data and a regularization tolerance to be used globally for all +connector behaviors. +Input File Usage: +*CONNECTOR BEHAVIOR, REGULARIZE=ON (default), +RTOL=tolerance +Abaqus/CAE Usage: +Interaction module: connector section editor: Table Options +tabbed page: Regularization: toggle on Regularize data +(Explicit only), Specify: tolerance +Specifying the use of user-defined tabular data without regularization for all connector behaviors +You can specify the use of user-defined tabular data directly by turning regularization off for all connector +behaviors. +Input File Usage: +Abaqus/CAE Usage: +*CONNECTOR BEHAVIOR, REGULARIZE=OFF +Interaction module: connector section editor: Table Options tabbed page: +Regularization: toggle off Regularize data (Explicit only) +Redefining the regularization options for individual connector behaviors +You can redefine the choice of regularization and regularization tolerance for individual connector +behaviors. +Input File Usage: +Use either of the following options: +Abaqus/CAE Usage: +*CONNECTOR BEHAVIOR OPTION, REGULARIZE=ON, RTOL=tolerance +*CONNECTOR BEHAVIOR OPTION, REGULARIZE=OFF +For example, use the following options to regularize the user-defined data for +all connector behaviors except for connector elasticity: +*CONNECTOR BEHAVIOR, REGULARIZE=ON, RTOL=0.05 +*CONNECTOR ELASTICITY, REGULARIZE=OFF +Use the following input for elasticity, damping, friction, plasticity, and damage +behaviors: +Interaction module: connector section editor: Behavior Options tabbed +page: Table Options button: Regularization: toggle off Use behavior +settings; toggle on Regularize data (Explicit only) and Specify: +tolerance, or toggle off Regularize data (Explicit only) +Use the following input for connector derived components: +Interaction module: derived component editor: Add: Table Options +button: Regularization: toggle off Use behavior settings; toggle +on Regularize data (Explicit only) and Specify: tolerance, or +toggle off Regularize data (Explicit only) +Evaluation of rate-dependent data +Data for the tabulated isotropic hardening in connector plasticity (“Defining the isotropic hardening +component by specifying tabular data” in “Connector plastic behavior,” Section 31.2.6) and plastic +motion–based damage initiation criterion (“Plastic motion–based damage initiation criterion” in +“Connector damage behavior,” Section 31.2.7) can be specified as dependent on the equivalent relative +plastic motion rate. Loading/unloading data for the rate-dependent connector uniaxial behavior model +can be specified as dependent on the rate of deformation. +Specifying linear intervals for interpolation of rate-dependent data +By default, both Abaqus/Standard and Abaqus/Explicit interpolate rate-dependent data using linear +intervals of the relative motion rate. +Input File Usage: +Use the following option to specify linear interpolation for isotropic hardening +data: +*CONNECTOR HARDENING, RATE INTERPOLATION=LINEAR +Use the following option to specify linear interpolation for damage initiation +data: +*CONNECTOR DAMAGE INITIATION, RATE INTERPOLATION= +LINEAR +Use both of the following options to specify linear interpolation for uniaxial +behavior loading/unloading data: +*CONNECTOR UNIAXIAL BEHAVIOR +*LOADING DATA, RATE INTERPOLATION=LINEAR +Abaqus/Standard always interpolates rate-dependent data using linear intervals +of the equivalent relative plastic motion rate. +Abaqus/CAE Usage: +Use the following input for isotropic hardening data: +Interaction module: connector section editor: Add→Plasticity: +Isotropic Hardening: Definition: Tabular, Table Options +button: Interpolation: Linear +Use the following input for damage initiation data: +Interaction module: connector section editor: Add→Damage: Initiation: +Table Options button: Interpolation: Linear +Connector uniaxial behavior cannot be defined in Abaqus/CAE. +Specifying logarithmic intervals for interpolation of rate-dependent data in Abaqus/Explicit +In Abaqus/Explicit you can specify that logarithmic intervals of the relative motion rate be used for +the interpolation of rate-dependent data if the rate dependence of the data is measured at logarithmic +intervals. +Input File Usage: +Use the following option to specify linear interpolation for isotropic hardening +data: +*CONNECTOR HARDENING, RATE INTERPOLATION=LOGARITHMIC +Abaqus/CAE Usage: +Use the following option to specify linear interpolation for damage initiation +data: +*CONNECTOR DAMAGE INITIATION, RATE +INTERPOLATION=LOGARITHMIC +Use both of the following options to specify linear interpolation for uniaxial +behavior loading/unloading data: +*CONNECTOR UNIAXIAL BEHAVIOR +*LOADING DATA, RATE INTERPOLATION=LOGARITHMIC +Use the following input for isotropic hardening data: +Interaction module: connector section editor: Add→Plasticity: +Isotropic Hardening: Definition: Tabular, Table Options +button: Interpolation: Logarithmic +Use the following input for damage initiation data: +Interaction module: connector section editor: Add→Damage: Initiation: +Table Options button: Interpolation: Logarithmic +Connector uniaxial behavior cannot be defined in Abaqus/CAE. +Filtering the equivalent plastic motion rate in Abaqus/Explicit +Rate-sensitive connector constitutive behavior may introduce nonphysical high-frequency oscillations +in an explicit dynamic analysis. To overcome this problem, Abaqus/Explicit uses a filtered equivalent +plastic motion rate +for the evaluation of rate-dependent data. +during the time increment +of the increment, respectively. The factor +associated with rate-dependent connector behavior. You can specify the value of the rate filter factor, +directly. The default value is 0.9. A value of +is the incremental change in equivalent plastic motion +are the plastic motion rates at the beginning and end +) facilitates filtering high-frequency oscillations +, +provides no filtering and should be used with caution. +, and +and +( +Input File Usage: +Use either of the following options: +*CONNECTOR HARDENING, RATE FILTER FACTOR= +*CONNECTOR DAMAGE INITIATION, RATE FILTER FACTOR= +Abaqus/CAE Usage: +Use the following input for isotropic hardening data: +Interaction module: connector section editor: Add→Plasticity: +Isotropic Hardening: Definition: Tabular, Table Options +button: Filter factor: Specify: +Use the following input for damage initiation data: +Interaction module: connector section editor: Add→Damage: Initiation: +Table Options button: Filter factor: Specify: +31.2.2 +CONNECTOR ELASTIC BEHAVIOR +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Connectors: overview,” Section 31.1.1 +• “Connector behavior,” Section 31.2.1 +• *CONNECTOR BEHAVIOR +• *CONNECTOR ELASTICITY +• “Defining elasticity,” Section 15.17.1 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +Spring-like elastic connector behavior: +• can be defined in any connector with available components of relative motion; +• can be specified for each available component of relative motion independently, in which case the +behavior can be linear or nonlinear; +• can be specified as dependent on relative positions or constitutive motions in several local directions; +and +• can be specified for all available components of relative motion as coupled linear elastic behavior. +Alternatively, rigid-like behavior can be specified in any of the available components of relative motion +using an automatically chosen stiff spring. +The directions in which the forces and moments act and the displacements and rotations +are measured are determined by the local directions as described in “Connection-type library,” +Section 31.1.5, for each connection type. +Defining linear uncoupled elastic behavior +In the simplest case of linear uncoupled elasticity you define the spring stiffnesses for the selected +components (i.e., +for component 2, etc.), which are used in the equation +for component 1, +(no sum on ) +is the force or moment in the +is the connector +where +displacement or rotation in the +direction. The elastic stiffness can depend on frequency (in +Abaqus/Standard), temperature, and field variables. See “Input syntax rules,” Section 1.2.1, for further +information about defining data as functions of frequency, temperature, and field variables. +component of relative motion and +If a frequency-dependent damping behavior is specified in an Abaqus/Standard analysis procedure +other than direction-solution steady-state dynamics, the data for the lowest frequency given will be used. +Input File Usage: +Use the following options to define linear uncoupled elastic connector behavior: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR ELASTICITY, COMPONENT=component number, +DEPENDENCIES=n +Abaqus/CAE Usage: +Interaction module: connector section editor: Add→Elasticity: Definition: +Linear, Force/Moment: component or components, Coupling: Uncoupled +Defining linear coupled elastic behavior +In the linear coupled case you define the spring stiffness matrix components, +equation +, which are used in the +where +component of relative motion, +is the force in the +is the coupling between the +component, and +is the motion of the +components. The D matrix is assumed to be symmetric, so +only the upper triangle of the matrix is specified. In connectors with kinematic constraints the entries that +correspond to the constrained components of relative motion will be ignored. The elastic stiffness can +depend on temperature and field variables. See “Input syntax rules,” Section 1.2.1, for further information +about defining data as functions of temperature and field variables. +and +Input File Usage: +Abaqus/CAE Usage: +Use the following options to define linear coupled elastic connector behavior: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR ELASTICITY, DEPENDENCIES=n +Interaction module: connector section editor: Add→Elasticity: Definition: +Linear, Force/Moment: component or components, Coupling: Coupled +Modeling coupled unsymmetric linear stiffness +By definition, linear elastic behavior should be defined by a symmetric spring stiffness matrix. However, +Abaqus/Standard allows you to define an unsymmetric coupled spring stiffness matrix. The intended use +case is to approximate fluid film bearings supporting a rotating structure in a rotordynamic analysis . Abaqus/Standard will not check the stability of +an unsymmetric spring stiffness matrix; therefore, you must ensure that it is defined properly. +In the linear coupled case you define the spring stiffness matrix components, +, which are used +in the equation +component, +is the motion of the +where +and +components. The D matrix in this case is assumed +to be unsymmetric, so the entire matrix is specified. The entries that correspond to the constrained +is the force in the +is the coupling between the +component of relative motion, +and +components of relative motion are ignored. When the unsymmetric matrix storage and solution scheme +are used, the stiffness can depend on frequency, temperature, and field variables. See “Input syntax +rules,” Section 1.2.1, for further information about defining data as functions of frequency, temperature +and field variables. +Input File Usage: +Use the following options to define unsymmetric linear coupled stiffness +connector behavior: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR ELASTICITY, UNSYMM, +FREQUENCY DEPENDENCE=ON +Abaqus/CAE Usage: +Unsymmetric linear coupled stiffness behavior +Abaqus/CAE. +is not +supported in +Defining nonlinear elastic behavior +For nonlinear elasticity you specify forces or moments as nonlinear functions of one or more available +components of relative motion, +. These functions can also depend on temperature and +field variables. See “Input syntax rules,” Section 1.2.1, for further information about defining data as +functions of temperature and field variables. +Defining nonlinear elastic behavior that depends on one component direction +By default, each nonlinear force or moment function depends only on the displacement or rotation in the +direction of the specified component of relative motion. +Input File Usage: +Use the following options: +Abaqus/CAE Usage: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR ELASTICITY, COMPONENT=component number, +NONLINEAR, DEPENDENCIES=n +Interaction module: connector section editor: Add→Elasticity: Definition: +Nonlinear, Force/Moment: component or components, Coupling: +Uncoupled +Defining nonlinear elastic behavior that depends on several component directions +Alternatively, the functions can depend on the relative positions or constitutive displacements/rotations +in several component directions, as described in “Defining nonlinear connector behavior properties +to depend on relative positions or constitutive displacements/rotations” in “Connector behavior,” +Section 31.2.1. In this case the operator matrices are unsymmetric when +, for +, and unsymmetric matrix storage and solution may be needed in Abaqus/Standard to improve +convergence. +Input File Usage: +Use the following options to define nonlinear elastic connector behavior that +depends on components of relative position: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR ELASTICITY, COMPONENT=component number, +NONLINEAR, INDEPENDENT COMPONENTS=POSITION, +DEPENDENCIES=n +Use the following options to define nonlinear elastic connector behavior that +depends on components of constitutive displacements or rotations: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR ELASTICITY, COMPONENT=component number, +NONLINEAR, INDEPENDENT COMPONENTS=CONSTITUTIVE MOTION, +DEPENDENCIES=n +Interaction module: connector section editor: Add→Elasticity: Definition: +Nonlinear, Force/Moment: component or components, Coupling: +Coupled on position or Coupled on motion +Abaqus/CAE Usage: +Examples +The combined connector in Figure 31.2.2–1 has two available components of relative motion: the relative +displacement along the 1-direction (from the SLOT connection) and the rotation around the 1-direction +(from the REVOLUTE connection)—see “Connection-type library,” Section 31.1.5. Thus, the connector +components of relative motion 1 and 4 can be used to specify connector behavior. +extensible +range +7.5 +node 12 +1 (local orientation) +node 11 +Figure 31.2.2–1 Simplified connector model of a shock absorber. +To define a nonlinear torsional spring to resist the relative rotation between the top and the bottom +connection point around the local 1-direction, use the following input: +*CONNECTOR SECTION, ELSET=shock, BEHAVIOR=sbehavior +slot, revolute +ori, +*CONNECTOR BEHAVIOR, NAME=sbehavior +*CONNECTOR ELASTICITY, COMPONENT=4, NONLINEAR +-900., -0.7 +0.0 +0.7 +0., +1250., +Although no elastic coupling is assumed to occur between the two available components of relative +motion, you could replace the nonlinear moment versus rotation data with coupled linear elastic behavior +to define the rotational stiffness around the shock’s axis coupled to the axial displacement. +In another application this same connector may have coupled linear elastic behavior, in the sense +that relative rotation and sliding affect each other through a linear coupling. To define a translational +stiffness of 2000.0 units, the +constant (the 1st entry of a symmetric matrix) is entered in the connector +elasticity definition. To define a torsional stiffness of 1000.0 units, the +constant (the 10th entry of +a symmetric matrix) is entered; and to define a coupling stiffness of 50.0 units between the available +rotation and displacement, the +constant (the 7th entry) is entered. +*CONNECTOR ELASTICITY +2000.0, , , , , , 50.0, +0.0, 1000.0, , , , , , +, , , , +Defining rigid connector behavior +Rigid-like elastic connector behavior can be used to make an otherwise available component of relative +motion rigid. Consider a CARTESIAN connector that has no intrinsic kinematic constraints. If rigid +behavior is specified in the local 2- and 3-directions, the connector will behave in a similar fashion to a +SLOT connector. +This technique of using connectors with available components of relative motion for which rigid +behavior is specified instead of connectors with intrinsically kinematic constraints is particularly useful +when you need to: +• customize the constrained components in a connector with available components of relative motion; +for example, you can constrain the local 1- and 2-directions in a CARTESIAN connector to define +a SLOT-like connector in the 3-direction; +• define rigid plastic behavior ; or +• define rigid damage behavior . +For example, if you use a SLOT connector, plasticity and damage behavior cannot be specified +in the intrinsically constrained 2- and 3-directions. To resolve the issue, you can use a CARTESIAN +connector with rigid behavior in components 2 and 3 as discussed above and then define rigid plasticity +(and/or damage) in these components. See the examples in “Connector plastic behavior,” Section 31.2.6, +for illustrations. +In Abaqus/Standard an overconstraint may occur if a rigid component is defined in the same local +direction as an active connector stop, connector lock, or specified connector motion. +Input File Usage: +Use the following option to define rigid connector behavior for a specified +component of relative motion: +*CONNECTOR ELASTICITY, RIGID, COMPONENT=n +Use the following option to define rigid connector behavior for multiple +specified components of relative motion: +*CONNECTOR ELASTICITY, RIGID +data line listing components to be made rigid +Use the following option to define rigid connector behavior for all available +components of relative motion: +*CONNECTOR ELASTICITY, RIGID +(no data lines) +Abaqus/CAE Usage: +Interaction module: connector section editor: Add→Elasticity: Definition: +Rigid, Components: component or components +Enforcing rigid-like elastic behavior +Rigid-like elastic behavior in a particular component is enforced by using a stiff, linear elastic spring in +that component. The stiffness of the spring is chosen automatically and depends on the circumstances +in which the connector is used. In Abaqus/Standard the stiffness is taken to be 10 times larger than the +average stiffness of the surrounding elements to which the connector element attaches. If the average +stiffness cannot be computed (as would be the case when the connector element does not attach to other +elements or attaches to rigid bodies), a stiffness of +is used. In Abaqus/Explicit a Courant stiffness +is first computed by considering the average mass at the connector element nodes and the stable time +increment in the analysis. +In most cases the Courant stiffness is then used to calculate the value of +the rigid-like elastic behavior using heuristics that depend on modeling circumstances and the precision +(single or double) of the analysis. For example, if plasticity is defined in the connector, the rigid-like +elastic stiffness in components involved in the plasticity definition does not exceed one thousandth of +the initial yield value. If plasticity is not defined, the rigid-like stiffness is computed as a multiple of the +Courant stiffness. +In most cases, the heuristics used in the computation of the rigid-like stiffness produces a stiffness +value that is adequate. If this stiffness does not serve the needs of your application, you can always +customize the elastic stiffness by specifying the linear stiffness value directly. +Due to the different stiffness values used for rigid-like elastic behavior in Abaqus/Standard and +Abaqus/Explicit, you may notice a discontinuity in the behavior when such a model is imported from +one solver to the other. +Defining elastic connector behavior in linear perturbation procedures +Available components of relative motion with connector elasticity use the linearized elastic stiffness +from the base state. In direct-solution steady-state dynamic and subspace-based steady-state dynamic +analyses, the linear elastic stiffness defined by an uncoupled connector elasticity behavior may be +frequency dependent. +Output +The Abaqus output variables available for connectors are listed in “Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2. The +following output variables are of particular interest when defining elasticity in connectors: +CU +CUE +CEF +Connector relative displacements/rotations. +Connector elastic displacements/rotations. +Connector elastic forces/moments. +Additional reference +• Genta, G., Dynamics of Rotating Systems, Springer, 2005. +31.2.3 +CONNECTOR DAMPING BEHAVIOR +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Connectors: overview,” Section 31.1.1 +• “Connector behavior,” Section 31.2.1 +• *CONNECTOR BEHAVIOR +• *CONNECTOR DAMPING +• “Defining damping,” Section 15.17.2 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +Connector damping behavior: +• can be of a dashpot-like viscous nature in transient or steady-state dynamic analyses; +• can be of a “structural” nature, related to complex stiffness, for steady-state dynamics procedures +that support non-diagonal damping; +• can be defined in any connector with available components of relative motion; +• can be specified for each available component of relative motion independently, in which case the +behavior can be linear or nonlinear for viscous nature damping; +• can be specified as dependent on relative positions or constitutive motions in several local directions +for viscous nature damping; and +• can be specified for all available components of relative motion as coupled damping behavior. +The directions in which the forces and moments act and the relative velocities are measured are +determined by the local directions as described in “Connection-type library,” Section 31.1.5, for each +In dynamic analysis the relative velocities are obtained as part of the integration +connection type. +operator; in quasi-static analysis in Abaqus/Standard the relative velocities are obtained by dividing the +relative displacement increments by the time increment. +Defining linear uncoupled viscous damping behavior +In the simplest case of linear uncoupled damping you define the damping coefficients for the selected +components (i.e., +for component 2, etc.), which are used in the equation +for component 1, +(no sum on ) +where +velocity in the +is the force or moment in the +is the velocity or angular +direction. The damping coefficient can depend on frequency (in Abaqus/Standard), +component of relative motion and +temperature, and field variables. See “Input syntax rules,” Section 1.2.1, for further information about +defining data as functions of frequency, temperature, and field variables. +If frequency-dependent damping behavior is specified in an Abaqus/Standard analysis procedure +other than direct solution steady-state dynamics, the data for the lowest frequency given will be used. +Input File Usage: +Use the following options to define linear uncoupled damping connector +behavior: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR DAMPING, COMPONENT=component number, +DEPENDENCIES=n +Abaqus/CAE Usage: +Interaction module: connector section editor: Add→Damping: Definition: +Linear, Force/Moment: component or components, Coupling: Uncoupled +Defining linear coupled viscous damping behavior +In the linear coupled case you define the damping coefficient matrix components, +the equation +, which are used in +where +component of relative motion, +is the force in the +is the coupling between the +component, and +is the velocity in the +components. The C matrix is assumed to be symmetric, so +only the upper triangle of the matrix is specified. In connectors with kinematic constraints the entries that +correspond to the constrained components of relative motion will be ignored. The damping coefficient +can depend on temperature and field variables. See “Input syntax rules,” Section 1.2.1, for further +information about defining data as functions of temperature and field variables. +and +Input File Usage: +Abaqus/CAE Usage: +Use the following options to define linear coupled damping connector behavior: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR DAMPING, DEPENDENCIES=n +Interaction module: connector section editor: Add→Damping: Definition: +Linear, Force/Moment: component or components, Coupling: Coupled +Defining unsymmetric linear coupled viscous damping behavior +As with linear coupled elastic behavior (“Connector elastic behavior,” Section 31.2.2), Abaqus/Standard +allows you to define an unsymmetric coupled viscous damping matrix. In the linear coupled case you +define the damping coefficient matrix components, +, which are used in the equation +where +is the force in the +is the coupling between the +component, and +is the velocity in the +components. The C matrix is assumed to be unsymmetric, +so the entire matrix is specified. The entries that correspond to the constrained components of relative +component of relative motion, +and +motion are ignored. When the unsymmetric matrix storage and solution scheme are used, the damping +coefficients can depend on frequency, temperature, and field variables. See “Input syntax rules,” +Section 1.2.1, for further information about defining data as functions of frequency, temperature and +field variables. +Input File Usage: +Use the following options to define unsymmetric linear coupled viscous +damping connector behavior: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR DAMPING, UNSYMM, +FREQUENCY DEPENDENCE=ON +Abaqus/CAE Usage: +Unsymmetric linear coupled viscous damping behavior is not supported in +Abaqus/CAE. +Defining nonlinear viscous damping behavior +For nonlinear damping you specify forces or moments as nonlinear functions of the velocity in the +available components of relative motion directions, +. These functions can also depend +on temperature and field variables. See “Input syntax rules,” Section 1.2.1, for further information about +defining data as functions of temperature and field variables. +Defining nonlinear viscous damping behavior that depends on one component direction +By default, each nonlinear force or moment function is dependent only on the velocity in the direction +of the specified component of relative motion. +Input File Usage: +Use the following options: +Abaqus/CAE Usage: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR DAMPING, COMPONENT=component number, +NONLINEAR, DEPENDENCIES=n +Interaction module: connector section editor: Add→Damping: +Definition: Nonlinear, Force/Moment: component or +components, Coupling: Uncoupled +Defining nonlinear viscous damping behavior that depends on several component directions +Alternatively, the functions can depend on the relative positions or constitutive displacements/rotations +in several component directions, as described in “Defining nonlinear connector behavior properties +to depend on relative positions or constitutive displacements/rotations” in “Connector behavior,” +Section 31.2.1. +Input File Usage: +Use the following options to define nonlinear damping connector behavior that +depends on components of relative position: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR DAMPING, COMPONENT=component number, +NONLINEAR, INDEPENDENT COMPONENTS=POSITION, +DEPENDENCIES=n +Use the following options to define nonlinear damping connector behavior that +depends on components of constitutive displacements or rotations: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR DAMPING, COMPONENT=component number, +NONLINEAR, INDEPENDENT COMPONENTS=CONSTITUTIVE +MOTION, DEPENDENCIES=n +Interaction module: connector section editor: Add→Damping: Definition: +Nonlinear, Force/Moment: component or components, Coupling: +Coupled on position or Coupled on motion +Abaqus/CAE Usage: +Example +Refer to the example in Figure 31.2.3–1. +extensible +range +7.5 +node 12 +1 (local orientation) +node 11 +Figure 31.2.3–1 Simplified connector model of a shock absorber. +In addition to the torsional spring resisting relative rotations, the shock absorber damps translational +motion along the line of the shock with a dashpot. To include a nonlinear dashpot behavior that is +dependent on the relative position between the attachment points, use the following input: +*CONNECTOR BEHAVIOR, NAME=sbehavior +... +*CONNECTOR DAMPING, COMPONENT=1, +INDEPENDENT COMPONENTS=POSITION, NONLINEAR +1500.0, 0.1, 0.0 +1625.0, 0.2, 0.0 +1750.0, 0.1, 10.0 +1925.0, 0.2, 10.0 +Defining linear structural damping behavior +Structural connector damping is supported in steady-state dynamics and modal transient procedures that +support non-diagonal damping (for example, direct solution steady-state dynamics). +Defining linear uncoupled structural damping behavior +You define the damping coefficients, +component 2, etc.), which are used in the equation +, for the selected components (i.e., +for component 1, +for +where +(no sum on ) +is the structural damping matrix, +relative motion, +coefficient can depend on frequency. +is the displacement in the +is the imaginary part of the force or moment in the +direction of +is the stiffness matrix. The damping +direction, and +Input File Usage: +Use the following options: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR DAMPING, COMPONENT=component number, +TYPE=STRUCTURAL +Abaqus/CAE Usage: +Linear uncoupled structural damping behavior +Abaqus/CAE. +is not +supported in +Defining linear coupled structural damping behavior +You define 21 +which are used in the equation +damping coefficients (the symmetric half of the 6 × 6 damping coefficient matrix), +where +(no sum on +) +is the structural damping matrix, +motion, +coefficient matrix cannot depend on frequency. +is the displacement in the +is the imaginary part of the force in the +direction of relative +is the stiffness matrix. The damping +direction, and +Input File Usage: +Use the following options: +Abaqus/CAE Usage: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR DAMPING, TYPE=STRUCTURAL +Linear coupled structural damping behavior is not supported in Abaqus/CAE. +Defining connector damping behavior in linear perturbation procedures +In both the direct-solution and subspace-based steady-state dynamic procedures, the viscous or structural +damping defined using an uncoupled connector damping behavior may be frequency dependent. In other +linear perturbation procedures connector damping behavior is ignored. +Output +The Abaqus output variables available for connectors are listed in “Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2. The +following output variables are of particular interest when defining damping in connectors: +CV +CVF +Connector relative velocities/angular velocities. +Connector viscous forces/moments. +31.2.4 +CONNECTOR FUNCTIONS FOR COUPLED BEHAVIOR +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Connectors: overview,” Section 31.1.1 +• “Connector friction behavior,” Section 31.2.5 +• “Connector plastic behavior,” Section 31.2.6 +• “Connector damage behavior,” Section 31.2.7 +• *CONNECTOR BEHAVIOR +• *CONNECTOR DERIVED COMPONENT +• *CONNECTOR POTENTIAL +• “Specifying connector derived components,” Section 15.17.15 of the Abaqus/CAE User’s Manual, +in the online HTML version of this manual +• “Specifying potential terms,” Section 15.17.16 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +This section describes how to define two special functions used to specify complex coupled behavior for +a connector element in Abaqus: derived components and potentials. +Connector derived components are user-specified component definitions based on a function of +intrinsic (1 through 6) connector components of relative motion. They can be used: +• to specify the friction-generating normal force in connectors as a complex combination of connector +forces and moments, and +• as an intermediate result in a connector potential function. +Connector potentials are user-defined functions of intrinsic components of relative motion or derived +components. These functions can be quadratic, elliptical, or maximum norms. They can be used to +define: +• the yield function for connector coupled plasticity when several available components of relative +motion are involved simultaneously, +• the potential function for coupled user-defined friction when the slip direction is not aligned with +an available component of relative motion, +• a magnitude measure as a coupled function of connector forces or motions used to detect the +initiation of damage in the connector, and +• an effective motion measure as a coupled function of connector motions to drive damage evolution +in the connector. +Defining derived components for connector elements +The definition of coupled behavior in connector elements beyond simple linear elasticity or damping +often requires the definition of a resultant force involving several intrinsic (1 through 6) components +or the definition of a “direction” not aligned with any of the intrinsic components. These user-defined +resultants or directions are called derived components. The forces and motions associated with these +derived components are functions of the forces and motions in the intrinsic relative components of motion +in the connector element. +Consider the case of a SLOT connector for which frictional effects are defined in the only available component of relative motion (the +1-direction). The two constraints enforced by this connection type will produce two reaction forces +( +), as shown in Figure 31.2.4–1. Both forces generate friction in the 1-direction in a coupled +and +fashion. +f3 +f2 +f1 +slot housing +Figure 31.2.4–1 Resultant contact force in a SLOT connector. +A reasonable estimate for the resulting contact force is +where +is the collection of connector forces and moments in the intrinsic components. The function +can be specified as a derived component. +Resultant forces that can be defined as derived components may take more complicated forms. +Consider a BUSHING connection type for which a tensile (Mode I) damage mechanism with failure is +to be specified in the 1-direction. You may wish to include the effects of the axial force +and of the +resultant of the “flexural” moments +in defining an overall resultant force in the axial direction +upon which damage initiation (and failure) can be triggered, as shown in Figure 31.2.4–2. One choice +would be to define the resultant axial force as +and +inner cylinder +outer cylinder +rubber +f1 +f axial +m2 +m3 +Figure 31.2.4–2 Resultant axial force in a BUSHING connector. +where +is a geometric factor relating translations to rotations with units of one over length. The function +can be specified as a derived component. +A derived component can also be interpreted as a user-specified direction that is not aligned with +the connector component directions. For example, if the motion-based damage with failure criterion in +a CARTESIAN connection with elastic behavior does not align with the intrinsic component directions, +the damage criterion can be defined in terms of a derived component representing a different direction, +as shown in Figure 31.2.4–3. One possible choice for the direction could be +where +interpreted as direction cosines ( +derived component. +is the collection of connector relative motions in the components and +, +, +). The function +, +, and +can be +can be specified as a +Functional form of the derived component +The functional form of a derived component +The derived component is specified as a sum of terms +in Abaqus is quite general; you specify its exact form. +U transf +Figure 31.2.4–3 User-defined direction in a CARTESIAN connector. +is a generic name for the connector intrinsic component values (such as forces, +where +), +are selected depending on the context in which the derived component is used. +, or motions, +is the number of terms. The appropriate component values for +is also a summation +term in the sum, and +is the +of several contributions and can take one of the following three forms: +• a norm ( +-type) +• a direct sum ( +-type) +• a Macauley sum ( +-type) +where +is the term’s sign (plus or minus), +is the Macauley bracket ( +, and +). In general, the units of +the scaling factors +depend on the context. In most cases they are either dimensionless, have units of +length, or have units of one over length. The scaling factors should be chosen such that all the terms in +the resulting derived component have the same units, and these units must be consistent with the use of +the derived component later on in a connector potential or connector contact force. +are scaling factors, +component of +is the +Defining a derived component with only one term (NT = 1) +Connector derived components are identified by the names given to them. If one term ( +to define the derived component g, specify only one connector derived component definition. +) is sufficient +Input File Usage: +*CONNECTOR DERIVED COMPONENT, +NAME=derived_component_name +Abaqus/CAE Usage: +Connector derived component names are not supported in Abaqus/CAE; you +define the individual derived component terms. +Use the following input to define a connector derived component term for a +friction-generating user-defined contact force: +Interaction module: connector section editor: Add→Friction: Friction +model: User-defined, Contact Force, Specify component: +Derived component, click Edit to display the derived component +editor: click Add and select components +Use the following input to define a connector derived component term as an +intermediate result in a connector potential function: +Interaction module: connector section editor: Add→Friction, Plasticity, or +Damage: potential contribution editors: Specify derived component, click +Edit to display the derived component editor: click Add and select components +Defining a derived component containing multiple terms (NT > 1) +If several terms ( +define the individual terms. +, +, etc.) are needed in the overall definition of the derived component g, you must +Input File Usage: +You must specify +connector derived component definitions with the same +name to define the individual terms. All definitions with the same name will +be summed together to produce the desired derived component g. See the spot +weld example below for an illustration. +*CONNECTOR DERIVED COMPONENT, +NAME=derived_component_name +*CONNECTOR DERIVED COMPONENT, NAME=derived_component_name +... +Abaqus/CAE Usage: +Connector derived component names are not supported in Abaqus/CAE; you +define the individual derived component terms. +Interaction module: derived component editor: click Add and select +components. Repeat, adding terms as necessary. +Specifying a term in the derived component as a norm +By default, a derived component term is computed as the square root of the sum of the squares of each +intrinsic component contribution. If the term has only one contribution ( +), the norm has the same +meaning as the absolute value. +Input File Usage: +*CONNECTOR DERIVED COMPONENT, +NAME=derived_component_name, OPERATOR=NORM (default) +component +For example, the following input can be used to define the +discussed above: +*CONNECTOR DERIVED COMPONENT, NAME=axial +1.0, +** +*CONNECTOR DERIVED COMPONENT, NAME=axial +5, 6 +, +** +Abaqus/CAE Usage: +The axial derived component is +Interaction module: derived component editor: Add: Term operator: +Square root of sum of squares +. +Specifying a term in the derived component as a direct sum +Alternatively, you can choose to compute a derived component term as the direct sum of the intrinsic +component contributions. +Input File Usage: +*CONNECTOR DERIVED COMPONENT, +NAME=derived_component_name, OPERATOR=SUM +component +For example, the following input can be used to define the +discussed above: +*CONNECTOR DERIVED COMPONENT, NAME=transf, +OPERATOR=SUM +1, 2, 3 +, +, +** +The transf derived component is +Interaction module: derived component editor: Add: Term +operator: Direct sum +. +31.2.4–6 +Specifying a term in the derived component as a Macauley sum +Alternatively, you can choose to compute a derived component term as the Macauley sum of the intrinsic +component contributions. +Input File Usage: +*CONNECTOR DERIVED COMPONENT, +NAME=derived_component_name, OPERATOR=MACAULEY SUM +For example, the following input can be used to define the first term of the +normal component of the force ( +) in the spotweld example discussed below: +*CONNECTOR DERIVED COMPONENT, NAME=normal, +OPERATOR=MACAULEY SUM +1.0 +** +Abaqus/CAE Usage: +Interaction module: derived component editor: Add: Term +operator: Macauley sum +Specifying the sign of a term +You can specify whether the sign of a derived component term should be positive or negative. +Input File Usage: +Abaqus/CAE Usage: +Use one of the following options: +*CONNECTOR DERIVED COMPONENT, +NAME=derived_component_name, SIGN=POSITIVE (default) +*CONNECTOR DERIVED COMPONENT, +NAME=derived_component_name, SIGN=NEGATIVE +Interaction module: derived component editor: Add: Overall +term sign: Positive or Negative +Defining the derived component contributions to depend on local directions +The scaling factors +used in the definition of the derived component can depend on the relative +positions or constitutive displacements/rotations in several component directions, as described in +“Defining nonlinear connector behavior properties to depend on relative positions or constitutive +displacements/rotations” in “Connector behavior,” Section 31.2.1. See the first example in “Connector +friction behavior,” Section 31.2.5, for an illustration. +Input File Usage: +Use the following option to define a connector derived component that depends +on components of relative position: +*CONNECTOR DERIVED COMPONENT, INDEPENDENT +COMPONENTS=POSITION +Use the following option to define a connector derived component that depends +on components of constitutive displacements or rotations: +*CONNECTOR DERIVED COMPONENT, INDEPENDENT +COMPONENTS=CONSTITUTIVE MOTION +Abaqus/CAE Usage: +Interaction module: derived component editor: Add: Use local +directions: Independent position components or Independent +constitutive motion components +Requirements for constructing a derived component used in plasticity or friction definitions +When a derived component is used to construct the yield function for a plasticity or friction definition, +the following simple requirements must be satisfied: +• All +terms of a derived component must be of a compatible type cannot be mixed with direct sum-type terms +-type) in the same derived component definition but can be mixed with Macauley sum-type +derived component”); norm-type terms ( +( +terms ( +-type). +• If all +terms are norm-type terms, the sign of each term must be positive (the default). +is greater than 1, the associated functions (potentials) in which the derived component is used +If +may become non-smooth. More precisely, the normal to the hyper-surface defined by the potential may +experience sudden changes in direction at certain locations. In these cases, Abaqus will automatically +smooth-out the defined functions by slightly changing the derived component functional definition. +These changes should be transparent to the user as the results of the analysis will change only by a +small margin. +Example: spot weld +The spot weld shown in Figure 31.2.4–4 is subjected to loading in the F-direction. +Fn +Figure 31.2.4–4 Loading of a spot weld connection. +The connector chosen to model the spot weld has six available components of relative motion: three +translations (components 1–3) and three rotations (components 4–6). You have chosen this connection +type because you are modeling a general deformation state. However, you would like to define inelastic +behavior in the connection in terms of a normal and a shear force, as shown in Figure 31.2.4–5, since +experimental data are available in this format. +plates +spot weld +Fn +Fs +Fn +f3 +m3 +m1 +m2 +f1 +Fs +f2 +Figure 31.2.4–5 Spot weld connection: derived component definitions. +Therefore, you want to derive the normal and shear components of the force, for example, as follows: +and +In these equations +have units of length; their interpretation is relatively straightforward if you +consider the spot weld as a short beam with the axis along the spot weld axis (3-direction). If the average +cross-section area of the spot weld is A and the beam’s second moment of inertia about one of the in-plane +axes is +). Furthermore, +if the cross-section is considered to be circular, +becomes equal to a fraction of the spot weld radius. +In all cases +can be taken to be +can be interpreted as the square root of the ratio +(or +(or +), +. +The reasoning above for the interpretation of the calibration constants in the equations is only a +suggestion. In general, any combination of constants that would lead to good comparisons with other +results (experimental, analytical, etc.) is equally valuable. +To define +with the same name: +, you would specify the following two connector derived component definitions, each +*PARAMETER +=30.68 +A=19.63 +=sqrt( += +) +*CONNECTOR DERIVED COMPONENT, NAME=normal, OPERATOR=MACAULEY SUM +1.0 +*CONNECTOR DERIVED COMPONENT, NAME=normal +4, 5 +, +symbols denote that +The +component +derived component defines the first term +is specified using a parameter definition. The normal force derived +. The first connector +, while the second defines the second term +is defined as the sum of two terms, +. +Similarly, +to define +, you would specify the following two connector derived component +definitions for the component shear: +*CONNECTOR DERIVED COMPONENT, NAME=shear +*CONNECTOR DERIVED COMPONENT, NAME=shear +1, 2 +1.0, 1.0 +Defining connector potentials +Connector potentials are user-defined mathematical functions that represent yield surfaces, limiting +surfaces, or magnitude measures in the space spanned by the components of relative motion in the +connector. The functions can be quadratic, general elliptical, or maximum norms. The connector +potential does not define a connector behavior by itself; instead, it is used to define the following +coupled connector behaviors: +• friction, +• plasticity, or +• damage. +Consider the case of a SLIDE-PLANE connection in which frictional sliding occurs in the +connection plane, as shown in Figure 31.2.4–6. The function governing the stick-slip frictional behavior + can be written as +where +is the connector potential defining the pseudo-yield function (the magnitude of the frictional +tangential tractions in the connector in a direction tangent to the connection plane on which contact +occurs), +is the friction coefficient. Frictional +stick occurs if +. In this case the potential can be defined as the +magnitude of the frictional tangential tractions, +is the friction-producing normal (contact) force, and +, and sliding occurs if +fn +f2 +normal direction +f3 +sliding with friction in this plane +Figure 31.2.4–6 Friction in the SLIDE-PLANE connection. +Connector potentials can also be useful in defining connector damage with a force-based coupled +damage initiation criterion. For example, in a connection type with six available components of relative +motion you could define a potential +Damage (with failure) can be initiated when the value of the potential +limiting value (usually 1.0). The units of the +and +final product. For example, if the intended units of +while the +coefficients have units of one over length. +is greater than a user-specified +coefficients must be consistent with the units of the +coefficients are dimensionless +are newtons, the +Connector potentials can take more complicated forms. Assume that coupled plasticity is to be +defined in a spot weld, in which case a plastic yield criterion can be defined as +where +potential could be defined as +is the connector potential defining the yield function and +is the yield force/moment. The +could be the named derived components normal and shear defined in the example +and +where +in “Defining derived components for connector elements” above. If +also have units of force, +are dimensionless. +and +has units of force and +and +Input File Usage: +Abaqus/CAE Usage: +*CONNECTOR POTENTIAL +Use the following input to define connector potentials for friction behavior: +Interaction module: connector section editor: Add→Friction: +Friction model: User-defined, Slip direction: Compute using +force potential, Force Potential +Use the following input to define connector potentials for plasticity behavior: +Interaction module: connector section editor: Add→Plasticity: +Coupling: Coupled, Force Potential +Use the following input to define connector potentials for damage behavior: +Interaction module: connector section editor: Add→Damage: Coupling: +Coupled, Initiation Potential or Evolution Potential +Functional form of the potential +The functional form of the potential +potential is specified as one of the following direct functions of several contributions: +in Abaqus is quite general; you specify its exact form. The +a quadratic form +a general elliptical form +a maximum form +where +), +is a generic name for the connector intrinsic component values (such as forces, +and +is the number of contributions, +contribution to the potential, +, or motions, +are positive +is the overall sign of the contribution (1.0 – default, or −1.0). +are selected depending on the context in which the potential is +), and +2.0, +is the +numbers (defaults +The appropriate component values for +used in. The positive exponents ( +yields a real number. +, +) and the sign +should be chosen such that the contribution +is a direct function of either an intrinsic connector component (1 through 6) or a derived connector +component. Since derived components are ultimately a function of intrinsic components , the contribution +is +defined as +is ultimately a function of +. +where +is the function used to generate the contribution: +• absolute value (default, +• Macauley bracket ( +• identity (X); +), +is the value of the identified component (intrinsic or derived); +is a shift factor (default 0.0); and +is a scaling factor (default 1.0). +), or +can be the identity function only if +The function +. The units of the various +coefficients in the equations above depend on the context in which the potential is used. In most cases +the coefficients in the equations above are either dimensionless, have units of length, or have units of one +over length. In all cases you must be careful in defining potentials for which the units are consistent. +Defining the potential as a quadratic or general elliptical form +To define a general elliptical form of the potential, you must specify the inverse of the overall exponent, +if they are different from the default value, which is the specified +. You can also define the exponents +value of +. +Input File Usage: +To define a quadratic form of the potential, you can omit specifying +default value is 2.0. Use the following option: +*CONNECTOR POTENTIAL +component name or number, +... +, +, +, +, +since its +Use the following option to define a general elliptical form of the potential: +*CONNECTOR POTENTIAL, OPERATOR=SUM, EXPONENT= +component name or number, +... +, +, +, +, +Abaqus/CAE Usage: +Each data line defines one contribution to the potential, +can be ABS (absolute value and the default), MACAULEY (Macauley bracket), +or NONE (identity). +. The function +Interaction module: connector section editor: friction, plasticity, or +damage behavior option: Force Potential, Initiation Potential, or +Evolution Potential: Operator: Sum, Exponent: 2 (for quadratic form) +or +(for elliptical form), select Add and enter data for the potential +contribution. Repeat, adding contributions as necessary. +Defining the potential as a maximum form +Alternatively, you can define the potential as a maximum form. +Input File Usage: +*CONNECTOR POTENTIAL, OPERATOR=MAX +component name or number, +... +Each data line defines one contribution to the potential, +can be ABS (absolute value and the default), MACAULEY (Macauley bracket), +or NONE (identity). +. The function +, +, +, +, +Abaqus/CAE Usage: +Interaction module: connector section editor: friction, plasticity, or damage +behavior option: Force Potential, Initiation Potential, or Evolution +Potential: Operator: Maximum, select Add and enter data for the potential +contribution. Repeat, adding contributions as necessary. +Requirements for constructing a potential used in plasticity or friction definitions +The connector potential, +, can be defined using intrinsic components of relative motion, derived +components, or both. A particular contribution to the potential may be one of the following two types: +• A norm-type contribution ( +) defined using the absolute value or the Macauley bracket functions +or using a combination of norm-type +derived components with +any of the available functions. +and Macauley sum-type +• A sum-type contribution ( +) defined using an intrinsic component of relative motion or a derived + together with the identity function. +When used in the context of connector plasticity or connector friction, the potential must be constructed +such that the following requirements are satisfied: +• All +contributions to the potential must be of the same type. Mixed +and +contributions are +not allowed in the same potential definition. +• If all +• The positive numbers +terms are +-type terms, the sign of each term must be positive (the default). +and +cannot be smaller than 1.0 and must be equal (the default). +Example: spot weld +Referring to the spot weld shown in Figure 31.2.4–5 and the yield function +defined above, you +would define this potential using the derived components normal and shear with the following input: +*PARAMETER +=0.02 +=0.05 +=1.5 +*CONNECTOR POTENTIAL, EXPONENT= +normal, +, , MACAULEY +shear, +, , ABS +Output +The Abaqus/Explicit output variables available for connectors are listed in “Abaqus/Explicit output +variable identifiers,” Section 4.2.2. The following variables (available only in Abaqus/Explicit ) are of +particular interest when defining connector functions for coupled behavior: +CDERF +CDERU +Connector derived force/moment with the connector derived component name +appended to the output variable. If the connector derived component is used with +connector plasticity, connector friction, and connector damage initiation (type +force), the derived components used to form the potential represent forces and this +quantity is available for both field and history output. If connector friction is used +with contact force, the derived components are not used to form a potential, and +the derived force is in fact the connector normal force CNF (which is available for +connector history output.) +Connector derived displacement/rotation with the connector derived component +name appended to the output variable. +If the connector derived component is +used with motion type for the connector damage initiation and connector damage +evolution, the derived components to form the potential represent displacements +and this quantity is available for both field and history output. +31.2.5 +CONNECTOR FRICTION BEHAVIOR +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Connectors: overview,” Section 31.1.1 +• “Connector behavior,” Section 31.2.1 +• “Connector functions for coupled behavior,” Section 31.2.4 +• *CHANGE FRICTION +• *CONNECTOR BEHAVIOR +• *CONNECTOR DERIVED COMPONENT +• *CONNECTOR FRICTION +• *CONNECTOR POTENTIAL +• *FRICTION +• “Defining friction,” Section 15.17.3 of the Abaqus/CAE User’s Manual, in the online HTML version +of this manual +Overview +Frictional effects can be defined in any connector with available components of relative motion. A +typical connector might have several pieces that are in relative motion and are contacting with friction. +Therefore, both frictional forces and frictional moments may develop in the connector available +components of relative motion. +To define connector friction in Abaqus, you must specify the following: +• the friction law as governed by a friction coefficient; +• the contributions to the friction-generating connector contact forces or moments; and +• the local “tangent” direction in which the friction forces/moments act. +The friction coefficient can be +• expressed in a general form in terms of slip rate, contact force, temperature, and field variables; +• defined by a static and kinetic term with a smooth transition zone defined by an exponential curve; +and +• limited by a tangential maximum force, +can be carried by the connector before sliding occurs. +, which is the maximum value of tangential force that +Abaqus provides two alternatives for specifying the other aspects of friction interactions in connectors: +• Predefined friction interactions for which you need to specify a set of parameters that are +characteristic of the connection type for which friction is modeled. Abaqus automatically +defines the contact force contributions and the local “tangent” directions in which friction occurs. +Predefined friction interactions represent common cases and are available for many connection +types . If desired, known internal contact forces +(such as from a press-fit assembly) can be defined as well. +• User-defined friction interactions for which you define all friction-generating contact force +contributions and the local “tangent” directions along which friction occurs. The user-defined +friction interactions can be used if predefined friction is not available for the connection type of +interest or if the predefined friction interaction does not adequately describe the mechanism being +analyzed. Although more complicated to utilize, user-defined interactions: +– are very general in nature due to flexibility in defining arbitrary sliding directions via connector +potentials and contact forces via connector derived components; +– allow for the specification of sliding directions, contact forces, and additional internal contact +forces as functions of connector relative position or motion, temperature, and field variables +(the internal contact forces can also be dependent on accumulated slip); and +– allow for several friction definitions to be used in the same connection applied in different +components of relative motion. +Friction formulation in connectors +The basic concept of Coulomb friction between two contacting bodies is the relation of the maximum +allowable frictional (shear) force across an interface to the contact force between the contacting bodies. +In the basic form of the Coulomb friction model, two contacting surfaces can carry shear forces, +, up +to a certain magnitude across their interface before they start sliding relative to one another; this state is +known as sticking. The Coulomb friction model defines this critical shear force as +is the +coefficient of friction and +is the contact force. The stick/slip calculations determine when a point +transitions from sticking to slipping or from slipping to sticking. Mathematically, the relationship can +be formalized as +, where +Frictional stick occurs if +; and sliding occurs if +, in which case the friction force is +. +Friction in connectors is based on the analogy that contacting surfaces of various parts inside +a connector device transmit tangential as well as normal forces across their interfaces. The normal +(contact) forces, +, are typically generated by kinematic constraints or by elastic forces/moments in the +connector. Connector friction can be used to model tangential (shear) forces, +, in the space spanned +by the available components of relative motion for both stick and slip conditions. Figure 31.2.5–1 +illustrates the simplest frictional mechanism in connectors, a SLOT connector in a two-dimensional +analysis. The local tangent direction in which frictional sliding occurs is the 1-direction (tangential +traction +), and the normal force is developed by the kinematic constraint enforcing the SLOT +constraint in the 2-direction, +. The friction model is defined in this case by +f2 +f1 +Figure 31.2.5–1 Friction in a two-dimensional SLOT connection. +which in case of slip predicts a friction force +as expected. In this case the friction model +is straightforward to understand as the slip direction is along an intrinsic (1 through 6) component of +relative motion and the normal force is given only by the force in one other single component orthogonal +to the sliding direction. +In many connectors the definition of the tangential tractions is more complex. For example, friction +may develop in a tangent direction that spans two or more available components of relative motion. +Consider the case of frictional sliding in a SLIDE-PLANE connection as illustrated in “Connector +In this case the friction-generating normal force is +functions for coupled behavior,” Section 31.2.4. +given by the constraint force in the 1-direction, +. However, the magnitude of the tangential +tractions is given by +thus including contributions from two components of relative motion. The instantaneous direction of +frictional slip in the 2–3 plane is not known a priori. +In many connectors the normal force may have contributions from several connector components. +Consider the case of a three-dimensional SLOT as illustrated in “Connector functions for coupled +behavior,” Section 31.2.4. In this case the magnitude of the tangential tractions is given by +, but +the normal force is generated by constraint forces in both the 2- and 3-directions and can be written as +In the most general case both the tangential tractions and the normal force may have contributions +from several components. Further, the component directions may include both translations (forces) and +rotations (moments). Thus, friction modeling in connectors is defined in a more general form, as follows. +First, the function +governing the stick-slip condition is defined as +where +is the connector potential , which represents the magnitude of the frictional +is the collection of forces in the connector; +tangential tractions in the connector in a direction tangent to the surface on which contact occurs; and +is the friction-producing normal (contact) force on the same contact surface. Frictional stick occurs +if +; and sliding occurs if +, in which case the friction force is +. +The normal force, +, is the sum of a magnitude measure of contact force-producing connector +, and a self-equilibrated internal contact force (such as from a press-fit assembly), +forces, +: +is given by a connector derived component definition as illustrated in “Connector +The function +functions for coupled behavior,” Section 31.2.4. Using this formalism, we can easily reconstruct the +examples illustrated above: +• In the two-dimensional SLOT case, +• In the SLIDE-PLANE case, +• In the three-dimensional SLOT case, +and +and +and +. +. +. +See the examples at the end of this section for more complex illustrations of friction definitions in +connectors. +If frictional effects are defined for a rotational component of relative motion (such as in a HINGE +connector), it is often more convenient to define “tangential” moments and “normal” moments instead +of tangential tractions/forces and normal forces. The pseudo-yield function governing the stick/slip +behavior is defined in a similar fashion: +where the “normal” moment +is written as +is the self-equilibrated friction-generating internal “contact” moment (for example, from press fit). +See “Specifying friction in a HINGE connection” at the end of this section for an illustration. +Predefined friction behavior +Predefined friction interactions allow you to model typical frictional mechanisms in commonly used +connector types without having to define the mechanics of the frictional response. Instead of specifying +the potential, +, directly to define the magnitude measure of the tangential tractions and the contact force +via a derived component, you specify: +• a set of friction-related parameters associated with the connection type, which include geometric +or contact +parameters specific to the connection type and, optionally, the internal contact force +moment +; and +• the friction law (governed by the friction coefficient) as described in “Defining the friction +coefficient.” +Abaqus then automatically generates internally the potential, +, based on +the connection type and geometric parameters provided. Table 31.2.5–1 shows the connection types for +which predefined friction interactions are available and the associated friction-related parameters. The +meanings of the geometric parameters as well as the corresponding potentials and derived components +automatically generated by Abaqus are described in “Connection-type library,” Section 31.1.5. +, and the contact force, +Table 31.2.5–1 Predefined friction-related parameters. +Connection type +Friction-related parameters +Geometric +parameters +Internal contact +force/moment +CYLINDRICAL +R, L +HINGE +PLANAR +SLIDE-PLANE +SLOT +TRANSLATOR +UJOINT +SLIPRING +, +, +, +None +None +, L +, +, +, +None +, +None +See the examples at the end of this section for illustrations of predefined friction. +Input File Usage: +*CONNECTOR FRICTION, PREDEFINED +friction-related parameters outlined in Table 31.2.5–1 +Abaqus/CAE Usage: +Interaction module: connector section editor: Add→Friction: Friction +model: Predefined, Predefined Friction Parameters, enter the +friction-related parameters outlined in Table 31.2.5–1 in the data table +User-defined friction behavior +User-defined friction behavior can be used if predefined friction is not available for the connection type +of interest or if the predefined friction interaction does not describe adequately the mechanism being +analyzed. For user-defined friction you must specify: +• “tangent” direction information, as follows: +– if the slip direction is known, you specify directly the direction in which friction +forces/moments act, from which Abaqus constructs the potential +; +– if the slip direction is unknown, you specify the potential +from which Abaqus computes +the instantaneous slip direction; +• the friction-producing normal force, +following: +, or normal moment, +, by defining at least one of the +– the contact force +– the internal contact force +or contact moment +; and/or +or contact moment +; and +• the friction law (governed by the friction coefficient) as described in “Defining the friction +coefficient.” +Specifying the slip direction aligned with an available component of relative motion +The friction tangent direction is identified by specifying an available component (1–6) to define friction +forces or moments in a specified intrinsic connector local direction. This is the natural choice in cases +when the connector element has only one available component of relative motion (for example, SLOT, +REVOLUTE, or TRANSLATOR); in these cases the relative slip between the various parts forming +the physical connection occurs in one local direction only. In connections with two or more available +components of relative motion, specifying a particular available component of relative motion allows you +to specify frictional effects in that direction only, if desired. For example, in the case of a CYLINDRICAL +connection, specifying component 1 defines frictional effects only in translation while rotation around +the axis is ignored for friction. +Abaqus constructs the potential, +, automatically as +where +is the force/moment in the specified component i. +Input File Usage: +Abaqus/CAE Usage: +*CONNECTOR FRICTION, COMPONENT=i +Interaction module: connector section editor: Add→Friction: Friction +model: User-defined, Slip direction: Specify direction, component +Specifying the potential when the slip direction is unknown +In connection types with two or more available components of relative motion, frictional slipping +is not necessarily solely along one of the available components of relative motion. +In such cases +the instantaneous slip direction is not known, as illustrated in the SLIDE-PLANE case in “Friction +formulation in connectors.” Another example is the CYLINDRICAL connection in which frictional +sliding occurs in a direction tangent to the cylindrical surface, +thus involving simultaneously a +translational slip in the local 1-direction and a rotational slip about the same axis . Thus, frictional slip may occur in a coupled fashion spanning +several available components simultaneously. +In such cases you must specify the magnitude measure of the tangential tractions on the assumed +contact surface using a connector potential definition, +. Abaqus then computes the instantaneous slip +direction simultaneously with the stick-slip determination similar to the surface-based three-dimensional +frictional contact computations described in “Coulomb friction,” Section 5.2.3 of the Abaqus Theory +Manual. This procedure is best illustrated for the SLIDE-PLANE case, as follows: +• First, the potential +is evaluated. +• Slipping occurs if the pseudo-yield function +• The two vector components (the local 2- and 3-directions) of the instantaneous slip direction are +, normalized by the magnitude of the potential. +and +given by the ratios of the two shear forces, +. +In general, this strategy is extended to the space spanned by the available components of relative +motion associated with the connection type that ultimately participate in the potential definition . For example, up to two components for +SLIDE-PLANE or CYLINDRICAL connections, three components for CARDAN connections, and six +components for a user-assembled connection using CARTESIAN and CARDAN connections can be +included in the potential. See the examples below for several illustrations. +Input File Usage: +Use the following two options to specify coupled user-defined friction: +Abaqus/CAE Usage: +*CONNECTOR FRICTION +*CONNECTOR POTENTIAL +Interaction module: connector section editor: Add→Friction: +Friction model: User-defined, Slip direction: Compute using +force potential, Force Potential +Specifying the contact force +You specify the friction-generating user-defined contact force, +, or contact moment, +, by referring to either an intrinsic component of relative motion number (1 through 6) or a named +connector derived component . +In the latter case the scaling parameters used in the definition of +can be made functions of +identified local directions, temperature, and field variables. It is often desirable to include contributions +from both connector forces and moments in the definition of the derived component. In these cases the +scaling parameters used to define the derived components should have units of length or one over length +for meaningful contact force/moment definitions. +Input File Usage: +Use the following option to define a contact force for connector friction using +an intrinsic connector component: +Abaqus/CAE Usage: +*CONNECTOR FRICTION, CONTACT FORCE=component number (1–6) +Use the following options to define a contact force for connector friction using +a connector derived component: +*CONNECTOR DERIVED COMPONENT, +NAME=derived_component_name +*CONNECTOR FRICTION, CONTACT FORCE=derived_component_name +Interaction module: connector section editor: Add→Friction: +Friction model: User-defined, Contact Force, Specify +component: Intrinsic component or Derived component, +component or specify derived component +Connector derived component names are not supported in Abaqus/CAE. +Specifying the internal contact force +Internal contact forces such as contact interference may occur in connectors during the physical +assembly of the various pieces forming the connector (for example, a press-fit shaft into the sleeve +of a CYLINDRICAL connection). When relative motion occurs between the connector parts, these +self-equilibrating contact stresses will produce contact forces, +; see +“Friction formulation in connectors.” +, or contact moments, +The internal contact forces/moments are created by specifying a contact force/moment curve +(positive values only) as a function of accumulated slip, +temperature, and field variables. The +accumulated slip is computed as the sum of the absolute values of all slip increments in an instantaneous +slip direction. Consequently, the accumulated slip is monotonically increasing for oscillatory or periodic +motion and can be used to model dependencies related to wear or heat generation in the connection. +Input File Usage: +Abaqus/CAE Usage: +The internal contact forces limiting curve is defined on the data lines +of the *CONNECTOR FRICTION option. +Interaction module: connector section editor: Add→Friction: +Friction model: User-defined, Contact Force, and enter the +Internal Contact Force in the data table +Specifying the internal contact force to depend on local directions +The internal contact force can also be defined as dependent on either connector relative positions or +constitutive relative motions. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to define an internal contact force that depends on +components of relative position: +*CONNECTOR FRICTION, INDEPENDENT COMPONENTS=POSITION +Use the following option to define an internal contact force that depends on +components of constitutive displacements or rotations: +*CONNECTOR FRICTION, +INDEPENDENT COMPONENTS=CONSTITUTIVE MOTION +Interaction module: connector section editor: Add→Friction: +Friction model: User-defined, Contact Force, Use independent +components: Position or Motion +Defining the friction coefficient +The connector friction definition uses the standard friction model described in “Frictional behavior,” +Section 36.1.5, to define the friction coefficient. The anisotropic friction and friction data associated +with the second contact direction are ignored for connector elements. If the friction coefficients are +not specified or are set to zero, the connector friction has no effect on the connector behavior. If the +equivalent shear force/moment limit, +, is specified , the limiting friction force + is replaced by +in the pseudo-yield function +. +Rough, Lagrange, and user-defined friction cannot be used in connector elements. +Input File Usage: +Use the following options: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR FRICTION +*FRICTION +Abaqus/CAE Usage: +Interaction module: connector section editor: Add→Friction: Tangential +Behavior, Friction Coefficient, and enter the Friction Coeff. in the data table +Changing the friction coefficients during an Abaqus/Standard analysis +In Abaqus/Standard the friction coefficients can be changed during the analysis as for any analysis +including friction . +Controlling the unsymmetric solver in Abaqus/Standard +In Abaqus/Standard friction constraints produce unsymmetric terms when the connector nodes are sliding +relative to each other. These terms have a strong effect on the convergence rate if frictional stresses have +a substantial influence on the overall displacement field and the magnitude of the frictional stresses is +highly solution dependent. Abaqus/Standard will automatically use the unsymmetric solution method +if the coefficient of friction is greater than 0.2. If desired, you can turn off the unsymmetric solution +method as described in “Defining an analysis,” Section 6.1.2. +Defining the stick stiffness +Abaqus determines whether the connector is sticking or slipping in a similar fashion as for all +contact interactions , as outlined in “Friction formulation in +connectors.” If the model is sticking, the elastic stiffness of the response is determined by the optional +stick stiffness that is specified as part of the connector friction definition. +If the stick stiffness is not specified, Abaqus will compute a usually appropriate stick stiffness. In +Abaqus/Standard a maximum allowable elastic slip length (or angle) is first defined using either the value +of the slip tolerance, +, together with an automatically computed characteristic length (angle) in the +model or the absolute magnitude of the allowable elastic slip, +, to be used in the stiffness method for +sticking friction directly . The elastic stick stiffness is then determined by simply dividing +the current connector limiting friction force by this maximum allowable elastic slip length (angle). In +Abaqus/Explicit the elastic stick stiffness is determined from the Courant (stability) condition. +Input File Usage: +Abaqus/CAE Usage: +*CONNECTOR FRICTION, STICK STIFFNESS=elastic stiffness +Interaction module: connector section editor: Add→Friction: Stick +stiffness: Specify: elastic stiffness +Using multiple connector friction definitions +Multiple connector frictions can be used as part of the same connector behavior definition. However, +only one connector friction definition can be used to define friction interactions for each available +component of relative motion. If predefined friction is used, only one connector friction definition can +be associated with a connector behavior definition. At most one coupled user-defined friction definition +can be associated with a connector behavior definition. Additional connector friction definitions are +permitted for the same connector behavior definition only if the component relative motion spaces +for each definition do not overlap; for example, you could define uncoupled connector friction in +components 1, 2, and 6 and coupled connector friction (by defining a potential) using components 3, 4, +and 5. All connector friction definitions act in parallel and will be summed if necessary. For a particular +connector element there will be as many stick-slip calculations as connector friction definitions. See the +examples below. +Examples +The following examples illustrate how to define friction in connector elements. +Equivalent ways of specifying friction behavior in a CYLINDRICAL connection +In the example in Figure 31.2.5–2 assume Coulomb-like friction affects the translational motion along +the shock and the rotational motion about the shock axis. +li +2r +Figure 31.2.5–2 Simplified connector model of a shock absorber. +The coefficient of friction is +, and the overlapping length for the two parts of the shock is +length units in the undeformed configuration. An average radius of the two cylinders is considered +to be +units. It is also assumed that the axial motion in the connection is relatively small so +that the overlapping length between the connector parts does not change much. The friction-generating +contact force has contributions from two sources: +• the normal force from the inner walls pushing against each other (the vector magnitude of the +Lagrange multipliers imposing the SLOT constraint), and +• the “bending” in the REVOLUTE constraint (the vector magnitude of the Lagrange multipliers +imposing the REVOLUTE constraint). +See “Connection-type library,” Section 31.1.5, for a detailed discussion of predefined contact forces +and tangential tractions in the CYLINDRICAL connection. Two equivalent alternatives to model these +frictional effects are shown below: +A. Using the Abaqus predefined friction behavior: +*PARAMETER +r=0.24 +=0.55 +... +*CONNECTOR FRICTION, PREDEFINED +, +*FRICTION +0.15 +Using a predefined connector friction behavior yields the most compact definition of frictional +effects. This definition requires only the specification of the two friction-relevant geometrical +scaling constants. +B. Using a user-defined frictional behavior: +*PARAMETER +r=0.24 +=0.55 +=1.0 +=2.0/ +... +*CONNECTOR BEHAVIOR, NAME=shock +*CONNECTOR DERIVED COMPONENT, NAME=normal +2, 3 +, +**( +) +*CONNECTOR DERIVED COMPONENT, NAME=normal, +5, 6 +, +) +**( +*CONNECTOR FRICTION, CONTACT FORCE=normal +*CONNECTOR POTENTIAL +1, +4, +*FRICTION +0.15 +The contact force “normal” is defined by +The connector potential defines the magnitude of the tangential tractions as +This force magnitude is tangent to the cylindrical surface of the connector on which contact occurs. +The choice of normal force definition and potential in this case ensures that the same frictional +effects defined in Case A are modeled. +Specifying friction interactions in a CYLINDRICAL connection accounting for position +dependencies +In the example in Figure 31.2.5–2 assume that large axial motion occurs between the two connector +parts and, hence, the overlapping length will change significantly during the analysis. For the sake of +discussion, assume that the two connector nodes are specified to be overlapped in the initial configuration. +Thus, at CP1=0.0 the initial overlap is +as specified above. If during the analysis the connector +relative position along the 1-component reaches CP1=0.45 units, the final overlap would be +. +If the connection is subjected to a “bending-like” loading, one can argue that as the +overlapping length decreases, the contact forces developed between the two parts become increasingly +higher. Use the following user-defined friction behavior definitions to model this dependence of the +contact force on relative positions: +*PARAMETER +r=0.24 +=0.55 +=0.1 +=1.0 +=2.0/ +=2.0/ +... +*CONNECTOR BEHAVIOR, NAME=shock +*CONNECTOR DERIVED COMPONENT, NAME=normal +2, 3 +, +**( +) +*CONNECTOR DERIVED COMPONENT, NAME=normal, +INDEPENDENT COMPONENTS=POSITION +5, 6 +**( +, +, +, 0 +, 0.45 +at CP1=0.0) +**( +*CONNECTOR FRICTION, CONTACT FORCE=normal +at CP1=0.45) +*CONNECTOR POTENTIAL +1, +4, +*FRICTION +0.15 +Specifying friction due to assembly contact interference +Assume a CYLINDRICAL connector element in which the shaft was press-fit into the sleeve, as shown +in the initial configuration (relative motion = 0.0) in Figure 31.2.5–3. +2r +Figure 31.2.5–3 CYLINDRICAL connection with slightly conical pin. +The shaft is not perfectly cylindrical but slightly conical so that its cross-section diameter is increasing in +a linear fashion along the shaft direction. If the relative displacement along the shaft direction becomes +positive, the contact forces will increase (more contact interference); if the relative displacements become +negative (less interference), they will decrease. An exponential decay model is assumed to model the +transition from a static coefficient of friction to a kinetic one. Only the positive contact force versus +displacement values need to be specified. The following user-defined friction behavior definitions can +be used: +*PARAMETER +r=0.24 +... +*CONNECTOR FRICTION, INDEPENDENT COMPONENTS=CONSTITUTIVE MOTION +** (independent component 1) +0.70, -0.7854 +0.85, -0.3927 +0.0 +1.0 , +0.3927 +1.15, +1.30, +0.7854 +*CONNECTOR POTENTIAL +1, +4, +*FRICTION, EXPONENTIAL DECAY +... +0.25, 0.10, 0.2 +The internal contact forces are specified directly on the data lines to model known contact interference +forces as a function of the connector constitutive component of relative motion along component 1. Since +no intrinsic component of relative motion number or named connector derived component was specified +to define the contact force, the only contribution to the contact force is the specified internal contact force. +Specifying friction in a HINGE connection +This example illustrates the use of a connector friction definition to specify frictional effects in a HINGE +connection. The friction behavior defines friction moments about the 1-direction, since there are no other +available components of relative motion. As illustrated in “Connection-type library,” Section 31.1.5, the +three geometrical scaling constants that need to be specified for predefined friction are the radius of the +pin cross-section, +=0.14; and the overlapping +length between the pin and the sleeve, +=0.65. The friction coefficient is assumed to be =0.15. It +is assumed that the connector has been assembled with initial known contact interference-producing +contact moments of +units. The following input could be used to specify the predefined +friction behavior in the HINGE connection: +=0.12; the effective friction arm in the axial direction, +*PARAMETER +=0.12 +=0.14 +=0.65 +... +*CONNECTOR FRICTION, PREDEFINED +, +, +, 100.0 +*FRICTION +0.15 +Alternatively, a user-defined friction behavior could be specified to define identical frictional effects +. Moreover, a reduction of the interference contact forces +as the pin wears due to accumulated sliding can be modeled in this case by specifying the internal contact +forces/moments to be functions of accumulated slip. The following input can be used: +*PARAMETER +=0.12 +=0.14 +=0.65 += += +=2.0* +... +*CONNECTOR DERIVED COMPONENT, NAME=contact_moment +1, +, +** ( +) +*CONNECTOR DERIVED COMPONENT, NAME=contact_moment +2, 3 +, +**( +*CONNECTOR DERIVED COMPONENT, NAME=contact_moment +5, 6 +) +, +) +**( +*CONNECTOR FRICTION, COMPONENT=4, CONTACT FORCE=contact_moment +100, 0.0 +90 , 1000.0 +** interference contact moments decreasing due to wear effects +*FRICTION +0.15 +The additional friction moments due to contact interference are modeled by specifying decreasing +internal contact moments as a function of accumulated rotational slip about the 1-direction. The +connector derived component definitions are used to define a contact moment-producing friction in the +same direction (component 4). The contact moment is defined by +The connector potential is defined automatically by Abaqus as +. +Specifying friction in a ball-in-socket connection +This example illustrates the specification of +frictional effects in a ball-in-socket connection. +While the first choice in defining a ball-in-socket connection is JOIN and ROTATION, other +rotation parameterizations could be used (JOIN and CARDAN, JOIN and EULER, or JOIN and +FLEXION-TORSION). Assuming that the radius of the ball is +and the coefficient of friction +is +, the following lines can be used to define the friction interactions: +*PARAMETER +=0.30 +... +*CONNECTOR DERIVED COMPONENT, NAME=normal +1, 2, 3 +1.0, 1.0, 1.0 +**( +) +*CONNECTOR FRICTION, CONTACT FORCE=normal +*CONNECTOR POTENTIAL +4, +5, +6, +*FRICTION +0.15 +The computed connector friction moments and the friction-induced moments at the connector nodes are +dependent on the connection type. +Defining connector friction behavior in linear perturbation procedures +Frictional slipping is not allowed in linear perturbation procedures. If a connector is slipping at the end +of the last general analysis step, it will slip freely during the current linear perturbation step. Otherwise, +Abaqus will allow the connector to slip elastically with the specified stick stiffness or enforce a sticking +condition if a stick stiffness is not specified. +Output +The Abaqus output variables available for connectors are listed in “Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2. The +following variables are of particular interest when defining friction in connectors: +CSF +CNF +CASU +CIVC +In addition to the usual six components +Connector friction forces/moments. +associated with connector output variables, CSF includes the scalar CSFC, which +is the friction force generated by a coupled friction definition. +Connector normal forces/moments. CNF includes the scalar CNFC, which is the +friction-generating normal force associated with a coupled friction definition. +Connector accumulated slip. CASU includes the scalar CASUC, which is the +accumulated slip associated with a coupled friction definition. +Connector instantaneous velocity associated with a coupled friction definition. +31.2.6 +CONNECTOR PLASTIC BEHAVIOR +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Connectors: overview,” Section 31.1.1 +• “Connector behavior,” Section 31.2.1 +• “Connector elastic behavior,” Section 31.2.2 +• “Connector functions for coupled behavior,” Section 31.2.4 +• *CONNECTOR BEHAVIOR +• *CONNECTOR DERIVED COMPONENT +• *CONNECTOR ELASTICITY +• *CONNECTOR HARDENING +• *CONNECTOR PLASTICITY +• *CONNECTOR POTENTIAL +• “Defining plasticity,” Section 15.17.6 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +Connector plasticity in Abaqus: +• can be used to model plastic/irreversible deformations of parts forming an actual connection device; +for example, +– the pin or the sleeve in a door hinge may deform plastically if the forces/moments acting on +them are large enough; +– connection elements in automotive suspension systems may deform irreversibly due to abusive +loading; or +– spot welds in a car frame and rivets in an airplane could undergo inelastic deformations if the +forces acting on the structural members they are a part of are larger than intended; +• is defined in terms of resultant forces and moments in the connector; +• uses perfect plasticity or isotropic/kinematic hardening behavior models; +• can be used when rate-dependent effects are important; +• can be specified in any connectors with available components of relative motion; +• can be used for available components of relative motion for which either elastic or rigid behavior +was specified; +• can be used in an uncoupled fashion to define elastic-plastic or rigid plastic response in individual +available components of relative motion; and +• can be used to specify coupled elastic-plastic or rigid plastic behavior, in which case the responses +in several available components of relative motion are involved simultaneously in a coupled fashion +to define plasticity effects. +To define connector plasticity in Abaqus, the following are necessary: +• the elastic or rigid behavior prior to the onset of plasticity; +• a yield function upon which plastic flow will be initiated; and +• hardening behavior to define the initial yield value and, optionally, the yield value evolution after +plastic motion initiation. +Plasticity formulation in connectors +The plasticity formulation in connectors is similar to the plasticity formulation in metal plasticity . In connectors the stress ( +) corresponds to the force ( ), +the strain ( ) corresponds to the constitutive motion ( ), the plastic strain ( +) corresponds to the plastic +relative motion ( +) corresponds to the equivalent plastic relative +), and the equivalent plastic strain ( +motion ( +). The yield function +is defined as +is the collection of forces and moments in the available components of relative motion that +where +ultimately contribute to the yield function; +, defines a magnitude of +connector tractions similar to defining an equivalent state of stress in Mises plasticity and is either +automatically defined by Abaqus or user-defined; and +is the yield force/moment. The connector +relative motions, +; and when plastic flow occurs, +, remain elastic as long as +the connector potential, +. +If yielding occurs, the plastic flow rule is assumed to be associated; thus, the plastic relative motions +are defined by +where +is the rate of plastic relative motion and +is the equivalent plastic relative motion rate. +Loading and unloading behavior +Abaqus allows for the following three types of behaviors associated with a plasticity definition when the +connector is not actively yielding: +• Linear elastic behavior, shown in Figure 31.2.6–1(a), is the most common case since similar +behavior can be modeled in metal plasticity, for example, by specifying the Young’s modulus. +Elastic motion occurs prior to plasticity onset, and unloading from a plastic state occurs on a +straight line parallel to the initial loading. +• Rigid behavior, shown in Figure 31.2.6–1(b), assumes that the slope in the linear elastic behavior is +infinite; thus, the elastic motion prior to plasticity onset is zero, and unloading from a plastic state +plasticity onset +linear elastic +unloading/reloading +0 +linear elasticity +U +plasticity onset +rigid +unloading/reloading +U +plasticity +onset +user-specified +nonlinear elasticity +nonlinear elastic +unloading/reloading +0 +F 0 +Fl0 +(a) +(b) +(c) +0 +0 c +U +Figure 31.2.6–1 Linear elastic-plastic (a), rigid plastic (b), +and nonlinear elastic-plastic (c) response. +occurs on a vertical line. In practice, the rigid behavior is enforced using an automatically chosen +high penalty stiffness. +• Nonlinear elastic behavior, shown in Figure 31.2.6–1(c), in which the initial elastic loading occurs +along the defined nonlinear path. Elastic unloading occurs along a nonlinear curve (C +Oc ) that +is simply the user-defined nonlinear elastic curve motion shifted such that it passes through point +C. The user-defined nonlinear elastic behavior must be such that the unloading path (C +Oc ) does +not intersect with the loading path (O +C); otherwise, a local instability will occur. +Other behaviors (such as damping or friction) can be specified in addition to the elastic/rigid/plastic +specifications but will not be considered in the plasticity calculations since they are considered to be in +parallel with the elastic-plastic/rigid plastic behavior . +Defining elastic-plastic or rigid plastic behavior +As is the case with any other connector behavior type, connector plasticity can be defined only for +available components of relative motion. For example, you cannot define plastic behavior in a BEAM +connector or in components 2 and 3 of a SLOT connector since these components are not available for +behavior definitions. The solution to this problem is to: +• define a connection type with available components of relative motion that best models the +kinematics of your connection device both before and after plasticity onset; +• define the desired components as rigid ; and +• specify rigid plastic behavior in some or all of these components. +For example, to define rigid plasticity for an otherwise rigid beam-like connector, you could +use a PROJECTION CARTESIAN connection together with a PROJECTION FLEXION-TORSION +connection, define all components as rigid, and proceed with your plasticity definitions. +Elastic-plastic behavior is usually specified for available components of relative motion for which +spring-like behavior is specified and for which plastic deformation may occur. +Input File Usage: +Abaqus/CAE Usage: +Use the following options to define rigid plasticity in connectors: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR ELASTICITY, RIGID +*CONNECTOR PLASTICITY +*CONNECTOR HARDENING +Use the following options to define elastic-plasticity in connectors: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR ELASTICITY +*CONNECTOR PLASTICITY +*CONNECTOR HARDENING +Use the following input to define rigid plasticity in connectors: +Interaction module: connector section editor: Add→Elasticity, +Definition: Rigid; Add→Plasticity +Use the following input to define elastic-plasticity in connectors: +Interaction module: connector section editor: Add→Elasticity; +Add→Plasticity +Defining uncoupled plastic behavior +Uncoupled elastic-plastic or rigid plastic behavior, specified for each component of relative motion +independently, is similar to one-dimensional plasticity. You must define elastic or rigid behavior in +the specified component of relative motion. +In this case the connector potential function is chosen +automatically as +where +behavior is specified. The associated plastic flow in this case becomes +is the force or moment in the +available component of relative motion for which plastic +where +is the rate of plastic relative motion and +is the equivalent plastic relative motion rate in the +component. +Input File Usage: +Use the following options to define uncoupled rigid plastic connector behavior: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR ELASTICITY, RIGID, COMPONENT=i +*CONNECTOR PLASTICITY, COMPONENT=i +*CONNECTOR HARDENING +Use the following options to define uncoupled elastic-plastic connector +behavior: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR ELASTICITY, COMPONENT=i +*CONNECTOR PLASTICITY, COMPONENT=i +*CONNECTOR HARDENING +Use the following input to define uncoupled rigid plastic connector behavior: +Interaction module: connector section editor: Add→Elasticity, Definition: +Rigid; Add→Plasticity, Coupling: Uncoupled +Use the following input to define uncoupled elastic-plastic connector behavior: +Interaction module: connector section editor: Add→Elasticity, +Definition: Linear or Nonlinear, Coupling: Uncoupled; +Add→Plasticity, Coupling: Uncoupled +31.2.6–5 +Defining coupled plastic behavior +You should define coupled plasticity in connectors when several available components of relative motion +are involved simultaneously in a coupled fashion in the definition of the yield function . In this case +you must define the potential, P, via a connector potential definition. Plastic flow eventually occurs only +in the intrinsic components of relative motion that are ultimately involved in the potential. Elastic or +rigid behavior should be specified for all components of relative motion that are involved in the potential +definition. The elastic/rigid behavior for these components can be specified in an uncoupled fashion, +in a coupled fashion, or in a combination of both. All elasticity definitions specified in a connector +behavior that are pertinent to the components of relative motion involved in the potential definition are +used collectively to define the elasticity for the coupled elastic-plastic or rigid plastic definition. +Input File Usage: +Use the following options to define coupled elastic-plastic or rigid plastic +connector behavior: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR ELASTICITY +*CONNECTOR PLASTICITY +*CONNECTOR POTENTIAL +*CONNECTOR HARDENING +Interaction module: connector section editor: Add→Elasticity; +Add→Plasticity, Coupling: Coupled, Force Potential +Abaqus/CAE Usage: +Mode-mix ratio +If the coupled plasticity definition includes at least two terms in the associated potential definition , a mode-mix ratio can be defined to reflect the relative weight of the first two terms in +their contribution to the potential. The mode-mix ratio can be used in plastic motion-based connector +damage definitions to specify dependencies in both +damage initiation and damage evolution. It is defined as +where +the force/moment in the second component specified for the same potential. +is the force/moment in the first component specified for the plasticity potential and +if +is +, +if +, and +is somewhere in between −1.0 and 1.0 if neither is 0.0. +Defining the plastic hardening behavior +Abaqus provides a number of hardening models varying from simple perfect plasticity to nonlinear +isotropic/kinematic hardening. Connector hardening is analogous to the hardening models used in +Abaqus for metals subjected to cyclic loading and described in “Models for metals subjected to cyclic +loading,” Section 23.2.2. +Defining perfect plasticity +Perfect plasticity means that the yield force does not change with plastic relative motion. +Input File Usage: +Use the following option to define perfect plasticity: +*CONNECTOR HARDENING +Abaqus/CAE Usage: +Interaction module: connector section editor: Add→Plasticity: +Specify isotropic hardening, Isotropic Hardening, and enter +the Yield Force/Moment in the data table +Defining nonlinear isotropic hardening +Isotropic hardening behavior defines the evolution of the yield surface size, +equivalent plastic relative motion, +function of +in tabular form or by using the simple exponential law +. This evolution can be introduced by specifying +, as a function of the +directly as a +is the yield value at zero plastic relative motion and +where +is the maximum change in the size of the yield surface, and b defines the rate at which the size of the +yield surface changes as plastic deformation develops. When the equivalent force defining the size of +the yield surface remains constant ( +), there is no isotropic hardening. +and b are material parameters. +Defining the isotropic hardening component by specifying tabular data +Isotropic hardening can be introduced by specifying the equivalent force defining the size of the yield +surface, +, and, if required, of the +, temperature, and/or other predefined field variables. The +equivalent relative plastic motion rate, +yield value at a given state is simply interpolated from this table of data. +, as a tabular function of the equivalent relative plastic motion, +Input File Usage: +*CONNECTOR HARDENING, TYPE=ISOTROPIC, +DEFINITION=TABULAR (default) +Abaqus/CAE Usage: +Interaction module: connector section editor: Add→Plasticity: Specify +isotropic hardening, Isotropic Hardening, Definition: Tabular +Defining the isotropic hardening component using the exponential law +Specify the material parameters of the exponential law ( +, and b) directly if they are already +calibrated from test data. These parameters can be specified as functions of temperature and/or field +variables. +, +Input File Usage: +*CONNECTOR HARDENING, TYPE=ISOTROPIC, +DEFINITION=EXPONENTIAL LAW +Abaqus/CAE Usage: +Interaction module: connector section editor: Add→Plasticity: Specify +isotropic hardening, Isotropic Hardening, Definition: Exponential law +Defining nonlinear kinematic hardening +When nonlinear kinematic hardening is specified, the center of the yield surface is allowed to translate +in the force space. The backforce, +, is the current center of the yield surface and is interpreted similar +to the backstress +discussed in “Classical metal plasticity,” Section 23.2.1. +The yield surface is defined by the function +where +is the yield value and +is the potential with respect to the backforce +. +The kinematic hardening component is defined to be an additive combination of a purely kinematic +term (the linear Ziegler hardening law) and a relaxation term (the recall term) that introduces the +nonlinearity. When temperature and field variable dependencies are omitted, the hardening law is +are material parameters that must be calibrated from cyclic test data. C is the initial +where C and +kinematic hardening modulus, and +determines the rate at which the kinematic hardening modulus +decreases with increasing plastic deformation. When C and +are zero, the model reduces to an isotropic +hardening model. When +is zero, the linear Ziegler hardening law is recovered. Refer to “Models +for metals subjected to cyclic loading,” Section 23.2.2, for a discussion of calibrating the material +parameters. +Defining the kinematic hardening component by specifying half-cycle test data +If limited test data are available, C and +can be based on the force-constitutive motion data obtained +from the first half cycle of a unidirectional tension or compression experiment. An example of such test +data is shown in Figure 31.2.6–2. This approach is usually adequate when the simulation will involve +only a few cycles of loading. +For each data point ( +is obtained from the test data as +) a value of +where +hardening definition or the initial yield force if the isotropic hardening component is not defined. +is the user-defined size of the yield surface at the corresponding plastic motion for the isotropic +Integration of the backforce evolution law over a half cycle yields the expression +which is used for calibrating C and . +When test data are given as functions of temperature and/or field variables, it is recommended that +a data check analysis be run first. During the data check run, Abaqus will determine several pairs of +material parameters (C, +), where each pair will correspond to a given combination of temperature and/or +F3, upl +F1, upl +F2, upl +F +upl +Figure 31.2.6–2 Half-cycle of force-motion data. +to be a constant, the data check analysis will +field variables. Since Abaqus requires the parameter +terminate with an error message if +is not a constant. However, an appropriate constant value of may +be determined from the information provided in the data file during the data check run. The values for +the parameter C and the constant +can then be entered directly as described below. +Input File Usage: +*CONNECTOR HARDENING, TYPE=KINEMATIC, +DEFINITION=HALF CYCLE (default) +Abaqus/CAE Usage: +Interaction module: connector section editor: Add→Plasticity: Specify +kinematic hardening, Kinematic Hardening, Definition: Half-cycle +Defining the kinematic hardening component by specifying test data from a stabilized cycle +Force-constitutive motion data can be obtained from the stabilized cycle of a specimen that is subjected +to symmetric cycles. A stabilized cycle is obtained by cycling the specimen over a fixed motion range +until a steady-state condition is reached; that is, until the force-motion curve no longer changes shape +from one cycle to the next. Such a stabilized cycle is shown in Figure 31.2.6–3. See “Models for metals +subjected to cyclic loading,” Section 23.2.2, for information on how the data should be processed before +they are specified in the connector hardening definition. +Input File Usage: +*CONNECTOR HARDENING, TYPE=KINEMATIC, +DEFINITION=STABILIZED +Abaqus/CAE Usage: +Interaction module: connector section editor: Add→Plasticity: Specify +kinematic hardening, Kinematic Hardening, Definition: Stabilized +Defining the kinematic hardening component by specifying the material parameters directly +The parameters C and +can be specified directly if they are already calibrated from test data. The +parameter C can be provided as a function of temperature and/or field variables, but temperature and +field variable dependence of +is not available. The algorithm currently used to integrate the nonlinear +isotropic/kinematic hardening model does not provide accurate solutions if the value of +changes +significantly in an increment due to temperature and/or field variable dependence. +Fn +F1 +Δu +F2 +up +Fi +ui +pl +ui += ui − i − +0up +Figure 31.2.6–3 Force-motion data for a stabilized cycle. +Input File Usage: +*CONNECTOR HARDENING, TYPE=KINEMATIC, +DEFINITION=PARAMETERS +Abaqus/CAE Usage: +Interaction module: connector section editor: Add→Plasticity: Specify +kinematic hardening, Kinematic Hardening, Definition: Parameters +Defining nonlinear isotropic/kinematic hardening +The evolution law of the combined isotropic/kinematic model consists of two components: an isotropic +hardening component, which describes the change in the equivalent force defining the size of the yield +surface, +, as a function of plastic relative motion, and a nonlinear kinematic hardening component, +which describes the translation of the yield surface in force space through the backforce, +. +At most two connector hardening definitions, one isotropic and one kinematic, can be associated +with a connector plasticity definition. If only one connector hardening definition is specified, it can be +either isotropic or kinematic. +Input File Usage: +Abaqus/CAE Usage: +Use the following two options to define nonlinear +hardening: +*CONNECTOR HARDENING, TYPE=KINEMATIC +*CONNECTOR HARDENING, TYPE=ISOTROPIC +Interaction module: connector section editor: Add→Plasticity: Specify +isotropic hardening and Specify kinematic hardening +isotropic/kinematic +Using multiple plasticity definitions +Multiple connector plasticity definitions can be used as part of the same connector behavior definition. +However, only one connector plasticity definition can be used to define plasticity for each available +component of relative motion. At most one coupled plasticity definition can be associated with a +connector behavior definition. Additional connector plasticity definitions are permitted for the same +connector behavior definition only if the two spaces do not overlap; for example, you could define +uncoupled connector plasticity for components 1, 2, and 6 and have one coupled connector plasticity +definition involving components 3, 4, and 5. +Each connector plasticity definition must have its own hardening definition. +Examples +Illustrations of uncoupled and coupled plasticity behaviors are shown in the following examples. +Uncoupled plasticity in a SLOT-like connector +Consider a SLOT connector that you have used to model a physical device efficiently. You have examined +the reaction forces enforcing the SLOT constraint in the local 2- and 3-directions; since they appear to +be quite large, you need to assess whether plastic deformations in the device may occur. One option that +you have is to create detailed meshes for the slot and the pin in the device, define the contact interactions +between them, and use elastic-plastic material definitions for the underlying materials. While this is the +most accurate modeling solution, it may be impractical, especially when the device you are modeling is +part of a larger model. Alternatively, you can do the following: +• use a CARTESIAN connection type instead of the SLOT connection with the first axis aligned with +the slot direction; +• define components 2 and 3 as rigid; and +• define rigid plasticity separately in each of the components. +The following input can be used: +*CONNECTOR SECTION, BEHAVIOR=slot +CARTESIAN +orientation at node a +*CONNECTOR BEHAVIOR, NAME=slot +*CONNECTOR ELASTICITY, RIGID +2, 3 +*CONNECTOR PLASTICITY, COMPONENT=2 +*CONNECTOR HARDENING, TYPE=ISOTROPIC +100, 0.0 +110, 0.12 +*CONNECTOR PLASTICITY, COMPONENT=3 +*CONNECTOR HARDENING, TYPE=ISOTROPIC +50, 0.0 +75, 0.23 +The yield forces that you specify in the connector hardening definitions are obtained from an experimental +result or are assessed from a “virtual experiment,” as follows: +• Use the meshed model of the slot discussed above. +• Run two simple separate analyses by constraining the slot part of the device and driving the pin into +the slot walls using a boundary condition. +• Plot the reaction force at the pin node against its motion. +• Use these data to create the force-motion hardening curve to be specified in the connector hardening +definition. +Coupled plasticity in a spot weld +Referring to the spot weld shown in Figure 31.2.6–4 and to the yield function described in “Defining +connector potentials” in “Connector functions for coupled behavior,” Section 31.2.4, +you could complete the plasticity definition, for example, by specifying tabular isotropic hardening and +kinematic hardening via parameters. +Fn +Figure 31.2.6–4 Spot weld connection. +*PARAMETER +=0.02 +=0.05 +*CONNECTOR ELASTICITY, RIGID +*CONNECTOR PLASTICITY +*CONNECTOR POTENTIAL, EXPONENT=a +normal, +, , MACAULEY +shear, +*CONNECTOR HARDENING, TYPE=ISOTROPIC +, , ABS +, +, +*CONNECTOR HARDENING, TYPE=KINEMATIC, DEFINITION=PARAMETERS +C, +Defining plastic connector behavior in linear perturbation procedures +Plastic relative motions are not allowed during linear perturbation analyses. Therefore, the connector +relative motions will be linear elastic perturbations about the plastically deformed base state, similar to +metal plasticity. +Output +The Abaqus output variables available for connectors are listed in “Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2. The +following output variables are of particular interest when defining plasticity in connectors: +CUE +CUP +CUPEQ +Connector elastic displacements/rotations. +Connector plastic displacements/rotations. +Connector equivalent plastic relative displacements/rotations. In addition to the +usual six components associated with connector output variables, CUPEQ includes +the scalar CUPEQC, which is the equivalent plastic relative motion associated with +a coupled plasticity definition. +CALPHAF +Connector kinematic hardening shift forces/moments. +31.2.7 +CONNECTOR DAMAGE BEHAVIOR +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Connectors: overview,” Section 31.1.1 +• “Connector behavior,” Section 31.2.1 +• *CONNECTOR BEHAVIOR +• *CONNECTOR DAMAGE EVOLUTION +• *CONNECTOR DAMAGE INITIATION +• *CONNECTOR ELASTICITY +• *CONNECTOR PLASTICITY +• *CONNECTOR POTENTIAL +• *SECTION CONTROLS +• “Defining damage,” Section 15.17.7 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +Connector damage behavior: +• can be specified in any connectors with available components of relative motion; +• can be used to degrade the elastic, elastic-plastic, or rigid plastic response in connector elements; +• can use a force-based, motion-based, or plastic motion–based damage initiation criterion upon +which response degradation may be triggered; +• can use either a (plastic) motion-based or an energy-based damage evolution law to degrade the +force response in the connector; +• can be defined in terms of several competing damage mechanisms; and +• can be used only as an indicator of proximity to the damage initiation point without degrading the +connector response. +Damage formulation in connectors +If relative forces or motions in a connection exceed critical values, the connector starts undergoing +irreversible damage (degradation). Upon additional loading there is further evolution of damage leading +to eventual failure. If damage has occurred, the force response in the connector component i will change +according to the following general form: +where +relative motion i if damage were not present (effective response). +is a scalar damage variable and +is the response in the available connector component of +To define a connector damage mechanism, you specify the following: +• a criterion for damage initiation; and +• a damage evolution law that specifies how the damage variable d evolves (optional). +Prior to damage initiation, d has a value of 0.0; thus, the force response in the connector does not change. +Once damage has been initiated, the damage variable will monotonically evolve up to the maximum +value of 1.0 if damage evolution is specified. Complete failure occurs when d = 1.0. +Abaqus allows you to specify a maximum degradation value (the default value is 1.0); damage +evolution will stop when the damage variable reaches this value, and the element will be deleted from +the mesh by default. Alternatively, you can specify that the damaged connector elements remain in +the analysis with no further damage evolution. The maximum degradation value is used to evaluate +the damaged stiffness in the remaining part of the analysis. This functionality is discussed in detail +in “Controlling element deletion and maximum degradation for materials with damage evolution” in +“Section controls,” Section 27.1.4. +Defining connector damage initiation +The degradation process in connectors initiates when forces or relative motions in the connector satisfy +certain criteria. Three different criteria types can be used to trigger damage in connectors: criteria +based on force, plastic motion, or constitutive motion. Connector damage initiation criteria for the +available components of relative motion can be specified for each component independently (uncoupled). +Alternatively, connector damage initiation criteria that couple all or some of the available components +of relative motion in the connector can be defined. +The damage initiation criterion can depend on temperature and field variables. See “Input syntax +rules,” Section 1.2.1, for further information about defining data as functions of temperature and field +variables. +Force-based damage initiation criterion +By default, the damage initiation criterion is specified in terms of forces/moments in the connector. +Elastic or rigid connector behavior must be defined for the components involved in the initiation. You +provide the lower (compression) limit, +, for the force/moment +damage initiation values. If the force is outside the range specified by the two limit values, damage is +initiated. The output variable CDIF can be used to monitor the proximity to the damage initiation point. +, and the upper (tension) limit, +Defining uncoupled force-based damage initiation +For an uncoupled force-based damage initiation criterion, the connector force in the specified component +is compared to the specified limit values. Damage is initiated when the force in the specified component +i, +, is for the first time outside the range ( +or +). +Input File Usage: +*CONNECTOR DAMAGE INITIATION, COMPONENT=component +number, CRITERION=FORCE (default), DEPENDENCIES=n +Abaqus/CAE Usage: +Interaction module: connector section editor: Add→Damage: Coupling: +Uncoupled, Initiation criterion: Force +Defining coupled force-based damage initiation +For a coupled force-based damage initiation criterion, a connector potential, +, must be specified +to define an equivalent force magnitude (scalar). The equivalent force magnitude is compared to +the specified limit values to assess damage initiation. Damage is initiated when the equivalent force +magnitude, +, is for the first time outside the range ( +or +). +Input File Usage: +Use the following options: +Abaqus/CAE Usage: +*CONNECTOR DAMAGE INITIATION, CRITERION=FORCE (default), +DEPENDENCIES=n +*CONNECTOR POTENTIAL +Interaction module: connector section editor: Add→Damage: Coupling: +Coupled, Initiation criterion: Force, Initiation Potential +Plastic motion–based damage initiation criterion +The damage initiation criterion can be specified in terms of an equivalent relative plastic motion in the +connector. You provide the relative equivalent plastic displacement/rotation at which damage will be +initiated as a function of the relative equivalent plastic rate. The output variable CDIP can be used to +monitor the proximity to the damage initiation point. +Defining uncoupled plastic damage initiation +For an uncoupled elastic-plastic or rigid plastic damage initiation criterion, uncoupled connector +plasticity in the specified component of relative motion must be defined . When the equivalent relative plastic motion as defined by the associated +plasticity definition is greater than the specified limit value for the first time, damage is initiated. +Input File Usage: +Use the following options: +*CONNECTOR DAMAGE INITIATION, COMPONENT=component +number, CRITERION=PLASTIC MOTION, DEPENDENCIES=n +*CONNECTOR PLASTICITY, COMPONENT=component number +or +*CONNECTOR PLASTICITY +Interaction module: connector section editor: Add→Damage: Initiation +criterion: Plastic motion; Add→Plasticity +Abaqus/CAE Usage: +Defining coupled plastic damage initiation +For a coupled elastic-plastic or rigid plastic damage initiation criterion, coupled connector plasticity +must be defined. The connector potential used in the coupled connector plasticity function defines an +equivalent relative plastic motion. This equivalent relative plastic motion is compared to the specified +limit values to assess damage initiation. The equivalent relative plastic motion at which damage is +initiated can be a function of the mode-mix ratio +. +Input File Usage: +Abaqus/CAE Usage: +Use the following options: +*CONNECTOR DAMAGE INITIATION, +CRITERION=PLASTIC MOTION, DEPENDENCIES=n +*CONNECTOR PLASTICITY +*CONNECTOR POTENTIAL +Interaction module: connector section editor: Add→Damage: Coupling: +Coupled, Initiation criterion: Plastic motion; Add→Plasticity: +Coupling: Coupled, Force Potential +Constitutive motion-based damage initiation criterion +The damage initiation criterion can be specified in terms of relative constitutive displacements/rotations +in the connector. You provide the lower (compression) limit, +, +for the constitutive displacement/rotation damage initiation values. If the motion is outside the range +specified by the two limit values, damage is initiated. The output variable CDIM can be used to monitor +the proximity to the damage initiation point. +, and the upper (tension) limit, +Defining uncoupled constitutive motion-based damage initiation +For an uncoupled motion-based damage initiation criterion, the connector relative constitutive motion in +the specified component is compared to the specified limit values. Damage is initiated when the relative +constitutive displacement/rotation in the specified component i, +, is for the first time outside the range +( +or +). +Input File Usage: +*CONNECTOR DAMAGE INITIATION, COMPONENT=component +number, CRITERION=MOTION, DEPENDENCIES=n +Abaqus/CAE Usage: +Interaction module: connector section editor: Add→Damage: Coupling: +Uncoupled, Initiation criterion: Motion +Defining coupled constitutive motion-based damage initiation +, must be specified +For a coupled motion-based damage initiation criterion, a connector potential, +to define an equivalent motion magnitude (scalar), where +is the collection of all available components +of relative motion in the connector. The equivalent motion magnitude is compared to the specified limit +values to assess damage initiation. Damage is initiated when the equivalent motion magnitude, +, is +for the first time outside the range ( +or +). +Input File Usage: +Abaqus/CAE Usage: +Use the following options: +*CONNECTOR DAMAGE INITIATION, CRITERION=MOTION, +DEPENDENCIES=n +*CONNECTOR POTENTIAL +Interaction module: connector section editor: Add→Damage: Coupling: +Coupled, Initiation criterion: Motion, Initiation Potential +Defining connector damage evolution +Connector damage evolution specifies the evolution law for the damage variable. Upon evolution, the +connector response will be degraded. The evolution of damage can be based on an energy dissipation +criterion or on relative (plastic) motions. In the motion-based criteria the damage variable, d, can be +defined as a linear, exponential, or tabular function of relative motions. +The damage evolution law can depend on temperature and field variables. See “Input syntax rules,” +Section 1.2.1, for further information about defining data as functions of temperature and field variables. +Specifying the affected components +By default (i.e., +the affected components are not specified explicitly), only the elastic/rigid or +elastic/rigid-plastic response in the connector will be damaged. The response due to friction, damping, +and stop/lock behavior will not be degraded. +For an uncoupled connector damage mechanism +(uncoupled damage initiation criterion), only the specified component of relative motion will undergo +damage. For coupled connector damage initiation, the components that will be degraded by default are +chosen as follows: +• If a force-based or constitutive motion-based damage initiation criterion is used, the intrinsic +available components (1 through 6) that ultimately contribute to the connector potential for damage +initiation will be affected. +• If a plastic motion–based damage initiation criterion is used, the intrinsic available components +that ultimately contribute to the connector potential used in the coupled plasticity definition will be +affected. +Alternatively, you can specify the available components of relative motion that will be affected +by the damage evolution law directly. In this case the entire connector response (elasto/rigid-plastic, +friction, damping, constraint forces and moments, etc.) in the affected components will be damaged. +*CONNECTOR DAMAGE EVOLUTION, AFFECTED COMPONENTS +Input File Usage: +Abaqus/CAE Usage: +The first data line identifies the component numbers that will be damaged, and +the additional data for the connector damage evolution definition begins on the +second data line. +Interaction module: connector section editor: Add→Damage: Specify +damage evolution, Evolution, Specify affected components +Defining a motion-based linear damage evolution law +The linear form of the damage evolution law is illustrated here in the context of linear elasticity, although +it can be used in any situation. Assume that the connector response is linear elastic and that after damage +initiation a linear damage evolution is desired, as illustrated in Figure 31.2.7–1. +Feff +Fc +linear elastic response +(no damage) +damage +initiation +effective response +(if damage was not present) +d Feff +actual current response in the +connector with damage +F = (1-d) Feff +damaged response +U o +U c +Uf +(1-d) E +unloading/reloading curve +Figure 31.2.7–1 Linear damage evolution law for linear elastic connector behavior. +If damage were not specified, the response would be linear elastic (a straight line passing through the +origin). Assume that damage has initiated at point I as triggered by a force-based or motion-based +criterion, for example; the corresponding constitutive motion at this point is +If the connector is +. +loaded further such that the constitutive motion increases to +, the connector force response at point C +becomes +. The response is diminished by +. If unloading occurs at point C, the +(the elastic response with no damage). Thus, +unloading curve of slope +, +the damage variable, d, stays constant at the value obtained when point C is first reached. If further +loading occurs, further damage occurs until the ultimate failure motion, +, is reached (d = 1) and the +connector component loses the ability to carry any load. Thus, one possible loading/unloading sequence +is O I C O C +is followed. As long as the constitutive motion does not exceed +when compared to the effective response +. +The linear damage evolution law defines a truly linear damaged force response only in the case +of linear elastic or rigid behavior with optional perfect plasticity. If nonlinear elasticity or plasticity +with hardening are defined for the damaged components, an approximate linear damaged response is +observed. +Defining the linear evolution law for a force-based or constitutive motion-based damage initiation +criterion +If an uncoupled damage initiation criterion is used in component i, you specify the difference between +the constitutive relative motion at ultimate failure, +, and the constitutive relative motion at damage +initiation, +, in the specified component ( +). +If a coupled damage initiation criterion is used, an equivalent constitutive relative motion, +be defined for damage evolution purposes. A connector potential definition is used to define +You specify the difference between the equivalent motion at ultimate failure, +motion at damage initiation, +). +( +, must +. +, and the equivalent +Input File Usage: +Use the following options to define a linear evolution law for an uncoupled +initiation criterion: +*CONNECTOR DAMAGE INITIATION, +COMPONENT=component number, CRITERION=FORCE or MOTION +*CONNECTOR DAMAGE EVOLUTION, TYPE=MOTION, +SOFTENING=LINEAR +Use the following options to define a linear evolution law for a coupled +initiation criterion: +*CONNECTOR DAMAGE INITIATION, +CRITERION=FORCE or MOTION +*CONNECTOR POTENTIAL +*CONNECTOR DAMAGE EVOLUTION, TYPE=MOTION, +SOFTENING=LINEAR +*CONNECTOR POTENTIAL +The second *CONNECTOR POTENTIAL option defines +Use the following input to define a linear evolution law for an uncoupled +initiation criterion: +. +Interaction module: connector section editor: Add→Damage: Coupling: +Uncoupled, Initiation criterion: Force or Motion; Specify damage +evolution, Evolution type: Motion, Evolution softening: Linear +Use the following input to define a linear evolution law for a coupled initiation +criterion: +Interaction module: connector section editor: Add→Damage: Coupling: +Coupled, Initiation criterion: Force or Motion; Specify damage +evolution, Evolution type: Motion, Evolution softening: Linear; +Initiation Potential; Evolution Potential +Abaqus/CAE Usage: +Defining the linear evolution law for a plastic motion–based damage initiation criterion +, and the associated equivalent plastic relative motion at damage initiation, +You can specify the difference between the associated equivalent plastic relative motion at ultimate +failure, +), +as a function of the mode-mix ratio, +, defined in “Connector plastic behavior,” Section 31.2.6. The +equivalent plastic relative motions are calculated from the associated plasticity definition (either coupled +or uncoupled). +( +Input File Usage: +Use the following options: +*CONNECTOR DAMAGE INITIATION, CRITERION=PLASTIC MOTION +Abaqus/CAE Usage: +*CONNECTOR DAMAGE EVOLUTION, TYPE=MOTION, +SOFTENING=LINEAR +Interaction module: connector section editor: Add→Damage: Initiation +criterion: Plastic motion; Specify damage evolution, Evolution +type: Motion, Evolution softening: Linear +Defining a motion-based exponential damage evolution law +The exponential damage evolution law is illustrated in the context of a linear elastic-plastic response +with hardening, although it can be used in any situation. The force response in a particular connector +component is shown in Figure 31.2.7–2. +plasticity with hardening +(no damage) +plasticity +onset +damage +initiation +Feff +elastic +response +Fc +d Feff +(1-d) E +actual response +with damage +unloading/reloading curve +pl +U o +pl +U c +pl +Uf +Figure 31.2.7–2 Exponential damage evolution law for linear +elastic-plastic connector behavior with hardening. +Assume that damage is initiated at point I as triggered by a plastic motion–based damage initiation +. Unloading from +criterion. If further loading occurs until point C, the response is +point C occurs along the damaged elastic line of slope +. Upon unloading/reloading, the damage +variable remains constant until point C is reached again. Further loading (beyond point C) leads to an +increasingly damaged response until the ultimate failure point, +, is reached (d = 1). The damage +variable d is given by the following equation: +The damaged response will appear to be truly exponential only if either linear elasticity or perfect +plasticity is used. An approximate exponential degradation is obtained if plasticity with hardening is +present. +You specify the difference between the relative motions at ultimate failure and at damage initiation +. The difference between the relative motions is interpreted in the same +and the exponential coefficient +way as described in “Defining a motion-based linear damage evolution law,” as follows: +• If an uncoupled force-based or constitutive motion-based damage initiation criterion is used, the +difference between the relative motions at ultimate failure and at damage initiation in the specified +component i, +, is specified. +• If a coupled force-based or constitutive motion-based damage initiation criterion is used, an +). The difference +, is specified. +equivalent relative motion is defined using a connector potential ( +between the relative motions at ultimate failure and at damage initiation, +• If a plastic motion–based damage initiation criterion is used, the difference between the equivalent +relative plastic motions at ultimate failure and at damage initiation, +, is specified. The +equivalent plastic relative motion is calculated from the associated plasticity definition. The data +can also be functions of the mode-mix ratio +. +In the first two cases the equation for the damage variable is similar to that given above for plastic +motion–based damage initiation except that (equivalent) constitutive relative motions are used instead +of equivalent relative plastic motions. +Input File Usage: +Abaqus/CAE Usage: +*CONNECTOR DAMAGE EVOLUTION, TYPE=MOTION, +SOFTENING=EXPONENTIAL +Interaction module: connector section editor: Add→Damage: +Specify damage evolution, Evolution type: Motion, +Evolution softening: Exponential +Defining a motion-based tabular damage evolution law +You can also specify the damage variable directly as a tabular function of the differences between the +relative motions at ultimate failure and the relative motions at damage initiation. The differences between +the relative motions are interpreted in the same way as described in “Defining a motion-based linear +damage evolution law,” as follows: +• If an uncoupled force-based or constitutive motion-based damage initiation criterion is used, the +differences between the constitutive relative motions at ultimate failure and at damage initiation in +the specified component i, +, are used to define the tabular data. +• If a coupled force-based or constitutive motion-based damage initiation criterion is used, an +). The differences +equivalent relative motion is defined using a connector potential ( +between the relative motions at ultimate failure and at damage initiation, +the tabular data. +, are used to define +• If a plastic motion–based damage initiation criterion is used, the differences between the equivalent +relative plastic motions at ultimate failure and at damage initiation, +, are used. The +equivalent plastic relative motion is calculated from the associated plasticity definition. The tabular +data can also be functions of the mode-mix ratio +. +Input File Usage: +Abaqus/CAE Usage: +*CONNECTOR DAMAGE EVOLUTION, TYPE=MOTION, +SOFTENING=TABULAR, DEPENDENCIES=n +Interaction module: connector section editor: Add→Damage: +Specify damage evolution, Evolution type: Motion, +Evolution softening: Tabular +Defining a damage evolution law using post-damage initiation dissipation energies +This damage evolution law is illustrated in the context of nonlinear elasticity, as shown in +Figure 31.2.7–3. +nonlinear elastic +response +Feff +Fc +damage initiation +d Feff +nonlinear elastic response +(no damage) +Gc +actual response +with damage +U o +U c +unloading/reloading curve +Figure 31.2.7–3 Post-damage initiation dissipation energy +evolution law for nonlinear elastic connector behavior. +as triggered by +Assume that damage is initiated at point I when the constitutive relative motion is +a force-based or a motion-based damage initiation criterion, for example. The response at point C will +be +. Unloading from point C occurs along the CO curve, which is the original +nonlinear elastic response curve (OE) scaled down by the ( +) factor. Damage remains constant on +the unloading/reloading curve (C O C), and it increases only if loading increases beyond point C. +Instantaneous failure can be specified upon initiation if +is specified as 0.0. In all other cases +ultimate failure (d = 1) would occur (in theory) at infinite motion since an exponential-like response +that asymptotically goes to zero is generated. Abaqus will set d = 1 when the damage dissipated energy +reaches 0.99 +. +You specify the post-damage initiation dissipated energy at ultimate failure, +. +motion–based initiation criterion is used, +can be specified as a function of the mode-mix ratio +If a plastic +. +Input File Usage: +*CONNECTOR DAMAGE EVOLUTION, TYPE=ENERGY, +DEPENDENCIES=n +Abaqus/CAE Usage: +Interaction module: connector section editor: Add→Damage: Specify +damage evolution, Evolution type: Energy +Using multiple damage mechanisms +At most three uncoupled damage mechanisms (pairs of connector damage initiation criteria and connector +damage evolution laws) can be defined for each available component of relative motion, one for each type +of initiation criterion (force, motion, and plastic motion). In addition, three coupled damage mechanisms +can be defined (one for each type of initiation criterion). Coupled and uncoupled damage definitions can +be combined; only one overall damage variable per component will be used to damage the response in a +particular available component of relative motion. Only the overall damage will be output. +Specifying the contribution of each damage mechanism +When several damage mechanisms are defined for the same connector behavior, you can specify the +contribution of each damage mechanism to the overall damage effect for a particular component of +relative motion. By default, the damage value associated with a particular mechanism will be compared +to the damage values from any other damage mechanisms defined for the connector behavior, and only +the maximum value will be considered for the overall damage. Alternatively, you can specify that the +damage values for the mechanisms associated with the connector behavior should be combined in a +multiplicative fashion to obtain the overall damage. See the last example below for an illustration. +Input File Usage: +Use the following option to specify that only the maximum damage value +associated with a particular connector behavior should contribute to the overall +damage effect: +*CONNECTOR DAMAGE EVOLUTION, DEGRADATION=MAXIMUM +Use the following option to specify that all the damage values associated with +a particular connector behavior should contribute in a multiplicative way to the +overall damage effect: +*CONNECTOR DAMAGE EVOLUTION, +DEGRADATION=MULTIPLICATIVE +Abaqus/CAE Usage: +Interaction module: connector section editor: Add→Damage: Specify +damage evolution, Evolution, Degradation: Maximum or Multiplicative +Examples +The examples that follow illustrate several methods for defining damage mechanisms. +Uncoupled damage +The following input could be used to define a simple uncoupled damage mechanism: +*CONNECTOR ELASTICITY, COMPONENT=1 +*CONNECTOR DAMAGE INITIATION, COMPONENT=1, CRITERION=FORCE +force_compress, force_tens +*CONNECTOR DAMAGE EVOLUTION, TYPE=ENERGY +0.0 +Damage will initiate when the elastic force in component 1 is either smaller than force_compress or larger +than force_tens. Only the elastic response in component 1 will be damaged. Since the dissipated energy +specified for damage evolution is 0.0, the damage evolves catastrophically instantaneously after it has +initiated. +Coupled rigid plasticity with plasticity-based damage +Referring to the spot weld in Figure 31.2.7–4 for which coupled plasticity is defined in “Connector plastic +behavior,” Section 31.2.6, a plastic motion–based damage initiation and evolution with dependencies on +the mode-mix ratio can be specified as follows: +Fn +Figure 31.2.7–4 Spot weld connection. +31.2.7–12 +*PARAMETER +=0.25 +=0.35 +=0.45 +=0.75 +=0.78 +=0.85 +*CONNECTOR DAMAGE INITIATION, CRITERION=PLASTIC MOTION +, 0.0 +, 0.5 +, 1.0 +*CONNECTOR DAMAGE EVOLUTION, TYPE=MOTION, SOFTENING=LINEAR +, 0.0 +, 0.3 +, 0.5 +, 1.0 +The equivalent plastic relative motion on the data lines is defined by the associated coupled plasticity +definition illustrated in “Connector plastic behavior,” Section 31.2.6. For the damage evolution the post- +damage-initiation equivalent plastic relative motion should be specified. The second column in all the +data lines represents the mode-mix ratios as defined in “Connector plastic behavior,” Section 31.2.6. In +this particular case the mode-mix ratio is +. The data point at 0.0 comes from a pure +“shear” experiment, and the data point at 1.0 comes from a pure “normal” experiment. Data for the +values in between come from combined “shear-normal” experiments. +Coupled rigid plasticity with force-based damage initiation and motion-based damage evolution +Referring to the spot weld in Figure 31.2.7–4 and using the derived components normal and shear +defined in “Defining derived components for connector elements” in “Connector functions for coupled +behavior,” Section 31.2.4, an alternative way to define damage in the spot weld is to use: +*PARAMETER +=2 +=0.85 +=120.0 +=115.0 +*CONNECTOR DAMAGE INITIATION, CRITERION=FORCE +, 1.0 +*CONNECTOR POTENTIAL +normal, +shear, +** +*CONNECTOR DAMAGE EVOLUTION, TYPE=MOTION, SOFTENING=EXPONENTIAL +, +*CONNECTOR POTENTIAL +** +and +Damage will be initiated when the force magnitude defined by the first connector potential definition +exceeds the specified value of 1.0. The scale factors +in the first potential definition are used in +this case to define a force magnitude that would be 1.0 at damage initiation. A motion-based exponential +decay damage evolution law is chosen. The second connector potential definition is associated with the +connector damage evolution definition and defines an equivalent motion, +, in the connection. When the +equivalent post-initiation motion, +, ultimate +failure occurs. All components (1 through 6) are affected in this case since they all ultimately contribute +to the first connector potential definition . +at damage initiation), reaches +(where +is +Elastic-plasticity with four competing damage mechanisms +This example illustrates how to specify the contributions of multiple damage mechanisms to the overall +damage effect and the components of relative motion affected by the damage evolution law. Most of the +data line entries or parameters are not given for conciseness. +** first damage mechanism: force-based damage initiation +** damage variable +*CONNECTOR DAMAGE INITIATION, COMPONENT=4, CRITERION=FORCE +*CONNECTOR DAMAGE EVOLUTION, TYPE=MOTION, SOFTENING=EXPONENTIAL, +DEGRADATION=MAXIMUM, AFFECTED COMPONENTS +4, 6 +** +** second damage mechanism: motion-based damage initiation +** damage variable +*CONNECTOR DAMAGE INITIATION, COMPONENT=4, CRITERION=MOTION +*CONNECTOR DAMAGE EVOLUTION, TYPE=MOTION, SOFTENING=LINEAR, +DEGRADATION=MULTIPLICATIVE, AFFECTED COMPONENTS +1, 2, 6 +** +** third damage mechanism: plastic motion–based damage initiation +** damage variable +*CONNECTOR DAMAGE INITIATION, COMPONENT=4, +CRITERION=PLASTIC MOTION +*CONNECTOR DAMAGE EVOLUTION, TYPE=MOTION, SOFTENING=TABULAR, +DEGRADATION=MULTIPLICATIVE, AFFECTED COMPONENTS +1, 2 +** +** fourth damage mechanism: coupled force-based damage initiation +** damage variable +*CONNECTOR DAMAGE INITIATION, CRITERION=FORCE +*CONNECTOR POTENTIAL +** using components 1, 2, 3, 4, 5, 6 +*CONNECTOR DAMAGE EVOLUTION, TYPE=ENERGY, DEGRADATION=MAXIMUM, +AFFECTED COMPONENTS +1, 3, 4, 6 +Four damage mechanisms (connector damage initiation/connector damage evolution pairs) are specified: +three uncoupled and one coupled. The first line of each damage evolution definition establishes the +components that will be damaged by the mechanism. The overall damage in a particular component +is determined by contributions from all the mechanisms that affect that component. For example, the +overall damage in component 1, +, is determined by the second, third, and fourth damage mechanisms +as follows: +use multiplicative degradation; therefore, they are multiplied first: +and +uses maximum degradation, so +is compared to +. +and the minimum +value is taken. +=0.6 (the only one increasing) while +For example, assume that at a particular time t, +, +stay the same. The overall damage variable gets +closer to the ultimate damage value faster when all three damage mechanisms are used than if we use +only the +=0.2 and at time +mechanism: +=0.3, and +=0.5, +and +while +Complete failure occurs when +reaches 0.0. +available component of relative motion. The overall +damage variables for the other components are determined as follows (based on the specified affected +components for each damage evolution law): +, where i refers to the +Maximum degradation and choice of element removal in Abaqus/Standard +You have control over how Abaqus/Standard treats connector elements with severe damage. By default, +the upper bound to the overall damage variable at a material point is +. You can reduce this +upper bound as discussed in “Controlling element deletion and maximum degradation for materials with +damage evolution” in “Section controls,” Section 27.1.4. +By default, once the overall damage variable in at least one component reaches +, the connector +elements are removed (deleted). See “Controlling element deletion and maximum degradation for +materials with damage evolution” in “Section controls,” Section 27.1.4, for details. Once removed, +connector elements offer no resistance to subsequent deformation. +Alternatively, you can specify that a connector element should remain in the model even after the +, +. In this case, once the overall damage variable reaches +overall damage variable reaches +the element stiffness remains constant at +times the undamaged stiffness. +Viscous regularization in Abaqus/Standard +Damage causes a softening response in connector elements, which often leads to convergence difficulties +in an implicit code such as Abaqus/Standard. One technique for overcoming convergence difficulties is +applying viscous regularization to the constitutive response by introducing a viscous damage variable, +, as defined by the evolution equation +where +representing the relaxation time. The damaged response of the viscous material is given as +is the damage variable evaluated in the inviscid backbone model and is the viscosity parameter +As a result of viscous regularization, the damped damage variable does not obey the specified evolution +law exactly (only the backbone damage variable does). +Input File Usage: +Abaqus/CAE Usage: +*SECTION CONTROLS, NAME=name, VISCOSITY= +*CONNECTOR SECTION, CONTROLS=name +Viscous regularization is not supported in Abaqus/CAE. +Defining connector damage behavior in linear perturbation procedures +Damage cannot be initiated and damage variables do not evolve during linear perturbation analyses. +Consequently, during a linear perturbation step damage is “frozen” in the state attained at the end of the +previous general step. +Output +The Abaqus output variables available for connectors are listed in “Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2. The +following variables are of particular interest when damage is defined in connectors: +CDMG +CDIF +CDIM +CDIP +Connector overall damage variable. +Force-based connector damage initiation variable. +In addition to the usual six +components associated with connector output variables, CDIF includes the scalar +CDIFC, which is the damage initiation criterion value associated with a coupled +force-based damage initiation criterion. +Motion-based connector damage initiation variable. CDIM includes the scalar +CDIMC, which is the damage initiation criterion value associated with a coupled +motion-based damage initiation criterion. +Plastic motion–based connector damage initiation variable. CDIP includes the +scalar CDIPC, which is the damage initiation criterion value associated with a +coupled plastic motion–based damage initiation criterion. +ALLDMD +ALLCD +Energy dissipated by damage. +Energy dissipated by viscous regularization. +31.2.8 +CONNECTOR STOPS AND LOCKS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Connectors: overview,” Section 31.1.1 +• “Connector behavior,” Section 31.2.1 +• *CONNECTOR BEHAVIOR +• *CONNECTOR LOCK +• *CONNECTOR STOP +• “Defining a stop,” Section 15.17.9 of the Abaqus/CAE User’s Manual, in the online HTML version +of this manual +• “Defining a lock,” Section 15.17.10 of the Abaqus/CAE User’s Manual, in the online HTML version +of this manual +Overview +Connector stops and locks can be: +• specified in any connector with available components of relative motion; +• used to specify contact-enforced stops in individual components of relative motion; and +• used to lock in position an available component of relative motion when a certain criterion is met. +Defining connector stops +In the physical construction of most connectors the admissible position of one body relative to the other +is limited by a certain range. In Abaqus these limits are modeled as built-in inequality constraints. You +specify the available components of relative motion for which the connector stops are to be defined and +the lower and upper limit values of the connector’s admissible range of positions in the directions of the +components of relative motion. +Input File Usage: +Use the following options to define a connector stop: +Abaqus/CAE Usage: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR STOP, COMPONENT=component number +lower limit, upper limit +Interaction module: connector section editor: Add→Stop: +Components: component or components, Lower bound: lower +limit, Upper bound: upper limit +Example +Since the shock in Figure 31.2.8–1 has finite length, contact with the ends of the shock determines the +upper and lower limit values of the distance that node b can be from node a. +extensible +range +7.5 +node 12 +1 (local orientation) +node 11 +Figure 31.2.8–1 Simplified connector model of a shock absorber. +Assume that the maximum length of the shock is 15.0 units and that the minimum length is 7.5 units. +Modify the input file presented in “Connectors: overview,” Section 31.1.1, that is associated with the +example in Figure 31.2.8–1 to include the following lines: +*CONNECTOR BEHAVIOR, NAME=sbehavior +... +*CONNECTOR STOP, COMPONENT=1 +7.5, 15.0 +Defining connector locks +Connector mechanisms may have devices designed to lock the connector in place once a desired +configuration is achieved. For example, a revolute connection might have a falling-pin mechanism that +locks the rotational motion after achieving a desired angle. A user-defined connector locking criterion +can be defined for connector elements that contain available components of relative motion. You can +select the component of relative motion for which the locking criterion is defined. +Connector locks can be used to specify connector behavior for constrained as well as available +components of relative motion. Limit values for force or moment can be specified for all components +of relative motion involved in the connection. The force/moment used in evaluating the criterion is +as computed in the output variable CTF. In addition, limit values can be specified for relative position +corresponding to the available components of relative motion. If no other behavior is specified for an +available component of relative motion, a force locking criterion will not be useful because CTF is zero. +In Abaqus/Explicit you can also specify the limiting values of velocity in the available components +as a criterion for locking. Velocity-dependent locking criteria are useful in modeling seatbelt systems in +automobiles . Moreover, the limiting values can be dependent on temperature and field variables. +Field variable dependencies can be used to model time-dependent locks. +If the locking criterion specified for the selected component of relative motion is met, either all +components lock or a single available component locks in place. By default, all components of relative +motion are locked in place upon meeting the locking criterion. In this case the connector element will +be completely kinematically locked from that point on. In dynamic analyses this locking may introduce +high accelerations. You can specify if only a selected component of relative motion is locked. +Input File Usage: +Use the following options to define a connector lock: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR LOCK, COMPONENT=component number, +LOCK=ALL or component number +Abaqus/CAE Usage: +Interaction module: connector section editor: Add→Lock: Components: +component or components, Lock: All or Specify component +Example +In the example in Figure 31.2.8–1 assume that relative rotations about the shock will lock if the force in +the local 3-direction exceeds 500.0 units of force. +*CONNECTOR BEHAVIOR, NAME=sbehavior +*CONNECTOR LOCK, COMPONENT=3, LOCK=4 +, , -500.0, 500.0 +Defining connector stops and locks in linear perturbation procedures +The status of connector locks or stops cannot change during a linear perturbation analysis; all connector +stop and connector lock definitions remain in the same status as in the base state. +Output +The Abaqus output variables available for connectors are listed in “Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2. The +following output variables are of particular interest when defining stops and locks in connectors: +CSLST +CRF +Flags for connector stops and locks. +Connector reaction forces/moments. +At a given time and for a particular component of relative motion i, the output variable CSLSTi +is 1 if the connector is actually stopped or locked in that component (stop or lock criteria are met). In +that case, the correspondent CRF output variable will most likely be nonzero and equal to the actual +force/moment required to enforce the stop or lock constraint. Since CRF is included in the calculation +of CTF, the latter will change as well when the lock or stop is active. +If the stop or lock criteria are not met at a given time for a particular component i, the output variable +CSLSTi is 0 and in most cases the corespondent reaction force CRF is zero (the only possible exception +is when a connector motion is also applied in that component). +31.2.9 +CONNECTOR FAILURE BEHAVIOR +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Connectors: overview,” Section 31.1.1 +• “Connector behavior,” Section 31.2.1 +• *CONNECTOR BEHAVIOR +• *CONNECTOR FAILURE +• “Defining failure,” Section 15.17.11 of the Abaqus/CAE User’s Manual, in the online HTML +version of this manual +Overview +Connector failure behavior: +• can be defined in any connector with available components of relative motion in Abaqus/Standard; +• can be defined in any connector in Abaqus/Explicit; +• can be used in Abaqus/Standard to fail all or specified components of relative motion if a failure +criterion is met; +• can be used in Abaqus/Explicit to fail all or specified components if a failure criterion is met; +• can be triggered if either a connector relative motion or connector force in a specified component +is outside a specified range; and +• can be replaced in most cases by the more sophisticated connector damage initiation/evolution +behavior . +Defining connector failure behavior +A typical connector might have pieces that break if a relative motion component, force, or moment +becomes too large. Abaqus provides a way to define which components of relative motion will break +and the criteria used to release these components. You can select the component of relative motion on +which the failure criterion is based. +In Abaqus/Standard connector failure can be used to specify connector behavior based on available +components of relative motion. In Abaqus/Explicit connector failure can be used to specify connector +behavior based on constrained as well as available components of relative motion. Limit values for force +or moment can be specified for all components of relative motion involved in the connection. In addition, +for connectors with available components of relative motion, limit values can be specified for the relative +positions corresponding to an available component. +In Abaqus/Standard if the failure criterion specified for the selected component of relative motion +is met, either all components of relative motion fail or a single available component fails. By default, +all components of relative motion are released upon meeting the failure criterion. The nodal force +contributions for all released components from the connector element will be removed during the +increment when the failure criterion is met. +In Abaqus/Explicit if the failure criterion specified for the selected component is met, either all +components or a single available component fails. By default, all components are released upon meeting +the failure criterion. The nodal force contributions for all released components from the connector +element will be removed during the increment when the failure criterion is met. +Input File Usage: +Use the following options to define connector failure: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR FAILURE, COMPONENT=component number, +RELEASE=ALL or component number +Abaqus/CAE Usage: +Interaction module: connector section editor: Add→Failure: Components: +component or components, Release: All or Specify component +Viscous damping in Abaqus/Standard +In Abaqus/Standard the sudden release of the failed connection may lead to convergence problems. To +avoid convergence problems, you can add viscous damping to the components. Damping forces in the +component are calculated as +is the +velocity of the failed component. Viscous damping is applied only if a selected available component of +relative motion is released. +is the user-defined damping coefficient and +, where +Input File Usage: +Abaqus/CAE Usage: +Example +Use the following options to add viscous damping to failed components in +Abaqus/Standard: +*SECTION CONTROLS, NAME=name, VISCOSITY= +*CONNECTOR SECTION, CONTROLS=name +Viscous regularization is not supported in Abaqus/CAE. +In the example in Figure 31.2.9–1 assume that the shock absorber pulls apart if the tensile force in the +shock exceeds 800.0 units of force. +extensible +range +7.5 +node 12 +1 (local orientation) +node 11 +Figure 31.2.9–1 Simplified connector model of a shock absorber. +... +*CONNECTOR BEHAVIOR, NAME=sbehavior +*CONNECTOR FAILURE, COMPONENT=1, RELEASE=ALL +, , , 800.0 +Output +The Abaqus output variables available for connectors are listed in “Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2. The +following output variables are of particular interest when defining failure in connectors: +CFAILST +ALLVD +Flags for connector failure status. +Energy dissipated by viscous damping added to failed components. +At any given time and for a particular component of relative motion i, the output variable CFAILSTi +is 1 if the connector fails in that particular component of relative motion (failure criteria are met). +If the failure criteria are not met at a given time for a particular component i, the output variable +CFAILSTi is 0. +31.2.10 +CONNECTOR UNIAXIAL BEHAVIOR +Product: Abaqus/Explicit +References +• “Connectors: overview,” Section 31.1.1 +• “Connector behavior,” Section 31.2.1 +• *CONNECTOR BEHAVIOR +• *LOADING DATA +• *UNLOADING DATA +Overview +Connector uniaxial behavior: +• can be defined in any connector with available components of relative motion by specifying the +loading and unloading behavior; +• can be specified for each available component of relative motion independently; +• can define separate response in the tensile and compressive directions; +• can exhibit nonlinear elastic behavior, damaged elastic behavior, or elastic-plastic type behavior +with permanent deformation upon complete unloading; +• can have an unloading response specified; and +• can be specified as dependent on constitutive motions in several local directions. +The local directions for each connection type (as described in “Connection-type library,” +Section 31.1.5) determine the directions in which the forces and moments act and in which the +displacements and rotations are measured. +Specifying uniaxial behavior for an available component of relative motion +Uniaxial behavior can be specified for an available component of relative motion by defining the loading +and unloading response for that component. For each component, separate loading/unloading response +data can be defined for the response in the tensile and compressive directions. The loading and unloading +response can be classified according to three available behavior types: +• nonlinear elastic behavior; +• damaged elastic behavior; and +• elastic-plastic type behavior with permanent deformation. +To define the loading response, you specify forces or moments as nonlinear functions of the +components of relative motion. These functions can also depend on temperature, field variables, and +constitutive displacements/rotations in the other component directions. See “Input syntax rules,” +Section 1.2.1, for further information about defining data as functions of temperature and field variables. +The unloading response can be defined in the following ways: +• You can specify several unloading curves that express the forces or moments as nonlinear functions +of the components of relative motion; Abaqus interpolates these curves to create an unloading curve +that passes through the point of unloading in an analysis. +• You can specify an energy dissipation factor (and a permanent deformation factor for models +with permanent deformation), from which Abaqus calculates an exponential/quadratic unloading +function. +• You can specify the forces or moments as nonlinear functions of the components of relative motion, +as well as a transition slope; the connector unloads along the specified transition slope until it +intersects the specified unloading function, at which point it unloads according to the function. +(This unloading definition is referred to as combined unloading.) +• You can specify the forces or moments as nonlinear functions of the components of relative motion; +Abaqus shifts the specified unloading function along the strain axis so that it passes through the +point of unloading in an analysis. +The behavior type that is specified for the loading response dictates the type of unloading you can define, +as summarized in Table 31.2.10–1. The different behavior types, as well as the associated loading and +unloading curves, are discussed in more detail in the sections that follow. +Table 31.2.10–1 Available unloading definitions for the uniaxial behavior types. +Unloading definition +Interpolated +Quadratic +Exponential +Combined +Shifted +Material behavior +type +Rate-dependent +elastic +Damaged elastic +Permanent +deformation +Input File Usage: +Use the following options to define connector uniaxial behavior: +*CONNECTOR BEHAVIOR, NAME=name +*CONNECTOR UNIAXIAL BEHAVIOR, COMPONENT=component number +*LOADING DATA, DIRECTION=deformation direction, +TYPE=behavior type +data lines to define loading data +*UNLOADING DATA +data lines to define unloading data +Defining the deformation direction +The loading/unloading data can be defined separately for tension and compression by specifying the +deformation direction. If the deformation direction is defined (tension or compression), the tabular values +defining tensile or compressive behavior should be specified with positive values of forces/moments and +displacements/rotations in the specified component of relative motion and the loading data must start at +the origin. If the behavior is not defined in a loading direction, the force response will be zero in that +direction (the connector has no resistance in that direction). +If the deformation direction is not defined, the data apply to both tension and compression. However, +the behavior is then considered to be nonlinear elastic and no damage or permanent deformation can be +specified. The response data will be considered to be symmetric about the origin if either tensile or +compressive data are omitted. +Input File Usage: +Use the following option to define tensile behavior: +*LOADING DATA, DIRECTION=TENSION +Use the following option to define compressive behavior: +*LOADING DATA, DIRECTION=COMPRESSION +Use the following option to define both tensile compressive behavior in a single +table: +*LOADING DATA +Behavior that depends on relative positions or motions in multiple component directions +By default, the loading and unloading functions depend only on the displacement or rotation in the +direction of the component of relative motion specified for the connector uniaxial behavior definition +. However, it is also possible to define loading and +unloading functions that depend on the constitutive displacements and rotations in multiple component +directions. +Input File Usage: +Use the following option to define connector uniaxial behavior that depends on +the relative displacements and/or rotations in several component directions: +*LOADING DATA, INDEPENDENT COMPONENTS=CONSTITUTIVE +MOTION +Defining rate-independent nonlinear elastic behavior +When the loading response is rate independent, the unloading response is also rate independent and +occurs along the same user-specified loading curve as illustrated in Figure 31.2.10–1. An unloading +curve does not need to be specified. +Loading curve +Figure 31.2.10–1 Nonlinear elastic loading. +Input File Usage: +*LOADING DATA, TYPE=ELASTIC +Defining rate-dependent behavior +The rate-dependent models require the specification of force-displacement curves at different rates of +deformation to describe both loading and unloading behavior. If unloading behavior is not specified, +the unloading occurs along the loading curve with the smallest rate of deformation. As the rate of +deformation changes, the response is obtained by interpolation of the specified loading/unloading data. +Unphysical jumps in the forces due to sudden changes in the rate of deformation are prevented using a +technique based on viscoplastic regularization. This technique also helps model relaxation effects in a +very simplistic manner, with the relaxation time given as +are +material parameters and +is a linear viscosity parameter that controls the relaxation +time when +is a nonlinear viscosity parameter +that controls the relaxation time at higher values of +. The smaller this value, the shorter the relaxation +time. +controls the sensitivity of the relaxation speed to the stretch in the component of relative motion. +Suggested values of these parameters are +. Figure 31.2.10–2 +, and +illustrates the loading/unloading behavior as the connector is loaded at a rate +and then unloaded at a +rate +. Small values of this parameter should be used. +is the stretch. +, where +, and +, +, +. +Figure 31.2.10–3 shows the loading/unloading response of a connector element for two different +. The larger the relaxation time, the longer it takes to achieve the +relaxation times +specified loading/unloading response for the applied deformation rate. +and with +uu +uu +uu +Figure 31.2.10–2 Rate-dependent loading/unloading. +Input File Usage: +Figure 31.2.10–3 Rate-dependent loading/unloading. +Use the following options when the unloading is also rate dependent: +*LOADING DATA, TYPE=ELASTIC, RATE DEPENDENT +*UNLOADING DATA, DEFINITION=INTERPOLATED CURVE, +RATE DEPENDENT +Use the following options when the unloading is rate independent: +*LOADING DATA, TYPE=ELASTIC, RATE DEPENDENT +*UNLOADING DATA, DEFINITION=INTERPOLATED CURVE +Defining models with damage +The damage models dissipate energy upon unloading, and there is no permanent deformation upon +complete unloading. The unloading behavior controls the amount of energy dissipated by damage +mechanisms and can be specified in one of the following ways: +• an analytical unloading curve (exponential/quadratic); +• an unloading curve interpolated from multiple user-specified unloading curves; or +• unloading along a transition unloading curve (constant slope specified by user) to the user-specified +unloading curve (combined unloading). +For an overview of the different available behaviors, see “Specifying uniaxial behavior for an available +component of relative motion” above. The various unloading types are discussed in the sections that +follow. +Defining onset of damage +You can specify the onset of damage by defining the displacement below which unloading occurs along +the loading curve. +Input File Usage: +*LOADING DATA, TYPE=DAMAGE, DAMAGE ONSET=value +Specifying exponential/quadratic unloading +The damage model in Figure 31.2.10–4 is based on an analytical unloading curve that is derived from +an energy dissipation factor, +(fraction of energy that is dissipated at any displacement level). As the +connector is loaded, the force follows the path given by the loading curve. If the connector is unloaded +(for example, at point B), the force follows the unloading curve +. Reloading after unloading follows +the unloading curve +, +after which the loading path follows the loading curve. The arrows shown in Figure 31.2.10–4 illustrate +the loading/unloading paths of this model. +until the loading is such that the displacement becomes greater than +The unloading response follows the loading curve when the calculated unloading curve lies above +the loading curve to prevent energy generation and follows a zero force response when the unloading +curve yields a negative response. In such cases the dissipated energy will be less than the value specified +by the energy dissipation factor. +Input File Usage: +Use the following option to define quadratic unloading behavior: +*UNLOADING DATA, DEFINITION=QUADRATIC +Use the following option to define exponential unloading behavior: +*UNLOADING DATA, DEFINITION=EXPONENTIAL +Specifying interpolated curve unloading +The damage model in Figure 31.2.10–5 illustrates an interpolated unloading response based on multiple +unloading curves that intersect the primary loading curve at increasing values of forces/displacements. +You can specify as many unloading curves as are necessary to define the unloading response. Each +Primary loading curve +exponential/quadratic +unloading +Umax +Figure 31.2.10–4 Exponential/quadratic unloading. +unloading curve always starts at point O, the point of zero force and zero displacements, since the damage +models do not allow any permanent deformation. The unloading curves are stored in normalized form +so that they intersect the loading curve at a unit force for a unit displacement, and the interpolation +occurs between these normalized curves. If unloading occurs from a maximum displacement for which +an unloading curve is not specified, the unloading is interpolated from neighboring unloading curves. As +the connector is loaded, the force follows the path given by the loading curve. If the connector is unloaded +(for example, at point B), the force follows the unloading curve +. Reloading after unloading follows +the unloading path +, after +which the loading path follows the loading curve. +until the loading is such that the displacement becomes greater than +Primary loading curve +Unloading curves +Umax +Figure 31.2.10–5 +Interpolated curve unloading +If the loading curve depends on the constitutive displacements/rotations in several component +directions, the unloading curves also depend on the same component directions. The unloading curves +also have the same temperature and field variable dependencies as the loading curve. +Input File Usage: +*UNLOADING DATA, DEFINITION=INTERPOLATED CURVE +Specifying combined unloading +in addition to the loading +As illustrated in Figure 31.2.10–6, you can specify an unloading curve +curve +as well as a constant transition slope that connects the loading curve to the unloading +curve. As the connector is loaded, the force follows the path given by the loading curve. If the connector +is unloaded (for example, at point B), the force follows the unloading curve +is +defined by the constant transition slope, and +lies on the specified unloading curve. Reloading after +unloading follows the unloading path +until the loading is such that the displacement becomes +greater than +, after which the loading path follows the loading curve. +. The path +Primary loading curve +transition curve +unloading curve +Umax +Figure 31.2.10–6 Combined unloading. +If the loading curve depends on the constitutive displacements/rotations in several component +directions, the unloading curve also depends on the same component directions. The unloading curve +also has the same temperature and field variable dependencies as the loading curve. +Input File Usage: +*UNLOADING DATA, DEFINITION=COMBINED +Defining models with permanent deformation +These models dissipate energy upon unloading and exhibit permanent deformation upon complete +unloading. The unloading behavior controls the amount of energy dissipated as well as the amount of +permanent deformation. The unloading behavior can be specified in one of the following ways: +• an analytical unloading curve (exponential/quadratic); +• an unloading curve interpolated from multiple user-specified unloading curves; or +• an unloading curve obtained by shifting the user-specified unloading curve to the point of unloading. +For an overview of the different available behaviors, see “Specifying uniaxial behavior for an available +component of relative motion” above. The various unloading types are discussed in the sections that +follow. +Defining the onset of permanent deformation +By default, the onset of yield will be obtained as soon as the slope of the loading curve decreases by 10% +from the maximum slope recorded up to that point while traversing along the loading curve. To override +the default method of determining the onset of yield, you can specify either a value for the decrease +in slope of the loading curve other than the default value of 10% (slope drop = 0.1) or by defining the +displacement below which unloading occurs along the loading curve. If a slope drop is specified, the +onset of yield will be obtained as soon as the slope of the loading curve decreases by the specified factor +from the maximum slope recorded up to that point. +Input File Usage: +Use the following options to specify the onset of yield by defining the +displacement below which unloading occurs along the loading curve: +*LOADING DATA, TYPE=PERMANENT DEFORMATION, +YIELD ONSET=value +Use the following options to specify the onset of yield by defining a slope drop +for the loading curve: +*LOADING DATA, TYPE=PERMANENT DEFORMATION, +SLOPE DROP=value +Specifying exponential/quadratic unloading +The model in Figure 31.2.10–7 illustrates an analytical unloading curve that is derived based on an energy +dissipation factor, +(fraction of energy that is dissipated at any displacement level) and a permanent +deformation factor, +. As the connector is loaded, the force follows the path given by the loading curve. +If the connector is unloaded (for example, at point B), the force follows the unloading curve +. The +point D corresponds to the permanent deformation, +. Reloading after unloading follows the +unloading curve +, after +which the loading path follows the loading curve. The arrows shown in Figure 31.2.10–7 illustrate the +loading/unloading paths of this model. +until the loading is such that the displacement becomes greater than +The unloading response follows the loading curve when the calculated unloading curve lies above +the loading curve to prevent energy generation and follows a zero force response when the unloading +curve yields a negative response. In such cases the dissipated energy will be less than the value specified +by the energy dissipation factor. +Input File Usage: +Use the following option to define quadratic unloading behavior: +*UNLOADING DATA, DEFINITION=QUADRATIC +Use the following option to define exponential unloading behavior: +*UNLOADING DATA, DEFINITION=EXPONENTIAL +Primary loading curve +Umax +DpUmax +exponential/quadratic +unloading +Figure 31.2.10–7 Exponential/quadratic unloading. +Specifying interpolated curve unloading +The model in Figure 31.2.10–8 illustrates an interpolated unloading response based on multiple unloading +curves that intersect the primary loading curve at increasing values of forces/displacements. You can +specify as many unloading curves as are necessary to define the unloading response. The first point of +each unloading curve defines the permanent deformation if the connector is completely unloaded. The +unloading curves are stored in normalized form so that they intersect the loading curve at a unit force for +a unit displacement, and the interpolation occurs between these normalized curves. If unloading occurs +from a maximum displacement for which an unloading curve is not specified, the unloading curve is +interpolated from neighboring unloading curves. As the connector is loaded, the force follows the path +given by the loading curve. If the connector is unloaded (for example, at point B), the force follows the +unloading curve +until the loading is +such that the displacement becomes greater than +, after which the loading path follows the loading +curve. +. Reloading after unloading follows the unloading path +If the loading curve depends on the constitutive displacements/rotations in several component +directions, the unloading curves also depends on the same component directions. The unloading curve +also has the same temperature and field variable dependencies as the loading curve. +Input File Usage: +*UNLOADING DATA, DEFINITION=INTERPOLATED CURVE +Specifying shifted curve unloading +You can specify an unloading curve passing through the origin in addition to the loading curve. The +actual unloading curve is obtained by horizontally shifting the user-specified unloading curve to pass +through the point of unloading as shown in Figure 31.2.10–9. The permanent deformation upon complete +unloading is the horizontal shift applied to the unloading curve. +Primary loading curve +Unloading curves +Umax +Figure 31.2.10–8 Interpolated curve unloading. +unloading curve +Primary loading curve +shifted unloading curve +Umax +Figure 31.2.10–9 Shifted curve unloading. +If the loading curve depends on the constitutive displacements/rotations in several component +directions, the unloading curve also depends on the same component directions. The unloading curve +also has the same temperature and field variable dependencies as the loading curve. +*UNLOADING DATA, DEFINITION=SHIFTED CURVE +Input File Usage: +Using different uniaxial models in tension and compression +When appropriate, different uniaxial behavior models can be used in tension and compression. For +example, a model with permanent deformation and exponential unloading in tension can be combined +with a nonlinear elastic model in compression . +Primary loading curve +unloading +nonlinear +elastic +Figure 31.2.10–10 Different uniaxial models in tension and compression. +Output +The Abaqus output variables available for connectors are listed in “Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2. The +following output variables are of particular interest when defining uniaxial behavior in connectors: +CU +CUF +Connector relative displacements/rotations. +Connector uniaxial forces/moments. +32. +Special-Purpose Elements +32.1 +32.2 +32.3 +32.4 +32.5 +32.6 +32.7 +32.8 +32.9 +32.10 +32.11 +32.12 +32.13 +32.14 +32.15 +Spring elements +Dashpot elements +Flexible joint elements +Distributing coupling elements +Cohesive elements +Gasket elements +Surface elements +Tube support elements +Line spring elements +Elastic-plastic joints +Drag chain elements +Pipe-soil elements +Acoustic interface elements +Eulerian elements +32.1 +Spring elements +• “Springs,” Section 32.1.1 +• “Spring element library,” Section 32.1.2 +32.1.1 +SPRINGS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Spring element library,” Section 32.1.2 +• *SPRING +• “Defining springs and dashpots,” Section 37.1 of the Abaqus/CAE User’s Manual +Overview +Spring elements: +• can couple a force with a relative displacement; +• in Abaqus/Standard can couple a moment with a relative rotation; +• can be linear or nonlinear; +• if linear, can be dependent on frequency in direct-solution steady-state dynamic analysis; +• can be dependent on temperature and field variables; and +• can be used to assign a structural damping factor to form the imaginary part of spring stiffness. +The terms “force” and “displacement” are used throughout the description of spring elements. When +the spring is associated with displacement degrees of freedom, these variables are the force and relative +displacement in the spring. If the springs are associated with rotational degrees of freedom, they are +torsional springs; these variables will then be the moment transmitted by the spring and the relative +rotation across the spring. +Viscoelastic spring behavior can be modeled in Abaqus/Standard by combining frequency- +dependent springs and frequency-dependent dashpots. +Typical applications +Spring elements are used to model actual physical springs as well as idealizations of axial or torsional +components. They can also model restraints to prevent rigid body motion. +They are also used to represent structural dampers by specifying structural damping factors to form +the imaginary part of the spring stiffness. +Choosing an appropriate element +SPRING1 and SPRING2 elements are available only in Abaqus/Standard. SPRING1 is between a node +and ground, acting in a fixed direction. SPRING2 is between two nodes, acting in a fixed direction. +The SPRINGA element is available in both Abaqus/Standard and Abaqus/Explicit. SPRINGA acts +between two nodes, with its line of action being the line joining the two nodes, so that this line of action +can rotate in large-displacement analysis. +The spring behavior can be linear or nonlinear in any of the spring elements in Abaqus. +Element types SPRING1 and SPRING2 can be associated with displacement or rotational degrees +of freedom (in the latter case, as torsional springs). However, the use of torsional springs in large- +displacement analysis requires careful consideration of the definition of total rotation at a node; therefore, +connector elements (“Connectors: overview,” Section 31.1.1) are usually a better approach to providing +torsional springs for large-displacement cases. +Input File Usage: +Use the following option to specify a spring element between a node and +ground, acting in a fixed direction: +Abaqus/CAE Usage: +*ELEMENT, TYPE=SPRING1 +Use the following option to specify a spring element between two nodes, acting +in a fixed direction: +*ELEMENT, TYPE=SPRING2 +Use the following option to specify a spring element between two nodes with +its line of action being the line joining the two nodes: +*ELEMENT, TYPE=SPRINGA +Property or Interaction module: Special→Springs/Dashpots→Create, +then select one of the following: +Connect points to ground: select points: toggle on Spring stiffness +(equivalent to SPRING1) +Connect two points: select points: Axis: Specify fixed direction: +toggle on Spring stiffness +(equivalent to SPRING2) +Connect two points: select points: Axis: Follow line of action: +toggle on Spring stiffness +(equivalent to SPRINGA) +Stability considerations in Abaqus/Explicit +A SPRINGA element introduces a stiffness between two degrees of freedom without introducing an +associated mass. In an explicit dynamic procedure this represents an unconditionally unstable element. +The nodes to which the spring is attached must have some mass contribution from adjacent elements; if +this condition is not satisfied, Abaqus/Explicit will issue an error message. If the spring is not too stiff +(relative to the stiffness of the adjacent elements), the stable time increment determined by the explicit +dynamics procedure (“Explicit dynamic analysis,” Section 6.3.3) will suffice to ensure stability of the +calculations. +Abaqus/Explicit does not use the springs in the determination of the stable time increment. During +the data check phase of the analysis, Abaqus/Explicit computes the minimum of the stable time increment +for all the elements in the mesh except the spring elements. The program then uses this minimum stable +time increment and the stiffness of each of the springs to determine the mass required for each spring +to give the same stable time increment. If this mass is too large compared to the mass of the model, +Abaqus/Explicit will issue an error message that the spring is too stiff compared to the model definition. +Relative displacement definition +The relative displacement definition depends on the element type. +SPRING1 elements +The relative displacement across a SPRING1 element is the ith component of displacement of the spring’s +node: +where i is defined as described below and can be in a local direction . +SPRING2 elements +The relative displacement across a SPRING2 element is the difference between the ith component of +displacement of the spring’s first node and the jth component of displacement of the spring’s second +node: +where i and j are defined as described below and can be in local directions . +It is important to understand how the SPRING2 element will behave according to the above relative +displacement equation since the element can produce counterintuitive results. For example, a SPRING2 +element set up in the following way will be a “compressive” spring: +If the nodes displace so that +, the spring appears to be in compression, while the +force in the SPRING2 element is positive. To obtain a “tensile” spring, the SPRING2 element should be +set up in the following way: +and +SPRINGA elements +For geometrically linear analysis the relative displacement is measured along the direction of the +SPRINGA element in the reference configuration: +where +second node. +is the reference position of the first node of the spring and +is the reference position of its +For geometrically nonlinear analysis the relative displacement across a SPRINGA element is the +change in length in the spring between the initial and the current configuration: +where +configuration. Here +is the current length of the spring and +is the value of l in the initial +and +are the current positions of the nodes of the spring. +In either case the force in a SPRINGA element is positive in tension. +Defining spring behavior +The spring behavior can be linear or nonlinear. In either case you must associate the spring behavior +with a region of your model. +Input File Usage: +*SPRING, ELSET=name +where the ELSET parameter refers to a set of spring elements. +Abaqus/CAE Usage: +Property or Interaction module: Special→Springs/Dashpots→Create: +select connectivity type: select points +Defining linear spring behavior +You define linear spring behavior by specifying a constant spring stiffness (force per relative +displacement). +The spring stiffness can depend on temperature and field variables. See “Input syntax rules,” +Section 1.2.1, for further information about defining data as functions of temperature and independent +field variables. +For direct-solution steady-state dynamic analysis the spring stiffness can depend on frequency, as +well as on temperature and field variables. If a frequency-dependent spring stiffness is specified for any +other analysis procedure in Abaqus/Standard, the data for the lowest frequency given will be used. +Input File Usage: +*SPRING, DEPENDENCIES=n +first data line +spring stiffness, frequency, temperature, field variable 1, etc. +... +Abaqus/CAE Usage: +Property or Interaction module: Special→Springs/Dashpots→Create: +select connectivity type: select points: Property: Spring stiffness: +spring stiffness +Defining the spring stiffness as a function of frequency, temperature, and +field variables is not supported in Abaqus/CAE when you define springs as +engineering features; instead, you can define connectors that have spring-like +elastic behavior . +Defining nonlinear spring behavior +You define nonlinear spring behavior by giving pairs of force–relative displacement values. These values +should be given in ascending order of relative displacement and should be provided over a sufficiently +wide range of relative displacement values so that the behavior is defined correctly. Abaqus assumes that +the force remains constant (which results in zero stiffness) outside the range given . +Force, F +F(0) +F1 +Continuation assumed +if u < u1 +Continuation assumed +if u > u4 +Displacement, u +Figure 32.1.1–1 Nonlinear spring force–relative displacement relationship. +Initial forces in nonlinear springs should be defined as part of the +relationship by giving a +nonzero force, +, at zero relative displacement. +The spring stiffness can depend on temperature and field variables. See “Input syntax rules,” +Section 1.2.1, for further information about defining data as functions of temperature and independent +field variables. +Abaqus/Explicit will regularize the data into tables that are defined in terms of even intervals of the +independent variables. In some cases where the force is defined at uneven intervals of the independent +variable (relative displacement) and the range of the independent variable is large compared to the +smallest interval, Abaqus/Explicit may fail to obtain an accurate regularization of your data in a +reasonable number of intervals. In this case the program will stop after all data are processed with an +error message that you must redefine the material data. See “Material data definition,” Section 21.1.2, +for a more detailed discussion of data regularization. +Input File Usage: +Abaqus/CAE Usage: +*SPRING, NONLINEAR, DEPENDENCIES=n +first data line +force, relative displacement, temperature, field variable 1, etc. +... +Defining nonlinear spring behavior is not supported in Abaqus/CAE when +you define springs as engineering features; instead, you can define connectors +that have spring-like elastic behavior . +Defining the direction of action for SPRING1 and SPRING2 elements +You define the direction of action for SPRING1 and SPRING2 elements by giving the degree of freedom +at each node of the element. This degree of freedom may be in a local coordinate system (“Orientations,” +Section 2.2.5). The local system is assumed to be fixed: even in large-displacement analysis SPRING1 +and SPRING2 elements act in a fixed direction throughout the analysis. +Input File Usage: +*SPRING, ORIENTATION=name +dof at node 1, dof at node 2 +Abaqus/CAE Usage: +Property or Interaction module: Special→Springs/Dashpots→Create, +then select one of the following: +Connect points to ground: select points: Orientation: Edit: +select orientation +Connect two points: select points: Axis: Specify fixed direction: +Orientation: Edit: select orientation +Defining linear spring behavior with complex stiffness +Springs can be used to simulate structural dampers that contribute to the imaginary part of the element +stiffness forming an elemental structural damping matrix. You specify both the real part of the spring +stiffness for particular degrees of freedom and the structural damping factor, s. The imaginary part of +the spring stiffness is calculated as +and represents structural damping. These data can be frequency +dependent. +Input File Usage: +*SPRING, COMPLEX STIFFNESS +first data line +real spring stiffness, structural damping factor, frequency +Abaqus/CAE Usage: +Linear spring behavior with complex stiffness is not supported in Abaqus/CAE. +32.1.2 +SPRING ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Springs,” Section 32.1.1 +• *SPRING +Overview +This section provides a reference to the spring elements available in Abaqus/Standard and +Abaqus/Explicit. +Element types +SPRINGA +SPRING1(S) +SPRING2(S) +Axial spring between two nodes, whose line of action is the line joining the two nodes. +This line of action may rotate in large-displacement analysis. +Spring between a node and ground, acting in a fixed direction +Spring between two nodes, acting in a fixed direction +Active degrees of freedom +SPRINGA: 1, 2, 3. The translational degree of freedom in the 3-direction is not activated in an +Abaqus/Standard analysis if both nodes of the element are connected to two-dimensional entities such +as two-dimensional analytical rigid surfaces, two-dimensional beam elements, etc. +SPRING1 or SPRING2: 1, 2, 3, 4, 5, or 6. If you specify a local orientation for the spring, these are +local degrees of freedom. Otherwise, these are global degrees of freedom. +Additional solution variables +None. +Nodal coordinates required +SPRINGA: X, Y, Z. These coordinates are used in the calculation of the action of the element. +SPRING1 or SPRING2: None. The element nodes do not need to have coordinates defined since the +action associated with these elements is defined by specifying the degrees of freedom involved. +Element property definition +Input File Usage: +Abaqus/CAE Usage: +*SPRING +Property or Interaction module: Special→Springs/Dashpots→Create +Element-based loading +None. +Element output +S11 +E11 +Force in the spring. +Relative displacement across the spring. +Node ordering on elements +SPRINGA +SPRING2 +SPRING1 +32.2 +Dashpot elements +• “Dashpots,” Section 32.2.1 +• “Dashpot element library,” Section 32.2.2 +32.2.1 +DASHPOTS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Dashpot element library,” Section 32.2.2 +• *DASHPOT +• “Defining springs and dashpots,” Section 37.1 of the Abaqus/CAE User’s Manual +Overview +Dashpot elements: +• can couple a force with a relative velocity; +• in Abaqus/Standard can couple a moment with a relative angular velocity; +• can be linear or nonlinear; +• if linear, can be dependent on frequency in direct-solution steady-state dynamic analysis; +• can be dependent on temperature and field variables; and +• can be used in any stress analysis procedure. +The terms “force” and “velocity” are used throughout the description of dashpot elements. When +the dashpot is associated with displacement degrees of freedom, these variables are the force and relative +velocity in the dashpot. +If the dashpots are associated with rotational degrees of freedom, they are +torsional dashpots; these variables will then be the moment transmitted by the dashpot and the relative +angular velocity across the dashpot. +In dynamic analysis the velocities are obtained as part of the integration operator; in quasi-static +analysis in Abaqus/Standard the velocities are obtained by dividing the displacement increments by the +time increment. +Typical applications +Dashpots are used to model relative velocity-dependent force or torsional resistance. They can also +provide viscous energy dissipation mechanisms. +Dashpots are often useful in unstable, nonlinear, static analyses where the modified Riks algorithm +is not appropriate and where the automatic time stepping algorithm is used because sudden +shifts in configuration can be controlled by the forces that arise in the dashpots. +In such cases the +magnitude of the damping must be chosen in conjunction with the time period so that enough damping is +available to control such difficulties but the damping forces are negligible when a stable static response is +obtained. See also the contact damping available with contact elements in Abaqus/Standard . +Choosing an appropriate element +DASHPOT1 and DASHPOT2 elements are available only in Abaqus/Standard. DASHPOT1 is between +a specified degree of freedom and ground. DASHPOT2 is between two specified degrees of freedom. +The DASHPOTA element is available in both Abaqus/Standard and Abaqus/Explicit. DASHPOTA +is between two nodes with its line of action being the line joining the two nodes. +The dashpot behavior can be linear or nonlinear in any of these elements. +Input File Usage: +Use the following option to specify a dashpot element between a specified +degree of freedom and ground: +Abaqus/CAE Usage: +*ELEMENT, TYPE=DASHPOT1 +Use the following option to specify a dashpot element between two degrees of +freedom: +*ELEMENT, TYPE=DASHPOT2 +Use the following option to specify a dashpot element between two nodes with +its line of action being the line joining the two nodes: +*ELEMENT, TYPE=DASHPOTA +Property or Interaction module: Special→Springs/Dashpots→Create, +then select one of the following: +Connect points to ground: select points: toggle on Dashpot coefficient +(equivalent to DASHPOT1) +Connect two points: select points: Axis: Specify fixed direction: +toggle on Dashpot coefficient +(equivalent to DASHPOT2) +Connect two points: select points: Axis: Follow line of action: +toggle on Dashpot coefficient +(equivalent to DASHPOTA) +Stability considerations in Abaqus/Explicit +Abaqus/Explicit does not take dashpots into account when determining the stable time step; therefore, +care should be taken when introducing dashpots into the mesh. +A DASHPOTA element introduces a damping force between two degrees of freedom without +introducing any stiffness between these degrees of freedom and without introducing any mass at the +nodes. This can cause a reduction in the stable time increment. For example, consider a simple system +of a truss element and a dashpot element as shown in Figure 32.2.1–1. +The dynamic equation for this system is +or +⇒ +k = +EA +m = +ρAL +Figure 32.2.1–1 A simple truss and dashpot system. +where +and +The stable time increment for the spring-dashpot system is +As the dashpot coefficient c is increased, the stable time increment, +, will be reduced. +To avoid this reduction in the stable time increment, dashpots should be used in parallel with spring +or truss elements, where the stiffness of the spring or truss elements is chosen so that the stable time +increment of the dashpot and spring or truss is larger than the stable critical time increment that is +calculated by Abaqus/Explicit. If this requires springs or trusses that have unacceptable forces, specify +the time increment size directly for the step . +Relative velocity definition +The relative velocity definition depends on the element type. +DASHPOT1 elements +The relative velocity across a DASHPOT1 element is the ith component of velocity of the dashpot’s +node: +where i is defined as described below and can be in a local direction . +DASHPOT2 elements +The relative velocity across a DASHPOT2 element is the difference between the ith component of +velocity at the dashpot’s first node and the jth component of velocity of the dashpot’s second node: +where i and j are defined as described below and can be in local directions . +It is important to understand how the DASHPOT2 element will behave according to the above +relative displacement equation since the element can produce counterintuitive results. For example, a +DASHPOT2 element set up in the following way will be a “compressive” dashpot: +If the nodes have velocities such that +, the dashpot is compressed while the force +and +in the dashpot is positive. To obtain a “tensile” dashpot, the DASHPOT2 element should be set up in the +following way: +DASHPOTA elements +The relative velocity across a DASHPOTA element is the difference between the velocity of the dashpot’s +second node and the dashpot’s first node, taken in the direction of the current axis of the dashpot. +For geometrically linear analysis, +where +second node, and +is the reference position of the dashpot’s first node, +is the reference length of the dashpot. +For geometrically nonlinear analysis, +is the reference position of the dashpot’s +where +second node, and l is the current length of the dashpot. +is the current position of the dashpot’s first node, +is the current position of the dashpot’s +In either case the force in a DASHPOTA element is positive if the dashpot is extending. +Defining dashpot behavior +The dashpot behavior can be linear or nonlinear. In either case you must associate the dashpot behavior +with a region of your model. +Input File Usage: +*DASHPOT, ELSET=name +where the ELSET parameter refers to a set of dashpot elements. +Abaqus/CAE Usage: +Property or Interaction module: Special→Springs/Dashpots→Create: +select connectivity type: select points +Linear dashpot behavior +You define linear dashpot behavior by specifying a constant dashpot coefficient (force per relative +velocity). +The dashpot coefficient can depend on temperature and field variables. See “Input syntax rules,” +Section 1.2.1, for further information about defining data as functions of temperature and independent +field variables. +For direct-solution steady-state dynamic analysis the dashpot coefficient can depend on frequency, +as well as on temperature and field variables. If a frequency-dependent dashpot coefficient is specified +for any other analysis procedure in Abaqus/Standard, the data for the lowest frequency given will be +used. +Input File Usage: +Abaqus/CAE Usage: +*DASHPOT, DEPENDENCIES=n +first data line +dashpot coefficient, frequency, temperature, field variable 1, etc. +... +Property or Interaction module: Special→Springs/Dashpots→Create: +select connectivity type: select points: Property: Dashpot coefficient: +dashpot coefficient +Defining the dashpot coefficient as a function of frequency, temperature, and +field variables is not supported in Abaqus/CAE when you define dashpots as +engineering features; instead, you can define connectors that have dashpot-like +damping behavior . +Nonlinear dashpot behavior +You define nonlinear dashpot behavior by giving pairs of force–relative velocity values. These values +should be given in ascending order of relative velocity and should be provided over a sufficiently wide +range of relative velocity values so that the behavior is defined correctly. Abaqus assumes that the force +remains constant outside the range given . In addition, the curve should pass through +the origin. That is, the force should be zero at zero relative velocity. +Force, F +F1 +Continuation assumed +if v < v1 +Continuation assumed +if v > v4 +Relative velocity, v +Figure 32.2.1–2 Nonlinear dashpot force-relative velocity relationship. +The dashpot coefficient can depend on temperature and field variables. See “Input syntax rules,” +Section 1.2.1, for further information about defining data as functions of temperature and independent +field variables. +Abaqus/Explicit will regularize the data into tables that are defined in terms of even intervals of the +independent variables. In some cases where the force is defined at uneven intervals of the independent +variable (relative velocity) and the range of the independent variable is large compared to the smallest +interval, Abaqus/Explicit may fail to obtain an accurate regularization of your data in a reasonable +number of intervals. In this case the program will stop after all data are processed with an error message +that you must redefine the material data. See “Material data definition,” Section 21.1.2, for a more +detailed discussion of data regularization. +Input File Usage: +Abaqus/CAE Usage: +*DASHPOT, NONLINEAR, DEPENDENCIES=n +first data line +force, relative velocity, temperature, field variable 1, etc. +... +Defining nonlinear dashpot behavior is not supported in Abaqus/CAE when +you define dashpots as engineering features; instead, you can define connectors +that have dashpot-like damping behavior . +Defining the direction of action for DASHPOT1 and DASHPOT2 elements +You define the direction of action for DASHPOT1 and DASHPOT2 elements by giving the degree of +freedom at each node of the element. This degree of freedom may be in a local coordinate system +(“Orientations,” Section 2.2.5). This local system is assumed to be fixed: even in large-displacement +analysis DASHPOT1 and DASHPOT2 elements act in a fixed direction throughout the analysis. +Input File Usage: +*DASHPOT, ORIENTATION=name +dof at node 1, dof at node 2 +Abaqus/CAE Usage: +Property or Interaction module: Special→Springs/Dashpots→Create, +then select one of the following: +Connect points to ground: select points: Orientation: Edit: +select orientation +Connect two points: select points: Axis: Specify fixed direction: +Orientation: Edit: select orientation +Dashpots within substructures +Dashpots cannot be used within substructures. You can define Rayleigh damping within the substructure +definition or on the usage level to create damping within a substructure; see “Defining substructure +damping” in “Using substructures,” Section 10.1.1, for more information. +32.2.2 +DASHPOT ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Dashpots,” Section 32.2.1 +• *DASHPOT +Overview +This section provides a reference to the dashpot elements available in Abaqus/Standard and +Abaqus/Explicit. +Element types +DASHPOTA +Axial dashpot between two nodes, whose line of action is the line joining the two nodes +DASHPOT1(S) Dashpot between a node and ground, acting in a fixed direction +DASHPOT2(S) Dashpot between two nodes, acting in a fixed direction +Active degrees of freedom +DASHPOTA: 1, 2, 3. The translational degree of freedom in the 3-direction is not activated in an +Abaqus/Standard analysis if both nodes of the element are connected to two-dimensional entities such +as two-dimensional analytical rigid surfaces, two-dimensional beam elements, etc. +DASHPOT1 or DASHPOT2: 1, 2, 3, 4, 5, or 6. If you specify a local orientation for the dashpot, these +are local degrees of freedom. Otherwise, these are global degrees of freedom. +Additional solution variables +None. +Nodal coordinates required +DASHPOTA: X, Y, Z. These coordinates are used in the calculation of the action of the element. +DASHPOT1 or DASHPOT2: None. The element nodes do not need to have coordinates defined since +the action associated with these elements is defined by specifying the degrees of freedom involved. +Element property definition +Input File Usage: +Abaqus/CAE Usage: +*DASHPOT +Property or Interaction module: Special→Springs/Dashpots→Create +Element-based loading +None. +Element output +S11 +E11 +ER11 +The force in the dashpot. +The relative displacement across the dashpot. +The relative velocity across the dashpot (available only from Abaqus/Standard). +Node ordering on elements +DASHPOTA +DASHPOT2 +DASHPOT1 +32.3 +Flexible joint elements +• “Flexible joint element,” Section 32.3.1 +• “Flexible joint element library,” Section 32.3.2 +32.3.1 +FLEXIBLE JOINT ELEMENT +Product: Abaqus/Standard +References +• “Flexible joint element library,” Section 32.3.2 +• *JOINT +• *DASHPOT +• *SPRING +Overview +JOINTC elements: +• are used to model joint interactions; and +• are made up of translational and rotational springs and parallel dashpots in a local, corotational +coordinate system. +Details of the element formulation can be found in “Flexible joint element,” Section 3.9.6 of the Abaqus +Theory Manual. +Typical applications +The JOINTC element is provided to model the interaction between two nodes that are (almost) coincident +geometrically and that represent a joint with internal stiffness and/or damping (such as a rubber bushing +in a car suspension system) so that the second node of the joint can displace and rotate slightly with +respect to the first node. +Joints that have only one or two axes of rotation and no relative displacement are better modeled by +the REVOLUTE- or UNIVERSAL-type MPCs . +Similar functionality is available using connectors; see “Connectors: overview,” Section 31.1.1. +Defining the joint behavior +The joint behavior consists of linear or nonlinear springs and dashpots in parallel, coupling the +corresponding components of relative displacement and of relative rotation in the joint. You define the +spring and dashpot behavior as described in “Springs,” Section 32.1.1, and “Dashpots,” Section 32.2.1. +Each spring or dashpot definition defines the behavior for one of the six local directions; up to six +spring and six dashpot definitions can be included. If no specification is given for a particular local +relative motion in the joint, the joint is assumed to have no stiffness with respect to that component. +The joint behavior can be defined in a local coordinate system that rotates with the motion of the +first node of the element (“Orientations,” Section 2.2.5). If a local coordinate system is not defined, the +global system is used. +You must associate the joint behavior with a set of JOINTC elements. +The kinematic behavior of JOINTC elements is described in detail in “Flexible joint element,” +Section 3.9.6 of the Abaqus Theory Manual. +Input File Usage: +Use the following options to define the joint behavior: +*JOINT, ELSET=name, ORIENTATION=name +*DASHPOT +*SPRING +Up to six *SPRING and *DASHPOT options can appear. +Using JOINTC elements in large-displacement analyses +In large-displacement analysis the formulation for the relationship between moments and rotations limits +the usefulness of these elements to small relative rotations. The relative rotation across a JOINTC +element should be of a magnitude to qualify as a small rotation. +32.3.2 +FLEXIBLE JOINT ELEMENT LIBRARY +Product: Abaqus/Standard +References +• “Flexible joint element,” Section 32.3.1 +• *JOINT +Overview +This section provides a reference to the flexible joint elements available in Abaqus/Standard. +Element types +JOINTC +Joint interaction element +Active degrees of freedom +1, 2, 3, 4, 5, 6 +Additional solution variables +None. +Nodal coordinates required +None. The element nodes do not need to have coordinates defined since the action associated with these +elements is defined by specifying the degrees of freedom involved. +Element property definition +Input File Usage: +*JOINT +Element-based loading +None. +Element output +S11 +S22 +S33 +S12 +S13 +S23 +Total direct force in the first local direction. +Total direct force in the second local direction. +Total direct force in the third local direction. +Total moment about the first local direction. +Total moment about the second local direction. +Total moment about the third local direction. +The relative displacements and rotations corresponding to the forces and moments above are chosen by +requesting the corresponding “strains.” +Nodes associated with the element +Two nodes. The rotation at the first node of the element defines the rotation of the local axis system. +{ +JOINT C +( local system, defined by a local orientation, attached to node 1 ) +32.4 +Distributing coupling elements +• “Distributing coupling elements,” Section 32.4.1 +• “Distributing coupling element library,” Section 32.4.2 +32.4.1 +DISTRIBUTING COUPLING ELEMENTS +Product: Abaqus/Standard +References +• “Distributing coupling element library,” Section 32.4.2 +• *DISTRIBUTING COUPLING +Overview +Distributing coupling elements: +• can be used to distribute forces and moments on a reference node to a collection of nodes; +• can be used to prescribe an average displacement and rotation to a collection of nodes; +• can be used to distribute mass to a collection of nodes; +• can control the force and mass distribution through the use of weight factors specified for each +coupling node; +• can be used to create a flexible coupling between structural and solid elements; and +• can be used with two- or three-dimensional stress/displacement elements. +If distribution of mass is not required, the preferred method for defining a distributing constraint is +described in “Coupling constraints,” Section 34.3.2. +Typical applications +The distributing coupling element constrains the motion of the coupling nodes to the translation and +rotation of the element node. This constraint is enforced in an average sense and in a way that enables +control of the transmission of loads. These characteristics make the distributing coupling element useful +in a number of applications: +• The element can be used to prescribe a displacement and rotation condition on a boundary in cases +where relative motion among the nodes on the boundary is required. An example of such a case is +prescribing a twist on the end of a structure that is expected to warp and/or deform within the end +surface . +• The element can be used to provide, through the motion of the reference node, a weighted average +of the motion of the coupling nodes. +• The element can be used to distribute loads, where the load distribution can be described with +moment-of-inertia expressions. Examples of such cases include the classic bolt-pattern and weld- +pattern load distribution expressions. +• The element can be used as a coupling between two parts (structural-solid) to transfer forces and +moments. In comparison to MPCs and the kinematic coupling constraint, the distributing coupling +element can be considered a more “flexible” connection. +DCOUP3D +element node +(NODE 1) +prescribed +rotation +warping is permitted +by the coupling element +Group of coupling +nodes (COUPLESET) +Figure 32.4.1–1 DCOUP3D element used to impart a rotation on the +surface of a structure without constraining motion within the surface. +Choosing an appropriate element +Two- and three-dimensional distributing coupling elements are available. Element DCOUP2D describes +behavior only in the global X–Y plane. Element DCOUP2D can be used in an axisymmetric analysis; +however, its use requires care in selecting the load distributing weight factors. For example, a uniform +axial load distribution to a structure would require specification of load distribution weight factors +in proportion to the radius of the coupling nodes. Since the radius of these nodes will change with +deformation, this use of DCOUP2D would only approximate the correct load distribution behavior in a +large-displacement analysis. +Defining the distributing coupling +To define a distributing coupling, you specify the coupling nodes to which loads and mass are to be +distributed, along with the corresponding weighting of the distribution. A minimum of two coupling +nodes is required. +Input File Usage: +*DISTRIBUTING COUPLING, ELSET=name +node number or node set, weight_factor_1 +node number or node set, weight_factor_2 +... +Example +This example illustrates the use of the DCOUP3D element to impart a rotation to +the surface of a structure that is expected to deform in a general way. In this case warping and motion +within the plane of the end surface are expected to occur. +*ELEMENT, TYPE=DCOUP3D, ELSET=ROTATEELEMENT +1001, 1 +*DISTRIBUTING COUPLING, ELSET=ROTATEELEMENT +COUPLESET, 1.0 +… +*STEP, NLGEOM +… +*BOUNDARY +1, 6, 6, 1.0 +… +*END STEP +Defining the load distribution +The element distributes loads such that the resultants of the forces on the coupling nodes are equal to the +forces and moments on the element node. For cases of more than a few coupling nodes, the distribution +of the forces is not determined by equilibrium alone, and the user-specified weight factors are used to +define the distribution. The weight factors are dimensionless and are normalized within each element +so that the sum of all weight factors is one. As a consequence, the normalized weight factors describe +the proportion of the total element force and moment that is transmitted through the particular coupling +node. In the case of transmission of forces alone, the proportion of force transmitted through the node is +simply the normalized weight factor. In the general case of transmission of forces and moments, the force +distribution follows that of a classic bolt-pattern analysis, where the weight factors could be considered +the areas of particular bolt cross-sections. Refer to “Distributing coupling elements,” Section 3.9.8 of +the Abaqus Theory Manual, for specific details of the load distribution. +In the example shown in Figure 32.4.1–1 the weight factor distribution chosen is homogeneous, +with a value of 1.0. For the rotation depicted, a more accurate load distribution would reflect the fact +that the shear forces on nodes near the edge of the slot will diminish to zero, which could be described +by choosing individual weight factors for nodes near the slot edge. If the loading on the element were +along the axis of the structure, the homogeneous distribution shown would be appropriate. For cases +where different loading modes require different descriptions of the weight factor distribution, multiple +distributing coupling elements with different element nodes and different weight factors can be used. +Colinear coupling node arrangements +The distributing coupling element transmits moments at the element node as a force distribution among +the coupling nodes, even if these nodes have rotational degrees of freedom. Thus, when the coupling +node arrangement is colinear, the element is not capable of transmitting all components of a moment +at the element node. Specifically, the moment component that is parallel to the colinear coupling node +arrangement will not be transmitted. When this case arises, a warning message is issued that identifies +the axis about which the element will not transmit a moment. +Use with nonuniform meshes +When the distributing coupling element is used with coupling nodes attached to elements of varying +size, care should be taken in selecting the weight factors. The weight factor selected for a node should +generally scale with the size of the elements attached to that node. +Defining the mass distribution +The mass distribution is analogous to the force distribution; the specified element mass is distributed to +the coupling nodes in proportion to the weight factors. +Input File Usage: +*DISTRIBUTING COUPLING, ELSET=name, MASS=total_element_mass +node number or node set, weight_factor_1 +node number or node set, weight_factor_2 +... +Output +Element nodal forces (the force the element places on the element and coupling nodes) are available +through element variable NFORC. Element kinetic energy is available in dynamic procedures through +the whole element variable ELKE. +32.4.2 +DISTRIBUTING COUPLING ELEMENT LIBRARY +Product: Abaqus/Standard +References +• “Distributing coupling elements,” Section 32.4.1 +• *DISTRIBUTING COUPLING +Overview +This section provides a reference to the distributing coupling elements available in Abaqus/Standard. +Element types +DCOUP2D +Two-dimensional distributing coupling element +DCOUP3D +Three-dimensional distributing coupling element +Active degrees of freedom +DCOUP2D: 1, 2, 6 +DCOUP3D: 1, 2, 3, 4, 5, 6 +Additional solution variables +None. +Nodal coordinates required +DCOUP2D: X, Y +DCOUP3D: X, Y, Z +Element property definition +You must identify a minimum of two nodes to which the distributing coupling element distributes loads +and mass; in addition, you can specify the element mass. +*DISTRIBUTING COUPLING +Input File Usage: +Element-based loading +None. +Element output +ELKE +Element kinetic energy. +NFORC +Element nodal forces. +Nodes associated with the element +1 node is defined with the element. Additional nodes forming the coupling are defined in the element +property definition. +32.5 +Cohesive elements +• “Cohesive elements: overview,” Section 32.5.1 +• “Choosing a cohesive element,” Section 32.5.2 +• “Modeling with cohesive elements,” Section 32.5.3 +• “Defining the cohesive element’s initial geometry,” Section 32.5.4 +• “Defining the constitutive response of cohesive elements using a continuum approach,” +Section 32.5.5 +• “Defining the constitutive response of cohesive elements using a traction-separation description,” +Section 32.5.6 +• “Defining the constitutive response of fluid within the cohesive element gap,” Section 32.5.7 +• “Two-dimensional cohesive element library,” Section 32.5.8 +• “Three-dimensional cohesive element library,” Section 32.5.9 +• “Axisymmetric cohesive element library,” Section 32.5.10 +32.5.1 +COHESIVE ELEMENTS: OVERVIEW +Abaqus offers a library of cohesive elements to model the behavior of adhesive joints, interfaces in composites, +and other situations where the integrity and strength of interfaces may be of interest. +Overview +Modeling with cohesive elements consists of: +• choosing the appropriate cohesive element type (“Choosing a cohesive element,” Section 32.5.2); +• including the cohesive elements in a finite element model, connecting them to other components, +and understanding typical modeling issues that arise during modeling using cohesive elements +(“Modeling with cohesive elements,” Section 32.5.3); +• defining the initial geometry of the cohesive elements (“Defining the cohesive element’s initial +geometry,” Section 32.5.4); and +• defining the mechanical, and optionally the fluid, constitutive behavior of the cohesive elements. +The mechanical constitutive behavior of the cohesive elements can be defined: +• with a continuum-based constitutive model (“Modeling of an adhesive layer of finite thickness” +in “Defining the constitutive response of cohesive elements using a continuum approach,” +Section 32.5.5), +• with a uniaxial stress-based constitutive model useful in modeling gaskets and/or single adhesive +patches (“Modeling of gaskets and/or small adhesive patches” in “Defining the constitutive response +of cohesive elements using a continuum approach,” Section 32.5.5), or +• by using a constitutive model specified directly in terms of traction versus separation (“Defining the +constitutive response of cohesive elements using a traction-separation description,” Section 32.5.6). +When pore pressure cohesive elements are used in soils procedures in Abaqus/Standard, the fluid +constitutive behavior of the cohesive elements can be defined (“Defining the constitutive response of +fluid within the cohesive element gap,” Section 32.5.7): +• by defining the tangential fluid flow relationship, and +• by defining a fluid leak-off coefficient that accounts for caking or fouling effects in rock fracture. +Typical applications +Cohesive elements are useful in modeling adhesives, bonded interfaces, gaskets, and rock fracture. +The constitutive response of these elements depends on the specific application and is based on certain +assumptions about the deformation and stress states that are appropriate for each application area. The +nature of the mechanical constitutive response may broadly be classified to be based on: +• a continuum description of the material; +• a traction-separation description of the interface; or +• a uniaxial stress state appropriate for modeling gaskets and/or laterally unconstrained adhesive +patches. +Each of these constitutive response types is discussed briefly below. +Continuum-based modeling +The modeling of adhesive joints involves situations where two bodies are connected together by a glue- +like material . A continuum-based modeling of the adhesive is appropriate when the +glue has a finite thickness. The macroscopic properties, such as stiffness and strength, of the adhesive +material can be measured experimentally and used directly for modeling purposes . +The adhesive material is generally more compliant than the surrounding material. The cohesive elements +model the initial loading, the initiation of damage, and the propagation of damage leading to eventual +failure in the material. +Figure 32.5.1–1 Typical peel test using cohesive elements to model finite-thickness adhesives. +In three-dimensional problems the continuum-based constitutive model assumes one direct +(through-thickness) strain, two transverse shear strains, and all (six) stress components to be active at +a material point. +In two-dimensional problems it assumes one direct (through-thickness) strain, one +transverse shear strain, and all (four) stress components to be active at a material point. +Traction-separation-based modeling +The modeling of bonded interfaces in composite materials often involves situations where the +intermediate glue material is very thin and for all practical purposes may be considered to be of zero +In this case the macroscopic material properties are not relevant +thickness . +directly, and the analyst must resort to concepts derived from fracture mechanics—such as the amount +of energy required to create new surfaces . The cohesive elements model the +stiffener +skin +debonding +bond line +Debonding along skin-stringer interface. +Figure 32.5.1–2 Debonding along a skin-stringer interface: typical situation for +traction-separation-based modeling. +initial loading, the initiation of damage, and the propagation of damage leading to eventual failure at the +bonded interface. The behavior of the interface prior to initiation of damage is often described as linear +elastic in terms of a penalty stiffness that degrades under tensile and/or shear loading but is unaffected +by pure compression. +You may use the cohesive elements in areas of the model where you expect cracks to develop. +However, the model need not have any crack to begin with. In fact, the precise locations (among all +areas modeled with cohesive elements) where cracks initiate, as well as the evolution characteristics of +such cracks, are determined as part of the solution. The cracks are restricted to propagate along the layer +of cohesive elements and will not deflect into the surrounding material. +In three-dimensional problems the traction-separation-based model assumes three components of +separation—one normal to the interface and two parallel to it; and the corresponding stress components +are assumed to be active at a material point. In two-dimensional problems the traction-separation-based +model assumes two components of separation—one normal to the interface and the other parallel to it; +and the corresponding stress components are assumed to be active at a material point. +Modeling of gaskets and/or laterally unconstrained adhesive patches +Cohesive elements also provide some limited capabilities for modeling gaskets . +The constitutive response of gaskets modeled with cohesive elements can be defined using only +macroscopic properties such as stiffness and strength . No specialized gasket +behavior (typically defined in terms of pressure versus closure) is available. Compared to the class +flanges +gasket +gasket +fasteners +Figure 32.5.1–3 Typical application involving gaskets. +of gasket elements available in Abaqus/Standard (“Gasket elements: overview,” Section 32.6.1), the +cohesive elements +• are fully nonlinear (can be used with finite strains and rotations); +• can have mass in a dynamic analysis; and +• are available in both Abaqus/Standard and Abaqus/Explicit. +It is assumed that the gaskets are subjected to a uniaxial stress state. A uniaxial stress state is also +appropriate for modeling small adhesive patches that are unconstrained in the lateral direction. +Any material model in Abaqus that is available for use with a one-dimensional element (beams, +trusses, or rebars)—including, for example, the hyperelastic and the elastomeric foam material models +(useful in this context for modeling gaskets, sealants, or shock absorbers made out of poron)—can be +used with this approach. +Spatial representation of a cohesive element +Figure 32.5.1–4 demonstrates the key geometrical features that are used to define cohesive elements. The +connectivity of cohesive elements is like that of continuum elements, but it is useful to think of cohesive +elements as being composed of two faces separated by a thickness. The relative motion of the bottom +and top faces measured along the thickness direction (local 3-direction for three-dimensional elements; +local 2-direction for two-dimensional elements—see “Defining the cohesive element’s initial geometry,” +Section 32.5.4, for further details on local directions) represents opening or closing of the interface. The +relative change in position of the bottom and top faces measured in the plane orthogonal to the thickness +thickness direction +COHESIVE ELEMENTS: OVERVIEW +cohesive element node +bottom face +midsurface +Figure 32.5.1–4 Spatial representation of a three-dimensional cohesive element. +direction quantifies the transverse shear behavior of the cohesive element. Stretching and shearing of +the midsurface of the element (the surface halfway between the bottom and top faces) are associated +with membrane strains in the cohesive element; however, it is assumed that the cohesive elements do not +generate any stresses in a purely membrane response. Figure 32.5.1–5 shows the different deformation +modes of a cohesive element. +cohesive +layer +through-thickness +behavior +transverse shear +membrane stretch +membrane stretch +membrane shear +Figure 32.5.1–5 Deformation modes of a cohesive element. +General issues related to modeling with cohesive elements +While using cohesive elements, you should be mindful of important issues that are specific to these +elements. Such issues include special considerations associated with using cohesive elements in +conjunction with contact interactions, potential degradation of the stable time increment size in +Abaqus/Explicit, and potential convergence problems in Abaqus/Standard. These issues are discussed +in detail in “Modeling with cohesive elements,” Section 32.5.3. Cohesive elements are typically used to +bond components together. “Modeling with cohesive elements,” Section 32.5.3, also discusses methods +for connecting a cohesive layer to adjacent components. +Procedures with which cohesive elements are allowed +Cohesive elements without pore pressure degrees of freedom can be used in all stress/displacement +analysis types. Although they do not have any degrees of freedom other than displacement, they can be +used in coupled procedures to bond together components made out of coupled temperature-displacement +elements, and in Abaqus/Standard coupled pore pressure-displacement elements and/or piezoelectric +elements, to simulate mechanical failure of interfaces. The response of the cohesive element in such +coupled procedures is mechanical only (for example, no heat transfer occurs across the interface in a +coupled temperature-displacement problem). +Cohesive elements with pore pressure degrees of freedom can be used in coupled pore fluid +diffusion/stress analyses (“Coupled pore fluid diffusion and stress analysis,” Section 6.8.1). The +mechanical response of the coupled pore pressure–displacement element is the same as the equivalent +displacement-only element, except that the gap fluid pressure is considered as a traction on open faces. +32.5.2 +CHOOSING A COHESIVE ELEMENT +Products: Abaqus/Standard Abaqus/Explicit +References +• “Cohesive elements: overview,” Section 32.5.1 +• “Two-dimensional cohesive element library,” Section 32.5.8 +• “Three-dimensional cohesive element library,” Section 32.5.9 +• “Axisymmetric cohesive element library,” Section 32.5.10 +Overview +The Abaqus cohesive element library includes: +• elements for two-dimensional analyses; +• elements for three-dimensional analyses; and +• elements for axisymmetric analyses. +Naming convention +The cohesive elements used in Abaqus are named as follows: +COH +3D +pore pressure (optional) +number of nodes +two-dimensional (2D), three-dimensional (3D), +or axisymmetric (AX) +cohesive element +For example, COH2D4 is a 4-node, two-dimensional cohesive element. +32.5.3 +MODELING WITH COHESIVE ELEMENTS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Cohesive elements: overview,” Section 32.5.1 +• “Choosing a cohesive element,” Section 32.5.2 +• *COHESIVE SECTION +• Chapter 21, “Adhesive joints and bonded interfaces,” of the Abaqus/CAE User’s Manual +Overview +Cohesive elements: +• are used to model adhesives between two components, each of which may be deformable or rigid; +• are used to model interfacial debonding using a cohesive zone framework; +• are used to model gaskets and/or small adhesive patches; +• can be connected to the adjacent components by sharing nodes, by using mesh tie constraints, or by +using MPCs type TIE or PIN; and +• may interact with other components via contact for gasket applications. +This section discusses the techniques that are available to discretize cohesive zones and assemble them +in a model representing several components that are bonded to one another. It also discusses several +common modeling issues related to cohesive elements. +Discretizing cohesive zones using cohesive elements +The cohesive zone must be discretized with a single layer of cohesive elements through the thickness. +If the cohesive zone represents an adhesive material with a finite thickness, the continuum macroscopic +properties of this material can be used directly for modeling the constitutive response of the cohesive +zone. Alternatively, if the cohesive zone represents an infinitesimally thin layer of adhesive at a bonded +interface, it may be more relevant to define the response of the interface directly in terms of the traction +at the interface versus the relative motion across the interface. Finally, if the cohesive zone represents +a small adhesive patch or a gasket with no lateral constraint, a uniaxial stress state provides a good +approximation to the state of these elements. Abaqus provides modeling capabilities for all the above +cases. The details are discussed in later sections. +Connecting cohesive elements to other components +At least one of either the top or the bottom face of the cohesive element must be constrained to another +component. In most applications it is appropriate to have both faces of the cohesive elements tied to +neighboring components. If only one face of the cohesive element is constrained and the other face +is free, the cohesive element exhibits one or (for three-dimensional elements) more singular modes of +deformation due to the lack of membrane stiffness. The singular modes can propagate from one cohesive +element to the adjacent one but can be suppressed by constraining the nodes on the side face at the end +of a series of cohesive elements. +In some cases it may be convenient and appropriate to have cohesive elements share nodes with the +elements on the surfaces of the adjacent components. More generally, when the mesh in the cohesive +zone is not matched to the mesh of the adjacent components, cohesive elements can be tied to other +components. When cohesive elements are used to model gaskets, it may be more appropriate to tie or +share nodes on one side and define contact on the other side as discussed below. This will prevent the +gaskets from being subjected to tensile stresses. +Having cohesive elements share nodes with other elements +When the cohesive elements and their neighboring parts have matched meshes, it is straightforward to +connect cohesive elements to other components in a model simply by sharing nodes . +Explicitly +defined node +Part 1 +pore pressure +cohesive elements +internally +generated nodes +Part 2 +Figure 32.5.3–1 Cohesive elements sharing nodes with other Abaqus elements. +When these elements are used as adhesives or to model debonding, this method can be used to obtain +initial results from a model—more accurate local results (in the decohesion zone) would typically be +obtained with the cohesive zone more refined than the elements of the surrounding components. When +these elements are used to model gaskets, this approach is suitable in situations when no frictional slip +occurs between the gaskets and the surrounding components. The method of sharing nodes in gasket +applications will lead to tensile stresses in the gasket should the parts connected to the gasket be pulled +apart. Defining contact on one side of the cohesive elements will avoid such tensile stresses. +Connecting cohesive elements to other components by using surface-based tie constraints +If the two neighboring parts do not have matched meshes, such as when the discretization level in the +cohesive layer is different (typically finer) from the discretization level in the surrounding structures, +the top and/or bottom surfaces of the cohesive layer can be tied to the surrounding structures using a tie +constraint (“Mesh tie constraints,” Section 34.3.1). Figure 32.5.3–2 shows an example in which a finer +discretization is used for the cohesive layer than for the neighboring parts. +tie constraints +Part 1 +Part 2 +cohesive elements +Figure 32.5.3–2 Independent meshes with tie constraints. +Contact interactions between cohesive elements and other components +For some applications involving gaskets it is appropriate to define contact on one side of the cohesive +element . Contact can be defined with either the general contact algorithm +interactions in Abaqus/Explicit,” Section 35.4.1) +in Abaqus/Explicit (“Defining general contact +or the contact pair algorithm in Abaqus/Standard (“Defining contact pairs in Abaqus/Standard,” +Section 35.3.1) or Abaqus/Explicit (“Defining contact pairs in Abaqus/Explicit,” Section 35.5.1). +If +pure master-slave contact is used, typically the surface of the cohesive elements should be the slave +surface and the surface of the neighboring part should be the master surface. This choice of master +and slave is based on the cohesive zone typically being composed of softer materials and having a +finer discretization. The second consideration also suggests that mismatched meshes will often be used +If mismatched meshes are used, the pressure distribution +in analyses involving cohesive elements. +contact interaction +tie constraints +Part 1 +Part 2 +cohesive elements +Figure 32.5.3–3 Contact interaction on one side of a cohesive zone. +on the cohesive elements may not be predicted accurately; submodeling (“Submodeling: overview,” +Section 10.2.1) may be required to obtain accurate local results. +Using cohesive elements in large-displacement analyses +Cohesive elements can be used in large-displacement analyses. The assembly containing the cohesive +elements can undergo finite displacement as well as finite rotation. +Selecting the broad class of the constitutive response of cohesive elements +As discussed earlier, cohesive elements can be used to model finite-thickness adhesives, negligibly thin +adhesive layers for debonding applications, as well as gaskets and/or small adhesive patches. You must +choose one of these broad classes of applications when you define the section properties of cohesive +elements. The detailed implications of each choice are discussed in “Defining the constitutive response of +cohesive elements using a continuum approach,” Section 32.5.5, and “Defining the constitutive response +of cohesive elements using a traction-separation description,” Section 32.5.6. +Input File Usage: +Use the following option to model a finite-thickness adhesive layer using a +continuum-based constitutive response: +*COHESIVE SECTION, RESPONSE=CONTINUUM +Use the following option to model a negligibly (geometrically) thin layer of +adhesive using a traction-separation-based response: +*COHESIVE SECTION, RESPONSE=TRACTION SEPARATION +Use the following option to use cohesive elements as gaskets and/or small +adhesive patches: +*COHESIVE SECTION, RESPONSE=GASKET +Property module: Create Section: select Other as the section Category +and Cohesive as the section Type: Response: Continuum, Traction +Separation, or Gasket +Abaqus/CAE Usage: +Assigning a material behavior to a cohesive element +You assign the name of a material definition to a particular element set. The constitutive behavior for this +element set is defined entirely by the constitutive thickness of the cohesive layer (discussed in “Specifying +the constitutive thickness” in “Defining the cohesive element’s initial geometry,” Section 32.5.4) and the +material properties referring to the same name. +The constitutive behavior of the cohesive elements can be defined either in terms of a material +model provided in Abaqus or a user-defined material model . When cohesive elements are used in applications involving a finite-thickness +adhesive, any available material model in Abaqus, including material models for progressive damage, can +be used. For applications involving gasket and/or small finite-thickness adhesive patches, any material +model that can be used with one-dimensional elements (such as beams, trusses, and rebars), including +material models for progressive damage, can be used. For further details, see “Defining the constitutive +response of cohesive elements using a continuum approach,” Section 32.5.5. For applications in which +the behavior of cohesive elements is defined directly in terms of traction versus separation, the response +can be defined only in terms of a linear elastic relation (between the traction and the separation) along +with progressive damage . +To define the constitutive behavior of cohesive elements, you assign the name of a material model +to a particular element set through the section definition. The actual material model for a user-defined +material model is defined in user subroutine UMAT in Abaqus/Standard or VUMAT in Abaqus/Explicit. +Input File Usage: +Abaqus/CAE Usage: +*COHESIVE SECTION, ELSET=name, MATERIAL=name +Property module: cohesive section editor: Material: name +Using cohesive elements in coupled pore fluid diffusion/stress analyses +Cohesive elements with, or without, pore pressure degrees of freedom can be used in coupled pore +fluid diffusion/stress analyses. Cohesive elements without pore pressure degrees of freedom will only +contribute mechanically, and surfaces exposed when cohesive elements open will be impermeable to +fluid flow. +Cohesive elements with pore pressure degrees of freedom provide a more general response, +including the ability to model tangential flow and leakage flow from the gap into the adjacent material. +These elements have additional pore pressure nodes in the gap interior, and you can choose to define +these nodes explicitly or have them generated automatically by Abaqus/Standard. +In a typical use you will have these gap interior nodes generated for you for the majority of cohesive +elements in the model. You invoke automatic node generation as discussed in “By defining the bottom- +face element connectivity and an integer offset” in “Defining the cohesive element’s initial geometry,” +Section 32.5.4. +Defining contact between surrounding components +Cohesive elements are used to bond two different components. Often the cohesive elements completely +degrade in tension and/or shear as a result of the deformation. Subsequently, the components that are +initially bonded together by cohesive elements may come into contact with each other. Approaches for +modeling this kind of contact include the following: +• In certain situations this kind of contact can be handled by the cohesive element itself. By default, +cohesive elements retain their resistance to compression even if their resistance to other deformation +modes is completely degraded. As a result, the cohesive elements resist interpenetration of the +surrounding components even after the cohesive element has completely degraded in tension and/or +shear. This approach works best when the top and the bottom faces of the cohesive element do not +displace tangentially by a significant amount relative to each other during the deformation. In other +words, to model the situation described above, the deformation of the cohesive elements should be +limited to “small sliding.” +• Another possible approach is to define contact between the surfaces of the surrounding components +that could potentially come into contact and to delete the cohesive elements once they are completely +damaged. Thus, contact is modeled throughout the analysis. This approach is not recommended if +the geometric thickness of the cohesive elements in the model is very small or zero (the geometric +thickness of the cohesive elements may be different from the constitutive thickness you specify +while defining the section properties of the cohesive elements—see “Specifying the constitutive +thickness” in “Defining the cohesive element’s initial geometry,” Section 32.5.4) because contact +will effectively cause nonphysical resistance to compression of the cohesive layer while the cohesive +elements are still active. If frictional contact is modeled, there may also be nonphysical shearing +forces. +This is the behavior that will occur by default with the general contact algorithm in +Abaqus/Explicit. Figure 32.5.3–4, Figure 32.5.3–5, and Figure 32.5.3–6 show the default surface +for general contact. This surface: +– is insensitive to whether the cohesive elements and neighboring elements share nodes, are tied +together, or are not connected; and +– does not include faces of cohesive elements. +tie constraints +Part 1 +⇒ +cohesive elements +Part 2 +all element-based +surfaces +Figure 32.5.3–4 Default surface when cohesive elements share nodes with surrounding elements. +tie constraints +Part 1 +⇒ +cohesive elements +Part 2 +all element-based +surfaces +Figure 32.5.3–5 Default surface when cohesive elements are tied to the surrounding elements. +contact interaction +tie constraints +Part 1 +⇒ +cohesive elements +Part 2 +all element- +based surfaces +Figure 32.5.3–6 Default surface when cohesive elements are tied on one side and +interact through contact on the other side. +Figure 32.5.3–7 shows the situation when the surfaces of the cohesive elements are also added to +the default surface. Abaqus/Explicit generates a contact exclusion automatically so that the general +contact algorithm avoids consideration of contact between the bottom surface of the cohesive +elements and the top surface of Part 2 since these surfaces are tied together. +contact interaction +tie constraints +Part 1 +⇒ +cohesive elements +Part 2 +all element- +based surfaces +Figure 32.5.3–7 Top and bottom faces of the cohesive element along with the default surface when +cohesive elements are tied on one side and interact through contact on the other side. +Input File Usage: +Use the following options to add the top and bottom faces of the cohesive +elements to the default general contact surface (the cohesive elements +are included in the element set COH_ELEMS): +*SURFACE, NAME=DEFAULT_PLUS_COH +, +COH_ELEMS, +*CONTACT +*CONTACT INCLUSIONS +DEFAULT_PLUS_COH, +Abaqus/CAE Usage: +Any module except Sketch, Job, and Visualization: +Tools→Surface→Create: Name: default_plus_coh: +pick faces in viewport +Interaction module: Create Interaction: General contact (Explicit): +Included surface pairs: Selected surface pairs: Edit, select +the surfaces in the columns on the left, and click the arrows in the +middle to transfer them to the list of included pairs +• For general contact in Abaqus/Explicit, yet another approach for modeling contact between the +surrounding structures involves activating contact only when the cohesive elements are completely +degraded and deleted from the model (see “Maximum degradation and choice of element removal” +in “Defining the constitutive response of cohesive elements using a traction-separation description,” +Section 32.5.6). For this approach the cohesive elements must share nodes with the neighboring +element and the general contact definition must include surfaces on the top and bottom faces of the +cohesive elements, as shown in Figure 32.5.3–8. Since each surface face of the cohesive elements +directly opposes a surface face of a neighboring element, the general contact algorithm does not +consider these faces active while both parent elements are active. However, if the cohesive element +fails, the opposing surface faces become active. +Input File Usage: +Use the following options to include the top and bottom faces of +the cohesive elements in the general contact definition (the cohesive +elements are included in the element set COH_ELEMS): +*SURFACE, NAME=gc_surf +, +COH_ELEMS, +*CONTACT +*CONTACT INCLUSIONS +gc_surf, +Abaqus/CAE Usage: +Any module except Sketch, Job, and Visualization: +Tools→Surface→Create: Name: gc_surf: pick faces in viewport +Interaction module: Create Interaction: General contact (Explicit): +Included surface pairs: Selected surface pairs: Edit, select +the surfaces in the columns on the left, and click the arrows in the +middle to transfer them to the list of included pairs +Part 1 +⇒ +cohesive elements +Part 2 +⇒ +all element- +based surfaces +and bottom +and top faces +of cohesive +elements +Figure 32.5.3–8 Surfaces that are involved in general contact when cohesive elements +are included in the surface definition and erosion is used. +Stable time increment in Abaqus/Explicit +The stable time increment for a cohesive element in Abaqus/Explicit is equal to the time, +for a stress wave to travel across the constitutive thickness, +, of the cohesive layer: +, required +is the wave speed and +represent the bulk stiffness and the density, respectively, +where +of the adhesive material. In terms of the expression for the wave speed, the stable time increment can be +written as +and +For cases in which the constitutive response is defined in terms of traction versus separation, +the slope of the traction versus separation relationship is +and the density is specified as +mass per unit area rather than per unit volume: +. Therefore, for traction versus separation the expression for the time increment becomes +It is quite common that the time increment of cohesive elements will be significantly less than that of +the other elements in the model, unless you take some action to alter one or more of the factors influencing +the time increment. This requires some judgement on your part. The following discussions provide some +recommendations for controlling the time increment for the different methods of defining the material +response. However, Abaqus/Standard may be preferable in some applications where it is necessary to +model a thin, stiff cohesive layer without approximations. +Constitutive response defined in terms of a continuum or uniaxial stress-state approach +For constitutive response defined in terms of a continuum or uniaxial stress-state approach, the ratio of +the stable time increment of the cohesive elements to that of the other elements is given by +where the subscripts “c” and “e” stand for the cohesive elements and the surrounding elements, +respectively. The thickness of the cohesive layer is often smaller than a characteristic length of the +other elements in the model, so the quantity +is often small. The quantity under the radical will +depend on the materials involved. For an epoxy adhesive between steel components, the quantity under +the radical is on the order of unity. The stable time increment of the cohesive element can be increased +by artificially +• increasing the constitutive thickness, +• increasing the density, +• reducing the stiffness, +• some combination of the above. +; +; or +; +In many cases the most attractive option will be to increase the density, which is also referred to as mass +scaling (“Mass scaling,” Section 11.6.1). However, if the thickness of the cohesive zone is very small, +the mass scaling required to achieve a reasonable time increment may affect the results significantly. +In such cases it may be necessary to artificially reduce the cohesive stiffness in addition to some mass +scaling. This approach involves the use of a stiffness that is different from the measured stiffness of the +interface; however, if the peak strength and the fracture energy remain unchanged, the global response +will not be affected significantly in many cases. +Constitutive response defined in terms of traction versus separation +For constitutive response defined in terms of traction versus separation, the ratio of the stable time +increment of the cohesive elements to that for the other elements is given by +where the subscripts “c” and “e” stand for the cohesive elements and the surrounding elements, +respectively. +One way to ensure that the cohesive elements will have no adverse effect on the stable time +increment is to choose material properties such that +, which implies +This is accomplished if, for example, the cohesive element stiffness and density per unit area are chosen +such that +where +represents the characteristic length of the neighboring non-cohesive elements. By choosing +, the stiffness in the cohesive layer relative to the surrounding elements will be similar to the +default stiffness used by penalty contact in Abaqus/Explicit (relative to the equivalent one-dimensional +stiffness of the surrounding elements). This approach involves the use of a stiffness that is likely to +be different from the measured stiffness of the interface; however, if the peak strength and the fracture +energy remain unchanged, the global response will not be affected significantly in many cases. +Convergence issues in Abaqus/Standard +In many problems cohesive elements are modeled as undergoing progressive damage leading to failure. +The modeling of progressive damage involves softening in the material response, which is known to lead +to convergence difficulties in an implicit solution procedure, such as in Abaqus/Standard. Convergence +difficulties may also occur during unstable crack propagation, when the energy available is higher than +the fracture toughness of the material. Several methods are available to help avoid these convergence +problems. +Using viscous regularization +Abaqus/Standard provides a viscous regularization capability that helps in improving the convergence +for these kinds of problems. This capability is discussed in detail in “Using viscous regularization +with cohesive elements, connector elements, and elements that can be used with the damage evolution +models for ductile metals and fiber-reinforced composites in Abaqus/Standard” in “Section controls,” +Section 27.1.4, and “Viscous regularization in Abaqus/Standard” in “Defining the constitutive response +of cohesive elements using a traction-separation description,” Section 32.5.6. +Using automatic stabilization +Another approach to help convergence behavior is the use of automatic stabilization , which is +useful when a problem is unstable due to local instabilities. Generally, if sufficient viscous regularization +is used (as measured by the viscosity coefficient—see “Viscous regularization in Abaqus/Standard” +in “Defining the constitutive response of cohesive elements using a traction-separation description,” +Section 32.5.6, for further details), the use of the automatic stabilization technique is not necessary. +In problems where a small amount or no viscous regularization is used, automatic stabilization will +improve the convergence characteristics. +Using nondefault solution controls +The use of nondefault solution controls and activation of the +line search technique (“Improving the efficiency of the solution by using the line search algorithm” in +“Convergence criteria for nonlinear problems,” Section 7.2.3) may be useful in improving the solution +efficiency. +DEFINING THE COHESIVE ELEMENT’S INITIAL GEOMETRY +COHESIVE GEOMETRY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Cohesive elements: overview,” Section 32.5.1 +• Chapter 21, “Adhesive joints and bonded interfaces,” of the Abaqus/CAE User’s Manual +Overview +The initial geometry of a cohesive element is defined: +• by the nodal connectivity of the element and the position of these nodes; +• by the stack direction, which can be used to specify the top and the bottom faces of the cohesive +element independent of the nodal connectivity; and +• by the magnitude of the initial constitutive thickness, which can either correspond to the geometric +thickness implied by the nodal positions and stack direction or be specified directly. +Defining the element connectivity +The connectivity of a cohesive element is like that of a continuum element; however, it is useful to think +of a cohesive element as being composed of two faces (a bottom and a top face) separated by the cohesive +zone thickness. The element has nodes on its bottom face and corresponding nodes on its top face. Pore +pressure cohesive elements include a third, middle face, which is used to model fluid flow within the +element. +Three methods are available to define the element connectivity. +By directly defining the element’s complete connectivity +The complete connectivity of a cohesive element can be given directly . +By defining the bottom-face element connectivity and an integer offset +Alternatively, you can specify the connectivity of the bottom face plus a positive integer offset that will be used to determine the +remaining cohesive element nodes. +Input File Usage: +Abaqus/CAE Usage: +*ELEMENT, OFFSET=n +Element offsets are not supported in Abaqus/CAE. +Use with displacement cohesive elements +The integer offset will be used to define node numbers of the top face of the cohesive element. Abaqus +will automatically position the nodes of the top face to be coincident with those of the bottom face unless +the nodes of the top face have already been assigned coordinates directly with a node definition (“Node +definition,” Section 2.1.1). +Use with pore pressure-displacement cohesive elements +When you define only the bottom face nodes, the integer offset will first be used to define the node +numbers of the top face of the cohesive element, with the numbering of the top-face nodes offset from +the bottom face node numbers. The integer offset will again be used to define the middle surface node +numbers offset, with the numbering of the middle-face nodes offset from the top face node numbers. +Abaqus will automatically position the nodes of the top and middle faces to be coincident with those of +the bottom face unless the nodes of the top face have already been assigned coordinates directly with a +node definition (“Node definition,” Section 2.1.1). +By defining the bottom- and top-face element connectivities and an integer offset +For pore pressure cohesive elements, you also can specify the connectivity of the bottom and top faces +plus a positive integer offset +that will be used to determine the middle face cohesive element nodes. +When you define the bottom and top face nodes, the integer offset will be used to define the node +numbers of the middle face, with the numbering of the middle-face nodes offset from the bottom face +node numbers. Abaqus will automatically position the nodes of the middle face to be halfway between +those of the bottom and top faces unless the nodes of the middle face have already been assigned +coordinates directly with a node definition (“Node definition,” Section 2.1.1). +*ELEMENT, OFFSET=n +Element offsets are not supported in Abaqus/CAE. +Abaqus/CAE Usage: +Input File Usage: +Specifying the out-of-plane thickness for two-dimensional elements +For two-dimensional cohesive elements the out-of-plane thickness is required. You specify this +additional information in the cohesive section definition; the default value is 1.0. +Input File Usage: +*COHESIVE SECTION +first data line +out-of-plane thickness +Abaqus/CAE Usage: +Property module: cohesive section editor: toggle on Out-of-plane thickness: +and specify the out-of-plane thickness +Specifying the constitutive thickness +You can specify the constitutive thickness of the cohesive element directly or allow Abaqus to compute +it based on nodal coordinates such that the constitutive thickness is equal to the geometric thickness. The +default behavior depends on the nature of the application. +If the geometric thickness of the cohesive element is very small compared to its surface dimensions, +the thickness computed from the nodal coordinates may be inaccurate. In such cases you can specify a +constant thickness directly when defining the section properties of these elements. +The characteristic element length of a cohesive element is equal to its constitutive thickness. The +characteristic element length is often useful in defining the evolution of damage in materials . +When the cohesive element response is based on a continuum approach +When the response of the cohesive elements is based on a continuum approach, by default the constitutive +thickness of the element is computed by Abaqus based on the nodal coordinates. You can override this +default by specifying the constitutive thickness directly. +Input File Usage: +Use the following option to have Abaqus compute the thickness based on the +nodal coordinates: +*COHESIVE SECTION, RESPONSE=CONTINUUM, +THICKNESS=GEOMETRY (default) +Use the following option to specify the thickness directly: +*COHESIVE SECTION, RESPONSE=CONTINUUM, +THICKNESS=SPECIFIED +thickness (1.0 by default) +Abaqus/CAE Usage: +Property module: cohesive section editor: Response: Continuum: Initial +thickness: Use nodal coordinates, Specify: thickness, or Use analysis +default +When the cohesive element response is based on a traction-separation approach +When the response of the cohesive elements is based on a traction-separation approach, Abaqus assumes +by default that the constitutive thickness is equal to one. This default value is motivated by the fact +that the geometric thickness of cohesive elements is often equal to (or very close to) zero for the kinds +of applications in which a traction-separation-based constitutive response is appropriate. This default +choice ensures that nominal strains are equal to the relative separation displacements . You can override this default by specifying another value or specifying that the +constitutive thickness should be equal to the geometric thickness. +Input File Usage: +Use the following option to specify the thickness directly: +*COHESIVE SECTION, RESPONSE=TRACTION SEPARATION, +THICKNESS=SPECIFIED (default) +thickness (1.0 by default) +Abaqus/CAE Usage: +Use the following option to have Abaqus compute the thickness based on the +nodal coordinates: +*COHESIVE SECTION, RESPONSE=TRACTION SEPARATION, +THICKNESS=GEOMETRY +Property module: cohesive section editor: Response: Traction Separation: +Initial thickness: Specify: thickness, Use analysis default, or Use nodal +coordinates +When the cohesive element response is based on a uniaxial stress state +When the response of the cohesive elements is based on a uniaxial stress state, there is no default method +for computing the constitutive thickness. You must indicate your choice of the method of determining +the constitutive thickness. +Input File Usage: +Use the following option to specify the thickness: +*COHESIVE SECTION, RESPONSE=GASKET, +THICKNESS=SPECIFIED +thickness (1.0 by default) +Use the following option to have Abaqus compute the thickness based on the +nodal coordinates: +*COHESIVE SECTION, RESPONSE=GASKET, +THICKNESS=GEOMETRY +Abaqus/CAE Usage: +Property module: cohesive section editor: Response: Gasket: +thickness: Specify: thickness or Use nodal coordinates +Initial +Element thickness direction definition +It is important to define the orientation of cohesive elements correctly, since the behavior of the elements +is different in the thickness and in-plane directions. By default, the top and bottom faces of cohesive +elements are as shown in Figure 32.5.4–1 for three-dimensional cohesive elements and Figure 32.5.4–2 +for two-dimensional and axisymmetric cohesive elements. Options for overriding the default orientation +of cohesive elements are discussed below along with an explanation of how the local thickness direction +and in-plane direction vectors are established. +Setting the stack direction equal to an isoparametric direction +The “stack direction” refers to the isoparametric direction along which the top and bottom faces of +a cohesive element are stacked. By default, the top and bottom faces are stacked along the third +isoparametric direction in three-dimensional cohesive elements and along the second isoparametric +direction in two-dimensional and axisymmetric cohesive elements. You can choose to stack the top +and bottom faces along an alternate isoparametric direction for most element types (the COH3D6 +element can have only the third isoparametric direction as the stack direction). The choice of the +isoparametric direction depends on the element connectivity. For a mesh-independent specification, +top face +bottom face +thickness +direction +thickness +direction +Figure 32.5.4–1 Default thickness direction for three-dimensional cohesive elements. +y (z) +x (r) +thickness +direction +Figure 32.5.4–2 Default thickness direction for two-dimensional +and axisymmetric cohesive elements. +use an orientation-based method as described below. +three-dimensional cohesive elements are shown in Figure 32.5.4–3. +The isoparametric direction choices for +F6 +F2 +F5 +F4 +F3 +F1 +Stack direction +F2 +F5 +F3 +F1 +F4 +Stack direction +Stack direction = 1 +from face 6 to face 4 +Stack direction = 2 +from face 3 to face 5 +Stack direction = 3 +from face 1 to face 2 +Stack direction = 3 +from face 1 to face 2 +Figure 32.5.4–3 Stack directions for COH3D8 (left) and COH3D6 (right) elements. +Input File Usage: +Use the following option to define the element top and bottom faces based on +the element’s isoparametric directions: +Abaqus/CAE Usage: +*COHESIVE SECTION, STACK DIRECTION=n +You cannot define the stack direction based on isoparametric directions in +Abaqus/CAE. The stack direction will correspond to the default discussed +above. +Setting the stack direction based on a user-defined orientation +You can also control the orientation of the stack direction through a user-defined local orientation +(“Orientations,” Section 2.2.5). When you define an orientation for cohesive elements, you also specify +an axis about which the local 1 and 2 material directions may be rotated. This axis also defines an +approximate normal direction. The stack direction will be the element isoparametric direction that is +closest to this approximate normal . +Cohesive section, stack direction +based on cylor1 +' +(10, 0, 0) +Local cylindrical orientation cylor1: +a = 0, 0, 0 +b = 10, 0, 0 +' +Global +(0, 0, 0) +ABAQUS selects the isoparametric direction  that is +closest to the 1st (i.e., x , or radial) axis, at the center. +Figure 32.5.4–4 Example illustrating the use of a cylindrical system to define the stack direction. +Input File Usage: +Use the following option to define the element thickness direction based on a +user-defined orientation: +Abaqus/CAE Usage: +*COHESIVE SECTION, STACK DIRECTION=ORIENTATION, +ORIENTATION=name +You cannot define the stack direction based on an orientation definition in +Abaqus/CAE. The stack direction will correspond to the default discussed +above. +Verifying the stack direction +The stack direction can be verified visually in Abaqus/CAE by using the stack direction query tool . For +three-dimensional elements Abaqus/CAE colors the top face purple and the bottom face brown. For +two-dimensional and axisymmetric elements, arrows indicate the orientation of the element. In addition, +Abaqus/CAE highlights any element faces and edges that have inconsistent orientations. +Alternatively, the material axes can be plotted in the Visualization module of Abaqus/CAE to verify +that the 3-axis points in the desired normal direction for three-dimensional elements; and if the element +is oriented improperly, one of the in-plane axes (either the 1- or 2-axis) will point in the normal direction. +For two-dimensional and axisymmetric elements, the stack direction is consistent with the 2-axis material +direction. +Thickness direction computation for two-dimensional and axisymmetric elements +To compute the thickness direction for two-dimensional and axisymmetric elements, Abaqus forms +a midsurface by averaging the coordinates of the node pairs forming the bottom and top surfaces +of the element. This midsurface passes through the integration points of the element, as shown in +Figure 32.5.4–5 for the default choice of the bottom and top surfaces. For each integration point Abaqus +computes a tangent whose direction is defined by the sequence of nodes given on the bottom and top +surfaces. The thickness direction is then obtained as the cross product of the out-of-plane and tangent +directions. +n1 +t1 +midsurface +n2 +t2 +Figure 32.5.4–5 Thickness direction for a two-dimensional or axisymmetric element. +Thickness direction computation for three-dimensional elements +To compute the thickness direction for three-dimensional elements, Abaqus forms a midsurface by +averaging the coordinates of the node pairs forming the bottom and top surfaces of the element. This +midsurface passes through the integration points of the element, as shown in Figure 32.5.4–6 for the +default choice of the bottom and top surfaces. Abaqus computes the thickness direction as the normal +to the midsurface at each integration point; the positive direction is obtained with the right-hand rule +going around the nodes of the element on the bottom or top surface. +n1 +midsurface +n4 +n2 +n3 +Figure 32.5.4–6 Thickness direction for a three-dimensional element. +Local directions at integration points +Abaqus computes default local directions at each integration point. The local directions are used for +output of all quantities that describe the current deformation state of a cohesive element. Details of local +directions are discussed separately below for cohesive elements with two versus three local directions. +Local directions for two-dimensional and axisymmetric cohesive elements +The local 2-direction for two-dimensional and axisymmetric cohesive elements corresponds to the +thickness direction, which is computed as discussed above in “Element thickness direction definition.” +The local 1-direction is defined such that the cross product between the local 1- and 2-directions gives +the out-of-plane direction . You cannot modify either local direction for these +elements for a given stack orientation. Transverse shear behavior is defined in the 1–2 plane for these +elements. +Figure 32.5.4–7 Local directions for two-dimensional and axisymmetric cohesive elements. +Local directions for three-dimensional cohesive elements +The local 3-direction for three-dimensional cohesive elements corresponds to the thickness direction, +which is computed as discussed above in “Element thickness direction definition” and cannot be modified +for a given stack orientation. The local 1- and 2-directions are normal to the thickness direction and, by +Section 1.2.2). The default local directions for a three-dimensional cohesive element are shown in +Figure 32.5.4–8. +COHESIVE GEOMETRY +projection of x-axis +onto surface +Figure 32.5.4–8 Local directions for three-dimensional cohesive elements. +Transverse shear behavior is defined in the local 1–3 and 2–3 planes for these elements. You can modify +the local 1- and 2-directions for three-dimensional cohesive elements in the plane normal to the thickness +direction by using a local orientation definition (“Orientations,” Section 2.2.5). +Input File Usage: +Abaqus/CAE Usage: +*COHESIVE SECTION, ELSET=name, ORIENTATION=name +Property module: Assign→Material Orientation: +orientation +select region: +select +32.5.5 +DEFINING THE CONSTITUTIVE RESPONSE OF COHESIVE ELEMENTS USING A +CONTINUUM APPROACH +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Cohesive elements: overview,” Section 32.5.1 +• “Defining the constitutive response of cohesive elements using a traction-separation description,” +Section 32.5.6 +• “Progressive damage and failure,” Section 24.1.1 +• *COHESIVE SECTION +• *TRANSVERSE SHEAR STIFFNESS +• Chapter 21, “Adhesive joints and bonded interfaces,” of the Abaqus/CAE User’s Manual +Overview +The features described in this section are used to model cohesive elements using a continuum approach, +which assumes that the cohesive zone contains material of finite thickness that can be modeled using the +conventional material models in Abaqus. If the cohesive zone is very thin and for all practical purposes +may be considered to be of zero thickness, the constitutive response is commonly described in terms of +a traction-separation law; this alternative approach is discussed in “Defining the constitutive response of +cohesive elements using a traction-separation description,” Section 32.5.6. +The constitutive response of cohesive elements modeled as a continuum: +• can be defined in terms of macroscopic material properties such as stiffness and strength using +conventional material models; +• can be specified in terms of either a built-in material model or a user-defined material model; +• can include the effects of material damage and failure in Abaqus/Explicit; and +• can also include the effects of material damage and failure in a low-cycle fatigue analysis in +Abaqus/Standard. +Behavior of cohesive elements with conventional material models +The implementation of the conventional material models (including user-defined models) in Abaqus for +cohesive elements is based on certain assumptions regarding the state of the deformation in the cohesive +layer. Two different classes of problems are considered: modeling of an adhesive layer of finite thickness +and modeling of gaskets. +Modeling of damage with cohesive elements for these classes of problems can be carried out only in +Abaqus/Explicit . You may need to alter the damage model for an adhesive +material to account for the fact that the failure of an adhesive bond may occur at the interface between +the adhesive and the adherend rather than within the adhesive material. +When used with conventional material models in Abaqus, cohesive elements use true stress and +strain measures. When used with a material model that is based on a traction-separation description +, cohesive elements use nominal stress and strain measures. +The frequency characteristics of cohesive elements are accounted for by the algorithms +to automatically choose the time increment +(“Explicit dynamic analysis,” +Section 6.3.3). In many applications involving adhesives or gaskets cohesive elements may be quite +thin compared to the other elements, which tends to decrease the stable time increment. See “Stable +time increment in Abaqus/Explicit” in “Modeling with cohesive elements,” Section 32.5.3, for further +discussion on this topic, including suggestions on how to avoid significant reductions in the stable time +increment when using cohesive elements. +in Abaqus/Explicit +Modeling of an adhesive layer of finite thickness +For adhesive layers with finite thickness it is assumed that the cohesive layer is subjected to only one +direct component of strain, which is the through-thickness strain, and to two transverse shear strain +components (one transverse shear strain component for two-dimensional problems). The other two direct +components of the strain (the direct membrane strains) and the in-plane (membrane) shear strain are +assumed to be zero for the constitutive calculations. More specifically, the through-thickness and the +transverse shear strains are computed from the element kinematics. However, the membrane strains are +not computed based on the element kinematics; they are simply assumed to be zero for the constitutive +calculations. These assumptions are appropriate in situations where a relatively thin and compliant +layer of adhesive bonds two relatively rigid (compared to the adhesive) parts. The above kinematic +assumptions are approximately correct everywhere inside the cohesive layer except around its outer +edges. +An additional linear elastic transverse shear behavior can be defined to provide more stability to +cohesive elements, particularly after damage has occurred. The transverse shear behavior is assumed to +be independent of the regular material response and does not undergo any damage. +Input File Usage: +Abaqus/CAE Usage: +Use the following options (the second option is needed only to define uncoupled +transverse shear response): +*COHESIVE SECTION, RESPONSE=CONTINUUM +*TRANSVERSE SHEAR STIFFNESS +Property module: Create Section: select Other as the section Category and +Cohesive as the section Type: Response: Continuum +Transverse shear behavior is not supported in Abaqus/CAE for cohesive +sections. +Modeling of gaskets and/or small adhesive patches +The modeling of gaskets and/or small adhesive patches involves situations where there are no lateral +constraints on the cohesive layer. Hence, the layers are free to expand in the lateral direction in a stress- +free manner. Application areas include individual spot welds and gaskets. The constitutive calculations +assume only one direct stress component, which is the through-thickness normal stress. All other stress +components, including the transverse shear stress components, are assumed to be zero. +The gasket modeling capability that is offered with this option has some advantages compared +to the family of gasket elements in Abaqus/Standard. The cohesive elements are fully nonlinear (the +element kinematics properly account for finite strains as well as finite rotations), can contribute mass +and damping in a dynamic analysis, and are available in Abaqus/Explicit. The gasket response modeled +in the above manner is similar to modeling using the special-purpose gasket elements in Abaqus/Standard +with thickness-direction behavior only . +Uncoupled, linear-elastic transverse shear behavior, if desired, can be defined. The transverse shear +behavior may either define the response of the gasket and/or adhesive patch or provide stability after +damage has occurred in the response in the thickness direction. There is no damage associated with the +transverse shear response. +Input File Usage: +Use the following options (the second option is needed only to define uncoupled +transverse shear response): +*COHESIVE SECTION, RESPONSE=GASKET +*TRANSVERSE SHEAR STIFFNESS +Property module: Create Section: select Other as the section Category and +Cohesive as the section Type: Response: Gasket +Transverse shear behavior is not supported in Abaqus/CAE for cohesive +sections. +Abaqus/CAE Usage: +Output +All standard output variables in Abaqus (“Abaqus/Standard output variable identifiers,” Section 4.2.1, +and “Abaqus/Explicit output variable identifiers,” Section 4.2.2) are available for cohesive elements that +are used with conventional material models. The stresses due to the additional transverse shear response +are reported separately using the output variables TSHR13 and (in three dimensions) TSHR23. These +stresses are not added to the usual material point stresses reported using the output variable S. +32.5.6 +DEFINING THE CONSTITUTIVE RESPONSE OF COHESIVE ELEMENTS USING A +TRACTION-SEPARATION DESCRIPTION +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Cohesive elements: overview,” Section 32.5.1 +• “Defining the constitutive response of cohesive elements using a continuum approach,” +Section 32.5.5 +• *COHESIVE SECTION +• *DAMAGE EVOLUTION +• *DAMAGE INITIATION +• “Defining damage,” Section 12.9.3 of the Abaqus/CAE User’s Manual, in the online HTML version +of this manual +• Chapter 21, “Adhesive joints and bonded interfaces,” of the Abaqus/CAE User’s Manual +Overview +The features described in this section are primarily intended for bonded interfaces where the interface +thickness is negligibly small. In such cases it may be straightforward to define the constitutive response +of the cohesive layer directly in terms of traction versus separation. If the interface adhesive layer has +a finite thickness and macroscopic properties (such as stiffness and strength) of the adhesive material +are available, it may be more appropriate to model the response using conventional material models. +The former approach is discussed in this section, while the latter approach is discussed in “Defining the +constitutive response of cohesive elements using a continuum approach,” Section 32.5.5. +Cohesive behavior defined directly in terms of a traction-separation law: +• can be used to model the delamination at interfaces in composites directly in terms of traction versus +separation; +• allows specification of material data such as the fracture energy as a function of the ratio of normal +to shear deformation (mode mix) at the interface; +• assumes a linear elastic traction-separation law prior to damage; +• can be used in combination with linear viscoelasticity in Abaqus/Explicit (“Defining viscoelastic +behavior for traction-separation elasticity in Abaqus/Explicit” in “Time domain viscoelasticity,” +Section 22.7.1) to describe rate-dependent delamination behavior; +• assumes that failure of the elements is characterized by progressive degradation of the material +stiffness, which is driven by a damage process; +• allows multiple damage mechanisms; and +• can be used with user subroutine UMAT in Abaqus/Standard or VUMAT in Abaqus/Explicit to specify +user-defined traction-separation laws. +Defining constitutive response in terms of traction-separation laws +To define the constitutive response of the cohesive element directly in terms of traction versus separation, +you choose a traction-separation response when defining the section behavior of the cohesive elements. +Input File Usage: +Abaqus/CAE Usage: +*COHESIVE SECTION, RESPONSE=TRACTION SEPARATION +Property module: Create Section: select Other as the section Category and +Cohesive as the section Type: Response: Traction Separation +Linear elastic traction-separation behavior +The available traction-separation model in Abaqus assumes initially linear elastic behavior followed by the initiation and evolution of damage. The elastic behavior is +written in terms of an elastic constitutive matrix that relates the nominal stresses to the nominal strains +across the interface. The nominal stresses are the force components divided by the original area at each +integration point, while the nominal strains are the separations divided by the original thickness at each +integration point. The default value of the original constitutive thickness is 1.0 if traction-separation +response is specified, which ensures that the nominal strain is equal to the separation (i.e., relative +displacements of the top and bottom faces). The constitutive thickness used for traction-separation +response is typically different from the geometric thickness (which is typically close or equal to zero). +See “Specifying the constitutive thickness” in “Defining the cohesive element’s initial geometry,” +Section 32.5.4, for a discussion on how to modify the constitutive thickness. +The nominal +traction stress vector, +, +, consists of three components (two components in +two-dimensional problems): +, which represent the normal +(along the local 3-direction in three dimensions and along the local 2-direction in two dimensions) and +the two shear tractions (along the local 1- and 2-directions in three dimensions and along the local +1-direction in two dimensions), respectively. The corresponding separations are denoted by +, and +the original thickness of the cohesive element, the nominal strains can be defined as +, and (in three-dimensional problems) +. Denoting by +, +The elastic behavior can then be written as +The elasticity matrix provides fully coupled behavior between all components of the traction vector and +separation vector and can depend on temperature and/or field variables. Set the off-diagonal terms in the +elasticity matrix to zero if uncoupled behavior between the normal and shear components is desired. +Input File Usage: +Use the following option to define uncoupled traction-separation behavior: +*ELASTIC, TYPE=TRACTION +Use the following option to define coupled traction-separation behavior: +Abaqus/CAE Usage: +*ELASTIC, TYPE=COUPLED TRACTION +Use the following option to define uncoupled traction-separation behavior: +Property module: material editor: Mechanical→Elasticity→Elastic: +Type: Traction +Use the following option to define coupled traction-separation behavior: +Property module: material editor: Mechanical→Elasticity→Elastic: +Type: Coupled Traction +Interpretation of material properties +The material parameters, such as the interfacial elastic stiffness, for a traction-separation model can be +better understood by studying the equation that represents the displacement of a truss of length L, elastic +stiffness E, and original area A, due to an axial load P: +This equation can be rewritten as +where +displacement. Likewise, the total mass of the truss, assuming a density , is given by +is the nominal stress and +is the stiffness that relates the nominal stress to the +The above equations suggest that the actual length L may be replaced with 1.0 (to ensure that the strain is +the same as the displacement) if the stiffness and the density are appropriately reinterpreted. In particular, +the stiffness is +, where the true length of the truss is used in +these equations. The density represents mass per unit area instead of mass per unit volume. +and the density is +and density +These ideas can be carried over to a cohesive layer of initial thickness +. If the adhesive material has +stiffness +, the stiffness of the interface (relating the nominal traction to the displacement) +is given by +. As discussed earlier, +and the density of the interface is given by +the default choice of the constitutive thickness for modeling the response in terms of traction versus +separation is 1.0 regardless of the actual thickness of the cohesive layer. With this choice, the nominal +strains are equal to the corresponding separations. When the constitutive thickness of the cohesive layer +is “artificially” set to 1.0, ideally you should specify +(if needed) as the material stiffness and +density, respectively, as calculated with the true thickness of the cohesive layer. +and +, tends to infinity and the density, +The above formulae provide a recipe for estimating the parameters required for modeling the +traction-separation behavior of an interface in terms of the material properties of the bulk adhesive +material. As the thickness of the interface layer tends to zero, the above equations imply that the +stiffness, +, tends to zero. This stiffness is often chosen as a penalty +parameter. A very large penalty stiffness is detrimental to the stable time increment in Abaqus/Explicit +and may result in ill-conditioning of the element operator in Abaqus/Standard. Recommendations for +the choice of the stiffness and density of an interface for an Abaqus/Explicit analysis such that the stable +time increment is not adversely affected are provided in “Stable time increment in Abaqus/Explicit” in +“Modeling with cohesive elements,” Section 32.5.3. +Modeling rate-dependent traction-separation behavior in Abaqus/Explicit +Time domain viscoelasticity can be used in Abaqus/Explicit to model rate-dependent behavior of +cohesive elements with traction-separation elasticity. The evolution equation for the normal and two +shear nominal tractions take the form: +, +, and +are the instantaneous nominal tractions at time t in the normal and the two +where +local shear directions, respectively. The functions +represent the dimensionless shear +and normal relaxation moduli, respectively. See “Defining viscoelastic behavior for traction-separation +elasticity in Abaqus/Explicit” in “Time domain viscoelasticity,” Section 22.7.1, for additional details and +usage information. +and +You can also combine time domain viscoelasticity with the models for progressive damage and +failure described in the next sections. This combination allows modeling rate-dependent behavior both +during the initial elastic response (prior to damage initiation), as well as during damage progression. +Damage modeling +Both Abaqus/Standard and Abaqus/Explicit allow modeling of progressive damage and failure in +cohesive layers whose response is defined in terms of traction-separation. By comparison, only +Abaqus/Explicit allows modeling of progressive damage and failure for cohesive elements modeled +with conventional materials (“Defining the constitutive response of cohesive elements using a +continuum approach,” Section 32.5.5). Damage of the traction-separation response is defined within +the same general framework used for conventional materials . This general framework allows the combination of several damage mechanisms acting +simultaneously on the same material. Each failure mechanism consists of three ingredients: a damage +initiation criterion, a damage evolution law, and a choice of element removal (or deletion) upon reaching +a completely damaged state. While this general framework is the same for traction-separation response +and conventional materials, many details of how the various ingredients are defined are different. +Therefore, the details of damage modeling for traction-separation response are presented below. +The initial response of the cohesive element is assumed to be linear as discussed above. However, +once a damage initiation criterion is met, material damage can occur according to a user-defined damage +evolution law. Figure 32.5.6–1 shows a typical traction-separation response with a failure mechanism. +If the damage initiation criterion is specified without a corresponding damage evolution model, Abaqus +will evaluate the damage initiation criterion for output purposes only; there is no effect on the response +of the cohesive element (i.e., no damage will occur). The cohesive layer does not undergo damage under +pure compression. +traction +t (t , t ) +n s t +δ (δ ,δ ) +δ (δ ,δ ) +separation +Figure 32.5.6–1 Typical traction-separation response. +Damage initiation +As the name implies, damage initiation refers to the beginning of degradation of the response of a material +point. The process of degradation begins when the stresses and/or strains satisfy certain damage initiation +criteria that you specify. Several damage initiation criteria are available and are discussed below. Each +damage initiation criterion also has an output variable associated with it to indicate whether the criterion +is met. A value of 1 or higher indicates that the initiation criterion has been met . Damage initiation criteria that do not have an associated evolution law affect only output. Thus, +you can use these criteria to evaluate the propensity of the material to undergo damage without actually +modeling the damage process (i.e., without actually specifying damage evolution). +, +, +, and +, and +In the discussion below, +represent the peak values of the nominal stress when the +deformation is either purely normal to the interface or purely in the first or the second shear direction, +respectively. Likewise, +represent the peak values of the nominal strain when the +deformation is either purely normal to the interface or purely in the first or the second shear direction, +respectively. With the initial constitutive thickness +, the nominal strain components are equal to +the respective components of the relative displacement— , +, and —between the top and bottom of +the cohesive layer. The symbol +used in the discussion below represents the Macaulay bracket with +the usual interpretation. The Macaulay brackets are used to signify that a pure compressive deformation +or stress state does not initiate damage. +Maximum nominal stress criterion +Damage is assumed to initiate when the maximum nominal stress ratio (as defined in the expression +below) reaches a value of one. This criterion can be represented as +Input File Usage: +Abaqus/CAE Usage: +*DAMAGE INITIATION, CRITERION=MAXS +Property module: material editor: Mechanical→Damage for Traction- +Separation Laws→Maxs Damage +Maximum nominal strain criterion +Damage is assumed to initiate when the maximum nominal strain ratio (as defined in the expression +below) reaches a value of one. This criterion can be represented as +Input File Usage: +Abaqus/CAE Usage: +*DAMAGE INITIATION, CRITERION=MAXE +Property module: material editor: Mechanical→Damage for Traction- +Separation Laws→Maxe Damage +Quadratic nominal stress criterion +Damage is assumed to initiate when a quadratic interaction function involving the nominal stress ratios +(as defined in the expression below) reaches a value of one. This criterion can be represented as +Input File Usage: +Abaqus/CAE Usage: +*DAMAGE INITIATION, CRITERION=QUADS +Property module: material editor: Mechanical→Damage for Traction- +Separation Laws→Quads Damage +Quadratic nominal strain criterion +Damage is assumed to initiate when a quadratic interaction function involving the nominal strain ratios +(as defined in the expression below) reaches a value of one. This criterion can be represented as +Input File Usage: +Abaqus/CAE Usage: +*DAMAGE INITIATION, CRITERION=QUADE +Property module: material editor: Mechanical→Damage for Traction- +Separation Laws→Quade Damage +Damage evolution +The damage evolution law describes the rate at which the material stiffness is degraded once the +corresponding initiation criterion is reached. The general framework for describing the evolution of +damage in bulk materials (as opposed to interfaces modeled using cohesive elements) is described in +“Damage evolution and element removal for ductile metals,” Section 24.2.3. Conceptually, similar +ideas apply for describing damage evolution in cohesive elements with a constitutive response that is +described in terms of traction versus separation; however, many details are different. +A scalar damage variable, D, represents the overall damage in the material and captures the +combined effects of all the active mechanisms. It initially has a value of 0. If damage evolution is +modeled, D monotonically evolves from 0 to 1 upon further loading after the initiation of damage. The +stress components of the traction-separation model are affected by the damage according to +otherwise (no damage to compressive stiffness); +, +where +current strains without damage. +and +are the stress components predicted by the elastic traction-separation behavior for the +To describe the evolution of damage under a combination of normal and shear deformation across +the interface, it is useful to introduce an effective displacement (Camanho and Davila, 2002) defined as +Mixed-mode definition +The mode mix of the deformation fields in the cohesive zone quantify the relative proportions of normal +and shear deformation. Abaqus uses two measures of mode mix, one based on energies and the other +based on tractions. You can choose one of these measures when you specify the mode dependence +of the damage evolution process. Denoting by +the work done by the tractions and +their conjugate relative displacements in the normal, first, and second shear directions, respectively, and +defining +, the mode-mix definitions based on energies are as follows: +, and +, +Clearly, only two of the three quantities defined above are independent. It is also useful to define the +quantity +to denote the portion of the total work done by the shear traction and the +corresponding relative displacement components. As discussed later, Abaqus requires that you specify +material properties related to damage evolution as functions of +(or, equivalently, +) and +. +The corresponding definitions of the mode mix based on traction components are given by +where +definition (before they are normalized by the factor +is a measure of the effective shear traction. The angular measures used in the above +) are illustrated in Figure 32.5.6–2. +The mode-mix ratios defined in terms of energies and tractions can be quite different in general. +The following example illustrates this point. In terms of energies a deformation in the purely normal +direction is one for which +, irrespective of the values of the normal and the +shear tractions. In particular, for a material with coupled traction-separation behavior both the normal +and shear tractions may be nonzero for a deformation in the purely normal direction. For this case +the definition of mode mix based on energies would indicate a purely normal deformation, while the +definition based on tractions would suggest a mix of both normal and shear deformation. +and +There are two components to the definition of the evolution of damage. The first component involves +specifying either the effective displacement at complete failure, +, relative to the effective displacement +at the initiation of damage, +. The +; or the energy dissipated due to failure, +second component to the definition of damage evolution is the specification of the nature of the evolution +t~ +normal +t n +t t +Shear 2 +t s +Shear 1 +traction +Figure 32.5.6–2 Mode mix measures based on traction. +δ o +δ f +separation +Figure 32.5.6–3 Linear damage evolution. +of the damage variable, D, between initiation of damage and final failure. This can be done by either +defining linear or exponential softening laws or specifying D directly as a tabular function of the effective +displacement relative to the effective displacement at damage initiation. The material data described +above will in general be functions of the mode mix, temperature, and/or field variables. +Figure 32.5.6–4 is a schematic representation of the dependence of damage initiation and evolution +on the mode mix, for a traction-separation response with isotropic shear behavior. +Figure 32.5.6–4 Illustration of mixed-mode response in cohesive elements. +The figure shows the traction on the vertical axis and the magnitudes of the normal and the shear +separations along the two horizontal axes. The unshaded triangles in the two vertical coordinate planes +represent the response under pure normal and pure shear deformation, respectively. All intermediate +vertical planes (that contain the vertical axis) represent the damage response under mixed mode +conditions with different mode mixes. The dependence of the damage evolution data on the mode mix +can be defined either in tabular form or, in the case of an energy-based definition, analytically. The +manner in which the damage evolution data are specified as a function of the mode mix is discussed +later in this section. +Unloading subsequent to damage initiation is always assumed to occur linearly toward the origin +of the traction-separation plane, as shown in Figure 32.5.6–3. Reloading subsequent to unloading also +occurs along the same linear path until the softening envelope (line AB) is reached. Once the softening +envelope is reached, further reloading follows this envelope as indicated by the arrow in Figure 32.5.6–3. +Input File Usage: +Use the following option to use the mode-mix definition based on energies: +Abaqus/CAE Usage: +*DAMAGE EVOLUTION, MODE MIX RATIO=ENERGY +Use the following option to use the mode-mix definition based on tractions: +*DAMAGE EVOLUTION, MODE MIX RATIO=TRACTION +Property module: material editor: Mechanical→Damage for Traction- +Separation Laws→Quade Damage, Maxe Damage, Quads Damage, +or Maxs Damage: Suboptions→Damage Evolution: Mode mix ratio: +Energy or Traction +Evolution based on effective displacement +(i.e., the effective displacement at complete failure, +, relative to +You specify the quantity +the effective displacement at damage initiation, +, as shown in Figure 32.5.6–3) as a tabular function +of the mode mix, temperature, and/or field variables. In addition, you also choose either a linear or an +exponential softening law that defines the detailed evolution (between initiation and complete failure) +of the damage variable, D, as a function of the effective displacement beyond damage initiation. +Alternatively, instead of using linear or exponential softening, you can specify the damage variable, +D, directly as a tabular function of the effective displacement after the initiation of damage, +; +mode mix; temperature; and/or field variables. +Linear damage evolution +For linear softening Abaqus uses an evolution of the damage variable, D, that +reduces (in the case of damage evolution under a constant mode mix, temperature, and field variables) +to the expression proposed by Camanho and Davila (2002), namely: +In the preceding expression and in all later references, +refers to the maximum value of the effective +displacement attained during the loading history. The assumption of a constant mode mix at a material +point between initiation of damage and final failure is customary for problems involving monotonic +damage (or monotonic fracture). +Input File Usage: +Use the following option to specify linear damage evolution: +Abaqus/CAE Usage: +*DAMAGE EVOLUTION, TYPE=DISPLACEMENT, +SOFTENING=LINEAR +Property module: material editor: Mechanical→Damage for Traction- +Separation Laws→Quade Damage, Maxe Damage, Quads Damage, or +Maxs Damage: Suboptions→Damage Evolution: Type: Displacement: +Softening: Linear +Exponential damage evolution +For exponential softening Abaqus uses an evolution of the damage variable, D, that +reduces (in the case of damage evolution under a constant mode mix, temperature, and field variables) to +In the expression above +evolution and +is the exponential function. +is a non-dimensional material parameter that defines the rate of damage +traction +δ o +δ f +separation +Figure 32.5.6–5 Exponential damage evolution. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to specify exponential softening: +*DAMAGE EVOLUTION, TYPE=DISPLACEMENT, +SOFTENING=EXPONENTIAL +Property module: material editor: Mechanical→Damage for Traction- +Separation Laws→Quade Damage, Maxe Damage, Quads Damage, or +Maxs Damage: Suboptions→Damage Evolution: Type: Displacement: +Softening: Exponential +Tabular damage evolution +For tabular softening you define the evolution of D directly in tabular form. D must be specified as +a function of the effective displacement relative to the effective displacement at initiation, mode mix, +temperature, and/or field variables. +Input File Usage: +Use the following option to define the damage variable directly in tabular form: +Abaqus/CAE Usage: +*DAMAGE EVOLUTION, TYPE=DISPLACEMENT, +SOFTENING=TABULAR +Property module: material editor: Mechanical→Damage for Traction- +Separation Laws→Quade Damage, Maxe Damage, Quads Damage, or +Maxs Damage: Suboptions→Damage Evolution: Type: Displacement: +Softening: Tabular +Evolution based on energy +Damage evolution can be defined based on the energy that is dissipated as a result of the damage process, +also called the fracture energy. The fracture energy is equal to the area under the traction-separation curve +. You specify the fracture energy as a material property and choose either a linear +or an exponential softening behavior. Abaqus ensures that the area under the linear or the exponential +damaged response is equal to the fracture energy. +The dependence of the fracture energy on the mode mix can be specified either directly in tabular +form or by using analytical forms as described below. When the analytical forms are used, the mode-mix +ratio is assumed to be defined in terms of energies. +Tabular form +The simplest way to define the dependence of the fracture energy is to specify it directly as a function of +the mode mix in tabular form. +Input File Usage: +Use the following option to specify fracture energy as a function of the mode +mix in tabular form: +*DAMAGE EVOLUTION, TYPE=ENERGY, +MIXED MODE BEHAVIOR=TABULAR +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Damage for Traction- +Separation Laws→Quade Damage, Maxe Damage, Quads Damage, or +Maxs Damage: Suboptions→Damage Evolution: Type: Energy: Mixed +mode behavior: Tabular +Power law form +The dependence of the fracture energy on the mode mix can be defined based on a power law fracture +criterion. The power law criterion states that failure under mixed-mode conditions is governed by a +power law interaction of the energies required to cause failure in the individual (normal and two shear) +modes. It is given by +The mixed-mode fracture energy +when the above condition is satisfied. In other words, +You specify the quantities +failure in the normal, the first, and the second shear directions, respectively. +, and +, +, which refer to the critical fracture energies required to cause +Input File Usage: +Abaqus/CAE Usage: +Use the following option to define the fracture energy as a function of the mode +mix using the analytical power law fracture criterion: +*DAMAGE EVOLUTION, TYPE=ENERGY, +MIXED MODE BEHAVIOR=POWER LAW, POWER= +Property module: material editor: Mechanical→Damage for Traction- +Separation Laws→Quade Damage, Maxe Damage, Quads Damage, or +Maxs Damage: Suboptions→Damage Evolution: Type: Energy: Mixed +mode behavior: Power Law: Toggle on Power and enter the exponent value +Benzeggagh-Kenane (BK) form +The Benzeggagh-Kenane fracture criterion (Benzeggagh and Kenane, 1996) is particularly useful when +the critical fracture energies during deformation purely along the first and the second shear directions are +the same; i.e., +. It is given by +where +, +, and +is a material parameter. You specify +, +, and . +Input File Usage: +Abaqus/CAE Usage: +Use the following option to define the fracture energy as a function of the mode +mix using the analytical BK fracture criterion: +*DAMAGE EVOLUTION, TYPE=ENERGY, +MIXED MODE BEHAVIOR=BK, POWER= +Property module: material editor: Mechanical→Damage for Traction- +Separation Laws→Quade Damage, Maxe Damage, Quads Damage, or +Maxs Damage: Suboptions→Damage Evolution: Type: Energy: Mixed +mode behavior: Bk: Toggle on Power and enter the exponent value +Linear damage evolution +For linear softening Abaqus uses an evolution of the damage variable, D, that +reduces to +where +as the effective traction at damage initiation. +maximum value of the effective displacement attained during the loading history. +with +refers to the +Input File Usage: +Use the following option to specify linear damage evolution: +Abaqus/CAE Usage: +*DAMAGE EVOLUTION, TYPE=ENERGY, SOFTENING=LINEAR +Property module: material editor: Mechanical→Damage for Traction- +Separation Laws→Quade Damage, Maxe Damage, Quads Damage, +or Maxs Damage: Suboptions→Damage Evolution: Type: Energy: +Softening: Linear +Exponential damage evolution +For exponential softening Abaqus uses an evolution of the damage variable, D, that reduces to +In the expression above +is the +elastic energy at damage initiation. In this case the traction might not drop immediately after damage +initiation, which is different from what is seen in Figure 32.5.6–5. +are the effective traction and displacement, respectively. +and +Input File Usage: +Use the following option to specify exponential softening: +*DAMAGE EVOLUTION, TYPE=ENERGY, +SOFTENING=EXPONENTIAL +Abaqus/CAE Usage: +Property module: material editor: Mechanical→Damage for Traction- +Separation Laws→Quade Damage, Maxe Damage, Quads Damage, +or Maxs Damage: Suboptions→Damage Evolution: Type: Energy: +Softening: Exponential +Defining damage evolution data as a tabular function of mode mix +As discussed earlier, the material data defining the evolution of damage can be tabular functions of the +mode mix. The manner in which this dependence must be defined in Abaqus is outlined below for mode- +mix definitions based on energy and traction, respectively. In the following discussion it is assumed +that the evolution is defined in terms of energy. Similar observations can also be made for evolution +definitions based on effective displacement. +Mode mix based on energy +For an energy-based definition of mode mix, in the most general case of a three-dimensional state of +deformation with anisotropic shear behavior the fracture energy, +, must be defined as a function of +is a measure of the fraction of +the total deformation that is shear, while +is a measure of the fraction of the +total shear deformation that is in the second shear direction. Figure 32.5.6–6 shows a schematic of the +fracture energy versus mode mix behavior. +. The quantity +and +Modes n-s +Modes s-t +Modes n-t +m + m = ( +2 3 +G s +G T +( +1.0 +1.0 +Figure 32.5.6–6 Fracture energy as a function of mode mix. + m + 3 +m + m = ( +2 3 +( +G t +GS +, +The limiting cases of pure normal and pure shear deformations in the first and second shear directions are +denoted in Figure 32.5.6–6 by +, respectively. The lines labeled “Modes n-s,” “Modes +n-t,” and “Modes s-t” show the transition in behavior between the pure normal and the pure shear in +the first direction, pure normal and pure shear in the second direction, and pure shears in the first and +second directions, respectively. In general, +at various +fixed values of +versus +as a “data block.” The following guidelines are +. In the discussion that follows we refer to a data set of +must be specified as a function of +corresponding to a fixed +, and +useful in defining the fracture energy as a function of the mode mix: +• For a two-dimensional problem +only. The data column corresponding to +only one “data block” is needed. +needs to be defined as a function of +in this case) +must be left blank. Hence, essentially +( +• For a three-dimensional problem with isotropic shear response, the shear behavior is defined by the +. Therefore, in this case a single +) also suffices to define the fracture energy +and not by the individual values of +and +sum +“data block” (the “data block” for +as a function of the mode mix. +• In the most general case of three-dimensional problems with anisotropic shear behavior, several +versus +can vary between +“data blocks” would be needed. As discussed earlier, each “data block” would contain +. In each “data block” +at a fixed value of +. The case +(the first data point in any “data block”), which corresponds to +0 and +a purely normal mode, can never be achieved when +(i.e., the only valid point +on line OB in Figure 32.5.6–6 is the point O, which corresponds to a purely normal deformation). +However, in the tabular definition of the fracture energy as a function of mode mix, this point simply +serves to set a limit that ensures a continuous change in fracture energy as a purely normal state +is approached from various combinations of normal and shear deformations. Hence, the fracture +energy of the first data point in each “data block” must always be set equal to the fracture energy in +a purely normal mode of deformation ( +). +As an example of the anisotropic shear case, consider that you want to input three “data blocks” +corresponding to fixed values of +0., 0.2, and 1.0, respectively. For each of the +three “data blocks,” the first data point must be +for the reasons discussed above. The rest +of the data points in each “data block” define the variation of the fracture energy with increasing +proportions of shear deformation. +Mode mix based on traction +needs to +The fracture energy needs to be specified in tabular form of +be specified as a function of +. A “data block” in this case corresponds +to a set of data for +may vary from 0 +(purely normal deformation) to 1 (purely shear deformation). An important restriction is that each data +block must specify the same value of the fracture energy for +. This restriction ensures that the +energy required for fracture as the traction vector approaches the normal direction does not depend on +the orientation of the projection of the traction vector on the shear plane . +at various fixed values of +, at a fixed value of +. In each “data block” +. Thus, +versus +versus +and +Evaluating damage when multiple criteria are active +When multiple damage initiation criteria and associated evolution definitions are used for the same +material, each evolution definition results in its own damage variable, +, where the subscript i represents +the ith damage system. The overall damage variable, D, is computed based on the individual +as +explained in “Evaluating overall damage when multiple criteria are active” in “Damage evolution and +element removal for ductile metals,” Section 24.2.3, for damage in bulk materials. +Maximum degradation and choice of element removal +You have control over how Abaqus treats cohesive elements with severe damage. By default, the upper +bound to the overall damage variable at a material point is +. You can reduce this upper bound +as discussed in “Controlling element deletion and maximum degradation for materials with damage +evolution” in “Section controls,” Section 27.1.4. You can control what happens to the cohesive element +when the damage reaches this limit, as discussed below. +By default, once the overall damage variable reaches +at all of its material points and none +of its material points are in compression, the cohesive elements, except for the pore pressure cohesive +elements, are removed (deleted). See “Controlling element deletion and maximum degradation for +materials with damage evolution” in “Section controls,” Section 27.1.4, for details. This element +removal approach is often appropriate for modeling complete fracture of the bond and separation of +components. Once removed, cohesive elements offer no resistance to subsequent penetration of the +components, so it may be necessary to model contact between the components as discussed in “Defining +contact between surrounding components” in “Modeling with cohesive elements,” Section 32.5.3. +Alternatively, you can specify that a cohesive element should remain in the model even after the +overall damage variable reaches +. In this case the stiffness of the element in tension and/or shear +remains constant (degraded by a factor of 1 − +over the initial undamaged stiffness). This choice +is appropriate if the cohesive elements must resist interpenetration of the surrounding components +even after they have completely degraded in tension and/or shear . In Abaqus/Explicit +it is recommended that you suppress bulk viscosity in the cohesive elements by setting the scale factors +for the linear and quadratic bulk viscosity parameters to zero using section controls . +Uncoupled transverse shear response +An optional linear elastic transverse shear behavior can be defined to provide additional stability to +cohesive elements, particularly after damage has occurred. The transverse shear behavior is assumed +to be independent of the regular material response and does not undergo any damage. +Input File Usage: +Abaqus/CAE Usage: +Use the following options: +*COHESIVE SECTION, RESPONSE=TRACTION SEPARATION +*TRANSVERSE SHEAR STIFFNESS +Transverse shear behavior is not supported in Abaqus/CAE for cohesive +sections. +Viscous regularization in Abaqus/Standard +Material models exhibiting softening behavior and stiffness degradation often lead to severe convergence +difficulties in implicit analysis programs, such as Abaqus/Standard. A common technique to overcome +some of these convergence difficulties is the use of viscous regularization of the constitutive equations, +which causes the tangent stiffness matrix of the softening material to be positive for sufficiently small +time increments. +The traction-separation laws can be regularized in Abaqus/Standard using viscosity by permitting +stresses to be outside the limits set by the traction-separation law. The regularization process involves +the use of a viscous stiffness degradation variable, +, which is defined by the evolution equation: +where +is the viscosity parameter representing the relaxation time of the viscous system and D is the +degradation variable evaluated in the inviscid backbone model. The damaged response of the viscous +material is given as +Using viscous regularization with a small value of the viscosity parameter (small compared to the +characteristic time increment) usually helps improve the rate of convergence of the model in the +softening regime, without compromising results. The basic idea is that the solution of the viscous +system relaxes to that of the inviscid case as +, where t represents time. You can specify +the value of the viscosity parameter as part of the section controls definition . If the viscosity parameter is different from zero, output results of +the stiffness degradation refer to the viscous value, +. The default value of the viscosity parameter +is zero so that no viscous regularization is performed. Use of viscous regularization for improving +the convergence behavior of delamination and debonding problems is discussed in “Delamination +analysis of laminated composites,” Section 2.7.1 of the Abaqus Benchmarks Manual, and “Analysis of +skin-stiffener debonding under tension,” Section 1.4.5 of the Abaqus Example Problems Manual. +The approximate amount of energy associated with viscous regularization over the whole model or +over an element set is available using output variable ALLCD. +Output +In addition to the standard output identifiers available in Abaqus (“Abaqus/Standard output variable +identifiers,” Section 4.2.1, and “Abaqus/Explicit output variable identifiers,” Section 4.2.2), +the +following variables have special meaning for cohesive elements with traction-separation behavior: +STATUS +SDEG +DMICRT +MAXSCRT +MAXECRT +QUADSCRT +QUADECRT +ALLCD +Status of element (the status of an element is 1.0 if the element is active, 0.0 if the +element is not). +Overall value of the scalar damage variable, D. +All damage initiation criteria components. +Maximum value of the nominal stress damage initiation criterion at a material point +during the analysis. It is evaluated as +Maximum value of the nominal strain damage initiation criterion at a material point +during the analysis. It is evaluated as +Maximum value of the quadratic nominal stress damage initiation criterion at a +material point during the analysis. It is evaluated as +Maximum value of the quadratic nominal strain damage initiation criterion at a +material point during the analysis. It is evaluated as +The approximate amount of energy over the whole model or over an element set +that is associated with viscous regularization in Abaqus/Standard. Corresponding +output variables (such as CENER, ELCD, and ECDDEN) represent the energy +associated with viscous regularization at the integration point level and element +level (the last quantity represents the energy per unit volume in the element), +respectively. +For the variables above that indicate whether a certain damage initiation criterion has been satisfied +or not, a value that is less than 1.0 indicates that the criterion has not been satisfied, while a value of 1.0 or +higher indicates that the criterion has been satisfied. If damage evolution is specified for this criterion, the +maximum value of this variable does not exceed 1.0. However, if damage evolution is not specified for +the initiation criterion, this variable can have values higher than 1.0. The extent to which the variable is +higher than 1.0 may be considered to be a measure of the extent to which this criterion has been violated. +Additional references +• Benzeggagh, M. L., and M. Kenane, “Measurement of Mixed-Mode Delamination Fracture +Toughness of Unidirectional Glass/Epoxy Composites with Mixed-Mode Bending Apparatus,” +Composites Science and Technology, vol. 56, pp. 439–449, 1996. +• Camanho, P. P., and C. G. Davila, “Mixed-Mode Decohesion Finite Elements for the Simulation +of Delamination in Composite Materials,” NASA/TM-2002–211737, pp. 1–37, 2002. +32.5.7 +DEFINING THE CONSTITUTIVE RESPONSE OF FLUID WITHIN THE COHESIVE +ELEMENT GAP +Products: Abaqus/Standard Abaqus/CAE +References +• “Cohesive elements: overview,” Section 32.5.1 +• “Defining the constitutive response of cohesive elements using a traction-separation description,” +Section 32.5.6 +• *FLUID LEAKOFF +• *GAP FLOW +• Chapter 21, “Adhesive joints and bonded interfaces,” of the Abaqus/CAE User’s Manual +Overview +The cohesive element fluid flow model: +• is typically used in geotechnical applications, where fluid flow continuity within the gap and through +the interface must be maintained; +• enables fluid pressure on the cohesive element surface to contribute to its mechanical behavior, +which enables the modeling of hydraulically driven fracture; +• enables modeling of an additional resistance layer on the surface of the cohesive element; and +• can be used only in conjunction with traction-separation behavior. +The features described in this section are used to model fluid flow within and across surfaces of pore +pressure cohesive elements. +Defining pore fluid flow properties +The fluid constitutive response comprises: +• Tangential flow within the gap, which can be modeled with either a Newtonian or power law model; +and +• Normal flow across the gap, which can reflect resistance due to caking or fouling effects. +The flow patterns of the pore fluid in the element are shown in Figure 32.5.7–1. The fluid is assumed to be +incompressible, and the formulation is based on a statement of flow continuity that considers tangential +and normal flow and the rate of opening of the cohesive element. +Specifying the fluid flow properties +You can assign tangential and normal flow properties separately. +cohesive elements +tangential flow +normal +flow +Figure 32.5.7–1 Flow within cohesive elements. +Tangential flow +By default, there is no tangential flow of pore fluid within the cohesive element. To allow tangential +flow, define a gap flow property in conjunction with the pore fluid material definition. +Newtonian fluid +In the case of a Newtonian fluid the volume flow rate density vector is given by the expression +is the tangential permeability (the resistance to the fluid flow), +is the pressure gradient along +where +the cohesive element, and +In Abaqus the gap opening, +is the gap opening. +, is defined as +where +and +and +are the current and original cohesive element geometrical thicknesses, respectively; +is the initial gap opening, which has a default value of 0.002. +Abaqus defines the tangential permeability, or the resistance to flow, according to Reynold’s +equation: +is the fluid viscosity and +is the gap opening. You can also specify an upper limit on the value +where +of +. +Input File Usage: +Abaqus/CAE Usage: +Use the following option to define the initial gap opening directly: +*SECTION CONTROLS, INITIAL GAP OPENING +Use the following option to define the tangential flow in a Newtonian fluid: +*GAP FLOW, TYPE=NEWTONIAN, KMAX +Initial gap opening is not supported in Abaqus/CAE. +Property module: material editor: Other→Pore Fluid→Gap Flow: Type: +Newtonian: Toggle on Maximum Permeability and enter the value of +Power law fluid +In the case of a power law fluid the constitutive relation is defined as +is the shear stress, +where +coefficient. Abaqus defines the tangential volume flow rate density as +is the shear strain rate, +is the fluid consistency, and +is the power law +where +is the gap opening. +Input File Usage: +Abaqus/CAE Usage: +*GAP FLOW, TYPE=POWER LAW +Property module: material editor: Other→Pore Fluid→Gap +Flow: Type: Power law +Normal flow across gap surfaces +You can permit normal flow by defining a fluid leakoff coefficient for the pore fluid material. This +coefficient defines a pressure-flow relationship between the cohesive element’s middle nodes and their +adjacent surface nodes. The fluid leakoff coefficients can be interpreted as the permeability of a finite +layer of material on the cohesive element surfaces, as shown in Figure 32.5.7–2. The normal flow is +defined as +and +where +and +pressure; and +are the flow rates into the top and bottom surfaces, respectively; +and +are the pore pressures on the top and bottom surfaces, respectively. +is the midface +Input File Usage: +Abaqus/CAE Usage: +*FLUID LEAKOFF +Property module: material editor: Other→Pore Fluid→Fluid +Leakoff: Type: Coefficients +Pt +Pi +Pb +permeable layer +Figure 32.5.7–2 Leakoff coefficient interpretation as a permeable layer. +Defining leakoff coefficients as a function of temperature and field variables +Input File Usage: +You can optionally define leakoff coefficients as functions of temperature and field variables. +*FLUID LEAKOFF, DEPENDENCIES +Property module: material editor: Other→Pore Fluid→Fluid Leakoff: +Type: Coefficients: Toggle on Use temperature-dependent data +and select the number of field variables. +Abaqus/CAE Usage: +Defining leakoff coefficients in a user subroutine +User subroutine UFLUIDLEAKOFF can also be used to define more complex leakoff behavior, including +the ability to define a time accumulated resistance, or fouling, through the use of solution-dependent state +variables. +Input File Usage: +Abaqus/CAE Usage: +*FLUID LEAKOFF, USER +Property module: material editor: Other→Pore Fluid→Fluid +Leakoff: Type: User +Tangential and normal flow combinations +Table 32.5.7–1 shows the permitted combinations of tangential and normal flow and the effects of each +combination. +Initially open elements +When the opening of the cohesive element is driven primarily by entry of fluid into the gap, you will +have to define one or more elements as initially open, since tangential flow is possible only in an open +element. Identify initially open elements as initial conditions. +Input File Usage: +Abaqus/CAE Usage: +*INITIAL CONDITIONS, TYPE=INITIAL GAP +Initial gap definition is not supported in Abaqus/CAE. +Table 32.5.7–1 Effects of flow property definition combinations. +Normal flow is defined +Normal flow is undefined +Tangential flow +is defined +Tangential and normal flow are +modeled. +Tangential flow +is undefined +Normal flow is modeled. +Tangential flow is modeled. Pore pressure +continuity is enforced between facing nodes +in the cohesive element only when the +element is closed. Otherwise, the surfaces +are impermeable in the normal direction. +Tangential flow is not modeled. Pore +pressure continuity is always enforced +between facing nodes in the cohesive +element. +Use of unsymmetric matrix storage and solution +The pore pressure cohesive element matrices are unsymmetric; therefore, unsymmetric matrix storage +and solution may be needed to improve convergence . +Additional considerations +Your use of cohesive element fluid properties and your property values can impact your solution in some +cases. +Large coefficient values +You must make sure that the tangential permeability or fluid leakoff coefficients are not excessively large. +If either coefficient is many orders of magnitude higher than the permeability in the adjacent continuum +elements, matrix conditioning problems may occur, leading to solver singularities and unreliable results. +Use in total pore pressure simulations +Definition of tangential flow properties may result in inaccurate results if the total pore pressure +formulation is used and the hydrostatic pressure gradient contributes significantly to the tangential flow +in the gap. The total pore pressure formulation is invoked if you apply gravity distributed loads to all +elements in the model. The results will be accurate if the hydrostatic pressure gradient (i.e., the gravity +vector) is perpendicular to the cohesive element. +Output +The following output variables are available when flow is enabled in pore pressure cohesive elements: +GFVR +PFOPEN +Gap fluid volume rate. +Fracture opening. +LEAKVRT +Leak-off flow rate at element top. +ALEAKVRT +Accumulated leak-off flow volume at element top. +LEAKVRB +Leak-off flow rate at element bottom. +ALEAKVRB +Accumulated leak-off flow volume at element bottom. +32.5.8 +TWO-DIMENSIONAL COHESIVE ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Cohesive elements: overview,” Section 32.5.1 +• “Choosing a cohesive element,” Section 32.5.2 +• *COHESIVE SECTION +• Chapter 21, “Adhesive joints and bonded interfaces,” of the Abaqus/CAE User’s Manual +Overview +This section provides a reference to the two-dimensional cohesive elements available in Abaqus/Standard +and Abaqus/Explicit. +Element types +General element +COH2D4 +4-node two-dimensional cohesive element +Active degrees of freedom +1, 2 +Additional solution variables +None. +Pore pressure element +COH2D4P(S) +6-node displacement and pore pressure two-dimensional cohesive element +Active degrees of freedom +1, 2, 8 at nodes on the top and bottom faces +8 at nodes on the middle face +Additional solution variables +None. +Nodal coordinates required +Element property definition +You can define the element’s initial constitutive thickness and the out-of-plane width. The default initial +constitutive thickness of cohesive elements depends on the response of these elements. For continuum +response, the default initial constitutive thickness is computed based on the nodal coordinates. For +traction-separation response, the default initial constitutive thickness is assumed to be 1.0. For response +based on a uniaxial stress state, there is no default; you must indicate your choice of the method for +computing the initial constitutive thickness. See “Specifying the constitutive thickness” in “Defining the +cohesive element’s initial geometry,” Section 32.5.4, for details. +Abaqus calculates the thickness direction automatically based on the midsurface of the element. +Input File Usage: +Abaqus/CAE Usage: +*COHESIVE SECTION +Property module: Create Section: select Other as the section +Category and Cohesive as the section Type +Element-based loading +Distributed loads +Distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +BX +BY +BXNU +Body force +Body force +Body force +FL−3 +FL−3 +FL−3 +BYNU +Body force +FL−3 +Body force in global X-direction. +Body force in global Y-direction. +Nonuniform body force in global +X-direction with magnitude supplied +subroutine DLOAD in +via +Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +user +Nonuniform body force in global +Y-direction with magnitude supplied +subroutine DLOAD in +via +user +and VDLOAD in +Abaqus/Standard +Abaqus/Explicit. +CENT(S) +Not supported +FL−4 (ML−3T−2) Centrifugal load (magnitude is input +is the mass density +, where +is the angular +as +per unit volume, +velocity). +(*DLOAD) +CENTRIF(S) +2-D COHESIVE ELEMENT LIBRARY +Abaqus/CAE +Load/Interaction +Units +Description +Rotational body +force +T−2 +Centrifugal load (magnitude is input +as +the angular +velocity). +, where +is +CORIO(S) +Coriolis force +FL−4 T +(ML−3 T−1 ) +GRAV +Gravity +Pn +PnNU +Pressure +Not supported +LT−2 +FL−2 +FL−2 +ROTA(S) +Rotational body +force +T−2 +SBF(E) +SPn(E) +VBF(E) +VPn(E) +Not supported +FL−5 T2 +Not supported +Not supported +FL−4 T2 +FL−4 T +Not supported +FL−3 T +Coriolis force (magnitude is input +is the mass density +as +, where +per unit volume, +is the angular +velocity). +Gravity +loading +direction (magnitude is +acceleration). +in +specified +input as +Pressure on face n. +on +Nonuniform pressure +with +magnitude +via +user +Abaqus/Standard +Abaqus/Explicit. +face +supplied +subroutine DLOAD in +and VDLOAD in +Rotary acceleration load (magnitude +is input as +is the rotary +acceleration). +, where +Stagnation body force in global X- +and Y-directions. +Stagnation pressure on face n. +Viscous body force in global X- and +Y-directions. +Viscous pressure on face n, applying +a pressure proportional to the velocity +normal to the face and opposing the +motion. +Surface-based loading +Distributed loads +Surface-based distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +PNU +SP(E) +VP(E) +Pressure +Pressure +FL−2 +FL−2 +Pressure +FL−4 T2 +Pressure +FL−3 T +Pressure on the element surface. +Nonuniform pressure on the element +surface with magnitude +supplied +subroutine DLOAD in +via +Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +user +Stagnation pressure on the element +surface. +Viscous pressure applied on the +element surface. The viscous pressure +is proportional to the velocity normal +to the element face and opposing the +motion. +Element output +Stress, strain, and other tensor components available for output depend on whether the cohesive elements +are used to model adhesive joints, gaskets, or delamination problems. You indicate the intended usage +of the cohesive elements by choosing an appropriate response type when defining the section properties +of these elements. The available response types are discussed in “Defining the constitutive response of +cohesive elements using a continuum approach,” Section 32.5.5, and “Defining the constitutive response +of cohesive elements using a traction-separation description,” Section 32.5.6. +Cohesive elements using a continuum response +Stress and other tensors (including strain tensors) are available for elements with continuum response. +Both the stress tensor and the strain tensor contain true values. For the constitutive calculations using +a continuum response, only the direct through-thickness and the transverse shear strains are assumed to +be nonzero. All the other strain components (i.e., the membrane strains) are assumed to be zero . All tensors have the same number +of components. For example, the stress components are as follows: +S11 +S22 +S33 +S12 +Direct membrane stress. +Direct through-thickness stress. +Direct membrane stress. +Transverse shear stress. +Cohesive elements using a uniaxial stress state +Stress and other tensors (including strain tensors) are available for cohesive elements with uniaxial stress +response. Both the stress tensor and the strain tensor contain true values. For the constitutive calculations +using a uniaxial stress response, only the direct through-thickness stress is assumed to be nonzero. All +the other stress components (i.e., the membrane and transverse shear stresses) are assumed to be zero . All tensors have the same number +of components. For example, the stress components are as follows: +S22 +Direct through-thickness stress. +Cohesive elements using a traction-separation response +Stress and other tensors (including strain tensors) are available for elements with traction-separation +response. Both the stress tensor and the strain tensor contain nominal values. The output variables E, +LE, and NE all contain the nominal strain when the response of cohesive elements is defined in terms +of traction versus separation. All tensors have the same number of components. For example, the stress +components are as follows: +S22 +S12 +Direct through-thickness stress. +Transverse shear stress. +Node ordering and face numbering on elements +face 3 +face 4 +face 2 + 5 +face 1 +4 - node element +6 - node element +Element faces +Face 1 +Face 2 +Face 3 +Face 4 +1 – 2 face +2 – 3 face +3 – 4 face +4 – 1 face +Numbering of integration points for output +5 1 +2 6 +4 - node element +6 - node element +32.5.9 +THREE-DIMENSIONAL COHESIVE ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Cohesive elements: overview,” Section 32.5.1 +• “Choosing a cohesive element,” Section 32.5.2 +• *COHESIVE SECTION +• Chapter 21, “Adhesive joints and bonded interfaces,” of the Abaqus/CAE User’s Manual +Overview +section provides a reference to the three-dimensional cohesive elements available in +This +Abaqus/Standard and Abaqus/Explicit. +Element types +General elements +COH3D6 +COH3D8 +6-node three-dimensional cohesive element +8-node three-dimensional cohesive element +Active degrees of freedom +1, 2, 3 +Additional solution variables +None. +Pore pressure elements +COH3D6P +9-node displacement and pore pressure three-dimensional cohesive element +COH3D8P +12-node displacement and pore pressure three-dimensional cohesive element +Active degrees of freedom +1, 2, 3, 8 at nodes on the top and bottom faces +8 at nodes on the middle face +Additional solution variables +None. +Nodal coordinates required +Element property definition +You can define the element’s initial constitutive thickness. The default initial constitutive thickness of +cohesive elements depends on the response of these elements. For continuum response, the default +initial constitutive thickness is computed based on the nodal coordinates. For traction-separation +response, the default initial constitutive thickness is assumed to be 1.0. For response based on a uniaxial +stress state, there is no default; you must indicate your choice of the method for computing the initial +constitutive thickness. See “Specifying the constitutive thickness” in “Defining the cohesive element’s +initial geometry,” Section 32.5.4, for details. +Abaqus computes the thickness direction automatically based on the midsurface of the element. +Input File Usage: +Abaqus/CAE Usage: +*COHESIVE SECTION +Property module: Create Section: select Other as the section +Category and Cohesive as the section Type +Element-based loading +Distributed loads +Distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +BX +BY +BZ +BXNU +Body force +Body force +Body force +Body force +FL−3 +FL−3 +FL−3 +FL−3 +BYNU +Body force +FL−3 +BZNU +Body force +FL−3 +Body force in global X-direction. +Body force in global Y-direction. +Body force in global Z-direction. +user +Nonuniform body force in global +X-direction with magnitude supplied +subroutine DLOAD in +via +Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +Nonuniform body force in global +Y-direction with magnitude supplied +subroutine DLOAD in +user +via +and VDLOAD in +Abaqus/Standard +Abaqus/Explicit. +Nonuniform body force in global +Z-direction with magnitude supplied +subroutine DLOAD in +via +user +and VDLOAD in +Abaqus/Standard +Abaqus/Explicit. +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +CENT(S) +Not supported +Units +Description +FL−4 (ML−3T−2) Centrifugal load (magnitude is input +is the mass density +, where +is the angular +as +per unit volume, +velocity). +Centrifugal load (magnitude is input +as +the angular +velocity). +, where +is +Coriolis force (magnitude is input +is the mass density +as +, where +per unit volume, +is the angular +velocity). +Gravity +loading +direction (magnitude is +acceleration). +in +specified +input as +Pressure on face n. +on +Nonuniform pressure +with +magnitude +via +user +Abaqus/Standard +Abaqus/Explicit. +face +supplied +subroutine DLOAD in +and VDLOAD in +Rotary acceleration load (magnitude +is input as +is the rotary +acceleration). +, where +Stagnation body force in global X-, +Y-, and Z-directions. +Stagnation pressure on face n. +Viscous body force in global X-, Y-, +and Z-directions. +Viscous pressure on face n, applying +a pressure proportional to the velocity +normal to the face and opposing the +motion. +CENTRIF(S) +Rotational body +force +T−2 +CORIO(S) +Coriolis force +FL−4 T +(ML−3 T−1 ) +GRAV +Gravity +Pn +PnNU +Pressure +Not supported +LT−2 +FL−2 +FL−2 +ROTA(S) +Rotational body +force +T−2 +SBF(E) +SPn(E) +VBF(E) +VPn(E) +Not supported +FL−5 T2 +Not supported +Not supported +FL−4 T2 +FL−4 T +Not supported +FL−3 T +Surface-based loading +Distributed loads +Surface-based distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +PNU +SP(E) +VP(E) +Pressure +Pressure +FL−2 +FL−2 +Pressure +Pressure +FL−4 T2 +FL−3 T +Pressure on the element surface. +Nonuniform pressure on the element +surface with magnitude +supplied +subroutine DLOAD in +via +user +and VDLOAD in +Abaqus/Standard +Abaqus/Explicit. +Stagnation pressure on the element +surface. +Viscous pressure applied on the +element surface. The viscous pressure +is proportional to the velocity normal +to the element face and opposing the +motion. +Element output +Stress, strain, and other tensor components available for output depend on whether the cohesive elements +are used to model adhesive joints, gaskets, or delamination problems. You indicate the intended usage +of the cohesive elements by choosing an appropriate response type when defining the section properties +of these elements. The available response types are discussed in “Defining the constitutive response of +cohesive elements using a continuum approach,” Section 32.5.5, and “Defining the constitutive response +of cohesive elements using a traction-separation description,” Section 32.5.6. +Cohesive elements using a continuum response +Stress and other tensors (including strain tensors) are available for elements with continuum response. +Both the stress tensor and the strain tensor contain true values. For the constitutive calculations using +a continuum response, only the direct through-thickness and the transverse shear strains are assumed to +be nonzero. All the other strain components (i.e., the membrane strains) are assumed to be zero . All tensors have the same number +of components. For example, the stress components are as follows: +S11 +Direct membrane stress. +S22 +S33 +S12 +S13 +S23 +Direct membrane stress. +Direct through-thickness stress. +In-plane membrane shear stress. +Transverse shear stress. +Transverse shear stress. +Cohesive elements using a uniaxial stress state +Stress and other tensors (including strain tensors) are available for cohesive elements with uniaxial stress +response. Both the stress tensor and the strain tensor contain true values. For the constitutive calculations +using a uniaxial stress response, only the direct through-thickness stress is assumed to be nonzero. All +the other stress components (i.e., the membrane and transverse shear stresses) are assumed to be zero . All tensors have the same number +of components. For example, the stress components are as follows: +S33 +Direct through-thickness stress. +Cohesive elements using a traction-separation response +Stress and other tensors (including strain tensors) are available for elements with traction-separation +response. Both the stress tensor and the strain tensor contain nominal values. The output variables E, +LE, and NE all contain the nominal strain when the response of cohesive elements is defined in terms +of traction versus separation. All tensors have the same number of components. For example, the stress +components are as follows: +S33 +S13 +S23 +Direct through-thickness stress. +Transverse shear stress. +Transverse shear stress. +Node ordering and face numbering on elements +face 3 +face 2 +face 5 +face 4 +face 1 +6 - node element +9 - node element +face 2 +face 5 +face 6 +face 4 +face 1 +face 3 +9 10 +12 11 +8 - node element +1 2 - node element +Element faces for COH3D6 +Face 1 +Face 2 +Face 3 +Face 4 +Face 5 +1 – 2 – 3 face +4 – 6 – 5 face +1 – 4 – 5 – 2 face +2 – 5 – 6 – 3 face +3 – 6 – 4 – 1 face +Element faces for COH3D8 +Face 1 +Face 2 +Face 3 +Face 4 +Face 5 +Face 6 +1 – 2 – 3 – 4 face +5 – 8 – 7 – 6 face +1 – 5 – 6 – 2 face +2 – 6 – 7 – 3 face +3 – 7 – 8 – 4 face +4 – 8 – 5 – 1 face +Numbering of integration points for output +7 1 +8 2 + 6 +9 3 +6 - node element +9 - node element +12 4 +11 +9 1 +10 +8 - node element +1 2 - node element +32.5.10 +AXISYMMETRIC COHESIVE ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Cohesive elements: overview,” Section 32.5.1 +• “Choosing a cohesive element,” Section 32.5.2 +• *COHESIVE SECTION +• Chapter 21, “Adhesive joints and bonded interfaces,” of the Abaqus/CAE User’s Manual +Overview +This section provides a reference to the axisymmetric cohesive elements available in Abaqus/Standard +and Abaqus/Explicit. +Element types +General element +COHAX4 +4-node axisymmetric cohesive element +Active degrees of freedom +, +1, 2 ( +) +Additional solution variables +None. +Pore pressure element +COHAX4P +6-node displacement and pore pressure axisymmetric cohesive element +Active degrees of freedom +1, 2, 8 +Additional solution variables +None. +Nodal coordinates required +Element property definition +You can define the element’s initial constitutive thickness. The default initial constitutive thickness of +cohesive elements depends on the response of these elements. For continuum response, the default +initial constitutive thickness is computed based on the nodal coordinates. For traction-separation +response, the default initial constitutive thickness is assumed to be 1.0. For response based on a uniaxial +stress state, there is no default; you must indicate your choice of the method for computing the initial +constitutive thickness. See “Specifying the constitutive thickness” in “Defining the cohesive element’s +initial geometry,” Section 32.5.4, for details. +Abaqus calculates the thickness direction automatically based on the midsurface of the element. +Input File Usage: +Abaqus/CAE Usage: +*COHESIVE SECTION +Property module: Create Section: select Other as the section +Category and Cohesive as the section Type +Element-based loading +Distributed loads +Distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +BR +BY +BRNU +Body force +Body force +Body force +FL−3 +FL−3 +FL−3 +BZNU +Body force +FL−3 +Body force in radial direction. +Body force in axial direction. +Nonuniform body force in radial +direction with magnitude supplied +subroutine DLOAD in +via +Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +user +Nonuniform body force in axial +direction with magnitude supplied +subroutine DLOAD in +via +user +and VDLOAD in +Abaqus/Standard +Abaqus/Explicit. +CENT(S) +Not supported +FL−4 (ML−3T−2) Centrifugal load (magnitude is input +is the mass density +, where +is the angular +as +per unit volume, +velocity). +Centrifugal load (magnitude is input +as +the angular +velocity). +, where +is +CENTRIF(S) +Rotational body +force +T−2 +(*DLOAD) +GRAV +Abaqus/CAE +Load/Interaction +Gravity +Pressure +Not supported +AXISYMMETRIC COHESIVE ELEMENT LIBRARY +Units +Description +LT−2 +FL−2 +FL−2 +Gravity +loading +direction (magnitude is +acceleration). +in +specified +input as +Pressure on face n. +on +with +user +face +Nonuniform pressure +supplied +magnitude +subroutine DLOAD in +via +Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +Not supported +FL−5 T2 +Not supported +Not supported +FL−4 T2 +FL−4 T +Not supported +FL−3 T +Stagnation body force in radial and +axial directions. +Stagnation pressure on face n. +Viscous body force in radial and axial +directions. +Viscous pressure on face n, applying +a pressure proportional to the velocity +normal to the face and opposing the +motion. +Pn +PnNU +SBF(E) +SPn(E) +VBF(E) +VPn(E) +Surface-based loading +Distributed loads +Surface-based distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +PNU +Pressure +Pressure +FL−2 +FL−2 +SP(E) +Pressure +FL−4 T2 +32.5.10–3 +Pressure on the element surface. +Nonuniform pressure on the element +surface with magnitude +supplied +subroutine DLOAD in +via +user +and VDLOAD in +Abaqus/Standard +Abaqus/Explicit. +Stagnation pressure on the element +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +VP(E) +Pressure +FL−3 T +Viscous pressure applied on the +element surface. The viscous pressure +is proportional to the velocity normal +to the element face and opposing the +motion. +Element output +Stress, strain, and other tensor components available for output depend on whether the cohesive elements +are used to model adhesive joints, gaskets, or delamination problems. You indicate the intended usage +of the cohesive elements by choosing an appropriate response type when defining the section properties +of these elements. The available response types are discussed in “Defining the constitutive response of +cohesive elements using a continuum approach,” Section 32.5.5, and “Defining the constitutive response +of cohesive elements using a traction-separation description,” Section 32.5.6. +Cohesive elements using a continuum response +Stress and other tensors (including strain tensors) are available for elements with continuum response. +Both the stress tensor and the strain tensor contain true values. For the constitutive calculations using +a continuum response, only the direct through-thickness and the transverse shear strains are assumed to +be nonzero. All the other strain components (i.e., the membrane strains) are assumed to be zero . All tensors have the same number +of components. For example, the stress components are as follows: +S11 +S22 +S33 +S12 +Direct membrane stress. +Direct through-thickness stress. +Direct membrane stress. +Transverse shear stress. +Cohesive elements using a uniaxial stress state +Stress and other tensors (including strain tensors) are available for cohesive elements with uniaxial stress +response. Both the stress tensor and the strain tensor contain true values. For the constitutive calculations +using a uniaxial stress response, only the direct through-thickness stress is assumed to be nonzero. All +the other stress components (i.e., the membrane and transverse shear stresses) are assumed to be zero . All tensors have the same number +of components. For example, the stress components are as follows: +S22 +Direct through-thickness stress. +Cohesive elements using a traction-separation response +Stress and other tensors (including strain tensors) are available for elements with traction-separation +response. Both the stress tensor and the strain tensor contain nominal values. The output variables E, +LE, and NE all contain the nominal strain when the response of cohesive elements is defined in terms +of traction versus separation. All tensors have the same number of components. For example, the stress +components are as follows: +S22 +S12 +Direct through-thickness stress. +Transverse shear stress. +Node ordering and face numbering on elements +face 3 +face 4 +face 2 +face 1 +4 - node element +6 - node element +Element faces +Face 1 +Face 2 +Face 3 +Face 4 +1 – 2 face +2 – 3 face +3 – 4 face +4 – 1 face +Numbering of integration points for output +5 1 +2 6 +4 - node element +6 - node element +32.6 +Gasket elements +• “Gasket elements: overview,” Section 32.6.1 +• “Choosing a gasket element,” Section 32.6.2 +• “Including gasket elements in a model,” Section 32.6.3 +• “Defining the gasket element’s initial geometry,” Section 32.6.4 +• “Defining the gasket behavior using a material model,” Section 32.6.5 +• “Defining the gasket behavior directly using a gasket behavior model,” Section 32.6.6 +• “Two-dimensional gasket element library,” Section 32.6.7 +• “Three-dimensional gasket element library,” Section 32.6.8 +• “Axisymmetric gasket element library,” Section 32.6.9 +32.6.1 +GASKET ELEMENTS: OVERVIEW +Abaqus/Standard offers a library of gasket elements to model the behavior of gaskets. +Overview +Gasket modeling consists of: +• choosing the appropriate gasket element type (“Choosing a gasket element,” Section 32.6.2); +• including the gasket elements in a finite element model (“Including gasket elements in a model,” +Section 32.6.3); +• defining the initial geometry of the gasket (“Defining the gasket element’s initial geometry,” +Section 32.6.4); and +• defining the gasket behavior with either a material model (“Defining the gasket behavior using a +material model,” Section 32.6.5) or a gasket behavior model (“Defining the gasket behavior directly +using a gasket behavior model,” Section 32.6.6). +Motivation for gasket elements +Gaskets are constructed in many ways and from many materials. Some types of gaskets consist of +several layers of preformed metal, possibly with thin elastomeric coatings or elastomeric inserts . Others use plastics together with elastomeric inserts. +Section A−A +Figure 32.6.1–1 Typical gasket consisting of several layers of preformed metal. +Gaskets are usually very thin and act as sealing components between structural components. They +are carefully designed to provide appropriate pressure-closure behaviors through their thickness (the +thin direction of the gaskets) so that they maintain their sealing action as the components undergo +It is difficult to use solid continuum elements +deformations due to thermal and mechanical loads. +to model the through-thickness behavior of gaskets with the material library available. Therefore, +Abaqus/Standard offers a variety of gasket elements that have through-thickness behaviors specifically +designed for the study of gaskets. +The gasket behavior models are separate from the models in the material library and assume that the +thickness-direction, transverse shear, and membrane behaviors are uncoupled . For a gasket behavior that +is not readily addressed by these special behavior models, such as occurs when coupled behaviors or +through-thickness tensile behavior must be considered, Abaqus/Standard provides a versatile alternative +by allowing a gasket element to use either a built-in or user-defined material model . +Spatial representation of a gasket element +Figure 32.6.1–2 demonstrates the key geometrical features that are used to define gasket elements. Gasket +elements are composed of two surfaces separated by a thickness. The relative motion of the bottom and +top surfaces measured along the thickness direction to the gasket quantifies the thickness-direction (local +1-direction) behavior of the gasket element. The relative change in position of the bottom and top surfaces +measured in the plane orthogonal to the thickness direction quantifies the transverse shear behavior of +the gasket element. The stretching and shearing of the midsurface of the element (the surface halfway +between the bottom and top surfaces) quantifies the membrane behavior of the gasket element. +top face (SPOS) +normal +direction +gasket element node +bottom face (SNEG) +midsurface +Figure 32.6.1–2 Spatial representation of a gasket element. +Local behavior directions defined at the integration points +The thickness direction defined at the integration points of gasket elements constitutes the local +1-direction. The transverse shear behavior is defined in the local 1–2 and 1–3 planes. The membrane +behavior is defined in the 2–3 plane. The local 2- and 3-directions are not defined for elements that have +nodes with only one degree of freedom because these elements consider only the thickness-direction +behavior of a gasket. The local directions are used to specify the gasket behavior and for output of all +quantities that describe the current deformation state of a gasket. Abaqus/Standard computes the local +directions by default. You can also define them for some element types. +Default local directions +Abaqus/Standard computes the local 1-direction as explained in “Defining the gasket element’s initial +geometry,” Section 32.6.4. +For two-dimensional and axisymmetric gasket elements, the local 2-direction is defined so that the +cross product between the local 1- and 2-directions gives the out-of-plane direction . +Figure 32.6.1–3 Local directions for two-dimensional and axisymmetric gasket elements. +For three-dimensional area and three-dimensional link elements, the local 2- and 3-directions are +normal to the local 1-direction and are defined by the standard Abaqus convention +for local directions on surfaces in space . +projection of x-axis +onto surface +Figure 32.6.1–4 Local directions for three-dimensional area +and three-dimensional link gasket elements. +For three-dimensional line elements, the local 2-direction is obtained by the projection of the tangent +to the midsurface of the element onto the plane orthogonal to the local 1-direction . +The local 3-direction is then obtained by the cross product of the local 1- and 2-directions. +midsurface +t = tangent vector +Figure 32.6.1–5 Local directions for three-dimensional line gasket elements. +Specifying the local directions +You can define the local 1-direction as explained in “Defining the gasket element’s initial geometry,” +Section 32.6.4. The local 2- and 3-directions can be defined using local orientations (“Orientations,” +Section 2.2.5) for three-dimensional area and three-dimensional link elements that consider transverse +shear and membrane deformations. +Input File Usage: +Use the following option to associate a local orientation with a particular gasket +element set: +Abaqus/CAE Usage: +*GASKET SECTION, ELSET=name, ORIENTATION=name +Property module: Assign→Material Orientation +Procedures with which gasket elements are allowed +Gasket elements can be used in static, static perturbation, quasi-static, dynamic, and frequency analyses. +However, gasket elements are assumed to have no mass; therefore, the density cannot be defined for +gasket elements. +32.6.2 +CHOOSING A GASKET ELEMENT +Products: Abaqus/Standard Abaqus/CAE +References +• “Gasket elements: overview,” Section 32.6.1 +• “Two-dimensional gasket element library,” Section 32.6.7 +• “Three-dimensional gasket element library,” Section 32.6.8 +• “Axisymmetric gasket element library,” Section 32.6.9 +• Chapter 32, “Gaskets,” of the Abaqus/CAE User’s Manual +Overview +The Abaqus/Standard gasket element library includes: +• elements for two-dimensional analyses; +• elements for three-dimensional analyses; +• elements for axisymmetric analyses; +• elements that account for the thickness-direction behavior of gaskets only; and +• elements that account for the thickness-direction, membrane, and transverse shear behaviors of +gaskets. +Naming convention +The gasket elements used in Abaqus/Standard are named as follows: +GK +3D +12 M N +Optional: +thickness-direction behavior only (N) +Optional: +line element (L), +element for use with modified +tetrahedral elements (M) +number of nodes +plane strain (PE), plane stress (PS), +two-dimensional (2D), three-dimensional (3D), +or axisymmetric (AX) +gasket element +For example, GKPE4 is a 4-node, plane strain gasket element that accounts for thickness-direction, +membrane, and transverse shear behaviors. +Elements for general use versus elements with thickness-direction behavior only +In both classes material properties can be +Abaqus/Standard offers two classes of gasket elements. +specified by either special gasket behavior models or built-in material models, including user-defined +materials . The first class is a collection +of gasket elements that have all displacement degrees of freedom active at their nodes. These elements +are necessary when the membrane and/or transverse shear behavior of the gasket is of importance . The thickness-direction, transverse shear, and membrane behaviors can be defined +as uncoupled behaviors only, when the elements are used in conjunction with special gasket behavior +models. In some cases the membrane effects are only secondary; in such cases it is possible to model +only the thickness-direction and transverse shear behaviors. These elements are suited for analyses +where both thickness-direction behavior and frictional effects are important. +gasket +normal +behavior +transverse shear +membrane stretch +membrane shear +membrane stretch +Figure 32.6.2–1 Different deformation modes of gaskets. +In the second class of gasket elements deformation is measured only in the thickness direction. The +response of the gasket to any other deformation mode is ignored. The nodes of these elements have +only one displacement degree of freedom, which lies in the thickness direction of the gasket. This class +of elements is intended as a means to reduce the computational cost of an analysis when the thickness- +direction behavior of the gasket is the only behavior of importance. This behavior can be specified easily +in terms of pressure in the gasket versus gasket closure. Frictional forces cannot be transmitted by such +elements, and any thermal expansion or stretching of the gasket in its plane is not accounted for. +Elements for two-dimensional, three-dimensional, and axisymmetric analyses +For both classes of gasket elements Abaqus/Standard offers a choice of +two-dimensional, +three-dimensional, and axisymmetric elements. Plane stress and plane strain elements are provided +for two-dimensional analyses to represent thin gaskets or thick gaskets in the out-of-plane direction, +respectively. Axisymmetric gasket elements are provided for cases where the geometry and loading of +the structure are axisymmetric. +Abaqus/Standard offers 2-node or link elements for two-dimensional, three-dimensional, and +axisymmetric analyses; three-dimensional line elements; and a three-dimensional 12-node element for +use with modified tetrahedral elements. These elements have specific characteristics that are useful +when modeling gaskets. +Link elements +Because link gasket elements have two nodes, their geometry defines only one dimension of the +gasket—the through-thickness dimension. A link gasket element might typically be used to model a +washer used under a bolt, when the bolt itself is modeled with a truss element. For two-dimensional and +three-dimensional link elements the cross-section of the gasket is undetermined. For axisymmetric link +elements the width of the element is undetermined. The reduction in dimensionality of these elements +offers flexibility in the specification of the gasket behavior and can prove to be very efficient in some +cases; see “Defining the gasket behavior directly using a gasket behavior model,” Section 32.6.6, for +further details. +Three-dimensional line elements +Three-dimensional line gasket elements are typically used to model narrow, thicker features in gaskets, +such as an elastomeric insert around a hole. Since they are used in three-dimensional analyses, their +width is undetermined from the element’s geometry. This reduction in dimensionality offers flexibility +in the specification of the gasket behavior and can prove to be very efficient in some cases; see “Defining +the gasket behavior directly using a gasket behavior model,” Section 32.6.6, for further details. +12-node elements for use with modified tetrahedral elements +The 12-node gasket elements have the same contact properties as the modified 10-node tetrahedra; these +elements have consistent nodal forces at the corner and midside nodes. They are primarily intended for +use with the modified tetrahedral elements but can also be used in conjunction with other solid continuum +elements by using contact pairs. In the latter case the solution may be noisy for badly mismatched meshes. +32.6.3 +INCLUDING GASKET ELEMENTS IN A MODEL +Products: Abaqus/Standard Abaqus/CAE +References +• “Gasket elements: overview,” Section 32.6.1 +• “Choosing a gasket element,” Section 32.6.2 +• “Contact interaction analysis: overview,” Section 35.1.1 +• “General multi-point constraints,” Section 34.2.2 +• Chapter 32, “Gaskets,” of the Abaqus/CAE User’s Manual +Overview +Gasket elements: +• are used to model gaskets and other seals between two components, each of which may be +deformable or rigid; and +• are connected to the adjacent components by sharing nodes, by using surface-based tie constraints, +by using MPCs type TIE or PIN, or by using contact pairs. +This section discusses the techniques that are available to discretize gaskets and assemble them in a +model representing several components, such as an internal combustion engine. The methods described +all apply to gasket elements that have all displacement degrees of freedom active at their nodes. For +the most part they also apply to gasket elements with only thickness-direction behavior; exceptions are +discussed later in this section. +Discretizing gaskets using gasket elements +Gaskets are generally manufactured as independent components. The gasket behavior is usually +measured by performing a compression experiment on the gasket. +In this case the gasket can be +discretized as a single layer of gasket elements. +Gaskets are sometimes made of several layers of materials. If the behavior of the gasket is obtained +by compression testing of the entire gasket, the gasket can again be discretized as a single layer of +gasket elements. However, if the behavior of the gasket is obtained by compression testing of each +layer constituting the gasket, the gasket can be discretized with a corresponding set of layers of gasket +elements. +Discretizing gaskets with multiple layers +If layers of gasket elements are used in the thickness direction and these layers do not have the same +element layout in the plane of the gasket, use surface-based tie constraints, mesh refinement MPCs, or +tied contact pairs to connect the different layers of the gasket. +If tied contact pairs are used, assign +a positive value to the adjustment zone depth, a, for the contact pairs (see “Adjusting initial surface +positions and specifying initial clearances in Abaqus/Standard contact pairs,” Section 35.3.5) so that all +slave nodes are properly tied at the beginning of the analysis. +Assembling gaskets to other components in a model +The easiest method to connect gasket elements that use all displacement components at their nodes to +other components in a model is to define the mesh so that the gasket elements can share nodes with +the elements on the surfaces of the adjacent components. More generally, when the gasket mesh is +not matched to the meshing of the surfaces of the adjacent components or when the gasket elements +that consider only thickness-direction behavior are used, gasket elements can be connected to other +components by using contact pairs. +Connecting gaskets to other components by using contact pairs or surface-based constraints +Gaskets are usually composed of materials that are softer than the materials that compose the neighboring +components. In addition, the discretization of gaskets will usually be finer than the discretization of +neighboring parts. These two facts suggest that the contacting surfaces of a gasket should be the slave +surfaces and that the contacting surfaces of neighboring parts should be the master surfaces. The second +consideration also suggests that mismatched meshes will often be used in analyses involving gaskets. +If mismatched meshes are used, the pressure distribution on a compressed gasket may not be predicted +accurately; submodeling (“Submodeling: overview,” Section 10.2.1) may be required to obtain accurate +local results. Two techniques are available to connect gasket elements to other parts in the model when +surface-based constraints are used. +Using a regular contact pair and a tied contact pair or a surface-based constraint +This technique is required when the gasket membrane behavior is not defined. Use a tied contact pair +(“Defining tied contact in Abaqus/Standard,” Section 35.3.7) or a tie constraint (“Mesh tie constraints,” +Section 34.3.1) on one side of the gasket and a regular contact pair on the other side, as shown in +Figure 32.6.3–1. Because a regular contact pair is used on one side of the gasket, tensile stresses cannot +develop in the gasket thickness direction should the components surrounding the gasket be pulled apart. +Assign a positive value to the adjustment zone depth, a, for the tied contact pair or, if necessary, specify a position tolerance for the tie constraint so that all slave nodes are properly tied at the beginning of the analysis. +This technique allows for frictional slip on only one side of the gasket. +Using a regular contact pair and a contact pair that does not allow separation +This technique allows for frictional slip to be transmitted on both sides of the gasket. It is recommended +when membrane behavior is defined for the gasket since it allows for the gasket membrane to stretch +or contract as a result of frictional effects considered on both sides of the gasket. A contact pair or +a constraint pair that does not allow for separation of the surfaces (“Contact pressure-overclosure +relationships,” Section 36.1.2) should be used on one side of the gasket and a regular contact pair on the +other, as shown in Figure 32.6.3–2. +or tied constraint pair +MODELING WITH GASKET ELEMENTS +part 1 +contact pair +gasket element +part 2 +Figure 32.6.3–1 Connecting gaskets to other parts using contact pairs. +contact pair or constraint pair +that does not allow for +separation of the surfaces +part 1 +contact pair +gasket element with +membrane behavior defined +part 2 +Figure 32.6.3–2 Connecting gaskets to other parts when the gasket membrane behavior is defined. +Assign a positive value to the adjustment zone depth, a, for the contact pair so +that the surfaces are in contact at the beginning of the analysis. Use the no separation contact pressure- +overclosure relationship so that these +surfaces do not separate during the analysis. This technique will prevent rigid body modes of the gasket +in its thickness direction. You may still need to prevent rigid body modes in the plane of the gasket until +frictional forces develop between the gasket and the adjacent components. +Having gasket elements share nodes with other elements +When the gaskets and their neighboring parts have matched meshes, it is straightforward to connect +gaskets to other components in a model simply by sharing nodes . +Part 1 +gasket element +Part 2 +Figure 32.6.3–3 Gasket elements sharing nodes with other Abaqus elements. +This method of connecting gaskets to other components is suited for cases when no frictional slip occurs +between the gasket and the other components. It can be used whether or not the membrane behavior of +the gasket elements is defined; however, if the gasket membrane behavior is defined, using a contact pair +approach will lead to more realistic results since the difference in membrane stiffness between the gasket +and its neighboring parts may lead to frictional slip. The method of sharing nodes will also lead to some +small tensile stresses in the gasket should the parts connected to the gasket be pulled apart, as a result +of the numerical stabilization technique added to the gasket thickness-direction behavior . The contact pair approach +will avoid such tensile stresses. This node-sharing approach cannot be used with the gasket elements +that consider only thickness-direction behavior. +Using gasket elements that model thickness-direction behavior only +In general, the modeling techniques discussed earlier can be used with gasket elements that model +these elements have only one displacement degree +thickness-direction behavior only. However, +of freedom per node and cannot share nodes with elements that have all displacement degrees of +freedom active at a node. They can, however, share nodes with other gasket elements that model +thickness-direction behavior only. +Discretizing a gasket with gasket elements that model thickness-direction behavior only +When discretizing a gasket with several layers of gasket elements along the gasket direction, it is +recommended that all the nodes belonging to a cross-section of the gasket have the same thickness +direction . An approximate solution will be generated if the thickness direction +changes, since only the magnitude of the force is transmitted from one gasket element to the next +through the thickness of the gasket. +cross +section +Figure 32.6.3–4 Discretizing a gasket using several layers of +elements with thickness-direction behavior only. +Connecting gaskets to other components when gasket elements with thickness-direction +behavior only are chosen +Contact pairs can be used to connect the gasket mesh to adjacent components, as explained above, but +only frictionless, small-sliding contact can be used. +MPC type PIN or TIE can also be used to connect a one degree of freedom node of a gasket element +to another coincident node that has all its displacement degrees of freedom active . +Abaqus/Standard automatically constrains the single displacement degree of freedom node to the global +displacements of the other node. +Surface-based tie constraints cannot be used to connect gasket elements +that model +thickness-direction behavior only. +Additional considerations when using gasket elements +Several cases require special consideration when using gasket elements. +part 1 +gasket +elements +part 2 +1 d.o.f. +Use +TIE- or +PIN-type +MPC +2 d.o.f. +coincident node +Figure 32.6.3–5 Connecting gasket elements with thickness-direction +behavior only to other parts by using MPCs. +Using gasket elements in large-displacement analyses +Gasket elements are small-strain, small-displacement elements. They can be used in large-displacement +analyses. However, the local directions of the gasket elements are not updated with the solution, +so incorrect results will be generated if the assembly containing the gasket elements undergoes any +significant amount of rotation. +Using 12-node gasket elements +These elements are primarily for use when the adjacent components are modeled with modified 10-node +tetrahedral elements (element type C3D10M). When the contact pair approach is used, such elements can +also be placed adjacent to other three-dimensional solid continuum elements; however, if the meshes are +badly mismatched, the solution may be noisy. +Using 18-node gasket elements +These elements are intended to share nodes with 21 to 27-node brick elements. They can also be +connected to a mesh composed of 21 to 27-node brick elements or a mesh composed of 20-node brick +elements when the contact pair approach is used. +Abaqus/Standard allows the node numbers and the coordinates of the midface nodes in the 18-node +gasket elements to be generated automatically if the faces are part of contact surfaces, similar to the way +that midface nodes are generated for 20-node brick element faces on which a contact surface is defined. +This feature is invoked by leaving the entries for nodes 17 and 18 in the element connectivity blank. +Using the three-dimensional line gasket elements +Three-dimensional line gasket elements are typically used to model narrow, thicker features in gaskets, +such as an elastomeric insert around a hole. A typical mesh for such a case is presented in Figure 32.6.3–6. +The gasket is discretized mainly with three-dimensional area elements. The insert is modeled with +three-dimensional line elements that may or may not be connected to the area elements. These gasket +elements are connected to surrounding components using two sets of contact pairs, and the area elements +will typically have initial gaps specified in the gasket property definition so that the thicker inserts develop +pressure on contact before the area elements do. +nodes of the line gasket elements +three-dimensional line gasket elements +area gasket elements +Figure 32.6.3–6 Typical use of three-dimensional line gasket +elements to model inserts in gaskets. +If three-dimensional line gasket elements that have all displacement degrees of freedom active at +their nodes are used to discretize a gasket and the local 3-direction is the same at all the nodes of these +elements (this is the case when all elements lie in a plane), the nodes of these elements can move in the +local 3-direction without creating any strain in the elements . +In such a case you should make sure that these elements are restrained +properly in the local 3-direction. +32.6.4 +DEFINING THE GASKET ELEMENT’S INITIAL GEOMETRY +Products: Abaqus/Standard Abaqus/CAE +References +• “Gasket elements: overview,” Section 32.6.1 +• *GASKET SECTION +• “Creating gasket sections,” Section 12.13.15 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +The initial gasket geometry: +• is defined by the nodal coordinates of the element; and +• is also defined by the thickness direction and initial thickness, each of which can be calculated by +Abaqus/Standard or user-defined. +Defining the element geometry +A gasket element is basically composed of two surfaces (a bottom and a top surface) separated by the +gasket thickness. The element has nodes on its bottom face and corresponding nodes on its top face. +Two methods are available to define the element geometry. +By defining the element’s nodes +You can define the geometry of the gasket element by defining the coordinates of all the element’s +nodes. You can define elements with constant or varying thickness. If the gasket element is very thin +in comparison to dimensions in its surfaces, the thickness of the element calculated from the nodal +coordinates may be inaccurate. In this case you can specify a constant thickness directly. +By defining the bottom surface of the element +You can specify a list of only the nodes on the bottom surface of the gasket element and the positive offset +number that will be used to define the corresponding nodes on the top surface of the gasket element. +Abaqus/Standard will create the nodes of the top face coincident with those of the bottom face unless +the nodes of the top face have already been assigned coordinates. If the bottom and top nodes coincide, +you must specify the thickness of the gasket element. +Specifying the element thickness +You can specify the gasket element thickness as part of its section property definition. +Input File Usage: +*GASKET SECTION +thickness +Abaqus/CAE Usage: +Property module: Create Section: select Other as the section Category and +Gasket as the section Type: Initial thickness: Specify: thickness +Additional quantities needed to specify the element geometry +For three-dimensional area elements, the element geometry is defined entirely by the location of the top +and bottom surfaces and the element thickness. For two- and three-dimensional link elements (elements +with two nodes, one on each face) you should specify the cross-sectional area of the element. For +axisymmetric link elements you should specify the width of the element. For general two-dimensional +elements the out-of-plane thickness is required. For three-dimensional line elements you should also +specify the width of the element. This additional information is specified as part of the gasket section +property definition; if it is not specified but is needed, it is assumed to have a value of 1.0. +Input File Usage: +*GASKET SECTION +, , , additional geometric data (cross-sectional area, width, +or out-of-plane thickness) +Abaqus/CAE Usage: +Property module: Create Section: select Other as the section Category +and Gasket as the section Type: Cross-sectional area, width, or +out-of-plane thickness: additional geometric data +Default element thickness-direction definition +Gaskets are usually manufactured to have a desired behavior in their thickness direction. Therefore, it is +important to define the thickness directions of gasket elements accurately. Abaqus/Standard computes +these directions by default. The method that Abaqus/Standard uses depends on the gasket element type. +Link elements +Abaqus/Standard computes the thickness direction for a two-dimensional, +three-dimensional, or +axisymmetric link element by subtracting the coordinates of node 1 from those of node 2, as shown in +Figure 32.6.4–1. The computed thickness direction is then assigned to each node. If the gasket element +is very thin, the thickness direction may not be predicted accurately. You can overwrite this direction, +as explained below in “Specifying the thickness direction explicitly.” +Two-dimensional and axisymmetric elements +To compute the thickness direction for two-dimensional and axisymmetric elements, Abaqus/Standard +forms a midsurface by averaging the coordinates of the node pairs forming the bottom and top surfaces +of the element. This midsurface passes through the integration points of the element, as shown in +Figure 32.6.4–2. For each integration point Abaqus/Standard computes a tangent whose direction is +defined by the sequence of nodes given on the bottom and top surfaces. The thickness direction is +then obtained as the cross product of the out-of-plane and tangent directions. The thickness direction +computed at each integration point is then assigned to the nodes on either side of the integration point. +Figure 32.6.4–1 Thickness direction for a link element. +n2 +n2 +n2 +t2 +t1 +n1 +n1 +n1 +midsurface +n3 +n3 +t3 +n3 +Figure 32.6.4–2 Thickness direction for a two-dimensional or axisymmetric element. +Three-dimensional area elements +To compute the thickness direction for three-dimensional area elements, Abaqus/Standard forms +a midsurface by averaging the coordinates of the node pairs forming the bottom and top surfaces +of the element. This midsurface passes through the integration points of the element, as shown +in Figure 32.6.4–3. Abaqus/Standard computes the thickness direction to the midsurface at each +integration point; the positive direction is obtained with the right-hand rule going around the nodes of +the element on the bottom or top surface. The thickness direction computed at each integration point is +assigned to the nodes on either side of the integration point. +Three-dimensional line elements +To compute the thickness direction for three-dimensional line elements, Abaqus/Standard computes +the thickness direction at each integration point of the line element by differencing the coordinates of +the element’s surface nodes associated with the integration point. The thickness direction will point +from the node on the bottom face to the node on the top face of the element. The thickness direction +computed at each integration point is then assigned to the nodes on either side of the integration point +. +n1 +n1 +n1 +n4 +n4 +n4 +midsurface +n2 +n2 +n2 +n3 +n3 +n3 +Figure 32.6.4–3 Thickness direction for a three-dimensional area element. +n1 +n1 +n1 +n2 +n2 +n2 +n3 +n3 +n3 +Figure 32.6.4–4 Thickness direction for a three-dimensional line element. +If the gasket element is very thin, the computation of the thickness direction may not be accurate. You +can overwrite this definition as explained below in “Specifying the thickness direction explicitly.” +Creating a smooth gasket +Gasket elements can be used in a single layer or can be stacked in multiple layers . The thickness directions computed at the nodes +of gasket elements on an element-by-element basis are averaged at nodes shared by two or more gasket +elements. This averaging process ensures that, if the gasket is not planar, it has a thickness direction +that varies smoothly even though the gasket has been discretized by elements. You must ensure that the +connectivities of the elements are such that the thickness direction does not reverse from one element +to the next for this process to work properly. Once the averaging process is complete, the thickness +directions at the nodes of a given element may vary significantly along the gasket midsurface and through +its thickness, as shown in Figure 32.6.4–5. The thickness directions at any of the nodes of an element +should not vary in direction by more than 20°. In addition, the thickness directions of two associated +nodes through the thickness direction should not vary in direction by more than 5°. Abaqus/Standard +will require that the gasket be remeshed when such conditions are not met. +multi-layered +gasket +thickness +direction +20° +5° +5° +midsurface +Figure 32.6.4–5 Result of the averaging process. +Specifying the thickness direction explicitly +For cases when the above averaging process is not satisfactory, two methods are provided to specify the +thickness direction of gasket elements. +Specifying the thickness direction as part of the gasket section definition +You can specify the components of the thickness direction as part of the gasket section definition. In +this case all nodes of the gasket elements using this section definition are assigned the same thickness +direction. The thickness direction specified at the nodes of the element will be averaged at nodes shared +by two or more elements. +Input File Usage: +*GASKET SECTION +, , , , component 1, component 2, component 3 +Abaqus/CAE Usage: +You cannot specify the gasket thickness direction in Abaqus/CAE. +Specifying the thickness direction by specifying a normal direction at the nodes +You can define the thickness direction at a particular integration point of a gasket element by specifying +a normal direction for the node on the bottom face of the element that is associated with the integration +point . The thickness direction will not be averaged if +this node belongs to more than one element. The thickness direction specified at the bottom node will +also be assigned at the top node associated with the same integration point. This thickness direction +will not be averaged if the top node belongs to more than one element; however, you can overwrite +this thickness direction by specifying a normal at this node if it is the bottom node of another element. +This last situation can occur only in cases when gasket elements are stacked up through the thickness +direction of the gasket. If this method is used to specify conflicting thickness directions at the same +node, Abaqus/Standard will issue an error message. Thickness directions specified using this method +will overwrite any thickness directions specified at a gasket node as part of the gasket section definition. +Input File Usage: +Abaqus/CAE Usage: +*NORMAL +User-specified nodal normals are not supported in Abaqus/CAE. +Creating fold lines +It is possible to introduce a fold line in a gasket by creating gaskets with coincident nodes and using +MPC type TIE or PIN (“General multi-point constraints,” Section 34.2.2) to constrain the displacement +of these nodes. However, fold lines are rarely needed in the analysis of gaskets, since almost all gaskets +are manufactured with smoothly varying surfaces. +Verifying the thickness direction +Thickness direction definitions can be checked by examining the analysis input file processor output. +The direction cosines of the thickness directions obtained at the nodes of gasket elements are listed under +GASKET THICKNESS DIRECTIONS in the data (.dat) file. +Specifying an initial gap and an initial void in the thickness direction of a gasket element +The construction of gaskets in their through-thickness direction may be complex; for example, certain +automotive gaskets are usually composed of several layers of metal and/or elastomeric inserts, and it is +likely that the layers do not all touch until the gasket is compressed. The inter-layer spaces in a gasket +are referred to in Abaqus as the initial void. The initial void is used only for calculating thermal strain +and creep strain. It is also possible that the gasket surface geometry is such that pressure will not start +building up until the gasket has been compressed by a certain amount. The gasket closure that is needed +to generate a pressure is referred to in Abaqus as the initial gap. Figure 32.6.4–6 shows a schematic +representation of the initial gap and initial void in a typical gasket. You can specify both the initial gap +and initial void as part of the gasket section property definition. The initial thickness of the element +should include the initial gap and the initial void. +Input File Usage: +*GASKET SECTION +, initial gap, initial void +Abaqus/CAE Usage: +Property module: Create Section: select Other as the section Category and +Gasket as the section Type: Initial gap: initial gap, Initial void: initial void +initial gap +metallic plate +metallic frame +initial void +spacers +Figure 32.6.4–6 Schematic representation of an initial gap +and an initial void in a typical gasket. +Stability of unsupported gasket elements +Gasket elements that extend outside neighboring components (unsupported gasket elements) can be +troublesome and should be avoided. If a gasket element is completely or partially unsupported, incorrect +areas can result in an incorrect stiffness, and numerical singularity problems can occur in the equation +solver. Minor extensions (caused by numerical roundoff in mesh generation) will not usually cause a +problem because Abaqus/Standard automatically extends the master surfaces a small amount beyond +the edge of the model. Numerical problems can occur in the direction tangential to the gasket (if general +gasket elements are used and no membrane stiffness is specified) as well as in the direction normal to +the gasket. The numerical singularity problems normal to the gasket can be treated by stabilizing the +elements with a small artificial stiffness. By default, Abaqus/Standard automatically applies a small +stabilization stiffness (on the order of 10−9 times the initial compressive stiffness in the thickness +direction) to all types of gasket elements except the link elements. For persistent numerical singularity +problems in unsupported gasket elements the following treatment methods can be considered. First, +make sure that an adequate membrane elasticity is specified. Second, specify a higher value for the +artificial stiffness for the gasket section. If problems still persist, consider trimming, “skinning,” and +using MPCs . +Input File Usage: +Use the following option to change the artificial stiffness for a gasket section: +Abaqus/CAE Usage: +*GASKET SECTION, STABILIZATION STIFFNESS=stiffness_value +Use the following option to change the artificial stiffness for a gasket section: +Property module: Create Section: select Other as the section Category and +Gasket as the section Type: Stabilization stiffness: Specify: stiffness_value +32.6.5 +DEFINING THE GASKET BEHAVIOR USING A MATERIAL MODEL +Products: Abaqus/Standard Abaqus/CAE +References +• “Gasket elements: overview,” Section 32.6.1 +• “UMAT,” Section 1.1.40 of the Abaqus User Subroutines Reference Manual +• “Creating and editing materials,” Section 12.7 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +The gasket behavior defined by a material model: +• can be specified in terms of a built-in material model or a user-defined small-strain material model; +• considers only the thickness behavior and assumes a uniaxial stress state for gasket elements that +model thickness-direction behavior only; +• admits both compressive and tensile stresses in the thickness direction; +• is defined in terms of small-strain measures and, hence, finite-strain material models such as +hyperelastic and hyperfoam cannot be used; +• is restricted to small-strain elasticity models for line gasket elements that use the built-in material +models; +• causes Abaqus/Standard to use the reference thickness to convert the relative displacements at the +top and bottom surfaces of the gasket to strains and uses these strains in conjunction with the +constitutive law to obtain the stresses; and +• makes the notions of “initial gap” and “initial void” in the thickness direction irrelevant +(consequently, Abaqus/Standard ignores such data specified as part of the gasket section property +definition). +Assigning a gasket behavior to a gasket element +To define the gasket behavior by a material model, you must assign a gasket section definition to a region +of your model and assign the name of a material definition to the gasket section definition. The gasket +behavior for this region is defined entirely by the gasket thickness and the material properties specified +by the material definition referring to the same name. +The gasket behavior can be defined in terms of a built-in or a user-defined material model. In the +latter case the actual material model is defined in user subroutine UMAT. +Input File Usage: +Use the following options to define the gasket behavior in terms of a built-in +material model: +*GASKET SECTION, ELSET=name, MATERIAL=name +*MATERIAL, NAME=name +Use the following options to define the gasket behavior in terms of a user- +defined material model: +*GASKET SECTION, ELSET=name, MATERIAL=name +*MATERIAL, NAME=name +*USER MATERIAL, CONSTANTS=n +Property module: +Create Material: Name: name, enter data for any materials that are valid for +gasket sections except those found under Other→Gasket +Create Section: select Other as the section Category and Gasket +as the section Type: Material: name +Abaqus/CAE Usage: +Tensile behavior modeling +Tensile behavior modeling can be desirable when gaskets carry (limited) tensile stresses, such as occurs +when adhesives are present. Undesired tensile behavior can be avoided by using appropriate contact +pairs and/or implementing a user-defined no-tension material model in user subroutine UMAT. +Specific output for material definition of gasket behavior +The output variables for stresses and strains are the same as those used for solid elements: tensile and +compressive stresses/strains are indicated as positive and negative quantities, respectively. However, for +all stress/strain output variables the 11-component refers to the through-thickness direction; the 22-, 33-, +and 23-components refer to two direct and one shear membrane component, respectively; the remaining +12- and 13-components refer to the transverse shear components. For details about these definitions, see +“Gasket elements: overview,” Section 32.6.1. The output variable NE is available to output nominal +(effective) strains for gasket elements defined using a material model; however, NE is identical to E in +this case. +32.6.6 +DEFINING THE GASKET BEHAVIOR DIRECTLY USING A GASKET BEHAVIOR +MODEL +Products: Abaqus/Standard Abaqus/CAE +References +• “Gasket elements: overview,” Section 32.6.1 +• “Defining the gasket element’s initial geometry,” Section 32.6.4 +• “Defining gasket behavior,” Section 12.12.4 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +The gasket behavior defined by a gasket behavior model: +• can be specified in terms of uncoupled thickness direction, membrane, and transverse shear behavior +only; +• can be nonlinear elastic with damage or nonlinear elastic-plastic in the thickness direction; +• can consider creep effects in the thickness direction when rate-independent elastic-plastic modeling +is used; +• can consider the dynamic stiffness and damping characteristics in the thickness direction when +elastic-damage modeling is used; +• will be linear elastic in the membrane and transverse shear directions; and +• can consider thermal effects in the thickness and membrane directions. +Assigning a gasket behavior to a gasket element +To define the gasket behavior by a gasket behavior model, you must assign a gasket section definition to a +region of your model and assign the name of a gasket behavior definition to the gasket section definition. +The gasket behavior for this region is defined entirely by the properties specified by the gasket behavior +definition referring to the same name. +Input File Usage: +Abaqus/CAE Usage: +Use both of the following options to define the gasket behavior in terms of a +gasket behavior model: +*GASKET SECTION, ELSET=name, BEHAVIOR=name +*GASKET BEHAVIOR, NAME=name +Property module: +Material editor: Name: name, enter data for any materials found under +Other→Gasket +Create Section: select Other as the section Category and Gasket +as the section Type: Material: name +Specifying a gasket behavior +The thickness-direction, transverse shear, and membrane behaviors are defined to be uncoupled. Each +behavior is specified independently. +You must specify the thickness-direction behavior. You can specify multiple thickness-direction +behaviors to define the loading and unloading characteristics. You can obtain an average contact pressure +output when the thickness-direction behavior is defined as force or force per unit length versus closure. +The transverse shear and membrane behaviors are optional for gasket elements that have all +displacement degrees of freedom active at their nodes. You can define one or both of these behaviors. +When thermal and rate-dependent effects are important, you can define thermal expansion and creep +behavior for gaskets; user subroutines UEXPAN and CREEP can be used to define these behaviors. +You cannot specify density for gasket elements since they have no mass matrix. +Input File Usage: +Use the first two options and any of the following options to specify a gasket +behavior: +*GASKET BEHAVIOR, NAME=name +*GASKET THICKNESS BEHAVIOR +*GASKET ELASTICITY +*GASKET CONTACT AREA +*EXPANSION +*CREEP +*DEPVAR +*USER OUTPUT VARIABLES +The *GASKET THICKNESS BEHAVIOR option can be repeated to define +the loading and unloading characteristics of the thickness-direction behavior. +The *GASKET ELASTICITY option can be repeated to define both transverse +shear and membrane behaviors. The other options cannot be repeated within +a single behavior definition. The order in which these options are specified +has no importance, but they must appear immediately after the *GASKET +BEHAVIOR option. +Abaqus/CAE Usage: +Use the first option and any of the following options to specify a gasket +behavior: +Property module: material editor: +Other→Gasket→Gasket Thickness Behavior +Other→Gasket→Gasket Transverse Shear Elasticity and/or Gasket +Membrane Elasticity +Mechanical→Expansion +Mechanical→Plasticity→Creep +General→Depvar +General→User Output Variables +Defining the thickness-direction behavior of the gasket +To define the thickness-direction behavior of gaskets, Abaqus/Standard offers a nonlinear elastic model +with damage and a nonlinear elastic-plastic model with the possibility of considering creep effects. +Thermal effects in the thickness direction can also be accounted for. +Abaqus/Standard measures the thickness-direction deformation as the closure between the bottom +and top faces of the gasket element; therefore, the thickness-direction behavior must always be defined +in terms of closure. The closure is the sum of the elastic closure, plastic closure, creep closure, thermal +closure, plus any initial gap in the thickness direction. As explained below, the behavior can be defined +as pressure versus closure, force versus closure, or force per unit length versus closure. In all cases the +thickness-direction behavior can be defined as a function of temperature and/or field variables. +Input File Usage: +Abaqus/CAE Usage: +*GASKET THICKNESS BEHAVIOR, DEPENDENCIES +Property module: material editor: Other→Gasket→Gasket +Thickness Behavior +Choosing a unit system used to define the thickness-direction behavior +The thickness-direction behavior can be defined in terms of pressure versus closure, force versus closure, +or force per unit length versus closure. +Prescribing the thickness-direction behavior as pressure versus closure +You can define the thickness-direction behavior in terms of pressure and closure for all gasket element +types. The pressure is available for output or visualization. +Input File Usage: +Abaqus/CAE Usage: +*GASKET THICKNESS BEHAVIOR, VARIABLE=STRESS +Property module: material editor: Other→Gasket→Gasket +Thickness Behavior: Units: Stress +Prescribing the thickness-direction behavior as force or force per unit length versus closure +You can define the thickness-direction behavior in terms of force or force per unit length and closure only +for link elements and three-dimensional line elements. This method is suited for cases where the gasket +cross-section in the 1–2 or 1–3 plane varies greatly with deformation because it would be too expensive +to model such a deformation with a full two- or three-dimensional model. In such cases a model with link +elements or three-dimensional line elements can give meaningful answers as long as the deformation is +quantified in terms of force or force per unit length . +When using two- or three-dimensional link elements, you must specify the thickness-direction +behavior as force versus closure. When using axisymmetric link elements or three-dimensional line +elements, you must specify the thickness-direction behavior as force per unit length versus closure. +Input File Usage: +Abaqus/CAE Usage: +*GASKET THICKNESS BEHAVIOR, VARIABLE=FORCE +Property module: material editor: Other→Gasket→Gasket +Thickness Behavior: Units: Force +top block +bottom +block +gasket +undeformed configuration +deformed configuration +bottom +block +gasket +element +force or force per unit length +top block +bottom block +model for analysis +Figure 32.6.6–1 Modeling complex deformations with link or three-dimensional line elements. +Defining a nonlinear elastic model with damage +The nonlinear elastic model with damage is illustrated in Figure 32.6.6–2. +pressure +loading +curves +unloading +curves +Cmax +closure +Cmax +Figure 32.6.6–2 Elastic model with damage. +As the gasket is compressed, the pressure (or force, or force per unit length) follows the path given by +the loading curve. If the gasket is unloaded, for example at point B, the pressure follows the unloading +curve +until the loading is such that +the closure becomes greater than +. The +arrows shown in the figure illustrate the loading/unloading paths of this model. +. Reloading after unloading follows the unloading curve +, after which the loading path follows the loading curve +Defining the loading curve +To define the loading curve in piecewise linear form, you provide data points of pressure versus elastic +closure, starting with point A. For negative elastic closures, the model gives zero pressure (or force). +For closures larger than the last user-specified closure, the pressure-closure relationship is extrapolated +based on the last slope computed from the user-specified data. +Input File Usage: +*GASKET THICKNESS BEHAVIOR, TYPE=DAMAGE, +DIRECTION=LOADING +Abaqus/CAE Usage: +Property module: material editor: Other→Gasket→Gasket Thickness +Behavior: Type: Damage, Loading +Defining the unloading curve +, +, and so on), you provide data points of pressure (or force) +To define the unloading curves ( +versus elastic closure up to a given maximum closure ( +, and so on). You can specify +as many unloading curves as are necessary. Each unloading curve always starts at point A, the point of +zero pressure for zero elastic closure, since the damaged elasticity model does not allow any permanent +deformation. If unloading occurs from a maximum closure for which an unloading curve is not specified, +the unloading is interpolated from neighboring unloading curves. The unloading curves are stored in +normalized form so that they intersect the loading curve at a unit stress (or unit force) for a unit elastic +closure, and the interpolation occurs between these normalized curves. +If unloading curves are not +specified, the loading/unloading will follow the loading curve. +, or +Input File Usage: +*GASKET THICKNESS BEHAVIOR, TYPE=DAMAGE, +DIRECTION=UNLOADING +Abaqus/CAE Usage: +Property module: material editor: Other→Gasket→Gasket +Thickness Behavior: Type: Damage, Unloading, toggle on +Include user-specified unloading curves +Defining the behavior for elements with an initial gap +For cases when the load in the gasket does not increase as soon as the gasket is compressed , you can specify an initial gap as part of the gasket section property definition and define the loading/unloading +curves as if the initial gap were not present (the case of Figure 32.6.6–2). This method is convenient +when many gasket elements refer to the same gasket behavior and the only difference is the initial gap. +pressure +loading +curves +unloading +curves +closure +initial gap +Figure 32.6.6–3 Elastic model with damage and initial gap. +Defining a nonlinear elastic-plastic model +The nonlinear elastic-plastic model is illustrated in Figure 32.6.6–4. As the gasket is compressed, the +pressure (or force) follows the path given by the loading curve +. The loading curve is a +nonlinear elastic curve until point B is reached. At point B the slope of the loading curves decreases +by more than 10%, which is assumed to correspond with the onset of plastic deformation. The value +of 10% was chosen as a reasonable minimum value that can be expected at the onset of yield. If yield +starts at a point at which no decrease in the slope occurs, numerical difficulties may occur. If the elastic +part of the loading curve has a changing slope, the curve should be defined such that the slope does not +decrease by more than 10% at any given point. After point B plastic deformation starts taking place. +If unloading occurs before point B is reached, unloading will take place along the initial loading curve. +Once loading has gone beyond point B, unloading will take place along an unloading curve such as curve +. The unloading is assumed to be entirely elastic. The amount of closure at point D represents the +plastic closure for the unloading curve +until +the gasket yields, after which the loading curve +is followed. Plastic deformation takes place until +the last point M on the loading curve is reached. Beyond point M, the curve +is followed for both +loading and unloading; this behavior represents the behavior of a crushed gasket, which is assumed to +be entirely elastic and can be specified in a piecewise-linear fashion, even beyond point M. The arrows +shown in the figure illustrate the loading/unloading paths for the elastic-plastic model. +. Reloading after unloading follows the same curve +Abaqus/Standard will automatically convert the curves so that the unloading curves become curves +of pressure (or force) versus elastic closure for a given plastic closure. The loading curve will be +transformed into an elastic loading/unloading curve defined at zero plastic closure (the portion +of +the curve) and a yield curve (the portion +of the curve). By default, the onset of yield (point B) +will be obtained as soon as the slope of the loading curve decreases by 10% from the maximum +slope recorded up to that point while traveling along the loading curve from point A to point M. +pressure +closure +plastic closure at point D +Figure 32.6.6–4 Elastic-plastic model. +Abaqus/Standard offers two alternatives to allow you to override this default method of determining the +onset of yield as described below. If only a loading curve is provided, the unloading will be based on +the curve +, independent of the level of plasticity. +Defining the loading curve +To define the loading curve in piecewise linear form, you provide data points of pressure (or force, or +force per unit length) versus closure (where closure represents the elastic plus the plastic closure), starting +with point A. The last closure value given represents the closure at which the gasket is assumed crushed +(point M in Figure 32.6.6–4); at this point, the maximum permanent deformation is reached. For negative +closures the model gives zero pressure (or force). +To override the default method of determining the onset of yield, you can specify either a value +for the decrease in slope other than the default value of 10% or the closure value at which onset of yield +occurs. The specified value must correspond to a point on the loading curve at which the slope decreases. +Input File Usage: +Use the following option to define the loading curve and use the default method +for determining the onset of yield: +*GASKET THICKNESS BEHAVIOR, TYPE=ELASTIC-PLASTIC, +DIRECTION=LOADING +Use the following option to define the loading curve and specify a nondefault +value for the decrease in slope that defines the onset of yield: +*GASKET THICKNESS BEHAVIOR, TYPE=ELASTIC-PLASTIC, +DIRECTION=LOADING, SLOPE DROP=drop +Use the following option to define the loading curve and specify the closure +value that defines the onset of yield: +*GASKET THICKNESS BEHAVIOR, TYPE=ELASTIC-PLASTIC, +DIRECTION=LOADING, YIELD ONSET=closure_value +Property module: material editor: Other→Gasket→Gasket Thickness +Behavior: Type: Elastic-Plastic, Loading, Yield onset method: Relative +slope drop drop or Yield onset method: Closure value closure_value +Abaqus/CAE Usage: +Defining the unloading curve +, +To define the unloading curves ( +, and so on), you provide data points of pressure (or force, +or force per unit length) versus closure (elastic plus plastic) for each given plastic closure (closure at +points D, F, and so on) in ascending values of closure. You can specify as many unloading curves as +are necessary. If unloading occurs at a plastic closure for which an unloading curve is not specified, the +unloading curve is interpolated from neighboring unloading curves. If no unloading curves are specified, +unloading is assumed to follow a curve similar to the initial nonlinear elastic segment of the loading +curve. The unloading curves are stored in normalized form so that they intersect the yield curve at a unit +stress (or unit force) for a unit elastic closure, and the interpolation occurs between these normalized +curves. +If the loading curve includes highly nonlinear behavior after the onset of yield, the interpolated +unloading may give unreasonable behavior (such as the interpolated unloading path crossing over the +user-defined loading curve). You should specify as many user-defined unloading curves as are needed to +create regions for which interpolated unloading response is appropriate. For example, Figure 32.6.6–5 +illustrates a loading curve that includes a sharp decrease in the hardening slope well after the onset of +yield. In this case it is insufficient to specify only one unloading curve at the gasket crush point (the +end of the loading data). If unloading were to take place from point C, the unloading path would cross +over the loading path. At least one additional unloading curve is required, after the sharp decrease in +hardening slope, to prevent the interpolated unloading path crossing the loading curve. +Input File Usage: +*GASKET THICKNESS BEHAVIOR, TYPE=ELASTIC-PLASTIC, +DIRECTION=UNLOADING +Abaqus/CAE Usage: +Property module: material editor: Other→Gasket→Gasket Thickness +Behavior: Type: Elastic-Plastic, Unloading, toggle on Include +user-specified unloading curves +Defining the behavior for elements with an initial gap +For cases when the load in the gasket does not increase as soon as the gasket is compressed , you can specify an initial gap as part of the gasket section property definition and define the loading/unloading +curves as if the initial gap were not present (the case of Figure 32.6.6–4). This method is convenient +when many gasket elements refer to the same gasket behavior and the only difference is the initial gap. +pressure +point where user-defined +unloading response +should be specified +gasket crush +point +interpolated +unloading +response +onset of yield +closure +Figure 32.6.6–5 Elastic-plastic behavior with complex loading curve. +pressure +closure +initial gap +Figure 32.6.6–6 Elastic-plastic model with initial gap. +Numerical stabilization of the thickness-direction behavior +The damage and elastic-plastic models described above have zero stiffness at zero pressure. To +overcome numerical problems caused by this zero stiffness, Abaqus/Standard automatically adds a +small stiffness (by default, equal to 10−3 times the initial compressive stiffness) in the thickness direction +of the gasket when the pressure obtained from the specified gasket thickness behavior is zero. This +numerical stabilization ensures that the gasket element always returns to its stress-free thickness when +it is totally unloaded. Hence, if the gasket surfaces are pulled apart, a small force will arise from the +stabilization process. You can change the default stiffness. +Input File Usage: +*GASKET THICKNESS BEHAVIOR, DIRECTION=LOADING, +TENSILE STIFFNESS FACTOR=factor +Abaqus/CAE Usage: +Property module: material editor: Other→Gasket→Gasket Thickness +Behavior: Loading, Tensile stiffness factor: factor +Defining the transverse shear behavior of the gasket +You can define the elastic transverse shear stiffness of the gasket. Abaqus/Standard measures the relative +displacement between the bottom and top of the gasket element along the local 2- or 3-directions to define +the transverse shear in the gasket. Therefore, you should always define the elastic transverse stiffness as +stress (or force, or force per unit length) per unit displacement. You can specify the stiffness as a function +of temperature and field variables. The same stiffness is used for the shear in the 1–2 plane and the shear +in the 1–3 plane. For each set of temperature and/or field variables, the first slope of the initial loading +curve for the gasket’s thickness-direction behavior will be used to compute the transverse shear stiffness +if the transverse shear behavior is not defined explicitly. +Input File Usage: +Abaqus/CAE Usage: +*GASKET ELASTICITY, COMPONENT=TRANSVERSE +SHEAR, DEPENDENCIES +Property module: material editor: Other→Gasket→Gasket +Transverse Shear Elasticity +Choosing a unit system to define the transverse shear behavior +The transverse shear stiffness is defined with units of stress per unit displacement, force per unit +displacement, or force per unit length per unit displacement. The unit system used to define the +transverse shear behavior must be consistent with the unit system used for the thickness-direction +behavior. +Providing the stiffness with units of stress per unit displacement +You can define the transverse shear stiffness in units of stress per unit displacement for all gasket element +types. The stiffness will be used to compute transverse shear stresses, which are available for output or +visualization. +Input File Usage: +*GASKET ELASTICITY, COMPONENT=TRANSVERSE +SHEAR, VARIABLE=STRESS +Abaqus/CAE Usage: +Property module: material editor: Other→Gasket→Gasket +Transverse Shear Elasticity: Units: Stress +Providing the stiffness with other units +You can define the transverse shear stiffness in units of force (or force per unit length) per unit +displacement only for link elements and three-dimensional line elements. This method is suited for +cases where the gasket cross-section in the 1–2 or 1–3 plane varies greatly with deformation because it +would be too expensive to model such a deformation mechanism with a full two- or three-dimensional +model, as explained earlier. +When using two- or three-dimensional link elements, you must specify the stiffness in terms of +units of force per unit displacement. Abaqus/Standard will use this stiffness to compute transverse shear +forces, which are available for output or visualization. When using axisymmetric link elements and +three-dimensional line elements, you must specify the stiffness in terms of units of force per unit length +per unit displacement. Abaqus/Standard will use this stiffness to compute transverse shear forces per +unit length, which are available for output or visualization. +Input File Usage: +Abaqus/CAE Usage: +*GASKET ELASTICITY, COMPONENT=TRANSVERSE +SHEAR, VARIABLE=FORCE +Property module: material editor: Other→Gasket→Gasket +Transverse Shear Elasticity: Units: Force +Defining the membrane behavior of the gasket +You can define the linear elastic behavior of the gasket by giving Young’s modulus and Poisson’s ratio. +These data can be provided as a function of temperature and/or field variables. If you do not specify the +linear elastic behavior of the gasket, the gasket has no membrane stiffness. In this case you must ensure +that the nodes of the elements are restrained adequately in the directions orthogonal to the thickness +direction of the gasket. +Input File Usage: +Abaqus/CAE Usage: +*GASKET ELASTICITY, COMPONENT=MEMBRANE, DEPENDENCIES +Property module: material editor: Other→Gasket→Gasket +Membrane Elasticity +Defining thermal expansion for the membrane and thickness-direction behaviors +You can define isotropic thermal expansion to specify the same coefficient of thermal expansion for the +membrane and thickness-direction behaviors. +Alternatively, you can define orthotropic thermal expansion to specify three different coefficients +of thermal expansion. The first coefficient will apply to the thermal expansion of the gasket in the +thickness direction; the other two coefficients will apply to the expansion of the gasket in the local 2- +and 3-directions, respectively. +The membrane thermal strains, +, are obtained as explained in “Thermal expansion,” +Section 26.1.2. Abaqus/Standard computes the thermal closure for the thickness direction as +initial gap +initial void +initial thickness +so that the “mechanical” closure is obtained as +You can specify the initial gap and initial void as part of the gasket section definition; the initial thickness +is obtained directly from the nodal coordinates of the gasket elements, or you can specify it as part of the +gasket section definition . +If user subroutine UEXPAN is used to define the thermal expansion of the gasket, the incremental +thermal strains must be provided in the subroutine. The thermal closure will be obtained from the thermal +strain in the thickness direction, as described above. +Input File Usage: +Use either of the following options to define the thermal expansion directly: +*EXPANSION, TYPE=ISO +*EXPANSION, TYPE=ORTHO +Use either of the following options to define the thermal expansion in user +subroutine UEXPAN: +*EXPANSION, TYPE=ISO, USER +*EXPANSION, TYPE=ORTHO, USER +Property module: material editor: Mechanical→Expansion: Use +user subroutine UEXPAN (optional) +Abaqus/CAE Usage: +Defining creep behavior for the thickness-direction behavior +You can define creep behavior in the thickness direction of the gasket only when the elastic-plastic model + is used. The creep closure rate will be obtained +as +initial thickness +initial gap +initial void +where +is obtained as explained in “Rate-dependent plasticity: creep and swelling,” Section 23.2.4. +You can specify the initial gap and initial void as part of the gasket section definition; the initial thickness +is obtained directly from the nodal coordinates of the gasket elements, or you can specify it as part of the +gasket section definition . +If user subroutine CREEP is used to define the rate-dependent thickness-direction response of the +gasket, the compressive creep strain increment must be provided in the subroutine. The creep closure +will be obtained from the creep strain, as described above. +Input File Usage: +Use the following option to define the creep behavior directly: +*CREEP +Use the following option to define the creep behavior in user subroutine CREEP: +Abaqus/CAE Usage: +*CREEP, LAW=USER +Property module: material editor: Mechanical→Plasticity→Creep: +Law: User-defined (optional) +Defining viscoelastic behavior for the thickness-direction behavior +You can define viscoelastic behavior in the thickness direction of the gasket only when the elastic- +damage model is used. Only frequency +domain viscoelastic behavior is supported. This behavior is useful for modeling the steady-state dynamic +response of automotive components with gaskets about some pre-loaded base state, such as would be +obtained at the end of a nonlinear sealing analysis, to determine the noise-vibration-harshness (NVH) +characteristics of the system. +During the nonlinear sealing analysis step the frequency-domain viscoelastic behavior is ignored, +and the material response is determined by the long-term elastic properties of the material. +It is +generally accepted (Zubeck and Marlow, 2002) that the dynamic stiffness and damping characteristics +of automotive components such as gaskets and grommets vary with the frequency of excitation as +well as the level of preload. These structural properties also depend on the geometry and the level of +confinement of the gasket. This capability allows the direct specification of such dynamic properties as +quantified by the effective storage and loss moduli in the thickness-direction, as tabular functions of the +frequency of excitation and the level of preload. The preload is quantified by the amount of closure in +the base state about which the steady-state dynamic response is desired. +In determining the dynamic response of the gasket, the long-term elastic response is assumed to be +defined by the nonlinear elastic model with damage. The steady-state dynamic response is assumed to +be a perturbation about a base state defined by this elastic damage behavior at a certain value of closure. +The viscoelastic response can be specified using two approaches, as discussed below. +Direct specification of the properties +The first approach involves direct (tabular) specification of the thickness-direction loss and storage +moduli as functions of excitation frequency at different levels of closure. +Input File Usage: +Abaqus/CAE Usage: +*VISCOELASTIC, TYPE=TRACTION, PRELOAD=UNIAXIAL +Property module: material editor: Mechanical→Elasticity→Viscoelastic: +Domain: Frequency and Frequency: Tabular +Specification of properties in terms of ratios +The second approach allows the specification of the ratio of both the thickness-direction storage and +the loss moduli to the long-term thickness-direction elastic modulus. These ratios can be specified +as tabular functions of the excitation frequency but are assumed to be independent of the amount of +closure. The actual storage or loss modulus at any given level of closure is computed by multiplying the +appropriate ratio with the long-term elastic modulus at the current value of closure (of the base state). +See “Frequency domain viscoelasticity,” Section 22.7.2, for a summary of the second approach in the +context of continuum material viscoelastic properties (the approach used here is just a one-dimensional +specialization of the more general approach presented there). +Input File Usage: +Abaqus/CAE Usage: +*VISCOELASTIC, TYPE=TRACTION +Property module: material editor: Mechanical→Elasticity→Viscoelastic: +Domain: Frequency and Frequency: Tabular +Defining the contact area for average contact pressure output +When the thickness-direction behavior of the gasket is defined in terms of force or force per unit length +versus closure, Abaqus/Standard will provide the thickness-direction force or force per unit length as +output variable S11. In this case you can define either a contact width or contact area versus closure +curve that will be used to obtain the average “contact” pressure at each integration point as output variable +CS11. This average pressure considers the changing contact area that occurs as a result of the deformation +of a gasket, as shown in Figure 32.6.6–1. The closure used for input of this curve corresponds to the total +mechanical closure, defined as the sum of the elastic, plastic, and creep closures. +When two- and three-dimensional link gasket elements are used, you should specify the contact +area versus mechanical closure in tabular form. When axisymmetric link and three-dimensional line +elements are used, you should specify the contact width versus mechanical closure in tabular form. A +typical curve is shown in Figure 32.6.6–7. +area +mechanical closure +Figure 32.6.6–7 Specification of contact area versus mechanical +closure for output of average pressure. +You must specify the area at zero closure, then the area at increasing closures. The area is constant +when the mechanical closure is negative and is extrapolated from the slope computed from the last two +user-specified data points if the closure reaches values that are greater than the last user-specified closure. +Area versus closure curves can be provided as a function of temperature and field variables. +Input File Usage: +*GASKET CONTACT AREA, DEPENDENCIES +Abaqus/CAE Usage: +Property module: material editor: Other→Gasket→Gasket Thickness +Behavior: Units: Force, Suboptions→Contact Area +Specific output for directly defined gasket behavior +Output variable E is usually used in Abaqus/Standard to output strain. For gasket elements with behavior +defined by a gasket behavior model this output variable has thickness-direction and transverse shear +components with units of displacement and membrane strains. Output variable NE is used to output an +effective strain. The effective strain components are computed as follows: +NE11 +NE11 +NE22 +NE33 +NE12 +NE13 +NE23 +E11 initial thickness +initial gap) for perturbation steps; otherwise +E11 +initial gap +initial thickness +initial gap)); and +E22 +E33 +E12 initial thickness +E13 (initial thickness +E23 +The output variables THE, PE, or CE can also be used for gasket elements to output generalized +thermal strains, plastic strains, or creep strains, respectively. +For all stress/strain output variables the 11-component refers to the through-thickness direction; +the 22-, 33- and 23-components refer to two direct and one shear membrane component, respectively; +the remaining 12- and 13-components refer to the transverse shear components. For details about these +definitions, see “Gasket elements: overview,” Section 32.6.1. +The output of the elastic strain energy (output variable ALLSE) also contains the energy due to +damage or change in elasticity as a function of plasticity. Therefore, this energy is usually not fully +recoverable. +Additional reference +• Zubeck, M. W., and R. S. Marlow, “Local-Global Finite Element Analysis for Cam Cover Noise +Reduction,” Society of Automotive Engineering, Inc., no. SAE 2003–01–1725, 2003. +32.6.7 +TWO-DIMENSIONAL GASKET ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/CAE +References +• “Gasket elements: overview,” Section 32.6.1 +• “Choosing a gasket element,” Section 32.6.2 +• *GASKET SECTION +Overview +This section provides a reference to the two-dimensional gasket elements available in Abaqus/Standard. +Element types +Link elements +GK2D2 +2-node, two-dimensional gasket element +GK2D2N +2-node, two-dimensional gasket element with thickness-direction behavior only +Active degrees of freedom +1 for gasket elements with thickness-direction behavior only. +1, 2 for other gasket elements. +Additional solution variables +None. +General elements +GKPS4 +GKPE4 +4-node, plane stress gasket element +4-node, plane strain gasket element +GKPS4N +4-node, two-dimensional gasket element with thickness-direction behavior only +GKPS6 +GKPE6 +6-node, plane stress gasket element +6-node, plane strain gasket element +GKPS6N +6-node, two-dimensional gasket element with thickness-direction behavior only +Active degrees of freedom +1 for gasket elements with thickness-direction behavior only. +1, 2 for other gasket elements. +Additional solution variables +None. +Nodal coordinates required +Element property definition +You must define the element’s cross-sectional area (for link elements) or out-of-plane width (for general +elements), initial gap, and initial void. +You can specify the thickness direction as part of the gasket section definition or by specifying a normal +direction at the nodes; you can specify the element thickness as part of the gasket section definition. +Otherwise, Abaqus/Standard will calculate the thickness direction. For link elements the thickness +direction is the direction from the first to the second node and the thickness is the distance between +the nodes. For general elements the thickness direction is based on the midsurface of the element and +the thicknesses at the integration points are based on the nodal positions. See “Defining the gasket +element’s initial geometry,” Section 32.6.4, for more details. +Input File Usage: +Abaqus/CAE Usage: +*GASKET SECTION +Property module: Create Section: select Other as the section +Category and Gasket as the section Type +Element-based loading +None. +Element output +GK2D2 elements +S11 +CS11 +S12 +E11 +E12 +NE11 +NE12 +Pressure or thickness-direction force in the gasket element. +Contact pressure in the gasket element (only available if S11 is the force in the gasket +element and the gasket response is not defined using a material model). +Shear stress or shear force. +Gasket closure if the gasket response is defined directly using a gasket behavior +model; strain if the gasket response is defined using a material model. +Shear motion if the gasket response is defined directly using a gasket behavior model; +strain if the gasket response is defined using a material model. +Effective thickness-direction strain in the gasket element. +Effective shear strain in the gasket element. +GK2D2N elements +S11 +CS11 +E11 +NE11 +Pressure or thickness-direction force in the gasket element. +Contact pressure in the gasket element (only available if S11 is the force in the gasket +element and the gasket response is not defined using a material model). +Gasket closure if the gasket response is defined directly using a gasket behavior +model; strain if the gasket response is defined using a material model. +Effective thickness-direction strain in the gasket element. +General elements with thickness-direction behavior only +S11 +E11 +Pressure in the gasket element. +Gasket closure if the gasket response is defined directly using a gasket behavior +model; strain if the gasket response is defined using a material model. +NE11 +Effective thickness-direction strain in the gasket element. +Other general elements +Pressure in the gasket element. +Direct membrane stress. +Direct membrane stress (only available for plane strain elements). +Shear stress. +Gasket closure if the gasket response is defined directly using a gasket behavior +model; strain if the gasket response is defined using a material model. +Direct membrane strain. +Direct membrane strain (only available for plane strain elements). +Shear motion if the gasket response is defined directly using a gasket behavior model; +strain if the gasket response is defined using a material model. +Effective thickness-direction strain in the gasket element. +Direct membrane strain. +Direct membrane strain (only available for plane strain elements). +Effective shear strain. +32.6.7–3 +S11 +S22 +S33 +S12 +E11 +E22 +E33 +E12 +NE11 +NE22 +NE33 +Node ordering and integration point numbering +Link elements +2 - node element +General elements +4 - node element +6 - node element +THREE-DIMENSIONAL GASKET ELEMENT LIBRARY +3-D GASKET ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/CAE +References +• “Gasket elements: overview,” Section 32.6.1 +• “Choosing a gasket element,” Section 32.6.2 +• *GASKET SECTION +Overview +This section provides a reference to the three-dimensional gasket elements available in Abaqus/Standard. +Element types +Link elements +GK3D2 +2-node, three-dimensional gasket element +GK3D2N +2-node, three-dimensional gasket element with thickness-direction behavior only +Active degrees of freedom +1 for gasket elements with thickness-direction behavior only. +1, 2, 3 for other gasket elements. +Additional solution variables +None. +Line elements +GK3D4L +4-node, three-dimensional line gasket element +GK3D4LN +4-node, three-dimensional line gasket element with thickness-direction behavior only +GK3D6L +6-node, three-dimensional line gasket element +GK3D6LN +6-node, three-dimensional line gasket element with thickness-direction behavior only +Active degrees of freedom +1 for gasket elements with thickness-direction behavior only. +1, 2, 3 for other gasket elements. +Additional solution variables +None. +Area elements +GK3D6 +6-node, three-dimensional gasket element +GK3D6N +6-node, three-dimensional gasket element with thickness-direction behavior only +GK3D8 +8-node, three-dimensional gasket element +GK3D8N +8-node, three-dimensional gasket element with thickness-direction behavior only +GK3D12M +12-node, three-dimensional gasket element +GK3D12MN +12-node, three-dimensional gasket element with thickness-direction behavior only +GK3D18 +18-node, three-dimensional gasket element +GK3D18N +18-node, three-dimensional gasket element with thickness-direction behavior only +Active degrees of freedom +1 for gasket elements with thickness-direction behavior only. +1, 2, 3 for other gasket elements. +Additional solution variables +None. +Nodal coordinates required +Element property definition +You must define the element’s initial gap and initial void, as well as the cross-sectional area (for link +elements) or width (for line elements). +You can specify the thickness direction as part of the gasket section definition or by specifying a normal +direction at the nodes; you can specify the element thickness as part of the gasket section definition. +Otherwise, Abaqus/Standard will calculate the thickness direction and the thickness. For link elements +the thickness direction is the direction from the first to the second node and the thickness is the distance +between the nodes. For line elements the thickness direction is the direction from the bottom node to +the top node associated with the integration point and the thicknesses are the distances between these +same bottom and top nodes. For area elements the thickness direction is based on the midsurface of the +element and the thicknesses at the integration points are based on the nodal positions. See “Defining the +gasket element’s initial geometry,” Section 32.6.4, for more details. +Input File Usage: +Abaqus/CAE Usage: +*GASKET SECTION +Property module: Create Section: select Other as the section +Category and Gasket as the section Type +Element-based loading +None. +Element output +GK3D2 elements +S11 +CS11 +S12 +S13 +E11 +E12 +E13 +NE11 +NE12 +NE13 +Pressure or thickness-direction force in the gasket element. +Contact pressure in the gasket element (only available if S11 is a force and the gasket +response is not defined using a material model). +Shear stress or shear force. +Shear stress or shear force. +Gasket closure if the gasket response is defined directly using a gasket behavior +model; strain if the gasket response is defined using a material model. +Shear motion if the gasket response is defined directly using a gasket behavior model; +strain if the gasket response is defined using a material model. +Shear motion if the gasket response is defined directly using a gasket behavior model; +strain if the gasket response is defined using a material model. +Effective thickness-direction strain in the gasket element. +Effective shear strain. +Effective shear strain. +GK3D2N elements +S11 +CS11 +E11 +NE11 +Pressure or thickness-direction force in the gasket element. +Contact pressure in the gasket element (only available if S11 is a force and the gasket +response is not defined using a material model.) +Gasket closure if the gasket response is defined directly using a gasket behavior +model; strain if the gasket response is defined using a material model. +Effective thickness-direction strain in the gasket element. +Line elements with thickness-direction behavior only +S11 +CS11 +E11 +NE11 +Pressure or thickness-direction force per unit length in the gasket element. +Contact pressure in the gasket element (only available if S11 is a force per unit length +and the gasket response is not defined using a material model). +Gasket closure if the gasket response is defined directly using a gasket behavior +model; strain if the gasket response is defined using a material model. +Effective thickness-direction strain in the gasket element. +Other line elements +S11 +CS11 +S22 +S12 +S13 +E11 +E22 +E12 +E13 +NE11 +NE22 +NE12 +NE13 +Pressure or thickness-direction force per unit length in the gasket element. +Contact pressure in the gasket element (only available if S11 is a force per unit length +and the gasket response is not defined using a material model). +Direct membrane stress. +Shear stress or shear force per unit length. +Shear stress or shear force per unit length. +Gasket closure if the gasket response is defined directly using a gasket behavior +model; strain if the gasket response is defined using a material model. +Direct membrane strain. +Shear motion if the gasket response is defined directly using a gasket behavior model; +strain if the gasket response is defined using a material model. +Shear motion if the gasket response is defined directly using a gasket behavior model; +strain if the gasket response is defined using a material model. +Effective thickness-direction strain in the gasket element. +Direct membrane strain. +Effective shear strain. +Effective shear strain. +Area elements with thickness-direction behavior only +S11 +E11 +NE11 +Pressure in the gasket element. +Gasket closure if the gasket response is defined directly using a gasket behavior +model; strain if the gasket response is defined using a material model. +Effective thickness-direction strain in the gasket element. +Other area elements +S11 +S22 +S33 +S12 +S13 +S23 +E11 +E22 +E33 +Pressure in the gasket element. +Direct membrane stress. +Direct membrane stress. +Transverse shear stress. +Transverse shear stress. +Membrane shear stress. +Gasket closure if the gasket response is defined directly using a gasket behavior +model; strain if the gasket response is defined using a material model. +Direct membrane strain. +Direct membrane strain. +Transverse shear motion if the gasket response is defined directly using a gasket +behavior model; strain if the gasket response is defined using a material model. +Transverse shear motion if the gasket response is defined directly using a gasket +behavior model; strain if the gasket response is defined using a material model. +Membrane shear strain. +Effective thickness-direction strain in the gasket element. +Direct membrane strain. +Direct membrane strain. +Effective shear strain. +Effective shear strain. +Membrane shear strain. +E12 +E13 +E23 +NE11 +NE22 +NE33 +NE12 +NE13 +NE12 +Node ordering and integration point numbering +Link elements +2 - node element +Line elements +4 - node element +6 - node element +32.6.8–5 +Area elements +6 - node element +12 +10 +11 +12 - node element +11 +12 +15 +14 +16 +18 +13 +17 +10 +8 - node element +18 - node element +Integration points are indicated with an X and have the same numbers as the bottom face nodes, except +that the point between nodes 17 and 18 in the 18-node gasket element is integration point number 9. +32.6.9 +AXISYMMETRIC GASKET ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/CAE +References +• “Gasket elements: overview,” Section 32.6.1 +• “Choosing a gasket element,” Section 32.6.2 +• *GASKET SECTION +Overview +This section provides a reference to the axisymmetric gasket elements available in Abaqus/Standard. +Element types +Link elements +GKAX2 +2-node, axisymmetric gasket element +GKAX2N +2-node, axisymmetric gasket element with thickness-direction behavior only +Active degrees of freedom +1 for gasket elements with thickness-direction behavior only. +1, 2 for other gasket elements. +Additional solution variables +None. +General elements +GKAX4 +4-node, axisymmetric gasket element +GKAX4N +4-node, axisymmetric gasket element with thickness-direction behavior only +GKAX6 +6-node, axisymmetric gasket element +GKAX6N +6-node, axisymmetric gasket element with thickness-direction behavior only +Active degrees of freedom +1 for gasket elements with thickness-direction behavior only. +1, 2 for other gasket elements. +Additional solution variables +None. +Nodal coordinates required +Element property definition +You must define the element’s initial gap and initial void. In addition, for link elements you must define +the element’s width. +You can specify the thickness direction as part of the gasket section definition or by specifying a normal +direction at the nodes; you can specify the element thickness as part of the gasket section definition. +Otherwise, Abaqus/Standard will calculate the thickness direction and the thickness. For link elements +the thickness direction is the direction from the first to the second node and the thickness is the distance +between the nodes. For general elements the thickness direction is based on the midsurface of the element +and the thicknesses at the integration points are based on the nodal positions. See “Defining the gasket +element’s initial geometry,” Section 32.6.4, for more details. +Input File Usage: +Abaqus/CAE Usage: +*GASKET SECTION +Property module: Create Section: select Other as the section +Category and Gasket as the section Type +Element-based loading +None. +Element output +GKAX2 elements +S11 +CS11 +S22 +S12 +E11 +E22 +E12 +NE11 +NE22 +NE12 +Pressure or thickness-direction force per unit length in the gasket element. +Contact pressure in the gasket element (only available if S11 is a force per unit length +and the gasket response is not defined using a material model). +Hoop stress. +Shear stress or shear force per unit length. +Gasket closure if the gasket response is defined directly using a gasket behavior +model; strain if the gasket response is defined using a material model. +Hoop strain. +Shear motion if the gasket response is defined directly using a gasket behavior model; +strain if the gasket response is defined using a material model. +Effective thickness-direction strain. +Hoop strain. +Effective shear strain. +GKAX2N elements +S11 +CS11 +E11 +NE11 +Pressure or thickness-direction force per unit length in the gasket element. +Contact pressure in the gasket element (only available if S11 is a force per unit length +and the gasket response is not defined using a material model). +Gasket closure if the gasket response is defined directly using a gasket behavior +model; strain if the gasket response is defined using a material model. +Effective thickness-direction strain. +General elements with thickness-direction behavior only +S11 +E11 +Pressure in the gasket element. +Gasket closure if the gasket response is defined directly using a gasket behavior +model; strain if the gasket response is defined using a material model. +NE11 +Effective thickness-direction strain. +Other general elements +S11 +S22 +S33 +S12 +E11 +E22 +E33 +E12 +NE11 +NE22 +NE33 +NE12 +Pressure in the gasket element. +Direct membrane stress. +Hoop stress. +Shear stress. +Gasket closure if the gasket response is defined directly using a gasket behavior +model; strain if the gasket response is defined using a material model. +Direct membrane strain. +Hoop strain. +Shear motion if the gasket response is defined directly using a gasket behavior model; +strain if the gasket response is defined using a material model. +Effective thickness-direction strain. +Direct membrane strain. +Direct membrane strain. +Effective shear strain. +Node ordering and integration point numbering +Link elements +2 - node element +General elements +4 - node element +6 - node element +32.7 +Surface elements +• “Surface elements,” Section 32.7.1 +• “General surface element library,” Section 32.7.2 +• “Cylindrical surface element library,” Section 32.7.3 +• “Axisymmetric surface element library,” Section 32.7.4 +32.7.1 +SURFACE ELEMENTS +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “General surface element library,” Section 32.7.2 +• “Cylindrical surface element library,” Section 32.7.3 +• “Axisymmetric surface element library,” Section 32.7.4 +• *SURFACE SECTION +• “Creating surface sections,” Section 12.13.9 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +Surface elements: +• are defined just like membrane elements—as surfaces in space; +• have no inherent stiffness; +• may have mass per unit area; +• may be used to define rigid bodies; +• may be used in the definition of surfaces and surface-based tie constraints; +• behave just like membrane elements with zero thickness; +• may be used with rebar layers; +• can be embedded in solid elements; +• can transmit only in-plane forces; and +• have no bending stiffness or transverse shear stiffness. +Typical applications +Surface elements are useful in several special modeling cases: +• They are used to carry rebar layers to represent thin stiffening components in solid structures. +The stiffness and mass of the rebar layers are added to the surface elements . The reinforced surface elements can also be embedded in “host” +solid elements . +• They are used to bring additional mass into the model in the form of a mass per unit area; for +example, to spread the mass of fuel in a tank over the tank surface, particularly when the tank is +modeled with solid elements. +• They are used to specify a surface used in a constraint, when that surface does not have structural +properties. +• When used in conjunction with a surface-based tie constraint, they are used to specify distributed +surface loading, such as incident wave loading, on beam elements. +• In Abaqus/Explicit (when used in conjunction with a surface-based tie constraint) they can be used +to specify a complex surface on beam elements for use in general contact. The stiffness of the +penalty springs used to enforce contact constraints is approximately proportional to the mass of the +surface nodes. Contact will not be enforced if the surface nodes have no mass. +• In Abaqus/Explicit they can be used to define all or part of the boundary for a surface-based fluid +cavity (for example, see “Hydrostatic fluid elements: modeling an airspring,” Section 1.1.9 of the +Abaqus Example Problems Manual). +Choosing an appropriate element +In addition to the general surface elements available in both Abaqus/Standard and Abaqus/Explicit, +cylindrical surface elements and axisymmetric surface elements are available in Abaqus/Standard only. +General surface elements +General surface elements should be used in three-dimensional models in which the deformation of the +structure can evolve in three dimensions. +Cylindrical surface elements +Cylindrical surface elements are available in Abaqus/Standard for precise modeling of regions in a +structure with circular geometry, such as a tire. The elements make use of trigonometric functions to +interpolate displacements along the circumferential direction and use regular isoparametric interpolation +in the in-plane direction. They use three nodes along the circumferential direction and can span a +segment between 0° and 180°. Elements with both first-order and second-order interpolation in the +in-plane direction are available. +The geometry of the element is defined by specifying nodal coordinates in a global Cartesian system. +These elements can be used in the same mesh with regular surface elements. They can also be +embedded in general solid and cylindrical elements. +Axisymmetric surface elements +The axisymmetric surface elements available in Abaqus/Standard are divided into two categories: those +that do not allow twist about the symmetry axis and those that do. These elements are referred to as the +regular and generalized axisymmetric surface elements, respectively. +The generalized axisymmetric surface elements (axisymmetric surface elements with twist) +allow a circumferential component of loading, which may cause twist about the symmetry axis. The +circumferential load component is independent of the circumferential coordinate . Since there is no +dependence of the loading on the circumferential coordinate, the deformation is axisymmetric. +The generalized axisymmetric surface elements cannot be used in dynamic or eigenfrequency +extraction procedures. +Naming convention +The naming convention for surface elements depends on the element dimensionality. +General surface elements +General surface elements in Abaqus are named as follows: +SF +3D 4 R +reduced integration (optional) +number of nodes +three-dimensional +membrane-like +surface +For example, SFM3D4R is a three-dimensional, 4-node surface element with reduced integration. +Cylindrical surface elements +Cylindrical surface elements in Abaqus/Standard are named as follows: +SF +M CL 6 +number of nodes +cylindrical +membrane-like +surface +For example, SFMCL6 is a 6-node cylindrical surface element with circumferential interpolation. +Axisymmetric surface elements +Axisymmetric surface elements in Abaqus/Standard are named as follows: +SF +G AX 2 +order of interpolation +axisymmetric +generalized (optional) +membrane-like +surface +For example, SFMAX2 is a regular axisymmetric, quadratic-interpolation surface element. +Element normal definition +The “top” surface of a surface element is the surface in the positive normal direction (defined below) and +is called the SPOS face for contact definition. The “bottom” surface is in the negative direction along +the normal and is called the SNEG face for contact definition. +General surface elements +For general surface elements the positive normal direction is defined by the right-hand rule going around +the nodes of the element in the order that they are specified in the element definition. See Figure 32.7.1–1. +face SPOS +face SNEG +Figure 32.7.1–1 Positive normals for general surface elements. +Cylindrical surface elements +The positive normal direction is defined by the right-hand rule going around the nodes of the element in +the order that they are specified in the element definition. See Figure 32.7.1–2. +face SNEG +face SPOS +Figure 32.7.1–2 Positive normals for cylindrical surface elements. +Axisymmetric surface elements +For axisymmetric surface elements the positive normal is defined by a 90° counterclockwise rotation +from the direction going from node 1 to node 2. See Figure 32.7.1–3. +face SPOS +face SNEG +Figure 32.7.1–3 Positive normals for axisymmetric surface elements. +Defining the element’s section properties +You must associate the surface section properties with a region of your model. +Input File Usage: +*SURFACE SECTION, ELSET=name +where the ELSET parameter refers to a set of surface elements. +Abaqus/CAE Usage: +Property module: +Create Section: select Shell as the section Category and Surface as the +section Type +Assign→Section: select regions +Using a surface element to carry rebar layers +You can define layers of reinforcement that are carried by the surface element. The stiffness and mass +due to the rebar layers are added to the surface element. +Input File Usage: +Use both of the following options: +Abaqus/CAE Usage: +*SURFACE SECTION, ELSET=name +*REBAR LAYER +Property module: Create Section: select Shell as the section Category +and Surface as the section Type, Rebar Layers +Using a surface element to bring additional mass into the model +You can define the mass per unit area carried by the surface element. +Input File Usage: +Abaqus/CAE Usage: +*SURFACE SECTION, ELSET=name, DENSITY=number +Property module: Create Section: select Shell as the section Category +and Surface as the section Type, toggle on Density: number +Using a surface element in a constraint +Surface elements can be used to define a surface in Abaqus, and this surface can be used in a surface- +based tie constraint . +Input File Usage: +Use the following options: +*SURFACE, NAME=surface_name +*TIE, NAME=name +surface_name, master_name +Abaqus/CAE Usage: +In Abaqus/CAE you can select one or more faces directly in the viewport when +you are prompted to select a surface. In addition, you can define surfaces as +collections of faces and edges using the Surface toolset. +Interaction module: Create Constraint: Tie +32.7.2 +GENERAL SURFACE ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/Explicit Abaqus/CAE +References +• “Surface elements,” Section 32.7.1 +• *SURFACE SECTION +• *REBAR LAYER +Overview +This section provides a reference to the surface elements available in Abaqus/Standard and +Abaqus/Explicit. +Element types +SFM3D3 +3-node triangle +SFM3D4(S) +4-node quadrilateral +SFM3D4R +4-node quadrilateral, reduced integration +SFM3D6(S) +SFM3D8(S) +6-node triangle +8-node quadrilateral +SFM3D8R(S) +8-node quadrilateral, reduced integration +Active degrees of freedom +1, 2, 3 +Additional solution variables +None. +Nodal coordinates required +X, Y, Z +Element property definition +Input File Usage: +Use the following option to define surface element properties: +*SURFACE SECTION +If rebar are being defined, use the following option in conjunction with the +*SURFACE SECTION option: +*REBAR LAYER +Use the following option to define a mass density per unit area: +*SURFACE SECTION, DENSITY=number +Property module: Create Section: select Shell as the section Category +and Surface as the section Type, Rebar Layers (optional) +You cannot define the mass per unit area for a surface section in Abaqus/CAE. +Abaqus/CAE Usage: +Element-based loading +Distributed loads +Distributed loads are specified as described in “Distributed loads,” Section 33.4.3. Gravity, centrifugal, +rotary acceleration, and Coriolis force loads apply only if the surface elements have rebar defined or if +the elements have a defined density. +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +BX +BY +BZ +BXNU +Body force +Body force +Body force +Body force +FL−2 +FL−2 +FL−2 +FL−2 +BYNU +Body force +FL−2 +BZNU +Body force +FL−2 +Body force in the global X-direction. +Body force in the global Y-direction. +Body force in the global Z-direction. +in +force +Nonuniform body +the +global X-direction with magnitude +supplied via user subroutine DLOAD +in Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +in +force +the +Nonuniform body +global Y-direction with magnitude +supplied via user subroutine DLOAD +in Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +in +force +Nonuniform body +the +global Z-direction with magnitude +supplied via user subroutine DLOAD +in Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +CENT(S) +Not supported +FL−3 +(ML−2 T−2 ) +CENTRIF(S) +Rotational body +force +T−2 +Centrifugal load (magnitude is input +is the mass density +as +per unit area, +is the angular speed). +, where +Centrifugal load (magnitude is input +as +is the angular speed). +, where +Units +Description +Load ID +(*DLOAD) +CORIO(S) +Abaqus/CAE +Load/Interaction +Coriolis force +FL−3 T +(ML−2 T−1 ) +GRAV +Gravity +LT−2 +HP(S) +Not supported +FL−2 +Pressure +FL−2 +PNU +Not supported +FL−2 +, where +Coriolis force (magnitude is input as +is the mass density per +unit area, +is the angular speed). The +load stiffness due to Coriolis loading +is not accounted for in direct steady- +state dynamics analysis. +loading +Gravity +direction (magnitude is +acceleration). +in +specified +input as +Hydrostatic pressure applied to the +element reference surface and linear +in global Z. The pressure is positive in +the direction of the positive element +normal. +Pressure +applied to the element +reference surface. The pressure is +positive in the direction of the positive +element normal. +applied +reference +to +Nonuniform pressure +surface +the +element +via +with magnitude +in +subroutine +user +VDLOAD +Abaqus/Standard +in Abaqus/Explicit. +The pressure +is positive in the direction of the +positive element normal. +supplied +DLOAD +and +ROTA(S) +SBF(E) +SP(E) +Rotational body +force +T−2 +Not supported +FL−5 T2 +Not supported +FL−4 T2 +TRSHR +Surface traction +FL−2 +Rotary acceleration load (magnitude +is input as +is the rotary +acceleration). +, where +Stagnation body force in global X-, +Y-, and Z-directions. +Stagnation pressure applied to the +element reference surface. +traction +Shear +reference surface. +on +the +element +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +TRSHRNU(S) +Not supported +FL−2 +TRVEC +Surface traction +FL−2 +TRVECNU(S) +Not supported +FL−2 +VBF(E) +VP(E) +Not supported +FL−4 T +Not supported +FL−3 T +traction on the +Nonuniform shear +element +surface with +reference +magnitude and direction supplied +via user subroutine UTRACLOAD. +General +reference surface. +traction on the element +traction +Nonuniform general +on +the element reference surface with +magnitude and direction supplied via +user subroutine UTRACLOAD. +Viscous body force in global X-, Y-, +and Z-directions. +surface pressure +Viscous +applied +reference surface. +to the element +The pressure is proportional to the +velocity normal to the element face +and opposing the motion. +Foundations +Foundations are available only in Abaqus/Standard and are specified as described in “Element +foundations,” Section 2.2.2. +Load ID +(*FOUNDATION) Load/Interaction +Abaqus/CAE +Elastic +foundation +Units +Description +FL−2 +Elastic foundation. +Surface-based loading +Distributed loads +Surface-based distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +HP(S) +Pressure +FL−2 +Hydrostatic pressure on the element +reference surface and linear in global +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +Pressure +FL−2 +PNU +Pressure +FL−2 +SP(E) +Pressure +FL−4 T2 +TRSHR +Surface traction +FL−2 +TRSHRNU(S) +Surface traction +FL−2 +TRVEC +Surface traction +FL−2 +TRVECNU(S) +Surface traction +FL−2 +VP(E) +Pressure +FL−3 T +Z. The pressure is positive in the +direction opposite to the surface +normal. +Pressure on the element reference +surface. The pressure is positive in +the direction opposite to the surface +normal. +Nonuniform pressure on the element +reference surface with magnitude +supplied via user subroutine DLOAD +in Abaqus/Standard and VDLOAD +in Abaqus/Explicit. The pressure is +positive in the direction opposite to +the surface normal. +Stagnation pressure applied to the +element reference surface. +traction +Shear +reference surface. +on +the +element +traction on the +Nonuniform shear +element +surface with +reference +magnitude and direction supplied +via user subroutine UTRACLOAD. +General +reference surface. +traction on the element +traction +on +Nonuniform general +the element reference surface with +magnitude and direction supplied via +user subroutine UTRACLOAD. +Viscous surface pressure applied to +the element reference surface. The +pressure is proportional to the velocity +normal to the element surface and +opposing the motion. +Incident wave loading +Surface-based incident wave loading is also available for these elements. See “Acoustic and shock +loads,” Section 33.4.6. +Element output +Output is currently available only when the surface element is used to carry rebar layers. See “Defining +reinforcement,” Section 2.2.3, for details. +Node ordering on elements +1 2 +3 - node element +4 - node element +6 5 +1 + 2 +4 7 3 +6 - node element +8 - node element +Numbering of integration points for output +6 5 +1 2 +1 + 2 +3 - node element +6 - node element +4 - node element +4 - node reduced +integration element +4 7 3 +4 7 3 +8 - node element +8 - node reduced +integration element +CYLINDRICAL SURFACE ELEMENT LIBRARY +CYLINDRICAL SURFACE ELEMENTS +Product: Abaqus/Standard +References +• “Surface elements,” Section 32.7.1 +• *SURFACE SECTION +• *REBAR LAYER +Overview +This section provides a reference to the cylindrical surface elements available in Abaqus/Standard. +Element types +SFMCL6 +6-node cylindrical surface +SFMCL9 +9-node cylindrical surface +Active degrees of freedom +1, 2, 3 +Additional solution variables +None. +Nodal coordinates required +X, Y, Z +Element property definition +Input File Usage: +Use the following option to define surface element properties: +*SURFACE SECTION +If rebar are being defined, use the following option in conjunction with the +*SURFACE SECTION option: +*REBAR LAYER +Use the following option to define a mass density per unit area: +*SURFACE SECTION, DENSITY=number +Element-based loading +Distributed loads +Distributed loads are specified as described in “Distributed loads,” Section 33.4.3. Gravity, centrifugal, +rotary acceleration, and Coriolis force loads apply only if the surface elements have rebar defined or if +the elements have a defined density. +Units +Description +Body force in the global X-direction. +Body force in the global Y-direction. +Body force in the global Z-direction. +Nonuniform body force in the global +X-direction with magnitude supplied via +user subroutine DLOAD. +Nonuniform body force in the global +Y-direction with magnitude supplied via +user subroutine DLOAD. +Nonuniform body force in the global +Z-direction with magnitude supplied via +user subroutine DLOAD. +Centrifugal load (magnitude is input as +where +is the angular speed). +is the mass density per unit area, +Centrifugal load (magnitude is input as +where +is the angular speed). +, +, +Coriolis force (magnitude is input as +where +, +is the mass density per unit area, +is the angular speed). The load stiffness +due to Coriolis loading is not accounted for +in direct steady-state dynamics analysis. +Gravity loading in a specified direction +(magnitude is input as acceleration). +Hydrostatic pressure applied to the element +reference surface and linear in global Z. The +32.7.3–2 +Load ID +(*DLOAD) +BX +BY +BZ +BXNU +BYNU +BZNU +FL−3 +FL−2 +FL−2 +FL−2 +FL−2 +FL−2 +CENT +FL−3 (ML−2 T−2 ) +CENTRIF +T−2 +CORIO +FL−3 T (ML−2 T−1 ) +GRAV +HP +LT−2 +Load ID +(*DLOAD) +Units +Description +PNU +ROTA +TRSHR +FL−2 +FL−2 +T−2 +FL−2 +TRSHRNU(S) +FL−2 +TRVEC +FL−2 +TRVECNU(S) +FL−2 +pressure is positive in the direction of the +positive element normal. +Pressure applied to the element reference +surface. The pressure is positive in the +direction of the positive element normal. +Nonuniform pressure applied to the element +reference surface with magnitude supplied +via user subroutine DLOAD. +Rotary acceleration load (magnitude is input +as +is the rotary acceleration). +, where +Shear traction on the element reference +surface. +Nonuniform shear traction on the element +reference surface with magnitude and +direction supplied via user +subroutine +UTRACLOAD. +General traction on the element reference +surface. +Nonuniform general traction on the element +reference surface with magnitude and +subroutine +direction supplied via user +UTRACLOAD. +Foundations +Foundations are specified as described in “Element foundations,” Section 2.2.2. +Load ID +(*FOUNDATION) +Units +Description +FL−2 +Elastic foundation. +Surface-based loading +Distributed loads +Surface-based distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DSLOAD) +Units +Description +HP +PNU +FL−2 +FL−2 +FL−2 +TRSHR +FL−2 +TRSHRNU(S) +FL−2 +TRVEC +FL−2 +TRVECNU(S) +FL−2 +on +pressure +Hydrostatic +element +reference surface and linear in global Z. +The pressure is positive in the direction +opposite to the surface normal. +the +Pressure on the element reference surface. +The pressure is positive in the direction +opposite to the surface normal. +Nonuniform pressure on the +element +reference surface with magnitude supplied +via user subroutine DLOAD. The pressure +is positive in the direction opposite to the +surface normal. +Shear traction on the element reference +surface. +Nonuniform shear traction on the element +reference surface with magnitude and +direction supplied via user +subroutine +UTRACLOAD. +General traction on the element reference +surface. +Nonuniform general traction on the element +reference surface with magnitude and +subroutine +direction supplied via user +UTRACLOAD. +Incident wave loading +Surface-based incident wave loading is also available for these elements. See “Acoustic and shock +loads,” Section 33.4.6. +Element output +Output is currently available only when the surface element is used to carry rebar layers. See “Defining +reinforcement,” Section 2.2.3, for details. +Node ordering and face numbering on elements +6-node element + 9-node element +Numbering of integration points for output +6-node element +9-node element +AXISYMMETRIC SURFACE ELEMENT LIBRARY +AXISYMMETRIC SURFACE LIBRARY +Products: Abaqus/Standard Abaqus/CAE +References +• “Surface elements,” Section 32.7.1 +• *SURFACE SECTION +• *REBAR LAYER +Overview +This section provides a reference to the axisymmetric surface elements available in Abaqus/Standard. +Conventions +Coordinate 1 is r, coordinate 2 is z. At +, the r-direction corresponds to the global X-direction +and the z-direction corresponds to the global Y-direction. This is important when data must be given in +global directions. Coordinate 1 should be greater than or equal to zero. +Degree of freedom 1 is +have an additional degree of freedom, 5, corresponding to the twist angle +, degree of freedom 2 is +. Generalized axisymmetric elements with twist +(in radians). +Abaqus/Standard does not automatically apply any boundary conditions to nodes located along the +symmetry axis. You must apply radial or symmetry boundary conditions on these nodes if desired. +Point loads and moments should be given as the value integrated around the circumference; that is, the +total value on the ring. +Element types +Regular axisymmetric surface elements +SFMAX1 +SFMAX2 +2-node linear, without twist +3-node quadratic, without twist +Active degrees of freedom +1, 2 +Additional solution variables +None. +Generalized axisymmetric surface elements +SFMGAX1 +2-node linear, with twist +SFMGAX2 +3-node quadratic, with twist +Active degrees of freedom +1, 2, 5 +Additional solution variables +None. +Nodal coordinates required +R, Z +Element property definition +Use the following option to define surface elements: +*SURFACE SECTION +If rebar are being defined, use the following option in conjunction with the +*SURFACE SECTION option: +*REBAR LAYER +Use the following option to define a mass density per unit area: +*SURFACE SECTION, DENSITY=number +Property module: Create Section: select Shell as the section Category +and Surface as the section Type, Rebar Layers (optional) +You cannot define the mass per unit area for a surface section in Abaqus/CAE. +Input File Usage: +Abaqus/CAE Usage: +Element-based loading +Distributed loads +Distributed loads are specified as described in “Distributed loads,” Section 33.4.3. Gravity and +centrifugal loads apply only if the surface elements have rebar defined or if the elements have a defined +density. +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +BR +BZ +Body force +Body force +BRNU +Body force +FL−2 +FL−2 +FL−2 +Body force in the radial (1 or r) +direction. +Body force in the axial (2 or z) +direction. +Nonuniform body force in the radial +direction with magnitude supplied via +user subroutine DLOAD. +Abaqus/CAE +Load/Interaction +Units +Description +Load ID +(*DLOAD) +BZNU +Body force +FL−2 +CENT +Not supported +FL−3 +(ML−2 T−2 ) +CENTRIF +Rotational body +force +T−2 +GRAV +Gravity +LT−2 +HP +Not supported +FL−2 +Pressure +FL−2 +PNU +Not supported +FL−2 +Nonuniform body force in the axial +direction with magnitude supplied via +user subroutine DLOAD. +Centrifugal load (magnitude is input +is the mass density +as +, where +per unit area, +is the angular +velocity). Since only axisymmetric +deformation is allowed, the spin axis +must be the z-axis. +, where +Centrifugal load (magnitude is input +as +the angular +velocity). Since only axisymmetric +deformation is allowed, the spin axis +must be the z-axis. +is +Gravity +direction +acceleration). +loading +in +(magnitude +specified +as +input +Hydrostatic pressure applied to the +element reference surface and linear +in global Z. The pressure is positive in +the direction of the positive element +normal. +Pressure +applied to the element +reference surface. The pressure is +positive in the direction of the positive +element normal. +applied +reference +to +Nonuniform pressure +the +surface +element +with magnitude supplied via user +subroutine DLOAD. The pressure is +positive in the direction of the positive +element normal. +TRSHR +Surface traction +FL−2 +TRSHRNU(S) +Not supported +FL−2 +traction +Shear +reference surface. +on +the +element +Nonuniform shear +reference +element +traction on the +surface with +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +TRVEC +Surface traction +FL−2 +TRVECNU(S) +Not supported +FL−2 +magnitude and direction supplied +via user subroutine UTRACLOAD. +General +reference surface. +traction on the element +traction +Nonuniform general +on +the element reference surface with +magnitude and direction supplied via +user subroutine UTRACLOAD. +Foundations +Foundations are specified as described in “Element foundations,” Section 2.2.2. +Load ID +(*FOUNDATION) Load/Interaction +Abaqus/CAE +Units +Description +Elastic +foundation +FL−2 +Surface-based loading +Distributed loads +Elastic foundation. For SFMGAX1 +and SFMGAX2 elements the elastic +foundations are applied to degrees of +freedom +only. +and +Surface-based distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +Hydrostatic pressure applied to the +element reference surface and linear +in global Z. The pressure is positive +in the direction opposite to the surface +normal. +Pressure +applied to the element +reference surface. The pressure is +positive in the direction opposite to +the surface normal. +Nonuniform pressure +element +the +reference +applied +to +surface +HP +Pressure +FL−2 +Pressure +FL−2 +PNU +Pressure +FL−2 +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +TRSHR +Surface traction +FL−2 +TRSHRNU(S) +Surface traction +FL−2 +TRVEC +Surface traction +FL−2 +TRVECNU(S) +Surface traction +FL−2 +with magnitude supplied via user +subroutine DLOAD. The pressure is +positive in the direction opposite to +the surface normal. +traction +Shear +reference surface. +on +the +element +traction on the +Nonuniform shear +element +surface with +reference +magnitude and direction supplied +via user subroutine UTRACLOAD. +General +reference surface. +traction on the element +traction +Nonuniform general +on +the element reference surface with +magnitude and direction supplied via +user subroutine UTRACLOAD. +Incident wave loading +Surface-based incident wave loading is also available for these elements. See “Acoustic and shock +loads,” Section 33.4.6. +Element output +Output is currently available only when the surface element is used to carry rebar layers. See “Defining +reinforcement,” Section 2.2.3, for details. +Node ordering on elements +2 - node element +3 - node element +Numbering of integration points for output +2 - node element +3 - node element +32.8 +Tube support elements +• “Tube support elements,” Section 32.8.1 +• “Tube support element library,” Section 32.8.2 +32.8.1 +TUBE SUPPORT ELEMENTS +Product: Abaqus/Standard +References +• “Tube support element library,” Section 32.8.2 +• *ITS +• *DASHPOT +• *FRICTION +• *SPRING +Overview +Tube support elements: +• are provided to model the interaction of a tube with a closely adjacent tube support, for cases where +intermittent contact between the tube and the support may occur; and +• are made up of a spring/friction link (to simulate direct contact between the tube and the support) +and a parallel dashpot (to simulate the effect of the fluid in the annulus between the tube and the +support), as shown in Figure 32.8.1–1. +Details of the element formulations can be found in “Tube support elements,” Section 3.9.4 of the Abaqus +Theory Manual. +Typical applications +An ITSCYL element can be used to model a drilled hole support . +Several ITSUNI elements can be attached to the same node of the beam elements representing the +tube to model the case of a tube support made up of a series of straight segments, as in an “egg-crate” +design . +Choosing an appropriate element +Two types of tube support elements are provided. +ITSUNI elements +ITSUNI is a “unidirectional” element, which always acts in a fixed direction in space. One node of the +element must be located on the axis of the tube, which is modeled using beam elements; and the other +node must be located equidistant between the two parallel support plates. The support plates are built +into the ITSUNI element definition. +P3 +Spring +( linear or nonlinear ) +Friction +Dashpot +( linear or nonlinear ) +P3 +Figure 32.8.1–1 Tube support element behavior. +ITSCYL elements +ITSCYL is a “cylindrical” element, which can be used to simulate the interaction between a circular tube +and a circular hole. One node of the element must be located on the axis of the tube, which is modeled +using beam elements, and the other node must be located at the center of the hole in the circular tube +support plate. The circular hole is built into the ITSCYL element definition. +Defining the behavior of ITS elements +You define the diameter of the tube and other geometric quantities that define the ITS element. You must +associate these quantities with a set of ITS elements. In addition, you must define the behavior of the +spring, friction link, and dashpot that make up a tube support element. +Tube center +Tube +C of tube +Tube +support +plate +Center of hole +ITSCYL +element +Figure 32.8.1–2 Use of an ITSCYL element for a drilled hole support. +The spring behavior of an ITS element is shown in Figure 32.8.1–4. Relative displacements in the +element are measured from the position where the tube and the hole in the support plate are aligned +exactly—when the nodes of the element are at the same location. As indicated in Figure 32.8.1–4, the +spring behavior of an ITS element is modified from that of the assigned spring definition to account for +any clearance between the tube and support when the nodes of the element are at the same location. +When there is no contact between the tube and the support, no force is transmitted by the spring; when +the tube is in contact with the support, the force increases as the tube wall is deformed. This force can +be modeled as a linear or a nonlinear function of the relative displacement between the axis of the tube +and the center of the hole in the support. +Tube +ITSUNI elements +Parallel support +plates for element 2 +C of tube +n2 +n1 +Center of opening +in support plates +Parallel support +plates for element 1 +Figure 32.8.1–3 Use of ITSUNI elements for an “egg-crate” support. +Friction between the tube and support will generate a moment at the tube node if the tube diameter +is greater than zero and a moment at the hole node if the hole size is greater than zero. At least one of +the following should be true for any node of an ITS element that will have a moment acting on it: +• the node should be associated with a beam or other element that can carry a moment; +• the nodal rotation should be set to zero with a boundary condition. +Input File Usage: +Use the following options to define the behavior of ITS elements: +*ITS, ELSET=name +*DASHPOT +*SPRING +*FRICTION +P3 +TUBE SUPPORT +Stiffness associated + with tube wall + flattening +-c0 +c0 +u3 +c0 = clearance between tube and support + side in fully aligned position +P3 +ITSCYL +Stiffness associated with +tube wall flattening +c0 +u3 +c0 = difference between support plate hole radius + and tube outside radius +Figure 32.8.1–4 Nonlinear spring behavior in ITS elements +to model clearance and tube flattening. +32.8.2 +TUBE SUPPORT ELEMENT LIBRARY +Product: Abaqus/Standard +References +• “Tube support elements,” Section 32.8.1 +• *ITS +Overview +This section provides a reference to the tube support elements available in Abaqus/Standard. +Element types +ITSUNI +ITSCYL +Unidirectional tube support element +Cylindrical geometry tube support element +Active degrees of freedom +1, 2, 3, 4, 5, 6 +Additional solution variables +None. +Nodal coordinates required +X, Y, Z +Element property definition +Input File Usage: +*ITS +Element-based loading +Total direct force in the element. +Tangential (shear) force component, caused by friction, in the plane of the cross- +section of the tube. +Tangential (shear) force component, caused by friction, parallel to the axis of the +tube. +32.8.2–1 +None. +Element output +S11 +S12 +The force in the spring link and the force in the dashpot are defined as generalized substresses and, +therefore, are available as substress selections in the output options, as follows: +SS1 +SS2 +Force in the spring link. +Force in the dashpot. +The relative axial and tangential displacements corresponding to the forces above are chosen by +requesting the corresponding “strains,” except that “strain” component E13 is not defined in element +type ITSCYL. +The relative tangential (shear) displacement components during slip are available as “plastic strain” +components PE12 and PE13. The “equivalent plastic strain” is defined in these elements as +where +and +are the two relative tangential displacement components. +Nodes associated with the element +ITSUNI: Two nodes—one on the axis of the tube and one equidistant between the two parallel support +plates. +ITSCYL: Two nodes—one on the axis of the tube and one at the center of the hole in the support plate. +32.9 +Line spring elements +• “Line spring elements for modeling part-through cracks in shells,” Section 32.9.1 +• “Line spring element library,” Section 32.9.2 +LINE SPRING ELEMENTS FOR MODELING PART-THROUGH CRACKS IN SHELLS +LINE SPRING ELEMENTS +Product: Abaqus/Standard +References +• “Line spring element library,” Section 32.9.2 +• *SHELL SECTION +• *SURFACE FLAW +Overview +Line spring elements: +• are used to evaluate part-through cracks (flaws) in shells inexpensively; +• are used together with shell elements; +• can be used with elastic or elastic-plastic (isotropic hardening, Mises yield) material behavior; +• do not include thermal strain effects; +• are written for small-displacement analysis only (large-rotation effects are not included); +• are not available in linear perturbation steps; +• use quite significant approximations (especially in the elastic-plastic case) and should, therefore, be +used with care; +• do not provide useful results for crack depths less than 2% or greater than 95% of the shell thickness; +and +• will not yield accurate results at the ends of the flaws or locations where the flaw depth varies rapidly +with position, due to the three-dimensional nature of the solution in such areas. +Typical applications +Line spring elements provide inexpensive evaluation of part-through cracks in shells. The basic concept +is that these elements introduce the local solution, dominated by the singularity at the crack tip, into a +shell model of the uncracked geometry. This is accomplished by allowing an additional freedom in the +model along the line of the crack, this freedom being provided by the line spring elements, as indicated +in Figure 32.9.1–1. +The compliance of the line spring with respect to these additional freedoms embeds the local +solution in the global response. From the relative displacements and rotations conjugate to that +compliance, Abaqus/Standard computes and prints out the J-integral and, in the linear case, stress +intensity factors at integration points in the line spring elements. Because the elements are simple, the +analysis is not significantly more expensive than a shell analysis of the uncracked geometry. The results +provide acceptable accuracy for many common applications. +shell elements +typical line spring element +Section A-A +'positive' crack +(open on +n surface) +'negative' crack +(open on -n surface) +nodes representing +opposite side +of crack +Figure 32.9.1–1 Line spring models. +See “Line spring elements,” Section 3.9.5 of the Abaqus Theory Manual, for details of the theory +behind these elements. +Choosing an appropriate element +Two versions of the element are provided—both are intended for use with the second-order shell elements +(S8R, S8R5, S9R5). Line spring element LS6 is for general cases, while line spring element LS3S is for +use when the flaw lies on a symmetry plane and only one side of the symmetry plane is modeled. +Defining the element’s section properties +You must associate the shell section properties with a set of line spring elements. +Input File Usage: +*SHELL SECTION, ELSET=name +Defining a constant section thickness +You can define a constant section thickness for the line spring element as part of the shell section +definition. +Input File Usage: +*SHELL SECTION +shell thickness +Defining a variable section thickness +Alternatively, you can define a line spring element with continuously varying thickness and specify +the thickness of the line spring element at the nodes. In this case any constant section thickness you +specify will be ignored, and the line spring thickness will be interpolated from the nodes . The thickness must be defined at all nodes connected to the element. +Input File Usage: +Use both of the following options: +*SHELL SECTION, NODAL THICKNESS +*NODAL THICKNESS +Assigning a material definition to a set of line spring elements +You must associate a material definition with each shell section definition. +Line spring elements can be used with isotropic elastic or elastic-plastic (isotropic hardening, Mises +yield) material behavior (“Linear elastic behavior,” Section 22.2.1, and “Classical metal plasticity,” +Section 23.2.1); these are the only material behavior definitions that are relevant to these elements. The +elastic behavior must be isotropic. Plasticity is included for Mode I (crack opening) response only; an +elastic-plastic analysis will be accurate only when Mode I behavior dominates. +The same material must be used through the section: a layered section cannot be defined with a line +spring. Thermal strain effects are not included in the line spring elements; however, most of the thermal +strain occurs in the shell, so this is not important in many cases (it is within the approximation made by +line springs). +Input File Usage: +*SHELL SECTION, ELSET=name, MATERIAL=name +Defining the flaw +The flaw is defined by specifying its depth at each node along the crack front. You must identify whether +the crack originates from the positive or negative surface of the shell (the positive surface is located a +positive distance along the surface normal from the shell’s middle surface, as shown in Figure 32.9.1–1). +At a point where the surface flaw depth is very small or zero, the compliance of the line spring +element is also very small. To avoid numerical problems when a small compliance is inverted to form a +stiffness, the minimum surface flaw depth used by Abaqus/Standard is 2% of the thickness specified for +the line spring element, even if you specify a smaller surface flaw depth. If you want to constrain the +two nodes where the surface flaw depth is zero to have the same displacements, you should tie the nodes +together with a linear constraint equation or a multi-point constraint (“Kinematic constraints: overview,” +Section 34.1.1). This is normally not required. +Input File Usage: +*SURFACE FLAW, SIDE=POSITIVE or NEGATIVE +node number or node set label, crack depth +... +Defining the shell model that contains the flaw +You must specify the uncracked thickness of the shell in the section definition. The geometry of the shell +at the flaw (coordinates and surface normals) is given in the usual way. +Including the effects of pressure loading on the crack faces +Cracks often occur on surfaces that are subjected to pressure; to include the effect of such loading on +the crack faces, suitable distributed loading types are provided. These loading types are not intended for +elastic-plastic line springs because the nodal equivalent forces calculated for the pressures are based on +superposition methods that are valid only in the linear elastic case. +J -integral output +If the material is linear elastic only, the J-integral value and the stress intensity factors are output; for the +elastic-plastic case local values of +are provided as well as their sum into a single J value. In +this case the J values will have acceptable accuracy only if +. See “Line spring +elements,” Section 3.9.5 of the Abaqus Theory Manual, for further details. +is much larger than +and +32.9.2 +LINE SPRING ELEMENT LIBRARY +Product: Abaqus/Standard +References +• “Line spring elements for modeling part-through cracks in shells,” Section 32.9.1 +• *SHELL SECTION +• *SURFACE FLAW +Overview +This section provides a reference to the line spring elements available in Abaqus/Standard. +Element types +LS6 +LS3S +6-node general second-order line spring +3-node second-order line spring for use on a symmetry plane +Active degrees of freedom +1, 2, 3, 4, 5, 6 +Additional solution variables +None. +Nodal coordinates required +X, Y, Z required at each node and, optionally, +at each node. +, +, +(direction cosines of the normal to the shell) +A user-defined normal definition can also be used to +specify +. If these are not specified, they are constructed as for all other shell elements—by +averaging over the shell elements attached to each node. +, +, +Element property definition +The only element property used is the thickness; the number of integration points is ignored, since the +elements work on the basis of section properties. +Input File Usage: +Use the following option to define line spring element properties: +*SHELL SECTION +Use the following option to define the depth of the crack as a function of +position: +*SURFACE FLAW +Element-based loading +Distributed loads +Distributed loads are specified as described in “Distributed loads,” Section 33.4.3. +Three Gauss points are used for crack face pressure loading. +Load ID +(*DLOAD) +HP +Element output +Units +Description +FL−2 +FL−2 +Hydrostatic surface pressure on the crack +faces, with magnitude varying linearly with +the global Z-direction. +Surface pressure on the crack faces. +Nodes 1, 2, and 3 on the element define side B and nodes 4, 5, and 6 define side A . +The sign of the crack is defined by the surface of the shell from which the crack originates, which +you identify when you define the depth of the crack . If the crack originates from the positive surface of the shell, +sign(crack)=1.0; if the crack originates from the negative surface of the shell, sign(crack)=−1.0. +is defined by the right-hand rule from the cross product of the tangent, +The vector +, which is positive +going from node 1 to node 3 of the element, and the normal, +, defined when the coordinates are given +(or by a user-defined normal definition). For element type LS3S the vector must point into the model +(away from the symmetry plane). For element type LS6 the vector must point from side A to side B. +“Strains” +E11 +E22 +Mode I opening displacement, +Mode I opening rotation, +The following strains exist only for LS6: +E33 +E12 +E13 +E23 +Mode II through thickness shear, +Mode II rotation, +(this strain plays no role) +Mode III anti-plane shear, +Mode III opening rotation, +The conjugate forces and moments are available by requesting “stress” output. +The J-integral is provided at each integration point. If elastic-plastic material behavior is defined, the +elastic and plastic parts of J are provided. The stress intensity factors, K, are also provided corresponding +to the elastic parts of J. +Figure 32.9.2–1 Notation for line spring strains. +Nodes associated with the element +LS6 +LS3S +side A +side B +side B +Numbering of integration points for output +Three points (these points are at the nodes) are used for integration and element output. +LS6 +LS3S +32.10 +Elastic-plastic joints +• “Elastic-plastic joints,” Section 32.10.1 +• “Elastic-plastic joint element library,” Section 32.10.2 +32.10.1 +ELASTIC-PLASTIC JOINTS +Product: Abaqus/Aqua +References +• *EPJOINT +• “Elastic-plastic joint element library,” Section 32.10.2 +Overview +JOINT2D and JOINT3D elements: +• are available for use only in Abaqus/Aqua used in conjunction with Abaqus/Standard +(“Abaqus/Aqua analysis,” Section 6.11.1); +• can be used to model flexible joints between structural members or the interaction between spud +cans and the ocean floor; +• are valid for small displacements and rotations; and +• can be purely elastic or elastic-plastic. +Elastic-plastic joint elements +Abaqus/Standard provides JOINT2D and JOINT3D elements for modeling a joint between structural +members or between a structural member and a fixed support. They can be used in an Abaqus/Aqua +analysis to model the interaction between a “spud can” and the sea floor for jack-up foundation analysis +in offshore applications. +The joint has two nodes. One of these nodes should be constrained fully (by using a boundary +condition) if the joint is between a structural member and a fixed support. +Kinematics and local coordinate system +The deformation of the joint is characterized by joint “strains,” which are relative displacements and +rotations between the nodes of the joint. The joint must be associated with a user-defined local orientation +system that is defined by three orthonormal directions: +. +The joint, when strained by relative extension or rotation of the two nodes, responds by applying +equal and opposite forces and/or moments to the nodes. These forces and moments, or joint “stresses,” +can be a linear (elastic) or nonlinear (elastic-plastic) function of the “strains,” depending on the type of +constitutive model used in the joint. +, and +, +The stresses and strains are named as shown in Figure 32.10.1–1. Positive stress indicates tension; +positive strain indicates extension. +joint between +structural +members +13 +22 +23 +11 +12 +33 +D0 +joint as a spud can +joint "stresses": +forces and moments +shown on node 2 +Figure 32.10.1–1 Local axis definition for joint elements. +Even when geometrically nonlinear analysis is requested (“Geometric nonlinearity” in “General and +linear perturbation procedures,” Section 6.1.3), the element kinematics are defined with the assumption +of small relative displacements and small rotations; therefore, these elements should not be used when +these assumptions are violated. If large rotations are required and there is no plasticity, JOINTC elements +can be used . +The “extensional” strains are defined through +and the “bending” strains through +where +are the relative displacements and rotations of the two nodes of the joint, respectively. +For two-dimensional elements only the axial strains +, +, and the bending strain +exist. For +three-dimensional elements all six components exist. +Input File Usage: +Use the following option to associate a local orientation system with an elastic- +plastic joint element: +*EPJOINT, ORIENTATION=name +Joint constitutive models +The elastic moduli for joint elasticity can be entered in one of two ways. You can specify a general, +anisotropic relation between the forces/moments and elastic extensions. Alternatively, you can enter +moduli specific for a spud can; the elastic stiffness matrix is diagonal and depends on the diameter of +the spud can at the soil surface, D, which can vary if spud can plasticity is defined and the spud can is +conical. See “Joint elasticity models” below for details. +Three joint plasticity models are provided. Two are specific to spud cans. The third is a parabolic +model for structural joints or members. See “Joint plasticity” below for details. +If plasticity is included, the plastic straining is assumed to occur in the local 1–2 plane so that the +. It is assumed that plasticity in the 3-direction can be +only nonzero plastic strains are +neglected. In a three-dimensional model strains out of the 1–2 plane produce purely elastic response. +, and +, +If the parabolic plasticity model for structural joints or members is used, the 1-direction is the axial +direction along the members, while the 2-direction is the transverse direction . In +the spud can plasticity models the 1-direction is the vertical direction, and the 2-direction is the horizontal +direction in which plastic extension can take place. In three-dimensional models the 3-direction is the +horizontal direction in which only elastic extension can take place. +Any combination of elastic and plastic models can be used. For example, usually spud can elastic +moduli will be used with spud can plasticity, but the use of general moduli with spud can plasticity is +allowed. +If plasticity is used in a three-dimensional model, coupling is not allowed through the elastic +) and the remaining, out-of-plane, +, +modulus between the strains or stresses in the 1–2 plane ( +strains ( +, +). Thus, in this case many of the general elastic moduli must be set to zero. +Input File Usage: +Use one or both of the following options immediately after the related +*EPJOINT option to define the joint constitutive model: +*JOINT ELASTICITY +*JOINT PLASTICITY +Orientation +Care must be taken in defining the local directions and node numbering so that the motion of node 2 +Incorrect +relative to node 1 in the positive 1-direction of the local axis corresponds to extension. +specification of the local directions or element node numbering can produce incorrect results in plastic +analysis because compression will be interpreted as extension. +If one of the nodes must be fixed to represent the ground, it is most convenient to let this node be +the first node of the element; extension is then represented by the motion of node 2 of the element in +the positive local 1-direction. If a spud can is being modeled in this way, the local 1-direction should be +the outward normal to the ocean floor. For a two-dimensional analysis that uses Abaqus/Aqua structural +loads, this direction must be the global y-direction. +For a three-dimensional analysis that uses Abaqus/Aqua structural loads, the local 1-direction +should point in the global z-direction. If plasticity is being used, the local 2-direction should be set so +that the 1–2 plane is the plane of greatest deformation. +Input File Usage: +Use the following orientation definition to model a spud can with the first node +fixed: +*ORIENTATION, NAME=name, TYPE=RECTANGULAR +0, 1, 0, −1, 0, 0 +Use the following orientation definition for a three-dimensional Abaqus/Aqua +analysis with plasticity: +*ORIENTATION, NAME=name, TYPE=RECTANGULAR +0, 0, 1, x, y, 0 +where (x, y, 0) defines the local 2-direction. +Spud can geometry +If either spud can elasticity or spud can plasticity is used, you must specify the constants to define the spud +can geometry. The entire spud can section definition has no effect if there is neither spud can elasticity +nor spud can plasticity. +The spud can, illustrated in Figure 32.10.1–1, can be either conical-based or flat-based. The spud +, the diameter of the cylindrical portion, and , the planar angle of the +. You can specify a flat-based spud can by omitting the specification +can geometry is defined by +conical portion, where +of +or by giving a value of 0 or 180 for +Input File Usage: +. +*EPJOINT, SECTION=SPUD CAN +, +Spud can initial embedment +If spud can plasticity is defined or if there is spud can elasticity and the spud can is conical, you must +specify the initial embedment of the spud can, +. +The embedment can be prescribed directly or by specifying a “preload” that produces the +embedment, as discussed below. Specification of both embedment and preload is not allowed. If either +embedment or preload is given, both embedment and equivalent preload (in the case of plasticity) can +be examined in the data file at the start of the analysis. +At any time in the analysis the spud can has a total (plastic) embedment of +, where +is the plastic embedment between the start of the analysis and time t. (The negative sign in this +equation reflects the fact that the sign convention for strain in Abaqus is positive for tensile strain. Most +often for spud can plasticity, +will be compressive, or negative.) The joint can be purely elastic, in +which case +always. +, so +The height of the conical portion of the spud can is given by +. The effective +diameter of the spud can at the soil surface, D, is defined by +1. For a flat-based spud can: +2. For a conical-based spud can: +a. Cone portion partially penetrating ( +): +b. Penetration beyond cone-cylinder transition ( +): +The current spud can area at the soil surface, A, is defined through +. The effective +diameter can vary throughout the analysis only for a conical spud can with plasticity. +The embedment has no effect and is not required if the spud can is cylindrical and spud can plasticity +is not defined. +Specifying the embedment directly +The embedment value can be prescribed directly using initial conditions . +Input File Usage: +*INITIAL CONDITIONS, TYPE=SPUD EMBEDMENT +Specifying the spud can preload +If spud can plasticity is defined, you can specify the initial compressive capacity (“preload”), +, +instead of the embedment. In this case Abaqus/Aqua will use the hardening law to calculate the plastic +embedment that follows when the preload is applied vertically. +The preload initial condition is used only to calculate the initial plastic embedment; the spud can +starts the analysis in a zero strain and stress state at this initial plastic embedment, and the preload is +assumed to be removed. You must apply any operational vertical load through loading within the history +definition. +Input File Usage: +*INITIAL CONDITIONS, TYPE=SPUD PRELOAD +Embedment in an elastic spud can analysis +If the spud can model is purely elastic, the spud can geometry is needed only for calculating the embedded +diameter of the spud can for spud can elastic moduli. The embedment is required for this calculation only +if the spud can is conical. +Output +Force and moment output in the element local system is available through the “stress” output variable S. +Extension and relative rotation are available through the “strain” output variable E. Elastic and plastic +strains are available through the output variables EE and PE. For spud cans the plastic embedment since +the start of the analysis is available through the vertical component of plastic strain, PE11, and will +usually be negative, indicating compression; the total vertical embedment, +, is available through +output variable PEEQ. Element nodal force (the force the element places on its nodes, in the global +system) is available through element variable NFORC. +Joint elasticity models +The elastic load-displacement behavior of the JOINT2D and JOINT3D elements is characterized by +elastic spring stiffnesses, which are assembled to form the elastic element stiffness matrix. A special +diagonal modulus for spud cans can be specified or, alternatively, a fully populated (general) elastic +modulus can be specified. +Spud can moduli +Spud can moduli can be prescribed for either two-dimensional or three-dimensional elements. +Two-dimensional spud can moduli +The elastic stiffness for a two-dimensional spud can is +where +is the vertical elastic spring stiffness, +is the horizontal elastic spring stiffness, +is the elastic spring stiffness in bending, +; +; +; +in which +, +displacements, respectively; +clay). +, and +are equivalent elastic shear moduli for vertical, horizontal, and rotational +is the Poisson’s ratio of the soil (suggested value: 0.2 for sand and 0.5 for +Input File Usage: +*JOINT ELASTICITY, MODULI=SPUD CAN, NDIM=2 +Three-dimensional spud can moduli +For a three-dimensional spud can the moduli are +where +is the vertical elastic spring stiffness, +is a horizontal elastic spring stiffness, +is a horizontal elastic spring stiffness, +is an elastic spring stiffness in bending, +is an elastic spring stiffness in bending, +is the torsional elastic spring stiffness, +; +; +; +; +; +; +in which +, +, +, and +are as before and +is a user-specified torsional stiffness value. +Straining out of the 1–2 plane through the strains +produces purely elastic response +in the three-dimensional model regardless of plasticity. The moduli related to these strains are assumed +not to be affected by the plasticity so that +are based on the initial embedded +diameter, while the other moduli depend on the current embedded diameter. +, and +, and +Input File Usage: +*JOINT ELASTICITY, MODULI=SPUD CAN, NDIM=3 +General moduli +General moduli can be specified for either two-dimensional or three-dimensional elements. +Two-dimensional general moduli +For the two-dimensional case six independent elastic moduli are needed. The stress-strain relations are +as follows: +Input File Usage: +*JOINT ELASTICITY, MODULI=GENERAL, NDIM=2 +Three-dimensional general moduli +For the three-dimensional case 21 independent elastic moduli are needed. The stress-strain relations are +as follows: +Input File Usage: +*JOINT ELASTICITY, MODULI=GENERAL, NDIM=3 +Joint plasticity +In what follows +horizontal load in the 1–2 plane, and the bending moment in the local 1–2 plane, respectively. +represent the vertical compressive load, the +, and +If plasticity is defined, the joint can yield axially, horizontally, or rotationally. The stress depends +linearly on the elastic strain. The elastic moduli can depend on the plasticity in the case of a conical spud +can, through the diameter at the surface, D. +The models are rate independent, with a yield equation of the form +where f is the yield function and +total vertical plastic embedment, +model. +is a set of hardening parameters, which in these models depend on +defines the type of plasticity +; the form of f and the definition of +The flow rule requires that the plastic flow direction is normal to the contours of the flow potential, +g. Associated flow is assumed in all of these models (except at vertices in the yield surface, as discussed +below). +Yield surface +The three available plasticity models all use parabolic yield surfaces. Each has a compressive and a +tensile limit for the stress in the 1-direction, which are termed +is zero for the +clay model. The sign convention for +always obeys +is such that they are always positive; thus, +, respectively; +and +and +The yield surface is most conveniently drawn in +vertical load and is defined as +-space, where +is normalized compressive +where +the length of the limiting range for V. The normalized load is, therefore, always within the range +is the middle value of the limiting elastic range for V, and +is +with +representing the tensile limit +and +representing the compressive limit +. +is the normalized equivalent horizontal load and is defined through +where +normalized horizontal force are defined through +and +The normalized yield function in +and +-space for each model is defined through +. +are the moment and horizontal yield stresses. The normalized moment and +and is a parabola as plotted in Figure 32.10.1–2. The yield surface in the space of the three normalized +stresses +is the surface of revolution of this parabola. +f, g = 0 +"tensile" yield +(softening) +compressive yield +(hardening) +-1 +V1 +g = 0 +f = 0 +.95 +Figure 32.10.1–2 Yield surface and flow potential contour. +Flow potential +The flow potential is the same as the yield function (associated flow) except that some smoothing is done +to the flow potential where the yield function has corners. +The yield surface has corners and, therefore, nonunique normals at points where it is intersected by +-axis. +the +To avoid problems with the indeterminate flow directions at these corners, Abaqus/Standard uses +a flow potential whose contours are rounded in the region of the vertex, as indicated in the detail of a +vertex shown in Figure 32.10.1–2. This rounding is achieved by fitting an elliptical segment to the flow +potential contour for +. +Integration of the plasticity equations +Abaqus/Aqua uses fully implicit integration for the plasticity equations. The corresponding tangent +stiffness is unsymmetric for these plasticity models. By default, the symmetrized tangent is used in the +global Newton loop. If the convergence rate seems to be poor, you may get some benefit out of using the +unsymmetric matrix storage and solution scheme for the step . +Joint plasticity models +The three models differ only in the definitions of +and in the hardening definitions. +, +We present the yield function for each model as it is presented in the literature rather than in normalized +form. The equivalent normalized form can be obtained by identifying +, which are explicit +in the given yield functions for clay and member plasticity; for the sand model they are provided for +reference. +, and +and +, +Sand model +A. Yield function: +and +where +The special case of +Osborne, et al. +are constant coefficients that determine the geometric shape of the yield function. +gives the yield function as proposed by +and +B. Work hardening equations: +i. Flat-base spud can: +is soil unit weight; +where +classical bearing capacity factors, which can be calculated as: +is an experimentally determined constant; and +and +are +where +is the soil friction angle. +ii. Conical-base spud can: +a. Cone portion partially penetrating: +b. Penetration beyond cone-cylinder transition: +where +is a “cone equivalency coefficient.” +The constants +centrifuge data: +and +are based on the following empirical relation, which has been derived from +in which the soil friction angle +is in degrees. +The sand model yield function can be put in normalized form by using +and +where +. For the model of Osborne et al. +. +This model requires a nonzero initial embedment or equivalent preload. +Input File Usage: +*JOINT PLASTICITY, TYPE=SAND +Clay model +A. Yield function: +where +is the undrained shear strength of clay; and +is the elevation area of the embedded portion of +the spud can, defined through: +i. Flat-base spud can: +ii. Conical-base spud can: +a. Cone portion penetrating: +b. Penetration beyond cone-cylinder transition: +B. Work hardening equations: +i. Flat-base spud can: +ii. Conical-base spud can: +where +, and c are user-defined empirical constants. +This model has zero yield strength in tension +and requires a nonzero initial embedment or +equivalent preload. +Input File Usage: +*JOINT PLASTICITY, TYPE=CLAY +Parabolic model for structural joints/members +A. Yield function: +where +are horizontal and moment capacities, respectively. +B. Work hardening: no work hardening is assumed (the model is perfectly plastic). +Input File Usage: +*JOINT PLASTICITY, TYPE=MEMBER +Plasticity analysis issues +Because associated flow is assumed in the spud can plasticity models, tensile vertical plastic strain can +occur whenever the yield surface is encountered with +. It is not required that the vertical force +itself be tensile for tensile plastic yield to occur; tensile plastic yield can occur on any part of the yield +surface where +. The spud can models soften during this tensile plastic yield; if there is insufficient +support from the rest of the model, an instability can occur and the analysis may fail to converge. When +this happens, the spud can is likely to be lifting out of the sea floor. +To make it easier to diagnose analysis problems that may arise due to these issues, a message is +printed to the message file in the following cases: if tensile plastic yield occurs for a spud can, if yield +occurs near the top of the parabolic yield surface ( +) where there is very little hardening, or if +the embedment of a spud can becomes less than 10% of the initial embedment. These messages are not +printed more than once in a given step. +The plasticity algorithm can fail in an iteration if the strain increment is excessively large. Some +details that may be of help in diagnosing failure in joint elements can be obtained by requesting detailed +printout to the message file of problems with the plasticity algorithms . +32.10.2 +ELASTIC-PLASTIC JOINT ELEMENT LIBRARY +Product: Abaqus/Aqua +References +• “Elastic-plastic joints,” Section 32.10.1 +• *EPJOINT +Overview +This section provides a reference to the elastic-plastic joint elements available in Abaqus/Aqua. +Element types +JOINT2D +Two-dimensional elastic-plastic joint element +JOINT3D +Three-dimensional elastic-plastic joint element +Active degrees of freedom +1, 2, 6 for JOINT2D +1, 2, 3, 4, 5, 6 for JOINT3D +Additional solution variables +None. +Nodal coordinates required +None. +Element property definition +Input File Usage: +*EPJOINT +Element-based loading +None. +Element output +The relative displacements and rotations corresponding to the forces and moments below are chosen +by requesting the corresponding “strains.” Elastic and plastic strains are available. For a spud can the +vertical (plastic) embedment since the start of the analysis is given by PE11; the total vertical embedment +is available as PEEQ. +JOINT2D +S11 +S22 +S12 +JOINT3D +S11 +S22 +S33 +S12 +S13 +S23 +Total direct force in the first local direction. +Total direct force in the second local direction. +Total moment about the third local direction. +Total direct force in the first local direction. +Total direct force in the second local direction. +Total direct force in the third local direction. +Total moment about the third local direction. +Total moment about the second local direction. +Total moment about the first local direction. +Nodes associated with the element +Two nodes. +32.11 +Drag chain elements +• “Drag chains,” Section 32.11.1 +• “Drag chain element library,” Section 32.11.2 +32.11.1 +DRAG CHAINS +Product: Abaqus/Standard +References +• “Drag chain element library,” Section 32.11.2 +• *DRAG CHAIN +• *RIGID SURFACE +Overview +Drag chain elements: +• are used for simulating the effects of drag chains on the seabed for near bottom bending simulation +modeling; and +• can be used in two-dimensional or three-dimensional problems. +Typical applications +The drag chain is modeled as a concentrated weight on the seabed, with a chain between it and an +attachment point on the pipe . +o o oooo +ooooooooooooooooooooo +o o o o o +° ° °°°°°°°°° +° +° +° ° ° +Figure 32.11.1–1 Drag chain model. +Given a uniform drag chain of total length +, weight per unit length w, and friction coefficient +between it and the seabed, attached to the pipeline at height h above the seabed, the length of chain on +the seabed at slip, +, is given by +and the horizontal projection of the suspended length, +, is +Thus, the equivalent model should have a friction limit of +taken as any value from to +, can be +. Comparison with experiment has shown that taking this length as +The horizontal length at slip, +is a reasonable choice. +When the pipeline attachment point is directly above the weight, there will be no horizontal force +or horizontal stiffness offered by a drag chain element; this position is assumed as the initial condition. +As the pipe moves relative to the seabed, the horizontal force on the pipeline caused by the drag chain +opposes the relative motion and gradually increases (an approximation to the catenary equation is used +to relate the force to the offset +) until the drag chain slips when the force reaches the friction limit. The +height, h, is assumed to be small compared to +. +Choosing an appropriate element +Two- and three-dimensional drag chain elements are available. +Element DRAG2D assumes that the seabed is flat and parallel to the plane in which the pipe is +moving; therefore, the seabed does not have to be modeled explicitly. +Element DRAG3D requires that the seabed be defined as an analytical rigid surface, which must be +flat and parallel to the global (X, Y) plane and is considered to be fixed throughout the analysis. +Defining the seabed for three-dimensional drag chains +The seabed is defined as an analytical rigid surface. This surface definition is used to determine if the +chain touches the seabed, depending on the separation between the pipe node and the position of the +seabed surface. See “Analytical rigid surface definition,” Section 2.3.4, for more information. +Since the seabed is considered to be fixed, boundary conditions must be applied to the rigid body +reference node of the seabed surface, which is also the second node of the DRAG3D element. +Input File Usage: +Use the following option to define the seabed surface for DRAG3D elements: +*RIGID SURFACE +In a model defined in terms of an assembly of part instances, the rigid surface +definition that defines the seabed must appear inside the same part definition as +the drag chain elements. +Defining the drag chain behavior +For DRAG2D elements you specify the maximum horizontal length, +, between the attachment point +and the concentrated weight. At this length the weight will start to slip on the seabed. In addition, you +specify the horizontal force between the weight and the seabed at slip (that is, the frictional limit). +For DRAG3D elements you specify the total length of the chain, the friction coefficient, and the +weight per unit length of chain. +You must associate the drag chain behavior with a set of drag chain elements. +Input File Usage: +*DRAG CHAIN, ELSET=name +drag chain data +32.11.2 +DRAG CHAIN ELEMENT LIBRARY +Product: Abaqus/Standard +References +• “Drag chains,” Section 32.11.1 +• *DRAG CHAIN +• *RIGID SURFACE +Overview +This section provides a reference to the drag chain elements available in Abaqus/Standard. +Element types +DRAG2D +Two-dimensional drag chain, for use in cases where only horizontal motion is being +studied +DRAG3D +Three-dimensional drag chain +Active degrees of freedom +DRAG2D: 1, 2 +DRAG3D: At the first node: 1, 2, 3. At the second node: 1, 2, 3, 4, 5, 6. +Additional solution variables +None. +Nodal coordinates required +DRAG2D: (X, Y) coordinates of the pipeline attachment node in the horizontal plane. +DRAG3D: (X, Y, Z) coordinates of both nodes. +Element property definition +Input File Usage: +Use the following option to define the horizontal length at slip and the friction +limit: +*DRAG CHAIN +Use the following option to define the seabed for DRAG3D elements: +*RIGID SURFACE +The rigid surface must be flat and parallel to the global (X, Y) plane. +Element-based loading +None. +Element output +S11 +S12 +E11 +E12 +The horizontal component of force supported by the drag chain in the plane parallel +to the seabed. +The vertical component of force in the drag chain for DRAG3D elements. +The horizontal length of the drag chain for DRAG2D elements. The length of chain +on the seabed floor (not suspended) for DRAG3D elements. +The orientation of the drag chain (angle from the global X-axis). +Nodes associated with the element +DRAG2D: One node at the position where the chain attaches to the pipe. +DRAG3D: Two nodes. The first node is the node where the chain attaches to the pipe; the second node +is the “reference node” of the rigid body containing the rigid surface that defines the seabed. +32.12 +Pipe-soil elements +• “Pipe-soil interaction elements,” Section 32.12.1 +• “Pipe-soil interaction element library,” Section 32.12.2 +32.12.1 +PIPE-SOIL INTERACTION ELEMENTS +Product: Abaqus/Standard +References +• “Pipe-soil interaction element library,” Section 32.12.2 +• *PIPE-SOIL INTERACTION +• *PIPE-SOIL STIFFNESS +Overview +The pipe-soil interaction elements in Abaqus/Standard: +• can be used to model the interaction between a buried pipeline and the surrounding soil; +• must be used with beam elements, pipe, or elbow elements ; and +• can have linear or nonlinear constitutive behavior. +Pipe foundation elements +Abaqus/Standard provides two-dimensional (PSI24 and PSI26) and three-dimensional (PSI34 and +PSI36) pipe-soil interaction elements for modeling the interaction between a buried pipeline and the +surrounding soil. +The pipeline itself is modeled with any of the beam, pipe, or elbow elements in the Abaqus/Standard +element library . The ground behavior and soil-pipe +interaction are modeled with the pipe-soil interaction (PSI) elements. These elements have only +displacement degrees of freedom at their nodes. One side or edge of the element shares nodes with the +underlying beam, pipe, or elbow element that models the pipeline . The nodes on +the other edge represent a far-field surface, such as the ground surface, and are used to prescribe the +far-field ground motion via boundary conditions together with amplitude references as needed. +The far-field side and the side that shares nodes with the pipeline are defined by the element +connectivity. Care must be taken in attaching the underlying elements to the correct edge of the PSI +element, since the connectivity of the pipe-soil element determines the local coordinate system as +defined below, and the depth, H, of the pipeline below the ground surface. The depth below the surface +is measured along the edge of the PSI element as shown in Figure 32.12.1–1 and is updated during +geometrically nonlinear analysis. +It is important to note that PSI elements do not discretize the actual domain of the surrounding soil. +The extent of the soil domain is reflected through the stiffness of the elements, which is defined by the +constitutive model as described later. +far-field edge +ground surface +PSI +element +e1 +e2 +e3 +pipe centerline +pipeline edge +pipeline discretized +with beam-type elements +Figure 32.12.1–1 Pipe-soil interaction model. +The pipe-soil interaction model does not include the density of the surrounding soil medium. +Mass can be associated with the model by applying concentrated MASS elements at the nodes of the pipe-soil interaction elements if needed. +Assigning the pipe-soil interaction behavior to a PSI element +You must assign the pipe-soil interaction behavior to a set of pipe-soil interaction elements. +Input File Usage: +Use the following option to assign the pipe-soil interaction behavior to a +particular element set: +*PIPE-SOIL INTERACTION, ELSET=name +Use the following option immediately after the*PIPE-SOIL INTERACTION +option to define the stiffness behavior for the element set: +*PIPE-SOIL STIFFNESS +Kinematics and local coordinate system +The deformation of the pipe-soil interaction element is characterized by the relative displacements +between the two edges of the element. When the element is “strained” by the relative displacements, +forces are applied to the pipeline nodes. These forces can be a linear (elastic) or nonlinear (elastic-plastic) +function of the “strains,” depending on the type of constitutive model used for the element. Positive +“strains” are defined by +where +are the relative displacements between the two edges ( +the pipeline displacements), +directions. For two-dimensional elements only the in-plane components of strain +three-dimensional elements all three strain components +are +are local directions, and the index i (=1, 2, 3) refers to the three local +exist. For +are the far-field displacements, and +exist. +, and +, +, +The local orientation system is defined by three orthonormal directions: +. The default +local directions are defined so that +is the +direction normal to the plane of the element (transverse horizontal direction), and +is +the direction in the plane of the element that defines the transverse vertical behavior. Positive default +directions are defined so that +points from the pipeline +edge toward the far-field edge, as shown in Figure 32.12.1–1. You can also define these local directions +by specifying a local orientation (“Orientations,” Section 2.2.5) for the pipe-soil interaction. +is the direction along the pipeline (axial direction), +points toward the second pipeline node and +, and +, +In a large-displacement analysis the local coordinate system rotates with the rigid body motion of the +underlying pipeline. In a small-displacement analysis the local system is defined by the initial geometry +of the PSI element and remains fixed in space during the analysis. +Input File Usage: +Use the following option to associate a local orientation with a pipe-soil +interaction behavior: +*PIPE-SOIL INTERACTION, ORIENTATION=name +Constitutive models +The constitutive behavior for a pipe-soil interaction is defined by the force per unit length, or “stress,” +at each point along the pipeline, +, between that point +and the point on the far-field surface: +, caused by relative displacement or “strain,” +where +are state variables (such as plastic strains), and +are temperatures and/or field variables. +You can define these +relationships quite generally by programming them in user subroutine UMAT. +Alternatively, you can define the relationships by specifying the data directly. In this case the assumption +is that the foundation behavior is separable: +in which case each of the independent relationships must be defined separately. Abaqus/Standard +assumes, by default, that these relationships are symmetric about the origin (as is generally appropriate +for the axial and transverse horizontal motions). However, you may give a nonsymmetric behavior for +any of the three relative motions (this is usually the case in the vertical direction when the pipeline is +not buried too deeply). These models assume that positive “strains” give rise to forces on the pipe that +act along the positive directions of the local coordinate system. +Specifying the constitutive behavior with a user subroutine +To define the +relationships quite generally, you can program them in user subroutine UMAT. +Input File Usage: +*PIPE-SOIL STIFFNESS, TYPE=USER +Specifying the constitutive behavior directly +Two methods are provided for specifying constitutive behavior data directly. One method is to define the +relationships directly in tabular (piecewise linear) form. The other method is to use ASCE formulae. +Forms of these relationships suitable for use with sands and clays are defined in the ASCE Guidelines +for the Seismic Design of Oil and Gas Pipeline Systems. +Specifying the constitutive behavior directly using tabular input +You can define a linear or nonlinear constitutive model with different behavior in tension and compression +using tabular input. +Linear model +To define a linear constitutive model, you specify the stiffness as a function of temperature and field +variables . You can enter different values for positive and negative “strain.” +Abaqus/Standard assumes, by default, that the relationship is symmetric about the origin. +Input File Usage: +*PIPE-SOIL STIFFNESS, TYPE=LINEAR +Nonlinear model +To define a nonlinear constitutive model, you specify the +relationship as a function of positive and +negative relative displacement (“strain”), temperature, and field variables . The +behavior is assumed symmetric about the origin if only positive or negative data are provided. +You must provide the data in ascending order of relative displacement; you should provide it over +a sufficiently wide range of relative displacement values so that the behavior is defined correctly. The +force remains constant outside the range of data points. You must separate positive and negative data by +specifying the data point at the origin of the force-relative displacement diagram. The two data points +immediately before and after the data point at the origin define the elastic stiffness, +, and the +initial elastic limits, +, as indicated in Figure 32.12.1–3. +and +and +The model provides linear elastic behavior if +where +respectively. Inelastic deformation occurs when the relative force exceeds these elastic limits. +are the equivalent plastic strains associated with negative and positive deformations, +and +Kn +Kp +Figure 32.12.1–2 Linear constitutive model. +qi, ε +qp +Kp +0, 0 +q1, ε +q2, ε +Kn +qn +Figure 32.12.1–3 Nonlinear constitutive relationship. +Hardening of the model is controlled by independent evolution of +and +. The model +assumes that +remains constant when the increment in relative displacement is negative, and +remains constant when the increment in relative displacement is positive. The response predicted by +this model during a full loading cycle is shown in Figure 32.12.1–4 for a simple constitutive law that +uses different bilinear behavior associated with positive and negative force. Figure 32.12.1–4 shows that +the yield stress associated with positive force is updated to +, while the initial yield stress associated +with negative force, +, remains constant during initial loading. Similarly, during subsequent reversed +loading the yield stress associated with negative force is updated to +, while the yield stress associated +with positive force remains constant. Consequently, yielding occurs at +during the next load reversal. +Such behavior is appropriate for the directions transverse to the pipeline where it is expected that relative +positive motion between the pipe and soil is independent from relative negative motion between the pipe +and soil. +Kn +qn +qp +Kp +Kp +Kp +Kn +qn +qn +qp +Figure 32.12.1–4 Cyclic loading for a bilinear model. +An isotropic hardening model is used if the behavior is symmetric about the origin (when only +positive or negative data are provided). In this case only one equivalent plastic strain variable, +, is +used, which is updated when either negative or positive inelastic deformation occurs. Such an evolution +model is more appropriate along the axial direction where it is expected that positive inelastic deformation +influences subsequent negative inelastic deformation. +Input File Usage: +*PIPE-SOIL STIFFNESS, TYPE=NONLINEAR +Specifying the constitutive behavior directly using ASCE formulae +Abaqus/Standard also provides analytical models to describe the pipe-soil interaction. These models +define the constant ultimate force that can be exerted on the pipeline. In other words, these models +describe elastic, perfectly plastic behavior. Forms of these formulae suitable for use with sands and +clays are described in detail in the ASCE Guidelines for the Seismic Design of Oil and Gas Pipeline +Systems. +The ASCE formulae can be applied in any arbitrary local system by associating an orientation +definition with the element. However, these formulae are intended to be used in the default local +coordinate system so that the formula for axial behavior is applied along the pipeline axis (the +1-direction), the formula for vertical behavior is applied along the 2-direction, and the formula for +horizontal behavior along the 3-direction. You must specify the direction in which the behavior is +specified when it is described by ASCE fomulae. +You specify all the parameters in the expressions below, except the depth, H, below the surface, +which is measured along the edge of the PSI element as shown in Figure 32.12.1–1 and is updated during +geometrically nonlinear analysis. Values for the remaining parameters can be found in standard soil +mechanics textbooks. Typical values are also provided in the ASCE Guidelines for the Seismic Design +of Oil and Gas Pipeline Systems. +Axial behavior +The ultimate axial load for sand, +, is given by +where +of the pipeline, D is the external diameter of the pipeline, +the interface angle of friction. +is the coefficient of soil pressure at rest, H is the depth from the ground surface to the center +is +is the effective unit weight of soil, and +The ultimate axial load for clay is given by +where S is the undrained soil shear strength and is an empirical adhesion factor that relates the undrained +soil shear strength to the cohesion, +. +The maximum load is reached at an ultimate relative displacement, +, of approximately 2.5 to +5.0 mm (0.1 to 0.2 inches) for sand and approximately 2.5 to 10.0 mm (0.2 to 0.4 inches) for clay. A +linear elastic response is assumed for +. +The axial behavior is assumed to be symmetric about the origin. Consequently, only one equivalent +, describes the evolution of the model. The equivalent plastic strain is updated +plastic strain variable, +when either negative or positive inelastic deformation occurs. +Input File Usage: +Use one of the following options to define the axial behavior: +*PIPE-SOIL STIFFNESS, DIRECTION=AXIAL, TYPE=SAND +*PIPE-SOIL STIFFNESS, DIRECTION=AXIAL, TYPE=CLAY +Transverse vertical behavior +The vertical behavior is described by different relationships for “upward” motion (when the pipeline rises +with respect to the ground surface) and “downward” motion. Downward motions give rise to positive +relative displacements so that positive forces are applied to the pipeline. Similarly, upward motions give +rise to negative relative displacements and pipeline forces. +The ultimate force for downward motion of the pipe in sand is given by +where +and +downward direction, and +section. The ultimate force for downward motion of the pipe in clay is given by +are bearing capacity factors for vertical strip footings, vertically loaded in the +is the total soil unit weight. Other parameters are defined in the previous +where +approximately +is a bearing capacity factor. The ultimate force is reached at a relative displacement of +for both sand and clay. +to +The ultimate force for upward motion of the pipe in sand is given by +and for clay by +where +and +are vertical uplift factors. +The ultimate force is reached at a relative displacement of approximately +to +to +for sand and +for clay. +The transverse vertical behavior is non-symmetric about the origin. Consequently, two equivalent +plastic strain variables—one associated with negative relative displacement, +, and the other with +positive relative displacement, —are used to describe the evolution of the model. The model assumes +that +remains +constant when the increment in relative displacement is positive. +remains constant when the increment in relative displacement is negative, and +Input File Usage: +Use one of the following options to define the vertical behavior: +*PIPE-SOIL STIFFNESS, DIRECTION=VERTICAL, TYPE=SAND +*PIPE-SOIL STIFFNESS, DIRECTION=VERTICAL, TYPE=CLAY +Transverse horizontal behavior +The horizontal force-relative displacement relationship for sand is given by +and for clay by +where +sections. The ultimate force is reached at a relative displacement of approximately +are horizontal bearing capacity factors. Other variables are defined in the previous +, +and +where +between 0.02 to 0.03 for dense sand. +is between 0.07 to 0.1 for loose sand, between 0.03 to 0.05 for medium sand and clay, and +The transverse horizontal behavior is assumed to be symmetric about the origin. Consequently, only +, describes the evolution of the model. The equivalent plastic +one equivalent plastic strain variable, +strain is updated when either negative or positive inelastic deformation occurs. +Input File Usage: +Use one of the following options to define the horizontal behavior: +*PIPE-SOIL STIFFNESS, DIRECTION=HORIZONTAL, TYPE=SAND +*PIPE-SOIL STIFFNESS, DIRECTION=HORIZONTAL, TYPE=CLAY +Specifying the directions for which the constitutive behavior is defined +If you are defining the constitutive behavior by specifying the data directly, by default an isotropic model +is assumed. If the model is not isotropic, you can specify different constitutive relationships in each +direction. For two-dimensional nonisotropic models you must specify the behavior in two directions; +for three-dimensional nonisotropic models you must specify the behavior in three directions. You must +indicate the direction in which the behavior is specified. You can specify the 1-direction, 2-direction, +3-direction, axial direction, vertical direction, or horizontal direction. Abaqus/Standard assumes that the +axial direction is equivalent to the 1-direction, the vertical direction is equivalent to the 2-direction, and +the horizontal direction is equivalent to the 3-direction. +Input File Usage: +Use the following option to define an isotropic constitutive model: +*PIPE-SOIL STIFFNESS +Use the following option to define the constitutive model in a particular +direction: +*PIPE-SOIL STIFFNESS, DIRECTION=direction +where direction can be 1, 2, 3, AXIAL, VERTICAL, or HORIZONTAL. Repeat +the *PIPE-SOIL STIFFNESS option with the DIRECTION parameter as many +times as necessary to define the behavior in each direction. +Output +The force per unit length in the element local system is available through the “stress” output variable S. +Relative deformation is available through the “strain” output variable E. Elastic and plastic “strains” are +available through the output variables EE and PE. +Element nodal force (the force the element places on the pipeline nodes, in the global system) is +available through element variable NFORC. +Additional reference +• Audibert, J. M. E., D. J. Nyman, and T. D. O’Rourke, “Differential Ground Movement Effects +on Buried Pipelines,” Guidelines for the Seismic Design of Oil and Gas Pipeline Systems, ASCE +publication, pp. 151–180, 1984. +32.12.2 +PIPE-SOIL INTERACTION ELEMENT LIBRARY +Product: Abaqus/Standard +References +• “Pipe-soil interaction elements,” Section 32.12.1 +• *PIPE-SOIL INTERACTION +Overview +This section provides a reference to the pipe-soil interaction elements available in Abaqus/Standard. +Element types +2-D elements +PSI24 +PSI26 +Two-dimensional 4-node pipe-soil interaction element +Two-dimensional 6-node pipe-soil interaction element +Active degrees of freedom +1, 2 +Additional solution variables +None. +3-D elements +PSI34 +PSI36 +Three-dimensional 4-node pipe-soil interaction element +Three-dimensional 6-node pipe-soil interaction element +Active degrees of freedom +1, 2, 3 +Additional solution variables +None. +Nodal coordinates required +2–D: X, Y +3–D: X, Y, Z +Element property definition +Input File Usage: +*PIPE-SOIL INTERACTION +Element-based loading +None. +Element output +The relative displacements corresponding to the forces below are chosen by requesting the corresponding +“strains.” Elastic and plastic strains are available. +Two-dimensional elements +S11 +S22 +Force per unit length in the first local direction. +Force per unit length in the second local direction. +Three-dimensional elements +S11 +S22 +S33 +Force per unit length in the first local direction. +Force per unit length in the second local direction. +Force per unit length in the third local direction. +Node ordering and integration point numbering +far-field edge +pipeline edge +PSI24 and PSI34 +far-field edge +pipeline edge +PSI26 and PSI36 +32.13 +Acoustic interface elements +• “Acoustic interface elements,” Section 32.13.1 +• “Acoustic interface element library,” Section 32.13.2 +32.13.1 +ACOUSTIC INTERFACE ELEMENTS +Products: Abaqus/Standard Abaqus/CAE +References +• “Acoustic interface element library,” Section 32.13.2 +• “Acoustic, shock, and coupled acoustic-structural analysis,” Section 6.10.1 +• *INTERFACE +• “Creating acoustic interface sections,” Section 12.13.18 of the Abaqus/CAE User’s Manual, in the +online HTML version of this manual +Overview +Acoustic interface elements: +• can be used to couple a model of an acoustic fluid to a structural model containing continuum or +structural elements; +• couple the accelerations of the surface of the structural model to the pressure in the acoustic medium; +• can be used in dynamic and steady-state dynamic procedures; +• must be defined with the nodes shared by the acoustic elements and the structural (or solid) elements; +• can be used only in small-displacement simulations and are not intended for use in nonlinear or +hydrostatic fluid-structure interactions; +• are ignored in eigenfrequency extraction analyses if the subspace iteration eigensolver is used; and +• if necessary, can be degenerated into triangular elements. +For most problems the surface-based, structural-acoustic capabilities described in “Mesh tie constraints,” +Section 34.3.1, and in “Defining tied contact in Abaqus/Standard,” Section 35.3.7, provide more general +and easy to use methods for modeling the interaction between an acoustic fluid and a structure. User- +specified acoustic interface elements give you increased control over the coupling specification, at the +expense of the convenience of the surface-based procedures. +Typical applications +The acoustic interface elements are used in simulations where the motion of a solid structure influences +the pressure in the acoustic fluid, such as when the vibrations of a car frame produce noise in the passenger +compartment; or where the pressure in the fluid affects a neighboring structure, such as when the small- +amplitude sloshing of a fluid inside a container affects its response. +User-specified acoustic interface elements are also useful in problems involving only an acoustic +medium because they allow you to specify displacement, velocity, or acceleration boundary conditions +directly on the nodes of the acoustic interface elements. +In this application, however, you must be +aware that the tangential displacements are not coupled to the fluid. Therefore, zero-energy modes may +arise involving the displacement degrees of freedom if these nodes are not constrained in the tangential +direction. When acoustic interface elements are used to couple fluid and solid elements, this problem +does not arise because of the stiffness and inertia of the solid. +Choosing an appropriate element +The order of the underlying acoustic and structural elements usually dictates which acoustic interface +element should be used. The general acoustic interface element, ASI1, can be used in any coupled +acoustic-structural simulation; however, normally it is used only with the acoustic link elements (AC1D2 +and AC1D3). +Defining the normal direction of the acoustic-structural interface +The connectivity of the acoustic interface elements and the right-hand rule define the normal direction +of the acoustic-structural interface, as shown in “Acoustic interface element library,” Section 32.13.2. +It is very important that this normal point into the acoustic fluid, as shown in Figure 32.13.1–1 and +Figure 32.13.1–2. The one exception is the ASI1 acoustic interface element, where you must define the +normal direction. +fluid +solid +ASI2D2 +ASIAX2 +fluid +solid +ASI2D3 +ASIAX3 +Figure 32.13.1–1 Normal directions for two-dimensional and +axisymmetric acoustic-structural interface elements. +Defining the acoustic interface element’s section properties +You must associate the acoustic interface section definition with a set of acoustic interface elements. This +section definition must be used with three-dimensional and axisymmetric acoustic interface elements, +even though there are no user-defined geometric properties for these elements. +Input File Usage: +Abaqus/CAE Usage: +*INTERFACE, ELSET=element_set_name +Property module: +Create Section: select Other as the section Category and +Acoustic interface as the section Type +Assign→Section: select regions +fluid +solid +ASI3D4 +fluid +fluid +solid +ASI3D3 +fluid +solid +solid +ASI3D6 +ASI3D8 +Figure 32.13.1–2 Normal directions for three-dimensional acoustic-structural interface elements. +Defining the geometric properties associated with ASI1 elements +The ASI1 elements consist of a single node. Abaqus/Standard cannot calculate the surface area +associated with these elements, so you must supply this information. +If accurate surface areas are +not given, Abaqus/Standard may calculate incorrect accelerations or acoustic fluid pressure at the +acoustic-structural interface. +In addition, Abaqus/Standard cannot calculate the direction of the interface normal associated with +these elements. You must provide the direction cosines, in the global Cartesian coordinate system, of the +interface normal for these elements. +Input File Usage: +Abaqus/CAE Usage: +*INTERFACE +surface area, X-direction cosine, Y-direction cosine, Z-direction cosine +General-use acoustic interface sections are not supported in Abaqus/CAE. +Defining the thickness for planar acoustic interface elements +You can specify the thickness of planar acoustic interface elements. The default value is unit thickness. +Input File Usage: +*INTERFACE +thickness +Abaqus/CAE Usage: +Property module: Create Section: select Other as the section +Category and Acoustic interface as the section Type: Plane +stress/strain thickness: thickness +Using acoustic interface elements when elements with different interpolation orders form the +acoustic-structural interface +It is normally assumed that the same order of interpolation will be used for both the acoustic fluid mesh +and the structural mesh (at least at the interface surfaces). If this is not the case, suitable MPCs must be +applied to the nodes along the acoustic-structural interface to maintain the compatibility in the pressure +(MPC type P LINEAR) or displacement fields (MPC type LINEAR). +32.13.2 +ACOUSTIC INTERFACE ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/CAE +References +• “Acoustic interface elements,” Section 32.13.1 +• *INTERFACE +Overview +This section provides a reference to the acoustic interface elements available in Abaqus/Standard. +Element types +Element for general use +ASI1 +1-node +Active degrees of freedom +1, 2, 3, 8 +Additional solution variables +None. +Elements for use in planar models +ASI2D2 +ASI2D3 +2-node linear +3-node quadratic +Active degrees of freedom +1, 2, 8 +Additional solution variables +None. +Elements for use in 3-D models +ASI3D3 +ASI3D4 +ASI3D6 +ASI3D8 +3-node linear +4-node linear +6-node quadratic +8-node quadratic +Active degrees of freedom +1, 2, 3, 8 +Additional solution variables +None. +Elements for use in axisymmetric models +ASIAX2 +ASIAX3 +2-node linear +3-node quadratic +Active degrees of freedom +1, 2, 8 +Additional solution variables +None. +Nodal coordinates required +General use element: None. +Planar: X, Y +3-D: X, Y, Z +Axisymmetric: r, z +Element property definition +For general-use elements, you must define the element’s surface area and the direction cosines of the +normal to the acoustic fluid-structural interface, pointing into the fluid. +For elements for use in planar models, you must specify the thickness (out-of-plane) of the element. The +default is unit thickness if no thickness is specified. +For elements for use in three-dimensional and axisymmetric models, no additional data are required. +Input File Usage: +Abaqus/CAE Usage: +*INTERFACE +Property module: Create Section: select Other as the section Category +and Acoustic interface as the section Type +General-use acoustic interface sections are not supported in Abaqus/CAE. +Element-based loading +Distributed impedances cannot be applied. +Element output +None. +Node ordering on elements +Planar +3-D +ASI2D2 +ASI2D3 +ASI3D3 +ASI3D4 +ASI3D6 +ASI3D8 +Axisymmetric +ASIAX2 +ASIAX3 +32.14 +Eulerian elements +• “Eulerian elements,” Section 32.14.1 +• “Eulerian element library,” Section 32.14.2 +32.14.1 +EULERIAN ELEMENTS +Products: Abaqus/Explicit Abaqus/CAE +References +• “Eulerian analysis,” Section 14.1.1 +• “Eulerian element library,” Section 32.14.2 +• *EULERIAN SECTION +• “Creating Eulerian sections,” Section 12.13.3 of the Abaqus/CAE User’s Manual, in the online +HTML version of this manual +Overview +Eulerian elements: +• can be used only in explicit dynamic analyses; +• must have eight unique nodes; +• are filled with void material by default; +• can be initialized with nonvoid material; +• can contain multiple materials simultaneously; and +• can be partially filled with material. +Typical applications +Eulerian elements are useful for simulations involving material that undergoes extreme deformation, up +to and including fluid flow. The Eulerian formulation allows material to flow from one element to another, +even as the Eulerian mesh remains fixed. Applications that utilize Eulerian elements are discussed in +“Eulerian analysis of a collapsing water column,” Section 1.7.1 of the Abaqus Benchmarks Manual, and +“Rivet forming,” Section 2.3.1 of the Abaqus Example Problems Manual. +For more information on Eulerian analyses, see “Eulerian analysis,” Section 14.1.1. +Choosing an appropriate element +The available Eulerian elements are the three-dimensional, 8-node element EC3D8R and the +three-dimensional, 8-node thermally coupled element EC3D8RT. Two-dimensional simulations can +be approximated using a one-element thick mesh or a wedge-shaped mesh with appropriate boundary +conditions. The Eulerian mesh is typically a simple rectangular grid of elements that does not conform +to the shape of the Eulerian materials. Complex material shapes can be represented inside this mesh +using a combination of fully and partially filled elements surrounded by void regions. +Defining the Eulerian element’s section properties +You must associate the Eulerian section definition with a set of Eulerian elements. This set of elements +must not share nodes with other types of elements. The section definition provides a list of materials that +may occupy the Eulerian elements. +Input File Usage: +*EULERIAN SECTION, ELSET=element_set_name +data lines giving list of materials +Abaqus/CAE Usage: +Property module: Create Section: select Solid as the section +Category and Eulerian as the section Type +Assign→Section: select part +32.14.2 +EULERIAN ELEMENT LIBRARY +Products: Abaqus/Explicit Abaqus/CAE +References +• “Eulerian analysis,” Section 14.1.1 +• *EULERIAN SECTION +Overview +This section provides a reference to the Eulerian elements available in Abaqus/Explicit. +Element types +Eulerian stress/displacement element +EC3D8R +8-node linear brick, multimaterial, reduced integration with hourglass control +Active degrees of freedom +1, 2, 3 +Additional solution variables +None. +Eulerian thermally coupled element +EC3D8RT +8-node thermally coupled linear brick, multimaterial, +hourglass control +reduced integration with +Active degrees of freedom +1, 2, 3,11 +Additional solution variables +None. +Nodal coordinates required +X, Y, Z +Element property definition +You must specify a list of materials that may be present in the Eulerian element. You can also assign +a material instance name to each material . +Input File Usage: +*EULERIAN SECTION +Abaqus/CAE Usage: +Property module: Create Section: select Solid as the section +Category and Eulerian as the section Type +Element-based loading +Distributed loads +Distributed loads are available only for Eulerian elements. They are specified as described in “Distributed +loads,” Section 33.4.3. +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +Body force in global X-direction. +Body force in global Y-direction. +Body force in global Z-direction. +Nonuniform body force in global +X-direction with magnitude supplied +subroutine DLOAD in +via +Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +user +Nonuniform body force in global +Y-direction with magnitude supplied +subroutine DLOAD in +via +user +and VDLOAD in +Abaqus/Standard +Abaqus/Explicit. +Nonuniform body force in global +Z-direction with magnitude supplied +subroutine DLOAD in +via +user +and VDLOAD in +Abaqus/Standard +Abaqus/Explicit. +Gravity +loading +direction (magnitude is +acceleration). +in +specified +input as +Pressure on face n. +Nonuniform pressure on face n +via +with magnitude +user +in +subroutine +VDLOAD +Abaqus/Standard +in Abaqus/Explicit. +supplied +DLOAD +and +BX +BY +BZ +BXNU +Body force +Body force +Body force +Body force +FL−3 +FL−3 +FL−3 +FL−3 +BYNU +Body force +FL−3 +BZNU +Body force +FL−3 +GRAV +Gravity +Pn +PnNU +Pressure +Not supported +LT−2 +FL−2 +FL−2 +Load ID +(*DLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +SBF +SPn +TRSHRn +TRVECn +VBF +VPn +Not supported +FL−5 T2 +Stagnation body force in global X-, +Y-, and Z-directions. +Not supported +FL−4 T2 +Stagnation pressure on face n. +Surface traction +Surface traction +FL−2 +FL−2 +Not supported +FL−4 T +Not supported +FL−3 T +Shear traction on face n. +General traction on face n. +Viscous body force in global X-, Y-, +and Z-directions. +Viscous pressure on face n, applying +a pressure proportional to the velocity +normal to the face and opposing the +motion. +Distributed heat fluxes +Distributed heat fluxes are available only for EC3D8RT elements. They are specified as described in +“Thermal loads,” Section 33.4.4. +Load ID +(*DFLUX) +Abaqus/CAE +Load/Interaction +Units +Description +BF +Sn +Body heat flux +Surface heat flux +JL−3 T−1 +JL−2 T−1 +Heat body flux per unit volume. +Heat surface flux per unit area into +face n. +Film conditions +Film conditions are available only for EC3D8RT elements. They are specified as described in “Thermal +loads,” Section 33.4.4. +Load ID +(*FILM) +Fn +Radiation types +Abaqus/CAE +Load/Interaction +Units +Description +Surface film +condition +JL−2 T−1 −1 +Film coefficient and sink temperature +(units of +) provided on face n. +Radiation conditions are available only for EC3D8RT elements. They are specified as described in +“Thermal loads,” Section 33.4.4. +Load ID +(*RADIATE) +Abaqus/CAE +Load/Interaction +Units +Description +Rn +Surface radiation Dimensionless +Emissivity and sink temperature +(units of +) provided on face n. +Surface-based loading +Distributed loads +Surface-based distributed loads are available for Eulerian elements. They are specified as described in +“Distributed loads,” Section 33.4.3. +Load ID +(*DSLOAD) +Abaqus/CAE +Load/Interaction +Units +Description +PNU +Pressure +Pressure +FL−2 +FL−2 +SP +Pressure +FL−4 T2 +TRSHR +TRVEC +Surface traction +Surface traction +FL−2 +FL−2 +VP +Pressure +FL−3 T +Pressure on the element surface. +Nonuniform pressure on the element +supplied +surface with magnitude +subroutine DLOAD in +via +Abaqus/Standard and VDLOAD in +Abaqus/Explicit. +user +Stagnation pressure on the element +surface. +Shear traction on the element surface. +General +surface. +traction on the element +Viscous pressure applied on the +element surface. The viscous pressure +is proportional to the velocity normal +to the element face and opposing the +motion. +Distributed heat fluxes +Surface-based heat fluxes are available only for EC3D8RT elements. They are specified as described in +“Thermal loads,” Section 33.4.4. +Load ID +(*DSFLUX) +Abaqus/CAE +Load/Interaction +Units +Description +Surface heat flux +JL−2 T−1 +Heat surface flux per unit area into the +element surface. +Film conditions +Surface-based film conditions are available only for EC3D8RT elements. They are specified as described +in “Thermal loads,” Section 33.4.4. +Load ID +(*SFILM) +Radiation types +Abaqus/CAE +Load/Interaction +Units +Description +Surface film +condition +JL−2 T−1 −1 +Film coefficient and sink temperature +(units of +) provided on the element +surface. +Surface-based radiation conditions are available only for EC3D8RT elements. They are specified as +described in “Thermal loads,” Section 33.4.4. +Load ID +(*SRADIATE) +Abaqus/CAE +Load/Interaction +Units +Description +Surface radiation Dimensionless +Emissivity and sink temperature +(units of +) provided on the element +surface. +Element output +A set of output variables is written for each Eulerian material instance listed in the Eulerian section +definition. The output variable names are automatically appended with the material instance names. For +example, if you define material instances named “steel” and “tin” and request stress output, the first stress +components will be written to separate output variables named “S11_steel” and “S11_tin.” +All output is given in global coordinates. +Stress and other tensor components +Stress and other tensors (excluding total strain tensors) are available. All tensors have the same +components. For example, the stress components are as follows: +S11 +S22 +S33 +S12 +S13 +S23 +, direct stress. +, direct stress. +, direct stress. +, shear stress. +, shear stress. +, shear stress. +Element-averaged quantities +Several output variables are also available as element-averaged quantities. These variables are computed +as a volume fraction weighted average of all materials present in the element. Use of these variables can +substantially decrease the size of the output database for models with many Eulerian materials. For +example: +SVAVG +Volume fraction averaged stress. +Node ordering and face numbering on elements +All elements must have eight nodes. Degenerate elements are not supported. +face 2 +face 5 +face 6 +face 4 +face 1 +face 3 +8 - node element +Element faces +Face 1 +Face 2 +Face 3 +Face 4 +Face 5 +Face 6 +1 – 2 – 3 – 4 face +5 – 8 – 7 – 6 face +1 – 5 – 6 – 2 face +2 – 6 – 7 – 3 face +3 – 7 – 8 – 4 face +4 – 8 – 5 – 1 face +Numbering of integration points for output +The single integration point is located at the centroid of the element. All materials within the element +are evaluated at this integration point. +32.15 +User-defined elements +• “User-defined elements,” Section 32.15.1 +• “User-defined element library,” Section 32.15.2 +32.15.1 +USER-DEFINED ELEMENTS +Products: Abaqus/Standard Abaqus/Explicit +References +• “User-defined element library,” Section 32.15.2 +• “UEL,” Section 1.1.27 of the Abaqus User Subroutines Reference Manual +• “UELMAT,” Section 1.1.28 of the Abaqus User Subroutines Reference Manual +• “VUEL,” Section 1.2.10 of the Abaqus User Subroutines Reference Manual +• “Accessing Abaqus thermal materials,” Section 2.1.18 of the Abaqus User Subroutines Reference +Manual +• “Accessing Abaqus materials,” Section 2.1.17 of the Abaqus User Subroutines Reference Manual +• *MATRIX +• *UEL PROPERTY +• *USER ELEMENT +Overview +User-defined elements: +• can be finite elements in the usual sense of representing a geometric part of the model; +• can be feedback links, supplying forces at some points as functions of values of displacement, +velocity, etc. at other points in the model; +• can be used to solve equations in terms of nonstandard degrees of freedom; +• can be linear or nonlinear; and +• can access selected materials from the Abaqus material library. +Assigning an element type key to a user-defined element +You must assign an element type key to a user-defined element. The element type key must be of the +form Un in Abaqus/Standard and VUn in Abaqus/Explicit, where n is a positive integer that identifies +the element type uniquely. For example, you can define element types U1, U2, U3, VU1, VU7, etc. In +Abaqus/Standard n must be less than 10000; while in Abaqus/Explicit n must be less than 9000. +The element type key is used to identify the element in the element definition. For general user +elements the integer part of the identifier is provided in user subroutines UEL, UELMAT and VUEL so +that you can distinguish between different element types. +Input File Usage: +*USER ELEMENT, TYPE=element_type +Invoking user-defined elements +User-defined elements are invoked in the same way as native Abaqus elements: you specify the element +type, Un or VUn, and define element numbers and nodes associated with each element . User elements can be assigned to element sets in the usual way, for +cross-reference to element property definitions, output requests, distributed load specifications, etc. +Material definitions (“Material data definition,” Section 21.1.2) are relevant only to user-defined +elements in Abaqus/Standard. If a material is assigned to a user-defined element (“Assigning an Abaqus +material to the user element”), user subroutine UELMAT will be used to define the element response. User +subroutine UELMAT allows access to selected Abaqus materials. If no material definition is specified, +all material behavior must be defined in user subroutines UEL and VUEL, based on user-defined material +constants and on solution-dependent state variables associated with the element and calculated in the +same subroutines. For linear user elements all material behavior must be defined through a user-defined +stiffness matrix. +Input File Usage: +Use the following options to invoke a user-defined element: +*USER ELEMENT, TYPE=element_type +*ELEMENT, TYPE=element_type +Defining the active degrees of freedom at the nodes +Any number of user element types can be defined and used in a model. Each user element can have any +number of nodes, at each of which a specified set of degrees of freedom is used by the element. The +activated degrees of freedom should follow the Abaqus convention (“Conventions,” Section 1.2.2). In +Abaqus/Standard this is important because the convergence criteria are based on the degrees of freedom +numbers. +In Abaqus/Explicit the activated degrees of freedom must follow the Abaqus convention +because these are the only degrees of freedom that can be updated. +Abaqus always works in the global system when passing information to or from a user element. +Therefore, the user element’s stiffness, mass, etc. should always be defined with respect to global +directions at its nodes, even if local transformations (“Transformed coordinate systems,” Section 2.1.5) +are applied to some of these nodes. +You define the ordering of the variables on a user element. The standard and recommended ordering +is such that the degrees of freedom at the first node appear first, followed by the degrees of freedom at +the second node, etc. For example, suppose that the user-defined element type is a planar beam with +three nodes. The element uses degrees of freedom 1, 2, and 6 ( +) at its first and last node +and degrees of freedom 1 and 2 at its second (middle) node. In this case the ordering of variables on the +element is: +, and +, +Element variable +number +Node +Degree of +freedom +Element variable +number +Node +Degree of +freedom +This ordering will be used in most cases. However, if you define an element matrix that does not have +its degrees of freedom ordered in this way, you can change the ordering of the degrees of freedom as +outlined below. +You specify the active degrees of freedom at each node of the element. If the degrees of freedom are +the same at all of the element’s nodes, you specify the list of degrees of freedom only once. Otherwise, +you specify a new list of degrees of freedom each time the degrees of freedom at a node are different from +those at previous nodes. Thus, different nodes of the element can use different degrees of freedom; this +is especially useful when the element is being used in a coupled field problem so that, for example, some +of its nodes have displacement degrees of freedom only, while others have displacement and temperature +degrees of freedom. This method will produce an ordering of the element variables such that all of the +degrees of freedom at the first node appear first, followed by the degrees of freedom at the second node, +etc. +In Abaqus/Standard there are two ways to define element variable numbers that order the degrees +of freedom on the element differently. +Since the user element can accept repeated node numbers when defining the nodal connectivity for +the element, the element can be declared to have one node per degree of freedom on the element. For +example, if the element is a planar, 3-node triangle for stress analysis, it has three nodes, each of which +has degrees of freedom 1 and 2. If all degrees of freedom 1 are to appear first in the element variables, +the element can be defined with six nodes, the first three of which have degree of freedom 1, while nodes +4–6 have degree of freedom 2. The element variables would be ordered as follows: +Element variable +number +Node +Degree of +freedom +32.15.1–3 +Alternatively, the user element variables can be defined so as to order the degrees of freedom on +the element in any arbitrary fashion. You specify a list of degrees of freedom for the first node on the +element. All nodes with a nodal connectivity number that is less than the next connectivity number for +which a list of degrees of freedom is specified will have the first list of degrees of freedom. The second +list of degrees of freedom will be used for all nodes until a new list is defined, etc. If a new list of degrees +of freedom is encountered with a nodal connectivity number that is less than or equal to that given with +the previous list, the previous list’s degrees of freedom will be assigned through the last node of the +element. This generation of degrees of freedom can be stopped before the last node on the element by +specifying a nodal connectivity number with an empty (blank) list of degrees of freedom. +Example +The above procedure continues using this new list to define additional degrees of freedom in accordance +with the new node and degrees of freedom. For example, consider a 3-node beam that has degrees of +freedom 1, 2, and 6 at nodes 1 and 3 and degrees of freedom 1 and 2 at node 2 (middle node). To order +degrees of freedom 1 first, followed by 2, followed by 6, the following input could be used: +*USER ELEMENT +1, 2 +1, 6 +2, +3, 6 +In this case the ordering of the variables on the element is: +Element variable +number +Node +Degree of +freedom +Requirements for activated degrees of freedom in Abaqus/Explicit +There are the following additional requirements with respect to activated degrees of freedom on a user +element of type VUn: +• Only degrees of freedom 1 through 6, 8, and 11 can be activated because these are the only degrees of +freedom numbers that can be updated in Abaqus/Explicit. (In Abaqus/Standard degrees of freedom +1 through 30 can be used.) +• If one translational degree of freedom is activated at a node, all translational degrees of freedom +up to the specified maximum number of coordinates must be activated at that node; moreover, the +translational degrees of freedom at the node must be in consecutive order. +• In three-dimensional analyses, if one rotational degree of freedom is activated at a node, all three +rotational degrees of freedom must be activated in consecutive order. +For example, if you define a 4-node three-dimensional user element that has translations and rotations +active at the first and fourth nodes, temperature only at the second node, and translations and temperature +at the third node, the following input could be used: +*USER ELEMENT +1,2,3,4,5,6 +2,11 +3,1,2,3,11 +4,1,2,3,4,5,6 +Rotation update in geometrically nonlinear analyses +If all three rotational degrees of freedom (4, 5, and 6) are used at a node in a geometrically nonlinear +analysis, Abaqus assumes that these rotations are finite rotations. In this case the incremental values of +these degrees of freedom are not simply added to the total values: the quaternion update formulae are used +instead. Similarly, the corrections are not simply added to the incremental values. The update procedure +is described in “Rotation variables,” Section 1.3.1 of the Abaqus Theory Manual, and is mentioned in +“Conventions,” Section 1.2.2. +To avoid the rotation update in a geometrically nonlinear analysis in Abaqus/Standard, you may +define repeated node numbers in the nodal connectivity of the element such that at least one of the degrees +of freedom 4, 5, or 6 is missing from the degree of freedom list at each node. +Visualizing user-defined elements in Abaqus/CAE +Plotting of user elements is not supported in Abaqus/CAE. However, if the user elements contain +displacement degrees of freedom, they can be overlaid with standard elements; and model plots of these +standard elements can be displayed, allowing you to see the shape of the user elements. If deformed +mesh plots of the user elements are required, the material properties of the overlaying standard elements +must be chosen so that the solution is not changed by including them. If this technique is used, nodes +of the user element will be tied to nodes of the standard elements. Therefore, degrees of freedom 1, 2, +and 3 in the user element must correspond to the displacement degrees of freedom at the nodes of the +standard elements. +Defining a linear user element in Abaqus/Standard +Linear user elements can be defined only in Abaqus/Standard. In the simplest case a linear user element +can be defined as a stiffness matrix and, if required, a mass matrix. In these matrices can be read from a +results file or defined directly. +Reading the element matrices from an Abaqus/Standard results file +To read the element matrices from an Abaqus/Standard results file, you must have written the stiffness +and/or mass matrices in a previous analysis to the results file as element matrix output (“Element matrix +output in Abaqus/Standard” in “Output,” Section 4.1.1) or substructure matrix output (“Writing the +recovery matrix, reduced stiffness matrix, mass matrix, load case vectors, and gravity vectors to a file” +in “Defining substructures,” Section 10.1.2). +You must specify the element number, n, or substructure identifier, Zn, to which the matrices +correspond. For models defined in terms of an assembly of part instances (“Defining an assembly,” +Section 2.10.1), the element numbers written to the results file are internal numbers generated by +Abaqus/Standard . A map between these internal numbers and the original +element numbers and part instance names is provided in the data file of the analysis from which the +element matrix output was written. +In addition, for element matrix output you must specify the step number and increment number at +which the element matrix was written. These items are not required if a substructure whose matrix was +output during its generation is used. +Input File Usage: +*USER ELEMENT, FILE=name, OLD ELEMENT=n or +Zn, STEP=n, INCREMENT=n +Defining the linear user element by specifying the matrices directly +If you define the stiffness and/or mass matrix directly, you must specify the number of nodes associated +with the element. +Input File Usage: +*USER ELEMENT, LINEAR, NODES=n +Defining whether or not the element matrices are symmetric +If the element matrices are not symmetric, you can request that Abaqus/Standard use its nonsymmetric +equation solution capability . +Input File Usage: +*USER ELEMENT, LINEAR, NODES=n, UNSYMM +Defining the mass or stiffness matrix +You define the element mass matrix and the element stiffness matrix separately. If the element is a heat +transfer element, the “stiffness matrix” is the conductivity matrix and the “mass matrix” is the specific +heat matrix. +You can define either one matrix for the element (mass or stiffness) or both types of matrices. +You can read the mass and/or stiffness matrices from a file or define them directly. In either case +Abaqus/Standard reads four values per line, using F20 format. This format ensures that the data are read +with adequate precision. Data written in E20.14 format can be read under this format. +Start with the first column of the matrix. Start a new line for each column. If you do not specify +that the element matrix is unsymmetric, give the matrix entries from the top of each column to the +diagonal term only: do not give the terms below the diagonal. If you specify that the element matrix is +unsymmetric, give all terms in each column, starting from the top of the column. +Input File Usage: +Use the following option to define the element mass matrix: +*MATRIX, TYPE=MASS +Use the following option to define the element stiffness matrix: +*MATRIX, TYPE=STIFFNESS +Use the following option to read the element mass or stiffness matrix from a +file: +*MATRIX, TYPE=MASS or STIFFNESS, INPUT=file_name +For example, if the matrix is symmetric, the following data lines should be used: +Etc. +If the matrix is unsymmetric, the following data lines should be used: +… +…, +Etc. +where m is the size of the matrix and +column j. +is the entry in the matrix for row i +Geometrically nonlinear analysis +When a linear user element is used in a geometrically nonlinear analysis, the stiffness matrix provided +will not be updated to account for any nonlinear effects such as finite rotations. +Defining the element properties +You must associate a property definition with every user element, even though no property values (except +Rayleigh damping factors) are associated with linear user elements. +Input File Usage: +Use the following option to associate a property definition with a user element +set: +*UEL PROPERTY, ELSET=name +Defining Rayleigh damping for direct-integration dynamic analysis +You can define the Rayleigh damping factors for direct-integration dynamic analysis (“Implicit dynamic +analysis using direct integration,” Section 6.3.2) for linear user elements. The Rayleigh damping factors +are defined as +is the damping matrix, +where +are +the user-specified damping factors. See “Material damping,” Section 26.1.1, for more information on +Rayleigh damping. +is the stiffness matrix, and +is the mass matrix, +and +Input File Usage: +*UEL PROPERTY, ELSET=name, ALPHA= , BETA= +Defining loads +to the nodes of linear user-defined elements in the +You can apply point loads, moments, fluxes, etc. +usual way using concentrated loads and concentrated fluxes (“Concentrated loads,” Section 33.4.2, and +“Thermal loads,” Section 33.4.4). +Distributed loads and fluxes cannot be defined for linear user-defined elements. +Defining a general user element +General user elements are defined in user subroutines UEL and UELMAT in Abaqus/Standard and in +user subroutine VUEL in Abaqus/Explicit. The implementation of user elements in user subroutines is +recommended only for advanced users. +Defining the number of nodes associated with the element +You must specify the number of nodes associated with a general user element. You can define “internal” +nodes that are not connected to other elements. +Input File Usage: +*USER ELEMENT, NODES=n +Defining whether or not the element matrices are symmetric in Abaqus/Standard +If the contribution of the element to the Jacobian operator matrix of the overall Newton method is not +symmetric (i.e., the element matrices are not symmetric), you can request that Abaqus/Standard use its +nonsymmetric equation solution capability . +Input File Usage: +*USER ELEMENT, NODES=n, UNSYMM +Defining the maximum number of coordinates needed at any nodal point +You can define the maximum number of coordinates needed in user subroutines UEL, UELMAT, or VUEL +at any node point of the element. Abaqus assigns space to store this many coordinate values at all of the +nodes associated with elements of this type. The default maximum number of coordinates at each node +is 1. +Abaqus will change the maximum number of coordinates to be the maximum of the user-specified +value or the value of the largest active degree of freedom of the user element that is less than or equal to 3. +For example, if you specify a maximum number of coordinates of 1 and the active degrees of freedom +of the user element are 2, 3, and 6, the maximum number of coordinates will be changed to 3. If you +specify a maximum number of coordinates of 2 and the active degrees of freedom of the user element +are 11 and 12, the maximum number of coordinates will remain as 2. +Input File Usage: +*USER ELEMENT, COORDINATES=n +Defining the element properties +You can define the number of properties associated with a particular user element and then specify their +numerical values. +Specifying the number of property values required +Any number of properties can be defined to be used in forming a general user element. You can specify +the number of integer property values required, n, and the number of real (floating point) property values +required, m; the total number of values required is the sum of these two numbers. The default number +of integer property values required is 0 and the default number of real property values required is 0. +Integer property values can be used inside user subroutines UEL, UELMAT, and VUEL as flags, +indices, counters, etc. Examples of real (floating point) property values are the cross-sectional area of a +beam or rod, thickness of a shell, and material properties to define the material behavior for the element. +Input File Usage: +*USER ELEMENT, I PROPERTIES=n, PROPERTIES=m +Specifying the numerical values of element properties +You must associate a user element property definition with each user-defined element, even if no +property values are required. The property values specified in the property definition are passed into +user subroutines UEL, UELMAT, and VUEL each time the subroutine is called for the user elements that +are in the specified element set. +Input File Usage: +Use the following option to associate a property definition with a user element +set: +*UEL PROPERTY, ELSET=name +To define the property values, enter all floating point values on the data lines +first, followed immediately by the integer values. Eight values should be +entered on all data lines except the last one, which may have fewer than eight +values. +Assigning an Abaqus material to the user element +If the Abaqus material library is accessed from a user element, a material must be defined and assigned +to the user element. +Input File Usage: +Use the following option to associate a material with the user element: +*UEL PROPERTY, MATERIAL=name +If this option is used, user subroutine UELMAT must be used to define the +contribution of the element to the model. Otherwise, user subroutine UEL must +be used. +Assigning an orientation definition +If the Abaqus material library is accessed from a user element, you can associate a material orientation +definition (“Orientations,” Section 2.2.5) with the user element. The orientation definition specifies a +local coordinate system for material calculations in the element. The local coordinate system is assumed +to be uniform in a given element and is based on the coordinates at the element centroid. +Input File Usage: +Use the following option to associate an orientation definition with a user +element: +*UEL PROPERTY, ORIENTATION=name +Specifying the element type +If the Abaqus material library is accessed from a user element, the element type must be specified. +Input File Usage: +Use the following option to define a three-dimensional element in a stress/ +displacement or a heat transfer analysis: +*USER ELEMENT, TENSOR=THREED +Use the following option to define a two-dimensional element in a heat transfer +analysis: +*USER ELEMENT, TENSOR=TWOD +Use the following option to define a plane strain element +displacement analysis: +*USER ELEMENT, TENSOR=PSTRAIN +Use the following option to define a plane stress element +displacement analysis: +*USER ELEMENT, TENSOR=PSTRESS +in a stress/ +in a stress/ +Specifying the number of integration points +If the Abaqus material library is accessed from a user element, the number of integration points must be +specified. +Input File Usage: +Use the following option to specify the number of integration points: +*USER ELEMENT, INTEGRATION=n +Defining the number of solution-dependent variables that must be stored within the element +You can define the number of solution-dependent state variables that must be stored within a general user +element. The default number of variables is 1. +Examples of such variables are strains, stresses, section forces, and other state variables (for +example, hardening measures in plasticity models) used in the calculations within the element. +These variables allow quite general nonlinear kinematic and material behavior to be modeled. These +solution-dependent state variables must be calculated and updated in user subroutines UEL, UELMAT, +and VUEL. +As an example, suppose the element has four numerical integration points, at each of which you +wish to store strain, stress, inelastic strain, and a scalar hardening variable to define the material state. +Assume that the element is a three-dimensional solid, so that there are six components of stress and strain +at each integration point. Then, the number of solution-dependent variables associated with each such +element is 4 × (6 × 3 + 1) = 76. +Input File Usage: +*USER ELEMENT, VARIABLES=n +Defining the contribution of the element to the model in user subroutine UEL +For a general user element in Abaqus/Standard, user subroutine UEL may be coded to define the +contribution of the element to the model. Abaqus/Standard calls this routine each time any information +about a user-defined element is needed. At each such call Abaqus/Standard provides the values +of the nodal coordinates and of all solution-dependent nodal variables (displacements, incremental +displacements, velocities, accelerations, etc.) at all degrees of freedom associated with the element, +as well as values, at the beginning of the current increment, of the solution-dependent state variables +associated with the element. Abaqus/Standard also provides the values of all user-defined properties +associated with this element and a control flag array indicating what functions the user subroutine must +perform. Depending on this set of control flags, the subroutine must define the contribution of the +element to the residual vector, define the contribution of the element to the Jacobian (stiffness) matrix, +update the solution-dependent state variables associated with the element, form the mass matrix, and so +on. Often, several of these functions must be performed in a single call to the routine. +Formulation of an element with user subroutine UEL +The element’s principal contribution to the model during general analysis steps is that it provides nodal +forces +and on the solution-dependent state +variables +that depend on the values of the nodal variables +within the element: +geometry, attributes, predefined field variables, distributed loads +Here we use the term “force” to mean that quantity in the variational statement that is conjugate to the +basic nodal variable: physical force when the associated degree of freedom is physical displacement, +moment when the associated degree of freedom is a rotation, heat flux when it is a temperature value, +and so on. The signs of the forces in +are such that external forces provide positive nodal force values +and “internal” forces caused by stresses, internal heat fluxes, etc. in the element provide negative nodal +force values. For example, in the case of mechanical equilibrium of a finite element subject to surface +tractions +and body forces with stress +, and with interpolation +, +In general procedures Abaqus/Standard solves the overall system of equations by Newton’s method: +Solve +Set +Iterate +, +, +where +is the residual at degree of freedom N and +is the Jacobian matrix. +During such iterations you must define +, which is the element’s contribution to the residual, +, +and +which is the element’s contribution to the Jacobian +we imply that the element’s contribution to +of the +include terms such as +. For example, the +on the +. By writing the total derivative +, +should include all direct and indirect dependencies +will +; therefore, +will generally depend on +Use in transient analysis procedures +In procedures such as transient heat transfer and dynamic analysis, the problem also involves time +integration of rates of change of the nodal degrees of freedom. The time integration schemes used by +Abaqus/Standard for the various procedures are described in more detail in the Theory Manual. For +example, in transient heat transfer analysis, the backward difference method is used: +Therefore, if +energy storage), the Jacobian contribution should include the term +depends on +and +(as would be the case if the user element includes thermal +where +is defined from the time integration procedure as +. +In all cases where Abaqus/Standard integrates first-order problems in time, the +are never stored +because they are readily available as +. However, for direct, +, where +implicit integration of dynamic systems Abaqus/Standard requires storage of +. These values are, therefore, passed +into subroutine UEL. If the user element contains effects that depend on these time derivatives (damping +and inertial effects), its Jacobian contribution will include +and +For the Hilber-Hughes-Taylor scheme +and +where +integration, the same expressions apply with +element’s damping matrix, and +are the (Newmark) parameters of the integration scheme. For backwark Euler time +is the +equal to unity. The term +and +is its mass matrix. +The Hilber-Hughes-Taylor scheme writes the overall dynamic equilibrium equations as +where +is often +is the total force at degree of freedom N, excluding d’Alembert (inertia) forces. +referred to as the “static residual.” Therefore, if a user element is to be used with Hilber-Hughes-Taylor +time integration, the element’s contribution +to the overall residual must be formulated in the same +way. Since Abaqus/Standard provides information only at the time point at which UEL is called, this +implies that each time UEL is called the +if half-increment +residual calculations are required, where +from the beginning of the previous increment) +and used to store +if half-increment residual calculations are required) for use in the next +increment. This complication can be avoided if the numerical damping control parameter, +, for the +dynamic step is set to zero; i.e., if the trapezoidal rule is used for integration of the dynamic equations +. This complication is +also avoided with the backward Euler time integration operator because dynamic equilibrium is enforced +at the end of the step. +array must be used to recover +indicates +(and +(and +If solution-dependent state variables ( +) are used in the element, a suitable time integration +method must be coded into subroutine UEL for these variables. Any of the +associated with the +element that are not shared with standard Abaqus/Standard elements may be integrated in time by any +, etc. at particular points +suitable technique. If, in such cases, it is necessary to store values of +in time, the solution-dependent state variable array, +, can be used for this purpose. Abaqus/Standard +will still compute and store values of +using the formulae associated with whatever time +integrator it is using, but these values need not be used. To ensure accurate, stable time integration, you +can control the size of the time increment used by Abaqus/Standard. +and +, +Constraints defined with Lagrange multipliers +Introduction of constraints with Lagrange multipliers should be avoided since Abaqus/Standard cannot +detect such variables and avoid eigensolver problems by proper ordering of the equations. +Defining the contribution of the element to the model in user subroutine UELMAT +Alternatively, for a general user element in Abaqus/Standard, user subroutine UELMAT may be coded to +define the contribution of the element to the model. User subroutine UELMAT is an enhanced version of +user subroutine UEL; consequently, all the information provided for user subroutine UEL is also valid +for user subroutine UELMAT. The enhancement allows you to access some of the material models from +the Abaqus material library from UELMAT. UELMAT works only with a subset of procedures for which +UEL is available: +• static; +• direct-integration dynamic; +• frequency extraction; +• steady-state uncouple heat transfer; and +• transient uncouple heat transfer. +User subroutine UELMAT will be called if an Abaqus material model is assigned to a user element ; otherwise, user subroutine UEL will be +called. +Accessing Abaqus materials from user subroutine UELMAT +Abaqus allows you to access some of the material models from the Abaqus material +library +from user subroutine UELMAT. The material models are accessed through the utility routines +MATERIAL_LIB_MECH and MATERIAL_LIB_HT (“Accessing Abaqus +thermal materials,” +Section 2.1.18 of the Abaqus User Subroutines Reference Manual, and “Accessing Abaqus materials,” +Section 2.1.17 of the Abaqus User Subroutines Reference Manual). Each time user subroutine UELMAT +is called with the flags set to values that require computation of the right-hand-side vector and the +element Jacobian, the material library must be called for each integration point, where the number of +integration points is specified in the element definition (“Specifying the number of integration points” +in “User-defined elements,” Section 32.15.1). The material models that are accessible from user +subroutine UELMAT are: +• linear elastic model; +• hyperelastic model; +• Ramberg-Osgood model; +• classical metal plasticity models (Mises and Hill); +• extended Drucker-Prager model; +• modified Drucker-Prager/Cap plasticity model; +• porous metal plasticity model; +• elastomeric foam material model; and +• crushable foam plasticity model. +Defining the contribution of the element to the model in user subroutine VUEL +For a general user element in Abaqus/Explicit, user subroutine VUEL must be coded to define the +contribution of the element to the model. Abaqus/Explicit calls this routine each time any information +about a user-defined element is needed. At each such call Abaqus/Explicit provides the values of the +nodal coordinates and of all solution-dependent nodal variables (displacements, velocities, accelerations, +etc.) at all degrees of freedom associated with the element, as well as values of the solution-dependent +state variables associated with the element at the beginning of the current increment. The incremental +displacements are those obtained in a previous increment. Abaqus/Explicit also provides the values of +all user-defined properties associated with this element and a control flag array indicating what functions +the user subroutine must perform. Depending on this set of control flags, the subroutine must define the +contribution of the element to the internal or external force/flux vector, form the mass/capacity matrix, +update the solution-dependent state variables associated with the element, and so on. +The element’s principal contribution to the model is that it provides nodal forces +that depend +, and on the solution-dependent +on the values of the nodal variables +state variables +within the element: +, the rate of nodal variables +geometry, attributes, predefined field variables, distributed loads +In addition, the element mass matrix +external load contribution from the element due to specified distributed loading. +Abaqus/Explicit solves for the accelerations at the end of the increment using +can be defined. Optionally, you can also define the +In each increment +where +using the central difference method +is the applied load vector. The solution (velocity, displacement) is then integrated in time +For coupled temperature/displacement elements the temperatures are computed at the beginning of +the increment using +where +vector. The temperature is integrated in time using the explicit forward-difference integration rule, +is the lumped capcitance matrix, +is the applied nodal source, and +is the internal flux +More details can be found in “Explicit dynamic analysis,” Section 6.3.3 and “Fully coupled thermal- +stress analysis,” Section 6.5.3. The signs of the forces defined in +are such that external forces provide +positive nodal force values and “internal” forces caused by stresses, damping effects, internal heat fluxes, +etc. in the element provide negative nodal force values. Internal forces due to bulk viscosity are dependent +on the scaled mass of the element. The necessary information (bulk viscosity constants and mass scaling +factors) is passed into the user subroutine for this purpose. +Requirements for defining the mass matrix +As explained in “Explicit dynamic analysis,” Section 6.3.3, what makes the explicit time integration +method efficient is that the mass inversion process is extremely effective. This is due to the fact that most +of the nonzero entries in the mass matrix are located on the diagonal positions. The only exception is for +rotational degrees of freedom in three-dimensional analyses in which case at each node an anisotropic +rotary inertia (symmetric 3 × 3 tensor) can be defined. In these cases some of the nonzero entries in +the mass matrix may be off-diagonal; but the inversion process is local and, hence, very effective. The +mass matrix defined in user subroutine VUEL must adhere to these requirements as illustrated in detail in +“VUEL,” Section 1.2.10 of the Abaqus User Subroutines Reference Manual. If you specify a zero mass +matrix or skip the definition of the mass matrix altogether, Abaqus/Explicit issues an error message. +The definition of a realistic mass matrix is not mandatory, but it is strongly recommended. +If +you choose to not define a realistic mass matrix using the user subroutine, you must provide realistic +mass, rotary inertia, heat capacity, etc. at all nodes and at all degrees of freedom associated with the +user element. This can be accomplished by various means, such as by defining mass and rotary inertia +elements at the nodes or by connecting the user element to other elements for which density, heat capacity, +etc. was specified. +Mass is computed only once at the beginning of the analysis. Consequently, the mass of the +user element cannot be changed arbitrarily during the analysis. If necessary, mass scaling is applied +accordingly to ensure the requested time incrementation. +Definition of the stable time increment +Since the central difference operator is conditionally stable, the time increments in Abaqus/Explicit must +be somewhat smaller than the stable time increment. You must provide an accurate estimate for the stable +time increment associated with the user element. This scalar value is highly dependent on the element +formulation, and sophisticated coding may be required inside the user subroutine to obtain a reliable +estimate. A conservative estimate will reduce the time increment size for the entire analysis and, hence, +lead to longer analysis times. +Defining loads +You can apply point loads, moments, fluxes, etc. to the nodes of general user-defined elements in the +usual way, using concentrated loads and concentrated fluxes (“Concentrated loads,” Section 33.4.2, and +“Thermal loads,” Section 33.4.4). +You can also define distributed loads and fluxes for general user-defined elements (“Distributed +loads,” Section 33.4.3, and “Thermal loads,” Section 33.4.4). These loads require a load type key. For +user-defined elements, you can define load type keys of the forms Un and, in Abaqus/Standard, UnNU, +where n is any positive integer. +If the load type key is of the form Un, the load magnitude is defined directly and follows +the standard Abaqus conventions with respect to its amplitude variation as a function of time. +In +Abaqus/Standard, if the load key is of the form UnNU, all of the load definition will be accomplished +inside subroutine UEL and UELMAT. Each time Abaqus/Standard calls subroutine UEL or UELMAT, it +tells the subroutine how many distributed loads/fluxes are currently active. For each active load or flux +of type Un Abaqus/Standard gives the current magnitude and current increment in magnitude of the +load. The coding in subroutine UEL or UELMAT must distribute the loads into consistent equivalent +nodal forces and, if necessary, provide their contribution to the Jacobian matrix—the “load stiffness +matrix.” +In Abaqus/Explicit only load keys of the form Un can be used, and they can be used only for +distributed loads (however, thermal fluxes can be defined in the coding in subroutine VUEL). Each time +Abaqus/Explicit calls subroutine VUEL, it tells the subroutine which load number is currently active +and the current magnitude of the load. The coding in subroutine VUEL must distribute the loads into +consistent equivalent nodal forces. +Defining output +All quantities to be output must be saved as solution-dependent state variables. In Abaqus/Standard, +the solution-dependent state variables can be printed or written to the results file using output variable +identifier SDV (“Abaqus/Standard output variable identifiers,” Section 4.2.1). +The components of solution-dependent state variables that belong to a user element are not +available in Abaqus/CAE. You can write output to separate files in a table format that can be accessed +in Abaqus/CAE to produce history output. +Defining wave kinematic data +A utility routine GETWAVE is provided in user subroutine UEL to access the wave kinematic data +defined for an Abaqus/Aqua analysis (“Abaqus/Aqua analysis,” Section 6.11.1). This utility is discussed +in “Obtaining wave kinematic data in an Abaqus/Aqua analysis,” Section 2.1.13 of the Abaqus User +Subroutines Reference Manual, where the arguments to GETWAVE and the syntax for its use are defined. +Use in contact +Only node-based surfaces (“Node-based surface definition,” Section 2.3.3) can be created on user-defined +elements. Hence, these elements can be used to define only slave surfaces in a contact analysis. In +Abaqus/Explicit the user elements will not be included in the general contact algorithm automatically. +Node-based surfaces can be defined using these nodes and then included in the general contact definition. +Import of user elements +User elements cannot be imported from an Abaqus/Standard analysis into an Abaqus/Explicit analysis +or vice versa. Equivalent user elements can be defined in both products to overcome this limitation. +However, the state variables associated with these elements will not be communicated. +32.15.2 +USER-DEFINED ELEMENT LIBRARY +Products: Abaqus/Standard Abaqus/Explicit +References +• “User-defined elements,” Section 32.15.1 +• “UEL,” Section 1.1.27 of the Abaqus User Subroutines Reference Manual +• “UELMAT,” Section 1.1.28 of the Abaqus User Subroutines Reference Manual +• “VUEL,” Section 1.2.10 of the Abaqus User Subroutines Reference Manual +• *MATRIX +• *UEL PROPERTY +• *USER ELEMENT +Overview +This section provides a reference to the user-defined elements available in Abaqus/Standard and +Abaqus/Explicit. +Element types +Un +VUn +n must be a positive integer ( +in Abaqus/Standard +n must be a positive integer ( +in Abaqus/Explicit +Active degrees of freedom +As defined in the user element definition. +Additional solution variables +) that will define the element type uniquely +) that will define the element type uniquely +You can define solution variables associated with nodes that are not connected to other elements. +However, in Abaqus/Standard, definition of constraints with Lagrange multipliers in user elements +should be avoided because of potential equation solver problems. +In Abaqus/Explicit definition of constraints with Lagrange multipliers is not possible because the stable +time increment would decrease to infinitesimally small values. +Nodal coordinates required +None required for linear user elements. +As needed in user subroutines UEL, UELMAT, or VUEL for general user elements. The maximum +number of coordinates per node is specified in the user element definition (see “Defining the maximum +number of coordinates needed at any nodal point” in “User-defined elements,” Section 32.15.1). The +first coordinate entries at each node should correspond to the standard Abaqus convention (X, Y, Z or +r, z for axisymmetric elements). +Element property definition +For a linear user element the properties are the stiffness and mass, defined via user-defined matrices or +read from an Abaqus/Standard results file. If necessary, you can specify Rayleigh damping values for +linear user elements in the element property definition. +For a general user element defined via user subroutines UEL, UELMAT, or VUEL, you define the number of +element properties in the user element definition and provide the numerical values in the element property +definition. The definition of these properties depends on your coding in subroutine UEL, UELMAT, or +VUEL. +Input File Usage: +*UEL PROPERTY +Element-based loading +None for linear user elements. +Un: Distributed load or flux whose magnitude is given via distributed load or distributed flux loading +definitions for a general +user element. n must be a positive integer that is passed into user subroutines UEL, UELMAT, or VUEL +to identify the particular load type. +UnNU: Available in Abaqus/Standard only. Distributed load or flux that is completely defined as +equivalent nodal values inside user subroutine UEL or UELMAT for a general user element. n must be +will be passed into subroutine UEL or UELMAT when such a load is active to +a positive integer: +identify the load type. The minus sign on n indicates that the load is of type NU. +Element output +For a linear user element there are no stress or strain components since the element only appears as a +stiffness and mass. +For a general user element any stress, strain, or other solution-dependent variables within the element +must be defined as solution-dependent state variables by your coding within subroutine UEL, UELMAT, +or VUEL. In Abaqus/Standard, they can be output using output variable SDV. +Currently element output to the output database is not supported for user-defined elements. +Node ordering on elements +As defined in the user element definition. +EI.1 +Abaqus/Standard ELEMENT INDEX +This index provides a reference to all of the element types that are available in Abaqus/Standard. Elements +are listed in alphabetical order, where numerical characters precede the letter “A” and two-digit numbers are +put in numerical, rather than “alphabetical,” order. Thus, AC1D2 precedes ACAX4, and AC3D20 follows +AC3D8. +For certain options, such as contact and surface-based distributing coupling, Abaqus may generate +internal elements (such as IDCOUP3D for surface-based distributing coupling). These internal element +names are not included in the index below but may appear in an output database (.odb) or data (.dat) file. +28.1.2 +28.1.2 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.3.2 +28.3.2 +28.3.2 +28.3.2 +28.3.2 +28.3.2 +28.3.2 +28.3.2 +32.13.2 +2-node acoustic link +3-node acoustic link +3-node linear 2-D acoustic triangle +4-node linear 2-D acoustic quadrilateral +6-node quadratic 2-D acoustic triangular prism +8-node quadratic 2-D acoustic quadrilateral +4-node linear acoustic tetrahedron +6-node linear acoustic triangular prism +8-node linear acoustic brick +10-node quadratic acoustic tetrahedron +15-node quadratic acoustic triangular prism +20-node quadratic acoustic brick +3-node linear axisymmetric acoustic triangle +4-node linear axisymmetric acoustic quadrilateral +6-node quadratic axisymmetric acoustic triangle +8-node quadratic axisymmetric acoustic quadrilateral +2-node linear 2-D acoustic infinite element +3-node quadratic 2-D acoustic infinite element +3-node linear 3-D acoustic infinite element +4-node linear 3-D acoustic infinite element +6-node quadratic 3-D acoustic infinite element +8-node quadratic 3-D acoustic infinite element +2-node linear axisymmetric acoustic infinite element +3-node quadratic axisymmetric acoustic infinite element +1-node acoustic interface element +EI.1–1 +AC1D2 +AC1D3 +AC2D3 +AC2D4 +AC2D6 +AC2D8 +AC3D4 +AC3D6 +AC3D8 +AC3D10 +AC3D15 +AC3D20 +ACAX3 +ACAX4 +ACAX6 +ACAX8 +ACIN2D2 +ACIN2D3 +ACIN3D3 +ACIN3D4 +ACIN3D6 +ACIN3D8 +ACINAX2 +ACINAX3 +2-node linear 2-D acoustic interface element (this element has been renamed to +ASI2D2) +2-node linear axisymmetric acoustic interface element (this element has been +renamed to ASIAX2) +2-node linear 2-D acoustic interface element +3-node quadratic 2-D acoustic interface element +3-node quadratic 2-D acoustic interface element (this element has been renamed +to ASI2D3) +3-node quadratic axisymmetric acoustic interface element (this element has been +renamed to ASIAX3) +3-node linear 3-D acoustic interface element +4-node linear 3-D acoustic interface element +6-node quadratic 3-D acoustic interface element +8-node quadratic 3-D acoustic interface element +4-node linear 3-D acoustic interface element (this element has been renamed to +ASI3D4) +8-node quadratic 3-D acoustic interface element (this element has been renamed +to ASI3D8) +2-node linear axisymmetric acoustic interface element +3-node quadratic axisymmetric acoustic interface element +2-node linear beam in a plane +2-node linear beam in a plane, hybrid formulation +3-node quadratic beam in a plane +3-node quadratic beam in a plane, hybrid formulation +2-node cubic beam in a plane +2-node cubic beam in a plane, hybrid formulation +2-node linear beam in space +2-node linear beam in space, hybrid formulation +2-node linear open-section beam in space +2-node linear open-section beam in space, hybrid formulation +3-node quadratic beam in space +3-node quadratic beam in space, hybrid formulation +3-node quadratic open-section beam in space +3-node quadratic open-section beam in space, hybrid formulation +2-node cubic beam in space +2-node cubic beam in space, hybrid formulation +4-node linear tetrahedron +32.13.2 +32.13.2 +32.13.2 +32.13.2 +32.13.2 +32.13.2 +32.13.2 +32.13.2 +32.13.2 +32.13.2 +32.13.2 +32.13.2 +32.13.2 +32.13.2 +29.3.8 +29.3.8 +29.3.8 +29.3.8 +29.3.8 +29.3.8 +29.3.8 +29.3.8 +29.3.8 +29.3.8 +29.3.8 +29.3.8 +29.3.8 +29.3.8 +29.3.8 +29.3.8 +28.1.4 +EI.1–2 +ASI2 +ASI2A +ASI2D2 +ASI2D3 +ASI3 +ASI3A +ASI3D3 +ASI3D4 +ASI3D6 +ASI3D8 +ASI4 +ASI8 +ASIAX2 +ASIAX3 +B21 +B21H +B22 +B22H +B23 +B23H +B31 +B31H +B31OS +B31OSH +B32 +B32H +B32OS +B32OSH +B33 +B33H +4-node linear piezoelectric tetrahedron +4-node linear tetrahedron, hybrid, linear pressure +4-node linear coupled pore pressure element +4-node thermally coupled tetrahedron, linear displacement and temperature +6-node linear triangular prism +6-node linear piezoelectric triangular prism +6-node linear triangular prism, hybrid, constant pressure +6-node linear coupled pore pressure element +6-node thermally coupled triangular prism, linear displacement and temperature +8-node linear brick +8-node linear piezoelectric brick +8-node linear brick, hybrid, constant pressure +8-node thermally coupled brick, trilinear displacement and temperature, hybrid, +constant pressure +8-node linear brick, incompatible modes +8-node linear brick, hybrid, linear pressure, incompatible modes +8-node brick, trilinear displacement, trilinear pore pressure +8-node brick, trilinear displacement, trilinear pore pressure, hybrid, constant +pressure +8-node brick, trilinear displacement, trilinear pore pressure, trilinear temperature, +hybrid, constant pressure +8-node brick, trilinear displacement, trilinear pore pressure, trilinear temperature +8-node linear brick, reduced integration, hourglass control +8-node linear brick, hybrid, constant pressure, reduced integration, hourglass +control +8-node thermally coupled brick, trilinear displacement and temperature, reduced +integration, hourglass control, hybrid, constant pressure +8-node brick, trilinear displacement, trilinear pore pressure, reduced integration +8-node brick, trilinear displacement, trilinear pore pressure, reduced integration, +hybrid, constant pressure +8-node brick, trilinear displacement, trilinear pore pressure, trilinear temperature, +reduced integration, hybrid, constant pressure +8-node brick, trilinear displacement, trilinear pore pressure, trilinear temperature, +reduced integration +8-node thermally coupled brick, trilinear displacement and temperature, reduced +integration, hourglass control +8-node thermally coupled brick, trilinear displacement and temperature +10-node quadratic tetrahedron +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +EI.1–3 +C3D4E +C3D4H +C3D4P +C3D4T +C3D6 +C3D6E +C3D6H +C3D6P +C3D6T +C3D8 +C3D8E +C3D8H +C3D8HT +C3D8I +C3D8IH +C3D8P +C3D8PH +C3D8PHT +C3D8PT +C3D8R +C3D8RH +C3D8RHT +C3D8RP +C3D8RPH +C3D8RPHT +C3D8RPT +C3D8RT +C3D8T +linear +improved surface stress +linear pressure, hourglass +10-node quadratic piezoelectric tetrahedron +10-node quadratic tetrahedron, hybrid, constant pressure +10-node general-purpose quadratic tetrahedron, +visualization +10-node modified tetrahedron, hourglass control +10-node modified quadratic tetrahedron, hybrid, +control +10-node thermally coupled modified quadratic tetrahedron, hybrid, +pressure, hourglass control +10-node modified displacement and pore pressure tetrahedron, hourglass control +10-node modified displacement and pore pressure tetrahedron, hybrid, linear +pressure, hourglass control +10-node modified displacement, pore pressure, and temperature tetrahedron, +linear pressure, hourglass control +10-node thermally coupled modified quadratic tetrahedron, hourglass control +15-node quadratic triangular prism +15-node quadratic piezoelectric triangular prism +15-node quadratic triangular prism, hybrid, linear pressure +15 to 18-node triangular prism +15 to 18-node triangular prism, hybrid, linear pressure +20-node quadratic brick +20-node quadratic piezoelectric brick +20-node quadratic brick, hybrid, linear pressure +20-node +thermally coupled brick, +temperature, hybrid, linear pressure +20-node brick, triquadratic displacement, trilinear pore pressure +20-node brick, triquadratic displacement, trilinear pore pressure, hybrid, linear +pressure +20-node quadratic brick, reduced integration +20-node quadratic piezoelectric brick, reduced integration +20-node quadratic brick, hybrid, linear pressure, reduced integration +20-node +triquadratic displacement, +temperature, hybrid, linear pressure, reduced integration +20-node brick, +integration +20-node brick, triquadratic displacement, trilinear pore pressure, hybrid, linear +pressure, reduced integration +thermally coupled brick, +triquadratic displacement, +triquadratic displacement, +trilinear pore pressure, +trilinear +trilinear +reduced +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +EI.1–4 +C3D10E +C3D10H +C3D10I +C3D10M +C3D10MH +C3D10MHT +C3D10MP +C3D10MPH +C3D10MPT +C3D10MT +C3D15 +C3D15E +C3D15H +C3D15V +C3D15VH +C3D20 +C3D20E +C3D20H +C3D20HT +C3D20P +C3D20PH +C3D20R +C3D20RE +C3D20RH +C3D20RHT +C3D20RP +thermally coupled brick, +20-node +temperature, reduced integration +20-node thermally coupled brick, triquadratic displacement, trilinear temperature +triquadratic displacement, +trilinear +21 to 27-node brick +21 to 27-node brick, hybrid, linear pressure +21 to 27-node brick, reduced integration +21 to 27-node brick, hybrid, linear pressure, reduced integration +3-node linear axisymmetric triangle +3-node linear axisymmetric piezoelectric triangle +3-node linear axisymmetric triangle, hybrid, constant pressure +3-node axisymmetric thermally coupled triangle, +temperature +linear displacement and +4-node bilinear axisymmetric quadrilateral +4-node bilinear axisymmetric piezoelectric quadrilateral +4-node bilinear axisymmetric quadrilateral, hybrid, constant pressure +4-node axisymmetric thermally coupled quadrilateral, bilinear displacement and +temperature, hybrid, constant pressure +4-node bilinear axisymmetric quadrilateral, incompatible modes +4-node bilinear axisymmetric quadrilateral, hybrid, linear pressure, incompatible +modes +4-node axisymmetric quadrilateral, bilinear displacement, bilinear pore pressure +4-node axisymmetric quadrilateral, bilinear displacement, bilinear pore pressure, +hybrid, constant pressure +4-node axisymmetric quadrilateral, bilinear displacement, bilinear pore pressure, +bilinear temperature +reduced integration, hourglass +4-node bilinear axisymmetric quadrilateral, +control +4-node bilinear axisymmetric quadrilateral, hybrid, constant pressure, reduced +integration, hourglass control +4-node thermally coupled axisymmetric quadrilateral, bilinear displacement and +temperature, reduced integration, hourglass control +4-node axisymmetric quadrilateral, bilinear displacement, bilinear pore pressure, +reduced integration +4-node axisymmetric quadrilateral, bilinear displacement, bilinear pore pressure, +hybrid, constant pressure, reduced integration +4-node axisymmetric quadrilateral, bilinear displacement, bilinear pore pressure, +bilinear temperature, hybrid, constant pressure, reduced integration +EI.1–5 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +C3D20RT +C3D20T +C3D27 +C3D27H +C3D27R +C3D27RH +CAX3 +CAX3E +CAX3H +CAX3T +CAX4 +CAX4E +CAX4H +CAX4HT +CAX4I +CAX4IH +CAX4P +CAX4PH +CAX4PT +CAX4R +CAX4RH +CAX4RHT +CAX4RP +CAX4RPH +CAX4RPT +4-node axisymmetric quadrilateral, bilinear displacement, bilinear pore pressure, +bilinear temperature, reduced integration +CAX4RT +CAX4T +CAX6 +CAX6E +CAX6H +CAX6M +CAX6MH +CAX6MHT +CAX6MP +CAX6MPH +CAX6MT +CAX8 +CAX8E +CAX8H +CAX8HT +CAX8P +CAX8PH +CAX8R +CAX8RE +CAX8RH +4-node thermally coupled axisymmetric quadrilateral, bilinear displacement and +temperature, hybrid, constant pressure, reduced integration, hourglass control +4-node axisymmetric thermally coupled quadrilateral, bilinear displacement and +temperature +6-node quadratic axisymmetric triangle +6-node quadratic axisymmetric piezoelectric triangle +6-node quadratic axisymmetric triangle, hybrid, linear pressure +6-node modified axisymmetric triangle, hourglass control +6-node modified quadratic axisymmetric triangle, hybrid, +hourglass control +linear pressure, +6-node modified axisymmetric thermally coupled triangle, hybrid, +pressure, hourglass control +linear +28.1.6 +6-node modified displacement and pore pressure axisymmetric triangle, +hourglass control +6-node modified displacement and pore pressure axisymmetric triangle, hybrid, +linear pressure, hourglass control +28.1.6 +28.1.6 +6-node modified axisymmetric thermally coupled triangle, +hourglass control +linear pressure, +28.1.6 +8-node biquadratic axisymmetric quadrilateral +8-node biquadratic axisymmetric piezoelectric quadrilateral +8-node biquadratic axisymmetric quadrilateral, hybrid, linear pressure +8-node axisymmetric thermally coupled quadrilateral, biquadratic displacement, +bilinear temperature, hybrid, linear pressure +8-node axisymmetric quadrilateral, biquadratic displacement, bilinear pore +pressure +8-node axisymmetric quadrilateral, biquadratic displacement, bilinear pore +pressure, hybrid, linear pressure +8-node biquadratic axisymmetric quadrilateral, reduced integration +8-node biquadratic axisymmetric piezoelectric quadrilateral, reduced integration +8-node biquadratic axisymmetric quadrilateral, hybrid, linear pressure, reduced +integration +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +CAX8RHT +CAX8RP +8-node axisymmetric thermally coupled quadrilateral, biquadratic displacement, +bilinear temperature, hybrid, linear pressure, reduced integration +8-node axisymmetric quadrilateral, biquadratic displacement, bilinear pore +pressure, reduced integration +CAX8RPH +CAX8RT +CAX8T +CAXA4N +CAXA4HN +CAXA4RN +8-node axisymmetric quadrilateral, biquadratic displacement, bilinear pore +pressure, hybrid, linear pressure, reduced integration +8-node axisymmetric thermally coupled quadrilateral, biquadratic displacement, +bilinear temperature, reduced integration +8-node axisymmetric thermally coupled quadrilateral, biquadratic displacement, +bilinear temperature +Bilinear asymmetric-axisymmetric, Fourier quadrilateral with 4 nodes per r–z +plane +Bilinear asymmetric-axisymmetric, Fourier quadrilateral with 4 nodes per r–z +plane, constant Fourier pressure, hybrid +Bilinear asymmetric-axisymmetric, Fourier quadrilateral with 4 nodes per r–z +plane, reduced integration in r–z planes, hourglass control +28.1.6 +28.1.6 +28.1.6 +28.1.7 +28.1.7 +28.1.7 +CAXA4RHN Bilinear asymmetric-axisymmetric, Fourier quadrilateral with 4 nodes per r–z +28.1.7 +CAXA8N +CAXA8HN +CAXA8PN +CAXA8RN +plane, constant Fourier pressure, hybrid, reduced integration in r–z planes +Biquadratic asymmetric-axisymmetric, Fourier quadrilateral with 8 nodes per r–z +plane +Biquadratic asymmetric-axisymmetric, Fourier quadrilateral with 8 nodes per r–z +plane, linear Fourier pressure, hybrid +Biquadratic asymmetric-axisymmetric, Fourier quadrilateral with 8 nodes per r–z +plane, bilinear Fourier pore pressure +Biquadratic asymmetric-axisymmetric, Fourier quadrilateral with 8 nodes per r–z +plane, reduced integration in r–z planes +28.1.7 +28.1.7 +28.1.7 +28.1.7 +CAXA8RHN Biquadratic asymmetric-axisymmetric, Fourier quadrilateral with 8 nodes per r–z +28.1.7 +CAXA8RPN +CCL9 +CCL9H +CCL12 +CCL12H +CCL18 +CCL18H +CCL24 +CCL24H +CCL24R +CCL24RH +CGAX3 +CGAX3H +plane, linear Fourier pressure, hybrid, reduced integration in r–z planes +Biquadratic asymmetric-axisymmetric, Fourier quadrilateral with 8 nodes per r–z +plane, bilinear Fourier pore pressure, reduced integration in r–z planes +9-node cylindrical prism +9-node cylindrical hybrid prism +12-node cylindrical brick +12-node cylindrical hybrid brick +18-node cylindrical prism +18-node cylindrical hybrid prism +24-node cylindrical brick +24-node cylindrical hybrid brick +24-node cylindrical brick with reduced integration +24-node cylindrical hybrid brick with reduced integration +3-node generalized linear axisymmetric triangle, twist +3-node generalized linear axisymmetric triangle, hybrid, constant pressure, twist +28.1.7 +28.1.5 +28.1.5 +28.1.5 +28.1.5 +28.1.5 +28.1.5 +28.1.5 +28.1.5 +28.1.5 +28.1.5 +28.1.6 +28.1.6 +CGAX3HT +CGAX3T +CGAX4 +CGAX4H +CGAX4HT +CGAX4R +CGAX4RH +CGAX4RHT +CGAX4RT +CGAX4T +CGAX6 +CGAX6H +CGAX6M +CGAX6MH +3-node generalized axisymmetric thermally coupled triangle, hybrid, constant +pressure, linear displacement and temperature, twist +3-node generalized axisymmetric thermally coupled triangle, linear displacement +and temperature, twist +4-node generalized bilinear axisymmetric quadrilateral, twist +4-node generalized bilinear axisymmetric quadrilateral, hybrid, constant +pressure, twist +4-node generalized axisymmetric thermally coupled quadrilateral, hybrid, +constant pressure, bilinear displacement and temperature, twist +4-node generalized bilinear axisymmetric quadrilateral, reduced integration, +hourglass control, twist +4-node generalized bilinear axisymmetric quadrilateral, hybrid, constant +pressure, reduced integration, hourglass control, twist +4-node generalized axisymmetric thermally coupled quadrilateral, bilinear +displacement and temperature, hybrid, constant pressure, reduced integration, +hourglass control, twist +4-node generalized axisymmetric thermally coupled quadrilateral, bilinear +displacement and temperature, reduced integration, hourglass control, twist +4-node generalized axisymmetric thermally coupled quadrilateral, bilinear +displacement and temperature, twist +6-node generalized quadratic axisymmetric triangle, twist +6-node generalized quadratic axisymmetric triangle, hybrid, linear pressure, twist +6-node generalized modified axisymmetric triangle, twist, hourglass control +6-node generalized modified axisymmetric triangle, +pressure, hourglass control +twist, hybrid, +linear +CGAX6MT +CGAX8 +CGAX8H +CGAX6MHT 6-node generalized modified thermally coupled axisymmetric triangle, quadratic +displacement, linear temperature, hybrid, linear pressure, twist, hourglass control +6-node generalized modified thermally coupled axisymmetric triangle, quadratic +displacement, linear temperature, twist, hourglass control +8-node generalized biquadratic axisymmetric quadrilateral, twist +8-node generalized biquadratic axisymmetric quadrilateral, hybrid, +pressure, twist +8-node generalized axisymmetric thermally coupled quadrilateral, biquadratic +displacement, bilinear temperature, hybrid, linear pressure, twist +8-node generalized biquadratic axisymmetric quadrilateral, reduced integration, +twist +8-node generalized biquadratic axisymmetric quadrilateral, hybrid, +pressure, reduced integration, twist +CGAX8RH +CGAX8HT +CGAX8R +linear +linear +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +8-node generalized axisymmetric thermally coupled quadrilateral, biquadratic +displacement, bilinear temperature, hybrid, linear pressure, reduced integration, +twist +8-node generalized axisymmetric thermally coupled quadrilateral, biquadratic +displacement, bilinear temperature, reduced integration, twist +8-node generalized axisymmetric thermally coupled quadrilateral, biquadratic +displacement, bilinear temperature, twist +8-node linear one-way infinite brick +12-node quadratic one-way infinite brick +18-node quadratic one-way infinite brick +4-node linear axisymmetric one-way infinite quadrilateral +5-node quadratic axisymmetric one-way infinite quadrilateral +4-node linear plane strain one-way infinite quadrilateral +5-node quadratic plane strain one-way infinite quadrilateral +4-node linear plane stress one-way infinite quadrilateral +5-node quadratic plane stress one-way infinite quadrilateral +4-node axisymmetric cohesive element +6-node axisymmetric pore pressure cohesive element +4-node two-dimensional cohesive element +6-node two-dimensional pore pressure cohesive element +6-node three-dimensional cohesive element +9-node three-dimensional pore pressure cohesive element +8-node three-dimensional cohesive element +12-node three-dimensional pore pressure cohesive element +Connector element in a plane between two nodes or ground and a node +Connector element in space between two nodes or ground and a node +3-node linear plane strain triangle +3-node linear plane strain piezoelectric triangle +3-node linear plane strain triangle, hybrid, constant pressure +3-node plane strain thermally coupled triangle, +temperature +4-node bilinear plane strain quadrilateral +4-node bilinear plane strain piezoelectric quadrilateral +4-node bilinear plane strain quadrilateral, hybrid, constant pressure +4-node plane strain thermally coupled quadrilateral, bilinear displacement and +temperature, hybrid, constant pressure +4-node bilinear plane strain quadrilateral, incompatible modes +linear displacement and +28.1.6 +28.1.6 +28.1.6 +28.3.2 +28.3.2 +28.3.2 +28.3.2 +28.3.2 +28.3.2 +28.3.2 +28.3.2 +28.3.2 +32.5.10 +32.5.10 +32.5.8 +32.5.8 +32.5.9 +32.5.9 +32.5.9 +32.5.9 +31.1.4 +31.1.4 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +EI.1–9 +CGAX8RHT +CGAX8RT +CGAX8T +CIN3D8 +CIN3D12R +CIN3D18R +CINAX4 +CINAX5R +CINPE4 +CINPE5R +CINPS4 +CINPS5R +COHAX4 +COHAX4P +COH2D4 +COH2D4P +COH3D6 +COH3D6P +COH3D8 +COH3D8P +CONN2D2 +CONN3D2 +CPE3 +CPE3E +CPE3H +CPE3T +CPE4 +CPE4E +CPE4H +CPE4HT +4-node bilinear plane strain quadrilateral, hybrid, linear pressure, incompatible +modes +4-node plane strain quadrilateral, bilinear displacement, bilinear pore pressure +4-node plane strain quadrilateral, bilinear displacement, bilinear pore pressure, +hybrid, constant pressure +4-node bilinear plane strain quadrilateral, reduced integration, hourglass control +4-node bilinear plane strain quadrilateral, hybrid, constant pressure, reduced +integration, hourglass control +4-node bilinear plane strain thermally coupled quadrilateral, hybrid, constant +pressure, reduced integration, hourglass control +4-node plane strain quadrilateral, bilinear displacement, bilinear pore pressure, +reduced integration, hourglass control +4-node plane strain quadrilateral, bilinear displacement, bilinear pore pressure, +hybrid, constant pressure, reduced integration, hourglass control +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +4-node bilinear plane +strain thermally coupled quadrilateral, +displacement and temperature, reduced integration, hourglass control +bilinear +28.1.3 +4-node plane strain thermally coupled quadrilateral, bilinear displacement and +temperature +6-node quadratic plane strain triangle +6-node quadratic plane strain piezoelectric triangle +6-node quadratic plane strain triangle, hybrid, linear pressure +6-node modified quadratic plane strain triangle, hourglass control +6-node modified quadratic plane strain triangle, hybrid, linear pressure, hourglass +control +6-node modified quadratic plane strain thermally coupled triangle, hybrid, linear +pressure, hourglass control +6-node modified displacement and pore pressure plane strain triangle, hourglass +control +6-node modified displacement and pore pressure plane strain triangle, hybrid, +linear pressure, hourglass control +6-node modified quadratic plane strain thermally coupled triangle, hourglass +control +8-node biquadratic plane strain quadrilateral +8-node biquadratic plane strain piezoelectric quadrilateral +8-node biquadratic plane strain quadrilateral, hybrid, linear pressure +8-node plane strain thermally coupled quadrilateral, biquadratic displacement, +bilinear temperature, hybrid, linear pressure +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +EI.1–10 +CPE4IH +CPE4P +CPE4PH +CPE4R +CPE4RH +CPE4RHT +CPE4RP +CPE4RPH +CPE4RT +CPE4T +CPE6 +CPE6E +CPE6H +CPE6M +CPE6MH +CPE6MHT +CPE6MP +CPE6MPH +CPE6MT +CPE8 +CPE8E +CPE8H +8-node plane strain quadrilateral, biquadratic displacement, bilinear pore +pressure +8-node plane strain quadrilateral, biquadratic displacement, bilinear pore +pressure, hybrid, linear pressure stress +8-node biquadratic plane strain quadrilateral, reduced integration +8-node biquadratic plane strain piezoelectric quadrilateral, reduced integration +8-node biquadratic plane strain quadrilateral, hybrid, linear pressure, reduced +integration +8-node plane strain thermally coupled quadrilateral, biquadratic displacement, +bilinear temperature, reduced integration, hybrid, linear pressure +8-node plane strain quadrilateral, biquadratic displacement, bilinear pore +pressure, reduced integration +8-node biquadratic displacement, bilinear pore pressure, reduced integration, +hybrid, linear pressure +8-node plane strain thermally coupled quadrilateral, biquadratic displacement, +bilinear temperature, reduced integration +8-node plane strain thermally coupled quadrilateral, biquadratic displacement, +bilinear temperature +3-node linear generalized plane strain triangle +3-node linear generalized plane strain triangle, hybrid, constant pressure +3-node generalized plane strain thermally coupled triangle, linear displacement +and temperature, hybrid, constant pressure +3-node generalized plane strain thermally coupled triangle, linear displacement +and temperature +4-node bilinear generalized plane strain quadrilateral +4-node bilinear generalized plane strain quadrilateral, hybrid, constant pressure +4-node generalized plane strain thermally coupled quadrilateral, bilinear +displacement and temperature, hybrid, constant pressure +4-node bilinear generalized plane strain quadrilateral, incompatible modes +4-node bilinear generalized plane strain quadrilateral, hybrid, linear pressure, +incompatible modes +4-node bilinear generalized plane strain quadrilateral, reduced integration, +hourglass control +4-node bilinear generalized plane strain quadrilateral, hybrid, constant pressure, +reduced integration, hourglass control +4-node generalized plane strain thermally coupled quadrilateral, bilinear +displacement and temperature, hybrid, constant pressure, reduced integration, +hourglass control +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +EI.1–11 +CPE8P +CPE8PH +CPE8R +CPE8RE +CPE8RH +CPE8RHT +CPE8RP +CPE8RPH +CPE8RT +CPE8T +CPEG3 +CPEG3H +CPEG3HT +CPEG3T +CPEG4 +CPEG4H +CPEG4HT +CPEG4I +CPEG4IH +CPEG4R +CPEG4RH +linear pressure, +4-node generalized plane strain thermally coupled quadrilateral, bilinear +displacement and temperature, reduced integration, hourglass control +4-node generalized plane strain thermally coupled quadrilateral, bilinear +displacement and temperature +6-node quadratic generalized plane strain triangle +6-node quadratic generalized plane strain triangle, hybrid, linear pressure +6-node modified generalized plane strain triangle, hourglass control +6-node modified generalized plane strain triangle, hybrid, +hourglass control +6-node modified generalized plane strain thermally coupled triangle, quadratic +displacement, linear temperature, hybrid, constant pressure, hourglass control +6-node modified generalized plane strain thermally coupled triangle, quadratic +displacement, linear temperature, hourglass control +8-node biquadratic generalized plane strain quadrilateral +8-node biquadratic generalized plane strain quadrilateral, hybrid, linear pressure +8-node generalized plane strain thermally coupled quadrilateral, biquadratic +displacement, bilinear temperature, hybrid, linear pressure +8-node biquadratic generalized plane strain quadrilateral, reduced integration +8-node biquadratic generalized plane strain quadrilateral, hybrid, linear pressure, +reduced integration +8-node generalized plane strain thermally coupled quadrilateral, biquadratic +displacement, bilinear temperature, hybrid, linear pressure, reduced integration +8-node generalized plane strain thermally coupled quadrilateral, biquadratic +displacement, bilinear temperature +3-node linear plane stress triangle +3-node linear plane stress piezoelectric triangle +3-node plane stress thermally coupled triangle, +temperature +4-node bilinear plane stress quadrilateral +4-node bilinear plane stress piezoelectric quadrilateral +4-node bilinear plane stress quadrilateral, incompatible modes +4-node bilinear plane stress quadrilateral, reduced integration, hourglass control +4-node plane stress thermally coupled quadrilateral, bilinear displacement and +temperature, reduced integration, hourglass control +4-node plane stress thermally coupled quadrilateral, bilinear displacement and +temperature +6-node quadratic plane stress triangle +6-node quadratic plane stress piezoelectric triangle +linear displacement and +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +EI.1–12 +CPEG4RT +CPEG4T +CPEG6 +CPEG6H +CPEG6M +CPEG6MH +CPEG6MHT +CPEG6MT +CPEG8 +CPEG8H +CPEG8HT +CPEG8R +CPEG8RH +CPEG8RHT +CPEG8T +CPS3 +CPS3E +CPS3T +CPS4 +CPS4E +CPS4I +CPS4R +CPS4RT +CPS4T +CPS6 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +32.2.2 +32.2.2 +32.2.2 +28.1.2 +28.1.2 +28.1.2 +28.1.2 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +CPS6M +CPS6MT +CPS8 +CPS8E +CPS8R +CPS8RE +CPS8RT +CPS8T +6-node modified second-order plane stress triangle, hourglass control +6-node modified second-order plane stress thermally coupled triangle, hourglass +control +8-node biquadratic plane stress quadrilateral +8-node biquadratic plane stress piezoelectric quadrilateral +8-node biquadratic plane stress quadrilateral, reduced integration +8-node biquadratic plane stress piezoelectric quadrilateral, reduced integration +8-node plane stress thermally coupled quadrilateral, biquadratic displacement, +bilinear temperature, reduced integration +8-node plane stress thermally coupled quadrilateral, biquadratic displacement, +bilinear temperature +Dashpot between a node and ground, acting in a fixed direction +Dashpot between two nodes, acting in a fixed direction +DASHPOT1 +DASHPOT2 +DASHPOTA Axial dashpot between two nodes, whose line of action is the line joining the two +nodes +2-node heat transfer link +2-node coupled thermal-electrical link +3-node heat transfer link +3-node coupled thermal-electrical link +3-node linear heat transfer triangle +3-node linear coupled thermal-electrical triangle +4-node linear heat transfer quadrilateral +4-node linear coupled thermal-electrical quadrilateral +6-node quadratic heat transfer triangle +6-node quadratic coupled thermal-electrical triangle +8-node quadratic heat transfer quadrilateral +8-node quadratic coupled thermal-electrical quadrilateral +4-node linear heat transfer tetrahedron +4-node linear coupled thermal-electrical tetrahedron +6-node linear heat transfer triangular prism +6-node linear coupled thermal-electrical triangular prism +8-node linear heat transfer brick +8-node linear coupled thermal-electrical brick +10-node quadratic heat transfer tetrahedron +10-node quadratic coupled thermal-electrical tetrahedron +15-node quadratic heat transfer triangular prism +15-node quadratic coupled thermal-electrical triangular prism +EI.1–13 +DC1D2 +DC1D2E +DC1D3 +DC1D3E +DC2D3 +DC2D3E +DC2D4 +DC2D4E +DC2D6 +DC2D6E +DC2D8 +DC2D8E +DC3D4 +DC3D4E +DC3D6 +DC3D6E +DC3D8 +DC3D8E +DC3D10 +DC3D10E +DC3D15 +DC3D20 +20-node quadratic heat transfer brick +DC3D20E +20-node quadratic coupled thermal-electrical brick +DCAX3 +3-node linear axisymmetric heat transfer triangle +DCAX3E +3-node linear axisymmetric coupled thermal-electrical triangle +DCAX4 +4-node linear axisymmetric heat transfer quadrilateral +DCAX4E +4-node linear axisymmetric coupled thermal-electrical quadrilateral +DCAX6 +6-node quadratic axisymmetric heat transfer triangle +DCAX6E +6-node quadratic axisymmetric coupled thermal-electrical triangle +DCAX8 +DCAX8E +DCC1D2 +8-node quadratic axisymmetric heat transfer quadrilateral +8-node quadratic axisymmetric coupled thermal-electrical quadrilateral +2-node convection/diffusion link +DCC1D2D +2-node convection/diffusion link, dispersion control +DCC2D4 +4-node convection/diffusion quadrilateral +DCC2D4D +4-node convection/diffusion quadrilateral, dispersion control +DCC3D8 +8-node convection/diffusion brick +DCC3D8D +8-node convection/diffusion brick, dispersion control +DCCAX2 +2-node axisymmetric convection/diffusion link +DCCAX2D +2-node axisymmetric convection/diffusion link, dispersion control +DCCAX4 +4-node axisymmetric convection/diffusion quadrilateral +DCCAX4D +4-node axisymmetric convection/diffusion quadrilateral, dispersion control +DCOUP2D +Two-dimensional distributing coupling element +DCOUP3D +Three-dimensional distributing coupling element +DGAP +DRAG2D +DRAG3D +DS3 +DS4 +DS6 +DS8 +Unidirectional thermal interactions between two nodes +2-D drag chain, for use in cases where only horizontal motion is being studied +3-D drag chain +3-node heat transfer triangular shell +4-node heat transfer quadrilateral shell +6-node heat transfer triangular shell +8-node heat transfer quadrilateral shell +DSAX1 +DSAX2 +2-node axisymmetric heat transfer shell +3-node axisymmetric heat transfer shell +ELBOW31 +2-node pipe in space with deforming section, linear interpolation along the pipe +ELBOW31B +2-node pipe in space with ovalization only, axial gradients of ovalization +neglected +28.1.4 +28.1.4 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.2 +28.1.2 +28.1.3 +28.1.3 +28.1.4 +28.1.4 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +32.4.2 +32.4.2 +39.2.2 +32.11.2 +32.11.2 +29.6.7 +29.6.7 +29.6.7 +29.6.7 +29.6.9 +29.6.9 +29.5.2 +29.5.2 +29.5.2 +29.5.2 +28.1.3 +28.1.3 +28.1.4 +28.1.4 +29.4.3 +29.4.3 +39.2.2 +39.2.2 +39.2.2 +39.2.2 +32.6.7 +32.6.7 +32.6.8 +32.6.8 +32.6.8 +32.6.8 +32.6.8 +32.6.8 +32.6.8 +32.6.8 +32.6.8 +32.6.8 +32.6.8 +32.6.8 +32.6.8 +32.6.8 +32.6.9 +ELBOW31C +ELBOW32 +EMC2D3 +EMC2D4 +EMC3D4 +EMC3D8 +FRAME2D +FRAME3D +GAPCYL +GAPSPHER +GAPUNI +GAPUNIT +GK2D2 +GK2D2N +GK3D2 +GK3D2N +GK3D4L +GK3D4LN +GK3D6L +GK3D6LN +2-node pipe in space with ovalization only, axial gradients of ovalization +neglected. This is the same as element type ELBOW31B except that the odd +numbered terms in the Fourier interpolation around the pipe, except the first +term, are neglected. +3-node pipe in space with deforming section, quadratic interpolation along the +pipe +3-node triangular zero-order electromagnetic element +4-node quadrilateral zero-order electromagnetic element +4-node tetrahedral zero-order electromagnetic element +8-node hexahedral zero-order electromagnetic element +2-node two-dimensional straight frame element +2-node three-dimensional straight frame element +Cylindrical gap between two nodes +Spherical gap between two nodes +Unidirectional gap between two nodes +Unidirectional gap and thermal interactions between two nodes +2-node two-dimensional gasket element +2-node two-dimensional gasket element with thickness-direction behavior only +2-node three-dimensional gasket element +2-node three-dimensional gasket element with thickness-direction behavior only +4-node three-dimensional line gasket element +4-node three-dimensional line gasket element with thickness-direction behavior +only +6-node three-dimensional line gasket element +6-node three-dimensional line gasket element with thickness-direction behavior +only +6-node three-dimensional gasket element +6-node three-dimensional gasket element with thickness-direction behavior only +8-node three-dimensional gasket element +8-node three-dimensional gasket element with thickness-direction behavior only +12-node three-dimensional gasket element +GK3D6 +GK3D6N +GK3D8 +GK3D8N +GK3D12M +GK3D12MN 12-node three-dimensional gasket element with thickness-direction behavior +GK3D18 +GK3D18N +GKAX2 +only +18-node three-dimensional gasket element +18-node three-dimensional gasket element with thickness-direction behavior +only +2-node axisymmetric gasket element +2-node axisymmetric gasket element with thickness-direction behavior only +4-node axisymmetric gasket element +4-node axisymmetric gasket element with thickness-direction behavior only +6-node axisymmetric gasket element +6-node axisymmetric gasket element with thickness-direction behavior only +4-node plane strain gasket element +6-node plane strain gasket element +4-node plane stress gasket element +4-node two-dimensional gasket element with thickness-direction behavior only +6-node plane stress gasket element +6-node two-dimensional gasket element with thickness-direction behavior only +Point heat capacitance +Axisymmetric rigid surface element (for use with first-order axisymmetric +elements) +Axisymmetric rigid surface element (for use with second-order axisymmetric +elements) +2-node axisymmetric slide line element (for use with first-order axisymmetric +elements) +3-node axisymmetric slide line element (for use with second-order axisymmetric +elements) +Cylindrical geometry tube support interaction element +Unidirectional tube support interaction element +Tube-tube element for use with first-order, 2-D beam and pipe elements +Tube-tube element for use with first-order, 3-D beam and pipe elements +Two-dimensional elastic-plastic joint interaction element. These elements are +available only for use in Abaqus/Aqua. +Three-dimensional elastic-plastic joint interaction element. These elements are +available only for use in Abaqus/Aqua. +Three-dimensional joint interaction element +3-node second-order line spring for use on a symmetry plane +6-node general second-order line spring. This element can be used only with +linear elastic material behavior. +3-node triangular membrane +4-node quadrilateral membrane +4-node quadrilateral membrane, reduced integration, hourglass control +6-node triangular membrane +8-node quadrilateral membrane +32.6.9 +32.6.9 +32.6.9 +32.6.9 +32.6.9 +32.6.7 +32.6.7 +32.6.7 +32.6.7 +32.6.7 +32.6.7 +30.4.2 +39.5.2 +39.5.2 +39.4.2 +39.4.2 +32.8.2 +32.8.2 +39.3.2 +39.3.2 +32.10.2 +32.10.2 +32.3.2 +32.9.2 +32.9.2 +29.1.2 +29.1.2 +29.1.2 +29.1.2 +29.1.2 +EI.1–16 +GKAX2N +GKAX4 +GKAX4N +GKAX6 +GKAX6N +GKPE4 +GKPE6 +GKPS4 +GKPS4N +GKPS6 +GKPS6N +HEATCAP +IRS21A +IRS22A +ISL21A +ISL22A +ITSCYL +ITSUNI +ITT21 +ITT31 +JOINT2D +JOINT3D +JOINTC +LS3S +LS6 +M3D3 +M3D4 +M3D4R +M3D6 +8-node quadrilateral membrane, reduced integration +9-node quadrilateral membrane +9-node quadrilateral membrane, reduced integration, hourglass control +Point mass +2-node linear axisymmetric membrane +3-node quadratic axisymmetric membrane +6-node cylindrical membrane +9-node cylindrical membrane +2-node linear axisymmetric membrane, twist +3-node quadratic axisymmetric membrane, twist +2-node linear pipe in a plane +2-node linear pipe in a plane, hybrid formulation +3-node quadratic pipe in a plane +3-node quadratic pipe in a plane, hybrid formulation +2-node linear pipe in space +2-node linear pipe in space, hybrid formulation +3-node quadratic pipe in space +3-node quadratic pipe in space, hybrid formulation +4-node 2-D pipe-soil interaction element +6-node 2-D pipe-soil interaction element +4-node 3-D pipe-soil interaction element +6-node 3-D pipe-soil interaction element +29.1.2 +29.1.2 +29.1.2 +30.1.2 +29.1.4 +29.1.4 +29.1.3 +29.1.3 +29.1.4 +29.1.4 +29.3.8 +29.3.8 +29.3.8 +29.3.8 +29.3.8 +29.3.8 +29.3.8 +29.3.8 +32.12.2 +32.12.2 +32.12.2 +32.12.2 +4-node tetrahedron, +temperature +linear displacement, +linear electric potential and linear +28.1.4 +6-node linear triangular prism, linear displacement, linear electric potential and +linear temperature +8-node brick, trilinear displacement, trilinear electric potential and trilinear +temperature +28.1.4 +28.1.4 +trilinear displacement, +8-node brick, +temperature, hybrid, constant pressure +8-node brick, +temperature, reduced integration, hourglass control +trilinear displacement, +trilinear electric potential, +trilinear electric potential, +trilinear +28.1.4 +trilinear +28.1.4 +8-node brick, +temperature, reduced integration, hourglass control, hybrid, constant pressure +trilinear electric potential, +trilinear displacement, +trilinear +28.1.4 +10-node modified displacement, electric potential, +tetrahedron, hourglass control +temperature quadratic +28.1.4 +EI.1–17 +M3D8R +M3D9 +M3D9R +MASS +MAX1 +MAX2 +MCL6 +MCL9 +MGAX1 +MGAX2 +PIPE21 +PIPE21H +PIPE22 +PIPE22H +PIPE31 +PIPE31H +PIPE32 +PIPE32H +PSI24 +PSI26 +PSI34 +PSI36 +Q3D4 +Q3D6 +Q3D8 +Q3D8H +Q3D8R +Q3D8RH +temperature quadratic +10-node modified displacement, electric potential, +tetrahedron, hybrid, linear pressure, hourglass control +20-node quadratic brick, triquadratic displacement, trilinear electric potential, +trilinear temperature +20-node quadratic brick, triquadratic displacement, trilinear electric potential, +trilinear temperature, hybrid, linear pressure +20-node quadratic brick, triquadratic displacement, trilinear electric potential, +trilinear temperature, reduced integration +20-node quadratic brick, triquadratic displacement, trilinear electric potential, +trilinear temperature, hybrid, linear pressure, reduced integration +2-node 2-D linear rigid link (for use in plane strain or plane stress) +3-node 3-D rigid triangular facet +4-node 3-D bilinear rigid quadrilateral +2-node linear axisymmetric rigid link (for use in axisymmetric planar geometries) +2-node 2-D rigid beam +2-node 3-D rigid beam +Rotary inertia at a point +3-node triangular general-purpose shell, finite membrane strains (identical to +element S3R) +3-node thermally coupled triangular general-purpose shell, finite membrane +strains (identical to element S3RT) +3-node triangular general-purpose shell, finite membrane strains (identical to +element S3) +3-node thermally coupled triangular general-purpose shell, finite membrane +strains (identical to element S3T) +4-node general-purpose shell, finite membrane strains +4-node thermally coupled general-purpose shell, finite membrane strains +4-node general-purpose shell, reduced integration, hourglass control, finite +membrane strains +4-node thermally coupled general-purpose shell, reduced integration, hourglass +control, finite membrane strains +4-node thin shell, reduced integration, hourglass control, using five degrees of +freedom per node +8-node doubly curved thick shell, reduced integration +8-node doubly curved thin shell, reduced integration, using five degrees of +freedom per node +8-node thermally coupled quadrilateral general +displacement, bilinear temperature in the shell surface +thick shell, biquadratic +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +30.3.2 +30.3.2 +30.3.2 +30.3.2 +30.3.2 +30.3.2 +30.2.2 +29.6.7 +29.6.7 +29.6.7 +29.6.7 +29.6.7 +29.6.7 +29.6.7 +29.6.7 +29.6.7 +29.6.7 +29.6.7 +29.6.7 +EI.1–18 +Q3D10MH +Q3D20 +Q3D20H +Q3D20R +Q3D20RH +R2D2 +R3D3 +R3D4 +RAX2 +RB2D2 +RB3D2 +ROTARYI +S3 +S3T +S3R +S3RT +S4 +S4T +S4R +S4RT +S4R5 +S8R +S8R5 +reduced +thick shell, quadratic +in-plane general-purpose continuum shell, +9-node doubly curved thin shell, reduced integration, using five degrees of +freedom per node +2-node linear axisymmetric thin or thick shell +3-node quadratic axisymmetric thin or thick shell +3-node axisymmetric thermally coupled thin or +displacement, linear temperature in the shell surface +Linear asymmetric-axisymmetric, Fourier shell element with 2 nodes in the +generator direction and N Fourier modes +Quadratic asymmetric-axisymmetric, Fourier shell element with 3 nodes in the +generator direction and N Fourier modes +6-node triangular in-plane continuum shell wedge, general-purpose continuum +shell, finite membrane strains. +8-node quadrilateral +integration with hourglass control, finite membrane strains. +6-node linear displacement and temperature, triangular in-plane continuum shell +wedge, general-purpose continuum shell, finite membrane strains. +8-node linear displacement and temperature, quadrilateral in-plane general- +purpose continuum shell, reduced integration with hourglass control, finite +membrane strains. +3-node triangular surface element +4-node quadrilateral surface element +4-node quadrilateral surface element, reduced integration +6-node triangular surface element +8-node quadrilateral surface element +8-node quadrilateral surface element, reduced integration +2-node linear axisymmetric surface element +3-node quadratic axisymmetric surface element +6-node cylindrical surface element +9-node cylindrical surface element +2-node linear axisymmetric surface element, twist +3-node quadratic axisymmetric surface element, twist +Spring between a node and ground, acting in a fixed direction +Spring between two nodes, acting in a fixed direction +Axial spring between two nodes, whose line of action is the line joining the two +nodes. This line of action may rotate in large-displacement analysis. +3-node triangular facet thin shell +6-node triangular thin shell, using five degrees of freedom per node +2-node linear 2-D truss +29.6.7 +29.6.9 +29.6.9 +29.6.9 +29.6.10 +29.6.10 +29.6.8 +29.6.8 +29.6.8 +29.6.8 +32.7.2 +32.7.2 +32.7.2 +32.7.2 +32.7.2 +32.7.2 +32.7.4 +32.7.4 +32.7.3 +32.7.3 +32.7.4 +32.7.4 +32.1.2 +32.1.2 +32.1.2 +29.6.7 +29.6.7 +29.2.2 +EI.1–19 +S9R5 +SAX1 +SAX2 +SAX2T +SAXA1N +SAXA2N +SC6R +SC8R +SC6RT +SC8RT +SFM3D3 +SFM3D4 +SFM3D4R +SFM3D6 +SFM3D8 +SFM3D8R +SFMAX1 +SFMAX2 +SFMCL6 +SFMCL9 +SFMGAX1 +SFMGAX2 +SPRING1 +SPRING2 +SPRINGA +STRI3 +STRI65 +T2D2E +T2D2H +T2D2T +T2D3 +T2D3E +T2D3H +T2D3T +T3D2 +T3D2E +T3D2H +T3D2T +T3D3 +T3D3E +T3D3H +T3D3T +2-node 2-D piezoelectric truss +2-node linear 2-D truss, hybrid +2-node 2-D thermally coupled truss +3-node quadratic 2-D truss +3-node 2-D piezoelectric truss +3-node quadratic 2-D truss, hybrid +3-node 2-D thermally coupled truss +2-node linear 3-D truss +2-node 3-D piezoelectric truss +2-node linear 3-D truss, hybrid +2-node 3-D thermally coupled truss +3-node quadratic 3-D truss +3-node 3-D piezoelectric truss +3-node quadratic 3-D truss, hybrid +3-node 3-D thermally coupled truss +WARP2D3 +3-node linear 2-D warping element +WARP2D4 +4-node bilinear 2-D warping element +29.2.2 +29.2.2 +29.2.2 +29.2.2 +29.2.2 +29.2.2 +29.2.2 +29.2.2 +29.2.2 +29.2.2 +29.2.2 +29.2.2 +29.2.2 +29.2.2 +29.2.2 +28.4.2 +28.4.2 +EI.2 +Abaqus/Explicit ELEMENT INDEX +This index provides a reference to all of the element types that are available in Abaqus/Explicit. Elements are +listed in alphabetical order, where numerical characters precede the letter “A” and two-digit numbers are put +in numerical, rather than “alphabetical,” order. For example, C3D8R precedes CAX3. +For certain options, such as contact and surface-based distributing coupling, Abaqus may generate +internal elements (such as IDCOUP3D for surface-based distributing coupling). These internal element +names are not included in the index below but may appear in an output database (.odb) or data (.dat) file. +3-node linear 2-D acoustic triangle +4-node linear 2-D acoustic quadrilateral, reduced integration, hourglass control +4-node linear acoustic tetrahedron +6-node linear acoustic triangular prism +8-node linear acoustic brick, reduced integration, hourglass control +3-node linear axisymmetric acoustic triangle +4-node linear axisymmetric acoustic quadrilateral, reduced integration, hourglass +control +2-node linear 2-D acoustic infinite element +3-node linear 3-D acoustic infinite element +4-node linear 3-D acoustic infinite element +2-node linear axisymmetric acoustic infinite element +2-node linear beam in a plane +3-node quadratic beam in a plane +2-node linear beam in space +3-node quadratic beam in space +4-node linear tetrahedron +4-node thermally coupled tetrahedron, linear displacement and temperature +6-node linear triangular prism, reduced integration, hourglass control +6-node thermally coupled triangular prism, linear displacement and temperature, +reduced integration, hourglass control +8-node linear brick +8-node linear brick, incompatible modes +8-node linear brick, reduced integration, hourglass control +8-node thermally coupled brick, trilinear displacement and temperature +8-node thermally coupled brick, trilinear displacement and temperature, reduced +integration, hourglass control +28.1.3 +28.1.3 +28.1.4 +28.1.4 +28.1.4 +28.1.6 +28.1.6 +28.3.2 +28.3.2 +28.3.2 +28.3.2 +29.3.8 +29.3.8 +29.3.8 +29.3.8 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +28.1.4 +EI.2–1 +AC2D3 +AC2D4R +AC3D4 +AC3D6 +AC3D8R +ACAX3 +ACAX4R +ACIN2D2 +ACIN3D3 +ACIN3D4 +ACINAX2 +B21 +B22 +B31 +B32 +C3D4 +C3D4T +C3D6 +C3D6T +C3D8 +C3D8I +C3D8R +C3D8T +linear displacement and +reduced integration, hourglass +10-node modified second-order tetrahedron +10-node modified thermally coupled second-order tetrahedron +3-node linear axisymmetric triangle +3-node thermally coupled axisymmetric triangle, +temperature +4-node bilinear axisymmetric quadrilateral, +control +4-node thermally coupled axisymmetric quadrilateral, bilinear displacement and +temperature, hybrid, constant pressure, reduced integration, hourglass control +6-node modified second-order axisymmetric triangle +6-node modified second-order axisymmetric thermally coupled triangle +8-node linear one-way infinite brick +4-node linear axisymmetric one-way infinite quadrilateral +4-node linear plane strain one-way infinite quadrilateral +4-node linear plane stress one-way infinite quadrilateral +4-node axisymmetric cohesive element +4-node two-dimensional cohesive element +6-node three-dimensional cohesive element +8-node three-dimensional cohesive element +Connector element in a plane between two nodes or ground and a node +Connector element in space between two nodes or ground and a node +3-node linear plane strain triangle +3-node plane strain thermally coupled triangle, +temperature +4-node bilinear plane strain quadrilateral, reduced integration, hourglass control +4-node bilinear plane +bilinear +strain thermally coupled quadrilateral, +displacement and temperature, reduced integration, hourglass control +6-node modified second-order plane strain triangle +6-node modified second-order plane strain thermally coupled triangle +3-node linear plane stress triangle +3-node plane stress thermally coupled triangle, +temperature +4-node bilinear plane stress quadrilateral, reduced integration, hourglass control +4-node plane stress thermally coupled quadrilateral, bilinear displacement and +temperature, reduced integration, hourglass control +6-node modified second-order plane stress triangle +6-node modified second-order plane stress thermally coupled triangle +linear displacement and +linear displacement and +28.1.4 +28.1.4 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.1.6 +28.3.2 +28.3.2 +28.3.2 +28.3.2 +32.5.10 +32.5.8 +32.5.9 +32.5.9 +31.1.4 +31.1.4 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +28.1.3 +EI.2–2 +C3D10M +C3D10MT +CAX3 +CAX3T +CAX4R +CAX4RT +CAX6M +CAX6MT +CIN3D8 +CINAX4 +CINPE4 +CINPS4 +COHAX4 +COH2D4 +COH3D6 +COH3D8 +CONN2D2 +CONN3D2 +CPE3 +CPE3T +CPE4R +CPE4RT +CPE6M +CPE6MT +CPS3 +CPS3T +CPS4R +CPS4RT +CPS6M +EC3D8R +Abaqus/Explicit ELEMENT INDEX +reduced +8-node linear multi-material Eulerian brick, reduced integration, hourglass +control +8-node thermally coupled linear multi-material Eulerian brick, +integration, hourglass control +Point heat capacitance +3-node triangular membrane +4-node quadrilateral membrane +4-node quadrilateral membrane, reduced integration, hourglass control +Point mass +1-node continuum particle element +2-node linear pipe in a plane +2-node linear pipe in space +2-node 2-D linear rigid link (for use in plane strain or plane stress) +3-node 3-D rigid triangular facet +4-node 3-D bilinear rigid quadrilateral +2-node linear axisymmetric rigid link (for use in axisymmetric geometries) +Rotary inertia at a point +3-node triangular shell, finite membrane strains +3-node triangular shell, small membrane strains +3-node thermally-coupled triangular shell, finite membrane strains +4-node general-purpose shell, finite membrane strains +4-node shell, reduced integration, hourglass control, finite membrane strains +4-node shell, reduced integration, hourglass control, small membrane strains +4-node shell, reduced integration, hourglass control, small membrane strains, +warping considered in small-strain formulation +4-node thermally-coupled shell, reduced integration, hourglass control, finite +membrane strains +2-node linear axisymmetric shell +6-node triangular in-plane continuum shell wedge, general-purpose continuum +shell, finite membrane strains. +8-node quadrilateral +integration with hourglass control, finite membrane strains. +6-node thermally coupled triangular in-plane continuum shell wedge, general- +purpose continuum shell, finite membrane strains. +8-node thermally coupled quadrilateral in-plane general-purpose continuum +shell, reduced integration with hourglass control, finite membrane strains. +in-plane general-purpose continuum shell, +reduced +32.2.2 +32.14.1 +32.14.1 +30.4.2 +29.1.2 +29.1.2 +29.1.2 +30.1.2 +28.5.2 +29.3.8 +29.3.8 +30.3.2 +30.3.2 +30.3.2 +30.3.2 +30.2.2 +29.6.7 +29.6.7 +29.6.7 +29.6.7 +29.6.7 +29.6.7 +29.6.7 +29.6.7 +29.6.9 +29.6.8 +29.6.8 +29.6.8 +29.6.8 +EI.2–3 +EC3D8RT +HEATCAP +M3D3 +M3D4 +M3D4R +MASS +PC3D +PIPE21 +PIPE31 +R2D2 +R3D3 +R3D4 +RAX2 +ROTARYI +S3R +S3RS +S3RT +S4 +S4R +S4RS +S4RSW +S4RT +SAX1 +SC6R +SC8R +SC6RT +SFM3D3 +3-node triangular surface element +SFM3D4R +4-node quadrilateral surface element, reduced integration +SPRINGA +Axial spring between two nodes +T2D2 +T3D2 +2-node linear 2-D truss +2-node linear 3-D truss +32.7.2 +32.7.2 +32.1.2 +29.2.2 +29.2.2 +EI.3 +Abaqus/CFD ELEMENT INDEX +This index provides a reference to all of the element types that are available in Abaqus/CFD. Elements are +listed in alphabetical order. +FC3D4 +FC3D6 +FC3D8 +4-node tetrahedron +6-node prism +8-node brick +28.2.2 +28.2.2 +28.2.2 +SIMULIA is the Dassault Systèmes brand that delivers a scalable portfolio of +Realistic Simulation solutions including the Abaqus product suite for Unified Finite +Element Analysis; multiphysics solutions for insight into challenging engineering +problems; and lifecycle management solutions for managing simulation data, +processes, and intellectual property. By building on established technology, +respected quality, and superior customer service, SIMULIA makes realistic +simulation an integral business practice that improves product performance, +reduces physical prototypes, and drives innovation. Headquartered in Providence, +RI, USA, with R&D centers in Providence and in Vélizy, France, SIMULIA provides +sales, services, and support through a global network of regional offices and +distributors. 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